0.00/0.01	% File    : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.00/0.01	% app-encoded or not : app
0.00/0.01	% Variant    : fo
0.00/0.01	% Ordering    : rpo6
0.00/0.01	% Command    : 
0.00/0.01	#!/bin/sh
0.00/0.01	
0.00/0.01	./zipperposition.native ${1:+"$1"} \
0.00/0.01	  -i tptp \
0.00/0.01	  -o tptp \
0.00/0.01	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.01	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.01	  --no-ho \
0.00/0.01	  --no-avatar \
0.00/0.01	  --no-induction \
0.00/0.01	  --no-unif-pattern \
0.00/0.01	  --ord $2 \
0.00/0.01	  --simultaneous-sup false \
0.00/0.01	  --no-max-vars \
0.00/0.01	  --no-fool
0.00/0.20	% Computer   : n094.star.cs.uiowa.edu
0.00/0.20	% Model      : x86_64 x86_64
0.00/0.20	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.20	% Memory     : 32218.625MB
0.00/0.20	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.20	% CPULimit   : 300
0.00/0.20	% DateTime   : Fri Feb  2 16:55:54 CST 2018
0.00/0.46	% done 491 iterations in 0.253s
0.00/0.46	% SZS status Theorem for 'stdin'
0.00/0.46	% SZS output start Refutation
0.00/0.47	tff(zf_stmt_3, conjecture,
0.00/0.47	  ((?[Xp:app_encode_fun($i,$o),Xq:app_encode_fun($i,$o),Xx,Xy]:
0.00/0.47	      (app_encode_app($i,$o,Xp,Xx) & (~app_encode_app($i,$o,Xp,Xy)) & 
0.00/0.47	       app_encode_app($i,$o,Xq,Xy) & (~app_encode_app($i,$o,Xq,z)))) <=>
0.00/0.47	   (?[Xp:app_encode_fun($i,$o),Xq:app_encode_fun($i,$o),Xx,Xy]:
0.00/0.47	      ((~app_encode_app($i,$o,Xq,z)) & app_encode_app($i,$o,Xq,Xy) & 
0.00/0.47	       app_encode_app($i,$o,Xp,Xx) & (~app_encode_app($i,$o,Xp,Xy)))))).
0.00/0.47	tff(zf_stmt_0, negated_conjecture,
0.00/0.47	  (~
0.00/0.47	    ((?[Xp:app_encode_fun($i,$o),Xq:app_encode_fun($i,$o),Xx,Xy]:
0.00/0.47	        (app_encode_app($i,$o,Xp,Xx) & (~app_encode_app($i,$o,Xp,Xy)) & 
0.00/0.47	         app_encode_app($i,$o,Xq,Xy) & (~app_encode_app($i,$o,Xq,z)))) <=>
0.00/0.47	     (?[Xp:app_encode_fun($i,$o),Xq:app_encode_fun($i,$o),Xx,Xy]:
0.00/0.47	        ((~app_encode_app($i,$o,Xq,z)) & app_encode_app($i,$o,Xq,Xy) & 
0.00/0.47	         app_encode_app($i,$o,Xp,Xx) & (~app_encode_app($i,$o,Xp,Xy))))))).
0.00/0.47	tff('0', plain,
0.00/0.47	    (app_encode_app($i, $o, sk_Xp, sk_Xx)
0.00/0.47	     | app_encode_app($i, $o, sk_Xp1, sk_Xx1)),
0.00/0.47	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.47	tff('1', plain,
0.00/0.47	    (app_encode_app($i, $o, sk_Xq, sk_Xy)
0.00/0.47	     | app_encode_app($i, $o, sk_Xp1, sk_Xx1)),
0.00/0.47	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.47	tff('2', plain,
0.00/0.47	    (app_encode_app($i, $o, sk_Xq, sk_Xy)
0.00/0.47	     | app_encode_app($i, $o, sk_Xq1, sk_Xy1)),
0.00/0.47	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.47	tff('3', plain,
0.00/0.47	    ![X0 : app_encode_fun($i, $o), X1, X2 : app_encode_fun($i, $o), X3, 
0.00/0.47	      X4 : app_encode_fun($i, $o), X5, X6 : app_encode_fun($i, $o), X7]:
0.00/0.47	      (~ app_encode_app($i, $o, X0, X1)
0.00/0.47	       | app_encode_app($i, $o, X2, X1)
0.00/0.47	       | ~ app_encode_app($i, $o, X2, X3)
0.00/0.47	       | app_encode_app($i, $o, X0, z)
0.00/0.47	       | app_encode_app($i, $o, X4, X5)
0.00/0.47	       | ~ app_encode_app($i, $o, X6, X5)
0.00/0.47	       | app_encode_app($i, $o, X6, z)
0.00/0.47	       | ~ app_encode_app($i, $o, X4, X7)),
0.00/0.47	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.47	tff('4', plain,
0.00/0.47	    ![X0, X1 : app_encode_fun($i, $o), X2 : app_encode_fun($i, $o), X3, X4, 
0.00/0.47	      X5 : app_encode_fun($i, $o)]:
0.00/0.47	      (~ $true
0.00/0.47	       | app_encode_app($i, $o, sk_Xq, sk_Xy)
0.00/0.47	       | ~ app_encode_app($i, $o, X1, X0)
0.00/0.47	       | app_encode_app($i, $o, X2, z)
0.00/0.47	       | ~ app_encode_app($i, $o, X2, X3)
0.00/0.47	       | app_encode_app($i, $o, X1, X3)
0.00/0.47	       | app_encode_app($i, $o, sk_Xq1, z)
0.00/0.47	       | ~ app_encode_app($i, $o, X5, X4)
0.00/0.47	       | app_encode_app($i, $o, X5, sk_Xy1)),
0.00/0.47	    inference('sup-', [status(thm)], ['2', '3'])).
0.00/0.47	tff('5', plain,
0.00/0.47	    ![X0, X1 : app_encode_fun($i, $o), X2 : app_encode_fun($i, $o), X3, X4, 
0.00/0.47	      X5 : app_encode_fun($i, $o)]:
0.00/0.47	      (app_encode_app($i, $o, X5, sk_Xy1)
0.00/0.47	       | ~ app_encode_app($i, $o, X5, X4)
0.00/0.47	       | app_encode_app($i, $o, sk_Xq1, z)
0.00/0.47	       | app_encode_app($i, $o, X1, X3)
0.00/0.47	       | ~ app_encode_app($i, $o, X2, X3)
0.00/0.47	       | app_encode_app($i, $o, X2, z)
0.00/0.47	       | ~ app_encode_app($i, $o, X1, X0)
0.00/0.47	       | app_encode_app($i, $o, sk_Xq, sk_Xy)),
0.00/0.47	    inference('simplify', [status(thm)], ['4'])).
0.00/0.47	tff('6', plain,
0.00/0.47	    (app_encode_app($i, $o, sk_Xp, sk_Xx)
0.00/0.47	     | ~ app_encode_app($i, $o, sk_Xq1, z)),
0.00/0.47	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.47	tff('7', plain,
0.00/0.47	    (app_encode_app($i, $o, sk_Xq, sk_Xy)
0.00/0.47	     | ~ app_encode_app($i, $o, sk_Xq1, z)),
0.00/0.47	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.47	tff('8', plain,
0.00/0.47	    ![X0, X1 : app_encode_fun($i, $o), X2 : app_encode_fun($i, $o), X3, X4, 
0.00/0.47	      X5 : app_encode_fun($i, $o)]:
0.00/0.47	      (~ $true
0.00/0.47	       | ~ app_encode_app($i, $o, sk_Xq1, z)
0.00/0.47	       | ~ app_encode_app($i, $o, X1, X0)
0.00/0.47	       | app_encode_app($i, $o, X2, z)
0.00/0.47	       | ~ app_encode_app($i, $o, X2, X3)
0.00/0.47	       | app_encode_app($i, $o, X1, X3)
0.00/0.47	       | app_encode_app($i, $o, sk_Xq, z)
0.00/0.47	       | ~ app_encode_app($i, $o, X5, X4)
0.00/0.47	       | app_encode_app($i, $o, X5, sk_Xy)),
0.00/0.47	    inference('sup-', [status(thm)], ['7', '3'])).
0.00/0.47	tff('9', plain,
0.00/0.47	    ![X0, X1 : app_encode_fun($i, $o), X2 : app_encode_fun($i, $o), X3, X4, 
0.00/0.47	      X5 : app_encode_fun($i, $o)]:
0.00/0.47	      (app_encode_app($i, $o, X5, sk_Xy)
0.00/0.47	       | ~ app_encode_app($i, $o, X5, X4)
0.00/0.47	       | app_encode_app($i, $o, sk_Xq, z)
0.00/0.47	       | app_encode_app($i, $o, X1, X3)
0.00/0.47	       | ~ app_encode_app($i, $o, X2, X3)
0.00/0.47	       | app_encode_app($i, $o, X2, z)
0.00/0.47	       | ~ app_encode_app($i, $o, X1, X0)
0.00/0.47	       | ~ app_encode_app($i, $o, sk_Xq1, z)),
0.00/0.47	    inference('simplify', [status(thm)], ['8'])).
0.00/0.47	tff('10', plain,
0.00/0.47	    (~ app_encode_app($i, $o, sk_Xq, z) | ~ app_encode_app($i, $o, sk_Xq1, z)),
0.00/0.47	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.47	tff('11', plain,
0.00/0.47	    ![X0, X1 : app_encode_fun($i, $o), X2 : app_encode_fun($i, $o), X3, X4, 
0.00/0.47	      X5 : app_encode_fun($i, $o)]:
0.00/0.47	      (~ app_encode_app($i, $o, sk_Xq1, z)
0.00/0.47	       | ~ app_encode_app($i, $o, X1, X0)
0.00/0.47	       | app_encode_app($i, $o, X2, z)
0.00/0.47	       | ~ app_encode_app($i, $o, X2, X3)
0.00/0.47	       | app_encode_app($i, $o, X1, X3)
0.00/0.47	       | ~ app_encode_app($i, $o, X5, X4)
0.00/0.47	       | app_encode_app($i, $o, X5, sk_Xy)),
0.00/0.47	    inference('clc', [status(thm)], ['9', '10'])).
0.00/0.47	tff('12', plain,
0.00/0.47	    ![X0 : app_encode_fun($i, $o), X1, X2, X3 : app_encode_fun($i, $o)]:
0.00/0.47	      (~ $true
0.00/0.47	       | ~ app_encode_app($i, $o, sk_Xq1, z)
0.00/0.47	       | app_encode_app($i, $o, X0, sk_Xy)
0.00/0.47	       | ~ app_encode_app($i, $o, X0, X1)
0.00/0.47	       | app_encode_app($i, $o, sk_Xp, X2)
0.00/0.47	       | ~ app_encode_app($i, $o, X3, X2)
0.00/0.47	       | app_encode_app($i, $o, X3, z)
0.00/0.47	       | ~ app_encode_app($i, $o, sk_Xq1, z)),
0.00/0.47	    inference('sup-', [status(thm)], ['6', '11'])).
0.00/0.47	tff('13', plain,
0.00/0.47	    ![X0 : app_encode_fun($i, $o), X1, X2, X3 : app_encode_fun($i, $o)]:
0.00/0.47	      (app_encode_app($i, $o, X3, z)
0.00/0.47	       | ~ app_encode_app($i, $o, X3, X2)
0.00/0.47	       | app_encode_app($i, $o, sk_Xp, X2)
0.00/0.47	       | ~ app_encode_app($i, $o, X0, X1)
0.00/0.47	       | app_encode_app($i, $o, X0, sk_Xy)
0.00/0.47	       | ~ app_encode_app($i, $o, sk_Xq1, z)),
0.00/0.47	    inference('simplify', [status(thm)], ['12'])).
0.00/0.47	tff('14', plain,
0.00/0.47	    ![X0 : app_encode_fun($i, $o), X1]:
0.00/0.47	      (~ $true
0.00/0.47	       | ~ app_encode_app($i, $o, sk_Xq1, z)
0.00/0.47	       | ~ app_encode_app($i, $o, sk_Xq1, z)
0.00/0.47	       | app_encode_app($i, $o, X0, sk_Xy)
0.00/0.47	       | ~ app_encode_app($i, $o, X0, X1)
0.00/0.47	       | app_encode_app($i, $o, sk_Xp, sk_Xy)
0.00/0.47	       | app_encode_app($i, $o, sk_Xq, z)),
0.00/0.47	    inference('sup-', [status(thm)], ['7', '13'])).
0.00/0.47	tff('15', plain,
0.00/0.47	    ![X0 : app_encode_fun($i, $o), X1]:
0.00/0.47	      (app_encode_app($i, $o, sk_Xq, z)
0.00/0.47	       | app_encode_app($i, $o, sk_Xp, sk_Xy)
0.00/0.47	       | ~ app_encode_app($i, $o, X0, X1)
0.00/0.47	       | app_encode_app($i, $o, X0, sk_Xy)
0.00/0.47	       | ~ app_encode_app($i, $o, sk_Xq1, z)),
0.00/0.47	    inference('simplify', [status(thm)], ['14'])).
0.00/0.47	tff('16', plain,
0.00/0.47	    ![X0 : app_encode_fun($i, $o), X1]:
0.00/0.47	      (~ app_encode_app($i, $o, sk_Xq1, z)
0.00/0.47	       | app_encode_app($i, $o, X0, sk_Xy)
0.00/0.47	       | ~ app_encode_app($i, $o, X0, X1)
0.00/0.47	       | app_encode_app($i, $o, sk_Xp, sk_Xy)),
0.00/0.47	    inference('clc', [status(thm)], ['15', '10'])).
0.00/0.47	tff('17', plain,
0.00/0.47	    (~ app_encode_app($i, $o, sk_Xp, sk_Xy)
0.00/0.47	     | ~ app_encode_app($i, $o, sk_Xq1, z)),
0.00/0.47	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.47	tff('18', plain,
0.00/0.47	    ![X0 : app_encode_fun($i, $o), X1]:
0.00/0.47	      (~ app_encode_app($i, $o, X0, X1)
0.00/0.47	       | app_encode_app($i, $o, X0, sk_Xy)
0.00/0.47	       | ~ app_encode_app($i, $o, sk_Xq1, z)),
0.00/0.47	    inference('clc', [status(thm)], ['16', '17'])).
0.00/0.47	tff('19', plain,
0.00/0.47	    (~ $true
0.00/0.47	     | ~ app_encode_app($i, $o, sk_Xq1, z)
0.00/0.47	     | ~ app_encode_app($i, $o, sk_Xq1, z)
0.00/0.47	     | app_encode_app($i, $o, sk_Xp, sk_Xy)),
0.00/0.47	    inference('sup-', [status(thm)], ['6', '18'])).
0.00/0.47	tff('20', plain,
0.00/0.47	    (app_encode_app($i, $o, sk_Xp, sk_Xy)
0.00/0.47	     | ~ app_encode_app($i, $o, sk_Xq1, z)),
0.00/0.47	    inference('simplify', [status(thm)], ['19'])).
0.00/0.47	tff('21', plain, ~ app_encode_app($i, $o, sk_Xq1, z),
0.00/0.47	    inference('clc', [status(thm)], ['20', '17'])).
0.00/0.47	tff('22', plain,
0.00/0.47	    ![X0, X1 : app_encode_fun($i, $o), X2 : app_encode_fun($i, $o), X3, X4, 
0.00/0.47	      X5 : app_encode_fun($i, $o)]:
0.00/0.47	      (app_encode_app($i, $o, sk_Xq, sk_Xy)
0.00/0.47	       | ~ app_encode_app($i, $o, X1, X0)
0.00/0.47	       | app_encode_app($i, $o, X2, z)
0.00/0.47	       | ~ app_encode_app($i, $o, X2, X3)
0.00/0.47	       | app_encode_app($i, $o, X1, X3)
0.00/0.47	       | ~ app_encode_app($i, $o, X5, X4)
0.00/0.47	       | app_encode_app($i, $o, X5, sk_Xy1)),
0.00/0.47	    inference('clc', [status(thm)], ['5', '21'])).
0.00/0.47	tff('23', plain,
0.00/0.47	    ![X0 : app_encode_fun($i, $o), X1, X2, X3 : app_encode_fun($i, $o)]:
0.00/0.47	      (~ $true
0.00/0.47	       | app_encode_app($i, $o, sk_Xq, sk_Xy)
0.00/0.47	       | app_encode_app($i, $o, X0, sk_Xy1)
0.00/0.47	       | ~ app_encode_app($i, $o, X0, X1)
0.00/0.47	       | app_encode_app($i, $o, sk_Xp1, X2)
0.00/0.47	       | ~ app_encode_app($i, $o, X3, X2)
0.00/0.47	       | app_encode_app($i, $o, X3, z)
0.00/0.47	       | app_encode_app($i, $o, sk_Xq, sk_Xy)),
0.00/0.47	    inference('sup-', [status(thm)], ['1', '22'])).
0.00/0.47	tff('24', plain,
0.00/0.47	    ![X0 : app_encode_fun($i, $o), X1, X2, X3 : app_encode_fun($i, $o)]:
0.00/0.47	      (app_encode_app($i, $o, X3, z)
0.00/0.47	       | ~ app_encode_app($i, $o, X3, X2)
0.00/0.47	       | app_encode_app($i, $o, sk_Xp1, X2)
0.00/0.47	       | ~ app_encode_app($i, $o, X0, X1)
0.00/0.47	       | app_encode_app($i, $o, X0, sk_Xy1)
0.00/0.47	       | app_encode_app($i, $o, sk_Xq, sk_Xy)),
0.00/0.47	    inference('simplify', [status(thm)], ['23'])).
0.00/0.47	tff('25', plain,
0.00/0.47	    ![X0 : app_encode_fun($i, $o), X1]:
0.00/0.47	      (~ $true
0.00/0.47	       | app_encode_app($i, $o, sk_Xq, sk_Xy)
0.00/0.47	       | app_encode_app($i, $o, sk_Xq, sk_Xy)
0.00/0.47	       | app_encode_app($i, $o, X0, sk_Xy1)
0.00/0.47	       | ~ app_encode_app($i, $o, X0, X1)
0.00/0.47	       | app_encode_app($i, $o, sk_Xp1, sk_Xy1)
0.00/0.47	       | app_encode_app($i, $o, sk_Xq1, z)),
0.00/0.47	    inference('sup-', [status(thm)], ['2', '24'])).
0.00/0.47	tff('26', plain,
0.00/0.47	    ![X0 : app_encode_fun($i, $o), X1]:
0.00/0.47	      (app_encode_app($i, $o, sk_Xq1, z)
0.00/0.47	       | app_encode_app($i, $o, sk_Xp1, sk_Xy1)
0.00/0.47	       | ~ app_encode_app($i, $o, X0, X1)
0.00/0.47	       | app_encode_app($i, $o, X0, sk_Xy1)
0.00/0.47	       | app_encode_app($i, $o, sk_Xq, sk_Xy)),
0.00/0.47	    inference('simplify', [status(thm)], ['25'])).
0.00/0.47	tff('27', plain,
0.00/0.47	    ![X0 : app_encode_fun($i, $o), X1]:
0.00/0.47	      (app_encode_app($i, $o, sk_Xq, sk_Xy)
0.00/0.47	       | app_encode_app($i, $o, X0, sk_Xy1)
0.00/0.47	       | ~ app_encode_app($i, $o, X0, X1)
0.00/0.47	       | app_encode_app($i, $o, sk_Xp1, sk_Xy1)),
0.00/0.47	    inference('clc', [status(thm)], ['26', '21'])).
0.00/0.47	tff('28', plain,
0.00/0.47	    (app_encode_app($i, $o, sk_Xq, sk_Xy)
0.00/0.47	     | ~ app_encode_app($i, $o, sk_Xp1, sk_Xy1)),
0.00/0.47	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.47	tff('29', plain,
0.00/0.47	    ![X0 : app_encode_fun($i, $o), X1]:
0.00/0.47	      (~ app_encode_app($i, $o, X0, X1)
0.00/0.47	       | app_encode_app($i, $o, X0, sk_Xy1)
0.00/0.47	       | app_encode_app($i, $o, sk_Xq, sk_Xy)),
0.00/0.47	    inference('clc', [status(thm)], ['27', '28'])).
0.00/0.47	tff('30', plain,
0.00/0.47	    (~ $true
0.00/0.47	     | app_encode_app($i, $o, sk_Xq, sk_Xy)
0.00/0.47	     | app_encode_app($i, $o, sk_Xq, sk_Xy)
0.00/0.47	     | app_encode_app($i, $o, sk_Xp1, sk_Xy1)),
0.00/0.47	    inference('sup-', [status(thm)], ['1', '29'])).
0.00/0.47	tff('31', plain,
0.00/0.47	    (app_encode_app($i, $o, sk_Xp1, sk_Xy1)
0.00/0.47	     | app_encode_app($i, $o, sk_Xq, sk_Xy)),
0.00/0.47	    inference('simplify', [status(thm)], ['30'])).
0.00/0.47	tff('32', plain, app_encode_app($i, $o, sk_Xq, sk_Xy),
0.00/0.47	    inference('clc', [status(thm)], ['31', '28'])).
0.00/0.47	tff('33', plain,
0.00/0.47	    ![X0, X1 : app_encode_fun($i, $o), X2 : app_encode_fun($i, $o), X3, X4, 
0.00/0.47	      X5 : app_encode_fun($i, $o)]:
0.00/0.47	      (~ $true
0.00/0.47	       | ~ app_encode_app($i, $o, X1, X0)
0.00/0.47	       | app_encode_app($i, $o, X2, z)
0.00/0.47	       | ~ app_encode_app($i, $o, X2, X3)
0.00/0.47	       | app_encode_app($i, $o, X1, X3)
0.00/0.47	       | app_encode_app($i, $o, sk_Xq, z)
0.00/0.47	       | ~ app_encode_app($i, $o, X5, X4)
0.00/0.47	       | app_encode_app($i, $o, X5, sk_Xy)),
0.00/0.47	    inference('sup-', [status(thm)], ['32', '3'])).
0.00/0.47	tff('34', plain,
0.00/0.47	    ![X0, X1 : app_encode_fun($i, $o), X2 : app_encode_fun($i, $o), X3, X4, 
0.00/0.47	      X5 : app_encode_fun($i, $o)]:
0.00/0.47	      (app_encode_app($i, $o, X5, sk_Xy)
0.00/0.47	       | ~ app_encode_app($i, $o, X5, X4)
0.00/0.47	       | app_encode_app($i, $o, sk_Xq, z)
0.00/0.47	       | app_encode_app($i, $o, X1, X3)
0.00/0.47	       | ~ app_encode_app($i, $o, X2, X3)
0.00/0.47	       | app_encode_app($i, $o, X2, z)
0.00/0.47	       | ~ app_encode_app($i, $o, X1, X0)),
0.00/0.47	    inference('simplify', [status(thm)], ['33'])).
0.00/0.47	tff('35', plain,
0.00/0.47	    (~ app_encode_app($i, $o, sk_Xq, z)
0.00/0.47	     | app_encode_app($i, $o, sk_Xp1, sk_Xx1)),
0.00/0.47	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.47	tff('36', plain,
0.00/0.47	    (~ app_encode_app($i, $o, sk_Xq, z)
0.00/0.47	     | app_encode_app($i, $o, sk_Xq1, sk_Xy1)),
0.00/0.47	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.47	tff('37', plain,
0.00/0.47	    ![X0, X1 : app_encode_fun($i, $o), X2 : app_encode_fun($i, $o), X3, X4, 
0.00/0.47	      X5 : app_encode_fun($i, $o)]:
0.00/0.47	      (~ $true
0.00/0.47	       | ~ app_encode_app($i, $o, sk_Xq, z)
0.00/0.47	       | ~ app_encode_app($i, $o, X1, X0)
0.00/0.47	       | app_encode_app($i, $o, X2, z)
0.00/0.47	       | ~ app_encode_app($i, $o, X2, X3)
0.00/0.47	       | app_encode_app($i, $o, X1, X3)
0.00/0.47	       | app_encode_app($i, $o, sk_Xq1, z)
0.00/0.47	       | ~ app_encode_app($i, $o, X5, X4)
0.00/0.47	       | app_encode_app($i, $o, X5, sk_Xy1)),
0.00/0.47	    inference('sup-', [status(thm)], ['36', '3'])).
0.00/0.47	tff('38', plain,
0.00/0.47	    ![X0, X1 : app_encode_fun($i, $o), X2 : app_encode_fun($i, $o), X3, X4, 
0.00/0.47	      X5 : app_encode_fun($i, $o)]:
0.00/0.47	      (app_encode_app($i, $o, X5, sk_Xy1)
0.00/0.47	       | ~ app_encode_app($i, $o, X5, X4)
0.00/0.47	       | app_encode_app($i, $o, sk_Xq1, z)
0.00/0.47	       | app_encode_app($i, $o, X1, X3)
0.00/0.47	       | ~ app_encode_app($i, $o, X2, X3)
0.00/0.47	       | app_encode_app($i, $o, X2, z)
0.00/0.47	       | ~ app_encode_app($i, $o, X1, X0)
0.00/0.47	       | ~ app_encode_app($i, $o, sk_Xq, z)),
0.00/0.47	    inference('simplify', [status(thm)], ['37'])).
0.00/0.47	tff('39', plain,
0.00/0.47	    ![X0, X1 : app_encode_fun($i, $o), X2 : app_encode_fun($i, $o), X3, X4, 
0.00/0.47	      X5 : app_encode_fun($i, $o)]:
0.00/0.47	      (~ app_encode_app($i, $o, sk_Xq, z)
0.00/0.47	       | ~ app_encode_app($i, $o, X1, X0)
0.00/0.47	       | app_encode_app($i, $o, X2, z)
0.00/0.47	       | ~ app_encode_app($i, $o, X2, X3)
0.00/0.47	       | app_encode_app($i, $o, X1, X3)
0.00/0.47	       | ~ app_encode_app($i, $o, X5, X4)
0.00/0.47	       | app_encode_app($i, $o, X5, sk_Xy1)),
0.00/0.47	    inference('clc', [status(thm)], ['38', '21'])).
0.00/0.47	tff('40', plain,
0.00/0.47	    ![X0 : app_encode_fun($i, $o), X1, X2, X3 : app_encode_fun($i, $o)]:
0.00/0.47	      (~ $true
0.00/0.47	       | ~ app_encode_app($i, $o, sk_Xq, z)
0.00/0.47	       | app_encode_app($i, $o, X0, sk_Xy1)
0.00/0.47	       | ~ app_encode_app($i, $o, X0, X1)
0.00/0.47	       | app_encode_app($i, $o, sk_Xp1, X2)
0.00/0.47	       | ~ app_encode_app($i, $o, X3, X2)
0.00/0.47	       | app_encode_app($i, $o, X3, z)
0.00/0.47	       | ~ app_encode_app($i, $o, sk_Xq, z)),
0.00/0.47	    inference('sup-', [status(thm)], ['35', '39'])).
0.00/0.47	tff('41', plain,
0.00/0.47	    ![X0 : app_encode_fun($i, $o), X1, X2, X3 : app_encode_fun($i, $o)]:
0.00/0.47	      (app_encode_app($i, $o, X3, z)
0.00/0.47	       | ~ app_encode_app($i, $o, X3, X2)
0.00/0.47	       | app_encode_app($i, $o, sk_Xp1, X2)
0.00/0.47	       | ~ app_encode_app($i, $o, X0, X1)
0.00/0.47	       | app_encode_app($i, $o, X0, sk_Xy1)
0.00/0.47	       | ~ app_encode_app($i, $o, sk_Xq, z)),
0.00/0.47	    inference('simplify', [status(thm)], ['40'])).
0.00/0.47	tff('42', plain,
0.00/0.47	    ![X0 : app_encode_fun($i, $o), X1]:
0.00/0.47	      (~ $true
0.00/0.47	       | ~ app_encode_app($i, $o, sk_Xq, z)
0.00/0.47	       | ~ app_encode_app($i, $o, sk_Xq, z)
0.00/0.47	       | app_encode_app($i, $o, X0, sk_Xy1)
0.00/0.47	       | ~ app_encode_app($i, $o, X0, X1)
0.00/0.47	       | app_encode_app($i, $o, sk_Xp1, sk_Xy1)
0.00/0.47	       | app_encode_app($i, $o, sk_Xq1, z)),
0.00/0.47	    inference('sup-', [status(thm)], ['36', '41'])).
0.00/0.47	tff('43', plain,
0.00/0.47	    ![X0 : app_encode_fun($i, $o), X1]:
0.00/0.47	      (app_encode_app($i, $o, sk_Xq1, z)
0.00/0.47	       | app_encode_app($i, $o, sk_Xp1, sk_Xy1)
0.00/0.47	       | ~ app_encode_app($i, $o, X0, X1)
0.00/0.47	       | app_encode_app($i, $o, X0, sk_Xy1)
0.00/0.47	       | ~ app_encode_app($i, $o, sk_Xq, z)),
0.00/0.47	    inference('simplify', [status(thm)], ['42'])).
0.00/0.47	tff('44', plain,
0.00/0.47	    ![X0 : app_encode_fun($i, $o), X1]:
0.00/0.47	      (~ app_encode_app($i, $o, sk_Xq, z)
0.00/0.47	       | app_encode_app($i, $o, X0, sk_Xy1)
0.00/0.47	       | ~ app_encode_app($i, $o, X0, X1)
0.00/0.47	       | app_encode_app($i, $o, sk_Xp1, sk_Xy1)),
0.00/0.47	    inference('clc', [status(thm)], ['43', '21'])).
0.00/0.47	tff('45', plain,
0.00/0.47	    (~ app_encode_app($i, $o, sk_Xq, z)
0.00/0.47	     | ~ app_encode_app($i, $o, sk_Xp1, sk_Xy1)),
0.00/0.47	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.47	tff('46', plain,
0.00/0.47	    ![X0 : app_encode_fun($i, $o), X1]:
0.00/0.47	      (~ app_encode_app($i, $o, X0, X1)
0.00/0.47	       | app_encode_app($i, $o, X0, sk_Xy1)
0.00/0.47	       | ~ app_encode_app($i, $o, sk_Xq, z)),
0.00/0.47	    inference('clc', [status(thm)], ['44', '45'])).
0.00/0.47	tff('47', plain,
0.00/0.47	    (~ $true
0.00/0.47	     | ~ app_encode_app($i, $o, sk_Xq, z)
0.00/0.47	     | ~ app_encode_app($i, $o, sk_Xq, z)
0.00/0.47	     | app_encode_app($i, $o, sk_Xp1, sk_Xy1)),
0.00/0.47	    inference('sup-', [status(thm)], ['35', '46'])).
0.00/0.47	tff('48', plain,
0.00/0.47	    (app_encode_app($i, $o, sk_Xp1, sk_Xy1)
0.00/0.47	     | ~ app_encode_app($i, $o, sk_Xq, z)),
0.00/0.47	    inference('simplify', [status(thm)], ['47'])).
0.00/0.47	tff('49', plain, ~ app_encode_app($i, $o, sk_Xq, z),
0.00/0.47	    inference('clc', [status(thm)], ['48', '45'])).
0.00/0.47	tff('50', plain,
0.00/0.47	    ![X0, X1 : app_encode_fun($i, $o), X2 : app_encode_fun($i, $o), X3, X4, 
0.00/0.47	      X5 : app_encode_fun($i, $o)]:
0.00/0.47	      (~ app_encode_app($i, $o, X1, X0)
0.00/0.47	       | app_encode_app($i, $o, X2, z)
0.00/0.47	       | ~ app_encode_app($i, $o, X2, X3)
0.00/0.47	       | app_encode_app($i, $o, X1, X3)
0.00/0.47	       | ~ app_encode_app($i, $o, X5, X4)
0.00/0.47	       | app_encode_app($i, $o, X5, sk_Xy)),
0.00/0.47	    inference('clc', [status(thm)], ['34', '49'])).
0.00/0.47	tff('51', plain,
0.00/0.47	    ![X0 : app_encode_fun($i, $o), X1, X2, X3 : app_encode_fun($i, $o)]:
0.00/0.47	      (~ $true
0.00/0.47	       | app_encode_app($i, $o, sk_Xp, sk_Xx)
0.00/0.47	       | app_encode_app($i, $o, X0, sk_Xy)
0.00/0.47	       | ~ app_encode_app($i, $o, X0, X1)
0.00/0.47	       | app_encode_app($i, $o, sk_Xp1, X2)
0.00/0.47	       | ~ app_encode_app($i, $o, X3, X2)
0.00/0.47	       | app_encode_app($i, $o, X3, z)),
0.00/0.47	    inference('sup-', [status(thm)], ['0', '50'])).
0.00/0.47	tff('52', plain,
0.00/0.47	    ![X0 : app_encode_fun($i, $o), X1, X2, X3 : app_encode_fun($i, $o)]:
0.00/0.47	      (app_encode_app($i, $o, X3, z)
0.00/0.47	       | ~ app_encode_app($i, $o, X3, X2)
0.00/0.47	       | app_encode_app($i, $o, sk_Xp1, X2)
0.00/0.47	       | ~ app_encode_app($i, $o, X0, X1)
0.00/0.47	       | app_encode_app($i, $o, X0, sk_Xy)
0.00/0.47	       | app_encode_app($i, $o, sk_Xp, sk_Xx)),
0.00/0.47	    inference('simplify', [status(thm)], ['51'])).
0.00/0.47	tff('53', plain,
0.00/0.47	    ![X0 : app_encode_fun($i, $o), X1]:
0.00/0.47	      (~ $true
0.00/0.47	       | app_encode_app($i, $o, sk_Xp, sk_Xx)
0.00/0.47	       | app_encode_app($i, $o, X0, sk_Xy)
0.00/0.47	       | ~ app_encode_app($i, $o, X0, X1)
0.00/0.47	       | app_encode_app($i, $o, sk_Xp1, sk_Xy)
0.00/0.47	       | app_encode_app($i, $o, sk_Xq, z)),
0.00/0.47	    inference('sup-', [status(thm)], ['32', '52'])).
0.00/0.47	tff('54', plain,
0.00/0.47	    ![X0 : app_encode_fun($i, $o), X1]:
0.00/0.47	      (app_encode_app($i, $o, sk_Xq, z)
0.00/0.47	       | app_encode_app($i, $o, sk_Xp1, sk_Xy)
0.00/0.47	       | ~ app_encode_app($i, $o, X0, X1)
0.00/0.47	       | app_encode_app($i, $o, X0, sk_Xy)
0.00/0.47	       | app_encode_app($i, $o, sk_Xp, sk_Xx)),
0.00/0.47	    inference('simplify', [status(thm)], ['53'])).
0.00/0.47	tff('55', plain,
0.00/0.47	    ![X0 : app_encode_fun($i, $o), X1]:
0.00/0.47	      (app_encode_app($i, $o, sk_Xp, sk_Xx)
0.00/0.47	       | app_encode_app($i, $o, X0, sk_Xy)
0.00/0.47	       | ~ app_encode_app($i, $o, X0, X1)
0.00/0.47	       | app_encode_app($i, $o, sk_Xp1, sk_Xy)),
0.00/0.47	    inference('clc', [status(thm)], ['54', '49'])).
0.00/0.47	tff('56', plain,
0.00/0.47	    (~ $true
0.00/0.47	     | app_encode_app($i, $o, sk_Xp, sk_Xx)
0.00/0.47	     | app_encode_app($i, $o, sk_Xp1, sk_Xy)
0.00/0.47	     | app_encode_app($i, $o, sk_Xp1, sk_Xy)
0.00/0.47	     | app_encode_app($i, $o, sk_Xp, sk_Xx)),
0.00/0.47	    inference('sup-', [status(thm)], ['0', '55'])).
0.00/0.47	tff('57', plain,
0.00/0.47	    (app_encode_app($i, $o, sk_Xp1, sk_Xy)
0.00/0.47	     | app_encode_app($i, $o, sk_Xp, sk_Xx)),
0.00/0.47	    inference('simplify', [status(thm)], ['56'])).
0.00/0.47	tff('58', plain,
0.00/0.47	    ![X0 : app_encode_fun($i, $o), X1, X2, X3 : app_encode_fun($i, $o)]:
0.00/0.47	      (~ $true
0.00/0.47	       | app_encode_app($i, $o, sk_Xp1, sk_Xy)
0.00/0.47	       | app_encode_app($i, $o, X0, sk_Xy)
0.00/0.47	       | ~ app_encode_app($i, $o, X0, X1)
0.00/0.47	       | app_encode_app($i, $o, sk_Xp, X2)
0.00/0.47	       | ~ app_encode_app($i, $o, X3, X2)
0.00/0.47	       | app_encode_app($i, $o, X3, z)),
0.00/0.47	    inference('sup-', [status(thm)], ['57', '50'])).
0.00/0.47	tff('59', plain,
0.00/0.47	    ![X0 : app_encode_fun($i, $o), X1, X2, X3 : app_encode_fun($i, $o)]:
0.00/0.47	      (app_encode_app($i, $o, X3, z)
0.00/0.47	       | ~ app_encode_app($i, $o, X3, X2)
0.00/0.47	       | app_encode_app($i, $o, sk_Xp, X2)
0.00/0.47	       | ~ app_encode_app($i, $o, X0, X1)
0.00/0.47	       | app_encode_app($i, $o, X0, sk_Xy)
0.00/0.47	       | app_encode_app($i, $o, sk_Xp1, sk_Xy)),
0.00/0.47	    inference('simplify', [status(thm)], ['58'])).
0.00/0.47	tff('60', plain,
0.00/0.47	    ![X0 : app_encode_fun($i, $o), X1]:
0.00/0.47	      (~ $true
0.00/0.47	       | app_encode_app($i, $o, sk_Xp1, sk_Xy)
0.00/0.47	       | app_encode_app($i, $o, X0, sk_Xy)
0.00/0.47	       | ~ app_encode_app($i, $o, X0, X1)
0.00/0.47	       | app_encode_app($i, $o, sk_Xp, sk_Xy)
0.00/0.47	       | app_encode_app($i, $o, sk_Xq, z)),
0.00/0.47	    inference('sup-', [status(thm)], ['32', '59'])).
0.00/0.47	tff('61', plain,
0.00/0.47	    ![X0 : app_encode_fun($i, $o), X1]:
0.00/0.47	      (app_encode_app($i, $o, sk_Xq, z)
0.00/0.47	       | app_encode_app($i, $o, sk_Xp, sk_Xy)
0.00/0.47	       | ~ app_encode_app($i, $o, X0, X1)
0.00/0.47	       | app_encode_app($i, $o, X0, sk_Xy)
0.00/0.47	       | app_encode_app($i, $o, sk_Xp1, sk_Xy)),
0.00/0.47	    inference('simplify', [status(thm)], ['60'])).
0.00/0.47	tff('62', plain,
0.00/0.47	    ![X0 : app_encode_fun($i, $o), X1]:
0.00/0.47	      (app_encode_app($i, $o, sk_Xp1, sk_Xy)
0.00/0.47	       | app_encode_app($i, $o, X0, sk_Xy)
0.00/0.47	       | ~ app_encode_app($i, $o, X0, X1)
0.00/0.47	       | app_encode_app($i, $o, sk_Xp, sk_Xy)),
0.00/0.47	    inference('clc', [status(thm)], ['61', '49'])).
0.00/0.47	tff('63', plain,
0.00/0.47	    (~ app_encode_app($i, $o, sk_Xp, sk_Xy)
0.00/0.47	     | app_encode_app($i, $o, sk_Xp1, sk_Xx1)),
0.00/0.47	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.47	tff('64', plain,
0.00/0.47	    (~ app_encode_app($i, $o, sk_Xp, sk_Xy)
0.00/0.47	     | app_encode_app($i, $o, sk_Xq1, sk_Xy1)),
0.00/0.47	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.47	tff('65', plain,
0.00/0.47	    ![X0, X1 : app_encode_fun($i, $o), X2 : app_encode_fun($i, $o), X3, X4, 
0.00/0.47	      X5 : app_encode_fun($i, $o)]:
0.00/0.47	      (~ $true
0.00/0.47	       | ~ app_encode_app($i, $o, sk_Xp, sk_Xy)
0.00/0.47	       | ~ app_encode_app($i, $o, X1, X0)
0.00/0.47	       | app_encode_app($i, $o, X2, z)
0.00/0.47	       | ~ app_encode_app($i, $o, X2, X3)
0.00/0.47	       | app_encode_app($i, $o, X1, X3)
0.00/0.47	       | app_encode_app($i, $o, sk_Xq1, z)
0.00/0.47	       | ~ app_encode_app($i, $o, X5, X4)
0.00/0.47	       | app_encode_app($i, $o, X5, sk_Xy1)),
0.00/0.47	    inference('sup-', [status(thm)], ['64', '3'])).
0.00/0.47	tff('66', plain,
0.00/0.47	    ![X0, X1 : app_encode_fun($i, $o), X2 : app_encode_fun($i, $o), X3, X4, 
0.00/0.47	      X5 : app_encode_fun($i, $o)]:
0.00/0.47	      (app_encode_app($i, $o, X5, sk_Xy1)
0.00/0.47	       | ~ app_encode_app($i, $o, X5, X4)
0.00/0.47	       | app_encode_app($i, $o, sk_Xq1, z)
0.00/0.47	       | app_encode_app($i, $o, X1, X3)
0.00/0.47	       | ~ app_encode_app($i, $o, X2, X3)
0.00/0.47	       | app_encode_app($i, $o, X2, z)
0.00/0.47	       | ~ app_encode_app($i, $o, X1, X0)
0.00/0.47	       | ~ app_encode_app($i, $o, sk_Xp, sk_Xy)),
0.00/0.47	    inference('simplify', [status(thm)], ['65'])).
0.00/0.47	tff('67', plain,
0.00/0.47	    ![X0, X1 : app_encode_fun($i, $o), X2 : app_encode_fun($i, $o), X3, X4, 
0.00/0.47	      X5 : app_encode_fun($i, $o)]:
0.00/0.47	      (~ app_encode_app($i, $o, sk_Xp, sk_Xy)
0.00/0.47	       | ~ app_encode_app($i, $o, X1, X0)
0.00/0.47	       | app_encode_app($i, $o, X2, z)
0.00/0.47	       | ~ app_encode_app($i, $o, X2, X3)
0.00/0.47	       | app_encode_app($i, $o, X1, X3)
0.00/0.47	       | ~ app_encode_app($i, $o, X5, X4)
0.00/0.47	       | app_encode_app($i, $o, X5, sk_Xy1)),
0.00/0.47	    inference('clc', [status(thm)], ['66', '21'])).
0.00/0.47	tff('68', plain,
0.00/0.47	    ![X0 : app_encode_fun($i, $o), X1, X2, X3 : app_encode_fun($i, $o)]:
0.00/0.47	      (~ $true
0.00/0.47	       | ~ app_encode_app($i, $o, sk_Xp, sk_Xy)
0.00/0.47	       | app_encode_app($i, $o, X0, sk_Xy1)
0.00/0.47	       | ~ app_encode_app($i, $o, X0, X1)
0.00/0.47	       | app_encode_app($i, $o, sk_Xp1, X2)
0.00/0.47	       | ~ app_encode_app($i, $o, X3, X2)
0.00/0.47	       | app_encode_app($i, $o, X3, z)
0.00/0.47	       | ~ app_encode_app($i, $o, sk_Xp, sk_Xy)),
0.00/0.47	    inference('sup-', [status(thm)], ['63', '67'])).
0.00/0.47	tff('69', plain,
0.00/0.47	    ![X0 : app_encode_fun($i, $o), X1, X2, X3 : app_encode_fun($i, $o)]:
0.00/0.47	      (app_encode_app($i, $o, X3, z)
0.00/0.47	       | ~ app_encode_app($i, $o, X3, X2)
0.00/0.47	       | app_encode_app($i, $o, sk_Xp1, X2)
0.00/0.47	       | ~ app_encode_app($i, $o, X0, X1)
0.00/0.47	       | app_encode_app($i, $o, X0, sk_Xy1)
0.00/0.47	       | ~ app_encode_app($i, $o, sk_Xp, sk_Xy)),
0.00/0.47	    inference('simplify', [status(thm)], ['68'])).
0.00/0.47	tff('70', plain,
0.00/0.47	    ![X0 : app_encode_fun($i, $o), X1]:
0.00/0.47	      (~ $true
0.00/0.47	       | ~ app_encode_app($i, $o, sk_Xp, sk_Xy)
0.00/0.47	       | ~ app_encode_app($i, $o, sk_Xp, sk_Xy)
0.00/0.47	       | app_encode_app($i, $o, X0, sk_Xy1)
0.00/0.47	       | ~ app_encode_app($i, $o, X0, X1)
0.00/0.47	       | app_encode_app($i, $o, sk_Xp1, sk_Xy1)
0.00/0.47	       | app_encode_app($i, $o, sk_Xq1, z)),
0.00/0.47	    inference('sup-', [status(thm)], ['64', '69'])).
0.00/0.47	tff('71', plain,
0.00/0.47	    ![X0 : app_encode_fun($i, $o), X1]:
0.00/0.47	      (app_encode_app($i, $o, sk_Xq1, z)
0.00/0.47	       | app_encode_app($i, $o, sk_Xp1, sk_Xy1)
0.00/0.47	       | ~ app_encode_app($i, $o, X0, X1)
0.00/0.47	       | app_encode_app($i, $o, X0, sk_Xy1)
0.00/0.47	       | ~ app_encode_app($i, $o, sk_Xp, sk_Xy)),
0.00/0.47	    inference('simplify', [status(thm)], ['70'])).
0.00/0.47	tff('72', plain,
0.00/0.47	    ![X0 : app_encode_fun($i, $o), X1]:
0.00/0.47	      (~ app_encode_app($i, $o, sk_Xp, sk_Xy)
0.00/0.47	       | app_encode_app($i, $o, X0, sk_Xy1)
0.00/0.47	       | ~ app_encode_app($i, $o, X0, X1)
0.00/0.47	       | app_encode_app($i, $o, sk_Xp1, sk_Xy1)),
0.00/0.47	    inference('clc', [status(thm)], ['71', '21'])).
0.00/0.47	tff('73', plain,
0.00/0.47	    (~ app_encode_app($i, $o, sk_Xp, sk_Xy)
0.00/0.47	     | ~ app_encode_app($i, $o, sk_Xp1, sk_Xy1)),
0.00/0.47	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.47	tff('74', plain,
0.00/0.47	    ![X0 : app_encode_fun($i, $o), X1]:
0.00/0.47	      (~ app_encode_app($i, $o, X0, X1)
0.00/0.47	       | app_encode_app($i, $o, X0, sk_Xy1)
0.00/0.47	       | ~ app_encode_app($i, $o, sk_Xp, sk_Xy)),
0.00/0.47	    inference('clc', [status(thm)], ['72', '73'])).
0.00/0.47	tff('75', plain,
0.00/0.47	    (~ $true
0.00/0.47	     | ~ app_encode_app($i, $o, sk_Xp, sk_Xy)
0.00/0.47	     | ~ app_encode_app($i, $o, sk_Xp, sk_Xy)
0.00/0.47	     | app_encode_app($i, $o, sk_Xp1, sk_Xy1)),
0.00/0.47	    inference('sup-', [status(thm)], ['63', '74'])).
0.00/0.47	tff('76', plain,
0.00/0.47	    (app_encode_app($i, $o, sk_Xp1, sk_Xy1)
0.00/0.47	     | ~ app_encode_app($i, $o, sk_Xp, sk_Xy)),
0.00/0.47	    inference('simplify', [status(thm)], ['75'])).
0.00/0.47	tff('77', plain, ~ app_encode_app($i, $o, sk_Xp, sk_Xy),
0.00/0.47	    inference('clc', [status(thm)], ['76', '73'])).
0.00/0.47	tff('78', plain,
0.00/0.47	    ![X0 : app_encode_fun($i, $o), X1]:
0.00/0.47	      (~ app_encode_app($i, $o, X0, X1)
0.00/0.47	       | app_encode_app($i, $o, X0, sk_Xy)
0.00/0.47	       | app_encode_app($i, $o, sk_Xp1, sk_Xy)),
0.00/0.47	    inference('clc', [status(thm)], ['62', '77'])).
0.00/0.47	tff('79', plain,
0.00/0.47	    (~ $true
0.00/0.47	     | app_encode_app($i, $o, sk_Xp1, sk_Xy)
0.00/0.47	     | app_encode_app($i, $o, sk_Xp1, sk_Xy)
0.00/0.47	     | app_encode_app($i, $o, sk_Xp, sk_Xy)),
0.00/0.47	    inference('sup-', [status(thm)], ['57', '78'])).
0.00/0.47	tff('80', plain,
0.00/0.47	    (app_encode_app($i, $o, sk_Xp, sk_Xy)
0.00/0.47	     | app_encode_app($i, $o, sk_Xp1, sk_Xy)),
0.00/0.47	    inference('simplify', [status(thm)], ['79'])).
0.00/0.47	tff('81', plain, app_encode_app($i, $o, sk_Xp1, sk_Xy),
0.00/0.47	    inference('clc', [status(thm)], ['80', '77'])).
0.00/0.47	tff('82', plain,
0.00/0.47	    (app_encode_app($i, $o, sk_Xp, sk_Xx)
0.00/0.47	     | app_encode_app($i, $o, sk_Xq1, sk_Xy1)),
0.00/0.47	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.47	tff('83', plain,
0.00/0.47	    ![X0 : app_encode_fun($i, $o), X1, X2, X3 : app_encode_fun($i, $o)]:
0.00/0.47	      (~ $true
0.00/0.47	       | app_encode_app($i, $o, sk_Xq1, sk_Xy1)
0.00/0.47	       | app_encode_app($i, $o, X0, sk_Xy)
0.00/0.47	       | ~ app_encode_app($i, $o, X0, X1)
0.00/0.47	       | app_encode_app($i, $o, sk_Xp, X2)
0.00/0.47	       | ~ app_encode_app($i, $o, X3, X2)
0.00/0.47	       | app_encode_app($i, $o, X3, z)),
0.00/0.47	    inference('sup-', [status(thm)], ['82', '50'])).
0.00/0.47	tff('84', plain,
0.00/0.47	    ![X0 : app_encode_fun($i, $o), X1, X2, X3 : app_encode_fun($i, $o)]:
0.00/0.47	      (app_encode_app($i, $o, X3, z)
0.00/0.47	       | ~ app_encode_app($i, $o, X3, X2)
0.00/0.47	       | app_encode_app($i, $o, sk_Xp, X2)
0.00/0.47	       | ~ app_encode_app($i, $o, X0, X1)
0.00/0.47	       | app_encode_app($i, $o, X0, sk_Xy)
0.00/0.47	       | app_encode_app($i, $o, sk_Xq1, sk_Xy1)),
0.00/0.47	    inference('simplify', [status(thm)], ['83'])).
0.00/0.47	tff('85', plain,
0.00/0.47	    ![X0 : app_encode_fun($i, $o), X1]:
0.00/0.47	      (~ $true
0.00/0.47	       | app_encode_app($i, $o, sk_Xq1, sk_Xy1)
0.00/0.47	       | app_encode_app($i, $o, X0, sk_Xy)
0.00/0.47	       | ~ app_encode_app($i, $o, X0, X1)
0.00/0.47	       | app_encode_app($i, $o, sk_Xp, sk_Xy)
0.00/0.47	       | app_encode_app($i, $o, sk_Xq, z)),
0.00/0.47	    inference('sup-', [status(thm)], ['32', '84'])).
0.00/0.47	tff('86', plain,
0.00/0.47	    ![X0 : app_encode_fun($i, $o), X1]:
0.00/0.47	      (app_encode_app($i, $o, sk_Xq, z)
0.00/0.47	       | app_encode_app($i, $o, sk_Xp, sk_Xy)
0.00/0.47	       | ~ app_encode_app($i, $o, X0, X1)
0.00/0.47	       | app_encode_app($i, $o, X0, sk_Xy)
0.00/0.47	       | app_encode_app($i, $o, sk_Xq1, sk_Xy1)),
0.00/0.47	    inference('simplify', [status(thm)], ['85'])).
0.00/0.47	tff('87', plain,
0.00/0.47	    ![X0 : app_encode_fun($i, $o), X1]:
0.00/0.47	      (app_encode_app($i, $o, sk_Xq1, sk_Xy1)
0.00/0.47	       | app_encode_app($i, $o, X0, sk_Xy)
0.00/0.47	       | ~ app_encode_app($i, $o, X0, X1)
0.00/0.47	       | app_encode_app($i, $o, sk_Xp, sk_Xy)),
0.00/0.47	    inference('clc', [status(thm)], ['86', '49'])).
0.00/0.47	tff('88', plain,
0.00/0.47	    ![X0 : app_encode_fun($i, $o), X1]:
0.00/0.47	      (~ app_encode_app($i, $o, X0, X1)
0.00/0.47	       | app_encode_app($i, $o, X0, sk_Xy)
0.00/0.47	       | app_encode_app($i, $o, sk_Xq1, sk_Xy1)),
0.00/0.47	    inference('clc', [status(thm)], ['87', '77'])).
0.00/0.47	tff('89', plain,
0.00/0.47	    (~ $true
0.00/0.47	     | app_encode_app($i, $o, sk_Xq1, sk_Xy1)
0.00/0.47	     | app_encode_app($i, $o, sk_Xq1, sk_Xy1)
0.00/0.47	     | app_encode_app($i, $o, sk_Xp, sk_Xy)),
0.00/0.47	    inference('sup-', [status(thm)], ['82', '88'])).
0.00/0.47	tff('90', plain,
0.00/0.47	    (app_encode_app($i, $o, sk_Xp, sk_Xy)
0.00/0.47	     | app_encode_app($i, $o, sk_Xq1, sk_Xy1)),
0.00/0.47	    inference('simplify', [status(thm)], ['89'])).
0.00/0.47	tff('91', plain, app_encode_app($i, $o, sk_Xq1, sk_Xy1),
0.00/0.47	    inference('clc', [status(thm)], ['90', '77'])).
0.00/0.47	tff('92', plain,
0.00/0.47	    ![X0, X1 : app_encode_fun($i, $o), X2 : app_encode_fun($i, $o), X3, X4, 
0.00/0.47	      X5 : app_encode_fun($i, $o)]:
0.00/0.47	      (~ $true
0.00/0.47	       | ~ app_encode_app($i, $o, X1, X0)
0.00/0.47	       | app_encode_app($i, $o, X2, z)
0.00/0.47	       | ~ app_encode_app($i, $o, X2, X3)
0.00/0.47	       | app_encode_app($i, $o, X1, X3)
0.00/0.47	       | app_encode_app($i, $o, sk_Xq1, z)
0.00/0.47	       | ~ app_encode_app($i, $o, X5, X4)
0.00/0.47	       | app_encode_app($i, $o, X5, sk_Xy1)),
0.00/0.47	    inference('sup-', [status(thm)], ['91', '3'])).
0.00/0.47	tff('93', plain,
0.00/0.47	    ![X0, X1 : app_encode_fun($i, $o), X2 : app_encode_fun($i, $o), X3, X4, 
0.00/0.47	      X5 : app_encode_fun($i, $o)]:
0.00/0.47	      (app_encode_app($i, $o, X5, sk_Xy1)
0.00/0.47	       | ~ app_encode_app($i, $o, X5, X4)
0.00/0.47	       | app_encode_app($i, $o, sk_Xq1, z)
0.00/0.47	       | app_encode_app($i, $o, X1, X3)
0.00/0.47	       | ~ app_encode_app($i, $o, X2, X3)
0.00/0.47	       | app_encode_app($i, $o, X2, z)
0.00/0.47	       | ~ app_encode_app($i, $o, X1, X0)),
0.00/0.47	    inference('simplify', [status(thm)], ['92'])).
0.00/0.47	tff('94', plain,
0.00/0.47	    ![X0, X1 : app_encode_fun($i, $o), X2 : app_encode_fun($i, $o), X3, X4, 
0.00/0.47	      X5 : app_encode_fun($i, $o)]:
0.00/0.47	      (~ app_encode_app($i, $o, X1, X0)
0.00/0.47	       | app_encode_app($i, $o, X2, z)
0.00/0.47	       | ~ app_encode_app($i, $o, X2, X3)
0.00/0.47	       | app_encode_app($i, $o, X1, X3)
0.00/0.47	       | ~ app_encode_app($i, $o, X5, X4)
0.00/0.47	       | app_encode_app($i, $o, X5, sk_Xy1)),
0.00/0.47	    inference('clc', [status(thm)], ['93', '21'])).
0.00/0.47	tff('95', plain,
0.00/0.47	    ![X0 : app_encode_fun($i, $o), X1, X2, X3 : app_encode_fun($i, $o)]:
0.00/0.47	      (~ $true
0.00/0.47	       | app_encode_app($i, $o, X0, sk_Xy1)
0.00/0.47	       | ~ app_encode_app($i, $o, X0, X1)
0.00/0.47	       | app_encode_app($i, $o, sk_Xq, X2)
0.00/0.47	       | ~ app_encode_app($i, $o, X3, X2)
0.00/0.47	       | app_encode_app($i, $o, X3, z)),
0.00/0.47	    inference('sup-', [status(thm)], ['32', '94'])).
0.00/0.47	tff('96', plain,
0.00/0.47	    ![X0 : app_encode_fun($i, $o), X1, X2, X3 : app_encode_fun($i, $o)]:
0.00/0.47	      (app_encode_app($i, $o, X3, z)
0.00/0.47	       | ~ app_encode_app($i, $o, X3, X2)
0.00/0.47	       | app_encode_app($i, $o, sk_Xq, X2)
0.00/0.47	       | ~ app_encode_app($i, $o, X0, X1)
0.00/0.47	       | app_encode_app($i, $o, X0, sk_Xy1)),
0.00/0.47	    inference('simplify', [status(thm)], ['95'])).
0.00/0.47	tff('97', plain,
0.00/0.47	    ![X0 : app_encode_fun($i, $o), X1]:
0.00/0.47	      (~ $true
0.00/0.47	       | app_encode_app($i, $o, X0, sk_Xy1)
0.00/0.47	       | ~ app_encode_app($i, $o, X0, X1)
0.00/0.47	       | app_encode_app($i, $o, sk_Xq, sk_Xy1)
0.00/0.47	       | app_encode_app($i, $o, sk_Xq1, z)),
0.00/0.47	    inference('sup-', [status(thm)], ['91', '96'])).
0.00/0.47	tff('98', plain,
0.00/0.47	    ![X0 : app_encode_fun($i, $o), X1]:
0.00/0.47	      (app_encode_app($i, $o, sk_Xq1, z)
0.00/0.47	       | app_encode_app($i, $o, sk_Xq, sk_Xy1)
0.00/0.47	       | ~ app_encode_app($i, $o, X0, X1)
0.00/0.47	       | app_encode_app($i, $o, X0, sk_Xy1)),
0.00/0.47	    inference('simplify', [status(thm)], ['97'])).
0.00/0.47	tff('99', plain,
0.00/0.47	    ![X0 : app_encode_fun($i, $o), X1]:
0.00/0.47	      (app_encode_app($i, $o, X0, sk_Xy1)
0.00/0.47	       | ~ app_encode_app($i, $o, X0, X1)
0.00/0.47	       | app_encode_app($i, $o, sk_Xq, sk_Xy1)),
0.00/0.47	    inference('clc', [status(thm)], ['98', '21'])).
0.00/0.47	tff('100', plain,
0.00/0.47	    (~ $true
0.00/0.47	     | app_encode_app($i, $o, sk_Xq, sk_Xy1)
0.00/0.47	     | app_encode_app($i, $o, sk_Xq, sk_Xy1)),
0.00/0.47	    inference('sup-', [status(thm)], ['32', '99'])).
0.00/0.47	tff('101', plain, app_encode_app($i, $o, sk_Xq, sk_Xy1),
0.00/0.47	    inference('simplify', [status(thm)], ['100'])).
0.00/0.47	tff('102', plain,
0.00/0.47	    ![X0 : app_encode_fun($i, $o), X1, X2, X3 : app_encode_fun($i, $o)]:
0.00/0.47	      (~ $true
0.00/0.47	       | app_encode_app($i, $o, X0, sk_Xy1)
0.00/0.47	       | ~ app_encode_app($i, $o, X0, X1)
0.00/0.47	       | app_encode_app($i, $o, sk_Xp1, X2)
0.00/0.47	       | ~ app_encode_app($i, $o, X3, X2)
0.00/0.47	       | app_encode_app($i, $o, X3, z)),
0.00/0.47	    inference('sup-', [status(thm)], ['81', '94'])).
0.00/0.47	tff('103', plain,
0.00/0.47	    ![X0 : app_encode_fun($i, $o), X1, X2, X3 : app_encode_fun($i, $o)]:
0.00/0.47	      (app_encode_app($i, $o, X3, z)
0.00/0.47	       | ~ app_encode_app($i, $o, X3, X2)
0.00/0.47	       | app_encode_app($i, $o, sk_Xp1, X2)
0.00/0.47	       | ~ app_encode_app($i, $o, X0, X1)
0.00/0.47	       | app_encode_app($i, $o, X0, sk_Xy1)),
0.00/0.47	    inference('simplify', [status(thm)], ['102'])).
0.00/0.47	tff('104', plain,
0.00/0.47	    ![X0 : app_encode_fun($i, $o), X1]:
0.00/0.47	      (~ $true
0.00/0.47	       | app_encode_app($i, $o, X0, sk_Xy1)
0.00/0.47	       | ~ app_encode_app($i, $o, X0, X1)
0.00/0.47	       | app_encode_app($i, $o, sk_Xp1, sk_Xy1)
0.00/0.47	       | app_encode_app($i, $o, sk_Xq, z)),
0.00/0.47	    inference('sup-', [status(thm)], ['101', '103'])).
0.00/0.47	tff('105', plain,
0.00/0.47	    ![X0 : app_encode_fun($i, $o), X1]:
0.00/0.47	      (app_encode_app($i, $o, sk_Xq, z)
0.00/0.47	       | app_encode_app($i, $o, sk_Xp1, sk_Xy1)
0.00/0.47	       | ~ app_encode_app($i, $o, X0, X1)
0.00/0.47	       | app_encode_app($i, $o, X0, sk_Xy1)),
0.00/0.47	    inference('simplify', [status(thm)], ['104'])).
0.00/0.47	tff('106', plain,
0.00/0.47	    ![X0 : app_encode_fun($i, $o), X1]:
0.00/0.47	      (app_encode_app($i, $o, X0, sk_Xy1)
0.00/0.47	       | ~ app_encode_app($i, $o, X0, X1)
0.00/0.47	       | app_encode_app($i, $o, sk_Xp1, sk_Xy1)),
0.00/0.47	    inference('clc', [status(thm)], ['105', '49'])).
0.00/0.47	tff('107', plain,
0.00/0.47	    (app_encode_app($i, $o, sk_Xp, sk_Xx)
0.00/0.47	     | ~ app_encode_app($i, $o, sk_Xp1, sk_Xy1)),
0.00/0.47	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.47	tff('108', plain,
0.00/0.47	    ![X0 : app_encode_fun($i, $o), X1, X2, X3 : app_encode_fun($i, $o)]:
0.00/0.47	      (~ $true
0.00/0.47	       | ~ app_encode_app($i, $o, sk_Xp1, sk_Xy1)
0.00/0.47	       | app_encode_app($i, $o, X0, sk_Xy)
0.00/0.47	       | ~ app_encode_app($i, $o, X0, X1)
0.00/0.47	       | app_encode_app($i, $o, sk_Xp, X2)
0.00/0.47	       | ~ app_encode_app($i, $o, X3, X2)
0.00/0.47	       | app_encode_app($i, $o, X3, z)),
0.00/0.47	    inference('sup-', [status(thm)], ['107', '50'])).
0.00/0.47	tff('109', plain,
0.00/0.47	    ![X0 : app_encode_fun($i, $o), X1, X2, X3 : app_encode_fun($i, $o)]:
0.00/0.47	      (app_encode_app($i, $o, X3, z)
0.00/0.47	       | ~ app_encode_app($i, $o, X3, X2)
0.00/0.47	       | app_encode_app($i, $o, sk_Xp, X2)
0.00/0.47	       | ~ app_encode_app($i, $o, X0, X1)
0.00/0.47	       | app_encode_app($i, $o, X0, sk_Xy)
0.00/0.47	       | ~ app_encode_app($i, $o, sk_Xp1, sk_Xy1)),
0.00/0.47	    inference('simplify', [status(thm)], ['108'])).
0.00/0.47	tff('110', plain,
0.00/0.47	    ![X0 : app_encode_fun($i, $o), X1]:
0.00/0.47	      (~ $true
0.00/0.47	       | ~ app_encode_app($i, $o, sk_Xp1, sk_Xy1)
0.00/0.47	       | app_encode_app($i, $o, X0, sk_Xy)
0.00/0.47	       | ~ app_encode_app($i, $o, X0, X1)
0.00/0.47	       | app_encode_app($i, $o, sk_Xp, sk_Xy)
0.00/0.47	       | app_encode_app($i, $o, sk_Xq, z)),
0.00/0.47	    inference('sup-', [status(thm)], ['32', '109'])).
0.00/0.47	tff('111', plain,
0.00/0.47	    ![X0 : app_encode_fun($i, $o), X1]:
0.00/0.47	      (app_encode_app($i, $o, sk_Xq, z)
0.00/0.47	       | app_encode_app($i, $o, sk_Xp, sk_Xy)
0.00/0.47	       | ~ app_encode_app($i, $o, X0, X1)
0.00/0.47	       | app_encode_app($i, $o, X0, sk_Xy)
0.00/0.47	       | ~ app_encode_app($i, $o, sk_Xp1, sk_Xy1)),
0.00/0.47	    inference('simplify', [status(thm)], ['110'])).
0.00/0.47	tff('112', plain,
0.00/0.47	    ![X0 : app_encode_fun($i, $o), X1]:
0.00/0.47	      (~ app_encode_app($i, $o, sk_Xp1, sk_Xy1)
0.00/0.47	       | app_encode_app($i, $o, X0, sk_Xy)
0.00/0.47	       | ~ app_encode_app($i, $o, X0, X1)
0.00/0.47	       | app_encode_app($i, $o, sk_Xp, sk_Xy)),
0.00/0.47	    inference('clc', [status(thm)], ['111', '49'])).
0.00/0.47	tff('113', plain,
0.00/0.47	    ![X0 : app_encode_fun($i, $o), X1]:
0.00/0.47	      (~ app_encode_app($i, $o, X0, X1)
0.00/0.47	       | app_encode_app($i, $o, X0, sk_Xy)
0.00/0.47	       | ~ app_encode_app($i, $o, sk_Xp1, sk_Xy1)),
0.00/0.47	    inference('clc', [status(thm)], ['112', '77'])).
0.00/0.47	tff('114', plain,
0.00/0.47	    (~ $true
0.00/0.47	     | ~ app_encode_app($i, $o, sk_Xp1, sk_Xy1)
0.00/0.47	     | ~ app_encode_app($i, $o, sk_Xp1, sk_Xy1)
0.00/0.47	     | app_encode_app($i, $o, sk_Xp, sk_Xy)),
0.00/0.47	    inference('sup-', [status(thm)], ['107', '113'])).
0.00/0.47	tff('115', plain,
0.00/0.47	    (app_encode_app($i, $o, sk_Xp, sk_Xy)
0.00/0.47	     | ~ app_encode_app($i, $o, sk_Xp1, sk_Xy1)),
0.00/0.47	    inference('simplify', [status(thm)], ['114'])).
0.00/0.47	tff('116', plain, ~ app_encode_app($i, $o, sk_Xp1, sk_Xy1),
0.00/0.47	    inference('clc', [status(thm)], ['115', '77'])).
0.00/0.47	tff('117', plain,
0.00/0.47	    ![X0 : app_encode_fun($i, $o), X1]:
0.00/0.47	      (~ app_encode_app($i, $o, X0, X1) | app_encode_app($i, $o, X0, sk_Xy1)),
0.00/0.47	    inference('clc', [status(thm)], ['106', '116'])).
0.00/0.47	tff('118', plain, (~ $true | app_encode_app($i, $o, sk_Xp1, sk_Xy1)),
0.00/0.47	    inference('sup-', [status(thm)], ['81', '117'])).
0.00/0.47	tff('119', plain, app_encode_app($i, $o, sk_Xp1, sk_Xy1),
0.00/0.47	    inference('simplify', [status(thm)], ['118'])).
0.00/0.47	tff('120', plain, ~ $true, inference('sup-', [status(thm)], ['119', '116'])).
0.00/0.47	tff('121', plain, $false, inference('simplify', [status(thm)], ['120'])).
0.00/0.47	
0.00/0.47	% SZS output end Refutation
0.00/0.47	EOF
