0.00/0.00	% File    : /export/starexec/sandbox/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : appext
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 $2 \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --no-fool
0.00/0.20	% Computer   : n068.star.cs.uiowa.edu
0.00/0.20	% Model      : x86_64 x86_64
0.00/0.20	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.20	% Memory     : 32218.625MB
0.00/0.20	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.20	% CPULimit   : 300
0.00/0.20	% DateTime   : Fri Feb  2 17:10:25 CST 2018
0.00/0.62	% done 1257 iterations in 0.416s
0.00/0.62	% SZS status Theorem for 'stdin'
0.00/0.62	% SZS output start Refutation
0.00/0.63	tff(zf_stmt_4, conjecture,
0.00/0.63	  (![X:app_encode_fun(a,$o),Y:app_encode_fun(a,$o),Z:app_encode_fun(a,$o)]:
0.00/0.63	     ((?[Xx:a]:
0.00/0.63	         ((app_encode_app(a,$o,Z,Xx) | app_encode_app(a,$o,Y,Xx)) & 
0.00/0.63	          app_encode_app(a,$o,X,Xx))) <=>
0.00/0.63	      ((?[Xx:a]: (app_encode_app(a,$o,Z,Xx) & app_encode_app(a,$o,X,Xx))) | 
0.00/0.63	       (?[Xx:a]: (app_encode_app(a,$o,Y,Xx) & app_encode_app(a,$o,X,Xx))))))).
0.00/0.63	tff(zf_stmt_0, type, zip_tseitin2 :
0.00/0.63	    (a * app_encode_fun(a,$o) * app_encode_fun(a,$o)) > $o).
0.00/0.63	tff(zf_stmt_1, axiom,
0.00/0.63	  (zip_tseitin2(Xx,Y,X) <=>
0.00/0.63	   (app_encode_app(a,$o,X,Xx) & app_encode_app(a,$o,Y,Xx)))).
0.00/0.63	tff(zf_stmt_2, type, zip_tseitin1 :
0.00/0.63	    (a * app_encode_fun(a,$o) * app_encode_fun(a,$o)) > $o).
0.00/0.63	tff(zf_stmt_3, axiom,
0.00/0.63	  (zip_tseitin1(Xx,Z,X) <=>
0.00/0.63	   (app_encode_app(a,$o,X,Xx) & app_encode_app(a,$o,Z,Xx)))).
0.00/0.63	tff(zf_stmt_4, type, zip_tseitin0 :
0.00/0.63	    (a * app_encode_fun(a,$o) * app_encode_fun(a,$o)) > $o).
0.00/0.63	tff(zf_stmt_5, axiom,
0.00/0.63	  (zip_tseitin0(Xx,Z,Y) <=>
0.00/0.63	   (app_encode_app(a,$o,Y,Xx) | app_encode_app(a,$o,Z,Xx)))).
0.00/0.63	tff(zf_stmt_6, conjecture,
0.00/0.63	  (![X:app_encode_fun(a,$o),Y:app_encode_fun(a,$o),Z:app_encode_fun(a,$o)]:
0.00/0.63	     ((?[Xx:a]: (app_encode_app(a,$o,X,Xx) & zip_tseitin0(Xx,Z,Y))) <=>
0.00/0.63	      ((?[Xx:a]: zip_tseitin2(Xx,Y,X)) | (?[Xx:a]: zip_tseitin1(Xx,Z,X)))))).
0.00/0.63	tff(zf_stmt_7, negated_conjecture,
0.00/0.63	  (~
0.00/0.63	    (![X:app_encode_fun(a,$o),Y:app_encode_fun(a,$o),Z:app_encode_fun(a,$o)]:
0.00/0.63	       ((?[Xx:a]: (app_encode_app(a,$o,X,Xx) & zip_tseitin0(Xx,Z,Y))) <=>
0.00/0.63	        ((?[Xx:a]: zip_tseitin2(Xx,Y,X)) | (?[Xx:a]: zip_tseitin1(Xx,Z,X))))))).
0.00/0.63	tff('0', plain,
0.00/0.63	    (zip_tseitin1(sk_Xx, sk_Z1, sk_X)
0.00/0.63	     | zip_tseitin2(sk_Xx1, sk_Y, sk_X)
0.00/0.63	     | app_encode_app(a, $o, sk_X, sk_Xx2)),
0.00/0.63	    inference('cnf', [status(esa)], [zf_stmt_7])).
0.00/0.63	tff('1', plain,
0.00/0.63	    ![X4 : app_encode_fun(a, $o), X5 : a, X6 : app_encode_fun(a, $o)]:
0.00/0.63	      (zip_tseitin0(X5, X4, X6) | ~ app_encode_app(a, $o, X4, X5)),
0.00/0.63	    inference('cnf', [status(esa)], [zf_stmt_5])).
0.00/0.63	tff('2', plain,
0.00/0.63	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.63	      (~ $true
0.00/0.63	       | zip_tseitin2(sk_Xx1, sk_Y, sk_X)
0.00/0.63	       | zip_tseitin1(sk_Xx, sk_Z1, sk_X)
0.00/0.63	       | zip_tseitin0(sk_Xx2, sk_X, X0)),
0.00/0.63	    inference('sup-', [status(thm)], ['0', '1'])).
0.00/0.63	tff('3', plain,
0.00/0.63	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.63	      (zip_tseitin0(sk_Xx2, sk_X, X0)
0.00/0.63	       | zip_tseitin1(sk_Xx, sk_Z1, sk_X)
0.00/0.63	       | zip_tseitin2(sk_Xx1, sk_Y, sk_X)),
0.00/0.63	    inference('simplify', [status(thm)], ['2'])).
0.00/0.63	tff('4', plain,
0.00/0.63	    ![X6 : app_encode_fun(a, $o), X7 : app_encode_fun(a, $o), X9 : a]:
0.00/0.63	      (app_encode_app(a, $o, X6, X9) | ~ zip_tseitin2(X9, X6, X7)),
0.00/0.63	    inference('cnf', [status(esa)], [zf_stmt_1])).
0.00/0.63	tff('5', plain,
0.00/0.63	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.63	      (~ $true
0.00/0.63	       | zip_tseitin1(sk_Xx, sk_Z1, sk_X)
0.00/0.63	       | zip_tseitin0(sk_Xx2, sk_X, X0)
0.00/0.63	       | app_encode_app(a, $o, sk_Y, sk_Xx1)),
0.00/0.63	    inference('sup-', [status(thm)], ['3', '4'])).
0.00/0.63	tff('6', plain,
0.00/0.63	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.63	      (app_encode_app(a, $o, sk_Y, sk_Xx1)
0.00/0.63	       | zip_tseitin0(sk_Xx2, sk_X, X0)
0.00/0.63	       | zip_tseitin1(sk_Xx, sk_Z1, sk_X)),
0.00/0.63	    inference('simplify', [status(thm)], ['5'])).
0.00/0.63	tff('7', plain,
0.00/0.63	    ![X4 : app_encode_fun(a, $o), X5 : a, X6 : app_encode_fun(a, $o)]:
0.00/0.63	      (zip_tseitin0(X5, X4, X6) | ~ app_encode_app(a, $o, X6, X5)),
0.00/0.63	    inference('cnf', [status(esa)], [zf_stmt_5])).
0.00/0.63	tff('8', plain,
0.00/0.63	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.00/0.63	      (~ $true
0.00/0.63	       | zip_tseitin1(sk_Xx, sk_Z1, sk_X)
0.00/0.63	       | zip_tseitin0(sk_Xx2, sk_X, X1)
0.00/0.63	       | zip_tseitin0(sk_Xx1, X0, sk_Y)),
0.00/0.63	    inference('sup-', [status(thm)], ['6', '7'])).
0.00/0.63	tff('9', plain,
0.00/0.63	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.00/0.63	      (zip_tseitin0(sk_Xx1, X0, sk_Y)
0.00/0.63	       | zip_tseitin0(sk_Xx2, sk_X, X1)
0.00/0.63	       | zip_tseitin1(sk_Xx, sk_Z1, sk_X)),
0.00/0.63	    inference('simplify', [status(thm)], ['8'])).
0.00/0.63	tff('10', plain,
0.00/0.63	    ![X4 : app_encode_fun(a, $o), X7 : app_encode_fun(a, $o), X8 : a]:
0.00/0.63	      (app_encode_app(a, $o, X7, X8) | ~ zip_tseitin1(X8, X4, X7)),
0.00/0.63	    inference('cnf', [status(esa)], [zf_stmt_3])).
0.00/0.63	tff('11', plain,
0.00/0.63	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.00/0.63	      (~ $true
0.00/0.63	       | zip_tseitin0(sk_Xx2, sk_X, X0)
0.00/0.63	       | zip_tseitin0(sk_Xx1, X1, sk_Y)
0.00/0.63	       | app_encode_app(a, $o, sk_X, sk_Xx)),
0.00/0.63	    inference('sup-', [status(thm)], ['9', '10'])).
0.00/0.63	tff('12', plain,
0.00/0.63	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.00/0.63	      (app_encode_app(a, $o, sk_X, sk_Xx)
0.00/0.63	       | zip_tseitin0(sk_Xx1, X1, sk_Y)
0.00/0.63	       | zip_tseitin0(sk_Xx2, sk_X, X0)),
0.00/0.63	    inference('simplify', [status(thm)], ['11'])).
0.00/0.63	tff('13', plain,
0.00/0.63	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
0.00/0.63	      X2 : app_encode_fun(a, $o)]:
0.00/0.63	      (~ $true
0.00/0.63	       | zip_tseitin0(sk_Xx2, sk_X, X1)
0.00/0.63	       | zip_tseitin0(sk_Xx1, X2, sk_Y)
0.00/0.63	       | zip_tseitin0(sk_Xx, sk_X, X0)),
0.00/0.63	    inference('sup-', [status(thm)], ['12', '1'])).
0.00/0.63	tff('14', plain,
0.00/0.63	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
0.00/0.63	      X2 : app_encode_fun(a, $o)]:
0.00/0.63	      (zip_tseitin0(sk_Xx, sk_X, X0)
0.00/0.63	       | zip_tseitin0(sk_Xx1, X2, sk_Y)
0.00/0.63	       | zip_tseitin0(sk_Xx2, sk_X, X1)),
0.00/0.63	    inference('simplify', [status(thm)], ['13'])).
0.00/0.63	tff('15', plain,
0.00/0.63	    ![X6 : app_encode_fun(a, $o), X7 : app_encode_fun(a, $o), X9 : a]:
0.00/0.63	      (app_encode_app(a, $o, X7, X9) | ~ zip_tseitin2(X9, X6, X7)),
0.00/0.63	    inference('cnf', [status(esa)], [zf_stmt_1])).
0.00/0.63	tff('16', plain,
0.00/0.63	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.63	      (~ $true
0.00/0.63	       | zip_tseitin1(sk_Xx, sk_Z1, sk_X)
0.00/0.63	       | zip_tseitin0(sk_Xx2, sk_X, X0)
0.00/0.63	       | app_encode_app(a, $o, sk_X, sk_Xx1)),
0.00/0.63	    inference('sup-', [status(thm)], ['3', '15'])).
0.00/0.63	tff('17', plain,
0.00/0.63	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.63	      (app_encode_app(a, $o, sk_X, sk_Xx1)
0.00/0.63	       | zip_tseitin0(sk_Xx2, sk_X, X0)
0.00/0.63	       | zip_tseitin1(sk_Xx, sk_Z1, sk_X)),
0.00/0.63	    inference('simplify', [status(thm)], ['16'])).
0.00/0.63	tff('18', plain,
0.00/0.63	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.00/0.63	      (~ $true
0.00/0.63	       | zip_tseitin1(sk_Xx, sk_Z1, sk_X)
0.00/0.63	       | zip_tseitin0(sk_Xx2, sk_X, X1)
0.00/0.63	       | zip_tseitin0(sk_Xx1, sk_X, X0)),
0.00/0.63	    inference('sup-', [status(thm)], ['17', '1'])).
0.00/0.63	tff('19', plain,
0.00/0.63	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.00/0.63	      (zip_tseitin0(sk_Xx1, sk_X, X0)
0.00/0.63	       | zip_tseitin0(sk_Xx2, sk_X, X1)
0.00/0.63	       | zip_tseitin1(sk_Xx, sk_Z1, sk_X)),
0.00/0.63	    inference('simplify', [status(thm)], ['18'])).
0.00/0.63	tff('20', plain,
0.00/0.63	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.00/0.63	      (~ $true
0.00/0.63	       | zip_tseitin0(sk_Xx2, sk_X, X0)
0.00/0.63	       | zip_tseitin0(sk_Xx1, sk_X, X1)
0.00/0.63	       | app_encode_app(a, $o, sk_X, sk_Xx)),
0.00/0.63	    inference('sup-', [status(thm)], ['19', '10'])).
0.00/0.63	tff('21', plain,
0.00/0.63	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.00/0.63	      (app_encode_app(a, $o, sk_X, sk_Xx)
0.00/0.63	       | zip_tseitin0(sk_Xx1, sk_X, X1)
0.00/0.63	       | zip_tseitin0(sk_Xx2, sk_X, X0)),
0.00/0.63	    inference('simplify', [status(thm)], ['20'])).
0.00/0.63	tff('22', plain,
0.00/0.63	    ![X10 : a, X11 : a]:
0.00/0.63	      (~ zip_tseitin2(X10, sk_Y, sk_X)
0.00/0.63	       | ~ zip_tseitin0(X11, sk_Z1, sk_Y)
0.00/0.63	       | ~ app_encode_app(a, $o, sk_X, X11)),
0.00/0.63	    inference('cnf', [status(esa)], [zf_stmt_7])).
0.00/0.63	tff('23', plain,
0.00/0.63	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
0.00/0.63	      (~ $true
0.00/0.63	       | zip_tseitin1(sk_Xx, sk_Z1, sk_X)
0.00/0.63	       | zip_tseitin0(sk_Xx2, sk_X, X1)
0.00/0.63	       | ~ app_encode_app(a, $o, sk_X, X0)
0.00/0.63	       | ~ zip_tseitin0(X0, sk_Z1, sk_Y)),
0.00/0.63	    inference('sup-', [status(thm)], ['3', '22'])).
0.00/0.63	tff('24', plain,
0.00/0.63	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
0.00/0.63	      (~ zip_tseitin0(X0, sk_Z1, sk_Y)
0.00/0.63	       | ~ app_encode_app(a, $o, sk_X, X0)
0.00/0.63	       | zip_tseitin0(sk_Xx2, sk_X, X1)
0.00/0.63	       | zip_tseitin1(sk_Xx, sk_Z1, sk_X)),
0.00/0.63	    inference('simplify', [status(thm)], ['23'])).
0.00/0.63	tff('25', plain,
0.00/0.63	    ![X11 : a, X12 : a]:
0.00/0.63	      (~ zip_tseitin1(X12, sk_Z1, sk_X)
0.00/0.63	       | ~ zip_tseitin0(X11, sk_Z1, sk_Y)
0.00/0.63	       | ~ app_encode_app(a, $o, sk_X, X11)),
0.00/0.63	    inference('cnf', [status(esa)], [zf_stmt_7])).
0.00/0.63	tff('26', plain,
0.00/0.63	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
0.00/0.63	      (zip_tseitin0(sk_Xx2, sk_X, X1)
0.00/0.63	       | ~ app_encode_app(a, $o, sk_X, X0)
0.00/0.63	       | ~ zip_tseitin0(X0, sk_Z1, sk_Y)),
0.00/0.63	    inference('clc', [status(thm)], ['24', '25'])).
0.00/0.63	tff('27', plain,
0.00/0.63	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
0.00/0.63	      X2 : app_encode_fun(a, $o)]:
0.00/0.63	      (~ $true
0.00/0.63	       | zip_tseitin0(sk_Xx2, sk_X, X1)
0.00/0.63	       | zip_tseitin0(sk_Xx1, sk_X, X2)
0.00/0.63	       | ~ zip_tseitin0(sk_Xx, sk_Z1, sk_Y)
0.00/0.63	       | zip_tseitin0(sk_Xx2, sk_X, X0)),
0.00/0.63	    inference('sup-', [status(thm)], ['21', '26'])).
0.00/0.63	tff('28', plain,
0.00/0.63	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
0.00/0.63	      X2 : app_encode_fun(a, $o)]:
0.00/0.63	      (zip_tseitin0(sk_Xx2, sk_X, X0)
0.00/0.63	       | ~ zip_tseitin0(sk_Xx, sk_Z1, sk_Y)
0.00/0.63	       | zip_tseitin0(sk_Xx1, sk_X, X2)
0.00/0.63	       | zip_tseitin0(sk_Xx2, sk_X, X1)),
0.00/0.63	    inference('simplify', [status(thm)], ['27'])).
0.00/0.63	tff('29', plain,
0.00/0.63	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.00/0.63	      (zip_tseitin0(sk_Xx2, sk_X, X0)
0.00/0.63	       | ~ zip_tseitin0(sk_Xx, sk_Z1, sk_Y)
0.00/0.63	       | zip_tseitin0(sk_Xx1, sk_X, X1)),
0.00/0.63	    inference('condensation', [status(thm)], ['28'])).
0.00/0.63	tff('30', plain,
0.00/0.63	    ![X4 : app_encode_fun(a, $o), X7 : app_encode_fun(a, $o), X8 : a]:
0.00/0.63	      (app_encode_app(a, $o, X4, X8) | ~ zip_tseitin1(X8, X4, X7)),
0.00/0.63	    inference('cnf', [status(esa)], [zf_stmt_3])).
0.00/0.63	tff('31', plain,
0.00/0.63	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.00/0.63	      (~ $true
0.00/0.63	       | zip_tseitin0(sk_Xx2, sk_X, X0)
0.00/0.63	       | zip_tseitin0(sk_Xx1, sk_X, X1)
0.00/0.63	       | app_encode_app(a, $o, sk_Z1, sk_Xx)),
0.00/0.63	    inference('sup-', [status(thm)], ['19', '30'])).
0.00/0.63	tff('32', plain,
0.00/0.63	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.00/0.63	      (app_encode_app(a, $o, sk_Z1, sk_Xx)
0.00/0.63	       | zip_tseitin0(sk_Xx1, sk_X, X1)
0.00/0.63	       | zip_tseitin0(sk_Xx2, sk_X, X0)),
0.00/0.63	    inference('simplify', [status(thm)], ['31'])).
0.00/0.63	tff('33', plain,
0.00/0.63	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
0.00/0.63	      X2 : app_encode_fun(a, $o)]:
0.00/0.63	      (~ $true
0.00/0.63	       | zip_tseitin0(sk_Xx2, sk_X, X1)
0.00/0.63	       | zip_tseitin0(sk_Xx1, sk_X, X2)
0.00/0.63	       | zip_tseitin0(sk_Xx, sk_Z1, X0)),
0.00/0.63	    inference('sup-', [status(thm)], ['32', '1'])).
0.00/0.63	tff('34', plain,
0.00/0.63	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
0.00/0.63	      X2 : app_encode_fun(a, $o)]:
0.00/0.63	      (zip_tseitin0(sk_Xx, sk_Z1, X0)
0.00/0.63	       | zip_tseitin0(sk_Xx1, sk_X, X2)
0.00/0.63	       | zip_tseitin0(sk_Xx2, sk_X, X1)),
0.00/0.63	    inference('simplify', [status(thm)], ['33'])).
0.00/0.63	tff('35', plain,
0.00/0.63	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.00/0.63	      (zip_tseitin0(sk_Xx1, sk_X, X1) | zip_tseitin0(sk_Xx2, sk_X, X0)),
0.00/0.63	    inference('clc', [status(thm)], ['29', '34'])).
0.00/0.63	tff('36', plain,
0.00/0.63	    ![X4 : app_encode_fun(a, $o), X5 : a, X6 : app_encode_fun(a, $o)]:
0.00/0.63	      (app_encode_app(a, $o, X4, X5)
0.00/0.63	       | app_encode_app(a, $o, X6, X5)
0.00/0.63	       | ~ zip_tseitin0(X5, X4, X6)),
0.00/0.63	    inference('cnf', [status(esa)], [zf_stmt_5])).
0.00/0.63	tff('37', plain,
0.00/0.63	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.00/0.63	      (~ $true
0.00/0.63	       | zip_tseitin0(sk_Xx2, sk_X, X1)
0.00/0.63	       | app_encode_app(a, $o, X0, sk_Xx1)
0.00/0.63	       | app_encode_app(a, $o, sk_X, sk_Xx1)),
0.00/0.63	    inference('sup-', [status(thm)], ['35', '36'])).
0.00/0.63	tff('38', plain,
0.00/0.63	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.00/0.63	      (app_encode_app(a, $o, sk_X, sk_Xx1)
0.00/0.63	       | app_encode_app(a, $o, X0, sk_Xx1)
0.00/0.63	       | zip_tseitin0(sk_Xx2, sk_X, X1)),
0.00/0.63	    inference('simplify', [status(thm)], ['37'])).
0.00/0.63	tff('39', plain,
0.00/0.63	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.63	      (app_encode_app(a, $o, sk_X, sk_Xx1) | zip_tseitin0(sk_Xx2, sk_X, X0)),
0.00/0.63	    inference('condensation', [status(thm)], ['38'])).
0.00/0.63	tff('40', plain,
0.00/0.63	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.00/0.63	      (~ $true
0.00/0.63	       | zip_tseitin0(sk_Xx2, sk_X, X1)
0.00/0.63	       | ~ zip_tseitin0(sk_Xx1, sk_Z1, sk_Y)
0.00/0.63	       | zip_tseitin0(sk_Xx2, sk_X, X0)),
0.00/0.63	    inference('sup-', [status(thm)], ['39', '26'])).
0.00/0.63	tff('41', plain,
0.00/0.63	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.00/0.63	      (zip_tseitin0(sk_Xx2, sk_X, X0)
0.00/0.63	       | ~ zip_tseitin0(sk_Xx1, sk_Z1, sk_Y)
0.00/0.63	       | zip_tseitin0(sk_Xx2, sk_X, X1)),
0.00/0.63	    inference('simplify', [status(thm)], ['40'])).
0.00/0.63	tff('42', plain,
0.00/0.63	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.63	      (zip_tseitin0(sk_Xx2, sk_X, X0) | ~ zip_tseitin0(sk_Xx1, sk_Z1, sk_Y)),
0.00/0.63	    inference('condensation', [status(thm)], ['41'])).
0.00/0.63	tff('43', plain,
0.00/0.63	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
0.00/0.63	      X2 : app_encode_fun(a, $o)]:
0.00/0.63	      (~ $true
0.00/0.63	       | zip_tseitin0(sk_Xx2, sk_X, X1)
0.00/0.63	       | zip_tseitin0(sk_Xx, sk_X, X2)
0.00/0.63	       | zip_tseitin0(sk_Xx2, sk_X, X0)),
0.00/0.63	    inference('sup-', [status(thm)], ['14', '42'])).
0.00/0.63	tff('44', plain,
0.00/0.63	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
0.00/0.63	      X2 : app_encode_fun(a, $o)]:
0.00/0.63	      (zip_tseitin0(sk_Xx2, sk_X, X0)
0.00/0.63	       | zip_tseitin0(sk_Xx, sk_X, X2)
0.00/0.63	       | zip_tseitin0(sk_Xx2, sk_X, X1)),
0.00/0.63	    inference('simplify', [status(thm)], ['43'])).
0.00/0.63	tff('45', plain,
0.00/0.63	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.00/0.63	      (zip_tseitin0(sk_Xx2, sk_X, X0) | zip_tseitin0(sk_Xx, sk_X, X1)),
0.00/0.63	    inference('condensation', [status(thm)], ['44'])).
0.00/0.63	tff('46', plain,
0.00/0.63	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.00/0.63	      (~ $true
0.00/0.63	       | zip_tseitin0(sk_Xx2, sk_X, X1)
0.00/0.63	       | app_encode_app(a, $o, X0, sk_Xx)
0.00/0.63	       | app_encode_app(a, $o, sk_X, sk_Xx)),
0.00/0.63	    inference('sup-', [status(thm)], ['45', '36'])).
0.00/0.63	tff('47', plain,
0.00/0.63	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.00/0.63	      (app_encode_app(a, $o, sk_X, sk_Xx)
0.00/0.63	       | app_encode_app(a, $o, X0, sk_Xx)
0.00/0.63	       | zip_tseitin0(sk_Xx2, sk_X, X1)),
0.00/0.63	    inference('simplify', [status(thm)], ['46'])).
0.00/0.63	tff('48', plain,
0.00/0.63	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.63	      (app_encode_app(a, $o, sk_X, sk_Xx) | zip_tseitin0(sk_Xx2, sk_X, X0)),
0.00/0.63	    inference('condensation', [status(thm)], ['47'])).
0.00/0.63	tff('49', plain,
0.00/0.63	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.00/0.63	      (~ $true
0.00/0.63	       | zip_tseitin0(sk_Xx2, sk_X, X1)
0.00/0.63	       | ~ zip_tseitin0(sk_Xx, sk_Z1, sk_Y)
0.00/0.63	       | zip_tseitin0(sk_Xx2, sk_X, X0)),
0.00/0.63	    inference('sup-', [status(thm)], ['48', '26'])).
0.00/0.63	tff('50', plain,
0.00/0.63	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.00/0.63	      (zip_tseitin0(sk_Xx2, sk_X, X0)
0.00/0.63	       | ~ zip_tseitin0(sk_Xx, sk_Z1, sk_Y)
0.00/0.63	       | zip_tseitin0(sk_Xx2, sk_X, X1)),
0.00/0.63	    inference('simplify', [status(thm)], ['49'])).
0.00/0.63	tff('51', plain,
0.00/0.63	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.63	      (zip_tseitin0(sk_Xx2, sk_X, X0) | ~ zip_tseitin0(sk_Xx, sk_Z1, sk_Y)),
0.00/0.63	    inference('condensation', [status(thm)], ['50'])).
0.00/0.63	tff('52', plain,
0.00/0.63	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.00/0.63	      (~ $true
0.00/0.63	       | zip_tseitin0(sk_Xx2, sk_X, X0)
0.00/0.63	       | zip_tseitin0(sk_Xx1, X1, sk_Y)
0.00/0.63	       | app_encode_app(a, $o, sk_Z1, sk_Xx)),
0.00/0.63	    inference('sup-', [status(thm)], ['9', '30'])).
0.00/0.63	tff('53', plain,
0.00/0.63	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.00/0.63	      (app_encode_app(a, $o, sk_Z1, sk_Xx)
0.00/0.63	       | zip_tseitin0(sk_Xx1, X1, sk_Y)
0.00/0.63	       | zip_tseitin0(sk_Xx2, sk_X, X0)),
0.00/0.63	    inference('simplify', [status(thm)], ['52'])).
0.00/0.63	tff('54', plain,
0.00/0.63	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
0.00/0.63	      X2 : app_encode_fun(a, $o)]:
0.00/0.63	      (~ $true
0.00/0.63	       | zip_tseitin0(sk_Xx2, sk_X, X1)
0.00/0.63	       | zip_tseitin0(sk_Xx1, X2, sk_Y)
0.00/0.63	       | zip_tseitin0(sk_Xx, sk_Z1, X0)),
0.00/0.63	    inference('sup-', [status(thm)], ['53', '1'])).
0.00/0.63	tff('55', plain,
0.00/0.63	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
0.00/0.63	      X2 : app_encode_fun(a, $o)]:
0.00/0.63	      (zip_tseitin0(sk_Xx, sk_Z1, X0)
0.00/0.63	       | zip_tseitin0(sk_Xx1, X2, sk_Y)
0.00/0.63	       | zip_tseitin0(sk_Xx2, sk_X, X1)),
0.00/0.63	    inference('simplify', [status(thm)], ['54'])).
0.00/0.63	tff('56', plain,
0.00/0.63	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
0.00/0.63	      X2 : app_encode_fun(a, $o)]:
0.00/0.63	      (~ $true
0.00/0.63	       | zip_tseitin0(sk_Xx2, sk_X, X1)
0.00/0.63	       | zip_tseitin0(sk_Xx, sk_Z1, X2)
0.00/0.63	       | zip_tseitin0(sk_Xx2, sk_X, X0)),
0.00/0.63	    inference('sup-', [status(thm)], ['55', '42'])).
0.00/0.63	tff('57', plain,
0.00/0.63	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
0.00/0.63	      X2 : app_encode_fun(a, $o)]:
0.00/0.63	      (zip_tseitin0(sk_Xx2, sk_X, X0)
0.00/0.63	       | zip_tseitin0(sk_Xx, sk_Z1, X2)
0.00/0.63	       | zip_tseitin0(sk_Xx2, sk_X, X1)),
0.00/0.63	    inference('simplify', [status(thm)], ['56'])).
0.00/0.63	tff('58', plain,
0.00/0.63	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.00/0.63	      (zip_tseitin0(sk_Xx2, sk_X, X0) | zip_tseitin0(sk_Xx, sk_Z1, X1)),
0.00/0.63	    inference('condensation', [status(thm)], ['57'])).
0.00/0.63	tff('59', plain,
0.00/0.63	    ![X0 : app_encode_fun(a, $o)]: zip_tseitin0(sk_Xx2, sk_X, X0),
0.00/0.63	    inference('clc', [status(thm)], ['51', '58'])).
0.00/0.63	tff('60', plain,
0.00/0.63	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.63	      (~ $true
0.00/0.63	       | app_encode_app(a, $o, X0, sk_Xx2)
0.00/0.63	       | app_encode_app(a, $o, sk_X, sk_Xx2)),
0.00/0.63	    inference('sup-', [status(thm)], ['59', '36'])).
0.00/0.63	tff('61', plain,
0.00/0.63	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.63	      (app_encode_app(a, $o, sk_X, sk_Xx2)
0.00/0.63	       | app_encode_app(a, $o, X0, sk_Xx2)),
0.00/0.63	    inference('simplify', [status(thm)], ['60'])).
0.00/0.63	tff('62', plain, app_encode_app(a, $o, sk_X, sk_Xx2),
0.00/0.63	    inference('condensation', [status(thm)], ['61'])).
0.00/0.63	tff('63', plain,
0.00/0.63	    (zip_tseitin1(sk_Xx, sk_Z1, sk_X)
0.00/0.63	     | zip_tseitin2(sk_Xx1, sk_Y, sk_X)
0.00/0.63	     | zip_tseitin0(sk_Xx2, sk_Z1, sk_Y)),
0.00/0.63	    inference('cnf', [status(esa)], [zf_stmt_7])).
0.00/0.63	tff('64', plain,
0.00/0.63	    (~ $true
0.00/0.63	     | zip_tseitin0(sk_Xx2, sk_Z1, sk_Y)
0.00/0.63	     | zip_tseitin1(sk_Xx, sk_Z1, sk_X)
0.00/0.63	     | app_encode_app(a, $o, sk_X, sk_Xx1)),
0.00/0.63	    inference('sup-', [status(thm)], ['63', '15'])).
0.00/0.63	tff('65', plain,
0.00/0.63	    (app_encode_app(a, $o, sk_X, sk_Xx1)
0.00/0.63	     | zip_tseitin1(sk_Xx, sk_Z1, sk_X)
0.00/0.63	     | zip_tseitin0(sk_Xx2, sk_Z1, sk_Y)),
0.00/0.63	    inference('simplify', [status(thm)], ['64'])).
0.00/0.63	tff('66', plain,
0.00/0.63	    ![X0 : a]:
0.00/0.63	      (~ $true
0.00/0.63	       | zip_tseitin0(sk_Xx2, sk_Z1, sk_Y)
0.00/0.63	       | zip_tseitin1(sk_Xx, sk_Z1, sk_X)
0.00/0.63	       | ~ app_encode_app(a, $o, sk_X, X0)
0.00/0.63	       | ~ zip_tseitin0(X0, sk_Z1, sk_Y)),
0.00/0.63	    inference('sup-', [status(thm)], ['63', '22'])).
0.00/0.63	tff('67', plain,
0.00/0.63	    ![X0 : a]:
0.00/0.63	      (~ zip_tseitin0(X0, sk_Z1, sk_Y)
0.00/0.63	       | ~ app_encode_app(a, $o, sk_X, X0)
0.00/0.63	       | zip_tseitin1(sk_Xx, sk_Z1, sk_X)
0.00/0.63	       | zip_tseitin0(sk_Xx2, sk_Z1, sk_Y)),
0.00/0.63	    inference('simplify', [status(thm)], ['66'])).
0.00/0.63	tff('68', plain,
0.00/0.63	    ![X0 : a]:
0.00/0.63	      (zip_tseitin0(sk_Xx2, sk_Z1, sk_Y)
0.00/0.63	       | ~ app_encode_app(a, $o, sk_X, X0)
0.00/0.63	       | ~ zip_tseitin0(X0, sk_Z1, sk_Y)),
0.00/0.63	    inference('clc', [status(thm)], ['67', '25'])).
0.00/0.63	tff('69', plain,
0.00/0.63	    (~ $true
0.00/0.63	     | zip_tseitin0(sk_Xx2, sk_Z1, sk_Y)
0.00/0.63	     | zip_tseitin1(sk_Xx, sk_Z1, sk_X)
0.00/0.63	     | ~ zip_tseitin0(sk_Xx1, sk_Z1, sk_Y)
0.00/0.63	     | zip_tseitin0(sk_Xx2, sk_Z1, sk_Y)),
0.00/0.63	    inference('sup-', [status(thm)], ['65', '68'])).
0.00/0.63	tff('70', plain,
0.00/0.63	    (~ zip_tseitin0(sk_Xx1, sk_Z1, sk_Y)
0.00/0.63	     | zip_tseitin1(sk_Xx, sk_Z1, sk_X)
0.00/0.63	     | zip_tseitin0(sk_Xx2, sk_Z1, sk_Y)),
0.00/0.63	    inference('simplify', [status(thm)], ['69'])).
0.00/0.63	tff('71', plain,
0.00/0.63	    (~ $true
0.00/0.63	     | zip_tseitin0(sk_Xx2, sk_Z1, sk_Y)
0.00/0.63	     | zip_tseitin1(sk_Xx, sk_Z1, sk_X)
0.00/0.63	     | app_encode_app(a, $o, sk_Y, sk_Xx1)),
0.00/0.63	    inference('sup-', [status(thm)], ['63', '4'])).
0.00/0.63	tff('72', plain,
0.00/0.63	    (app_encode_app(a, $o, sk_Y, sk_Xx1)
0.00/0.63	     | zip_tseitin1(sk_Xx, sk_Z1, sk_X)
0.00/0.63	     | zip_tseitin0(sk_Xx2, sk_Z1, sk_Y)),
0.00/0.63	    inference('simplify', [status(thm)], ['71'])).
0.00/0.63	tff('73', plain,
0.00/0.63	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.63	      (~ $true
0.00/0.63	       | zip_tseitin0(sk_Xx2, sk_Z1, sk_Y)
0.00/0.63	       | zip_tseitin1(sk_Xx, sk_Z1, sk_X)
0.00/0.63	       | zip_tseitin0(sk_Xx1, X0, sk_Y)),
0.00/0.63	    inference('sup-', [status(thm)], ['72', '7'])).
0.00/0.63	tff('74', plain,
0.00/0.63	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.63	      (zip_tseitin0(sk_Xx1, X0, sk_Y)
0.00/0.63	       | zip_tseitin1(sk_Xx, sk_Z1, sk_X)
0.00/0.63	       | zip_tseitin0(sk_Xx2, sk_Z1, sk_Y)),
0.00/0.63	    inference('simplify', [status(thm)], ['73'])).
0.00/0.63	tff('75', plain,
0.00/0.63	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.63	      (~ $true
0.00/0.63	       | zip_tseitin0(sk_Xx2, sk_Z1, sk_Y)
0.00/0.63	       | zip_tseitin0(sk_Xx1, X0, sk_Y)
0.00/0.63	       | app_encode_app(a, $o, sk_X, sk_Xx)),
0.00/0.63	    inference('sup-', [status(thm)], ['74', '10'])).
0.00/0.63	tff('76', plain,
0.00/0.63	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.63	      (app_encode_app(a, $o, sk_X, sk_Xx)
0.00/0.63	       | zip_tseitin0(sk_Xx1, X0, sk_Y)
0.00/0.63	       | zip_tseitin0(sk_Xx2, sk_Z1, sk_Y)),
0.00/0.63	    inference('simplify', [status(thm)], ['75'])).
0.00/0.63	tff('77', plain,
0.00/0.63	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.63	      (~ $true
0.00/0.63	       | zip_tseitin0(sk_Xx2, sk_Z1, sk_Y)
0.00/0.63	       | zip_tseitin0(sk_Xx1, X0, sk_Y)
0.00/0.63	       | ~ zip_tseitin0(sk_Xx, sk_Z1, sk_Y)
0.00/0.63	       | zip_tseitin0(sk_Xx2, sk_Z1, sk_Y)),
0.00/0.63	    inference('sup-', [status(thm)], ['76', '68'])).
0.00/0.63	tff('78', plain,
0.00/0.63	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.63	      (~ zip_tseitin0(sk_Xx, sk_Z1, sk_Y)
0.00/0.63	       | zip_tseitin0(sk_Xx1, X0, sk_Y)
0.00/0.63	       | zip_tseitin0(sk_Xx2, sk_Z1, sk_Y)),
0.00/0.63	    inference('simplify', [status(thm)], ['77'])).
0.00/0.63	tff('79', plain,
0.00/0.63	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.63	      (~ $true
0.00/0.63	       | zip_tseitin0(sk_Xx2, sk_Z1, sk_Y)
0.00/0.63	       | zip_tseitin0(sk_Xx1, X0, sk_Y)
0.00/0.63	       | app_encode_app(a, $o, sk_Z1, sk_Xx)),
0.00/0.63	    inference('sup-', [status(thm)], ['74', '30'])).
0.00/0.63	tff('80', plain,
0.00/0.63	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.63	      (app_encode_app(a, $o, sk_Z1, sk_Xx)
0.00/0.63	       | zip_tseitin0(sk_Xx1, X0, sk_Y)
0.00/0.63	       | zip_tseitin0(sk_Xx2, sk_Z1, sk_Y)),
0.00/0.63	    inference('simplify', [status(thm)], ['79'])).
0.00/0.63	tff('81', plain,
0.00/0.63	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.00/0.63	      (~ $true
0.00/0.63	       | zip_tseitin0(sk_Xx2, sk_Z1, sk_Y)
0.00/0.63	       | zip_tseitin0(sk_Xx1, X1, sk_Y)
0.00/0.63	       | zip_tseitin0(sk_Xx, sk_Z1, X0)),
0.00/0.63	    inference('sup-', [status(thm)], ['80', '1'])).
0.00/0.63	tff('82', plain,
0.00/0.63	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.00/0.63	      (zip_tseitin0(sk_Xx, sk_Z1, X0)
0.00/0.63	       | zip_tseitin0(sk_Xx1, X1, sk_Y)
0.00/0.63	       | zip_tseitin0(sk_Xx2, sk_Z1, sk_Y)),
0.00/0.63	    inference('simplify', [status(thm)], ['81'])).
0.00/0.63	tff('83', plain,
0.00/0.63	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.63	      (zip_tseitin0(sk_Xx2, sk_Z1, sk_Y) | zip_tseitin0(sk_Xx1, X0, sk_Y)),
0.00/0.63	    inference('clc', [status(thm)], ['78', '82'])).
0.00/0.63	tff('84', plain,
0.00/0.63	    (zip_tseitin0(sk_Xx2, sk_Z1, sk_Y) | zip_tseitin1(sk_Xx, sk_Z1, sk_X)),
0.00/0.63	    inference('clc', [status(thm)], ['70', '83'])).
0.00/0.63	tff('85', plain,
0.00/0.63	    (~ $true
0.00/0.63	     | zip_tseitin0(sk_Xx2, sk_Z1, sk_Y)
0.00/0.63	     | app_encode_app(a, $o, sk_X, sk_Xx)),
0.00/0.63	    inference('sup-', [status(thm)], ['84', '10'])).
0.00/0.63	tff('86', plain,
0.00/0.63	    (app_encode_app(a, $o, sk_X, sk_Xx) | zip_tseitin0(sk_Xx2, sk_Z1, sk_Y)),
0.00/0.63	    inference('simplify', [status(thm)], ['85'])).
0.00/0.63	tff('87', plain,
0.00/0.63	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.63	      (~ $true
0.00/0.63	       | zip_tseitin0(sk_Xx2, sk_Z1, sk_Y)
0.00/0.63	       | ~ zip_tseitin0(sk_Xx, sk_Z1, sk_Y)
0.00/0.63	       | zip_tseitin0(sk_Xx2, sk_X, X0)),
0.00/0.63	    inference('sup-', [status(thm)], ['86', '26'])).
0.00/0.63	tff('88', plain,
0.00/0.63	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.63	      (zip_tseitin0(sk_Xx2, sk_X, X0)
0.00/0.63	       | ~ zip_tseitin0(sk_Xx, sk_Z1, sk_Y)
0.00/0.63	       | zip_tseitin0(sk_Xx2, sk_Z1, sk_Y)),
0.00/0.63	    inference('simplify', [status(thm)], ['87'])).
0.00/0.63	tff('89', plain,
0.00/0.63	    (~ $true
0.00/0.63	     | zip_tseitin0(sk_Xx2, sk_Z1, sk_Y)
0.00/0.63	     | ~ zip_tseitin0(sk_Xx, sk_Z1, sk_Y)
0.00/0.63	     | zip_tseitin0(sk_Xx2, sk_Z1, sk_Y)),
0.00/0.63	    inference('sup-', [status(thm)], ['86', '68'])).
0.00/0.63	tff('90', plain,
0.00/0.63	    (~ zip_tseitin0(sk_Xx, sk_Z1, sk_Y) | zip_tseitin0(sk_Xx2, sk_Z1, sk_Y)),
0.00/0.63	    inference('simplify', [status(thm)], ['89'])).
0.00/0.63	tff('91', plain,
0.00/0.63	    (zip_tseitin0(sk_Xx2, sk_Z1, sk_Y) | ~ zip_tseitin0(sk_Xx, sk_Z1, sk_Y)),
0.00/0.63	    inference('clc', [status(thm)], ['88', '90'])).
0.00/0.63	tff('92', plain,
0.00/0.63	    (~ $true
0.00/0.63	     | zip_tseitin0(sk_Xx2, sk_Z1, sk_Y)
0.00/0.63	     | app_encode_app(a, $o, sk_Z1, sk_Xx)),
0.00/0.63	    inference('sup-', [status(thm)], ['84', '30'])).
0.00/0.63	tff('93', plain,
0.00/0.63	    (app_encode_app(a, $o, sk_Z1, sk_Xx) | zip_tseitin0(sk_Xx2, sk_Z1, sk_Y)),
0.00/0.63	    inference('simplify', [status(thm)], ['92'])).
0.00/0.63	tff('94', plain,
0.00/0.63	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.63	      (~ $true
0.00/0.63	       | zip_tseitin0(sk_Xx2, sk_Z1, sk_Y)
0.00/0.63	       | zip_tseitin0(sk_Xx, sk_Z1, X0)),
0.00/0.63	    inference('sup-', [status(thm)], ['93', '1'])).
0.00/0.63	tff('95', plain,
0.00/0.63	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.63	      (zip_tseitin0(sk_Xx, sk_Z1, X0) | zip_tseitin0(sk_Xx2, sk_Z1, sk_Y)),
0.00/0.63	    inference('simplify', [status(thm)], ['94'])).
0.00/0.63	tff('96', plain, zip_tseitin0(sk_Xx2, sk_Z1, sk_Y),
0.00/0.63	    inference('clc', [status(thm)], ['91', '95'])).
0.00/0.63	tff('97', plain,
0.00/0.63	    (~ $true
0.00/0.63	     | app_encode_app(a, $o, sk_Y, sk_Xx2)
0.00/0.63	     | app_encode_app(a, $o, sk_Z1, sk_Xx2)),
0.00/0.63	    inference('sup-', [status(thm)], ['96', '36'])).
0.00/0.63	tff('98', plain,
0.00/0.63	    (app_encode_app(a, $o, sk_Z1, sk_Xx2)
0.00/0.63	     | app_encode_app(a, $o, sk_Y, sk_Xx2)),
0.00/0.63	    inference('simplify', [status(thm)], ['97'])).
0.00/0.63	tff('99', plain,
0.00/0.63	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.63	      (~ $true
0.00/0.63	       | app_encode_app(a, $o, sk_Y, sk_Xx2)
0.00/0.63	       | zip_tseitin0(sk_Xx2, sk_Z1, X0)),
0.00/0.63	    inference('sup-', [status(thm)], ['98', '1'])).
0.00/0.63	tff('100', plain,
0.00/0.63	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.63	      (zip_tseitin0(sk_Xx2, sk_Z1, X0) | app_encode_app(a, $o, sk_Y, sk_Xx2)),
0.00/0.63	    inference('simplify', [status(thm)], ['99'])).
0.00/0.63	tff('101', plain,
0.00/0.63	    ![X6 : app_encode_fun(a, $o), X7 : app_encode_fun(a, $o), X9 : a]:
0.00/0.63	      (zip_tseitin2(X9, X6, X7)
0.00/0.63	       | ~ app_encode_app(a, $o, X6, X9)
0.00/0.63	       | ~ app_encode_app(a, $o, X7, X9)),
0.00/0.63	    inference('cnf', [status(esa)], [zf_stmt_1])).
0.00/0.63	tff('102', plain,
0.00/0.63	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.00/0.63	      (~ $true
0.00/0.63	       | zip_tseitin0(sk_Xx2, sk_Z1, X1)
0.00/0.63	       | ~ app_encode_app(a, $o, X0, sk_Xx2)
0.00/0.63	       | zip_tseitin2(sk_Xx2, sk_Y, X0)),
0.00/0.63	    inference('sup-', [status(thm)], ['100', '101'])).
0.00/0.63	tff('103', plain,
0.00/0.63	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.00/0.63	      (zip_tseitin2(sk_Xx2, sk_Y, X0)
0.00/0.63	       | ~ app_encode_app(a, $o, X0, sk_Xx2)
0.00/0.63	       | zip_tseitin0(sk_Xx2, sk_Z1, X1)),
0.00/0.63	    inference('simplify', [status(thm)], ['102'])).
0.00/0.63	tff('104', plain,
0.00/0.63	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.63	      (~ $true
0.00/0.63	       | zip_tseitin0(sk_Xx2, sk_Z1, X0)
0.00/0.63	       | zip_tseitin2(sk_Xx2, sk_Y, sk_X)),
0.00/0.63	    inference('sup-', [status(thm)], ['62', '103'])).
0.00/0.63	tff('105', plain,
0.00/0.63	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.63	      (zip_tseitin2(sk_Xx2, sk_Y, sk_X) | zip_tseitin0(sk_Xx2, sk_Z1, X0)),
0.00/0.63	    inference('simplify', [status(thm)], ['104'])).
0.00/0.63	tff('106', plain,
0.00/0.63	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
0.00/0.63	      (~ $true
0.00/0.63	       | zip_tseitin0(sk_Xx2, sk_Z1, X1)
0.00/0.63	       | ~ app_encode_app(a, $o, sk_X, X0)
0.00/0.63	       | ~ zip_tseitin0(X0, sk_Z1, sk_Y)),
0.00/0.63	    inference('sup-', [status(thm)], ['105', '22'])).
0.00/0.63	tff('107', plain,
0.00/0.63	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
0.00/0.63	      (~ zip_tseitin0(X0, sk_Z1, sk_Y)
0.00/0.63	       | ~ app_encode_app(a, $o, sk_X, X0)
0.00/0.63	       | zip_tseitin0(sk_Xx2, sk_Z1, X1)),
0.00/0.63	    inference('simplify', [status(thm)], ['106'])).
0.00/0.63	tff('108', plain,
0.00/0.63	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.63	      (~ $true
0.00/0.63	       | zip_tseitin0(sk_Xx2, sk_Z1, X0)
0.00/0.63	       | ~ zip_tseitin0(sk_Xx2, sk_Z1, sk_Y)),
0.00/0.63	    inference('sup-', [status(thm)], ['62', '107'])).
0.00/0.63	tff('109', plain,
0.00/0.63	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.63	      (~ $true | zip_tseitin0(sk_Xx2, sk_Z1, X0) | ~ $true),
0.00/0.63	    inference('demod', [status(thm)], ['108', '96'])).
0.00/0.63	tff('110', plain,
0.00/0.63	    ![X0 : app_encode_fun(a, $o)]: zip_tseitin0(sk_Xx2, sk_Z1, X0),
0.00/0.63	    inference('simplify', [status(thm)], ['109'])).
0.00/0.63	tff('111', plain,
0.00/0.63	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.63	      (~ $true
0.00/0.63	       | app_encode_app(a, $o, X0, sk_Xx2)
0.00/0.63	       | app_encode_app(a, $o, sk_Z1, sk_Xx2)),
0.00/0.63	    inference('sup-', [status(thm)], ['110', '36'])).
0.00/0.63	tff('112', plain,
0.00/0.63	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.63	      (app_encode_app(a, $o, sk_Z1, sk_Xx2)
0.00/0.63	       | app_encode_app(a, $o, X0, sk_Xx2)),
0.00/0.63	    inference('simplify', [status(thm)], ['111'])).
0.00/0.63	tff('113', plain, app_encode_app(a, $o, sk_Z1, sk_Xx2),
0.00/0.63	    inference('condensation', [status(thm)], ['112'])).
0.00/0.63	tff('114', plain,
0.00/0.63	    ![X4 : app_encode_fun(a, $o), X7 : app_encode_fun(a, $o), X8 : a]:
0.00/0.63	      (zip_tseitin1(X8, X4, X7)
0.00/0.63	       | ~ app_encode_app(a, $o, X4, X8)
0.00/0.63	       | ~ app_encode_app(a, $o, X7, X8)),
0.00/0.63	    inference('cnf', [status(esa)], [zf_stmt_3])).
0.00/0.63	tff('115', plain,
0.00/0.63	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.63	      (~ $true
0.00/0.63	       | ~ app_encode_app(a, $o, X0, sk_Xx2)
0.00/0.63	       | zip_tseitin1(sk_Xx2, sk_Z1, X0)),
0.00/0.63	    inference('sup-', [status(thm)], ['113', '114'])).
0.00/0.63	tff('116', plain,
0.00/0.63	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.63	      (zip_tseitin1(sk_Xx2, sk_Z1, X0) | ~ app_encode_app(a, $o, X0, sk_Xx2)),
0.00/0.63	    inference('simplify', [status(thm)], ['115'])).
0.00/0.63	tff('117', plain, (~ $true | zip_tseitin1(sk_Xx2, sk_Z1, sk_X)),
0.00/0.63	    inference('sup-', [status(thm)], ['62', '116'])).
0.00/0.63	tff('118', plain, zip_tseitin1(sk_Xx2, sk_Z1, sk_X),
0.00/0.63	    inference('simplify', [status(thm)], ['117'])).
0.00/0.63	tff('119', plain,
0.00/0.63	    ![X0 : a]:
0.00/0.63	      (~ $true
0.00/0.63	       | ~ app_encode_app(a, $o, sk_X, X0)
0.00/0.63	       | ~ zip_tseitin0(X0, sk_Z1, sk_Y)),
0.00/0.63	    inference('sup-', [status(thm)], ['118', '25'])).
0.00/0.63	tff('120', plain,
0.00/0.63	    ![X0 : a]:
0.00/0.63	      (~ zip_tseitin0(X0, sk_Z1, sk_Y) | ~ app_encode_app(a, $o, sk_X, X0)),
0.00/0.63	    inference('simplify', [status(thm)], ['119'])).
0.00/0.63	tff('121', plain, (~ $true | ~ zip_tseitin0(sk_Xx2, sk_Z1, sk_Y)),
0.00/0.63	    inference('sup-', [status(thm)], ['62', '120'])).
0.00/0.63	tff('122', plain, (~ $true | ~ $true),
0.00/0.63	    inference('demod', [status(thm)], ['121', '110'])).
0.00/0.63	tff('123', plain, $false, inference('simplify', [status(thm)], ['122'])).
0.00/0.63	
0.00/0.63	% SZS output end Refutation
0.00/0.63	EOF
