0.00/0.01	% File    : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.00/0.01	% app-encoded or not : appext
0.00/0.01	% Variant    : fo
0.00/0.01	% Ordering    : kbo
0.00/0.01	% Command    : 
0.00/0.01	#!/bin/sh
0.00/0.01	
0.00/0.01	./zipperposition.native ${1:+"$1"} \
0.00/0.01	  -i tptp \
0.00/0.01	  -o tptp \
0.00/0.01	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.01	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.01	  --no-ho \
0.00/0.01	  --no-avatar \
0.00/0.01	  --no-induction \
0.00/0.01	  --no-unif-pattern \
0.00/0.01	  --ord $2 \
0.00/0.01	  --simultaneous-sup false \
0.00/0.01	  --no-max-vars \
0.00/0.01	  --no-fool
0.00/0.20	% Computer   : n119.star.cs.uiowa.edu
0.00/0.20	% Model      : x86_64 x86_64
0.00/0.20	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.20	% Memory     : 32218.625MB
0.00/0.20	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.20	% CPULimit   : 300
0.00/0.20	% DateTime   : Fri Feb  2 17:19:54 CST 2018
0.82/1.07	% done 2378 iterations in 0.868s
0.82/1.07	% SZS status Theorem for 'stdin'
0.82/1.07	% SZS output start Refutation
0.82/1.08	tff(zf_stmt_4, conjecture,
0.82/1.08	  (![S:app_encode_fun(a,$o),T:app_encode_fun(a,$o),U:app_encode_fun(a,$o)]:
0.82/1.08	     (((![Xx:a]: (app_encode_app(a,$o,T,Xx) => app_encode_app(a,$o,U,Xx))) & 
0.82/1.08	       (![Xx:a]: (app_encode_app(a,$o,S,Xx) => app_encode_app(a,$o,U,Xx)))) =>
0.82/1.08	      ((![Xx:a]: (app_encode_app(a,$o,S,Xx) => app_encode_app(a,$o,T,Xx))) <=>
0.82/1.08	       (![Xx:a]:
0.82/1.08	          (((~app_encode_app(a,$o,T,Xx)) & app_encode_app(a,$o,U,Xx) & 
0.82/1.08	            app_encode_app(a,$o,S,Xx)) =>
0.82/1.08	           app_encode_app(a,$o,T,Xx))))))).
0.82/1.08	tff(zf_stmt_0, axiom,
0.82/1.08	  (zip_tseitin0(Xx,T,S) <=>
0.82/1.08	   (app_encode_app(a,$o,S,Xx) => app_encode_app(a,$o,T,Xx)))).
0.82/1.08	tff('0', plain,
0.82/1.08	    ![X4 : app_encode_fun(a, $o), X5 : a, X6 : app_encode_fun(a, $o)]:
0.82/1.08	      (zip_tseitin0(X5, X6, X4) | app_encode_app(a, $o, X4, X5)),
0.82/1.08	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.82/1.08	tff(zf_stmt_1, type, zip_tseitin2 :
0.82/1.08	    (a * app_encode_fun(a,$o) * app_encode_fun(a,$o) * app_encode_fun(a,$o)) >
0.82/1.08	      $o).
0.82/1.08	tff(zf_stmt_2, axiom,
0.82/1.08	  (zip_tseitin2(Xx,U,T,S) <=>
0.82/1.08	   (zip_tseitin1(Xx,U,T,S) => app_encode_app(a,$o,T,Xx)))).
0.82/1.08	tff(zf_stmt_3, type, zip_tseitin1 :
0.82/1.08	    (a * app_encode_fun(a,$o) * app_encode_fun(a,$o) * app_encode_fun(a,$o)) >
0.82/1.08	      $o).
0.82/1.08	tff(zf_stmt_4, axiom,
0.82/1.08	  (zip_tseitin1(Xx,U,T,S) <=>
0.82/1.08	   (app_encode_app(a,$o,S,Xx) & app_encode_app(a,$o,U,Xx) & 
0.82/1.08	    (~app_encode_app(a,$o,T,Xx))))).
0.82/1.08	tff(zf_stmt_5, type, zip_tseitin0 :
0.82/1.08	    (a * app_encode_fun(a,$o) * app_encode_fun(a,$o)) > $o).
0.82/1.08	tff(zf_stmt_6, conjecture,
0.82/1.08	  (![S:app_encode_fun(a,$o),T:app_encode_fun(a,$o),U:app_encode_fun(a,$o)]:
0.82/1.08	     (((![Xx:a]: (app_encode_app(a,$o,S,Xx) => app_encode_app(a,$o,U,Xx))) & 
0.82/1.08	       (![Xx:a]: (app_encode_app(a,$o,T,Xx) => app_encode_app(a,$o,U,Xx)))) =>
0.82/1.08	      ((![Xx:a]: zip_tseitin0(Xx,T,S)) <=> (![Xx:a]: zip_tseitin2(Xx,U,T,S)))))).
0.82/1.08	tff(zf_stmt_7, negated_conjecture,
0.82/1.08	  (~
0.82/1.08	    (![S:app_encode_fun(a,$o),T:app_encode_fun(a,$o),U:app_encode_fun(a,$o)]:
0.82/1.08	       (((![Xx:a]: (app_encode_app(a,$o,S,Xx) => app_encode_app(a,$o,U,Xx))) & 
0.82/1.08	         (![Xx:a]: (app_encode_app(a,$o,T,Xx) => app_encode_app(a,$o,U,Xx)))) =>
0.82/1.08	        ((![Xx:a]: zip_tseitin0(Xx,T,S)) <=>
0.82/1.08	         (![Xx:a]: zip_tseitin2(Xx,U,T,S))))))).
0.82/1.08	tff('1', plain,
0.82/1.08	    ![X9 : a]:
0.82/1.08	      (app_encode_app(a, $o, sk_U, X9) | ~ app_encode_app(a, $o, sk_S, X9)),
0.82/1.08	    inference('cnf', [status(esa)], [zf_stmt_7])).
0.82/1.08	tff('2', plain,
0.82/1.08	    ![X4 : app_encode_fun(a, $o), X5 : a, X6 : app_encode_fun(a, $o)]:
0.82/1.08	      (zip_tseitin0(X5, X6, X4) | ~ app_encode_app(a, $o, X6, X5)),
0.82/1.08	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.82/1.08	tff('3', plain,
0.82/1.08	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ $true
0.82/1.08	       | ~ app_encode_app(a, $o, sk_S, X0)
0.82/1.08	       | zip_tseitin0(X0, sk_U, X1)),
0.82/1.08	    inference('sup-', [status(thm)], ['1', '2'])).
0.82/1.08	tff('4', plain,
0.82/1.08	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
0.82/1.08	      (zip_tseitin0(X0, sk_U, X1) | ~ app_encode_app(a, $o, sk_S, X0)),
0.82/1.08	    inference('simplify', [status(thm)], ['3'])).
0.82/1.08	tff('5', plain,
0.82/1.08	    ![X0 : a, X1 : app_encode_fun(a, $o), X2 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ $true | zip_tseitin0(X0, X2, sk_S) | zip_tseitin0(X0, sk_U, X1)),
0.82/1.08	    inference('sup-', [status(thm)], ['0', '4'])).
0.82/1.08	tff('6', plain,
0.82/1.08	    ![X0 : a, X1 : app_encode_fun(a, $o), X2 : app_encode_fun(a, $o)]:
0.82/1.08	      (zip_tseitin0(X0, sk_U, X1) | zip_tseitin0(X0, X2, sk_S)),
0.82/1.08	    inference('simplify', [status(thm)], ['5'])).
0.82/1.08	tff('7', plain, ![X0 : a]: (~ $true | zip_tseitin0(X0, sk_U, sk_S)),
0.82/1.08	    inference('eq_fact', [status(thm)], ['6'])).
0.82/1.08	tff('8', plain, ![X0 : a]: zip_tseitin0(X0, sk_U, sk_S),
0.82/1.08	    inference('simplify', [status(thm)], ['7'])).
0.82/1.08	tff('9', plain,
0.82/1.08	    ![X4 : app_encode_fun(a, $o), X5 : a, X6 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ app_encode_app(a, $o, X4, X5)
0.82/1.08	       | app_encode_app(a, $o, X6, X5)
0.82/1.08	       | ~ zip_tseitin0(X5, X6, X4)),
0.82/1.08	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.82/1.08	tff('10', plain,
0.82/1.08	    ![X0 : a, X1 : app_encode_fun(a, $o), X2 : app_encode_fun(a, $o), 
0.82/1.08	      X3 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ $true
0.82/1.08	       | zip_tseitin0(X0, X3, X1)
0.82/1.08	       | ~ zip_tseitin0(X0, X2, X1)
0.82/1.08	       | app_encode_app(a, $o, X2, X0)),
0.82/1.08	    inference('sup-', [status(thm)], ['0', '9'])).
0.82/1.08	tff('11', plain,
0.82/1.08	    ![X0 : a, X1 : app_encode_fun(a, $o), X2 : app_encode_fun(a, $o), 
0.82/1.08	      X3 : app_encode_fun(a, $o)]:
0.82/1.08	      (app_encode_app(a, $o, X2, X0)
0.82/1.08	       | ~ zip_tseitin0(X0, X2, X1)
0.82/1.08	       | zip_tseitin0(X0, X3, X1)),
0.82/1.08	    inference('simplify', [status(thm)], ['10'])).
0.82/1.08	tff('12', plain,
0.82/1.08	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ $true | zip_tseitin0(X0, X1, sk_S) | app_encode_app(a, $o, sk_U, X0)),
0.82/1.08	    inference('sup-', [status(thm)], ['8', '11'])).
0.82/1.08	tff('13', plain,
0.82/1.08	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
0.82/1.08	      (app_encode_app(a, $o, sk_U, X0) | zip_tseitin0(X0, X1, sk_S)),
0.82/1.08	    inference('simplify', [status(thm)], ['12'])).
0.82/1.08	tff('14', plain,
0.82/1.08	    ![X4 : app_encode_fun(a, $o), X6 : app_encode_fun(a, $o), X7 : a, 
0.82/1.08	      X8 : app_encode_fun(a, $o)]:
0.82/1.08	      (zip_tseitin1(X7, X8, X6, X4)
0.82/1.08	       | app_encode_app(a, $o, X6, X7)
0.82/1.08	       | ~ app_encode_app(a, $o, X8, X7)
0.82/1.08	       | ~ app_encode_app(a, $o, X4, X7)),
0.82/1.08	    inference('cnf', [status(esa)], [zf_stmt_4])).
0.82/1.08	tff('15', plain,
0.82/1.08	    ![X0 : a, X1 : app_encode_fun(a, $o), X2 : app_encode_fun(a, $o), 
0.82/1.08	      X3 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ $true
0.82/1.08	       | zip_tseitin0(X0, X3, sk_S)
0.82/1.08	       | ~ app_encode_app(a, $o, X1, X0)
0.82/1.08	       | app_encode_app(a, $o, X2, X0)
0.82/1.08	       | zip_tseitin1(X0, sk_U, X2, X1)),
0.82/1.08	    inference('sup-', [status(thm)], ['13', '14'])).
0.82/1.08	tff('16', plain,
0.82/1.08	    ![X0 : a, X1 : app_encode_fun(a, $o), X2 : app_encode_fun(a, $o), 
0.82/1.08	      X3 : app_encode_fun(a, $o)]:
0.82/1.08	      (zip_tseitin1(X0, sk_U, X2, X1)
0.82/1.08	       | app_encode_app(a, $o, X2, X0)
0.82/1.08	       | ~ app_encode_app(a, $o, X1, X0)
0.82/1.08	       | zip_tseitin0(X0, X3, sk_S)),
0.82/1.08	    inference('simplify', [status(thm)], ['15'])).
0.82/1.08	tff('17', plain,
0.82/1.08	    ![X11 : a, X12 : a]:
0.82/1.08	      (zip_tseitin2(X11, sk_U, sk_T, sk_S) | zip_tseitin0(X12, sk_T, sk_S)),
0.82/1.08	    inference('cnf', [status(esa)], [zf_stmt_7])).
0.82/1.08	tff('18', plain,
0.82/1.08	    ![X0 : a, X1 : app_encode_fun(a, $o), X2 : a]:
0.82/1.08	      (~ $true
0.82/1.08	       | zip_tseitin2(X2, sk_U, sk_T, sk_S)
0.82/1.08	       | zip_tseitin0(X0, X1, sk_S)
0.82/1.08	       | app_encode_app(a, $o, sk_T, X0)),
0.82/1.08	    inference('sup-', [status(thm)], ['17', '11'])).
0.82/1.08	tff('19', plain,
0.82/1.08	    ![X0 : a, X1 : app_encode_fun(a, $o), X2 : a]:
0.82/1.08	      (app_encode_app(a, $o, sk_T, X0)
0.82/1.08	       | zip_tseitin0(X0, X1, sk_S)
0.82/1.08	       | zip_tseitin2(X2, sk_U, sk_T, sk_S)),
0.82/1.08	    inference('simplify', [status(thm)], ['18'])).
0.82/1.08	tff('20', plain,
0.82/1.08	    ![X4 : app_encode_fun(a, $o), X6 : app_encode_fun(a, $o), X7 : a, 
0.82/1.08	      X8 : app_encode_fun(a, $o)]:
0.82/1.08	      (zip_tseitin2(X7, X8, X6, X4) | ~ app_encode_app(a, $o, X6, X7)),
0.82/1.08	    inference('cnf', [status(esa)], [zf_stmt_2])).
0.82/1.08	tff('21', plain,
0.82/1.08	    ![X0 : a, X1 : app_encode_fun(a, $o), X2 : app_encode_fun(a, $o), 
0.82/1.08	      X3 : a, X4 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ $true
0.82/1.08	       | zip_tseitin2(X3, sk_U, sk_T, sk_S)
0.82/1.08	       | zip_tseitin0(X0, X4, sk_S)
0.82/1.08	       | zip_tseitin2(X0, X2, sk_T, X1)),
0.82/1.08	    inference('sup-', [status(thm)], ['19', '20'])).
0.82/1.08	tff('22', plain,
0.82/1.08	    ![X0 : a, X1 : app_encode_fun(a, $o), X2 : app_encode_fun(a, $o), 
0.82/1.08	      X3 : a, X4 : app_encode_fun(a, $o)]:
0.82/1.08	      (zip_tseitin2(X0, X2, sk_T, X1)
0.82/1.08	       | zip_tseitin0(X0, X4, sk_S)
0.82/1.08	       | zip_tseitin2(X3, sk_U, sk_T, sk_S)),
0.82/1.08	    inference('simplify', [status(thm)], ['21'])).
0.82/1.08	tff('23', plain,
0.82/1.08	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ $true
0.82/1.08	       | zip_tseitin2(X0, sk_U, sk_T, sk_S)
0.82/1.08	       | zip_tseitin0(X0, X1, sk_S)),
0.82/1.08	    inference('eq_fact', [status(thm)], ['22'])).
0.82/1.08	tff('24', plain,
0.82/1.08	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
0.82/1.08	      (zip_tseitin0(X0, X1, sk_S) | zip_tseitin2(X0, sk_U, sk_T, sk_S)),
0.82/1.08	    inference('simplify', [status(thm)], ['23'])).
0.82/1.08	tff('25', plain,
0.82/1.08	    ![X4 : app_encode_fun(a, $o), X6 : app_encode_fun(a, $o), X7 : a, 
0.82/1.08	      X8 : app_encode_fun(a, $o)]:
0.82/1.08	      (zip_tseitin2(X7, X8, X6, X4) | zip_tseitin1(X7, X8, X6, X4)),
0.82/1.08	    inference('cnf', [status(esa)], [zf_stmt_2])).
0.82/1.08	tff('26', plain,
0.82/1.08	    (~ zip_tseitin2(sk_Xx, sk_U, sk_T, sk_S)
0.82/1.08	     | ~ zip_tseitin0(sk_Xx1, sk_T, sk_S)),
0.82/1.08	    inference('cnf', [status(esa)], [zf_stmt_7])).
0.82/1.08	tff('27', plain,
0.82/1.08	    (~ $true
0.82/1.08	     | zip_tseitin1(sk_Xx, sk_U, sk_T, sk_S)
0.82/1.08	     | ~ zip_tseitin0(sk_Xx1, sk_T, sk_S)),
0.82/1.08	    inference('sup-', [status(thm)], ['25', '26'])).
0.82/1.08	tff('28', plain,
0.82/1.08	    (~ zip_tseitin0(sk_Xx1, sk_T, sk_S)
0.82/1.08	     | zip_tseitin1(sk_Xx, sk_U, sk_T, sk_S)),
0.82/1.08	    inference('simplify', [status(thm)], ['27'])).
0.82/1.08	tff('29', plain,
0.82/1.08	    ![X0 : a, X1 : app_encode_fun(a, $o), X2 : app_encode_fun(a, $o), 
0.82/1.08	      X3 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ $true | zip_tseitin0(X0, X3, X1) | zip_tseitin0(X0, X1, X2)),
0.82/1.08	    inference('sup-', [status(thm)], ['0', '2'])).
0.82/1.08	tff('30', plain,
0.82/1.08	    ![X0 : a, X1 : app_encode_fun(a, $o), X2 : app_encode_fun(a, $o), 
0.82/1.08	      X3 : app_encode_fun(a, $o)]:
0.82/1.08	      (zip_tseitin0(X0, X1, X2) | zip_tseitin0(X0, X3, X1)),
0.82/1.08	    inference('simplify', [status(thm)], ['29'])).
0.82/1.08	tff('31', plain,
0.82/1.08	    ![X0 : a]:
0.82/1.08	      (~ $true
0.82/1.08	       | zip_tseitin0(X0, sk_T, sk_S)
0.82/1.08	       | ~ zip_tseitin0(sk_Xx1, sk_T, sk_S)),
0.82/1.08	    inference('sup-', [status(thm)], ['17', '26'])).
0.82/1.08	tff('32', plain,
0.82/1.08	    ![X0 : a]:
0.82/1.08	      (~ zip_tseitin0(sk_Xx1, sk_T, sk_S) | zip_tseitin0(X0, sk_T, sk_S)),
0.82/1.08	    inference('simplify', [status(thm)], ['31'])).
0.82/1.08	tff('33', plain,
0.82/1.08	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ $true
0.82/1.08	       | zip_tseitin0(sk_Xx1, sk_S, X1)
0.82/1.08	       | zip_tseitin0(X0, sk_T, sk_S)),
0.82/1.08	    inference('sup-', [status(thm)], ['30', '32'])).
0.82/1.08	tff('34', plain,
0.82/1.08	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
0.82/1.08	      (zip_tseitin0(X0, sk_T, sk_S) | zip_tseitin0(sk_Xx1, sk_S, X1)),
0.82/1.08	    inference('simplify', [status(thm)], ['33'])).
0.82/1.08	tff('35', plain,
0.82/1.08	    ![X4 : app_encode_fun(a, $o), X6 : app_encode_fun(a, $o), X7 : a, 
0.82/1.08	      X8 : app_encode_fun(a, $o)]:
0.82/1.08	      (app_encode_app(a, $o, X4, X7) | ~ zip_tseitin1(X7, X8, X6, X4)),
0.82/1.08	    inference('cnf', [status(esa)], [zf_stmt_4])).
0.82/1.08	tff('36', plain,
0.82/1.08	    (~ $true
0.82/1.08	     | ~ zip_tseitin0(sk_Xx1, sk_T, sk_S)
0.82/1.08	     | app_encode_app(a, $o, sk_S, sk_Xx)),
0.82/1.08	    inference('sup-', [status(thm)], ['28', '35'])).
0.82/1.08	tff('37', plain,
0.82/1.08	    (app_encode_app(a, $o, sk_S, sk_Xx) | ~ zip_tseitin0(sk_Xx1, sk_T, sk_S)),
0.82/1.08	    inference('simplify', [status(thm)], ['36'])).
0.82/1.08	tff('38', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ $true
0.82/1.08	       | ~ zip_tseitin0(sk_Xx1, sk_T, sk_S)
0.82/1.08	       | ~ zip_tseitin0(sk_Xx, X0, sk_S)
0.82/1.08	       | app_encode_app(a, $o, X0, sk_Xx)),
0.82/1.08	    inference('sup-', [status(thm)], ['37', '9'])).
0.82/1.08	tff('39', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o)]:
0.82/1.08	      (app_encode_app(a, $o, X0, sk_Xx)
0.82/1.08	       | ~ zip_tseitin0(sk_Xx, X0, sk_S)
0.82/1.08	       | ~ zip_tseitin0(sk_Xx1, sk_T, sk_S)),
0.82/1.08	    inference('simplify', [status(thm)], ['38'])).
0.82/1.08	tff('40', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ $true
0.82/1.08	       | zip_tseitin0(sk_Xx1, sk_S, X1)
0.82/1.08	       | ~ zip_tseitin0(sk_Xx, X0, sk_S)
0.82/1.08	       | app_encode_app(a, $o, X0, sk_Xx)),
0.82/1.08	    inference('sup-', [status(thm)], ['34', '39'])).
0.82/1.08	tff('41', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.82/1.08	      (app_encode_app(a, $o, X0, sk_Xx)
0.82/1.08	       | ~ zip_tseitin0(sk_Xx, X0, sk_S)
0.82/1.08	       | zip_tseitin0(sk_Xx1, sk_S, X1)),
0.82/1.08	    inference('simplify', [status(thm)], ['40'])).
0.82/1.08	tff('42', plain,
0.82/1.08	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ $true
0.82/1.08	       | ~ app_encode_app(a, $o, sk_S, X0)
0.82/1.08	       | ~ zip_tseitin0(X0, X1, sk_U)
0.82/1.08	       | app_encode_app(a, $o, X1, X0)),
0.82/1.08	    inference('sup-', [status(thm)], ['1', '9'])).
0.82/1.08	tff('43', plain,
0.82/1.08	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
0.82/1.08	      (app_encode_app(a, $o, X1, X0)
0.82/1.08	       | ~ zip_tseitin0(X0, X1, sk_U)
0.82/1.08	       | ~ app_encode_app(a, $o, sk_S, X0)),
0.82/1.08	    inference('simplify', [status(thm)], ['42'])).
0.82/1.08	tff('44', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ $true
0.82/1.08	       | zip_tseitin0(sk_Xx1, sk_S, X1)
0.82/1.08	       | ~ zip_tseitin0(sk_Xx, sk_S, sk_S)
0.82/1.08	       | ~ zip_tseitin0(sk_Xx, X0, sk_U)
0.82/1.08	       | app_encode_app(a, $o, X0, sk_Xx)),
0.82/1.08	    inference('sup-', [status(thm)], ['41', '43'])).
0.82/1.08	tff('45', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : a]:
0.82/1.08	      (~ $true | zip_tseitin0(X1, X0, X0)),
0.82/1.08	    inference('eq_fact', [status(thm)], ['30'])).
0.82/1.08	tff('46', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : a]: zip_tseitin0(X1, X0, X0),
0.82/1.08	    inference('simplify', [status(thm)], ['45'])).
0.82/1.08	tff('47', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ $true
0.82/1.08	       | zip_tseitin0(sk_Xx1, sk_S, X1)
0.82/1.08	       | ~ $true
0.82/1.08	       | ~ zip_tseitin0(sk_Xx, X0, sk_U)
0.82/1.08	       | app_encode_app(a, $o, X0, sk_Xx)),
0.82/1.08	    inference('demod', [status(thm)], ['44', '46'])).
0.82/1.08	tff('48', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.82/1.08	      (app_encode_app(a, $o, X0, sk_Xx)
0.82/1.08	       | ~ zip_tseitin0(sk_Xx, X0, sk_U)
0.82/1.08	       | zip_tseitin0(sk_Xx1, sk_S, X1)),
0.82/1.08	    inference('simplify', [status(thm)], ['47'])).
0.82/1.08	tff('49', plain,
0.82/1.08	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ $true
0.82/1.08	       | zip_tseitin0(sk_Xx1, sk_U, X1)
0.82/1.08	       | zip_tseitin0(X0, sk_T, sk_S)),
0.82/1.08	    inference('sup-', [status(thm)], ['6', '32'])).
0.82/1.08	tff('50', plain,
0.82/1.08	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
0.82/1.08	      (zip_tseitin0(X0, sk_T, sk_S) | zip_tseitin0(sk_Xx1, sk_U, X1)),
0.82/1.08	    inference('simplify', [status(thm)], ['49'])).
0.82/1.08	tff('51', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ $true
0.82/1.08	       | zip_tseitin0(sk_Xx1, sk_U, X1)
0.82/1.08	       | ~ zip_tseitin0(sk_Xx, X0, sk_S)
0.82/1.08	       | app_encode_app(a, $o, X0, sk_Xx)),
0.82/1.08	    inference('sup-', [status(thm)], ['50', '39'])).
0.82/1.08	tff('52', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.82/1.08	      (app_encode_app(a, $o, X0, sk_Xx)
0.82/1.08	       | ~ zip_tseitin0(sk_Xx, X0, sk_S)
0.82/1.08	       | zip_tseitin0(sk_Xx1, sk_U, X1)),
0.82/1.08	    inference('simplify', [status(thm)], ['51'])).
0.82/1.08	tff('53', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ $true
0.82/1.08	       | zip_tseitin0(sk_Xx1, sk_U, X1)
0.82/1.08	       | ~ zip_tseitin0(sk_Xx, sk_S, sk_S)
0.82/1.08	       | ~ zip_tseitin0(sk_Xx, X0, sk_U)
0.82/1.08	       | app_encode_app(a, $o, X0, sk_Xx)),
0.82/1.08	    inference('sup-', [status(thm)], ['52', '43'])).
0.82/1.08	tff('54', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ $true
0.82/1.08	       | zip_tseitin0(sk_Xx1, sk_U, X1)
0.82/1.08	       | ~ $true
0.82/1.08	       | ~ zip_tseitin0(sk_Xx, X0, sk_U)
0.82/1.08	       | app_encode_app(a, $o, X0, sk_Xx)),
0.82/1.08	    inference('demod', [status(thm)], ['53', '46'])).
0.82/1.08	tff('55', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.82/1.08	      (app_encode_app(a, $o, X0, sk_Xx)
0.82/1.08	       | ~ zip_tseitin0(sk_Xx, X0, sk_U)
0.82/1.08	       | zip_tseitin0(sk_Xx1, sk_U, X1)),
0.82/1.08	    inference('simplify', [status(thm)], ['54'])).
0.82/1.08	tff('56', plain,
0.82/1.08	    ![X4 : app_encode_fun(a, $o), X6 : app_encode_fun(a, $o), X7 : a, 
0.82/1.08	      X8 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ app_encode_app(a, $o, X6, X7) | ~ zip_tseitin1(X7, X8, X6, X4)),
0.82/1.08	    inference('cnf', [status(esa)], [zf_stmt_4])).
0.82/1.08	tff('57', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
0.82/1.08	      X2 : app_encode_fun(a, $o), X3 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ $true
0.82/1.08	       | zip_tseitin0(sk_Xx1, sk_U, X3)
0.82/1.08	       | ~ zip_tseitin0(sk_Xx, X0, sk_U)
0.82/1.08	       | ~ zip_tseitin1(sk_Xx, X2, X0, X1)),
0.82/1.08	    inference('sup-', [status(thm)], ['55', '56'])).
0.82/1.08	tff('58', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
0.82/1.08	      X2 : app_encode_fun(a, $o), X3 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ zip_tseitin1(sk_Xx, X2, X0, X1)
0.82/1.08	       | ~ zip_tseitin0(sk_Xx, X0, sk_U)
0.82/1.08	       | zip_tseitin0(sk_Xx1, sk_U, X3)),
0.82/1.08	    inference('simplify', [status(thm)], ['57'])).
0.82/1.08	tff('59', plain,
0.82/1.08	    ![X0 : a, X1 : app_encode_fun(a, $o), X2 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ $true
0.82/1.08	       | zip_tseitin0(X0, X2, sk_S)
0.82/1.08	       | ~ zip_tseitin0(X0, X1, sk_U)
0.82/1.08	       | app_encode_app(a, $o, X1, X0)),
0.82/1.08	    inference('sup-', [status(thm)], ['0', '43'])).
0.82/1.08	tff('60', plain,
0.82/1.08	    ![X0 : a, X1 : app_encode_fun(a, $o), X2 : app_encode_fun(a, $o)]:
0.82/1.08	      (app_encode_app(a, $o, X1, X0)
0.82/1.08	       | ~ zip_tseitin0(X0, X1, sk_U)
0.82/1.08	       | zip_tseitin0(X0, X2, sk_S)),
0.82/1.08	    inference('simplify', [status(thm)], ['59'])).
0.82/1.08	tff('61', plain,
0.82/1.08	    ![X0 : a, X1 : app_encode_fun(a, $o), X2 : app_encode_fun(a, $o), 
0.82/1.08	      X3 : app_encode_fun(a, $o), X4 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ $true
0.82/1.08	       | zip_tseitin0(X0, X4, sk_S)
0.82/1.08	       | ~ zip_tseitin0(X0, X1, sk_U)
0.82/1.08	       | ~ zip_tseitin1(X0, X3, X1, X2)),
0.82/1.08	    inference('sup-', [status(thm)], ['60', '56'])).
0.82/1.08	tff('62', plain,
0.82/1.08	    ![X0 : a, X1 : app_encode_fun(a, $o), X2 : app_encode_fun(a, $o), 
0.82/1.08	      X3 : app_encode_fun(a, $o), X4 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ zip_tseitin1(X0, X3, X1, X2)
0.82/1.08	       | ~ zip_tseitin0(X0, X1, sk_U)
0.82/1.08	       | zip_tseitin0(X0, X4, sk_S)),
0.82/1.08	    inference('simplify', [status(thm)], ['61'])).
0.82/1.08	tff('63', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ $true
0.82/1.08	       | ~ zip_tseitin0(sk_Xx1, sk_T, sk_S)
0.82/1.08	       | zip_tseitin0(sk_Xx, X0, sk_S)
0.82/1.08	       | ~ zip_tseitin0(sk_Xx, sk_T, sk_U)),
0.82/1.08	    inference('sup-', [status(thm)], ['28', '62'])).
0.82/1.08	tff('64', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ zip_tseitin0(sk_Xx, sk_T, sk_U)
0.82/1.08	       | zip_tseitin0(sk_Xx, X0, sk_S)
0.82/1.08	       | ~ zip_tseitin0(sk_Xx1, sk_T, sk_S)),
0.82/1.08	    inference('simplify', [status(thm)], ['63'])).
0.82/1.08	tff('65', plain,
0.82/1.08	    ![X0 : a, X1 : app_encode_fun(a, $o), X2 : a, X3 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ $true
0.82/1.08	       | zip_tseitin2(X2, sk_U, sk_T, sk_S)
0.82/1.08	       | zip_tseitin0(X0, X3, sk_S)
0.82/1.08	       | zip_tseitin0(X0, sk_T, X1)),
0.82/1.08	    inference('sup-', [status(thm)], ['19', '2'])).
0.82/1.08	tff('66', plain,
0.82/1.08	    ![X0 : a, X1 : app_encode_fun(a, $o), X2 : a, X3 : app_encode_fun(a, $o)]:
0.82/1.08	      (zip_tseitin0(X0, sk_T, X1)
0.82/1.08	       | zip_tseitin0(X0, X3, sk_S)
0.82/1.08	       | zip_tseitin2(X2, sk_U, sk_T, sk_S)),
0.82/1.08	    inference('simplify', [status(thm)], ['65'])).
0.82/1.08	tff('67', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : a, X2 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ $true
0.82/1.08	       | zip_tseitin0(X1, X0, sk_S)
0.82/1.08	       | zip_tseitin0(X1, sk_T, X2)
0.82/1.08	       | ~ zip_tseitin0(sk_Xx1, sk_T, sk_S)),
0.82/1.08	    inference('sup-', [status(thm)], ['66', '26'])).
0.82/1.08	tff('68', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : a, X2 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ zip_tseitin0(sk_Xx1, sk_T, sk_S)
0.82/1.08	       | zip_tseitin0(X1, sk_T, X2)
0.82/1.08	       | zip_tseitin0(X1, X0, sk_S)),
0.82/1.08	    inference('simplify', [status(thm)], ['67'])).
0.82/1.08	tff('69', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ zip_tseitin0(sk_Xx1, sk_T, sk_S) | zip_tseitin0(sk_Xx, X0, sk_S)),
0.82/1.08	    inference('clc', [status(thm)], ['64', '68'])).
0.82/1.08	tff('70', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ $true
0.82/1.08	       | zip_tseitin0(sk_Xx1, sk_U, X1)
0.82/1.08	       | zip_tseitin0(sk_Xx, X0, sk_S)),
0.82/1.08	    inference('sup-', [status(thm)], ['50', '69'])).
0.82/1.08	tff('71', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.82/1.08	      (zip_tseitin0(sk_Xx, X0, sk_S) | zip_tseitin0(sk_Xx1, sk_U, X1)),
0.82/1.08	    inference('simplify', [status(thm)], ['70'])).
0.82/1.08	tff('72', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
0.82/1.08	      X2 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ $true
0.82/1.08	       | zip_tseitin0(sk_Xx1, sk_U, X2)
0.82/1.08	       | ~ zip_tseitin0(sk_Xx, X0, sk_S)
0.82/1.08	       | zip_tseitin0(sk_Xx, X0, X1)),
0.82/1.08	    inference('sup-', [status(thm)], ['52', '2'])).
0.82/1.08	tff('73', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
0.82/1.08	      X2 : app_encode_fun(a, $o)]:
0.82/1.08	      (zip_tseitin0(sk_Xx, X0, X1)
0.82/1.08	       | ~ zip_tseitin0(sk_Xx, X0, sk_S)
0.82/1.08	       | zip_tseitin0(sk_Xx1, sk_U, X2)),
0.82/1.08	    inference('simplify', [status(thm)], ['72'])).
0.82/1.08	tff('74', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
0.82/1.08	      X2 : app_encode_fun(a, $o), X3 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ $true
0.82/1.08	       | zip_tseitin0(sk_Xx1, sk_U, X3)
0.82/1.08	       | zip_tseitin0(sk_Xx1, sk_U, X1)
0.82/1.08	       | zip_tseitin0(sk_Xx, X0, X2)),
0.82/1.08	    inference('sup-', [status(thm)], ['71', '73'])).
0.82/1.08	tff('75', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
0.82/1.08	      X2 : app_encode_fun(a, $o), X3 : app_encode_fun(a, $o)]:
0.82/1.08	      (zip_tseitin0(sk_Xx, X0, X2)
0.82/1.08	       | zip_tseitin0(sk_Xx1, sk_U, X1)
0.82/1.08	       | zip_tseitin0(sk_Xx1, sk_U, X3)),
0.82/1.08	    inference('simplify', [status(thm)], ['74'])).
0.82/1.08	tff('76', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
0.82/1.08	      X2 : app_encode_fun(a, $o)]:
0.82/1.08	      (zip_tseitin0(sk_Xx, X1, X0) | zip_tseitin0(sk_Xx1, sk_U, X2)),
0.82/1.08	    inference('condensation', [status(thm)], ['75'])).
0.82/1.08	tff('77', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
0.82/1.08	      X2 : app_encode_fun(a, $o), X3 : app_encode_fun(a, $o)]:
0.82/1.08	      (zip_tseitin0(sk_Xx1, sk_U, X3) | ~ zip_tseitin1(sk_Xx, X2, X0, X1)),
0.82/1.08	    inference('clc', [status(thm)], ['58', '76'])).
0.82/1.08	tff('78', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ $true
0.82/1.08	       | ~ zip_tseitin0(sk_Xx1, sk_T, sk_S)
0.82/1.08	       | zip_tseitin0(sk_Xx1, sk_U, X0)),
0.82/1.08	    inference('sup-', [status(thm)], ['28', '77'])).
0.82/1.08	tff('79', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o)]:
0.82/1.08	      (zip_tseitin0(sk_Xx1, sk_U, X0) | ~ zip_tseitin0(sk_Xx1, sk_T, sk_S)),
0.82/1.08	    inference('simplify', [status(thm)], ['78'])).
0.82/1.08	tff('80', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o)]: zip_tseitin0(sk_Xx1, sk_U, X0),
0.82/1.08	    inference('clc', [status(thm)], ['79', '50'])).
0.82/1.08	tff('81', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ $true
0.82/1.08	       | zip_tseitin0(sk_Xx1, X1, X0)
0.82/1.08	       | app_encode_app(a, $o, sk_U, sk_Xx1)),
0.82/1.08	    inference('sup-', [status(thm)], ['80', '11'])).
0.82/1.08	tff('82', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.82/1.08	      (app_encode_app(a, $o, sk_U, sk_Xx1) | zip_tseitin0(sk_Xx1, X1, X0)),
0.82/1.08	    inference('simplify', [status(thm)], ['81'])).
0.82/1.08	tff('83', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
0.82/1.08	      X2 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ $true
0.82/1.08	       | zip_tseitin0(sk_Xx1, X2, X1)
0.82/1.08	       | ~ zip_tseitin0(sk_Xx1, X0, sk_U)
0.82/1.08	       | app_encode_app(a, $o, X0, sk_Xx1)),
0.82/1.08	    inference('sup-', [status(thm)], ['82', '9'])).
0.82/1.08	tff('84', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
0.82/1.08	      X2 : app_encode_fun(a, $o)]:
0.82/1.08	      (app_encode_app(a, $o, X0, sk_Xx1)
0.82/1.08	       | ~ zip_tseitin0(sk_Xx1, X0, sk_U)
0.82/1.08	       | zip_tseitin0(sk_Xx1, X2, X1)),
0.82/1.08	    inference('simplify', [status(thm)], ['83'])).
0.82/1.08	tff('85', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
0.82/1.08	      X2 : app_encode_fun(a, $o), X3 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ $true
0.82/1.08	       | zip_tseitin0(sk_Xx1, X3, X2)
0.82/1.08	       | ~ zip_tseitin0(sk_Xx1, X0, sk_U)
0.82/1.08	       | zip_tseitin0(sk_Xx1, X0, X1)),
0.82/1.08	    inference('sup-', [status(thm)], ['84', '2'])).
0.82/1.08	tff('86', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
0.82/1.08	      X2 : app_encode_fun(a, $o), X3 : app_encode_fun(a, $o)]:
0.82/1.08	      (zip_tseitin0(sk_Xx1, X0, X1)
0.82/1.08	       | ~ zip_tseitin0(sk_Xx1, X0, sk_U)
0.82/1.08	       | zip_tseitin0(sk_Xx1, X3, X2)),
0.82/1.08	    inference('simplify', [status(thm)], ['85'])).
0.82/1.08	tff('87', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.82/1.08	      (zip_tseitin0(sk_Xx1, X1, X0) | ~ zip_tseitin0(sk_Xx1, X1, sk_U)),
0.82/1.08	    inference('condensation', [status(thm)], ['86'])).
0.82/1.08	tff('88', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ $true
0.82/1.08	       | ~ zip_tseitin0(sk_Xx, X1, sk_U)
0.82/1.08	       | app_encode_app(a, $o, X1, sk_Xx)
0.82/1.08	       | zip_tseitin0(sk_Xx1, sk_S, X0)),
0.82/1.08	    inference('sup-', [status(thm)], ['48', '87'])).
0.82/1.08	tff('89', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.82/1.08	      (zip_tseitin0(sk_Xx1, sk_S, X0)
0.82/1.08	       | app_encode_app(a, $o, X1, sk_Xx)
0.82/1.08	       | ~ zip_tseitin0(sk_Xx, X1, sk_U)),
0.82/1.08	    inference('simplify', [status(thm)], ['88'])).
0.82/1.08	tff('90', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ $true
0.82/1.08	       | zip_tseitin0(sk_Xx1, sk_S, X1)
0.82/1.08	       | zip_tseitin0(sk_Xx, X0, sk_S)),
0.82/1.08	    inference('sup-', [status(thm)], ['34', '69'])).
0.82/1.08	tff('91', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.82/1.08	      (zip_tseitin0(sk_Xx, X0, sk_S) | zip_tseitin0(sk_Xx1, sk_S, X1)),
0.82/1.08	    inference('simplify', [status(thm)], ['90'])).
0.82/1.08	tff('92', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
0.82/1.08	      X2 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ $true
0.82/1.08	       | zip_tseitin0(sk_Xx1, sk_S, X2)
0.82/1.08	       | ~ zip_tseitin0(sk_Xx, X0, sk_S)
0.82/1.08	       | zip_tseitin0(sk_Xx, X0, X1)),
0.82/1.08	    inference('sup-', [status(thm)], ['41', '2'])).
0.82/1.08	tff('93', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
0.82/1.08	      X2 : app_encode_fun(a, $o)]:
0.82/1.08	      (zip_tseitin0(sk_Xx, X0, X1)
0.82/1.08	       | ~ zip_tseitin0(sk_Xx, X0, sk_S)
0.82/1.08	       | zip_tseitin0(sk_Xx1, sk_S, X2)),
0.82/1.08	    inference('simplify', [status(thm)], ['92'])).
0.82/1.08	tff('94', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
0.82/1.08	      X2 : app_encode_fun(a, $o), X3 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ $true
0.82/1.08	       | zip_tseitin0(sk_Xx1, sk_S, X3)
0.82/1.08	       | zip_tseitin0(sk_Xx1, sk_S, X1)
0.82/1.08	       | zip_tseitin0(sk_Xx, X0, X2)),
0.82/1.08	    inference('sup-', [status(thm)], ['91', '93'])).
0.82/1.08	tff('95', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
0.82/1.08	      X2 : app_encode_fun(a, $o), X3 : app_encode_fun(a, $o)]:
0.82/1.08	      (zip_tseitin0(sk_Xx, X0, X2)
0.82/1.08	       | zip_tseitin0(sk_Xx1, sk_S, X1)
0.82/1.08	       | zip_tseitin0(sk_Xx1, sk_S, X3)),
0.82/1.08	    inference('simplify', [status(thm)], ['94'])).
0.82/1.08	tff('96', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
0.82/1.08	      X2 : app_encode_fun(a, $o)]:
0.82/1.08	      (zip_tseitin0(sk_Xx, X1, X0) | zip_tseitin0(sk_Xx1, sk_S, X2)),
0.82/1.08	    inference('condensation', [status(thm)], ['95'])).
0.82/1.08	tff('97', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.82/1.08	      (app_encode_app(a, $o, X1, sk_Xx) | zip_tseitin0(sk_Xx1, sk_S, X0)),
0.82/1.08	    inference('clc', [status(thm)], ['89', '96'])).
0.82/1.08	tff('98', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
0.82/1.08	      X2 : app_encode_fun(a, $o), X3 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ $true
0.82/1.08	       | zip_tseitin0(sk_Xx1, sk_S, X3)
0.82/1.08	       | ~ zip_tseitin1(sk_Xx, X2, X0, X1)),
0.82/1.08	    inference('sup-', [status(thm)], ['97', '56'])).
0.82/1.08	tff('99', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
0.82/1.08	      X2 : app_encode_fun(a, $o), X3 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ zip_tseitin1(sk_Xx, X2, X0, X1) | zip_tseitin0(sk_Xx1, sk_S, X3)),
0.82/1.08	    inference('simplify', [status(thm)], ['98'])).
0.82/1.08	tff('100', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ $true
0.82/1.08	       | ~ zip_tseitin0(sk_Xx1, sk_T, sk_S)
0.82/1.08	       | zip_tseitin0(sk_Xx1, sk_S, X0)),
0.82/1.08	    inference('sup-', [status(thm)], ['28', '99'])).
0.82/1.08	tff('101', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o)]:
0.82/1.08	      (zip_tseitin0(sk_Xx1, sk_S, X0) | ~ zip_tseitin0(sk_Xx1, sk_T, sk_S)),
0.82/1.08	    inference('simplify', [status(thm)], ['100'])).
0.82/1.08	tff('102', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o)]: zip_tseitin0(sk_Xx1, sk_S, X0),
0.82/1.08	    inference('clc', [status(thm)], ['101', '30'])).
0.82/1.08	tff('103', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ $true
0.82/1.08	       | zip_tseitin0(sk_Xx1, X1, X0)
0.82/1.08	       | app_encode_app(a, $o, sk_S, sk_Xx1)),
0.82/1.08	    inference('sup-', [status(thm)], ['102', '11'])).
0.82/1.08	tff('104', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.82/1.08	      (app_encode_app(a, $o, sk_S, sk_Xx1) | zip_tseitin0(sk_Xx1, X1, X0)),
0.82/1.08	    inference('simplify', [status(thm)], ['103'])).
0.82/1.08	tff('105', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
0.82/1.08	      X2 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ $true
0.82/1.08	       | zip_tseitin0(sk_Xx1, X2, X1)
0.82/1.08	       | ~ zip_tseitin0(sk_Xx1, X0, sk_S)
0.82/1.08	       | app_encode_app(a, $o, X0, sk_Xx1)),
0.82/1.08	    inference('sup-', [status(thm)], ['104', '9'])).
0.82/1.08	tff('106', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
0.82/1.08	      X2 : app_encode_fun(a, $o)]:
0.82/1.08	      (app_encode_app(a, $o, X0, sk_Xx1)
0.82/1.08	       | ~ zip_tseitin0(sk_Xx1, X0, sk_S)
0.82/1.08	       | zip_tseitin0(sk_Xx1, X2, X1)),
0.82/1.08	    inference('simplify', [status(thm)], ['105'])).
0.82/1.08	tff('107', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
0.82/1.08	      X2 : app_encode_fun(a, $o), X3 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ $true
0.82/1.08	       | zip_tseitin0(sk_Xx1, X3, X2)
0.82/1.08	       | ~ zip_tseitin0(sk_Xx1, X0, sk_S)
0.82/1.08	       | zip_tseitin0(sk_Xx1, X0, X1)),
0.82/1.08	    inference('sup-', [status(thm)], ['106', '2'])).
0.82/1.08	tff('108', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
0.82/1.08	      X2 : app_encode_fun(a, $o), X3 : app_encode_fun(a, $o)]:
0.82/1.08	      (zip_tseitin0(sk_Xx1, X0, X1)
0.82/1.08	       | ~ zip_tseitin0(sk_Xx1, X0, sk_S)
0.82/1.08	       | zip_tseitin0(sk_Xx1, X3, X2)),
0.82/1.08	    inference('simplify', [status(thm)], ['107'])).
0.82/1.08	tff('109', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.82/1.08	      (zip_tseitin0(sk_Xx1, X1, X0) | ~ zip_tseitin0(sk_Xx1, X1, sk_S)),
0.82/1.08	    inference('condensation', [status(thm)], ['108'])).
0.82/1.08	tff('110', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ $true
0.82/1.08	       | zip_tseitin2(sk_Xx1, sk_U, sk_T, sk_S)
0.82/1.08	       | zip_tseitin0(sk_Xx1, X0, X1)),
0.82/1.08	    inference('sup-', [status(thm)], ['24', '109'])).
0.82/1.08	tff('111', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.82/1.08	      (zip_tseitin0(sk_Xx1, X0, X1) | zip_tseitin2(sk_Xx1, sk_U, sk_T, sk_S)),
0.82/1.08	    inference('simplify', [status(thm)], ['110'])).
0.82/1.08	tff('112', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ $true
0.82/1.08	       | ~ zip_tseitin0(sk_Xx1, X1, sk_U)
0.82/1.08	       | app_encode_app(a, $o, X1, sk_Xx1)
0.82/1.08	       | ~ zip_tseitin0(sk_Xx, X0, sk_S)
0.82/1.08	       | app_encode_app(a, $o, X0, sk_Xx)),
0.82/1.08	    inference('sup-', [status(thm)], ['60', '39'])).
0.82/1.08	tff('113', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.82/1.08	      (app_encode_app(a, $o, X0, sk_Xx)
0.82/1.08	       | ~ zip_tseitin0(sk_Xx, X0, sk_S)
0.82/1.08	       | app_encode_app(a, $o, X1, sk_Xx1)
0.82/1.08	       | ~ zip_tseitin0(sk_Xx1, X1, sk_U)),
0.82/1.08	    inference('simplify', [status(thm)], ['112'])).
0.82/1.08	tff('114', plain,
0.82/1.08	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ $true
0.82/1.08	       | ~ zip_tseitin0(sk_Xx1, X1, sk_U)
0.82/1.08	       | app_encode_app(a, $o, X1, sk_Xx1)
0.82/1.08	       | zip_tseitin0(X0, sk_T, sk_S)),
0.82/1.08	    inference('sup-', [status(thm)], ['60', '32'])).
0.82/1.08	tff('115', plain,
0.82/1.08	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
0.82/1.08	      (zip_tseitin0(X0, sk_T, sk_S)
0.82/1.08	       | app_encode_app(a, $o, X1, sk_Xx1)
0.82/1.08	       | ~ zip_tseitin0(sk_Xx1, X1, sk_U)),
0.82/1.08	    inference('simplify', [status(thm)], ['114'])).
0.82/1.08	tff('116', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ $true
0.82/1.08	       | ~ zip_tseitin0(sk_Xx1, X1, sk_U)
0.82/1.08	       | app_encode_app(a, $o, X1, sk_Xx1)
0.82/1.08	       | zip_tseitin0(sk_Xx, X0, sk_S)),
0.82/1.08	    inference('sup-', [status(thm)], ['115', '69'])).
0.82/1.08	tff('117', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.82/1.08	      (zip_tseitin0(sk_Xx, X0, sk_S)
0.82/1.08	       | app_encode_app(a, $o, X1, sk_Xx1)
0.82/1.08	       | ~ zip_tseitin0(sk_Xx1, X1, sk_U)),
0.82/1.08	    inference('simplify', [status(thm)], ['116'])).
0.82/1.08	tff('118', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ zip_tseitin0(sk_Xx1, X1, sk_U)
0.82/1.08	       | app_encode_app(a, $o, X1, sk_Xx1)
0.82/1.08	       | app_encode_app(a, $o, X0, sk_Xx)),
0.82/1.08	    inference('clc', [status(thm)], ['113', '117'])).
0.82/1.08	tff('119', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
0.82/1.08	      X2 : app_encode_fun(a, $o), X3 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ $true
0.82/1.08	       | app_encode_app(a, $o, X3, sk_Xx1)
0.82/1.08	       | ~ zip_tseitin0(sk_Xx1, X3, sk_U)
0.82/1.08	       | ~ zip_tseitin1(sk_Xx, X2, X0, X1)),
0.82/1.08	    inference('sup-', [status(thm)], ['118', '56'])).
0.82/1.08	tff('120', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
0.82/1.08	      X2 : app_encode_fun(a, $o), X3 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ zip_tseitin1(sk_Xx, X2, X0, X1)
0.82/1.08	       | ~ zip_tseitin0(sk_Xx1, X3, sk_U)
0.82/1.08	       | app_encode_app(a, $o, X3, sk_Xx1)),
0.82/1.08	    inference('simplify', [status(thm)], ['119'])).
0.82/1.08	tff('121', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ $true
0.82/1.08	       | ~ zip_tseitin0(sk_Xx1, sk_T, sk_S)
0.82/1.08	       | app_encode_app(a, $o, X0, sk_Xx1)
0.82/1.08	       | ~ zip_tseitin0(sk_Xx1, X0, sk_U)),
0.82/1.08	    inference('sup-', [status(thm)], ['28', '120'])).
0.82/1.08	tff('122', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ zip_tseitin0(sk_Xx1, X0, sk_U)
0.82/1.08	       | app_encode_app(a, $o, X0, sk_Xx1)
0.82/1.08	       | ~ zip_tseitin0(sk_Xx1, sk_T, sk_S)),
0.82/1.08	    inference('simplify', [status(thm)], ['121'])).
0.82/1.08	tff('123', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o)]:
0.82/1.08	      (app_encode_app(a, $o, X0, sk_Xx1) | ~ zip_tseitin0(sk_Xx1, X0, sk_U)),
0.82/1.08	    inference('clc', [status(thm)], ['122', '60'])).
0.82/1.08	tff('124', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
0.82/1.08	      X2 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ $true
0.82/1.08	       | ~ zip_tseitin0(sk_Xx1, X0, sk_U)
0.82/1.08	       | zip_tseitin2(sk_Xx1, X2, X0, X1)),
0.82/1.08	    inference('sup-', [status(thm)], ['123', '20'])).
0.82/1.08	tff('125', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
0.82/1.08	      X2 : app_encode_fun(a, $o)]:
0.82/1.08	      (zip_tseitin2(sk_Xx1, X2, X0, X1) | ~ zip_tseitin0(sk_Xx1, X0, sk_U)),
0.82/1.08	    inference('simplify', [status(thm)], ['124'])).
0.82/1.08	tff('126', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
0.82/1.08	      X2 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ $true
0.82/1.08	       | zip_tseitin2(sk_Xx1, sk_U, sk_T, sk_S)
0.82/1.08	       | zip_tseitin2(sk_Xx1, X2, X0, X1)),
0.82/1.08	    inference('sup-', [status(thm)], ['111', '125'])).
0.82/1.08	tff('127', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
0.82/1.08	      X2 : app_encode_fun(a, $o)]:
0.82/1.08	      (zip_tseitin2(sk_Xx1, X2, X0, X1)
0.82/1.08	       | zip_tseitin2(sk_Xx1, sk_U, sk_T, sk_S)),
0.82/1.08	    inference('simplify', [status(thm)], ['126'])).
0.82/1.08	tff('128', plain, zip_tseitin2(sk_Xx1, sk_U, sk_T, sk_S),
0.82/1.08	    inference('condensation', [status(thm)], ['127'])).
0.82/1.08	tff('129', plain,
0.82/1.08	    ![X4 : app_encode_fun(a, $o), X6 : app_encode_fun(a, $o), X7 : a, 
0.82/1.08	      X8 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ zip_tseitin1(X7, X8, X6, X4)
0.82/1.08	       | app_encode_app(a, $o, X6, X7)
0.82/1.08	       | ~ zip_tseitin2(X7, X8, X6, X4)),
0.82/1.08	    inference('cnf', [status(esa)], [zf_stmt_2])).
0.82/1.08	tff('130', plain,
0.82/1.08	    ![X4 : app_encode_fun(a, $o), X6 : app_encode_fun(a, $o), X7 : a, 
0.82/1.08	      X8 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ zip_tseitin2(X7, X8, X6, X4) | ~ zip_tseitin1(X7, X8, X6, X4)),
0.82/1.08	    inference('clc', [status(thm)], ['129', '56'])).
0.82/1.08	tff('131', plain, (~ $true | ~ zip_tseitin1(sk_Xx1, sk_U, sk_T, sk_S)),
0.82/1.08	    inference('sup-', [status(thm)], ['128', '130'])).
0.82/1.08	tff('132', plain, ~ zip_tseitin1(sk_Xx1, sk_U, sk_T, sk_S),
0.82/1.08	    inference('simplify', [status(thm)], ['131'])).
0.82/1.08	tff('133', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ $true
0.82/1.08	       | zip_tseitin0(sk_Xx1, X0, sk_S)
0.82/1.08	       | ~ app_encode_app(a, $o, sk_S, sk_Xx1)
0.82/1.08	       | app_encode_app(a, $o, sk_T, sk_Xx1)),
0.82/1.08	    inference('sup-', [status(thm)], ['16', '132'])).
0.82/1.08	tff('134', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o)]:
0.82/1.08	      (app_encode_app(a, $o, sk_T, sk_Xx1)
0.82/1.08	       | ~ app_encode_app(a, $o, sk_S, sk_Xx1)
0.82/1.08	       | zip_tseitin0(sk_Xx1, X0, sk_S)),
0.82/1.08	    inference('simplify', [status(thm)], ['133'])).
0.82/1.08	tff('135', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ $true
0.82/1.08	       | ~ zip_tseitin0(sk_Xx1, X0, sk_U)
0.82/1.08	       | ~ zip_tseitin0(sk_Xx1, X1, X0)
0.82/1.08	       | app_encode_app(a, $o, X1, sk_Xx1)),
0.82/1.08	    inference('sup-', [status(thm)], ['123', '9'])).
0.82/1.08	tff('136', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.82/1.08	      (app_encode_app(a, $o, X1, sk_Xx1)
0.82/1.08	       | ~ zip_tseitin0(sk_Xx1, X1, X0)
0.82/1.08	       | ~ zip_tseitin0(sk_Xx1, X0, sk_U)),
0.82/1.08	    inference('simplify', [status(thm)], ['135'])).
0.82/1.08	tff('137', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ $true
0.82/1.08	       | ~ zip_tseitin0(sk_Xx1, X0, sk_U)
0.82/1.08	       | app_encode_app(a, $o, sk_S, sk_Xx1)),
0.82/1.08	    inference('sup-', [status(thm)], ['102', '136'])).
0.82/1.08	tff('138', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o)]:
0.82/1.08	      (app_encode_app(a, $o, sk_S, sk_Xx1) | ~ zip_tseitin0(sk_Xx1, X0, sk_U)),
0.82/1.08	    inference('simplify', [status(thm)], ['137'])).
0.82/1.08	tff('139', plain, app_encode_app(a, $o, sk_S, sk_Xx1),
0.82/1.08	    inference('clc', [status(thm)], ['138', '104'])).
0.82/1.08	tff('140', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o)]:
0.82/1.08	      (app_encode_app(a, $o, sk_T, sk_Xx1)
0.82/1.08	       | ~ $true
0.82/1.08	       | zip_tseitin0(sk_Xx1, X0, sk_S)),
0.82/1.08	    inference('demod', [status(thm)], ['134', '139'])).
0.82/1.08	tff('141', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o)]:
0.82/1.08	      (zip_tseitin0(sk_Xx1, X0, sk_S) | app_encode_app(a, $o, sk_T, sk_Xx1)),
0.82/1.08	    inference('simplify', [status(thm)], ['140'])).
0.82/1.08	tff('142', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ $true
0.82/1.08	       | zip_tseitin0(sk_Xx1, X1, sk_S)
0.82/1.08	       | zip_tseitin0(sk_Xx1, sk_T, X0)),
0.82/1.08	    inference('sup-', [status(thm)], ['141', '2'])).
0.82/1.08	tff('143', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.82/1.08	      (zip_tseitin0(sk_Xx1, sk_T, X0) | zip_tseitin0(sk_Xx1, X1, sk_S)),
0.82/1.08	    inference('simplify', [status(thm)], ['142'])).
0.82/1.08	tff('144', plain, (~ $true | zip_tseitin0(sk_Xx1, sk_T, sk_S)),
0.82/1.08	    inference('eq_fact', [status(thm)], ['143'])).
0.82/1.08	tff('145', plain, zip_tseitin0(sk_Xx1, sk_T, sk_S),
0.82/1.08	    inference('simplify', [status(thm)], ['144'])).
0.82/1.08	tff('146', plain, ![X0 : a]: (~ $true | zip_tseitin0(X0, sk_T, sk_S)),
0.82/1.08	    inference('sup-', [status(thm)], ['145', '32'])).
0.82/1.08	tff('147', plain, ![X0 : a]: zip_tseitin0(X0, sk_T, sk_S),
0.82/1.08	    inference('simplify', [status(thm)], ['146'])).
0.82/1.08	tff('148', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o)]: (~ $true | zip_tseitin0(sk_Xx1, sk_T, X0)),
0.82/1.08	    inference('sup-', [status(thm)], ['147', '109'])).
0.82/1.08	tff('149', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o)]: zip_tseitin0(sk_Xx1, sk_T, X0),
0.82/1.08	    inference('simplify', [status(thm)], ['148'])).
0.82/1.08	tff('150', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ $true
0.82/1.08	       | ~ zip_tseitin0(sk_Xx, X0, sk_S)
0.82/1.08	       | app_encode_app(a, $o, X0, sk_Xx)),
0.82/1.08	    inference('sup-', [status(thm)], ['149', '39'])).
0.82/1.08	tff('151', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o)]: (~ $true | zip_tseitin0(sk_Xx, X0, sk_S)),
0.82/1.08	    inference('sup-', [status(thm)], ['145', '69'])).
0.82/1.08	tff('152', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o)]: zip_tseitin0(sk_Xx, X0, sk_S),
0.82/1.08	    inference('simplify', [status(thm)], ['151'])).
0.82/1.08	tff('153', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ $true | ~ $true | app_encode_app(a, $o, X0, sk_Xx)),
0.82/1.08	    inference('demod', [status(thm)], ['150', '152'])).
0.82/1.08	tff('154', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o)]: app_encode_app(a, $o, X0, sk_Xx),
0.82/1.08	    inference('simplify', [status(thm)], ['153'])).
0.82/1.08	tff('155', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
0.82/1.08	      X2 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ $true | zip_tseitin2(sk_Xx, X2, X0, X1)),
0.82/1.08	    inference('sup-', [status(thm)], ['154', '20'])).
0.82/1.08	tff('156', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
0.82/1.08	      X2 : app_encode_fun(a, $o)]: zip_tseitin2(sk_Xx, X2, X0, X1),
0.82/1.08	    inference('simplify', [status(thm)], ['155'])).
0.82/1.08	tff('157', plain, (~ $true | ~ zip_tseitin0(sk_Xx1, sk_T, sk_S)),
0.82/1.08	    inference('sup-', [status(thm)], ['156', '26'])).
0.82/1.08	tff('158', plain,
0.82/1.08	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ $true
0.82/1.08	       | zip_tseitin0(sk_Xx1, X1, sk_T)
0.82/1.08	       | zip_tseitin0(X0, sk_T, sk_S)),
0.82/1.08	    inference('sup-', [status(thm)], ['30', '32'])).
0.82/1.08	tff('159', plain,
0.82/1.08	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
0.82/1.08	      (zip_tseitin0(X0, sk_T, sk_S) | zip_tseitin0(sk_Xx1, X1, sk_T)),
0.82/1.08	    inference('simplify', [status(thm)], ['158'])).
0.82/1.08	tff('160', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ $true
0.82/1.08	       | zip_tseitin0(sk_Xx1, X1, sk_T)
0.82/1.08	       | ~ zip_tseitin0(sk_Xx, X0, sk_S)
0.82/1.08	       | app_encode_app(a, $o, X0, sk_Xx)),
0.82/1.08	    inference('sup-', [status(thm)], ['159', '39'])).
0.82/1.08	tff('161', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.82/1.08	      (app_encode_app(a, $o, X0, sk_Xx)
0.82/1.08	       | ~ zip_tseitin0(sk_Xx, X0, sk_S)
0.82/1.08	       | zip_tseitin0(sk_Xx1, X1, sk_T)),
0.82/1.08	    inference('simplify', [status(thm)], ['160'])).
0.82/1.08	tff('162', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ $true
0.82/1.08	       | zip_tseitin0(sk_Xx1, X1, sk_T)
0.82/1.08	       | ~ zip_tseitin0(sk_Xx, sk_S, sk_S)
0.82/1.08	       | ~ zip_tseitin0(sk_Xx, X0, sk_U)
0.82/1.08	       | app_encode_app(a, $o, X0, sk_Xx)),
0.82/1.08	    inference('sup-', [status(thm)], ['161', '43'])).
0.82/1.08	tff('163', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ $true
0.82/1.08	       | zip_tseitin0(sk_Xx1, X1, sk_T)
0.82/1.08	       | ~ $true
0.82/1.08	       | ~ zip_tseitin0(sk_Xx, X0, sk_U)
0.82/1.08	       | app_encode_app(a, $o, X0, sk_Xx)),
0.82/1.08	    inference('demod', [status(thm)], ['162', '46'])).
0.82/1.08	tff('164', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.82/1.08	      (app_encode_app(a, $o, X0, sk_Xx)
0.82/1.08	       | ~ zip_tseitin0(sk_Xx, X0, sk_U)
0.82/1.08	       | zip_tseitin0(sk_Xx1, X1, sk_T)),
0.82/1.08	    inference('simplify', [status(thm)], ['163'])).
0.82/1.08	tff('165', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
0.82/1.08	      X2 : app_encode_fun(a, $o), X3 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ $true
0.82/1.08	       | zip_tseitin0(sk_Xx1, X3, sk_T)
0.82/1.08	       | ~ zip_tseitin0(sk_Xx, X0, sk_U)
0.82/1.08	       | ~ zip_tseitin1(sk_Xx, X2, X0, X1)),
0.82/1.08	    inference('sup-', [status(thm)], ['164', '56'])).
0.82/1.08	tff('166', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
0.82/1.08	      X2 : app_encode_fun(a, $o), X3 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ zip_tseitin1(sk_Xx, X2, X0, X1)
0.82/1.08	       | ~ zip_tseitin0(sk_Xx, X0, sk_U)
0.82/1.08	       | zip_tseitin0(sk_Xx1, X3, sk_T)),
0.82/1.08	    inference('simplify', [status(thm)], ['165'])).
0.82/1.08	tff('167', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ $true
0.82/1.08	       | zip_tseitin0(sk_Xx1, X1, sk_T)
0.82/1.08	       | zip_tseitin0(sk_Xx, X0, sk_S)),
0.82/1.08	    inference('sup-', [status(thm)], ['159', '69'])).
0.82/1.08	tff('168', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.82/1.08	      (zip_tseitin0(sk_Xx, X0, sk_S) | zip_tseitin0(sk_Xx1, X1, sk_T)),
0.82/1.08	    inference('simplify', [status(thm)], ['167'])).
0.82/1.08	tff('169', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
0.82/1.08	      X2 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ $true
0.82/1.08	       | zip_tseitin0(sk_Xx1, X2, sk_T)
0.82/1.08	       | ~ zip_tseitin0(sk_Xx, X0, sk_S)
0.82/1.08	       | zip_tseitin0(sk_Xx, X0, X1)),
0.82/1.08	    inference('sup-', [status(thm)], ['161', '2'])).
0.82/1.08	tff('170', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
0.82/1.08	      X2 : app_encode_fun(a, $o)]:
0.82/1.08	      (zip_tseitin0(sk_Xx, X0, X1)
0.82/1.08	       | ~ zip_tseitin0(sk_Xx, X0, sk_S)
0.82/1.08	       | zip_tseitin0(sk_Xx1, X2, sk_T)),
0.82/1.08	    inference('simplify', [status(thm)], ['169'])).
0.82/1.08	tff('171', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
0.82/1.08	      X2 : app_encode_fun(a, $o), X3 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ $true
0.82/1.08	       | zip_tseitin0(sk_Xx1, X3, sk_T)
0.82/1.08	       | zip_tseitin0(sk_Xx1, X1, sk_T)
0.82/1.08	       | zip_tseitin0(sk_Xx, X0, X2)),
0.82/1.08	    inference('sup-', [status(thm)], ['168', '170'])).
0.82/1.08	tff('172', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
0.82/1.08	      X2 : app_encode_fun(a, $o), X3 : app_encode_fun(a, $o)]:
0.82/1.08	      (zip_tseitin0(sk_Xx, X0, X2)
0.82/1.08	       | zip_tseitin0(sk_Xx1, X1, sk_T)
0.82/1.08	       | zip_tseitin0(sk_Xx1, X3, sk_T)),
0.82/1.08	    inference('simplify', [status(thm)], ['171'])).
0.82/1.08	tff('173', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
0.82/1.08	      X2 : app_encode_fun(a, $o)]:
0.82/1.08	      (zip_tseitin0(sk_Xx, X1, X0) | zip_tseitin0(sk_Xx1, X2, sk_T)),
0.82/1.08	    inference('condensation', [status(thm)], ['172'])).
0.82/1.08	tff('174', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
0.82/1.08	      X2 : app_encode_fun(a, $o), X3 : app_encode_fun(a, $o)]:
0.82/1.08	      (zip_tseitin0(sk_Xx1, X3, sk_T) | ~ zip_tseitin1(sk_Xx, X2, X0, X1)),
0.82/1.08	    inference('clc', [status(thm)], ['166', '173'])).
0.82/1.08	tff('175', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ $true
0.82/1.08	       | ~ zip_tseitin0(sk_Xx1, sk_T, sk_S)
0.82/1.08	       | zip_tseitin0(sk_Xx1, X0, sk_T)),
0.82/1.08	    inference('sup-', [status(thm)], ['28', '174'])).
0.82/1.08	tff('176', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o)]:
0.82/1.08	      (zip_tseitin0(sk_Xx1, X0, sk_T) | ~ zip_tseitin0(sk_Xx1, sk_T, sk_S)),
0.82/1.08	    inference('simplify', [status(thm)], ['175'])).
0.82/1.08	tff('177', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o)]: zip_tseitin0(sk_Xx1, X0, sk_T),
0.82/1.08	    inference('clc', [status(thm)], ['176', '30'])).
0.82/1.08	tff('178', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ $true
0.82/1.08	       | ~ zip_tseitin0(sk_Xx1, X0, sk_S)
0.82/1.08	       | app_encode_app(a, $o, X0, sk_Xx1)),
0.82/1.08	    inference('sup-', [status(thm)], ['139', '9'])).
0.82/1.08	tff('179', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o)]:
0.82/1.08	      (app_encode_app(a, $o, X0, sk_Xx1) | ~ zip_tseitin0(sk_Xx1, X0, sk_S)),
0.82/1.08	    inference('simplify', [status(thm)], ['178'])).
0.82/1.08	tff('180', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ $true
0.82/1.08	       | ~ zip_tseitin0(sk_Xx1, X0, sk_S)
0.82/1.08	       | ~ zip_tseitin0(sk_Xx1, X1, X0)
0.82/1.08	       | app_encode_app(a, $o, X1, sk_Xx1)),
0.82/1.08	    inference('sup-', [status(thm)], ['179', '9'])).
0.82/1.08	tff('181', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.82/1.08	      (app_encode_app(a, $o, X1, sk_Xx1)
0.82/1.08	       | ~ zip_tseitin0(sk_Xx1, X1, X0)
0.82/1.08	       | ~ zip_tseitin0(sk_Xx1, X0, sk_S)),
0.82/1.08	    inference('simplify', [status(thm)], ['180'])).
0.82/1.08	tff('182', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ $true
0.82/1.08	       | ~ zip_tseitin0(sk_Xx1, sk_T, sk_S)
0.82/1.08	       | app_encode_app(a, $o, X0, sk_Xx1)),
0.82/1.08	    inference('sup-', [status(thm)], ['177', '181'])).
0.82/1.08	tff('183', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o)]:
0.82/1.08	      (app_encode_app(a, $o, X0, sk_Xx1) | ~ zip_tseitin0(sk_Xx1, sk_T, sk_S)),
0.82/1.08	    inference('simplify', [status(thm)], ['182'])).
0.82/1.08	tff('184', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ $true | app_encode_app(a, $o, X0, sk_Xx1)),
0.82/1.08	    inference('sup-', [status(thm)], ['147', '183'])).
0.82/1.08	tff('185', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o)]: app_encode_app(a, $o, X0, sk_Xx1),
0.82/1.08	    inference('simplify', [status(thm)], ['184'])).
0.82/1.08	tff('186', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.82/1.08	      (~ $true | zip_tseitin0(sk_Xx1, X0, X1)),
0.82/1.08	    inference('sup-', [status(thm)], ['185', '2'])).
0.82/1.08	tff('187', plain,
0.82/1.08	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
0.82/1.08	      zip_tseitin0(sk_Xx1, X0, X1),
0.82/1.08	    inference('simplify', [status(thm)], ['186'])).
0.82/1.08	tff('188', plain, (~ $true | ~ $true),
0.82/1.08	    inference('demod', [status(thm)], ['157', '187'])).
0.82/1.08	tff('189', plain, $false, inference('simplify', [status(thm)], ['188'])).
0.82/1.08	
0.82/1.08	% SZS output end Refutation
0.82/1.09	EOF
