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 $2 \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --no-fool
0.00/0.20	% Computer   : n060.star.cs.uiowa.edu
0.00/0.20	% Model      : x86_64 x86_64
0.00/0.20	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.20	% Memory     : 32218.625MB
0.00/0.20	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.20	% CPULimit   : 300
0.00/0.20	% DateTime   : Fri Feb  2 17:19:54 CST 2018
2.28/2.51	% done 4758 iterations in 2.309s
2.28/2.51	% SZS status Theorem for 'stdin'
2.28/2.51	% SZS output start Refutation
2.28/2.52	tff(zf_stmt_4, conjecture,
2.28/2.52	  (![S:app_encode_fun(a,$o),T:app_encode_fun(a,$o),U:app_encode_fun(a,$o)]:
2.28/2.52	     (((![Xx:a]: (app_encode_app(a,$o,T,Xx) => app_encode_app(a,$o,U,Xx))) & 
2.28/2.52	       (![Xx:a]: (app_encode_app(a,$o,S,Xx) => app_encode_app(a,$o,U,Xx)))) =>
2.28/2.52	      ((![Xx:a]: (app_encode_app(a,$o,S,Xx) => app_encode_app(a,$o,T,Xx))) <=>
2.28/2.52	       (![Xx:a]:
2.28/2.52	          (((~app_encode_app(a,$o,T,Xx)) & app_encode_app(a,$o,U,Xx) & 
2.28/2.52	            app_encode_app(a,$o,S,Xx)) =>
2.28/2.52	           ((~app_encode_app(a,$o,S,Xx)) & app_encode_app(a,$o,U,Xx)))))))).
2.28/2.52	tff(zf_stmt_0, axiom,
2.28/2.52	  (zip_tseitin3(Xx,U,T,S) <=>
2.28/2.52	   (zip_tseitin1(Xx,U,T,S) => zip_tseitin2(Xx,U,S)))).
2.28/2.52	tff('0', plain,
2.28/2.52	    ![X4 : app_encode_fun(a, $o), X6 : app_encode_fun(a, $o), X7 : a, 
2.28/2.52	      X8 : app_encode_fun(a, $o)]:
2.28/2.52	      (zip_tseitin3(X7, X8, X6, X4) | zip_tseitin1(X7, X8, X6, X4)),
2.28/2.52	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.28/2.52	tff(zf_stmt_1, type, zip_tseitin3 :
2.28/2.52	    (a * app_encode_fun(a,$o) * app_encode_fun(a,$o) * app_encode_fun(a,$o)) >
2.28/2.52	      $o).
2.28/2.52	tff(zf_stmt_2, type, zip_tseitin2 :
2.28/2.52	    (a * app_encode_fun(a,$o) * app_encode_fun(a,$o)) > $o).
2.28/2.52	tff(zf_stmt_3, axiom,
2.28/2.52	  (zip_tseitin2(Xx,U,S) <=>
2.28/2.52	   (app_encode_app(a,$o,U,Xx) & (~app_encode_app(a,$o,S,Xx))))).
2.28/2.52	tff(zf_stmt_4, type, zip_tseitin1 :
2.28/2.52	    (a * app_encode_fun(a,$o) * app_encode_fun(a,$o) * app_encode_fun(a,$o)) >
2.28/2.52	      $o).
2.28/2.52	tff(zf_stmt_5, axiom,
2.28/2.52	  (zip_tseitin1(Xx,U,T,S) <=>
2.28/2.52	   (app_encode_app(a,$o,S,Xx) & app_encode_app(a,$o,U,Xx) & 
2.28/2.52	    (~app_encode_app(a,$o,T,Xx))))).
2.28/2.52	tff(zf_stmt_6, type, zip_tseitin0 :
2.28/2.52	    (a * app_encode_fun(a,$o) * app_encode_fun(a,$o)) > $o).
2.28/2.52	tff(zf_stmt_7, axiom,
2.28/2.52	  (zip_tseitin0(Xx,T,S) <=>
2.28/2.52	   (app_encode_app(a,$o,S,Xx) => app_encode_app(a,$o,T,Xx)))).
2.28/2.52	tff(zf_stmt_8, conjecture,
2.28/2.52	  (![S:app_encode_fun(a,$o),T:app_encode_fun(a,$o),U:app_encode_fun(a,$o)]:
2.28/2.52	     (((![Xx:a]: (app_encode_app(a,$o,S,Xx) => app_encode_app(a,$o,U,Xx))) & 
2.28/2.52	       (![Xx:a]: (app_encode_app(a,$o,T,Xx) => app_encode_app(a,$o,U,Xx)))) =>
2.28/2.52	      ((![Xx:a]: zip_tseitin0(Xx,T,S)) <=> (![Xx:a]: zip_tseitin3(Xx,U,T,S)))))).
2.28/2.52	tff(zf_stmt_9, negated_conjecture,
2.28/2.52	  (~
2.28/2.52	    (![S:app_encode_fun(a,$o),T:app_encode_fun(a,$o),U:app_encode_fun(a,$o)]:
2.28/2.52	       (((![Xx:a]: (app_encode_app(a,$o,S,Xx) => app_encode_app(a,$o,U,Xx))) & 
2.28/2.52	         (![Xx:a]: (app_encode_app(a,$o,T,Xx) => app_encode_app(a,$o,U,Xx)))) =>
2.28/2.52	        ((![Xx:a]: zip_tseitin0(Xx,T,S)) <=>
2.28/2.52	         (![Xx:a]: zip_tseitin3(Xx,U,T,S))))))).
2.28/2.52	tff('1', plain,
2.28/2.52	    (~ zip_tseitin3(sk_Xx, sk_U, sk_T, sk_S)
2.28/2.52	     | ~ zip_tseitin0(sk_Xx1, sk_T, sk_S)),
2.28/2.52	    inference('cnf', [status(esa)], [zf_stmt_9])).
2.28/2.52	tff('2', plain,
2.28/2.52	    (~ $true
2.28/2.52	     | zip_tseitin1(sk_Xx, sk_U, sk_T, sk_S)
2.28/2.52	     | ~ zip_tseitin0(sk_Xx1, sk_T, sk_S)),
2.28/2.52	    inference('sup-', [status(thm)], ['0', '1'])).
2.28/2.52	tff('3', plain,
2.28/2.52	    (~ zip_tseitin0(sk_Xx1, sk_T, sk_S)
2.28/2.52	     | zip_tseitin1(sk_Xx, sk_U, sk_T, sk_S)),
2.28/2.52	    inference('simplify', [status(thm)], ['2'])).
2.28/2.52	tff('4', plain,
2.28/2.52	    ![X4 : app_encode_fun(a, $o), X5 : a, X6 : app_encode_fun(a, $o)]:
2.28/2.52	      (zip_tseitin0(X5, X6, X4) | app_encode_app(a, $o, X4, X5)),
2.28/2.52	    inference('cnf', [status(esa)], [zf_stmt_7])).
2.28/2.52	tff('5', plain,
2.28/2.52	    ![X9 : a]:
2.28/2.52	      (app_encode_app(a, $o, sk_U, X9) | ~ app_encode_app(a, $o, sk_S, X9)),
2.28/2.52	    inference('cnf', [status(esa)], [zf_stmt_9])).
2.28/2.52	tff('6', plain,
2.28/2.52	    ![X4 : app_encode_fun(a, $o), X5 : a, X6 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ app_encode_app(a, $o, X4, X5)
2.28/2.52	       | app_encode_app(a, $o, X6, X5)
2.28/2.52	       | ~ zip_tseitin0(X5, X6, X4)),
2.28/2.52	    inference('cnf', [status(esa)], [zf_stmt_7])).
2.28/2.52	tff('7', plain,
2.28/2.52	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ $true
2.28/2.52	       | ~ app_encode_app(a, $o, sk_S, X0)
2.28/2.52	       | ~ zip_tseitin0(X0, X1, sk_U)
2.28/2.52	       | app_encode_app(a, $o, X1, X0)),
2.28/2.52	    inference('sup-', [status(thm)], ['5', '6'])).
2.28/2.52	tff('8', plain,
2.28/2.52	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
2.28/2.52	      (app_encode_app(a, $o, X1, X0)
2.28/2.52	       | ~ zip_tseitin0(X0, X1, sk_U)
2.28/2.52	       | ~ app_encode_app(a, $o, sk_S, X0)),
2.28/2.52	    inference('simplify', [status(thm)], ['7'])).
2.28/2.52	tff('9', plain,
2.28/2.52	    ![X0 : a, X1 : app_encode_fun(a, $o), X2 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ $true
2.28/2.52	       | zip_tseitin0(X0, X2, sk_S)
2.28/2.52	       | ~ zip_tseitin0(X0, X1, sk_U)
2.28/2.52	       | app_encode_app(a, $o, X1, X0)),
2.28/2.52	    inference('sup-', [status(thm)], ['4', '8'])).
2.28/2.52	tff('10', plain,
2.28/2.52	    ![X0 : a, X1 : app_encode_fun(a, $o), X2 : app_encode_fun(a, $o)]:
2.28/2.52	      (app_encode_app(a, $o, X1, X0)
2.28/2.52	       | ~ zip_tseitin0(X0, X1, sk_U)
2.28/2.52	       | zip_tseitin0(X0, X2, sk_S)),
2.28/2.52	    inference('simplify', [status(thm)], ['9'])).
2.28/2.52	tff('11', plain,
2.28/2.52	    ![X4 : app_encode_fun(a, $o), X6 : app_encode_fun(a, $o), X7 : a, 
2.28/2.52	      X8 : app_encode_fun(a, $o)]:
2.28/2.52	      (app_encode_app(a, $o, X4, X7) | ~ zip_tseitin1(X7, X8, X6, X4)),
2.28/2.52	    inference('cnf', [status(esa)], [zf_stmt_5])).
2.28/2.52	tff('12', plain,
2.28/2.52	    (~ $true
2.28/2.52	     | ~ zip_tseitin0(sk_Xx1, sk_T, sk_S)
2.28/2.52	     | app_encode_app(a, $o, sk_S, sk_Xx)),
2.28/2.52	    inference('sup-', [status(thm)], ['3', '11'])).
2.28/2.52	tff('13', plain,
2.28/2.52	    (app_encode_app(a, $o, sk_S, sk_Xx) | ~ zip_tseitin0(sk_Xx1, sk_T, sk_S)),
2.28/2.52	    inference('simplify', [status(thm)], ['12'])).
2.28/2.52	tff('14', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ $true
2.28/2.52	       | ~ zip_tseitin0(sk_Xx1, sk_T, sk_S)
2.28/2.52	       | ~ zip_tseitin0(sk_Xx, X0, sk_S)
2.28/2.52	       | app_encode_app(a, $o, X0, sk_Xx)),
2.28/2.52	    inference('sup-', [status(thm)], ['13', '6'])).
2.28/2.52	tff('15', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o)]:
2.28/2.52	      (app_encode_app(a, $o, X0, sk_Xx)
2.28/2.52	       | ~ zip_tseitin0(sk_Xx, X0, sk_S)
2.28/2.52	       | ~ zip_tseitin0(sk_Xx1, sk_T, sk_S)),
2.28/2.52	    inference('simplify', [status(thm)], ['14'])).
2.28/2.52	tff('16', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ $true
2.28/2.52	       | ~ zip_tseitin0(sk_Xx1, X1, sk_U)
2.28/2.52	       | app_encode_app(a, $o, X1, sk_Xx1)
2.28/2.52	       | ~ zip_tseitin0(sk_Xx, X0, sk_S)
2.28/2.52	       | app_encode_app(a, $o, X0, sk_Xx)),
2.28/2.52	    inference('sup-', [status(thm)], ['10', '15'])).
2.28/2.52	tff('17', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
2.28/2.52	      (app_encode_app(a, $o, X0, sk_Xx)
2.28/2.52	       | ~ zip_tseitin0(sk_Xx, X0, sk_S)
2.28/2.52	       | app_encode_app(a, $o, X1, sk_Xx1)
2.28/2.52	       | ~ zip_tseitin0(sk_Xx1, X1, sk_U)),
2.28/2.52	    inference('simplify', [status(thm)], ['16'])).
2.28/2.52	tff('18', plain,
2.28/2.52	    ![X4 : app_encode_fun(a, $o), X5 : a, X6 : app_encode_fun(a, $o)]:
2.28/2.52	      (zip_tseitin0(X5, X6, X4) | ~ app_encode_app(a, $o, X6, X5)),
2.28/2.52	    inference('cnf', [status(esa)], [zf_stmt_7])).
2.28/2.52	tff('19', plain,
2.28/2.52	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ $true
2.28/2.52	       | ~ app_encode_app(a, $o, sk_S, X0)
2.28/2.52	       | zip_tseitin0(X0, sk_U, X1)),
2.28/2.52	    inference('sup-', [status(thm)], ['5', '18'])).
2.28/2.52	tff('20', plain,
2.28/2.52	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
2.28/2.52	      (zip_tseitin0(X0, sk_U, X1) | ~ app_encode_app(a, $o, sk_S, X0)),
2.28/2.52	    inference('simplify', [status(thm)], ['19'])).
2.28/2.52	tff('21', plain,
2.28/2.52	    ![X0 : a, X1 : app_encode_fun(a, $o), X2 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ $true | zip_tseitin0(X0, X2, sk_S) | zip_tseitin0(X0, sk_U, X1)),
2.28/2.52	    inference('sup-', [status(thm)], ['4', '20'])).
2.28/2.52	tff('22', plain,
2.28/2.52	    ![X0 : a, X1 : app_encode_fun(a, $o), X2 : app_encode_fun(a, $o)]:
2.28/2.52	      (zip_tseitin0(X0, sk_U, X1) | zip_tseitin0(X0, X2, sk_S)),
2.28/2.52	    inference('simplify', [status(thm)], ['21'])).
2.28/2.52	tff('23', plain,
2.28/2.52	    ![X11 : a, X12 : a]:
2.28/2.52	      (zip_tseitin3(X11, sk_U, sk_T, sk_S) | zip_tseitin0(X12, sk_T, sk_S)),
2.28/2.52	    inference('cnf', [status(esa)], [zf_stmt_9])).
2.28/2.52	tff('24', plain,
2.28/2.52	    ![X0 : a]:
2.28/2.52	      (~ $true
2.28/2.52	       | zip_tseitin0(X0, sk_T, sk_S)
2.28/2.52	       | ~ zip_tseitin0(sk_Xx1, sk_T, sk_S)),
2.28/2.52	    inference('sup-', [status(thm)], ['23', '1'])).
2.28/2.52	tff('25', plain,
2.28/2.52	    ![X0 : a]:
2.28/2.52	      (~ zip_tseitin0(sk_Xx1, sk_T, sk_S) | zip_tseitin0(X0, sk_T, sk_S)),
2.28/2.52	    inference('simplify', [status(thm)], ['24'])).
2.28/2.52	tff('26', plain,
2.28/2.52	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ $true
2.28/2.52	       | zip_tseitin0(sk_Xx1, sk_U, X1)
2.28/2.52	       | zip_tseitin0(X0, sk_T, sk_S)),
2.28/2.52	    inference('sup-', [status(thm)], ['22', '25'])).
2.28/2.52	tff('27', plain,
2.28/2.52	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
2.28/2.52	      (zip_tseitin0(X0, sk_T, sk_S) | zip_tseitin0(sk_Xx1, sk_U, X1)),
2.28/2.52	    inference('simplify', [status(thm)], ['26'])).
2.28/2.52	tff('28', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ $true
2.28/2.52	       | zip_tseitin0(sk_Xx1, sk_U, X1)
2.28/2.52	       | ~ zip_tseitin0(sk_Xx, X0, sk_S)
2.28/2.52	       | app_encode_app(a, $o, X0, sk_Xx)),
2.28/2.52	    inference('sup-', [status(thm)], ['27', '15'])).
2.28/2.52	tff('29', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
2.28/2.52	      (app_encode_app(a, $o, X0, sk_Xx)
2.28/2.52	       | ~ zip_tseitin0(sk_Xx, X0, sk_S)
2.28/2.52	       | zip_tseitin0(sk_Xx1, sk_U, X1)),
2.28/2.52	    inference('simplify', [status(thm)], ['28'])).
2.28/2.52	tff('30', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
2.28/2.52	      X2 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ $true
2.28/2.52	       | zip_tseitin0(sk_Xx1, sk_U, X2)
2.28/2.52	       | ~ zip_tseitin0(sk_Xx, X0, sk_S)
2.28/2.52	       | ~ zip_tseitin0(sk_Xx, X1, X0)
2.28/2.52	       | app_encode_app(a, $o, X1, sk_Xx)),
2.28/2.52	    inference('sup-', [status(thm)], ['29', '6'])).
2.28/2.52	tff('31', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
2.28/2.52	      X2 : app_encode_fun(a, $o)]:
2.28/2.52	      (app_encode_app(a, $o, X1, sk_Xx)
2.28/2.52	       | ~ zip_tseitin0(sk_Xx, X1, X0)
2.28/2.52	       | ~ zip_tseitin0(sk_Xx, X0, sk_S)
2.28/2.52	       | zip_tseitin0(sk_Xx1, sk_U, X2)),
2.28/2.52	    inference('simplify', [status(thm)], ['30'])).
2.28/2.52	tff('32', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ $true
2.28/2.52	       | zip_tseitin0(sk_Xx1, sk_U, X1)
2.28/2.52	       | zip_tseitin0(sk_Xx1, sk_U, X0)
2.28/2.52	       | ~ zip_tseitin0(sk_Xx, sk_S, sk_S)
2.28/2.52	       | app_encode_app(a, $o, sk_T, sk_Xx)),
2.28/2.52	    inference('sup-', [status(thm)], ['27', '31'])).
2.28/2.52	tff('33', plain,
2.28/2.52	    ![X0 : a, X1 : app_encode_fun(a, $o), X2 : app_encode_fun(a, $o), 
2.28/2.52	      X3 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ $true | zip_tseitin0(X0, X3, X1) | zip_tseitin0(X0, X1, X2)),
2.28/2.52	    inference('sup-', [status(thm)], ['4', '18'])).
2.28/2.52	tff('34', plain,
2.28/2.52	    ![X0 : a, X1 : app_encode_fun(a, $o), X2 : app_encode_fun(a, $o), 
2.28/2.52	      X3 : app_encode_fun(a, $o)]:
2.28/2.52	      (zip_tseitin0(X0, X1, X2) | zip_tseitin0(X0, X3, X1)),
2.28/2.52	    inference('simplify', [status(thm)], ['33'])).
2.28/2.52	tff('35', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o), X1 : a]:
2.28/2.52	      (~ $true | zip_tseitin0(X1, X0, X0)),
2.28/2.52	    inference('eq_fact', [status(thm)], ['34'])).
2.28/2.52	tff('36', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o), X1 : a]: zip_tseitin0(X1, X0, X0),
2.28/2.52	    inference('simplify', [status(thm)], ['35'])).
2.28/2.52	tff('37', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ $true
2.28/2.52	       | zip_tseitin0(sk_Xx1, sk_U, X1)
2.28/2.52	       | zip_tseitin0(sk_Xx1, sk_U, X0)
2.28/2.52	       | ~ $true
2.28/2.52	       | app_encode_app(a, $o, sk_T, sk_Xx)),
2.28/2.52	    inference('demod', [status(thm)], ['32', '36'])).
2.28/2.52	tff('38', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
2.28/2.52	      (app_encode_app(a, $o, sk_T, sk_Xx)
2.28/2.52	       | zip_tseitin0(sk_Xx1, sk_U, X0)
2.28/2.52	       | zip_tseitin0(sk_Xx1, sk_U, X1)),
2.28/2.52	    inference('simplify', [status(thm)], ['37'])).
2.28/2.52	tff('39', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o)]:
2.28/2.52	      (app_encode_app(a, $o, sk_T, sk_Xx) | zip_tseitin0(sk_Xx1, sk_U, X0)),
2.28/2.52	    inference('condensation', [status(thm)], ['38'])).
2.28/2.52	tff('40', plain,
2.28/2.52	    ![X4 : app_encode_fun(a, $o), X6 : app_encode_fun(a, $o), X7 : a, 
2.28/2.52	      X8 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ app_encode_app(a, $o, X6, X7) | ~ zip_tseitin1(X7, X8, X6, X4)),
2.28/2.52	    inference('cnf', [status(esa)], [zf_stmt_5])).
2.28/2.52	tff('41', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
2.28/2.52	      X2 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ $true
2.28/2.52	       | zip_tseitin0(sk_Xx1, sk_U, X2)
2.28/2.52	       | ~ zip_tseitin1(sk_Xx, X1, sk_T, X0)),
2.28/2.52	    inference('sup-', [status(thm)], ['39', '40'])).
2.28/2.52	tff('42', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
2.28/2.52	      X2 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ zip_tseitin1(sk_Xx, X1, sk_T, X0) | zip_tseitin0(sk_Xx1, sk_U, X2)),
2.28/2.52	    inference('simplify', [status(thm)], ['41'])).
2.28/2.52	tff('43', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ $true
2.28/2.52	       | ~ zip_tseitin0(sk_Xx1, sk_T, sk_S)
2.28/2.52	       | zip_tseitin0(sk_Xx1, sk_U, X0)),
2.28/2.52	    inference('sup-', [status(thm)], ['3', '42'])).
2.28/2.52	tff('44', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o)]:
2.28/2.52	      (zip_tseitin0(sk_Xx1, sk_U, X0) | ~ zip_tseitin0(sk_Xx1, sk_T, sk_S)),
2.28/2.52	    inference('simplify', [status(thm)], ['43'])).
2.28/2.52	tff('45', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o)]: zip_tseitin0(sk_Xx1, sk_U, X0),
2.28/2.52	    inference('clc', [status(thm)], ['44', '27'])).
2.28/2.52	tff('46', plain,
2.28/2.52	    ![X0 : a, X1 : app_encode_fun(a, $o), X2 : app_encode_fun(a, $o), 
2.28/2.52	      X3 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ $true
2.28/2.52	       | zip_tseitin0(X0, X3, X1)
2.28/2.52	       | ~ zip_tseitin0(X0, X2, X1)
2.28/2.52	       | app_encode_app(a, $o, X2, X0)),
2.28/2.52	    inference('sup-', [status(thm)], ['4', '6'])).
2.28/2.52	tff('47', plain,
2.28/2.52	    ![X0 : a, X1 : app_encode_fun(a, $o), X2 : app_encode_fun(a, $o), 
2.28/2.52	      X3 : app_encode_fun(a, $o)]:
2.28/2.52	      (app_encode_app(a, $o, X2, X0)
2.28/2.52	       | ~ zip_tseitin0(X0, X2, X1)
2.28/2.52	       | zip_tseitin0(X0, X3, X1)),
2.28/2.52	    inference('simplify', [status(thm)], ['46'])).
2.28/2.52	tff('48', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ $true
2.28/2.52	       | zip_tseitin0(sk_Xx1, X1, X0)
2.28/2.52	       | app_encode_app(a, $o, sk_U, sk_Xx1)),
2.28/2.52	    inference('sup-', [status(thm)], ['45', '47'])).
2.28/2.52	tff('49', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
2.28/2.52	      (app_encode_app(a, $o, sk_U, sk_Xx1) | zip_tseitin0(sk_Xx1, X1, X0)),
2.28/2.52	    inference('simplify', [status(thm)], ['48'])).
2.28/2.52	tff('50', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
2.28/2.52	      X2 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ $true
2.28/2.52	       | zip_tseitin0(sk_Xx1, X2, X1)
2.28/2.52	       | ~ zip_tseitin0(sk_Xx1, X0, sk_U)
2.28/2.52	       | app_encode_app(a, $o, X0, sk_Xx1)),
2.28/2.52	    inference('sup-', [status(thm)], ['49', '6'])).
2.28/2.52	tff('51', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
2.28/2.52	      X2 : app_encode_fun(a, $o)]:
2.28/2.52	      (app_encode_app(a, $o, X0, sk_Xx1)
2.28/2.52	       | ~ zip_tseitin0(sk_Xx1, X0, sk_U)
2.28/2.52	       | zip_tseitin0(sk_Xx1, X2, X1)),
2.28/2.52	    inference('simplify', [status(thm)], ['50'])).
2.28/2.52	tff('52', plain,
2.28/2.52	    ![X0 : a, X1 : app_encode_fun(a, $o), X2 : app_encode_fun(a, $o), 
2.28/2.52	      X3 : app_encode_fun(a, $o), X4 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ $true
2.28/2.52	       | zip_tseitin0(X0, X4, sk_S)
2.28/2.52	       | ~ zip_tseitin0(X0, X1, sk_U)
2.28/2.52	       | ~ zip_tseitin1(X0, X3, X1, X2)),
2.28/2.52	    inference('sup-', [status(thm)], ['10', '40'])).
2.28/2.52	tff('53', plain,
2.28/2.52	    ![X0 : a, X1 : app_encode_fun(a, $o), X2 : app_encode_fun(a, $o), 
2.28/2.52	      X3 : app_encode_fun(a, $o), X4 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ zip_tseitin1(X0, X3, X1, X2)
2.28/2.52	       | ~ zip_tseitin0(X0, X1, sk_U)
2.28/2.52	       | zip_tseitin0(X0, X4, sk_S)),
2.28/2.52	    inference('simplify', [status(thm)], ['52'])).
2.28/2.52	tff('54', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ $true
2.28/2.52	       | ~ zip_tseitin0(sk_Xx1, sk_T, sk_S)
2.28/2.52	       | zip_tseitin0(sk_Xx, X0, sk_S)
2.28/2.52	       | ~ zip_tseitin0(sk_Xx, sk_T, sk_U)),
2.28/2.52	    inference('sup-', [status(thm)], ['3', '53'])).
2.28/2.52	tff('55', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ zip_tseitin0(sk_Xx, sk_T, sk_U)
2.28/2.52	       | zip_tseitin0(sk_Xx, X0, sk_S)
2.28/2.52	       | ~ zip_tseitin0(sk_Xx1, sk_T, sk_S)),
2.28/2.52	    inference('simplify', [status(thm)], ['54'])).
2.28/2.52	tff('56', plain,
2.28/2.52	    ![X0 : a, X1 : app_encode_fun(a, $o), X2 : a]:
2.28/2.52	      (~ $true
2.28/2.52	       | zip_tseitin3(X2, sk_U, sk_T, sk_S)
2.28/2.52	       | zip_tseitin0(X0, X1, sk_S)
2.28/2.52	       | app_encode_app(a, $o, sk_T, X0)),
2.28/2.52	    inference('sup-', [status(thm)], ['23', '47'])).
2.28/2.52	tff('57', plain,
2.28/2.52	    ![X0 : a, X1 : app_encode_fun(a, $o), X2 : a]:
2.28/2.52	      (app_encode_app(a, $o, sk_T, X0)
2.28/2.52	       | zip_tseitin0(X0, X1, sk_S)
2.28/2.52	       | zip_tseitin3(X2, sk_U, sk_T, sk_S)),
2.28/2.52	    inference('simplify', [status(thm)], ['56'])).
2.28/2.52	tff('58', plain,
2.28/2.52	    ![X0 : a, X1 : app_encode_fun(a, $o), X2 : a, X3 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ $true
2.28/2.52	       | zip_tseitin3(X2, sk_U, sk_T, sk_S)
2.28/2.52	       | zip_tseitin0(X0, X3, sk_S)
2.28/2.52	       | zip_tseitin0(X0, sk_T, X1)),
2.28/2.52	    inference('sup-', [status(thm)], ['57', '18'])).
2.28/2.52	tff('59', plain,
2.28/2.52	    ![X0 : a, X1 : app_encode_fun(a, $o), X2 : a, X3 : app_encode_fun(a, $o)]:
2.28/2.52	      (zip_tseitin0(X0, sk_T, X1)
2.28/2.52	       | zip_tseitin0(X0, X3, sk_S)
2.28/2.52	       | zip_tseitin3(X2, sk_U, sk_T, sk_S)),
2.28/2.52	    inference('simplify', [status(thm)], ['58'])).
2.28/2.52	tff('60', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o), X1 : a, X2 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ $true
2.28/2.52	       | zip_tseitin0(X1, X0, sk_S)
2.28/2.52	       | zip_tseitin0(X1, sk_T, X2)
2.28/2.52	       | ~ zip_tseitin0(sk_Xx1, sk_T, sk_S)),
2.28/2.52	    inference('sup-', [status(thm)], ['59', '1'])).
2.28/2.52	tff('61', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o), X1 : a, X2 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ zip_tseitin0(sk_Xx1, sk_T, sk_S)
2.28/2.52	       | zip_tseitin0(X1, sk_T, X2)
2.28/2.52	       | zip_tseitin0(X1, X0, sk_S)),
2.28/2.52	    inference('simplify', [status(thm)], ['60'])).
2.28/2.52	tff('62', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ zip_tseitin0(sk_Xx1, sk_T, sk_S) | zip_tseitin0(sk_Xx, X0, sk_S)),
2.28/2.52	    inference('clc', [status(thm)], ['55', '61'])).
2.28/2.52	tff('63', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ $true
2.28/2.52	       | ~ zip_tseitin0(sk_Xx1, X1, sk_U)
2.28/2.52	       | app_encode_app(a, $o, X1, sk_Xx1)
2.28/2.52	       | zip_tseitin0(sk_Xx, X0, sk_S)),
2.28/2.52	    inference('sup-', [status(thm)], ['51', '62'])).
2.28/2.52	tff('64', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
2.28/2.52	      (zip_tseitin0(sk_Xx, X0, sk_S)
2.28/2.52	       | app_encode_app(a, $o, X1, sk_Xx1)
2.28/2.52	       | ~ zip_tseitin0(sk_Xx1, X1, sk_U)),
2.28/2.52	    inference('simplify', [status(thm)], ['63'])).
2.28/2.52	tff('65', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ zip_tseitin0(sk_Xx1, X1, sk_U)
2.28/2.52	       | app_encode_app(a, $o, X1, sk_Xx1)
2.28/2.52	       | app_encode_app(a, $o, X0, sk_Xx)),
2.28/2.52	    inference('clc', [status(thm)], ['17', '64'])).
2.28/2.52	tff('66', plain,
2.28/2.52	    ![X4 : app_encode_fun(a, $o), X7 : a, X8 : app_encode_fun(a, $o)]:
2.28/2.52	      (zip_tseitin2(X7, X8, X4)
2.28/2.52	       | app_encode_app(a, $o, X4, X7)
2.28/2.52	       | ~ app_encode_app(a, $o, X8, X7)),
2.28/2.52	    inference('cnf', [status(esa)], [zf_stmt_3])).
2.28/2.52	tff('67', plain,
2.28/2.52	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ $true
2.28/2.52	       | ~ app_encode_app(a, $o, sk_S, X0)
2.28/2.52	       | app_encode_app(a, $o, X1, X0)
2.28/2.52	       | zip_tseitin2(X0, sk_U, X1)),
2.28/2.52	    inference('sup-', [status(thm)], ['5', '66'])).
2.28/2.52	tff('68', plain,
2.28/2.52	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
2.28/2.52	      (zip_tseitin2(X0, sk_U, X1)
2.28/2.52	       | app_encode_app(a, $o, X1, X0)
2.28/2.52	       | ~ app_encode_app(a, $o, sk_S, X0)),
2.28/2.52	    inference('simplify', [status(thm)], ['67'])).
2.28/2.52	tff('69', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ $true
2.28/2.52	       | app_encode_app(a, $o, X1, sk_Xx)
2.28/2.52	       | ~ zip_tseitin0(sk_Xx1, sk_S, sk_U)
2.28/2.52	       | app_encode_app(a, $o, X0, sk_Xx1)
2.28/2.52	       | zip_tseitin2(sk_Xx1, sk_U, X0)),
2.28/2.52	    inference('sup-', [status(thm)], ['65', '68'])).
2.28/2.52	tff('70', plain,
2.28/2.52	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ $true
2.28/2.52	       | zip_tseitin0(sk_Xx1, sk_S, X1)
2.28/2.52	       | zip_tseitin0(X0, sk_T, sk_S)),
2.28/2.52	    inference('sup-', [status(thm)], ['34', '25'])).
2.28/2.52	tff('71', plain,
2.28/2.52	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
2.28/2.52	      (zip_tseitin0(X0, sk_T, sk_S) | zip_tseitin0(sk_Xx1, sk_S, X1)),
2.28/2.52	    inference('simplify', [status(thm)], ['70'])).
2.28/2.52	tff('72', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ $true
2.28/2.52	       | zip_tseitin0(sk_Xx1, sk_S, X1)
2.28/2.52	       | ~ zip_tseitin0(sk_Xx, X0, sk_S)
2.28/2.52	       | app_encode_app(a, $o, X0, sk_Xx)),
2.28/2.52	    inference('sup-', [status(thm)], ['71', '15'])).
2.28/2.52	tff('73', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
2.28/2.52	      (app_encode_app(a, $o, X0, sk_Xx)
2.28/2.52	       | ~ zip_tseitin0(sk_Xx, X0, sk_S)
2.28/2.52	       | zip_tseitin0(sk_Xx1, sk_S, X1)),
2.28/2.52	    inference('simplify', [status(thm)], ['72'])).
2.28/2.52	tff('74', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
2.28/2.52	      X2 : app_encode_fun(a, $o), X3 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ $true
2.28/2.52	       | zip_tseitin0(sk_Xx1, sk_S, X3)
2.28/2.52	       | ~ zip_tseitin0(sk_Xx, X0, sk_S)
2.28/2.52	       | ~ zip_tseitin1(sk_Xx, X2, X0, X1)),
2.28/2.52	    inference('sup-', [status(thm)], ['73', '40'])).
2.28/2.52	tff('75', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
2.28/2.52	      X2 : app_encode_fun(a, $o), X3 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ zip_tseitin1(sk_Xx, X2, X0, X1)
2.28/2.52	       | ~ zip_tseitin0(sk_Xx, X0, sk_S)
2.28/2.52	       | zip_tseitin0(sk_Xx1, sk_S, X3)),
2.28/2.52	    inference('simplify', [status(thm)], ['74'])).
2.28/2.52	tff('76', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ $true
2.28/2.52	       | zip_tseitin0(sk_Xx1, sk_S, X1)
2.28/2.52	       | zip_tseitin0(sk_Xx, X0, sk_S)),
2.28/2.52	    inference('sup-', [status(thm)], ['71', '62'])).
2.28/2.52	tff('77', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
2.28/2.52	      (zip_tseitin0(sk_Xx, X0, sk_S) | zip_tseitin0(sk_Xx1, sk_S, X1)),
2.28/2.52	    inference('simplify', [status(thm)], ['76'])).
2.28/2.52	tff('78', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
2.28/2.52	      X2 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ $true
2.28/2.52	       | zip_tseitin0(sk_Xx1, sk_S, X2)
2.28/2.52	       | ~ zip_tseitin0(sk_Xx, X0, sk_S)
2.28/2.52	       | zip_tseitin0(sk_Xx, X0, X1)),
2.28/2.52	    inference('sup-', [status(thm)], ['73', '18'])).
2.28/2.52	tff('79', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
2.28/2.52	      X2 : app_encode_fun(a, $o)]:
2.28/2.52	      (zip_tseitin0(sk_Xx, X0, X1)
2.28/2.52	       | ~ zip_tseitin0(sk_Xx, X0, sk_S)
2.28/2.52	       | zip_tseitin0(sk_Xx1, sk_S, X2)),
2.28/2.52	    inference('simplify', [status(thm)], ['78'])).
2.28/2.52	tff('80', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
2.28/2.52	      X2 : app_encode_fun(a, $o), X3 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ $true
2.28/2.52	       | zip_tseitin0(sk_Xx1, sk_S, X3)
2.28/2.52	       | zip_tseitin0(sk_Xx1, sk_S, X1)
2.28/2.52	       | zip_tseitin0(sk_Xx, X0, X2)),
2.28/2.52	    inference('sup-', [status(thm)], ['77', '79'])).
2.28/2.52	tff('81', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
2.28/2.52	      X2 : app_encode_fun(a, $o), X3 : app_encode_fun(a, $o)]:
2.28/2.52	      (zip_tseitin0(sk_Xx, X0, X2)
2.28/2.52	       | zip_tseitin0(sk_Xx1, sk_S, X1)
2.28/2.52	       | zip_tseitin0(sk_Xx1, sk_S, X3)),
2.28/2.52	    inference('simplify', [status(thm)], ['80'])).
2.28/2.52	tff('82', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
2.28/2.52	      X2 : app_encode_fun(a, $o)]:
2.28/2.52	      (zip_tseitin0(sk_Xx, X1, X0) | zip_tseitin0(sk_Xx1, sk_S, X2)),
2.28/2.52	    inference('condensation', [status(thm)], ['81'])).
2.28/2.52	tff('83', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
2.28/2.52	      X2 : app_encode_fun(a, $o), X3 : app_encode_fun(a, $o)]:
2.28/2.52	      (zip_tseitin0(sk_Xx1, sk_S, X3) | ~ zip_tseitin1(sk_Xx, X2, X0, X1)),
2.28/2.52	    inference('clc', [status(thm)], ['75', '82'])).
2.28/2.52	tff('84', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ $true
2.28/2.52	       | ~ zip_tseitin0(sk_Xx1, sk_T, sk_S)
2.28/2.52	       | zip_tseitin0(sk_Xx1, sk_S, X0)),
2.28/2.52	    inference('sup-', [status(thm)], ['3', '83'])).
2.28/2.52	tff('85', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o)]:
2.28/2.52	      (zip_tseitin0(sk_Xx1, sk_S, X0) | ~ zip_tseitin0(sk_Xx1, sk_T, sk_S)),
2.28/2.52	    inference('simplify', [status(thm)], ['84'])).
2.28/2.52	tff('86', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o)]: zip_tseitin0(sk_Xx1, sk_S, X0),
2.28/2.52	    inference('clc', [status(thm)], ['85', '34'])).
2.28/2.52	tff('87', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ $true
2.28/2.52	       | app_encode_app(a, $o, X1, sk_Xx)
2.28/2.52	       | ~ $true
2.28/2.52	       | app_encode_app(a, $o, X0, sk_Xx1)
2.28/2.52	       | zip_tseitin2(sk_Xx1, sk_U, X0)),
2.28/2.52	    inference('demod', [status(thm)], ['69', '86'])).
2.28/2.52	tff('88', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
2.28/2.52	      (zip_tseitin2(sk_Xx1, sk_U, X0)
2.28/2.52	       | app_encode_app(a, $o, X0, sk_Xx1)
2.28/2.52	       | app_encode_app(a, $o, X1, sk_Xx)),
2.28/2.52	    inference('simplify', [status(thm)], ['87'])).
2.28/2.52	tff('89', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
2.28/2.52	      X2 : app_encode_fun(a, $o), X3 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ $true
2.28/2.52	       | app_encode_app(a, $o, X3, sk_Xx1)
2.28/2.52	       | zip_tseitin2(sk_Xx1, sk_U, X3)
2.28/2.52	       | ~ zip_tseitin1(sk_Xx, X2, X0, X1)),
2.28/2.52	    inference('sup-', [status(thm)], ['88', '40'])).
2.28/2.52	tff('90', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
2.28/2.52	      X2 : app_encode_fun(a, $o), X3 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ zip_tseitin1(sk_Xx, X2, X0, X1)
2.28/2.52	       | zip_tseitin2(sk_Xx1, sk_U, X3)
2.28/2.52	       | app_encode_app(a, $o, X3, sk_Xx1)),
2.28/2.52	    inference('simplify', [status(thm)], ['89'])).
2.28/2.52	tff('91', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ $true
2.28/2.52	       | ~ zip_tseitin0(sk_Xx1, sk_T, sk_S)
2.28/2.52	       | app_encode_app(a, $o, X0, sk_Xx1)
2.28/2.52	       | zip_tseitin2(sk_Xx1, sk_U, X0)),
2.28/2.52	    inference('sup-', [status(thm)], ['3', '90'])).
2.28/2.52	tff('92', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o)]:
2.28/2.52	      (zip_tseitin2(sk_Xx1, sk_U, X0)
2.28/2.52	       | app_encode_app(a, $o, X0, sk_Xx1)
2.28/2.52	       | ~ zip_tseitin0(sk_Xx1, sk_T, sk_S)),
2.28/2.52	    inference('simplify', [status(thm)], ['91'])).
2.28/2.52	tff('93', plain, ![X0 : a]: (~ $true | zip_tseitin0(X0, sk_U, sk_S)),
2.28/2.52	    inference('eq_fact', [status(thm)], ['22'])).
2.28/2.52	tff('94', plain, ![X0 : a]: zip_tseitin0(X0, sk_U, sk_S),
2.28/2.52	    inference('simplify', [status(thm)], ['93'])).
2.28/2.52	tff('95', plain,
2.28/2.52	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ $true | zip_tseitin0(X0, X1, sk_S) | app_encode_app(a, $o, sk_U, X0)),
2.28/2.52	    inference('sup-', [status(thm)], ['94', '47'])).
2.28/2.52	tff('96', plain,
2.28/2.52	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
2.28/2.52	      (app_encode_app(a, $o, sk_U, X0) | zip_tseitin0(X0, X1, sk_S)),
2.28/2.52	    inference('simplify', [status(thm)], ['95'])).
2.28/2.52	tff('97', plain,
2.28/2.52	    ![X0 : a, X1 : app_encode_fun(a, $o), X2 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ $true
2.28/2.52	       | zip_tseitin0(X0, X2, sk_S)
2.28/2.52	       | app_encode_app(a, $o, X1, X0)
2.28/2.52	       | zip_tseitin2(X0, sk_U, X1)),
2.28/2.52	    inference('sup-', [status(thm)], ['96', '66'])).
2.28/2.52	tff('98', plain,
2.28/2.52	    ![X0 : a, X1 : app_encode_fun(a, $o), X2 : app_encode_fun(a, $o)]:
2.28/2.52	      (zip_tseitin2(X0, sk_U, X1)
2.28/2.52	       | app_encode_app(a, $o, X1, X0)
2.28/2.52	       | zip_tseitin0(X0, X2, sk_S)),
2.28/2.52	    inference('simplify', [status(thm)], ['97'])).
2.28/2.52	tff('99', plain,
2.28/2.52	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ $true
2.28/2.52	       | app_encode_app(a, $o, X1, sk_Xx1)
2.28/2.52	       | zip_tseitin2(sk_Xx1, sk_U, X1)
2.28/2.52	       | zip_tseitin0(X0, sk_T, sk_S)),
2.28/2.52	    inference('sup-', [status(thm)], ['98', '25'])).
2.28/2.52	tff('100', plain,
2.28/2.52	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
2.28/2.52	      (zip_tseitin0(X0, sk_T, sk_S)
2.28/2.52	       | zip_tseitin2(sk_Xx1, sk_U, X1)
2.28/2.52	       | app_encode_app(a, $o, X1, sk_Xx1)),
2.28/2.52	    inference('simplify', [status(thm)], ['99'])).
2.28/2.52	tff('101', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o)]:
2.28/2.52	      (app_encode_app(a, $o, X0, sk_Xx1) | zip_tseitin2(sk_Xx1, sk_U, X0)),
2.28/2.52	    inference('clc', [status(thm)], ['92', '100'])).
2.28/2.52	tff('102', plain,
2.28/2.52	    ![X10 : a]:
2.28/2.52	      (app_encode_app(a, $o, sk_U, X10) | ~ app_encode_app(a, $o, sk_T, X10)),
2.28/2.52	    inference('cnf', [status(esa)], [zf_stmt_9])).
2.28/2.52	tff('103', plain,
2.28/2.52	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ $true
2.28/2.52	       | ~ app_encode_app(a, $o, sk_T, X0)
2.28/2.52	       | ~ zip_tseitin0(X0, X1, sk_U)
2.28/2.52	       | app_encode_app(a, $o, X1, X0)),
2.28/2.52	    inference('sup-', [status(thm)], ['102', '6'])).
2.28/2.52	tff('104', plain,
2.28/2.52	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
2.28/2.52	      (app_encode_app(a, $o, X1, X0)
2.28/2.52	       | ~ zip_tseitin0(X0, X1, sk_U)
2.28/2.52	       | ~ app_encode_app(a, $o, sk_T, X0)),
2.28/2.52	    inference('simplify', [status(thm)], ['103'])).
2.28/2.52	tff('105', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ $true
2.28/2.52	       | zip_tseitin2(sk_Xx1, sk_U, sk_T)
2.28/2.52	       | ~ zip_tseitin0(sk_Xx1, X0, sk_U)
2.28/2.52	       | app_encode_app(a, $o, X0, sk_Xx1)),
2.28/2.52	    inference('sup-', [status(thm)], ['101', '104'])).
2.28/2.52	tff('106', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o)]:
2.28/2.52	      (app_encode_app(a, $o, X0, sk_Xx1)
2.28/2.52	       | ~ zip_tseitin0(sk_Xx1, X0, sk_U)
2.28/2.52	       | zip_tseitin2(sk_Xx1, sk_U, sk_T)),
2.28/2.52	    inference('simplify', [status(thm)], ['105'])).
2.28/2.52	tff('107', plain,
2.28/2.52	    ![X0 : a, X1 : app_encode_fun(a, $o), X2 : app_encode_fun(a, $o), 
2.28/2.52	      X3 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ $true
2.28/2.52	       | zip_tseitin0(X0, X3, X1)
2.28/2.52	       | app_encode_app(a, $o, X2, X0)
2.28/2.52	       | zip_tseitin2(X0, X1, X2)),
2.28/2.52	    inference('sup-', [status(thm)], ['4', '66'])).
2.28/2.52	tff('108', plain,
2.28/2.52	    ![X0 : a, X1 : app_encode_fun(a, $o), X2 : app_encode_fun(a, $o), 
2.28/2.52	      X3 : app_encode_fun(a, $o)]:
2.28/2.52	      (zip_tseitin2(X0, X1, X2)
2.28/2.52	       | app_encode_app(a, $o, X2, X0)
2.28/2.52	       | zip_tseitin0(X0, X3, X1)),
2.28/2.52	    inference('simplify', [status(thm)], ['107'])).
2.28/2.52	tff('109', plain,
2.28/2.52	    ![X0 : a, X1 : app_encode_fun(a, $o), X2 : app_encode_fun(a, $o), 
2.28/2.52	      X3 : app_encode_fun(a, $o), X4 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ $true
2.28/2.52	       | zip_tseitin0(X0, X4, X3)
2.28/2.52	       | zip_tseitin2(X0, X3, X1)
2.28/2.52	       | zip_tseitin0(X0, X1, X2)),
2.28/2.52	    inference('sup-', [status(thm)], ['108', '18'])).
2.28/2.52	tff('110', plain,
2.28/2.52	    ![X0 : a, X1 : app_encode_fun(a, $o), X2 : app_encode_fun(a, $o), 
2.28/2.52	      X3 : app_encode_fun(a, $o), X4 : app_encode_fun(a, $o)]:
2.28/2.52	      (zip_tseitin0(X0, X1, X2)
2.28/2.52	       | zip_tseitin2(X0, X3, X1)
2.28/2.52	       | zip_tseitin0(X0, X4, X3)),
2.28/2.52	    inference('simplify', [status(thm)], ['109'])).
2.28/2.52	tff('111', plain,
2.28/2.52	    ![X0 : a, X1 : app_encode_fun(a, $o), X2 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ $true
2.28/2.52	       | zip_tseitin0(sk_Xx1, X2, X1)
2.28/2.52	       | zip_tseitin2(sk_Xx1, X1, sk_T)
2.28/2.52	       | zip_tseitin0(X0, sk_T, sk_S)),
2.28/2.52	    inference('sup-', [status(thm)], ['110', '25'])).
2.28/2.52	tff('112', plain,
2.28/2.52	    ![X0 : a, X1 : app_encode_fun(a, $o), X2 : app_encode_fun(a, $o)]:
2.28/2.52	      (zip_tseitin0(X0, sk_T, sk_S)
2.28/2.52	       | zip_tseitin2(sk_Xx1, X1, sk_T)
2.28/2.52	       | zip_tseitin0(sk_Xx1, X2, X1)),
2.28/2.52	    inference('simplify', [status(thm)], ['111'])).
2.28/2.52	tff('113', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
2.28/2.52	      X2 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ $true
2.28/2.52	       | zip_tseitin0(sk_Xx1, X2, X1)
2.28/2.52	       | zip_tseitin2(sk_Xx1, X1, sk_T)
2.28/2.52	       | ~ zip_tseitin0(sk_Xx, X0, sk_S)
2.28/2.52	       | app_encode_app(a, $o, X0, sk_Xx)),
2.28/2.52	    inference('sup-', [status(thm)], ['112', '15'])).
2.28/2.52	tff('114', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
2.28/2.52	      X2 : app_encode_fun(a, $o)]:
2.28/2.52	      (app_encode_app(a, $o, X0, sk_Xx)
2.28/2.52	       | ~ zip_tseitin0(sk_Xx, X0, sk_S)
2.28/2.52	       | zip_tseitin2(sk_Xx1, X1, sk_T)
2.28/2.52	       | zip_tseitin0(sk_Xx1, X2, X1)),
2.28/2.52	    inference('simplify', [status(thm)], ['113'])).
2.28/2.52	tff('115', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
2.28/2.52	      X2 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ $true
2.28/2.52	       | zip_tseitin0(sk_Xx1, X2, X1)
2.28/2.52	       | zip_tseitin2(sk_Xx1, X1, sk_T)
2.28/2.52	       | zip_tseitin0(sk_Xx, X0, sk_S)),
2.28/2.52	    inference('sup-', [status(thm)], ['110', '62'])).
2.28/2.52	tff('116', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
2.28/2.52	      X2 : app_encode_fun(a, $o)]:
2.28/2.52	      (zip_tseitin0(sk_Xx, X0, sk_S)
2.28/2.52	       | zip_tseitin2(sk_Xx1, X1, sk_T)
2.28/2.52	       | zip_tseitin0(sk_Xx1, X2, X1)),
2.28/2.52	    inference('simplify', [status(thm)], ['115'])).
2.28/2.52	tff('117', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
2.28/2.52	      X2 : app_encode_fun(a, $o)]:
2.28/2.52	      (zip_tseitin0(sk_Xx1, X2, X1)
2.28/2.52	       | zip_tseitin2(sk_Xx1, X1, sk_T)
2.28/2.52	       | app_encode_app(a, $o, X0, sk_Xx)),
2.28/2.52	    inference('clc', [status(thm)], ['114', '116'])).
2.28/2.52	tff('118', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
2.28/2.52	      X2 : app_encode_fun(a, $o), X3 : app_encode_fun(a, $o), 
2.28/2.52	      X4 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ $true
2.28/2.52	       | zip_tseitin2(sk_Xx1, X3, sk_T)
2.28/2.52	       | zip_tseitin0(sk_Xx1, X4, X3)
2.28/2.52	       | ~ zip_tseitin1(sk_Xx, X2, X0, X1)),
2.28/2.52	    inference('sup-', [status(thm)], ['117', '40'])).
2.28/2.52	tff('119', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
2.28/2.52	      X2 : app_encode_fun(a, $o), X3 : app_encode_fun(a, $o), 
2.28/2.52	      X4 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ zip_tseitin1(sk_Xx, X2, X0, X1)
2.28/2.52	       | zip_tseitin0(sk_Xx1, X4, X3)
2.28/2.52	       | zip_tseitin2(sk_Xx1, X3, sk_T)),
2.28/2.52	    inference('simplify', [status(thm)], ['118'])).
2.28/2.52	tff('120', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ $true
2.28/2.52	       | ~ zip_tseitin0(sk_Xx1, sk_T, sk_S)
2.28/2.52	       | zip_tseitin2(sk_Xx1, X0, sk_T)
2.28/2.52	       | zip_tseitin0(sk_Xx1, X1, X0)),
2.28/2.52	    inference('sup-', [status(thm)], ['3', '119'])).
2.28/2.52	tff('121', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
2.28/2.52	      (zip_tseitin0(sk_Xx1, X1, X0)
2.28/2.52	       | zip_tseitin2(sk_Xx1, X0, sk_T)
2.28/2.52	       | ~ zip_tseitin0(sk_Xx1, sk_T, sk_S)),
2.28/2.52	    inference('simplify', [status(thm)], ['120'])).
2.28/2.52	tff('122', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ $true
2.28/2.52	       | zip_tseitin0(sk_Xx1, X1, X0)
2.28/2.52	       | app_encode_app(a, $o, sk_S, sk_Xx1)),
2.28/2.52	    inference('sup-', [status(thm)], ['86', '47'])).
2.28/2.52	tff('123', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
2.28/2.52	      (app_encode_app(a, $o, sk_S, sk_Xx1) | zip_tseitin0(sk_Xx1, X1, X0)),
2.28/2.52	    inference('simplify', [status(thm)], ['122'])).
2.28/2.52	tff('124', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
2.28/2.52	      X2 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ $true
2.28/2.52	       | zip_tseitin0(sk_Xx1, X2, X1)
2.28/2.52	       | ~ zip_tseitin0(sk_Xx1, X0, sk_S)
2.28/2.52	       | app_encode_app(a, $o, X0, sk_Xx1)),
2.28/2.52	    inference('sup-', [status(thm)], ['123', '6'])).
2.28/2.52	tff('125', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
2.28/2.52	      X2 : app_encode_fun(a, $o)]:
2.28/2.52	      (app_encode_app(a, $o, X0, sk_Xx1)
2.28/2.52	       | ~ zip_tseitin0(sk_Xx1, X0, sk_S)
2.28/2.52	       | zip_tseitin0(sk_Xx1, X2, X1)),
2.28/2.52	    inference('simplify', [status(thm)], ['124'])).
2.28/2.52	tff('126', plain,
2.28/2.52	    ![X4 : app_encode_fun(a, $o), X7 : a, X8 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ app_encode_app(a, $o, X4, X7) | ~ zip_tseitin2(X7, X8, X4)),
2.28/2.52	    inference('cnf', [status(esa)], [zf_stmt_3])).
2.28/2.52	tff('127', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
2.28/2.52	      X2 : app_encode_fun(a, $o), X3 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ $true
2.28/2.52	       | zip_tseitin0(sk_Xx1, X3, X2)
2.28/2.52	       | ~ zip_tseitin0(sk_Xx1, X0, sk_S)
2.28/2.52	       | ~ zip_tseitin2(sk_Xx1, X1, X0)),
2.28/2.52	    inference('sup-', [status(thm)], ['125', '126'])).
2.28/2.52	tff('128', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
2.28/2.52	      X2 : app_encode_fun(a, $o), X3 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ zip_tseitin2(sk_Xx1, X1, X0)
2.28/2.52	       | ~ zip_tseitin0(sk_Xx1, X0, sk_S)
2.28/2.52	       | zip_tseitin0(sk_Xx1, X3, X2)),
2.28/2.52	    inference('simplify', [status(thm)], ['127'])).
2.28/2.52	tff('129', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ zip_tseitin0(sk_Xx1, sk_T, sk_S) | zip_tseitin0(sk_Xx1, X1, X0)),
2.28/2.52	    inference('clc', [status(thm)], ['121', '128'])).
2.28/2.52	tff('130', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
2.28/2.52	      X2 : app_encode_fun(a, $o), X3 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ $true
2.28/2.52	       | zip_tseitin0(sk_Xx1, X3, X2)
2.28/2.52	       | zip_tseitin2(sk_Xx1, X2, sk_T)
2.28/2.52	       | zip_tseitin0(sk_Xx1, X1, X0)),
2.28/2.52	    inference('sup-', [status(thm)], ['112', '129'])).
2.28/2.52	tff('131', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
2.28/2.52	      X2 : app_encode_fun(a, $o), X3 : app_encode_fun(a, $o)]:
2.28/2.52	      (zip_tseitin0(sk_Xx1, X1, X0)
2.28/2.52	       | zip_tseitin2(sk_Xx1, X2, sk_T)
2.28/2.52	       | zip_tseitin0(sk_Xx1, X3, X2)),
2.28/2.52	    inference('simplify', [status(thm)], ['130'])).
2.28/2.52	tff('132', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
2.28/2.52	      (zip_tseitin0(sk_Xx1, X1, X0) | zip_tseitin2(sk_Xx1, X0, sk_T)),
2.28/2.52	    inference('condensation', [status(thm)], ['131'])).
2.28/2.52	tff('133', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
2.28/2.52	      X2 : app_encode_fun(a, $o), X3 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ $true
2.28/2.52	       | zip_tseitin0(sk_Xx1, X3, X2)
2.28/2.52	       | ~ zip_tseitin0(sk_Xx1, X0, sk_U)
2.28/2.52	       | zip_tseitin0(sk_Xx1, X0, X1)),
2.28/2.52	    inference('sup-', [status(thm)], ['51', '18'])).
2.28/2.52	tff('134', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
2.28/2.52	      X2 : app_encode_fun(a, $o), X3 : app_encode_fun(a, $o)]:
2.28/2.52	      (zip_tseitin0(sk_Xx1, X0, X1)
2.28/2.52	       | ~ zip_tseitin0(sk_Xx1, X0, sk_U)
2.28/2.52	       | zip_tseitin0(sk_Xx1, X3, X2)),
2.28/2.52	    inference('simplify', [status(thm)], ['133'])).
2.28/2.52	tff('135', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
2.28/2.52	      (zip_tseitin0(sk_Xx1, X1, X0) | ~ zip_tseitin0(sk_Xx1, X1, sk_U)),
2.28/2.52	    inference('condensation', [status(thm)], ['134'])).
2.28/2.52	tff('136', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ $true
2.28/2.52	       | zip_tseitin2(sk_Xx1, sk_U, sk_T)
2.28/2.52	       | zip_tseitin0(sk_Xx1, X0, X1)),
2.28/2.52	    inference('sup-', [status(thm)], ['132', '135'])).
2.28/2.52	tff('137', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
2.28/2.52	      (zip_tseitin0(sk_Xx1, X0, X1) | zip_tseitin2(sk_Xx1, sk_U, sk_T)),
2.28/2.52	    inference('simplify', [status(thm)], ['136'])).
2.28/2.52	tff('138', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o)]:
2.28/2.52	      (zip_tseitin2(sk_Xx1, sk_U, sk_T) | app_encode_app(a, $o, X0, sk_Xx1)),
2.28/2.52	    inference('clc', [status(thm)], ['106', '137'])).
2.28/2.52	tff('139', plain,
2.28/2.52	    ![X4 : app_encode_fun(a, $o), X7 : a, X8 : app_encode_fun(a, $o)]:
2.28/2.52	      (app_encode_app(a, $o, X8, X7) | ~ zip_tseitin2(X7, X8, X4)),
2.28/2.52	    inference('cnf', [status(esa)], [zf_stmt_3])).
2.28/2.52	tff('140', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ $true
2.28/2.52	       | app_encode_app(a, $o, X0, sk_Xx1)
2.28/2.52	       | app_encode_app(a, $o, sk_U, sk_Xx1)),
2.28/2.52	    inference('sup-', [status(thm)], ['138', '139'])).
2.28/2.52	tff('141', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o)]:
2.28/2.52	      (app_encode_app(a, $o, sk_U, sk_Xx1)
2.28/2.52	       | app_encode_app(a, $o, X0, sk_Xx1)),
2.28/2.52	    inference('simplify', [status(thm)], ['140'])).
2.28/2.52	tff('142', plain, app_encode_app(a, $o, sk_U, sk_Xx1),
2.28/2.52	    inference('condensation', [status(thm)], ['141'])).
2.28/2.52	tff('143', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ $true
2.28/2.52	       | ~ zip_tseitin0(sk_Xx1, X0, sk_U)
2.28/2.52	       | app_encode_app(a, $o, X0, sk_Xx1)),
2.28/2.52	    inference('sup-', [status(thm)], ['142', '6'])).
2.28/2.52	tff('144', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o)]:
2.28/2.52	      (app_encode_app(a, $o, X0, sk_Xx1) | ~ zip_tseitin0(sk_Xx1, X0, sk_U)),
2.28/2.52	    inference('simplify', [status(thm)], ['143'])).
2.28/2.52	tff('145', plain,
2.28/2.52	    ![X4 : app_encode_fun(a, $o), X6 : app_encode_fun(a, $o), X7 : a, 
2.28/2.52	      X8 : app_encode_fun(a, $o)]:
2.28/2.52	      (zip_tseitin1(X7, X8, X6, X4)
2.28/2.52	       | app_encode_app(a, $o, X6, X7)
2.28/2.52	       | ~ app_encode_app(a, $o, X8, X7)
2.28/2.52	       | ~ app_encode_app(a, $o, X4, X7)),
2.28/2.52	    inference('cnf', [status(esa)], [zf_stmt_5])).
2.28/2.52	tff('146', plain,
2.28/2.52	    ![X0 : a, X1 : app_encode_fun(a, $o), X2 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ $true
2.28/2.52	       | ~ app_encode_app(a, $o, sk_S, X0)
2.28/2.52	       | ~ app_encode_app(a, $o, X1, X0)
2.28/2.52	       | app_encode_app(a, $o, X2, X0)
2.28/2.52	       | zip_tseitin1(X0, sk_U, X2, X1)),
2.28/2.52	    inference('sup-', [status(thm)], ['5', '145'])).
2.28/2.52	tff('147', plain,
2.28/2.52	    ![X0 : a, X1 : app_encode_fun(a, $o), X2 : app_encode_fun(a, $o)]:
2.28/2.52	      (zip_tseitin1(X0, sk_U, X2, X1)
2.28/2.52	       | app_encode_app(a, $o, X2, X0)
2.28/2.52	       | ~ app_encode_app(a, $o, X1, X0)
2.28/2.52	       | ~ app_encode_app(a, $o, sk_S, X0)),
2.28/2.52	    inference('simplify', [status(thm)], ['146'])).
2.28/2.52	tff('148', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ $true
2.28/2.52	       | ~ zip_tseitin0(sk_Xx1, sk_S, sk_U)
2.28/2.52	       | ~ app_encode_app(a, $o, X0, sk_Xx1)
2.28/2.52	       | app_encode_app(a, $o, X1, sk_Xx1)
2.28/2.52	       | zip_tseitin1(sk_Xx1, sk_U, X1, X0)),
2.28/2.52	    inference('sup-', [status(thm)], ['144', '147'])).
2.28/2.52	tff('149', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ $true
2.28/2.52	       | ~ $true
2.28/2.52	       | ~ app_encode_app(a, $o, X0, sk_Xx1)
2.28/2.52	       | app_encode_app(a, $o, X1, sk_Xx1)
2.28/2.52	       | zip_tseitin1(sk_Xx1, sk_U, X1, X0)),
2.28/2.52	    inference('demod', [status(thm)], ['148', '86'])).
2.28/2.52	tff('150', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
2.28/2.52	      (zip_tseitin1(sk_Xx1, sk_U, X1, X0)
2.28/2.52	       | app_encode_app(a, $o, X1, sk_Xx1)
2.28/2.52	       | ~ app_encode_app(a, $o, X0, sk_Xx1)),
2.28/2.52	    inference('simplify', [status(thm)], ['149'])).
2.28/2.52	tff('151', plain,
2.28/2.52	    ![X4 : app_encode_fun(a, $o), X6 : app_encode_fun(a, $o), X7 : a, 
2.28/2.52	      X8 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ zip_tseitin1(X7, X8, X6, X4)
2.28/2.52	       | zip_tseitin2(X7, X8, X4)
2.28/2.52	       | ~ zip_tseitin3(X7, X8, X6, X4)),
2.28/2.52	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.28/2.52	tff('152', plain,
2.28/2.52	    ![X0 : a, X1 : a]:
2.28/2.52	      (~ $true
2.28/2.52	       | zip_tseitin0(X1, sk_T, sk_S)
2.28/2.52	       | zip_tseitin2(X0, sk_U, sk_S)
2.28/2.52	       | ~ zip_tseitin1(X0, sk_U, sk_T, sk_S)),
2.28/2.52	    inference('sup-', [status(thm)], ['23', '151'])).
2.28/2.52	tff('153', plain,
2.28/2.52	    ![X0 : a, X1 : a]:
2.28/2.52	      (~ zip_tseitin1(X0, sk_U, sk_T, sk_S)
2.28/2.52	       | zip_tseitin2(X0, sk_U, sk_S)
2.28/2.52	       | zip_tseitin0(X1, sk_T, sk_S)),
2.28/2.52	    inference('simplify', [status(thm)], ['152'])).
2.28/2.52	tff('154', plain,
2.28/2.52	    ![X0 : a]:
2.28/2.52	      (~ $true
2.28/2.52	       | ~ app_encode_app(a, $o, sk_S, sk_Xx1)
2.28/2.52	       | app_encode_app(a, $o, sk_T, sk_Xx1)
2.28/2.52	       | zip_tseitin0(X0, sk_T, sk_S)
2.28/2.52	       | zip_tseitin2(sk_Xx1, sk_U, sk_S)),
2.28/2.52	    inference('sup-', [status(thm)], ['150', '153'])).
2.28/2.52	tff('155', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ $true
2.28/2.52	       | zip_tseitin2(sk_Xx1, sk_U, X0)
2.28/2.52	       | ~ zip_tseitin0(sk_Xx1, X1, X0)
2.28/2.52	       | app_encode_app(a, $o, X1, sk_Xx1)),
2.28/2.52	    inference('sup-', [status(thm)], ['101', '6'])).
2.28/2.52	tff('156', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
2.28/2.52	      (app_encode_app(a, $o, X1, sk_Xx1)
2.28/2.52	       | ~ zip_tseitin0(sk_Xx1, X1, X0)
2.28/2.52	       | zip_tseitin2(sk_Xx1, sk_U, X0)),
2.28/2.52	    inference('simplify', [status(thm)], ['155'])).
2.28/2.52	tff('157', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ $true
2.28/2.52	       | zip_tseitin2(sk_Xx1, sk_U, X0)
2.28/2.52	       | app_encode_app(a, $o, sk_S, sk_Xx1)),
2.28/2.52	    inference('sup-', [status(thm)], ['86', '156'])).
2.28/2.52	tff('158', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o)]:
2.28/2.52	      (app_encode_app(a, $o, sk_S, sk_Xx1) | zip_tseitin2(sk_Xx1, sk_U, X0)),
2.28/2.52	    inference('simplify', [status(thm)], ['157'])).
2.28/2.52	tff('159', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ $true
2.28/2.52	       | ~ zip_tseitin0(sk_Xx1, X0, sk_U)
2.28/2.52	       | ~ zip_tseitin2(sk_Xx1, X1, X0)),
2.28/2.52	    inference('sup-', [status(thm)], ['144', '126'])).
2.28/2.52	tff('160', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ zip_tseitin2(sk_Xx1, X1, X0) | ~ zip_tseitin0(sk_Xx1, X0, sk_U)),
2.28/2.52	    inference('simplify', [status(thm)], ['159'])).
2.28/2.52	tff('161', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ $true
2.28/2.52	       | app_encode_app(a, $o, sk_S, sk_Xx1)
2.28/2.52	       | ~ zip_tseitin0(sk_Xx1, X0, sk_U)),
2.28/2.52	    inference('sup-', [status(thm)], ['158', '160'])).
2.28/2.52	tff('162', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ zip_tseitin0(sk_Xx1, X0, sk_U) | app_encode_app(a, $o, sk_S, sk_Xx1)),
2.28/2.52	    inference('simplify', [status(thm)], ['161'])).
2.28/2.52	tff('163', plain, app_encode_app(a, $o, sk_S, sk_Xx1),
2.28/2.52	    inference('clc', [status(thm)], ['162', '123'])).
2.28/2.52	tff('164', plain,
2.28/2.52	    ![X0 : a]:
2.28/2.52	      (~ $true
2.28/2.52	       | ~ $true
2.28/2.52	       | app_encode_app(a, $o, sk_T, sk_Xx1)
2.28/2.52	       | zip_tseitin0(X0, sk_T, sk_S)
2.28/2.52	       | zip_tseitin2(sk_Xx1, sk_U, sk_S)),
2.28/2.52	    inference('demod', [status(thm)], ['154', '163'])).
2.28/2.52	tff('165', plain,
2.28/2.52	    ![X0 : a]:
2.28/2.52	      (zip_tseitin2(sk_Xx1, sk_U, sk_S)
2.28/2.52	       | zip_tseitin0(X0, sk_T, sk_S)
2.28/2.52	       | app_encode_app(a, $o, sk_T, sk_Xx1)),
2.28/2.52	    inference('simplify', [status(thm)], ['164'])).
2.28/2.52	tff('166', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ $true | ~ zip_tseitin2(sk_Xx1, X0, sk_S)),
2.28/2.52	    inference('sup-', [status(thm)], ['163', '126'])).
2.28/2.52	tff('167', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o)]: ~ zip_tseitin2(sk_Xx1, X0, sk_S),
2.28/2.52	    inference('simplify', [status(thm)], ['166'])).
2.28/2.52	tff('168', plain,
2.28/2.52	    ![X0 : a]:
2.28/2.52	      (app_encode_app(a, $o, sk_T, sk_Xx1) | zip_tseitin0(X0, sk_T, sk_S)),
2.28/2.52	    inference('clc', [status(thm)], ['165', '167'])).
2.28/2.52	tff('169', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o), X1 : a]:
2.28/2.52	      (~ $true
2.28/2.52	       | zip_tseitin0(X1, sk_T, sk_S)
2.28/2.52	       | zip_tseitin0(sk_Xx1, sk_T, X0)),
2.28/2.52	    inference('sup-', [status(thm)], ['168', '18'])).
2.28/2.52	tff('170', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o), X1 : a]:
2.28/2.52	      (zip_tseitin0(sk_Xx1, sk_T, X0) | zip_tseitin0(X1, sk_T, sk_S)),
2.28/2.52	    inference('simplify', [status(thm)], ['169'])).
2.28/2.52	tff('171', plain, (~ $true | zip_tseitin0(sk_Xx1, sk_T, sk_S)),
2.28/2.52	    inference('eq_fact', [status(thm)], ['170'])).
2.28/2.52	tff('172', plain, zip_tseitin0(sk_Xx1, sk_T, sk_S),
2.28/2.52	    inference('simplify', [status(thm)], ['171'])).
2.28/2.52	tff('173', plain, ![X0 : a]: (~ $true | zip_tseitin0(X0, sk_T, sk_S)),
2.28/2.52	    inference('sup-', [status(thm)], ['172', '25'])).
2.28/2.52	tff('174', plain, ![X0 : a]: zip_tseitin0(X0, sk_T, sk_S),
2.28/2.52	    inference('simplify', [status(thm)], ['173'])).
2.28/2.52	tff('175', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ $true | zip_tseitin0(sk_Xx1, X1, X0)),
2.28/2.52	    inference('sup-', [status(thm)], ['174', '129'])).
2.28/2.52	tff('176', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
2.28/2.52	      zip_tseitin0(sk_Xx1, X1, X0),
2.28/2.52	    inference('simplify', [status(thm)], ['175'])).
2.28/2.52	tff('177', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ $true
2.28/2.52	       | ~ zip_tseitin0(sk_Xx, X0, sk_S)
2.28/2.52	       | app_encode_app(a, $o, X0, sk_Xx)),
2.28/2.52	    inference('sup-', [status(thm)], ['176', '15'])).
2.28/2.52	tff('178', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o)]: (~ $true | zip_tseitin0(sk_Xx, X0, sk_S)),
2.28/2.52	    inference('sup-', [status(thm)], ['172', '62'])).
2.28/2.52	tff('179', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o)]: zip_tseitin0(sk_Xx, X0, sk_S),
2.28/2.52	    inference('simplify', [status(thm)], ['178'])).
2.28/2.52	tff('180', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ $true | ~ $true | app_encode_app(a, $o, X0, sk_Xx)),
2.28/2.52	    inference('demod', [status(thm)], ['177', '179'])).
2.28/2.52	tff('181', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o)]: app_encode_app(a, $o, X0, sk_Xx),
2.28/2.52	    inference('simplify', [status(thm)], ['180'])).
2.28/2.52	tff('182', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
2.28/2.52	      X2 : app_encode_fun(a, $o)]:
2.28/2.52	      (~ $true | ~ zip_tseitin1(sk_Xx, X2, X0, X1)),
2.28/2.52	    inference('sup-', [status(thm)], ['181', '40'])).
2.28/2.52	tff('183', plain,
2.28/2.52	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
2.28/2.52	      X2 : app_encode_fun(a, $o)]: ~ zip_tseitin1(sk_Xx, X2, X0, X1),
2.28/2.52	    inference('simplify', [status(thm)], ['182'])).
2.28/2.52	tff('184', plain, (~ $true | ~ zip_tseitin0(sk_Xx1, sk_T, sk_S)),
2.28/2.52	    inference('sup-', [status(thm)], ['3', '183'])).
2.28/2.52	tff('185', plain, (~ $true | ~ $true),
2.28/2.52	    inference('demod', [status(thm)], ['184', '176'])).
2.28/2.52	tff('186', plain, $false, inference('simplify', [status(thm)], ['185'])).
2.28/2.52	
2.28/2.52	% SZS output end Refutation
2.28/2.52	EOF
