0.00/0.00	% File    : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : app
0.00/0.00	% Variant    : fo
0.00/0.00	% Ordering    : kbo
0.00/0.00	% Command    : 
0.00/0.00	#!/bin/sh
0.00/0.00	
0.00/0.00	./zipperposition.native ${1:+"$1"} \
0.00/0.00	  -i tptp \
0.00/0.00	  -o tptp \
0.00/0.00	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.00	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.00	  --no-ho \
0.00/0.00	  --no-avatar \
0.00/0.00	  --no-induction \
0.00/0.00	  --no-unif-pattern \
0.00/0.00	  --ord $2 \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --no-fool
0.00/0.19	% Computer   : n041.star.cs.uiowa.edu
0.00/0.19	% Model      : x86_64 x86_64
0.00/0.19	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.19	% Memory     : 32218.625MB
0.00/0.19	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.19	% CPULimit   : 300
0.00/0.19	% DateTime   : Fri Feb  2 17:19:54 CST 2018
1.34/1.55	% done 3277 iterations in 1.353s
1.34/1.55	% SZS status Theorem for 'stdin'
1.34/1.55	% SZS output start Refutation
1.38/1.56	tff(zf_stmt_3, conjecture,
1.38/1.56	  (![S:app_encode_fun(a,$o),T:app_encode_fun(a,$o),U:app_encode_fun(a,$o)]:
1.38/1.56	     (((![Xx:a]: (app_encode_app(a,$o,T,Xx) => app_encode_app(a,$o,U,Xx))) & 
1.38/1.56	       (![Xx:a]: (app_encode_app(a,$o,S,Xx) => app_encode_app(a,$o,U,Xx)))) =>
1.38/1.56	      ((![Xx:a]: (app_encode_app(a,$o,S,Xx) => app_encode_app(a,$o,T,Xx))) <=>
1.38/1.56	       (![Xx:a]:
1.38/1.56	          (((~app_encode_app(a,$o,T,Xx)) & app_encode_app(a,$o,U,Xx) & 
1.38/1.56	            app_encode_app(a,$o,S,Xx)) =>
1.38/1.56	           ((~app_encode_app(a,$o,S,Xx)) & app_encode_app(a,$o,U,Xx)))))))).
1.38/1.56	tff(zf_stmt_0, axiom,
1.38/1.56	  (zip_tseitin3(Xx,U,T,S) <=>
1.38/1.56	   (zip_tseitin1(Xx,U,T,S) => zip_tseitin2(Xx,U,S)))).
1.38/1.56	tff('0', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X2 : app_encode_fun(a, $o), X3 : a, 
1.38/1.56	      X4 : app_encode_fun(a, $o)]:
1.38/1.56	      (zip_tseitin3(X3, X4, X2, X0) | zip_tseitin1(X3, X4, X2, X0)),
1.38/1.56	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.38/1.56	tff(zf_stmt_1, type, zip_tseitin3 :
1.38/1.56	    (a * app_encode_fun(a,$o) * app_encode_fun(a,$o) * app_encode_fun(a,$o)) >
1.38/1.56	      $o).
1.38/1.56	tff(zf_stmt_2, type, zip_tseitin2 :
1.38/1.56	    (a * app_encode_fun(a,$o) * app_encode_fun(a,$o)) > $o).
1.38/1.56	tff(zf_stmt_3, axiom,
1.38/1.56	  (zip_tseitin2(Xx,U,S) <=>
1.38/1.56	   (app_encode_app(a,$o,U,Xx) & (~app_encode_app(a,$o,S,Xx))))).
1.38/1.56	tff(zf_stmt_4, type, zip_tseitin1 :
1.38/1.56	    (a * app_encode_fun(a,$o) * app_encode_fun(a,$o) * app_encode_fun(a,$o)) >
1.38/1.56	      $o).
1.38/1.56	tff(zf_stmt_5, axiom,
1.38/1.56	  (zip_tseitin1(Xx,U,T,S) <=>
1.38/1.56	   (app_encode_app(a,$o,S,Xx) & app_encode_app(a,$o,U,Xx) & 
1.38/1.56	    (~app_encode_app(a,$o,T,Xx))))).
1.38/1.56	tff(zf_stmt_6, type, zip_tseitin0 :
1.38/1.56	    (a * app_encode_fun(a,$o) * app_encode_fun(a,$o)) > $o).
1.38/1.56	tff(zf_stmt_7, axiom,
1.38/1.56	  (zip_tseitin0(Xx,T,S) <=>
1.38/1.56	   (app_encode_app(a,$o,S,Xx) => app_encode_app(a,$o,T,Xx)))).
1.38/1.56	tff(zf_stmt_8, conjecture,
1.38/1.56	  (![S:app_encode_fun(a,$o),T:app_encode_fun(a,$o),U:app_encode_fun(a,$o)]:
1.38/1.56	     (((![Xx:a]: (app_encode_app(a,$o,S,Xx) => app_encode_app(a,$o,U,Xx))) & 
1.38/1.56	       (![Xx:a]: (app_encode_app(a,$o,T,Xx) => app_encode_app(a,$o,U,Xx)))) =>
1.38/1.56	      ((![Xx:a]: zip_tseitin0(Xx,T,S)) <=> (![Xx:a]: zip_tseitin3(Xx,U,T,S)))))).
1.38/1.56	tff(zf_stmt_9, negated_conjecture,
1.38/1.56	  (~
1.38/1.56	    (![S:app_encode_fun(a,$o),T:app_encode_fun(a,$o),U:app_encode_fun(a,$o)]:
1.38/1.56	       (((![Xx:a]: (app_encode_app(a,$o,S,Xx) => app_encode_app(a,$o,U,Xx))) & 
1.38/1.56	         (![Xx:a]: (app_encode_app(a,$o,T,Xx) => app_encode_app(a,$o,U,Xx)))) =>
1.38/1.56	        ((![Xx:a]: zip_tseitin0(Xx,T,S)) <=>
1.38/1.56	         (![Xx:a]: zip_tseitin3(Xx,U,T,S))))))).
1.38/1.56	tff('1', plain,
1.38/1.56	    (~ zip_tseitin3(sk_Xx, sk_U, sk_T, sk_S)
1.38/1.56	     | ~ zip_tseitin0(sk_Xx1, sk_T, sk_S)),
1.38/1.56	    inference('cnf', [status(esa)], [zf_stmt_9])).
1.38/1.56	tff('2', plain,
1.38/1.56	    (~ $true
1.38/1.56	     | zip_tseitin1(sk_Xx, sk_U, sk_T, sk_S)
1.38/1.56	     | ~ zip_tseitin0(sk_Xx1, sk_T, sk_S)),
1.38/1.56	    inference('sup-', [status(thm)], ['0', '1'])).
1.38/1.56	tff('3', plain,
1.38/1.56	    (~ zip_tseitin0(sk_Xx1, sk_T, sk_S)
1.38/1.56	     | zip_tseitin1(sk_Xx, sk_U, sk_T, sk_S)),
1.38/1.56	    inference('simplify', [status(thm)], ['2'])).
1.38/1.56	tff('4', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : a, X2 : app_encode_fun(a, $o)]:
1.38/1.56	      (zip_tseitin0(X1, X2, X0) | app_encode_app(a, $o, X0, X1)),
1.38/1.56	    inference('cnf', [status(esa)], [zf_stmt_7])).
1.38/1.56	tff('5', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : a, X2 : app_encode_fun(a, $o)]:
1.38/1.56	      (zip_tseitin0(X1, X2, X0) | ~ app_encode_app(a, $o, X2, X1)),
1.38/1.56	    inference('cnf', [status(esa)], [zf_stmt_7])).
1.38/1.56	tff('6', plain,
1.38/1.56	    ![X0 : a, X1 : app_encode_fun(a, $o), X2 : app_encode_fun(a, $o), 
1.38/1.56	      X3 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ $true | zip_tseitin0(X0, X3, X1) | zip_tseitin0(X0, X1, X2)),
1.38/1.56	    inference('sup-', [status(thm)], ['4', '5'])).
1.38/1.56	tff('7', plain,
1.38/1.56	    ![X0 : a, X1 : app_encode_fun(a, $o), X2 : app_encode_fun(a, $o), 
1.38/1.56	      X3 : app_encode_fun(a, $o)]:
1.38/1.56	      (zip_tseitin0(X0, X1, X2) | zip_tseitin0(X0, X3, X1)),
1.38/1.56	    inference('simplify', [status(thm)], ['6'])).
1.38/1.56	tff('8', plain,
1.38/1.56	    ![X7 : a, X8 : a]:
1.38/1.56	      (zip_tseitin3(X7, sk_U, sk_T, sk_S) | zip_tseitin0(X8, sk_T, sk_S)),
1.38/1.56	    inference('cnf', [status(esa)], [zf_stmt_9])).
1.38/1.56	tff('9', plain,
1.38/1.56	    ![X0 : a]:
1.38/1.56	      (~ $true
1.38/1.56	       | zip_tseitin0(X0, sk_T, sk_S)
1.38/1.56	       | ~ zip_tseitin0(sk_Xx1, sk_T, sk_S)),
1.38/1.56	    inference('sup-', [status(thm)], ['8', '1'])).
1.38/1.56	tff('10', plain,
1.38/1.56	    ![X0 : a]:
1.38/1.56	      (~ zip_tseitin0(sk_Xx1, sk_T, sk_S) | zip_tseitin0(X0, sk_T, sk_S)),
1.38/1.56	    inference('simplify', [status(thm)], ['9'])).
1.38/1.56	tff('11', plain,
1.38/1.56	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ $true
1.38/1.56	       | zip_tseitin0(sk_Xx1, sk_S, X1)
1.38/1.56	       | zip_tseitin0(X0, sk_T, sk_S)),
1.38/1.56	    inference('sup-', [status(thm)], ['7', '10'])).
1.38/1.56	tff('12', plain,
1.38/1.56	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
1.38/1.56	      (zip_tseitin0(X0, sk_T, sk_S) | zip_tseitin0(sk_Xx1, sk_S, X1)),
1.38/1.56	    inference('simplify', [status(thm)], ['11'])).
1.38/1.56	tff('13', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X2 : app_encode_fun(a, $o), X3 : a, 
1.38/1.56	      X4 : app_encode_fun(a, $o)]:
1.38/1.56	      (app_encode_app(a, $o, X0, X3) | ~ zip_tseitin1(X3, X4, X2, X0)),
1.38/1.56	    inference('cnf', [status(esa)], [zf_stmt_5])).
1.38/1.56	tff('14', plain,
1.38/1.56	    (~ $true
1.38/1.56	     | ~ zip_tseitin0(sk_Xx1, sk_T, sk_S)
1.38/1.56	     | app_encode_app(a, $o, sk_S, sk_Xx)),
1.38/1.56	    inference('sup-', [status(thm)], ['3', '13'])).
1.38/1.56	tff('15', plain,
1.38/1.56	    (app_encode_app(a, $o, sk_S, sk_Xx) | ~ zip_tseitin0(sk_Xx1, sk_T, sk_S)),
1.38/1.56	    inference('simplify', [status(thm)], ['14'])).
1.38/1.56	tff('16', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : a, X2 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ app_encode_app(a, $o, X0, X1)
1.38/1.56	       | app_encode_app(a, $o, X2, X1)
1.38/1.56	       | ~ zip_tseitin0(X1, X2, X0)),
1.38/1.56	    inference('cnf', [status(esa)], [zf_stmt_7])).
1.38/1.56	tff('17', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ $true
1.38/1.56	       | ~ zip_tseitin0(sk_Xx1, sk_T, sk_S)
1.38/1.56	       | ~ zip_tseitin0(sk_Xx, X0, sk_S)
1.38/1.56	       | app_encode_app(a, $o, X0, sk_Xx)),
1.38/1.56	    inference('sup-', [status(thm)], ['15', '16'])).
1.38/1.56	tff('18', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o)]:
1.38/1.56	      (app_encode_app(a, $o, X0, sk_Xx)
1.38/1.56	       | ~ zip_tseitin0(sk_Xx, X0, sk_S)
1.38/1.56	       | ~ zip_tseitin0(sk_Xx1, sk_T, sk_S)),
1.38/1.56	    inference('simplify', [status(thm)], ['17'])).
1.38/1.56	tff('19', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ $true
1.38/1.56	       | zip_tseitin0(sk_Xx1, sk_S, X1)
1.38/1.56	       | ~ zip_tseitin0(sk_Xx, X0, sk_S)
1.38/1.56	       | app_encode_app(a, $o, X0, sk_Xx)),
1.38/1.56	    inference('sup-', [status(thm)], ['12', '18'])).
1.38/1.56	tff('20', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
1.38/1.56	      (app_encode_app(a, $o, X0, sk_Xx)
1.38/1.56	       | ~ zip_tseitin0(sk_Xx, X0, sk_S)
1.38/1.56	       | zip_tseitin0(sk_Xx1, sk_S, X1)),
1.38/1.56	    inference('simplify', [status(thm)], ['19'])).
1.38/1.56	tff('21', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
1.38/1.56	      X2 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ $true
1.38/1.56	       | zip_tseitin0(sk_Xx1, sk_S, X2)
1.38/1.56	       | ~ zip_tseitin0(sk_Xx, X0, sk_S)
1.38/1.56	       | ~ zip_tseitin0(sk_Xx, X1, X0)
1.38/1.56	       | app_encode_app(a, $o, X1, sk_Xx)),
1.38/1.56	    inference('sup-', [status(thm)], ['20', '16'])).
1.38/1.56	tff('22', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
1.38/1.56	      X2 : app_encode_fun(a, $o)]:
1.38/1.56	      (app_encode_app(a, $o, X1, sk_Xx)
1.38/1.56	       | ~ zip_tseitin0(sk_Xx, X1, X0)
1.38/1.56	       | ~ zip_tseitin0(sk_Xx, X0, sk_S)
1.38/1.56	       | zip_tseitin0(sk_Xx1, sk_S, X2)),
1.38/1.56	    inference('simplify', [status(thm)], ['21'])).
1.38/1.56	tff('23', plain,
1.38/1.56	    ![X5 : a]:
1.38/1.56	      (app_encode_app(a, $o, sk_U, X5) | ~ app_encode_app(a, $o, sk_S, X5)),
1.38/1.56	    inference('cnf', [status(esa)], [zf_stmt_9])).
1.38/1.56	tff('24', plain,
1.38/1.56	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ $true
1.38/1.56	       | ~ app_encode_app(a, $o, sk_S, X0)
1.38/1.56	       | ~ zip_tseitin0(X0, X1, sk_U)
1.38/1.56	       | app_encode_app(a, $o, X1, X0)),
1.38/1.56	    inference('sup-', [status(thm)], ['23', '16'])).
1.38/1.56	tff('25', plain,
1.38/1.56	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
1.38/1.56	      (app_encode_app(a, $o, X1, X0)
1.38/1.56	       | ~ zip_tseitin0(X0, X1, sk_U)
1.38/1.56	       | ~ app_encode_app(a, $o, sk_S, X0)),
1.38/1.56	    inference('simplify', [status(thm)], ['24'])).
1.38/1.56	tff('26', plain,
1.38/1.56	    ![X0 : a, X1 : app_encode_fun(a, $o), X2 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ $true
1.38/1.56	       | zip_tseitin0(X0, X2, sk_S)
1.38/1.56	       | ~ zip_tseitin0(X0, X1, sk_U)
1.38/1.56	       | app_encode_app(a, $o, X1, X0)),
1.38/1.56	    inference('sup-', [status(thm)], ['4', '25'])).
1.38/1.56	tff('27', plain,
1.38/1.56	    ![X0 : a, X1 : app_encode_fun(a, $o), X2 : app_encode_fun(a, $o)]:
1.38/1.56	      (app_encode_app(a, $o, X1, X0)
1.38/1.56	       | ~ zip_tseitin0(X0, X1, sk_U)
1.38/1.56	       | zip_tseitin0(X0, X2, sk_S)),
1.38/1.56	    inference('simplify', [status(thm)], ['26'])).
1.38/1.56	tff('28', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X2 : app_encode_fun(a, $o), X3 : a, 
1.38/1.56	      X4 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ app_encode_app(a, $o, X2, X3) | ~ zip_tseitin1(X3, X4, X2, X0)),
1.38/1.56	    inference('cnf', [status(esa)], [zf_stmt_5])).
1.38/1.56	tff('29', plain,
1.38/1.56	    ![X0 : a, X1 : app_encode_fun(a, $o), X2 : app_encode_fun(a, $o), 
1.38/1.56	      X3 : app_encode_fun(a, $o), X4 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ $true
1.38/1.56	       | zip_tseitin0(X0, X4, sk_S)
1.38/1.56	       | ~ zip_tseitin0(X0, X1, sk_U)
1.38/1.56	       | ~ zip_tseitin1(X0, X3, X1, X2)),
1.38/1.56	    inference('sup-', [status(thm)], ['27', '28'])).
1.38/1.56	tff('30', plain,
1.38/1.56	    ![X0 : a, X1 : app_encode_fun(a, $o), X2 : app_encode_fun(a, $o), 
1.38/1.56	      X3 : app_encode_fun(a, $o), X4 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ zip_tseitin1(X0, X3, X1, X2)
1.38/1.56	       | ~ zip_tseitin0(X0, X1, sk_U)
1.38/1.56	       | zip_tseitin0(X0, X4, sk_S)),
1.38/1.56	    inference('simplify', [status(thm)], ['29'])).
1.38/1.56	tff('31', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ $true
1.38/1.56	       | ~ zip_tseitin0(sk_Xx1, sk_T, sk_S)
1.38/1.56	       | zip_tseitin0(sk_Xx, X0, sk_S)
1.38/1.56	       | ~ zip_tseitin0(sk_Xx, sk_T, sk_U)),
1.38/1.56	    inference('sup-', [status(thm)], ['3', '30'])).
1.38/1.56	tff('32', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ zip_tseitin0(sk_Xx, sk_T, sk_U)
1.38/1.56	       | zip_tseitin0(sk_Xx, X0, sk_S)
1.38/1.56	       | ~ zip_tseitin0(sk_Xx1, sk_T, sk_S)),
1.38/1.56	    inference('simplify', [status(thm)], ['31'])).
1.38/1.56	tff('33', plain,
1.38/1.56	    ![X0 : a, X1 : app_encode_fun(a, $o), X2 : app_encode_fun(a, $o), 
1.38/1.56	      X3 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ $true
1.38/1.56	       | zip_tseitin0(X0, X3, X1)
1.38/1.56	       | ~ zip_tseitin0(X0, X2, X1)
1.38/1.56	       | app_encode_app(a, $o, X2, X0)),
1.38/1.56	    inference('sup-', [status(thm)], ['4', '16'])).
1.38/1.56	tff('34', plain,
1.38/1.56	    ![X0 : a, X1 : app_encode_fun(a, $o), X2 : app_encode_fun(a, $o), 
1.38/1.56	      X3 : app_encode_fun(a, $o)]:
1.38/1.56	      (app_encode_app(a, $o, X2, X0)
1.38/1.56	       | ~ zip_tseitin0(X0, X2, X1)
1.38/1.56	       | zip_tseitin0(X0, X3, X1)),
1.38/1.56	    inference('simplify', [status(thm)], ['33'])).
1.38/1.56	tff('35', plain,
1.38/1.56	    ![X0 : a, X1 : app_encode_fun(a, $o), X2 : a]:
1.38/1.56	      (~ $true
1.38/1.56	       | zip_tseitin3(X2, sk_U, sk_T, sk_S)
1.38/1.56	       | zip_tseitin0(X0, X1, sk_S)
1.38/1.56	       | app_encode_app(a, $o, sk_T, X0)),
1.38/1.56	    inference('sup-', [status(thm)], ['8', '34'])).
1.38/1.56	tff('36', plain,
1.38/1.56	    ![X0 : a, X1 : app_encode_fun(a, $o), X2 : a]:
1.38/1.56	      (app_encode_app(a, $o, sk_T, X0)
1.38/1.56	       | zip_tseitin0(X0, X1, sk_S)
1.38/1.56	       | zip_tseitin3(X2, sk_U, sk_T, sk_S)),
1.38/1.56	    inference('simplify', [status(thm)], ['35'])).
1.38/1.56	tff('37', plain,
1.38/1.56	    ![X0 : a, X1 : app_encode_fun(a, $o), X2 : a, X3 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ $true
1.38/1.56	       | zip_tseitin3(X2, sk_U, sk_T, sk_S)
1.38/1.56	       | zip_tseitin0(X0, X3, sk_S)
1.38/1.56	       | zip_tseitin0(X0, sk_T, X1)),
1.38/1.56	    inference('sup-', [status(thm)], ['36', '5'])).
1.38/1.56	tff('38', plain,
1.38/1.56	    ![X0 : a, X1 : app_encode_fun(a, $o), X2 : a, X3 : app_encode_fun(a, $o)]:
1.38/1.56	      (zip_tseitin0(X0, sk_T, X1)
1.38/1.56	       | zip_tseitin0(X0, X3, sk_S)
1.38/1.56	       | zip_tseitin3(X2, sk_U, sk_T, sk_S)),
1.38/1.56	    inference('simplify', [status(thm)], ['37'])).
1.38/1.56	tff('39', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : a, X2 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ $true
1.38/1.56	       | zip_tseitin0(X1, X0, sk_S)
1.38/1.56	       | zip_tseitin0(X1, sk_T, X2)
1.38/1.56	       | ~ zip_tseitin0(sk_Xx1, sk_T, sk_S)),
1.38/1.56	    inference('sup-', [status(thm)], ['38', '1'])).
1.38/1.56	tff('40', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : a, X2 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ zip_tseitin0(sk_Xx1, sk_T, sk_S)
1.38/1.56	       | zip_tseitin0(X1, sk_T, X2)
1.38/1.56	       | zip_tseitin0(X1, X0, sk_S)),
1.38/1.56	    inference('simplify', [status(thm)], ['39'])).
1.38/1.56	tff('41', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ zip_tseitin0(sk_Xx1, sk_T, sk_S) | zip_tseitin0(sk_Xx, X0, sk_S)),
1.38/1.56	    inference('clc', [status(thm)], ['32', '40'])).
1.38/1.56	tff('42', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ $true
1.38/1.56	       | zip_tseitin0(sk_Xx1, sk_S, X1)
1.38/1.56	       | zip_tseitin0(sk_Xx, X0, sk_S)),
1.38/1.56	    inference('sup-', [status(thm)], ['12', '41'])).
1.38/1.56	tff('43', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
1.38/1.56	      (zip_tseitin0(sk_Xx, X0, sk_S) | zip_tseitin0(sk_Xx1, sk_S, X1)),
1.38/1.56	    inference('simplify', [status(thm)], ['42'])).
1.38/1.56	tff('44', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
1.38/1.56	      X2 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ $true
1.38/1.56	       | zip_tseitin0(sk_Xx1, sk_S, X2)
1.38/1.56	       | ~ zip_tseitin0(sk_Xx, X0, sk_S)
1.38/1.56	       | zip_tseitin0(sk_Xx, X0, X1)),
1.38/1.56	    inference('sup-', [status(thm)], ['20', '5'])).
1.38/1.56	tff('45', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
1.38/1.56	      X2 : app_encode_fun(a, $o)]:
1.38/1.56	      (zip_tseitin0(sk_Xx, X0, X1)
1.38/1.56	       | ~ zip_tseitin0(sk_Xx, X0, sk_S)
1.38/1.56	       | zip_tseitin0(sk_Xx1, sk_S, X2)),
1.38/1.56	    inference('simplify', [status(thm)], ['44'])).
1.38/1.56	tff('46', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
1.38/1.56	      X2 : app_encode_fun(a, $o), X3 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ $true
1.38/1.56	       | zip_tseitin0(sk_Xx1, sk_S, X3)
1.38/1.56	       | zip_tseitin0(sk_Xx1, sk_S, X1)
1.38/1.56	       | zip_tseitin0(sk_Xx, X0, X2)),
1.38/1.56	    inference('sup-', [status(thm)], ['43', '45'])).
1.38/1.56	tff('47', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
1.38/1.56	      X2 : app_encode_fun(a, $o), X3 : app_encode_fun(a, $o)]:
1.38/1.56	      (zip_tseitin0(sk_Xx, X0, X2)
1.38/1.56	       | zip_tseitin0(sk_Xx1, sk_S, X1)
1.38/1.56	       | zip_tseitin0(sk_Xx1, sk_S, X3)),
1.38/1.56	    inference('simplify', [status(thm)], ['46'])).
1.38/1.56	tff('48', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
1.38/1.56	      X2 : app_encode_fun(a, $o)]:
1.38/1.56	      (zip_tseitin0(sk_Xx, X1, X0) | zip_tseitin0(sk_Xx1, sk_S, X2)),
1.38/1.56	    inference('condensation', [status(thm)], ['47'])).
1.38/1.56	tff('49', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
1.38/1.56	      X2 : app_encode_fun(a, $o)]:
1.38/1.56	      (zip_tseitin0(sk_Xx1, sk_S, X2)
1.38/1.56	       | ~ zip_tseitin0(sk_Xx, X0, sk_S)
1.38/1.56	       | app_encode_app(a, $o, X1, sk_Xx)),
1.38/1.56	    inference('clc', [status(thm)], ['22', '48'])).
1.38/1.56	tff('50', plain,
1.38/1.56	    ![X1 : app_encode_fun(a, $o), X2 : app_encode_fun(a, $o)]:
1.38/1.56	      (app_encode_app(a, $o, X1, sk_Xx) | zip_tseitin0(sk_Xx1, sk_S, X2)),
1.38/1.56	    inference('clc', [status(thm)], ['49', '48'])).
1.38/1.56	tff('51', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
1.38/1.56	      X2 : app_encode_fun(a, $o), X3 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ $true
1.38/1.56	       | zip_tseitin0(sk_Xx1, sk_S, X3)
1.38/1.56	       | ~ zip_tseitin1(sk_Xx, X2, X0, X1)),
1.38/1.56	    inference('sup-', [status(thm)], ['50', '28'])).
1.38/1.56	tff('52', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
1.38/1.56	      X2 : app_encode_fun(a, $o), X3 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ zip_tseitin1(sk_Xx, X2, X0, X1) | zip_tseitin0(sk_Xx1, sk_S, X3)),
1.38/1.56	    inference('simplify', [status(thm)], ['51'])).
1.38/1.56	tff('53', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ $true
1.38/1.56	       | ~ zip_tseitin0(sk_Xx1, sk_T, sk_S)
1.38/1.56	       | zip_tseitin0(sk_Xx1, sk_S, X0)),
1.38/1.56	    inference('sup-', [status(thm)], ['3', '52'])).
1.38/1.56	tff('54', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o)]:
1.38/1.56	      (zip_tseitin0(sk_Xx1, sk_S, X0) | ~ zip_tseitin0(sk_Xx1, sk_T, sk_S)),
1.38/1.56	    inference('simplify', [status(thm)], ['53'])).
1.38/1.56	tff('55', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o)]: zip_tseitin0(sk_Xx1, sk_S, X0),
1.38/1.56	    inference('clc', [status(thm)], ['54', '7'])).
1.38/1.56	tff('56', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ $true
1.38/1.56	       | ~ zip_tseitin0(sk_Xx1, X1, sk_U)
1.38/1.56	       | app_encode_app(a, $o, X1, sk_Xx1)
1.38/1.56	       | ~ zip_tseitin0(sk_Xx, X0, sk_S)
1.38/1.56	       | app_encode_app(a, $o, X0, sk_Xx)),
1.38/1.56	    inference('sup-', [status(thm)], ['27', '18'])).
1.38/1.56	tff('57', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
1.38/1.56	      (app_encode_app(a, $o, X0, sk_Xx)
1.38/1.56	       | ~ zip_tseitin0(sk_Xx, X0, sk_S)
1.38/1.56	       | app_encode_app(a, $o, X1, sk_Xx1)
1.38/1.56	       | ~ zip_tseitin0(sk_Xx1, X1, sk_U)),
1.38/1.56	    inference('simplify', [status(thm)], ['56'])).
1.38/1.56	tff('58', plain,
1.38/1.56	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ $true
1.38/1.56	       | ~ app_encode_app(a, $o, sk_S, X0)
1.38/1.56	       | zip_tseitin0(X0, sk_U, X1)),
1.38/1.56	    inference('sup-', [status(thm)], ['23', '5'])).
1.38/1.56	tff('59', plain,
1.38/1.56	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
1.38/1.56	      (zip_tseitin0(X0, sk_U, X1) | ~ app_encode_app(a, $o, sk_S, X0)),
1.38/1.56	    inference('simplify', [status(thm)], ['58'])).
1.38/1.56	tff('60', plain,
1.38/1.56	    ![X0 : a, X1 : app_encode_fun(a, $o), X2 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ $true | zip_tseitin0(X0, X2, sk_S) | zip_tseitin0(X0, sk_U, X1)),
1.38/1.56	    inference('sup-', [status(thm)], ['4', '59'])).
1.38/1.56	tff('61', plain,
1.38/1.56	    ![X0 : a, X1 : app_encode_fun(a, $o), X2 : app_encode_fun(a, $o)]:
1.38/1.56	      (zip_tseitin0(X0, sk_U, X1) | zip_tseitin0(X0, X2, sk_S)),
1.38/1.56	    inference('simplify', [status(thm)], ['60'])).
1.38/1.56	tff('62', plain,
1.38/1.56	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ $true
1.38/1.56	       | zip_tseitin0(sk_Xx1, sk_U, X1)
1.38/1.56	       | zip_tseitin0(X0, sk_T, sk_S)),
1.38/1.56	    inference('sup-', [status(thm)], ['61', '10'])).
1.38/1.56	tff('63', plain,
1.38/1.56	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
1.38/1.56	      (zip_tseitin0(X0, sk_T, sk_S) | zip_tseitin0(sk_Xx1, sk_U, X1)),
1.38/1.56	    inference('simplify', [status(thm)], ['62'])).
1.38/1.56	tff('64', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ $true
1.38/1.56	       | zip_tseitin0(sk_Xx1, sk_U, X1)
1.38/1.56	       | ~ zip_tseitin0(sk_Xx, X0, sk_S)
1.38/1.56	       | app_encode_app(a, $o, X0, sk_Xx)),
1.38/1.56	    inference('sup-', [status(thm)], ['63', '18'])).
1.38/1.56	tff('65', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
1.38/1.56	      (app_encode_app(a, $o, X0, sk_Xx)
1.38/1.56	       | ~ zip_tseitin0(sk_Xx, X0, sk_S)
1.38/1.56	       | zip_tseitin0(sk_Xx1, sk_U, X1)),
1.38/1.56	    inference('simplify', [status(thm)], ['64'])).
1.38/1.56	tff('66', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
1.38/1.56	      X2 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ $true
1.38/1.56	       | zip_tseitin0(sk_Xx1, sk_U, X2)
1.38/1.56	       | ~ zip_tseitin0(sk_Xx, X0, sk_S)
1.38/1.56	       | ~ zip_tseitin0(sk_Xx, X1, X0)
1.38/1.56	       | app_encode_app(a, $o, X1, sk_Xx)),
1.38/1.56	    inference('sup-', [status(thm)], ['65', '16'])).
1.38/1.56	tff('67', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
1.38/1.56	      X2 : app_encode_fun(a, $o)]:
1.38/1.56	      (app_encode_app(a, $o, X1, sk_Xx)
1.38/1.56	       | ~ zip_tseitin0(sk_Xx, X1, X0)
1.38/1.56	       | ~ zip_tseitin0(sk_Xx, X0, sk_S)
1.38/1.56	       | zip_tseitin0(sk_Xx1, sk_U, X2)),
1.38/1.56	    inference('simplify', [status(thm)], ['66'])).
1.38/1.56	tff('68', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ $true
1.38/1.56	       | zip_tseitin0(sk_Xx1, sk_U, X1)
1.38/1.56	       | zip_tseitin0(sk_Xx1, sk_U, X0)
1.38/1.56	       | ~ zip_tseitin0(sk_Xx, sk_S, sk_S)
1.38/1.56	       | app_encode_app(a, $o, sk_T, sk_Xx)),
1.38/1.56	    inference('sup-', [status(thm)], ['63', '67'])).
1.38/1.56	tff('69', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : a]:
1.38/1.56	      (~ $true | zip_tseitin0(X1, X0, X0)),
1.38/1.56	    inference('eq_fact', [status(thm)], ['7'])).
1.38/1.56	tff('70', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : a]: zip_tseitin0(X1, X0, X0),
1.38/1.56	    inference('simplify', [status(thm)], ['69'])).
1.38/1.56	tff('71', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ $true
1.38/1.56	       | zip_tseitin0(sk_Xx1, sk_U, X1)
1.38/1.56	       | zip_tseitin0(sk_Xx1, sk_U, X0)
1.38/1.56	       | ~ $true
1.38/1.56	       | app_encode_app(a, $o, sk_T, sk_Xx)),
1.38/1.56	    inference('demod', [status(thm)], ['68', '70'])).
1.38/1.56	tff('72', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
1.38/1.56	      (app_encode_app(a, $o, sk_T, sk_Xx)
1.38/1.56	       | zip_tseitin0(sk_Xx1, sk_U, X0)
1.38/1.56	       | zip_tseitin0(sk_Xx1, sk_U, X1)),
1.38/1.56	    inference('simplify', [status(thm)], ['71'])).
1.38/1.56	tff('73', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o)]:
1.38/1.56	      (app_encode_app(a, $o, sk_T, sk_Xx) | zip_tseitin0(sk_Xx1, sk_U, X0)),
1.38/1.56	    inference('condensation', [status(thm)], ['72'])).
1.38/1.56	tff('74', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
1.38/1.56	      X2 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ $true
1.38/1.56	       | zip_tseitin0(sk_Xx1, sk_U, X2)
1.38/1.56	       | ~ zip_tseitin1(sk_Xx, X1, sk_T, X0)),
1.38/1.56	    inference('sup-', [status(thm)], ['73', '28'])).
1.38/1.56	tff('75', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
1.38/1.56	      X2 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ zip_tseitin1(sk_Xx, X1, sk_T, X0) | zip_tseitin0(sk_Xx1, sk_U, X2)),
1.38/1.56	    inference('simplify', [status(thm)], ['74'])).
1.38/1.56	tff('76', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ $true
1.38/1.56	       | ~ zip_tseitin0(sk_Xx1, sk_T, sk_S)
1.38/1.56	       | zip_tseitin0(sk_Xx1, sk_U, X0)),
1.38/1.56	    inference('sup-', [status(thm)], ['3', '75'])).
1.38/1.56	tff('77', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o)]:
1.38/1.56	      (zip_tseitin0(sk_Xx1, sk_U, X0) | ~ zip_tseitin0(sk_Xx1, sk_T, sk_S)),
1.38/1.56	    inference('simplify', [status(thm)], ['76'])).
1.38/1.56	tff('78', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o)]: zip_tseitin0(sk_Xx1, sk_U, X0),
1.38/1.56	    inference('clc', [status(thm)], ['77', '63'])).
1.38/1.56	tff('79', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ $true
1.38/1.56	       | zip_tseitin0(sk_Xx1, X1, X0)
1.38/1.56	       | app_encode_app(a, $o, sk_U, sk_Xx1)),
1.38/1.56	    inference('sup-', [status(thm)], ['78', '34'])).
1.38/1.56	tff('80', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
1.38/1.56	      (app_encode_app(a, $o, sk_U, sk_Xx1) | zip_tseitin0(sk_Xx1, X1, X0)),
1.38/1.56	    inference('simplify', [status(thm)], ['79'])).
1.38/1.56	tff('81', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
1.38/1.56	      X2 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ $true
1.38/1.56	       | zip_tseitin0(sk_Xx1, X2, X1)
1.38/1.56	       | ~ zip_tseitin0(sk_Xx1, X0, sk_U)
1.38/1.56	       | app_encode_app(a, $o, X0, sk_Xx1)),
1.38/1.56	    inference('sup-', [status(thm)], ['80', '16'])).
1.38/1.56	tff('82', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
1.38/1.56	      X2 : app_encode_fun(a, $o)]:
1.38/1.56	      (app_encode_app(a, $o, X0, sk_Xx1)
1.38/1.56	       | ~ zip_tseitin0(sk_Xx1, X0, sk_U)
1.38/1.56	       | zip_tseitin0(sk_Xx1, X2, X1)),
1.38/1.56	    inference('simplify', [status(thm)], ['81'])).
1.38/1.56	tff('83', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ $true
1.38/1.56	       | ~ zip_tseitin0(sk_Xx1, X1, sk_U)
1.38/1.56	       | app_encode_app(a, $o, X1, sk_Xx1)
1.38/1.56	       | zip_tseitin0(sk_Xx, X0, sk_S)),
1.38/1.56	    inference('sup-', [status(thm)], ['82', '41'])).
1.38/1.56	tff('84', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
1.38/1.56	      (zip_tseitin0(sk_Xx, X0, sk_S)
1.38/1.56	       | app_encode_app(a, $o, X1, sk_Xx1)
1.38/1.56	       | ~ zip_tseitin0(sk_Xx1, X1, sk_U)),
1.38/1.56	    inference('simplify', [status(thm)], ['83'])).
1.38/1.56	tff('85', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ zip_tseitin0(sk_Xx1, X1, sk_U)
1.38/1.56	       | app_encode_app(a, $o, X1, sk_Xx1)
1.38/1.56	       | app_encode_app(a, $o, X0, sk_Xx)),
1.38/1.56	    inference('clc', [status(thm)], ['57', '84'])).
1.38/1.56	tff('86', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X3 : a, X4 : app_encode_fun(a, $o)]:
1.38/1.56	      (zip_tseitin2(X3, X4, X0)
1.38/1.56	       | app_encode_app(a, $o, X0, X3)
1.38/1.56	       | ~ app_encode_app(a, $o, X4, X3)),
1.38/1.56	    inference('cnf', [status(esa)], [zf_stmt_3])).
1.38/1.56	tff('87', plain,
1.38/1.56	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ $true
1.38/1.56	       | ~ app_encode_app(a, $o, sk_S, X0)
1.38/1.56	       | app_encode_app(a, $o, X1, X0)
1.38/1.56	       | zip_tseitin2(X0, sk_U, X1)),
1.38/1.56	    inference('sup-', [status(thm)], ['23', '86'])).
1.38/1.56	tff('88', plain,
1.38/1.56	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
1.38/1.56	      (zip_tseitin2(X0, sk_U, X1)
1.38/1.56	       | app_encode_app(a, $o, X1, X0)
1.38/1.56	       | ~ app_encode_app(a, $o, sk_S, X0)),
1.38/1.56	    inference('simplify', [status(thm)], ['87'])).
1.38/1.56	tff('89', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ $true
1.38/1.56	       | app_encode_app(a, $o, X1, sk_Xx)
1.38/1.56	       | ~ zip_tseitin0(sk_Xx1, sk_S, sk_U)
1.38/1.56	       | app_encode_app(a, $o, X0, sk_Xx1)
1.38/1.56	       | zip_tseitin2(sk_Xx1, sk_U, X0)),
1.38/1.56	    inference('sup-', [status(thm)], ['85', '88'])).
1.38/1.56	tff('90', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ $true
1.38/1.56	       | app_encode_app(a, $o, X1, sk_Xx)
1.38/1.56	       | ~ $true
1.38/1.56	       | app_encode_app(a, $o, X0, sk_Xx1)
1.38/1.56	       | zip_tseitin2(sk_Xx1, sk_U, X0)),
1.38/1.56	    inference('demod', [status(thm)], ['89', '55'])).
1.38/1.56	tff('91', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
1.38/1.56	      (zip_tseitin2(sk_Xx1, sk_U, X0)
1.38/1.56	       | app_encode_app(a, $o, X0, sk_Xx1)
1.38/1.56	       | app_encode_app(a, $o, X1, sk_Xx)),
1.38/1.56	    inference('simplify', [status(thm)], ['90'])).
1.38/1.56	tff('92', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
1.38/1.56	      X2 : app_encode_fun(a, $o), X3 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ $true
1.38/1.56	       | app_encode_app(a, $o, X3, sk_Xx1)
1.38/1.56	       | zip_tseitin2(sk_Xx1, sk_U, X3)
1.38/1.56	       | ~ zip_tseitin1(sk_Xx, X2, X0, X1)),
1.38/1.56	    inference('sup-', [status(thm)], ['91', '28'])).
1.38/1.56	tff('93', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
1.38/1.56	      X2 : app_encode_fun(a, $o), X3 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ zip_tseitin1(sk_Xx, X2, X0, X1)
1.38/1.56	       | zip_tseitin2(sk_Xx1, sk_U, X3)
1.38/1.56	       | app_encode_app(a, $o, X3, sk_Xx1)),
1.38/1.56	    inference('simplify', [status(thm)], ['92'])).
1.38/1.56	tff('94', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ $true
1.38/1.56	       | ~ zip_tseitin0(sk_Xx1, sk_T, sk_S)
1.38/1.56	       | app_encode_app(a, $o, X0, sk_Xx1)
1.38/1.56	       | zip_tseitin2(sk_Xx1, sk_U, X0)),
1.38/1.56	    inference('sup-', [status(thm)], ['3', '93'])).
1.38/1.56	tff('95', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o)]:
1.38/1.56	      (zip_tseitin2(sk_Xx1, sk_U, X0)
1.38/1.56	       | app_encode_app(a, $o, X0, sk_Xx1)
1.38/1.56	       | ~ zip_tseitin0(sk_Xx1, sk_T, sk_S)),
1.38/1.56	    inference('simplify', [status(thm)], ['94'])).
1.38/1.56	tff('96', plain, ![X0 : a]: (~ $true | zip_tseitin0(X0, sk_U, sk_S)),
1.38/1.56	    inference('eq_fact', [status(thm)], ['61'])).
1.38/1.56	tff('97', plain, ![X0 : a]: zip_tseitin0(X0, sk_U, sk_S),
1.38/1.56	    inference('simplify', [status(thm)], ['96'])).
1.38/1.56	tff('98', plain,
1.38/1.56	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ $true | zip_tseitin0(X0, X1, sk_S) | app_encode_app(a, $o, sk_U, X0)),
1.38/1.56	    inference('sup-', [status(thm)], ['97', '34'])).
1.38/1.56	tff('99', plain,
1.38/1.56	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
1.38/1.56	      (app_encode_app(a, $o, sk_U, X0) | zip_tseitin0(X0, X1, sk_S)),
1.38/1.56	    inference('simplify', [status(thm)], ['98'])).
1.38/1.56	tff('100', plain,
1.38/1.56	    ![X0 : a, X1 : app_encode_fun(a, $o), X2 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ $true
1.38/1.56	       | zip_tseitin0(X0, X2, sk_S)
1.38/1.56	       | app_encode_app(a, $o, X1, X0)
1.38/1.56	       | zip_tseitin2(X0, sk_U, X1)),
1.38/1.56	    inference('sup-', [status(thm)], ['99', '86'])).
1.38/1.56	tff('101', plain,
1.38/1.56	    ![X0 : a, X1 : app_encode_fun(a, $o), X2 : app_encode_fun(a, $o)]:
1.38/1.56	      (zip_tseitin2(X0, sk_U, X1)
1.38/1.56	       | app_encode_app(a, $o, X1, X0)
1.38/1.56	       | zip_tseitin0(X0, X2, sk_S)),
1.38/1.56	    inference('simplify', [status(thm)], ['100'])).
1.38/1.56	tff('102', plain,
1.38/1.56	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ $true
1.38/1.56	       | app_encode_app(a, $o, X1, sk_Xx1)
1.38/1.56	       | zip_tseitin2(sk_Xx1, sk_U, X1)
1.38/1.56	       | zip_tseitin0(X0, sk_T, sk_S)),
1.38/1.56	    inference('sup-', [status(thm)], ['101', '10'])).
1.38/1.56	tff('103', plain,
1.38/1.56	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
1.38/1.56	      (zip_tseitin0(X0, sk_T, sk_S)
1.38/1.56	       | zip_tseitin2(sk_Xx1, sk_U, X1)
1.38/1.56	       | app_encode_app(a, $o, X1, sk_Xx1)),
1.38/1.56	    inference('simplify', [status(thm)], ['102'])).
1.38/1.56	tff('104', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o)]:
1.38/1.56	      (app_encode_app(a, $o, X0, sk_Xx1) | zip_tseitin2(sk_Xx1, sk_U, X0)),
1.38/1.56	    inference('clc', [status(thm)], ['95', '103'])).
1.38/1.56	tff('105', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ $true
1.38/1.56	       | zip_tseitin2(sk_Xx1, sk_U, X0)
1.38/1.56	       | ~ zip_tseitin0(sk_Xx1, X1, X0)
1.38/1.56	       | app_encode_app(a, $o, X1, sk_Xx1)),
1.38/1.56	    inference('sup-', [status(thm)], ['104', '16'])).
1.38/1.56	tff('106', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
1.38/1.56	      (app_encode_app(a, $o, X1, sk_Xx1)
1.38/1.56	       | ~ zip_tseitin0(sk_Xx1, X1, X0)
1.38/1.56	       | zip_tseitin2(sk_Xx1, sk_U, X0)),
1.38/1.56	    inference('simplify', [status(thm)], ['105'])).
1.38/1.56	tff('107', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ $true
1.38/1.56	       | zip_tseitin2(sk_Xx1, sk_U, X0)
1.38/1.56	       | app_encode_app(a, $o, sk_S, sk_Xx1)),
1.38/1.56	    inference('sup-', [status(thm)], ['55', '106'])).
1.38/1.56	tff('108', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o)]:
1.38/1.56	      (app_encode_app(a, $o, sk_S, sk_Xx1) | zip_tseitin2(sk_Xx1, sk_U, X0)),
1.38/1.56	    inference('simplify', [status(thm)], ['107'])).
1.38/1.56	tff('109', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ $true
1.38/1.56	       | zip_tseitin2(sk_Xx1, sk_U, X0)
1.38/1.56	       | app_encode_app(a, $o, sk_U, sk_Xx1)),
1.38/1.56	    inference('sup-', [status(thm)], ['78', '106'])).
1.38/1.56	tff('110', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o)]:
1.38/1.56	      (app_encode_app(a, $o, sk_U, sk_Xx1) | zip_tseitin2(sk_Xx1, sk_U, X0)),
1.38/1.56	    inference('simplify', [status(thm)], ['109'])).
1.38/1.56	tff('111', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X3 : a, X4 : app_encode_fun(a, $o)]:
1.38/1.56	      (app_encode_app(a, $o, X4, X3) | ~ zip_tseitin2(X3, X4, X0)),
1.38/1.56	    inference('cnf', [status(esa)], [zf_stmt_3])).
1.38/1.56	tff('112', plain, app_encode_app(a, $o, sk_U, sk_Xx1),
1.38/1.56	    inference('clc', [status(thm)], ['110', '111'])).
1.38/1.56	tff('113', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ $true
1.38/1.56	       | ~ zip_tseitin0(sk_Xx1, X0, sk_U)
1.38/1.56	       | app_encode_app(a, $o, X0, sk_Xx1)),
1.38/1.56	    inference('sup-', [status(thm)], ['112', '16'])).
1.38/1.56	tff('114', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o)]:
1.38/1.56	      (app_encode_app(a, $o, X0, sk_Xx1) | ~ zip_tseitin0(sk_Xx1, X0, sk_U)),
1.38/1.56	    inference('simplify', [status(thm)], ['113'])).
1.38/1.56	tff('115', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X3 : a, X4 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ app_encode_app(a, $o, X0, X3) | ~ zip_tseitin2(X3, X4, X0)),
1.38/1.56	    inference('cnf', [status(esa)], [zf_stmt_3])).
1.38/1.56	tff('116', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ $true
1.38/1.56	       | ~ zip_tseitin0(sk_Xx1, X0, sk_U)
1.38/1.56	       | ~ zip_tseitin2(sk_Xx1, X1, X0)),
1.38/1.56	    inference('sup-', [status(thm)], ['114', '115'])).
1.38/1.56	tff('117', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ zip_tseitin2(sk_Xx1, X1, X0) | ~ zip_tseitin0(sk_Xx1, X0, sk_U)),
1.38/1.56	    inference('simplify', [status(thm)], ['116'])).
1.38/1.56	tff('118', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ $true
1.38/1.56	       | app_encode_app(a, $o, sk_S, sk_Xx1)
1.38/1.56	       | ~ zip_tseitin0(sk_Xx1, X0, sk_U)),
1.38/1.56	    inference('sup-', [status(thm)], ['108', '117'])).
1.38/1.56	tff('119', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ zip_tseitin0(sk_Xx1, X0, sk_U) | app_encode_app(a, $o, sk_S, sk_Xx1)),
1.38/1.56	    inference('simplify', [status(thm)], ['118'])).
1.38/1.56	tff('120', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ $true
1.38/1.56	       | zip_tseitin0(sk_Xx1, X1, X0)
1.38/1.56	       | app_encode_app(a, $o, sk_S, sk_Xx1)),
1.38/1.56	    inference('sup-', [status(thm)], ['55', '34'])).
1.38/1.56	tff('121', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
1.38/1.56	      (app_encode_app(a, $o, sk_S, sk_Xx1) | zip_tseitin0(sk_Xx1, X1, X0)),
1.38/1.56	    inference('simplify', [status(thm)], ['120'])).
1.38/1.56	tff('122', plain, app_encode_app(a, $o, sk_S, sk_Xx1),
1.38/1.56	    inference('clc', [status(thm)], ['119', '121'])).
1.38/1.56	tff('123', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X2 : app_encode_fun(a, $o), X3 : a, 
1.38/1.56	      X4 : app_encode_fun(a, $o)]:
1.38/1.56	      (zip_tseitin1(X3, X4, X2, X0)
1.38/1.56	       | app_encode_app(a, $o, X2, X3)
1.38/1.56	       | ~ app_encode_app(a, $o, X4, X3)
1.38/1.56	       | ~ app_encode_app(a, $o, X0, X3)),
1.38/1.56	    inference('cnf', [status(esa)], [zf_stmt_5])).
1.38/1.56	tff('124', plain,
1.38/1.56	    ![X0 : a, X1 : app_encode_fun(a, $o), X2 : app_encode_fun(a, $o), 
1.38/1.56	      X3 : app_encode_fun(a, $o), X4 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ $true
1.38/1.56	       | zip_tseitin0(X0, X4, X1)
1.38/1.56	       | ~ app_encode_app(a, $o, X2, X0)
1.38/1.56	       | app_encode_app(a, $o, X3, X0)
1.38/1.56	       | zip_tseitin1(X0, X1, X3, X2)),
1.38/1.56	    inference('sup-', [status(thm)], ['4', '123'])).
1.38/1.56	tff('125', plain,
1.38/1.56	    ![X0 : a, X1 : app_encode_fun(a, $o), X2 : app_encode_fun(a, $o), 
1.38/1.56	      X3 : app_encode_fun(a, $o), X4 : app_encode_fun(a, $o)]:
1.38/1.56	      (zip_tseitin1(X0, X1, X3, X2)
1.38/1.56	       | app_encode_app(a, $o, X3, X0)
1.38/1.56	       | ~ app_encode_app(a, $o, X2, X0)
1.38/1.56	       | zip_tseitin0(X0, X4, X1)),
1.38/1.56	    inference('simplify', [status(thm)], ['124'])).
1.38/1.56	tff('126', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
1.38/1.56	      X2 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ $true
1.38/1.56	       | zip_tseitin0(sk_Xx1, X1, X0)
1.38/1.56	       | app_encode_app(a, $o, X2, sk_Xx1)
1.38/1.56	       | zip_tseitin1(sk_Xx1, X0, X2, sk_S)),
1.38/1.56	    inference('sup-', [status(thm)], ['122', '125'])).
1.38/1.56	tff('127', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
1.38/1.56	      X2 : app_encode_fun(a, $o)]:
1.38/1.56	      (zip_tseitin1(sk_Xx1, X0, X2, sk_S)
1.38/1.56	       | app_encode_app(a, $o, X2, sk_Xx1)
1.38/1.56	       | zip_tseitin0(sk_Xx1, X1, X0)),
1.38/1.56	    inference('simplify', [status(thm)], ['126'])).
1.38/1.56	tff('128', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
1.38/1.56	      X2 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ $true
1.38/1.56	       | zip_tseitin0(sk_Xx1, X2, X1)
1.38/1.56	       | ~ zip_tseitin0(sk_Xx1, X0, sk_S)
1.38/1.56	       | app_encode_app(a, $o, X0, sk_Xx1)),
1.38/1.56	    inference('sup-', [status(thm)], ['121', '16'])).
1.38/1.56	tff('129', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
1.38/1.56	      X2 : app_encode_fun(a, $o)]:
1.38/1.56	      (app_encode_app(a, $o, X0, sk_Xx1)
1.38/1.56	       | ~ zip_tseitin0(sk_Xx1, X0, sk_S)
1.38/1.56	       | zip_tseitin0(sk_Xx1, X2, X1)),
1.38/1.56	    inference('simplify', [status(thm)], ['128'])).
1.38/1.56	tff('130', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
1.38/1.56	      X2 : app_encode_fun(a, $o), X3 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ $true
1.38/1.56	       | zip_tseitin0(sk_Xx1, X3, X2)
1.38/1.56	       | ~ zip_tseitin0(sk_Xx1, X0, sk_S)
1.38/1.56	       | zip_tseitin0(sk_Xx1, X0, X1)),
1.38/1.56	    inference('sup-', [status(thm)], ['129', '5'])).
1.38/1.56	tff('131', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
1.38/1.56	      X2 : app_encode_fun(a, $o), X3 : app_encode_fun(a, $o)]:
1.38/1.56	      (zip_tseitin0(sk_Xx1, X0, X1)
1.38/1.56	       | ~ zip_tseitin0(sk_Xx1, X0, sk_S)
1.38/1.56	       | zip_tseitin0(sk_Xx1, X3, X2)),
1.38/1.56	    inference('simplify', [status(thm)], ['130'])).
1.38/1.56	tff('132', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
1.38/1.56	      (zip_tseitin0(sk_Xx1, X1, X0) | ~ zip_tseitin0(sk_Xx1, X1, sk_S)),
1.38/1.56	    inference('condensation', [status(thm)], ['131'])).
1.38/1.56	tff('133', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), X2 : a, 
1.38/1.56	      X3 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ $true
1.38/1.56	       | zip_tseitin3(X2, sk_U, sk_T, sk_S)
1.38/1.56	       | zip_tseitin0(sk_Xx1, sk_T, X3)
1.38/1.56	       | zip_tseitin0(sk_Xx1, X0, X1)),
1.38/1.56	    inference('sup-', [status(thm)], ['38', '132'])).
1.38/1.56	tff('134', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), X2 : a, 
1.38/1.56	      X3 : app_encode_fun(a, $o)]:
1.38/1.56	      (zip_tseitin0(sk_Xx1, X0, X1)
1.38/1.56	       | zip_tseitin0(sk_Xx1, sk_T, X3)
1.38/1.56	       | zip_tseitin3(X2, sk_U, sk_T, sk_S)),
1.38/1.56	    inference('simplify', [status(thm)], ['133'])).
1.38/1.56	tff('135', plain,
1.38/1.56	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
1.38/1.56	      (zip_tseitin3(X0, sk_U, sk_T, sk_S) | zip_tseitin0(sk_Xx1, sk_T, X1)),
1.38/1.56	    inference('condensation', [status(thm)], ['134'])).
1.38/1.56	tff('136', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ $true
1.38/1.56	       | ~ zip_tseitin0(sk_Xx1, X0, sk_U)
1.38/1.56	       | ~ zip_tseitin0(sk_Xx1, X1, X0)
1.38/1.56	       | app_encode_app(a, $o, X1, sk_Xx1)),
1.38/1.56	    inference('sup-', [status(thm)], ['114', '16'])).
1.38/1.56	tff('137', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
1.38/1.56	      (app_encode_app(a, $o, X1, sk_Xx1)
1.38/1.56	       | ~ zip_tseitin0(sk_Xx1, X1, X0)
1.38/1.56	       | ~ zip_tseitin0(sk_Xx1, X0, sk_U)),
1.38/1.56	    inference('simplify', [status(thm)], ['136'])).
1.38/1.56	tff('138', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : a]:
1.38/1.56	      (~ $true
1.38/1.56	       | zip_tseitin3(X1, sk_U, sk_T, sk_S)
1.38/1.56	       | ~ zip_tseitin0(sk_Xx1, X0, sk_U)
1.38/1.56	       | app_encode_app(a, $o, sk_T, sk_Xx1)),
1.38/1.56	    inference('sup-', [status(thm)], ['135', '137'])).
1.38/1.56	tff('139', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : a]:
1.38/1.56	      (app_encode_app(a, $o, sk_T, sk_Xx1)
1.38/1.56	       | ~ zip_tseitin0(sk_Xx1, X0, sk_U)
1.38/1.56	       | zip_tseitin3(X1, sk_U, sk_T, sk_S)),
1.38/1.56	    inference('simplify', [status(thm)], ['138'])).
1.38/1.56	tff('140', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), X2 : a]:
1.38/1.56	      (~ $true
1.38/1.56	       | zip_tseitin3(X2, sk_U, sk_T, sk_S)
1.38/1.56	       | app_encode_app(a, $o, sk_T, sk_Xx1)
1.38/1.56	       | zip_tseitin0(sk_Xx1, X0, X1)),
1.38/1.56	    inference('sup-', [status(thm)], ['36', '132'])).
1.38/1.56	tff('141', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), X2 : a]:
1.38/1.56	      (zip_tseitin0(sk_Xx1, X0, X1)
1.38/1.56	       | app_encode_app(a, $o, sk_T, sk_Xx1)
1.38/1.56	       | zip_tseitin3(X2, sk_U, sk_T, sk_S)),
1.38/1.56	    inference('simplify', [status(thm)], ['140'])).
1.38/1.56	tff('142', plain,
1.38/1.56	    ![X1 : a]:
1.38/1.56	      (zip_tseitin3(X1, sk_U, sk_T, sk_S)
1.38/1.56	       | app_encode_app(a, $o, sk_T, sk_Xx1)),
1.38/1.56	    inference('clc', [status(thm)], ['139', '141'])).
1.38/1.56	tff('143', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X2 : app_encode_fun(a, $o), X3 : a, 
1.38/1.56	      X4 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ zip_tseitin1(X3, X4, X2, X0)
1.38/1.56	       | zip_tseitin2(X3, X4, X0)
1.38/1.56	       | ~ zip_tseitin3(X3, X4, X2, X0)),
1.38/1.56	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.38/1.56	tff('144', plain,
1.38/1.56	    ![X0 : a]:
1.38/1.56	      (~ $true
1.38/1.56	       | app_encode_app(a, $o, sk_T, sk_Xx1)
1.38/1.56	       | zip_tseitin2(X0, sk_U, sk_S)
1.38/1.56	       | ~ zip_tseitin1(X0, sk_U, sk_T, sk_S)),
1.38/1.56	    inference('sup-', [status(thm)], ['142', '143'])).
1.38/1.56	tff('145', plain,
1.38/1.56	    ![X0 : a]:
1.38/1.56	      (~ zip_tseitin1(X0, sk_U, sk_T, sk_S)
1.38/1.56	       | zip_tseitin2(X0, sk_U, sk_S)
1.38/1.56	       | app_encode_app(a, $o, sk_T, sk_Xx1)),
1.38/1.56	    inference('simplify', [status(thm)], ['144'])).
1.38/1.56	tff('146', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ $true
1.38/1.56	       | zip_tseitin0(sk_Xx1, X0, sk_U)
1.38/1.56	       | app_encode_app(a, $o, sk_T, sk_Xx1)
1.38/1.56	       | app_encode_app(a, $o, sk_T, sk_Xx1)
1.38/1.56	       | zip_tseitin2(sk_Xx1, sk_U, sk_S)),
1.38/1.56	    inference('sup-', [status(thm)], ['127', '145'])).
1.38/1.56	tff('147', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o)]:
1.38/1.56	      (zip_tseitin2(sk_Xx1, sk_U, sk_S)
1.38/1.56	       | app_encode_app(a, $o, sk_T, sk_Xx1)
1.38/1.56	       | zip_tseitin0(sk_Xx1, X0, sk_U)),
1.38/1.56	    inference('simplify', [status(thm)], ['146'])).
1.38/1.56	tff('148', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ $true | ~ zip_tseitin2(sk_Xx1, X0, sk_S)),
1.38/1.56	    inference('sup-', [status(thm)], ['122', '115'])).
1.38/1.56	tff('149', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o)]: ~ zip_tseitin2(sk_Xx1, X0, sk_S),
1.38/1.56	    inference('simplify', [status(thm)], ['148'])).
1.38/1.56	tff('150', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o)]:
1.38/1.56	      (zip_tseitin0(sk_Xx1, X0, sk_U) | app_encode_app(a, $o, sk_T, sk_Xx1)),
1.38/1.56	    inference('clc', [status(thm)], ['147', '149'])).
1.38/1.56	tff('151', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ $true
1.38/1.56	       | zip_tseitin0(sk_Xx1, X1, sk_U)
1.38/1.56	       | zip_tseitin0(sk_Xx1, sk_T, X0)),
1.38/1.56	    inference('sup-', [status(thm)], ['150', '5'])).
1.38/1.56	tff('152', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
1.38/1.56	      (zip_tseitin0(sk_Xx1, sk_T, X0) | zip_tseitin0(sk_Xx1, X1, sk_U)),
1.38/1.56	    inference('simplify', [status(thm)], ['151'])).
1.38/1.56	tff('153', plain, (~ $true | zip_tseitin0(sk_Xx1, sk_T, sk_U)),
1.38/1.56	    inference('eq_fact', [status(thm)], ['152'])).
1.38/1.56	tff('154', plain, zip_tseitin0(sk_Xx1, sk_T, sk_U),
1.38/1.56	    inference('simplify', [status(thm)], ['153'])).
1.38/1.56	tff('155', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ $true
1.38/1.56	       | zip_tseitin2(sk_Xx1, sk_U, X0)
1.38/1.56	       | app_encode_app(a, $o, X1, sk_Xx1)
1.38/1.56	       | zip_tseitin2(sk_Xx1, X0, X1)),
1.38/1.56	    inference('sup-', [status(thm)], ['104', '86'])).
1.38/1.56	tff('156', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
1.38/1.56	      (zip_tseitin2(sk_Xx1, X0, X1)
1.38/1.56	       | app_encode_app(a, $o, X1, sk_Xx1)
1.38/1.56	       | zip_tseitin2(sk_Xx1, sk_U, X0)),
1.38/1.56	    inference('simplify', [status(thm)], ['155'])).
1.38/1.56	tff('157', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
1.38/1.56	      X2 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ $true
1.38/1.56	       | zip_tseitin2(sk_Xx1, sk_U, X2)
1.38/1.56	       | zip_tseitin2(sk_Xx1, X2, X0)
1.38/1.56	       | zip_tseitin0(sk_Xx1, X0, X1)),
1.38/1.56	    inference('sup-', [status(thm)], ['156', '5'])).
1.38/1.56	tff('158', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
1.38/1.56	      X2 : app_encode_fun(a, $o)]:
1.38/1.56	      (zip_tseitin0(sk_Xx1, X0, X1)
1.38/1.56	       | zip_tseitin2(sk_Xx1, X2, X0)
1.38/1.56	       | zip_tseitin2(sk_Xx1, sk_U, X2)),
1.38/1.56	    inference('simplify', [status(thm)], ['157'])).
1.38/1.56	tff('159', plain,
1.38/1.56	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ $true
1.38/1.56	       | zip_tseitin2(sk_Xx1, sk_U, X1)
1.38/1.56	       | zip_tseitin2(sk_Xx1, X1, sk_T)
1.38/1.56	       | zip_tseitin0(X0, sk_T, sk_S)),
1.38/1.56	    inference('sup-', [status(thm)], ['158', '10'])).
1.38/1.56	tff('160', plain,
1.38/1.56	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
1.38/1.56	      (zip_tseitin0(X0, sk_T, sk_S)
1.38/1.56	       | zip_tseitin2(sk_Xx1, X1, sk_T)
1.38/1.56	       | zip_tseitin2(sk_Xx1, sk_U, X1)),
1.38/1.56	    inference('simplify', [status(thm)], ['159'])).
1.38/1.56	tff('161', plain,
1.38/1.56	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ $true
1.38/1.56	       | ~ app_encode_app(a, $o, sk_S, X0)
1.38/1.56	       | ~ zip_tseitin2(X0, X1, sk_U)),
1.38/1.56	    inference('sup-', [status(thm)], ['23', '115'])).
1.38/1.56	tff('162', plain,
1.38/1.56	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ zip_tseitin2(X0, X1, sk_U) | ~ app_encode_app(a, $o, sk_S, X0)),
1.38/1.56	    inference('simplify', [status(thm)], ['161'])).
1.38/1.56	tff('163', plain,
1.38/1.56	    ![X0 : a]:
1.38/1.56	      (~ $true
1.38/1.56	       | zip_tseitin2(sk_Xx1, sk_U, sk_T)
1.38/1.56	       | zip_tseitin0(X0, sk_T, sk_S)
1.38/1.56	       | ~ app_encode_app(a, $o, sk_S, sk_Xx1)),
1.38/1.56	    inference('sup-', [status(thm)], ['160', '162'])).
1.38/1.56	tff('164', plain,
1.38/1.56	    ![X0 : a]:
1.38/1.56	      (~ $true
1.38/1.56	       | zip_tseitin2(sk_Xx1, sk_U, sk_T)
1.38/1.56	       | zip_tseitin0(X0, sk_T, sk_S)
1.38/1.56	       | ~ $true),
1.38/1.56	    inference('demod', [status(thm)], ['163', '122'])).
1.38/1.56	tff('165', plain,
1.38/1.56	    ![X0 : a]:
1.38/1.56	      (zip_tseitin0(X0, sk_T, sk_S) | zip_tseitin2(sk_Xx1, sk_U, sk_T)),
1.38/1.56	    inference('simplify', [status(thm)], ['164'])).
1.38/1.56	tff('166', plain,
1.38/1.56	    ![X0 : a]:
1.38/1.56	      (~ $true
1.38/1.56	       | zip_tseitin0(X0, sk_T, sk_S)
1.38/1.56	       | ~ zip_tseitin0(sk_Xx1, sk_T, sk_U)),
1.38/1.56	    inference('sup-', [status(thm)], ['165', '117'])).
1.38/1.56	tff('167', plain,
1.38/1.56	    ![X0 : a]:
1.38/1.56	      (~ zip_tseitin0(sk_Xx1, sk_T, sk_U) | zip_tseitin0(X0, sk_T, sk_S)),
1.38/1.56	    inference('simplify', [status(thm)], ['166'])).
1.38/1.56	tff('168', plain, ![X0 : a]: (~ $true | zip_tseitin0(X0, sk_T, sk_S)),
1.38/1.56	    inference('sup-', [status(thm)], ['154', '167'])).
1.38/1.56	tff('169', plain, ![X0 : a]: zip_tseitin0(X0, sk_T, sk_S),
1.38/1.56	    inference('simplify', [status(thm)], ['168'])).
1.38/1.56	tff('170', plain,
1.38/1.56	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ $true
1.38/1.56	       | zip_tseitin0(sk_Xx1, X1, sk_T)
1.38/1.56	       | zip_tseitin0(X0, sk_T, sk_S)),
1.38/1.56	    inference('sup-', [status(thm)], ['7', '10'])).
1.38/1.56	tff('171', plain,
1.38/1.56	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
1.38/1.56	      (zip_tseitin0(X0, sk_T, sk_S) | zip_tseitin0(sk_Xx1, X1, sk_T)),
1.38/1.56	    inference('simplify', [status(thm)], ['170'])).
1.38/1.56	tff('172', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ $true
1.38/1.56	       | zip_tseitin0(sk_Xx1, X1, sk_T)
1.38/1.56	       | ~ zip_tseitin0(sk_Xx, X0, sk_S)
1.38/1.56	       | app_encode_app(a, $o, X0, sk_Xx)),
1.38/1.56	    inference('sup-', [status(thm)], ['171', '18'])).
1.38/1.56	tff('173', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
1.38/1.56	      (app_encode_app(a, $o, X0, sk_Xx)
1.38/1.56	       | ~ zip_tseitin0(sk_Xx, X0, sk_S)
1.38/1.56	       | zip_tseitin0(sk_Xx1, X1, sk_T)),
1.38/1.56	    inference('simplify', [status(thm)], ['172'])).
1.38/1.56	tff('174', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
1.38/1.56	      X2 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ $true
1.38/1.56	       | zip_tseitin0(sk_Xx1, X2, sk_T)
1.38/1.56	       | ~ zip_tseitin0(sk_Xx, X0, sk_S)
1.38/1.56	       | ~ zip_tseitin0(sk_Xx, X1, X0)
1.38/1.56	       | app_encode_app(a, $o, X1, sk_Xx)),
1.38/1.56	    inference('sup-', [status(thm)], ['173', '16'])).
1.38/1.56	tff('175', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
1.38/1.56	      X2 : app_encode_fun(a, $o)]:
1.38/1.56	      (app_encode_app(a, $o, X1, sk_Xx)
1.38/1.56	       | ~ zip_tseitin0(sk_Xx, X1, X0)
1.38/1.56	       | ~ zip_tseitin0(sk_Xx, X0, sk_S)
1.38/1.56	       | zip_tseitin0(sk_Xx1, X2, sk_T)),
1.38/1.56	    inference('simplify', [status(thm)], ['174'])).
1.38/1.56	tff('176', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ $true
1.38/1.56	       | zip_tseitin0(sk_Xx1, X1, sk_T)
1.38/1.56	       | zip_tseitin0(sk_Xx1, X0, sk_T)
1.38/1.56	       | ~ zip_tseitin0(sk_Xx, sk_S, sk_S)
1.38/1.56	       | app_encode_app(a, $o, sk_T, sk_Xx)),
1.38/1.56	    inference('sup-', [status(thm)], ['171', '175'])).
1.38/1.56	tff('177', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ $true
1.38/1.56	       | zip_tseitin0(sk_Xx1, X1, sk_T)
1.38/1.56	       | zip_tseitin0(sk_Xx1, X0, sk_T)
1.38/1.56	       | ~ $true
1.38/1.56	       | app_encode_app(a, $o, sk_T, sk_Xx)),
1.38/1.56	    inference('demod', [status(thm)], ['176', '70'])).
1.38/1.56	tff('178', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
1.38/1.56	      (app_encode_app(a, $o, sk_T, sk_Xx)
1.38/1.56	       | zip_tseitin0(sk_Xx1, X0, sk_T)
1.38/1.56	       | zip_tseitin0(sk_Xx1, X1, sk_T)),
1.38/1.56	    inference('simplify', [status(thm)], ['177'])).
1.38/1.56	tff('179', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o)]:
1.38/1.56	      (app_encode_app(a, $o, sk_T, sk_Xx) | zip_tseitin0(sk_Xx1, X0, sk_T)),
1.38/1.56	    inference('condensation', [status(thm)], ['178'])).
1.38/1.56	tff('180', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
1.38/1.56	      X2 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ $true
1.38/1.56	       | zip_tseitin0(sk_Xx1, X2, sk_T)
1.38/1.56	       | ~ zip_tseitin1(sk_Xx, X1, sk_T, X0)),
1.38/1.56	    inference('sup-', [status(thm)], ['179', '28'])).
1.38/1.56	tff('181', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
1.38/1.56	      X2 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ zip_tseitin1(sk_Xx, X1, sk_T, X0) | zip_tseitin0(sk_Xx1, X2, sk_T)),
1.38/1.56	    inference('simplify', [status(thm)], ['180'])).
1.38/1.56	tff('182', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ $true
1.38/1.56	       | ~ zip_tseitin0(sk_Xx1, sk_T, sk_S)
1.38/1.56	       | zip_tseitin0(sk_Xx1, X0, sk_T)),
1.38/1.56	    inference('sup-', [status(thm)], ['3', '181'])).
1.38/1.56	tff('183', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o)]:
1.38/1.56	      (zip_tseitin0(sk_Xx1, X0, sk_T) | ~ zip_tseitin0(sk_Xx1, sk_T, sk_S)),
1.38/1.56	    inference('simplify', [status(thm)], ['182'])).
1.38/1.56	tff('184', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o)]: zip_tseitin0(sk_Xx1, X0, sk_T),
1.38/1.56	    inference('clc', [status(thm)], ['183', '7'])).
1.38/1.56	tff('185', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ $true
1.38/1.56	       | zip_tseitin2(sk_Xx1, sk_U, sk_T)
1.38/1.56	       | app_encode_app(a, $o, X0, sk_Xx1)),
1.38/1.56	    inference('sup-', [status(thm)], ['184', '106'])).
1.38/1.56	tff('186', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o)]:
1.38/1.56	      (app_encode_app(a, $o, X0, sk_Xx1) | zip_tseitin2(sk_Xx1, sk_U, sk_T)),
1.38/1.56	    inference('simplify', [status(thm)], ['185'])).
1.38/1.56	tff('187', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ $true
1.38/1.56	       | zip_tseitin2(sk_Xx1, sk_U, sk_T)
1.38/1.56	       | zip_tseitin0(sk_Xx1, X0, X1)),
1.38/1.56	    inference('sup-', [status(thm)], ['186', '5'])).
1.38/1.56	tff('188', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
1.38/1.56	      (zip_tseitin0(sk_Xx1, X0, X1) | zip_tseitin2(sk_Xx1, sk_U, sk_T)),
1.38/1.56	    inference('simplify', [status(thm)], ['187'])).
1.38/1.56	tff('189', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ $true
1.38/1.56	       | ~ zip_tseitin0(sk_Xx1, X0, sk_S)
1.38/1.56	       | app_encode_app(a, $o, X0, sk_Xx1)),
1.38/1.56	    inference('sup-', [status(thm)], ['122', '16'])).
1.38/1.56	tff('190', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o)]:
1.38/1.56	      (app_encode_app(a, $o, X0, sk_Xx1) | ~ zip_tseitin0(sk_Xx1, X0, sk_S)),
1.38/1.56	    inference('simplify', [status(thm)], ['189'])).
1.38/1.56	tff('191', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ $true
1.38/1.56	       | ~ zip_tseitin0(sk_Xx1, X0, sk_S)
1.38/1.56	       | ~ zip_tseitin2(sk_Xx1, X1, X0)),
1.38/1.56	    inference('sup-', [status(thm)], ['190', '115'])).
1.38/1.56	tff('192', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ zip_tseitin2(sk_Xx1, X1, X0) | ~ zip_tseitin0(sk_Xx1, X0, sk_S)),
1.38/1.56	    inference('simplify', [status(thm)], ['191'])).
1.38/1.56	tff('193', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ $true
1.38/1.56	       | zip_tseitin0(sk_Xx1, X1, X0)
1.38/1.56	       | ~ zip_tseitin0(sk_Xx1, sk_T, sk_S)),
1.38/1.56	    inference('sup-', [status(thm)], ['188', '192'])).
1.38/1.56	tff('194', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ zip_tseitin0(sk_Xx1, sk_T, sk_S) | zip_tseitin0(sk_Xx1, X1, X0)),
1.38/1.56	    inference('simplify', [status(thm)], ['193'])).
1.38/1.56	tff('195', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ $true | zip_tseitin0(sk_Xx1, X1, X0)),
1.38/1.56	    inference('sup-', [status(thm)], ['169', '194'])).
1.38/1.56	tff('196', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
1.38/1.56	      zip_tseitin0(sk_Xx1, X1, X0),
1.38/1.56	    inference('simplify', [status(thm)], ['195'])).
1.38/1.56	tff('197', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ $true
1.38/1.56	       | ~ zip_tseitin0(sk_Xx, X0, sk_S)
1.38/1.56	       | app_encode_app(a, $o, X0, sk_Xx)),
1.38/1.56	    inference('sup-', [status(thm)], ['196', '18'])).
1.38/1.56	tff('198', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o)]: (~ $true | zip_tseitin0(sk_Xx, X0, sk_S)),
1.38/1.56	    inference('sup-', [status(thm)], ['169', '41'])).
1.38/1.56	tff('199', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o)]: zip_tseitin0(sk_Xx, X0, sk_S),
1.38/1.56	    inference('simplify', [status(thm)], ['198'])).
1.38/1.56	tff('200', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ $true | ~ $true | app_encode_app(a, $o, X0, sk_Xx)),
1.38/1.56	    inference('demod', [status(thm)], ['197', '199'])).
1.38/1.56	tff('201', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o)]: app_encode_app(a, $o, X0, sk_Xx),
1.38/1.56	    inference('simplify', [status(thm)], ['200'])).
1.38/1.56	tff('202', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
1.38/1.56	      X2 : app_encode_fun(a, $o)]:
1.38/1.56	      (~ $true | ~ zip_tseitin1(sk_Xx, X2, X0, X1)),
1.38/1.56	    inference('sup-', [status(thm)], ['201', '28'])).
1.38/1.56	tff('203', plain,
1.38/1.56	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
1.38/1.56	      X2 : app_encode_fun(a, $o)]: ~ zip_tseitin1(sk_Xx, X2, X0, X1),
1.38/1.56	    inference('simplify', [status(thm)], ['202'])).
1.38/1.56	tff('204', plain, (~ $true | ~ zip_tseitin0(sk_Xx1, sk_T, sk_S)),
1.38/1.56	    inference('sup-', [status(thm)], ['3', '203'])).
1.38/1.56	tff('205', plain, (~ $true | ~ $true),
1.38/1.56	    inference('demod', [status(thm)], ['204', '196'])).
1.38/1.56	tff('206', plain, $false, inference('simplify', [status(thm)], ['205'])).
1.38/1.56	
1.38/1.56	% SZS output end Refutation
1.38/1.56	EOF
