0.00/0.00	% File    : /export/starexec/sandbox/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : original
0.00/0.00	% Variant    : purification_ext
0.00/0.00	% Ordering    : rpo6
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-avatar \
0.00/0.00	  --ho \
0.00/0.00	  --force-ho \
0.00/0.00	  --no-ho-elim-pred-var \
0.00/0.00	  --ho-general-ext-pos \
0.00/0.00	  --no-ho-unif \
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	  --ho-purify ext \
0.00/0.00	  --ho-ext-axiom \
0.00/0.00	  --restrict-hidden-sup-at-vars \
0.00/0.00	  --ho-prim-enum none \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --dont-select-ho-var-lits \
0.00/0.00	  --no-fool
0.00/0.19	% Computer   : n119.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 08:22:23 CST 2018
106.80/106.99	% done 6865 iterations in 106.795s
106.80/106.99	% SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
106.80/106.99	% SZS output start Refutation
106.80/107.00	tff(prove_this, conjecture,
106.80/107.00	  (~(?[X1:algorithm]: (![Y1:program,Z1:input]: decides(X1,Y1,Z1))))).
106.80/107.00	tff(zf_stmt_0, negated_conjecture,
106.80/107.00	  (?[X1:algorithm]: (![Y1:program,Z1:input]: decides(X1,Y1,Z1)))).
106.80/107.00	tff('0', plain, ![X21 : program, X22 : input]: decides(sk_X1, X21, X22),
106.80/107.00	    inference('cnf', [status(esa)], [zf_stmt_0])).
106.80/107.00	tff(p1, axiom,
106.80/107.00	  ((?[X:algorithm]: (![Y:program,Z:input]: decides(X,Y,Z))) =>
106.80/107.00	   (?[W:program]: (![Y:program,Z:input]: decides(algorithm_of(W),Y,Z))))).
106.80/107.00	tff('1', plain,
106.80/107.00	    ![X0 : program, X1 : input, X2 : algorithm]:
106.80/107.00	      (decides(algorithm_of(sk_W), X0, X1)
106.80/107.00	       | ~ decides(X2, sk_Y(X2), sk_Z(X2))),
106.80/107.00	    inference('cnf', [status(esa)], [p1])).
106.80/107.00	tff('2', plain,
106.80/107.00	    ![X0 : input, X1 : program]:
106.80/107.00	      (~ $true | decides(algorithm_of(sk_W), X1, X0)),
106.80/107.00	    inference('sup-', [status(thm)], ['0', '1'])).
106.80/107.00	tff('3', plain,
106.80/107.00	    ![X0 : input, X1 : program]: decides(algorithm_of(sk_W), X1, X0),
106.80/107.00	    inference('simplify', [status(thm)], ['2'])).
106.80/107.00	tff(p2, axiom,
106.80/107.00	  (![W:program,Y:program,Z:input]:
106.80/107.00	     (decides(algorithm_of(W),Y,Z) =>
106.80/107.00	      (![Y:program,Z:input]:
106.80/107.00	         (((~halts2(Y,Z)) => (outputs(W,bad) & halts3(W,Y,Z))) & 
106.80/107.00	          (halts2(Y,Z) => (outputs(W,good) & halts3(W,Y,Z)))))))).
106.80/107.00	tff('4', plain,
106.80/107.00	    ![X3 : program, X5 : program, X6 : program, X7 : input, X8 : input]:
106.80/107.00	      (~ halts2(X3, X8)
106.80/107.00	       | halts3(X5, X3, X8)
106.80/107.00	       | ~ decides(algorithm_of(X5), X6, X7)),
106.80/107.00	    inference('cnf', [status(esa)], [p2])).
106.80/107.00	tff('5', plain,
106.80/107.00	    ![X3 : program, X4 : input, X5 : program, X6 : program, X7 : input]:
106.80/107.00	      (halts2(X3, X4)
106.80/107.00	       | halts3(X5, X3, X4)
106.80/107.00	       | ~ decides(algorithm_of(X5), X6, X7)),
106.80/107.00	    inference('cnf', [status(esa)], [p2])).
106.80/107.00	tff('6', plain,
106.80/107.00	    ![X3 : program, X5 : program, X6 : program, X7 : input, X8 : input]:
106.80/107.00	      (~ decides(algorithm_of(X5), X6, X7) | halts3(X5, X3, X8)),
106.80/107.00	    inference('clc', [status(thm)], ['4', '5'])).
106.80/107.00	tff('7', plain,
106.80/107.00	    ![X2 : input, X3 : program]: (~ $true | halts3(sk_W, X3, X2)),
106.80/107.00	    inference('sup-', [status(thm)], ['3', '6'])).
106.80/107.00	tff('8', plain, ![X2 : input, X3 : program]: halts3(sk_W, X3, X2),
106.80/107.00	    inference('simplify', [status(thm)], ['7'])).
106.80/107.00	tff(p3, axiom,
106.80/107.00	  ((?[W:program]:
106.80/107.00	      (![Y:program]:
106.80/107.00	         ((halts2(Y,as_input(Y)) =>
106.80/107.00	           (halts3(W,Y,as_input(Y)) & outputs(W,good))) & 
106.80/107.00	          ((~halts2(Y,as_input(Y))) =>
106.80/107.00	           (halts3(W,Y,as_input(Y)) & outputs(W,bad)))))) =>
106.80/107.00	   (?[V:program]:
106.80/107.00	      (![Y:program]:
106.80/107.00	         ((halts2(Y,as_input(Y)) => (halts2(V,as_input(Y)) & outputs(V,good))) & 
106.80/107.00	          ((~halts2(Y,as_input(Y))) =>
106.80/107.00	           (halts2(V,as_input(Y)) & outputs(V,bad)))))))).
106.80/107.00	tff(zf_stmt_1, axiom,
106.80/107.00	  ((halts2(Y,as_input(Y)) => (outputs(W,good) & halts3(W,Y,as_input(Y)))) =>
106.80/107.00	   zip_tseitin0(Y,W))).
106.80/107.00	tff('9', plain,
106.80/107.00	    ![X9 : program, X10 : program]:
106.80/107.00	      (zip_tseitin0(X9, X10) | halts2(X9, as_input(X9))),
106.80/107.00	    inference('cnf', [status(esa)], [zf_stmt_1])).
106.80/107.00	tff(zf_stmt_2, axiom,
106.80/107.00	  (((~halts2(Y,as_input(Y))) => (outputs(W,bad) & halts3(W,Y,as_input(Y)))) =>
106.80/107.00	   zip_tseitin1(Y,W))).
106.80/107.00	tff('10', plain,
106.80/107.00	    ![X9 : program, X10 : program]:
106.80/107.00	      (zip_tseitin1(X9, X10)
106.80/107.00	       | ~ outputs(X10, bad)
106.80/107.00	       | ~ halts3(X10, X9, as_input(X9))),
106.80/107.00	    inference('cnf', [status(esa)], [zf_stmt_2])).
106.80/107.00	tff(zf_stmt_3, type, zip_tseitin4 : (program * program) > $o).
106.80/107.00	tff(zf_stmt_4, axiom,
106.80/107.00	  (zip_tseitin4(Y,V) =>
106.80/107.00	   (((~halts2(Y,as_input(Y))) => zip_tseitin3(Y,V)) & 
106.80/107.00	    (halts2(Y,as_input(Y)) => zip_tseitin2(Y,V))))).
106.80/107.00	tff(zf_stmt_5, type, zip_tseitin3 : (program * program) > $o).
106.80/107.00	tff(zf_stmt_6, axiom,
106.80/107.00	  (zip_tseitin3(Y,V) => (outputs(V,bad) & halts2(V,as_input(Y))))).
106.80/107.00	tff(zf_stmt_7, type, zip_tseitin2 : (program * program) > $o).
106.80/107.00	tff(zf_stmt_8, axiom,
106.80/107.00	  (zip_tseitin2(Y,V) => (outputs(V,good) & halts2(V,as_input(Y))))).
106.80/107.00	tff(zf_stmt_9, type, zip_tseitin1 : (program * program) > $o).
106.80/107.00	tff(zf_stmt_10, type, zip_tseitin0 : (program * program) > $o).
106.80/107.00	tff(zf_stmt_11, axiom,
106.80/107.00	  ((?[W:program]: (![Y:program]: (zip_tseitin1(Y,W) & zip_tseitin0(Y,W)))) =>
106.80/107.00	   (?[V:program]: (![Y:program]: zip_tseitin4(Y,V))))).
106.80/107.00	tff('11', plain,
106.80/107.00	    ![X13 : program, X14 : program]:
106.80/107.00	      (zip_tseitin4(X13, sk_V)
106.80/107.00	       | ~ zip_tseitin0(sk_Y1(X14), X14)
106.80/107.00	       | ~ zip_tseitin1(sk_Y1(X14), X14)),
106.80/107.00	    inference('cnf', [status(esa)], [zf_stmt_11])).
106.80/107.00	tff('12', plain,
106.80/107.00	    ![X0 : program, X1 : program]:
106.80/107.00	      (~ $true
106.80/107.00	       | ~ halts3(X0, sk_Y1(X0), as_input(sk_Y1(X0)))
106.80/107.00	       | ~ outputs(X0, bad)
106.80/107.00	       | ~ zip_tseitin0(sk_Y1(X0), X0)
106.80/107.00	       | zip_tseitin4(X1, sk_V)),
106.80/107.00	    inference('sup-', [status(thm)], ['10', '11'])).
106.80/107.00	tff('13', plain,
106.80/107.00	    ![X0 : program, X1 : program]:
106.80/107.00	      (zip_tseitin4(X1, sk_V)
106.80/107.00	       | ~ zip_tseitin0(sk_Y1(X0), X0)
106.80/107.00	       | ~ outputs(X0, bad)
106.80/107.00	       | ~ halts3(X0, sk_Y1(X0), as_input(sk_Y1(X0)))),
106.80/107.00	    inference('simplify', [status(thm)], ['12'])).
106.80/107.00	tff('14', plain,
106.80/107.00	    ![X0 : program, X1 : program]:
106.80/107.00	      (~ $true
106.80/107.00	       | halts2(sk_Y1(X0), as_input(sk_Y1(X0)))
106.80/107.00	       | ~ halts3(X0, sk_Y1(X0), as_input(sk_Y1(X0)))
106.80/107.00	       | ~ outputs(X0, bad)
106.80/107.00	       | zip_tseitin4(X1, sk_V)),
106.80/107.00	    inference('sup-', [status(thm)], ['9', '13'])).
106.80/107.00	tff('15', plain,
106.80/107.00	    ![X0 : program, X1 : program]:
106.80/107.00	      (zip_tseitin4(X1, sk_V)
106.80/107.00	       | ~ outputs(X0, bad)
106.80/107.00	       | ~ halts3(X0, sk_Y1(X0), as_input(sk_Y1(X0)))
106.80/107.00	       | halts2(sk_Y1(X0), as_input(sk_Y1(X0)))),
106.80/107.00	    inference('simplify', [status(thm)], ['14'])).
106.80/107.00	tff('16', plain,
106.80/107.00	    ![X0 : program]:
106.80/107.00	      (~ $true
106.80/107.00	       | halts2(sk_Y1(sk_W), as_input(sk_Y1(sk_W)))
106.80/107.00	       | ~ outputs(sk_W, bad)
106.80/107.00	       | zip_tseitin4(X0, sk_V)),
106.80/107.00	    inference('sup-', [status(thm)], ['8', '15'])).
106.80/107.00	tff('17', plain,
106.80/107.00	    ![X3 : program, X4 : input, X5 : program, X6 : program, X7 : input]:
106.80/107.00	      (halts2(X3, X4)
106.80/107.00	       | outputs(X5, bad)
106.80/107.00	       | ~ decides(algorithm_of(X5), X6, X7)),
106.80/107.00	    inference('cnf', [status(esa)], [p2])).
106.80/107.00	tff('18', plain,
106.80/107.00	    ![X2 : input, X3 : program]:
106.80/107.00	      (~ $true | outputs(sk_W, bad) | halts2(X3, X2)),
106.80/107.00	    inference('sup-', [status(thm)], ['3', '17'])).
106.80/107.00	tff('19', plain,
106.80/107.00	    ![X2 : input, X3 : program]: (halts2(X3, X2) | outputs(sk_W, bad)),
106.80/107.00	    inference('simplify', [status(thm)], ['18'])).
106.80/107.00	tff('20', plain,
106.80/107.00	    ![X3 : program, X5 : program, X6 : program, X7 : input, X8 : input]:
106.80/107.00	      (~ halts2(X3, X8)
106.80/107.00	       | outputs(X5, good)
106.80/107.00	       | ~ decides(algorithm_of(X5), X6, X7)),
106.80/107.00	    inference('cnf', [status(esa)], [p2])).
106.80/107.00	tff('21', plain,
106.80/107.00	    ![X2 : input, X3 : program, X4 : program]:
106.80/107.00	      (~ $true
106.80/107.00	       | outputs(sk_W, bad)
106.80/107.00	       | ~ decides(algorithm_of(X4), X3, X2)
106.80/107.00	       | outputs(X4, good)),
106.80/107.00	    inference('sup-', [status(thm)], ['19', '20'])).
106.80/107.00	tff('22', plain,
106.80/107.00	    ![X2 : input, X3 : program, X4 : program]:
106.80/107.00	      (outputs(X4, good)
106.80/107.00	       | ~ decides(algorithm_of(X4), X3, X2)
106.80/107.00	       | outputs(sk_W, bad)),
106.80/107.00	    inference('simplify', [status(thm)], ['21'])).
106.80/107.00	tff('23', plain, (~ $true | outputs(sk_W, bad) | outputs(sk_W, good)),
106.80/107.00	    inference('sup-', [status(thm)], ['3', '22'])).
106.80/107.00	tff('24', plain, (outputs(sk_W, good) | outputs(sk_W, bad)),
106.80/107.00	    inference('simplify', [status(thm)], ['23'])).
106.80/107.00	tff(p4, axiom,
106.80/107.00	  ((?[V:program]:
106.80/107.00	      (![Y:program]:
106.80/107.00	         ((halts2(Y,as_input(Y)) => (halts2(V,as_input(Y)) & outputs(V,good))) & 
106.80/107.00	          ((~halts2(Y,as_input(Y))) =>
106.80/107.00	           (halts2(V,as_input(Y)) & outputs(V,bad)))))) =>
106.80/107.00	   (?[U:program]:
106.80/107.00	      (![Y:program]:
106.80/107.00	         ((halts2(Y,as_input(Y)) => (~halts2(U,as_input(Y)))) & 
106.80/107.00	          ((~halts2(Y,as_input(Y))) =>
106.80/107.00	           (halts2(U,as_input(Y)) & outputs(U,bad)))))))).
106.80/107.00	tff(zf_stmt_12, axiom,
106.80/107.00	  ((halts2(Y,as_input(Y)) => (outputs(V,good) & halts2(V,as_input(Y)))) =>
106.80/107.00	   zip_tseitin5(Y,V))).
106.80/107.00	tff('25', plain,
106.80/107.00	    ![X15 : program, X16 : program]:
106.80/107.00	      (zip_tseitin5(X15, X16)
106.80/107.00	       | ~ outputs(X16, good)
106.80/107.00	       | ~ halts2(X16, as_input(X15))),
106.80/107.00	    inference('cnf', [status(esa)], [zf_stmt_12])).
106.80/107.00	tff(zf_stmt_13, axiom,
106.80/107.00	  (((~halts2(Y,as_input(Y))) => (outputs(V,bad) & halts2(V,as_input(Y)))) =>
106.80/107.00	   zip_tseitin6(Y,V))).
106.80/107.00	tff('26', plain,
106.80/107.00	    ![X15 : program, X16 : program]:
106.80/107.00	      (zip_tseitin6(X15, X16) | ~ halts2(X15, as_input(X15))),
106.80/107.00	    inference('cnf', [status(esa)], [zf_stmt_13])).
106.80/107.00	tff(zf_stmt_14, type, zip_tseitin8 : (program * program) > $o).
106.80/107.00	tff(zf_stmt_15, axiom,
106.80/107.00	  (zip_tseitin8(Y,U) =>
106.80/107.00	   (((~halts2(Y,as_input(Y))) => zip_tseitin7(Y,U)) & 
106.80/107.00	    (halts2(Y,as_input(Y)) => (~halts2(U,as_input(Y))))))).
106.80/107.00	tff(zf_stmt_16, type, zip_tseitin7 : (program * program) > $o).
106.80/107.00	tff(zf_stmt_17, axiom,
106.80/107.00	  (zip_tseitin7(Y,U) => (outputs(U,bad) & halts2(U,as_input(Y))))).
106.80/107.00	tff(zf_stmt_18, type, zip_tseitin6 : (program * program) > $o).
106.80/107.00	tff(zf_stmt_19, type, zip_tseitin5 : (program * program) > $o).
106.80/107.00	tff(zf_stmt_20, axiom,
106.80/107.00	  ((?[V:program]: (![Y:program]: (zip_tseitin6(Y,V) & zip_tseitin5(Y,V)))) =>
106.80/107.00	   (?[U:program]: (![Y:program]: zip_tseitin8(Y,U))))).
106.80/107.00	tff('27', plain,
106.80/107.00	    ![X19 : program, X20 : program]:
106.80/107.00	      (zip_tseitin8(X19, sk_U)
106.80/107.00	       | ~ zip_tseitin5(sk_Y2(X20), X20)
106.80/107.00	       | ~ zip_tseitin6(sk_Y2(X20), X20)),
106.80/107.00	    inference('cnf', [status(esa)], [zf_stmt_20])).
106.80/107.00	tff('28', plain,
106.80/107.00	    ![X0 : program, X1 : program]:
106.80/107.00	      (~ $true
106.80/107.00	       | ~ halts2(sk_Y2(X0), as_input(sk_Y2(X0)))
106.80/107.00	       | ~ zip_tseitin5(sk_Y2(X0), X0)
106.80/107.00	       | zip_tseitin8(X1, sk_U)),
106.80/107.00	    inference('sup-', [status(thm)], ['26', '27'])).
106.80/107.00	tff('29', plain,
106.80/107.00	    ![X0 : program, X1 : program]:
106.80/107.00	      (zip_tseitin8(X1, sk_U)
106.80/107.00	       | ~ zip_tseitin5(sk_Y2(X0), X0)
106.80/107.00	       | ~ halts2(sk_Y2(X0), as_input(sk_Y2(X0)))),
106.80/107.00	    inference('simplify', [status(thm)], ['28'])).
106.80/107.00	tff('30', plain,
106.80/107.00	    ![X0 : program, X1 : program]:
106.80/107.00	      (~ $true
106.80/107.00	       | ~ halts2(X0, as_input(sk_Y2(X0)))
106.80/107.00	       | ~ outputs(X0, good)
106.80/107.00	       | ~ halts2(sk_Y2(X0), as_input(sk_Y2(X0)))
106.80/107.00	       | zip_tseitin8(X1, sk_U)),
106.80/107.00	    inference('sup-', [status(thm)], ['25', '29'])).
106.80/107.00	tff('31', plain,
106.80/107.00	    ![X0 : program, X1 : program]:
106.80/107.00	      (zip_tseitin8(X1, sk_U)
106.80/107.00	       | ~ halts2(sk_Y2(X0), as_input(sk_Y2(X0)))
106.80/107.00	       | ~ outputs(X0, good)
106.80/107.00	       | ~ halts2(X0, as_input(sk_Y2(X0)))),
106.80/107.00	    inference('simplify', [status(thm)], ['30'])).
106.80/107.00	tff('32', plain,
106.80/107.00	    ![X0 : program, X1 : program]:
106.80/107.00	      (~ $true
106.80/107.00	       | outputs(sk_W, bad)
106.80/107.00	       | ~ halts2(X0, as_input(sk_Y2(X0)))
106.80/107.00	       | ~ outputs(X0, good)
106.80/107.00	       | zip_tseitin8(X1, sk_U)),
106.80/107.00	    inference('sup-', [status(thm)], ['19', '31'])).
106.80/107.00	tff('33', plain,
106.80/107.00	    ![X0 : program, X1 : program]:
106.80/107.00	      (zip_tseitin8(X1, sk_U)
106.80/107.00	       | ~ outputs(X0, good)
106.80/107.00	       | ~ halts2(X0, as_input(sk_Y2(X0)))
106.80/107.00	       | outputs(sk_W, bad)),
106.80/107.00	    inference('simplify', [status(thm)], ['32'])).
106.80/107.00	tff('34', plain,
106.80/107.00	    ![X0 : program, X1 : program]:
106.80/107.00	      (outputs(sk_W, bad) | ~ outputs(X0, good) | zip_tseitin8(X1, sk_U)),
106.80/107.00	    inference('clc', [status(thm)], ['33', '19'])).
106.80/107.00	tff('35', plain,
106.80/107.00	    ![X0 : program]:
106.80/107.00	      (~ $true
106.80/107.00	       | outputs(sk_W, bad)
106.80/107.00	       | zip_tseitin8(X0, sk_U)
106.80/107.00	       | outputs(sk_W, bad)),
106.80/107.00	    inference('sup-', [status(thm)], ['24', '34'])).
106.80/107.00	tff('36', plain,
106.80/107.00	    ![X0 : program]: (zip_tseitin8(X0, sk_U) | outputs(sk_W, bad)),
106.80/107.00	    inference('simplify', [status(thm)], ['35'])).
106.80/107.00	tff('37', plain,
106.80/107.00	    ![X17 : program, X18 : program]:
106.80/107.00	      (~ halts2(X18, as_input(X18))
106.80/107.00	       | ~ halts2(X17, as_input(X18))
106.80/107.00	       | ~ zip_tseitin8(X18, X17)),
106.80/107.00	    inference('cnf', [status(esa)], [zf_stmt_15])).
106.80/107.00	tff('38', plain,
106.80/107.00	    ![X0 : program]:
106.80/107.00	      (~ $true
106.80/107.00	       | outputs(sk_W, bad)
106.80/107.00	       | ~ halts2(sk_U, as_input(X0))
106.80/107.00	       | ~ halts2(X0, as_input(X0))),
106.80/107.00	    inference('sup-', [status(thm)], ['36', '37'])).
106.80/107.00	tff('39', plain,
106.80/107.00	    ![X0 : program]:
106.80/107.00	      (~ halts2(X0, as_input(X0))
106.80/107.00	       | ~ halts2(sk_U, as_input(X0))
106.80/107.00	       | outputs(sk_W, bad)),
106.80/107.00	    inference('simplify', [status(thm)], ['38'])).
106.80/107.00	tff('40', plain,
106.80/107.00	    ![X0 : program]: (outputs(sk_W, bad) | ~ halts2(sk_U, as_input(X0))),
106.80/107.00	    inference('clc', [status(thm)], ['39', '19'])).
106.80/107.00	tff('41', plain, outputs(sk_W, bad),
106.80/107.00	    inference('clc', [status(thm)], ['40', '19'])).
106.80/107.00	tff('42', plain,
106.80/107.00	    ![X0 : program]:
106.80/107.00	      (~ $true
106.80/107.00	       | halts2(sk_Y1(sk_W), as_input(sk_Y1(sk_W)))
106.80/107.00	       | ~ $true
106.80/107.00	       | zip_tseitin4(X0, sk_V)),
106.80/107.00	    inference('demod', [status(thm)], ['16', '41'])).
106.80/107.00	tff('43', plain,
106.80/107.00	    ![X0 : program]:
106.80/107.00	      (zip_tseitin4(X0, sk_V) | halts2(sk_Y1(sk_W), as_input(sk_Y1(sk_W)))),
106.80/107.00	    inference('simplify', [status(thm)], ['42'])).
106.80/107.00	tff('44', plain,
106.80/107.00	    ![X0 : $tType, X1 : $tType, X2 : X0 > X1, X3 : X0 > X1]:
106.80/107.00	      (X2 = X3 | X2(zf_ext_diff(X2, X3)) != X3(zf_ext_diff(X2, X3))),
106.80/107.00	    trivial([status(thm)])).
106.80/107.00	tff('45', plain,
106.80/107.00	    ![X0 : $tType, X1 : $tType, X2 : X0 > X1, X3 : X0 > X1, X4 : X0 > X1, 
106.80/107.00	      X5 : X0 > X1]:
106.80/107.00	      (X5 != X3
106.80/107.00	       | X4 != X2
106.80/107.00	       | X2 = X3
106.80/107.00	       | X2(zf_ext_diff(X4, X3)) != X5(zf_ext_diff(X4, X3))),
106.80/107.00	    inference('ho.purify_applied_variable', [status(thm)], ['44'])).
106.80/107.00	tff('46', plain,
106.80/107.00	    ![X0 : program, X1 : input > $o, X2 : input > $o, X3 : input > $o]:
106.80/107.00	      (X3(zf_ext_diff(X2, X1)) != $true
106.80/107.00	       | X3 = X1
106.80/107.00	       | X2 != X3
106.80/107.00	       | decides(sk_X1, X0) != X1),
106.80/107.00	    inference('sup-', [status(thm)], ['0', '45'])).
106.80/107.00	tff('47', plain,
106.80/107.00	    ![X0 : program, X1 : input > $o, X2 : input > $o, X3 : program]:
106.80/107.00	      ($true != $true
106.80/107.00	       | decides(sk_X1, X3) != X1
106.80/107.00	       | X2 != decides(sk_X1, X0)
106.80/107.00	       | decides(sk_X1, X0) = X1),
106.80/107.00	    inference('sup-', [status(thm)], ['0', '46'])).
106.80/107.00	tff('48', plain,
106.80/107.00	    ![X0 : program, X1 : input > $o, X2 : input > $o, X3 : program]:
106.80/107.00	      (decides(sk_X1, X0) = X1
106.80/107.00	       | X2 != decides(sk_X1, X0)
106.80/107.00	       | decides(sk_X1, X3) != X1),
106.80/107.00	    inference('simplify', [status(thm)], ['47'])).
106.80/107.00	tff('49', plain,
106.80/107.00	    ![X0 : program, X1 : input > $o, X2 : program]:
106.80/107.00	      (decides(sk_X1, X0) != X1 | decides(sk_X1, X2) = X1),
106.80/107.00	    inference('eq_res', [status(thm)], ['48'])).
106.80/107.00	tff('50', plain,
106.80/107.00	    ![X0 : program, X1 : program]: decides(sk_X1, X0) = decides(sk_X1, X1),
106.80/107.00	    inference('eq_res', [status(thm)], ['49'])).
106.80/107.00	tff('51', plain,
106.80/107.00	    ![X0 : program, X1 : (program * input) > $o, 
106.80/107.00	      X2 : (program * input) > $o, X3 : (program * input) > $o]:
106.80/107.00	      (decides(sk_X1, X0) != X1(zf_ext_diff(X3, X2))
106.80/107.00	       | decides(sk_X1) = X2
106.80/107.00	       | X3 != decides(sk_X1)
106.80/107.00	       | X1 != X2),
106.80/107.00	    inference('sup-', [status(thm)], ['50', '45'])).
106.80/107.00	tff('52', plain,
106.80/107.00	    ![X0 : program, X1 : (program * input) > $o, 
106.80/107.00	      X2 : (program * input) > $o, X3 : (program * input) > $o]:
106.80/107.00	      (decides(sk_X1, X0, '#k4'(X0, X1, X2, X3))
106.80/107.00	        != X1(zf_ext_diff(X3, X2), '#k4'(X0, X1, X2, X3))
106.80/107.00	       | decides(sk_X1) = X2
106.80/107.00	       | X3 != decides(sk_X1)
106.80/107.00	       | X1 != X2),
106.80/107.00	    inference('rw_lit', [status(thm)], ['51'])).
106.80/107.00	tff('53', plain,
106.80/107.00	    ![X0 : program, X1 : (program * input) > $o, 
106.80/107.00	      X2 : (program * input) > $o, X3 : (program * input) > $o, 
106.80/107.00	      X4 : (program * input) > $o]:
106.80/107.00	      (X4 != X1
106.80/107.00	       | decides(sk_X1, X0, '#k4'(X0, X1, X2, X3))
106.80/107.00	          != X4(zf_ext_diff(X3, X2), '#k4'(X0, X1, X2, X3))
106.80/107.00	       | decides(sk_X1) = X2
106.80/107.00	       | X3 != decides(sk_X1)
106.80/107.00	       | X1 != X2),
106.80/107.00	    inference('ho.purify_applied_variable', [status(thm)], ['52'])).
106.80/107.00	tff('54', plain,
106.80/107.00	    ![X0 : program, X1 : (program * input) > $o, 
106.80/107.00	      X2 : (program * input) > $o, X3 : (program * input) > $o, 
106.80/107.00	      X4 : (program * input) > $o]:
106.80/107.00	      (X4 != X1
106.80/107.00	       | $true != X4(zf_ext_diff(X3, X2), '#k4'(X0, X1, X2, X3))
106.80/107.00	       | decides(sk_X1) = X2
106.80/107.00	       | X3 != decides(sk_X1)
106.80/107.00	       | X1 != X2),
106.80/107.00	    inference('demod', [status(thm)], ['53', '0'])).
106.80/107.00	tff('55', plain,
106.80/107.00	    ![X0 : (program * input) > $o, X1 : (program * input) > $o, 
106.80/107.00	      X2 : (program * input) > $o]:
106.80/107.00	      ($true != $true
106.80/107.00	       | X2 != X1
106.80/107.00	       | X0 != decides(sk_X1)
106.80/107.00	       | decides(sk_X1) = X1
106.80/107.00	       | halts3(sk_W) != X2),
106.80/107.00	    inference('sup-', [status(thm)], ['8', '54'])).
106.80/107.00	tff('56', plain,
106.80/107.00	    ![X0 : (program * input) > $o, X1 : (program * input) > $o, 
106.80/107.00	      X2 : (program * input) > $o]:
106.80/107.00	      (halts3(sk_W) != X2
106.80/107.00	       | decides(sk_X1) = X1
106.80/107.00	       | X0 != decides(sk_X1)
106.80/107.00	       | X2 != X1),
106.80/107.00	    inference('simplify', [status(thm)], ['55'])).
106.80/107.00	tff('57', plain,
106.80/107.00	    ![X0 : (program * input) > $o, X1 : (program * input) > $o]:
106.80/107.00	      (X0 != X1 | decides(sk_X1) = X1 | halts3(sk_W) != X0),
106.80/107.00	    inference('eq_res', [status(thm)], ['56'])).
106.80/107.00	tff('58', plain,
106.80/107.00	    ![X0 : (program * input) > $o, X1 : (program * input) > $o, 
106.80/107.00	      X2 : program, X3 : input]:
106.80/107.00	      (decides(sk_X1, X2, X3) = X1(X2, X3) | halts3(sk_W) != X0 | X0 != X1),
106.80/107.00	    inference('ho_complete_eq', [status(thm)], ['57'])).
106.80/107.00	tff('59', plain,
106.80/107.00	    ![X0 : (program * input) > $o, X1 : (program * input) > $o, 
106.80/107.00	      X2 : program, X3 : input]:
106.80/107.00	      ($true = X1(X2, X3) | halts3(sk_W) != X0 | X0 != X1),
106.80/107.00	    inference('demod', [status(thm)], ['58', '0'])).
106.80/107.00	tff('60', plain,
106.80/107.00	    ![X0 : (program * input) > $o]:
106.80/107.00	      (halts3(sk_W) != X0 | decides(sk_X1) = X0),
106.80/107.00	    inference('eq_res', [status(thm)], ['57'])).
106.80/107.00	tff('61', plain,
106.80/107.00	    ![X0 : (program * input) > $o, X1 : program]:
106.80/107.00	      (decides(sk_X1, X1) = X0(X1) | halts3(sk_W) != X0),
106.80/107.00	    inference('ho_complete_eq', [status(thm)], ['60'])).
106.80/107.00	tff('62', plain,
106.80/107.00	    ![X0 : (program * input) > $o, X1 : program, X2 : (program * input) > $o]:
106.80/107.00	      (X2 != X0 | decides(sk_X1, X1) = X0(X1) | halts3(sk_W) != X2),
106.80/107.00	    inference('ho.purify_applied_variable', [status(thm)], ['61'])).
106.80/107.00	tff('63', plain,
106.80/107.00	    ![X0 : input > $o, X1 : input > $o, X2 : input > $o, X3 : program]:
106.80/107.00	      ($true != X0(zf_ext_diff(X2, X1))
106.80/107.00	       | decides(sk_X1, X3) = X1
106.80/107.00	       | X2 != decides(sk_X1, X3)
106.80/107.00	       | X0 != X1),
106.80/107.00	    inference('sup-', [status(thm)], ['0', '45'])).
106.80/107.00	tff('64', plain,
106.80/107.00	    ![X0 : input > $o, X1 : input > $o, X2 : program]:
106.80/107.00	      (X0 != X1
106.80/107.00	       | decides(sk_X1, X2) = X1
106.80/107.00	       | ~ X0(zf_ext_diff(decides(sk_X1, X2), X1))),
106.80/107.00	    inference('eq_res', [status(thm)], ['63'])).
106.80/107.00	tff('65', plain,
106.80/107.00	    ![X0 : program, X1 : input > $o, X2 : program]:
106.80/107.00	      (~ $true
106.80/107.00	       | decides(sk_X1, X2) = X1
106.80/107.00	       | decides(algorithm_of(sk_W), X0) != X1),
106.80/107.00	    inference('sup-', [status(thm)], ['3', '64'])).
106.80/107.00	tff('66', plain,
106.80/107.00	    ![X0 : program, X1 : input > $o, X2 : program]:
106.80/107.00	      (decides(algorithm_of(sk_W), X0) != X1 | decides(sk_X1, X2) = X1),
106.80/107.00	    inference('simplify', [status(thm)], ['65'])).
106.80/107.00	tff('67', plain,
106.80/107.00	    ![X0 : program, X1 : program]:
106.80/107.00	      decides(sk_X1, X0) = decides(algorithm_of(sk_W), X1),
106.80/107.00	    inference('eq_res', [status(thm)], ['66'])).
106.80/107.00	tff('68', plain,
106.80/107.00	    ![X0 : (program * input) > $o, X1 : program, X2 : (program * input) > $o]:
106.80/107.00	      (X2 != X0
106.80/107.00	       | decides(algorithm_of(sk_W), X1) = X0(X1)
106.80/107.00	       | halts3(sk_W) != X2),
106.80/107.00	    inference('demod', [status(thm)], ['62', '67'])).
106.80/107.00	tff('69', plain,
106.80/107.00	    ![X0 : (program * input) > $o, X2 : (program * input) > $o]:
106.80/107.00	      (decides(algorithm_of(sk_W)) = X0 | halts3(sk_W) != X2 | X2 != X0),
106.80/107.00	    inference('ho_ext_pos_general', [status(thm)], ['68'])).
106.80/107.00	tff('70', plain,
106.80/107.00	    ![X0 : (program * input) > $o]:
106.80/107.00	      (halts3(sk_W) != X0 | decides(algorithm_of(sk_W)) = X0),
106.80/107.00	    inference('eq_res', [status(thm)], ['69'])).
106.80/107.00	tff('71', plain, decides(algorithm_of(sk_W)) = halts3(sk_W),
106.80/107.00	    inference('eq_res', [status(thm)], ['70'])).
106.80/107.00	tff('72', plain,
106.80/107.00	    ![X0 : (program * input) > $o, X1 : (program * input) > $o, 
106.80/107.00	      X2 : program, X3 : input]:
106.80/107.00	      ($true = X1(X2, X3) | decides(algorithm_of(sk_W)) != X0 | X0 != X1),
106.80/107.00	    inference('demod', [status(thm)], ['59', '71'])).
106.80/107.00	tff('73', plain,
106.80/107.00	    ![X2 : program, X3 : input, X4 : program, X5 : (program * input) > $o]:
106.80/107.00	      (~ $true
106.80/107.00	       | X5 != decides(algorithm_of(X2))
106.80/107.00	       | decides(algorithm_of(sk_W)) != X5
106.80/107.00	       | halts3(X2, X4, X3)),
106.80/107.00	    inference('sup-', [status(thm)], ['72', '6'])).
106.80/107.00	tff('74', plain,
106.80/107.00	    ![X2 : program, X3 : input, X4 : program, X5 : (program * input) > $o]:
106.80/107.00	      (halts3(X2, X4, X3)
106.80/107.00	       | decides(algorithm_of(sk_W)) != X5
106.80/107.00	       | X5 != decides(algorithm_of(X2))),
106.80/107.00	    inference('simplify', [status(thm)], ['73'])).
106.80/107.00	tff('75', plain,
106.80/107.00	    ![X0 : program, X1 : input, X2 : program]:
106.80/107.00	      (decides(algorithm_of(sk_W)) != decides(algorithm_of(X0))
106.80/107.00	       | halts3(X0, X2, X1)),
106.80/107.00	    inference('eq_res', [status(thm)], ['74'])).
106.80/107.00	tff('76', plain,
106.80/107.00	    ![X0 : program, X1 : input, X2 : program]:
106.80/107.00	      (decides(algorithm_of(sk_W), '#k90'(X0), '#k91'(X0))
106.80/107.00	        != decides(algorithm_of(X0), '#k90'(X0), '#k91'(X0))
106.80/107.00	       | halts3(X0, X2, X1)),
106.80/107.00	    inference('rw_lit', [status(thm)], ['75'])).
106.80/107.00	tff('77', plain,
106.80/107.00	    ![X0 : program, X1 : input, X2 : program]:
106.80/107.00	      ($true != decides(algorithm_of(X0), '#k90'(X0), '#k91'(X0))
106.80/107.00	       | halts3(X0, X2, X1)),
106.80/107.00	    inference('demod', [status(thm)], ['76', '3'])).
106.80/107.00	tff('78', plain,
106.80/107.00	    ![X9 : program, X10 : program]:
106.80/107.00	      (zip_tseitin0(X9, X10)
106.80/107.00	       | ~ outputs(X10, good)
106.80/107.00	       | ~ halts3(X10, X9, as_input(X9))),
106.80/107.00	    inference('cnf', [status(esa)], [zf_stmt_1])).
106.80/107.00	tff('79', plain,
106.80/107.00	    ![X9 : program, X10 : program]:
106.80/107.00	      (zip_tseitin1(X9, X10) | ~ halts2(X9, as_input(X9))),
106.80/107.00	    inference('cnf', [status(esa)], [zf_stmt_2])).
106.80/107.00	tff('80', plain,
106.80/107.00	    ![X0 : program, X1 : program]:
106.80/107.00	      (~ $true
106.80/107.00	       | ~ halts2(sk_Y1(X0), as_input(sk_Y1(X0)))
106.80/107.00	       | ~ zip_tseitin0(sk_Y1(X0), X0)
106.80/107.00	       | zip_tseitin4(X1, sk_V)),
106.80/107.00	    inference('sup-', [status(thm)], ['79', '11'])).
106.80/107.00	tff('81', plain,
106.80/107.00	    ![X0 : program, X1 : program]:
106.80/107.00	      (zip_tseitin4(X1, sk_V)
106.80/107.00	       | ~ zip_tseitin0(sk_Y1(X0), X0)
106.80/107.00	       | ~ halts2(sk_Y1(X0), as_input(sk_Y1(X0)))),
106.80/107.00	    inference('simplify', [status(thm)], ['80'])).
106.80/107.00	tff('82', plain,
106.80/107.00	    ![X0 : program, X1 : program]:
106.80/107.00	      (~ $true
106.80/107.00	       | ~ halts3(X0, sk_Y1(X0), as_input(sk_Y1(X0)))
106.80/107.00	       | ~ outputs(X0, good)
106.80/107.00	       | ~ halts2(sk_Y1(X0), as_input(sk_Y1(X0)))
106.80/107.00	       | zip_tseitin4(X1, sk_V)),
106.80/107.00	    inference('sup-', [status(thm)], ['78', '81'])).
106.80/107.00	tff('83', plain,
106.80/107.00	    ![X0 : program, X1 : program]:
106.80/107.00	      (zip_tseitin4(X1, sk_V)
106.80/107.00	       | ~ halts2(sk_Y1(X0), as_input(sk_Y1(X0)))
106.80/107.00	       | ~ outputs(X0, good)
106.80/107.00	       | ~ halts3(X0, sk_Y1(X0), as_input(sk_Y1(X0)))),
106.80/107.00	    inference('simplify', [status(thm)], ['82'])).
106.80/107.00	tff('84', plain,
106.80/107.00	    ![X0 : program, X1 : program]:
106.80/107.00	      (~ $true
106.80/107.00	       | ~ decides(algorithm_of(X0), '#k90'(X0), '#k91'(X0))
106.80/107.00	       | ~ outputs(X0, good)
106.80/107.00	       | ~ halts2(sk_Y1(X0), as_input(sk_Y1(X0)))
106.80/107.00	       | zip_tseitin4(X1, sk_V)),
106.80/107.00	    inference('sup-', [status(thm)], ['77', '83'])).
106.80/107.00	tff('85', plain,
106.80/107.00	    ![X0 : program, X1 : program]:
106.80/107.00	      (zip_tseitin4(X1, sk_V)
106.80/107.00	       | ~ halts2(sk_Y1(X0), as_input(sk_Y1(X0)))
106.80/107.00	       | ~ outputs(X0, good)
106.80/107.00	       | ~ decides(algorithm_of(X0), '#k90'(X0), '#k91'(X0))),
106.80/107.00	    inference('simplify', [status(thm)], ['84'])).
106.80/107.00	tff('86', plain,
106.80/107.00	    ![X0 : program, X1 : program]:
106.80/107.00	      (~ decides(algorithm_of(X0), '#k90'(X0), '#k91'(X0))
106.80/107.00	       | ~ halts2(sk_Y1(X0), as_input(sk_Y1(X0)))
106.80/107.00	       | zip_tseitin4(X1, sk_V)),
106.80/107.00	    inference('clc', [status(thm)], ['85', '20'])).
106.80/107.00	tff('87', plain,
106.80/107.00	    ![X0 : program, X1 : program]:
106.80/107.00	      (~ $true
106.80/107.00	       | zip_tseitin4(X1, sk_V)
106.80/107.00	       | zip_tseitin4(X0, sk_V)
106.80/107.00	       | ~ decides(algorithm_of(sk_W), '#k90'(sk_W), '#k91'(sk_W))),
106.80/107.00	    inference('sup-', [status(thm)], ['43', '86'])).
106.80/107.00	tff('88', plain,
106.80/107.00	    ![X0 : program, X1 : program]:
106.80/107.00	      (~ $true | zip_tseitin4(X1, sk_V) | zip_tseitin4(X0, sk_V) | ~ $true),
106.80/107.00	    inference('demod', [status(thm)], ['87', '3'])).
106.80/107.00	tff('89', plain,
106.80/107.00	    ![X0 : program, X1 : program]:
106.80/107.00	      (zip_tseitin4(X0, sk_V) | zip_tseitin4(X1, sk_V)),
106.80/107.00	    inference('simplify', [status(thm)], ['88'])).
106.80/107.00	tff('90', plain, ![X0 : program]: zip_tseitin4(X0, sk_V),
106.80/107.00	    inference('condensation', [status(thm)], ['89'])).
106.80/107.00	tff('91', plain,
106.80/107.00	    ![X11 : program, X12 : program]:
106.80/107.00	      (halts2(X12, as_input(X12))
106.80/107.00	       | zip_tseitin3(X12, X11)
106.80/107.00	       | ~ zip_tseitin4(X12, X11)),
106.80/107.00	    inference('cnf', [status(esa)], [zf_stmt_4])).
106.80/107.00	tff('92', plain,
106.80/107.00	    ![X0 : program]:
106.80/107.00	      (~ $true | zip_tseitin3(X0, sk_V) | halts2(X0, as_input(X0))),
106.80/107.00	    inference('sup-', [status(thm)], ['90', '91'])).
106.80/107.00	tff('93', plain,
106.80/107.00	    ![X0 : program]: (halts2(X0, as_input(X0)) | zip_tseitin3(X0, sk_V)),
106.80/107.00	    inference('simplify', [status(thm)], ['92'])).
106.80/107.00	tff('94', plain,
106.80/107.00	    ![X11 : program, X12 : program]:
106.80/107.00	      (outputs(X11, bad) | ~ zip_tseitin3(X12, X11)),
106.80/107.00	    inference('cnf', [status(esa)], [zf_stmt_6])).
106.80/107.00	tff('95', plain,
106.80/107.00	    ![X0 : program]:
106.80/107.00	      (~ $true | halts2(X0, as_input(X0)) | outputs(sk_V, bad)),
106.80/107.00	    inference('sup-', [status(thm)], ['93', '94'])).
106.80/107.00	tff('96', plain,
106.80/107.00	    ![X0 : program]: (outputs(sk_V, bad) | halts2(X0, as_input(X0))),
106.80/107.00	    inference('simplify', [status(thm)], ['95'])).
106.80/107.00	tff('97', plain,
106.80/107.00	    ![X11 : program, X12 : program]:
106.80/107.00	      (~ halts2(X12, as_input(X12))
106.80/107.00	       | zip_tseitin2(X12, X11)
106.80/107.00	       | ~ zip_tseitin4(X12, X11)),
106.80/107.00	    inference('cnf', [status(esa)], [zf_stmt_4])).
106.80/107.00	tff('98', plain,
106.80/107.00	    ![X0 : program]:
106.80/107.00	      (~ $true | zip_tseitin2(X0, sk_V) | ~ halts2(X0, as_input(X0))),
106.80/107.00	    inference('sup-', [status(thm)], ['90', '97'])).
106.80/107.00	tff('99', plain,
106.80/107.00	    ![X0 : program]: (~ halts2(X0, as_input(X0)) | zip_tseitin2(X0, sk_V)),
106.80/107.00	    inference('simplify', [status(thm)], ['98'])).
106.80/107.00	tff('100', plain,
106.80/107.00	    ![X11 : program, X12 : program]:
106.80/107.00	      (halts2(X11, as_input(X12)) | ~ zip_tseitin2(X12, X11)),
106.80/107.00	    inference('cnf', [status(esa)], [zf_stmt_8])).
106.80/107.00	tff('101', plain,
106.80/107.00	    ![X0 : program]:
106.80/107.00	      (~ $true | ~ halts2(X0, as_input(X0)) | halts2(sk_V, as_input(X0))),
106.80/107.00	    inference('sup-', [status(thm)], ['99', '100'])).
106.80/107.00	tff('102', plain,
106.80/107.00	    ![X0 : program]:
106.80/107.00	      (halts2(sk_V, as_input(X0)) | ~ halts2(X0, as_input(X0))),
106.80/107.00	    inference('simplify', [status(thm)], ['101'])).
106.80/107.00	tff('103', plain,
106.80/107.00	    ![X11 : program, X12 : program]:
106.80/107.00	      (halts2(X11, as_input(X12)) | ~ zip_tseitin3(X12, X11)),
106.80/107.00	    inference('cnf', [status(esa)], [zf_stmt_6])).
106.80/107.00	tff('104', plain,
106.80/107.00	    ![X0 : program]:
106.80/107.00	      (~ $true | halts2(X0, as_input(X0)) | halts2(sk_V, as_input(X0))),
106.80/107.00	    inference('sup-', [status(thm)], ['93', '103'])).
106.80/107.00	tff('105', plain,
106.80/107.00	    ![X0 : program]: (halts2(sk_V, as_input(X0)) | halts2(X0, as_input(X0))),
106.80/107.00	    inference('simplify', [status(thm)], ['104'])).
106.80/107.00	tff('106', plain, ![X0 : program]: halts2(sk_V, as_input(X0)),
106.80/107.00	    inference('clc', [status(thm)], ['102', '105'])).
106.80/107.00	tff('107', plain,
106.80/107.00	    ![X15 : program, X16 : program]:
106.80/107.00	      (zip_tseitin6(X15, X16)
106.80/107.00	       | ~ outputs(X16, bad)
106.80/107.00	       | ~ halts2(X16, as_input(X15))),
106.80/107.00	    inference('cnf', [status(esa)], [zf_stmt_13])).
106.80/107.00	tff('108', plain,
106.80/107.00	    ![X0 : program, X1 : program]:
106.80/107.00	      (~ $true
106.80/107.00	       | ~ halts2(X0, as_input(sk_Y2(X0)))
106.80/107.00	       | ~ outputs(X0, bad)
106.80/107.00	       | ~ zip_tseitin5(sk_Y2(X0), X0)
106.80/107.00	       | zip_tseitin8(X1, sk_U)),
106.80/107.00	    inference('sup-', [status(thm)], ['107', '27'])).
106.80/107.00	tff('109', plain,
106.80/107.00	    ![X0 : program, X1 : program]:
106.80/107.00	      (zip_tseitin8(X1, sk_U)
106.80/107.00	       | ~ zip_tseitin5(sk_Y2(X0), X0)
106.80/107.00	       | ~ outputs(X0, bad)
106.80/107.00	       | ~ halts2(X0, as_input(sk_Y2(X0)))),
106.80/107.00	    inference('simplify', [status(thm)], ['108'])).
106.80/107.00	tff('110', plain,
106.80/107.00	    ![X0 : program, X1 : program]:
106.80/107.00	      (~ $true
106.80/107.00	       | ~ halts2(X0, as_input(sk_Y2(X0)))
106.80/107.00	       | ~ outputs(X0, good)
106.80/107.00	       | ~ halts2(X0, as_input(sk_Y2(X0)))
106.80/107.00	       | ~ outputs(X0, bad)
106.80/107.00	       | zip_tseitin8(X1, sk_U)),
106.80/107.00	    inference('sup-', [status(thm)], ['25', '109'])).
106.80/107.00	tff('111', plain,
106.80/107.00	    ![X0 : program, X1 : program]:
106.80/107.00	      (zip_tseitin8(X1, sk_U)
106.80/107.00	       | ~ outputs(X0, bad)
106.80/107.00	       | ~ outputs(X0, good)
106.80/107.00	       | ~ halts2(X0, as_input(sk_Y2(X0)))),
106.80/107.00	    inference('simplify', [status(thm)], ['110'])).
106.80/107.00	tff('112', plain,
106.80/107.00	    ![X0 : program]:
106.80/107.00	      (~ $true
106.80/107.00	       | ~ outputs(sk_V, good)
106.80/107.00	       | ~ outputs(sk_V, bad)
106.80/107.00	       | zip_tseitin8(X0, sk_U)),
106.80/107.00	    inference('sup-', [status(thm)], ['106', '111'])).
106.80/107.00	tff('113', plain, (~ $true | halts2(sk_V, as_input(sk_V))),
106.80/107.00	    inference('eq_fact', [status(thm)], ['105'])).
106.80/107.00	tff('114', plain, halts2(sk_V, as_input(sk_V)),
106.80/107.00	    inference('simplify', [status(thm)], ['113'])).
106.80/107.00	tff('115', plain,
106.80/107.00	    ![X11 : program, X12 : program]:
106.80/107.00	      (outputs(X11, good) | ~ zip_tseitin2(X12, X11)),
106.80/107.00	    inference('cnf', [status(esa)], [zf_stmt_8])).
106.80/107.00	tff('116', plain,
106.80/107.00	    ![X0 : program]:
106.80/107.00	      (~ $true | ~ halts2(X0, as_input(X0)) | outputs(sk_V, good)),
106.80/107.00	    inference('sup-', [status(thm)], ['99', '115'])).
106.80/107.00	tff('117', plain,
106.80/107.00	    ![X0 : program]: (outputs(sk_V, good) | ~ halts2(X0, as_input(X0))),
106.80/107.00	    inference('simplify', [status(thm)], ['116'])).
106.80/107.00	tff('118', plain, (~ $true | outputs(sk_V, good)),
106.80/107.00	    inference('sup-', [status(thm)], ['114', '117'])).
106.80/107.00	tff('119', plain, outputs(sk_V, good),
106.80/107.00	    inference('simplify', [status(thm)], ['118'])).
106.80/107.00	tff('120', plain,
106.80/107.00	    ![X0 : program]:
106.80/107.00	      (~ $true | ~ $true | ~ outputs(sk_V, bad) | zip_tseitin8(X0, sk_U)),
106.80/107.00	    inference('demod', [status(thm)], ['112', '119'])).
106.80/107.00	tff('121', plain,
106.80/107.00	    ![X0 : program]: (zip_tseitin8(X0, sk_U) | ~ outputs(sk_V, bad)),
106.80/107.00	    inference('simplify', [status(thm)], ['120'])).
106.80/107.00	tff('122', plain,
106.80/107.00	    ![X0 : program, X1 : program]:
106.80/107.00	      (~ $true | halts2(X1, as_input(X1)) | zip_tseitin8(X0, sk_U)),
106.80/107.00	    inference('sup-', [status(thm)], ['96', '121'])).
106.80/107.00	tff('123', plain,
106.80/107.00	    ![X0 : program, X1 : program]:
106.80/107.00	      (zip_tseitin8(X0, sk_U) | halts2(X1, as_input(X1))),
106.80/107.00	    inference('simplify', [status(thm)], ['122'])).
106.80/107.00	tff('124', plain,
106.80/107.00	    ![X17 : program, X18 : program]:
106.80/107.00	      (halts2(X18, as_input(X18))
106.80/107.00	       | zip_tseitin7(X18, X17)
106.80/107.00	       | ~ zip_tseitin8(X18, X17)),
106.80/107.00	    inference('cnf', [status(esa)], [zf_stmt_15])).
106.80/107.00	tff('125', plain,
106.80/107.00	    ![X0 : program, X1 : program]:
106.80/107.00	      (~ $true
106.80/107.00	       | halts2(X1, as_input(X1))
106.80/107.00	       | zip_tseitin7(X0, sk_U)
106.80/107.00	       | halts2(X0, as_input(X0))),
106.80/107.00	    inference('sup-', [status(thm)], ['123', '124'])).
106.80/107.00	tff('126', plain,
106.80/107.00	    ![X0 : program, X1 : program]:
106.80/107.00	      (halts2(X0, as_input(X0))
106.80/107.00	       | zip_tseitin7(X0, sk_U)
106.80/107.00	       | halts2(X1, as_input(X1))),
106.80/107.00	    inference('simplify', [status(thm)], ['125'])).
106.80/107.00	tff('127', plain,
106.80/107.00	    ![X0 : program]: (halts2(X0, as_input(X0)) | zip_tseitin7(X0, sk_U)),
106.80/107.00	    inference('condensation', [status(thm)], ['126'])).
106.80/107.00	tff('128', plain,
106.80/107.00	    ![X17 : program, X18 : program]:
106.80/107.00	      (halts2(X17, as_input(X18)) | ~ zip_tseitin7(X18, X17)),
106.80/107.00	    inference('cnf', [status(esa)], [zf_stmt_17])).
106.80/107.00	tff('129', plain,
106.80/107.00	    ![X0 : program]:
106.80/107.00	      (~ $true | halts2(X0, as_input(X0)) | halts2(sk_U, as_input(X0))),
106.80/107.00	    inference('sup-', [status(thm)], ['127', '128'])).
106.80/107.00	tff('130', plain,
106.80/107.00	    ![X0 : program]: (halts2(sk_U, as_input(X0)) | halts2(X0, as_input(X0))),
106.80/107.00	    inference('simplify', [status(thm)], ['129'])).
106.80/107.00	tff('131', plain, (~ $true | halts2(sk_U, as_input(sk_U))),
106.80/107.00	    inference('eq_fact', [status(thm)], ['130'])).
106.80/107.00	tff('132', plain, halts2(sk_U, as_input(sk_U)),
106.80/107.00	    inference('simplify', [status(thm)], ['131'])).
106.80/107.00	tff('133', plain,
106.80/107.00	    ![X0 : program, X1 : program]:
106.80/107.00	      (~ $true
106.80/107.00	       | halts2(X1, as_input(X1))
106.80/107.00	       | ~ halts2(sk_U, as_input(X0))
106.80/107.00	       | ~ halts2(X0, as_input(X0))),
106.80/107.00	    inference('sup-', [status(thm)], ['123', '37'])).
106.80/107.00	tff('134', plain,
106.80/107.00	    ![X0 : program, X1 : program]:
106.80/107.00	      (~ halts2(X0, as_input(X0))
106.80/107.00	       | ~ halts2(sk_U, as_input(X0))
106.80/107.00	       | halts2(X1, as_input(X1))),
106.80/107.00	    inference('simplify', [status(thm)], ['133'])).
106.80/107.00	tff('135', plain,
106.80/107.00	    ![X0 : program]:
106.80/107.00	      (~ $true | halts2(X0, as_input(X0)) | ~ halts2(sk_U, as_input(sk_U))),
106.80/107.00	    inference('sup-', [status(thm)], ['132', '134'])).
106.80/107.00	tff('136', plain,
106.80/107.00	    ![X0 : program]: (~ $true | halts2(X0, as_input(X0)) | ~ $true),
106.80/107.00	    inference('demod', [status(thm)], ['135', '132'])).
106.80/107.00	tff('137', plain, ![X0 : program]: halts2(X0, as_input(X0)),
106.80/107.00	    inference('simplify', [status(thm)], ['136'])).
106.80/107.00	tff('138', plain,
106.80/107.00	    ![X0 : program, X1 : program]:
106.80/107.00	      (~ $true
106.80/107.00	       | ~ halts2(X0, as_input(sk_Y2(X0)))
106.80/107.00	       | ~ outputs(X0, good)
106.80/107.00	       | zip_tseitin8(X1, sk_U)),
106.80/107.00	    inference('sup-', [status(thm)], ['137', '31'])).
106.80/107.00	tff('139', plain,
106.80/107.00	    ![X0 : program, X1 : program]:
106.80/107.00	      (zip_tseitin8(X1, sk_U)
106.80/107.00	       | ~ outputs(X0, good)
106.80/107.00	       | ~ halts2(X0, as_input(sk_Y2(X0)))),
106.80/107.00	    inference('simplify', [status(thm)], ['138'])).
106.80/107.00	tff('140', plain,
106.80/107.00	    ![X0 : program]:
106.80/107.00	      (~ $true | ~ outputs(sk_V, good) | zip_tseitin8(X0, sk_U)),
106.80/107.00	    inference('sup-', [status(thm)], ['106', '139'])).
106.80/107.00	tff('141', plain,
106.80/107.00	    ![X0 : program]: (~ $true | ~ $true | zip_tseitin8(X0, sk_U)),
106.80/107.00	    inference('demod', [status(thm)], ['140', '119'])).
106.80/107.00	tff('142', plain, ![X0 : program]: zip_tseitin8(X0, sk_U),
106.80/107.00	    inference('simplify', [status(thm)], ['141'])).
106.80/107.00	tff('143', plain,
106.80/107.00	    ![X0 : program]:
106.80/107.00	      (~ $true | ~ halts2(sk_U, as_input(X0)) | ~ halts2(X0, as_input(X0))),
106.80/107.00	    inference('sup-', [status(thm)], ['142', '37'])).
106.80/107.00	tff('144', plain,
106.80/107.00	    ![X0 : program]: (~ $true | ~ halts2(sk_U, as_input(X0)) | ~ $true),
106.80/107.00	    inference('demod', [status(thm)], ['143', '137'])).
106.80/107.00	tff('145', plain, ![X0 : program]: ~ halts2(sk_U, as_input(X0)),
106.80/107.00	    inference('simplify', [status(thm)], ['144'])).
106.80/107.00	tff('146', plain, ~ $true, inference('sup-', [status(thm)], ['137', '145'])).
106.80/107.00	tff('147', plain, $false, inference('simplify', [status(thm)], ['146'])).
106.80/107.00	
106.80/107.00	% SZS output end Refutation
106.80/107.00	EOF
