0.00/0.01	% File    : /export/starexec/sandbox/benchmark/theBenchmark.p
0.00/0.01	% app-encoded or not : original
0.00/0.01	% Variant    : purification_ext
0.00/0.01	% Ordering    : kbo
0.00/0.01	% Command    : 
0.00/0.01	#!/bin/sh
0.00/0.01	
0.00/0.01	./zipperposition.native ${1:+"$1"} \
0.00/0.01	  -i tptp \
0.00/0.01	  -o tptp \
0.00/0.01	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.01	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.01	  --no-avatar \
0.00/0.01	  --ho \
0.00/0.01	  --force-ho \
0.00/0.01	  --no-ho-elim-pred-var \
0.00/0.01	  --ho-general-ext-pos \
0.00/0.01	  --no-ho-unif \
0.00/0.01	  --no-induction \
0.00/0.01	  --no-unif-pattern \
0.00/0.01	  --ord $2  \
0.00/0.01	  --simultaneous-sup false \
0.00/0.01	  --ho-purify ext \
0.00/0.01	  --ho-ext-axiom \
0.00/0.01	  --restrict-hidden-sup-at-vars \
0.00/0.01	  --ho-prim-enum none \
0.00/0.01	  --no-max-vars \
0.00/0.01	  --dont-select-ho-var-lits \
0.00/0.01	  --no-fool
0.00/0.20	% Computer   : n031.star.cs.uiowa.edu
0.00/0.20	% Model      : x86_64 x86_64
0.00/0.20	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.20	% Memory     : 32218.625MB
0.00/0.20	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.20	% CPULimit   : 300
0.00/0.20	% DateTime   : Fri Feb  2 08:22:09 CST 2018
1.33/1.53	% done 895 iterations in 1.327s
1.33/1.53	% SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
1.33/1.53	% SZS output start Refutation
1.33/1.54	tff(prove_this, conjecture,
1.33/1.54	  (~(?[X1:algorithm]: (![Y1:program,Z1:input]: decides(X1,Y1,Z1))))).
1.33/1.54	tff(zf_stmt_0, negated_conjecture,
1.33/1.54	  (?[X1:algorithm]: (![Y1:program,Z1:input]: decides(X1,Y1,Z1)))).
1.33/1.54	tff('0', plain, ![X21 : program, X22 : input]: decides(sk_X1, X21, X22),
1.33/1.54	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.33/1.54	tff(p1, axiom,
1.33/1.54	  ((?[X:algorithm]: (![Y:program,Z:input]: decides(X,Y,Z))) =>
1.33/1.54	   (?[W:program]: (![Y:program,Z:input]: decides(algorithm_of(W),Y,Z))))).
1.33/1.54	tff('1', plain,
1.33/1.54	    ![X0 : program, X1 : input, X2 : algorithm]:
1.33/1.54	      (decides(algorithm_of(sk_W), X0, X1)
1.33/1.54	       | ~ decides(X2, sk_Y(X2), sk_Z(X2))),
1.33/1.54	    inference('cnf', [status(esa)], [p1])).
1.33/1.54	tff('2', plain,
1.33/1.54	    ![X0 : input, X1 : program]:
1.33/1.54	      (~ $true | decides(algorithm_of(sk_W), X1, X0)),
1.33/1.54	    inference('sup-', [status(thm)], ['0', '1'])).
1.33/1.54	tff('3', plain,
1.33/1.54	    ![X0 : input, X1 : program]: decides(algorithm_of(sk_W), X1, X0),
1.33/1.54	    inference('simplify', [status(thm)], ['2'])).
1.33/1.54	tff(p3, axiom,
1.33/1.54	  ((?[W:program]:
1.33/1.54	      (![Y:program]:
1.33/1.54	         ((halts2(Y,as_input(Y)) =>
1.33/1.54	           (halts3(W,Y,as_input(Y)) & outputs(W,good))) & 
1.33/1.54	          ((~halts2(Y,as_input(Y))) =>
1.33/1.54	           (halts3(W,Y,as_input(Y)) & outputs(W,bad)))))) =>
1.33/1.54	   (?[V:program]:
1.33/1.54	      (![Y:program]:
1.33/1.54	         ((halts2(Y,as_input(Y)) => (halts2(V,as_input(Y)) & outputs(V,good))) & 
1.33/1.54	          ((~halts2(Y,as_input(Y))) =>
1.33/1.54	           (halts2(V,as_input(Y)) & outputs(V,bad)))))))).
1.33/1.54	tff(zf_stmt_1, axiom,
1.33/1.54	  ((halts2(Y,as_input(Y)) => (outputs(W,good) & halts3(W,Y,as_input(Y)))) =>
1.33/1.54	   zip_tseitin0(Y,W))).
1.33/1.54	tff('4', plain,
1.33/1.54	    ![X9 : program, X10 : program]:
1.33/1.54	      (zip_tseitin0(X9, X10) | halts2(X9, as_input(X9))),
1.33/1.54	    inference('cnf', [status(esa)], [zf_stmt_1])).
1.33/1.54	tff(p2, axiom,
1.33/1.54	  (![W:program,Y:program,Z:input]:
1.33/1.54	     (decides(algorithm_of(W),Y,Z) =>
1.33/1.54	      (![Y:program,Z:input]:
1.33/1.54	         (((~halts2(Y,Z)) => (outputs(W,bad) & halts3(W,Y,Z))) & 
1.33/1.54	          (halts2(Y,Z) => (outputs(W,good) & halts3(W,Y,Z)))))))).
1.33/1.54	tff('5', plain,
1.33/1.54	    ![X3 : program, X5 : program, X6 : program, X7 : input, X8 : input]:
1.33/1.54	      (~ halts2(X3, X8)
1.33/1.54	       | outputs(X5, good)
1.33/1.54	       | ~ decides(algorithm_of(X5), X6, X7)),
1.33/1.54	    inference('cnf', [status(esa)], [p2])).
1.33/1.54	tff('6', plain,
1.33/1.54	    ![X0 : program, X1 : input, X2 : program, X3 : program, X4 : program]:
1.33/1.54	      (~ $true
1.33/1.54	       | zip_tseitin0(X0, X4)
1.33/1.54	       | ~ decides(algorithm_of(X3), X2, X1)
1.33/1.54	       | outputs(X3, good)),
1.33/1.54	    inference('sup-', [status(thm)], ['4', '5'])).
1.33/1.54	tff('7', plain,
1.33/1.54	    ![X0 : program, X1 : input, X2 : program, X3 : program, X4 : program]:
1.33/1.54	      (outputs(X3, good)
1.33/1.54	       | ~ decides(algorithm_of(X3), X2, X1)
1.33/1.54	       | zip_tseitin0(X0, X4)),
1.33/1.54	    inference('simplify', [status(thm)], ['6'])).
1.33/1.54	tff('8', plain,
1.33/1.54	    ![X2 : program, X3 : program]:
1.33/1.54	      (~ $true | zip_tseitin0(X3, X2) | outputs(sk_W, good)),
1.33/1.54	    inference('sup-', [status(thm)], ['3', '7'])).
1.33/1.54	tff('9', plain,
1.33/1.54	    ![X2 : program, X3 : program]:
1.33/1.54	      (outputs(sk_W, good) | zip_tseitin0(X3, X2)),
1.33/1.54	    inference('simplify', [status(thm)], ['8'])).
1.33/1.54	tff('10', plain,
1.33/1.54	    ![X3 : program, X5 : program, X6 : program, X7 : input, X8 : input]:
1.33/1.54	      (~ halts2(X3, X8)
1.33/1.54	       | halts3(X5, X3, X8)
1.33/1.54	       | ~ decides(algorithm_of(X5), X6, X7)),
1.33/1.54	    inference('cnf', [status(esa)], [p2])).
1.33/1.54	tff('11', plain,
1.33/1.54	    ![X3 : program, X4 : input, X5 : program, X6 : program, X7 : input]:
1.33/1.54	      (halts2(X3, X4)
1.33/1.54	       | halts3(X5, X3, X4)
1.33/1.54	       | ~ decides(algorithm_of(X5), X6, X7)),
1.33/1.54	    inference('cnf', [status(esa)], [p2])).
1.33/1.54	tff('12', plain,
1.33/1.54	    ![X3 : program, X5 : program, X6 : program, X7 : input, X8 : input]:
1.33/1.54	      (~ decides(algorithm_of(X5), X6, X7) | halts3(X5, X3, X8)),
1.33/1.54	    inference('clc', [status(thm)], ['10', '11'])).
1.33/1.54	tff('13', plain,
1.33/1.54	    ![X2 : input, X3 : program]: (~ $true | halts3(sk_W, X3, X2)),
1.33/1.54	    inference('sup-', [status(thm)], ['3', '12'])).
1.33/1.54	tff('14', plain, ![X2 : input, X3 : program]: halts3(sk_W, X3, X2),
1.33/1.54	    inference('simplify', [status(thm)], ['13'])).
1.33/1.54	tff('15', plain,
1.33/1.54	    ![X9 : program, X10 : program]:
1.33/1.54	      (zip_tseitin0(X9, X10)
1.33/1.54	       | ~ outputs(X10, good)
1.33/1.54	       | ~ halts3(X10, X9, as_input(X9))),
1.33/1.54	    inference('cnf', [status(esa)], [zf_stmt_1])).
1.33/1.54	tff('16', plain,
1.33/1.54	    ![X0 : program]:
1.33/1.54	      (~ $true | ~ outputs(sk_W, good) | zip_tseitin0(X0, sk_W)),
1.33/1.54	    inference('sup-', [status(thm)], ['14', '15'])).
1.33/1.54	tff('17', plain,
1.33/1.54	    ![X0 : program]: (zip_tseitin0(X0, sk_W) | ~ outputs(sk_W, good)),
1.33/1.54	    inference('simplify', [status(thm)], ['16'])).
1.33/1.54	tff('18', plain,
1.33/1.54	    ![X0 : program, X1 : program, X2 : program]:
1.33/1.54	      (~ $true | zip_tseitin0(X2, X1) | zip_tseitin0(X0, sk_W)),
1.33/1.54	    inference('sup-', [status(thm)], ['9', '17'])).
1.33/1.54	tff('19', plain,
1.33/1.54	    ![X0 : program, X1 : program, X2 : program]:
1.33/1.54	      (zip_tseitin0(X0, sk_W) | zip_tseitin0(X2, X1)),
1.33/1.54	    inference('simplify', [status(thm)], ['18'])).
1.33/1.54	tff('20', plain, ![X0 : program]: zip_tseitin0(X0, sk_W),
1.33/1.54	    inference('condensation', [status(thm)], ['19'])).
1.33/1.54	tff(zf_stmt_2, axiom,
1.33/1.54	  (((~halts2(Y,as_input(Y))) => (outputs(W,bad) & halts3(W,Y,as_input(Y)))) =>
1.33/1.54	   zip_tseitin1(Y,W))).
1.33/1.54	tff('21', plain,
1.33/1.54	    ![X9 : program, X10 : program]:
1.33/1.54	      (zip_tseitin1(X9, X10)
1.33/1.54	       | ~ outputs(X10, bad)
1.33/1.54	       | ~ halts3(X10, X9, as_input(X9))),
1.33/1.54	    inference('cnf', [status(esa)], [zf_stmt_2])).
1.33/1.54	tff('22', plain,
1.33/1.54	    ![X0 : program]:
1.33/1.54	      (~ $true | ~ outputs(sk_W, bad) | zip_tseitin1(X0, sk_W)),
1.33/1.54	    inference('sup-', [status(thm)], ['14', '21'])).
1.33/1.54	tff('23', plain,
1.33/1.54	    ![X0 : program]: (zip_tseitin1(X0, sk_W) | ~ outputs(sk_W, bad)),
1.33/1.54	    inference('simplify', [status(thm)], ['22'])).
1.33/1.54	tff('24', plain,
1.33/1.54	    ![X3 : program, X4 : input, X5 : program, X6 : program, X7 : input]:
1.33/1.54	      (halts2(X3, X4)
1.33/1.54	       | outputs(X5, bad)
1.33/1.54	       | ~ decides(algorithm_of(X5), X6, X7)),
1.33/1.54	    inference('cnf', [status(esa)], [p2])).
1.33/1.54	tff('25', plain,
1.33/1.54	    ![X2 : input, X3 : program]:
1.33/1.54	      (~ $true | outputs(sk_W, bad) | halts2(X3, X2)),
1.33/1.54	    inference('sup-', [status(thm)], ['3', '24'])).
1.33/1.54	tff('26', plain,
1.33/1.54	    ![X2 : input, X3 : program]: (halts2(X3, X2) | outputs(sk_W, bad)),
1.33/1.54	    inference('simplify', [status(thm)], ['25'])).
1.33/1.54	tff('27', plain,
1.33/1.54	    ![X9 : program, X10 : program]:
1.33/1.54	      (zip_tseitin1(X9, X10) | ~ halts2(X9, as_input(X9))),
1.33/1.54	    inference('cnf', [status(esa)], [zf_stmt_2])).
1.33/1.54	tff('28', plain,
1.33/1.54	    ![X0 : program, X1 : program]:
1.33/1.54	      (~ $true | outputs(sk_W, bad) | zip_tseitin1(X0, X1)),
1.33/1.54	    inference('sup-', [status(thm)], ['26', '27'])).
1.33/1.54	tff('29', plain,
1.33/1.54	    ![X0 : program, X1 : program]:
1.33/1.54	      (zip_tseitin1(X0, X1) | outputs(sk_W, bad)),
1.33/1.54	    inference('simplify', [status(thm)], ['28'])).
1.33/1.54	tff('30', plain, ![X0 : program]: zip_tseitin1(X0, sk_W),
1.33/1.54	    inference('clc', [status(thm)], ['23', '29'])).
1.33/1.54	tff(zf_stmt_3, type, zip_tseitin4 : (program * program) > $o).
1.33/1.54	tff(zf_stmt_4, axiom,
1.33/1.54	  (zip_tseitin4(Y,V) =>
1.33/1.54	   (((~halts2(Y,as_input(Y))) => zip_tseitin3(Y,V)) & 
1.33/1.54	    (halts2(Y,as_input(Y)) => zip_tseitin2(Y,V))))).
1.33/1.54	tff(zf_stmt_5, type, zip_tseitin3 : (program * program) > $o).
1.33/1.54	tff(zf_stmt_6, axiom,
1.33/1.54	  (zip_tseitin3(Y,V) => (outputs(V,bad) & halts2(V,as_input(Y))))).
1.33/1.54	tff(zf_stmt_7, type, zip_tseitin2 : (program * program) > $o).
1.33/1.54	tff(zf_stmt_8, axiom,
1.33/1.54	  (zip_tseitin2(Y,V) => (outputs(V,good) & halts2(V,as_input(Y))))).
1.33/1.54	tff(zf_stmt_9, type, zip_tseitin1 : (program * program) > $o).
1.33/1.54	tff(zf_stmt_10, type, zip_tseitin0 : (program * program) > $o).
1.33/1.54	tff(zf_stmt_11, axiom,
1.33/1.54	  ((?[W:program]: (![Y:program]: (zip_tseitin1(Y,W) & zip_tseitin0(Y,W)))) =>
1.33/1.54	   (?[V:program]: (![Y:program]: zip_tseitin4(Y,V))))).
1.33/1.54	tff('31', plain,
1.33/1.54	    ![X13 : program, X14 : program]:
1.33/1.54	      (zip_tseitin4(X13, sk_V)
1.33/1.54	       | ~ zip_tseitin0(sk_Y1(X14), X14)
1.33/1.54	       | ~ zip_tseitin1(sk_Y1(X14), X14)),
1.33/1.54	    inference('cnf', [status(esa)], [zf_stmt_11])).
1.33/1.54	tff('32', plain,
1.33/1.54	    ![X0 : program]:
1.33/1.54	      (~ $true | ~ zip_tseitin0(sk_Y1(sk_W), sk_W) | zip_tseitin4(X0, sk_V)),
1.33/1.54	    inference('sup-', [status(thm)], ['30', '31'])).
1.33/1.54	tff('33', plain,
1.33/1.54	    ![X0 : program]:
1.33/1.54	      (zip_tseitin4(X0, sk_V) | ~ zip_tseitin0(sk_Y1(sk_W), sk_W)),
1.33/1.54	    inference('simplify', [status(thm)], ['32'])).
1.33/1.54	tff('34', plain, ![X0 : program]: (~ $true | zip_tseitin4(X0, sk_V)),
1.33/1.54	    inference('sup-', [status(thm)], ['20', '33'])).
1.33/1.54	tff('35', plain, ![X0 : program]: zip_tseitin4(X0, sk_V),
1.33/1.54	    inference('simplify', [status(thm)], ['34'])).
1.33/1.54	tff('36', plain,
1.33/1.54	    ![X11 : program, X12 : program]:
1.33/1.54	      (halts2(X12, as_input(X12))
1.33/1.54	       | zip_tseitin3(X12, X11)
1.33/1.54	       | ~ zip_tseitin4(X12, X11)),
1.33/1.54	    inference('cnf', [status(esa)], [zf_stmt_4])).
1.33/1.54	tff('37', plain,
1.33/1.54	    ![X0 : program]:
1.33/1.54	      (~ $true | zip_tseitin3(X0, sk_V) | halts2(X0, as_input(X0))),
1.33/1.54	    inference('sup-', [status(thm)], ['35', '36'])).
1.33/1.54	tff('38', plain,
1.33/1.54	    ![X0 : program]: (halts2(X0, as_input(X0)) | zip_tseitin3(X0, sk_V)),
1.33/1.54	    inference('simplify', [status(thm)], ['37'])).
1.33/1.54	tff(p4, axiom,
1.33/1.54	  ((?[V:program]:
1.33/1.54	      (![Y:program]:
1.33/1.54	         ((halts2(Y,as_input(Y)) => (halts2(V,as_input(Y)) & outputs(V,good))) & 
1.33/1.54	          ((~halts2(Y,as_input(Y))) =>
1.33/1.54	           (halts2(V,as_input(Y)) & outputs(V,bad)))))) =>
1.33/1.54	   (?[U:program]:
1.33/1.54	      (![Y:program]:
1.33/1.54	         ((halts2(Y,as_input(Y)) => (~halts2(U,as_input(Y)))) & 
1.33/1.54	          ((~halts2(Y,as_input(Y))) =>
1.33/1.54	           (halts2(U,as_input(Y)) & outputs(U,bad)))))))).
1.33/1.54	tff(zf_stmt_12, axiom,
1.33/1.54	  (((~halts2(Y,as_input(Y))) => (outputs(V,bad) & halts2(V,as_input(Y)))) =>
1.33/1.54	   zip_tseitin6(Y,V))).
1.33/1.54	tff('39', plain,
1.33/1.54	    ![X15 : program, X16 : program]:
1.33/1.54	      (zip_tseitin6(X15, X16) | ~ halts2(X15, as_input(X15))),
1.33/1.54	    inference('cnf', [status(esa)], [zf_stmt_12])).
1.33/1.54	tff('40', plain,
1.33/1.54	    ![X0 : program, X1 : program]:
1.33/1.54	      (~ $true | zip_tseitin3(X0, sk_V) | zip_tseitin6(X0, X1)),
1.33/1.54	    inference('sup-', [status(thm)], ['38', '39'])).
1.33/1.54	tff('41', plain,
1.33/1.54	    ![X0 : program, X1 : program]:
1.33/1.54	      (zip_tseitin6(X0, X1) | zip_tseitin3(X0, sk_V)),
1.33/1.54	    inference('simplify', [status(thm)], ['40'])).
1.33/1.54	tff('42', plain,
1.33/1.54	    ![X11 : program, X12 : program]:
1.33/1.54	      (~ halts2(X12, as_input(X12))
1.33/1.54	       | zip_tseitin2(X12, X11)
1.33/1.54	       | ~ zip_tseitin4(X12, X11)),
1.33/1.54	    inference('cnf', [status(esa)], [zf_stmt_4])).
1.33/1.54	tff('43', plain,
1.33/1.54	    ![X0 : program, X1 : program]:
1.33/1.54	      (~ $true
1.33/1.54	       | zip_tseitin3(X0, sk_V)
1.33/1.54	       | ~ zip_tseitin4(X0, X1)
1.33/1.54	       | zip_tseitin2(X0, X1)),
1.33/1.54	    inference('sup-', [status(thm)], ['38', '42'])).
1.33/1.54	tff('44', plain,
1.33/1.54	    ![X0 : program, X1 : program]:
1.33/1.54	      (zip_tseitin2(X0, X1) | ~ zip_tseitin4(X0, X1) | zip_tseitin3(X0, sk_V)),
1.33/1.54	    inference('simplify', [status(thm)], ['43'])).
1.33/1.54	tff('45', plain,
1.33/1.54	    ![X0 : program]:
1.33/1.54	      (~ $true | zip_tseitin3(X0, sk_V) | zip_tseitin2(X0, sk_V)),
1.33/1.54	    inference('sup-', [status(thm)], ['35', '44'])).
1.33/1.54	tff('46', plain,
1.33/1.54	    ![X0 : program]: (zip_tseitin2(X0, sk_V) | zip_tseitin3(X0, sk_V)),
1.33/1.54	    inference('simplify', [status(thm)], ['45'])).
1.33/1.54	tff('47', plain,
1.33/1.54	    ![X11 : program, X12 : program]:
1.33/1.54	      (halts2(X11, as_input(X12)) | ~ zip_tseitin3(X12, X11)),
1.33/1.54	    inference('cnf', [status(esa)], [zf_stmt_6])).
1.33/1.54	tff('48', plain,
1.33/1.54	    ![X0 : program, X1 : program]:
1.33/1.54	      (~ $true
1.33/1.54	       | ~ zip_tseitin3(X0, X0)
1.33/1.54	       | ~ zip_tseitin4(X0, X1)
1.33/1.54	       | zip_tseitin2(X0, X1)),
1.33/1.54	    inference('sup-', [status(thm)], ['47', '42'])).
1.33/1.54	tff('49', plain,
1.33/1.54	    ![X0 : program, X1 : program]:
1.33/1.54	      (zip_tseitin2(X0, X1) | ~ zip_tseitin4(X0, X1) | ~ zip_tseitin3(X0, X0)),
1.33/1.54	    inference('simplify', [status(thm)], ['48'])).
1.33/1.54	tff('50', plain,
1.33/1.54	    ![X0 : program]:
1.33/1.54	      (~ $true | ~ zip_tseitin3(X0, X0) | zip_tseitin2(X0, sk_V)),
1.33/1.54	    inference('sup-', [status(thm)], ['35', '49'])).
1.33/1.54	tff('51', plain,
1.33/1.54	    ![X0 : program]: (zip_tseitin2(X0, sk_V) | ~ zip_tseitin3(X0, X0)),
1.33/1.54	    inference('simplify', [status(thm)], ['50'])).
1.33/1.54	tff('52', plain,
1.33/1.54	    (~ $true | zip_tseitin2(sk_V, sk_V) | zip_tseitin2(sk_V, sk_V)),
1.33/1.54	    inference('sup-', [status(thm)], ['46', '51'])).
1.33/1.54	tff('53', plain, zip_tseitin2(sk_V, sk_V),
1.33/1.54	    inference('simplify', [status(thm)], ['52'])).
1.33/1.54	tff('54', plain,
1.33/1.54	    ![X11 : program, X12 : program]:
1.33/1.54	      (outputs(X11, good) | ~ zip_tseitin2(X12, X11)),
1.33/1.54	    inference('cnf', [status(esa)], [zf_stmt_8])).
1.33/1.54	tff('55', plain, (~ $true | outputs(sk_V, good)),
1.33/1.54	    inference('sup-', [status(thm)], ['53', '54'])).
1.33/1.54	tff('56', plain, outputs(sk_V, good),
1.33/1.54	    inference('simplify', [status(thm)], ['55'])).
1.33/1.54	tff(zf_stmt_13, axiom,
1.33/1.54	  ((halts2(Y,as_input(Y)) => (outputs(V,good) & halts2(V,as_input(Y)))) =>
1.33/1.54	   zip_tseitin5(Y,V))).
1.33/1.54	tff('57', plain,
1.33/1.54	    ![X15 : program, X16 : program]:
1.33/1.54	      (zip_tseitin5(X15, X16)
1.33/1.54	       | ~ outputs(X16, good)
1.33/1.54	       | ~ halts2(X16, as_input(X15))),
1.33/1.54	    inference('cnf', [status(esa)], [zf_stmt_13])).
1.33/1.54	tff('58', plain,
1.33/1.54	    ![X0 : program, X1 : program]:
1.33/1.54	      (~ $true
1.33/1.54	       | ~ zip_tseitin3(X0, X1)
1.33/1.54	       | ~ outputs(X1, good)
1.33/1.54	       | zip_tseitin5(X0, X1)),
1.33/1.54	    inference('sup-', [status(thm)], ['47', '57'])).
1.33/1.54	tff('59', plain,
1.33/1.54	    ![X0 : program, X1 : program]:
1.33/1.54	      (zip_tseitin5(X0, X1) | ~ outputs(X1, good) | ~ zip_tseitin3(X0, X1)),
1.33/1.54	    inference('simplify', [status(thm)], ['58'])).
1.33/1.54	tff('60', plain,
1.33/1.54	    ![X0 : program]:
1.33/1.54	      (~ $true | ~ zip_tseitin3(X0, sk_V) | zip_tseitin5(X0, sk_V)),
1.33/1.54	    inference('sup-', [status(thm)], ['56', '59'])).
1.33/1.54	tff('61', plain,
1.33/1.54	    ![X0 : program]: (zip_tseitin5(X0, sk_V) | ~ zip_tseitin3(X0, sk_V)),
1.33/1.54	    inference('simplify', [status(thm)], ['60'])).
1.33/1.54	tff('62', plain,
1.33/1.54	    ![X15 : program, X16 : program]:
1.33/1.54	      (zip_tseitin6(X15, X16)
1.33/1.54	       | ~ outputs(X16, bad)
1.33/1.54	       | ~ halts2(X16, as_input(X15))),
1.33/1.54	    inference('cnf', [status(esa)], [zf_stmt_12])).
1.33/1.54	tff('63', plain,
1.33/1.54	    ![X0 : program, X1 : program]:
1.33/1.54	      (~ $true
1.33/1.54	       | ~ zip_tseitin3(X0, X1)
1.33/1.54	       | ~ outputs(X1, bad)
1.33/1.54	       | zip_tseitin6(X0, X1)),
1.33/1.54	    inference('sup-', [status(thm)], ['47', '62'])).
1.33/1.54	tff('64', plain,
1.33/1.54	    ![X0 : program, X1 : program]:
1.33/1.54	      (zip_tseitin6(X0, X1) | ~ outputs(X1, bad) | ~ zip_tseitin3(X0, X1)),
1.33/1.54	    inference('simplify', [status(thm)], ['63'])).
1.33/1.54	tff('65', plain,
1.33/1.54	    ![X11 : program, X12 : program]:
1.33/1.54	      (outputs(X11, bad) | ~ zip_tseitin3(X12, X11)),
1.33/1.54	    inference('cnf', [status(esa)], [zf_stmt_6])).
1.33/1.54	tff('66', plain,
1.33/1.54	    ![X0 : program, X1 : program]:
1.33/1.54	      (~ zip_tseitin3(X0, X1) | zip_tseitin6(X0, X1)),
1.33/1.54	    inference('clc', [status(thm)], ['64', '65'])).
1.33/1.54	tff(zf_stmt_14, type, zip_tseitin8 : (program * program) > $o).
1.33/1.54	tff(zf_stmt_15, axiom,
1.33/1.54	  (zip_tseitin8(Y,U) =>
1.33/1.54	   (((~halts2(Y,as_input(Y))) => zip_tseitin7(Y,U)) & 
1.33/1.54	    (halts2(Y,as_input(Y)) => (~halts2(U,as_input(Y))))))).
1.33/1.54	tff(zf_stmt_16, type, zip_tseitin7 : (program * program) > $o).
1.33/1.54	tff(zf_stmt_17, axiom,
1.33/1.54	  (zip_tseitin7(Y,U) => (outputs(U,bad) & halts2(U,as_input(Y))))).
1.33/1.54	tff(zf_stmt_18, type, zip_tseitin6 : (program * program) > $o).
1.33/1.54	tff(zf_stmt_19, type, zip_tseitin5 : (program * program) > $o).
1.33/1.54	tff(zf_stmt_20, axiom,
1.33/1.54	  ((?[V:program]: (![Y:program]: (zip_tseitin6(Y,V) & zip_tseitin5(Y,V)))) =>
1.33/1.54	   (?[U:program]: (![Y:program]: zip_tseitin8(Y,U))))).
1.33/1.54	tff('67', plain,
1.33/1.54	    ![X19 : program, X20 : program]:
1.33/1.54	      (zip_tseitin8(X19, sk_U)
1.33/1.54	       | ~ zip_tseitin5(sk_Y2(X20), X20)
1.33/1.54	       | ~ zip_tseitin6(sk_Y2(X20), X20)),
1.33/1.54	    inference('cnf', [status(esa)], [zf_stmt_20])).
1.33/1.54	tff('68', plain,
1.33/1.54	    ![X0 : program, X1 : program]:
1.33/1.54	      (~ $true
1.33/1.54	       | ~ zip_tseitin3(sk_Y2(X0), X0)
1.33/1.54	       | ~ zip_tseitin5(sk_Y2(X0), X0)
1.33/1.54	       | zip_tseitin8(X1, sk_U)),
1.33/1.54	    inference('sup-', [status(thm)], ['66', '67'])).
1.33/1.54	tff('69', plain,
1.33/1.54	    ![X0 : program, X1 : program]:
1.33/1.54	      (zip_tseitin8(X1, sk_U)
1.33/1.54	       | ~ zip_tseitin5(sk_Y2(X0), X0)
1.33/1.54	       | ~ zip_tseitin3(sk_Y2(X0), X0)),
1.33/1.54	    inference('simplify', [status(thm)], ['68'])).
1.33/1.54	tff('70', plain,
1.33/1.54	    ![X0 : program]:
1.33/1.54	      (~ $true
1.33/1.54	       | ~ zip_tseitin3(sk_Y2(sk_V), sk_V)
1.33/1.54	       | ~ zip_tseitin3(sk_Y2(sk_V), sk_V)
1.33/1.54	       | zip_tseitin8(X0, sk_U)),
1.33/1.54	    inference('sup-', [status(thm)], ['61', '69'])).
1.33/1.54	tff('71', plain,
1.33/1.54	    ![X0 : program]:
1.33/1.54	      (zip_tseitin8(X0, sk_U) | ~ zip_tseitin3(sk_Y2(sk_V), sk_V)),
1.33/1.54	    inference('simplify', [status(thm)], ['70'])).
1.33/1.54	tff('72', plain,
1.33/1.54	    ![X0 : program, X1 : program]:
1.33/1.54	      (~ $true | zip_tseitin6(sk_Y2(sk_V), X1) | zip_tseitin8(X0, sk_U)),
1.33/1.54	    inference('sup-', [status(thm)], ['41', '71'])).
1.33/1.54	tff('73', plain,
1.33/1.54	    ![X0 : program, X1 : program]:
1.33/1.54	      (zip_tseitin8(X0, sk_U) | zip_tseitin6(sk_Y2(sk_V), X1)),
1.33/1.54	    inference('simplify', [status(thm)], ['72'])).
1.33/1.54	tff('74', plain,
1.33/1.54	    ![X0 : program, X1 : program]:
1.33/1.54	      (~ $true
1.33/1.54	       | zip_tseitin8(X1, sk_U)
1.33/1.54	       | ~ zip_tseitin5(sk_Y2(sk_V), sk_V)
1.33/1.54	       | zip_tseitin8(X0, sk_U)),
1.33/1.54	    inference('sup-', [status(thm)], ['73', '67'])).
1.33/1.54	tff('75', plain,
1.33/1.54	    ![X0 : program, X1 : program]:
1.33/1.54	      (zip_tseitin8(X0, sk_U)
1.33/1.54	       | ~ zip_tseitin5(sk_Y2(sk_V), sk_V)
1.33/1.54	       | zip_tseitin8(X1, sk_U)),
1.33/1.54	    inference('simplify', [status(thm)], ['74'])).
1.33/1.54	tff('76', plain,
1.33/1.54	    ![X0 : program]:
1.33/1.54	      (zip_tseitin8(X0, sk_U) | ~ zip_tseitin5(sk_Y2(sk_V), sk_V)),
1.33/1.54	    inference('condensation', [status(thm)], ['75'])).
1.33/1.54	tff('77', plain,
1.33/1.54	    ![X0 : program]:
1.33/1.54	      (~ $true | zip_tseitin2(sk_Y2(sk_V), sk_V) | zip_tseitin8(X0, sk_U)),
1.33/1.54	    inference('sup-', [status(thm)], ['46', '71'])).
1.33/1.54	tff('78', plain,
1.33/1.54	    ![X0 : program]:
1.33/1.54	      (zip_tseitin8(X0, sk_U) | zip_tseitin2(sk_Y2(sk_V), sk_V)),
1.33/1.54	    inference('simplify', [status(thm)], ['77'])).
1.33/1.54	tff('79', plain,
1.33/1.54	    ![X11 : program, X12 : program]:
1.33/1.54	      (halts2(X11, as_input(X12)) | ~ zip_tseitin2(X12, X11)),
1.33/1.54	    inference('cnf', [status(esa)], [zf_stmt_8])).
1.33/1.54	tff('80', plain,
1.33/1.54	    ![X0 : program, X1 : program]:
1.33/1.54	      (~ $true
1.33/1.54	       | ~ zip_tseitin2(X0, X1)
1.33/1.54	       | ~ outputs(X1, good)
1.33/1.54	       | zip_tseitin5(X0, X1)),
1.33/1.54	    inference('sup-', [status(thm)], ['79', '57'])).
1.33/1.54	tff('81', plain,
1.33/1.54	    ![X0 : program, X1 : program]:
1.33/1.54	      (zip_tseitin5(X0, X1) | ~ outputs(X1, good) | ~ zip_tseitin2(X0, X1)),
1.33/1.54	    inference('simplify', [status(thm)], ['80'])).
1.33/1.54	tff('82', plain,
1.33/1.54	    ![X0 : program, X1 : program]:
1.33/1.54	      (~ zip_tseitin2(X0, X1) | zip_tseitin5(X0, X1)),
1.33/1.54	    inference('clc', [status(thm)], ['81', '54'])).
1.33/1.54	tff('83', plain,
1.33/1.54	    ![X15 : program, X16 : program]:
1.33/1.54	      (zip_tseitin5(X15, X16) | halts2(X15, as_input(X15))),
1.33/1.54	    inference('cnf', [status(esa)], [zf_stmt_13])).
1.33/1.54	tff('84', plain,
1.33/1.54	    ![X0 : program, X1 : program, X2 : program]:
1.33/1.54	      (~ $true | zip_tseitin5(X0, X2) | zip_tseitin6(X0, X1)),
1.33/1.54	    inference('sup-', [status(thm)], ['83', '39'])).
1.33/1.54	tff('85', plain,
1.33/1.54	    ![X0 : program, X1 : program, X2 : program]:
1.33/1.54	      (zip_tseitin6(X0, X1) | zip_tseitin5(X0, X2)),
1.33/1.54	    inference('simplify', [status(thm)], ['84'])).
1.33/1.54	tff('86', plain,
1.33/1.54	    ![X0 : program, X1 : program, X2 : program]:
1.33/1.54	      (~ $true
1.33/1.54	       | zip_tseitin5(sk_Y2(X0), X2)
1.33/1.54	       | ~ zip_tseitin5(sk_Y2(X0), X0)
1.33/1.54	       | zip_tseitin8(X1, sk_U)),
1.33/1.54	    inference('sup-', [status(thm)], ['85', '67'])).
1.33/1.54	tff('87', plain,
1.33/1.54	    ![X0 : program, X1 : program, X2 : program]:
1.33/1.54	      (zip_tseitin8(X1, sk_U)
1.33/1.54	       | ~ zip_tseitin5(sk_Y2(X0), X0)
1.33/1.54	       | zip_tseitin5(sk_Y2(X0), X2)),
1.33/1.54	    inference('simplify', [status(thm)], ['86'])).
1.33/1.54	tff('88', plain,
1.33/1.54	    ![X0 : program, X1 : program, X2 : program]:
1.33/1.54	      (~ $true
1.33/1.54	       | ~ zip_tseitin2(sk_Y2(X0), X0)
1.33/1.54	       | zip_tseitin5(sk_Y2(X0), X1)
1.33/1.54	       | zip_tseitin8(X2, sk_U)),
1.33/1.54	    inference('sup-', [status(thm)], ['82', '87'])).
1.33/1.54	tff('89', plain,
1.33/1.54	    ![X0 : program, X1 : program, X2 : program]:
1.33/1.54	      (zip_tseitin8(X2, sk_U)
1.33/1.54	       | zip_tseitin5(sk_Y2(X0), X1)
1.33/1.54	       | ~ zip_tseitin2(sk_Y2(X0), X0)),
1.33/1.54	    inference('simplify', [status(thm)], ['88'])).
1.33/1.54	tff('90', plain,
1.33/1.54	    ![X0 : program, X1 : program, X2 : program]:
1.33/1.54	      (~ $true
1.33/1.54	       | zip_tseitin8(X2, sk_U)
1.33/1.54	       | zip_tseitin5(sk_Y2(sk_V), X0)
1.33/1.54	       | zip_tseitin8(X1, sk_U)),
1.33/1.54	    inference('sup-', [status(thm)], ['78', '89'])).
1.33/1.54	tff('91', plain,
1.33/1.54	    ![X0 : program, X1 : program, X2 : program]:
1.33/1.54	      (zip_tseitin8(X1, sk_U)
1.33/1.54	       | zip_tseitin5(sk_Y2(sk_V), X0)
1.33/1.54	       | zip_tseitin8(X2, sk_U)),
1.33/1.54	    inference('simplify', [status(thm)], ['90'])).
1.33/1.54	tff('92', plain,
1.33/1.54	    ![X0 : program, X1 : program]:
1.33/1.54	      (zip_tseitin8(X0, sk_U) | zip_tseitin5(sk_Y2(sk_V), X1)),
1.33/1.54	    inference('condensation', [status(thm)], ['91'])).
1.33/1.54	tff('93', plain, ![X0 : program]: zip_tseitin8(X0, sk_U),
1.33/1.54	    inference('clc', [status(thm)], ['76', '92'])).
1.33/1.54	tff('94', plain,
1.33/1.54	    ![X17 : program, X18 : program]:
1.33/1.54	      (halts2(X18, as_input(X18))
1.33/1.54	       | zip_tseitin7(X18, X17)
1.33/1.54	       | ~ zip_tseitin8(X18, X17)),
1.33/1.54	    inference('cnf', [status(esa)], [zf_stmt_15])).
1.33/1.54	tff('95', plain,
1.33/1.54	    ![X0 : program]:
1.33/1.54	      (~ $true | zip_tseitin7(X0, sk_U) | halts2(X0, as_input(X0))),
1.33/1.54	    inference('sup-', [status(thm)], ['93', '94'])).
1.33/1.54	tff('96', plain,
1.33/1.54	    ![X0 : program]: (halts2(X0, as_input(X0)) | zip_tseitin7(X0, sk_U)),
1.33/1.54	    inference('simplify', [status(thm)], ['95'])).
1.33/1.54	tff('97', plain,
1.33/1.54	    ![X17 : program, X18 : program]:
1.33/1.54	      (~ halts2(X18, as_input(X18))
1.33/1.54	       | ~ halts2(X17, as_input(X18))
1.33/1.54	       | ~ zip_tseitin8(X18, X17)),
1.33/1.54	    inference('cnf', [status(esa)], [zf_stmt_15])).
1.33/1.54	tff('98', plain,
1.33/1.54	    ![X0 : program, X1 : program]:
1.33/1.54	      (~ $true
1.33/1.54	       | zip_tseitin7(X0, sk_U)
1.33/1.54	       | ~ zip_tseitin8(X0, X1)
1.33/1.54	       | ~ halts2(X1, as_input(X0))),
1.33/1.54	    inference('sup-', [status(thm)], ['96', '97'])).
1.33/1.54	tff('99', plain,
1.33/1.54	    ![X0 : program, X1 : program]:
1.33/1.54	      (~ halts2(X1, as_input(X0))
1.33/1.54	       | ~ zip_tseitin8(X0, X1)
1.33/1.54	       | zip_tseitin7(X0, sk_U)),
1.33/1.54	    inference('simplify', [status(thm)], ['98'])).
1.33/1.54	tff('100', plain,
1.33/1.54	    ![X0 : program]:
1.33/1.54	      (~ $true
1.33/1.54	       | zip_tseitin7(X0, sk_U)
1.33/1.54	       | zip_tseitin7(X0, sk_U)
1.33/1.54	       | ~ zip_tseitin8(X0, X0)),
1.33/1.54	    inference('sup-', [status(thm)], ['96', '99'])).
1.33/1.54	tff('101', plain,
1.33/1.54	    ![X0 : program]: (~ zip_tseitin8(X0, X0) | zip_tseitin7(X0, sk_U)),
1.33/1.54	    inference('simplify', [status(thm)], ['100'])).
1.33/1.54	tff('102', plain, (~ $true | zip_tseitin7(sk_U, sk_U)),
1.33/1.54	    inference('sup-', [status(thm)], ['93', '101'])).
1.33/1.54	tff('103', plain, zip_tseitin7(sk_U, sk_U),
1.33/1.54	    inference('simplify', [status(thm)], ['102'])).
1.33/1.54	tff('104', plain,
1.33/1.54	    ![X17 : program, X18 : program]:
1.33/1.54	      (halts2(X17, as_input(X18)) | ~ zip_tseitin7(X18, X17)),
1.33/1.54	    inference('cnf', [status(esa)], [zf_stmt_17])).
1.33/1.54	tff('105', plain,
1.33/1.54	    ![X0 : program, X1 : program]:
1.33/1.54	      (~ $true
1.33/1.54	       | ~ zip_tseitin7(X0, X0)
1.33/1.54	       | ~ zip_tseitin8(X0, X1)
1.33/1.54	       | ~ halts2(X1, as_input(X0))),
1.33/1.54	    inference('sup-', [status(thm)], ['104', '97'])).
1.33/1.54	tff('106', plain,
1.33/1.54	    ![X0 : program, X1 : program]:
1.33/1.54	      (~ halts2(X1, as_input(X0))
1.33/1.54	       | ~ zip_tseitin8(X0, X1)
1.33/1.54	       | ~ zip_tseitin7(X0, X0)),
1.33/1.54	    inference('simplify', [status(thm)], ['105'])).
1.33/1.54	tff('107', plain,
1.33/1.54	    ![X0 : program]:
1.33/1.54	      (~ $true
1.33/1.54	       | zip_tseitin7(X0, sk_U)
1.33/1.54	       | ~ zip_tseitin7(X0, X0)
1.33/1.54	       | ~ zip_tseitin8(X0, X0)),
1.33/1.54	    inference('sup-', [status(thm)], ['96', '106'])).
1.33/1.54	tff('108', plain,
1.33/1.54	    ![X0 : program]:
1.33/1.54	      (~ zip_tseitin8(X0, X0)
1.33/1.54	       | ~ zip_tseitin7(X0, X0)
1.33/1.54	       | zip_tseitin7(X0, sk_U)),
1.33/1.54	    inference('simplify', [status(thm)], ['107'])).
1.33/1.54	tff('109', plain,
1.33/1.54	    ![X0 : program, X1 : program]:
1.33/1.54	      (~ $true
1.33/1.54	       | ~ zip_tseitin7(X0, X1)
1.33/1.54	       | ~ zip_tseitin7(X0, X0)
1.33/1.54	       | ~ zip_tseitin8(X0, X1)),
1.33/1.54	    inference('sup-', [status(thm)], ['104', '106'])).
1.33/1.54	tff('110', plain,
1.33/1.54	    ![X0 : program, X1 : program]:
1.33/1.54	      (~ zip_tseitin8(X0, X1)
1.33/1.54	       | ~ zip_tseitin7(X0, X0)
1.33/1.54	       | ~ zip_tseitin7(X0, X1)),
1.33/1.54	    inference('simplify', [status(thm)], ['109'])).
1.33/1.54	tff('111', plain,
1.33/1.54	    ![X0 : program]:
1.33/1.54	      (~ $true | ~ zip_tseitin7(X0, sk_U) | ~ zip_tseitin7(X0, X0)),
1.33/1.54	    inference('sup-', [status(thm)], ['93', '110'])).
1.33/1.54	tff('112', plain,
1.33/1.54	    ![X0 : program]: (~ zip_tseitin7(X0, X0) | ~ zip_tseitin7(X0, sk_U)),
1.33/1.54	    inference('simplify', [status(thm)], ['111'])).
1.33/1.54	tff('113', plain,
1.33/1.54	    ![X0 : program]: (~ zip_tseitin7(X0, X0) | ~ zip_tseitin8(X0, X0)),
1.33/1.54	    inference('clc', [status(thm)], ['108', '112'])).
1.33/1.54	tff('114', plain, (~ $true | ~ zip_tseitin7(sk_U, sk_U)),
1.33/1.54	    inference('sup-', [status(thm)], ['93', '113'])).
1.33/1.54	tff('115', plain, ~ zip_tseitin7(sk_U, sk_U),
1.33/1.54	    inference('simplify', [status(thm)], ['114'])).
1.33/1.54	tff('116', plain, ~ $true, inference('sup-', [status(thm)], ['103', '115'])).
1.33/1.54	tff('117', plain, $false, inference('simplify', [status(thm)], ['116'])).
1.33/1.54	
1.33/1.54	% SZS output end Refutation
1.33/1.54	EOF
