0.00/0.00	% File    : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : original
0.00/0.00	% Variant    : supatvars_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	  --sup-at-vars \
0.00/0.00	  --restrict-hidden-sup-at-vars \
0.00/0.00	  --ho-ext-axiom \
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
0.00/0.20	% Computer   : n064.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 08:23:23 CST 2018
231.26/231.56	% done 52307 iterations in 231.349s
231.26/231.56	% SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
231.26/231.56	% SZS output start Refutation
231.26/231.56	tff(prove_this, conjecture,
231.26/231.56	  (~(?[X1:algorithm]: (![Y1:program,Z1:input]: decides(X1,Y1,Z1))))).
231.26/231.56	tff(zf_stmt_0, negated_conjecture,
231.26/231.56	  (?[X1:algorithm]: (![Y1:program,Z1:input]: decides(X1,Y1,Z1)))).
231.26/231.56	tff('0', plain, ![X21 : program, X22 : input]: decides(sk_X1, X21, X22),
231.26/231.56	    inference('cnf', [status(esa)], [zf_stmt_0])).
231.26/231.56	tff(p1, axiom,
231.26/231.56	  ((?[X:algorithm]: (![Y:program,Z:input]: decides(X,Y,Z))) =>
231.26/231.56	   (?[W:program]: (![Y:program,Z:input]: decides(algorithm_of(W),Y,Z))))).
231.26/231.56	tff('1', plain,
231.26/231.56	    ![X0 : program, X1 : input, X2 : algorithm]:
231.26/231.56	      (decides(algorithm_of(sk_W), X0, X1)
231.26/231.56	       | ~ decides(X2, sk_Y(X2), sk_Z(X2))),
231.26/231.56	    inference('cnf', [status(esa)], [p1])).
231.26/231.56	tff('2', plain,
231.26/231.56	    ![X0 : input, X1 : program]:
231.26/231.56	      (~ $true | decides(algorithm_of(sk_W), X1, X0)),
231.26/231.56	    inference('sup-', [status(thm)], ['0', '1'])).
231.26/231.56	tff('3', plain,
231.26/231.56	    ![X0 : input, X1 : program]: decides(algorithm_of(sk_W), X1, X0),
231.26/231.56	    inference('simplify', [status(thm)], ['2'])).
231.26/231.56	tff(p2, axiom,
231.26/231.56	  (![W:program,Y:program,Z:input]:
231.26/231.56	     (decides(algorithm_of(W),Y,Z) =>
231.26/231.56	      (![Y:program,Z:input]:
231.26/231.56	         (((~halts2(Y,Z)) => (outputs(W,bad) & halts3(W,Y,Z))) & 
231.26/231.56	          (halts2(Y,Z) => (outputs(W,good) & halts3(W,Y,Z)))))))).
231.26/231.56	tff('4', plain,
231.26/231.56	    ![X3 : program, X4 : input, X5 : program, X6 : program, X7 : input]:
231.26/231.56	      (halts2(X3, X4)
231.26/231.56	       | outputs(X5, bad)
231.26/231.56	       | ~ decides(algorithm_of(X5), X6, X7)),
231.26/231.56	    inference('cnf', [status(esa)], [p2])).
231.26/231.56	tff('5', plain,
231.26/231.56	    ![X2 : input, X3 : program]:
231.26/231.56	      (~ $true | outputs(sk_W, bad) | halts2(X3, X2)),
231.26/231.56	    inference('sup-', [status(thm)], ['3', '4'])).
231.26/231.56	tff('6', plain,
231.26/231.56	    ![X2 : input, X3 : program]: (halts2(X3, X2) | outputs(sk_W, bad)),
231.26/231.56	    inference('simplify', [status(thm)], ['5'])).
231.26/231.56	tff('7', plain,
231.26/231.56	    ![X3 : program, X5 : program, X6 : program, X7 : input, X8 : input]:
231.26/231.56	      (~ halts2(X3, X8)
231.26/231.56	       | halts3(X5, X3, X8)
231.26/231.56	       | ~ decides(algorithm_of(X5), X6, X7)),
231.26/231.56	    inference('cnf', [status(esa)], [p2])).
231.26/231.56	tff('8', plain,
231.26/231.56	    ![X3 : program, X4 : input, X5 : program, X6 : program, X7 : input]:
231.26/231.56	      (halts2(X3, X4)
231.26/231.56	       | halts3(X5, X3, X4)
231.26/231.56	       | ~ decides(algorithm_of(X5), X6, X7)),
231.26/231.56	    inference('cnf', [status(esa)], [p2])).
231.26/231.56	tff('9', plain,
231.26/231.56	    ![X3 : program, X5 : program, X6 : program, X7 : input, X8 : input]:
231.26/231.56	      (~ decides(algorithm_of(X5), X6, X7) | halts3(X5, X3, X8)),
231.26/231.56	    inference('clc', [status(thm)], ['7', '8'])).
231.26/231.56	tff('10', plain,
231.26/231.56	    ![X2 : input, X3 : program]: (~ $true | halts3(sk_W, X3, X2)),
231.26/231.56	    inference('sup-', [status(thm)], ['3', '9'])).
231.26/231.56	tff('11', plain, ![X2 : input, X3 : program]: halts3(sk_W, X3, X2),
231.26/231.56	    inference('simplify', [status(thm)], ['10'])).
231.26/231.56	tff(p3, axiom,
231.26/231.56	  ((?[W:program]:
231.26/231.56	      (![Y:program]:
231.26/231.56	         ((halts2(Y,as_input(Y)) =>
231.26/231.56	           (halts3(W,Y,as_input(Y)) & outputs(W,good))) & 
231.26/231.56	          ((~halts2(Y,as_input(Y))) =>
231.26/231.56	           (halts3(W,Y,as_input(Y)) & outputs(W,bad)))))) =>
231.26/231.56	   (?[V:program]:
231.26/231.56	      (![Y:program]:
231.26/231.56	         ((halts2(Y,as_input(Y)) => (halts2(V,as_input(Y)) & outputs(V,good))) & 
231.26/231.56	          ((~halts2(Y,as_input(Y))) =>
231.26/231.56	           (halts2(V,as_input(Y)) & outputs(V,bad)))))))).
231.26/231.56	tff(zf_stmt_1, axiom,
231.26/231.56	  ((halts2(Y,as_input(Y)) => (outputs(W,good) & halts3(W,Y,as_input(Y)))) =>
231.26/231.56	   zip_tseitin0(Y,W))).
231.26/231.56	tff('12', plain,
231.26/231.56	    ![X9 : program, X10 : program]:
231.26/231.56	      (zip_tseitin0(X9, X10) | halts2(X9, as_input(X9))),
231.26/231.56	    inference('cnf', [status(esa)], [zf_stmt_1])).
231.26/231.56	tff(zf_stmt_2, axiom,
231.26/231.56	  (((~halts2(Y,as_input(Y))) => (outputs(W,bad) & halts3(W,Y,as_input(Y)))) =>
231.26/231.56	   zip_tseitin1(Y,W))).
231.26/231.56	tff('13', plain,
231.26/231.56	    ![X9 : program, X10 : program]:
231.26/231.56	      (zip_tseitin1(X9, X10)
231.26/231.56	       | ~ outputs(X10, bad)
231.26/231.56	       | ~ halts3(X10, X9, as_input(X9))),
231.26/231.56	    inference('cnf', [status(esa)], [zf_stmt_2])).
231.26/231.56	tff(zf_stmt_3, type, zip_tseitin4 : (program * program) > $o).
231.26/231.56	tff(zf_stmt_4, axiom,
231.26/231.56	  (zip_tseitin4(Y,V) =>
231.26/231.56	   (((~halts2(Y,as_input(Y))) => zip_tseitin3(Y,V)) & 
231.26/231.56	    (halts2(Y,as_input(Y)) => zip_tseitin2(Y,V))))).
231.26/231.56	tff(zf_stmt_5, type, zip_tseitin3 : (program * program) > $o).
231.26/231.56	tff(zf_stmt_6, axiom,
231.26/231.56	  (zip_tseitin3(Y,V) => (outputs(V,bad) & halts2(V,as_input(Y))))).
231.26/231.56	tff(zf_stmt_7, type, zip_tseitin2 : (program * program) > $o).
231.26/231.56	tff(zf_stmt_8, axiom,
231.26/231.56	  (zip_tseitin2(Y,V) => (outputs(V,good) & halts2(V,as_input(Y))))).
231.26/231.56	tff(zf_stmt_9, type, zip_tseitin1 : (program * program) > $o).
231.26/231.56	tff(zf_stmt_10, type, zip_tseitin0 : (program * program) > $o).
231.26/231.56	tff(zf_stmt_11, axiom,
231.26/231.56	  ((?[W:program]: (![Y:program]: (zip_tseitin1(Y,W) & zip_tseitin0(Y,W)))) =>
231.26/231.56	   (?[V:program]: (![Y:program]: zip_tseitin4(Y,V))))).
231.26/231.56	tff('14', plain,
231.26/231.56	    ![X13 : program, X14 : program]:
231.26/231.56	      (zip_tseitin4(X13, sk_V)
231.26/231.56	       | ~ zip_tseitin0(sk_Y1(X14), X14)
231.26/231.56	       | ~ zip_tseitin1(sk_Y1(X14), X14)),
231.26/231.56	    inference('cnf', [status(esa)], [zf_stmt_11])).
231.26/231.56	tff('15', plain,
231.26/231.56	    ![X0 : program, X1 : program]:
231.26/231.56	      (~ $true
231.26/231.56	       | ~ halts3(X0, sk_Y1(X0), as_input(sk_Y1(X0)))
231.26/231.56	       | ~ outputs(X0, bad)
231.26/231.56	       | ~ zip_tseitin0(sk_Y1(X0), X0)
231.26/231.56	       | zip_tseitin4(X1, sk_V)),
231.26/231.56	    inference('sup-', [status(thm)], ['13', '14'])).
231.26/231.56	tff('16', plain,
231.26/231.56	    ![X0 : program, X1 : program]:
231.26/231.56	      (zip_tseitin4(X1, sk_V)
231.26/231.56	       | ~ zip_tseitin0(sk_Y1(X0), X0)
231.26/231.56	       | ~ outputs(X0, bad)
231.26/231.56	       | ~ halts3(X0, sk_Y1(X0), as_input(sk_Y1(X0)))),
231.26/231.56	    inference('simplify', [status(thm)], ['15'])).
231.26/231.56	tff('17', plain,
231.26/231.56	    ![X0 : program, X1 : program]:
231.26/231.56	      (~ $true
231.26/231.56	       | halts2(sk_Y1(X0), as_input(sk_Y1(X0)))
231.26/231.56	       | ~ halts3(X0, sk_Y1(X0), as_input(sk_Y1(X0)))
231.26/231.56	       | ~ outputs(X0, bad)
231.26/231.56	       | zip_tseitin4(X1, sk_V)),
231.26/231.56	    inference('sup-', [status(thm)], ['12', '16'])).
231.26/231.56	tff('18', plain,
231.26/231.56	    ![X0 : program, X1 : program]:
231.26/231.56	      (zip_tseitin4(X1, sk_V)
231.26/231.56	       | ~ outputs(X0, bad)
231.26/231.56	       | ~ halts3(X0, sk_Y1(X0), as_input(sk_Y1(X0)))
231.26/231.56	       | halts2(sk_Y1(X0), as_input(sk_Y1(X0)))),
231.26/231.56	    inference('simplify', [status(thm)], ['17'])).
231.26/231.56	tff('19', plain,
231.26/231.56	    ![X0 : program]:
231.26/231.56	      (~ $true
231.26/231.56	       | halts2(sk_Y1(sk_W), as_input(sk_Y1(sk_W)))
231.26/231.56	       | ~ outputs(sk_W, bad)
231.26/231.56	       | zip_tseitin4(X0, sk_V)),
231.26/231.56	    inference('sup-', [status(thm)], ['11', '18'])).
231.26/231.56	tff('20', plain,
231.26/231.56	    ![X0 : program]:
231.26/231.56	      (zip_tseitin4(X0, sk_V)
231.26/231.56	       | ~ outputs(sk_W, bad)
231.26/231.56	       | halts2(sk_Y1(sk_W), as_input(sk_Y1(sk_W)))),
231.26/231.56	    inference('simplify', [status(thm)], ['19'])).
231.26/231.56	tff('21', plain,
231.26/231.56	    ![X0 : program]:
231.26/231.56	      (halts2(sk_Y1(sk_W), as_input(sk_Y1(sk_W))) | zip_tseitin4(X0, sk_V)),
231.26/231.56	    inference('clc', [status(thm)], ['20', '6'])).
231.26/231.56	tff('22', plain,
231.26/231.56	    ![X11 : program, X12 : program]:
231.26/231.56	      (halts2(X12, as_input(X12))
231.26/231.56	       | zip_tseitin3(X12, X11)
231.26/231.56	       | ~ zip_tseitin4(X12, X11)),
231.26/231.56	    inference('cnf', [status(esa)], [zf_stmt_4])).
231.26/231.56	tff('23', plain,
231.26/231.56	    ![X0 : program]:
231.26/231.56	      (~ $true
231.26/231.56	       | halts2(sk_Y1(sk_W), as_input(sk_Y1(sk_W)))
231.26/231.56	       | zip_tseitin3(X0, sk_V)
231.26/231.56	       | halts2(X0, as_input(X0))),
231.26/231.56	    inference('sup-', [status(thm)], ['21', '22'])).
231.26/231.56	tff('24', plain,
231.26/231.56	    ![X0 : program]:
231.26/231.56	      (halts2(X0, as_input(X0))
231.26/231.56	       | zip_tseitin3(X0, sk_V)
231.26/231.56	       | halts2(sk_Y1(sk_W), as_input(sk_Y1(sk_W)))),
231.26/231.56	    inference('simplify', [status(thm)], ['23'])).
231.26/231.56	tff('25', plain,
231.26/231.56	    ![X11 : program, X12 : program]:
231.26/231.56	      (halts2(X11, as_input(X12)) | ~ zip_tseitin3(X12, X11)),
231.26/231.56	    inference('cnf', [status(esa)], [zf_stmt_6])).
231.26/231.56	tff('26', plain,
231.26/231.56	    ![X0 : program]:
231.26/231.56	      (~ $true
231.26/231.56	       | halts2(sk_Y1(sk_W), as_input(sk_Y1(sk_W)))
231.26/231.56	       | halts2(X0, as_input(X0))
231.26/231.56	       | halts2(sk_V, as_input(X0))),
231.26/231.56	    inference('sup-', [status(thm)], ['24', '25'])).
231.26/231.56	tff('27', plain,
231.26/231.56	    ![X0 : program]:
231.26/231.56	      (halts2(sk_V, as_input(X0))
231.26/231.56	       | halts2(X0, as_input(X0))
231.26/231.56	       | halts2(sk_Y1(sk_W), as_input(sk_Y1(sk_W)))),
231.26/231.56	    inference('simplify', [status(thm)], ['26'])).
231.26/231.56	tff('28', plain,
231.26/231.56	    (~ $true
231.26/231.56	     | halts2(sk_Y1(sk_W), as_input(sk_Y1(sk_W)))
231.26/231.56	     | halts2(sk_V, as_input(sk_Y1(sk_W)))),
231.26/231.56	    inference('eq_fact', [status(thm)], ['27'])).
231.26/231.56	tff('29', plain,
231.26/231.56	    (halts2(sk_V, as_input(sk_Y1(sk_W)))
231.26/231.56	     | halts2(sk_Y1(sk_W), as_input(sk_Y1(sk_W)))),
231.26/231.56	    inference('simplify', [status(thm)], ['28'])).
231.26/231.56	tff('30', plain,
231.26/231.56	    ![X3 : program, X5 : program, X6 : program, X7 : input, X8 : input]:
231.26/231.56	      (~ halts2(X3, X8)
231.26/231.56	       | outputs(X5, good)
231.26/231.56	       | ~ decides(algorithm_of(X5), X6, X7)),
231.26/231.56	    inference('cnf', [status(esa)], [p2])).
231.26/231.56	tff('31', plain,
231.26/231.56	    ![X0 : input, X1 : program, X2 : program]:
231.26/231.56	      (~ $true
231.26/231.56	       | halts2(sk_V, as_input(sk_Y1(sk_W)))
231.26/231.56	       | ~ decides(algorithm_of(X2), X1, X0)
231.26/231.56	       | outputs(X2, good)),
231.26/231.56	    inference('sup-', [status(thm)], ['29', '30'])).
231.26/231.56	tff('32', plain,
231.26/231.56	    ![X0 : input, X1 : program, X2 : program]:
231.26/231.56	      (outputs(X2, good)
231.26/231.56	       | ~ decides(algorithm_of(X2), X1, X0)
231.26/231.56	       | halts2(sk_V, as_input(sk_Y1(sk_W)))),
231.26/231.56	    inference('simplify', [status(thm)], ['31'])).
231.26/231.56	tff('33', plain,
231.26/231.56	    ![X0 : input, X1 : program, X2 : program]:
231.26/231.56	      (~ decides(algorithm_of(X2), X1, X0) | outputs(X2, good)),
231.26/231.56	    inference('clc', [status(thm)], ['32', '30'])).
231.26/231.56	tff('34', plain, (~ $true | outputs(sk_W, good)),
231.26/231.56	    inference('sup-', [status(thm)], ['3', '33'])).
231.26/231.56	tff('35', plain, outputs(sk_W, good),
231.26/231.56	    inference('simplify', [status(thm)], ['34'])).
231.26/231.56	tff('36', plain,
231.26/231.56	    ![X9 : program, X10 : program]:
231.26/231.56	      (zip_tseitin0(X9, X10)
231.26/231.56	       | ~ outputs(X10, good)
231.26/231.56	       | ~ halts3(X10, X9, as_input(X9))),
231.26/231.56	    inference('cnf', [status(esa)], [zf_stmt_1])).
231.26/231.56	tff('37', plain,
231.26/231.56	    ![X0 : program, X1 : program]:
231.26/231.56	      (~ $true
231.26/231.56	       | ~ halts3(X0, sk_Y1(X0), as_input(sk_Y1(X0)))
231.26/231.56	       | ~ outputs(X0, good)
231.26/231.56	       | ~ halts3(X0, sk_Y1(X0), as_input(sk_Y1(X0)))
231.26/231.56	       | ~ outputs(X0, bad)
231.26/231.56	       | zip_tseitin4(X1, sk_V)),
231.26/231.56	    inference('sup-', [status(thm)], ['36', '16'])).
231.26/231.56	tff('38', plain,
231.26/231.56	    ![X0 : program, X1 : program]:
231.26/231.56	      (zip_tseitin4(X1, sk_V)
231.26/231.56	       | ~ outputs(X0, bad)
231.26/231.56	       | ~ outputs(X0, good)
231.26/231.56	       | ~ halts3(X0, sk_Y1(X0), as_input(sk_Y1(X0)))),
231.26/231.56	    inference('simplify', [status(thm)], ['37'])).
231.26/231.56	tff('39', plain,
231.26/231.56	    ![X0 : program]:
231.26/231.56	      (~ $true
231.26/231.56	       | ~ outputs(sk_W, good)
231.26/231.56	       | ~ outputs(sk_W, bad)
231.26/231.56	       | zip_tseitin4(X0, sk_V)),
231.26/231.56	    inference('sup-', [status(thm)], ['11', '38'])).
231.26/231.56	tff('40', plain,
231.26/231.56	    ![X0 : program]:
231.26/231.56	      (zip_tseitin4(X0, sk_V) | ~ outputs(sk_W, bad) | ~ outputs(sk_W, good)),
231.26/231.56	    inference('simplify', [status(thm)], ['39'])).
231.26/231.56	tff('41', plain,
231.26/231.56	    ![X0 : program]:
231.26/231.56	      (~ $true | ~ outputs(sk_W, bad) | zip_tseitin4(X0, sk_V)),
231.26/231.56	    inference('sup-', [status(thm)], ['35', '40'])).
231.26/231.56	tff('42', plain,
231.26/231.56	    ![X0 : program]: (zip_tseitin4(X0, sk_V) | ~ outputs(sk_W, bad)),
231.26/231.56	    inference('simplify', [status(thm)], ['41'])).
231.26/231.56	tff('43', plain,
231.26/231.56	    ![X0 : program, X1 : input, X2 : program]:
231.26/231.56	      (~ $true | halts2(X2, X1) | zip_tseitin4(X0, sk_V)),
231.26/231.56	    inference('sup-', [status(thm)], ['6', '42'])).
231.26/231.56	tff('44', plain,
231.26/231.56	    ![X0 : program, X1 : input, X2 : program]:
231.26/231.56	      (zip_tseitin4(X0, sk_V) | halts2(X2, X1)),
231.26/231.56	    inference('simplify', [status(thm)], ['43'])).
231.26/231.56	tff('45', plain,
231.26/231.56	    ![X0 : program, X1 : input, X2 : program]:
231.26/231.56	      (~ $true
231.26/231.56	       | halts2(X2, X1)
231.26/231.56	       | zip_tseitin3(X0, sk_V)
231.26/231.56	       | halts2(X0, as_input(X0))),
231.26/231.56	    inference('sup-', [status(thm)], ['44', '22'])).
231.26/231.56	tff('46', plain,
231.26/231.56	    ![X0 : program, X1 : input, X2 : program]:
231.26/231.56	      (halts2(X0, as_input(X0)) | zip_tseitin3(X0, sk_V) | halts2(X2, X1)),
231.26/231.56	    inference('simplify', [status(thm)], ['45'])).
231.26/231.56	tff('47', plain,
231.26/231.56	    ![X0 : program]: (halts2(X0, as_input(X0)) | zip_tseitin3(X0, sk_V)),
231.26/231.56	    inference('condensation', [status(thm)], ['46'])).
231.26/231.56	tff('48', plain,
231.26/231.56	    ![X11 : program, X12 : program]:
231.26/231.56	      (outputs(X11, bad) | ~ zip_tseitin3(X12, X11)),
231.26/231.56	    inference('cnf', [status(esa)], [zf_stmt_6])).
231.26/231.56	tff('49', plain,
231.26/231.56	    ![X0 : program]:
231.26/231.56	      (~ $true | halts2(X0, as_input(X0)) | outputs(sk_V, bad)),
231.26/231.56	    inference('sup-', [status(thm)], ['47', '48'])).
231.26/231.56	tff('50', plain,
231.26/231.56	    ![X0 : program]: (outputs(sk_V, bad) | halts2(X0, as_input(X0))),
231.26/231.56	    inference('simplify', [status(thm)], ['49'])).
231.26/231.56	tff('51', plain,
231.26/231.56	    ![X11 : program, X12 : program]:
231.26/231.56	      (~ halts2(X12, as_input(X12))
231.26/231.56	       | zip_tseitin2(X12, X11)
231.26/231.56	       | ~ zip_tseitin4(X12, X11)),
231.26/231.56	    inference('cnf', [status(esa)], [zf_stmt_4])).
231.26/231.56	tff('52', plain,
231.26/231.56	    ![X0 : program, X1 : input, X2 : program]:
231.26/231.56	      (~ $true
231.26/231.56	       | halts2(X2, X1)
231.26/231.56	       | zip_tseitin2(X0, sk_V)
231.26/231.56	       | ~ halts2(X0, as_input(X0))),
231.26/231.56	    inference('sup-', [status(thm)], ['44', '51'])).
231.26/231.56	tff('53', plain,
231.26/231.56	    ![X0 : program, X1 : input, X2 : program]:
231.26/231.56	      (~ halts2(X0, as_input(X0)) | zip_tseitin2(X0, sk_V) | halts2(X2, X1)),
231.26/231.56	    inference('simplify', [status(thm)], ['52'])).
231.26/231.56	tff('54', plain,
231.26/231.56	    ![X11 : program, X12 : program]:
231.26/231.56	      (halts2(X11, as_input(X12)) | ~ zip_tseitin2(X12, X11)),
231.26/231.56	    inference('cnf', [status(esa)], [zf_stmt_8])).
231.26/231.56	tff('55', plain,
231.26/231.56	    ![X0 : program, X1 : input, X2 : program]:
231.26/231.56	      (~ $true
231.26/231.56	       | halts2(X2, X1)
231.26/231.56	       | ~ halts2(X0, as_input(X0))
231.26/231.56	       | halts2(sk_V, as_input(X0))),
231.26/231.56	    inference('sup-', [status(thm)], ['53', '54'])).
231.26/231.56	tff('56', plain,
231.26/231.56	    ![X0 : program, X1 : input, X2 : program]:
231.26/231.56	      (halts2(sk_V, as_input(X0))
231.26/231.56	       | ~ halts2(X0, as_input(X0))
231.26/231.56	       | halts2(X2, X1)),
231.26/231.56	    inference('simplify', [status(thm)], ['55'])).
231.26/231.56	tff('57', plain,
231.26/231.56	    ![X0 : program]:
231.26/231.56	      (halts2(sk_V, as_input(X0)) | ~ halts2(X0, as_input(X0))),
231.26/231.56	    inference('condensation', [status(thm)], ['56'])).
231.26/231.56	tff('58', plain,
231.26/231.56	    ![X0 : program]:
231.26/231.56	      (~ $true | halts2(X0, as_input(X0)) | halts2(sk_V, as_input(X0))),
231.26/231.56	    inference('sup-', [status(thm)], ['47', '25'])).
231.26/231.56	tff('59', plain,
231.26/231.56	    ![X0 : program]: (halts2(sk_V, as_input(X0)) | halts2(X0, as_input(X0))),
231.26/231.56	    inference('simplify', [status(thm)], ['58'])).
231.26/231.56	tff('60', plain, ![X0 : program]: halts2(sk_V, as_input(X0)),
231.26/231.56	    inference('clc', [status(thm)], ['57', '59'])).
231.26/231.56	tff(p4, axiom,
231.26/231.56	  ((?[V:program]:
231.26/231.56	      (![Y:program]:
231.26/231.56	         ((halts2(Y,as_input(Y)) => (halts2(V,as_input(Y)) & outputs(V,good))) & 
231.26/231.56	          ((~halts2(Y,as_input(Y))) =>
231.26/231.56	           (halts2(V,as_input(Y)) & outputs(V,bad)))))) =>
231.26/231.56	   (?[U:program]:
231.26/231.56	      (![Y:program]:
231.26/231.56	         ((halts2(Y,as_input(Y)) => (~halts2(U,as_input(Y)))) & 
231.26/231.56	          ((~halts2(Y,as_input(Y))) =>
231.26/231.56	           (halts2(U,as_input(Y)) & outputs(U,bad)))))))).
231.26/231.56	tff(zf_stmt_12, axiom,
231.26/231.56	  ((halts2(Y,as_input(Y)) => (outputs(V,good) & halts2(V,as_input(Y)))) =>
231.26/231.56	   zip_tseitin5(Y,V))).
231.26/231.56	tff('61', plain,
231.26/231.56	    ![X15 : program, X16 : program]:
231.26/231.56	      (zip_tseitin5(X15, X16)
231.26/231.56	       | ~ outputs(X16, good)
231.26/231.56	       | ~ halts2(X16, as_input(X15))),
231.26/231.56	    inference('cnf', [status(esa)], [zf_stmt_12])).
231.26/231.56	tff(zf_stmt_13, axiom,
231.26/231.56	  (((~halts2(Y,as_input(Y))) => (outputs(V,bad) & halts2(V,as_input(Y)))) =>
231.26/231.56	   zip_tseitin6(Y,V))).
231.26/231.56	tff('62', plain,
231.26/231.56	    ![X15 : program, X16 : program]:
231.26/231.56	      (zip_tseitin6(X15, X16)
231.26/231.56	       | ~ outputs(X16, bad)
231.26/231.56	       | ~ halts2(X16, as_input(X15))),
231.26/231.56	    inference('cnf', [status(esa)], [zf_stmt_13])).
231.26/231.56	tff(zf_stmt_14, type, zip_tseitin8 : (program * program) > $o).
231.26/231.56	tff(zf_stmt_15, axiom,
231.26/231.56	  (zip_tseitin8(Y,U) =>
231.26/231.56	   (((~halts2(Y,as_input(Y))) => zip_tseitin7(Y,U)) & 
231.26/231.56	    (halts2(Y,as_input(Y)) => (~halts2(U,as_input(Y))))))).
231.26/231.56	tff(zf_stmt_16, type, zip_tseitin7 : (program * program) > $o).
231.26/231.56	tff(zf_stmt_17, axiom,
231.26/231.56	  (zip_tseitin7(Y,U) => (outputs(U,bad) & halts2(U,as_input(Y))))).
231.26/231.56	tff(zf_stmt_18, type, zip_tseitin6 : (program * program) > $o).
231.26/231.56	tff(zf_stmt_19, type, zip_tseitin5 : (program * program) > $o).
231.26/231.56	tff(zf_stmt_20, axiom,
231.26/231.56	  ((?[V:program]: (![Y:program]: (zip_tseitin6(Y,V) & zip_tseitin5(Y,V)))) =>
231.26/231.56	   (?[U:program]: (![Y:program]: zip_tseitin8(Y,U))))).
231.26/231.56	tff('63', plain,
231.26/231.56	    ![X19 : program, X20 : program]:
231.26/231.56	      (zip_tseitin8(X19, sk_U)
231.26/231.56	       | ~ zip_tseitin5(sk_Y2(X20), X20)
231.26/231.56	       | ~ zip_tseitin6(sk_Y2(X20), X20)),
231.26/231.56	    inference('cnf', [status(esa)], [zf_stmt_20])).
231.26/231.56	tff('64', plain,
231.26/231.56	    ![X0 : program, X1 : program]:
231.26/231.56	      (~ $true
231.26/231.56	       | ~ halts2(X0, as_input(sk_Y2(X0)))
231.26/231.56	       | ~ outputs(X0, bad)
231.26/231.56	       | ~ zip_tseitin5(sk_Y2(X0), X0)
231.26/231.56	       | zip_tseitin8(X1, sk_U)),
231.26/231.56	    inference('sup-', [status(thm)], ['62', '63'])).
231.26/231.56	tff('65', plain,
231.26/231.56	    ![X0 : program, X1 : program]:
231.26/231.56	      (zip_tseitin8(X1, sk_U)
231.26/231.56	       | ~ zip_tseitin5(sk_Y2(X0), X0)
231.26/231.56	       | ~ outputs(X0, bad)
231.26/231.56	       | ~ halts2(X0, as_input(sk_Y2(X0)))),
231.26/231.56	    inference('simplify', [status(thm)], ['64'])).
231.26/231.56	tff('66', plain,
231.26/231.56	    ![X0 : program, X1 : program]:
231.26/231.56	      (~ $true
231.26/231.56	       | ~ halts2(X0, as_input(sk_Y2(X0)))
231.26/231.56	       | ~ outputs(X0, good)
231.26/231.56	       | ~ halts2(X0, as_input(sk_Y2(X0)))
231.26/231.56	       | ~ outputs(X0, bad)
231.26/231.56	       | zip_tseitin8(X1, sk_U)),
231.26/231.56	    inference('sup-', [status(thm)], ['61', '65'])).
231.26/231.56	tff('67', plain,
231.26/231.56	    ![X0 : program, X1 : program]:
231.26/231.56	      (zip_tseitin8(X1, sk_U)
231.26/231.56	       | ~ outputs(X0, bad)
231.26/231.56	       | ~ outputs(X0, good)
231.26/231.56	       | ~ halts2(X0, as_input(sk_Y2(X0)))),
231.26/231.56	    inference('simplify', [status(thm)], ['66'])).
231.26/231.56	tff('68', plain,
231.26/231.56	    ![X0 : program]:
231.26/231.56	      (~ $true
231.26/231.56	       | ~ outputs(sk_V, good)
231.26/231.56	       | ~ outputs(sk_V, bad)
231.26/231.56	       | zip_tseitin8(X0, sk_U)),
231.26/231.56	    inference('sup-', [status(thm)], ['60', '67'])).
231.26/231.56	tff('69', plain,
231.26/231.56	    ![X9 : program, X10 : program]:
231.26/231.56	      (zip_tseitin1(X9, X10) | ~ halts2(X9, as_input(X9))),
231.26/231.56	    inference('cnf', [status(esa)], [zf_stmt_2])).
231.26/231.56	tff('70', plain,
231.26/231.56	    ![X0 : program, X1 : program]:
231.26/231.56	      (~ $true
231.26/231.56	       | ~ halts2(sk_Y1(X0), as_input(sk_Y1(X0)))
231.26/231.56	       | ~ zip_tseitin0(sk_Y1(X0), X0)
231.26/231.56	       | zip_tseitin4(X1, sk_V)),
231.26/231.56	    inference('sup-', [status(thm)], ['69', '14'])).
231.26/231.56	tff('71', plain,
231.26/231.56	    ![X0 : program, X1 : program]:
231.26/231.56	      (zip_tseitin4(X1, sk_V)
231.26/231.56	       | ~ zip_tseitin0(sk_Y1(X0), X0)
231.26/231.56	       | ~ halts2(sk_Y1(X0), as_input(sk_Y1(X0)))),
231.26/231.56	    inference('simplify', [status(thm)], ['70'])).
231.26/231.56	tff('72', plain,
231.26/231.56	    ![X0 : program, X1 : program]:
231.26/231.56	      (~ $true
231.26/231.56	       | ~ halts3(X0, sk_Y1(X0), as_input(sk_Y1(X0)))
231.26/231.56	       | ~ outputs(X0, good)
231.26/231.56	       | ~ halts2(sk_Y1(X0), as_input(sk_Y1(X0)))
231.26/231.56	       | zip_tseitin4(X1, sk_V)),
231.26/231.56	    inference('sup-', [status(thm)], ['36', '71'])).
231.26/231.56	tff('73', plain,
231.26/231.56	    ![X0 : program, X1 : program]:
231.26/231.56	      (zip_tseitin4(X1, sk_V)
231.26/231.56	       | ~ halts2(sk_Y1(X0), as_input(sk_Y1(X0)))
231.26/231.56	       | ~ outputs(X0, good)
231.26/231.56	       | ~ halts3(X0, sk_Y1(X0), as_input(sk_Y1(X0)))),
231.26/231.56	    inference('simplify', [status(thm)], ['72'])).
231.26/231.56	tff('74', plain,
231.26/231.56	    ![X0 : program, X1 : program]:
231.26/231.56	      (~ halts3(X0, sk_Y1(X0), as_input(sk_Y1(X0)))
231.26/231.56	       | ~ outputs(X0, good)
231.26/231.56	       | zip_tseitin4(X1, sk_V)),
231.26/231.56	    inference('clc', [status(thm)], ['73', '44'])).
231.26/231.56	tff('75', plain,
231.26/231.56	    ![X0 : program]:
231.26/231.56	      (~ $true | zip_tseitin4(X0, sk_V) | ~ outputs(sk_W, good)),
231.26/231.56	    inference('sup-', [status(thm)], ['11', '74'])).
231.26/231.56	tff('76', plain,
231.26/231.56	    ![X0 : program]: (~ $true | zip_tseitin4(X0, sk_V) | ~ $true),
231.26/231.56	    inference('demod', [status(thm)], ['75', '35'])).
231.26/231.56	tff('77', plain, ![X0 : program]: zip_tseitin4(X0, sk_V),
231.26/231.56	    inference('simplify', [status(thm)], ['76'])).
231.26/231.56	tff('78', plain,
231.26/231.56	    ![X0 : program]:
231.26/231.56	      (~ $true | zip_tseitin2(X0, sk_V) | ~ halts2(X0, as_input(X0))),
231.26/231.56	    inference('sup-', [status(thm)], ['77', '51'])).
231.26/231.56	tff('79', plain,
231.26/231.56	    ![X0 : program]: (~ halts2(X0, as_input(X0)) | zip_tseitin2(X0, sk_V)),
231.26/231.56	    inference('simplify', [status(thm)], ['78'])).
231.26/231.56	tff('80', plain,
231.26/231.56	    ![X11 : program, X12 : program]:
231.26/231.56	      (outputs(X11, good) | ~ zip_tseitin2(X12, X11)),
231.26/231.56	    inference('cnf', [status(esa)], [zf_stmt_8])).
231.26/231.56	tff('81', plain,
231.26/231.56	    ![X0 : program]:
231.26/231.56	      (~ $true | ~ halts2(X0, as_input(X0)) | outputs(sk_V, good)),
231.26/231.56	    inference('sup-', [status(thm)], ['79', '80'])).
231.26/231.56	tff('82', plain,
231.26/231.56	    ![X0 : program]: (outputs(sk_V, good) | ~ halts2(X0, as_input(X0))),
231.26/231.56	    inference('simplify', [status(thm)], ['81'])).
231.26/231.56	tff('83', plain, (~ $true | halts2(sk_V, as_input(sk_V))),
231.26/231.56	    inference('eq_fact', [status(thm)], ['59'])).
231.26/231.56	tff('84', plain, halts2(sk_V, as_input(sk_V)),
231.26/231.56	    inference('simplify', [status(thm)], ['83'])).
231.26/231.56	tff('85', plain,
231.26/231.56	    ![X0 : program, X1 : input, X2 : program]:
231.26/231.56	      (~ $true
231.26/231.56	       | halts2(X2, X1)
231.26/231.56	       | ~ halts2(X0, as_input(X0))
231.26/231.56	       | outputs(sk_V, good)),
231.26/231.56	    inference('sup-', [status(thm)], ['53', '80'])).
231.26/231.56	tff('86', plain,
231.26/231.56	    ![X0 : program, X1 : input, X2 : program]:
231.26/231.56	      (outputs(sk_V, good) | ~ halts2(X0, as_input(X0)) | halts2(X2, X1)),
231.26/231.56	    inference('simplify', [status(thm)], ['85'])).
231.26/231.56	tff('87', plain,
231.26/231.56	    ![X0 : input, X1 : program]:
231.26/231.56	      (~ $true | halts2(X1, X0) | outputs(sk_V, good)),
231.26/231.56	    inference('sup-', [status(thm)], ['84', '86'])).
231.26/231.56	tff('88', plain,
231.26/231.56	    ![X0 : input, X1 : program]: (outputs(sk_V, good) | halts2(X1, X0)),
231.26/231.56	    inference('simplify', [status(thm)], ['87'])).
231.26/231.56	tff('89', plain, outputs(sk_V, good),
231.26/231.56	    inference('clc', [status(thm)], ['82', '88'])).
231.26/231.56	tff('90', plain,
231.26/231.56	    ![X0 : program]:
231.26/231.56	      (~ $true | ~ $true | ~ outputs(sk_V, bad) | zip_tseitin8(X0, sk_U)),
231.26/231.56	    inference('demod', [status(thm)], ['68', '89'])).
231.26/231.56	tff('91', plain,
231.26/231.56	    ![X0 : program]: (zip_tseitin8(X0, sk_U) | ~ outputs(sk_V, bad)),
231.26/231.56	    inference('simplify', [status(thm)], ['90'])).
231.26/231.56	tff('92', plain,
231.26/231.56	    ![X0 : program, X1 : program]:
231.26/231.56	      (~ $true | halts2(X1, as_input(X1)) | zip_tseitin8(X0, sk_U)),
231.26/231.56	    inference('sup-', [status(thm)], ['50', '91'])).
231.26/231.56	tff('93', plain,
231.26/231.56	    ![X0 : program, X1 : program]:
231.26/231.56	      (zip_tseitin8(X0, sk_U) | halts2(X1, as_input(X1))),
231.26/231.56	    inference('simplify', [status(thm)], ['92'])).
231.26/231.56	tff('94', plain,
231.26/231.56	    ![X17 : program, X18 : program]:
231.26/231.56	      (halts2(X18, as_input(X18))
231.26/231.56	       | zip_tseitin7(X18, X17)
231.26/231.56	       | ~ zip_tseitin8(X18, X17)),
231.26/231.56	    inference('cnf', [status(esa)], [zf_stmt_15])).
231.26/231.56	tff('95', plain,
231.26/231.56	    ![X0 : program, X1 : program]:
231.26/231.56	      (~ $true
231.26/231.56	       | halts2(X1, as_input(X1))
231.26/231.56	       | zip_tseitin7(X0, sk_U)
231.26/231.56	       | halts2(X0, as_input(X0))),
231.26/231.56	    inference('sup-', [status(thm)], ['93', '94'])).
231.26/231.56	tff('96', plain,
231.26/231.56	    ![X0 : program, X1 : program]:
231.26/231.56	      (halts2(X0, as_input(X0))
231.26/231.56	       | zip_tseitin7(X0, sk_U)
231.26/231.56	       | halts2(X1, as_input(X1))),
231.26/231.56	    inference('simplify', [status(thm)], ['95'])).
231.26/231.56	tff('97', plain,
231.26/231.56	    ![X0 : program]: (halts2(X0, as_input(X0)) | zip_tseitin7(X0, sk_U)),
231.26/231.56	    inference('condensation', [status(thm)], ['96'])).
231.26/231.56	tff('98', plain,
231.26/231.56	    ![X17 : program, X18 : program]:
231.26/231.56	      (halts2(X17, as_input(X18)) | ~ zip_tseitin7(X18, X17)),
231.26/231.56	    inference('cnf', [status(esa)], [zf_stmt_17])).
231.26/231.56	tff('99', plain,
231.26/231.56	    ![X0 : program]:
231.26/231.56	      (~ $true | halts2(X0, as_input(X0)) | halts2(sk_U, as_input(X0))),
231.26/231.56	    inference('sup-', [status(thm)], ['97', '98'])).
231.26/231.56	tff('100', plain,
231.26/231.56	    ![X0 : program]: (halts2(sk_U, as_input(X0)) | halts2(X0, as_input(X0))),
231.26/231.56	    inference('simplify', [status(thm)], ['99'])).
231.26/231.56	tff('101', plain, (~ $true | halts2(sk_U, as_input(sk_U))),
231.26/231.56	    inference('eq_fact', [status(thm)], ['100'])).
231.26/231.56	tff('102', plain, halts2(sk_U, as_input(sk_U)),
231.26/231.56	    inference('simplify', [status(thm)], ['101'])).
231.26/231.56	tff('103', plain,
231.26/231.56	    ![X15 : program, X16 : program]:
231.26/231.56	      (zip_tseitin6(X15, X16) | ~ halts2(X15, as_input(X15))),
231.26/231.56	    inference('cnf', [status(esa)], [zf_stmt_13])).
231.26/231.56	tff('104', plain,
231.26/231.56	    ![X0 : program, X1 : program]:
231.26/231.56	      (~ $true
231.26/231.56	       | ~ halts2(sk_Y2(X0), as_input(sk_Y2(X0)))
231.26/231.56	       | ~ zip_tseitin5(sk_Y2(X0), X0)
231.26/231.56	       | zip_tseitin8(X1, sk_U)),
231.26/231.56	    inference('sup-', [status(thm)], ['103', '63'])).
231.26/231.56	tff('105', plain,
231.26/231.56	    ![X0 : program, X1 : program]:
231.26/231.56	      (zip_tseitin8(X1, sk_U)
231.26/231.56	       | ~ zip_tseitin5(sk_Y2(X0), X0)
231.26/231.56	       | ~ halts2(sk_Y2(X0), as_input(sk_Y2(X0)))),
231.26/231.56	    inference('simplify', [status(thm)], ['104'])).
231.26/231.56	tff('106', plain,
231.26/231.56	    ![X0 : program, X1 : program]:
231.26/231.56	      (~ $true
231.26/231.56	       | ~ halts2(X0, as_input(sk_Y2(X0)))
231.26/231.56	       | ~ outputs(X0, good)
231.26/231.56	       | ~ halts2(sk_Y2(X0), as_input(sk_Y2(X0)))
231.26/231.56	       | zip_tseitin8(X1, sk_U)),
231.26/231.56	    inference('sup-', [status(thm)], ['61', '105'])).
231.26/231.56	tff('107', plain,
231.26/231.56	    ![X0 : program, X1 : program]:
231.26/231.56	      (zip_tseitin8(X1, sk_U)
231.26/231.56	       | ~ halts2(sk_Y2(X0), as_input(sk_Y2(X0)))
231.26/231.56	       | ~ outputs(X0, good)
231.26/231.56	       | ~ halts2(X0, as_input(sk_Y2(X0)))),
231.26/231.56	    inference('simplify', [status(thm)], ['106'])).
231.26/231.56	tff('108', plain,
231.26/231.56	    ![X0 : program, X1 : program]:
231.26/231.56	      (~ halts2(X0, as_input(sk_Y2(X0)))
231.26/231.56	       | ~ outputs(X0, good)
231.26/231.56	       | zip_tseitin8(X1, sk_U)),
231.26/231.56	    inference('clc', [status(thm)], ['107', '93'])).
231.26/231.56	tff('109', plain,
231.26/231.56	    ![X0 : program]:
231.26/231.56	      (~ $true | zip_tseitin8(X0, sk_U) | ~ outputs(sk_V, good)),
231.26/231.56	    inference('sup-', [status(thm)], ['60', '108'])).
231.26/231.56	tff('110', plain,
231.26/231.56	    ![X0 : program]: (~ $true | zip_tseitin8(X0, sk_U) | ~ $true),
231.26/231.56	    inference('demod', [status(thm)], ['109', '89'])).
231.26/231.56	tff('111', plain, ![X0 : program]: zip_tseitin8(X0, sk_U),
231.26/231.56	    inference('simplify', [status(thm)], ['110'])).
231.26/231.56	tff('112', plain,
231.26/231.56	    ![X17 : program, X18 : program]:
231.26/231.56	      (~ halts2(X18, as_input(X18))
231.26/231.56	       | ~ halts2(X17, as_input(X18))
231.26/231.56	       | ~ zip_tseitin8(X18, X17)),
231.26/231.56	    inference('cnf', [status(esa)], [zf_stmt_15])).
231.26/231.56	tff('113', plain,
231.26/231.56	    ![X0 : program]:
231.26/231.56	      (~ $true | ~ halts2(sk_U, as_input(X0)) | ~ halts2(X0, as_input(X0))),
231.26/231.56	    inference('sup-', [status(thm)], ['111', '112'])).
231.26/231.56	tff('114', plain,
231.26/231.56	    ![X0 : program]:
231.26/231.56	      (~ halts2(X0, as_input(X0)) | ~ halts2(sk_U, as_input(X0))),
231.26/231.56	    inference('simplify', [status(thm)], ['113'])).
231.26/231.56	tff('115', plain, (~ $true | ~ halts2(sk_U, as_input(sk_U))),
231.26/231.56	    inference('sup-', [status(thm)], ['102', '114'])).
231.26/231.56	tff('116', plain, (~ $true | ~ $true),
231.26/231.56	    inference('demod', [status(thm)], ['115', '102'])).
231.26/231.56	tff('117', plain, $false, inference('simplify', [status(thm)], ['116'])).
231.26/231.56	
231.26/231.56	% SZS output end Refutation
231.26/231.57	EOF
