%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : COM003+2 : TPTP v9.0.0. Bugfixed v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Jul 24 10:54:53 AM UTC 2025
% Result : Theorem 6.83s 1.20s
% Output : CNFRefutation 6.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 10
% Syntax : Number of formulae : 60 ( 5 unt; 0 def)
% Number of atoms : 170 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 203 ( 93 ~; 86 |; 13 &)
% ( 5 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 14 ( 13 usr; 1 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-1 aty)
% Number of variables : 56 ( 9 sgn 18 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_this,plain,
~ ? [X] : algorithm_program_decides(X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
fof(prove_this_negated,plain,
~ ~ ? [X] : algorithm_program_decides(X),
inference(negate_conjecture,[status(cth)],[prove_this]) ).
cnf(42,plain,
algorithm_program_decides(sK8),
inference(cnf,[status(esa)],[prove_this_negated]) ).
cnf(l0,plain,
algorithm_program_decides(sK8),
inference(instantiation,[status(thm)],[42]) ).
fof(p1,plain,
( ? [X] : algorithm_program_decides(X)
=> ? [W] : program_program_decides(W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
cnf(33,plain,
( ~ algorithm_program_decides(X0)
| program_program_decides(sK3) ),
inference(cnf,[status(esa)],[p1]) ).
cnf(l1,plain,
( ~ algorithm_program_decides(sK8)
| program_program_decides(sK3) ),
inference(instantiation,[status(thm)],[33]) ).
fof(p2,plain,
! [W] :
( program_program_decides(W)
=> ! [Y,Z] :
( program_halts2_halts3_outputs(W,Y,Z,good)
& program_not_halts2_halts3_outputs(W,Y,Z,bad) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2) ).
cnf(35,plain,
( ~ program_program_decides(X0)
| program_not_halts2_halts3_outputs(X0,X1,X2,bad) ),
inference(cnf,[status(esa)],[p2]) ).
cnf(l2,plain,
( ~ program_program_decides(sK3)
| program_not_halts2_halts3_outputs(sK3,sK4(sK3),sK4(sK3),bad) ),
inference(instantiation,[status(thm)],[35]) ).
fof(p3,plain,
( ? [W] :
( program(W)
& ! [Y] :
( program_halts2_halts3_outputs(W,Y,Y,good)
& program_not_halts2_halts3_outputs(W,Y,Y,bad) ) )
=> ? [V] :
( program(V)
& ! [Y] :
( program_halts2_halts2_outputs(V,Y,good)
& program_not_halts2_halts2_outputs(V,Y,bad) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3) ).
cnf(38,plain,
( ~ program_not_halts2_halts3_outputs(X0,sK4(X0),sK4(X0),bad)
| ~ program(X0)
| ~ program_halts2_halts3_outputs(X0,sK4(X0),sK4(X0),good)
| program_not_halts2_halts2_outputs(sK5,X1,bad) ),
inference(cnf,[status(esa)],[p3]) ).
cnf(l3,plain,
( ~ program_not_halts2_halts3_outputs(sK3,sK4(sK3),sK4(sK3),bad)
| ~ program(sK3)
| ~ program_halts2_halts3_outputs(sK3,sK4(sK3),sK4(sK3),good)
| program_not_halts2_halts2_outputs(sK5,sK6(sK5),bad) ),
inference(instantiation,[status(thm)],[38]) ).
fof(program_program_decides_def,plain,
! [X] :
( program_program_decides(X)
<=> ( program(X)
& program_decides(X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',program_program_decides_def) ).
cnf(3,plain,
( ~ program_program_decides(X0)
| program(X0) ),
inference(cnf,[status(esa)],[program_program_decides_def]) ).
cnf(l82,plain,
( ~ program_program_decides(sK3)
| program(sK3) ),
inference(instantiation,[status(thm)],[3]) ).
fof(p4,plain,
( ? [V] :
( program(V)
& ! [Y] :
( program_halts2_halts2_outputs(V,Y,good)
& program_not_halts2_halts2_outputs(V,Y,bad) ) )
=> ? [U] :
( program(U)
& ! [Y] :
( ( program_halts2(Y,Y)
=> ~ halts2(U,Y) )
& program_not_halts2_halts2_outputs(U,Y,good) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p4) ).
cnf(39,plain,
( ~ program(X0)
| ~ program_not_halts2_halts2_outputs(X0,sK6(X0),bad)
| ~ program_halts2_halts2_outputs(X0,sK6(X0),good)
| program(sK7) ),
inference(cnf,[status(esa)],[p4]) ).
cnf(l86,plain,
( ~ program(sK5)
| ~ program_not_halts2_halts2_outputs(sK5,sK6(sK5),bad)
| ~ program_halts2_halts2_outputs(sK5,sK6(sK5),good)
| program(sK7) ),
inference(instantiation,[status(thm)],[39]) ).
cnf(37,plain,
( ~ program_not_halts2_halts3_outputs(X0,sK4(X0),sK4(X0),bad)
| ~ program(X0)
| ~ program_halts2_halts3_outputs(X0,sK4(X0),sK4(X0),good)
| program_halts2_halts2_outputs(sK5,X1,good) ),
inference(cnf,[status(esa)],[p3]) ).
cnf(l87,plain,
( ~ program_not_halts2_halts3_outputs(sK3,sK4(sK3),sK4(sK3),bad)
| ~ program(sK3)
| ~ program_halts2_halts3_outputs(sK3,sK4(sK3),sK4(sK3),good)
| program_halts2_halts2_outputs(sK5,sK6(sK5),good) ),
inference(instantiation,[status(thm)],[37]) ).
cnf(34,plain,
( ~ program_program_decides(X0)
| program_halts2_halts3_outputs(X0,X1,X2,good) ),
inference(cnf,[status(esa)],[p2]) ).
cnf(l146,plain,
( ~ program_program_decides(sK3)
| program_halts2_halts3_outputs(sK3,sK4(sK3),sK4(sK3),good) ),
inference(instantiation,[status(thm)],[34]) ).
cnf(36,plain,
( ~ program_not_halts2_halts3_outputs(X0,sK4(X0),sK4(X0),bad)
| ~ program(X0)
| ~ program_halts2_halts3_outputs(X0,sK4(X0),sK4(X0),good)
| program(sK5) ),
inference(cnf,[status(esa)],[p3]) ).
cnf(l88,plain,
( ~ program_not_halts2_halts3_outputs(sK3,sK4(sK3),sK4(sK3),bad)
| ~ program(sK3)
| ~ program_halts2_halts3_outputs(sK3,sK4(sK3),sK4(sK3),good)
| program(sK5) ),
inference(instantiation,[status(thm)],[36]) ).
cnf(l84,plain,
( ~ program_program_decides(sK3)
| program_halts2_halts3_outputs(sK3,sK4(sK3),sK4(sK3),good) ),
inference(instantiation,[status(thm)],[34]) ).
cnf(l90,plain,
( ~ program_program_decides(sK3)
| program_halts2_halts3_outputs(sK3,sK4(sK3),sK4(sK3),good) ),
inference(instantiation,[status(thm)],[34]) ).
cnf(l91,plain,
( ~ program_program_decides(sK3)
| program(sK3) ),
inference(instantiation,[status(thm)],[3]) ).
cnf(l96,plain,
( ~ program_program_decides(sK3)
| program(sK3) ),
inference(instantiation,[status(thm)],[3]) ).
fof(program_not_halts2_def,plain,
! [X,Y] :
( program_not_halts2(X,Y)
<=> ( program(X)
& ~ halts2(X,Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',program_not_halts2_def) ).
cnf(17,plain,
( ~ program(X0)
| program_not_halts2(X0,X1)
| halts2(X0,X1) ),
inference(cnf,[status(esa)],[program_not_halts2_def]) ).
cnf(l113,plain,
( ~ program(sK7)
| program_not_halts2(sK7,sK7)
| halts2(sK7,sK7) ),
inference(instantiation,[status(thm)],[17]) ).
cnf(40,plain,
( ~ program(X0)
| ~ halts2(sK7,X1)
| ~ program_halts2(X1,X1)
| ~ program_not_halts2_halts2_outputs(X0,sK6(X0),bad)
| ~ program_halts2_halts2_outputs(X0,sK6(X0),good) ),
inference(cnf,[status(esa)],[p4]) ).
cnf(l118,plain,
( ~ program(sK5)
| ~ halts2(sK7,sK7)
| ~ program_halts2(sK7,sK7)
| ~ program_not_halts2_halts2_outputs(sK5,sK6(sK5),bad)
| ~ program_halts2_halts2_outputs(sK5,sK6(sK5),good) ),
inference(instantiation,[status(thm)],[40]) ).
fof(program_halts2_def,plain,
! [X,Y] :
( program_halts2(X,Y)
<=> ( program(X)
& halts2(X,Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',program_halts2_def) ).
cnf(11,plain,
( ~ program(X0)
| ~ halts2(X0,X1)
| program_halts2(X0,X1) ),
inference(cnf,[status(esa)],[program_halts2_def]) ).
cnf(l844,plain,
( ~ program(sK7)
| ~ halts2(sK7,sK7)
| program_halts2(sK7,sK7) ),
inference(instantiation,[status(thm)],[11]) ).
cnf(l835,plain,
( ~ program_not_halts2_halts3_outputs(sK3,sK4(sK3),sK4(sK3),bad)
| ~ program(sK3)
| ~ program_halts2_halts3_outputs(sK3,sK4(sK3),sK4(sK3),good)
| program(sK5) ),
inference(instantiation,[status(thm)],[36]) ).
cnf(l1096,plain,
( ~ program_program_decides(sK3)
| program_halts2_halts3_outputs(sK3,sK4(sK3),sK4(sK3),good) ),
inference(instantiation,[status(thm)],[34]) ).
fof(program_not_halts2_halts2_outputs_def,plain,
! [X,Y,W] :
( program_not_halts2_halts2_outputs(X,Y,W)
<=> ( program_not_halts2(Y,Y)
=> halts2_outputs(X,Y,W) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',program_not_halts2_halts2_outputs_def) ).
cnf(30,plain,
( ~ program_not_halts2(X0,X0)
| ~ program_not_halts2_halts2_outputs(X1,X0,X2)
| halts2_outputs(X1,X0,X2) ),
inference(cnf,[status(esa)],[program_not_halts2_halts2_outputs_def]) ).
cnf(l823,plain,
( ~ program_not_halts2(sK7,sK7)
| ~ program_not_halts2_halts2_outputs(sK7,sK7,good)
| halts2_outputs(sK7,sK7,good) ),
inference(instantiation,[status(thm)],[30]) ).
cnf(41,plain,
( ~ program(X0)
| ~ program_not_halts2_halts2_outputs(X0,sK6(X0),bad)
| ~ program_halts2_halts2_outputs(X0,sK6(X0),good)
| program_not_halts2_halts2_outputs(sK7,X1,good) ),
inference(cnf,[status(esa)],[p4]) ).
cnf(l824,plain,
( ~ program(sK5)
| ~ program_not_halts2_halts2_outputs(sK5,sK6(sK5),bad)
| ~ program_halts2_halts2_outputs(sK5,sK6(sK5),good)
| program_not_halts2_halts2_outputs(sK7,sK7,good) ),
inference(instantiation,[status(thm)],[41]) ).
cnf(l944,plain,
( ~ program_program_decides(sK3)
| program(sK3) ),
inference(instantiation,[status(thm)],[3]) ).
cnf(l975,plain,
( ~ program_not_halts2_halts3_outputs(sK3,sK4(sK3),sK4(sK3),bad)
| ~ program(sK3)
| ~ program_halts2_halts3_outputs(sK3,sK4(sK3),sK4(sK3),good)
| program_halts2_halts2_outputs(sK5,sK6(sK5),good) ),
inference(instantiation,[status(thm)],[37]) ).
cnf(l1099,plain,
( ~ program_program_decides(sK3)
| program_halts2_halts3_outputs(sK3,sK4(sK3),sK4(sK3),good) ),
inference(instantiation,[status(thm)],[34]) ).
fof(halts2_outputs_def,plain,
! [X,Y,W] :
( halts2_outputs(X,Y,W)
<=> ( halts2(X,Y)
& outputs(X,W) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',halts2_outputs_def) ).
cnf(18,plain,
( ~ halts2_outputs(X0,X1,X2)
| halts2(X0,X1) ),
inference(cnf,[status(esa)],[halts2_outputs_def]) ).
cnf(l848,plain,
( ~ halts2_outputs(sK7,sK7,good)
| halts2(sK7,sK7) ),
inference(instantiation,[status(thm)],[18]) ).
cnf(l1118,plain,
( ~ program_program_decides(sK3)
| program(sK3) ),
inference(instantiation,[status(thm)],[3]) ).
cnf(16,plain,
( ~ program_not_halts2(X0,X1)
| ~ halts2(X0,X1) ),
inference(cnf,[status(esa)],[program_not_halts2_def]) ).
cnf(l951,plain,
( ~ program_not_halts2(sK7,sK7)
| ~ halts2(sK7,sK7) ),
inference(instantiation,[status(thm)],[16]) ).
cnf(l956,plain,
( ~ program_not_halts2_halts3_outputs(sK3,sK4(sK3),sK4(sK3),bad)
| ~ program(sK3)
| ~ program_halts2_halts3_outputs(sK3,sK4(sK3),sK4(sK3),good)
| program_halts2_halts2_outputs(sK5,sK6(sK5),good) ),
inference(instantiation,[status(thm)],[37]) ).
cnf(l1086,plain,
( ~ program_program_decides(sK3)
| program_halts2_halts3_outputs(sK3,sK4(sK3),sK4(sK3),good) ),
inference(instantiation,[status(thm)],[34]) ).
cnf(l957,plain,
( ~ program_program_decides(sK3)
| program(sK3) ),
inference(instantiation,[status(thm)],[3]) ).
cnf(l853,plain,
( ~ program_not_halts2_halts3_outputs(sK3,sK4(sK3),sK4(sK3),bad)
| ~ program(sK3)
| ~ program_halts2_halts3_outputs(sK3,sK4(sK3),sK4(sK3),good)
| program(sK5) ),
inference(instantiation,[status(thm)],[36]) ).
cnf(l1092,plain,
( ~ program_program_decides(sK3)
| program_halts2_halts3_outputs(sK3,sK4(sK3),sK4(sK3),good) ),
inference(instantiation,[status(thm)],[34]) ).
cnf(l942,plain,
( ~ program_program_decides(sK3)
| program(sK3) ),
inference(instantiation,[status(thm)],[3]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l2,l3,l82,l86,l87,l146,l88,l84,l90,l91,l96,l113,l118,l844,l835,l1096,l823,l824,l944,l975,l1099,l848,l1118,l951,l956,l1086,l957,l853,l1092,l942]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : COM003+2 : TPTP v9.0.0. Bugfixed v2.2.0.
% 0.10/0.13 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.34 % Computer : n026.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sun Jul 20 06:07:04 EDT 2025
% 0.14/0.34 % CPUTime :
% 0.14/0.35 % launching worker at depth: 3
% 0.14/0.35 % launching worker at depth: 1
% 0.14/0.35 % launching worker at depth: 5
% 0.14/0.35 % launching worker at depth: 6
% 0.14/0.35 % launching worker at depth: 8
% 0.14/0.35 % launching worker at depth: 2
% 0.14/0.35 % launching worker at depth: 7
% 0.14/0.35 % launching worker at depth: 4
% 0.14/0.35 % launching worker at depth: 9
% 0.14/0.35 % launching worker at depth: 10
% 0.14/0.35 % launching worker at depth: 11
% 0.14/0.35 % launching worker at depth: 12
% 0.14/0.36 % launching worker at depth: 13
% 0.14/0.39 % launching worker at depth: 14
% 0.21/0.53 % launching worker at depth: 15
% 6.83/1.20 % SZS status Theorem for theBenchmark
% 6.83/1.20 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------