%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : GRA010+2 : TPTP v9.0.0. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 01:41:52 PM UTC 2025
% Result : Theorem 0.12s 0.38s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 2
% Syntax : Number of formulae : 24 ( 11 unt; 0 def)
% Number of atoms : 63 ( 16 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 61 ( 22 ~; 22 |; 9 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 2 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 33 ( 1 sgn 15 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(complete_means_sequential_pairs_and_triangles,plain,
( complete
=> ! [P,V1,V2] :
( ( path(V1,V2,P)
& ! [E1,E2] :
( ( on_path(E1,P)
& on_path(E2,P)
& sequential(E1,E2) )
=> ? [E3] : triangle(E1,E2,E3) ) )
=> number_of_in(sequential_pairs,P) = number_of_in(triangles,P) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complete_means_sequential_pairs_and_triangles) ).
fof(complete_means_sequential_pairs_and_triangles_negated,plain,
~ ( complete
=> ! [P,V1,V2] :
( ( path(V1,V2,P)
& ! [E1,E2] :
( ( on_path(E1,P)
& on_path(E2,P)
& sequential(E1,E2) )
=> ? [E3] : triangle(E1,E2,E3) ) )
=> number_of_in(sequential_pairs,P) = number_of_in(triangles,P) ) ),
inference(negate_conjecture,[status(cth)],[complete_means_sequential_pairs_and_triangles]) ).
cnf(62,plain,
( ~ sequential(X0,X1)
| ~ on_path(X0,sK12)
| ~ on_path(X1,sK12)
| triangle(X0,X1,sK15(X0,X1)) ),
inference(cnf,[status(esa)],[complete_means_sequential_pairs_and_triangles_negated]) ).
cnf(l0,plain,
( ~ sequential(sK9(sK12,sK13,sK14),sK10(sK12,sK13,sK14))
| ~ on_path(sK9(sK12,sK13,sK14),sK12)
| ~ on_path(sK10(sK12,sK13,sK14),sK12)
| triangle(sK9(sK12,sK13,sK14),sK10(sK12,sK13,sK14),sK15(sK9(sK12,sK13,sK14),sK10(sK12,sK13,sK14))) ),
inference(instantiation,[status(thm)],[62]) ).
fof(sequential_pairs_and_triangles,plain,
! [P,V1,V2] :
( ( path(V1,V2,P)
& ! [E1,E2] :
( ( on_path(E1,P)
& on_path(E2,P)
& sequential(E1,E2) )
=> ? [E3] : triangle(E1,E2,E3) ) )
=> number_of_in(sequential_pairs,P) = number_of_in(triangles,P) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sequential_pairs_and_triangles) ).
cnf(55,plain,
( ~ path(X0,X1,X2)
| number_of_in(sequential_pairs,X2) = number_of_in(triangles,X2)
| on_path(sK10(X2,X0,X1),X2) ),
inference(cnf,[status(esa)],[sequential_pairs_and_triangles]) ).
cnf(l13,plain,
( ~ path(sK13,sK14,sK12)
| number_of_in(sequential_pairs,sK12) = number_of_in(triangles,sK12)
| on_path(sK10(sK12,sK13,sK14),sK12) ),
inference(instantiation,[status(thm)],[55]) ).
cnf(61,plain,
path(sK13,sK14,sK12),
inference(cnf,[status(esa)],[complete_means_sequential_pairs_and_triangles_negated]) ).
cnf(l17,plain,
path(sK13,sK14,sK12),
inference(instantiation,[status(thm)],[61]) ).
cnf(54,plain,
( ~ path(X0,X1,X2)
| number_of_in(sequential_pairs,X2) = number_of_in(triangles,X2)
| on_path(sK9(X2,X0,X1),X2) ),
inference(cnf,[status(esa)],[sequential_pairs_and_triangles]) ).
cnf(l12,plain,
( ~ path(sK13,sK14,sK12)
| number_of_in(sequential_pairs,sK12) = number_of_in(triangles,sK12)
| on_path(sK9(sK12,sK13,sK14),sK12) ),
inference(instantiation,[status(thm)],[54]) ).
cnf(l15,plain,
path(sK13,sK14,sK12),
inference(instantiation,[status(thm)],[61]) ).
cnf(63,plain,
number_of_in(sequential_pairs,sK12) != number_of_in(triangles,sK12),
inference(cnf,[status(esa)],[complete_means_sequential_pairs_and_triangles_negated]) ).
cnf(l16,plain,
number_of_in(sequential_pairs,sK12) != number_of_in(triangles,sK12),
inference(instantiation,[status(thm)],[63]) ).
cnf(56,plain,
( ~ path(X0,X1,X2)
| number_of_in(sequential_pairs,X2) = number_of_in(triangles,X2)
| sequential(sK9(X2,X0,X1),sK10(X2,X0,X1)) ),
inference(cnf,[status(esa)],[sequential_pairs_and_triangles]) ).
cnf(l1,plain,
( ~ path(sK13,sK14,sK12)
| number_of_in(sequential_pairs,sK12) = number_of_in(triangles,sK12)
| sequential(sK9(sK12,sK13,sK14),sK10(sK12,sK13,sK14)) ),
inference(instantiation,[status(thm)],[56]) ).
cnf(l2,plain,
path(sK13,sK14,sK12),
inference(instantiation,[status(thm)],[61]) ).
cnf(l3,plain,
number_of_in(sequential_pairs,sK12) != number_of_in(triangles,sK12),
inference(instantiation,[status(thm)],[63]) ).
cnf(57,plain,
( ~ path(X0,X1,X2)
| ~ triangle(sK9(X2,X0,X1),sK10(X2,X0,X1),X3)
| number_of_in(sequential_pairs,X2) = number_of_in(triangles,X2) ),
inference(cnf,[status(esa)],[sequential_pairs_and_triangles]) ).
cnf(l11,plain,
( ~ path(sK13,sK14,sK12)
| ~ triangle(sK9(sK12,sK13,sK14),sK10(sK12,sK13,sK14),sK15(sK9(sK12,sK13,sK14),sK10(sK12,sK13,sK14)))
| number_of_in(sequential_pairs,sK12) = number_of_in(triangles,sK12) ),
inference(instantiation,[status(thm)],[57]) ).
cnf(l23,plain,
path(sK13,sK14,sK12),
inference(instantiation,[status(thm)],[61]) ).
cnf(l18,plain,
number_of_in(sequential_pairs,sK12) != number_of_in(triangles,sK12),
inference(instantiation,[status(thm)],[63]) ).
cnf(l22,plain,
number_of_in(sequential_pairs,sK12) != number_of_in(triangles,sK12),
inference(instantiation,[status(thm)],[63]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l13,l17,l12,l15,l16,l1,l2,l3,l11,l23,l18,l22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRA010+2 : TPTP v9.0.0. Bugfixed v3.2.0.
% 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.34 % Computer : n018.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sun Jul 20 13:09:19 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.34 % launching worker at depth: 1
% 0.12/0.34 % launching worker at depth: 3
% 0.12/0.34 % launching worker at depth: 6
% 0.12/0.34 % launching worker at depth: 7
% 0.12/0.34 % launching worker at depth: 4
% 0.12/0.34 % launching worker at depth: 5
% 0.12/0.34 % launching worker at depth: 2
% 0.12/0.34 % launching worker at depth: 8
% 0.12/0.35 % launching worker at depth: 9
% 0.12/0.38 % SZS status Theorem for theBenchmark
% 0.12/0.38 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------