%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : GRA002+4 : TPTP v9.0.0. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n028.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 01:41:51 PM UTC 2025
% Result : Theorem 210.79s 26.84s
% Output : CNFRefutation 210.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of formulae : 21 ( 10 unt; 0 def)
% Number of atoms : 40 ( 7 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 31 ( 12 ~; 8 |; 2 &)
% ( 1 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 2 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 29 ( 5 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(maximal_path_length,plain,
( complete
=> ! [P,V1,V2] :
( shortest_path(V1,V2,P)
=> less_or_equal(minus(length_of(P),n1),number_of_in(triangles,graph)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maximal_path_length) ).
fof(maximal_path_length_negated,plain,
~ ( complete
=> ! [P,V1,V2] :
( shortest_path(V1,V2,P)
=> less_or_equal(minus(length_of(P),n1),number_of_in(triangles,graph)) ) ),
inference(negate_conjecture,[status(cth)],[maximal_path_length]) ).
cnf(61,plain,
shortest_path(sK12,sK13,sK11),
inference(cnf,[status(esa)],[maximal_path_length_negated]) ).
cnf(l0,plain,
shortest_path(sK12,sK13,sK11),
inference(instantiation,[status(thm)],[61]) ).
fof(shortest_path_defn,plain,
! [V1,V2,SP] :
( shortest_path(V1,V2,SP)
<=> ( path(V1,V2,SP)
& V1 != V2
& ! [P] :
( path(V1,V2,P)
=> less_or_equal(length_of(SP),length_of(P)) ) ) ),
file('Axioms/GRA001+0.ax',shortest_path_defn) ).
cnf(38,plain,
( ~ shortest_path(X0,X1,X2)
| path(X0,X1,X2) ),
inference(cnf,[status(esa)],[shortest_path_defn]) ).
cnf(l1,plain,
( ~ shortest_path(sK12,sK13,sK11)
| path(sK12,sK13,sK11) ),
inference(instantiation,[status(thm)],[38]) ).
fof(path_length_sequential_pairs,plain,
! [V1,V2,P] :
( path(V1,V2,P)
=> number_of_in(sequential_pairs,P) = minus(length_of(P),n1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',path_length_sequential_pairs) ).
cnf(53,plain,
( ~ path(X0,X1,X2)
| number_of_in(sequential_pairs,X2) = minus(length_of(X2),n1) ),
inference(cnf,[status(esa)],[path_length_sequential_pairs]) ).
cnf(l3,plain,
( ~ path(sK12,sK13,sK11)
| number_of_in(sequential_pairs,sK11) = minus(length_of(sK11),n1) ),
inference(instantiation,[status(thm)],[53]) ).
fof(triangles_and_sequential_pairs,plain,
( complete
=> ! [P,V1,V2] :
( shortest_path(V1,V2,P)
=> number_of_in(sequential_pairs,P) = number_of_in(triangles,P) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',triangles_and_sequential_pairs) ).
cnf(59,plain,
( ~ complete
| ~ shortest_path(X0,X1,X2)
| number_of_in(sequential_pairs,X2) = number_of_in(triangles,X2) ),
inference(cnf,[status(esa)],[triangles_and_sequential_pairs]) ).
cnf(l248,plain,
( ~ complete
| ~ shortest_path(sK12,sK13,sK11)
| number_of_in(sequential_pairs,sK11) = number_of_in(triangles,sK11) ),
inference(instantiation,[status(thm)],[59]) ).
fof(graph_has_them_all,plain,
! [Things,InThese] : less_or_equal(number_of_in(Things,InThese),number_of_in(Things,graph)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',graph_has_them_all) ).
cnf(58,plain,
less_or_equal(number_of_in(X0,X1),number_of_in(X0,graph)),
inference(cnf,[status(esa)],[graph_has_them_all]) ).
cnf(l262,plain,
less_or_equal(number_of_in(triangles,sK11),number_of_in(triangles,graph)),
inference(instantiation,[status(thm)],[58]) ).
cnf(62,plain,
~ less_or_equal(minus(length_of(sK11),n1),number_of_in(triangles,graph)),
inference(cnf,[status(esa)],[maximal_path_length_negated]) ).
cnf(l1299,plain,
~ less_or_equal(minus(length_of(sK11),n1),number_of_in(triangles,graph)),
inference(instantiation,[status(thm)],[62]) ).
cnf(60,plain,
complete,
inference(cnf,[status(esa)],[maximal_path_length_negated]) ).
cnf(l2132,plain,
complete,
inference(instantiation,[status(thm)],[60]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l3,l248,l262,l1299,l2132]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRA002+4 : TPTP v9.0.0. Bugfixed v3.2.0.
% 0.03/0.12 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n028.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sun Jul 20 13:07:19 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.34 % launching worker at depth: 2
% 0.12/0.34 % launching worker at depth: 8
% 0.12/0.34 % launching worker at depth: 4
% 0.12/0.34 % launching worker at depth: 3
% 0.12/0.34 % launching worker at depth: 5
% 0.12/0.34 % launching worker at depth: 1
% 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: 9
% 0.12/0.34 % launching worker at depth: 10
% 0.19/0.44 % launching worker at depth: 11
% 6.61/1.17 % launching worker at depth: 12
% 210.79/26.84 % SZS status Theorem for theBenchmark
% 210.79/26.84 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------