%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : GRA005+1 : 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 01:41:52 PM UTC 2025
% Result : Theorem 0.12s 0.34s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 2
% Syntax : Number of formulae : 14 ( 9 unt; 0 def)
% Number of atoms : 32 ( 14 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 31 ( 13 ~; 6 |; 9 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-1 aty)
% Number of variables : 24 ( 2 sgn 15 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(no_short_cut_edge,plain,
! [V1,V2,E1,E2,P] :
( ( shortest_path(V1,V2,P)
& precedes(E1,E2,P) )
=> ~ ? [E3] :
( edge(E3)
& tail_of(E3) = tail_of(E1)
& head_of(E3) = head_of(E2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',no_short_cut_edge) ).
fof(no_short_cut_edge_negated,plain,
~ ! [V1,V2,E1,E2,P] :
( ( shortest_path(V1,V2,P)
& precedes(E1,E2,P) )
=> ~ ? [E3] :
( edge(E3)
& tail_of(E3) = tail_of(E1)
& head_of(E3) = head_of(E2) ) ),
inference(negate_conjecture,[status(cth)],[no_short_cut_edge]) ).
cnf(59,plain,
shortest_path(sK11,sK12,sK15),
inference(cnf,[status(esa)],[no_short_cut_edge_negated]) ).
cnf(l0,plain,
shortest_path(sK11,sK12,sK15),
inference(instantiation,[status(thm)],[59]) ).
fof(shortest_path_properties,plain,
! [V1,V2,E1,E2,P] :
( ( shortest_path(V1,V2,P)
& precedes(E1,E2,P) )
=> ( ~ ? [E3] :
( tail_of(E3) = tail_of(E1)
& head_of(E3) = head_of(E2) )
& ~ precedes(E2,E1,P) ) ),
file('Axioms/GRA001+0.ax',shortest_path_properties) ).
cnf(43,plain,
( tail_of(X0) != tail_of(X1)
| head_of(X0) != head_of(X2)
| ~ shortest_path(X3,X4,X5)
| ~ precedes(X1,X2,X5) ),
inference(cnf,[status(esa)],[shortest_path_properties]) ).
cnf(l1,plain,
( tail_of(sK16) != tail_of(sK13)
| head_of(sK16) != head_of(sK14)
| ~ shortest_path(sK11,sK12,sK15)
| ~ precedes(sK13,sK14,sK15) ),
inference(instantiation,[status(thm)],[43]) ).
cnf(62,plain,
tail_of(sK16) = tail_of(sK13),
inference(cnf,[status(esa)],[no_short_cut_edge_negated]) ).
cnf(l3,plain,
tail_of(sK16) = tail_of(sK13),
inference(instantiation,[status(thm)],[62]) ).
cnf(63,plain,
head_of(sK16) = head_of(sK14),
inference(cnf,[status(esa)],[no_short_cut_edge_negated]) ).
cnf(l2,plain,
head_of(sK16) = head_of(sK14),
inference(instantiation,[status(thm)],[63]) ).
cnf(60,plain,
precedes(sK13,sK14,sK15),
inference(cnf,[status(esa)],[no_short_cut_edge_negated]) ).
cnf(l6,plain,
precedes(sK13,sK14,sK15),
inference(instantiation,[status(thm)],[60]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l3,l2,l6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRA005+1 : TPTP v9.0.0. Bugfixed v3.2.0.
% 0.07/0.12 % 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 13:07:49 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.34 % launching worker at depth: 1
% 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: 2
% 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: 5
% 0.12/0.34 % launching worker at depth: 9
% 0.12/0.34 % SZS status Theorem for theBenchmark
% 0.12/0.34 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------