%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRA005+1 : TPTP v9.3.1. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:18:43 AM UTC 2026
% Result : Theorem 4.83s 4.05s
% Output : CNFRefutation 4.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 2
% Syntax : Number of formulae : 14 ( 6 unt; 0 def)
% Number of atoms : 37 ( 14 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 45 ( 22 ~; 11 |; 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 : 39 ( 10 sgn 15 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(shortest_path_properties,axiom,
! [X0,X1,X2,X3,X4] :
( ( precedes(X2,X3,X4)
& 'shortest$upath'(X0,X1,X4) )
=> ( ~ precedes(X3,X2,X4)
& ~ ? [X5] :
( 'head$uof'(X5) = 'head$uof'(X3)
& 'tail$uof'(X5) = 'tail$uof'(X2) ) ) ) ).
fof(no_short_cut_edge,conjecture,
! [X0,X1,X2,X3,X4] :
( ( precedes(X2,X3,X4)
& 'shortest$upath'(X0,X1,X4) )
=> ~ ? [X5] :
( 'head$uof'(X5) = 'head$uof'(X3)
& 'tail$uof'(X5) = 'tail$uof'(X2)
& edge(X5) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2,X3,X4] :
( ( precedes(X2,X3,X4)
& 'shortest$upath'(X0,X1,X4) )
=> ~ ? [X5] :
( 'head$uof'(X5) = 'head$uof'(X3)
& 'tail$uof'(X5) = 'tail$uof'(X2)
& edge(X5) ) ),
inference(negate_conjecture,[status(cth)],[no_short_cut_edge]) ).
cnf(c76,plain,
( 'head$uof'(X5) != 'head$uof'(X4)
| 'tail$uof'(X5) != 'tail$uof'(X3)
| ~ precedes(X3,X4,X2)
| ~ 'shortest$upath'(X0,X1,X2) ),
inference(clausification,[status(esa)],[shortest_path_properties]) ).
cnf(c78,plain,
'shortest$upath'(sK75,sK76,sK79),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c79,plain,
precedes(sK77,sK78,sK79),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c81,plain,
'tail$uof'(sK80) = 'tail$uof'(sK77),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c82,plain,
'head$uof'(sK80) = 'head$uof'(sK78),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ 'shortest$upath'(X3,X4,X2)
| ~ precedes(sK77,X1,X2)
| 'head$uof'(X0) != 'head$uof'(X1)
| 'tail$uof'(X0) != 'tail$uof'(sK80) ),
inference(superposition,[status(thm)],[c81,c76]) ).
cnf(d1,plain,
( ~ 'shortest$upath'(X2,X3,X1)
| ~ precedes(sK77,X0,X1)
| 'head$uof'(sK80) != 'head$uof'(X0) ),
inference(equality_resolution,[status(thm)],[d0]) ).
cnf(d2,plain,
( ~ 'shortest$upath'(X1,X2,X0)
| ~ precedes(sK77,sK78,X0)
| 'head$uof'(sK80) != 'head$uof'(sK80) ),
inference(superposition,[status(thm)],[c82,d1]) ).
cnf(d3,plain,
( ~ 'shortest$upath'(X1,X2,X0)
| ~ precedes(sK77,sK78,X0) ),
inference(equality_resolution,[status(thm)],[d2]) ).
cnf(d4,plain,
~ precedes(sK77,sK78,sK79),
inference(resolution,[status(thm)],[d3,c78]) ).
cnf(d5,plain,
$false,
inference(resolution,[status(thm)],[c79,d4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRA005+1 : TPTP v9.3.1. Bugfixed v3.2.0.
% 0.00/0.05 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n007.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Fri Sep 25 13:45:53 UTC 2026
% 0.17/0.42 % CPUTime :
% 0.17/0.42 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.83/4.05 % SZS status Theorem for theBenchmark.p
% 4.83/4.05 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------