%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRA005+1 : TPTP v9.3.1. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 07:19:22 AM UTC 2026
% Result : Theorem 0.12s 0.60s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 2
% Syntax : Number of formulae : 15 ( 7 unt; 0 def)
% Number of atoms : 41 ( 20 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 42 ( 16 ~; 6 |; 17 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 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 : 34 ( 2 sgn 15 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(shortest_path_properties,axiom,
! [V1,V2,E1,E2,P] :
( ( precedes(E1,E2,P)
& shortest_path(V1,V2,P) )
=> ( ~ precedes(E2,E1,P)
& ~ ? [E3] :
( head_of(E3) = head_of(E2)
& tail_of(E3) = tail_of(E1) ) ) ),
file('theBenchmark.p',shortest_path_properties) ).
fof(no_short_cut_edge,conjecture,
! [V1,V2,E1,E2,P] :
( ( precedes(E1,E2,P)
& shortest_path(V1,V2,P) )
=> ~ ? [E3] :
( head_of(E3) = head_of(E2)
& tail_of(E3) = tail_of(E1)
& edge(E3) ) ),
file('theBenchmark.p',no_short_cut_edge) ).
fof(no_short_cut_edge_neg,negated_conjecture,
~ ! [V1,V2,E1,E2,P] :
( ( precedes(E1,E2,P)
& shortest_path(V1,V2,P) )
=> ~ ? [E3] :
( head_of(E3) = head_of(E2)
& tail_of(E3) = tail_of(E1)
& edge(E3) ) ),
inference(assume_negation,[status(cth)],[no_short_cut_edge]) ).
fof(nnf_18,plain,
? [V1,V2,E1,E2,P] :
( ? [E3] :
( head_of(E3) = head_of(E2)
& tail_of(E3) = tail_of(E1)
& edge(E3) )
& precedes(E1,E2,P)
& shortest_path(V1,V2,P) ),
inference(fof_nnf,[status(thm)],[no_short_cut_edge_neg]) ).
fof(sk_no_short_cut_edge_neg,plain,
( head_of(sK5) = head_of(sK4)
& tail_of(sK5) = tail_of(sK3)
& edge(sK5)
& precedes(sK3,sK4,sK2)
& shortest_path(sK0,sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5]),skolemize(V1,sK0),skolemize(V2,sK1),skolemize(E1,sK3),skolemize(E2,sK4),skolemize(P,sK2),skolemize(E3,sK5)],[nnf_18]) ).
cnf(c_25,negated_conjecture,
shortest_path(sK0,sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_no_short_cut_edge_neg]) ).
cnf(c_26,plain,
( head_of(F) != head_of(E)
| tail_of(F) != tail_of(D)
| ~ precedes(D,E,C)
| ~ shortest_path(A,B,C) ),
inference(clausify,[status(thm)],[shortest_path_properties]) ).
cnf(c_41,negated_conjecture,
( head_of(C) != head_of(B)
| tail_of(C) != tail_of(A)
| ~ precedes(A,B,sK2) ),
inference(resolve,[status(thm)],[c_26,c_25]) ).
cnf(c_91,negated_conjecture,
precedes(sK3,sK4,sK2),
inference(split_conjunct,[status(thm)],[sk_no_short_cut_edge_neg]) ).
cnf(c_93,negated_conjecture,
tail_of(sK5) = tail_of(sK3),
inference(split_conjunct,[status(thm)],[sk_no_short_cut_edge_neg]) ).
cnf(c_94,negated_conjecture,
head_of(sK5) = head_of(sK4),
inference(split_conjunct,[status(thm)],[sk_no_short_cut_edge_neg]) ).
cnf(c_168,negated_conjecture,
( head_of(A) != head_of(sK4)
| tail_of(A) != tail_of(sK3) ),
inference(resolve,[status(thm)],[c_41,c_91]) ).
cnf(c_169,negated_conjecture,
head_of(sK5) != head_of(sK4),
inference(resolve,[status(thm)],[c_168,c_93]) ).
cnf(c_170,negated_conjecture,
head_of(sK4) != head_of(sK4),
inference(paramod,[status(thm)],[c_94,c_169]) ).
cnf(c_167,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_170]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRA005+1 : TPTP v9.3.1. Bugfixed v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.56 % Computer : n009.cluster.edu
% 0.09/0.56 % Model : x86_64 x86_64
% 0.09/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.56 % Memory : 8046.5625MB
% 0.09/0.56 % OS : Linux 6.8.0-71-generic
% 0.09/0.56 % CPULimit : 300
% 0.09/0.56 % WCLimit : 300
% 0.09/0.56 % DateTime : Fri Sep 25 13:48:14 UTC 2026
% 0.12/0.56 % CPUTime :
% 0.12/0.56 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.56 % Process 1731583 was started by sandbox on n009,
% 0.12/0.56 % Fri Sep 25 13:48:14 2026
% 0.12/0.56 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.57
% 0.12/0.57 % From the command line: assign(max_seconds, 300).
% 0.12/0.60
% 0.12/0.60 % SZS status Theorem for theBenchmark
% 0.12/0.60
% 0.12/0.60 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.12/0.60 % Length of proof is 9.
% 0.12/0.60 % Level of proof is 3.
% 0.12/0.60 % Maximum clause weight is 14.000.
% 0.12/0.60 % Given clauses 61.
% 0.12/0.60
% 0.12/0.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------