%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRA005+1 : TPTP v9.3.1. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 : Thu Sep 24 12:30:38 PM UTC 2026
% Result : Theorem 0.14s 5.40s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 2
% Syntax : Number of formulae : 18 ( 7 unt; 0 def)
% Number of atoms : 56 ( 26 equ)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 64 ( 26 ~; 12 |; 23 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 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 : 52 ( 37 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f12,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('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,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('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,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(negated_conjecture,[status(cth)],[f18]) ).
fof(f89,plain,
! [V1,V2,E1,E2,P] :
( ( ~ precedes(E2,E1,P)
& ! [E3] :
( head_of(E3) != head_of(E2)
| tail_of(E3) != tail_of(E1) ) )
| ~ precedes(E1,E2,P)
| ~ shortest_path(V1,V2,P) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f90,plain,
! [E1,E2,P] :
( ( ~ precedes(E2,E1,P)
& ! [E3] :
( head_of(E3) != head_of(E2)
| tail_of(E3) != tail_of(E1) ) )
| ~ precedes(E1,E2,P)
| ! [V1,V2] : ~ shortest_path(V1,V2,P) ),
inference(miniscoping,[status(thm)],[f89]) ).
fof(f91,plain,
! [X0,X1,X2,X3,X4,X5] :
( head_of(X5) != head_of(X4)
| tail_of(X5) != tail_of(X3)
| ~ precedes(X3,X4,X2)
| ~ shortest_path(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f90]) ).
fof(f116,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(pre_NNF_transformation,[status(thm)],[f19]) ).
fof(f117,plain,
? [E1,E2] :
( ? [E3] :
( head_of(E3) = head_of(E2)
& tail_of(E3) = tail_of(E1)
& edge(E3) )
& ? [P] :
( precedes(E1,E2,P)
& ? [V1,V2] : shortest_path(V1,V2,P) ) ),
inference(miniscoping,[status(thm)],[f116]) ).
fof(f118,plain,
( head_of(sK13_skl) = head_of(sK9_skl)
& tail_of(sK13_skl) = tail_of(sK8_skl)
& edge(sK13_skl)
& precedes(sK8_skl,sK9_skl,sK10_skl)
& shortest_path(sK11_skl,sK12_skl,sK10_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl,sK9_skl,sK10_skl,sK11_skl,sK12_skl,sK13_skl]),skolemize(E1,sK8_skl),skolemize(E2,sK9_skl),skolemize(P,sK10_skl),skolemize(V1,sK11_skl),skolemize(V2,sK12_skl),skolemize(E3,sK13_skl)],[f117]) ).
fof(f119,plain,
shortest_path(sK11_skl,sK12_skl,sK10_skl),
inference(cnf_transformation,[status(thm)],[f118]) ).
fof(f120,plain,
precedes(sK8_skl,sK9_skl,sK10_skl),
inference(cnf_transformation,[status(thm)],[f118]) ).
fof(f122,plain,
tail_of(sK13_skl) = tail_of(sK8_skl),
inference(cnf_transformation,[status(thm)],[f118]) ).
fof(f123,plain,
head_of(sK13_skl) = head_of(sK9_skl),
inference(cnf_transformation,[status(thm)],[f118]) ).
fof(f167,plain,
! [X0,X1,X2] :
( head_of(X2) != head_of(sK9_skl)
| tail_of(X2) != tail_of(sK8_skl)
| ~ shortest_path(X0,X1,sK10_skl) ),
inference(resolution,[status(thm)],[f91,f120]) ).
fof(f168,plain,
! [X0] :
( head_of(X0) != head_of(sK9_skl)
| tail_of(X0) != tail_of(sK8_skl) ),
inference(resolution,[status(thm)],[f167,f119]) ).
fof(f169,plain,
head_of(sK13_skl) != head_of(sK9_skl),
inference(resolution,[status(thm)],[f168,f122]) ).
fof(f172,plain,
head_of(sK9_skl) != head_of(sK9_skl),
inference(forward_demodulation,[status(thm)],[f123,f169]) ).
fof(f173,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f172]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRA005+1 : TPTP v9.3.1. Bugfixed v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/5.37 % Computer : n002.cluster.edu
% 0.11/5.37 % Model : x86_64 x86_64
% 0.11/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.37 % Memory : 8046.5625MB
% 0.11/5.37 % OS : Linux 6.8.0-71-generic
% 0.11/5.37 % CPULimit : 300
% 0.11/5.37 % WCLimit : 300
% 0.11/5.38 % DateTime : Sun Sep 20 18:20:24 UTC 2026
% 0.11/5.38 % CPUTime :
% 0.11/5.39 % Drodi V4.1.1
% 0.14/5.40 % Refutation found
% 0.14/5.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/5.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/5.44 % Elapsed time: 0.043883 seconds
% 0.14/5.44 % CPU time: 0.144607 seconds
% 0.14/5.44 % Total memory used: 100.758 MB
% 0.14/5.44 % Net memory used: 100.675 MB
%------------------------------------------------------------------------------