%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRA002+4 : TPTP v9.3.1. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(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 : Thu Sep 24 12:30:38 PM UTC 2026
% Result : Theorem 0.10s 0.39s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 31 ( 11 unt; 0 def)
% Number of atoms : 90 ( 19 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 95 ( 36 ~; 27 |; 22 &)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 2 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-3 aty)
% Number of variables : 74 ( 66 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f11,axiom,
! [V1,V2,SP] :
( shortest_path(V1,V2,SP)
<=> ( ! [P] :
( path(V1,V2,P)
=> less_or_equal(length_of(SP),length_of(P)) )
& V1 != V2
& path(V1,V2,SP) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [V1,V2,P] :
( path(V1,V2,P)
=> number_of_in(sequential_pairs,P) = minus(length_of(P),n1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [Things,InThese] : less_or_equal(number_of_in(Things,InThese),number_of_in(Things,graph)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,lemma,
( complete
=> ! [P,V1,V2] :
( shortest_path(V1,V2,P)
=> number_of_in(sequential_pairs,P) = number_of_in(triangles,P) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,conjecture,
( 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/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
~ ( complete
=> ! [P,V1,V2] :
( shortest_path(V1,V2,P)
=> less_or_equal(minus(length_of(P),n1),number_of_in(triangles,graph)) ) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f81,plain,
! [V1,V2,SP] :
( shortest_path(V1,V2,SP)
<=> ( ! [P] :
( less_or_equal(length_of(SP),length_of(P))
| ~ path(V1,V2,P) )
& V1 != V2
& path(V1,V2,SP) ) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f82,plain,
! [V1,V2,SP] :
( ( ? [P] :
( ~ less_or_equal(length_of(SP),length_of(P))
& path(V1,V2,P) )
| V1 = V2
| ~ path(V1,V2,SP)
| shortest_path(V1,V2,SP) )
& ( ( ! [P] :
( less_or_equal(length_of(SP),length_of(P))
| ~ path(V1,V2,P) )
& V1 != V2
& path(V1,V2,SP) )
| ~ shortest_path(V1,V2,SP) ) ),
inference(NNF_transformation,[status(thm)],[f81]) ).
fof(f83,plain,
( ! [V1,V2,SP] :
( ? [P] :
( ~ less_or_equal(length_of(SP),length_of(P))
& path(V1,V2,P) )
| V1 = V2
| ~ path(V1,V2,SP)
| shortest_path(V1,V2,SP) )
& ! [V1,V2,SP] :
( ( ! [P] :
( less_or_equal(length_of(SP),length_of(P))
| ~ path(V1,V2,P) )
& V1 != V2
& path(V1,V2,SP) )
| ~ shortest_path(V1,V2,SP) ) ),
inference(miniscoping,[status(thm)],[f82]) ).
fof(f84,plain,
( ! [V1,V2,SP] :
( ( ~ less_or_equal(length_of(SP),length_of(sK5_skl(SP,V2,V1)))
& path(V1,V2,sK5_skl(SP,V2,V1)) )
| V1 = V2
| ~ path(V1,V2,SP)
| shortest_path(V1,V2,SP) )
& ! [V1,V2,SP] :
( ( ! [P] :
( less_or_equal(length_of(SP),length_of(P))
| ~ path(V1,V2,P) )
& V1 != V2
& path(V1,V2,SP) )
| ~ shortest_path(V1,V2,SP) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(P,sK5_skl(SP,V2,V1))],[f83]) ).
fof(f85,plain,
! [X0,X1,X2] :
( path(X0,X1,X2)
| ~ shortest_path(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f84]) ).
fof(f106,plain,
! [V1,V2,P] :
( number_of_in(sequential_pairs,P) = minus(length_of(P),n1)
| ~ path(V1,V2,P) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f107,plain,
! [P] :
( number_of_in(sequential_pairs,P) = minus(length_of(P),n1)
| ! [V1,V2] : ~ path(V1,V2,P) ),
inference(miniscoping,[status(thm)],[f106]) ).
fof(f108,plain,
! [X0,X1,X2] :
( number_of_in(sequential_pairs,X2) = minus(length_of(X2),n1)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f107]) ).
fof(f116,plain,
! [X0,X1] : less_or_equal(number_of_in(X0,X1),number_of_in(X0,graph)),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f117,plain,
( ! [P,V1,V2] :
( number_of_in(sequential_pairs,P) = number_of_in(triangles,P)
| ~ shortest_path(V1,V2,P) )
| ~ complete ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f118,plain,
( ! [P] :
( number_of_in(sequential_pairs,P) = number_of_in(triangles,P)
| ! [V1,V2] : ~ shortest_path(V1,V2,P) )
| ~ complete ),
inference(miniscoping,[status(thm)],[f117]) ).
fof(f119,plain,
! [X0,X1,X2] :
( number_of_in(sequential_pairs,X2) = number_of_in(triangles,X2)
| ~ shortest_path(X0,X1,X2)
| ~ complete ),
inference(cnf_transformation,[status(thm)],[f118]) ).
fof(f120,plain,
( ? [P,V1,V2] :
( ~ less_or_equal(minus(length_of(P),n1),number_of_in(triangles,graph))
& shortest_path(V1,V2,P) )
& complete ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f121,plain,
( ? [P] :
( ~ less_or_equal(minus(length_of(P),n1),number_of_in(triangles,graph))
& ? [V1,V2] : shortest_path(V1,V2,P) )
& complete ),
inference(miniscoping,[status(thm)],[f120]) ).
fof(f122,plain,
( ~ less_or_equal(minus(length_of(sK8_skl),n1),number_of_in(triangles,graph))
& shortest_path(sK9_skl,sK10_skl,sK8_skl)
& complete ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl,sK9_skl,sK10_skl]),skolemize(P,sK8_skl),skolemize(V1,sK9_skl),skolemize(V2,sK10_skl)],[f121]) ).
fof(f123,plain,
complete,
inference(cnf_transformation,[status(thm)],[f122]) ).
fof(f124,plain,
shortest_path(sK9_skl,sK10_skl,sK8_skl),
inference(cnf_transformation,[status(thm)],[f122]) ).
fof(f125,plain,
~ less_or_equal(minus(length_of(sK8_skl),n1),number_of_in(triangles,graph)),
inference(cnf_transformation,[status(thm)],[f122]) ).
fof(f138,plain,
path(sK9_skl,sK10_skl,sK8_skl),
inference(resolution,[status(thm)],[f85,f124]) ).
fof(f141,plain,
number_of_in(sequential_pairs,sK8_skl) = minus(length_of(sK8_skl),n1),
inference(resolution,[status(thm)],[f108,f138]) ).
fof(f142,plain,
~ less_or_equal(number_of_in(sequential_pairs,sK8_skl),number_of_in(triangles,graph)),
inference(backward_demodulation,[status(thm)],[f141,f125]) ).
fof(f143,plain,
! [X0,X1,X2] :
( number_of_in(sequential_pairs,X2) = number_of_in(triangles,X2)
| ~ shortest_path(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f119,f123]) ).
fof(f144,plain,
number_of_in(sequential_pairs,sK8_skl) = number_of_in(triangles,sK8_skl),
inference(resolution,[status(thm)],[f143,f124]) ).
fof(f145,plain,
~ less_or_equal(number_of_in(triangles,sK8_skl),number_of_in(triangles,graph)),
inference(backward_demodulation,[status(thm)],[f144,f142]) ).
fof(f148,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f145,f116]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRA002+4 : TPTP v9.3.1. Bugfixed v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n007.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 20 18:15:05 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.10/0.39 % Refutation found
% 0.10/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.43 % Elapsed time: 0.055500 seconds
% 0.10/0.43 % CPU time: 0.151201 seconds
% 0.10/0.43 % Total memory used: 82.336 MB
% 0.10/0.43 % Net memory used: 82.258 MB
%------------------------------------------------------------------------------