%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO059-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 12:23:56 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.42s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 22 ( 16 unt; 0 def)
% Number of atoms : 31 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 23 ( 14 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-4 aty)
% Number of variables : 54 ( 54 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] : equidistant(X,Y,Y,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y,Z,V,V2,W] :
( equidistant(Z,V,V2,W)
| ~ equidistant(X,Y,V2,W)
| ~ equidistant(X,Y,Z,V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [Y,X,W,V] : equidistant(Y,extension(X,Y,W,V),W,V),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [U,V] : reflection(U,V) = extension(U,V,U,V),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
~ equidistant(v,u,v,reflection(reflection(u,v),v)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,plain,
! [X0,X1] : equidistant(X0,X1,X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f22,plain,
! [Z,V,V2,W] :
( equidistant(Z,V,V2,W)
| ! [X,Y] :
( ~ equidistant(X,Y,V2,W)
| ~ equidistant(X,Y,Z,V) ) ),
inference(miniscoping,[status(thm)],[f2]) ).
fof(f23,plain,
! [X0,X1,X2,X3,X4,X5] :
( equidistant(X2,X3,X4,X5)
| ~ equidistant(X0,X1,X4,X5)
| ~ equidistant(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f27,plain,
! [X0,X1,X2,X3] : equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f43,plain,
! [X0,X1] : reflection(X0,X1) = extension(X0,X1,X0,X1),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f44,plain,
~ equidistant(v,u,v,reflection(reflection(u,v),v)),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f46,plain,
! [X0,X1,X2,X3] :
( equidistant(X2,X3,X1,X0)
| ~ equidistant(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[f23,f21]) ).
fof(f47,plain,
! [X0,X1] :
( ~ equidistant(X0,X1,v,reflection(reflection(u,v),v))
| ~ equidistant(X0,X1,v,u) ),
inference(resolution,[status(thm)],[f23,f44]) ).
fof(f52,plain,
! [X0,X1] : equidistant(X0,X1,X0,X1),
inference(resolution,[status(thm)],[f46,f21]) ).
fof(f55,plain,
! [X0,X1,X2,X3] :
( equidistant(X2,X3,X0,X1)
| ~ equidistant(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[f52,f23]) ).
fof(f82,plain,
! [X0,X1] : equidistant(X0,reflection(X1,X0),X1,X0),
inference(paramodulation,[status(thm)],[f43,f27]) ).
fof(f125,plain,
! [X0,X1] : equidistant(X0,X1,reflection(X0,X1),X1),
inference(resolution,[status(thm)],[f82,f46]) ).
fof(f133,plain,
! [X0,X1] : equidistant(reflection(X0,X1),X1,X1,X0),
inference(resolution,[status(thm)],[f125,f46]) ).
fof(f141,plain,
! [X0,X1] : equidistant(X0,X1,X0,reflection(X1,X0)),
inference(resolution,[status(thm)],[f133,f46]) ).
fof(f145,plain,
~ equidistant(v,reflection(u,v),v,u),
inference(resolution,[status(thm)],[f141,f47]) ).
fof(f192,plain,
~ equidistant(v,u,v,reflection(u,v)),
inference(resolution,[status(thm)],[f55,f145]) ).
fof(f205,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f192,f141]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO059-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.38 % Computer : n001.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8046.5625MB
% 0.09/0.38 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Sun Sep 20 09:08:26 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.14/0.39 % Drodi V4.1.1
% 0.14/0.42 % Refutation found
% 0.14/0.42 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.45 % Elapsed time: 0.062171 seconds
% 0.14/0.45 % CPU time: 0.209013 seconds
% 0.14/0.45 % Total memory used: 102.643 MB
% 0.14/0.45 % Net memory used: 102.156 MB
%------------------------------------------------------------------------------