%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO059-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/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 12:23:56 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.45s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 19 ( 9 unt; 0 def)
% Number of atoms : 32 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 28 ( 15 ~; 13 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-4 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 58 ( 58 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [U,V,W,X] :
( equidistant(W,X,U,V)
| ~ equidistant(U,V,W,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [U,V,W,X] :
( equidistant(V,U,X,W)
| ~ equidistant(U,V,W,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [U,V,W,X] :
( equidistant(X,W,V,U)
| ~ equidistant(U,V,W,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,axiom,
! [V,U] : equidistant(V,reflection(U,V),U,V),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,negated_conjecture,
~ equidistant(v,u,v,reflection(reflection(u,v),v)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,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(f45,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)],[f44]) ).
fof(f67,plain,
! [X0,X1,X2,X3] :
( equidistant(X2,X3,X0,X1)
| ~ equidistant(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f70,plain,
! [X0,X1,X2,X3] :
( equidistant(X1,X0,X3,X2)
| ~ equidistant(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f73,plain,
! [X0,X1,X2,X3] :
( equidistant(X3,X2,X1,X0)
| ~ equidistant(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f80,plain,
! [X0,X1] : equidistant(X0,reflection(X1,X0),X1,X0),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f93,plain,
~ equidistant(v,u,v,reflection(reflection(u,v),v)),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f106,plain,
! [X0,X1,X2,X3] :
( equidistant(X2,X3,X1,X0)
| ~ equidistant(X0,reflection(X1,X0),X2,X3) ),
inference(resolution,[status(thm)],[f80,f45]) ).
fof(f108,plain,
! [X0,X1] : equidistant(X0,X1,X1,reflection(X0,X1)),
inference(resolution,[status(thm)],[f67,f80]) ).
fof(f126,plain,
! [X0,X1] : equidistant(X0,X1,reflection(X1,X0),X0),
inference(resolution,[status(thm)],[f70,f108]) ).
fof(f466,plain,
! [X0,X1] : equidistant(reflection(reflection(X0,X1),X1),X1,X0,X1),
inference(resolution,[status(thm)],[f106,f126]) ).
fof(f475,plain,
! [X0,X1] : equidistant(X0,X1,X0,reflection(reflection(X1,X0),X0)),
inference(resolution,[status(thm)],[f466,f73]) ).
fof(f533,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f93,f475]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO059-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n007.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 20 09:01:52 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.10/0.45 % Refutation found
% 0.10/0.45 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.48 % Elapsed time: 0.092503 seconds
% 0.10/0.48 % CPU time: 0.415558 seconds
% 0.10/0.48 % Total memory used: 105.403 MB
% 0.10/0.48 % Net memory used: 104.827 MB
%------------------------------------------------------------------------------