%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO024-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 12:23:48 PM UTC 2026
% Result : Unsatisfiable 0.11s 0.41s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 15 ( 11 unt; 0 def)
% Number of atoms : 22 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 19 ( 12 ~; 7 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-4 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-4 aty)
% Number of variables : 41 ( 41 !; 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(f5,axiom,
! [Y,X,W,V] : equidistant(Y,extension(X,Y,W,V),W,V),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [U,V] : equidistant(U,V,U,V),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,axiom,
! [V,U,W] : V = extension(U,V,W,W),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
~ equidistant(u,u,v,v),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,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(f39,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)],[f38]) ).
fof(f43,plain,
! [X0,X1,X2,X3] : equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f60,plain,
! [X0,X1] : equidistant(X0,X1,X0,X1),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f70,plain,
! [X0,X1,X2] : X0 = extension(X1,X0,X2,X2),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f78,plain,
~ equidistant(u,u,v,v),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f83,plain,
! [X0,X1] :
( ~ equidistant(X0,X1,v,v)
| ~ equidistant(X0,X1,u,u) ),
inference(resolution,[status(thm)],[f39,f78]) ).
fof(f115,plain,
! [X0,X1] : ~ equidistant(X0,extension(X1,X0,v,v),u,u),
inference(resolution,[status(thm)],[f83,f43]) ).
fof(f122,plain,
! [X0] : ~ equidistant(X0,X0,u,u),
inference(forward_demodulation,[status(thm)],[f70,f115]) ).
fof(f126,plain,
$false,
inference(resolution,[status(thm)],[f122,f60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO024-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n026.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 20 08:20:22 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.39 % Drodi V4.1.1
% 0.11/0.41 % Refutation found
% 0.11/0.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.11/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.43 % Elapsed time: 0.049300 seconds
% 0.11/0.43 % CPU time: 0.151582 seconds
% 0.11/0.43 % Total memory used: 89.556 MB
% 0.11/0.43 % Net memory used: 89.430 MB
%------------------------------------------------------------------------------