%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO058-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 0.13s 5.40s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 23 ( 14 unt; 0 def)
% Number of atoms : 36 ( 15 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 28 ( 15 ~; 13 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 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 : 56 ( 56 !; 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(f3,axiom,
! [X,Y,Z] :
( X = Y
| ~ equidistant(X,Y,Z,Z) ),
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(f19,axiom,
! [U,V] : reflection(U,V) = extension(U,V,U,V),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,hypothesis,
v = reflection(u,v),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
u != v,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,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(f24,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)],[f23]) ).
fof(f25,plain,
! [X,Y] :
( X = Y
| ! [Z] : ~ equidistant(X,Y,Z,Z) ),
inference(miniscoping,[status(thm)],[f3]) ).
fof(f26,plain,
! [X0,X1,X2] :
( X0 = X1
| ~ equidistant(X0,X1,X2,X2) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f28,plain,
! [X0,X1,X2,X3] : equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f44,plain,
! [X0,X1] : reflection(X0,X1) = extension(X0,X1,X0,X1),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f45,plain,
v = reflection(u,v),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f46,plain,
u != v,
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f47,plain,
! [X0,X1,X2,X3,X4] :
( ~ equidistant(X2,X3,X4,X4)
| ~ equidistant(X2,X3,X0,X1)
| X0 = X1 ),
inference(resolution,[status(thm)],[f26,f24]) ).
fof(f51,plain,
! [X0,X1,X2] : X0 = extension(X1,X0,X2,X2),
inference(resolution,[status(thm)],[f28,f26]) ).
fof(f52,plain,
! [X0,X1] : equidistant(X0,reflection(X1,X0),X1,X0),
inference(paramodulation,[status(thm)],[f44,f28]) ).
fof(f54,plain,
! [X0] : X0 = reflection(X0,X0),
inference(paramodulation,[status(thm)],[f44,f51]) ).
fof(f62,plain,
equidistant(v,v,u,v),
inference(paramodulation,[status(thm)],[f45,f52]) ).
fof(f64,plain,
! [X0,X1,X2] :
( ~ equidistant(X2,reflection(X2,X2),X0,X1)
| X0 = X1 ),
inference(resolution,[status(thm)],[f47,f52]) ).
fof(f70,plain,
! [X0,X1,X2] :
( ~ equidistant(X2,X2,X0,X1)
| X0 = X1 ),
inference(forward_demodulation,[status(thm)],[f54,f64]) ).
fof(f72,plain,
u = v,
inference(resolution,[status(thm)],[f70,f62]) ).
fof(f77,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f72,f46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO058-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/5.36 % Computer : n019.cluster.edu
% 0.07/5.36 % Model : x86_64 x86_64
% 0.07/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/5.36 % Memory : 8046.5625MB
% 0.07/5.36 % OS : Linux 6.8.0-71-generic
% 0.07/5.36 % CPULimit : 300
% 0.07/5.36 % WCLimit : 300
% 0.07/5.36 % DateTime : Sun Sep 20 09:01:58 UTC 2026
% 0.07/5.36 % CPUTime :
% 0.07/5.38 % Drodi V4.1.1
% 0.13/5.40 % Refutation found
% 0.13/5.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/5.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/5.42 % Elapsed time: 0.055463 seconds
% 0.13/5.42 % CPU time: 0.156110 seconds
% 0.13/5.42 % Total memory used: 102.078 MB
% 0.13/5.42 % Net memory used: 101.720 MB
%------------------------------------------------------------------------------