%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO037-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 12:23:51 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.41s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 35 ( 23 unt; 0 def)
% Number of atoms : 52 ( 9 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 37 ( 20 ~; 17 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-4 aty)
% Number of variables : 103 ( 103 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] : equidistant(X,Y,Y,X),
file('/export/starexec/sandbox/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/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(f4,axiom,
! [X,Y,W,V] : between(X,Y,extension(X,Y,W,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(f12,axiom,
~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( ~ between(u,v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2))
| ~ equidistant(v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2),x,extension(w,x,lower_dimension_point_1,lower_dimension_point_2))
| v = extension(u,v,lower_dimension_point_1,lower_dimension_point_2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,plain,
! [X0,X1] : equidistant(X0,X1,X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f21,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(f22,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)],[f21]) ).
fof(f23,plain,
! [X,Y] :
( X = Y
| ! [Z] : ~ equidistant(X,Y,Z,Z) ),
inference(miniscoping,[status(thm)],[f3]) ).
fof(f24,plain,
! [X0,X1,X2] :
( X0 = X1
| ~ equidistant(X0,X1,X2,X2) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f25,plain,
! [X0,X1,X2,X3] : between(X0,X1,extension(X0,X1,X2,X3)),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f26,plain,
! [X0,X1,X2,X3] : equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f34,plain,
~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f42,plain,
( ~ between(u,v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2))
| ~ equidistant(v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2),x,extension(w,x,lower_dimension_point_1,lower_dimension_point_2))
| v = extension(u,v,lower_dimension_point_1,lower_dimension_point_2) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f44,plain,
( ~ equidistant(v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2),x,extension(w,x,lower_dimension_point_1,lower_dimension_point_2))
| v = extension(u,v,lower_dimension_point_1,lower_dimension_point_2) ),
inference(backward_subsumption_resolution,[status(thm)],[f42,f25]) ).
fof(f45,plain,
! [X0,X1,X2,X3] :
( equidistant(X1,X0,X2,X3)
| ~ equidistant(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[f22,f20]) ).
fof(f46,plain,
! [X0,X1,X2,X3,X4,X5] :
( equidistant(X2,X3,X4,X5)
| ~ equidistant(X0,extension(X1,X0,X2,X3),X4,X5) ),
inference(resolution,[status(thm)],[f26,f22]) ).
fof(f47,plain,
! [X0,X1,X2] : X0 = extension(X1,X0,X2,X2),
inference(resolution,[status(thm)],[f26,f24]) ).
fof(f49,plain,
! [X0,X1] : between(X0,X1,X1),
inference(paramodulation,[status(thm)],[f47,f25]) ).
fof(f55,plain,
! [X0,X1] : equidistant(X0,X1,X0,X1),
inference(resolution,[status(thm)],[f45,f20]) ).
fof(f67,plain,
! [X0,X1,X2,X3] : equidistant(X0,X1,X2,extension(X3,X2,X0,X1)),
inference(resolution,[status(thm)],[f46,f55]) ).
fof(f68,plain,
! [X0,X1,X2,X3] : equidistant(X0,X1,extension(X2,X3,X0,X1),X3),
inference(resolution,[status(thm)],[f46,f20]) ).
fof(f73,plain,
! [X0,X1,X2,X3,X4,X5] :
( equidistant(X4,extension(X5,X4,X0,X1),X2,X3)
| ~ equidistant(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[f67,f22]) ).
fof(f78,plain,
! [X0,X1,X2,X3] : equidistant(X0,X1,extension(X2,X3,X1,X0),X3),
inference(resolution,[status(thm)],[f68,f45]) ).
fof(f102,plain,
! [X0,X1,X2,X3,X4,X5] : equidistant(X0,X1,extension(X2,X3,extension(X4,X5,X0,X1),X5),X3),
inference(resolution,[status(thm)],[f78,f46]) ).
fof(f141,plain,
! [X0,X1,X2,X3,X4,X5] : equidistant(X0,X1,extension(X2,X3,extension(X4,X5,X1,X0),X5),X3),
inference(resolution,[status(thm)],[f102,f45]) ).
fof(f214,plain,
! [X0,X1,X2,X3,X4,X5] : equidistant(X0,extension(X1,X0,X2,X3),X4,extension(X5,X4,X2,X3)),
inference(resolution,[status(thm)],[f73,f67]) ).
fof(f290,plain,
v = extension(u,v,lower_dimension_point_1,lower_dimension_point_2),
inference(backward_subsumption_resolution,[status(thm)],[f44,f214]) ).
fof(f314,plain,
! [X0,X1] : equidistant(lower_dimension_point_2,lower_dimension_point_1,extension(X0,X1,v,v),X1),
inference(paramodulation,[status(thm)],[f290,f141]) ).
fof(f332,plain,
! [X0] : equidistant(lower_dimension_point_2,lower_dimension_point_1,X0,X0),
inference(forward_demodulation,[status(thm)],[f47,f314]) ).
fof(f352,plain,
lower_dimension_point_2 = lower_dimension_point_1,
inference(resolution,[status(thm)],[f332,f24]) ).
fof(f356,plain,
~ between(lower_dimension_point_3,lower_dimension_point_2,lower_dimension_point_2),
inference(backward_demodulation,[status(thm)],[f352,f34]) ).
fof(f359,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f356,f49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO037-2 : 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 : n002.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 08:35:46 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.14/0.39 % Drodi V4.1.1
% 0.14/0.41 % Refutation found
% 0.14/0.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.44 % Elapsed time: 0.055810 seconds
% 0.14/0.44 % CPU time: 0.211126 seconds
% 0.14/0.44 % Total memory used: 79.449 MB
% 0.14/0.44 % Net memory used: 78.951 MB
%------------------------------------------------------------------------------