%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO027-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 12:23:49 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.41s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 19 ( 13 unt; 0 def)
% Number of atoms : 37 ( 17 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 36 ( 18 ~; 18 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-4 aty)
% Number of variables : 35 ( 35 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(f38,axiom,
! [U,V,W,X] :
( W = X
| U = V
| ~ equidistant(V,W,V,X)
| ~ between(U,V,X)
| ~ between(U,V,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,hypothesis,
between(u,v,w),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,hypothesis,
u != v,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f41,negated_conjecture,
w != extension(u,v,v,w),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f47,plain,
! [X0,X1,X2,X3] : between(X0,X1,extension(X0,X1,X2,X3)),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f48,plain,
! [X0,X1,X2,X3] : equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f86,plain,
! [W,X] :
( W = X
| ! [U,V] :
( U = V
| ~ equidistant(V,W,V,X)
| ~ between(U,V,X)
| ~ between(U,V,W) ) ),
inference(miniscoping,[status(thm)],[f38]) ).
fof(f87,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| X0 = X1
| ~ equidistant(X1,X2,X1,X3)
| ~ between(X0,X1,X3)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f88,plain,
between(u,v,w),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f89,plain,
u != v,
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f90,plain,
w != extension(u,v,v,w),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f103,plain,
! [X0,X1,X2,X3] :
( extension(X2,X1,X1,X3) = X3
| X0 = X1
| ~ between(X0,X1,X3)
| ~ between(X0,X1,extension(X2,X1,X1,X3)) ),
inference(resolution,[status(thm)],[f87,f48]) ).
fof(f105,plain,
! [X0,X1,X2] :
( extension(X0,X1,X1,X2) = X2
| X0 = X1
| ~ between(X0,X1,X2) ),
inference(resolution,[status(thm)],[f103,f47]) ).
fof(f110,plain,
( u = v
| ~ between(u,v,w) ),
inference(resolution,[status(thm)],[f105,f90]) ).
fof(f113,plain,
u != u,
inference(backward_demodulation,[status(thm)],[f116,f89]) ).
fof(f116,plain,
u = v,
inference(forward_subsumption_resolution,[status(thm)],[f110,f88]) ).
fof(f117,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f113]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO027-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n003.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 20 08:19:44 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.13/0.36 % Drodi V4.1.1
% 0.13/0.41 % Refutation found
% 0.13/0.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.42 % Elapsed time: 0.065241 seconds
% 0.13/0.42 % CPU time: 0.279634 seconds
% 0.13/0.42 % Total memory used: 100.732 MB
% 0.13/0.42 % Net memory used: 100.432 MB
%------------------------------------------------------------------------------