%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO029-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.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 12:23:50 PM UTC 2026
% Result : Unsatisfiable 1.44s 0.77s
% Output : CNFRefutation 1.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 31 ( 19 unt; 0 def)
% Number of atoms : 58 ( 18 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 58 ( 31 ~; 27 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-4 aty)
% Number of variables : 77 ( 77 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X,Y,W,V] : between(X,Y,extension(X,Y,W,V)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [Y,X,W,V] : equidistant(Y,extension(X,Y,W,V),W,V),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [U,V] : reflection(U,V) = extension(U,V,U,V),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [U,V,W,X] :
( equidistant(X,W,U,V)
| ~ equidistant(U,V,W,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [U,V,W,X,Y,Z] :
( equidistant(U,V,Y,Z)
| ~ equidistant(W,X,Y,Z)
| ~ equidistant(U,V,W,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,axiom,
! [U,V] : between(U,V,reflection(U,V)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,axiom,
! [V,U] : equidistant(V,reflection(U,V),U,V),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,hypothesis,
u != v,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,negated_conjecture,
extension(u,v,u,v) != extension(u,v,v,u),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f46,plain,
! [X0,X1,X2,X3] : between(X0,X1,extension(X0,X1,X2,X3)),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f47,plain,
! [X0,X1,X2,X3] : equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f63,plain,
! [X0,X1] : reflection(X0,X1) = extension(X0,X1,X0,X1),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f70,plain,
! [X0,X1,X2,X3] :
( equidistant(X3,X2,X0,X1)
| ~ equidistant(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f72,plain,
! [U,V,Y,Z] :
( equidistant(U,V,Y,Z)
| ! [W,X] :
( ~ equidistant(W,X,Y,Z)
| ~ equidistant(U,V,W,X) ) ),
inference(miniscoping,[status(thm)],[f28]) ).
fof(f73,plain,
! [X0,X1,X2,X3,X4,X5] :
( equidistant(X0,X1,X4,X5)
| ~ equidistant(X2,X3,X4,X5)
| ~ equidistant(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f77,plain,
! [X0,X1] : between(X0,X1,reflection(X0,X1)),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f78,plain,
! [X0,X1] : equidistant(X0,reflection(X1,X0),X1,X0),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f85,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(f86,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)],[f85]) ).
fof(f87,plain,
u != v,
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f88,plain,
extension(u,v,u,v) != extension(u,v,v,u),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f106,plain,
reflection(u,v) != extension(u,v,v,u),
inference(backward_demodulation,[status(thm)],[f63,f88]) ).
fof(f227,plain,
! [X0,X1,X2,X3,X4] :
( X2 = extension(X0,X1,X3,X4)
| X0 = X1
| ~ equidistant(X1,X2,X1,extension(X0,X1,X3,X4))
| ~ between(X0,X1,X2) ),
inference(resolution,[status(thm)],[f86,f46]) ).
fof(f239,plain,
! [X0,X1,X2,X3] :
( reflection(X1,X0) = extension(X1,X0,X2,X3)
| X1 = X0
| ~ equidistant(X0,reflection(X1,X0),X0,extension(X1,X0,X2,X3)) ),
inference(resolution,[status(thm)],[f227,f77]) ).
fof(f246,plain,
( u = v
| ~ equidistant(v,reflection(u,v),v,extension(u,v,v,u)) ),
inference(resolution,[status(thm)],[f239,f106]) ).
fof(f249,plain,
~ equidistant(v,reflection(u,v),v,extension(u,v,v,u)),
inference(forward_subsumption_resolution,[status(thm)],[f246,f87]) ).
fof(f252,plain,
! [X0,X1] :
( ~ equidistant(X0,X1,v,extension(u,v,v,u))
| ~ equidistant(v,reflection(u,v),X0,X1) ),
inference(resolution,[status(thm)],[f249,f73]) ).
fof(f579,plain,
~ equidistant(u,v,v,extension(u,v,v,u)),
inference(resolution,[status(thm)],[f252,f78]) ).
fof(f701,plain,
~ equidistant(v,extension(u,v,v,u),v,u),
inference(resolution,[status(thm)],[f579,f70]) ).
fof(f709,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f701,f47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO029-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n008.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 20 08:24:38 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.15/0.38 % Drodi V4.1.1
% 1.44/0.77 % Refutation found
% 1.44/0.77 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 1.44/0.77 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.44/0.79 % Elapsed time: 0.407274 seconds
% 1.44/0.79 % CPU time: 2.837637 seconds
% 1.44/0.79 % Total memory used: 118.677 MB
% 1.44/0.79 % Net memory used: 115.659 MB
%------------------------------------------------------------------------------