%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO034-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 180.14s 23.15s
% Output : CNFRefutation 180.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 13
% Syntax : Number of formulae : 56 ( 26 unt; 0 def)
% Number of atoms : 129 ( 27 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 145 ( 72 ~; 73 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 110 ( 110 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X,Y,Z] :
( X = Y
| ~ equidistant(X,Y,Z,Z) ),
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(f27,axiom,
! [U,V,W,X] :
( equidistant(X,W,V,U)
| ~ equidistant(U,V,W,X) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f36,axiom,
! [U,V] : equidistant(U,U,V,V),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,axiom,
! [U,V] : between(U,V,V),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f46,axiom,
! [U,V,W] :
( between(W,V,U)
| ~ between(U,V,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f65,axiom,
! [U,V,W,W1] :
( W = W1
| U = V
| ~ equidistant(V,W,V,W1)
| ~ equidistant(U,W,U,W1)
| ~ between(U,V,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f66,axiom,
! [U,V,U1,V1,W,W1,X,X1] :
( equidistant(V,X,V1,X1)
| ~ between(U1,V1,W1)
| ~ between(U,V,W)
| ~ equidistant(W,X,W1,X1)
| ~ equidistant(U,X,U1,X1)
| ~ equidistant(U,W,U1,W1)
| ~ equidistant(U,V,U1,V1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f69,hypothesis,
between(u,v,w),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f70,hypothesis,
equidistant(u,v,u,x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f71,hypothesis,
equidistant(w,v,w,x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f72,negated_conjecture,
v != x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f76,plain,
! [X,Y] :
( X = Y
| ! [Z] : ~ equidistant(X,Y,Z,Z) ),
inference(miniscoping,[status(thm)],[f3]) ).
fof(f77,plain,
! [X0,X1,X2] :
( X0 = X1
| ~ equidistant(X0,X1,X2,X2) ),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f96,plain,
! [X0,X1] : equidistant(X0,X1,X0,X1),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f103,plain,
! [X0,X1,X2,X3] :
( ~ equidistant(X3,X2,X1,X0)
| equidistant(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f104,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(f105,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)],[f104]) ).
fof(f114,plain,
! [X0,X1] : equidistant(X0,X0,X1,X1),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f125,plain,
! [X0,X1] : between(X0,X1,X1),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f128,plain,
! [X0,X1,X2] :
( ~ between(X2,X1,X0)
| between(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f157,plain,
! [W,W1] :
( W = W1
| ! [U,V] :
( U = V
| ~ equidistant(V,W,V,W1)
| ~ equidistant(U,W,U,W1)
| ~ between(U,V,W) ) ),
inference(miniscoping,[status(thm)],[f65]) ).
fof(f158,plain,
! [X0,X1,X2,X3] :
( ~ equidistant(X0,X2,X0,X3)
| ~ between(X1,X0,X2)
| ~ equidistant(X1,X2,X1,X3)
| X2 = X3
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f157]) ).
fof(f159,plain,
! [V,V1,X,X1] :
( equidistant(V,X,V1,X1)
| ! [U1,W1] :
( ~ between(U1,V1,W1)
| ! [U,W] :
( ~ between(U,V,W)
| ~ equidistant(W,X,W1,X1)
| ~ equidistant(U,X,U1,X1)
| ~ equidistant(U,W,U1,W1)
| ~ equidistant(U,V,U1,V1) ) ) ),
inference(miniscoping,[status(thm)],[f66]) ).
fof(f160,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ equidistant(X4,X1,X6,X3)
| ~ between(X6,X7,X2)
| ~ equidistant(X4,X0,X6,X2)
| equidistant(X5,X1,X7,X3)
| ~ between(X4,X5,X0)
| ~ equidistant(X4,X5,X6,X7)
| ~ equidistant(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f159]) ).
fof(f165,plain,
between(u,v,w),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f166,plain,
equidistant(u,v,u,x),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f167,plain,
equidistant(w,v,w,x),
inference(cnf_transformation,[status(thm)],[f71]) ).
fof(f168,plain,
x != v,
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f210,plain,
! [X0,X1,X2,X3] :
( ~ equidistant(X3,X3,X1,X2)
| equidistant(X0,X0,X1,X2) ),
inference(resolution,[status(thm)],[f114,f105]) ).
fof(f537,plain,
between(w,v,u),
inference(resolution,[status(thm)],[f128,f165]) ).
fof(f890,plain,
! [X0] :
( ~ equidistant(X0,v,X0,x)
| ~ between(u,X0,v)
| v = x
| X0 = u ),
inference(resolution,[status(thm)],[f158,f166]) ).
fof(f892,plain,
! [X0] :
( ~ equidistant(X0,v,X0,x)
| ~ between(w,X0,v)
| v = x
| X0 = w ),
inference(resolution,[status(thm)],[f158,f167]) ).
fof(f901,plain,
! [X0] :
( ~ between(w,X0,v)
| ~ equidistant(X0,v,X0,x)
| X0 = w ),
inference(forward_subsumption_resolution,[status(thm)],[f892,f168]) ).
fof(f902,plain,
! [X0] :
( ~ between(u,X0,v)
| ~ equidistant(X0,v,X0,x)
| X0 = u ),
inference(forward_subsumption_resolution,[status(thm)],[f890,f168]) ).
fof(f947,plain,
( w = u
| ~ between(u,w,v) ),
inference(resolution,[status(thm)],[f902,f167]) ).
fof(f1112,plain,
! [X0,X1,X2,X3] :
( equidistant(X3,v,X1,x)
| ~ equidistant(X2,v,X0,x)
| ~ equidistant(X2,X3,X0,X1)
| ~ equidistant(X2,u,X0,u)
| ~ between(X2,X3,u)
| ~ between(X0,X1,u) ),
inference(resolution,[status(thm)],[f160,f166]) ).
fof(f1336,plain,
! [X0,X1] :
( equidistant(X1,v,X1,x)
| ~ equidistant(X0,v,X0,x)
| ~ equidistant(X0,u,X0,u)
| ~ between(X0,X1,u)
| ~ between(X0,X1,u) ),
inference(resolution,[status(thm)],[f1112,f96]) ).
fof(f1349,plain,
! [X0,X1] :
( equidistant(X1,v,X1,x)
| ~ equidistant(X0,v,X0,x)
| ~ equidistant(X0,u,X0,u)
| ~ between(X0,X1,u) ),
inference(duplicate_literals_removal,[status(thm)],[f1336]) ).
fof(f1350,plain,
! [X0,X1] :
( ~ equidistant(X1,v,X1,x)
| ~ between(X1,X0,u)
| equidistant(X0,v,X0,x) ),
inference(forward_subsumption_resolution,[status(thm)],[f1349,f96]) ).
fof(f4072,plain,
( ~ equidistant(w,v,w,x)
| equidistant(v,v,v,x) ),
inference(resolution,[status(thm)],[f1350,f537]) ).
fof(f4085,plain,
equidistant(v,v,v,x),
inference(forward_subsumption_resolution,[status(thm)],[f4072,f167]) ).
fof(f4093,plain,
( ~ between(u,v,v)
| v = u ),
inference(resolution,[status(thm)],[f4085,f902]) ).
fof(f4094,plain,
( ~ between(w,v,v)
| v = w ),
inference(resolution,[status(thm)],[f4085,f901]) ).
fof(f4100,plain,
! [X0] : equidistant(X0,X0,v,x),
inference(resolution,[status(thm)],[f4085,f210]) ).
fof(f4133,plain,
w = v,
inference(forward_subsumption_resolution,[status(thm)],[f4094,f125]) ).
fof(f4140,plain,
u = v,
inference(forward_subsumption_resolution,[status(thm)],[f4093,f125]) ).
fof(f4248,plain,
( w = u
| ~ between(u,w,w) ),
inference(backward_demodulation,[status(thm)],[f4133,f947]) ).
fof(f4300,plain,
x != w,
inference(backward_demodulation,[status(thm)],[f4133,f168]) ).
fof(f4383,plain,
w = u,
inference(forward_subsumption_resolution,[status(thm)],[f4248,f125]) ).
fof(f4509,plain,
x != u,
inference(backward_demodulation,[status(thm)],[f4383,f4300]) ).
fof(f4545,plain,
! [X0] : equidistant(X0,X0,u,x),
inference(forward_demodulation,[status(thm)],[f4140,f4100]) ).
fof(f4559,plain,
! [X0] : equidistant(x,u,X0,X0),
inference(resolution,[status(thm)],[f4545,f103]) ).
fof(f4593,plain,
x = u,
inference(resolution,[status(thm)],[f4559,f77]) ).
fof(f4605,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f4593,f4509]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO034-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n001.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 20 08:35:14 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Drodi V4.1.1
% 180.14/23.15 % Refutation found
% 180.14/23.15 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 180.14/23.15 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 11.14/23.96 % Elapsed time: 23.581007 seconds
% 11.14/23.96 % CPU time: 181.550851 seconds
% 11.14/23.96 % Total memory used: 319.216 MB
% 11.14/23.96 % Net memory used: 263.596 MB
%------------------------------------------------------------------------------