%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO030-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 0.13s 0.59s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 38 ( 20 unt; 0 def)
% Number of atoms : 92 ( 14 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 107 ( 53 ~; 54 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-4 aty)
% Number of variables : 95 ( 95 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] : equidistant(X,Y,Y,X),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] :
( X = Y
| ~ equidistant(X,Y,Z,Z) ),
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(f6,axiom,
! [X,Y,X1,Y1,Z,Z1,V,V1] :
( equidistant(Z,V,Z1,V1)
| X = Y
| ~ between(X1,Y1,Z1)
| ~ between(X,Y,Z)
| ~ equidistant(Y,V,Y1,V1)
| ~ equidistant(X,V,X1,V1)
| ~ equidistant(Y,Z,Y1,Z1)
| ~ equidistant(X,Y,X1,Y1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,hypothesis,
between(u,v,w),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,hypothesis,
equidistant(u,w,u,w1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,hypothesis,
equidistant(v,w,v,w1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,hypothesis,
u != v,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
w != w1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,plain,
! [X0,X1] : equidistant(X0,X1,X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f25,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(f26,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)],[f25]) ).
fof(f27,plain,
! [X,Y] :
( X = Y
| ! [Z] : ~ equidistant(X,Y,Z,Z) ),
inference(miniscoping,[status(thm)],[f3]) ).
fof(f28,plain,
! [X0,X1,X2] :
( X0 = X1
| ~ equidistant(X0,X1,X2,X2) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f30,plain,
! [X0,X1,X2,X3] : equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f31,plain,
! [Z,Z1,V,V1] :
( equidistant(Z,V,Z1,V1)
| ! [X,Y] :
( X = Y
| ! [X1,Y1] :
( ~ between(X1,Y1,Z1)
| ~ between(X,Y,Z)
| ~ equidistant(Y,V,Y1,V1)
| ~ equidistant(X,V,X1,V1)
| ~ equidistant(Y,Z,Y1,Z1)
| ~ equidistant(X,Y,X1,Y1) ) ) ),
inference(miniscoping,[status(thm)],[f6]) ).
fof(f32,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( equidistant(X4,X6,X5,X7)
| X0 = X1
| ~ between(X2,X3,X5)
| ~ between(X0,X1,X4)
| ~ equidistant(X1,X6,X3,X7)
| ~ equidistant(X0,X6,X2,X7)
| ~ equidistant(X1,X4,X3,X5)
| ~ equidistant(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f46,plain,
between(u,v,w),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f47,plain,
equidistant(u,w,u,w1),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f48,plain,
equidistant(v,w,v,w1),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f49,plain,
u != v,
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f50,plain,
w != w1,
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f53,plain,
! [X0,X1,X2,X3] :
( equidistant(X2,X3,X1,X0)
| ~ equidistant(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[f26,f24]) ).
fof(f59,plain,
! [X0,X1,X2] : X0 = extension(X1,X0,X2,X2),
inference(resolution,[status(thm)],[f30,f28]) ).
fof(f60,plain,
! [X0,X1,X2,X3,X4,X5] :
( equidistant(X4,X5,X2,X3)
| ~ equidistant(X0,extension(X1,X0,X2,X3),X4,X5) ),
inference(resolution,[status(thm)],[f30,f26]) ).
fof(f77,plain,
! [X0,X1,X2,X3] :
( equidistant(X2,w,X3,w1)
| X0 = v
| ~ between(X1,v,X3)
| ~ between(X0,v,X2)
| ~ equidistant(X0,w,X1,w1)
| ~ equidistant(v,X2,v,X3)
| ~ equidistant(X0,v,X1,v) ),
inference(resolution,[status(thm)],[f32,f48]) ).
fof(f131,plain,
! [X0,X1] :
( equidistant(X0,w,X1,w1)
| u = v
| ~ between(u,v,X1)
| ~ between(u,v,X0)
| ~ equidistant(v,X0,v,X1)
| ~ equidistant(u,v,u,v) ),
inference(resolution,[status(thm)],[f77,f47]) ).
fof(f134,plain,
! [X0,X1] :
( equidistant(X0,w,X1,w1)
| ~ between(u,v,X1)
| ~ between(u,v,X0)
| ~ equidistant(v,X0,v,X1)
| ~ equidistant(u,v,u,v) ),
inference(forward_subsumption_resolution,[status(thm)],[f131,f49]) ).
fof(f242,plain,
! [X0,X1] : equidistant(X0,X1,X0,X1),
inference(resolution,[status(thm)],[f53,f24]) ).
fof(f295,plain,
! [X0,X1,X2,X3] :
( equidistant(X1,X2,X3,X3)
| ~ equidistant(X0,X0,X1,X2) ),
inference(paramodulation,[status(thm)],[f59,f60]) ).
fof(f870,plain,
! [X0,X1] :
( equidistant(X0,w,X1,w1)
| ~ between(u,v,X1)
| ~ between(u,v,X0)
| ~ equidistant(v,X0,v,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f134,f242]) ).
fof(f874,plain,
! [X0] :
( equidistant(X0,w,X0,w1)
| ~ between(u,v,X0)
| ~ between(u,v,X0) ),
inference(resolution,[status(thm)],[f870,f242]) ).
fof(f877,plain,
! [X0] :
( equidistant(X0,w,X0,w1)
| ~ between(u,v,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f874]) ).
fof(f1230,plain,
equidistant(w,w,w,w1),
inference(resolution,[status(thm)],[f877,f46]) ).
fof(f1268,plain,
! [X0] : equidistant(w,w1,X0,X0),
inference(resolution,[status(thm)],[f1230,f295]) ).
fof(f1341,plain,
w = w1,
inference(resolution,[status(thm)],[f1268,f28]) ).
fof(f1350,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1341,f50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO030-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n018.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 08:29:43 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.37 % Drodi V4.1.1
% 0.13/0.59 % Refutation found
% 0.13/0.59 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.59 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.56/0.61 % Elapsed time: 0.236024 seconds
% 0.56/0.61 % CPU time: 1.550719 seconds
% 0.56/0.61 % Total memory used: 99.058 MB
% 0.56/0.61 % Net memory used: 96.132 MB
%------------------------------------------------------------------------------