%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO002-1 : TPTP v9.3.1. Bugfixed v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 12:23:42 PM UTC 2026
% Result : Unsatisfiable 0.13s 5.41s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 24 ( 11 unt; 0 def)
% Number of atoms : 43 ( 9 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 40 ( 21 ~; 19 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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; 0-5 aty)
% Number of variables : 69 ( 69 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] :
( X = Y
| ~ between(X,Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y,Z] :
( X = Y
| ~ equidistant(X,Y,Z,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,W,V,Y,Z] :
( between(X,outer_pasch(W,X,Y,Z,V),Y)
| ~ between(Y,V,Z)
| ~ between(X,W,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,W,V,Y,Z] :
( between(Z,W,outer_pasch(W,X,Y,Z,V))
| ~ between(Y,V,Z)
| ~ between(X,W,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X,Y,W,V] : between(X,Y,extension(X,Y,W,V)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [Y,X,W,V] : equidistant(Y,extension(X,Y,W,V),W,V),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
~ between(a,a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,plain,
! [X0,X1] :
( X0 = X1
| ~ between(X0,X1,X0) ),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f28,plain,
! [X,Y] :
( X = Y
| ! [Z] : ~ equidistant(X,Y,Z,Z) ),
inference(miniscoping,[status(thm)],[f5]) ).
fof(f29,plain,
! [X0,X1,X2] :
( X0 = X1
| ~ equidistant(X0,X1,X2,X2) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f32,plain,
! [X0,X1,X2,X3,X4] :
( between(X0,outer_pasch(X1,X0,X3,X4,X2),X3)
| ~ between(X3,X2,X4)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f33,plain,
! [X0,X1,X2,X3,X4] :
( between(X4,X1,outer_pasch(X1,X0,X3,X4,X2))
| ~ between(X3,X2,X4)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f39,plain,
! [X0,X1,X2,X3] : between(X0,X1,extension(X0,X1,X2,X3)),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f40,plain,
! [X0,X1,X2,X3] : equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f48,plain,
~ between(a,a,b),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f64,plain,
! [X0,X1,X2] : X0 = extension(X1,X0,X2,X2),
inference(resolution,[status(thm)],[f40,f29]) ).
fof(f71,plain,
! [X0,X1] : between(X0,X1,X1),
inference(paramodulation,[status(thm)],[f64,f39]) ).
fof(f105,plain,
! [X0,X1,X2,X3] :
( X0 = outer_pasch(X1,X0,X0,X3,X2)
| ~ between(X0,X2,X3)
| ~ between(X0,X1,X2) ),
inference(resolution,[status(thm)],[f32,f22]) ).
fof(f118,plain,
! [X0,X1,X2] :
( X0 = outer_pasch(X1,X0,X0,X2,X2)
| ~ between(X0,X1,X2) ),
inference(resolution,[status(thm)],[f105,f71]) ).
fof(f125,plain,
! [X0,X1] : X0 = outer_pasch(X1,X0,X0,X1,X1),
inference(resolution,[status(thm)],[f118,f71]) ).
fof(f126,plain,
! [X0,X1] :
( between(X1,X1,X0)
| ~ between(X0,X1,X1)
| ~ between(X0,X1,X1) ),
inference(paramodulation,[status(thm)],[f125,f33]) ).
fof(f128,plain,
! [X0,X1] :
( between(X1,X1,X0)
| ~ between(X0,X1,X1) ),
inference(duplicate_literals_removal,[status(thm)],[f126]) ).
fof(f129,plain,
! [X0,X1] : between(X0,X0,X1),
inference(forward_subsumption_resolution,[status(thm)],[f128,f71]) ).
fof(f132,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f48,f129]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO002-1 : TPTP v9.3.1. Bugfixed v2.5.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.36 % Computer : n004.cluster.edu
% 0.09/5.36 % Model : x86_64 x86_64
% 0.09/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.36 % Memory : 8046.5625MB
% 0.09/5.36 % OS : Linux 6.8.0-71-generic
% 0.09/5.36 % CPULimit : 300
% 0.09/5.36 % WCLimit : 300
% 0.09/5.36 % DateTime : Sun Sep 20 08:13:54 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.38 % Drodi V4.1.1
% 0.13/5.41 % Refutation found
% 0.13/5.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/5.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/5.44 % Elapsed time: 0.057909 seconds
% 0.13/5.44 % CPU time: 0.197851 seconds
% 0.13/5.44 % Total memory used: 81.647 MB
% 0.13/5.44 % Net memory used: 81.032 MB
%------------------------------------------------------------------------------