%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO002-4 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 0.11s 0.42s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 34 ( 15 unt; 0 def)
% Number of atoms : 63 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 60 ( 31 ~; 29 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-5 aty)
% Number of variables : 114 ( 114 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,V,Z] :
( between(X,Y,Z)
| ~ between(Y,Z,V)
| ~ between(X,Y,V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y,Z] :
( equalish(X,Y)
| ~ equidistant(X,Y,Z,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y,W,V] : between(X,Y,extension(X,Y,W,V)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [Y,X,W,V] : equidistant(Y,extension(X,Y,W,V),W,V),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Y,W,Z] :
( between(W,Z,Y)
| ~ between(W,Z,X)
| ~ equalish(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
~ between(a,a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,plain,
! [X,Y,Z] :
( between(X,Y,Z)
| ! [V] :
( ~ between(Y,Z,V)
| ~ between(X,Y,V) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f10,plain,
! [X0,X1,X2,X3] :
( between(X0,X1,X3)
| ~ between(X1,X3,X2)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f11,plain,
! [X,Y] :
( equalish(X,Y)
| ! [Z] : ~ equidistant(X,Y,Z,Z) ),
inference(miniscoping,[status(thm)],[f2]) ).
fof(f12,plain,
! [X0,X1,X2] :
( equalish(X0,X1)
| ~ equidistant(X0,X1,X2,X2) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f13,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)],[f3]) ).
fof(f14,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)],[f4]) ).
fof(f15,plain,
! [X0,X1,X2,X3] : between(X0,X1,extension(X0,X1,X2,X3)),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f16,plain,
! [X0,X1,X2,X3] : equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f17,plain,
! [Y,W,Z] :
( between(W,Z,Y)
| ! [X] :
( ~ between(W,Z,X)
| ~ equalish(X,Y) ) ),
inference(miniscoping,[status(thm)],[f7]) ).
fof(f18,plain,
! [X0,X1,X2,X3] :
( between(X2,X3,X1)
| ~ between(X2,X3,X0)
| ~ equalish(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f19,plain,
~ between(a,a,b),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f20,plain,
! [X0,X1,X2,X3,X4] :
( between(X2,X0,X1)
| ~ between(X0,X1,extension(X2,X0,X3,X4)) ),
inference(resolution,[status(thm)],[f10,f15]) ).
fof(f21,plain,
! [X0,X1,X2] : equalish(X0,extension(X1,X0,X2,X2)),
inference(resolution,[status(thm)],[f16,f12]) ).
fof(f22,plain,
! [X0,X1,X2,X3,X4] :
( between(X0,X1,extension(X3,X2,X4,X4))
| ~ between(X0,X1,X2) ),
inference(resolution,[status(thm)],[f18,f21]) ).
fof(f24,plain,
! [X0] : between(X0,X0,X0),
inference(resolution,[status(thm)],[f20,f15]) ).
fof(f31,plain,
! [X0,X1,X2] : between(X0,X0,extension(X1,X0,X2,X2)),
inference(resolution,[status(thm)],[f22,f24]) ).
fof(f32,plain,
! [X0,X1] : between(X0,X1,X1),
inference(resolution,[status(thm)],[f31,f20]) ).
fof(f39,plain,
! [X0,X1,X2,X3] :
( between(X2,X1,outer_pasch(X1,X3,X0,X2,X1))
| ~ between(X0,X1,X2) ),
inference(resolution,[status(thm)],[f32,f14]) ).
fof(f41,plain,
! [X0,X1,X2,X3] :
( between(X3,outer_pasch(X1,X3,X0,X2,X1),X0)
| ~ between(X0,X1,X2) ),
inference(resolution,[status(thm)],[f32,f13]) ).
fof(f42,plain,
! [X0,X1,X2] :
( between(X2,X0,X1)
| ~ between(X0,X1,X0) ),
inference(resolution,[status(thm)],[f32,f10]) ).
fof(f196,plain,
! [X0,X1,X2] : between(X0,X0,outer_pasch(X0,X1,X2,X0,X0)),
inference(resolution,[status(thm)],[f39,f32]) ).
fof(f204,plain,
! [X0,X1,X2,X3] :
( between(X0,X0,X1)
| ~ between(X0,X1,outer_pasch(X0,X2,X3,X0,X0)) ),
inference(resolution,[status(thm)],[f196,f10]) ).
fof(f227,plain,
! [X0,X1,X2] : between(X0,outer_pasch(X1,X0,X2,X1,X1),X2),
inference(resolution,[status(thm)],[f41,f32]) ).
fof(f232,plain,
! [X0,X1,X2] : between(X0,X1,outer_pasch(X2,X1,X1,X2,X2)),
inference(resolution,[status(thm)],[f227,f42]) ).
fof(f477,plain,
! [X0,X1] : between(X0,X0,X1),
inference(resolution,[status(thm)],[f204,f232]) ).
fof(f489,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f19,f477]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO002-4 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n002.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 20 08:17:01 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Drodi V4.1.1
% 0.11/0.42 % Refutation found
% 0.11/0.42 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.11/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.45 % Elapsed time: 0.070092 seconds
% 0.11/0.45 % CPU time: 0.330722 seconds
% 0.11/0.45 % Total memory used: 57.873 MB
% 0.11/0.45 % Net memory used: 57.439 MB
%------------------------------------------------------------------------------