%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO002-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 0.16s 0.51s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 24 ( 13 unt; 0 def)
% Number of atoms : 39 ( 7 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 32 ( 17 ~; 15 |; 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 : 72 ( 72 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X,Y,Z] :
( X = Y
| ~ equidistant(X,Y,Z,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y,W,V] : between(X,Y,extension(X,Y,W,V)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [Y,X,W,V] : equidistant(Y,extension(X,Y,W,V),W,V),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Y] :
( X = Y
| ~ between(X,Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [U,V,W,Y,X] :
( between(V,inner_pasch(U,V,W,X,Y),Y)
| ~ between(Y,X,W)
| ~ between(U,V,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [U,V,W,Y,X] :
( between(X,inner_pasch(U,V,W,X,Y),U)
| ~ between(Y,X,W)
| ~ between(U,V,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
~ between(a,a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,plain,
! [X,Y] :
( X = Y
| ! [Z] : ~ equidistant(X,Y,Z,Z) ),
inference(miniscoping,[status(thm)],[f3]) ).
fof(f24,plain,
! [X0,X1,X2] :
( X0 = X1
| ~ equidistant(X0,X1,X2,X2) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f25,plain,
! [X0,X1,X2,X3] : between(X0,X1,extension(X0,X1,X2,X3)),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f26,plain,
! [X0,X1,X2,X3] : equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f29,plain,
! [X0,X1] :
( X0 = X1
| ~ between(X0,X1,X0) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f30,plain,
! [X0,X1,X2,X3,X4] :
( between(X1,inner_pasch(X0,X1,X2,X4,X3),X3)
| ~ between(X3,X4,X2)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f31,plain,
! [X0,X1,X2,X3,X4] :
( between(X4,inner_pasch(X0,X1,X2,X4,X3),X0)
| ~ between(X3,X4,X2)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f42,plain,
~ between(a,a,b),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f45,plain,
! [X0,X1,X2] : X0 = extension(X1,X0,X2,X2),
inference(resolution,[status(thm)],[f26,f24]) ).
fof(f49,plain,
! [X0,X1] : between(X0,X1,X1),
inference(paramodulation,[status(thm)],[f45,f25]) ).
fof(f50,plain,
! [X0,X1,X2,X3] :
( between(X1,inner_pasch(X0,X1,X2,X2,X3),X3)
| ~ between(X0,X1,X2) ),
inference(resolution,[status(thm)],[f49,f30]) ).
fof(f63,plain,
! [X0,X1,X2] : between(X0,inner_pasch(X1,X0,X0,X0,X2),X2),
inference(resolution,[status(thm)],[f50,f49]) ).
fof(f67,plain,
! [X0,X1] : X0 = inner_pasch(X1,X0,X0,X0,X0),
inference(resolution,[status(thm)],[f63,f29]) ).
fof(f70,plain,
! [X0,X1,X2,X3] :
( between(X2,inner_pasch(X0,X1,X2,X2,X3),X0)
| ~ between(X0,X1,X2) ),
inference(resolution,[status(thm)],[f31,f49]) ).
fof(f89,plain,
! [X0,X1,X2] : between(X0,inner_pasch(X1,X0,X0,X0,X2),X1),
inference(resolution,[status(thm)],[f70,f49]) ).
fof(f97,plain,
! [X0,X1] : between(X0,X0,X1),
inference(paramodulation,[status(thm)],[f67,f89]) ).
fof(f103,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f42,f97]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO002-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.43 % Computer : n010.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Sun Sep 20 08:14:39 UTC 2026
% 0.16/0.44 % CPUTime :
% 0.16/0.45 % Drodi V4.1.1
% 0.16/0.51 % Refutation found
% 0.16/0.51 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.16/0.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.24/0.57 % Elapsed time: 0.123292 seconds
% 0.24/0.57 % CPU time: 0.134167 seconds
% 0.24/0.57 % Total memory used: 15.396 MB
% 0.24/0.57 % Net memory used: 15.347 MB
%------------------------------------------------------------------------------