%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO041-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/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 12:23:52 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.40s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 24 ( 9 unt; 2 def)
% Number of atoms : 43 ( 9 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 38 ( 19 ~; 17 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 18 ( 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f46,axiom,
! [U,V,W] :
( between(W,V,U)
| ~ between(U,V,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f48,axiom,
! [U,V,W] :
( U = V
| ~ between(V,U,W)
| ~ between(U,V,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f49,hypothesis,
between(u,v,w),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f50,hypothesis,
between(u,w,v),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f51,negated_conjecture,
v != w,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f107,plain,
! [X0,X1,X2] :
( between(X2,X1,X0)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f109,plain,
! [U,V] :
( U = V
| ! [W] :
( ~ between(V,U,W)
| ~ between(U,V,W) ) ),
inference(miniscoping,[status(thm)],[f48]) ).
fof(f110,plain,
! [X0,X1,X2] :
( X0 = X1
| ~ between(X1,X0,X2)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f109]) ).
fof(f111,plain,
between(u,v,w),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f112,plain,
between(u,w,v),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f113,plain,
v != w,
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f250,plain,
! [X0,X1,X2] :
( ~ between(X2,X0,X1)
| X0 = X1
| ~ between(X0,X1,X2) ),
inference(resolution,[status(thm)],[f110,f107]) ).
fof(f276,definition,
( sQ13_spl
<=> between(w,v,u) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f278,plain,
( sQ13_spl
| ~ between(w,v,u) ),
inference(component_clause,[status(thm)],[f276]) ).
fof(f306,definition,
( sQ15_spl
<=> v = w ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f307,plain,
( ~ sQ15_spl
| v = w ),
inference(component_clause,[status(thm)],[f306]) ).
fof(f312,plain,
( ~ sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f307,f113]) ).
fof(f313,plain,
~ sQ15_spl,
inference(contradiction_clause,[status(thm)],[f312]) ).
fof(f371,plain,
( w = v
| ~ between(w,v,u) ),
inference(resolution,[status(thm)],[f250,f112]) ).
fof(f389,plain,
( sQ15_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f371,f276,f306]) ).
fof(f397,plain,
( sQ13_spl
| ~ between(u,v,w) ),
inference(resolution,[status(thm)],[f278,f107]) ).
fof(f400,plain,
( sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f397,f111]) ).
fof(f401,plain,
sQ13_spl,
inference(contradiction_clause,[status(thm)],[f400]) ).
fof(f402,plain,
$false,
inference(sat_refutation,[status(thm)],[f313,f389,f401]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO041-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.35 % Computer : n002.cluster.edu
% 0.06/0.35 % Model : x86_64 x86_64
% 0.06/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.35 % Memory : 8046.5625MB
% 0.06/0.35 % OS : Linux 6.8.0-71-generic
% 0.06/0.35 % CPULimit : 300
% 0.06/0.35 % WCLimit : 300
% 0.06/0.35 % DateTime : Sun Sep 20 08:37:32 UTC 2026
% 0.06/0.35 % CPUTime :
% 0.06/0.36 % Drodi V4.1.1
% 0.12/0.40 % Refutation found
% 0.12/0.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.47 % Elapsed time: 0.111342 seconds
% 0.12/0.47 % CPU time: 0.289236 seconds
% 0.12/0.47 % Total memory used: 90.874 MB
% 0.12/0.47 % Net memory used: 90.714 MB
%------------------------------------------------------------------------------