%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO051-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/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 12:23:54 PM UTC 2026
% Result : Unsatisfiable 9.16s 1.77s
% Output : CNFRefutation 9.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 11
% Syntax : Number of formulae : 40 ( 14 unt; 4 def)
% Number of atoms : 86 ( 9 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 85 ( 39 ~; 42 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 5 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 29 ( 29 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f54,axiom,
! [U,V,W,X] :
( between(V,W,X)
| ~ between(U,W,X)
| ~ between(U,V,W) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f77,axiom,
! [U,V,W,X] :
( between(U,X,W)
| between(U,W,X)
| U = V
| ~ between(U,V,X)
| ~ between(U,V,W) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f78,hypothesis,
between(u,v,w),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f79,hypothesis,
between(u,v,x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f80,hypothesis,
u != v,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f81,hypothesis,
~ between(v,w,x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f82,negated_conjecture,
~ between(v,x,w),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f151,plain,
! [V,W,X] :
( between(V,W,X)
| ! [U] :
( ~ between(U,W,X)
| ~ between(U,V,W) ) ),
inference(miniscoping,[status(thm)],[f54]) ).
fof(f152,plain,
! [X0,X1,X2,X3] :
( between(X1,X2,X3)
| ~ between(X0,X2,X3)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f151]) ).
fof(f187,plain,
! [U,W,X] :
( between(U,X,W)
| between(U,W,X)
| ! [V] :
( U = V
| ~ between(U,V,X)
| ~ between(U,V,W) ) ),
inference(miniscoping,[status(thm)],[f77]) ).
fof(f188,plain,
! [X0,X1,X2,X3] :
( between(X0,X3,X2)
| between(X0,X2,X3)
| X0 = X1
| ~ between(X0,X1,X3)
| ~ between(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f187]) ).
fof(f189,plain,
between(u,v,w),
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f190,plain,
between(u,v,x),
inference(cnf_transformation,[status(thm)],[f79]) ).
fof(f191,plain,
u != v,
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f192,plain,
~ between(v,w,x),
inference(cnf_transformation,[status(thm)],[f81]) ).
fof(f193,plain,
~ between(v,x,w),
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f212,definition,
( sQ1_spl
<=> u = v ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f213,plain,
( ~ sQ1_spl
| u = v ),
inference(component_clause,[status(thm)],[f212]) ).
fof(f227,plain,
( ~ sQ1_spl
| u != u ),
inference(forward_demodulation,[status(thm)],[f213,f191]) ).
fof(f228,plain,
( ~ sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f227]) ).
fof(f229,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f228]) ).
fof(f336,plain,
! [X0] :
( between(v,x,X0)
| ~ between(u,x,X0) ),
inference(resolution,[status(thm)],[f190,f152]) ).
fof(f353,plain,
! [X0] :
( between(u,X0,x)
| between(u,x,X0)
| u = v
| ~ between(u,v,X0) ),
inference(resolution,[status(thm)],[f188,f190]) ).
fof(f359,definition,
! [X0] :
( sQ16_spl
<=> ( between(u,X0,x)
| between(u,x,X0)
| ~ between(u,v,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f360,plain,
! [X0] :
( ~ sQ16_spl
| between(u,X0,x)
| between(u,x,X0)
| ~ between(u,v,X0) ),
inference(component_clause,[status(thm)],[f359]) ).
fof(f362,plain,
( sQ1_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f353,f359,f212]) ).
fof(f412,definition,
( sQ24_spl
<=> between(u,x,w) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f413,plain,
( ~ sQ24_spl
| between(u,x,w) ),
inference(component_clause,[status(thm)],[f412]) ).
fof(f474,plain,
! [X0] :
( between(v,w,X0)
| ~ between(u,w,X0) ),
inference(resolution,[status(thm)],[f189,f152]) ).
fof(f1220,plain,
( ~ sQ16_spl
| between(u,w,x)
| between(u,x,w) ),
inference(resolution,[status(thm)],[f360,f189]) ).
fof(f1225,definition,
( sQ71_spl
<=> between(u,w,x) ),
introduced(definition,[new_symbols(definition,[sQ71_spl])],[split_symbol_definition]) ).
fof(f1226,plain,
( ~ sQ71_spl
| between(u,w,x) ),
inference(component_clause,[status(thm)],[f1225]) ).
fof(f1228,plain,
( ~ sQ16_spl
| sQ71_spl
| sQ24_spl ),
inference(split_clause,[status(thm)],[f1220,f412,f1225,f359]) ).
fof(f1315,plain,
( ~ sQ24_spl
| between(v,x,w) ),
inference(resolution,[status(thm)],[f413,f336]) ).
fof(f1340,plain,
( ~ sQ24_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1315,f193]) ).
fof(f1341,plain,
~ sQ24_spl,
inference(contradiction_clause,[status(thm)],[f1340]) ).
fof(f2405,plain,
( ~ sQ71_spl
| between(v,w,x) ),
inference(resolution,[status(thm)],[f474,f1226]) ).
fof(f2409,plain,
( ~ sQ71_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2405,f192]) ).
fof(f2410,plain,
~ sQ71_spl,
inference(contradiction_clause,[status(thm)],[f2409]) ).
fof(f2411,plain,
$false,
inference(sat_refutation,[status(thm)],[f229,f362,f1228,f1341,f2410]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO051-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.41 % Computer : n010.cluster.edu
% 0.12/0.41 % Model : x86_64 x86_64
% 0.12/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.41 % Memory : 8046.5625MB
% 0.12/0.41 % OS : Linux 6.8.0-71-generic
% 0.12/0.41 % CPULimit : 300
% 0.12/0.41 % WCLimit : 300
% 0.12/0.41 % DateTime : Sun Sep 20 08:45:25 UTC 2026
% 0.12/0.42 % CPUTime :
% 0.16/0.44 % Drodi V4.1.1
% 9.16/1.77 % Refutation found
% 9.16/1.77 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 9.16/1.77 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 9.16/1.81 % Elapsed time: 1.374600 seconds
% 9.16/1.81 % CPU time: 10.538718 seconds
% 9.16/1.81 % Total memory used: 138.694 MB
% 9.16/1.81 % Net memory used: 132.806 MB
%------------------------------------------------------------------------------