%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO027-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 12:23:49 PM UTC 2026
% Result : Unsatisfiable 3.80s 0.96s
% Output : CNFRefutation 3.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 15
% Syntax : Number of formulae : 57 ( 17 unt; 7 def)
% Number of atoms : 146 ( 11 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 177 ( 88 ~; 82 |; 0 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 8 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-4 aty)
% Number of variables : 98 ( 98 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X,Y,Z,V,V2,W] :
( equidistant(Z,V,V2,W)
| ~ equidistant(X,Y,V2,W)
| ~ equidistant(X,Y,Z,V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] :
( X = Y
| ~ equidistant(X,Y,Z,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y,W,V] : between(X,Y,extension(X,Y,W,V)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [Y,X,W,V] : equidistant(Y,extension(X,Y,W,V),W,V),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y,X1,Y1,Z,Z1,V,V1] :
( equidistant(Z,V,Z1,V1)
| X = Y
| ~ between(X1,Y1,Z1)
| ~ between(X,Y,Z)
| ~ equidistant(Y,V,Y1,V1)
| ~ equidistant(X,V,X1,V1)
| ~ equidistant(Y,Z,Y1,Z1)
| ~ equidistant(X,Y,X1,Y1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,hypothesis,
between(u,v,w),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,hypothesis,
u != v,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
w != extension(u,v,v,w),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,plain,
! [Z,V,V2,W] :
( equidistant(Z,V,V2,W)
| ! [X,Y] :
( ~ equidistant(X,Y,V2,W)
| ~ equidistant(X,Y,Z,V) ) ),
inference(miniscoping,[status(thm)],[f2]) ).
fof(f24,plain,
! [X0,X1,X2,X3,X4,X5] :
( equidistant(X2,X3,X4,X5)
| ~ equidistant(X0,X1,X4,X5)
| ~ equidistant(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f25,plain,
! [X,Y] :
( X = Y
| ! [Z] : ~ equidistant(X,Y,Z,Z) ),
inference(miniscoping,[status(thm)],[f3]) ).
fof(f26,plain,
! [X0,X1,X2] :
( X0 = X1
| ~ equidistant(X0,X1,X2,X2) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f27,plain,
! [X0,X1,X2,X3] : between(X0,X1,extension(X0,X1,X2,X3)),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f28,plain,
! [X0,X1,X2,X3] : equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f29,plain,
! [Z,Z1,V,V1] :
( equidistant(Z,V,Z1,V1)
| ! [X,Y] :
( X = Y
| ! [X1,Y1] :
( ~ between(X1,Y1,Z1)
| ~ between(X,Y,Z)
| ~ equidistant(Y,V,Y1,V1)
| ~ equidistant(X,V,X1,V1)
| ~ equidistant(Y,Z,Y1,Z1)
| ~ equidistant(X,Y,X1,Y1) ) ) ),
inference(miniscoping,[status(thm)],[f6]) ).
fof(f30,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( equidistant(X4,X6,X5,X7)
| X0 = X1
| ~ between(X2,X3,X5)
| ~ between(X0,X1,X4)
| ~ equidistant(X1,X6,X3,X7)
| ~ equidistant(X0,X6,X2,X7)
| ~ equidistant(X1,X4,X3,X5)
| ~ equidistant(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f44,plain,
between(u,v,w),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f45,plain,
u != v,
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f46,plain,
w != extension(u,v,v,w),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f54,plain,
! [X0] : ~ equidistant(extension(u,v,v,w),w,X0,X0),
inference(resolution,[status(thm)],[f26,f46]) ).
fof(f73,plain,
! [X0,X1,X2,X3,X4] :
( X0 = X1
| ~ between(X2,X3,X4)
| ~ between(X0,X1,extension(u,v,v,w))
| ~ equidistant(X1,w,X3,X4)
| ~ equidistant(X0,w,X2,X4)
| ~ equidistant(X1,extension(u,v,v,w),X3,X4)
| ~ equidistant(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[f54,f30]) ).
fof(f325,plain,
! [X0,X1,X2] :
( ~ between(X0,X1,X2)
| ~ between(u,v,extension(u,v,v,w))
| ~ equidistant(v,w,X1,X2)
| ~ equidistant(u,w,X0,X2)
| ~ equidistant(v,extension(u,v,v,w),X1,X2)
| ~ equidistant(u,v,X0,X1) ),
inference(resolution,[status(thm)],[f73,f45]) ).
fof(f329,definition,
! [X0,X1,X2] :
( sQ37_spl
<=> ( ~ between(X0,X1,X2)
| ~ equidistant(v,w,X1,X2)
| ~ equidistant(u,w,X0,X2)
| ~ equidistant(v,extension(u,v,v,w),X1,X2)
| ~ equidistant(u,v,X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f330,plain,
! [X0,X1,X2] :
( ~ sQ37_spl
| ~ between(X0,X1,X2)
| ~ equidistant(v,w,X1,X2)
| ~ equidistant(u,w,X0,X2)
| ~ equidistant(v,extension(u,v,v,w),X1,X2)
| ~ equidistant(u,v,X0,X1) ),
inference(component_clause,[status(thm)],[f329]) ).
fof(f332,definition,
( sQ38_spl
<=> between(u,v,extension(u,v,v,w)) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f334,plain,
( sQ38_spl
| ~ between(u,v,extension(u,v,v,w)) ),
inference(component_clause,[status(thm)],[f332]) ).
fof(f335,plain,
( ~ sQ38_spl
| sQ37_spl ),
inference(split_clause,[status(thm)],[f325,f329,f332]) ).
fof(f354,plain,
( sQ38_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f334,f27]) ).
fof(f355,plain,
sQ38_spl,
inference(contradiction_clause,[status(thm)],[f354]) ).
fof(f411,definition,
( sQ54_spl
<=> equidistant(v,extension(u,v,v,w),v,w) ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f413,plain,
( sQ54_spl
| ~ equidistant(v,extension(u,v,v,w),v,w) ),
inference(component_clause,[status(thm)],[f411]) ).
fof(f415,plain,
( sQ54_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f413,f28]) ).
fof(f416,plain,
sQ54_spl,
inference(contradiction_clause,[status(thm)],[f415]) ).
fof(f543,definition,
! [X1,X2] :
( sQ67_spl
<=> ( ~ equidistant(X1,X2,u,v)
| ~ equidistant(X1,X2,u,v) ) ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f544,plain,
! [X0,X1] :
( ~ sQ67_spl
| ~ equidistant(X0,X1,u,v)
| ~ equidistant(X0,X1,u,v) ),
inference(component_clause,[status(thm)],[f543]) ).
fof(f547,definition,
( sQ68_spl
<=> equidistant(u,v,u,v) ),
introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition]) ).
fof(f549,plain,
( sQ68_spl
| ~ equidistant(u,v,u,v) ),
inference(component_clause,[status(thm)],[f547]) ).
fof(f551,plain,
! [X0,X1] :
( ~ sQ67_spl
| ~ equidistant(X0,X1,u,v) ),
inference(duplicate_literals_removal,[status(thm)],[f544]) ).
fof(f552,plain,
( ~ sQ67_spl
| $false ),
inference(resolution,[status(thm)],[f551,f28]) ).
fof(f556,plain,
~ sQ67_spl,
inference(contradiction_clause,[status(thm)],[f552]) ).
fof(f560,plain,
! [X0,X1] :
( sQ68_spl
| ~ equidistant(X0,X1,u,v)
| ~ equidistant(X0,X1,u,v) ),
inference(resolution,[status(thm)],[f549,f24]) ).
fof(f561,plain,
( sQ68_spl
| sQ67_spl ),
inference(split_clause,[status(thm)],[f560,f543,f547]) ).
fof(f1387,definition,
( sQ168_spl
<=> equidistant(v,w,v,w) ),
introduced(definition,[new_symbols(definition,[sQ168_spl])],[split_symbol_definition]) ).
fof(f1389,plain,
( sQ168_spl
| ~ equidistant(v,w,v,w) ),
inference(component_clause,[status(thm)],[f1387]) ).
fof(f1448,plain,
! [X0,X1] :
( sQ168_spl
| ~ equidistant(X0,X1,v,w)
| ~ equidistant(X0,X1,v,w) ),
inference(resolution,[status(thm)],[f1389,f24]) ).
fof(f1449,plain,
! [X0,X1] :
( sQ168_spl
| ~ equidistant(X0,X1,v,w) ),
inference(duplicate_literals_removal,[status(thm)],[f1448]) ).
fof(f1450,plain,
( sQ168_spl
| $false ),
inference(resolution,[status(thm)],[f1449,f28]) ).
fof(f1454,plain,
sQ168_spl,
inference(contradiction_clause,[status(thm)],[f1450]) ).
fof(f2250,plain,
( ~ sQ37_spl
| ~ equidistant(v,w,v,w)
| ~ equidistant(u,w,u,w)
| ~ equidistant(v,extension(u,v,v,w),v,w)
| ~ equidistant(u,v,u,v) ),
inference(resolution,[status(thm)],[f330,f44]) ).
fof(f2272,definition,
( sQ225_spl
<=> equidistant(u,w,u,w) ),
introduced(definition,[new_symbols(definition,[sQ225_spl])],[split_symbol_definition]) ).
fof(f2274,plain,
( sQ225_spl
| ~ equidistant(u,w,u,w) ),
inference(component_clause,[status(thm)],[f2272]) ).
fof(f2275,plain,
( ~ sQ37_spl
| ~ sQ168_spl
| ~ sQ225_spl
| ~ sQ54_spl
| ~ sQ68_spl ),
inference(split_clause,[status(thm)],[f2250,f547,f411,f2272,f1387,f329]) ).
fof(f2282,plain,
! [X0,X1] :
( sQ225_spl
| ~ equidistant(X0,X1,u,w)
| ~ equidistant(X0,X1,u,w) ),
inference(resolution,[status(thm)],[f2274,f24]) ).
fof(f2283,plain,
! [X0,X1] :
( sQ225_spl
| ~ equidistant(X0,X1,u,w) ),
inference(duplicate_literals_removal,[status(thm)],[f2282]) ).
fof(f2284,plain,
( sQ225_spl
| $false ),
inference(resolution,[status(thm)],[f2283,f28]) ).
fof(f2288,plain,
sQ225_spl,
inference(contradiction_clause,[status(thm)],[f2284]) ).
fof(f2289,plain,
$false,
inference(sat_refutation,[status(thm)],[f335,f355,f416,f556,f561,f1454,f2275,f2288]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO027-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.38 % Computer : n026.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 20 08:25:21 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.39 % Drodi V4.1.1
% 3.80/0.96 % Refutation found
% 3.80/0.96 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 3.80/0.96 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.80/0.98 % Elapsed time: 0.582498 seconds
% 3.80/0.98 % CPU time: 4.305438 seconds
% 3.80/0.98 % Total memory used: 115.455 MB
% 3.80/0.98 % Net memory used: 109.958 MB
%------------------------------------------------------------------------------