%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO026-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 0.89s 0.71s
% Output : CNFRefutation 0.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 15
% Syntax : Number of formulae : 56 ( 19 unt; 6 def)
% Number of atoms : 140 ( 11 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 164 ( 80 ~; 78 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 7 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-4 aty)
% Number of variables : 86 ( 86 !; 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(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,
between(u,v,x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,hypothesis,
equidistant(v,w,v,x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,hypothesis,
u != v,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
w != x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,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(f26,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)],[f25]) ).
fof(f27,plain,
! [X,Y] :
( X = Y
| ! [Z] : ~ equidistant(X,Y,Z,Z) ),
inference(miniscoping,[status(thm)],[f3]) ).
fof(f28,plain,
! [X0,X1,X2] :
( X0 = X1
| ~ equidistant(X0,X1,X2,X2) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f30,plain,
! [X0,X1,X2,X3] : equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f31,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(f32,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)],[f31]) ).
fof(f46,plain,
between(u,v,w),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f47,plain,
between(u,v,x),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f48,plain,
equidistant(v,w,v,x),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f49,plain,
u != v,
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f50,plain,
w != x,
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f56,plain,
! [X0] : ~ equidistant(w,x,X0,X0),
inference(resolution,[status(thm)],[f28,f50]) ).
fof(f66,plain,
! [X0,X1,X2,X3,X4] :
( X0 = X1
| ~ between(X2,X3,X4)
| ~ between(X0,X1,w)
| ~ equidistant(X1,x,X3,X4)
| ~ equidistant(X0,x,X2,X4)
| ~ equidistant(X1,w,X3,X4)
| ~ equidistant(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[f32,f56]) ).
fof(f137,plain,
! [X0,X1,X2] :
( ~ between(X0,X1,X2)
| ~ between(u,v,w)
| ~ equidistant(v,x,X1,X2)
| ~ equidistant(u,x,X0,X2)
| ~ equidistant(v,w,X1,X2)
| ~ equidistant(u,v,X0,X1) ),
inference(resolution,[status(thm)],[f66,f49]) ).
fof(f141,definition,
! [X0,X1,X2] :
( sQ8_spl
<=> ( ~ between(X0,X1,X2)
| ~ equidistant(v,x,X1,X2)
| ~ equidistant(u,x,X0,X2)
| ~ equidistant(v,w,X1,X2)
| ~ equidistant(u,v,X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f142,plain,
! [X0,X1,X2] :
( ~ sQ8_spl
| ~ between(X0,X1,X2)
| ~ equidistant(v,x,X1,X2)
| ~ equidistant(u,x,X0,X2)
| ~ equidistant(v,w,X1,X2)
| ~ equidistant(u,v,X0,X1) ),
inference(component_clause,[status(thm)],[f141]) ).
fof(f144,definition,
( sQ9_spl
<=> between(u,v,w) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f146,plain,
( sQ9_spl
| ~ between(u,v,w) ),
inference(component_clause,[status(thm)],[f144]) ).
fof(f147,plain,
( ~ sQ9_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f137,f141,f144]) ).
fof(f703,definition,
( sQ82_spl
<=> equidistant(v,w,v,x) ),
introduced(definition,[new_symbols(definition,[sQ82_spl])],[split_symbol_definition]) ).
fof(f705,plain,
( sQ82_spl
| ~ equidistant(v,w,v,x) ),
inference(component_clause,[status(thm)],[f703]) ).
fof(f721,plain,
( sQ82_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f705,f48]) ).
fof(f722,plain,
sQ82_spl,
inference(contradiction_clause,[status(thm)],[f721]) ).
fof(f1057,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f146,f46]) ).
fof(f1058,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f1057]) ).
fof(f1447,definition,
( sQ183_spl
<=> equidistant(u,v,u,v) ),
introduced(definition,[new_symbols(definition,[sQ183_spl])],[split_symbol_definition]) ).
fof(f1449,plain,
( sQ183_spl
| ~ equidistant(u,v,u,v) ),
inference(component_clause,[status(thm)],[f1447]) ).
fof(f1460,definition,
( sQ187_spl
<=> equidistant(v,x,v,x) ),
introduced(definition,[new_symbols(definition,[sQ187_spl])],[split_symbol_definition]) ).
fof(f1462,plain,
( sQ187_spl
| ~ equidistant(v,x,v,x) ),
inference(component_clause,[status(thm)],[f1460]) ).
fof(f1727,plain,
( ~ sQ8_spl
| ~ equidistant(v,x,v,x)
| ~ equidistant(u,x,u,x)
| ~ equidistant(v,w,v,x)
| ~ equidistant(u,v,u,v) ),
inference(resolution,[status(thm)],[f142,f47]) ).
fof(f1746,definition,
( sQ203_spl
<=> equidistant(u,x,u,x) ),
introduced(definition,[new_symbols(definition,[sQ203_spl])],[split_symbol_definition]) ).
fof(f1748,plain,
( sQ203_spl
| ~ equidistant(u,x,u,x) ),
inference(component_clause,[status(thm)],[f1746]) ).
fof(f1749,plain,
( ~ sQ8_spl
| ~ sQ187_spl
| ~ sQ203_spl
| ~ sQ82_spl
| ~ sQ183_spl ),
inference(split_clause,[status(thm)],[f1727,f1447,f703,f1746,f1460,f141]) ).
fof(f2003,plain,
! [X0,X1] :
( sQ183_spl
| ~ equidistant(X0,X1,u,v)
| ~ equidistant(X0,X1,u,v) ),
inference(resolution,[status(thm)],[f1449,f26]) ).
fof(f2004,plain,
! [X0,X1] :
( sQ183_spl
| ~ equidistant(X0,X1,u,v) ),
inference(duplicate_literals_removal,[status(thm)],[f2003]) ).
fof(f2005,plain,
( sQ183_spl
| $false ),
inference(resolution,[status(thm)],[f2004,f30]) ).
fof(f2009,plain,
sQ183_spl,
inference(contradiction_clause,[status(thm)],[f2005]) ).
fof(f2091,plain,
! [X0,X1] :
( sQ187_spl
| ~ equidistant(X0,X1,v,x)
| ~ equidistant(X0,X1,v,x) ),
inference(resolution,[status(thm)],[f1462,f26]) ).
fof(f2092,plain,
! [X0,X1] :
( sQ187_spl
| ~ equidistant(X0,X1,v,x) ),
inference(duplicate_literals_removal,[status(thm)],[f2091]) ).
fof(f2093,plain,
( sQ187_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f48,f2092]) ).
fof(f2098,plain,
sQ187_spl,
inference(contradiction_clause,[status(thm)],[f2093]) ).
fof(f2177,plain,
! [X0,X1] :
( sQ203_spl
| ~ equidistant(X0,X1,u,x)
| ~ equidistant(X0,X1,u,x) ),
inference(resolution,[status(thm)],[f1748,f26]) ).
fof(f2178,plain,
! [X0,X1] :
( sQ203_spl
| ~ equidistant(X0,X1,u,x) ),
inference(duplicate_literals_removal,[status(thm)],[f2177]) ).
fof(f2179,plain,
( sQ203_spl
| $false ),
inference(resolution,[status(thm)],[f2178,f30]) ).
fof(f2183,plain,
sQ203_spl,
inference(contradiction_clause,[status(thm)],[f2179]) ).
fof(f2184,plain,
$false,
inference(sat_refutation,[status(thm)],[f147,f722,f1058,f1749,f2009,f2098,f2183]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO026-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n017.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 08:18:11 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.14/0.37 % Drodi V4.1.1
% 0.89/0.71 % Refutation found
% 0.89/0.71 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.89/0.71 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.80/0.74 % Elapsed time: 0.364697 seconds
% 1.80/0.74 % CPU time: 2.554208 seconds
% 1.80/0.74 % Total memory used: 107.079 MB
% 1.80/0.74 % Net memory used: 102.327 MB
%------------------------------------------------------------------------------