%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO026-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 0.12s 0.41s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 11
% Syntax : Number of formulae : 38 ( 16 unt; 3 def)
% Number of atoms : 96 ( 16 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 111 ( 53 ~; 55 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 53 ( 53 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X,Y,Z] :
( X = Y
| ~ equidistant(X,Y,Z,Z) ),
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(f20,axiom,
! [U,V] : equidistant(U,V,U,V),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,hypothesis,
between(u,v,w),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,hypothesis,
between(u,v,x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,hypothesis,
equidistant(v,w,v,x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f41,hypothesis,
u != v,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f42,negated_conjecture,
w != x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f46,plain,
! [X,Y] :
( X = Y
| ! [Z] : ~ equidistant(X,Y,Z,Z) ),
inference(miniscoping,[status(thm)],[f3]) ).
fof(f47,plain,
! [X0,X1,X2] :
( X0 = X1
| ~ equidistant(X0,X1,X2,X2) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f50,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(f51,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)],[f50]) ).
fof(f66,plain,
! [X0,X1] : equidistant(X0,X1,X0,X1),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f87,plain,
between(u,v,w),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f88,plain,
between(u,v,x),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f89,plain,
equidistant(v,w,v,x),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f90,plain,
u != v,
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f91,plain,
w != x,
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f110,plain,
! [X0,X1,X2,X3,X4] :
( equidistant(X2,X3,x,X4)
| X0 = X1
| ~ between(X0,X1,X2)
| ~ equidistant(X1,X3,v,X4)
| ~ equidistant(X0,X3,u,X4)
| ~ equidistant(X1,X2,v,x)
| ~ equidistant(X0,X1,u,v) ),
inference(resolution,[status(thm)],[f51,f88]) ).
fof(f119,plain,
! [X0,X1,X2] :
( equidistant(w,X1,x,X2)
| X0 = v
| ~ between(X0,v,w)
| ~ equidistant(v,X1,v,X2)
| ~ equidistant(X0,X1,u,X2)
| ~ equidistant(X0,v,u,v) ),
inference(resolution,[status(thm)],[f110,f89]) ).
fof(f163,plain,
! [X0,X1] :
( equidistant(w,X0,x,X1)
| u = v
| ~ between(u,v,w)
| ~ equidistant(v,X0,v,X1)
| ~ equidistant(u,X0,u,X1) ),
inference(resolution,[status(thm)],[f119,f66]) ).
fof(f165,definition,
! [X0,X1] :
( sQ5_spl
<=> ( equidistant(w,X0,x,X1)
| ~ equidistant(v,X0,v,X1)
| ~ equidistant(u,X0,u,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f166,plain,
! [X0,X1] :
( ~ sQ5_spl
| equidistant(w,X0,x,X1)
| ~ equidistant(v,X0,v,X1)
| ~ equidistant(u,X0,u,X1) ),
inference(component_clause,[status(thm)],[f165]) ).
fof(f168,definition,
( sQ6_spl
<=> between(u,v,w) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f170,plain,
( sQ6_spl
| ~ between(u,v,w) ),
inference(component_clause,[status(thm)],[f168]) ).
fof(f171,definition,
( sQ7_spl
<=> u = v ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f172,plain,
( ~ sQ7_spl
| u = v ),
inference(component_clause,[status(thm)],[f171]) ).
fof(f174,plain,
( sQ7_spl
| ~ sQ6_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f163,f165,f168,f171]) ).
fof(f175,plain,
( ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f172,f90]) ).
fof(f176,plain,
~ sQ7_spl,
inference(contradiction_clause,[status(thm)],[f175]) ).
fof(f284,plain,
! [X0] :
( ~ sQ5_spl
| equidistant(w,X0,x,X0)
| ~ equidistant(u,X0,u,X0) ),
inference(resolution,[status(thm)],[f166,f66]) ).
fof(f318,plain,
! [X0] :
( ~ sQ5_spl
| equidistant(w,X0,x,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f284,f66]) ).
fof(f328,plain,
( ~ sQ5_spl
| w = x ),
inference(resolution,[status(thm)],[f318,f47]) ).
fof(f330,plain,
( ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f328,f91]) ).
fof(f331,plain,
~ sQ5_spl,
inference(contradiction_clause,[status(thm)],[f330]) ).
fof(f332,plain,
( sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f170,f87]) ).
fof(f333,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f332]) ).
fof(f334,plain,
$false,
inference(sat_refutation,[status(thm)],[f174,f176,f331,f333]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO026-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n015.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 20 08:25:34 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.12/0.41 % Refutation found
% 0.12/0.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.44 % Elapsed time: 0.077531 seconds
% 0.12/0.44 % CPU time: 0.329528 seconds
% 0.12/0.44 % Total memory used: 104.555 MB
% 0.12/0.44 % Net memory used: 104.182 MB
%------------------------------------------------------------------------------