%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO037-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : 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 12:23:51 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.47s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of formulae : 36 ( 11 unt; 3 def)
% Number of atoms : 68 ( 10 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 62 ( 30 ~; 29 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-4 aty)
% Number of variables : 57 ( 57 !; 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(f21,axiom,
! [U,V,W,X] :
( equidistant(W,X,U,V)
| ~ equidistant(U,V,W,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f58,axiom,
lower_dimension_point_1 != lower_dimension_point_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f61,negated_conjecture,
( ~ between(u,v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2))
| ~ equidistant(v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2),x,extension(w,x,lower_dimension_point_1,lower_dimension_point_2))
| v = extension(u,v,lower_dimension_point_1,lower_dimension_point_2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f63,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(f64,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)],[f63]) ).
fof(f65,plain,
! [X,Y] :
( X = Y
| ! [Z] : ~ equidistant(X,Y,Z,Z) ),
inference(miniscoping,[status(thm)],[f3]) ).
fof(f66,plain,
! [X0,X1,X2] :
( X0 = X1
| ~ equidistant(X0,X1,X2,X2) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f67,plain,
! [X0,X1,X2,X3] : between(X0,X1,extension(X0,X1,X2,X3)),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f68,plain,
! [X0,X1,X2,X3] : equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f86,plain,
! [X0,X1,X2,X3] :
( equidistant(X2,X3,X0,X1)
| ~ equidistant(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f139,plain,
lower_dimension_point_1 != lower_dimension_point_2,
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f142,plain,
( ~ between(u,v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2))
| ~ equidistant(v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2),x,extension(w,x,lower_dimension_point_1,lower_dimension_point_2))
| v = extension(u,v,lower_dimension_point_1,lower_dimension_point_2) ),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f143,definition,
( sQ0_spl
<=> v = extension(u,v,lower_dimension_point_1,lower_dimension_point_2) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f144,plain,
( ~ sQ0_spl
| v = extension(u,v,lower_dimension_point_1,lower_dimension_point_2) ),
inference(component_clause,[status(thm)],[f143]) ).
fof(f146,definition,
( sQ1_spl
<=> equidistant(v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2),x,extension(w,x,lower_dimension_point_1,lower_dimension_point_2)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f148,plain,
( sQ1_spl
| ~ equidistant(v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2),x,extension(w,x,lower_dimension_point_1,lower_dimension_point_2)) ),
inference(component_clause,[status(thm)],[f146]) ).
fof(f149,definition,
( sQ2_spl
<=> between(u,v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2)) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f151,plain,
( sQ2_spl
| ~ between(u,v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2)) ),
inference(component_clause,[status(thm)],[f149]) ).
fof(f152,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f142,f143,f146,f149]) ).
fof(f167,plain,
( sQ2_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f151,f67]) ).
fof(f169,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f167]) ).
fof(f294,plain,
( ~ sQ0_spl
| equidistant(v,v,lower_dimension_point_1,lower_dimension_point_2) ),
inference(paramodulation,[status(thm)],[f144,f68]) ).
fof(f324,plain,
! [X0,X1] :
( sQ1_spl
| ~ equidistant(X0,X1,x,extension(w,x,lower_dimension_point_1,lower_dimension_point_2))
| ~ equidistant(X0,X1,v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2)) ),
inference(resolution,[status(thm)],[f148,f64]) ).
fof(f361,plain,
! [X0,X1,X2,X3] : equidistant(X0,X1,X2,extension(X3,X2,X0,X1)),
inference(resolution,[status(thm)],[f86,f68]) ).
fof(f408,plain,
( sQ1_spl
| ~ equidistant(lower_dimension_point_1,lower_dimension_point_2,x,extension(w,x,lower_dimension_point_1,lower_dimension_point_2)) ),
inference(resolution,[status(thm)],[f361,f324]) ).
fof(f423,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f408,f361]) ).
fof(f424,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f423]) ).
fof(f425,plain,
( ~ sQ0_spl
| equidistant(lower_dimension_point_1,lower_dimension_point_2,v,v) ),
inference(resolution,[status(thm)],[f294,f86]) ).
fof(f444,plain,
( ~ sQ0_spl
| lower_dimension_point_1 = lower_dimension_point_2 ),
inference(resolution,[status(thm)],[f425,f66]) ).
fof(f459,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f444,f139]) ).
fof(f460,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f459]) ).
fof(f461,plain,
$false,
inference(sat_refutation,[status(thm)],[f152,f169,f424,f460]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO037-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n002.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 08:35:47 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.13/0.47 % Refutation found
% 0.13/0.47 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.50 % Elapsed time: 0.124723 seconds
% 0.13/0.50 % CPU time: 0.797819 seconds
% 0.13/0.50 % Total memory used: 110.537 MB
% 0.13/0.50 % Net memory used: 109.408 MB
%------------------------------------------------------------------------------