%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO037-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.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 12:25:36 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.41s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO037-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n006.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 20 08:33:13 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % 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
% 0.12/0.41 fof(f2,axiom,(
% 0.12/0.41 (![X,Y,Z,V,V2,W]: (( ~ equidistant(X,Y,Z,V)| ~ equidistant(X,Y,V2,W)| equidistant(Z,V,V2,W) ) ))),
% 0.12/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.41 fof(f3,axiom,(
% 0.12/0.41 (![X,Y,Z]: (( ~ equidistant(X,Y,Z,Z)| X = Y ) ))),
% 0.12/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.41 fof(f4,axiom,(
% 0.12/0.41 (![X,Y,W,V]: (between(X,Y,extension(X,Y,W,V)) ))),
% 0.12/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.41 fof(f5,axiom,(
% 0.12/0.41 (![Y,X,W,V]: (equidistant(Y,extension(X,Y,W,V),W,V) ))),
% 0.12/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.41 fof(f21,axiom,(
% 0.12/0.41 (![U,V,W,X]: (( ~ equidistant(U,V,W,X)| equidistant(W,X,U,V) ) ))),
% 0.12/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.41 fof(f58,axiom,(
% 0.12/0.41 lower_dimension_point_1 != lower_dimension_point_2 ),
% 0.12/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.41 fof(f61,negated_conjecture,(
% 0.12/0.41 ( 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))| ~ between(u,v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2)) ) ),
% 0.12/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.41 fof(f63,plain,(
% 0.12/0.41 ![Z,V,V2,W]: ((![X,Y]: (~equidistant(X,Y,Z,V)|~equidistant(X,Y,V2,W)))|equidistant(Z,V,V2,W))),
% 0.12/0.41 inference(miniscoping,[status(thm)],[f2])).
% 0.12/0.41 fof(f64,plain,(
% 0.12/0.41 ![X0,X1,X2,X3,X4,X5]: (~equidistant(X0,X1,X2,X3)|~equidistant(X0,X1,X4,X5)|equidistant(X2,X3,X4,X5))),
% 0.12/0.41 inference(cnf_transformation,[status(thm)],[f63])).
% 0.12/0.41 fof(f65,plain,(
% 0.12/0.41 ![X,Y]: ((![Z]: ~equidistant(X,Y,Z,Z))|X=Y)),
% 0.12/0.41 inference(miniscoping,[status(thm)],[f3])).
% 0.12/0.41 fof(f66,plain,(
% 0.12/0.41 ![X0,X1,X2]: (~equidistant(X0,X1,X2,X2)|X0=X1)),
% 0.12/0.41 inference(cnf_transformation,[status(thm)],[f65])).
% 0.12/0.41 fof(f67,plain,(
% 0.12/0.41 ![X0,X1,X2,X3]: (between(X0,X1,extension(X0,X1,X2,X3)))),
% 0.12/0.41 inference(cnf_transformation,[status(thm)],[f4])).
% 0.12/0.41 fof(f68,plain,(
% 0.12/0.41 ![X0,X1,X2,X3]: (equidistant(X0,extension(X1,X0,X2,X3),X2,X3))),
% 0.12/0.41 inference(cnf_transformation,[status(thm)],[f5])).
% 0.12/0.41 fof(f86,plain,(
% 0.12/0.41 ![X0,X1,X2,X3]: (~equidistant(X0,X1,X2,X3)|equidistant(X2,X3,X0,X1))),
% 0.12/0.41 inference(cnf_transformation,[status(thm)],[f21])).
% 0.12/0.41 fof(f139,plain,(
% 0.12/0.41 ~lower_dimension_point_1=lower_dimension_point_2),
% 0.12/0.41 inference(cnf_transformation,[status(thm)],[f58])).
% 0.12/0.41 fof(f142,plain,(
% 0.12/0.41 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))|~between(u,v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2))),
% 0.12/0.41 inference(cnf_transformation,[status(thm)],[f61])).
% 0.12/0.41 fof(f143,definition,(
% 0.12/0.41 sQ0_spl <=> (v=extension(u,v,lower_dimension_point_1,lower_dimension_point_2))),
% 0.12/0.41 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.12/0.41 fof(f144,plain,(
% 0.12/0.41 v=extension(u,v,lower_dimension_point_1,lower_dimension_point_2)|~sQ0_spl),
% 0.12/0.41 inference(component_clause,[status(thm)],[f143])).
% 0.12/0.41 fof(f146,definition,(
% 0.12/0.41 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)))),
% 0.12/0.41 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.12/0.41 fof(f148,plain,(
% 0.12/0.41 ~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))|sQ1_spl),
% 0.12/0.41 inference(component_clause,[status(thm)],[f146])).
% 0.12/0.41 fof(f149,definition,(
% 0.12/0.41 sQ2_spl <=> (between(u,v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2)))),
% 0.12/0.41 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.12/0.41 fof(f151,plain,(
% 0.12/0.41 ~between(u,v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2))|sQ2_spl),
% 0.12/0.41 inference(component_clause,[status(thm)],[f149])).
% 0.12/0.41 fof(f152,plain,(
% 0.12/0.41 sQ0_spl|~sQ1_spl|~sQ2_spl),
% 0.12/0.42 inference(split_clause,[status(thm)],[f142,f143,f146,f149])).
% 0.12/0.42 fof(f167,plain,(
% 0.12/0.42 $false|sQ2_spl),
% 0.12/0.42 inference(backward_subsumption_resolution,[status(thm)],[f151,f67])).
% 0.12/0.42 fof(f169,plain,(
% 0.12/0.42 sQ2_spl),
% 0.12/0.42 inference(contradiction_clause,[status(thm)],[f167])).
% 0.12/0.42 fof(f294,plain,(
% 0.12/0.42 equidistant(v,v,lower_dimension_point_1,lower_dimension_point_2)|~sQ0_spl),
% 0.12/0.42 inference(paramodulation,[status(thm)],[f144,f68])).
% 0.12/0.42 fof(f324,plain,(
% 0.12/0.42 ![X0,X1]: (~equidistant(X0,X1,v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2))|~equidistant(X0,X1,x,extension(w,x,lower_dimension_point_1,lower_dimension_point_2))|sQ1_spl)),
% 0.12/0.42 inference(resolution,[status(thm)],[f148,f64])).
% 0.12/0.42 fof(f361,plain,(
% 0.12/0.42 ![X0,X1,X2,X3]: (equidistant(X0,X1,X2,extension(X3,X2,X0,X1)))),
% 0.12/0.42 inference(resolution,[status(thm)],[f86,f68])).
% 0.12/0.42 fof(f408,plain,(
% 0.12/0.42 ~equidistant(lower_dimension_point_1,lower_dimension_point_2,x,extension(w,x,lower_dimension_point_1,lower_dimension_point_2))|sQ1_spl),
% 0.12/0.42 inference(resolution,[status(thm)],[f361,f324])).
% 0.12/0.42 fof(f423,plain,(
% 0.12/0.42 $false|sQ1_spl),
% 0.12/0.42 inference(forward_subsumption_resolution,[status(thm)],[f408,f361])).
% 0.12/0.42 fof(f424,plain,(
% 0.12/0.42 sQ1_spl),
% 0.12/0.42 inference(contradiction_clause,[status(thm)],[f423])).
% 0.12/0.42 fof(f425,plain,(
% 0.12/0.42 equidistant(lower_dimension_point_1,lower_dimension_point_2,v,v)|~sQ0_spl),
% 0.12/0.42 inference(resolution,[status(thm)],[f294,f86])).
% 0.12/0.42 fof(f444,plain,(
% 0.12/0.42 lower_dimension_point_1=lower_dimension_point_2|~sQ0_spl),
% 0.12/0.42 inference(resolution,[status(thm)],[f425,f66])).
% 0.12/0.42 fof(f459,plain,(
% 0.12/0.42 $false|~sQ0_spl),
% 0.12/0.42 inference(forward_subsumption_resolution,[status(thm)],[f444,f139])).
% 0.12/0.42 fof(f460,plain,(
% 0.12/0.42 ~sQ0_spl),
% 0.12/0.42 inference(contradiction_clause,[status(thm)],[f459])).
% 0.12/0.42 fof(f461,plain,(
% 0.12/0.42 $false),
% 0.12/0.42 inference(sat_refutation,[status(thm)],[f152,f169,f424,f460])).
% 0.12/0.42 % SZS output end CNFRefutation for theBenchmark.p
% 0.12/0.45 % Elapsed time: 0.070900 seconds
% 0.12/0.45 % CPU time: 0.281952 seconds
% 0.12/0.45 % Total memory used: 104.769 MB
% 0.12/0.45 % Net memory used: 104.444 MB
%------------------------------------------------------------------------------