%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO041-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 12:25:37 PM UTC 2026
% Result : Unsatisfiable 0.14s 5.79s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO041-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.37 % Computer : n020.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.38 % CPULimit : 300
% 0.09/5.38 % WCLimit : 300
% 0.09/5.38 % DateTime : Sun Sep 20 08:35:23 UTC 2026
% 0.09/5.38 % CPUTime :
% 0.09/5.39 % Drodi V4.1.1
% 0.14/5.79 % Refutation found
% 0.14/5.79 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/5.79 % SZS output start CNFRefutation for theBenchmark
% 0.14/5.79 fof(f3,axiom,(
% 0.14/5.79 (![X,Y,Z]: (( ~ equidistant(X,Y,Z,Z)| X = Y ) ))),
% 0.14/5.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/5.79 fof(f4,axiom,(
% 0.14/5.79 (![X,Y,W,V]: (between(X,Y,extension(X,Y,W,V)) ))),
% 0.14/5.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/5.79 fof(f5,axiom,(
% 0.14/5.79 (![Y,X,W,V]: (equidistant(Y,extension(X,Y,W,V),W,V) ))),
% 0.14/5.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/5.79 fof(f7,axiom,(
% 0.14/5.79 (![X,Y]: (( ~ between(X,Y,X)| X = Y ) ))),
% 0.14/5.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/5.79 fof(f8,axiom,(
% 0.14/5.79 (![U,V,W,Y,X]: (( ~ between(U,V,W)| ~ between(Y,X,W)| between(V,inner_pasch(U,V,W,X,Y),Y) ) ))),
% 0.14/5.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/5.79 fof(f9,axiom,(
% 0.14/5.79 (![U,V,W,Y,X]: (( ~ between(U,V,W)| ~ between(Y,X,W)| between(X,inner_pasch(U,V,W,X,Y),U) ) ))),
% 0.14/5.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/5.79 fof(f19,hypothesis,(
% 0.14/5.79 between(u,v,w) ),
% 0.14/5.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/5.79 fof(f20,hypothesis,(
% 0.14/5.79 between(u,w,v) ),
% 0.14/5.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/5.79 fof(f21,negated_conjecture,(
% 0.14/5.79 v != w ),
% 0.14/5.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/5.79 fof(f25,plain,(
% 0.14/5.79 ![X,Y]: ((![Z]: ~equidistant(X,Y,Z,Z))|X=Y)),
% 0.14/5.79 inference(miniscoping,[status(thm)],[f3])).
% 0.14/5.79 fof(f26,plain,(
% 0.14/5.79 ![X0,X1,X2]: (~equidistant(X0,X1,X2,X2)|X0=X1)),
% 0.14/5.79 inference(cnf_transformation,[status(thm)],[f25])).
% 0.14/5.79 fof(f27,plain,(
% 0.14/5.79 ![X0,X1,X2,X3]: (between(X0,X1,extension(X0,X1,X2,X3)))),
% 0.14/5.79 inference(cnf_transformation,[status(thm)],[f4])).
% 0.14/5.79 fof(f28,plain,(
% 0.14/5.79 ![X0,X1,X2,X3]: (equidistant(X0,extension(X1,X0,X2,X3),X2,X3))),
% 0.14/5.79 inference(cnf_transformation,[status(thm)],[f5])).
% 0.14/5.79 fof(f31,plain,(
% 0.14/5.79 ![X0,X1]: (~between(X0,X1,X0)|X0=X1)),
% 0.14/5.79 inference(cnf_transformation,[status(thm)],[f7])).
% 0.14/5.79 fof(f32,plain,(
% 0.14/5.79 ![X0,X1,X2,X3,X4]: (~between(X0,X1,X2)|~between(X3,X4,X2)|between(X1,inner_pasch(X0,X1,X2,X4,X3),X3))),
% 0.14/5.79 inference(cnf_transformation,[status(thm)],[f8])).
% 0.14/5.79 fof(f33,plain,(
% 0.14/5.79 ![X0,X1,X2,X3,X4]: (~between(X0,X1,X2)|~between(X3,X4,X2)|between(X4,inner_pasch(X0,X1,X2,X4,X3),X0))),
% 0.14/5.79 inference(cnf_transformation,[status(thm)],[f9])).
% 0.14/5.79 fof(f44,plain,(
% 0.14/5.79 between(u,v,w)),
% 0.14/5.79 inference(cnf_transformation,[status(thm)],[f19])).
% 0.14/5.79 fof(f45,plain,(
% 0.14/5.79 between(u,w,v)),
% 0.14/5.79 inference(cnf_transformation,[status(thm)],[f20])).
% 0.14/5.79 fof(f46,plain,(
% 0.14/5.79 ~v=w),
% 0.14/5.79 inference(cnf_transformation,[status(thm)],[f21])).
% 0.14/5.79 fof(f47,plain,(
% 0.14/5.79 ![X0,X1,X2,X3]: (~between(X0,X1,X2)|~between(X1,X3,X2)|X1=inner_pasch(X0,X1,X2,X3,X1))),
% 0.14/5.79 inference(resolution,[status(thm)],[f32,f31])).
% 0.14/5.79 fof(f49,plain,(
% 0.14/5.79 ![X0,X1,X2,X3,X4]: (~between(X0,X1,extension(X1,X2,X3,X4))|X1=inner_pasch(X0,X1,extension(X1,X2,X3,X4),X2,X1))),
% 0.14/5.79 inference(resolution,[status(thm)],[f47,f27])).
% 0.14/5.79 fof(f51,plain,(
% 0.14/5.79 ![X0,X1,X2,X3]: (~between(X0,X1,X2)|~between(X3,X0,X2)|X0=inner_pasch(X0,X1,X2,X0,X3))),
% 0.14/5.79 inference(resolution,[status(thm)],[f33,f31])).
% 0.14/5.79 fof(f86,plain,(
% 0.14/5.79 ![X0,X1,X2]: (X0=extension(X1,X0,X2,X2))),
% 0.14/5.79 inference(resolution,[status(thm)],[f28,f26])).
% 0.14/5.79 fof(f107,plain,(
% 0.14/5.79 ![X0,X1,X2,X3]: (~between(X0,X1,X2)|X1=inner_pasch(X0,X1,extension(X1,X2,X3,X3),X2,X1))),
% 0.14/5.79 inference(paramodulation,[status(thm)],[f86,f49])).
% 0.14/5.79 fof(f108,plain,(
% 0.14/5.79 ![X0,X1]: (between(X0,X1,X1))),
% 0.14/5.79 inference(paramodulation,[status(thm)],[f86,f27])).
% 0.14/5.79 fof(f110,plain,(
% 0.14/5.79 ![X0,X1,X2]: (~between(X0,X1,X2)|X1=inner_pasch(X0,X1,X2,X2,X1))),
% 0.14/5.79 inference(forward_demodulation,[status(thm)],[f86,f107])).
% 0.14/5.79 fof(f119,plain,(
% 0.14/5.79 w=inner_pasch(u,w,v,v,w)),
% 0.14/5.79 inference(resolution,[status(thm)],[f110,f45])).
% 0.14/5.79 fof(f120,plain,(
% 0.14/5.79 v=inner_pasch(u,v,w,w,v)),
% 0.14/5.79 inference(resolution,[status(thm)],[f110,f44])).
% 0.14/5.79 fof(f278,plain,(
% 0.14/5.79 ~between(u,w,v)|~between(w,v,v)|between(v,w,u)),
% 0.14/5.79 inference(paramodulation,[status(thm)],[f119,f33])).
% 0.14/5.79 fof(f280,definition,(
% 0.14/5.79 sQ0_spl <=> (between(u,w,v))),
% 0.14/5.79 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.14/5.79 fof(f282,plain,(
% 0.14/5.79 ~between(u,w,v)|sQ0_spl),
% 0.14/5.79 inference(component_clause,[status(thm)],[f280])).
% 0.14/5.79 fof(f283,definition,(
% 0.14/5.79 sQ1_spl <=> (between(w,v,v))),
% 0.14/5.79 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.14/5.79 fof(f285,plain,(
% 0.14/5.79 ~between(w,v,v)|sQ1_spl),
% 0.14/5.79 inference(component_clause,[status(thm)],[f283])).
% 0.14/5.79 fof(f286,definition,(
% 0.14/5.79 sQ2_spl <=> (between(v,w,u))),
% 0.14/5.79 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.14/5.79 fof(f287,plain,(
% 0.14/5.79 between(v,w,u)|~sQ2_spl),
% 0.14/5.79 inference(component_clause,[status(thm)],[f286])).
% 0.14/5.79 fof(f289,plain,(
% 0.14/5.79 ~sQ0_spl|~sQ1_spl|sQ2_spl),
% 0.14/5.79 inference(split_clause,[status(thm)],[f278,f280,f283,f286])).
% 0.14/5.79 fof(f294,plain,(
% 0.14/5.79 $false|sQ1_spl),
% 0.14/5.79 inference(forward_subsumption_resolution,[status(thm)],[f285,f108])).
% 0.14/5.79 fof(f295,plain,(
% 0.14/5.79 sQ1_spl),
% 0.14/5.79 inference(contradiction_clause,[status(thm)],[f294])).
% 0.14/5.79 fof(f296,plain,(
% 0.14/5.79 $false|sQ0_spl),
% 0.14/5.79 inference(forward_subsumption_resolution,[status(thm)],[f282,f45])).
% 0.14/5.79 fof(f297,plain,(
% 0.14/5.79 sQ0_spl),
% 0.14/5.79 inference(contradiction_clause,[status(thm)],[f296])).
% 0.14/5.79 fof(f301,plain,(
% 0.14/5.79 ![X0]: (~between(w,X0,u)|w=inner_pasch(w,X0,u,w,v)|~sQ2_spl)),
% 0.14/5.79 inference(resolution,[status(thm)],[f287,f51])).
% 0.14/5.79 fof(f303,plain,(
% 0.14/5.79 ~between(u,v,w)|~between(v,w,w)|between(w,v,u)),
% 0.14/5.79 inference(paramodulation,[status(thm)],[f120,f33])).
% 0.14/5.79 fof(f305,definition,(
% 0.14/5.79 sQ4_spl <=> (between(u,v,w))),
% 0.14/5.79 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 0.14/5.79 fof(f307,plain,(
% 0.14/5.79 ~between(u,v,w)|sQ4_spl),
% 0.14/5.79 inference(component_clause,[status(thm)],[f305])).
% 0.14/5.79 fof(f308,definition,(
% 0.14/5.79 sQ5_spl <=> (between(v,w,w))),
% 0.14/5.79 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 0.14/5.79 fof(f310,plain,(
% 0.14/5.79 ~between(v,w,w)|sQ5_spl),
% 0.14/5.79 inference(component_clause,[status(thm)],[f308])).
% 0.14/5.79 fof(f311,definition,(
% 0.14/5.79 sQ6_spl <=> (between(w,v,u))),
% 0.14/5.79 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.14/5.79 fof(f312,plain,(
% 0.14/5.79 between(w,v,u)|~sQ6_spl),
% 0.14/5.79 inference(component_clause,[status(thm)],[f311])).
% 0.14/5.79 fof(f314,plain,(
% 0.14/5.79 ~sQ4_spl|~sQ5_spl|sQ6_spl),
% 0.14/5.79 inference(split_clause,[status(thm)],[f303,f305,f308,f311])).
% 0.14/5.79 fof(f319,plain,(
% 0.14/5.79 $false|sQ5_spl),
% 0.14/5.79 inference(forward_subsumption_resolution,[status(thm)],[f310,f108])).
% 0.14/5.79 fof(f320,plain,(
% 0.14/5.79 sQ5_spl),
% 0.14/5.79 inference(contradiction_clause,[status(thm)],[f319])).
% 0.14/5.79 fof(f321,plain,(
% 0.14/5.79 $false|sQ4_spl),
% 0.14/5.79 inference(forward_subsumption_resolution,[status(thm)],[f307,f44])).
% 0.14/5.79 fof(f322,plain,(
% 0.14/5.79 sQ4_spl),
% 0.14/5.79 inference(contradiction_clause,[status(thm)],[f321])).
% 0.14/5.79 fof(f865,plain,(
% 0.14/5.79 w=inner_pasch(w,v,u,w,v)|~sQ2_spl|~sQ6_spl),
% 0.14/5.79 inference(resolution,[status(thm)],[f301,f312])).
% 0.14/5.79 fof(f872,plain,(
% 0.14/5.79 ~between(w,v,u)|~between(v,w,u)|between(v,w,v)|~sQ2_spl|~sQ6_spl),
% 0.14/5.79 inference(paramodulation,[status(thm)],[f865,f32])).
% 0.14/5.79 fof(f874,definition,(
% 0.14/5.79 sQ17_spl <=> (between(v,w,v))),
% 0.14/5.79 introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition])).
% 0.14/5.79 fof(f875,plain,(
% 0.14/5.79 between(v,w,v)|~sQ17_spl),
% 0.14/5.79 inference(component_clause,[status(thm)],[f874])).
% 0.14/5.79 fof(f877,plain,(
% 0.14/5.79 ~sQ6_spl|~sQ2_spl|sQ17_spl),
% 0.14/5.79 inference(split_clause,[status(thm)],[f872,f311,f286,f874])).
% 0.14/5.79 fof(f895,plain,(
% 0.14/5.79 v=w|~sQ17_spl),
% 0.14/5.79 inference(resolution,[status(thm)],[f875,f31])).
% 0.14/5.79 fof(f897,plain,(
% 0.14/5.79 $false|~sQ17_spl),
% 0.14/5.79 inference(forward_subsumption_resolution,[status(thm)],[f895,f46])).
% 0.14/5.79 fof(f898,plain,(
% 0.14/5.79 ~sQ17_spl),
% 0.14/5.79 inference(contradiction_clause,[status(thm)],[f897])).
% 0.14/5.79 fof(f899,plain,(
% 0.14/5.79 $false),
% 0.14/5.79 inference(sat_refutation,[status(thm)],[f289,f295,f297,f314,f320,f322,f877,f898])).
% 0.14/5.79 % SZS output end CNFRefutation for theBenchmark.p
% 0.14/5.81 % Elapsed time: 0.414868 seconds
% 0.14/5.81 % CPU time: 3.091938 seconds
% 0.14/5.81 % Total memory used: 102.106 MB
% 0.14/5.81 % Net memory used: 98.599 MB
%------------------------------------------------------------------------------