%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO025-2 : 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 : n003.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 12:25:34 PM UTC 2026
% Result : Unsatisfiable 9.18s 1.83s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO025-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n003.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 20 08:19:14 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.12/0.36 % Drodi V4.1.1
% 9.18/1.83 % Refutation found
% 9.18/1.83 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 9.18/1.83 % SZS output start CNFRefutation for theBenchmark
% 9.18/1.83 fof(f1,axiom,(
% 9.18/1.83 (![X,Y]: (equidistant(X,Y,Y,X) ))),
% 9.18/1.83 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 9.18/1.83 fof(f2,axiom,(
% 9.18/1.83 (![X,Y,Z,V,V2,W]: (( ~ equidistant(X,Y,Z,V)| ~ equidistant(X,Y,V2,W)| equidistant(Z,V,V2,W) ) ))),
% 9.18/1.83 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 9.18/1.83 fof(f3,axiom,(
% 9.18/1.83 (![X,Y,Z]: (( ~ equidistant(X,Y,Z,Z)| X = Y ) ))),
% 9.18/1.83 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 9.18/1.83 fof(f4,axiom,(
% 9.18/1.83 (![X,Y,W,V]: (between(X,Y,extension(X,Y,W,V)) ))),
% 9.18/1.83 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 9.18/1.83 fof(f5,axiom,(
% 9.18/1.83 (![Y,X,W,V]: (equidistant(Y,extension(X,Y,W,V),W,V) ))),
% 9.18/1.83 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 9.18/1.83 fof(f6,axiom,(
% 9.18/1.83 (![X,Y,X1,Y1,Z,Z1,V,V1]: (( ~ equidistant(X,Y,X1,Y1)| ~ equidistant(Y,Z,Y1,Z1)| ~ equidistant(X,V,X1,V1)| ~ equidistant(Y,V,Y1,V1)| ~ between(X,Y,Z)| ~ between(X1,Y1,Z1)| X = Y| equidistant(Z,V,Z1,V1) ) ))),
% 9.18/1.83 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 9.18/1.83 fof(f7,axiom,(
% 9.18/1.83 (![X,Y]: (( ~ between(X,Y,X)| X = Y ) ))),
% 9.18/1.83 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 9.18/1.83 fof(f8,axiom,(
% 9.18/1.83 (![U,V,W,Y,X]: (( ~ between(U,V,W)| ~ between(Y,X,W)| between(V,inner_pasch(U,V,W,X,Y),Y) ) ))),
% 9.18/1.83 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 9.18/1.83 fof(f9,axiom,(
% 9.18/1.83 (![U,V,W,Y,X]: (( ~ between(U,V,W)| ~ between(Y,X,W)| between(X,inner_pasch(U,V,W,X,Y),U) ) ))),
% 9.18/1.83 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 9.18/1.83 fof(f19,hypothesis,(
% 9.18/1.83 equidistant(u,v,u1,v1) ),
% 9.18/1.83 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 9.18/1.83 fof(f20,hypothesis,(
% 9.18/1.83 equidistant(v,w,v1,w1) ),
% 9.18/1.83 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 9.18/1.83 fof(f21,hypothesis,(
% 9.18/1.83 between(u,v,w) ),
% 9.18/1.83 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 9.18/1.83 fof(f22,hypothesis,(
% 9.18/1.83 between(u1,v1,w1) ),
% 9.18/1.83 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 9.18/1.83 fof(f23,negated_conjecture,(
% 9.18/1.83 ~ equidistant(u,w,u1,w1) ),
% 9.18/1.83 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 9.18/1.83 fof(f24,plain,(
% 9.18/1.83 ![X0,X1]: (equidistant(X0,X1,X1,X0))),
% 9.18/1.83 inference(cnf_transformation,[status(thm)],[f1])).
% 9.18/1.83 fof(f25,plain,(
% 9.18/1.83 ![Z,V,V2,W]: ((![X,Y]: (~equidistant(X,Y,Z,V)|~equidistant(X,Y,V2,W)))|equidistant(Z,V,V2,W))),
% 9.18/1.83 inference(miniscoping,[status(thm)],[f2])).
% 9.18/1.83 fof(f26,plain,(
% 9.18/1.83 ![X0,X1,X2,X3,X4,X5]: (~equidistant(X0,X1,X2,X3)|~equidistant(X0,X1,X4,X5)|equidistant(X2,X3,X4,X5))),
% 9.18/1.83 inference(cnf_transformation,[status(thm)],[f25])).
% 9.18/1.83 fof(f27,plain,(
% 9.18/1.83 ![X,Y]: ((![Z]: ~equidistant(X,Y,Z,Z))|X=Y)),
% 9.18/1.83 inference(miniscoping,[status(thm)],[f3])).
% 9.18/1.83 fof(f28,plain,(
% 9.18/1.83 ![X0,X1,X2]: (~equidistant(X0,X1,X2,X2)|X0=X1)),
% 9.18/1.83 inference(cnf_transformation,[status(thm)],[f27])).
% 9.18/1.83 fof(f29,plain,(
% 9.18/1.83 ![X0,X1,X2,X3]: (between(X0,X1,extension(X0,X1,X2,X3)))),
% 9.18/1.83 inference(cnf_transformation,[status(thm)],[f4])).
% 9.18/1.83 fof(f30,plain,(
% 9.18/1.83 ![X0,X1,X2,X3]: (equidistant(X0,extension(X1,X0,X2,X3),X2,X3))),
% 9.18/1.83 inference(cnf_transformation,[status(thm)],[f5])).
% 9.18/1.83 fof(f31,plain,(
% 9.18/1.83 ![Z,Z1,V,V1]: ((![X,Y]: ((![X1,Y1]: (((((~equidistant(X,Y,X1,Y1)|~equidistant(Y,Z,Y1,Z1))|~equidistant(X,V,X1,V1))|~equidistant(Y,V,Y1,V1))|~between(X,Y,Z))|~between(X1,Y1,Z1)))|X=Y))|equidistant(Z,V,Z1,V1))),
% 9.18/1.83 inference(miniscoping,[status(thm)],[f6])).
% 9.18/1.83 fof(f32,plain,(
% 9.18/1.83 ![X0,X1,X2,X3,X4,X5,X6,X7]: (~equidistant(X0,X1,X2,X3)|~equidistant(X1,X4,X3,X5)|~equidistant(X0,X6,X2,X7)|~equidistant(X1,X6,X3,X7)|~between(X0,X1,X4)|~between(X2,X3,X5)|X0=X1|equidistant(X4,X6,X5,X7))),
% 9.18/1.83 inference(cnf_transformation,[status(thm)],[f31])).
% 9.18/1.83 fof(f33,plain,(
% 9.18/1.83 ![X0,X1]: (~between(X0,X1,X0)|X0=X1)),
% 9.18/1.83 inference(cnf_transformation,[status(thm)],[f7])).
% 9.18/1.83 fof(f34,plain,(
% 9.18/1.83 ![X0,X1,X2,X3,X4]: (~between(X0,X1,X2)|~between(X3,X4,X2)|between(X1,inner_pasch(X0,X1,X2,X4,X3),X3))),
% 9.18/1.83 inference(cnf_transformation,[status(thm)],[f8])).
% 9.18/1.83 fof(f35,plain,(
% 9.18/1.83 ![X0,X1,X2,X3,X4]: (~between(X0,X1,X2)|~between(X3,X4,X2)|between(X4,inner_pasch(X0,X1,X2,X4,X3),X0))),
% 9.18/1.83 inference(cnf_transformation,[status(thm)],[f9])).
% 9.18/1.83 fof(f46,plain,(
% 9.18/1.83 equidistant(u,v,u1,v1)),
% 9.18/1.83 inference(cnf_transformation,[status(thm)],[f19])).
% 9.18/1.83 fof(f47,plain,(
% 9.18/1.83 equidistant(v,w,v1,w1)),
% 9.18/1.83 inference(cnf_transformation,[status(thm)],[f20])).
% 9.18/1.83 fof(f48,plain,(
% 9.18/1.83 between(u,v,w)),
% 9.18/1.83 inference(cnf_transformation,[status(thm)],[f21])).
% 9.18/1.83 fof(f49,plain,(
% 9.18/1.83 between(u1,v1,w1)),
% 9.18/1.83 inference(cnf_transformation,[status(thm)],[f22])).
% 9.18/1.83 fof(f50,plain,(
% 9.18/1.83 ~equidistant(u,w,u1,w1)),
% 9.18/1.83 inference(cnf_transformation,[status(thm)],[f23])).
% 9.18/1.83 fof(f52,plain,(
% 9.18/1.83 ![X0,X1,X2,X3]: (~equidistant(X0,X1,X2,X3)|equidistant(X2,X3,X1,X0))),
% 9.18/1.83 inference(resolution,[status(thm)],[f26,f24])).
% 9.18/1.83 fof(f54,plain,(
% 9.18/1.83 ![X0,X1]: (~equidistant(v,w,X0,X1)|equidistant(X0,X1,v1,w1))),
% 9.18/1.83 inference(resolution,[status(thm)],[f47,f26])).
% 9.18/1.83 fof(f55,plain,(
% 9.18/1.83 equidistant(v1,w1,w,v)),
% 9.18/1.83 inference(resolution,[status(thm)],[f52,f47])).
% 9.18/1.83 fof(f56,plain,(
% 9.18/1.83 equidistant(u1,v1,v,u)),
% 9.18/1.83 inference(resolution,[status(thm)],[f52,f46])).
% 9.18/1.83 fof(f57,plain,(
% 9.18/1.83 ![X0,X1]: (equidistant(X0,X1,X0,X1))),
% 9.18/1.83 inference(resolution,[status(thm)],[f52,f24])).
% 9.18/1.83 fof(f59,plain,(
% 9.18/1.83 ![X0,X1,X2,X3]: (~equidistant(X0,X1,X2,X3)|equidistant(X2,X3,X0,X1))),
% 9.18/1.83 inference(resolution,[status(thm)],[f57,f26])).
% 9.18/1.83 fof(f61,plain,(
% 9.18/1.83 equidistant(w,v,w1,v1)),
% 9.18/1.83 inference(resolution,[status(thm)],[f55,f52])).
% 9.18/1.83 fof(f63,plain,(
% 9.18/1.83 equidistant(v,u,v1,u1)),
% 9.18/1.83 inference(resolution,[status(thm)],[f56,f52])).
% 9.18/1.83 fof(f119,plain,(
% 9.18/1.83 ![X0,X1,X2,X3]: (~equidistant(X0,v,X1,v1)|~equidistant(v,X2,v1,X3)|~equidistant(X0,w,X1,w1)|~between(X0,v,X2)|~between(X1,v1,X3)|X0=v|equidistant(X2,w,X3,w1))),
% 9.18/1.83 inference(resolution,[status(thm)],[f32,f47])).
% 9.18/1.83 fof(f141,plain,(
% 9.18/1.83 ![X0,X1,X2,X3]: (equidistant(X0,X1,extension(X2,X3,X0,X1),X3))),
% 9.18/1.83 inference(resolution,[status(thm)],[f30,f52])).
% 9.18/1.83 fof(f143,plain,(
% 9.18/1.83 ![X0,X1,X2]: (X0=extension(X1,X0,X2,X2))),
% 9.18/1.83 inference(resolution,[status(thm)],[f30,f28])).
% 9.18/1.83 fof(f144,plain,(
% 9.18/1.83 ![X0,X1]: (equidistant(X0,X0,X1,X1))),
% 9.18/1.83 inference(paramodulation,[status(thm)],[f143,f30])).
% 9.18/1.83 fof(f145,plain,(
% 9.18/1.83 ![X0,X1]: (between(X0,X1,X1))),
% 9.18/1.83 inference(paramodulation,[status(thm)],[f143,f29])).
% 9.18/1.83 fof(f229,plain,(
% 9.18/1.83 ![X0,X1,X2,X3]: (~between(X0,X1,X2)|between(X2,inner_pasch(X3,X2,X2,X1,X0),X0))),
% 9.18/1.83 inference(resolution,[status(thm)],[f34,f145])).
% 9.18/1.83 fof(f233,plain,(
% 9.18/1.83 ![X0,X1,X2,X3]: (~between(X0,X1,X2)|between(X1,inner_pasch(X3,X2,X2,X1,X0),X3))),
% 9.18/1.83 inference(resolution,[status(thm)],[f35,f145])).
% 9.18/1.83 fof(f353,plain,(
% 9.18/1.83 ![X0,X1]: (equidistant(extension(X0,X1,v,w),X1,v1,w1))),
% 9.18/1.83 inference(resolution,[status(thm)],[f54,f141])).
% 9.18/1.83 fof(f431,plain,(
% 9.18/1.83 ![X0,X1]: (equidistant(v1,w1,extension(X0,X1,v,w),X1))),
% 9.18/1.83 inference(resolution,[status(thm)],[f353,f59])).
% 9.18/1.83 fof(f573,plain,(
% 9.18/1.83 ![X0,X1]: (equidistant(extension(X0,X1,v,w),X1,w1,v1))),
% 9.18/1.83 inference(resolution,[status(thm)],[f431,f52])).
% 9.18/1.83 fof(f836,plain,(
% 9.18/1.83 ![X0,X1]: (equidistant(w1,v1,X0,extension(X1,X0,v,w)))),
% 9.18/1.83 inference(resolution,[status(thm)],[f573,f52])).
% 9.18/1.83 fof(f1196,plain,(
% 9.18/1.83 ![X0,X1]: (~equidistant(X0,v,X1,v1)|~equidistant(X0,w,X1,w1)|~between(X0,v,u)|~between(X1,v1,u1)|X0=v|equidistant(u,w,u1,w1))),
% 9.18/1.83 inference(resolution,[status(thm)],[f119,f63])).
% 9.18/1.83 fof(f1208,plain,(
% 9.18/1.83 ![X0,X1]: (~equidistant(X0,v,X1,v1)|~equidistant(X0,w,X1,w1)|~between(X0,v,u)|~between(X1,v1,u1)|X0=v)),
% 9.18/1.83 inference(forward_subsumption_resolution,[status(thm)],[f1196,f50])).
% 9.18/1.83 fof(f1730,plain,(
% 9.18/1.83 ~equidistant(w,w,w1,w1)|~between(w,v,u)|~between(w1,v1,u1)|w=v),
% 9.18/1.83 inference(resolution,[status(thm)],[f1208,f61])).
% 9.18/1.83 fof(f1736,plain,(
% 9.18/1.83 ~between(w,v,u)|~between(w1,v1,u1)|w=v),
% 9.18/1.83 inference(forward_subsumption_resolution,[status(thm)],[f1730,f144])).
% 9.18/1.83 fof(f2254,plain,(
% 9.18/1.83 ![X0]: (between(w1,inner_pasch(X0,w1,w1,v1,u1),u1))),
% 9.18/1.83 inference(resolution,[status(thm)],[f229,f49])).
% 9.18/1.83 fof(f2255,plain,(
% 9.18/1.83 ![X0]: (between(w,inner_pasch(X0,w,w,v,u),u))),
% 9.18/1.83 inference(resolution,[status(thm)],[f229,f48])).
% 9.18/1.83 fof(f2294,plain,(
% 9.18/1.83 ![X0]: (between(v1,inner_pasch(X0,w1,w1,v1,u1),X0))),
% 9.18/1.83 inference(resolution,[status(thm)],[f233,f49])).
% 9.18/1.83 fof(f2295,plain,(
% 9.18/1.83 ![X0]: (between(v,inner_pasch(X0,w,w,v,u),X0))),
% 9.18/1.83 inference(resolution,[status(thm)],[f233,f48])).
% 9.18/1.83 fof(f2657,plain,(
% 9.18/1.83 v1=inner_pasch(v1,w1,w1,v1,u1)),
% 9.18/1.83 inference(resolution,[status(thm)],[f2294,f33])).
% 9.18/1.83 fof(f2679,plain,(
% 9.18/1.83 v=inner_pasch(v,w,w,v,u)),
% 9.18/1.83 inference(resolution,[status(thm)],[f2295,f33])).
% 9.18/1.83 fof(f4826,plain,(
% 9.18/1.83 between(w1,v1,u1)),
% 9.18/1.83 inference(paramodulation,[status(thm)],[f2657,f2254])).
% 9.18/1.83 fof(f4993,plain,(
% 9.18/1.83 ~between(w,v,u)|w=v),
% 9.18/1.83 inference(backward_subsumption_resolution,[status(thm)],[f1736,f4826])).
% 9.18/1.83 fof(f5084,plain,(
% 9.18/1.83 between(w,v,u)),
% 9.18/1.83 inference(paramodulation,[status(thm)],[f2679,f2255])).
% 9.18/1.83 fof(f5085,plain,(
% 9.18/1.83 w=v),
% 9.18/1.83 inference(backward_subsumption_resolution,[status(thm)],[f4993,f5084])).
% 9.18/1.83 fof(f5190,plain,(
% 9.18/1.83 ![X0,X1]: (equidistant(w1,v1,X0,extension(X1,X0,w,w)))),
% 9.18/1.83 inference(backward_demodulation,[status(thm)],[f5085,f836])).
% 9.18/1.83 fof(f5243,plain,(
% 9.18/1.83 equidistant(u,w,u1,v1)),
% 9.18/1.83 inference(backward_demodulation,[status(thm)],[f5085,f46])).
% 9.18/1.83 fof(f5360,plain,(
% 9.18/1.83 ![X0]: (equidistant(w1,v1,X0,X0))),
% 9.18/1.83 inference(forward_demodulation,[status(thm)],[f143,f5190])).
% 9.18/1.83 fof(f5417,plain,(
% 9.18/1.83 w1=v1),
% 9.18/1.83 inference(resolution,[status(thm)],[f5360,f28])).
% 9.18/1.83 fof(f5475,plain,(
% 9.18/1.83 equidistant(u,w,u1,w1)),
% 9.18/1.83 inference(backward_demodulation,[status(thm)],[f5417,f5243])).
% 9.18/1.83 fof(f5504,plain,(
% 9.18/1.83 $false),
% 9.18/1.83 inference(forward_subsumption_resolution,[status(thm)],[f5475,f50])).
% 9.18/1.83 % SZS output end CNFRefutation for theBenchmark.p
% 9.18/1.83 % Elapsed time: 1.476396 seconds
% 9.18/1.83 % CPU time: 11.497705 seconds
% 9.18/1.83 % Total memory used: 132.804 MB
% 9.18/1.83 % Net memory used: 121.686 MB
%------------------------------------------------------------------------------