%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO069-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 12:25:42 PM UTC 2026
% Result : Unsatisfiable 0.19s 6.02s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO069-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/5.41 % Computer : n009.cluster.edu
% 0.13/5.41 % Model : x86_64 x86_64
% 0.13/5.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.41 % Memory : 8046.5625MB
% 0.13/5.41 % OS : Linux 6.8.0-71-generic
% 0.13/5.41 % CPULimit : 300
% 0.13/5.41 % WCLimit : 300
% 0.13/5.41 % DateTime : Sun Sep 20 09:32:17 UTC 2026
% 0.13/5.41 % CPUTime :
% 0.13/5.44 % Drodi V4.1.1
% 0.19/6.02 % Refutation found
% 0.19/6.02 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.19/6.02 % SZS output start CNFRefutation for theBenchmark
% 0.19/6.02 fof(f19,axiom,(
% 0.19/6.02 (![X,Y,Z]: (( ~ between(X,Y,Z)| colinear(X,Y,Z) ) ))),
% 0.19/6.02 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/6.02 fof(f20,axiom,(
% 0.19/6.02 (![Y,Z,X]: (( ~ between(Y,Z,X)| colinear(X,Y,Z) ) ))),
% 0.19/6.02 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/6.02 fof(f21,axiom,(
% 0.19/6.02 (![Z,X,Y]: (( ~ between(Z,X,Y)| colinear(X,Y,Z) ) ))),
% 0.19/6.02 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/6.02 fof(f22,axiom,(
% 0.19/6.02 (![X,Y,Z]: (( ~ colinear(X,Y,Z)| between(X,Y,Z)| between(Y,Z,X)| between(Z,X,Y) ) ))),
% 0.19/6.02 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/6.02 fof(f88,axiom,(
% 0.19/6.02 (![W,V,U]: (( ~ between(W,V,U)| colinear(U,V,W) ) ))),
% 0.19/6.02 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/6.02 fof(f89,axiom,(
% 0.19/6.02 (![U,W,V]: (( ~ between(U,W,V)| colinear(U,V,W) ) ))),
% 0.19/6.02 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/6.02 fof(f90,axiom,(
% 0.19/6.02 (![V,U,W]: (( ~ between(V,U,W)| colinear(U,V,W) ) ))),
% 0.19/6.02 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/6.02 fof(f91,axiom,(
% 0.19/6.02 (![U,V,W]: (( ~ colinear(U,V,W)| colinear(W,V,U) ) ))),
% 0.19/6.02 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/6.02 fof(f97,axiom,(
% 0.19/6.02 (![X,Y]: (colinear(X,X,Y) ))),
% 0.19/6.02 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/6.02 fof(f98,axiom,(
% 0.19/6.02 (![X,Y]: (colinear(X,Y,X) ))),
% 0.19/6.02 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/6.02 fof(f99,axiom,(
% 0.19/6.02 (![Y,X]: (colinear(Y,X,X) ))),
% 0.19/6.02 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/6.02 fof(f102,axiom,(
% 0.19/6.02 (![U,V,W,X]: (( ~ colinear(U,V,W)| ~ colinear(U,V,X)| colinear(U,W,X)| U = V ) ))),
% 0.19/6.02 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/6.02 fof(f103,axiom,(
% 0.19/6.02 (![U,V,W,X]: (( ~ colinear(U,V,W)| ~ colinear(U,V,X)| colinear(V,W,X)| U = V ) ))),
% 0.19/6.02 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/6.02 fof(f104,hypothesis,(
% 0.19/6.02 u != v ),
% 0.19/6.02 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/6.02 fof(f105,hypothesis,(
% 0.19/6.02 colinear(w,v,u) ),
% 0.19/6.02 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/6.02 fof(f106,hypothesis,(
% 0.19/6.02 colinear(x,v,u) ),
% 0.19/6.02 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/6.02 fof(f107,negated_conjecture,(
% 0.19/6.02 ( ~ colinear(x,w,u)| ~ colinear(x,w,v) ) ),
% 0.19/6.02 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/6.02 fof(f130,plain,(
% 0.19/6.02 ![X0,X1,X2]: (~between(X0,X1,X2)|colinear(X0,X1,X2))),
% 0.19/6.02 inference(cnf_transformation,[status(thm)],[f19])).
% 0.19/6.02 fof(f131,plain,(
% 0.19/6.02 ![X0,X1,X2]: (~between(X0,X1,X2)|colinear(X2,X0,X1))),
% 0.19/6.02 inference(cnf_transformation,[status(thm)],[f20])).
% 0.19/6.02 fof(f132,plain,(
% 0.19/6.02 ![X0,X1,X2]: (~between(X0,X1,X2)|colinear(X1,X2,X0))),
% 0.19/6.02 inference(cnf_transformation,[status(thm)],[f21])).
% 0.19/6.02 fof(f133,plain,(
% 0.19/6.02 ![X0,X1,X2]: (~colinear(X0,X1,X2)|between(X0,X1,X2)|between(X1,X2,X0)|between(X2,X0,X1))),
% 0.19/6.02 inference(cnf_transformation,[status(thm)],[f22])).
% 0.19/6.02 fof(f230,plain,(
% 0.19/6.02 ![X0,X1,X2]: (~between(X0,X1,X2)|colinear(X2,X1,X0))),
% 0.19/6.02 inference(cnf_transformation,[status(thm)],[f88])).
% 0.19/6.02 fof(f231,plain,(
% 0.19/6.02 ![X0,X1,X2]: (~between(X0,X1,X2)|colinear(X0,X2,X1))),
% 0.19/6.02 inference(cnf_transformation,[status(thm)],[f89])).
% 0.19/6.02 fof(f232,plain,(
% 0.19/6.02 ![X0,X1,X2]: (~between(X0,X1,X2)|colinear(X1,X0,X2))),
% 0.19/6.02 inference(cnf_transformation,[status(thm)],[f90])).
% 0.19/6.02 fof(f233,plain,(
% 0.19/6.02 ![X0,X1,X2]: (~colinear(X0,X1,X2)|colinear(X2,X1,X0))),
% 0.19/6.02 inference(cnf_transformation,[status(thm)],[f91])).
% 0.19/6.02 fof(f239,plain,(
% 0.19/6.02 ![X0,X1]: (colinear(X0,X0,X1))),
% 0.19/6.02 inference(cnf_transformation,[status(thm)],[f97])).
% 0.19/6.02 fof(f240,plain,(
% 0.19/6.02 ![X0,X1]: (colinear(X0,X1,X0))),
% 0.19/6.02 inference(cnf_transformation,[status(thm)],[f98])).
% 0.19/6.02 fof(f241,plain,(
% 0.19/6.02 ![X0,X1]: (colinear(X0,X1,X1))),
% 0.19/6.02 inference(cnf_transformation,[status(thm)],[f99])).
% 0.19/6.02 fof(f246,plain,(
% 0.19/6.02 ![U,V]: ((![W,X]: ((~colinear(U,V,W)|~colinear(U,V,X))|colinear(U,W,X)))|U=V)),
% 0.19/6.02 inference(miniscoping,[status(thm)],[f102])).
% 0.19/6.02 fof(f247,plain,(
% 0.19/6.02 ![X0,X1,X2,X3]: (~colinear(X0,X1,X2)|~colinear(X0,X1,X3)|colinear(X0,X2,X3)|X0=X1)),
% 0.19/6.02 inference(cnf_transformation,[status(thm)],[f246])).
% 0.19/6.02 fof(f248,plain,(
% 0.19/6.02 ![U,V]: ((![W,X]: ((~colinear(U,V,W)|~colinear(U,V,X))|colinear(V,W,X)))|U=V)),
% 0.19/6.02 inference(miniscoping,[status(thm)],[f103])).
% 0.19/6.02 fof(f249,plain,(
% 0.19/6.02 ![X0,X1,X2,X3]: (~colinear(X0,X1,X2)|~colinear(X0,X1,X3)|colinear(X1,X2,X3)|X0=X1)),
% 0.19/6.02 inference(cnf_transformation,[status(thm)],[f248])).
% 0.19/6.02 fof(f250,plain,(
% 0.19/6.02 ~u=v),
% 0.19/6.02 inference(cnf_transformation,[status(thm)],[f104])).
% 0.19/6.02 fof(f251,plain,(
% 0.19/6.02 colinear(w,v,u)),
% 0.19/6.02 inference(cnf_transformation,[status(thm)],[f105])).
% 0.19/6.02 fof(f252,plain,(
% 0.19/6.02 colinear(x,v,u)),
% 0.19/6.02 inference(cnf_transformation,[status(thm)],[f106])).
% 0.19/6.02 fof(f253,plain,(
% 0.19/6.02 ~colinear(x,w,u)|~colinear(x,w,v)),
% 0.19/6.02 inference(cnf_transformation,[status(thm)],[f107])).
% 0.19/6.02 fof(f290,plain,(
% 0.19/6.02 ![X0]: (~colinear(x,v,X0)|colinear(x,X0,u)|x=v)),
% 0.19/6.02 inference(resolution,[status(thm)],[f247,f252])).
% 0.19/6.02 fof(f292,plain,(
% 0.19/6.02 ![X0,X1,X2]: (~colinear(X0,X1,X2)|colinear(X0,X2,X1)|X0=X1)),
% 0.19/6.02 inference(resolution,[status(thm)],[f247,f241])).
% 0.19/6.02 fof(f295,plain,(
% 0.19/6.02 colinear(x,u,v)|x=v),
% 0.19/6.02 inference(resolution,[status(thm)],[f292,f252])).
% 0.19/6.02 fof(f296,plain,(
% 0.19/6.02 colinear(w,u,v)|w=v),
% 0.19/6.02 inference(resolution,[status(thm)],[f292,f251])).
% 0.19/6.02 fof(f302,plain,(
% 0.19/6.02 x=v|colinear(v,u,x)),
% 0.19/6.02 inference(resolution,[status(thm)],[f295,f233])).
% 0.19/6.02 fof(f305,plain,(
% 0.19/6.02 w=v|colinear(v,u,w)),
% 0.19/6.02 inference(resolution,[status(thm)],[f296,f233])).
% 0.19/6.02 fof(f307,plain,(
% 0.19/6.02 ![X0]: (x=v|~colinear(v,u,X0)|colinear(v,X0,x)|v=u)),
% 0.19/6.02 inference(resolution,[status(thm)],[f302,f247])).
% 0.19/6.02 fof(f310,plain,(
% 0.19/6.02 ![X0]: (x=v|~colinear(v,u,X0)|colinear(v,X0,x))),
% 0.19/6.02 inference(forward_subsumption_resolution,[status(thm)],[f307,f250])).
% 0.19/6.02 fof(f312,plain,(
% 0.19/6.02 ![X0]: (w=v|~colinear(v,u,X0)|colinear(v,X0,w)|v=u)),
% 0.19/6.02 inference(resolution,[status(thm)],[f305,f247])).
% 0.19/6.02 fof(f315,plain,(
% 0.19/6.02 ![X0]: (w=v|~colinear(v,u,X0)|colinear(v,X0,w))),
% 0.19/6.02 inference(forward_subsumption_resolution,[status(thm)],[f312,f250])).
% 0.19/6.02 fof(f353,plain,(
% 0.19/6.02 ![X0,X1,X2]: (~colinear(X0,X1,X2)|colinear(X1,X2,X0)|X0=X1)),
% 0.19/6.02 inference(resolution,[status(thm)],[f249,f240])).
% 0.19/6.02 fof(f393,plain,(
% 0.19/6.02 between(x,v,u)|between(v,u,x)|between(u,x,v)),
% 0.19/6.02 inference(resolution,[status(thm)],[f133,f252])).
% 0.19/6.02 fof(f395,plain,(
% 0.19/6.02 between(w,v,u)|between(v,u,w)|between(u,w,v)),
% 0.19/6.02 inference(resolution,[status(thm)],[f133,f251])).
% 0.19/6.02 fof(f408,plain,(
% 0.19/6.02 between(v,u,x)|between(u,x,v)|colinear(v,u,x)),
% 0.19/6.02 inference(resolution,[status(thm)],[f393,f132])).
% 0.19/6.02 fof(f414,plain,(
% 0.19/6.02 between(v,u,x)|colinear(v,u,x)),
% 0.19/6.02 inference(forward_subsumption_resolution,[status(thm)],[f408,f131])).
% 0.19/6.02 fof(f459,plain,(
% 0.19/6.02 colinear(v,u,x)),
% 0.19/6.02 inference(forward_subsumption_resolution,[status(thm)],[f414,f130])).
% 0.19/6.02 fof(f476,plain,(
% 0.19/6.02 x=v|colinear(v,w,x)|w=v),
% 0.19/6.02 inference(resolution,[status(thm)],[f310,f305])).
% 0.19/6.02 fof(f485,plain,(
% 0.19/6.02 x=v|w=v|colinear(x,w,v)),
% 0.19/6.02 inference(resolution,[status(thm)],[f476,f233])).
% 0.19/6.02 fof(f506,plain,(
% 0.19/6.02 x=v|w=v|~colinear(x,w,u)),
% 0.19/6.02 inference(resolution,[status(thm)],[f485,f253])).
% 0.19/6.02 fof(f514,plain,(
% 0.19/6.02 w=v|colinear(v,x,w)),
% 0.19/6.02 inference(resolution,[status(thm)],[f315,f459])).
% 0.19/6.02 fof(f523,plain,(
% 0.19/6.02 w=v|colinear(w,x,v)),
% 0.19/6.02 inference(resolution,[status(thm)],[f514,f233])).
% 0.19/6.02 fof(f525,plain,(
% 0.19/6.02 w=v|colinear(x,v,w)|w=x),
% 0.19/6.02 inference(resolution,[status(thm)],[f523,f353])).
% 0.19/6.02 fof(f531,plain,(
% 0.19/6.02 w=v|w=x|colinear(x,w,u)|x=v),
% 0.19/6.02 inference(resolution,[status(thm)],[f525,f290])).
% 0.19/6.02 fof(f538,plain,(
% 0.19/6.02 w=v|w=x|x=v),
% 0.19/6.02 inference(forward_subsumption_resolution,[status(thm)],[f531,f506])).
% 0.19/6.02 fof(f542,plain,(
% 0.19/6.02 x=v|w=v|~colinear(w,w,u)|w=v|x=v),
% 0.19/6.02 inference(paramodulation,[status(thm)],[f538,f506])).
% 0.19/6.02 fof(f559,plain,(
% 0.19/6.02 x=v|w=v|~colinear(w,w,u)),
% 0.19/6.02 inference(duplicate_literals_removal,[status(thm)],[f542])).
% 0.19/6.02 fof(f560,plain,(
% 0.19/6.02 x=v|w=v),
% 0.19/6.02 inference(forward_subsumption_resolution,[status(thm)],[f559,f239])).
% 0.19/6.02 fof(f577,plain,(
% 0.19/6.02 ~colinear(x,w,u)|~colinear(v,w,v)|w=v),
% 0.19/6.02 inference(paramodulation,[status(thm)],[f560,f253])).
% 0.19/6.02 fof(f581,plain,(
% 0.19/6.02 ~colinear(x,w,u)|w=v),
% 0.19/6.02 inference(forward_subsumption_resolution,[status(thm)],[f577,f240])).
% 0.19/6.02 fof(f651,plain,(
% 0.19/6.02 between(v,u,w)|between(u,w,v)|colinear(v,w,u)),
% 0.19/6.02 inference(resolution,[status(thm)],[f395,f232])).
% 0.19/6.02 fof(f657,plain,(
% 0.19/6.02 between(u,w,v)|colinear(v,w,u)),
% 0.19/6.02 inference(forward_subsumption_resolution,[status(thm)],[f651,f231])).
% 0.19/6.03 fof(f662,plain,(
% 0.19/6.03 colinear(v,w,u)),
% 0.19/6.03 inference(forward_subsumption_resolution,[status(thm)],[f657,f230])).
% 0.19/6.03 fof(f1078,plain,(
% 0.19/6.03 ~colinear(v,w,u)|w=v|w=v),
% 0.19/6.03 inference(paramodulation,[status(thm)],[f560,f581])).
% 0.19/6.03 fof(f1079,plain,(
% 0.19/6.03 ~colinear(v,w,u)|w=v),
% 0.19/6.03 inference(duplicate_literals_removal,[status(thm)],[f1078])).
% 0.19/6.03 fof(f1080,plain,(
% 0.19/6.03 w=v),
% 0.19/6.03 inference(forward_subsumption_resolution,[status(thm)],[f1079,f662])).
% 0.19/6.03 fof(f1123,plain,(
% 0.19/6.03 ~colinear(x,w,u)|~colinear(x,v,v)),
% 0.19/6.03 inference(backward_demodulation,[status(thm)],[f1080,f253])).
% 0.19/6.03 fof(f1140,plain,(
% 0.19/6.03 ~colinear(x,v,u)|~colinear(x,v,v)),
% 0.19/6.03 inference(forward_demodulation,[status(thm)],[f1080,f1123])).
% 0.19/6.03 fof(f1141,plain,(
% 0.19/6.03 ~colinear(x,v,v)),
% 0.19/6.03 inference(forward_subsumption_resolution,[status(thm)],[f1140,f252])).
% 0.19/6.03 fof(f1142,plain,(
% 0.19/6.03 $false),
% 0.19/6.03 inference(forward_subsumption_resolution,[status(thm)],[f1141,f241])).
% 0.19/6.03 % SZS output end CNFRefutation for theBenchmark.p
% 0.19/6.04 % Elapsed time: 0.611933 seconds
% 0.19/6.04 % CPU time: 4.482312 seconds
% 0.19/6.04 % Total memory used: 122.714 MB
% 0.19/6.04 % Net memory used: 119.886 MB
%------------------------------------------------------------------------------