%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO124+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 12:25:49 PM UTC 2026
% Result : Theorem 0.13s 0.49s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO124+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n004.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 20 11:53:51 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.37 % Drodi V4.1.1
% 0.13/0.49 % Refutation found
% 0.13/0.49 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.49 % SZS output start CNFRefutation for theBenchmark
% 0.13/0.49 fof(f17,axiom,(
% 0.13/0.49 (! [C,P,Q,R] :( between_c(C,P,Q,R)<=> ( P != R& (? [Cpp] :( part_of(Cpp,C)& end_point(P,Cpp)& end_point(R,Cpp)& inner_point(Q,Cpp) ) )) ) )),
% 0.13/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.49 fof(f18,axiom,(
% 0.13/0.49 (! [O,P,Q,R] :( between_o(O,P,Q,R)<=> ( ( ordered_by(O,P,Q)& ordered_by(O,Q,R) )| ( ordered_by(O,R,Q)& ordered_by(O,Q,P) ) ) ) )),
% 0.13/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.49 fof(f19,axiom,(
% 0.13/0.49 (! [P,O] :( start_point(P,O)<=> ( incident_o(P,O)& (! [Q] :( ( P != Q& incident_o(Q,O) )=> ordered_by(O,P,Q) ) )) ) )),
% 0.13/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.49 fof(f21,axiom,(
% 0.13/0.49 (! [O,P,Q] :( ordered_by(O,P,Q)=> ( incident_o(P,O)& incident_o(Q,O) ) ) )),
% 0.13/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.49 fof(f23,axiom,(
% 0.13/0.49 (! [P,Q,R,O] :( between_o(O,P,Q,R)<=> (? [C] :( (! [P] :( incident_o(P,O)<=> incident_c(P,C) ))& between_c(C,P,Q,R) ) )) )),
% 0.13/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.49 fof(f28,conjecture,(
% 0.13/0.49 (! [O,P,Q] :( ( start_point(P,O)& start_point(Q,O) )=> P = Q ) )),
% 0.13/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.49 fof(f29,negated_conjecture,(
% 0.13/0.49 ~((! [O,P,Q] :( ( start_point(P,O)& start_point(Q,O) )=> P = Q ) ))),
% 0.13/0.49 inference(negated_conjecture,[status(cth)],[f28])).
% 0.13/0.49 fof(f115,plain,(
% 0.13/0.49 ![C,P,Q,R]: ((~between_c(C,P,Q,R)|(~P=R&(?[Cpp]: (((part_of(Cpp,C)&end_point(P,Cpp))&end_point(R,Cpp))&inner_point(Q,Cpp)))))&(between_c(C,P,Q,R)|(P=R|(![Cpp]: (((~part_of(Cpp,C)|~end_point(P,Cpp))|~end_point(R,Cpp))|~inner_point(Q,Cpp))))))),
% 0.13/0.49 inference(NNF_transformation,[status(thm)],[f17])).
% 0.13/0.49 fof(f116,plain,(
% 0.13/0.49 (![C,P,Q,R]: (~between_c(C,P,Q,R)|(~P=R&(?[Cpp]: (((part_of(Cpp,C)&end_point(P,Cpp))&end_point(R,Cpp))&inner_point(Q,Cpp))))))&(![C,P,Q,R]: (between_c(C,P,Q,R)|(P=R|(![Cpp]: (((~part_of(Cpp,C)|~end_point(P,Cpp))|~end_point(R,Cpp))|~inner_point(Q,Cpp))))))),
% 0.13/0.49 inference(miniscoping,[status(thm)],[f115])).
% 0.13/0.49 fof(f117,plain,(
% 0.13/0.49 (![C,P,Q,R]: (~between_c(C,P,Q,R)|(~P=R&(((part_of(sK13_skl(R,Q,P,C),C)&end_point(P,sK13_skl(R,Q,P,C)))&end_point(R,sK13_skl(R,Q,P,C)))&inner_point(Q,sK13_skl(R,Q,P,C))))))&(![C,P,Q,R]: (between_c(C,P,Q,R)|(P=R|(![Cpp]: (((~part_of(Cpp,C)|~end_point(P,Cpp))|~end_point(R,Cpp))|~inner_point(Q,Cpp))))))),
% 0.13/0.49 inference(skolemize,[status(esa),new_symbols(skolem,[sK13_skl]),skolemize(Cpp,sK13_skl(R,Q,P,C))],[f116])).
% 0.13/0.49 fof(f118,plain,(
% 0.13/0.49 ![X0,X1,X2,X3]: (~between_c(X0,X1,X2,X3)|~X1=X3)),
% 0.13/0.49 inference(cnf_transformation,[status(thm)],[f117])).
% 0.13/0.49 fof(f124,plain,(
% 0.13/0.49 ![O,P,Q,R]: ((~between_o(O,P,Q,R)|((ordered_by(O,P,Q)&ordered_by(O,Q,R))|(ordered_by(O,R,Q)&ordered_by(O,Q,P))))&(between_o(O,P,Q,R)|((~ordered_by(O,P,Q)|~ordered_by(O,Q,R))&(~ordered_by(O,R,Q)|~ordered_by(O,Q,P)))))),
% 0.13/0.49 inference(NNF_transformation,[status(thm)],[f18])).
% 0.13/0.49 fof(f125,plain,(
% 0.13/0.49 (![O,P,Q,R]: (~between_o(O,P,Q,R)|((ordered_by(O,P,Q)&ordered_by(O,Q,R))|(ordered_by(O,R,Q)&ordered_by(O,Q,P)))))&(![O,P,Q,R]: (between_o(O,P,Q,R)|((~ordered_by(O,P,Q)|~ordered_by(O,Q,R))&(~ordered_by(O,R,Q)|~ordered_by(O,Q,P)))))),
% 0.13/0.49 inference(miniscoping,[status(thm)],[f124])).
% 0.13/0.49 fof(f127,plain,(
% 0.13/0.49 ![X0,X1,X2,X3]: (~between_o(X0,X1,X2,X3)|ordered_by(X0,X1,X2)|ordered_by(X0,X2,X1))),
% 0.13/0.49 inference(cnf_transformation,[status(thm)],[f125])).
% 0.13/0.49 fof(f131,plain,(
% 0.13/0.49 ![X0,X1,X2,X3]: (between_o(X0,X1,X2,X3)|~ordered_by(X0,X3,X2)|~ordered_by(X0,X2,X1))),
% 0.13/0.49 inference(cnf_transformation,[status(thm)],[f125])).
% 0.13/0.49 fof(f132,plain,(
% 0.13/0.49 ![P,O]: (start_point(P,O)<=>(incident_o(P,O)&(![Q]: ((P=Q|~incident_o(Q,O))|ordered_by(O,P,Q)))))),
% 0.13/0.49 inference(pre_NNF_transformation,[status(thm)],[f19])).
% 0.13/0.49 fof(f133,plain,(
% 0.13/0.49 ![P,O]: ((~start_point(P,O)|(incident_o(P,O)&(![Q]: ((P=Q|~incident_o(Q,O))|ordered_by(O,P,Q)))))&(start_point(P,O)|(~incident_o(P,O)|(?[Q]: ((~P=Q&incident_o(Q,O))&~ordered_by(O,P,Q))))))),
% 0.13/0.49 inference(NNF_transformation,[status(thm)],[f132])).
% 0.13/0.49 fof(f134,plain,(
% 0.13/0.49 (![P,O]: (~start_point(P,O)|(incident_o(P,O)&(![Q]: ((P=Q|~incident_o(Q,O))|ordered_by(O,P,Q))))))&(![P,O]: (start_point(P,O)|(~incident_o(P,O)|(?[Q]: ((~P=Q&incident_o(Q,O))&~ordered_by(O,P,Q))))))),
% 0.13/0.49 inference(miniscoping,[status(thm)],[f133])).
% 0.13/0.49 fof(f135,plain,(
% 0.13/0.49 (![P,O]: (~start_point(P,O)|(incident_o(P,O)&(![Q]: ((P=Q|~incident_o(Q,O))|ordered_by(O,P,Q))))))&(![P,O]: (start_point(P,O)|(~incident_o(P,O)|((~P=sK14_skl(O,P)&incident_o(sK14_skl(O,P),O))&~ordered_by(O,P,sK14_skl(O,P))))))),
% 0.13/0.49 inference(skolemize,[status(esa),new_symbols(skolem,[sK14_skl]),skolemize(Q,sK14_skl(O,P))],[f134])).
% 0.13/0.49 fof(f136,plain,(
% 0.13/0.49 ![X0,X1]: (~start_point(X0,X1)|incident_o(X0,X1))),
% 0.13/0.49 inference(cnf_transformation,[status(thm)],[f135])).
% 0.13/0.49 fof(f137,plain,(
% 0.13/0.49 ![X0,X1,X2]: (~start_point(X0,X1)|X0=X2|~incident_o(X2,X1)|ordered_by(X1,X0,X2))),
% 0.13/0.49 inference(cnf_transformation,[status(thm)],[f135])).
% 0.13/0.49 fof(f150,plain,(
% 0.13/0.49 ![O,P,Q]: (~ordered_by(O,P,Q)|(incident_o(P,O)&incident_o(Q,O)))),
% 0.13/0.49 inference(pre_NNF_transformation,[status(thm)],[f21])).
% 0.13/0.49 fof(f151,plain,(
% 0.13/0.49 ![X0,X1,X2]: (~ordered_by(X0,X1,X2)|incident_o(X1,X0))),
% 0.13/0.49 inference(cnf_transformation,[status(thm)],[f150])).
% 0.13/0.49 fof(f159,plain,(
% 0.13/0.49 ![P,Q,R,O]: ((~between_o(O,P,Q,R)|(?[C]: ((![P]: ((~incident_o(P,O)|incident_c(P,C))&(incident_o(P,O)|~incident_c(P,C))))&between_c(C,P,Q,R))))&(between_o(O,P,Q,R)|(![C]: ((?[P]: ((~incident_o(P,O)|~incident_c(P,C))&(incident_o(P,O)|incident_c(P,C))))|~between_c(C,P,Q,R)))))),
% 0.13/0.49 inference(NNF_transformation,[status(thm)],[f23])).
% 0.13/0.49 fof(f160,plain,(
% 0.13/0.49 (![P,Q,R,O]: (~between_o(O,P,Q,R)|(?[C]: (((![P]: (~incident_o(P,O)|incident_c(P,C)))&(![P]: (incident_o(P,O)|~incident_c(P,C))))&between_c(C,P,Q,R)))))&(![P,Q,R,O]: (between_o(O,P,Q,R)|(![C]: ((?[P]: ((~incident_o(P,O)|~incident_c(P,C))&(incident_o(P,O)|incident_c(P,C))))|~between_c(C,P,Q,R)))))),
% 0.13/0.49 inference(miniscoping,[status(thm)],[f159])).
% 0.13/0.49 fof(f161,plain,(
% 0.13/0.49 (![P,Q,R,O]: (~between_o(O,P,Q,R)|(((![P]: (~incident_o(P,O)|incident_c(P,sK17_skl(O,R,Q,P))))&(![P]: (incident_o(P,O)|~incident_c(P,sK17_skl(O,R,Q,P)))))&between_c(sK17_skl(O,R,Q,P),P,Q,R))))&(![P,Q,R,O]: (between_o(O,P,Q,R)|(![C]: (((~incident_o(sK18_skl(C,O,R,Q,P),O)|~incident_c(sK18_skl(C,O,R,Q,P),C))&(incident_o(sK18_skl(C,O,R,Q,P),O)|incident_c(sK18_skl(C,O,R,Q,P),C)))|~between_c(C,P,Q,R)))))),
% 0.13/0.49 inference(skolemize,[status(esa),new_symbols(skolem,[sK17_skl,sK18_skl]),skolemize(C,sK17_skl(O,R,Q,P)),skolemize(P,sK18_skl(C,O,R,Q,P))],[f160])).
% 0.13/0.49 fof(f164,plain,(
% 0.13/0.49 ![X0,X1,X2,X3]: (~between_o(X0,X1,X2,X3)|between_c(sK17_skl(X0,X3,X2,X1),X1,X2,X3))),
% 0.13/0.49 inference(cnf_transformation,[status(thm)],[f161])).
% 0.13/0.49 fof(f188,plain,(
% 0.13/0.49 (?[O,P,Q]: ((start_point(P,O)&start_point(Q,O))&~P=Q))),
% 0.13/0.49 inference(pre_NNF_transformation,[status(thm)],[f29])).
% 0.13/0.49 fof(f189,plain,(
% 0.13/0.49 ?[P,Q]: ((?[O]: (start_point(P,O)&start_point(Q,O)))&~P=Q)),
% 0.13/0.49 inference(miniscoping,[status(thm)],[f188])).
% 0.13/0.49 fof(f190,plain,(
% 0.13/0.49 ((start_point(sK24_skl,sK26_skl)&start_point(sK25_skl,sK26_skl))&~sK24_skl=sK25_skl)),
% 0.13/0.49 inference(skolemize,[status(esa),new_symbols(skolem,[sK24_skl,sK25_skl,sK26_skl]),skolemize(P,sK24_skl),skolemize(Q,sK25_skl),skolemize(O,sK26_skl)],[f189])).
% 0.13/0.49 fof(f191,plain,(
% 0.13/0.49 start_point(sK24_skl,sK26_skl)),
% 0.13/0.49 inference(cnf_transformation,[status(thm)],[f190])).
% 0.13/0.49 fof(f192,plain,(
% 0.13/0.49 start_point(sK25_skl,sK26_skl)),
% 0.13/0.49 inference(cnf_transformation,[status(thm)],[f190])).
% 0.13/0.49 fof(f193,plain,(
% 0.13/0.49 ~sK24_skl=sK25_skl),
% 0.13/0.49 inference(cnf_transformation,[status(thm)],[f190])).
% 0.13/0.49 fof(f198,plain,(
% 0.13/0.49 ![X0,X1,X2]: (~between_c(X0,X1,X2,X1))),
% 0.13/0.49 inference(destructive_equality_resolution,[status(thm)],[f118])).
% 0.13/0.49 fof(f203,plain,(
% 0.13/0.49 incident_o(sK25_skl,sK26_skl)),
% 0.13/0.49 inference(resolution,[status(thm)],[f136,f192])).
% 0.13/0.49 fof(f580,plain,(
% 0.13/0.49 ![X0,X1,X2,X3]: (between_o(X0,X1,X2,X3)|~ordered_by(X0,X2,X1)|~start_point(X3,X0)|X3=X2|~incident_o(X2,X0))),
% 0.13/0.49 inference(resolution,[status(thm)],[f131,f137])).
% 0.13/0.49 fof(f581,plain,(
% 0.13/0.49 ![X0,X1,X2,X3]: (between_o(X0,X1,X2,X3)|~ordered_by(X0,X2,X1)|~start_point(X3,X0)|X3=X2)),
% 0.13/0.49 inference(forward_subsumption_resolution,[status(thm)],[f580,f151])).
% 0.13/0.49 fof(f637,plain,(
% 0.13/0.49 ![X0,X1]: (between_o(sK26_skl,X0,X1,sK25_skl)|~ordered_by(sK26_skl,X1,X0)|sK25_skl=X1)),
% 0.13/0.49 inference(resolution,[status(thm)],[f581,f192])).
% 0.13/0.51 fof(f638,plain,(
% 0.13/0.51 ![X0,X1]: (between_o(sK26_skl,X0,X1,sK24_skl)|~ordered_by(sK26_skl,X1,X0)|sK24_skl=X1)),
% 0.13/0.51 inference(resolution,[status(thm)],[f581,f191])).
% 0.13/0.51 fof(f648,plain,(
% 0.13/0.51 ![X0,X1]: (between_o(sK26_skl,X0,X1,sK25_skl)|sK25_skl=X1|~start_point(X1,sK26_skl)|X1=X0|~incident_o(X0,sK26_skl))),
% 0.13/0.51 inference(resolution,[status(thm)],[f637,f137])).
% 0.13/0.51 fof(f749,plain,(
% 0.13/0.51 ![X0]: (between_o(sK26_skl,X0,sK24_skl,sK25_skl)|sK25_skl=sK24_skl|sK24_skl=X0|~incident_o(X0,sK26_skl))),
% 0.13/0.51 inference(resolution,[status(thm)],[f648,f191])).
% 0.13/0.51 fof(f751,plain,(
% 0.13/0.51 ![X0]: (between_o(sK26_skl,X0,sK24_skl,sK25_skl)|sK24_skl=X0|~incident_o(X0,sK26_skl))),
% 0.13/0.51 inference(forward_subsumption_resolution,[status(thm)],[f749,f193])).
% 0.13/0.51 fof(f757,plain,(
% 0.13/0.51 ![X0]: (sK24_skl=X0|~incident_o(X0,sK26_skl)|ordered_by(sK26_skl,X0,sK24_skl)|ordered_by(sK26_skl,sK24_skl,X0))),
% 0.13/0.51 inference(resolution,[status(thm)],[f751,f127])).
% 0.13/0.51 fof(f776,plain,(
% 0.13/0.51 sK24_skl=sK25_skl|ordered_by(sK26_skl,sK25_skl,sK24_skl)|ordered_by(sK26_skl,sK24_skl,sK25_skl)),
% 0.13/0.51 inference(resolution,[status(thm)],[f757,f203])).
% 0.13/0.51 fof(f778,plain,(
% 0.13/0.51 ordered_by(sK26_skl,sK25_skl,sK24_skl)|ordered_by(sK26_skl,sK24_skl,sK25_skl)),
% 0.13/0.51 inference(forward_subsumption_resolution,[status(thm)],[f776,f193])).
% 0.13/0.51 fof(f782,plain,(
% 0.13/0.51 ordered_by(sK26_skl,sK25_skl,sK24_skl)|between_o(sK26_skl,sK25_skl,sK24_skl,sK25_skl)|sK25_skl=sK24_skl),
% 0.13/0.51 inference(resolution,[status(thm)],[f778,f637])).
% 0.13/0.51 fof(f793,plain,(
% 0.13/0.51 ordered_by(sK26_skl,sK25_skl,sK24_skl)|between_o(sK26_skl,sK25_skl,sK24_skl,sK25_skl)),
% 0.13/0.51 inference(forward_subsumption_resolution,[status(thm)],[f782,f193])).
% 0.13/0.51 fof(f799,plain,(
% 0.13/0.51 ordered_by(sK26_skl,sK25_skl,sK24_skl)|between_c(sK17_skl(sK26_skl,sK25_skl,sK24_skl,sK25_skl),sK25_skl,sK24_skl,sK25_skl)),
% 0.13/0.51 inference(resolution,[status(thm)],[f793,f164])).
% 0.13/0.51 fof(f806,plain,(
% 0.13/0.51 ordered_by(sK26_skl,sK25_skl,sK24_skl)),
% 0.13/0.51 inference(forward_subsumption_resolution,[status(thm)],[f799,f198])).
% 0.13/0.51 fof(f813,plain,(
% 0.13/0.51 between_o(sK26_skl,sK24_skl,sK25_skl,sK24_skl)|sK24_skl=sK25_skl),
% 0.13/0.51 inference(resolution,[status(thm)],[f806,f638])).
% 0.13/0.51 fof(f824,plain,(
% 0.13/0.51 between_o(sK26_skl,sK24_skl,sK25_skl,sK24_skl)),
% 0.13/0.51 inference(forward_subsumption_resolution,[status(thm)],[f813,f193])).
% 0.13/0.51 fof(f826,plain,(
% 0.13/0.51 between_c(sK17_skl(sK26_skl,sK24_skl,sK25_skl,sK24_skl),sK24_skl,sK25_skl,sK24_skl)),
% 0.13/0.51 inference(resolution,[status(thm)],[f824,f164])).
% 0.13/0.51 fof(f833,plain,(
% 0.13/0.51 $false),
% 0.13/0.51 inference(forward_subsumption_resolution,[status(thm)],[f826,f198])).
% 0.13/0.51 % SZS output end CNFRefutation for theBenchmark.p
% 0.13/0.52 % Elapsed time: 0.154595 seconds
% 0.13/0.52 % CPU time: 0.899545 seconds
% 0.13/0.52 % Total memory used: 94.088 MB
% 0.13/0.52 % Net memory used: 92.949 MB
%------------------------------------------------------------------------------