%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO111+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 12:25:47 PM UTC 2026
% Result : Theorem 0.11s 0.50s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO111+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n015.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 20 11:27:04 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.37 % Drodi V4.1.1
% 0.11/0.50 % Refutation found
% 0.11/0.50 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.50 % SZS output start CNFRefutation for theBenchmark
% 0.11/0.50 fof(f1,axiom,(
% 0.11/0.50 (! [C,C1] :( part_of(C1,C)<=> (! [P] :( incident_c(P,C1)=> incident_c(P,C) ) )) )),
% 0.11/0.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.50 fof(f3,axiom,(
% 0.11/0.50 (! [P,C] :( end_point(P,C)<=> ( incident_c(P,C)& (! [C1,C2] :( ( part_of(C1,C)& part_of(C2,C)& incident_c(P,C1)& incident_c(P,C2) )=> ( part_of(C1,C2)| part_of(C2,C1) ) ) )) ) )),
% 0.11/0.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.50 fof(f4,axiom,(
% 0.11/0.50 (! [P,C] :( inner_point(P,C)<=> ( incident_c(P,C)& ~ end_point(P,C) ) ) )),
% 0.11/0.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.50 fof(f17,axiom,(
% 0.11/0.50 (! [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) ) )) ) )),
% 0.11/0.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.50 fof(f18,conjecture,(
% 0.11/0.50 (! [C,P,Q,R] :( between_c(C,P,Q,R)=> ( incident_c(P,C)& incident_c(Q,C)& incident_c(R,C)& P != Q& Q != R& P != R ) ) )),
% 0.11/0.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.50 fof(f19,negated_conjecture,(
% 0.11/0.50 ~((! [C,P,Q,R] :( between_c(C,P,Q,R)=> ( incident_c(P,C)& incident_c(Q,C)& incident_c(R,C)& P != Q& Q != R& P != R ) ) ))),
% 0.11/0.50 inference(negated_conjecture,[status(cth)],[f18])).
% 0.11/0.50 fof(f20,plain,(
% 0.11/0.50 ![C,C1]: (part_of(C1,C)<=>(![P]: (~incident_c(P,C1)|incident_c(P,C))))),
% 0.11/0.50 inference(pre_NNF_transformation,[status(thm)],[f1])).
% 0.11/0.50 fof(f21,plain,(
% 0.11/0.50 ![C,C1]: ((~part_of(C1,C)|(![P]: (~incident_c(P,C1)|incident_c(P,C))))&(part_of(C1,C)|(?[P]: (incident_c(P,C1)&~incident_c(P,C)))))),
% 0.11/0.50 inference(NNF_transformation,[status(thm)],[f20])).
% 0.11/0.50 fof(f22,plain,(
% 0.11/0.50 (![C,C1]: (~part_of(C1,C)|(![P]: (~incident_c(P,C1)|incident_c(P,C)))))&(![C,C1]: (part_of(C1,C)|(?[P]: (incident_c(P,C1)&~incident_c(P,C)))))),
% 0.11/0.50 inference(miniscoping,[status(thm)],[f21])).
% 0.11/0.50 fof(f23,plain,(
% 0.11/0.50 (![C,C1]: (~part_of(C1,C)|(![P]: (~incident_c(P,C1)|incident_c(P,C)))))&(![C,C1]: (part_of(C1,C)|(incident_c(sK0_skl(C1,C),C1)&~incident_c(sK0_skl(C1,C),C))))),
% 0.11/0.50 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(P,sK0_skl(C1,C))],[f22])).
% 0.11/0.50 fof(f24,plain,(
% 0.11/0.50 ![X0,X1,X2]: (~part_of(X0,X1)|~incident_c(X2,X0)|incident_c(X2,X1))),
% 0.11/0.50 inference(cnf_transformation,[status(thm)],[f23])).
% 0.11/0.50 fof(f36,plain,(
% 0.11/0.50 ![P,C]: (end_point(P,C)<=>(incident_c(P,C)&(![C1,C2]: ((((~part_of(C1,C)|~part_of(C2,C))|~incident_c(P,C1))|~incident_c(P,C2))|(part_of(C1,C2)|part_of(C2,C1))))))),
% 0.11/0.50 inference(pre_NNF_transformation,[status(thm)],[f3])).
% 0.11/0.50 fof(f37,plain,(
% 0.11/0.50 ![P,C]: ((~end_point(P,C)|(incident_c(P,C)&(![C1,C2]: ((((~part_of(C1,C)|~part_of(C2,C))|~incident_c(P,C1))|~incident_c(P,C2))|(part_of(C1,C2)|part_of(C2,C1))))))&(end_point(P,C)|(~incident_c(P,C)|(?[C1,C2]: ((((part_of(C1,C)&part_of(C2,C))&incident_c(P,C1))&incident_c(P,C2))&(~part_of(C1,C2)&~part_of(C2,C1)))))))),
% 0.11/0.50 inference(NNF_transformation,[status(thm)],[f36])).
% 0.11/0.50 fof(f38,plain,(
% 0.11/0.50 (![P,C]: (~end_point(P,C)|(incident_c(P,C)&(![C1,C2]: ((((~part_of(C1,C)|~part_of(C2,C))|~incident_c(P,C1))|~incident_c(P,C2))|(part_of(C1,C2)|part_of(C2,C1)))))))&(![P,C]: (end_point(P,C)|(~incident_c(P,C)|(?[C1,C2]: ((((part_of(C1,C)&part_of(C2,C))&incident_c(P,C1))&incident_c(P,C2))&(~part_of(C1,C2)&~part_of(C2,C1)))))))),
% 0.11/0.50 inference(miniscoping,[status(thm)],[f37])).
% 0.11/0.50 fof(f39,plain,(
% 0.11/0.50 (![P,C]: (~end_point(P,C)|(incident_c(P,C)&(![C1,C2]: ((((~part_of(C1,C)|~part_of(C2,C))|~incident_c(P,C1))|~incident_c(P,C2))|(part_of(C1,C2)|part_of(C2,C1)))))))&(![P,C]: (end_point(P,C)|(~incident_c(P,C)|((((part_of(sK2_skl(C,P),C)&part_of(sK3_skl(C,P),C))&incident_c(P,sK2_skl(C,P)))&incident_c(P,sK3_skl(C,P)))&(~part_of(sK2_skl(C,P),sK3_skl(C,P))&~part_of(sK3_skl(C,P),sK2_skl(C,P)))))))),
% 0.11/0.50 inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(C1,sK2_skl(C,P)),skolemize(C2,sK3_skl(C,P))],[f38])).
% 0.11/0.50 fof(f40,plain,(
% 0.11/0.50 ![X0,X1]: (~end_point(X0,X1)|incident_c(X0,X1))),
% 0.11/0.50 inference(cnf_transformation,[status(thm)],[f39])).
% 0.11/0.50 fof(f48,plain,(
% 0.11/0.50 ![P,C]: ((~inner_point(P,C)|(incident_c(P,C)&~end_point(P,C)))&(inner_point(P,C)|(~incident_c(P,C)|end_point(P,C))))),
% 0.11/0.50 inference(NNF_transformation,[status(thm)],[f4])).
% 0.11/0.50 fof(f49,plain,(
% 0.11/0.50 (![P,C]: (~inner_point(P,C)|(incident_c(P,C)&~end_point(P,C))))&(![P,C]: (inner_point(P,C)|(~incident_c(P,C)|end_point(P,C))))),
% 0.11/0.50 inference(miniscoping,[status(thm)],[f48])).
% 0.11/0.50 fof(f50,plain,(
% 0.11/0.50 ![X0,X1]: (~inner_point(X0,X1)|incident_c(X0,X1))),
% 0.11/0.50 inference(cnf_transformation,[status(thm)],[f49])).
% 0.11/0.50 fof(f51,plain,(
% 0.11/0.50 ![X0,X1]: (~inner_point(X0,X1)|~end_point(X0,X1))),
% 0.11/0.50 inference(cnf_transformation,[status(thm)],[f49])).
% 0.11/0.50 fof(f105,plain,(
% 0.11/0.50 ![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))))))),
% 0.11/0.50 inference(NNF_transformation,[status(thm)],[f17])).
% 0.11/0.50 fof(f106,plain,(
% 0.11/0.50 (![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))))))),
% 0.11/0.50 inference(miniscoping,[status(thm)],[f105])).
% 0.11/0.50 fof(f107,plain,(
% 0.11/0.50 (![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))))))),
% 0.11/0.50 inference(skolemize,[status(esa),new_symbols(skolem,[sK13_skl]),skolemize(Cpp,sK13_skl(R,Q,P,C))],[f106])).
% 0.11/0.50 fof(f108,plain,(
% 0.11/0.50 ![X0,X1,X2,X3]: (~between_c(X0,X1,X2,X3)|~X1=X3)),
% 0.11/0.50 inference(cnf_transformation,[status(thm)],[f107])).
% 0.11/0.50 fof(f109,plain,(
% 0.11/0.50 ![X0,X1,X2,X3]: (~between_c(X0,X1,X2,X3)|part_of(sK13_skl(X3,X2,X1,X0),X0))),
% 0.11/0.50 inference(cnf_transformation,[status(thm)],[f107])).
% 0.11/0.50 fof(f110,plain,(
% 0.11/0.50 ![X0,X1,X2,X3]: (~between_c(X0,X1,X2,X3)|end_point(X1,sK13_skl(X3,X2,X1,X0)))),
% 0.11/0.50 inference(cnf_transformation,[status(thm)],[f107])).
% 0.11/0.50 fof(f111,plain,(
% 0.11/0.50 ![X0,X1,X2,X3]: (~between_c(X0,X1,X2,X3)|end_point(X3,sK13_skl(X3,X2,X1,X0)))),
% 0.11/0.50 inference(cnf_transformation,[status(thm)],[f107])).
% 0.11/0.50 fof(f112,plain,(
% 0.11/0.50 ![X0,X1,X2,X3]: (~between_c(X0,X1,X2,X3)|inner_point(X2,sK13_skl(X3,X2,X1,X0)))),
% 0.11/0.50 inference(cnf_transformation,[status(thm)],[f107])).
% 0.11/0.50 fof(f114,plain,(
% 0.11/0.50 (?[C,P,Q,R]: (between_c(C,P,Q,R)&(((((~incident_c(P,C)|~incident_c(Q,C))|~incident_c(R,C))|P=Q)|Q=R)|P=R)))),
% 0.11/0.50 inference(pre_NNF_transformation,[status(thm)],[f19])).
% 0.11/0.50 fof(f115,plain,(
% 0.11/0.50 (between_c(sK14_skl,sK15_skl,sK16_skl,sK17_skl)&(((((~incident_c(sK15_skl,sK14_skl)|~incident_c(sK16_skl,sK14_skl))|~incident_c(sK17_skl,sK14_skl))|sK15_skl=sK16_skl)|sK16_skl=sK17_skl)|sK15_skl=sK17_skl))),
% 0.11/0.50 inference(skolemize,[status(esa),new_symbols(skolem,[sK14_skl,sK15_skl,sK16_skl,sK17_skl]),skolemize(C,sK14_skl),skolemize(P,sK15_skl),skolemize(Q,sK16_skl),skolemize(R,sK17_skl)],[f114])).
% 0.11/0.50 fof(f116,plain,(
% 0.11/0.50 between_c(sK14_skl,sK15_skl,sK16_skl,sK17_skl)),
% 0.11/0.50 inference(cnf_transformation,[status(thm)],[f115])).
% 0.11/0.50 fof(f117,plain,(
% 0.11/0.50 ~incident_c(sK15_skl,sK14_skl)|~incident_c(sK16_skl,sK14_skl)|~incident_c(sK17_skl,sK14_skl)|sK15_skl=sK16_skl|sK16_skl=sK17_skl|sK15_skl=sK17_skl),
% 0.11/0.50 inference(cnf_transformation,[status(thm)],[f115])).
% 0.11/0.50 fof(f118,plain,(
% 0.11/0.50 ![X0,X1,X2]: (~between_c(X0,X1,X2,X1))),
% 0.11/0.50 inference(destructive_equality_resolution,[status(thm)],[f108])).
% 0.11/0.50 fof(f131,plain,(
% 0.11/0.50 part_of(sK13_skl(sK17_skl,sK16_skl,sK15_skl,sK14_skl),sK14_skl)),
% 0.11/0.50 inference(resolution,[status(thm)],[f109,f116])).
% 0.11/0.50 fof(f132,plain,(
% 0.11/0.50 end_point(sK15_skl,sK13_skl(sK17_skl,sK16_skl,sK15_skl,sK14_skl))),
% 0.11/0.50 inference(resolution,[status(thm)],[f110,f116])).
% 0.11/0.50 fof(f133,plain,(
% 0.11/0.50 end_point(sK17_skl,sK13_skl(sK17_skl,sK16_skl,sK15_skl,sK14_skl))),
% 0.11/0.50 inference(resolution,[status(thm)],[f111,f116])).
% 0.11/0.50 fof(f134,plain,(
% 0.11/0.50 inner_point(sK16_skl,sK13_skl(sK17_skl,sK16_skl,sK15_skl,sK14_skl))),
% 0.11/0.50 inference(resolution,[status(thm)],[f112,f116])).
% 0.11/0.50 fof(f138,plain,(
% 0.11/0.50 ![X0]: (~incident_c(X0,sK13_skl(sK17_skl,sK16_skl,sK15_skl,sK14_skl))|incident_c(X0,sK14_skl))),
% 0.11/0.51 inference(resolution,[status(thm)],[f131,f24])).
% 0.11/0.51 fof(f139,plain,(
% 0.11/0.51 incident_c(sK15_skl,sK13_skl(sK17_skl,sK16_skl,sK15_skl,sK14_skl))),
% 0.11/0.51 inference(resolution,[status(thm)],[f132,f40])).
% 0.11/0.51 fof(f142,plain,(
% 0.11/0.51 incident_c(sK17_skl,sK13_skl(sK17_skl,sK16_skl,sK15_skl,sK14_skl))),
% 0.11/0.51 inference(resolution,[status(thm)],[f133,f40])).
% 0.11/0.51 fof(f147,plain,(
% 0.11/0.51 ~end_point(sK16_skl,sK13_skl(sK17_skl,sK16_skl,sK15_skl,sK14_skl))),
% 0.11/0.51 inference(resolution,[status(thm)],[f134,f51])).
% 0.11/0.51 fof(f148,plain,(
% 0.11/0.51 incident_c(sK16_skl,sK13_skl(sK17_skl,sK16_skl,sK15_skl,sK14_skl))),
% 0.11/0.51 inference(resolution,[status(thm)],[f134,f50])).
% 0.11/0.51 fof(f153,plain,(
% 0.11/0.51 incident_c(sK16_skl,sK14_skl)),
% 0.11/0.51 inference(resolution,[status(thm)],[f138,f148])).
% 0.11/0.51 fof(f154,plain,(
% 0.11/0.51 incident_c(sK17_skl,sK14_skl)),
% 0.11/0.51 inference(resolution,[status(thm)],[f138,f142])).
% 0.11/0.51 fof(f155,plain,(
% 0.11/0.51 incident_c(sK15_skl,sK14_skl)),
% 0.11/0.51 inference(resolution,[status(thm)],[f138,f139])).
% 0.11/0.51 fof(f158,plain,(
% 0.11/0.51 ~incident_c(sK15_skl,sK14_skl)|~incident_c(sK17_skl,sK14_skl)|sK15_skl=sK16_skl|sK16_skl=sK17_skl|sK15_skl=sK17_skl),
% 0.11/0.51 inference(backward_subsumption_resolution,[status(thm)],[f117,f153])).
% 0.11/0.51 fof(f159,plain,(
% 0.11/0.51 ~incident_c(sK17_skl,sK14_skl)|sK15_skl=sK16_skl|sK16_skl=sK17_skl|sK15_skl=sK17_skl),
% 0.11/0.51 inference(forward_subsumption_resolution,[status(thm)],[f158,f155])).
% 0.11/0.51 fof(f163,plain,(
% 0.11/0.51 sK15_skl=sK16_skl|sK16_skl=sK17_skl|sK15_skl=sK17_skl),
% 0.11/0.51 inference(resolution,[status(thm)],[f154,f159])).
% 0.11/0.51 fof(f263,plain,(
% 0.11/0.51 end_point(sK16_skl,sK13_skl(sK17_skl,sK16_skl,sK15_skl,sK14_skl))|sK15_skl=sK16_skl|sK15_skl=sK17_skl),
% 0.11/0.51 inference(paramodulation,[status(thm)],[f163,f133])).
% 0.11/0.51 fof(f269,plain,(
% 0.11/0.51 sK15_skl=sK16_skl|sK15_skl=sK17_skl),
% 0.11/0.51 inference(forward_subsumption_resolution,[status(thm)],[f263,f147])).
% 0.11/0.51 fof(f286,plain,(
% 0.11/0.51 between_c(sK14_skl,sK15_skl,sK16_skl,sK15_skl)|sK15_skl=sK16_skl),
% 0.11/0.51 inference(paramodulation,[status(thm)],[f269,f116])).
% 0.11/0.51 fof(f293,plain,(
% 0.11/0.51 ~end_point(sK16_skl,sK13_skl(sK17_skl,sK15_skl,sK15_skl,sK14_skl))),
% 0.11/0.51 inference(backward_demodulation,[status(thm)],[f335,f147])).
% 0.11/0.51 fof(f300,plain,(
% 0.11/0.51 end_point(sK15_skl,sK13_skl(sK17_skl,sK15_skl,sK15_skl,sK14_skl))),
% 0.11/0.51 inference(backward_demodulation,[status(thm)],[f335,f132])).
% 0.11/0.51 fof(f335,plain,(
% 0.11/0.51 sK15_skl=sK16_skl),
% 0.11/0.51 inference(forward_subsumption_resolution,[status(thm)],[f286,f118])).
% 0.11/0.51 fof(f340,plain,(
% 0.11/0.51 ~end_point(sK15_skl,sK13_skl(sK17_skl,sK15_skl,sK15_skl,sK14_skl))),
% 0.11/0.51 inference(forward_demodulation,[status(thm)],[f335,f293])).
% 0.11/0.51 fof(f342,plain,(
% 0.11/0.51 $false),
% 0.11/0.51 inference(forward_subsumption_resolution,[status(thm)],[f300,f340])).
% 0.11/0.51 % SZS output end CNFRefutation for theBenchmark.p
% 0.63/0.53 % Elapsed time: 0.156194 seconds
% 0.63/0.53 % CPU time: 0.956551 seconds
% 0.63/0.53 % Total memory used: 93.424 MB
% 0.63/0.53 % Net memory used: 92.146 MB
%------------------------------------------------------------------------------