%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO126+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 : n011.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 12:25:50 PM UTC 2026
% Result : Theorem 0.19s 0.62s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO126+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.45 % Computer : n011.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Sun Sep 20 11:57:25 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.48 % Drodi V4.1.1
% 0.19/0.62 % Refutation found
% 0.19/0.62 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/0.62 % SZS output start CNFRefutation for theBenchmark
% 0.19/0.62 fof(f3,axiom,(
% 0.19/0.62 (! [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) ) ) )) ) )),
% 0.19/0.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.19/0.62 fof(f4,axiom,(
% 0.19/0.62 (! [P,C] :( inner_point(P,C)<=> ( incident_c(P,C)& ~ end_point(P,C) ) ) )),
% 0.19/0.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.19/0.62 fof(f7,axiom,(
% 0.19/0.62 (! [C] :( open(C)<=> (? [P] : end_point(P,C) )) )),
% 0.19/0.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.19/0.62 fof(f10,axiom,(
% 0.19/0.62 (! [C] :(? [P] : inner_point(P,C) ))),
% 0.19/0.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.19/0.62 fof(f19,axiom,(
% 0.19/0.62 (! [P,O] :( start_point(P,O)<=> ( incident_o(P,O)& (! [Q] :( ( P != Q& incident_o(Q,O) )=> ordered_by(O,P,Q) ) )) ) )),
% 0.19/0.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.19/0.62 fof(f22,axiom,(
% 0.19/0.62 (! [O] :(? [C] :( open(C)& (! [P] :( incident_o(P,O)<=> incident_c(P,C) ) )) ))),
% 0.19/0.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.19/0.62 fof(f24,axiom,(
% 0.19/0.62 (! [O] :(? [P] : start_point(P,O) ))),
% 0.19/0.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.19/0.62 fof(f28,conjecture,(
% 0.19/0.62 (! [O] :(? [P,Q] :( ordered_by(O,P,Q)& P != Q ) ))),
% 0.19/0.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.19/0.62 fof(f29,negated_conjecture,(
% 0.19/0.62 ~((! [O] :(? [P,Q] :( ordered_by(O,P,Q)& P != Q ) )))),
% 0.19/0.62 inference(negated_conjecture,[status(cth)],[f28])).
% 0.19/0.62 fof(f46,plain,(
% 0.19/0.62 ![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))))))),
% 0.19/0.62 inference(pre_NNF_transformation,[status(thm)],[f3])).
% 0.19/0.62 fof(f47,plain,(
% 0.19/0.62 ![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)))))))),
% 0.19/0.62 inference(NNF_transformation,[status(thm)],[f46])).
% 0.19/0.62 fof(f48,plain,(
% 0.19/0.62 (![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)))))))),
% 0.19/0.62 inference(miniscoping,[status(thm)],[f47])).
% 0.19/0.62 fof(f49,plain,(
% 0.19/0.62 (![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)))))))),
% 0.19/0.62 inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(C1,sK2_skl(C,P)),skolemize(C2,sK3_skl(C,P))],[f48])).
% 0.19/0.62 fof(f50,plain,(
% 0.19/0.62 ![X0,X1]: (~end_point(X0,X1)|incident_c(X0,X1))),
% 0.19/0.62 inference(cnf_transformation,[status(thm)],[f49])).
% 0.19/0.62 fof(f58,plain,(
% 0.19/0.62 ![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))))),
% 0.19/0.62 inference(NNF_transformation,[status(thm)],[f4])).
% 0.19/0.62 fof(f59,plain,(
% 0.19/0.62 (![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))))),
% 0.19/0.62 inference(miniscoping,[status(thm)],[f58])).
% 0.19/0.62 fof(f60,plain,(
% 0.19/0.62 ![X0,X1]: (~inner_point(X0,X1)|incident_c(X0,X1))),
% 0.19/0.62 inference(cnf_transformation,[status(thm)],[f59])).
% 0.19/0.62 fof(f61,plain,(
% 0.19/0.62 ![X0,X1]: (~inner_point(X0,X1)|~end_point(X0,X1))),
% 0.19/0.62 inference(cnf_transformation,[status(thm)],[f59])).
% 0.19/0.62 fof(f80,plain,(
% 0.19/0.62 ![C]: ((~open(C)|(?[P]: end_point(P,C)))&(open(C)|(![P]: ~end_point(P,C))))),
% 0.19/0.62 inference(NNF_transformation,[status(thm)],[f7])).
% 0.19/0.62 fof(f81,plain,(
% 0.19/0.62 (![C]: (~open(C)|(?[P]: end_point(P,C))))&(![C]: (open(C)|(![P]: ~end_point(P,C))))),
% 0.19/0.62 inference(miniscoping,[status(thm)],[f80])).
% 0.19/0.62 fof(f82,plain,(
% 0.19/0.62 (![C]: (~open(C)|end_point(sK6_skl(C),C)))&(![C]: (open(C)|(![P]: ~end_point(P,C))))),
% 0.19/0.62 inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl]),skolemize(P,sK6_skl(C))],[f81])).
% 0.19/0.62 fof(f83,plain,(
% 0.19/0.62 ![X0]: (~open(X0)|end_point(sK6_skl(X0),X0))),
% 0.19/0.62 inference(cnf_transformation,[status(thm)],[f82])).
% 0.19/0.62 fof(f91,plain,(
% 0.19/0.62 ![C]: inner_point(sK7_skl(C),C)),
% 0.19/0.62 inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl]),skolemize(P,sK7_skl(C))],[f10])).
% 0.19/0.62 fof(f92,plain,(
% 0.19/0.62 ![X0]: (inner_point(sK7_skl(X0),X0))),
% 0.19/0.62 inference(cnf_transformation,[status(thm)],[f91])).
% 0.19/0.62 fof(f132,plain,(
% 0.19/0.62 ![P,O]: (start_point(P,O)<=>(incident_o(P,O)&(![Q]: ((P=Q|~incident_o(Q,O))|ordered_by(O,P,Q)))))),
% 0.19/0.62 inference(pre_NNF_transformation,[status(thm)],[f19])).
% 0.19/0.62 fof(f133,plain,(
% 0.19/0.62 ![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))))))),
% 0.19/0.62 inference(NNF_transformation,[status(thm)],[f132])).
% 0.19/0.62 fof(f134,plain,(
% 0.19/0.62 (![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))))))),
% 0.19/0.62 inference(miniscoping,[status(thm)],[f133])).
% 0.19/0.62 fof(f135,plain,(
% 0.19/0.62 (![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))))))),
% 0.19/0.62 inference(skolemize,[status(esa),new_symbols(skolem,[sK14_skl]),skolemize(Q,sK14_skl(O,P))],[f134])).
% 0.19/0.62 fof(f137,plain,(
% 0.19/0.62 ![X0,X1,X2]: (~start_point(X0,X1)|X0=X2|~incident_o(X2,X1)|ordered_by(X1,X0,X2))),
% 0.19/0.62 inference(cnf_transformation,[status(thm)],[f135])).
% 0.19/0.62 fof(f153,plain,(
% 0.19/0.62 ![O]: ?[C]: (open(C)&(![P]: ((~incident_o(P,O)|incident_c(P,C))&(incident_o(P,O)|~incident_c(P,C)))))),
% 0.19/0.62 inference(NNF_transformation,[status(thm)],[f22])).
% 0.19/0.62 fof(f154,plain,(
% 0.19/0.62 ![O]: ?[C]: (open(C)&((![P]: (~incident_o(P,O)|incident_c(P,C)))&(![P]: (incident_o(P,O)|~incident_c(P,C)))))),
% 0.19/0.62 inference(miniscoping,[status(thm)],[f153])).
% 0.19/0.62 fof(f155,plain,(
% 0.19/0.62 ![O]: (open(sK16_skl(O))&((![P]: (~incident_o(P,O)|incident_c(P,sK16_skl(O))))&(![P]: (incident_o(P,O)|~incident_c(P,sK16_skl(O))))))),
% 0.19/0.62 inference(skolemize,[status(esa),new_symbols(skolem,[sK16_skl]),skolemize(C,sK16_skl(O))],[f154])).
% 0.19/0.62 fof(f156,plain,(
% 0.19/0.62 ![X0]: (open(sK16_skl(X0)))),
% 0.19/0.62 inference(cnf_transformation,[status(thm)],[f155])).
% 0.19/0.62 fof(f158,plain,(
% 0.19/0.62 ![X0,X1]: (incident_o(X0,X1)|~incident_c(X0,sK16_skl(X1)))),
% 0.19/0.62 inference(cnf_transformation,[status(thm)],[f155])).
% 0.19/0.62 fof(f167,plain,(
% 0.19/0.62 ![O]: start_point(sK19_skl(O),O)),
% 0.19/0.62 inference(skolemize,[status(esa),new_symbols(skolem,[sK19_skl]),skolemize(P,sK19_skl(O))],[f24])).
% 0.19/0.62 fof(f168,plain,(
% 0.19/0.62 ![X0]: (start_point(sK19_skl(X0),X0))),
% 0.19/0.62 inference(cnf_transformation,[status(thm)],[f167])).
% 0.19/0.62 fof(f188,plain,(
% 0.19/0.62 (?[O]: ![P,Q]: (~ordered_by(O,P,Q)|P=Q))),
% 0.19/0.62 inference(pre_NNF_transformation,[status(thm)],[f29])).
% 0.19/0.62 fof(f189,plain,(
% 0.19/0.62 ![P,Q]: (~ordered_by(sK24_skl,P,Q)|P=Q)),
% 0.19/0.62 inference(skolemize,[status(esa),new_symbols(skolem,[sK24_skl]),skolemize(O,sK24_skl)],[f188])).
% 0.19/0.62 fof(f190,plain,(
% 0.19/0.62 ![X0,X1]: (~ordered_by(sK24_skl,X0,X1)|X0=X1)),
% 0.19/0.62 inference(cnf_transformation,[status(thm)],[f189])).
% 0.19/0.62 fof(f194,plain,(
% 0.19/0.62 ![X0]: (incident_c(sK7_skl(X0),X0))),
% 0.19/0.62 inference(resolution,[status(thm)],[f60,f92])).
% 0.19/0.62 fof(f195,plain,(
% 0.19/0.62 ![X0]: (~end_point(sK7_skl(X0),X0))),
% 0.19/0.62 inference(resolution,[status(thm)],[f61,f92])).
% 0.19/0.62 fof(f198,plain,(
% 0.19/0.62 ![X0]: (end_point(sK6_skl(sK16_skl(X0)),sK16_skl(X0)))),
% 0.19/0.62 inference(resolution,[status(thm)],[f83,f156])).
% 0.19/0.62 fof(f203,plain,(
% 0.19/0.62 ![X0]: (incident_o(sK7_skl(sK16_skl(X0)),X0))),
% 0.19/0.62 inference(resolution,[status(thm)],[f158,f194])).
% 0.19/0.62 fof(f210,plain,(
% 0.19/0.62 ![X0]: (incident_c(sK6_skl(sK16_skl(X0)),sK16_skl(X0)))),
% 0.19/0.62 inference(resolution,[status(thm)],[f198,f50])).
% 0.19/0.62 fof(f211,plain,(
% 0.19/0.62 ![X0]: (incident_o(sK6_skl(sK16_skl(X0)),X0))),
% 0.19/0.62 inference(resolution,[status(thm)],[f210,f158])).
% 0.19/0.63 fof(f215,plain,(
% 0.19/0.63 ![X0,X1]: (sK19_skl(X0)=X1|~incident_o(X1,X0)|ordered_by(X0,sK19_skl(X0),X1))),
% 0.19/0.63 inference(resolution,[status(thm)],[f137,f168])).
% 0.19/0.63 fof(f220,plain,(
% 0.19/0.63 ![X0]: (sK19_skl(X0)=sK6_skl(sK16_skl(X0))|ordered_by(X0,sK19_skl(X0),sK6_skl(sK16_skl(X0))))),
% 0.19/0.63 inference(resolution,[status(thm)],[f215,f211])).
% 0.19/0.63 fof(f221,plain,(
% 0.19/0.63 ![X0]: (sK19_skl(X0)=sK7_skl(sK16_skl(X0))|ordered_by(X0,sK19_skl(X0),sK7_skl(sK16_skl(X0))))),
% 0.19/0.63 inference(resolution,[status(thm)],[f215,f203])).
% 0.19/0.63 fof(f232,plain,(
% 0.19/0.63 sK19_skl(sK24_skl)=sK6_skl(sK16_skl(sK24_skl))|sK19_skl(sK24_skl)=sK6_skl(sK16_skl(sK24_skl))),
% 0.19/0.63 inference(resolution,[status(thm)],[f220,f190])).
% 0.19/0.63 fof(f235,plain,(
% 0.19/0.63 sK19_skl(sK24_skl)=sK6_skl(sK16_skl(sK24_skl))),
% 0.19/0.63 inference(duplicate_literals_removal,[status(thm)],[f232])).
% 0.19/0.63 fof(f239,plain,(
% 0.19/0.63 end_point(sK19_skl(sK24_skl),sK16_skl(sK24_skl))),
% 0.19/0.63 inference(paramodulation,[status(thm)],[f235,f198])).
% 0.19/0.63 fof(f240,plain,(
% 0.19/0.63 sK19_skl(sK24_skl)=sK7_skl(sK16_skl(sK24_skl))|sK19_skl(sK24_skl)=sK7_skl(sK16_skl(sK24_skl))),
% 0.19/0.63 inference(resolution,[status(thm)],[f221,f190])).
% 0.19/0.63 fof(f243,plain,(
% 0.19/0.63 sK19_skl(sK24_skl)=sK7_skl(sK16_skl(sK24_skl))),
% 0.19/0.63 inference(duplicate_literals_removal,[status(thm)],[f240])).
% 0.19/0.63 fof(f246,plain,(
% 0.19/0.63 ~end_point(sK19_skl(sK24_skl),sK16_skl(sK24_skl))),
% 0.19/0.63 inference(paramodulation,[status(thm)],[f243,f195])).
% 0.19/0.63 fof(f249,plain,(
% 0.19/0.63 $false),
% 0.19/0.63 inference(forward_subsumption_resolution,[status(thm)],[f246,f239])).
% 0.19/0.63 % SZS output end CNFRefutation for theBenchmark.p
% 0.43/0.66 % Elapsed time: 0.192879 seconds
% 0.43/0.66 % CPU time: 1.054792 seconds
% 0.43/0.66 % Total memory used: 90.946 MB
% 0.43/0.66 % Net memory used: 89.908 MB
%------------------------------------------------------------------------------