%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : PRO009+2 : TPTP v9.3.1. Released v4.0.0.
% 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 01:59:23 PM UTC 2026
% Result : Theorem 0.61s 0.71s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PRO009+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n003.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 03:43:46 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.61/0.71 % Refutation found
% 0.61/0.71 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.61/0.71 % SZS output start CNFRefutation for theBenchmark
% 0.61/0.71 fof(f1,axiom,(
% 0.61/0.71 (! [X0,X1,X2,X3] :( ( min_precedes(X0,X1,X3)& min_precedes(X1,X2,X3) )=> min_precedes(X0,X2,X3) ) )),
% 0.61/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.61/0.71 fof(f5,axiom,(
% 0.61/0.71 (! [X15,X16,X17] :( next_subocc(X15,X16,X17)<=> ( min_precedes(X15,X16,X17)& ~ (? [X18] :( min_precedes(X15,X18,X17)& min_precedes(X18,X16,X17) ) )) ) )),
% 0.61/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.61/0.71 fof(f33,axiom,(
% 0.61/0.71 (! [X95] :( occurrence_of(X95,tptp0)=> (? [X96,X97,X98] :( occurrence_of(X96,tptp3)& root_occ(X96,X95)& occurrence_of(X97,tptp4)& next_subocc(X96,X97,tptp0)& ( occurrence_of(X98,tptp2)| occurrence_of(X98,tptp1) )& next_subocc(X97,X98,tptp0)& leaf_occ(X98,X95) ) )) )),
% 0.61/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.61/0.71 fof(f46,conjecture,(
% 0.61/0.71 (! [X99] :( occurrence_of(X99,tptp0)=> (? [X100,X101] :( occurrence_of(X100,tptp3)& root_occ(X100,X99)& ( occurrence_of(X101,tptp2)| occurrence_of(X101,tptp1) )& min_precedes(X100,X101,tptp0)& leaf_occ(X101,X99) ) )) )),
% 0.61/0.71 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.61/0.71 fof(f47,negated_conjecture,(
% 0.61/0.71 ~((! [X99] :( occurrence_of(X99,tptp0)=> (? [X100,X101] :( occurrence_of(X100,tptp3)& root_occ(X100,X99)& ( occurrence_of(X101,tptp2)| occurrence_of(X101,tptp1) )& min_precedes(X100,X101,tptp0)& leaf_occ(X101,X99) ) )) ))),
% 0.61/0.71 inference(negated_conjecture,[status(cth)],[f46])).
% 0.61/0.71 fof(f48,plain,(
% 0.61/0.71 ![X0,X1,X2,X3]: ((~min_precedes(X0,X1,X3)|~min_precedes(X1,X2,X3))|min_precedes(X0,X2,X3))),
% 0.61/0.71 inference(pre_NNF_transformation,[status(thm)],[f1])).
% 0.61/0.71 fof(f49,plain,(
% 0.61/0.71 ![X0,X2,X3]: ((![X1]: (~min_precedes(X0,X1,X3)|~min_precedes(X1,X2,X3)))|min_precedes(X0,X2,X3))),
% 0.61/0.71 inference(miniscoping,[status(thm)],[f48])).
% 0.61/0.71 fof(f50,plain,(
% 0.61/0.71 ![X0,X1,X2,X3]: (~min_precedes(X0,X1,X2)|~min_precedes(X1,X3,X2)|min_precedes(X0,X3,X2))),
% 0.61/0.71 inference(cnf_transformation,[status(thm)],[f49])).
% 0.61/0.71 fof(f60,plain,(
% 0.61/0.71 ![X15,X16,X17]: (next_subocc(X15,X16,X17)<=>(min_precedes(X15,X16,X17)&(![X18]: (~min_precedes(X15,X18,X17)|~min_precedes(X18,X16,X17)))))),
% 0.61/0.71 inference(pre_NNF_transformation,[status(thm)],[f5])).
% 0.61/0.71 fof(f61,plain,(
% 0.61/0.71 ![X15,X16,X17]: ((~next_subocc(X15,X16,X17)|(min_precedes(X15,X16,X17)&(![X18]: (~min_precedes(X15,X18,X17)|~min_precedes(X18,X16,X17)))))&(next_subocc(X15,X16,X17)|(~min_precedes(X15,X16,X17)|(?[X18]: (min_precedes(X15,X18,X17)&min_precedes(X18,X16,X17))))))),
% 0.61/0.71 inference(NNF_transformation,[status(thm)],[f60])).
% 0.61/0.71 fof(f62,plain,(
% 0.61/0.71 (![X15,X16,X17]: (~next_subocc(X15,X16,X17)|(min_precedes(X15,X16,X17)&(![X18]: (~min_precedes(X15,X18,X17)|~min_precedes(X18,X16,X17))))))&(![X15,X16,X17]: (next_subocc(X15,X16,X17)|(~min_precedes(X15,X16,X17)|(?[X18]: (min_precedes(X15,X18,X17)&min_precedes(X18,X16,X17))))))),
% 0.61/0.71 inference(miniscoping,[status(thm)],[f61])).
% 0.61/0.71 fof(f63,plain,(
% 0.61/0.71 (![X15,X16,X17]: (~next_subocc(X15,X16,X17)|(min_precedes(X15,X16,X17)&(![X18]: (~min_precedes(X15,X18,X17)|~min_precedes(X18,X16,X17))))))&(![X15,X16,X17]: (next_subocc(X15,X16,X17)|(~min_precedes(X15,X16,X17)|(min_precedes(X15,sK0_skl(X17,X16,X15),X17)&min_precedes(sK0_skl(X17,X16,X15),X16,X17)))))),
% 0.61/0.71 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X18,sK0_skl(X17,X16,X15))],[f62])).
% 0.61/0.71 fof(f64,plain,(
% 0.61/0.71 ![X0,X1,X2]: (~next_subocc(X0,X1,X2)|min_precedes(X0,X1,X2))),
% 0.61/0.71 inference(cnf_transformation,[status(thm)],[f63])).
% 0.61/0.71 fof(f177,plain,(
% 0.61/0.71 ![X95]: (~occurrence_of(X95,tptp0)|(?[X96,X97,X98]: ((((((occurrence_of(X96,tptp3)&root_occ(X96,X95))&occurrence_of(X97,tptp4))&next_subocc(X96,X97,tptp0))&(occurrence_of(X98,tptp2)|occurrence_of(X98,tptp1)))&next_subocc(X97,X98,tptp0))&leaf_occ(X98,X95))))),
% 0.61/0.71 inference(pre_NNF_transformation,[status(thm)],[f33])).
% 0.61/0.71 fof(f178,plain,(
% 0.61/0.71 ![X95]: (~occurrence_of(X95,tptp0)|(?[X98]: ((?[X97]: (((?[X96]: (((occurrence_of(X96,tptp3)&root_occ(X96,X95))&occurrence_of(X97,tptp4))&next_subocc(X96,X97,tptp0)))&(occurrence_of(X98,tptp2)|occurrence_of(X98,tptp1)))&next_subocc(X97,X98,tptp0)))&leaf_occ(X98,X95))))),
% 0.61/0.71 inference(miniscoping,[status(thm)],[f177])).
% 0.61/0.71 fof(f179,plain,(
% 0.61/0.71 ![X95]: (~occurrence_of(X95,tptp0)|((((((occurrence_of(sK16_skl(X95),tptp3)&root_occ(sK16_skl(X95),X95))&occurrence_of(sK15_skl(X95),tptp4))&next_subocc(sK16_skl(X95),sK15_skl(X95),tptp0))&(occurrence_of(sK14_skl(X95),tptp2)|occurrence_of(sK14_skl(X95),tptp1)))&next_subocc(sK15_skl(X95),sK14_skl(X95),tptp0))&leaf_occ(sK14_skl(X95),X95)))),
% 0.61/0.71 inference(skolemize,[status(esa),new_symbols(skolem,[sK14_skl,sK15_skl,sK16_skl]),skolemize(X98,sK14_skl(X95)),skolemize(X97,sK15_skl(X95)),skolemize(X96,sK16_skl(X95))],[f178])).
% 0.61/0.71 fof(f180,plain,(
% 0.61/0.71 ![X0]: (~occurrence_of(X0,tptp0)|occurrence_of(sK16_skl(X0),tptp3))),
% 0.61/0.71 inference(cnf_transformation,[status(thm)],[f179])).
% 0.61/0.71 fof(f181,plain,(
% 0.61/0.71 ![X0]: (~occurrence_of(X0,tptp0)|root_occ(sK16_skl(X0),X0))),
% 0.61/0.71 inference(cnf_transformation,[status(thm)],[f179])).
% 0.61/0.71 fof(f183,plain,(
% 0.61/0.71 ![X0]: (~occurrence_of(X0,tptp0)|next_subocc(sK16_skl(X0),sK15_skl(X0),tptp0))),
% 0.61/0.71 inference(cnf_transformation,[status(thm)],[f179])).
% 0.61/0.71 fof(f184,plain,(
% 0.61/0.71 ![X0]: (~occurrence_of(X0,tptp0)|occurrence_of(sK14_skl(X0),tptp2)|occurrence_of(sK14_skl(X0),tptp1))),
% 0.61/0.71 inference(cnf_transformation,[status(thm)],[f179])).
% 0.61/0.71 fof(f185,plain,(
% 0.61/0.71 ![X0]: (~occurrence_of(X0,tptp0)|next_subocc(sK15_skl(X0),sK14_skl(X0),tptp0))),
% 0.61/0.71 inference(cnf_transformation,[status(thm)],[f179])).
% 0.61/0.71 fof(f186,plain,(
% 0.61/0.71 ![X0]: (~occurrence_of(X0,tptp0)|leaf_occ(sK14_skl(X0),X0))),
% 0.61/0.71 inference(cnf_transformation,[status(thm)],[f179])).
% 0.61/0.71 fof(f199,plain,(
% 0.61/0.71 (?[X99]: (occurrence_of(X99,tptp0)&(![X100,X101]: ((((~occurrence_of(X100,tptp3)|~root_occ(X100,X99))|(~occurrence_of(X101,tptp2)&~occurrence_of(X101,tptp1)))|~min_precedes(X100,X101,tptp0))|~leaf_occ(X101,X99)))))),
% 0.61/0.71 inference(pre_NNF_transformation,[status(thm)],[f47])).
% 0.61/0.71 fof(f200,plain,(
% 0.61/0.71 ?[X99]: (occurrence_of(X99,tptp0)&(![X101]: ((![X100]: (((~occurrence_of(X100,tptp3)|~root_occ(X100,X99))|(~occurrence_of(X101,tptp2)&~occurrence_of(X101,tptp1)))|~min_precedes(X100,X101,tptp0)))|~leaf_occ(X101,X99))))),
% 0.61/0.71 inference(miniscoping,[status(thm)],[f199])).
% 0.61/0.71 fof(f201,plain,(
% 0.61/0.71 (occurrence_of(sK17_skl,tptp0)&(![X101]: ((![X100]: (((~occurrence_of(X100,tptp3)|~root_occ(X100,sK17_skl))|(~occurrence_of(X101,tptp2)&~occurrence_of(X101,tptp1)))|~min_precedes(X100,X101,tptp0)))|~leaf_occ(X101,sK17_skl))))),
% 0.61/0.71 inference(skolemize,[status(esa),new_symbols(skolem,[sK17_skl]),skolemize(X99,sK17_skl)],[f200])).
% 0.61/0.71 fof(f202,plain,(
% 0.61/0.71 occurrence_of(sK17_skl,tptp0)),
% 0.61/0.71 inference(cnf_transformation,[status(thm)],[f201])).
% 0.61/0.71 fof(f203,plain,(
% 0.61/0.71 ![X0,X1]: (~occurrence_of(X0,tptp3)|~root_occ(X0,sK17_skl)|~occurrence_of(X1,tptp2)|~min_precedes(X0,X1,tptp0)|~leaf_occ(X1,sK17_skl))),
% 0.61/0.71 inference(cnf_transformation,[status(thm)],[f201])).
% 0.61/0.71 fof(f204,plain,(
% 0.61/0.71 ![X0,X1]: (~occurrence_of(X0,tptp3)|~root_occ(X0,sK17_skl)|~occurrence_of(X1,tptp1)|~min_precedes(X0,X1,tptp0)|~leaf_occ(X1,sK17_skl))),
% 0.61/0.71 inference(cnf_transformation,[status(thm)],[f201])).
% 0.61/0.71 fof(f334,plain,(
% 0.61/0.71 root_occ(sK16_skl(sK17_skl),sK17_skl)),
% 0.61/0.71 inference(resolution,[status(thm)],[f181,f202])).
% 0.61/0.71 fof(f349,plain,(
% 0.61/0.71 leaf_occ(sK14_skl(sK17_skl),sK17_skl)),
% 0.61/0.71 inference(resolution,[status(thm)],[f186,f202])).
% 0.61/0.71 fof(f427,plain,(
% 0.61/0.71 occurrence_of(sK16_skl(sK17_skl),tptp3)),
% 0.61/0.71 inference(resolution,[status(thm)],[f180,f202])).
% 0.61/0.71 fof(f429,plain,(
% 0.61/0.71 ![X0]: (~root_occ(sK16_skl(sK17_skl),sK17_skl)|~occurrence_of(X0,tptp1)|~min_precedes(sK16_skl(sK17_skl),X0,tptp0)|~leaf_occ(X0,sK17_skl))),
% 0.61/0.71 inference(resolution,[status(thm)],[f427,f204])).
% 0.61/0.71 fof(f430,plain,(
% 0.61/0.71 ![X0]: (~root_occ(sK16_skl(sK17_skl),sK17_skl)|~occurrence_of(X0,tptp2)|~min_precedes(sK16_skl(sK17_skl),X0,tptp0)|~leaf_occ(X0,sK17_skl))),
% 0.61/0.71 inference(resolution,[status(thm)],[f427,f203])).
% 0.61/0.71 fof(f441,plain,(
% 0.61/0.71 ![X0]: (~occurrence_of(X0,tptp1)|~min_precedes(sK16_skl(sK17_skl),X0,tptp0)|~leaf_occ(X0,sK17_skl))),
% 0.61/0.71 inference(forward_subsumption_resolution,[status(thm)],[f429,f334])).
% 0.61/0.71 fof(f442,plain,(
% 0.61/0.71 ![X0]: (~occurrence_of(X0,tptp2)|~min_precedes(sK16_skl(sK17_skl),X0,tptp0)|~leaf_occ(X0,sK17_skl))),
% 0.61/0.71 inference(forward_subsumption_resolution,[status(thm)],[f430,f334])).
% 0.61/0.71 fof(f709,plain,(
% 0.61/0.71 next_subocc(sK16_skl(sK17_skl),sK15_skl(sK17_skl),tptp0)),
% 0.61/0.71 inference(resolution,[status(thm)],[f183,f202])).
% 0.61/0.71 fof(f712,plain,(
% 0.61/0.71 occurrence_of(sK14_skl(sK17_skl),tptp2)|occurrence_of(sK14_skl(sK17_skl),tptp1)),
% 0.61/0.71 inference(resolution,[status(thm)],[f184,f202])).
% 0.61/0.71 fof(f715,plain,(
% 0.61/0.71 next_subocc(sK15_skl(sK17_skl),sK14_skl(sK17_skl),tptp0)),
% 0.61/0.71 inference(resolution,[status(thm)],[f185,f202])).
% 0.61/0.71 fof(f716,plain,(
% 0.61/0.71 min_precedes(sK16_skl(sK17_skl),sK15_skl(sK17_skl),tptp0)),
% 0.61/0.71 inference(resolution,[status(thm)],[f709,f64])).
% 0.61/0.71 fof(f719,plain,(
% 0.61/0.71 min_precedes(sK15_skl(sK17_skl),sK14_skl(sK17_skl),tptp0)),
% 0.61/0.71 inference(resolution,[status(thm)],[f715,f64])).
% 0.61/0.71 fof(f951,plain,(
% 0.61/0.71 ![X0]: (~min_precedes(X0,sK15_skl(sK17_skl),tptp0)|min_precedes(X0,sK14_skl(sK17_skl),tptp0))),
% 0.61/0.71 inference(resolution,[status(thm)],[f719,f50])).
% 0.61/0.71 fof(f1545,plain,(
% 0.61/0.71 min_precedes(sK16_skl(sK17_skl),sK14_skl(sK17_skl),tptp0)),
% 0.61/0.71 inference(resolution,[status(thm)],[f951,f716])).
% 0.61/0.71 fof(f1547,plain,(
% 0.61/0.71 ~occurrence_of(sK14_skl(sK17_skl),tptp2)|~leaf_occ(sK14_skl(sK17_skl),sK17_skl)),
% 0.61/0.71 inference(resolution,[status(thm)],[f1545,f442])).
% 0.61/0.71 fof(f1548,plain,(
% 0.61/0.71 ~occurrence_of(sK14_skl(sK17_skl),tptp1)|~leaf_occ(sK14_skl(sK17_skl),sK17_skl)),
% 0.61/0.71 inference(resolution,[status(thm)],[f1545,f441])).
% 0.61/0.71 fof(f1656,plain,(
% 0.61/0.71 ~occurrence_of(sK14_skl(sK17_skl),tptp2)),
% 0.61/0.71 inference(forward_subsumption_resolution,[status(thm)],[f1547,f349])).
% 0.61/0.71 fof(f1657,plain,(
% 0.61/0.71 ~occurrence_of(sK14_skl(sK17_skl),tptp1)),
% 0.61/0.71 inference(forward_subsumption_resolution,[status(thm)],[f1548,f349])).
% 0.61/0.71 fof(f1672,plain,(
% 0.61/0.71 occurrence_of(sK14_skl(sK17_skl),tptp1)),
% 0.61/0.71 inference(backward_subsumption_resolution,[status(thm)],[f712,f1656])).
% 0.61/0.71 fof(f1677,plain,(
% 0.61/0.71 $false),
% 0.61/0.71 inference(forward_subsumption_resolution,[status(thm)],[f1672,f1657])).
% 0.61/0.71 % SZS output end CNFRefutation for theBenchmark.p
% 0.37/0.73 % Elapsed time: 0.350624 seconds
% 0.37/0.73 % CPU time: 2.156723 seconds
% 0.37/0.73 % Total memory used: 100.510 MB
% 0.37/0.73 % Net memory used: 99.531 MB
%------------------------------------------------------------------------------