%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SWC355+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 : n016.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 02:42:14 PM UTC 2026
% Result : Theorem 18.21s 2.77s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC355+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
% 0.10/0.35 % Computer : n016.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
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Mon Sep 21 08:23:07 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.14/0.37 % Drodi V4.1.1
% 18.21/2.77 % Refutation found
% 18.21/2.77 % SZS status Theorem for theBenchmark: Theorem is valid
% 18.21/2.77 % SZS output start CNFRefutation for theBenchmark
% 18.21/2.77 fof(f7,axiom,(
% 18.21/2.77 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> ( segmentP(U,V)<=> (? [W] :( ssList(W)& (? [X] :( ssList(X)& app(app(W,V),X) = U ) )) )) ) )) )),
% 18.21/2.77 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 18.21/2.77 fof(f16,axiom,(
% 18.21/2.77 (! [U] :( ssList(U)=> (! [V] :( ssItem(V)=> ssList(cons(V,U)) ) )) )),
% 18.21/2.77 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 18.21/2.77 fof(f17,axiom,(
% 18.21/2.77 ssList(nil) ),
% 18.21/2.77 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 18.21/2.77 fof(f26,axiom,(
% 18.21/2.77 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> ssList(app(U,V)) ) )) )),
% 18.21/2.77 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 18.21/2.77 fof(f28,axiom,(
% 18.21/2.77 (! [U] :( ssList(U)=> app(nil,U) = U ) )),
% 18.21/2.77 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 18.21/2.77 fof(f96,conjecture,(
% 18.21/2.77 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> (! [X] :( ssList(X)=> ( V != X| U != W| ( ( ~ neq(V,nil)| (! [Y] :( ssItem(Y)=> app(W,cons(Y,nil)) != X ))| segmentP(V,U) )& ( ~ neq(V,nil)| neq(X,nil) ) ) ) ) )) )) )) )),
% 18.21/2.77 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 18.21/2.77 fof(f97,negated_conjecture,(
% 18.21/2.77 ~((! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> (! [X] :( ssList(X)=> ( V != X| U != W| ( ( ~ neq(V,nil)| (! [Y] :( ssItem(Y)=> app(W,cons(Y,nil)) != X ))| segmentP(V,U) )& ( ~ neq(V,nil)| neq(X,nil) ) ) ) ) )) )) )) ))),
% 18.21/2.77 inference(negated_conjecture,[status(cth)],[f96])).
% 18.21/2.77 fof(f131,plain,(
% 18.21/2.77 ![U]: (~ssList(U)|(![V]: (~ssList(V)|(segmentP(U,V)<=>(?[W]: (ssList(W)&(?[X]: (ssList(X)&app(app(W,V),X)=U))))))))),
% 18.21/2.77 inference(pre_NNF_transformation,[status(thm)],[f7])).
% 18.21/2.77 fof(f132,plain,(
% 18.21/2.77 ![U]: (~ssList(U)|(![V]: (~ssList(V)|((~segmentP(U,V)|(?[W]: (ssList(W)&(?[X]: (ssList(X)&app(app(W,V),X)=U)))))&(segmentP(U,V)|(![W]: (~ssList(W)|(![X]: (~ssList(X)|~app(app(W,V),X)=U)))))))))),
% 18.21/2.77 inference(NNF_transformation,[status(thm)],[f131])).
% 18.21/2.77 fof(f133,plain,(
% 18.21/2.77 ![U]: (~ssList(U)|(![V]: (~ssList(V)|((~segmentP(U,V)|(ssList(sK7_skl(V,U))&(ssList(sK8_skl(V,U))&app(app(sK7_skl(V,U),V),sK8_skl(V,U))=U)))&(segmentP(U,V)|(![W]: (~ssList(W)|(![X]: (~ssList(X)|~app(app(W,V),X)=U)))))))))),
% 18.21/2.77 inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl,sK8_skl]),skolemize(W,sK7_skl(V,U)),skolemize(X,sK8_skl(V,U))],[f132])).
% 18.21/2.77 fof(f137,plain,(
% 18.21/2.77 ![X0,X1,X2,X3]: (~ssList(X0)|~ssList(X1)|segmentP(X0,X1)|~ssList(X2)|~ssList(X3)|~app(app(X2,X1),X3)=X0)),
% 18.21/2.77 inference(cnf_transformation,[status(thm)],[f133])).
% 18.21/2.77 fof(f221,plain,(
% 18.21/2.77 ![U]: (~ssList(U)|(![V]: (~ssItem(V)|ssList(cons(V,U)))))),
% 18.21/2.77 inference(pre_NNF_transformation,[status(thm)],[f16])).
% 18.21/2.77 fof(f222,plain,(
% 18.21/2.77 ![X0,X1]: (~ssList(X0)|~ssItem(X1)|ssList(cons(X1,X0)))),
% 18.21/2.77 inference(cnf_transformation,[status(thm)],[f221])).
% 18.21/2.77 fof(f223,plain,(
% 18.21/2.77 ssList(nil)),
% 18.21/2.77 inference(cnf_transformation,[status(thm)],[f17])).
% 18.21/2.77 fof(f244,plain,(
% 18.21/2.77 ![U]: (~ssList(U)|(![V]: (~ssList(V)|ssList(app(U,V)))))),
% 18.21/2.77 inference(pre_NNF_transformation,[status(thm)],[f26])).
% 18.21/2.77 fof(f245,plain,(
% 18.21/2.77 ![X0,X1]: (~ssList(X0)|~ssList(X1)|ssList(app(X0,X1)))),
% 18.21/2.77 inference(cnf_transformation,[status(thm)],[f244])).
% 18.21/2.77 fof(f248,plain,(
% 18.21/2.77 ![U]: (~ssList(U)|app(nil,U)=U)),
% 18.21/2.77 inference(pre_NNF_transformation,[status(thm)],[f28])).
% 18.21/2.77 fof(f249,plain,(
% 18.21/2.77 ![X0]: (~ssList(X0)|app(nil,X0)=X0)),
% 18.21/2.77 inference(cnf_transformation,[status(thm)],[f248])).
% 18.21/2.77 fof(f415,plain,(
% 18.21/2.77 (?[U]: (ssList(U)&(?[V]: (ssList(V)&(?[W]: (ssList(W)&(?[X]: (ssList(X)&((V=X&U=W)&(((neq(V,nil)&(?[Y]: (ssItem(Y)&app(W,cons(Y,nil))=X)))&~segmentP(V,U))|(neq(V,nil)&~neq(X,nil))))))))))))),
% 18.21/2.77 inference(pre_NNF_transformation,[status(thm)],[f97])).
% 18.21/2.77 fof(f416,definition,(
% 18.21/2.77 ![U,V,W,X]: (sP0_prd(X,W,V,U)<=>((neq(V,nil)&(?[Y]: (ssItem(Y)&app(W,cons(Y,nil))=X)))&~segmentP(V,U)))),
% 18.21/2.77 introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 18.21/2.77 fof(f417,plain,(
% 18.21/2.77 ?[U]: (ssList(U)&(?[V]: (ssList(V)&(?[W]: (ssList(W)&(?[X]: (ssList(X)&((V=X&U=W)&(sP0_prd(X,W,V,U)|(neq(V,nil)&~neq(X,nil)))))))))))),
% 18.21/2.77 inference(formula_renaming,[status(thm)],[f415,f416])).
% 18.21/2.77 fof(f418,plain,(
% 18.21/2.77 (ssList(sK47_skl)&(ssList(sK48_skl)&(ssList(sK49_skl)&(ssList(sK50_skl)&((sK48_skl=sK50_skl&sK47_skl=sK49_skl)&(sP0_prd(sK50_skl,sK49_skl,sK48_skl,sK47_skl)|(neq(sK48_skl,nil)&~neq(sK50_skl,nil))))))))),
% 18.21/2.77 inference(skolemize,[status(esa),new_symbols(skolem,[sK47_skl,sK48_skl,sK49_skl,sK50_skl]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl)],[f417])).
% 18.21/2.77 fof(f419,plain,(
% 18.21/2.77 ssList(sK47_skl)),
% 18.21/2.77 inference(cnf_transformation,[status(thm)],[f418])).
% 18.21/2.77 fof(f423,plain,(
% 18.21/2.77 sK48_skl=sK50_skl),
% 18.21/2.77 inference(cnf_transformation,[status(thm)],[f418])).
% 18.21/2.77 fof(f424,plain,(
% 18.21/2.77 sK47_skl=sK49_skl),
% 18.21/2.77 inference(cnf_transformation,[status(thm)],[f418])).
% 18.21/2.77 fof(f425,plain,(
% 18.21/2.77 sP0_prd(sK50_skl,sK49_skl,sK48_skl,sK47_skl)|neq(sK48_skl,nil)),
% 18.21/2.77 inference(cnf_transformation,[status(thm)],[f418])).
% 18.21/2.77 fof(f426,plain,(
% 18.21/2.77 sP0_prd(sK50_skl,sK49_skl,sK48_skl,sK47_skl)|~neq(sK50_skl,nil)),
% 18.21/2.77 inference(cnf_transformation,[status(thm)],[f418])).
% 18.21/2.77 fof(f427,plain,(
% 18.21/2.77 ![U,V,W,X]: ((~sP0_prd(X,W,V,U)|((neq(V,nil)&(?[Y]: (ssItem(Y)&app(W,cons(Y,nil))=X)))&~segmentP(V,U)))&(sP0_prd(X,W,V,U)|((~neq(V,nil)|(![Y]: (~ssItem(Y)|~app(W,cons(Y,nil))=X)))|segmentP(V,U))))),
% 18.21/2.77 inference(NNF_transformation,[status(thm)],[f416])).
% 18.21/2.77 fof(f428,plain,(
% 18.21/2.77 (![U,V,W,X]: (~sP0_prd(X,W,V,U)|((neq(V,nil)&(?[Y]: (ssItem(Y)&app(W,cons(Y,nil))=X)))&~segmentP(V,U))))&(![U,V,W,X]: (sP0_prd(X,W,V,U)|((~neq(V,nil)|(![Y]: (~ssItem(Y)|~app(W,cons(Y,nil))=X)))|segmentP(V,U))))),
% 18.21/2.77 inference(miniscoping,[status(thm)],[f427])).
% 18.21/2.77 fof(f429,plain,(
% 18.21/2.77 (![U,V,W,X]: (~sP0_prd(X,W,V,U)|((neq(V,nil)&(ssItem(sK51_skl(X,W,V,U))&app(W,cons(sK51_skl(X,W,V,U),nil))=X))&~segmentP(V,U))))&(![U,V,W,X]: (sP0_prd(X,W,V,U)|((~neq(V,nil)|(![Y]: (~ssItem(Y)|~app(W,cons(Y,nil))=X)))|segmentP(V,U))))),
% 18.21/2.77 inference(skolemize,[status(esa),new_symbols(skolem,[sK51_skl]),skolemize(Y,sK51_skl(X,W,V,U))],[f428])).
% 18.21/2.77 fof(f431,plain,(
% 18.21/2.77 ![X0,X1,X2,X3]: (~sP0_prd(X0,X1,X2,X3)|ssItem(sK51_skl(X0,X1,X2,X3)))),
% 18.21/2.77 inference(cnf_transformation,[status(thm)],[f429])).
% 18.21/2.77 fof(f432,plain,(
% 18.21/2.77 ![X0,X1,X2,X3]: (~sP0_prd(X0,X1,X2,X3)|app(X1,cons(sK51_skl(X0,X1,X2,X3),nil))=X0)),
% 18.21/2.77 inference(cnf_transformation,[status(thm)],[f429])).
% 18.21/2.77 fof(f433,plain,(
% 18.21/2.77 ![X0,X1,X2,X3]: (~sP0_prd(X0,X1,X2,X3)|~segmentP(X2,X3))),
% 18.21/2.77 inference(cnf_transformation,[status(thm)],[f429])).
% 18.21/2.77 fof(f441,plain,(
% 18.21/2.77 ![X0,X1,X2]: (~ssList(app(app(X0,X1),X2))|~ssList(X1)|segmentP(app(app(X0,X1),X2),X1)|~ssList(X0)|~ssList(X2))),
% 18.21/2.77 inference(destructive_equality_resolution,[status(thm)],[f137])).
% 18.21/2.77 fof(f469,plain,(
% 18.21/2.77 sP0_prd(sK48_skl,sK49_skl,sK48_skl,sK47_skl)|neq(sK48_skl,nil)),
% 18.21/2.77 inference(forward_demodulation,[status(thm)],[f423,f425])).
% 18.21/2.77 fof(f470,plain,(
% 18.21/2.77 sP0_prd(sK48_skl,sK47_skl,sK48_skl,sK47_skl)|neq(sK48_skl,nil)),
% 18.21/2.77 inference(forward_demodulation,[status(thm)],[f424,f469])).
% 18.21/2.77 fof(f471,plain,(
% 18.21/2.77 sP0_prd(sK48_skl,sK49_skl,sK48_skl,sK47_skl)|~neq(sK50_skl,nil)),
% 18.21/2.77 inference(forward_demodulation,[status(thm)],[f423,f426])).
% 18.21/2.77 fof(f472,plain,(
% 18.21/2.77 sP0_prd(sK48_skl,sK47_skl,sK48_skl,sK47_skl)|~neq(sK50_skl,nil)),
% 18.21/2.77 inference(forward_demodulation,[status(thm)],[f424,f471])).
% 18.21/2.77 fof(f473,plain,(
% 18.21/2.77 sP0_prd(sK48_skl,sK47_skl,sK48_skl,sK47_skl)|~neq(sK48_skl,nil)),
% 18.21/2.77 inference(forward_demodulation,[status(thm)],[f423,f472])).
% 18.21/2.77 fof(f474,plain,(
% 18.21/2.77 sP0_prd(sK48_skl,sK47_skl,sK48_skl,sK47_skl)),
% 18.21/2.77 inference(forward_subsumption_resolution,[status(thm)],[f473,f470])).
% 18.21/2.77 fof(f477,plain,(
% 18.21/2.77 app(nil,sK47_skl)=sK47_skl),
% 18.21/2.77 inference(resolution,[status(thm)],[f249,f419])).
% 18.21/2.77 fof(f480,plain,(
% 18.21/2.77 ~segmentP(sK48_skl,sK47_skl)),
% 18.21/2.77 inference(resolution,[status(thm)],[f433,f474])).
% 18.21/2.77 fof(f488,plain,(
% 18.21/2.77 ![X0]: (~ssList(app(sK47_skl,X0))|~ssList(sK47_skl)|segmentP(app(app(nil,sK47_skl),X0),sK47_skl)|~ssList(nil)|~ssList(X0))),
% 18.21/2.77 inference(paramodulation,[status(thm)],[f477,f441])).
% 18.21/2.77 fof(f489,plain,(
% 18.21/2.77 ![X0]: (~ssList(app(sK47_skl,X0))|~ssList(sK47_skl)|segmentP(app(sK47_skl,X0),sK47_skl)|~ssList(nil)|~ssList(X0))),
% 18.21/2.77 inference(forward_demodulation,[status(thm)],[f477,f488])).
% 18.21/2.77 fof(f490,plain,(
% 18.21/2.77 ![X0]: (~ssList(sK47_skl)|segmentP(app(sK47_skl,X0),sK47_skl)|~ssList(nil)|~ssList(X0))),
% 18.21/2.77 inference(forward_subsumption_resolution,[status(thm)],[f489,f245])).
% 18.21/2.79 fof(f521,plain,(
% 18.21/2.79 ssItem(sK51_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl))),
% 18.21/2.79 inference(resolution,[status(thm)],[f431,f474])).
% 18.21/2.79 fof(f531,plain,(
% 18.21/2.79 ![X0]: (~ssList(sK47_skl)|segmentP(app(sK47_skl,X0),sK47_skl)|~ssList(X0))),
% 18.21/2.79 inference(resolution,[status(thm)],[f223,f490])).
% 18.21/2.79 fof(f538,plain,(
% 18.21/2.79 ![X0]: (~ssItem(X0)|ssList(cons(X0,nil)))),
% 18.21/2.79 inference(resolution,[status(thm)],[f223,f222])).
% 18.21/2.79 fof(f544,plain,(
% 18.21/2.79 ![X0]: (segmentP(app(sK47_skl,X0),sK47_skl)|~ssList(X0))),
% 18.21/2.79 inference(forward_subsumption_resolution,[status(thm)],[f531,f419])).
% 18.21/2.79 fof(f589,plain,(
% 18.21/2.79 app(sK47_skl,cons(sK51_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl),nil))=sK48_skl),
% 18.21/2.79 inference(resolution,[status(thm)],[f432,f474])).
% 18.21/2.79 fof(f2197,plain,(
% 18.21/2.79 ssList(cons(sK51_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl),nil))),
% 18.21/2.79 inference(resolution,[status(thm)],[f521,f538])).
% 18.21/2.79 fof(f2561,plain,(
% 18.21/2.79 segmentP(sK48_skl,sK47_skl)|~ssList(cons(sK51_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl),nil))),
% 18.21/2.79 inference(paramodulation,[status(thm)],[f589,f544])).
% 18.21/2.79 fof(f2573,plain,(
% 18.21/2.79 ~ssList(cons(sK51_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl),nil))),
% 18.21/2.79 inference(forward_subsumption_resolution,[status(thm)],[f2561,f480])).
% 18.21/2.79 fof(f2574,plain,(
% 18.21/2.79 $false),
% 18.21/2.79 inference(backward_subsumption_resolution,[status(thm)],[f2197,f2573])).
% 18.21/2.79 % SZS output end CNFRefutation for theBenchmark.p
% 6.45/2.80 % Elapsed time: 2.436818 seconds
% 6.45/2.80 % CPU time: 18.942194 seconds
% 6.45/2.80 % Total memory used: 276.569 MB
% 6.45/2.80 % Net memory used: 263.811 MB
%------------------------------------------------------------------------------