%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SWC371+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 : 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 02:42:17 PM UTC 2026
% Result : Theorem 0.13s 0.49s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC371+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
% 0.09/0.35 % Computer : n011.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 08:19:26 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(f7,axiom,(
% 0.13/0.49 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> ( segmentP(U,V)<=> (? [W] :( ssList(W)& (? [X] :( ssList(X)& app(app(W,V),X) = U ) )) )) ) )) )),
% 0.13/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.49 fof(f17,axiom,(
% 0.13/0.49 ssList(nil) ),
% 0.13/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.49 fof(f28,axiom,(
% 0.13/0.49 (! [U] :( ssList(U)=> app(nil,U) = U ) )),
% 0.13/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.49 fof(f96,conjecture,(
% 0.13/0.49 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> (! [X] :( ssList(X)=> ( V != X| U != W| (! [Y] :( ssList(Y)=> ( app(W,Y) != X| ~ totalorderedP(W)| (? [Z] :( ssItem(Z)& (? [X1] :( ssList(X1)& app(cons(Z,nil),X1) = Y& (? [X2] :( ssItem(X2)& (? [X3] :( ssList(X3)& app(X3,cons(X2,nil)) = W& leq(X2,Z) ) )) )) )) )) ))| segmentP(V,U)| ( nil != X& nil = W ) ) ) )) )) )) )),
% 0.13/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.49 fof(f97,negated_conjecture,(
% 0.13/0.49 ~((! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> (! [X] :( ssList(X)=> ( V != X| U != W| (! [Y] :( ssList(Y)=> ( app(W,Y) != X| ~ totalorderedP(W)| (? [Z] :( ssItem(Z)& (? [X1] :( ssList(X1)& app(cons(Z,nil),X1) = Y& (? [X2] :( ssItem(X2)& (? [X3] :( ssList(X3)& app(X3,cons(X2,nil)) = W& leq(X2,Z) ) )) )) )) )) ))| segmentP(V,U)| ( nil != X& nil = W ) ) ) )) )) )) ))),
% 0.13/0.49 inference(negated_conjecture,[status(cth)],[f96])).
% 0.13/0.49 fof(f131,plain,(
% 0.13/0.49 ![U]: (~ssList(U)|(![V]: (~ssList(V)|(segmentP(U,V)<=>(?[W]: (ssList(W)&(?[X]: (ssList(X)&app(app(W,V),X)=U))))))))),
% 0.13/0.49 inference(pre_NNF_transformation,[status(thm)],[f7])).
% 0.13/0.49 fof(f132,plain,(
% 0.13/0.49 ![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)))))))))),
% 0.13/0.49 inference(NNF_transformation,[status(thm)],[f131])).
% 0.13/0.49 fof(f133,plain,(
% 0.13/0.49 ![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)))))))))),
% 0.13/0.49 inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl,sK8_skl]),skolemize(W,sK7_skl(V,U)),skolemize(X,sK8_skl(V,U))],[f132])).
% 0.13/0.49 fof(f137,plain,(
% 0.13/0.49 ![X0,X1,X2,X3]: (~ssList(X0)|~ssList(X1)|segmentP(X0,X1)|~ssList(X2)|~ssList(X3)|~app(app(X2,X1),X3)=X0)),
% 0.13/0.49 inference(cnf_transformation,[status(thm)],[f133])).
% 0.13/0.49 fof(f223,plain,(
% 0.13/0.49 ssList(nil)),
% 0.13/0.49 inference(cnf_transformation,[status(thm)],[f17])).
% 0.13/0.49 fof(f248,plain,(
% 0.13/0.49 ![U]: (~ssList(U)|app(nil,U)=U)),
% 0.13/0.49 inference(pre_NNF_transformation,[status(thm)],[f28])).
% 0.13/0.49 fof(f249,plain,(
% 0.13/0.49 ![X0]: (~ssList(X0)|app(nil,X0)=X0)),
% 0.13/0.49 inference(cnf_transformation,[status(thm)],[f248])).
% 0.13/0.49 fof(f415,plain,(
% 0.13/0.49 (?[U]: (ssList(U)&(?[V]: (ssList(V)&(?[W]: (ssList(W)&(?[X]: (ssList(X)&((((V=X&U=W)&(?[Y]: (ssList(Y)&((app(W,Y)=X&totalorderedP(W))&(![Z]: (~ssItem(Z)|(![X1]: ((~ssList(X1)|~app(cons(Z,nil),X1)=Y)|(![X2]: (~ssItem(X2)|(![X3]: ((~ssList(X3)|~app(X3,cons(X2,nil))=W)|~leq(X2,Z)))))))))))))&~segmentP(V,U))&(nil=X|~nil=W))))))))))),
% 0.13/0.49 inference(pre_NNF_transformation,[status(thm)],[f97])).
% 0.13/0.49 fof(f416,plain,(
% 0.13/0.49 ?[U]: (ssList(U)&(?[V]: (ssList(V)&(?[W]: (ssList(W)&(?[X]: (ssList(X)&((((V=X&U=W)&(?[Y]: (ssList(Y)&((app(W,Y)=X&totalorderedP(W))&(![Z]: (~ssItem(Z)|((![X1]: (~ssList(X1)|~app(cons(Z,nil),X1)=Y))|(![X2]: (~ssItem(X2)|((![X3]: (~ssList(X3)|~app(X3,cons(X2,nil))=W))|~leq(X2,Z)))))))))))&~segmentP(V,U))&(nil=X|~nil=W)))))))))),
% 0.13/0.49 inference(miniscoping,[status(thm)],[f415])).
% 0.13/0.49 fof(f417,plain,(
% 0.13/0.49 (ssList(sK47_skl)&(ssList(sK48_skl)&(ssList(sK49_skl)&(ssList(sK50_skl)&((((sK48_skl=sK50_skl&sK47_skl=sK49_skl)&(ssList(sK51_skl)&((app(sK49_skl,sK51_skl)=sK50_skl&totalorderedP(sK49_skl))&(![Z]: (~ssItem(Z)|((![X1]: (~ssList(X1)|~app(cons(Z,nil),X1)=sK51_skl))|(![X2]: (~ssItem(X2)|((![X3]: (~ssList(X3)|~app(X3,cons(X2,nil))=sK49_skl))|~leq(X2,Z))))))))))&~segmentP(sK48_skl,sK47_skl))&(nil=sK50_skl|~nil=sK49_skl))))))),
% 0.13/0.49 inference(skolemize,[status(esa),new_symbols(skolem,[sK47_skl,sK48_skl,sK49_skl,sK50_skl,sK51_skl]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl),skolemize(Y,sK51_skl)],[f416])).
% 0.13/0.49 fof(f418,plain,(
% 0.13/0.49 ssList(sK47_skl)),
% 0.13/0.49 inference(cnf_transformation,[status(thm)],[f417])).
% 0.13/0.49 fof(f419,plain,(
% 0.13/0.49 ssList(sK48_skl)),
% 0.13/0.49 inference(cnf_transformation,[status(thm)],[f417])).
% 0.13/0.49 fof(f422,plain,(
% 0.13/0.49 sK48_skl=sK50_skl),
% 0.13/0.49 inference(cnf_transformation,[status(thm)],[f417])).
% 0.13/0.49 fof(f423,plain,(
% 0.13/0.49 sK47_skl=sK49_skl),
% 0.13/0.49 inference(cnf_transformation,[status(thm)],[f417])).
% 0.13/0.49 fof(f424,plain,(
% 0.13/0.49 ssList(sK51_skl)),
% 0.13/0.49 inference(cnf_transformation,[status(thm)],[f417])).
% 0.13/0.49 fof(f425,plain,(
% 0.13/0.49 app(sK49_skl,sK51_skl)=sK50_skl),
% 0.13/0.49 inference(cnf_transformation,[status(thm)],[f417])).
% 0.13/0.49 fof(f428,plain,(
% 0.13/0.49 ~segmentP(sK48_skl,sK47_skl)),
% 0.13/0.49 inference(cnf_transformation,[status(thm)],[f417])).
% 0.13/0.49 fof(f456,definition,(
% 0.13/0.49 sQ2_spl <=> (ssList(nil))),
% 0.13/0.49 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.13/0.49 fof(f458,plain,(
% 0.13/0.49 ~ssList(nil)|sQ2_spl),
% 0.13/0.49 inference(component_clause,[status(thm)],[f456])).
% 0.13/0.49 fof(f459,definition,(
% 0.13/0.49 sQ3_spl <=> (ssList(sK47_skl))),
% 0.13/0.49 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.13/0.49 fof(f461,plain,(
% 0.13/0.49 ~ssList(sK47_skl)|sQ3_spl),
% 0.13/0.49 inference(component_clause,[status(thm)],[f459])).
% 0.13/0.49 fof(f471,plain,(
% 0.13/0.49 ![X0,X1]: (~ssList(sK48_skl)|~ssList(sK47_skl)|~ssList(X0)|~ssList(X1)|~app(app(X0,sK47_skl),X1)=sK48_skl)),
% 0.13/0.49 inference(resolution,[status(thm)],[f428,f137])).
% 0.13/0.49 fof(f472,definition,(
% 0.13/0.49 sQ5_spl <=> (ssList(sK48_skl))),
% 0.13/0.49 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 0.13/0.49 fof(f474,plain,(
% 0.13/0.49 ~ssList(sK48_skl)|sQ5_spl),
% 0.13/0.49 inference(component_clause,[status(thm)],[f472])).
% 0.13/0.49 fof(f475,definition,(
% 0.13/0.49 ![X0,X1]: (sQ6_spl <=> (~ssList(X0)|~ssList(X1)|~app(app(X0,sK47_skl),X1)=sK48_skl))),
% 0.13/0.49 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.13/0.49 fof(f476,plain,(
% 0.13/0.49 ![X0,X1]: (~ssList(X0)|~ssList(X1)|~app(app(X0,sK47_skl),X1)=sK48_skl|~sQ6_spl)),
% 0.13/0.49 inference(component_clause,[status(thm)],[f475])).
% 0.13/0.49 fof(f478,plain,(
% 0.13/0.49 ~sQ5_spl|~sQ3_spl|sQ6_spl),
% 0.13/0.49 inference(split_clause,[status(thm)],[f471,f472,f459,f475])).
% 0.13/0.49 fof(f479,plain,(
% 0.13/0.49 $false|sQ3_spl),
% 0.13/0.49 inference(forward_subsumption_resolution,[status(thm)],[f461,f418])).
% 0.13/0.49 fof(f480,plain,(
% 0.13/0.49 sQ3_spl),
% 0.13/0.49 inference(contradiction_clause,[status(thm)],[f479])).
% 0.13/0.49 fof(f481,plain,(
% 0.13/0.49 $false|sQ5_spl),
% 0.13/0.49 inference(forward_subsumption_resolution,[status(thm)],[f474,f419])).
% 0.13/0.49 fof(f482,plain,(
% 0.13/0.49 sQ5_spl),
% 0.13/0.49 inference(contradiction_clause,[status(thm)],[f481])).
% 0.13/0.49 fof(f485,plain,(
% 0.13/0.49 app(sK47_skl,sK51_skl)=sK50_skl),
% 0.13/0.49 inference(forward_demodulation,[status(thm)],[f423,f425])).
% 0.13/0.49 fof(f486,plain,(
% 0.13/0.49 app(sK47_skl,sK51_skl)=sK48_skl),
% 0.13/0.49 inference(forward_demodulation,[status(thm)],[f422,f485])).
% 0.13/0.49 fof(f515,plain,(
% 0.13/0.49 app(nil,sK47_skl)=sK47_skl),
% 0.13/0.49 inference(resolution,[status(thm)],[f249,f418])).
% 0.13/0.49 fof(f517,plain,(
% 0.13/0.49 ![X0]: (~ssList(nil)|~ssList(X0)|~app(sK47_skl,X0)=sK48_skl|~sQ6_spl)),
% 0.13/0.49 inference(paramodulation,[status(thm)],[f515,f476])).
% 0.13/0.49 fof(f522,definition,(
% 0.13/0.49 ![X0]: (sQ12_spl <=> (~ssList(X0)|~app(sK47_skl,X0)=sK48_skl))),
% 0.13/0.49 introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition])).
% 0.13/0.49 fof(f523,plain,(
% 0.13/0.49 ![X0]: (~ssList(X0)|~app(sK47_skl,X0)=sK48_skl|~sQ12_spl)),
% 0.13/0.49 inference(component_clause,[status(thm)],[f522])).
% 0.13/0.49 fof(f525,plain,(
% 0.13/0.49 ~sQ2_spl|sQ12_spl|~sQ6_spl),
% 0.13/0.49 inference(split_clause,[status(thm)],[f517,f456,f522,f475])).
% 0.13/0.49 fof(f526,plain,(
% 0.13/0.49 $false|sQ2_spl),
% 0.13/0.49 inference(forward_subsumption_resolution,[status(thm)],[f458,f223])).
% 0.13/0.49 fof(f527,plain,(
% 0.13/0.49 sQ2_spl),
% 0.13/0.49 inference(contradiction_clause,[status(thm)],[f526])).
% 0.13/0.49 fof(f556,plain,(
% 0.13/0.49 ~app(sK47_skl,sK51_skl)=sK48_skl|~sQ12_spl),
% 0.13/0.49 inference(resolution,[status(thm)],[f523,f424])).
% 0.13/0.49 fof(f559,plain,(
% 0.13/0.49 ~sK48_skl=sK48_skl|~sQ12_spl),
% 0.13/0.49 inference(forward_demodulation,[status(thm)],[f486,f556])).
% 0.13/0.49 fof(f560,plain,(
% 0.13/0.49 $false|~sQ12_spl),
% 0.13/0.49 inference(trivial_equality_resolution,[status(thm)],[f559])).
% 0.13/0.49 fof(f561,plain,(
% 0.13/0.49 ~sQ12_spl),
% 0.13/0.49 inference(contradiction_clause,[status(thm)],[f560])).
% 0.13/0.49 fof(f562,plain,(
% 0.13/0.49 $false),
% 0.13/0.49 inference(sat_refutation,[status(thm)],[f478,f480,f482,f525,f527,f561])).
% 0.13/0.49 % SZS output end CNFRefutation for theBenchmark.p
% 0.13/0.50 % Elapsed time: 0.135433 seconds
% 0.13/0.50 % CPU time: 0.716613 seconds
% 0.13/0.50 % Total memory used: 121.122 MB
% 0.13/0.50 % Net memory used: 120.167 MB
%------------------------------------------------------------------------------