%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SWC398+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 : n005.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 02:42:22 PM UTC 2026
% Result : Theorem 0.19s 0.67s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWC398+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.42 % Computer : n005.cluster.edu
% 0.19/0.42 % Model : x86_64 x86_64
% 0.19/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.42 % Memory : 8046.5625MB
% 0.19/0.42 % OS : Linux 6.8.0-71-generic
% 0.19/0.42 % CPULimit : 300
% 0.19/0.42 % WCLimit : 300
% 0.19/0.42 % DateTime : Mon Sep 21 08:21:20 UTC 2026
% 0.19/0.42 % CPUTime :
% 0.19/0.45 % Drodi V4.1.1
% 0.19/0.67 % Refutation found
% 0.19/0.67 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/0.67 % SZS output start CNFRefutation for theBenchmark
% 0.19/0.67 fof(f36,axiom,(
% 0.19/0.67 (! [U] :( ssItem(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> ( memberP(app(V,W),U)<=> ( memberP(V,U)| memberP(W,U) ) ) ) )) )) )),
% 0.19/0.67 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.67 fof(f96,conjecture,(
% 0.19/0.67 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> (! [X] :( ssList(X)=> ( V != X| U != W| (! [Y] :( ssList(Y)=> ( app(W,Y) != X| ~ equalelemsP(W)| (? [Z] :( ssItem(Z)& (? [X1] :( ssList(X1)& app(cons(Z,nil),X1) = Y& (? [X2] :( ssList(X2)& app(X2,cons(Z,nil)) = W ) )) )) )) ))| (! [X3] :( ssItem(X3)=> ( ~ memberP(U,X3)| memberP(V,X3) ) ))| ( nil != X& nil = W ) ) ) )) )) )) )),
% 0.19/0.67 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.67 fof(f97,negated_conjecture,(
% 0.19/0.67 ~((! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> (! [X] :( ssList(X)=> ( V != X| U != W| (! [Y] :( ssList(Y)=> ( app(W,Y) != X| ~ equalelemsP(W)| (? [Z] :( ssItem(Z)& (? [X1] :( ssList(X1)& app(cons(Z,nil),X1) = Y& (? [X2] :( ssList(X2)& app(X2,cons(Z,nil)) = W ) )) )) )) ))| (! [X3] :( ssItem(X3)=> ( ~ memberP(U,X3)| memberP(V,X3) ) ))| ( nil != X& nil = W ) ) ) )) )) )) ))),
% 0.19/0.67 inference(negated_conjecture,[status(cth)],[f96])).
% 0.19/0.67 fof(f268,plain,(
% 0.19/0.67 ![U]: (~ssItem(U)|(![V]: (~ssList(V)|(![W]: (~ssList(W)|(memberP(app(V,W),U)<=>(memberP(V,U)|memberP(W,U))))))))),
% 0.19/0.67 inference(pre_NNF_transformation,[status(thm)],[f36])).
% 0.19/0.67 fof(f269,plain,(
% 0.19/0.67 ![U]: (~ssItem(U)|(![V]: (~ssList(V)|(![W]: (~ssList(W)|((~memberP(app(V,W),U)|(memberP(V,U)|memberP(W,U)))&(memberP(app(V,W),U)|(~memberP(V,U)&~memberP(W,U)))))))))),
% 0.19/0.67 inference(NNF_transformation,[status(thm)],[f268])).
% 0.19/0.67 fof(f271,plain,(
% 0.19/0.67 ![X0,X1,X2]: (~ssItem(X0)|~ssList(X1)|~ssList(X2)|memberP(app(X1,X2),X0)|~memberP(X1,X0))),
% 0.19/0.67 inference(cnf_transformation,[status(thm)],[f269])).
% 0.19/0.67 fof(f415,plain,(
% 0.19/0.67 (?[U]: (ssList(U)&(?[V]: (ssList(V)&(?[W]: (ssList(W)&(?[X]: (ssList(X)&((((V=X&U=W)&(?[Y]: (ssList(Y)&((app(W,Y)=X&equalelemsP(W))&(![Z]: (~ssItem(Z)|(![X1]: ((~ssList(X1)|~app(cons(Z,nil),X1)=Y)|(![X2]: (~ssList(X2)|~app(X2,cons(Z,nil))=W))))))))))&(?[X3]: (ssItem(X3)&(memberP(U,X3)&~memberP(V,X3)))))&(nil=X|~nil=W))))))))))),
% 0.19/0.67 inference(pre_NNF_transformation,[status(thm)],[f97])).
% 0.19/0.67 fof(f416,plain,(
% 0.19/0.67 ?[U]: (ssList(U)&(?[V]: (ssList(V)&(?[W]: (ssList(W)&(?[X]: (ssList(X)&((((V=X&U=W)&(?[Y]: (ssList(Y)&((app(W,Y)=X&equalelemsP(W))&(![Z]: (~ssItem(Z)|((![X1]: (~ssList(X1)|~app(cons(Z,nil),X1)=Y))|(![X2]: (~ssList(X2)|~app(X2,cons(Z,nil))=W)))))))))&(?[X3]: (ssItem(X3)&(memberP(U,X3)&~memberP(V,X3)))))&(nil=X|~nil=W)))))))))),
% 0.19/0.67 inference(miniscoping,[status(thm)],[f415])).
% 0.19/0.67 fof(f417,plain,(
% 0.19/0.67 (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&equalelemsP(sK49_skl))&(![Z]: (~ssItem(Z)|((![X1]: (~ssList(X1)|~app(cons(Z,nil),X1)=sK51_skl))|(![X2]: (~ssList(X2)|~app(X2,cons(Z,nil))=sK49_skl))))))))&(ssItem(sK52_skl)&(memberP(sK47_skl,sK52_skl)&~memberP(sK48_skl,sK52_skl))))&(nil=sK50_skl|~nil=sK49_skl))))))),
% 0.19/0.67 inference(skolemize,[status(esa),new_symbols(skolem,[sK47_skl,sK48_skl,sK49_skl,sK50_skl,sK51_skl,sK52_skl]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl),skolemize(Y,sK51_skl),skolemize(X3,sK52_skl)],[f416])).
% 0.19/0.67 fof(f418,plain,(
% 0.19/0.67 ssList(sK47_skl)),
% 0.19/0.67 inference(cnf_transformation,[status(thm)],[f417])).
% 0.19/0.67 fof(f422,plain,(
% 0.19/0.67 sK48_skl=sK50_skl),
% 0.19/0.67 inference(cnf_transformation,[status(thm)],[f417])).
% 0.19/0.67 fof(f423,plain,(
% 0.19/0.67 sK47_skl=sK49_skl),
% 0.19/0.67 inference(cnf_transformation,[status(thm)],[f417])).
% 0.19/0.67 fof(f424,plain,(
% 0.19/0.67 ssList(sK51_skl)),
% 0.19/0.67 inference(cnf_transformation,[status(thm)],[f417])).
% 0.19/0.67 fof(f425,plain,(
% 0.19/0.67 app(sK49_skl,sK51_skl)=sK50_skl),
% 0.19/0.67 inference(cnf_transformation,[status(thm)],[f417])).
% 0.19/0.67 fof(f428,plain,(
% 0.19/0.67 ssItem(sK52_skl)),
% 0.19/0.67 inference(cnf_transformation,[status(thm)],[f417])).
% 0.19/0.67 fof(f429,plain,(
% 0.19/0.67 memberP(sK47_skl,sK52_skl)),
% 0.19/0.67 inference(cnf_transformation,[status(thm)],[f417])).
% 0.19/0.68 fof(f430,plain,(
% 0.19/0.68 ~memberP(sK48_skl,sK52_skl)),
% 0.19/0.68 inference(cnf_transformation,[status(thm)],[f417])).
% 0.19/0.68 fof(f501,plain,(
% 0.19/0.68 ![X0,X1]: (~ssItem(X0)|~ssList(X1)|memberP(app(X1,sK51_skl),X0)|~memberP(X1,X0))),
% 0.19/0.68 inference(resolution,[status(thm)],[f424,f271])).
% 0.19/0.68 fof(f505,plain,(
% 0.19/0.68 app(sK47_skl,sK51_skl)=sK50_skl),
% 0.19/0.68 inference(forward_demodulation,[status(thm)],[f423,f425])).
% 0.19/0.68 fof(f506,plain,(
% 0.19/0.68 app(sK47_skl,sK51_skl)=sK48_skl),
% 0.19/0.68 inference(forward_demodulation,[status(thm)],[f422,f505])).
% 0.19/0.68 fof(f511,definition,(
% 0.19/0.68 sQ3_spl <=> (ssList(sK47_skl))),
% 0.19/0.68 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.19/0.68 fof(f513,plain,(
% 0.19/0.68 ~ssList(sK47_skl)|sQ3_spl),
% 0.19/0.68 inference(component_clause,[status(thm)],[f511])).
% 0.19/0.68 fof(f538,plain,(
% 0.19/0.68 $false|sQ3_spl),
% 0.19/0.68 inference(forward_subsumption_resolution,[status(thm)],[f513,f418])).
% 0.19/0.68 fof(f539,plain,(
% 0.19/0.68 sQ3_spl),
% 0.19/0.68 inference(contradiction_clause,[status(thm)],[f538])).
% 0.19/0.68 fof(f667,definition,(
% 0.19/0.68 sQ26_spl <=> (ssItem(sK52_skl))),
% 0.19/0.68 introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition])).
% 0.19/0.68 fof(f669,plain,(
% 0.19/0.68 ~ssItem(sK52_skl)|sQ26_spl),
% 0.19/0.68 inference(component_clause,[status(thm)],[f667])).
% 0.19/0.68 fof(f678,plain,(
% 0.19/0.68 $false|sQ26_spl),
% 0.19/0.68 inference(forward_subsumption_resolution,[status(thm)],[f669,f428])).
% 0.19/0.68 fof(f679,plain,(
% 0.19/0.68 sQ26_spl),
% 0.19/0.68 inference(contradiction_clause,[status(thm)],[f678])).
% 0.19/0.68 fof(f2865,plain,(
% 0.19/0.68 ~ssItem(sK52_skl)|~ssList(sK47_skl)|memberP(app(sK47_skl,sK51_skl),sK52_skl)),
% 0.19/0.68 inference(resolution,[status(thm)],[f501,f429])).
% 0.19/0.68 fof(f2930,definition,(
% 0.19/0.68 sQ365_spl <=> (memberP(app(sK47_skl,sK51_skl),sK52_skl))),
% 0.19/0.68 introduced(definition,[new_symbols(definition,[sQ365_spl])],[split_symbol_definition])).
% 0.19/0.68 fof(f2931,plain,(
% 0.19/0.68 memberP(app(sK47_skl,sK51_skl),sK52_skl)|~sQ365_spl),
% 0.19/0.68 inference(component_clause,[status(thm)],[f2930])).
% 0.19/0.68 fof(f2933,plain,(
% 0.19/0.68 ~sQ26_spl|~sQ3_spl|sQ365_spl),
% 0.19/0.68 inference(split_clause,[status(thm)],[f2865,f667,f511,f2930])).
% 0.19/0.68 fof(f2934,plain,(
% 0.19/0.68 memberP(sK48_skl,sK52_skl)|~sQ365_spl),
% 0.19/0.68 inference(forward_demodulation,[status(thm)],[f506,f2931])).
% 0.19/0.68 fof(f2935,plain,(
% 0.19/0.68 $false|~sQ365_spl),
% 0.19/0.68 inference(forward_subsumption_resolution,[status(thm)],[f2934,f430])).
% 0.19/0.68 fof(f2936,plain,(
% 0.19/0.68 ~sQ365_spl),
% 0.19/0.68 inference(contradiction_clause,[status(thm)],[f2935])).
% 0.19/0.68 fof(f2937,plain,(
% 0.19/0.68 $false),
% 0.19/0.68 inference(sat_refutation,[status(thm)],[f539,f679,f2933,f2936])).
% 0.19/0.68 % SZS output end CNFRefutation for theBenchmark.p
% 0.19/0.71 % Elapsed time: 0.266608 seconds
% 0.19/0.71 % CPU time: 1.587218 seconds
% 0.19/0.71 % Total memory used: 126.018 MB
% 0.19/0.71 % Net memory used: 124.763 MB
%------------------------------------------------------------------------------