%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SWC041+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 : n018.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 02:41:25 PM UTC 2026
% Result : Theorem 0.12s 5.41s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC041+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.35 % Computer : n018.cluster.edu
% 0.09/5.35 % Model : x86_64 x86_64
% 0.09/5.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.35 % Memory : 8046.5625MB
% 0.09/5.35 % OS : Linux 6.8.0-71-generic
% 0.09/5.35 % CPULimit : 300
% 0.09/5.35 % WCLimit : 300
% 0.09/5.35 % DateTime : Mon Sep 21 07:53:05 UTC 2026
% 0.09/5.35 % CPUTime :
% 0.09/5.37 % Drodi V4.1.1
% 0.12/5.41 % Refutation found
% 0.12/5.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/5.41 % SZS output start CNFRefutation for theBenchmark
% 0.12/5.41 fof(f83,axiom,(
% 0.12/5.41 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> ( nil = app(U,V)<=> ( nil = V& nil = U ) ) ) )) )),
% 0.12/5.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/5.41 fof(f96,conjecture,(
% 0.12/5.41 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> (! [X] :( ssList(X)=> ( nil != V| V != X| U != W| nil = U| (! [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 ) )) )) )) ))| ( nil != X& nil = W ) ) ) )) )) )) )),
% 0.12/5.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/5.41 fof(f97,negated_conjecture,(
% 0.12/5.41 ~((! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> (! [X] :( ssList(X)=> ( nil != V| V != X| U != W| nil = U| (! [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 ) )) )) )) ))| ( nil != X& nil = W ) ) ) )) )) )) ))),
% 0.12/5.41 inference(negated_conjecture,[status(cth)],[f96])).
% 0.12/5.41 fof(f383,plain,(
% 0.12/5.41 ![U]: (~ssList(U)|(![V]: (~ssList(V)|(nil=app(U,V)<=>(nil=V&nil=U)))))),
% 0.12/5.41 inference(pre_NNF_transformation,[status(thm)],[f83])).
% 0.12/5.41 fof(f384,plain,(
% 0.12/5.41 ![U]: (~ssList(U)|(![V]: (~ssList(V)|((~nil=app(U,V)|(nil=V&nil=U))&(nil=app(U,V)|(~nil=V|~nil=U))))))),
% 0.12/5.41 inference(NNF_transformation,[status(thm)],[f383])).
% 0.12/5.41 fof(f386,plain,(
% 0.12/5.41 ![X0,X1]: (~ssList(X0)|~ssList(X1)|~nil=app(X0,X1)|nil=X0)),
% 0.12/5.41 inference(cnf_transformation,[status(thm)],[f384])).
% 0.12/5.41 fof(f415,plain,(
% 0.12/5.41 (?[U]: (ssList(U)&(?[V]: (ssList(V)&(?[W]: (ssList(W)&(?[X]: (ssList(X)&(((((nil=V&V=X)&U=W)&~nil=U)&(?[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))))))))))&(nil=X|~nil=W))))))))))),
% 0.12/5.41 inference(pre_NNF_transformation,[status(thm)],[f97])).
% 0.12/5.41 fof(f416,plain,(
% 0.12/5.41 ?[U]: (ssList(U)&(?[V]: (ssList(V)&(?[W]: (ssList(W)&(?[X]: (ssList(X)&(((((nil=V&V=X)&U=W)&~nil=U)&(?[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)))))))))&(nil=X|~nil=W)))))))))),
% 0.12/5.41 inference(miniscoping,[status(thm)],[f415])).
% 0.12/5.41 fof(f417,plain,(
% 0.12/5.41 (ssList(sK47_skl)&(ssList(sK48_skl)&(ssList(sK49_skl)&(ssList(sK50_skl)&(((((nil=sK48_skl&sK48_skl=sK50_skl)&sK47_skl=sK49_skl)&~nil=sK47_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))))))))&(nil=sK50_skl|~nil=sK49_skl))))))),
% 0.12/5.41 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])).
% 0.12/5.41 fof(f420,plain,(
% 0.12/5.41 ssList(sK49_skl)),
% 0.12/5.41 inference(cnf_transformation,[status(thm)],[f417])).
% 0.12/5.41 fof(f422,plain,(
% 0.12/5.41 nil=sK48_skl),
% 0.12/5.41 inference(cnf_transformation,[status(thm)],[f417])).
% 0.12/5.41 fof(f423,plain,(
% 0.12/5.41 sK48_skl=sK50_skl),
% 0.12/5.41 inference(cnf_transformation,[status(thm)],[f417])).
% 0.12/5.41 fof(f424,plain,(
% 0.12/5.41 sK47_skl=sK49_skl),
% 0.12/5.41 inference(cnf_transformation,[status(thm)],[f417])).
% 0.12/5.41 fof(f425,plain,(
% 0.12/5.41 ~nil=sK47_skl),
% 0.12/5.41 inference(cnf_transformation,[status(thm)],[f417])).
% 0.12/5.41 fof(f426,plain,(
% 0.12/5.41 ssList(sK51_skl)),
% 0.12/5.41 inference(cnf_transformation,[status(thm)],[f417])).
% 0.12/5.41 fof(f427,plain,(
% 0.12/5.41 app(sK49_skl,sK51_skl)=sK50_skl),
% 0.12/5.41 inference(cnf_transformation,[status(thm)],[f417])).
% 0.12/5.41 fof(f468,plain,(
% 0.12/5.41 nil=sK50_skl),
% 0.12/5.41 inference(backward_demodulation,[status(thm)],[f423,f422])).
% 0.12/5.41 fof(f471,plain,(
% 0.12/5.41 ~nil=sK49_skl),
% 0.12/5.41 inference(forward_demodulation,[status(thm)],[f424,f425])).
% 0.12/5.41 fof(f715,definition,(
% 0.12/5.41 sQ29_spl <=> (ssList(sK51_skl))),
% 0.12/5.41 introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition])).
% 0.12/5.41 fof(f717,plain,(
% 0.12/5.41 ~ssList(sK51_skl)|sQ29_spl),
% 0.12/5.41 inference(component_clause,[status(thm)],[f715])).
% 0.12/5.41 fof(f729,definition,(
% 0.12/5.41 sQ33_spl <=> (ssList(sK49_skl))),
% 0.12/5.41 introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition])).
% 0.12/5.41 fof(f731,plain,(
% 0.12/5.41 ~ssList(sK49_skl)|sQ33_spl),
% 0.12/5.41 inference(component_clause,[status(thm)],[f729])).
% 0.12/5.41 fof(f736,plain,(
% 0.12/5.41 $false|sQ33_spl),
% 0.12/5.41 inference(forward_subsumption_resolution,[status(thm)],[f731,f420])).
% 0.12/5.41 fof(f737,plain,(
% 0.12/5.41 sQ33_spl),
% 0.12/5.41 inference(contradiction_clause,[status(thm)],[f736])).
% 0.12/5.41 fof(f740,plain,(
% 0.12/5.41 $false|sQ29_spl),
% 0.12/5.41 inference(forward_subsumption_resolution,[status(thm)],[f717,f426])).
% 0.12/5.41 fof(f741,plain,(
% 0.12/5.41 sQ29_spl),
% 0.12/5.41 inference(contradiction_clause,[status(thm)],[f740])).
% 0.12/5.41 fof(f743,plain,(
% 0.12/5.41 ~sK50_skl=sK49_skl),
% 0.12/5.41 inference(forward_demodulation,[status(thm)],[f468,f471])).
% 0.12/5.41 fof(f1701,definition,(
% 0.12/5.41 sQ132_spl <=> (sK50_skl=sK49_skl)),
% 0.12/5.41 introduced(definition,[new_symbols(definition,[sQ132_spl])],[split_symbol_definition])).
% 0.12/5.41 fof(f1702,plain,(
% 0.12/5.41 sK50_skl=sK49_skl|~sQ132_spl),
% 0.12/5.41 inference(component_clause,[status(thm)],[f1701])).
% 0.12/5.41 fof(f1709,plain,(
% 0.12/5.41 ![X0,X1]: (~ssList(X0)|~ssList(X1)|~sK50_skl=app(X0,X1)|nil=X0)),
% 0.12/5.41 inference(forward_demodulation,[status(thm)],[f468,f386])).
% 0.12/5.41 fof(f1710,plain,(
% 0.12/5.41 ![X0,X1]: (~ssList(X0)|~ssList(X1)|~sK50_skl=app(X0,X1)|sK50_skl=X0)),
% 0.12/5.41 inference(forward_demodulation,[status(thm)],[f468,f1709])).
% 0.12/5.41 fof(f1712,plain,(
% 0.12/5.41 ~ssList(sK49_skl)|~ssList(sK51_skl)|sK50_skl=sK49_skl),
% 0.12/5.41 inference(resolution,[status(thm)],[f1710,f427])).
% 0.12/5.41 fof(f1720,plain,(
% 0.12/5.41 ~sQ33_spl|~sQ29_spl|sQ132_spl),
% 0.12/5.41 inference(split_clause,[status(thm)],[f1712,f729,f715,f1701])).
% 0.12/5.41 fof(f1727,plain,(
% 0.12/5.41 $false|~sQ132_spl),
% 0.12/5.41 inference(forward_subsumption_resolution,[status(thm)],[f1702,f743])).
% 0.12/5.41 fof(f1728,plain,(
% 0.12/5.41 ~sQ132_spl),
% 0.12/5.41 inference(contradiction_clause,[status(thm)],[f1727])).
% 0.12/5.41 fof(f1729,plain,(
% 0.12/5.41 $false),
% 0.12/5.41 inference(sat_refutation,[status(thm)],[f737,f741,f1720,f1728])).
% 0.12/5.41 % SZS output end CNFRefutation for theBenchmark.p
% 0.12/5.44 % Elapsed time: 0.076146 seconds
% 0.12/5.44 % CPU time: 0.283292 seconds
% 0.12/5.44 % Total memory used: 92.123 MB
% 0.12/5.44 % Net memory used: 91.857 MB
%------------------------------------------------------------------------------