%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SWC009+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 02:41:19 PM UTC 2026
% Result : Theorem 0.12s 0.41s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC009+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
% 0.08/0.35 % Computer : n011.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 07:48:40 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.12/0.37 % Drodi V4.1.1
% 0.12/0.41 % Refutation found
% 0.12/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.41 % SZS output start CNFRefutation for theBenchmark
% 0.12/0.41 fof(f17,axiom,(
% 0.12/0.41 ssList(nil) ),
% 0.12/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.41 fof(f84,axiom,(
% 0.12/0.41 (! [U] :( ssList(U)=> app(U,nil) = U ) )),
% 0.12/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.41 fof(f96,conjecture,(
% 0.12/0.41 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> (! [X] :( ssList(X)=> ( V != X| U != W| (? [Y] :( ssList(Y)& (? [Z] :( ssList(Z)& (? [X1] :( ssList(X1)& app(app(Y,Z),X1) = V& app(Y,X1) = U ) )) )))| (! [X2] :( ssList(X2)=> ( app(W,X2) != X| ~ strictorderedP(W)| (? [X3] :( ssItem(X3)& (? [X4] :( ssList(X4)& app(cons(X3,nil),X4) = X2& (? [X5] :( ssItem(X5)& (? [X6] :( ssList(X6)& app(X6,cons(X5,nil)) = W& lt(X5,X3) ) )) )) )) )) ))| ( nil != X& nil = W ) ) ) )) )) )) )),
% 0.12/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.41 fof(f97,negated_conjecture,(
% 0.12/0.41 ~((! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> (! [X] :( ssList(X)=> ( V != X| U != W| (? [Y] :( ssList(Y)& (? [Z] :( ssList(Z)& (? [X1] :( ssList(X1)& app(app(Y,Z),X1) = V& app(Y,X1) = U ) )) )))| (! [X2] :( ssList(X2)=> ( app(W,X2) != X| ~ strictorderedP(W)| (? [X3] :( ssItem(X3)& (? [X4] :( ssList(X4)& app(cons(X3,nil),X4) = X2& (? [X5] :( ssItem(X5)& (? [X6] :( ssList(X6)& app(X6,cons(X5,nil)) = W& lt(X5,X3) ) )) )) )) )) ))| ( nil != X& nil = W ) ) ) )) )) )) ))),
% 0.12/0.41 inference(negated_conjecture,[status(cth)],[f96])).
% 0.12/0.41 fof(f223,plain,(
% 0.12/0.41 ssList(nil)),
% 0.12/0.41 inference(cnf_transformation,[status(thm)],[f17])).
% 0.12/0.41 fof(f388,plain,(
% 0.12/0.41 ![U]: (~ssList(U)|app(U,nil)=U)),
% 0.12/0.41 inference(pre_NNF_transformation,[status(thm)],[f84])).
% 0.12/0.41 fof(f389,plain,(
% 0.12/0.41 ![X0]: (~ssList(X0)|app(X0,nil)=X0)),
% 0.12/0.41 inference(cnf_transformation,[status(thm)],[f388])).
% 0.12/0.41 fof(f415,plain,(
% 0.12/0.41 (?[U]: (ssList(U)&(?[V]: (ssList(V)&(?[W]: (ssList(W)&(?[X]: (ssList(X)&((((V=X&U=W)&(![Y]: (~ssList(Y)|(![Z]: (~ssList(Z)|(![X1]: ((~ssList(X1)|~app(app(Y,Z),X1)=V)|~app(Y,X1)=U)))))))&(?[X2]: (ssList(X2)&((app(W,X2)=X&strictorderedP(W))&(![X3]: (~ssItem(X3)|(![X4]: ((~ssList(X4)|~app(cons(X3,nil),X4)=X2)|(![X5]: (~ssItem(X5)|(![X6]: ((~ssList(X6)|~app(X6,cons(X5,nil))=W)|~lt(X5,X3)))))))))))))&(nil=X|~nil=W))))))))))),
% 0.12/0.41 inference(pre_NNF_transformation,[status(thm)],[f97])).
% 0.12/0.41 fof(f416,plain,(
% 0.12/0.41 ?[U]: (ssList(U)&(?[V]: (ssList(V)&(?[W]: (ssList(W)&(?[X]: (ssList(X)&((((V=X&U=W)&(![Y]: (~ssList(Y)|(![Z]: (~ssList(Z)|(![X1]: ((~ssList(X1)|~app(app(Y,Z),X1)=V)|~app(Y,X1)=U)))))))&(?[X2]: (ssList(X2)&((app(W,X2)=X&strictorderedP(W))&(![X3]: (~ssItem(X3)|((![X4]: (~ssList(X4)|~app(cons(X3,nil),X4)=X2))|(![X5]: (~ssItem(X5)|((![X6]: (~ssList(X6)|~app(X6,cons(X5,nil))=W))|~lt(X5,X3)))))))))))&(nil=X|~nil=W)))))))))),
% 0.12/0.41 inference(miniscoping,[status(thm)],[f415])).
% 0.12/0.41 fof(f417,plain,(
% 0.12/0.41 (ssList(sK47_skl)&(ssList(sK48_skl)&(ssList(sK49_skl)&(ssList(sK50_skl)&((((sK48_skl=sK50_skl&sK47_skl=sK49_skl)&(![Y]: (~ssList(Y)|(![Z]: (~ssList(Z)|(![X1]: ((~ssList(X1)|~app(app(Y,Z),X1)=sK48_skl)|~app(Y,X1)=sK47_skl)))))))&(ssList(sK51_skl)&((app(sK49_skl,sK51_skl)=sK50_skl&strictorderedP(sK49_skl))&(![X3]: (~ssItem(X3)|((![X4]: (~ssList(X4)|~app(cons(X3,nil),X4)=sK51_skl))|(![X5]: (~ssItem(X5)|((![X6]: (~ssList(X6)|~app(X6,cons(X5,nil))=sK49_skl))|~lt(X5,X3))))))))))&(nil=sK50_skl|~nil=sK49_skl))))))),
% 0.12/0.41 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(X2,sK51_skl)],[f416])).
% 0.12/0.41 fof(f420,plain,(
% 0.12/0.41 ssList(sK49_skl)),
% 0.12/0.41 inference(cnf_transformation,[status(thm)],[f417])).
% 0.12/0.41 fof(f421,plain,(
% 0.12/0.41 ssList(sK50_skl)),
% 0.12/0.41 inference(cnf_transformation,[status(thm)],[f417])).
% 0.12/0.41 fof(f422,plain,(
% 0.12/0.41 sK48_skl=sK50_skl),
% 0.12/0.41 inference(cnf_transformation,[status(thm)],[f417])).
% 0.12/0.41 fof(f423,plain,(
% 0.12/0.41 sK47_skl=sK49_skl),
% 0.12/0.41 inference(cnf_transformation,[status(thm)],[f417])).
% 0.12/0.41 fof(f424,plain,(
% 0.12/0.41 ![X0,X1,X2]: (~ssList(X0)|~ssList(X1)|~ssList(X2)|~app(app(X0,X1),X2)=sK48_skl|~app(X0,X2)=sK47_skl)),
% 0.12/0.41 inference(cnf_transformation,[status(thm)],[f417])).
% 0.12/0.41 fof(f425,plain,(
% 0.12/0.41 ssList(sK51_skl)),
% 0.12/0.41 inference(cnf_transformation,[status(thm)],[f417])).
% 0.12/0.41 fof(f426,plain,(
% 0.12/0.41 app(sK49_skl,sK51_skl)=sK50_skl),
% 0.12/0.41 inference(cnf_transformation,[status(thm)],[f417])).
% 0.12/0.41 fof(f493,plain,(
% 0.12/0.41 ![X0,X1,X2]: (~ssList(X0)|~ssList(X1)|~ssList(X2)|~app(app(X0,X1),X2)=sK50_skl|~app(X0,X2)=sK47_skl)),
% 0.12/0.41 inference(forward_demodulation,[status(thm)],[f422,f424])).
% 0.12/0.41 fof(f494,plain,(
% 0.12/0.41 ![X0,X1,X2]: (~ssList(X0)|~ssList(X1)|~ssList(X2)|~app(app(X0,X1),X2)=sK50_skl|~app(X0,X2)=sK49_skl)),
% 0.12/0.41 inference(forward_demodulation,[status(thm)],[f423,f493])).
% 0.12/0.41 fof(f498,plain,(
% 0.12/0.41 ![X0]: (~ssList(sK49_skl)|~ssList(sK51_skl)|~ssList(X0)|~app(sK50_skl,X0)=sK50_skl|~app(sK49_skl,X0)=sK49_skl)),
% 0.12/0.41 inference(paramodulation,[status(thm)],[f426,f494])).
% 0.12/0.41 fof(f502,definition,(
% 0.12/0.41 sQ3_spl <=> (ssList(sK49_skl))),
% 0.12/0.41 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.12/0.41 fof(f504,plain,(
% 0.12/0.41 ~ssList(sK49_skl)|sQ3_spl),
% 0.12/0.41 inference(component_clause,[status(thm)],[f502])).
% 0.12/0.41 fof(f513,definition,(
% 0.12/0.41 sQ6_spl <=> (ssList(sK51_skl))),
% 0.12/0.41 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.12/0.41 fof(f515,plain,(
% 0.12/0.41 ~ssList(sK51_skl)|sQ6_spl),
% 0.12/0.41 inference(component_clause,[status(thm)],[f513])).
% 0.12/0.41 fof(f520,definition,(
% 0.12/0.41 ![X0]: (sQ8_spl <=> (~ssList(X0)|~app(sK50_skl,X0)=sK50_skl|~app(sK49_skl,X0)=sK49_skl))),
% 0.12/0.41 introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition])).
% 0.12/0.41 fof(f521,plain,(
% 0.12/0.41 ![X0]: (~ssList(X0)|~app(sK50_skl,X0)=sK50_skl|~app(sK49_skl,X0)=sK49_skl|~sQ8_spl)),
% 0.12/0.41 inference(component_clause,[status(thm)],[f520])).
% 0.12/0.41 fof(f523,plain,(
% 0.12/0.41 ~sQ3_spl|~sQ6_spl|sQ8_spl),
% 0.12/0.41 inference(split_clause,[status(thm)],[f498,f502,f513,f520])).
% 0.12/0.41 fof(f526,plain,(
% 0.12/0.41 $false|sQ6_spl),
% 0.12/0.41 inference(forward_subsumption_resolution,[status(thm)],[f515,f425])).
% 0.12/0.41 fof(f527,plain,(
% 0.12/0.41 sQ6_spl),
% 0.12/0.41 inference(contradiction_clause,[status(thm)],[f526])).
% 0.12/0.41 fof(f528,plain,(
% 0.12/0.41 $false|sQ3_spl),
% 0.12/0.41 inference(forward_subsumption_resolution,[status(thm)],[f504,f420])).
% 0.12/0.41 fof(f529,plain,(
% 0.12/0.41 sQ3_spl),
% 0.12/0.41 inference(contradiction_clause,[status(thm)],[f528])).
% 0.12/0.41 fof(f536,plain,(
% 0.12/0.41 app(sK50_skl,nil)=sK50_skl),
% 0.12/0.41 inference(resolution,[status(thm)],[f389,f421])).
% 0.12/0.41 fof(f537,plain,(
% 0.12/0.41 app(sK49_skl,nil)=sK49_skl),
% 0.12/0.41 inference(resolution,[status(thm)],[f389,f420])).
% 0.12/0.41 fof(f539,definition,(
% 0.12/0.41 sQ9_spl <=> (ssList(nil))),
% 0.12/0.41 introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition])).
% 0.12/0.41 fof(f541,plain,(
% 0.12/0.41 ~ssList(nil)|sQ9_spl),
% 0.12/0.41 inference(component_clause,[status(thm)],[f539])).
% 0.12/0.41 fof(f546,plain,(
% 0.12/0.41 $false|sQ9_spl),
% 0.12/0.41 inference(forward_subsumption_resolution,[status(thm)],[f541,f223])).
% 0.12/0.41 fof(f547,plain,(
% 0.12/0.41 sQ9_spl),
% 0.12/0.41 inference(contradiction_clause,[status(thm)],[f546])).
% 0.12/0.41 fof(f1534,plain,(
% 0.12/0.41 ~ssList(nil)|~app(sK50_skl,nil)=sK50_skl|~sQ8_spl),
% 0.12/0.41 inference(resolution,[status(thm)],[f521,f537])).
% 0.12/0.41 fof(f1537,definition,(
% 0.12/0.41 sQ142_spl <=> (app(sK50_skl,nil)=sK50_skl)),
% 0.12/0.41 introduced(definition,[new_symbols(definition,[sQ142_spl])],[split_symbol_definition])).
% 0.12/0.41 fof(f1539,plain,(
% 0.12/0.41 ~app(sK50_skl,nil)=sK50_skl|sQ142_spl),
% 0.12/0.41 inference(component_clause,[status(thm)],[f1537])).
% 0.12/0.41 fof(f1540,plain,(
% 0.12/0.41 ~sQ9_spl|~sQ142_spl|~sQ8_spl),
% 0.12/0.41 inference(split_clause,[status(thm)],[f1534,f539,f1537,f520])).
% 0.12/0.41 fof(f1552,plain,(
% 0.12/0.41 ~sK50_skl=sK50_skl|sQ142_spl),
% 0.12/0.41 inference(forward_demodulation,[status(thm)],[f536,f1539])).
% 0.12/0.41 fof(f1553,plain,(
% 0.12/0.41 $false|sQ142_spl),
% 0.12/0.41 inference(trivial_equality_resolution,[status(thm)],[f1552])).
% 0.12/0.41 fof(f1554,plain,(
% 0.12/0.41 sQ142_spl),
% 0.12/0.41 inference(contradiction_clause,[status(thm)],[f1553])).
% 0.12/0.41 fof(f1555,plain,(
% 0.12/0.41 $false),
% 0.12/0.41 inference(sat_refutation,[status(thm)],[f523,f527,f529,f547,f1540,f1554])).
% 0.12/0.41 % SZS output end CNFRefutation for theBenchmark.p
% 0.12/0.44 % Elapsed time: 0.080502 seconds
% 0.12/0.44 % CPU time: 0.277011 seconds
% 0.12/0.44 % Total memory used: 112.557 MB
% 0.12/0.44 % Net memory used: 112.221 MB
%------------------------------------------------------------------------------