%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SWC254+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 : n015.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 02:41:58 PM UTC 2026
% Result : Theorem 0.13s 0.41s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC254+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n015.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 08:12:36 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.13/0.41 % Refutation found
% 0.13/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.41 % SZS output start CNFRefutation for theBenchmark
% 0.13/0.41 fof(f4,axiom,(
% 0.13/0.41 (! [U] :( ssList(U)=> ( singletonP(U)<=> (? [V] :( ssItem(V)& cons(V,nil) = U ) )) ) )),
% 0.13/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.41 fof(f96,conjecture,(
% 0.13/0.41 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> (! [X] :( ssList(X)=> ( V != X| U != W| ( ( ~ neq(V,nil)| (! [Y] :( ssItem(Y)=> (! [Z] :( ssList(Z)=> ( cons(Y,nil) != W| app(Z,cons(Y,nil)) != X ) ) )))| singletonP(U) )& ( ~ neq(V,nil)| neq(X,nil) ) ) ) ) )) )) )) )),
% 0.13/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.41 fof(f97,negated_conjecture,(
% 0.13/0.41 ~((! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> (! [X] :( ssList(X)=> ( V != X| U != W| ( ( ~ neq(V,nil)| (! [Y] :( ssItem(Y)=> (! [Z] :( ssList(Z)=> ( cons(Y,nil) != W| app(Z,cons(Y,nil)) != X ) ) )))| singletonP(U) )& ( ~ neq(V,nil)| neq(X,nil) ) ) ) ) )) )) )) ))),
% 0.13/0.41 inference(negated_conjecture,[status(cth)],[f96])).
% 0.13/0.41 fof(f113,plain,(
% 0.13/0.41 ![U]: (~ssList(U)|(singletonP(U)<=>(?[V]: (ssItem(V)&cons(V,nil)=U))))),
% 0.13/0.41 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 0.13/0.41 fof(f114,plain,(
% 0.13/0.41 ![U]: (~ssList(U)|((~singletonP(U)|(?[V]: (ssItem(V)&cons(V,nil)=U)))&(singletonP(U)|(![V]: (~ssItem(V)|~cons(V,nil)=U)))))),
% 0.13/0.41 inference(NNF_transformation,[status(thm)],[f113])).
% 0.13/0.41 fof(f115,plain,(
% 0.13/0.41 ![U]: (~ssList(U)|((~singletonP(U)|(ssItem(sK4_skl(U))&cons(sK4_skl(U),nil)=U))&(singletonP(U)|(![V]: (~ssItem(V)|~cons(V,nil)=U)))))),
% 0.13/0.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(V,sK4_skl(U))],[f114])).
% 0.13/0.41 fof(f118,plain,(
% 0.13/0.41 ![X0,X1]: (~ssList(X0)|singletonP(X0)|~ssItem(X1)|~cons(X1,nil)=X0)),
% 0.13/0.41 inference(cnf_transformation,[status(thm)],[f115])).
% 0.13/0.41 fof(f415,plain,(
% 0.13/0.41 (?[U]: (ssList(U)&(?[V]: (ssList(V)&(?[W]: (ssList(W)&(?[X]: (ssList(X)&((V=X&U=W)&(((neq(V,nil)&(?[Y]: (ssItem(Y)&(?[Z]: (ssList(Z)&(cons(Y,nil)=W&app(Z,cons(Y,nil))=X))))))&~singletonP(U))|(neq(V,nil)&~neq(X,nil))))))))))))),
% 0.13/0.41 inference(pre_NNF_transformation,[status(thm)],[f97])).
% 0.13/0.41 fof(f416,definition,(
% 0.13/0.41 ![U,V,W,X]: (sP0_prd(X,W,V,U)<=>((neq(V,nil)&(?[Y]: (ssItem(Y)&(?[Z]: (ssList(Z)&(cons(Y,nil)=W&app(Z,cons(Y,nil))=X))))))&~singletonP(U)))),
% 0.13/0.41 introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 0.13/0.41 fof(f417,plain,(
% 0.13/0.41 ?[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)))))))))))),
% 0.13/0.41 inference(formula_renaming,[status(thm)],[f415,f416])).
% 0.13/0.41 fof(f418,plain,(
% 0.13/0.41 (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))))))))),
% 0.13/0.41 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])).
% 0.13/0.41 fof(f419,plain,(
% 0.13/0.41 ssList(sK47_skl)),
% 0.13/0.41 inference(cnf_transformation,[status(thm)],[f418])).
% 0.13/0.41 fof(f423,plain,(
% 0.13/0.41 sK48_skl=sK50_skl),
% 0.13/0.41 inference(cnf_transformation,[status(thm)],[f418])).
% 0.13/0.41 fof(f424,plain,(
% 0.13/0.41 sK47_skl=sK49_skl),
% 0.13/0.41 inference(cnf_transformation,[status(thm)],[f418])).
% 0.13/0.41 fof(f425,plain,(
% 0.13/0.41 sP0_prd(sK50_skl,sK49_skl,sK48_skl,sK47_skl)|neq(sK48_skl,nil)),
% 0.13/0.41 inference(cnf_transformation,[status(thm)],[f418])).
% 0.13/0.41 fof(f426,plain,(
% 0.13/0.41 sP0_prd(sK50_skl,sK49_skl,sK48_skl,sK47_skl)|~neq(sK50_skl,nil)),
% 0.13/0.41 inference(cnf_transformation,[status(thm)],[f418])).
% 0.13/0.41 fof(f427,plain,(
% 0.13/0.41 ![U,V,W,X]: ((~sP0_prd(X,W,V,U)|((neq(V,nil)&(?[Y]: (ssItem(Y)&(?[Z]: (ssList(Z)&(cons(Y,nil)=W&app(Z,cons(Y,nil))=X))))))&~singletonP(U)))&(sP0_prd(X,W,V,U)|((~neq(V,nil)|(![Y]: (~ssItem(Y)|(![Z]: (~ssList(Z)|(~cons(Y,nil)=W|~app(Z,cons(Y,nil))=X))))))|singletonP(U))))),
% 0.13/0.41 inference(NNF_transformation,[status(thm)],[f416])).
% 0.13/0.41 fof(f428,plain,(
% 0.13/0.41 (![U,V,W,X]: (~sP0_prd(X,W,V,U)|((neq(V,nil)&(?[Y]: (ssItem(Y)&(?[Z]: (ssList(Z)&(cons(Y,nil)=W&app(Z,cons(Y,nil))=X))))))&~singletonP(U))))&(![U,V,W,X]: (sP0_prd(X,W,V,U)|((~neq(V,nil)|(![Y]: (~ssItem(Y)|(![Z]: (~ssList(Z)|(~cons(Y,nil)=W|~app(Z,cons(Y,nil))=X))))))|singletonP(U))))),
% 0.13/0.41 inference(miniscoping,[status(thm)],[f427])).
% 0.13/0.41 fof(f429,plain,(
% 0.13/0.41 (![U,V,W,X]: (~sP0_prd(X,W,V,U)|((neq(V,nil)&(ssItem(sK51_skl(X,W,V,U))&(ssList(sK52_skl(X,W,V,U))&(cons(sK51_skl(X,W,V,U),nil)=W&app(sK52_skl(X,W,V,U),cons(sK51_skl(X,W,V,U),nil))=X))))&~singletonP(U))))&(![U,V,W,X]: (sP0_prd(X,W,V,U)|((~neq(V,nil)|(![Y]: (~ssItem(Y)|(![Z]: (~ssList(Z)|(~cons(Y,nil)=W|~app(Z,cons(Y,nil))=X))))))|singletonP(U))))),
% 0.13/0.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK51_skl,sK52_skl]),skolemize(Y,sK51_skl(X,W,V,U)),skolemize(Z,sK52_skl(X,W,V,U))],[f428])).
% 0.13/0.41 fof(f431,plain,(
% 0.13/0.41 ![X0,X1,X2,X3]: (~sP0_prd(X0,X1,X2,X3)|ssItem(sK51_skl(X0,X1,X2,X3)))),
% 0.13/0.41 inference(cnf_transformation,[status(thm)],[f429])).
% 0.13/0.41 fof(f433,plain,(
% 0.13/0.41 ![X0,X1,X2,X3]: (~sP0_prd(X0,X1,X2,X3)|cons(sK51_skl(X0,X1,X2,X3),nil)=X1)),
% 0.13/0.41 inference(cnf_transformation,[status(thm)],[f429])).
% 0.13/0.41 fof(f435,plain,(
% 0.13/0.41 ![X0,X1,X2,X3]: (~sP0_prd(X0,X1,X2,X3)|~singletonP(X3))),
% 0.13/0.41 inference(cnf_transformation,[status(thm)],[f429])).
% 0.13/0.41 fof(f440,plain,(
% 0.13/0.41 ![X0]: (~ssList(cons(X0,nil))|singletonP(cons(X0,nil))|~ssItem(X0))),
% 0.13/0.41 inference(destructive_equality_resolution,[status(thm)],[f118])).
% 0.13/0.41 fof(f471,plain,(
% 0.13/0.41 sP0_prd(sK48_skl,sK49_skl,sK48_skl,sK47_skl)|neq(sK48_skl,nil)),
% 0.13/0.41 inference(forward_demodulation,[status(thm)],[f423,f425])).
% 0.13/0.41 fof(f472,plain,(
% 0.13/0.41 sP0_prd(sK48_skl,sK47_skl,sK48_skl,sK47_skl)|neq(sK48_skl,nil)),
% 0.13/0.41 inference(forward_demodulation,[status(thm)],[f424,f471])).
% 0.13/0.41 fof(f473,plain,(
% 0.13/0.41 sP0_prd(sK48_skl,sK49_skl,sK48_skl,sK47_skl)|~neq(sK50_skl,nil)),
% 0.13/0.41 inference(forward_demodulation,[status(thm)],[f423,f426])).
% 0.13/0.41 fof(f474,plain,(
% 0.13/0.41 sP0_prd(sK48_skl,sK47_skl,sK48_skl,sK47_skl)|~neq(sK50_skl,nil)),
% 0.13/0.41 inference(forward_demodulation,[status(thm)],[f424,f473])).
% 0.13/0.41 fof(f475,plain,(
% 0.13/0.41 sP0_prd(sK48_skl,sK47_skl,sK48_skl,sK47_skl)|~neq(sK48_skl,nil)),
% 0.13/0.41 inference(forward_demodulation,[status(thm)],[f423,f474])).
% 0.13/0.41 fof(f476,plain,(
% 0.13/0.41 sP0_prd(sK48_skl,sK47_skl,sK48_skl,sK47_skl)),
% 0.13/0.41 inference(forward_subsumption_resolution,[status(thm)],[f475,f472])).
% 0.13/0.41 fof(f482,plain,(
% 0.13/0.41 ~singletonP(sK47_skl)),
% 0.13/0.41 inference(resolution,[status(thm)],[f476,f435])).
% 0.13/0.41 fof(f491,plain,(
% 0.13/0.41 ssItem(sK51_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl))),
% 0.13/0.41 inference(resolution,[status(thm)],[f431,f476])).
% 0.13/0.41 fof(f511,plain,(
% 0.13/0.41 cons(sK51_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl),nil)=sK47_skl),
% 0.13/0.41 inference(resolution,[status(thm)],[f433,f476])).
% 0.13/0.41 fof(f512,plain,(
% 0.13/0.41 ~ssList(cons(sK51_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl),nil))|singletonP(sK47_skl)|~ssItem(sK51_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl))),
% 0.13/0.41 inference(paramodulation,[status(thm)],[f511,f440])).
% 0.13/0.41 fof(f515,plain,(
% 0.13/0.41 ~ssList(sK47_skl)|singletonP(sK47_skl)|~ssItem(sK51_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl))),
% 0.13/0.41 inference(forward_demodulation,[status(thm)],[f511,f512])).
% 0.13/0.41 fof(f516,plain,(
% 0.13/0.41 singletonP(sK47_skl)|~ssItem(sK51_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl))),
% 0.13/0.41 inference(forward_subsumption_resolution,[status(thm)],[f515,f419])).
% 0.13/0.41 fof(f633,plain,(
% 0.13/0.41 singletonP(sK47_skl)),
% 0.13/0.41 inference(resolution,[status(thm)],[f516,f491])).
% 0.13/0.41 fof(f634,plain,(
% 0.13/0.41 $false),
% 0.13/0.41 inference(forward_subsumption_resolution,[status(thm)],[f633,f482])).
% 0.13/0.41 % SZS output end CNFRefutation for theBenchmark.p
% 0.13/0.44 % Elapsed time: 0.075418 seconds
% 0.13/0.44 % CPU time: 0.315141 seconds
% 0.13/0.44 % Total memory used: 48.651 MB
% 0.13/0.44 % Net memory used: 48.322 MB
%------------------------------------------------------------------------------