%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SWC096+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 : n004.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 02:41:34 PM UTC 2026
% Result : Theorem 30.45s 4.41s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWC096+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
% 0.16/0.43 % Computer : n004.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Mon Sep 21 07:55:04 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.47 % Drodi V4.1.1
% 30.45/4.41 % Refutation found
% 30.45/4.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 30.45/4.41 % SZS output start CNFRefutation for theBenchmark
% 30.45/4.41 fof(f96,conjecture,(
% 30.45/4.41 (! [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) = U& app(Z,cons(Y,nil)) = V ) )))| (! [X1] :( ssItem(X1)=> (! [X2] :( ~ ssList(X2)| cons(X1,nil) != W| app(X2,cons(X1,nil)) != X ) )) ))& ( ~ neq(V,nil)| neq(X,nil) ) ) ) )) )) )) )),
% 30.45/4.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 30.45/4.41 fof(f97,negated_conjecture,(
% 30.45/4.41 ~((! [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) = U& app(Z,cons(Y,nil)) = V ) )))| (! [X1] :( ssItem(X1)=> (! [X2] :( ~ ssList(X2)| cons(X1,nil) != W| app(X2,cons(X1,nil)) != X ) )) ))& ( ~ neq(V,nil)| neq(X,nil) ) ) ) )) )) )) ))),
% 30.45/4.41 inference(negated_conjecture,[status(cth)],[f96])).
% 30.45/4.41 fof(f415,plain,(
% 30.45/4.41 (?[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)=U)|~app(Z,cons(Y,nil))=V)))))&(?[X1]: (ssItem(X1)&(?[X2]: ((ssList(X2)&cons(X1,nil)=W)&app(X2,cons(X1,nil))=X)))))|(neq(V,nil)&~neq(X,nil)))))))))))),
% 30.45/4.41 inference(pre_NNF_transformation,[status(thm)],[f97])).
% 30.45/4.41 fof(f416,definition,(
% 30.45/4.41 ![U,V,W,X]: (sP0_prd(X,W,V,U)<=>((neq(V,nil)&(![Y]: (~ssItem(Y)|(![Z]: ((~ssList(Z)|~cons(Y,nil)=U)|~app(Z,cons(Y,nil))=V)))))&(?[X1]: (ssItem(X1)&(?[X2]: ((ssList(X2)&cons(X1,nil)=W)&app(X2,cons(X1,nil))=X))))))),
% 30.45/4.41 introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 30.45/4.41 fof(f417,plain,(
% 30.45/4.41 ?[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))))))))))),
% 30.45/4.41 inference(formula_renaming,[status(thm)],[f415,f416])).
% 30.45/4.41 fof(f418,plain,(
% 30.45/4.41 (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)))))))),
% 30.45/4.41 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])).
% 30.45/4.41 fof(f423,plain,(
% 30.45/4.41 sK48_skl=sK50_skl),
% 30.45/4.41 inference(cnf_transformation,[status(thm)],[f418])).
% 30.45/4.41 fof(f424,plain,(
% 30.45/4.41 sK47_skl=sK49_skl),
% 30.45/4.41 inference(cnf_transformation,[status(thm)],[f418])).
% 30.45/4.41 fof(f425,plain,(
% 30.45/4.41 sP0_prd(sK50_skl,sK49_skl,sK48_skl,sK47_skl)|neq(sK48_skl,nil)),
% 30.45/4.41 inference(cnf_transformation,[status(thm)],[f418])).
% 30.45/4.41 fof(f426,plain,(
% 30.45/4.41 sP0_prd(sK50_skl,sK49_skl,sK48_skl,sK47_skl)|~neq(sK50_skl,nil)),
% 30.45/4.41 inference(cnf_transformation,[status(thm)],[f418])).
% 30.45/4.41 fof(f427,plain,(
% 30.45/4.41 ![U,V,W,X]: ((~sP0_prd(X,W,V,U)|((neq(V,nil)&(![Y]: (~ssItem(Y)|(![Z]: ((~ssList(Z)|~cons(Y,nil)=U)|~app(Z,cons(Y,nil))=V)))))&(?[X1]: (ssItem(X1)&(?[X2]: ((ssList(X2)&cons(X1,nil)=W)&app(X2,cons(X1,nil))=X))))))&(sP0_prd(X,W,V,U)|((~neq(V,nil)|(?[Y]: (ssItem(Y)&(?[Z]: ((ssList(Z)&cons(Y,nil)=U)&app(Z,cons(Y,nil))=V)))))|(![X1]: (~ssItem(X1)|(![X2]: ((~ssList(X2)|~cons(X1,nil)=W)|~app(X2,cons(X1,nil))=X)))))))),
% 30.45/4.41 inference(NNF_transformation,[status(thm)],[f416])).
% 30.45/4.41 fof(f428,plain,(
% 30.45/4.41 (![U,V,W,X]: (~sP0_prd(X,W,V,U)|((neq(V,nil)&(![Y]: (~ssItem(Y)|(![Z]: ((~ssList(Z)|~cons(Y,nil)=U)|~app(Z,cons(Y,nil))=V)))))&(?[X1]: (ssItem(X1)&(?[X2]: ((ssList(X2)&cons(X1,nil)=W)&app(X2,cons(X1,nil))=X)))))))&(![U,V,W,X]: (sP0_prd(X,W,V,U)|((~neq(V,nil)|(?[Y]: (ssItem(Y)&(?[Z]: ((ssList(Z)&cons(Y,nil)=U)&app(Z,cons(Y,nil))=V)))))|(![X1]: (~ssItem(X1)|(![X2]: ((~ssList(X2)|~cons(X1,nil)=W)|~app(X2,cons(X1,nil))=X)))))))),
% 30.45/4.41 inference(miniscoping,[status(thm)],[f427])).
% 30.45/4.41 fof(f429,plain,(
% 30.45/4.41 (![U,V,W,X]: (~sP0_prd(X,W,V,U)|((neq(V,nil)&(![Y]: (~ssItem(Y)|(![Z]: ((~ssList(Z)|~cons(Y,nil)=U)|~app(Z,cons(Y,nil))=V)))))&(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)))))&(![U,V,W,X]: (sP0_prd(X,W,V,U)|((~neq(V,nil)|(ssItem(sK53_skl(X,W,V,U))&((ssList(sK54_skl(X,W,V,U))&cons(sK53_skl(X,W,V,U),nil)=U)&app(sK54_skl(X,W,V,U),cons(sK53_skl(X,W,V,U),nil))=V)))|(![X1]: (~ssItem(X1)|(![X2]: ((~ssList(X2)|~cons(X1,nil)=W)|~app(X2,cons(X1,nil))=X)))))))),
% 30.45/4.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK51_skl,sK52_skl,sK53_skl,sK54_skl]),skolemize(X1,sK51_skl(X,W,V,U)),skolemize(X2,sK52_skl(X,W,V,U)),skolemize(Y,sK53_skl(X,W,V,U)),skolemize(Z,sK54_skl(X,W,V,U))],[f428])).
% 30.45/4.41 fof(f431,plain,(
% 30.45/4.41 ![X0,X1,X2,X3,X4,X5]: (~sP0_prd(X0,X1,X2,X3)|~ssItem(X4)|~ssList(X5)|~cons(X4,nil)=X3|~app(X5,cons(X4,nil))=X2)),
% 30.45/4.41 inference(cnf_transformation,[status(thm)],[f429])).
% 30.45/4.41 fof(f432,plain,(
% 30.45/4.41 ![X0,X1,X2,X3]: (~sP0_prd(X0,X1,X2,X3)|ssItem(sK51_skl(X0,X1,X2,X3)))),
% 30.45/4.41 inference(cnf_transformation,[status(thm)],[f429])).
% 30.45/4.41 fof(f433,plain,(
% 30.45/4.41 ![X0,X1,X2,X3]: (~sP0_prd(X0,X1,X2,X3)|ssList(sK52_skl(X0,X1,X2,X3)))),
% 30.45/4.41 inference(cnf_transformation,[status(thm)],[f429])).
% 30.45/4.41 fof(f434,plain,(
% 30.45/4.41 ![X0,X1,X2,X3]: (~sP0_prd(X0,X1,X2,X3)|cons(sK51_skl(X0,X1,X2,X3),nil)=X1)),
% 30.45/4.41 inference(cnf_transformation,[status(thm)],[f429])).
% 30.45/4.41 fof(f435,plain,(
% 30.45/4.41 ![X0,X1,X2,X3]: (~sP0_prd(X0,X1,X2,X3)|app(sK52_skl(X0,X1,X2,X3),cons(sK51_skl(X0,X1,X2,X3),nil))=X0)),
% 30.45/4.41 inference(cnf_transformation,[status(thm)],[f429])).
% 30.45/4.41 fof(f474,plain,(
% 30.45/4.41 sP0_prd(sK48_skl,sK49_skl,sK48_skl,sK47_skl)|neq(sK48_skl,nil)),
% 30.45/4.41 inference(forward_demodulation,[status(thm)],[f423,f425])).
% 30.45/4.41 fof(f475,plain,(
% 30.45/4.41 sP0_prd(sK48_skl,sK47_skl,sK48_skl,sK47_skl)|neq(sK48_skl,nil)),
% 30.45/4.41 inference(forward_demodulation,[status(thm)],[f424,f474])).
% 30.45/4.41 fof(f476,plain,(
% 30.45/4.41 sP0_prd(sK48_skl,sK49_skl,sK48_skl,sK47_skl)|~neq(sK50_skl,nil)),
% 30.45/4.41 inference(forward_demodulation,[status(thm)],[f423,f426])).
% 30.45/4.41 fof(f477,plain,(
% 30.45/4.41 sP0_prd(sK48_skl,sK47_skl,sK48_skl,sK47_skl)|~neq(sK50_skl,nil)),
% 30.45/4.41 inference(forward_demodulation,[status(thm)],[f424,f476])).
% 30.45/4.41 fof(f478,plain,(
% 30.45/4.41 sP0_prd(sK48_skl,sK47_skl,sK48_skl,sK47_skl)|~neq(sK48_skl,nil)),
% 30.45/4.41 inference(forward_demodulation,[status(thm)],[f423,f477])).
% 30.45/4.41 fof(f479,plain,(
% 30.45/4.41 sP0_prd(sK48_skl,sK47_skl,sK48_skl,sK47_skl)),
% 30.45/4.41 inference(forward_subsumption_resolution,[status(thm)],[f478,f475])).
% 30.45/4.41 fof(f480,plain,(
% 30.45/4.41 ![X0,X1,X2,X3]: (~sP0_prd(X0,X1,app(X2,cons(X3,nil)),cons(X3,nil))|~ssItem(X3)|~ssList(X2))),
% 30.45/4.41 inference(destructive_equality_resolution,[status(thm)],[f431])).
% 30.45/4.41 fof(f508,plain,(
% 30.45/4.41 ssItem(sK51_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl))),
% 30.45/4.41 inference(resolution,[status(thm)],[f432,f479])).
% 30.45/4.41 fof(f513,plain,(
% 30.45/4.41 ![X0,X1,X2]: (~sP0_prd(X0,X1,app(X2,cons(sK51_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl),nil)),cons(sK51_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl),nil))|~ssList(X2))),
% 30.45/4.41 inference(resolution,[status(thm)],[f508,f480])).
% 30.45/4.41 fof(f517,plain,(
% 30.45/4.41 ssList(sK52_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl))),
% 30.45/4.41 inference(resolution,[status(thm)],[f433,f479])).
% 30.45/4.41 fof(f583,plain,(
% 30.45/4.41 cons(sK51_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl),nil)=sK47_skl),
% 30.45/4.41 inference(resolution,[status(thm)],[f434,f479])).
% 30.45/4.41 fof(f585,plain,(
% 30.45/4.41 ![X0,X1,X2]: (~sP0_prd(X0,X1,app(X2,cons(sK51_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl),nil)),sK47_skl)|~ssList(X2))),
% 30.45/4.41 inference(backward_demodulation,[status(thm)],[f583,f513])).
% 30.45/4.41 fof(f590,plain,(
% 30.45/4.41 ![X0,X1,X2]: (~sP0_prd(X0,X1,app(X2,sK47_skl),sK47_skl)|~ssList(X2))),
% 30.45/4.41 inference(forward_demodulation,[status(thm)],[f583,f585])).
% 30.45/4.41 fof(f691,plain,(
% 30.45/4.41 app(sK52_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl),cons(sK51_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl),nil))=sK48_skl),
% 30.45/4.41 inference(resolution,[status(thm)],[f435,f479])).
% 30.45/4.41 fof(f692,plain,(
% 30.45/4.41 app(sK52_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl),sK47_skl)=sK48_skl),
% 30.45/4.41 inference(forward_demodulation,[status(thm)],[f583,f691])).
% 30.45/4.41 fof(f2268,plain,(
% 30.45/4.41 ![X0,X1]: (~sP0_prd(X0,X1,sK48_skl,sK47_skl)|~ssList(sK52_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl)))),
% 30.45/4.41 inference(paramodulation,[status(thm)],[f692,f590])).
% 30.45/4.41 fof(f2271,plain,(
% 30.45/4.41 ![X0,X1]: (~sP0_prd(X0,X1,sK48_skl,sK47_skl))),
% 30.45/4.41 inference(forward_subsumption_resolution,[status(thm)],[f2268,f517])).
% 30.45/4.41 fof(f2272,plain,(
% 30.45/4.41 $false),
% 30.45/4.41 inference(backward_subsumption_resolution,[status(thm)],[f479,f2271])).
% 30.45/4.41 % SZS output end CNFRefutation for theBenchmark.p
% 4.60/4.46 % Elapsed time: 4.008739 seconds
% 4.60/4.46 % CPU time: 31.151878 seconds
% 4.60/4.46 % Total memory used: 275.952 MB
% 4.60/4.46 % Net memory used: 265.127 MB
%------------------------------------------------------------------------------