%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SWC012+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 : n014.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 38.09s 5.31s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC012+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
% 0.10/0.35 % Computer : n014.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Mon Sep 21 07:48:50 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 38.09/5.31 % Refutation found
% 38.09/5.31 % SZS status Theorem for theBenchmark: Theorem is valid
% 38.09/5.31 % SZS output start CNFRefutation for theBenchmark
% 38.09/5.31 fof(f17,axiom,(
% 38.09/5.31 ssList(nil) ),
% 38.09/5.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 38.09/5.31 fof(f84,axiom,(
% 38.09/5.31 (! [U] :( ssList(U)=> app(U,nil) = U ) )),
% 38.09/5.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 38.09/5.31 fof(f96,conjecture,(
% 38.09/5.31 (! [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)& (? [X1] :( ssList(X1)& app(app(Z,cons(Y,nil)),X1) = V& app(Z,X1) = U ) )) )))| (! [X2] :( ssItem(X2)=> app(W,cons(X2,nil)) != X ) ))& ( ~ neq(V,nil)| neq(X,nil) ) ) ) ) )) )) )) )),
% 38.09/5.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 38.09/5.31 fof(f97,negated_conjecture,(
% 38.09/5.31 ~((! [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)& (? [X1] :( ssList(X1)& app(app(Z,cons(Y,nil)),X1) = V& app(Z,X1) = U ) )) )))| (! [X2] :( ssItem(X2)=> app(W,cons(X2,nil)) != X ) ))& ( ~ neq(V,nil)| neq(X,nil) ) ) ) ) )) )) )) ))),
% 38.09/5.31 inference(negated_conjecture,[status(cth)],[f96])).
% 38.09/5.31 fof(f223,plain,(
% 38.09/5.31 ssList(nil)),
% 38.09/5.31 inference(cnf_transformation,[status(thm)],[f17])).
% 38.09/5.31 fof(f388,plain,(
% 38.09/5.31 ![U]: (~ssList(U)|app(U,nil)=U)),
% 38.09/5.31 inference(pre_NNF_transformation,[status(thm)],[f84])).
% 38.09/5.31 fof(f389,plain,(
% 38.09/5.31 ![X0]: (~ssList(X0)|app(X0,nil)=X0)),
% 38.09/5.31 inference(cnf_transformation,[status(thm)],[f388])).
% 38.09/5.31 fof(f415,plain,(
% 38.09/5.31 (?[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)|(![X1]: ((~ssList(X1)|~app(app(Z,cons(Y,nil)),X1)=V)|~app(Z,X1)=U)))))))&(?[X2]: (ssItem(X2)&app(W,cons(X2,nil))=X)))|(neq(V,nil)&~neq(X,nil))))))))))))),
% 38.09/5.31 inference(pre_NNF_transformation,[status(thm)],[f97])).
% 38.09/5.31 fof(f416,definition,(
% 38.09/5.31 ![U,V,W,X]: (sP0_prd(X,W,V,U)<=>((neq(V,nil)&(![Y]: (~ssItem(Y)|(![Z]: (~ssList(Z)|(![X1]: ((~ssList(X1)|~app(app(Z,cons(Y,nil)),X1)=V)|~app(Z,X1)=U)))))))&(?[X2]: (ssItem(X2)&app(W,cons(X2,nil))=X))))),
% 38.09/5.31 introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 38.09/5.31 fof(f417,plain,(
% 38.09/5.31 ?[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)))))))))))),
% 38.09/5.31 inference(formula_renaming,[status(thm)],[f415,f416])).
% 38.09/5.31 fof(f418,plain,(
% 38.09/5.31 (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))))))))),
% 38.09/5.31 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])).
% 38.09/5.31 fof(f421,plain,(
% 38.09/5.31 ssList(sK49_skl)),
% 38.09/5.31 inference(cnf_transformation,[status(thm)],[f418])).
% 38.09/5.31 fof(f422,plain,(
% 38.09/5.31 ssList(sK50_skl)),
% 38.09/5.31 inference(cnf_transformation,[status(thm)],[f418])).
% 38.09/5.31 fof(f423,plain,(
% 38.09/5.31 sK48_skl=sK50_skl),
% 38.09/5.31 inference(cnf_transformation,[status(thm)],[f418])).
% 38.09/5.31 fof(f424,plain,(
% 38.09/5.31 sK47_skl=sK49_skl),
% 38.09/5.31 inference(cnf_transformation,[status(thm)],[f418])).
% 38.09/5.31 fof(f425,plain,(
% 38.09/5.31 sP0_prd(sK50_skl,sK49_skl,sK48_skl,sK47_skl)|neq(sK48_skl,nil)),
% 38.09/5.31 inference(cnf_transformation,[status(thm)],[f418])).
% 38.09/5.31 fof(f426,plain,(
% 38.09/5.31 sP0_prd(sK50_skl,sK49_skl,sK48_skl,sK47_skl)|~neq(sK50_skl,nil)),
% 38.09/5.31 inference(cnf_transformation,[status(thm)],[f418])).
% 38.09/5.31 fof(f427,plain,(
% 38.09/5.31 ![U,V,W,X]: ((~sP0_prd(X,W,V,U)|((neq(V,nil)&(![Y]: (~ssItem(Y)|(![Z]: (~ssList(Z)|(![X1]: ((~ssList(X1)|~app(app(Z,cons(Y,nil)),X1)=V)|~app(Z,X1)=U)))))))&(?[X2]: (ssItem(X2)&app(W,cons(X2,nil))=X))))&(sP0_prd(X,W,V,U)|((~neq(V,nil)|(?[Y]: (ssItem(Y)&(?[Z]: (ssList(Z)&(?[X1]: ((ssList(X1)&app(app(Z,cons(Y,nil)),X1)=V)&app(Z,X1)=U)))))))|(![X2]: (~ssItem(X2)|~app(W,cons(X2,nil))=X)))))),
% 38.09/5.31 inference(NNF_transformation,[status(thm)],[f416])).
% 38.09/5.31 fof(f428,plain,(
% 38.09/5.31 (![U,V,W,X]: (~sP0_prd(X,W,V,U)|((neq(V,nil)&(![Y]: (~ssItem(Y)|(![Z]: (~ssList(Z)|(![X1]: ((~ssList(X1)|~app(app(Z,cons(Y,nil)),X1)=V)|~app(Z,X1)=U)))))))&(?[X2]: (ssItem(X2)&app(W,cons(X2,nil))=X)))))&(![U,V,W,X]: (sP0_prd(X,W,V,U)|((~neq(V,nil)|(?[Y]: (ssItem(Y)&(?[Z]: (ssList(Z)&(?[X1]: ((ssList(X1)&app(app(Z,cons(Y,nil)),X1)=V)&app(Z,X1)=U)))))))|(![X2]: (~ssItem(X2)|~app(W,cons(X2,nil))=X)))))),
% 38.09/5.31 inference(miniscoping,[status(thm)],[f427])).
% 38.09/5.31 fof(f429,plain,(
% 38.09/5.31 (![U,V,W,X]: (~sP0_prd(X,W,V,U)|((neq(V,nil)&(![Y]: (~ssItem(Y)|(![Z]: (~ssList(Z)|(![X1]: ((~ssList(X1)|~app(app(Z,cons(Y,nil)),X1)=V)|~app(Z,X1)=U)))))))&(ssItem(sK51_skl(X,W,V,U))&app(W,cons(sK51_skl(X,W,V,U),nil))=X))))&(![U,V,W,X]: (sP0_prd(X,W,V,U)|((~neq(V,nil)|(ssItem(sK52_skl(X,W,V,U))&(ssList(sK53_skl(X,W,V,U))&((ssList(sK54_skl(X,W,V,U))&app(app(sK53_skl(X,W,V,U),cons(sK52_skl(X,W,V,U),nil)),sK54_skl(X,W,V,U))=V)&app(sK53_skl(X,W,V,U),sK54_skl(X,W,V,U))=U))))|(![X2]: (~ssItem(X2)|~app(W,cons(X2,nil))=X)))))),
% 38.09/5.31 inference(skolemize,[status(esa),new_symbols(skolem,[sK51_skl,sK52_skl,sK53_skl,sK54_skl]),skolemize(X2,sK51_skl(X,W,V,U)),skolemize(Y,sK52_skl(X,W,V,U)),skolemize(Z,sK53_skl(X,W,V,U)),skolemize(X1,sK54_skl(X,W,V,U))],[f428])).
% 38.09/5.31 fof(f430,plain,(
% 38.09/5.31 ![X0,X1,X2,X3]: (~sP0_prd(X0,X1,X2,X3)|neq(X2,nil))),
% 38.09/5.31 inference(cnf_transformation,[status(thm)],[f429])).
% 38.09/5.31 fof(f431,plain,(
% 38.09/5.31 ![X0,X1,X2,X3,X4,X5,X6]: (~sP0_prd(X0,X1,X2,X3)|~ssItem(X4)|~ssList(X5)|~ssList(X6)|~app(app(X5,cons(X4,nil)),X6)=X2|~app(X5,X6)=X3)),
% 38.09/5.31 inference(cnf_transformation,[status(thm)],[f429])).
% 38.09/5.31 fof(f432,plain,(
% 38.09/5.31 ![X0,X1,X2,X3]: (~sP0_prd(X0,X1,X2,X3)|ssItem(sK51_skl(X0,X1,X2,X3)))),
% 38.09/5.31 inference(cnf_transformation,[status(thm)],[f429])).
% 38.09/5.31 fof(f433,plain,(
% 38.09/5.31 ![X0,X1,X2,X3]: (~sP0_prd(X0,X1,X2,X3)|app(X1,cons(sK51_skl(X0,X1,X2,X3),nil))=X0)),
% 38.09/5.31 inference(cnf_transformation,[status(thm)],[f429])).
% 38.09/5.31 fof(f469,plain,(
% 38.09/5.31 ![X0,X1,X2,X3,X4]: (~sP0_prd(X0,X1,app(app(X2,cons(X3,nil)),X4),app(X2,X4))|~ssItem(X3)|~ssList(X2)|~ssList(X4))),
% 38.09/5.31 inference(destructive_equality_resolution,[status(thm)],[f431])).
% 38.09/5.31 fof(f490,plain,(
% 38.09/5.31 sP0_prd(sK50_skl,sK49_skl,sK50_skl,sK47_skl)|neq(sK48_skl,nil)),
% 38.09/5.31 inference(forward_demodulation,[status(thm)],[f423,f425])).
% 38.09/5.31 fof(f491,plain,(
% 38.09/5.31 sP0_prd(sK50_skl,sK49_skl,sK50_skl,sK49_skl)|neq(sK48_skl,nil)),
% 38.09/5.31 inference(forward_demodulation,[status(thm)],[f424,f490])).
% 38.09/5.31 fof(f492,plain,(
% 38.09/5.31 sP0_prd(sK50_skl,sK49_skl,sK50_skl,sK49_skl)|neq(sK50_skl,nil)),
% 38.09/5.31 inference(forward_demodulation,[status(thm)],[f423,f491])).
% 38.09/5.31 fof(f493,plain,(
% 38.09/5.31 neq(sK50_skl,nil)),
% 38.09/5.31 inference(forward_subsumption_resolution,[status(thm)],[f492,f430])).
% 38.09/5.31 fof(f495,plain,(
% 38.09/5.31 app(sK50_skl,nil)=sK50_skl),
% 38.09/5.31 inference(resolution,[status(thm)],[f389,f422])).
% 38.09/5.31 fof(f496,plain,(
% 38.09/5.31 app(sK49_skl,nil)=sK49_skl),
% 38.09/5.31 inference(resolution,[status(thm)],[f389,f421])).
% 38.09/5.31 fof(f522,plain,(
% 38.09/5.31 sP0_prd(sK50_skl,sK49_skl,sK50_skl,sK47_skl)|~neq(sK50_skl,nil)),
% 38.09/5.31 inference(forward_demodulation,[status(thm)],[f423,f426])).
% 38.09/5.31 fof(f523,plain,(
% 38.09/5.31 sP0_prd(sK50_skl,sK49_skl,sK50_skl,sK49_skl)|~neq(sK50_skl,nil)),
% 38.09/5.31 inference(forward_demodulation,[status(thm)],[f424,f522])).
% 38.09/5.31 fof(f524,plain,(
% 38.09/5.31 sP0_prd(sK50_skl,sK49_skl,sK50_skl,sK49_skl)),
% 38.09/5.31 inference(forward_subsumption_resolution,[status(thm)],[f523,f493])).
% 38.09/5.31 fof(f682,plain,(
% 38.09/5.31 ![X0,X1,X2]: (~sP0_prd(X0,X1,app(app(sK49_skl,cons(X2,nil)),nil),sK49_skl)|~ssItem(X2)|~ssList(sK49_skl)|~ssList(nil))),
% 38.09/5.31 inference(paramodulation,[status(thm)],[f496,f469])).
% 38.09/5.31 fof(f687,plain,(
% 38.09/5.31 ![X0,X1,X2]: (~sP0_prd(X0,X1,app(app(sK49_skl,cons(X2,nil)),nil),sK49_skl)|~ssItem(X2)|~ssList(nil))),
% 38.09/5.31 inference(forward_subsumption_resolution,[status(thm)],[f682,f421])).
% 38.09/5.31 fof(f848,plain,(
% 38.09/5.31 ssItem(sK51_skl(sK50_skl,sK49_skl,sK50_skl,sK49_skl))),
% 38.09/5.31 inference(resolution,[status(thm)],[f432,f524])).
% 38.09/5.31 fof(f1067,plain,(
% 38.09/5.31 app(sK49_skl,cons(sK51_skl(sK50_skl,sK49_skl,sK50_skl,sK49_skl),nil))=sK50_skl),
% 38.09/5.31 inference(resolution,[status(thm)],[f433,f524])).
% 38.09/5.31 fof(f44617,plain,(
% 38.09/5.31 ![X0,X1,X2]: (~sP0_prd(X0,X1,app(app(sK49_skl,cons(X2,nil)),nil),sK49_skl)|~ssItem(X2))),
% 38.09/5.31 inference(forward_subsumption_resolution,[status(thm)],[f687,f223])).
% 38.09/5.31 fof(f44618,plain,(
% 38.09/5.31 ![X0,X1]: (~sP0_prd(X0,X1,app(sK50_skl,nil),sK49_skl)|~ssItem(sK51_skl(sK50_skl,sK49_skl,sK50_skl,sK49_skl)))),
% 38.09/5.31 inference(paramodulation,[status(thm)],[f1067,f44617])).
% 38.90/5.36 fof(f44619,plain,(
% 38.90/5.36 ![X0,X1]: (~sP0_prd(X0,X1,sK50_skl,sK49_skl)|~ssItem(sK51_skl(sK50_skl,sK49_skl,sK50_skl,sK49_skl)))),
% 38.90/5.36 inference(forward_demodulation,[status(thm)],[f495,f44618])).
% 38.90/5.36 fof(f44620,plain,(
% 38.90/5.36 ![X0,X1]: (~sP0_prd(X0,X1,sK50_skl,sK49_skl))),
% 38.90/5.36 inference(forward_subsumption_resolution,[status(thm)],[f44619,f848])).
% 38.90/5.36 fof(f44623,plain,(
% 38.90/5.36 $false),
% 38.90/5.36 inference(backward_subsumption_resolution,[status(thm)],[f524,f44620])).
% 38.90/5.36 % SZS output end CNFRefutation for theBenchmark.p
% 38.90/5.37 % Elapsed time: 4.999413 seconds
% 38.90/5.37 % CPU time: 39.275985 seconds
% 38.90/5.37 % Total memory used: 413.763 MB
% 38.90/5.37 % Net memory used: 392.883 MB
%------------------------------------------------------------------------------