%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SWC101+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 : n012.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 02:41:35 PM UTC 2026
% Result : Theorem 0.07s 0.34s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWC101+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.02 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.29 % CPULimit : 300
% 0.03/0.29 % WCLimit : 300
% 0.03/0.29 % DateTime : Mon Sep 21 07:55:06 UTC 2026
% 0.03/0.29 % CPUTime :
% 0.03/0.30 % Drodi V4.1.1
% 0.07/0.34 % Refutation found
% 0.07/0.34 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.07/0.34 % SZS output start CNFRefutation for theBenchmark
% 0.07/0.34 fof(f5,axiom,(
% 0.07/0.34 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> ( frontsegP(U,V)<=> (? [W] :( ssList(W)& app(V,W) = U ) )) ) )) )),
% 0.07/0.34 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.07/0.34 fof(f15,axiom,(
% 0.07/0.34 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> ( neq(U,V)<=> U != V ) ) )) )),
% 0.07/0.34 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.07/0.34 fof(f17,axiom,(
% 0.07/0.34 ssList(nil) ),
% 0.07/0.34 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.07/0.34 fof(f96,conjecture,(
% 0.07/0.34 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> (! [X] :( ssList(X)=> ( V != X| U != W| (! [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 )| ( nil = V& nil = U )| ( neq(U,nil)& frontsegP(V,U) ) ) ) )) )) )) )),
% 0.07/0.34 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.07/0.34 fof(f97,negated_conjecture,(
% 0.07/0.34 ~((! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> (! [X] :( ssList(X)=> ( V != X| U != W| (! [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 )| ( nil = V& nil = U )| ( neq(U,nil)& frontsegP(V,U) ) ) ) )) )) )) ))),
% 0.07/0.34 inference(negated_conjecture,[status(cth)],[f96])).
% 0.07/0.34 fof(f119,plain,(
% 0.07/0.34 ![U]: (~ssList(U)|(![V]: (~ssList(V)|(frontsegP(U,V)<=>(?[W]: (ssList(W)&app(V,W)=U))))))),
% 0.07/0.34 inference(pre_NNF_transformation,[status(thm)],[f5])).
% 0.07/0.34 fof(f120,plain,(
% 0.07/0.34 ![U]: (~ssList(U)|(![V]: (~ssList(V)|((~frontsegP(U,V)|(?[W]: (ssList(W)&app(V,W)=U)))&(frontsegP(U,V)|(![W]: (~ssList(W)|~app(V,W)=U)))))))),
% 0.07/0.34 inference(NNF_transformation,[status(thm)],[f119])).
% 0.07/0.34 fof(f121,plain,(
% 0.07/0.34 ![U]: (~ssList(U)|(![V]: (~ssList(V)|((~frontsegP(U,V)|(ssList(sK5_skl(V,U))&app(V,sK5_skl(V,U))=U))&(frontsegP(U,V)|(![W]: (~ssList(W)|~app(V,W)=U)))))))),
% 0.07/0.34 inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(W,sK5_skl(V,U))],[f120])).
% 0.07/0.34 fof(f124,plain,(
% 0.07/0.34 ![X0,X1,X2]: (~ssList(X0)|~ssList(X1)|frontsegP(X0,X1)|~ssList(X2)|~app(X1,X2)=X0)),
% 0.07/0.34 inference(cnf_transformation,[status(thm)],[f121])).
% 0.07/0.34 fof(f217,plain,(
% 0.07/0.34 ![U]: (~ssList(U)|(![V]: (~ssList(V)|(neq(U,V)<=>~U=V))))),
% 0.07/0.34 inference(pre_NNF_transformation,[status(thm)],[f15])).
% 0.07/0.34 fof(f218,plain,(
% 0.07/0.34 ![U]: (~ssList(U)|(![V]: (~ssList(V)|((~neq(U,V)|~U=V)&(neq(U,V)|U=V)))))),
% 0.07/0.34 inference(NNF_transformation,[status(thm)],[f217])).
% 0.07/0.34 fof(f220,plain,(
% 0.07/0.34 ![X0,X1]: (~ssList(X0)|~ssList(X1)|neq(X0,X1)|X0=X1)),
% 0.07/0.34 inference(cnf_transformation,[status(thm)],[f218])).
% 0.07/0.34 fof(f223,plain,(
% 0.07/0.34 ssList(nil)),
% 0.07/0.34 inference(cnf_transformation,[status(thm)],[f17])).
% 0.07/0.34 fof(f415,plain,(
% 0.07/0.34 (?[U]: (ssList(U)&(?[V]: (ssList(V)&(?[W]: (ssList(W)&(?[X]: (ssList(X)&(((((V=X&U=W)&(?[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))&(~nil=V|~nil=U))&(~neq(U,nil)|~frontsegP(V,U)))))))))))),
% 0.07/0.34 inference(pre_NNF_transformation,[status(thm)],[f97])).
% 0.07/0.34 fof(f416,plain,(
% 0.07/0.34 ?[U]: (ssList(U)&(?[V]: (ssList(V)&(?[W]: (ssList(W)&(?[X]: (ssList(X)&(((((V=X&U=W)&(?[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))&(~nil=V|~nil=U))&(~neq(U,nil)|~frontsegP(V,U))))))))))),
% 0.07/0.34 inference(miniscoping,[status(thm)],[f415])).
% 0.07/0.34 fof(f417,plain,(
% 0.07/0.34 (ssList(sK47_skl)&(ssList(sK48_skl)&(ssList(sK49_skl)&(ssList(sK50_skl)&(((((sK48_skl=sK50_skl&sK47_skl=sK49_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))&(~nil=sK48_skl|~nil=sK47_skl))&(~neq(sK47_skl,nil)|~frontsegP(sK48_skl,sK47_skl)))))))),
% 0.07/0.34 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])).
% 0.07/0.34 fof(f418,plain,(
% 0.07/0.34 ssList(sK47_skl)),
% 0.07/0.34 inference(cnf_transformation,[status(thm)],[f417])).
% 0.07/0.34 fof(f419,plain,(
% 0.07/0.34 ssList(sK48_skl)),
% 0.07/0.34 inference(cnf_transformation,[status(thm)],[f417])).
% 0.07/0.34 fof(f422,plain,(
% 0.07/0.34 sK48_skl=sK50_skl),
% 0.07/0.34 inference(cnf_transformation,[status(thm)],[f417])).
% 0.07/0.34 fof(f423,plain,(
% 0.07/0.34 sK47_skl=sK49_skl),
% 0.07/0.34 inference(cnf_transformation,[status(thm)],[f417])).
% 0.07/0.34 fof(f424,plain,(
% 0.07/0.34 ssList(sK51_skl)),
% 0.07/0.34 inference(cnf_transformation,[status(thm)],[f417])).
% 0.07/0.34 fof(f425,plain,(
% 0.07/0.34 app(sK49_skl,sK51_skl)=sK50_skl),
% 0.07/0.34 inference(cnf_transformation,[status(thm)],[f417])).
% 0.07/0.34 fof(f428,plain,(
% 0.07/0.34 nil=sK50_skl|~nil=sK49_skl),
% 0.07/0.34 inference(cnf_transformation,[status(thm)],[f417])).
% 0.07/0.34 fof(f429,plain,(
% 0.07/0.34 ~nil=sK48_skl|~nil=sK47_skl),
% 0.07/0.34 inference(cnf_transformation,[status(thm)],[f417])).
% 0.07/0.34 fof(f430,plain,(
% 0.07/0.34 ~neq(sK47_skl,nil)|~frontsegP(sK48_skl,sK47_skl)),
% 0.07/0.34 inference(cnf_transformation,[status(thm)],[f417])).
% 0.07/0.34 fof(f435,plain,(
% 0.07/0.34 ![X0,X1]: (~ssList(app(X0,X1))|~ssList(X0)|frontsegP(app(X0,X1),X0)|~ssList(X1))),
% 0.07/0.34 inference(destructive_equality_resolution,[status(thm)],[f124])).
% 0.07/0.34 fof(f474,plain,(
% 0.07/0.34 app(sK47_skl,sK51_skl)=sK50_skl),
% 0.07/0.34 inference(forward_demodulation,[status(thm)],[f423,f425])).
% 0.07/0.34 fof(f475,plain,(
% 0.07/0.34 app(sK47_skl,sK51_skl)=sK48_skl),
% 0.07/0.34 inference(forward_demodulation,[status(thm)],[f422,f474])).
% 0.07/0.34 fof(f477,plain,(
% 0.07/0.34 ~ssList(sK48_skl)|~ssList(sK47_skl)|frontsegP(app(sK47_skl,sK51_skl),sK47_skl)|~ssList(sK51_skl)),
% 0.07/0.34 inference(paramodulation,[status(thm)],[f475,f435])).
% 0.07/0.34 fof(f480,plain,(
% 0.07/0.34 ~ssList(sK48_skl)|~ssList(sK47_skl)|frontsegP(sK48_skl,sK47_skl)|~ssList(sK51_skl)),
% 0.07/0.34 inference(forward_demodulation,[status(thm)],[f475,f477])).
% 0.07/0.34 fof(f481,plain,(
% 0.07/0.34 ~ssList(sK47_skl)|frontsegP(sK48_skl,sK47_skl)|~ssList(sK51_skl)),
% 0.07/0.34 inference(forward_subsumption_resolution,[status(thm)],[f480,f419])).
% 0.07/0.34 fof(f485,plain,(
% 0.07/0.34 nil=sK48_skl|~nil=sK49_skl),
% 0.07/0.34 inference(forward_demodulation,[status(thm)],[f422,f428])).
% 0.07/0.34 fof(f486,plain,(
% 0.07/0.34 nil=sK48_skl|~nil=sK47_skl),
% 0.07/0.34 inference(forward_demodulation,[status(thm)],[f423,f485])).
% 0.07/0.34 fof(f514,plain,(
% 0.07/0.34 ~nil=sK47_skl),
% 0.07/0.34 inference(forward_subsumption_resolution,[status(thm)],[f429,f486])).
% 0.07/0.34 fof(f557,plain,(
% 0.07/0.34 frontsegP(sK48_skl,sK47_skl)|~ssList(sK51_skl)),
% 0.07/0.34 inference(forward_subsumption_resolution,[status(thm)],[f481,f418])).
% 0.07/0.34 fof(f558,plain,(
% 0.07/0.34 frontsegP(sK48_skl,sK47_skl)),
% 0.07/0.34 inference(resolution,[status(thm)],[f557,f424])).
% 0.07/0.34 fof(f559,plain,(
% 0.07/0.34 ~neq(sK47_skl,nil)),
% 0.07/0.34 inference(backward_subsumption_resolution,[status(thm)],[f430,f558])).
% 0.07/0.34 fof(f566,plain,(
% 0.07/0.34 ~ssList(sK47_skl)|~ssList(nil)|sK47_skl=nil),
% 0.07/0.34 inference(resolution,[status(thm)],[f559,f220])).
% 0.07/0.34 fof(f567,plain,(
% 0.07/0.34 ~ssList(nil)|sK47_skl=nil),
% 0.07/0.34 inference(forward_subsumption_resolution,[status(thm)],[f566,f418])).
% 0.07/0.34 fof(f722,plain,(
% 0.07/0.34 ~sK47_skl=sK47_skl),
% 0.07/0.34 inference(backward_demodulation,[status(thm)],[f735,f514])).
% 0.07/0.34 fof(f735,plain,(
% 0.07/0.34 sK47_skl=nil),
% 0.07/0.34 inference(forward_subsumption_resolution,[status(thm)],[f567,f223])).
% 0.07/0.34 fof(f744,plain,(
% 0.07/0.34 $false),
% 0.07/0.34 inference(trivial_equality_resolution,[status(thm)],[f722])).
% 0.07/0.34 % SZS output end CNFRefutation for theBenchmark.p
% 0.07/0.36 % Elapsed time: 0.054366 seconds
% 0.07/0.36 % CPU time: 0.147782 seconds
% 0.07/0.36 % Total memory used: 112.349 MB
% 0.07/0.36 % Net memory used: 112.117 MB
%------------------------------------------------------------------------------