%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SWC032+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 02:41:23 PM UTC 2026
% Result : Theorem 0.17s 5.83s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC032+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/5.56 % Computer : n013.cluster.edu
% 0.12/5.56 % Model : x86_64 x86_64
% 0.12/5.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.56 % Memory : 8046.5625MB
% 0.12/5.56 % OS : Linux 6.8.0-71-generic
% 0.12/5.56 % CPULimit : 300
% 0.12/5.56 % WCLimit : 300
% 0.12/5.56 % DateTime : Mon Sep 21 07:50:14 UTC 2026
% 0.12/5.57 % CPUTime :
% 0.12/5.59 % Drodi V4.1.1
% 0.17/5.83 % Refutation found
% 0.17/5.83 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/5.83 % SZS output start CNFRefutation for theBenchmark
% 0.17/5.83 fof(f5,axiom,(
% 0.17/5.83 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> ( frontsegP(U,V)<=> (? [W] :( ssList(W)& app(V,W) = U ) )) ) )) )),
% 0.17/5.83 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/5.83 fof(f26,axiom,(
% 0.17/5.83 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> ssList(app(U,V)) ) )) )),
% 0.17/5.83 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/5.83 fof(f46,axiom,(
% 0.17/5.83 (! [U] :( ssList(U)=> ( frontsegP(nil,U)<=> nil = U ) ) )),
% 0.17/5.83 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/5.83 fof(f96,conjecture,(
% 0.17/5.83 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> (! [X] :( ssList(X)=> ( V != X| U != W| (! [Y] :( ssList(Y)=> ( app(W,Y) != X| ~ strictorderedP(W)| (? [Z] :( ssItem(Z)& (? [X1] :( ssList(X1)& app(cons(Z,nil),X1) = Y& (? [X2] :( ssItem(X2)& (? [X3] :( ssList(X3)& app(X3,cons(X2,nil)) = W& lt(X2,Z) ) )) )) )) )) ))| ( nil != X& nil = W )| ( ( nil != V| nil = U )& ( nil != U| nil = V ) ) ) ) )) )) )) )),
% 0.17/5.83 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/5.83 fof(f97,negated_conjecture,(
% 0.17/5.83 ~((! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> (! [X] :( ssList(X)=> ( V != X| U != W| (! [Y] :( ssList(Y)=> ( app(W,Y) != X| ~ strictorderedP(W)| (? [Z] :( ssItem(Z)& (? [X1] :( ssList(X1)& app(cons(Z,nil),X1) = Y& (? [X2] :( ssItem(X2)& (? [X3] :( ssList(X3)& app(X3,cons(X2,nil)) = W& lt(X2,Z) ) )) )) )) )) ))| ( nil != X& nil = W )| ( ( nil != V| nil = U )& ( nil != U| nil = V ) ) ) ) )) )) )) ))),
% 0.17/5.83 inference(negated_conjecture,[status(cth)],[f96])).
% 0.17/5.83 fof(f119,plain,(
% 0.17/5.83 ![U]: (~ssList(U)|(![V]: (~ssList(V)|(frontsegP(U,V)<=>(?[W]: (ssList(W)&app(V,W)=U))))))),
% 0.17/5.83 inference(pre_NNF_transformation,[status(thm)],[f5])).
% 0.17/5.83 fof(f120,plain,(
% 0.17/5.83 ![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)))))))),
% 0.17/5.83 inference(NNF_transformation,[status(thm)],[f119])).
% 0.17/5.83 fof(f121,plain,(
% 0.17/5.83 ![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)))))))),
% 0.17/5.83 inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(W,sK5_skl(V,U))],[f120])).
% 0.17/5.83 fof(f124,plain,(
% 0.17/5.83 ![X0,X1,X2]: (~ssList(X0)|~ssList(X1)|frontsegP(X0,X1)|~ssList(X2)|~app(X1,X2)=X0)),
% 0.17/5.83 inference(cnf_transformation,[status(thm)],[f121])).
% 0.17/5.83 fof(f244,plain,(
% 0.17/5.83 ![U]: (~ssList(U)|(![V]: (~ssList(V)|ssList(app(U,V)))))),
% 0.17/5.83 inference(pre_NNF_transformation,[status(thm)],[f26])).
% 0.17/5.83 fof(f245,plain,(
% 0.17/5.83 ![X0,X1]: (~ssList(X0)|~ssList(X1)|ssList(app(X0,X1)))),
% 0.17/5.83 inference(cnf_transformation,[status(thm)],[f244])).
% 0.17/5.83 fof(f296,plain,(
% 0.17/5.83 ![U]: (~ssList(U)|(frontsegP(nil,U)<=>nil=U))),
% 0.17/5.83 inference(pre_NNF_transformation,[status(thm)],[f46])).
% 0.17/5.83 fof(f297,plain,(
% 0.17/5.83 ![U]: (~ssList(U)|((~frontsegP(nil,U)|nil=U)&(frontsegP(nil,U)|~nil=U)))),
% 0.17/5.83 inference(NNF_transformation,[status(thm)],[f296])).
% 0.17/5.83 fof(f298,plain,(
% 0.17/5.83 ![X0]: (~ssList(X0)|~frontsegP(nil,X0)|nil=X0)),
% 0.17/5.83 inference(cnf_transformation,[status(thm)],[f297])).
% 0.17/5.83 fof(f415,plain,(
% 0.17/5.83 (?[U]: (ssList(U)&(?[V]: (ssList(V)&(?[W]: (ssList(W)&(?[X]: (ssList(X)&((((V=X&U=W)&(?[Y]: (ssList(Y)&((app(W,Y)=X&strictorderedP(W))&(![Z]: (~ssItem(Z)|(![X1]: ((~ssList(X1)|~app(cons(Z,nil),X1)=Y)|(![X2]: (~ssItem(X2)|(![X3]: ((~ssList(X3)|~app(X3,cons(X2,nil))=W)|~lt(X2,Z)))))))))))))&(nil=X|~nil=W))&((nil=V&~nil=U)|(nil=U&~nil=V)))))))))))),
% 0.17/5.83 inference(pre_NNF_transformation,[status(thm)],[f97])).
% 0.17/5.83 fof(f416,definition,(
% 0.17/5.83 ![U,V]: (sP0_prd(V,U)<=>(nil=V&~nil=U))),
% 0.17/5.83 introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 0.17/5.83 fof(f417,plain,(
% 0.17/5.83 ?[U]: (ssList(U)&(?[V]: (ssList(V)&(?[W]: (ssList(W)&(?[X]: (ssList(X)&((((V=X&U=W)&(?[Y]: (ssList(Y)&((app(W,Y)=X&strictorderedP(W))&(![Z]: (~ssItem(Z)|(![X1]: ((~ssList(X1)|~app(cons(Z,nil),X1)=Y)|(![X2]: (~ssItem(X2)|(![X3]: ((~ssList(X3)|~app(X3,cons(X2,nil))=W)|~lt(X2,Z)))))))))))))&(nil=X|~nil=W))&(sP0_prd(V,U)|(nil=U&~nil=V))))))))))),
% 0.17/5.83 inference(formula_renaming,[status(thm)],[f415,f416])).
% 0.17/5.83 fof(f418,plain,(
% 0.17/5.83 ?[U]: (ssList(U)&(?[V]: (ssList(V)&(?[W]: (ssList(W)&(?[X]: (ssList(X)&((((V=X&U=W)&(?[Y]: (ssList(Y)&((app(W,Y)=X&strictorderedP(W))&(![Z]: (~ssItem(Z)|((![X1]: (~ssList(X1)|~app(cons(Z,nil),X1)=Y))|(![X2]: (~ssItem(X2)|((![X3]: (~ssList(X3)|~app(X3,cons(X2,nil))=W))|~lt(X2,Z)))))))))))&(nil=X|~nil=W))&(sP0_prd(V,U)|(nil=U&~nil=V))))))))))),
% 0.17/5.83 inference(miniscoping,[status(thm)],[f417])).
% 0.17/5.83 fof(f419,plain,(
% 0.17/5.83 (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&strictorderedP(sK49_skl))&(![Z]: (~ssItem(Z)|((![X1]: (~ssList(X1)|~app(cons(Z,nil),X1)=sK51_skl))|(![X2]: (~ssItem(X2)|((![X3]: (~ssList(X3)|~app(X3,cons(X2,nil))=sK49_skl))|~lt(X2,Z))))))))))&(nil=sK50_skl|~nil=sK49_skl))&(sP0_prd(sK48_skl,sK47_skl)|(nil=sK47_skl&~nil=sK48_skl)))))))),
% 0.17/5.83 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)],[f418])).
% 0.17/5.83 fof(f420,plain,(
% 0.17/5.83 ssList(sK47_skl)),
% 0.17/5.83 inference(cnf_transformation,[status(thm)],[f419])).
% 0.17/5.83 fof(f424,plain,(
% 0.17/5.83 sK48_skl=sK50_skl),
% 0.17/5.83 inference(cnf_transformation,[status(thm)],[f419])).
% 0.17/5.83 fof(f425,plain,(
% 0.17/5.83 sK47_skl=sK49_skl),
% 0.17/5.83 inference(cnf_transformation,[status(thm)],[f419])).
% 0.17/5.83 fof(f426,plain,(
% 0.17/5.83 ssList(sK51_skl)),
% 0.17/5.83 inference(cnf_transformation,[status(thm)],[f419])).
% 0.17/5.83 fof(f427,plain,(
% 0.17/5.83 app(sK49_skl,sK51_skl)=sK50_skl),
% 0.17/5.83 inference(cnf_transformation,[status(thm)],[f419])).
% 0.17/5.83 fof(f430,plain,(
% 0.17/5.83 nil=sK50_skl|~nil=sK49_skl),
% 0.17/5.83 inference(cnf_transformation,[status(thm)],[f419])).
% 0.17/5.83 fof(f431,plain,(
% 0.17/5.83 sP0_prd(sK48_skl,sK47_skl)|nil=sK47_skl),
% 0.17/5.83 inference(cnf_transformation,[status(thm)],[f419])).
% 0.17/5.83 fof(f432,plain,(
% 0.17/5.83 sP0_prd(sK48_skl,sK47_skl)|~nil=sK48_skl),
% 0.17/5.83 inference(cnf_transformation,[status(thm)],[f419])).
% 0.17/5.83 fof(f433,plain,(
% 0.17/5.83 ![U,V]: ((~sP0_prd(V,U)|(nil=V&~nil=U))&(sP0_prd(V,U)|(~nil=V|nil=U)))),
% 0.17/5.83 inference(NNF_transformation,[status(thm)],[f416])).
% 0.17/5.83 fof(f434,plain,(
% 0.17/5.83 (![U,V]: (~sP0_prd(V,U)|(nil=V&~nil=U)))&(![U,V]: (sP0_prd(V,U)|(~nil=V|nil=U)))),
% 0.17/5.83 inference(miniscoping,[status(thm)],[f433])).
% 0.17/5.83 fof(f435,plain,(
% 0.17/5.83 ![X0,X1]: (~sP0_prd(X0,X1)|nil=X0)),
% 0.17/5.83 inference(cnf_transformation,[status(thm)],[f434])).
% 0.17/5.83 fof(f436,plain,(
% 0.17/5.83 ![X0,X1]: (~sP0_prd(X0,X1)|~nil=X1)),
% 0.17/5.83 inference(cnf_transformation,[status(thm)],[f434])).
% 0.17/5.83 fof(f442,plain,(
% 0.17/5.83 ![X0,X1]: (~ssList(app(X0,X1))|~ssList(X0)|frontsegP(app(X0,X1),X0)|~ssList(X1))),
% 0.17/5.83 inference(destructive_equality_resolution,[status(thm)],[f124])).
% 0.17/5.83 fof(f456,plain,(
% 0.17/5.83 ![X0,X1]: (~ssList(X0)|frontsegP(app(X0,X1),X0)|~ssList(X1))),
% 0.17/5.83 inference(backward_subsumption_resolution,[status(thm)],[f442,f245])).
% 0.17/5.83 fof(f472,plain,(
% 0.17/5.83 app(sK47_skl,sK51_skl)=sK50_skl),
% 0.17/5.83 inference(forward_demodulation,[status(thm)],[f425,f427])).
% 0.17/5.83 fof(f473,plain,(
% 0.17/5.83 app(sK47_skl,sK51_skl)=sK48_skl),
% 0.17/5.83 inference(forward_demodulation,[status(thm)],[f424,f472])).
% 0.17/5.83 fof(f476,plain,(
% 0.17/5.83 nil=sK48_skl|~nil=sK49_skl),
% 0.17/5.83 inference(forward_demodulation,[status(thm)],[f424,f430])).
% 0.17/5.83 fof(f477,plain,(
% 0.17/5.83 nil=sK48_skl|~nil=sK47_skl),
% 0.17/5.83 inference(forward_demodulation,[status(thm)],[f425,f476])).
% 0.17/5.83 fof(f478,plain,(
% 0.17/5.83 ![X0]: (~sP0_prd(X0,nil))),
% 0.17/5.83 inference(destructive_equality_resolution,[status(thm)],[f436])).
% 0.17/5.83 fof(f496,plain,(
% 0.17/5.83 nil=sK47_skl|nil=sK48_skl),
% 0.17/5.83 inference(resolution,[status(thm)],[f431,f435])).
% 0.17/5.83 fof(f513,plain,(
% 0.17/5.83 ![X0]: (~sP0_prd(X0,sK48_skl))),
% 0.17/5.83 inference(backward_demodulation,[status(thm)],[f561,f478])).
% 0.17/5.83 fof(f517,plain,(
% 0.17/5.83 sP0_prd(sK48_skl,sK47_skl)|~sK48_skl=sK48_skl),
% 0.17/5.83 inference(backward_demodulation,[status(thm)],[f561,f432])).
% 0.17/5.83 fof(f551,plain,(
% 0.17/5.83 ![X0]: (~ssList(X0)|~frontsegP(nil,X0)|sK48_skl=X0)),
% 0.17/5.83 inference(backward_demodulation,[status(thm)],[f561,f298])).
% 0.17/5.83 fof(f561,plain,(
% 0.17/5.83 nil=sK48_skl),
% 0.17/5.83 inference(forward_subsumption_resolution,[status(thm)],[f496,f477])).
% 0.17/5.83 fof(f565,plain,(
% 0.17/5.83 sP0_prd(sK48_skl,sK47_skl)),
% 0.17/5.83 inference(trivial_equality_resolution,[status(thm)],[f517])).
% 0.17/5.83 fof(f572,plain,(
% 0.17/5.83 ![X0]: (~ssList(X0)|~frontsegP(sK48_skl,X0)|sK48_skl=X0)),
% 0.17/5.83 inference(forward_demodulation,[status(thm)],[f561,f551])).
% 0.17/5.83 fof(f646,plain,(
% 0.17/5.83 ![X0]: (~ssList(X0)|frontsegP(app(X0,sK51_skl),X0))),
% 0.17/5.83 inference(resolution,[status(thm)],[f456,f426])).
% 0.17/5.83 fof(f650,plain,(
% 0.17/5.83 ~ssList(sK47_skl)|frontsegP(sK48_skl,sK47_skl)),
% 0.17/5.83 inference(paramodulation,[status(thm)],[f473,f646])).
% 0.17/5.83 fof(f652,plain,(
% 0.17/5.83 frontsegP(sK48_skl,sK47_skl)),
% 0.17/5.83 inference(forward_subsumption_resolution,[status(thm)],[f650,f420])).
% 0.17/5.83 fof(f657,plain,(
% 0.17/5.83 ~ssList(sK47_skl)|sK48_skl=sK47_skl),
% 0.17/5.83 inference(resolution,[status(thm)],[f652,f572])).
% 0.17/5.83 fof(f689,plain,(
% 0.17/5.83 sP0_prd(sK47_skl,sK47_skl)),
% 0.17/5.83 inference(backward_demodulation,[status(thm)],[f742,f565])).
% 0.17/5.83 fof(f691,plain,(
% 0.17/5.83 ![X0]: (~sP0_prd(X0,sK47_skl))),
% 0.17/5.83 inference(backward_demodulation,[status(thm)],[f742,f513])).
% 0.17/5.83 fof(f742,plain,(
% 0.17/5.83 sK48_skl=sK47_skl),
% 0.17/5.83 inference(forward_subsumption_resolution,[status(thm)],[f657,f420])).
% 0.17/5.83 fof(f772,plain,(
% 0.17/5.83 $false),
% 0.17/5.83 inference(backward_subsumption_resolution,[status(thm)],[f689,f691])).
% 0.17/5.83 % SZS output end CNFRefutation for theBenchmark.p
% 0.17/5.85 % Elapsed time: 0.269939 seconds
% 0.17/5.85 % CPU time: 1.838201 seconds
% 0.17/5.85 % Total memory used: 127.061 MB
% 0.17/5.85 % Net memory used: 125.494 MB
%------------------------------------------------------------------------------