%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SWC029+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 : n011.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 0.10s 0.49s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC029+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
% 0.10/0.36 % Computer : n011.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 07:50:11 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.10/0.49 % Refutation found
% 0.10/0.49 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.49 % SZS output start CNFRefutation for theBenchmark
% 0.10/0.49 fof(f1,axiom,(
% 0.10/0.49 (! [U] :( ssItem(U)=> (! [V] :( ssItem(V)=> ( neq(U,V)<=> U != V ) ) )) )),
% 0.10/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.49 fof(f3,axiom,(
% 0.10/0.49 (! [U] :( ssList(U)=> (! [V] :( ssItem(V)=> ( memberP(U,V)<=> (? [W] :( ssList(W)& (? [X] :( ssList(X)& app(W,cons(V,X)) = U ) )) )) ) )) )),
% 0.10/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.49 fof(f4,axiom,(
% 0.10/0.49 (! [U] :( ssList(U)=> ( singletonP(U)<=> (? [V] :( ssItem(V)& cons(V,nil) = U ) )) ) )),
% 0.10/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.49 fof(f5,axiom,(
% 0.10/0.49 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> ( frontsegP(U,V)<=> (? [W] :( ssList(W)& app(V,W) = U ) )) ) )) )),
% 0.10/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.49 fof(f15,axiom,(
% 0.10/0.49 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> ( neq(U,V)<=> U != V ) ) )) )),
% 0.10/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.49 fof(f16,axiom,(
% 0.10/0.49 (! [U] :( ssList(U)=> (! [V] :( ssItem(V)=> ssList(cons(V,U)) ) )) )),
% 0.10/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.49 fof(f17,axiom,(
% 0.10/0.49 ssList(nil) ),
% 0.10/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.49 fof(f38,axiom,(
% 0.10/0.49 (! [U] :( ssItem(U)=> ~ memberP(nil,U) ) )),
% 0.10/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.49 fof(f45,axiom,(
% 0.10/0.49 (! [U] :( ssList(U)=> frontsegP(U,nil) ) )),
% 0.10/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.49 fof(f96,conjecture,(
% 0.10/0.49 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> (! [X] :( ssList(X)=> ( V != X| U != W| ( nil != W& nil = X )| ( (! [Y] :( ssItem(Y)=> (! [Z] :( ssList(Z)=> ( app(cons(Y,nil),Z) != X| app(Z,cons(Y,nil)) != W ) ) )))& neq(X,nil) )| ( ( nil != V| nil = U )& ( nil != U| nil = V ) ) ) ) )) )) )) )),
% 0.10/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.49 fof(f97,negated_conjecture,(
% 0.10/0.49 ~((! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> (! [X] :( ssList(X)=> ( V != X| U != W| ( nil != W& nil = X )| ( (! [Y] :( ssItem(Y)=> (! [Z] :( ssList(Z)=> ( app(cons(Y,nil),Z) != X| app(Z,cons(Y,nil)) != W ) ) )))& neq(X,nil) )| ( ( nil != V| nil = U )& ( nil != U| nil = V ) ) ) ) )) )) )) ))),
% 0.10/0.49 inference(negated_conjecture,[status(cth)],[f96])).
% 0.10/0.49 fof(f98,plain,(
% 0.10/0.49 ![U]: (~ssItem(U)|(![V]: (~ssItem(V)|(neq(U,V)<=>~U=V))))),
% 0.10/0.49 inference(pre_NNF_transformation,[status(thm)],[f1])).
% 0.10/0.49 fof(f99,plain,(
% 0.10/0.49 ![U]: (~ssItem(U)|(![V]: (~ssItem(V)|((~neq(U,V)|~U=V)&(neq(U,V)|U=V)))))),
% 0.10/0.49 inference(NNF_transformation,[status(thm)],[f98])).
% 0.10/0.49 fof(f100,plain,(
% 0.10/0.49 ![X0,X1]: (~ssItem(X0)|~ssItem(X1)|~neq(X0,X1)|~X0=X1)),
% 0.10/0.49 inference(cnf_transformation,[status(thm)],[f99])).
% 0.10/0.49 fof(f101,plain,(
% 0.10/0.49 ![X0,X1]: (~ssItem(X0)|~ssItem(X1)|neq(X0,X1)|X0=X1)),
% 0.10/0.49 inference(cnf_transformation,[status(thm)],[f99])).
% 0.10/0.49 fof(f106,plain,(
% 0.10/0.49 ![U]: (~ssList(U)|(![V]: (~ssItem(V)|(memberP(U,V)<=>(?[W]: (ssList(W)&(?[X]: (ssList(X)&app(W,cons(V,X))=U))))))))),
% 0.10/0.49 inference(pre_NNF_transformation,[status(thm)],[f3])).
% 0.10/0.49 fof(f107,plain,(
% 0.10/0.49 ![U]: (~ssList(U)|(![V]: (~ssItem(V)|((~memberP(U,V)|(?[W]: (ssList(W)&(?[X]: (ssList(X)&app(W,cons(V,X))=U)))))&(memberP(U,V)|(![W]: (~ssList(W)|(![X]: (~ssList(X)|~app(W,cons(V,X))=U)))))))))),
% 0.10/0.49 inference(NNF_transformation,[status(thm)],[f106])).
% 0.10/0.49 fof(f108,plain,(
% 0.10/0.49 ![U]: (~ssList(U)|(![V]: (~ssItem(V)|((~memberP(U,V)|(ssList(sK2_skl(V,U))&(ssList(sK3_skl(V,U))&app(sK2_skl(V,U),cons(V,sK3_skl(V,U)))=U)))&(memberP(U,V)|(![W]: (~ssList(W)|(![X]: (~ssList(X)|~app(W,cons(V,X))=U)))))))))),
% 0.10/0.49 inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(W,sK2_skl(V,U)),skolemize(X,sK3_skl(V,U))],[f107])).
% 0.10/0.49 fof(f112,plain,(
% 0.10/0.49 ![X0,X1,X2,X3]: (~ssList(X0)|~ssItem(X1)|memberP(X0,X1)|~ssList(X2)|~ssList(X3)|~app(X2,cons(X1,X3))=X0)),
% 0.10/0.49 inference(cnf_transformation,[status(thm)],[f108])).
% 0.10/0.49 fof(f113,plain,(
% 0.10/0.49 ![U]: (~ssList(U)|(singletonP(U)<=>(?[V]: (ssItem(V)&cons(V,nil)=U))))),
% 0.10/0.49 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 0.10/0.49 fof(f114,plain,(
% 0.10/0.49 ![U]: (~ssList(U)|((~singletonP(U)|(?[V]: (ssItem(V)&cons(V,nil)=U)))&(singletonP(U)|(![V]: (~ssItem(V)|~cons(V,nil)=U)))))),
% 0.10/0.49 inference(NNF_transformation,[status(thm)],[f113])).
% 0.10/0.49 fof(f115,plain,(
% 0.10/0.49 ![U]: (~ssList(U)|((~singletonP(U)|(ssItem(sK4_skl(U))&cons(sK4_skl(U),nil)=U))&(singletonP(U)|(![V]: (~ssItem(V)|~cons(V,nil)=U)))))),
% 0.10/0.49 inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(V,sK4_skl(U))],[f114])).
% 0.10/0.49 fof(f118,plain,(
% 0.10/0.49 ![X0,X1]: (~ssList(X0)|singletonP(X0)|~ssItem(X1)|~cons(X1,nil)=X0)),
% 0.10/0.49 inference(cnf_transformation,[status(thm)],[f115])).
% 0.10/0.49 fof(f119,plain,(
% 0.10/0.49 ![U]: (~ssList(U)|(![V]: (~ssList(V)|(frontsegP(U,V)<=>(?[W]: (ssList(W)&app(V,W)=U))))))),
% 0.10/0.49 inference(pre_NNF_transformation,[status(thm)],[f5])).
% 0.10/0.49 fof(f120,plain,(
% 0.10/0.49 ![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)))))))),
% 0.10/0.49 inference(NNF_transformation,[status(thm)],[f119])).
% 0.10/0.49 fof(f121,plain,(
% 0.10/0.49 ![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)))))))),
% 0.10/0.49 inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(W,sK5_skl(V,U))],[f120])).
% 0.10/0.49 fof(f122,plain,(
% 0.10/0.49 ![X0,X1]: (~ssList(X0)|~ssList(X1)|~frontsegP(X0,X1)|ssList(sK5_skl(X1,X0)))),
% 0.10/0.49 inference(cnf_transformation,[status(thm)],[f121])).
% 0.10/0.49 fof(f123,plain,(
% 0.10/0.49 ![X0,X1]: (~ssList(X0)|~ssList(X1)|~frontsegP(X0,X1)|app(X1,sK5_skl(X1,X0))=X0)),
% 0.10/0.49 inference(cnf_transformation,[status(thm)],[f121])).
% 0.10/0.49 fof(f217,plain,(
% 0.10/0.49 ![U]: (~ssList(U)|(![V]: (~ssList(V)|(neq(U,V)<=>~U=V))))),
% 0.10/0.49 inference(pre_NNF_transformation,[status(thm)],[f15])).
% 0.10/0.49 fof(f218,plain,(
% 0.10/0.49 ![U]: (~ssList(U)|(![V]: (~ssList(V)|((~neq(U,V)|~U=V)&(neq(U,V)|U=V)))))),
% 0.10/0.49 inference(NNF_transformation,[status(thm)],[f217])).
% 0.10/0.49 fof(f220,plain,(
% 0.10/0.49 ![X0,X1]: (~ssList(X0)|~ssList(X1)|neq(X0,X1)|X0=X1)),
% 0.10/0.49 inference(cnf_transformation,[status(thm)],[f218])).
% 0.10/0.49 fof(f221,plain,(
% 0.10/0.49 ![U]: (~ssList(U)|(![V]: (~ssItem(V)|ssList(cons(V,U)))))),
% 0.10/0.49 inference(pre_NNF_transformation,[status(thm)],[f16])).
% 0.10/0.49 fof(f222,plain,(
% 0.10/0.49 ![X0,X1]: (~ssList(X0)|~ssItem(X1)|ssList(cons(X1,X0)))),
% 0.10/0.49 inference(cnf_transformation,[status(thm)],[f221])).
% 0.10/0.49 fof(f223,plain,(
% 0.10/0.49 ssList(nil)),
% 0.10/0.49 inference(cnf_transformation,[status(thm)],[f17])).
% 0.10/0.49 fof(f278,plain,(
% 0.10/0.49 ![U]: (~ssItem(U)|~memberP(nil,U))),
% 0.10/0.49 inference(pre_NNF_transformation,[status(thm)],[f38])).
% 0.10/0.49 fof(f279,plain,(
% 0.10/0.49 ![X0]: (~ssItem(X0)|~memberP(nil,X0))),
% 0.10/0.49 inference(cnf_transformation,[status(thm)],[f278])).
% 0.10/0.49 fof(f294,plain,(
% 0.10/0.49 ![U]: (~ssList(U)|frontsegP(U,nil))),
% 0.10/0.49 inference(pre_NNF_transformation,[status(thm)],[f45])).
% 0.10/0.49 fof(f295,plain,(
% 0.10/0.49 ![X0]: (~ssList(X0)|frontsegP(X0,nil))),
% 0.10/0.49 inference(cnf_transformation,[status(thm)],[f294])).
% 0.10/0.49 fof(f415,plain,(
% 0.10/0.49 (?[U]: (ssList(U)&(?[V]: (ssList(V)&(?[W]: (ssList(W)&(?[X]: (ssList(X)&((((V=X&U=W)&(nil=W|~nil=X))&((?[Y]: (ssItem(Y)&(?[Z]: (ssList(Z)&(app(cons(Y,nil),Z)=X&app(Z,cons(Y,nil))=W)))))|~neq(X,nil)))&((nil=V&~nil=U)|(nil=U&~nil=V)))))))))))),
% 0.10/0.49 inference(pre_NNF_transformation,[status(thm)],[f97])).
% 0.10/0.49 fof(f416,definition,(
% 0.10/0.49 ![U,V]: (sP0_prd(V,U)<=>(nil=V&~nil=U))),
% 0.10/0.49 introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 0.10/0.49 fof(f417,plain,(
% 0.10/0.49 ?[U]: (ssList(U)&(?[V]: (ssList(V)&(?[W]: (ssList(W)&(?[X]: (ssList(X)&((((V=X&U=W)&(nil=W|~nil=X))&((?[Y]: (ssItem(Y)&(?[Z]: (ssList(Z)&(app(cons(Y,nil),Z)=X&app(Z,cons(Y,nil))=W)))))|~neq(X,nil)))&(sP0_prd(V,U)|(nil=U&~nil=V))))))))))),
% 0.10/0.49 inference(formula_renaming,[status(thm)],[f415,f416])).
% 0.10/0.49 fof(f418,plain,(
% 0.10/0.49 (ssList(sK47_skl)&(ssList(sK48_skl)&(ssList(sK49_skl)&(ssList(sK50_skl)&((((sK48_skl=sK50_skl&sK47_skl=sK49_skl)&(nil=sK49_skl|~nil=sK50_skl))&((ssItem(sK51_skl)&(ssList(sK52_skl)&(app(cons(sK51_skl,nil),sK52_skl)=sK50_skl&app(sK52_skl,cons(sK51_skl,nil))=sK49_skl)))|~neq(sK50_skl,nil)))&(sP0_prd(sK48_skl,sK47_skl)|(nil=sK47_skl&~nil=sK48_skl)))))))),
% 0.10/0.49 inference(skolemize,[status(esa),new_symbols(skolem,[sK47_skl,sK48_skl,sK49_skl,sK50_skl,sK51_skl,sK52_skl]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl),skolemize(Y,sK51_skl),skolemize(Z,sK52_skl)],[f417])).
% 0.10/0.49 fof(f420,plain,(
% 0.10/0.49 ssList(sK48_skl)),
% 0.10/0.49 inference(cnf_transformation,[status(thm)],[f418])).
% 0.10/0.49 fof(f423,plain,(
% 0.10/0.49 sK48_skl=sK50_skl),
% 0.10/0.49 inference(cnf_transformation,[status(thm)],[f418])).
% 0.10/0.49 fof(f424,plain,(
% 0.10/0.49 sK47_skl=sK49_skl),
% 0.10/0.49 inference(cnf_transformation,[status(thm)],[f418])).
% 0.10/0.49 fof(f425,plain,(
% 0.10/0.49 nil=sK49_skl|~nil=sK50_skl),
% 0.10/0.49 inference(cnf_transformation,[status(thm)],[f418])).
% 0.10/0.49 fof(f426,plain,(
% 0.10/0.49 ssItem(sK51_skl)|~neq(sK50_skl,nil)),
% 0.10/0.49 inference(cnf_transformation,[status(thm)],[f418])).
% 0.10/0.49 fof(f427,plain,(
% 0.10/0.49 ssList(sK52_skl)|~neq(sK50_skl,nil)),
% 0.10/0.49 inference(cnf_transformation,[status(thm)],[f418])).
% 0.10/0.49 fof(f428,plain,(
% 0.10/0.49 app(cons(sK51_skl,nil),sK52_skl)=sK50_skl|~neq(sK50_skl,nil)),
% 0.10/0.49 inference(cnf_transformation,[status(thm)],[f418])).
% 0.10/0.49 fof(f429,plain,(
% 0.10/0.49 app(sK52_skl,cons(sK51_skl,nil))=sK49_skl|~neq(sK50_skl,nil)),
% 0.10/0.49 inference(cnf_transformation,[status(thm)],[f418])).
% 0.10/0.49 fof(f430,plain,(
% 0.10/0.49 sP0_prd(sK48_skl,sK47_skl)|nil=sK47_skl),
% 0.10/0.49 inference(cnf_transformation,[status(thm)],[f418])).
% 0.10/0.49 fof(f431,plain,(
% 0.10/0.49 sP0_prd(sK48_skl,sK47_skl)|~nil=sK48_skl),
% 0.10/0.49 inference(cnf_transformation,[status(thm)],[f418])).
% 0.10/0.49 fof(f432,plain,(
% 0.10/0.49 ![U,V]: ((~sP0_prd(V,U)|(nil=V&~nil=U))&(sP0_prd(V,U)|(~nil=V|nil=U)))),
% 0.10/0.49 inference(NNF_transformation,[status(thm)],[f416])).
% 0.10/0.49 fof(f433,plain,(
% 0.10/0.49 (![U,V]: (~sP0_prd(V,U)|(nil=V&~nil=U)))&(![U,V]: (sP0_prd(V,U)|(~nil=V|nil=U)))),
% 0.10/0.49 inference(miniscoping,[status(thm)],[f432])).
% 0.10/0.49 fof(f434,plain,(
% 0.10/0.49 ![X0,X1]: (~sP0_prd(X0,X1)|nil=X0)),
% 0.10/0.49 inference(cnf_transformation,[status(thm)],[f433])).
% 0.10/0.49 fof(f435,plain,(
% 0.10/0.49 ![X0,X1]: (~sP0_prd(X0,X1)|~nil=X1)),
% 0.10/0.49 inference(cnf_transformation,[status(thm)],[f433])).
% 0.10/0.49 fof(f437,definition,(
% 0.10/0.49 sQ0_spl <=> (nil=sK49_skl)),
% 0.10/0.49 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.10/0.49 fof(f438,plain,(
% 0.10/0.49 nil=sK49_skl|~sQ0_spl),
% 0.10/0.49 inference(component_clause,[status(thm)],[f437])).
% 0.10/0.49 fof(f440,definition,(
% 0.10/0.49 sQ1_spl <=> (nil=sK50_skl)),
% 0.10/0.49 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.10/0.49 fof(f442,plain,(
% 0.10/0.49 ~nil=sK50_skl|sQ1_spl),
% 0.10/0.49 inference(component_clause,[status(thm)],[f440])).
% 0.10/0.49 fof(f443,plain,(
% 0.10/0.49 sQ0_spl|~sQ1_spl),
% 0.10/0.49 inference(split_clause,[status(thm)],[f425,f437,f440])).
% 0.10/0.49 fof(f444,definition,(
% 0.10/0.49 sQ2_spl <=> (ssItem(sK51_skl))),
% 0.10/0.49 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.10/0.49 fof(f445,plain,(
% 0.10/0.49 ssItem(sK51_skl)|~sQ2_spl),
% 0.10/0.49 inference(component_clause,[status(thm)],[f444])).
% 0.10/0.49 fof(f447,definition,(
% 0.10/0.49 sQ3_spl <=> (neq(sK50_skl,nil))),
% 0.10/0.49 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.10/0.49 fof(f449,plain,(
% 0.10/0.49 ~neq(sK50_skl,nil)|sQ3_spl),
% 0.10/0.49 inference(component_clause,[status(thm)],[f447])).
% 0.10/0.49 fof(f450,plain,(
% 0.10/0.49 sQ2_spl|~sQ3_spl),
% 0.10/0.49 inference(split_clause,[status(thm)],[f426,f444,f447])).
% 0.10/0.49 fof(f451,definition,(
% 0.10/0.49 sQ4_spl <=> (ssList(sK52_skl))),
% 0.10/0.49 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 0.10/0.49 fof(f454,plain,(
% 0.10/0.49 sQ4_spl|~sQ3_spl),
% 0.10/0.49 inference(split_clause,[status(thm)],[f427,f451,f447])).
% 0.10/0.49 fof(f455,definition,(
% 0.10/0.49 sQ5_spl <=> (app(cons(sK51_skl,nil),sK52_skl)=sK50_skl)),
% 0.10/0.49 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 0.10/0.49 fof(f458,plain,(
% 0.10/0.49 sQ5_spl|~sQ3_spl),
% 0.10/0.49 inference(split_clause,[status(thm)],[f428,f455,f447])).
% 0.10/0.49 fof(f459,definition,(
% 0.10/0.49 sQ6_spl <=> (app(sK52_skl,cons(sK51_skl,nil))=sK49_skl)),
% 0.10/0.49 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.10/0.49 fof(f460,plain,(
% 0.10/0.49 app(sK52_skl,cons(sK51_skl,nil))=sK49_skl|~sQ6_spl),
% 0.10/0.49 inference(component_clause,[status(thm)],[f459])).
% 0.10/0.49 fof(f462,plain,(
% 0.10/0.49 sQ6_spl|~sQ3_spl),
% 0.10/0.49 inference(split_clause,[status(thm)],[f429,f459,f447])).
% 0.10/0.49 fof(f463,definition,(
% 0.10/0.49 sQ7_spl <=> (sP0_prd(sK48_skl,sK47_skl))),
% 0.10/0.49 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 0.10/0.49 fof(f464,plain,(
% 0.10/0.49 sP0_prd(sK48_skl,sK47_skl)|~sQ7_spl),
% 0.10/0.49 inference(component_clause,[status(thm)],[f463])).
% 0.10/0.49 fof(f466,definition,(
% 0.10/0.49 sQ8_spl <=> (nil=sK47_skl)),
% 0.10/0.49 introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition])).
% 0.10/0.49 fof(f467,plain,(
% 0.10/0.49 nil=sK47_skl|~sQ8_spl),
% 0.10/0.49 inference(component_clause,[status(thm)],[f466])).
% 0.10/0.49 fof(f469,plain,(
% 0.10/0.49 sQ7_spl|sQ8_spl),
% 0.10/0.49 inference(split_clause,[status(thm)],[f430,f463,f466])).
% 0.10/0.49 fof(f470,definition,(
% 0.10/0.49 sQ9_spl <=> (nil=sK48_skl)),
% 0.10/0.49 introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition])).
% 0.10/0.49 fof(f473,plain,(
% 0.10/0.49 sQ7_spl|~sQ9_spl),
% 0.10/0.49 inference(split_clause,[status(thm)],[f431,f463,f470])).
% 0.10/0.49 fof(f474,plain,(
% 0.10/0.49 ![X1]: (~ssItem(X1)|~ssItem(X1)|~neq(X1,X1))),
% 0.10/0.49 inference(destructive_equality_resolution,[status(thm)],[f100])).
% 0.10/0.49 fof(f475,plain,(
% 0.10/0.49 ![X0]: (~ssItem(X0)|~neq(X0,X0))),
% 0.10/0.49 inference(duplicate_literals_removal,[status(thm)],[f474])).
% 0.10/0.49 fof(f476,plain,(
% 0.10/0.49 ![X0,X1,X2]: (~ssList(app(X0,cons(X1,X2)))|~ssItem(X1)|memberP(app(X0,cons(X1,X2)),X1)|~ssList(X0)|~ssList(X2))),
% 0.10/0.49 inference(destructive_equality_resolution,[status(thm)],[f112])).
% 0.10/0.49 fof(f477,plain,(
% 0.10/0.49 ![X0]: (~ssList(cons(X0,nil))|singletonP(cons(X0,nil))|~ssItem(X0))),
% 0.10/0.49 inference(destructive_equality_resolution,[status(thm)],[f118])).
% 0.10/0.49 fof(f508,plain,(
% 0.10/0.49 ![X0]: (~sP0_prd(X0,nil))),
% 0.10/0.49 inference(destructive_equality_resolution,[status(thm)],[f435])).
% 0.10/0.49 fof(f510,plain,(
% 0.10/0.49 ~neq(sK48_skl,nil)|sQ3_spl),
% 0.10/0.49 inference(forward_demodulation,[status(thm)],[f423,f449])).
% 0.10/0.49 fof(f511,plain,(
% 0.10/0.49 sP0_prd(sK48_skl,sK49_skl)|~sQ7_spl),
% 0.10/0.49 inference(forward_demodulation,[status(thm)],[f424,f464])).
% 0.10/0.49 fof(f512,plain,(
% 0.10/0.49 sP0_prd(sK48_skl,nil)|~sQ0_spl|~sQ7_spl),
% 0.10/0.49 inference(backward_demodulation,[status(thm)],[f438,f511])).
% 0.10/0.49 fof(f516,plain,(
% 0.10/0.49 $false|~sQ0_spl|~sQ7_spl),
% 0.10/0.49 inference(forward_subsumption_resolution,[status(thm)],[f512,f508])).
% 0.10/0.49 fof(f517,plain,(
% 0.10/0.49 ~sQ0_spl|~sQ7_spl),
% 0.10/0.49 inference(contradiction_clause,[status(thm)],[f516])).
% 0.10/0.49 fof(f518,plain,(
% 0.10/0.49 ~nil=sK48_skl|sQ1_spl),
% 0.10/0.49 inference(forward_demodulation,[status(thm)],[f423,f442])).
% 0.10/0.49 fof(f520,plain,(
% 0.10/0.49 nil=sK49_skl|~sQ8_spl),
% 0.10/0.49 inference(forward_demodulation,[status(thm)],[f467,f424])).
% 0.10/0.49 fof(f535,plain,(
% 0.10/0.49 ~ssList(sK48_skl)|~ssList(nil)|sK48_skl=nil|sQ3_spl),
% 0.10/0.49 inference(resolution,[status(thm)],[f220,f510])).
% 0.10/0.49 fof(f537,definition,(
% 0.10/0.49 sQ12_spl <=> (ssList(sK48_skl))),
% 0.10/0.49 introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition])).
% 0.10/0.49 fof(f539,plain,(
% 0.10/0.49 ~ssList(sK48_skl)|sQ12_spl),
% 0.10/0.49 inference(component_clause,[status(thm)],[f537])).
% 0.10/0.49 fof(f540,definition,(
% 0.10/0.49 sQ13_spl <=> (ssList(nil))),
% 0.10/0.49 introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition])).
% 0.10/0.49 fof(f542,plain,(
% 0.10/0.49 ~ssList(nil)|sQ13_spl),
% 0.10/0.49 inference(component_clause,[status(thm)],[f540])).
% 0.10/0.49 fof(f543,plain,(
% 0.10/0.49 ~sQ12_spl|~sQ13_spl|sQ9_spl|sQ3_spl),
% 0.10/0.49 inference(split_clause,[status(thm)],[f535,f537,f540,f470,f447])).
% 0.10/0.49 fof(f544,plain,(
% 0.10/0.49 $false|sQ13_spl),
% 0.10/0.49 inference(forward_subsumption_resolution,[status(thm)],[f542,f223])).
% 0.10/0.49 fof(f545,plain,(
% 0.10/0.49 sQ13_spl),
% 0.10/0.49 inference(contradiction_clause,[status(thm)],[f544])).
% 0.10/0.49 fof(f546,plain,(
% 0.10/0.49 $false|sQ12_spl),
% 0.10/0.49 inference(forward_subsumption_resolution,[status(thm)],[f539,f420])).
% 0.10/0.49 fof(f547,plain,(
% 0.10/0.49 sQ12_spl),
% 0.10/0.49 inference(contradiction_clause,[status(thm)],[f546])).
% 0.10/0.49 fof(f554,plain,(
% 0.10/0.49 ![X0]: (~ssItem(X0)|neq(X0,sK51_skl)|X0=sK51_skl|~sQ2_spl)),
% 0.10/0.49 inference(resolution,[status(thm)],[f445,f101])).
% 0.10/0.49 fof(f555,plain,(
% 0.10/0.49 ~neq(sK51_skl,sK51_skl)|~sQ2_spl),
% 0.10/0.49 inference(resolution,[status(thm)],[f445,f475])).
% 0.10/0.49 fof(f576,definition,(
% 0.10/0.49 sQ19_spl <=> (sK51_skl=sK51_skl)),
% 0.10/0.49 introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition])).
% 0.10/0.49 fof(f580,plain,(
% 0.10/0.49 nil=sK48_skl|~sQ7_spl),
% 0.10/0.49 inference(resolution,[status(thm)],[f434,f511])).
% 0.10/0.49 fof(f581,plain,(
% 0.10/0.49 $false|sQ1_spl|~sQ7_spl),
% 0.10/0.49 inference(forward_subsumption_resolution,[status(thm)],[f580,f518])).
% 0.10/0.49 fof(f582,plain,(
% 0.10/0.49 sQ1_spl|~sQ7_spl),
% 0.10/0.49 inference(contradiction_clause,[status(thm)],[f581])).
% 0.10/0.49 fof(f585,plain,(
% 0.10/0.49 app(sK52_skl,cons(sK51_skl,nil))=nil|~sQ8_spl|~sQ6_spl),
% 0.10/0.49 inference(backward_demodulation,[status(thm)],[f520,f460])).
% 0.10/0.49 fof(f633,plain,(
% 0.10/0.49 ![X0]: (singletonP(cons(X0,nil))|~ssItem(X0)|~ssList(nil)|~ssItem(X0))),
% 0.10/0.49 inference(resolution,[status(thm)],[f477,f222])).
% 0.10/0.49 fof(f634,definition,(
% 0.10/0.49 ![X0]: (sQ20_spl <=> (singletonP(cons(X0,nil))|~ssItem(X0)|~ssItem(X0)))),
% 0.10/0.49 introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition])).
% 0.10/0.49 fof(f637,plain,(
% 0.10/0.49 sQ20_spl|~sQ13_spl),
% 0.10/0.49 inference(split_clause,[status(thm)],[f633,f634,f540])).
% 0.10/0.49 fof(f639,plain,(
% 0.10/0.49 ![X0]: (~ssList(X0)|~ssList(nil)|ssList(sK5_skl(nil,X0))|~ssList(X0))),
% 0.10/0.49 inference(resolution,[status(thm)],[f122,f295])).
% 0.10/0.49 fof(f641,definition,(
% 0.10/0.49 ![X0]: (sQ21_spl <=> (~ssList(X0)|ssList(sK5_skl(nil,X0))|~ssList(X0)))),
% 0.10/0.49 introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition])).
% 0.10/0.49 fof(f644,plain,(
% 0.10/0.49 sQ21_spl|~sQ13_spl),
% 0.10/0.49 inference(split_clause,[status(thm)],[f639,f641,f540])).
% 0.10/0.49 fof(f647,plain,(
% 0.10/0.49 ![X0]: (~ssList(X0)|~ssList(nil)|app(nil,sK5_skl(nil,X0))=X0|~ssList(X0))),
% 0.10/0.49 inference(resolution,[status(thm)],[f123,f295])).
% 0.10/0.49 fof(f649,definition,(
% 0.10/0.49 ![X0]: (sQ22_spl <=> (~ssList(X0)|app(nil,sK5_skl(nil,X0))=X0|~ssList(X0)))),
% 0.10/0.49 introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition])).
% 0.10/0.49 fof(f652,plain,(
% 0.10/0.49 sQ22_spl|~sQ13_spl),
% 0.10/0.49 inference(split_clause,[status(thm)],[f647,f649,f540])).
% 0.10/0.49 fof(f655,plain,(
% 0.10/0.49 ~ssItem(sK51_skl)|sK51_skl=sK51_skl|~sQ2_spl),
% 0.10/0.49 inference(resolution,[status(thm)],[f554,f555])).
% 0.10/0.49 fof(f657,plain,(
% 0.10/0.49 ~sQ2_spl|sQ19_spl),
% 0.10/0.49 inference(split_clause,[status(thm)],[f655,f444,f576])).
% 0.10/0.49 fof(f659,plain,(
% 0.10/0.49 ~ssList(nil)|~ssItem(sK51_skl)|memberP(app(sK52_skl,cons(sK51_skl,nil)),sK51_skl)|~ssList(sK52_skl)|~ssList(nil)|~sQ8_spl|~sQ6_spl),
% 0.10/0.49 inference(paramodulation,[status(thm)],[f585,f476])).
% 0.10/0.49 fof(f660,definition,(
% 0.10/0.49 sQ23_spl <=> (memberP(app(sK52_skl,cons(sK51_skl,nil)),sK51_skl))),
% 0.10/0.49 introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition])).
% 0.10/0.49 fof(f661,plain,(
% 0.10/0.49 memberP(app(sK52_skl,cons(sK51_skl,nil)),sK51_skl)|~sQ23_spl),
% 0.10/0.49 inference(component_clause,[status(thm)],[f660])).
% 0.10/0.49 fof(f663,plain,(
% 0.10/0.49 ~sQ13_spl|~sQ2_spl|sQ23_spl|~sQ4_spl|~sQ8_spl|~sQ6_spl),
% 0.10/0.49 inference(split_clause,[status(thm)],[f659,f540,f444,f660,f451,f466,f459])).
% 0.10/0.49 fof(f664,plain,(
% 0.10/0.49 memberP(nil,sK51_skl)|~sQ8_spl|~sQ6_spl|~sQ23_spl),
% 0.10/0.49 inference(forward_demodulation,[status(thm)],[f585,f661])).
% 0.10/0.49 fof(f665,plain,(
% 0.10/0.49 ~ssItem(sK51_skl)|~sQ8_spl|~sQ6_spl|~sQ23_spl),
% 0.10/0.49 inference(resolution,[status(thm)],[f664,f279])).
% 0.10/0.49 fof(f667,plain,(
% 0.10/0.49 $false|~sQ2_spl|~sQ8_spl|~sQ6_spl|~sQ23_spl),
% 0.10/0.49 inference(forward_subsumption_resolution,[status(thm)],[f665,f445])).
% 0.10/0.49 fof(f668,plain,(
% 0.10/0.49 ~sQ2_spl|~sQ8_spl|~sQ6_spl|~sQ23_spl),
% 0.10/0.49 inference(contradiction_clause,[status(thm)],[f667])).
% 0.10/0.49 fof(f669,plain,(
% 0.10/0.49 $false),
% 0.10/0.49 inference(sat_refutation,[status(thm)],[f443,f450,f454,f458,f462,f469,f473,f517,f543,f545,f547,f582,f637,f644,f652,f657,f663,f668])).
% 0.10/0.49 % SZS output end CNFRefutation for theBenchmark.p
% 0.10/0.50 % Elapsed time: 0.136882 seconds
% 0.10/0.50 % CPU time: 0.823547 seconds
% 0.10/0.50 % Total memory used: 122.155 MB
% 0.10/0.50 % Net memory used: 121.144 MB
%------------------------------------------------------------------------------