%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SWC097+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 : n009.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 0.12s 0.46s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC097+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
% 0.09/0.35 % Computer : n009.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 07:55:43 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.12/0.36 % Drodi V4.1.1
% 0.12/0.46 % Refutation found
% 0.12/0.46 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.46 % SZS output start CNFRefutation for theBenchmark
% 0.12/0.46 fof(f4,axiom,(
% 0.12/0.46 (! [U] :( ssList(U)=> ( singletonP(U)<=> (? [V] :( ssItem(V)& cons(V,nil) = U ) )) ) )),
% 0.12/0.46 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.46 fof(f5,axiom,(
% 0.12/0.46 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> ( frontsegP(U,V)<=> (? [W] :( ssList(W)& app(V,W) = U ) )) ) )) )),
% 0.12/0.46 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.46 fof(f6,axiom,(
% 0.12/0.46 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> ( rearsegP(U,V)<=> (? [W] :( ssList(W)& app(W,V) = U ) )) ) )) )),
% 0.12/0.46 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.46 fof(f7,axiom,(
% 0.12/0.46 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> ( segmentP(U,V)<=> (? [W] :( ssList(W)& (? [X] :( ssList(X)& app(app(W,V),X) = U ) )) )) ) )) )),
% 0.12/0.46 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.46 fof(f15,axiom,(
% 0.12/0.46 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> ( neq(U,V)<=> U != V ) ) )) )),
% 0.12/0.46 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.46 fof(f16,axiom,(
% 0.12/0.46 (! [U] :( ssList(U)=> (! [V] :( ssItem(V)=> ssList(cons(V,U)) ) )) )),
% 0.12/0.46 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.46 fof(f17,axiom,(
% 0.12/0.46 ssList(nil) ),
% 0.12/0.46 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.46 fof(f26,axiom,(
% 0.12/0.46 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> ssList(app(U,V)) ) )) )),
% 0.12/0.46 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.46 fof(f28,axiom,(
% 0.12/0.46 (! [U] :( ssList(U)=> app(nil,U) = U ) )),
% 0.12/0.46 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.46 fof(f45,axiom,(
% 0.12/0.46 (! [U] :( ssList(U)=> frontsegP(U,nil) ) )),
% 0.12/0.46 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.46 fof(f51,axiom,(
% 0.12/0.46 (! [U] :( ssList(U)=> rearsegP(U,nil) ) )),
% 0.12/0.46 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.46 fof(f57,axiom,(
% 0.12/0.46 (! [U] :( ssList(U)=> segmentP(U,nil) ) )),
% 0.12/0.46 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.46 fof(f84,axiom,(
% 0.12/0.46 (! [U] :( ssList(U)=> app(U,nil) = U ) )),
% 0.12/0.46 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.46 fof(f96,conjecture,(
% 0.12/0.46 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> (! [X] :( ssList(X)=> ( V != X| U != W| ( ( ~ neq(V,nil)| (? [Y] :( ssItem(Y)& app(U,cons(Y,nil)) = V ))| (! [Z] :( ssItem(Z)=> app(W,cons(Z,nil)) != X ) ))& ( ~ neq(V,nil)| neq(X,nil) ) ) ) ) )) )) )) )),
% 0.12/0.46 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.46 fof(f97,negated_conjecture,(
% 0.12/0.46 ~((! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> (! [X] :( ssList(X)=> ( V != X| U != W| ( ( ~ neq(V,nil)| (? [Y] :( ssItem(Y)& app(U,cons(Y,nil)) = V ))| (! [Z] :( ssItem(Z)=> app(W,cons(Z,nil)) != X ) ))& ( ~ neq(V,nil)| neq(X,nil) ) ) ) ) )) )) )) ))),
% 0.12/0.46 inference(negated_conjecture,[status(cth)],[f96])).
% 0.12/0.46 fof(f113,plain,(
% 0.12/0.46 ![U]: (~ssList(U)|(singletonP(U)<=>(?[V]: (ssItem(V)&cons(V,nil)=U))))),
% 0.12/0.46 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 0.12/0.46 fof(f114,plain,(
% 0.12/0.46 ![U]: (~ssList(U)|((~singletonP(U)|(?[V]: (ssItem(V)&cons(V,nil)=U)))&(singletonP(U)|(![V]: (~ssItem(V)|~cons(V,nil)=U)))))),
% 0.12/0.46 inference(NNF_transformation,[status(thm)],[f113])).
% 0.12/0.46 fof(f115,plain,(
% 0.12/0.46 ![U]: (~ssList(U)|((~singletonP(U)|(ssItem(sK4_skl(U))&cons(sK4_skl(U),nil)=U))&(singletonP(U)|(![V]: (~ssItem(V)|~cons(V,nil)=U)))))),
% 0.12/0.46 inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(V,sK4_skl(U))],[f114])).
% 0.12/0.46 fof(f118,plain,(
% 0.12/0.46 ![X0,X1]: (~ssList(X0)|singletonP(X0)|~ssItem(X1)|~cons(X1,nil)=X0)),
% 0.12/0.46 inference(cnf_transformation,[status(thm)],[f115])).
% 0.12/0.46 fof(f119,plain,(
% 0.12/0.46 ![U]: (~ssList(U)|(![V]: (~ssList(V)|(frontsegP(U,V)<=>(?[W]: (ssList(W)&app(V,W)=U))))))),
% 0.12/0.46 inference(pre_NNF_transformation,[status(thm)],[f5])).
% 0.12/0.46 fof(f120,plain,(
% 0.12/0.46 ![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)))))))),
% 0.12/0.46 inference(NNF_transformation,[status(thm)],[f119])).
% 0.12/0.46 fof(f121,plain,(
% 0.12/0.46 ![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)))))))),
% 0.12/0.46 inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(W,sK5_skl(V,U))],[f120])).
% 0.12/0.46 fof(f122,plain,(
% 0.12/0.46 ![X0,X1]: (~ssList(X0)|~ssList(X1)|~frontsegP(X0,X1)|ssList(sK5_skl(X1,X0)))),
% 0.12/0.46 inference(cnf_transformation,[status(thm)],[f121])).
% 0.12/0.46 fof(f123,plain,(
% 0.12/0.46 ![X0,X1]: (~ssList(X0)|~ssList(X1)|~frontsegP(X0,X1)|app(X1,sK5_skl(X1,X0))=X0)),
% 0.12/0.46 inference(cnf_transformation,[status(thm)],[f121])).
% 0.12/0.46 fof(f125,plain,(
% 0.12/0.46 ![U]: (~ssList(U)|(![V]: (~ssList(V)|(rearsegP(U,V)<=>(?[W]: (ssList(W)&app(W,V)=U))))))),
% 0.12/0.46 inference(pre_NNF_transformation,[status(thm)],[f6])).
% 0.12/0.46 fof(f126,plain,(
% 0.12/0.46 ![U]: (~ssList(U)|(![V]: (~ssList(V)|((~rearsegP(U,V)|(?[W]: (ssList(W)&app(W,V)=U)))&(rearsegP(U,V)|(![W]: (~ssList(W)|~app(W,V)=U)))))))),
% 0.12/0.46 inference(NNF_transformation,[status(thm)],[f125])).
% 0.12/0.46 fof(f127,plain,(
% 0.12/0.46 ![U]: (~ssList(U)|(![V]: (~ssList(V)|((~rearsegP(U,V)|(ssList(sK6_skl(V,U))&app(sK6_skl(V,U),V)=U))&(rearsegP(U,V)|(![W]: (~ssList(W)|~app(W,V)=U)))))))),
% 0.12/0.46 inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl]),skolemize(W,sK6_skl(V,U))],[f126])).
% 0.12/0.46 fof(f128,plain,(
% 0.12/0.46 ![X0,X1]: (~ssList(X0)|~ssList(X1)|~rearsegP(X0,X1)|ssList(sK6_skl(X1,X0)))),
% 0.12/0.46 inference(cnf_transformation,[status(thm)],[f127])).
% 0.12/0.46 fof(f129,plain,(
% 0.12/0.46 ![X0,X1]: (~ssList(X0)|~ssList(X1)|~rearsegP(X0,X1)|app(sK6_skl(X1,X0),X1)=X0)),
% 0.12/0.46 inference(cnf_transformation,[status(thm)],[f127])).
% 0.12/0.46 fof(f130,plain,(
% 0.12/0.46 ![X0,X1,X2]: (~ssList(X0)|~ssList(X1)|rearsegP(X0,X1)|~ssList(X2)|~app(X2,X1)=X0)),
% 0.12/0.46 inference(cnf_transformation,[status(thm)],[f127])).
% 0.12/0.46 fof(f131,plain,(
% 0.12/0.46 ![U]: (~ssList(U)|(![V]: (~ssList(V)|(segmentP(U,V)<=>(?[W]: (ssList(W)&(?[X]: (ssList(X)&app(app(W,V),X)=U))))))))),
% 0.12/0.46 inference(pre_NNF_transformation,[status(thm)],[f7])).
% 0.12/0.46 fof(f132,plain,(
% 0.12/0.46 ![U]: (~ssList(U)|(![V]: (~ssList(V)|((~segmentP(U,V)|(?[W]: (ssList(W)&(?[X]: (ssList(X)&app(app(W,V),X)=U)))))&(segmentP(U,V)|(![W]: (~ssList(W)|(![X]: (~ssList(X)|~app(app(W,V),X)=U)))))))))),
% 0.12/0.46 inference(NNF_transformation,[status(thm)],[f131])).
% 0.12/0.46 fof(f133,plain,(
% 0.12/0.46 ![U]: (~ssList(U)|(![V]: (~ssList(V)|((~segmentP(U,V)|(ssList(sK7_skl(V,U))&(ssList(sK8_skl(V,U))&app(app(sK7_skl(V,U),V),sK8_skl(V,U))=U)))&(segmentP(U,V)|(![W]: (~ssList(W)|(![X]: (~ssList(X)|~app(app(W,V),X)=U)))))))))),
% 0.12/0.46 inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl,sK8_skl]),skolemize(W,sK7_skl(V,U)),skolemize(X,sK8_skl(V,U))],[f132])).
% 0.12/0.46 fof(f134,plain,(
% 0.12/0.46 ![X0,X1]: (~ssList(X0)|~ssList(X1)|~segmentP(X0,X1)|ssList(sK7_skl(X1,X0)))),
% 0.12/0.46 inference(cnf_transformation,[status(thm)],[f133])).
% 0.12/0.46 fof(f135,plain,(
% 0.12/0.46 ![X0,X1]: (~ssList(X0)|~ssList(X1)|~segmentP(X0,X1)|ssList(sK8_skl(X1,X0)))),
% 0.12/0.46 inference(cnf_transformation,[status(thm)],[f133])).
% 0.12/0.46 fof(f136,plain,(
% 0.12/0.46 ![X0,X1]: (~ssList(X0)|~ssList(X1)|~segmentP(X0,X1)|app(app(sK7_skl(X1,X0),X1),sK8_skl(X1,X0))=X0)),
% 0.12/0.46 inference(cnf_transformation,[status(thm)],[f133])).
% 0.12/0.46 fof(f137,plain,(
% 0.12/0.46 ![X0,X1,X2,X3]: (~ssList(X0)|~ssList(X1)|segmentP(X0,X1)|~ssList(X2)|~ssList(X3)|~app(app(X2,X1),X3)=X0)),
% 0.12/0.46 inference(cnf_transformation,[status(thm)],[f133])).
% 0.12/0.46 fof(f217,plain,(
% 0.12/0.46 ![U]: (~ssList(U)|(![V]: (~ssList(V)|(neq(U,V)<=>~U=V))))),
% 0.12/0.46 inference(pre_NNF_transformation,[status(thm)],[f15])).
% 0.12/0.46 fof(f218,plain,(
% 0.12/0.46 ![U]: (~ssList(U)|(![V]: (~ssList(V)|((~neq(U,V)|~U=V)&(neq(U,V)|U=V)))))),
% 0.12/0.46 inference(NNF_transformation,[status(thm)],[f217])).
% 0.12/0.46 fof(f220,plain,(
% 0.12/0.46 ![X0,X1]: (~ssList(X0)|~ssList(X1)|neq(X0,X1)|X0=X1)),
% 0.12/0.46 inference(cnf_transformation,[status(thm)],[f218])).
% 0.12/0.46 fof(f221,plain,(
% 0.12/0.46 ![U]: (~ssList(U)|(![V]: (~ssItem(V)|ssList(cons(V,U)))))),
% 0.12/0.46 inference(pre_NNF_transformation,[status(thm)],[f16])).
% 0.12/0.46 fof(f222,plain,(
% 0.12/0.46 ![X0,X1]: (~ssList(X0)|~ssItem(X1)|ssList(cons(X1,X0)))),
% 0.12/0.46 inference(cnf_transformation,[status(thm)],[f221])).
% 0.12/0.46 fof(f223,plain,(
% 0.12/0.46 ssList(nil)),
% 0.12/0.46 inference(cnf_transformation,[status(thm)],[f17])).
% 0.12/0.46 fof(f244,plain,(
% 0.12/0.46 ![U]: (~ssList(U)|(![V]: (~ssList(V)|ssList(app(U,V)))))),
% 0.12/0.46 inference(pre_NNF_transformation,[status(thm)],[f26])).
% 0.12/0.46 fof(f245,plain,(
% 0.12/0.46 ![X0,X1]: (~ssList(X0)|~ssList(X1)|ssList(app(X0,X1)))),
% 0.12/0.46 inference(cnf_transformation,[status(thm)],[f244])).
% 0.12/0.46 fof(f248,plain,(
% 0.12/0.46 ![U]: (~ssList(U)|app(nil,U)=U)),
% 0.12/0.46 inference(pre_NNF_transformation,[status(thm)],[f28])).
% 0.12/0.46 fof(f249,plain,(
% 0.12/0.46 ![X0]: (~ssList(X0)|app(nil,X0)=X0)),
% 0.12/0.46 inference(cnf_transformation,[status(thm)],[f248])).
% 0.12/0.46 fof(f294,plain,(
% 0.12/0.46 ![U]: (~ssList(U)|frontsegP(U,nil))),
% 0.12/0.46 inference(pre_NNF_transformation,[status(thm)],[f45])).
% 0.12/0.46 fof(f295,plain,(
% 0.12/0.46 ![X0]: (~ssList(X0)|frontsegP(X0,nil))),
% 0.12/0.46 inference(cnf_transformation,[status(thm)],[f294])).
% 0.12/0.46 fof(f308,plain,(
% 0.12/0.46 ![U]: (~ssList(U)|rearsegP(U,nil))),
% 0.12/0.46 inference(pre_NNF_transformation,[status(thm)],[f51])).
% 0.12/0.46 fof(f309,plain,(
% 0.12/0.46 ![X0]: (~ssList(X0)|rearsegP(X0,nil))),
% 0.12/0.46 inference(cnf_transformation,[status(thm)],[f308])).
% 0.12/0.46 fof(f322,plain,(
% 0.12/0.46 ![U]: (~ssList(U)|segmentP(U,nil))),
% 0.12/0.46 inference(pre_NNF_transformation,[status(thm)],[f57])).
% 0.12/0.46 fof(f323,plain,(
% 0.12/0.46 ![X0]: (~ssList(X0)|segmentP(X0,nil))),
% 0.12/0.46 inference(cnf_transformation,[status(thm)],[f322])).
% 0.12/0.46 fof(f388,plain,(
% 0.12/0.46 ![U]: (~ssList(U)|app(U,nil)=U)),
% 0.12/0.46 inference(pre_NNF_transformation,[status(thm)],[f84])).
% 0.12/0.46 fof(f389,plain,(
% 0.12/0.46 ![X0]: (~ssList(X0)|app(X0,nil)=X0)),
% 0.12/0.46 inference(cnf_transformation,[status(thm)],[f388])).
% 0.12/0.46 fof(f415,plain,(
% 0.12/0.46 (?[U]: (ssList(U)&(?[V]: (ssList(V)&(?[W]: (ssList(W)&(?[X]: (ssList(X)&((V=X&U=W)&(((neq(V,nil)&(![Y]: (~ssItem(Y)|~app(U,cons(Y,nil))=V)))&(?[Z]: (ssItem(Z)&app(W,cons(Z,nil))=X)))|(neq(V,nil)&~neq(X,nil))))))))))))),
% 0.12/0.46 inference(pre_NNF_transformation,[status(thm)],[f97])).
% 0.12/0.46 fof(f416,definition,(
% 0.12/0.46 ![U,V,W,X]: (sP0_prd(X,W,V,U)<=>((neq(V,nil)&(![Y]: (~ssItem(Y)|~app(U,cons(Y,nil))=V)))&(?[Z]: (ssItem(Z)&app(W,cons(Z,nil))=X))))),
% 0.12/0.46 introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 0.12/0.46 fof(f417,plain,(
% 0.12/0.46 ?[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)))))))))))),
% 0.12/0.46 inference(formula_renaming,[status(thm)],[f415,f416])).
% 0.12/0.46 fof(f418,plain,(
% 0.12/0.46 (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))))))))),
% 0.12/0.46 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])).
% 0.12/0.46 fof(f419,plain,(
% 0.12/0.46 ssList(sK47_skl)),
% 0.12/0.46 inference(cnf_transformation,[status(thm)],[f418])).
% 0.12/0.46 fof(f420,plain,(
% 0.12/0.46 ssList(sK48_skl)),
% 0.12/0.46 inference(cnf_transformation,[status(thm)],[f418])).
% 0.12/0.46 fof(f423,plain,(
% 0.12/0.46 sK48_skl=sK50_skl),
% 0.12/0.46 inference(cnf_transformation,[status(thm)],[f418])).
% 0.12/0.46 fof(f424,plain,(
% 0.12/0.46 sK47_skl=sK49_skl),
% 0.12/0.46 inference(cnf_transformation,[status(thm)],[f418])).
% 0.12/0.46 fof(f425,plain,(
% 0.12/0.46 sP0_prd(sK50_skl,sK49_skl,sK48_skl,sK47_skl)|neq(sK48_skl,nil)),
% 0.12/0.46 inference(cnf_transformation,[status(thm)],[f418])).
% 0.12/0.46 fof(f426,plain,(
% 0.12/0.46 sP0_prd(sK50_skl,sK49_skl,sK48_skl,sK47_skl)|~neq(sK50_skl,nil)),
% 0.12/0.46 inference(cnf_transformation,[status(thm)],[f418])).
% 0.12/0.46 fof(f427,plain,(
% 0.12/0.46 ![U,V,W,X]: ((~sP0_prd(X,W,V,U)|((neq(V,nil)&(![Y]: (~ssItem(Y)|~app(U,cons(Y,nil))=V)))&(?[Z]: (ssItem(Z)&app(W,cons(Z,nil))=X))))&(sP0_prd(X,W,V,U)|((~neq(V,nil)|(?[Y]: (ssItem(Y)&app(U,cons(Y,nil))=V)))|(![Z]: (~ssItem(Z)|~app(W,cons(Z,nil))=X)))))),
% 0.12/0.46 inference(NNF_transformation,[status(thm)],[f416])).
% 0.12/0.46 fof(f428,plain,(
% 0.12/0.46 (![U,V,W,X]: (~sP0_prd(X,W,V,U)|((neq(V,nil)&(![Y]: (~ssItem(Y)|~app(U,cons(Y,nil))=V)))&(?[Z]: (ssItem(Z)&app(W,cons(Z,nil))=X)))))&(![U,V,W,X]: (sP0_prd(X,W,V,U)|((~neq(V,nil)|(?[Y]: (ssItem(Y)&app(U,cons(Y,nil))=V)))|(![Z]: (~ssItem(Z)|~app(W,cons(Z,nil))=X)))))),
% 0.12/0.46 inference(miniscoping,[status(thm)],[f427])).
% 0.12/0.46 fof(f429,plain,(
% 0.12/0.46 (![U,V,W,X]: (~sP0_prd(X,W,V,U)|((neq(V,nil)&(![Y]: (~ssItem(Y)|~app(U,cons(Y,nil))=V)))&(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))&app(U,cons(sK52_skl(X,W,V,U),nil))=V))|(![Z]: (~ssItem(Z)|~app(W,cons(Z,nil))=X)))))),
% 0.12/0.46 inference(skolemize,[status(esa),new_symbols(skolem,[sK51_skl,sK52_skl]),skolemize(Z,sK51_skl(X,W,V,U)),skolemize(Y,sK52_skl(X,W,V,U))],[f428])).
% 0.12/0.46 fof(f431,plain,(
% 0.12/0.46 ![X0,X1,X2,X3,X4]: (~sP0_prd(X0,X1,X2,X3)|~ssItem(X4)|~app(X3,cons(X4,nil))=X2)),
% 0.12/0.46 inference(cnf_transformation,[status(thm)],[f429])).
% 0.12/0.46 fof(f432,plain,(
% 0.12/0.46 ![X0,X1,X2,X3]: (~sP0_prd(X0,X1,X2,X3)|ssItem(sK51_skl(X0,X1,X2,X3)))),
% 0.12/0.46 inference(cnf_transformation,[status(thm)],[f429])).
% 0.12/0.46 fof(f433,plain,(
% 0.12/0.46 ![X0,X1,X2,X3]: (~sP0_prd(X0,X1,X2,X3)|app(X1,cons(sK51_skl(X0,X1,X2,X3),nil))=X0)),
% 0.12/0.46 inference(cnf_transformation,[status(thm)],[f429])).
% 0.12/0.46 fof(f434,plain,(
% 0.12/0.46 ![X0,X1,X2,X3,X4]: (sP0_prd(X0,X1,X2,X3)|~neq(X2,nil)|ssItem(sK52_skl(X0,X1,X2,X3))|~ssItem(X4)|~app(X1,cons(X4,nil))=X0)),
% 0.12/0.46 inference(cnf_transformation,[status(thm)],[f429])).
% 0.12/0.46 fof(f435,plain,(
% 0.12/0.46 ![X0,X1,X2,X3,X4]: (sP0_prd(X0,X1,X2,X3)|~neq(X2,nil)|app(X3,cons(sK52_skl(X0,X1,X2,X3),nil))=X2|~ssItem(X4)|~app(X1,cons(X4,nil))=X0)),
% 0.12/0.46 inference(cnf_transformation,[status(thm)],[f429])).
% 0.12/0.46 fof(f436,definition,(
% 0.12/0.46 sQ0_spl <=> (sP0_prd(sK50_skl,sK49_skl,sK48_skl,sK47_skl))),
% 0.12/0.46 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.12/0.46 fof(f437,plain,(
% 0.12/0.46 sP0_prd(sK50_skl,sK49_skl,sK48_skl,sK47_skl)|~sQ0_spl),
% 0.12/0.46 inference(component_clause,[status(thm)],[f436])).
% 0.12/0.46 fof(f439,definition,(
% 0.12/0.46 sQ1_spl <=> (neq(sK48_skl,nil))),
% 0.12/0.46 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.12/0.46 fof(f440,plain,(
% 0.12/0.46 neq(sK48_skl,nil)|~sQ1_spl),
% 0.12/0.46 inference(component_clause,[status(thm)],[f439])).
% 0.12/0.46 fof(f442,plain,(
% 0.12/0.46 sQ0_spl|sQ1_spl),
% 0.12/0.46 inference(split_clause,[status(thm)],[f425,f436,f439])).
% 0.12/0.46 fof(f443,definition,(
% 0.12/0.46 sQ2_spl <=> (neq(sK50_skl,nil))),
% 0.12/0.46 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.12/0.46 fof(f445,plain,(
% 0.12/0.46 ~neq(sK50_skl,nil)|sQ2_spl),
% 0.12/0.46 inference(component_clause,[status(thm)],[f443])).
% 0.12/0.46 fof(f446,plain,(
% 0.12/0.46 sQ0_spl|~sQ2_spl),
% 0.12/0.46 inference(split_clause,[status(thm)],[f426,f436,f443])).
% 0.12/0.46 fof(f450,plain,(
% 0.12/0.46 ![X0]: (~ssList(cons(X0,nil))|singletonP(cons(X0,nil))|~ssItem(X0))),
% 0.12/0.46 inference(destructive_equality_resolution,[status(thm)],[f118])).
% 0.12/0.46 fof(f452,plain,(
% 0.12/0.46 ![X0,X1]: (~ssList(app(X0,X1))|~ssList(X1)|rearsegP(app(X0,X1),X1)|~ssList(X0))),
% 0.12/0.46 inference(destructive_equality_resolution,[status(thm)],[f130])).
% 0.12/0.46 fof(f453,plain,(
% 0.12/0.46 ![X0,X1,X2]: (~ssList(app(app(X0,X1),X2))|~ssList(X1)|segmentP(app(app(X0,X1),X2),X1)|~ssList(X0)|~ssList(X2))),
% 0.12/0.46 inference(destructive_equality_resolution,[status(thm)],[f137])).
% 0.12/0.46 fof(f477,plain,(
% 0.12/0.46 ![X0,X1,X2,X3]: (~sP0_prd(X0,X1,app(X2,cons(X3,nil)),X2)|~ssItem(X3))),
% 0.12/0.46 inference(destructive_equality_resolution,[status(thm)],[f431])).
% 0.12/0.46 fof(f478,plain,(
% 0.12/0.46 ![X0,X1,X2,X3]: (sP0_prd(app(X0,cons(X1,nil)),X0,X2,X3)|~neq(X2,nil)|ssItem(sK52_skl(app(X0,cons(X1,nil)),X0,X2,X3))|~ssItem(X1))),
% 0.12/0.46 inference(destructive_equality_resolution,[status(thm)],[f434])).
% 0.12/0.46 fof(f479,plain,(
% 0.12/0.46 ![X0,X1,X2,X3]: (sP0_prd(app(X0,cons(X1,nil)),X0,X2,X3)|~neq(X2,nil)|app(X3,cons(sK52_skl(app(X0,cons(X1,nil)),X0,X2,X3),nil))=X2|~ssItem(X1))),
% 0.12/0.46 inference(destructive_equality_resolution,[status(thm)],[f435])).
% 0.12/0.46 fof(f482,plain,(
% 0.12/0.46 app(nil,nil)=nil),
% 0.12/0.46 inference(resolution,[status(thm)],[f249,f223])).
% 0.12/0.46 fof(f483,plain,(
% 0.12/0.46 app(nil,sK48_skl)=sK48_skl),
% 0.12/0.46 inference(resolution,[status(thm)],[f249,f420])).
% 0.12/0.46 fof(f484,plain,(
% 0.12/0.46 app(nil,sK47_skl)=sK47_skl),
% 0.12/0.46 inference(resolution,[status(thm)],[f249,f419])).
% 0.12/0.46 fof(f490,plain,(
% 0.12/0.46 sP0_prd(sK48_skl,sK49_skl,sK48_skl,sK47_skl)|~sQ0_spl),
% 0.12/0.46 inference(forward_demodulation,[status(thm)],[f423,f437])).
% 0.12/0.46 fof(f491,plain,(
% 0.12/0.46 sP0_prd(sK48_skl,sK47_skl,sK48_skl,sK47_skl)|~sQ0_spl),
% 0.12/0.46 inference(forward_demodulation,[status(thm)],[f424,f490])).
% 0.12/0.46 fof(f512,plain,(
% 0.12/0.46 ssItem(sK51_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl))|~sQ0_spl),
% 0.12/0.46 inference(resolution,[status(thm)],[f432,f491])).
% 0.12/0.46 fof(f516,plain,(
% 0.12/0.46 app(sK47_skl,cons(sK51_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl),nil))=sK48_skl|~sQ0_spl),
% 0.12/0.46 inference(resolution,[status(thm)],[f433,f491])).
% 0.12/0.46 fof(f519,plain,(
% 0.12/0.46 app(sK48_skl,nil)=sK48_skl),
% 0.12/0.46 inference(resolution,[status(thm)],[f389,f420])).
% 0.12/0.46 fof(f520,plain,(
% 0.12/0.46 app(sK47_skl,nil)=sK47_skl),
% 0.12/0.46 inference(resolution,[status(thm)],[f389,f419])).
% 0.12/0.46 fof(f535,plain,(
% 0.12/0.46 ![X0]: (singletonP(cons(X0,nil))|~ssItem(X0)|~ssList(nil)|~ssItem(X0))),
% 0.12/0.46 inference(resolution,[status(thm)],[f450,f222])).
% 0.12/0.46 fof(f536,definition,(
% 0.12/0.46 ![X0]: (sQ7_spl <=> (singletonP(cons(X0,nil))|~ssItem(X0)|~ssItem(X0)))),
% 0.12/0.46 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 0.12/0.46 fof(f539,definition,(
% 0.12/0.46 sQ8_spl <=> (ssList(nil))),
% 0.12/0.46 introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition])).
% 0.12/0.46 fof(f541,plain,(
% 0.12/0.46 ~ssList(nil)|sQ8_spl),
% 0.12/0.46 inference(component_clause,[status(thm)],[f539])).
% 0.12/0.46 fof(f542,plain,(
% 0.12/0.46 sQ7_spl|~sQ8_spl),
% 0.12/0.46 inference(split_clause,[status(thm)],[f535,f536,f539])).
% 0.12/0.46 fof(f544,plain,(
% 0.12/0.46 ![X0]: (~ssList(X0)|~ssList(nil)|ssList(sK5_skl(nil,X0))|~ssList(X0))),
% 0.12/0.46 inference(resolution,[status(thm)],[f122,f295])).
% 0.12/0.46 fof(f546,definition,(
% 0.12/0.46 ![X0]: (sQ9_spl <=> (~ssList(X0)|ssList(sK5_skl(nil,X0))|~ssList(X0)))),
% 0.12/0.46 introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition])).
% 0.12/0.46 fof(f549,plain,(
% 0.12/0.46 sQ9_spl|~sQ8_spl),
% 0.12/0.46 inference(split_clause,[status(thm)],[f544,f546,f539])).
% 0.12/0.46 fof(f551,plain,(
% 0.12/0.46 $false|sQ8_spl),
% 0.12/0.46 inference(forward_subsumption_resolution,[status(thm)],[f541,f223])).
% 0.12/0.46 fof(f552,plain,(
% 0.12/0.46 sQ8_spl),
% 0.12/0.46 inference(contradiction_clause,[status(thm)],[f551])).
% 0.12/0.46 fof(f554,plain,(
% 0.12/0.46 ![X0]: (~ssList(X0)|~ssList(nil)|app(nil,sK5_skl(nil,X0))=X0|~ssList(X0))),
% 0.12/0.46 inference(resolution,[status(thm)],[f123,f295])).
% 0.12/0.46 fof(f556,definition,(
% 0.12/0.46 ![X0]: (sQ10_spl <=> (~ssList(X0)|app(nil,sK5_skl(nil,X0))=X0|~ssList(X0)))),
% 0.12/0.46 introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition])).
% 0.12/0.46 fof(f559,plain,(
% 0.12/0.46 sQ10_spl|~sQ8_spl),
% 0.12/0.46 inference(split_clause,[status(thm)],[f554,f556,f539])).
% 0.12/0.46 fof(f567,plain,(
% 0.12/0.46 ![X0,X1,X2,X3]: (sP0_prd(app(X0,cons(X1,nil)),X0,X2,X3)|ssItem(sK52_skl(app(X0,cons(X1,nil)),X0,X2,X3))|~ssItem(X1)|~ssList(X2)|~ssList(nil)|X2=nil)),
% 0.12/0.46 inference(resolution,[status(thm)],[f478,f220])).
% 0.12/0.46 fof(f568,definition,(
% 0.12/0.46 ![X0,X1,X2,X3]: (sQ11_spl <=> (sP0_prd(app(X0,cons(X1,nil)),X0,X2,X3)|ssItem(sK52_skl(app(X0,cons(X1,nil)),X0,X2,X3))|~ssItem(X1)|~ssList(X2)|X2=nil))),
% 0.12/0.46 introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition])).
% 0.12/0.46 fof(f571,plain,(
% 0.12/0.46 sQ11_spl|~sQ8_spl),
% 0.12/0.46 inference(split_clause,[status(thm)],[f567,f568,f539])).
% 0.12/0.46 fof(f638,plain,(
% 0.12/0.46 ![X0]: (~ssList(X0)|~ssList(nil)|ssList(sK6_skl(nil,X0))|~ssList(X0))),
% 0.12/0.46 inference(resolution,[status(thm)],[f128,f309])).
% 0.12/0.46 fof(f640,definition,(
% 0.12/0.46 ![X0]: (sQ14_spl <=> (~ssList(X0)|ssList(sK6_skl(nil,X0))|~ssList(X0)))),
% 0.12/0.46 introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition])).
% 0.12/0.46 fof(f643,plain,(
% 0.12/0.46 sQ14_spl|~sQ8_spl),
% 0.12/0.46 inference(split_clause,[status(thm)],[f638,f640,f539])).
% 0.12/0.46 fof(f646,plain,(
% 0.12/0.46 ![X0]: (~ssList(X0)|~ssList(nil)|app(sK6_skl(nil,X0),nil)=X0|~ssList(X0))),
% 0.12/0.46 inference(resolution,[status(thm)],[f129,f309])).
% 0.12/0.46 fof(f648,definition,(
% 0.12/0.46 ![X0]: (sQ15_spl <=> (~ssList(X0)|app(sK6_skl(nil,X0),nil)=X0|~ssList(X0)))),
% 0.12/0.46 introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition])).
% 0.12/0.46 fof(f651,plain,(
% 0.12/0.46 sQ15_spl|~sQ8_spl),
% 0.12/0.46 inference(split_clause,[status(thm)],[f646,f648,f539])).
% 0.12/0.46 fof(f683,plain,(
% 0.12/0.46 ![X0,X1,X2,X3]: (sP0_prd(app(X0,cons(X1,nil)),X0,X2,X3)|app(X3,cons(sK52_skl(app(X0,cons(X1,nil)),X0,X2,X3),nil))=X2|~ssItem(X1)|~ssList(X2)|~ssList(nil)|X2=nil)),
% 0.12/0.46 inference(resolution,[status(thm)],[f479,f220])).
% 0.12/0.46 fof(f684,definition,(
% 0.12/0.46 ![X0,X1,X2,X3]: (sQ16_spl <=> (sP0_prd(app(X0,cons(X1,nil)),X0,X2,X3)|app(X3,cons(sK52_skl(app(X0,cons(X1,nil)),X0,X2,X3),nil))=X2|~ssItem(X1)|~ssList(X2)|X2=nil))),
% 0.12/0.46 introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition])).
% 0.12/0.46 fof(f687,plain,(
% 0.12/0.46 sQ16_spl|~sQ8_spl),
% 0.12/0.46 inference(split_clause,[status(thm)],[f683,f684,f539])).
% 0.12/0.46 fof(f892,plain,(
% 0.12/0.46 ![X0,X1]: (~ssList(X0)|rearsegP(app(X1,X0),X0)|~ssList(X1))),
% 0.12/0.46 inference(forward_subsumption_resolution,[status(thm)],[f452,f245])).
% 0.12/0.46 fof(f895,plain,(
% 0.12/0.46 ~ssList(nil)|rearsegP(sK47_skl,nil)|~ssList(sK47_skl)),
% 0.12/0.46 inference(paramodulation,[status(thm)],[f520,f892])).
% 0.12/0.46 fof(f896,plain,(
% 0.12/0.46 ~ssList(nil)|rearsegP(sK48_skl,nil)|~ssList(sK48_skl)),
% 0.12/0.46 inference(paramodulation,[status(thm)],[f519,f892])).
% 0.12/0.46 fof(f897,plain,(
% 0.12/0.46 ~ssList(nil)|rearsegP(nil,nil)|~ssList(nil)),
% 0.12/0.46 inference(paramodulation,[status(thm)],[f482,f892])).
% 0.12/0.46 fof(f898,plain,(
% 0.12/0.46 ~ssList(sK47_skl)|rearsegP(sK47_skl,sK47_skl)|~ssList(nil)),
% 0.12/0.46 inference(paramodulation,[status(thm)],[f484,f892])).
% 0.12/0.46 fof(f899,plain,(
% 0.12/0.46 ~ssList(sK48_skl)|rearsegP(sK48_skl,sK48_skl)|~ssList(nil)),
% 0.12/0.46 inference(paramodulation,[status(thm)],[f483,f892])).
% 0.12/0.46 fof(f904,definition,(
% 0.12/0.46 sQ17_spl <=> (rearsegP(sK47_skl,nil))),
% 0.12/0.46 introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition])).
% 0.12/0.46 fof(f905,plain,(
% 0.12/0.46 rearsegP(sK47_skl,nil)|~sQ17_spl),
% 0.12/0.46 inference(component_clause,[status(thm)],[f904])).
% 0.12/0.46 fof(f907,definition,(
% 0.12/0.46 sQ18_spl <=> (ssList(sK47_skl))),
% 0.12/0.46 introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition])).
% 0.12/0.46 fof(f909,plain,(
% 0.12/0.46 ~ssList(sK47_skl)|sQ18_spl),
% 0.12/0.46 inference(component_clause,[status(thm)],[f907])).
% 0.12/0.46 fof(f910,plain,(
% 0.12/0.46 ~sQ8_spl|sQ17_spl|~sQ18_spl),
% 0.12/0.46 inference(split_clause,[status(thm)],[f895,f539,f904,f907])).
% 0.12/0.46 fof(f911,definition,(
% 0.12/0.46 sQ19_spl <=> (rearsegP(sK48_skl,nil))),
% 0.12/0.46 introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition])).
% 0.12/0.46 fof(f912,plain,(
% 0.12/0.46 rearsegP(sK48_skl,nil)|~sQ19_spl),
% 0.12/0.46 inference(component_clause,[status(thm)],[f911])).
% 0.12/0.46 fof(f914,definition,(
% 0.12/0.46 sQ20_spl <=> (ssList(sK48_skl))),
% 0.12/0.46 introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition])).
% 0.12/0.46 fof(f916,plain,(
% 0.12/0.46 ~ssList(sK48_skl)|sQ20_spl),
% 0.12/0.46 inference(component_clause,[status(thm)],[f914])).
% 0.12/0.46 fof(f917,plain,(
% 0.12/0.46 ~sQ8_spl|sQ19_spl|~sQ20_spl),
% 0.12/0.46 inference(split_clause,[status(thm)],[f896,f539,f911,f914])).
% 0.12/0.46 fof(f918,definition,(
% 0.12/0.46 sQ21_spl <=> (rearsegP(nil,nil))),
% 0.12/0.46 introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition])).
% 0.12/0.46 fof(f919,plain,(
% 0.12/0.46 rearsegP(nil,nil)|~sQ21_spl),
% 0.12/0.46 inference(component_clause,[status(thm)],[f918])).
% 0.12/0.46 fof(f921,plain,(
% 0.12/0.46 ~sQ8_spl|sQ21_spl),
% 0.12/0.46 inference(split_clause,[status(thm)],[f897,f539,f918])).
% 0.12/0.46 fof(f922,definition,(
% 0.12/0.46 sQ22_spl <=> (rearsegP(sK47_skl,sK47_skl))),
% 0.12/0.46 introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition])).
% 0.12/0.46 fof(f923,plain,(
% 0.12/0.46 rearsegP(sK47_skl,sK47_skl)|~sQ22_spl),
% 0.12/0.46 inference(component_clause,[status(thm)],[f922])).
% 0.12/0.46 fof(f925,plain,(
% 0.12/0.46 ~sQ18_spl|sQ22_spl|~sQ8_spl),
% 0.12/0.46 inference(split_clause,[status(thm)],[f898,f907,f922,f539])).
% 0.12/0.46 fof(f926,definition,(
% 0.12/0.46 sQ23_spl <=> (rearsegP(sK48_skl,sK48_skl))),
% 0.12/0.46 introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition])).
% 0.12/0.46 fof(f927,plain,(
% 0.12/0.46 rearsegP(sK48_skl,sK48_skl)|~sQ23_spl),
% 0.12/0.46 inference(component_clause,[status(thm)],[f926])).
% 0.12/0.46 fof(f929,plain,(
% 0.12/0.46 ~sQ20_spl|sQ23_spl|~sQ8_spl),
% 0.12/0.46 inference(split_clause,[status(thm)],[f899,f914,f926,f539])).
% 0.12/0.46 fof(f930,plain,(
% 0.12/0.46 $false|sQ18_spl),
% 0.12/0.46 inference(forward_subsumption_resolution,[status(thm)],[f909,f419])).
% 0.12/0.46 fof(f931,plain,(
% 0.12/0.46 sQ18_spl),
% 0.12/0.46 inference(contradiction_clause,[status(thm)],[f930])).
% 0.12/0.46 fof(f932,plain,(
% 0.12/0.46 $false|sQ20_spl),
% 0.12/0.46 inference(forward_subsumption_resolution,[status(thm)],[f916,f420])).
% 0.12/0.46 fof(f933,plain,(
% 0.12/0.46 sQ20_spl),
% 0.12/0.46 inference(contradiction_clause,[status(thm)],[f932])).
% 0.12/0.46 fof(f934,plain,(
% 0.12/0.46 ![X0]: (~ssList(X0)|~ssList(nil)|ssList(sK7_skl(nil,X0))|~ssList(X0))),
% 0.12/0.46 inference(resolution,[status(thm)],[f134,f323])).
% 0.12/0.46 fof(f936,definition,(
% 0.12/0.46 ![X0]: (sQ24_spl <=> (~ssList(X0)|ssList(sK7_skl(nil,X0))|~ssList(X0)))),
% 0.12/0.46 introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition])).
% 0.12/0.46 fof(f939,plain,(
% 0.12/0.46 sQ24_spl|~sQ8_spl),
% 0.12/0.46 inference(split_clause,[status(thm)],[f934,f936,f539])).
% 0.12/0.46 fof(f942,plain,(
% 0.12/0.46 ![X0]: (~ssList(X0)|~ssList(nil)|ssList(sK8_skl(nil,X0))|~ssList(X0))),
% 0.12/0.46 inference(resolution,[status(thm)],[f135,f323])).
% 0.12/0.46 fof(f944,definition,(
% 0.12/0.46 ![X0]: (sQ25_spl <=> (~ssList(X0)|ssList(sK8_skl(nil,X0))|~ssList(X0)))),
% 0.12/0.46 introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition])).
% 0.12/0.46 fof(f947,plain,(
% 0.12/0.46 sQ25_spl|~sQ8_spl),
% 0.12/0.46 inference(split_clause,[status(thm)],[f942,f944,f539])).
% 0.12/0.46 fof(f950,plain,(
% 0.12/0.46 ~ssList(sK47_skl)|~ssList(nil)|app(sK6_skl(nil,sK47_skl),nil)=sK47_skl|~sQ17_spl),
% 0.12/0.46 inference(resolution,[status(thm)],[f905,f129])).
% 0.12/0.46 fof(f951,plain,(
% 0.12/0.46 ~ssList(sK47_skl)|~ssList(nil)|ssList(sK6_skl(nil,sK47_skl))|~sQ17_spl),
% 0.12/0.46 inference(resolution,[status(thm)],[f905,f128])).
% 0.12/0.46 fof(f952,definition,(
% 0.12/0.46 sQ26_spl <=> (app(sK6_skl(nil,sK47_skl),nil)=sK47_skl)),
% 0.12/0.46 introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition])).
% 0.12/0.46 fof(f955,plain,(
% 0.12/0.46 ~sQ18_spl|~sQ8_spl|sQ26_spl|~sQ17_spl),
% 0.12/0.46 inference(split_clause,[status(thm)],[f950,f907,f539,f952,f904])).
% 0.12/0.46 fof(f956,definition,(
% 0.12/0.46 sQ27_spl <=> (ssList(sK6_skl(nil,sK47_skl)))),
% 0.12/0.46 introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition])).
% 0.12/0.46 fof(f959,plain,(
% 0.12/0.46 ~sQ18_spl|~sQ8_spl|sQ27_spl|~sQ17_spl),
% 0.12/0.46 inference(split_clause,[status(thm)],[f951,f907,f539,f956,f904])).
% 0.12/0.46 fof(f960,plain,(
% 0.12/0.46 ~ssList(sK47_skl)|~ssList(sK47_skl)|app(sK6_skl(sK47_skl,sK47_skl),sK47_skl)=sK47_skl|~sQ22_spl),
% 0.12/0.46 inference(resolution,[status(thm)],[f923,f129])).
% 0.12/0.46 fof(f961,plain,(
% 0.12/0.46 ~ssList(sK47_skl)|~ssList(sK47_skl)|ssList(sK6_skl(sK47_skl,sK47_skl))|~sQ22_spl),
% 0.12/0.46 inference(resolution,[status(thm)],[f923,f128])).
% 0.12/0.46 fof(f962,definition,(
% 0.12/0.46 sQ28_spl <=> (app(sK6_skl(sK47_skl,sK47_skl),sK47_skl)=sK47_skl)),
% 0.12/0.46 introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition])).
% 0.12/0.46 fof(f965,plain,(
% 0.12/0.46 ~sQ18_spl|sQ28_spl|~sQ22_spl),
% 0.12/0.46 inference(split_clause,[status(thm)],[f960,f907,f962,f922])).
% 0.12/0.46 fof(f966,definition,(
% 0.12/0.46 sQ29_spl <=> (ssList(sK6_skl(sK47_skl,sK47_skl)))),
% 0.12/0.46 introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition])).
% 0.12/0.46 fof(f969,plain,(
% 0.12/0.46 ~sQ18_spl|sQ29_spl|~sQ22_spl),
% 0.12/0.46 inference(split_clause,[status(thm)],[f961,f907,f966,f922])).
% 0.12/0.46 fof(f970,plain,(
% 0.12/0.46 ~ssList(sK48_skl)|~ssList(nil)|app(sK6_skl(nil,sK48_skl),nil)=sK48_skl|~sQ19_spl),
% 0.12/0.46 inference(resolution,[status(thm)],[f912,f129])).
% 0.12/0.46 fof(f971,plain,(
% 0.12/0.46 ~ssList(sK48_skl)|~ssList(nil)|ssList(sK6_skl(nil,sK48_skl))|~sQ19_spl),
% 0.12/0.46 inference(resolution,[status(thm)],[f912,f128])).
% 0.12/0.46 fof(f972,definition,(
% 0.12/0.46 sQ30_spl <=> (app(sK6_skl(nil,sK48_skl),nil)=sK48_skl)),
% 0.12/0.46 introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition])).
% 0.12/0.46 fof(f975,plain,(
% 0.12/0.46 ~sQ20_spl|~sQ8_spl|sQ30_spl|~sQ19_spl),
% 0.12/0.46 inference(split_clause,[status(thm)],[f970,f914,f539,f972,f911])).
% 0.12/0.46 fof(f976,definition,(
% 0.12/0.46 sQ31_spl <=> (ssList(sK6_skl(nil,sK48_skl)))),
% 0.12/0.46 introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition])).
% 0.12/0.46 fof(f979,plain,(
% 0.12/0.46 ~sQ20_spl|~sQ8_spl|sQ31_spl|~sQ19_spl),
% 0.12/0.46 inference(split_clause,[status(thm)],[f971,f914,f539,f976,f911])).
% 0.12/0.46 fof(f980,plain,(
% 0.12/0.46 ![X0,X1]: (~sP0_prd(X0,X1,sK48_skl,sK47_skl)|~ssItem(sK51_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl))|~sQ0_spl)),
% 0.12/0.46 inference(paramodulation,[status(thm)],[f516,f477])).
% 0.12/0.46 fof(f983,definition,(
% 0.12/0.46 ![X0,X1]: (sQ32_spl <=> (~sP0_prd(X0,X1,sK48_skl,sK47_skl)))),
% 0.12/0.46 introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition])).
% 0.12/0.46 fof(f984,plain,(
% 0.12/0.46 ![X0,X1]: (~sP0_prd(X0,X1,sK48_skl,sK47_skl)|~sQ32_spl)),
% 0.12/0.46 inference(component_clause,[status(thm)],[f983])).
% 0.12/0.46 fof(f986,definition,(
% 0.12/0.46 sQ33_spl <=> (ssItem(sK51_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl)))),
% 0.12/0.46 introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition])).
% 0.12/0.46 fof(f988,plain,(
% 0.12/0.46 ~ssItem(sK51_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl))|sQ33_spl),
% 0.12/0.46 inference(component_clause,[status(thm)],[f986])).
% 0.12/0.46 fof(f989,plain,(
% 0.12/0.46 sQ32_spl|~sQ33_spl|~sQ0_spl),
% 0.12/0.46 inference(split_clause,[status(thm)],[f980,f983,f986,f436])).
% 0.12/0.46 fof(f1001,plain,(
% 0.12/0.46 $false|~sQ0_spl|sQ33_spl),
% 0.12/0.46 inference(forward_subsumption_resolution,[status(thm)],[f988,f512])).
% 0.12/0.46 fof(f1002,plain,(
% 0.12/0.46 ~sQ0_spl|sQ33_spl),
% 0.12/0.46 inference(contradiction_clause,[status(thm)],[f1001])).
% 0.12/0.46 fof(f1003,plain,(
% 0.12/0.46 ~neq(sK48_skl,nil)|sQ2_spl),
% 0.12/0.46 inference(forward_demodulation,[status(thm)],[f423,f445])).
% 0.12/0.46 fof(f1006,plain,(
% 0.12/0.46 ~ssList(nil)|~ssList(nil)|app(sK6_skl(nil,nil),nil)=nil|~sQ21_spl),
% 0.12/0.46 inference(resolution,[status(thm)],[f919,f129])).
% 0.12/0.46 fof(f1007,plain,(
% 0.12/0.46 ~ssList(nil)|~ssList(nil)|ssList(sK6_skl(nil,nil))|~sQ21_spl),
% 0.12/0.46 inference(resolution,[status(thm)],[f919,f128])).
% 0.12/0.46 fof(f1008,definition,(
% 0.12/0.46 sQ37_spl <=> (app(sK6_skl(nil,nil),nil)=nil)),
% 0.12/0.46 introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition])).
% 0.12/0.46 fof(f1011,plain,(
% 0.12/0.46 ~sQ8_spl|sQ37_spl|~sQ21_spl),
% 0.12/0.46 inference(split_clause,[status(thm)],[f1006,f539,f1008,f918])).
% 0.12/0.46 fof(f1012,definition,(
% 0.12/0.46 sQ38_spl <=> (ssList(sK6_skl(nil,nil)))),
% 0.12/0.46 introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition])).
% 0.12/0.46 fof(f1015,plain,(
% 0.12/0.46 ~sQ8_spl|sQ38_spl|~sQ21_spl),
% 0.12/0.46 inference(split_clause,[status(thm)],[f1007,f539,f1012,f918])).
% 0.12/0.46 fof(f1016,plain,(
% 0.12/0.46 ~ssList(sK48_skl)|~ssList(sK48_skl)|app(sK6_skl(sK48_skl,sK48_skl),sK48_skl)=sK48_skl|~sQ23_spl),
% 0.12/0.46 inference(resolution,[status(thm)],[f927,f129])).
% 0.12/0.46 fof(f1017,plain,(
% 0.12/0.46 ~ssList(sK48_skl)|~ssList(sK48_skl)|ssList(sK6_skl(sK48_skl,sK48_skl))|~sQ23_spl),
% 0.12/0.46 inference(resolution,[status(thm)],[f927,f128])).
% 0.12/0.46 fof(f1018,definition,(
% 0.12/0.46 sQ39_spl <=> (app(sK6_skl(sK48_skl,sK48_skl),sK48_skl)=sK48_skl)),
% 0.12/0.46 introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition])).
% 0.12/0.46 fof(f1021,plain,(
% 0.12/0.46 ~sQ20_spl|sQ39_spl|~sQ23_spl),
% 0.12/0.46 inference(split_clause,[status(thm)],[f1016,f914,f1018,f926])).
% 0.12/0.46 fof(f1022,definition,(
% 0.12/0.46 sQ40_spl <=> (ssList(sK6_skl(sK48_skl,sK48_skl)))),
% 0.12/0.46 introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition])).
% 0.12/0.46 fof(f1025,plain,(
% 0.12/0.46 ~sQ20_spl|sQ40_spl|~sQ23_spl),
% 0.12/0.46 inference(split_clause,[status(thm)],[f1017,f914,f1022,f926])).
% 0.12/0.46 fof(f1315,plain,(
% 0.12/0.46 ![X0]: (~ssList(X0)|~ssList(nil)|app(app(sK7_skl(nil,X0),nil),sK8_skl(nil,X0))=X0|~ssList(X0))),
% 0.12/0.46 inference(resolution,[status(thm)],[f136,f323])).
% 0.12/0.46 fof(f1317,definition,(
% 0.12/0.46 ![X0]: (sQ41_spl <=> (~ssList(X0)|app(app(sK7_skl(nil,X0),nil),sK8_skl(nil,X0))=X0|~ssList(X0)))),
% 0.12/0.46 introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition])).
% 0.12/0.46 fof(f1320,plain,(
% 0.12/0.46 sQ41_spl|~sQ8_spl),
% 0.12/0.46 inference(split_clause,[status(thm)],[f1315,f1317,f539])).
% 0.12/0.46 fof(f1323,plain,(
% 0.12/0.46 ![X0]: (~ssList(app(sK47_skl,X0))|~ssList(nil)|segmentP(app(app(sK47_skl,nil),X0),nil)|~ssList(sK47_skl)|~ssList(X0))),
% 0.12/0.46 inference(paramodulation,[status(thm)],[f520,f453])).
% 0.12/0.46 fof(f1324,plain,(
% 0.12/0.46 ![X0]: (~ssList(app(sK48_skl,X0))|~ssList(nil)|segmentP(app(app(sK48_skl,nil),X0),nil)|~ssList(sK48_skl)|~ssList(X0))),
% 0.12/0.46 inference(paramodulation,[status(thm)],[f519,f453])).
% 0.12/0.46 fof(f1325,plain,(
% 0.12/0.46 ![X0]: (~ssList(app(nil,X0))|~ssList(nil)|segmentP(app(app(nil,nil),X0),nil)|~ssList(nil)|~ssList(X0))),
% 0.12/0.46 inference(paramodulation,[status(thm)],[f482,f453])).
% 0.12/0.46 fof(f1326,plain,(
% 0.12/0.46 ![X0]: (~ssList(app(sK47_skl,X0))|~ssList(sK47_skl)|segmentP(app(app(nil,sK47_skl),X0),sK47_skl)|~ssList(nil)|~ssList(X0))),
% 0.12/0.46 inference(paramodulation,[status(thm)],[f484,f453])).
% 0.12/0.46 fof(f1327,plain,(
% 0.12/0.46 ![X0]: (~ssList(app(sK48_skl,X0))|~ssList(sK48_skl)|segmentP(app(app(nil,sK48_skl),X0),sK48_skl)|~ssList(nil)|~ssList(X0))),
% 0.12/0.46 inference(paramodulation,[status(thm)],[f483,f453])).
% 0.12/0.46 fof(f1328,definition,(
% 0.12/0.46 ![X0]: (sQ42_spl <=> (~ssList(app(sK47_skl,X0))|segmentP(app(app(sK47_skl,nil),X0),nil)|~ssList(X0)))),
% 0.12/0.46 introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition])).
% 0.12/0.46 fof(f1331,plain,(
% 0.12/0.46 sQ42_spl|~sQ8_spl|~sQ18_spl),
% 0.12/0.46 inference(split_clause,[status(thm)],[f1323,f1328,f539,f907])).
% 0.12/0.46 fof(f1332,definition,(
% 0.12/0.46 ![X0]: (sQ43_spl <=> (~ssList(app(sK48_skl,X0))|segmentP(app(app(sK48_skl,nil),X0),nil)|~ssList(X0)))),
% 0.12/0.46 introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition])).
% 0.12/0.46 fof(f1335,plain,(
% 0.12/0.46 sQ43_spl|~sQ8_spl|~sQ20_spl),
% 0.12/0.46 inference(split_clause,[status(thm)],[f1324,f1332,f539,f914])).
% 0.12/0.46 fof(f1336,definition,(
% 0.12/0.46 ![X0]: (sQ44_spl <=> (~ssList(app(nil,X0))|segmentP(app(app(nil,nil),X0),nil)|~ssList(X0)))),
% 0.12/0.46 introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition])).
% 0.12/0.46 fof(f1339,plain,(
% 0.12/0.46 sQ44_spl|~sQ8_spl),
% 0.12/0.46 inference(split_clause,[status(thm)],[f1325,f1336,f539])).
% 0.12/0.46 fof(f1340,definition,(
% 0.12/0.46 ![X0]: (sQ45_spl <=> (~ssList(app(sK47_skl,X0))|segmentP(app(app(nil,sK47_skl),X0),sK47_skl)|~ssList(X0)))),
% 0.12/0.46 introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition])).
% 0.12/0.46 fof(f1343,plain,(
% 0.12/0.46 sQ45_spl|~sQ18_spl|~sQ8_spl),
% 0.12/0.46 inference(split_clause,[status(thm)],[f1326,f1340,f907,f539])).
% 0.12/0.46 fof(f1344,definition,(
% 0.12/0.46 ![X0]: (sQ46_spl <=> (~ssList(app(sK48_skl,X0))|segmentP(app(app(nil,sK48_skl),X0),sK48_skl)|~ssList(X0)))),
% 0.12/0.46 introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition])).
% 0.12/0.46 fof(f1347,plain,(
% 0.12/0.46 sQ46_spl|~sQ20_spl|~sQ8_spl),
% 0.12/0.46 inference(split_clause,[status(thm)],[f1327,f1344,f914,f539])).
% 0.12/0.46 fof(f1353,plain,(
% 0.12/0.46 $false|~sQ32_spl|~sQ0_spl),
% 0.12/0.46 inference(forward_subsumption_resolution,[status(thm)],[f491,f984])).
% 0.12/0.46 fof(f1354,plain,(
% 0.12/0.46 ~sQ32_spl|~sQ0_spl),
% 0.12/0.46 inference(contradiction_clause,[status(thm)],[f1353])).
% 0.12/0.46 fof(f1357,plain,(
% 0.12/0.46 $false|~sQ1_spl|sQ2_spl),
% 0.12/0.46 inference(forward_subsumption_resolution,[status(thm)],[f1003,f440])).
% 0.12/0.46 fof(f1358,plain,(
% 0.12/0.46 ~sQ1_spl|sQ2_spl),
% 0.12/0.46 inference(contradiction_clause,[status(thm)],[f1357])).
% 0.12/0.46 fof(f1359,plain,(
% 0.12/0.46 $false),
% 0.12/0.46 inference(sat_refutation,[status(thm)],[f442,f446,f542,f549,f552,f559,f571,f643,f651,f687,f910,f917,f921,f925,f929,f931,f933,f939,f947,f955,f959,f965,f969,f975,f979,f989,f1002,f1011,f1015,f1021,f1025,f1320,f1331,f1335,f1339,f1343,f1347,f1354,f1358])).
% 0.12/0.46 % SZS output end CNFRefutation for theBenchmark.p
% 0.12/0.46 % Elapsed time: 0.109651 seconds
% 0.12/0.46 % CPU time: 0.589910 seconds
% 0.12/0.46 % Total memory used: 119.424 MB
% 0.12/0.46 % Net memory used: 118.745 MB
%------------------------------------------------------------------------------