%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SWC098+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 : n008.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 0.15s 0.49s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC098+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
% 0.11/0.37 % Computer : n008.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 07:56:25 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.15/0.39 % Drodi V4.1.1
% 0.15/0.49 % Refutation found
% 0.15/0.49 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.49 % SZS output start CNFRefutation for theBenchmark
% 0.15/0.49 fof(f4,axiom,(
% 0.15/0.49 (! [U] :( ssList(U)=> ( singletonP(U)<=> (? [V] :( ssItem(V)& cons(V,nil) = U ) )) ) )),
% 0.15/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.49 fof(f5,axiom,(
% 0.15/0.49 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> ( frontsegP(U,V)<=> (? [W] :( ssList(W)& app(V,W) = U ) )) ) )) )),
% 0.15/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.49 fof(f6,axiom,(
% 0.15/0.49 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> ( rearsegP(U,V)<=> (? [W] :( ssList(W)& app(W,V) = U ) )) ) )) )),
% 0.15/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.49 fof(f7,axiom,(
% 0.15/0.49 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> ( segmentP(U,V)<=> (? [W] :( ssList(W)& (? [X] :( ssList(X)& app(app(W,V),X) = U ) )) )) ) )) )),
% 0.15/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.49 fof(f8,axiom,(
% 0.15/0.49 (! [U] :( ssList(U)=> ( cyclefreeP(U)<=> (! [V] :( ssItem(V)=> (! [W] :( ssItem(W)=> (! [X] :( ssList(X)=> (! [Y] :( ssList(Y)=> (! [Z] :( ssList(Z)=> ( app(app(X,cons(V,Y)),cons(W,Z)) = U=> ~ ( leq(V,W)& leq(W,V) ) ) ) )) )) )) )) )) ) )),
% 0.15/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.49 fof(f16,axiom,(
% 0.15/0.49 (! [U] :( ssList(U)=> (! [V] :( ssItem(V)=> ssList(cons(V,U)) ) )) )),
% 0.15/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.49 fof(f17,axiom,(
% 0.15/0.49 ssList(nil) ),
% 0.15/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.49 fof(f28,axiom,(
% 0.15/0.49 (! [U] :( ssList(U)=> app(nil,U) = U ) )),
% 0.15/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.49 fof(f36,axiom,(
% 0.15/0.49 (! [U] :( ssItem(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> ( memberP(app(V,W),U)<=> ( memberP(V,U)| memberP(W,U) ) ) ) )) )) )),
% 0.15/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.49 fof(f45,axiom,(
% 0.15/0.49 (! [U] :( ssList(U)=> frontsegP(U,nil) ) )),
% 0.15/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.49 fof(f51,axiom,(
% 0.15/0.49 (! [U] :( ssList(U)=> rearsegP(U,nil) ) )),
% 0.15/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.49 fof(f57,axiom,(
% 0.15/0.49 (! [U] :( ssList(U)=> segmentP(U,nil) ) )),
% 0.15/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.49 fof(f84,axiom,(
% 0.15/0.49 (! [U] :( ssList(U)=> app(U,nil) = U ) )),
% 0.15/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.49 fof(f96,conjecture,(
% 0.15/0.49 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> (! [X] :( ssList(X)=> ( V != X| U != W| (? [Y] :( ssItem(Y)& cons(Y,nil) = U& (! [Z] :( ssItem(Z)=> ( ~ memberP(V,Z)| ~ leq(Y,Z)| Y = Z ) ))& memberP(V,Y) ))| ( nil = V& nil = U )| ( (! [X1] :( ssItem(X1)=> ( cons(X1,nil) != W| ~ memberP(X,X1)| (? [X2] :( ssItem(X2)& X1 != X2& memberP(X,X2)& leq(X1,X2) ) )) ))& ( nil != X| nil != W ) ) ) ) )) )) )) )),
% 0.15/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.49 fof(f97,negated_conjecture,(
% 0.15/0.49 ~((! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> (! [X] :( ssList(X)=> ( V != X| U != W| (? [Y] :( ssItem(Y)& cons(Y,nil) = U& (! [Z] :( ssItem(Z)=> ( ~ memberP(V,Z)| ~ leq(Y,Z)| Y = Z ) ))& memberP(V,Y) ))| ( nil = V& nil = U )| ( (! [X1] :( ssItem(X1)=> ( cons(X1,nil) != W| ~ memberP(X,X1)| (? [X2] :( ssItem(X2)& X1 != X2& memberP(X,X2)& leq(X1,X2) ) )) ))& ( nil != X| nil != W ) ) ) ) )) )) )) ))),
% 0.15/0.49 inference(negated_conjecture,[status(cth)],[f96])).
% 0.15/0.49 fof(f113,plain,(
% 0.15/0.49 ![U]: (~ssList(U)|(singletonP(U)<=>(?[V]: (ssItem(V)&cons(V,nil)=U))))),
% 0.15/0.49 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 0.15/0.49 fof(f114,plain,(
% 0.15/0.49 ![U]: (~ssList(U)|((~singletonP(U)|(?[V]: (ssItem(V)&cons(V,nil)=U)))&(singletonP(U)|(![V]: (~ssItem(V)|~cons(V,nil)=U)))))),
% 0.15/0.49 inference(NNF_transformation,[status(thm)],[f113])).
% 0.15/0.49 fof(f115,plain,(
% 0.15/0.49 ![U]: (~ssList(U)|((~singletonP(U)|(ssItem(sK4_skl(U))&cons(sK4_skl(U),nil)=U))&(singletonP(U)|(![V]: (~ssItem(V)|~cons(V,nil)=U)))))),
% 0.15/0.49 inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(V,sK4_skl(U))],[f114])).
% 0.15/0.49 fof(f118,plain,(
% 0.15/0.49 ![X0,X1]: (~ssList(X0)|singletonP(X0)|~ssItem(X1)|~cons(X1,nil)=X0)),
% 0.15/0.49 inference(cnf_transformation,[status(thm)],[f115])).
% 0.15/0.49 fof(f119,plain,(
% 0.15/0.49 ![U]: (~ssList(U)|(![V]: (~ssList(V)|(frontsegP(U,V)<=>(?[W]: (ssList(W)&app(V,W)=U))))))),
% 0.15/0.49 inference(pre_NNF_transformation,[status(thm)],[f5])).
% 0.15/0.49 fof(f120,plain,(
% 0.15/0.49 ![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)))))))),
% 0.15/0.49 inference(NNF_transformation,[status(thm)],[f119])).
% 0.15/0.49 fof(f121,plain,(
% 0.15/0.49 ![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)))))))),
% 0.15/0.49 inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(W,sK5_skl(V,U))],[f120])).
% 0.15/0.49 fof(f122,plain,(
% 0.15/0.49 ![X0,X1]: (~ssList(X0)|~ssList(X1)|~frontsegP(X0,X1)|ssList(sK5_skl(X1,X0)))),
% 0.15/0.49 inference(cnf_transformation,[status(thm)],[f121])).
% 0.15/0.49 fof(f123,plain,(
% 0.15/0.49 ![X0,X1]: (~ssList(X0)|~ssList(X1)|~frontsegP(X0,X1)|app(X1,sK5_skl(X1,X0))=X0)),
% 0.15/0.49 inference(cnf_transformation,[status(thm)],[f121])).
% 0.15/0.49 fof(f124,plain,(
% 0.15/0.49 ![X0,X1,X2]: (~ssList(X0)|~ssList(X1)|frontsegP(X0,X1)|~ssList(X2)|~app(X1,X2)=X0)),
% 0.15/0.49 inference(cnf_transformation,[status(thm)],[f121])).
% 0.15/0.49 fof(f125,plain,(
% 0.15/0.49 ![U]: (~ssList(U)|(![V]: (~ssList(V)|(rearsegP(U,V)<=>(?[W]: (ssList(W)&app(W,V)=U))))))),
% 0.15/0.49 inference(pre_NNF_transformation,[status(thm)],[f6])).
% 0.15/0.49 fof(f126,plain,(
% 0.15/0.49 ![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)))))))),
% 0.15/0.49 inference(NNF_transformation,[status(thm)],[f125])).
% 0.15/0.49 fof(f127,plain,(
% 0.15/0.49 ![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)))))))),
% 0.15/0.49 inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl]),skolemize(W,sK6_skl(V,U))],[f126])).
% 0.15/0.49 fof(f129,plain,(
% 0.15/0.49 ![X0,X1]: (~ssList(X0)|~ssList(X1)|~rearsegP(X0,X1)|app(sK6_skl(X1,X0),X1)=X0)),
% 0.15/0.49 inference(cnf_transformation,[status(thm)],[f127])).
% 0.15/0.49 fof(f130,plain,(
% 0.15/0.49 ![X0,X1,X2]: (~ssList(X0)|~ssList(X1)|rearsegP(X0,X1)|~ssList(X2)|~app(X2,X1)=X0)),
% 0.15/0.49 inference(cnf_transformation,[status(thm)],[f127])).
% 0.15/0.49 fof(f131,plain,(
% 0.15/0.49 ![U]: (~ssList(U)|(![V]: (~ssList(V)|(segmentP(U,V)<=>(?[W]: (ssList(W)&(?[X]: (ssList(X)&app(app(W,V),X)=U))))))))),
% 0.15/0.49 inference(pre_NNF_transformation,[status(thm)],[f7])).
% 0.15/0.49 fof(f132,plain,(
% 0.15/0.49 ![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)))))))))),
% 0.15/0.49 inference(NNF_transformation,[status(thm)],[f131])).
% 0.15/0.49 fof(f133,plain,(
% 0.15/0.49 ![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)))))))))),
% 0.15/0.49 inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl,sK8_skl]),skolemize(W,sK7_skl(V,U)),skolemize(X,sK8_skl(V,U))],[f132])).
% 0.15/0.49 fof(f134,plain,(
% 0.15/0.49 ![X0,X1]: (~ssList(X0)|~ssList(X1)|~segmentP(X0,X1)|ssList(sK7_skl(X1,X0)))),
% 0.15/0.49 inference(cnf_transformation,[status(thm)],[f133])).
% 0.15/0.49 fof(f135,plain,(
% 0.15/0.49 ![X0,X1]: (~ssList(X0)|~ssList(X1)|~segmentP(X0,X1)|ssList(sK8_skl(X1,X0)))),
% 0.15/0.49 inference(cnf_transformation,[status(thm)],[f133])).
% 0.15/0.49 fof(f136,plain,(
% 0.15/0.49 ![X0,X1]: (~ssList(X0)|~ssList(X1)|~segmentP(X0,X1)|app(app(sK7_skl(X1,X0),X1),sK8_skl(X1,X0))=X0)),
% 0.15/0.49 inference(cnf_transformation,[status(thm)],[f133])).
% 0.15/0.49 fof(f137,plain,(
% 0.15/0.49 ![X0,X1,X2,X3]: (~ssList(X0)|~ssList(X1)|segmentP(X0,X1)|~ssList(X2)|~ssList(X3)|~app(app(X2,X1),X3)=X0)),
% 0.15/0.49 inference(cnf_transformation,[status(thm)],[f133])).
% 0.15/0.49 fof(f138,plain,(
% 0.15/0.49 ![U]: (~ssList(U)|(cyclefreeP(U)<=>(![V]: (~ssItem(V)|(![W]: (~ssItem(W)|(![X]: (~ssList(X)|(![Y]: (~ssList(Y)|(![Z]: (~ssList(Z)|(~app(app(X,cons(V,Y)),cons(W,Z))=U|(~leq(V,W)|~leq(W,V)))))))))))))))),
% 0.15/0.49 inference(pre_NNF_transformation,[status(thm)],[f8])).
% 0.15/0.49 fof(f139,plain,(
% 0.15/0.49 ![U]: (~ssList(U)|((~cyclefreeP(U)|(![V]: (~ssItem(V)|(![W]: (~ssItem(W)|(![X]: (~ssList(X)|(![Y]: (~ssList(Y)|(![Z]: (~ssList(Z)|(~app(app(X,cons(V,Y)),cons(W,Z))=U|(~leq(V,W)|~leq(W,V))))))))))))))&(cyclefreeP(U)|(?[V]: (ssItem(V)&(?[W]: (ssItem(W)&(?[X]: (ssList(X)&(?[Y]: (ssList(Y)&(?[Z]: (ssList(Z)&(app(app(X,cons(V,Y)),cons(W,Z))=U&(leq(V,W)&leq(W,V))))))))))))))))),
% 0.15/0.49 inference(NNF_transformation,[status(thm)],[f138])).
% 0.15/0.49 fof(f140,plain,(
% 0.15/0.49 ![U]: (~ssList(U)|((~cyclefreeP(U)|(![V]: (~ssItem(V)|(![W]: (~ssItem(W)|(![X]: (~ssList(X)|(![Y]: (~ssList(Y)|(![Z]: (~ssList(Z)|(~app(app(X,cons(V,Y)),cons(W,Z))=U|(~leq(V,W)|~leq(W,V))))))))))))))&(cyclefreeP(U)|(ssItem(sK9_skl(U))&(ssItem(sK10_skl(U))&(ssList(sK11_skl(U))&(ssList(sK12_skl(U))&(ssList(sK13_skl(U))&(app(app(sK11_skl(U),cons(sK9_skl(U),sK12_skl(U))),cons(sK10_skl(U),sK13_skl(U)))=U&(leq(sK9_skl(U),sK10_skl(U))&leq(sK10_skl(U),sK9_skl(U))))))))))))),
% 0.15/0.49 inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl,sK10_skl,sK11_skl,sK12_skl,sK13_skl]),skolemize(V,sK9_skl(U)),skolemize(W,sK10_skl(U)),skolemize(X,sK11_skl(U)),skolemize(Y,sK12_skl(U)),skolemize(Z,sK13_skl(U))],[f139])).
% 0.15/0.49 fof(f147,plain,(
% 0.15/0.49 ![X0]: (~ssList(X0)|cyclefreeP(X0)|app(app(sK11_skl(X0),cons(sK9_skl(X0),sK12_skl(X0))),cons(sK10_skl(X0),sK13_skl(X0)))=X0)),
% 0.15/0.49 inference(cnf_transformation,[status(thm)],[f140])).
% 0.15/0.49 fof(f221,plain,(
% 0.15/0.49 ![U]: (~ssList(U)|(![V]: (~ssItem(V)|ssList(cons(V,U)))))),
% 0.15/0.49 inference(pre_NNF_transformation,[status(thm)],[f16])).
% 0.15/0.49 fof(f222,plain,(
% 0.15/0.49 ![X0,X1]: (~ssList(X0)|~ssItem(X1)|ssList(cons(X1,X0)))),
% 0.15/0.49 inference(cnf_transformation,[status(thm)],[f221])).
% 0.15/0.49 fof(f223,plain,(
% 0.15/0.49 ssList(nil)),
% 0.15/0.49 inference(cnf_transformation,[status(thm)],[f17])).
% 0.15/0.49 fof(f248,plain,(
% 0.15/0.49 ![U]: (~ssList(U)|app(nil,U)=U)),
% 0.15/0.49 inference(pre_NNF_transformation,[status(thm)],[f28])).
% 0.15/0.49 fof(f249,plain,(
% 0.15/0.49 ![X0]: (~ssList(X0)|app(nil,X0)=X0)),
% 0.15/0.49 inference(cnf_transformation,[status(thm)],[f248])).
% 0.15/0.49 fof(f268,plain,(
% 0.15/0.49 ![U]: (~ssItem(U)|(![V]: (~ssList(V)|(![W]: (~ssList(W)|(memberP(app(V,W),U)<=>(memberP(V,U)|memberP(W,U))))))))),
% 0.15/0.49 inference(pre_NNF_transformation,[status(thm)],[f36])).
% 0.15/0.49 fof(f269,plain,(
% 0.15/0.49 ![U]: (~ssItem(U)|(![V]: (~ssList(V)|(![W]: (~ssList(W)|((~memberP(app(V,W),U)|(memberP(V,U)|memberP(W,U)))&(memberP(app(V,W),U)|(~memberP(V,U)&~memberP(W,U)))))))))),
% 0.15/0.49 inference(NNF_transformation,[status(thm)],[f268])).
% 0.15/0.49 fof(f270,plain,(
% 0.15/0.49 ![X0,X1,X2]: (~ssItem(X0)|~ssList(X1)|~ssList(X2)|~memberP(app(X1,X2),X0)|memberP(X1,X0)|memberP(X2,X0))),
% 0.15/0.49 inference(cnf_transformation,[status(thm)],[f269])).
% 0.15/0.49 fof(f294,plain,(
% 0.15/0.49 ![U]: (~ssList(U)|frontsegP(U,nil))),
% 0.15/0.49 inference(pre_NNF_transformation,[status(thm)],[f45])).
% 0.15/0.49 fof(f295,plain,(
% 0.15/0.49 ![X0]: (~ssList(X0)|frontsegP(X0,nil))),
% 0.15/0.49 inference(cnf_transformation,[status(thm)],[f294])).
% 0.15/0.49 fof(f308,plain,(
% 0.15/0.49 ![U]: (~ssList(U)|rearsegP(U,nil))),
% 0.15/0.49 inference(pre_NNF_transformation,[status(thm)],[f51])).
% 0.15/0.49 fof(f309,plain,(
% 0.15/0.49 ![X0]: (~ssList(X0)|rearsegP(X0,nil))),
% 0.15/0.49 inference(cnf_transformation,[status(thm)],[f308])).
% 0.15/0.49 fof(f322,plain,(
% 0.15/0.49 ![U]: (~ssList(U)|segmentP(U,nil))),
% 0.15/0.49 inference(pre_NNF_transformation,[status(thm)],[f57])).
% 0.15/0.49 fof(f323,plain,(
% 0.15/0.49 ![X0]: (~ssList(X0)|segmentP(X0,nil))),
% 0.15/0.49 inference(cnf_transformation,[status(thm)],[f322])).
% 0.15/0.49 fof(f388,plain,(
% 0.15/0.49 ![U]: (~ssList(U)|app(U,nil)=U)),
% 0.15/0.49 inference(pre_NNF_transformation,[status(thm)],[f84])).
% 0.15/0.49 fof(f389,plain,(
% 0.15/0.49 ![X0]: (~ssList(X0)|app(X0,nil)=X0)),
% 0.15/0.49 inference(cnf_transformation,[status(thm)],[f388])).
% 0.15/0.49 fof(f415,plain,(
% 0.15/0.49 (?[U]: (ssList(U)&(?[V]: (ssList(V)&(?[W]: (ssList(W)&(?[X]: (ssList(X)&((((V=X&U=W)&(![Y]: (((~ssItem(Y)|~cons(Y,nil)=U)|(?[Z]: (ssItem(Z)&((memberP(V,Z)&leq(Y,Z))&~Y=Z))))|~memberP(V,Y))))&(~nil=V|~nil=U))&((?[X1]: (ssItem(X1)&((cons(X1,nil)=W&memberP(X,X1))&(![X2]: (((~ssItem(X2)|X1=X2)|~memberP(X,X2))|~leq(X1,X2))))))|(nil=X&nil=W)))))))))))),
% 0.15/0.49 inference(pre_NNF_transformation,[status(thm)],[f97])).
% 0.15/0.49 fof(f416,definition,(
% 0.15/0.49 ![W,X,X1]: (sP0_prd(X1,X,W)<=>(ssItem(X1)&((cons(X1,nil)=W&memberP(X,X1))&(![X2]: (((~ssItem(X2)|X1=X2)|~memberP(X,X2))|~leq(X1,X2))))))),
% 0.15/0.49 introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 0.15/0.49 fof(f417,plain,(
% 0.15/0.49 ?[U]: (ssList(U)&(?[V]: (ssList(V)&(?[W]: (ssList(W)&(?[X]: (ssList(X)&((((V=X&U=W)&(![Y]: (((~ssItem(Y)|~cons(Y,nil)=U)|(?[Z]: (ssItem(Z)&((memberP(V,Z)&leq(Y,Z))&~Y=Z))))|~memberP(V,Y))))&(~nil=V|~nil=U))&((?[X1]: sP0_prd(X1,X,W))|(nil=X&nil=W))))))))))),
% 0.15/0.49 inference(formula_renaming,[status(thm)],[f415,f416])).
% 0.15/0.49 fof(f418,plain,(
% 0.15/0.49 (ssList(sK47_skl)&(ssList(sK48_skl)&(ssList(sK49_skl)&(ssList(sK50_skl)&((((sK48_skl=sK50_skl&sK47_skl=sK49_skl)&(![Y]: (((~ssItem(Y)|~cons(Y,nil)=sK47_skl)|(ssItem(sK51_skl(Y))&((memberP(sK48_skl,sK51_skl(Y))&leq(Y,sK51_skl(Y)))&~Y=sK51_skl(Y))))|~memberP(sK48_skl,Y))))&(~nil=sK48_skl|~nil=sK47_skl))&(sP0_prd(sK52_skl,sK50_skl,sK49_skl)|(nil=sK50_skl&nil=sK49_skl)))))))),
% 0.15/0.49 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(Z,sK51_skl(Y)),skolemize(X1,sK52_skl)],[f417])).
% 0.15/0.49 fof(f421,plain,(
% 0.15/0.49 ssList(sK49_skl)),
% 0.15/0.49 inference(cnf_transformation,[status(thm)],[f418])).
% 0.15/0.49 fof(f422,plain,(
% 0.15/0.49 ssList(sK50_skl)),
% 0.15/0.49 inference(cnf_transformation,[status(thm)],[f418])).
% 0.15/0.49 fof(f423,plain,(
% 0.15/0.49 sK48_skl=sK50_skl),
% 0.15/0.49 inference(cnf_transformation,[status(thm)],[f418])).
% 0.15/0.49 fof(f424,plain,(
% 0.15/0.49 sK47_skl=sK49_skl),
% 0.15/0.49 inference(cnf_transformation,[status(thm)],[f418])).
% 0.15/0.49 fof(f425,plain,(
% 0.15/0.49 ![X0]: (~ssItem(X0)|~cons(X0,nil)=sK47_skl|ssItem(sK51_skl(X0))|~memberP(sK48_skl,X0))),
% 0.15/0.49 inference(cnf_transformation,[status(thm)],[f418])).
% 0.15/0.49 fof(f426,plain,(
% 0.15/0.49 ![X0]: (~ssItem(X0)|~cons(X0,nil)=sK47_skl|memberP(sK48_skl,sK51_skl(X0))|~memberP(sK48_skl,X0))),
% 0.15/0.49 inference(cnf_transformation,[status(thm)],[f418])).
% 0.15/0.49 fof(f427,plain,(
% 0.15/0.49 ![X0]: (~ssItem(X0)|~cons(X0,nil)=sK47_skl|leq(X0,sK51_skl(X0))|~memberP(sK48_skl,X0))),
% 0.15/0.49 inference(cnf_transformation,[status(thm)],[f418])).
% 0.15/0.49 fof(f428,plain,(
% 0.15/0.49 ![X0]: (~ssItem(X0)|~cons(X0,nil)=sK47_skl|~X0=sK51_skl(X0)|~memberP(sK48_skl,X0))),
% 0.15/0.49 inference(cnf_transformation,[status(thm)],[f418])).
% 0.15/0.49 fof(f429,plain,(
% 0.15/0.49 ~nil=sK48_skl|~nil=sK47_skl),
% 0.15/0.49 inference(cnf_transformation,[status(thm)],[f418])).
% 0.15/0.49 fof(f430,plain,(
% 0.15/0.49 sP0_prd(sK52_skl,sK50_skl,sK49_skl)|nil=sK50_skl),
% 0.15/0.49 inference(cnf_transformation,[status(thm)],[f418])).
% 0.15/0.49 fof(f431,plain,(
% 0.15/0.49 sP0_prd(sK52_skl,sK50_skl,sK49_skl)|nil=sK49_skl),
% 0.15/0.49 inference(cnf_transformation,[status(thm)],[f418])).
% 0.15/0.49 fof(f432,plain,(
% 0.15/0.49 ![W,X,X1]: ((~sP0_prd(X1,X,W)|(ssItem(X1)&((cons(X1,nil)=W&memberP(X,X1))&(![X2]: (((~ssItem(X2)|X1=X2)|~memberP(X,X2))|~leq(X1,X2))))))&(sP0_prd(X1,X,W)|(~ssItem(X1)|((~cons(X1,nil)=W|~memberP(X,X1))|(?[X2]: (((ssItem(X2)&~X1=X2)&memberP(X,X2))&leq(X1,X2)))))))),
% 0.15/0.49 inference(NNF_transformation,[status(thm)],[f416])).
% 0.15/0.49 fof(f433,plain,(
% 0.15/0.49 (![W,X,X1]: (~sP0_prd(X1,X,W)|(ssItem(X1)&((cons(X1,nil)=W&memberP(X,X1))&(![X2]: (((~ssItem(X2)|X1=X2)|~memberP(X,X2))|~leq(X1,X2)))))))&(![W,X,X1]: (sP0_prd(X1,X,W)|(~ssItem(X1)|((~cons(X1,nil)=W|~memberP(X,X1))|(?[X2]: (((ssItem(X2)&~X1=X2)&memberP(X,X2))&leq(X1,X2)))))))),
% 0.15/0.49 inference(miniscoping,[status(thm)],[f432])).
% 0.15/0.49 fof(f434,plain,(
% 0.15/0.49 (![W,X,X1]: (~sP0_prd(X1,X,W)|(ssItem(X1)&((cons(X1,nil)=W&memberP(X,X1))&(![X2]: (((~ssItem(X2)|X1=X2)|~memberP(X,X2))|~leq(X1,X2)))))))&(![W,X,X1]: (sP0_prd(X1,X,W)|(~ssItem(X1)|((~cons(X1,nil)=W|~memberP(X,X1))|(((ssItem(sK53_skl(X1,X,W))&~X1=sK53_skl(X1,X,W))&memberP(X,sK53_skl(X1,X,W)))&leq(X1,sK53_skl(X1,X,W)))))))),
% 0.15/0.49 inference(skolemize,[status(esa),new_symbols(skolem,[sK53_skl]),skolemize(X2,sK53_skl(X1,X,W))],[f433])).
% 0.15/0.49 fof(f435,plain,(
% 0.15/0.49 ![X0,X1,X2]: (~sP0_prd(X0,X1,X2)|ssItem(X0))),
% 0.15/0.49 inference(cnf_transformation,[status(thm)],[f434])).
% 0.15/0.49 fof(f436,plain,(
% 0.15/0.49 ![X0,X1,X2]: (~sP0_prd(X0,X1,X2)|cons(X0,nil)=X2)),
% 0.15/0.49 inference(cnf_transformation,[status(thm)],[f434])).
% 0.15/0.49 fof(f437,plain,(
% 0.15/0.49 ![X0,X1,X2]: (~sP0_prd(X0,X1,X2)|memberP(X1,X0))),
% 0.15/0.49 inference(cnf_transformation,[status(thm)],[f434])).
% 0.15/0.49 fof(f438,plain,(
% 0.15/0.49 ![X0,X1,X2,X3]: (~sP0_prd(X0,X1,X2)|~ssItem(X3)|X0=X3|~memberP(X1,X3)|~leq(X0,X3))),
% 0.15/0.49 inference(cnf_transformation,[status(thm)],[f434])).
% 0.15/0.49 fof(f443,definition,(
% 0.15/0.49 sQ0_spl <=> (nil=sK48_skl)),
% 0.15/0.49 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.15/0.49 fof(f445,plain,(
% 0.15/0.49 ~nil=sK48_skl|sQ0_spl),
% 0.15/0.49 inference(component_clause,[status(thm)],[f443])).
% 0.15/0.49 fof(f446,definition,(
% 0.15/0.49 sQ1_spl <=> (nil=sK47_skl)),
% 0.15/0.49 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.15/0.49 fof(f448,plain,(
% 0.15/0.49 ~nil=sK47_skl|sQ1_spl),
% 0.15/0.49 inference(component_clause,[status(thm)],[f446])).
% 0.15/0.49 fof(f449,plain,(
% 0.15/0.49 ~sQ0_spl|~sQ1_spl),
% 0.15/0.49 inference(split_clause,[status(thm)],[f429,f443,f446])).
% 0.15/0.49 fof(f450,definition,(
% 0.15/0.49 sQ2_spl <=> (sP0_prd(sK52_skl,sK50_skl,sK49_skl))),
% 0.15/0.49 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.15/0.49 fof(f451,plain,(
% 0.15/0.49 sP0_prd(sK52_skl,sK50_skl,sK49_skl)|~sQ2_spl),
% 0.15/0.49 inference(component_clause,[status(thm)],[f450])).
% 0.15/0.49 fof(f453,definition,(
% 0.15/0.49 sQ3_spl <=> (nil=sK50_skl)),
% 0.15/0.49 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.15/0.49 fof(f454,plain,(
% 0.15/0.49 nil=sK50_skl|~sQ3_spl),
% 0.15/0.49 inference(component_clause,[status(thm)],[f453])).
% 0.15/0.49 fof(f456,plain,(
% 0.15/0.49 sQ2_spl|sQ3_spl),
% 0.15/0.49 inference(split_clause,[status(thm)],[f430,f450,f453])).
% 0.15/0.49 fof(f457,definition,(
% 0.15/0.49 sQ4_spl <=> (nil=sK49_skl)),
% 0.15/0.49 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 0.15/0.49 fof(f458,plain,(
% 0.15/0.49 nil=sK49_skl|~sQ4_spl),
% 0.15/0.49 inference(component_clause,[status(thm)],[f457])).
% 0.15/0.49 fof(f460,plain,(
% 0.15/0.49 sQ2_spl|sQ4_spl),
% 0.15/0.49 inference(split_clause,[status(thm)],[f431,f450,f457])).
% 0.15/0.49 fof(f464,plain,(
% 0.15/0.49 ![X0]: (~ssList(cons(X0,nil))|singletonP(cons(X0,nil))|~ssItem(X0))),
% 0.15/0.49 inference(destructive_equality_resolution,[status(thm)],[f118])).
% 0.15/0.49 fof(f465,plain,(
% 0.15/0.49 ![X0,X1]: (~ssList(app(X0,X1))|~ssList(X0)|frontsegP(app(X0,X1),X0)|~ssList(X1))),
% 0.15/0.49 inference(destructive_equality_resolution,[status(thm)],[f124])).
% 0.15/0.49 fof(f466,plain,(
% 0.15/0.49 ![X0,X1]: (~ssList(app(X0,X1))|~ssList(X1)|rearsegP(app(X0,X1),X1)|~ssList(X0))),
% 0.15/0.49 inference(destructive_equality_resolution,[status(thm)],[f130])).
% 0.15/0.49 fof(f467,plain,(
% 0.15/0.49 ![X0,X1,X2]: (~ssList(app(app(X0,X1),X2))|~ssList(X1)|segmentP(app(app(X0,X1),X2),X1)|~ssList(X0)|~ssList(X2))),
% 0.15/0.49 inference(destructive_equality_resolution,[status(thm)],[f137])).
% 0.15/0.49 fof(f497,plain,(
% 0.15/0.49 ~nil=sK50_skl|sQ0_spl),
% 0.15/0.49 inference(forward_demodulation,[status(thm)],[f423,f445])).
% 0.15/0.49 fof(f503,plain,(
% 0.15/0.49 ssItem(sK52_skl)|~sQ2_spl),
% 0.15/0.49 inference(resolution,[status(thm)],[f451,f435])).
% 0.15/0.49 fof(f506,plain,(
% 0.15/0.49 ![X0]: (~ssItem(X0)|~cons(X0,nil)=sK49_skl|ssItem(sK51_skl(X0))|~memberP(sK48_skl,X0))),
% 0.15/0.49 inference(forward_demodulation,[status(thm)],[f424,f425])).
% 0.15/0.49 fof(f507,plain,(
% 0.15/0.49 ![X0]: (~ssItem(X0)|~cons(X0,nil)=sK49_skl|ssItem(sK51_skl(X0))|~memberP(sK50_skl,X0))),
% 0.15/0.49 inference(forward_demodulation,[status(thm)],[f423,f506])).
% 0.15/0.49 fof(f515,plain,(
% 0.15/0.49 memberP(sK50_skl,sK52_skl)|~sQ2_spl),
% 0.15/0.49 inference(resolution,[status(thm)],[f437,f451])).
% 0.15/0.49 fof(f516,plain,(
% 0.15/0.49 ~ssItem(sK52_skl)|~cons(sK52_skl,nil)=sK49_skl|ssItem(sK51_skl(sK52_skl))|~sQ2_spl),
% 0.15/0.49 inference(resolution,[status(thm)],[f515,f507])).
% 0.15/0.49 fof(f518,definition,(
% 0.15/0.49 sQ5_spl <=> (ssItem(sK52_skl))),
% 0.15/0.49 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 0.15/0.49 fof(f520,plain,(
% 0.15/0.49 ~ssItem(sK52_skl)|sQ5_spl),
% 0.15/0.49 inference(component_clause,[status(thm)],[f518])).
% 0.15/0.49 fof(f521,definition,(
% 0.15/0.49 sQ6_spl <=> (cons(sK52_skl,nil)=sK49_skl)),
% 0.15/0.49 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.15/0.49 fof(f523,plain,(
% 0.15/0.49 ~cons(sK52_skl,nil)=sK49_skl|sQ6_spl),
% 0.15/0.49 inference(component_clause,[status(thm)],[f521])).
% 0.15/0.49 fof(f524,definition,(
% 0.15/0.49 sQ7_spl <=> (ssItem(sK51_skl(sK52_skl)))),
% 0.15/0.49 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 0.15/0.49 fof(f527,plain,(
% 0.15/0.49 ~sQ5_spl|~sQ6_spl|sQ7_spl|~sQ2_spl),
% 0.15/0.49 inference(split_clause,[status(thm)],[f516,f518,f521,f524,f450])).
% 0.15/0.49 fof(f528,definition,(
% 0.15/0.49 sQ8_spl <=> (ssList(sK50_skl))),
% 0.15/0.49 introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition])).
% 0.15/0.49 fof(f530,plain,(
% 0.15/0.49 ~ssList(sK50_skl)|sQ8_spl),
% 0.15/0.49 inference(component_clause,[status(thm)],[f528])).
% 0.15/0.49 fof(f535,plain,(
% 0.15/0.49 $false|sQ0_spl|~sQ3_spl),
% 0.15/0.49 inference(forward_subsumption_resolution,[status(thm)],[f454,f497])).
% 0.15/0.49 fof(f536,plain,(
% 0.15/0.49 sQ0_spl|~sQ3_spl),
% 0.15/0.49 inference(contradiction_clause,[status(thm)],[f535])).
% 0.15/0.49 fof(f537,plain,(
% 0.15/0.49 ~nil=sK49_skl|sQ1_spl),
% 0.15/0.49 inference(forward_demodulation,[status(thm)],[f424,f448])).
% 0.15/0.49 fof(f538,plain,(
% 0.15/0.49 ![X0]: (~ssItem(X0)|~cons(X0,nil)=sK49_skl|memberP(sK48_skl,sK51_skl(X0))|~memberP(sK48_skl,X0))),
% 0.15/0.49 inference(forward_demodulation,[status(thm)],[f424,f426])).
% 0.15/0.49 fof(f539,plain,(
% 0.15/0.49 ![X0]: (~ssItem(X0)|~cons(X0,nil)=sK49_skl|memberP(sK50_skl,sK51_skl(X0))|~memberP(sK48_skl,X0))),
% 0.15/0.49 inference(forward_demodulation,[status(thm)],[f423,f538])).
% 0.15/0.49 fof(f540,plain,(
% 0.15/0.49 ![X0]: (~ssItem(X0)|~cons(X0,nil)=sK49_skl|memberP(sK50_skl,sK51_skl(X0))|~memberP(sK50_skl,X0))),
% 0.15/0.49 inference(forward_demodulation,[status(thm)],[f423,f539])).
% 0.15/0.49 fof(f542,plain,(
% 0.15/0.49 $false|sQ5_spl|~sQ2_spl),
% 0.15/0.49 inference(forward_subsumption_resolution,[status(thm)],[f503,f520])).
% 0.15/0.49 fof(f543,plain,(
% 0.15/0.49 sQ5_spl|~sQ2_spl),
% 0.15/0.49 inference(contradiction_clause,[status(thm)],[f542])).
% 0.15/0.49 fof(f544,plain,(
% 0.15/0.49 $false|sQ8_spl),
% 0.15/0.49 inference(forward_subsumption_resolution,[status(thm)],[f530,f422])).
% 0.15/0.49 fof(f545,plain,(
% 0.15/0.49 sQ8_spl),
% 0.15/0.49 inference(contradiction_clause,[status(thm)],[f544])).
% 0.15/0.49 fof(f563,plain,(
% 0.15/0.49 $false|sQ1_spl|~sQ4_spl),
% 0.15/0.49 inference(forward_subsumption_resolution,[status(thm)],[f458,f537])).
% 0.15/0.49 fof(f564,plain,(
% 0.15/0.49 sQ1_spl|~sQ4_spl),
% 0.15/0.49 inference(contradiction_clause,[status(thm)],[f563])).
% 0.15/0.49 fof(f572,plain,(
% 0.15/0.49 ![X0]: (singletonP(cons(X0,nil))|~ssItem(X0)|~ssList(nil)|~ssItem(X0))),
% 0.15/0.49 inference(resolution,[status(thm)],[f464,f222])).
% 0.15/0.49 fof(f573,definition,(
% 0.15/0.49 ![X0]: (sQ10_spl <=> (singletonP(cons(X0,nil))|~ssItem(X0)|~ssItem(X0)))),
% 0.15/0.49 introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition])).
% 0.15/0.49 fof(f576,definition,(
% 0.15/0.49 sQ11_spl <=> (ssList(nil))),
% 0.15/0.49 introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition])).
% 0.15/0.49 fof(f578,plain,(
% 0.15/0.49 ~ssList(nil)|sQ11_spl),
% 0.15/0.49 inference(component_clause,[status(thm)],[f576])).
% 0.15/0.49 fof(f579,plain,(
% 0.15/0.49 sQ10_spl|~sQ11_spl),
% 0.15/0.49 inference(split_clause,[status(thm)],[f572,f573,f576])).
% 0.15/0.49 fof(f589,definition,(
% 0.15/0.49 sQ13_spl <=> (leq(sK52_skl,sK51_skl(sK52_skl)))),
% 0.15/0.49 introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition])).
% 0.15/0.49 fof(f591,plain,(
% 0.15/0.49 ~leq(sK52_skl,sK51_skl(sK52_skl))|sQ13_spl),
% 0.15/0.49 inference(component_clause,[status(thm)],[f589])).
% 0.15/0.49 fof(f602,plain,(
% 0.15/0.49 app(nil,sK50_skl)=sK50_skl),
% 0.15/0.49 inference(resolution,[status(thm)],[f249,f422])).
% 0.15/0.49 fof(f606,plain,(
% 0.15/0.49 app(nil,nil)=nil),
% 0.15/0.49 inference(resolution,[status(thm)],[f249,f223])).
% 0.15/0.49 fof(f607,plain,(
% 0.15/0.49 ![X0]: (~ssList(X0)|~ssList(nil)|app(nil,sK5_skl(nil,X0))=X0|~ssList(X0))),
% 0.15/0.49 inference(resolution,[status(thm)],[f123,f295])).
% 0.15/0.49 fof(f609,definition,(
% 0.15/0.49 ![X0]: (sQ14_spl <=> (~ssList(X0)|app(nil,sK5_skl(nil,X0))=X0|~ssList(X0)))),
% 0.15/0.49 introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition])).
% 0.15/0.49 fof(f612,plain,(
% 0.15/0.49 sQ14_spl|~sQ11_spl),
% 0.15/0.49 inference(split_clause,[status(thm)],[f607,f609,f576])).
% 0.15/0.49 fof(f614,plain,(
% 0.15/0.49 $false|sQ11_spl),
% 0.15/0.49 inference(forward_subsumption_resolution,[status(thm)],[f578,f223])).
% 0.15/0.49 fof(f615,plain,(
% 0.15/0.49 sQ11_spl),
% 0.15/0.49 inference(contradiction_clause,[status(thm)],[f614])).
% 0.15/0.49 fof(f617,plain,(
% 0.15/0.49 ~ssList(nil)|~ssList(nil)|frontsegP(app(nil,nil),nil)|~ssList(nil)),
% 0.15/0.49 inference(paramodulation,[status(thm)],[f606,f465])).
% 0.15/0.49 fof(f618,plain,(
% 0.15/0.49 ~ssList(sK50_skl)|~ssList(nil)|frontsegP(app(nil,sK50_skl),nil)|~ssList(sK50_skl)),
% 0.15/0.49 inference(paramodulation,[status(thm)],[f602,f465])).
% 0.15/0.49 fof(f619,definition,(
% 0.15/0.49 sQ15_spl <=> (frontsegP(app(nil,nil),nil))),
% 0.15/0.49 introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition])).
% 0.15/0.49 fof(f620,plain,(
% 0.15/0.49 frontsegP(app(nil,nil),nil)|~sQ15_spl),
% 0.15/0.49 inference(component_clause,[status(thm)],[f619])).
% 0.15/0.49 fof(f622,plain,(
% 0.15/0.49 ~sQ11_spl|sQ15_spl),
% 0.15/0.49 inference(split_clause,[status(thm)],[f617,f576,f619])).
% 0.15/0.49 fof(f623,definition,(
% 0.15/0.49 sQ16_spl <=> (frontsegP(app(nil,sK50_skl),nil))),
% 0.15/0.49 introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition])).
% 0.15/0.49 fof(f624,plain,(
% 0.15/0.49 frontsegP(app(nil,sK50_skl),nil)|~sQ16_spl),
% 0.15/0.49 inference(component_clause,[status(thm)],[f623])).
% 0.15/0.49 fof(f626,plain,(
% 0.15/0.49 ~sQ8_spl|~sQ11_spl|sQ16_spl),
% 0.15/0.49 inference(split_clause,[status(thm)],[f618,f528,f576,f623])).
% 0.15/0.49 fof(f627,plain,(
% 0.15/0.49 frontsegP(sK50_skl,nil)|~sQ16_spl),
% 0.15/0.49 inference(forward_demodulation,[status(thm)],[f602,f624])).
% 0.15/0.49 fof(f628,plain,(
% 0.15/0.49 frontsegP(nil,nil)|~sQ15_spl),
% 0.15/0.49 inference(forward_demodulation,[status(thm)],[f606,f620])).
% 0.15/0.49 fof(f630,plain,(
% 0.15/0.49 ~ssList(sK50_skl)|~ssList(nil)|app(nil,sK5_skl(nil,sK50_skl))=sK50_skl|~sQ16_spl),
% 0.15/0.49 inference(resolution,[status(thm)],[f627,f123])).
% 0.15/0.49 fof(f631,definition,(
% 0.15/0.49 sQ17_spl <=> (app(nil,sK5_skl(nil,sK50_skl))=sK50_skl)),
% 0.15/0.49 introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition])).
% 0.15/0.49 fof(f632,plain,(
% 0.15/0.49 app(nil,sK5_skl(nil,sK50_skl))=sK50_skl|~sQ17_spl),
% 0.15/0.49 inference(component_clause,[status(thm)],[f631])).
% 0.15/0.49 fof(f634,plain,(
% 0.15/0.49 ~sQ8_spl|~sQ11_spl|sQ17_spl|~sQ16_spl),
% 0.15/0.49 inference(split_clause,[status(thm)],[f630,f528,f576,f631,f623])).
% 0.15/0.49 fof(f645,definition,(
% 0.15/0.49 sQ18_spl <=> (sK52_skl=sK51_skl(sK52_skl))),
% 0.15/0.49 introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition])).
% 0.15/0.49 fof(f649,plain,(
% 0.15/0.49 ![X0]: (~ssItem(X0)|~cons(X0,nil)=sK47_skl|~X0=sK51_skl(X0)|~memberP(sK50_skl,X0))),
% 0.15/0.49 inference(forward_demodulation,[status(thm)],[f423,f428])).
% 0.15/0.49 fof(f650,plain,(
% 0.15/0.49 ![X0]: (~ssItem(X0)|~cons(X0,nil)=sK47_skl|leq(X0,sK51_skl(X0))|~memberP(sK50_skl,X0))),
% 0.15/0.49 inference(forward_demodulation,[status(thm)],[f423,f427])).
% 0.15/0.49 fof(f652,plain,(
% 0.15/0.49 app(nil,sK49_skl)=sK49_skl),
% 0.15/0.49 inference(resolution,[status(thm)],[f421,f249])).
% 0.15/0.49 fof(f653,plain,(
% 0.15/0.49 ~ssList(nil)|~ssList(nil)|app(nil,sK5_skl(nil,nil))=nil|~sQ15_spl),
% 0.15/0.49 inference(resolution,[status(thm)],[f628,f123])).
% 0.15/0.49 fof(f654,definition,(
% 0.15/0.49 sQ19_spl <=> (app(nil,sK5_skl(nil,nil))=nil)),
% 0.15/0.49 introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition])).
% 0.15/0.49 fof(f657,plain,(
% 0.15/0.49 ~sQ11_spl|sQ19_spl|~sQ15_spl),
% 0.15/0.49 inference(split_clause,[status(thm)],[f653,f576,f654,f619])).
% 0.15/0.49 fof(f658,plain,(
% 0.15/0.49 ![X0]: (~ssItem(X0)|~ssList(nil)|~ssList(nil)|~memberP(nil,X0)|memberP(nil,X0)|memberP(nil,X0))),
% 0.15/0.49 inference(paramodulation,[status(thm)],[f606,f270])).
% 0.15/0.49 fof(f659,plain,(
% 0.15/0.49 ![X0]: (~ssItem(X0)|~ssList(nil)|~ssList(sK50_skl)|~memberP(sK50_skl,X0)|memberP(nil,X0)|memberP(sK50_skl,X0))),
% 0.15/0.49 inference(paramodulation,[status(thm)],[f602,f270])).
% 0.15/0.49 fof(f660,definition,(
% 0.15/0.49 ![X0]: (sQ20_spl <=> (~ssItem(X0)|~memberP(nil,X0)|memberP(nil,X0)|memberP(nil,X0)))),
% 0.15/0.49 introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition])).
% 0.15/0.49 fof(f663,plain,(
% 0.15/0.49 sQ20_spl|~sQ11_spl),
% 0.15/0.49 inference(split_clause,[status(thm)],[f658,f660,f576])).
% 0.15/0.49 fof(f664,definition,(
% 0.15/0.49 ![X0]: (sQ21_spl <=> (~ssItem(X0)|~memberP(sK50_skl,X0)|memberP(nil,X0)|memberP(sK50_skl,X0)))),
% 0.15/0.49 introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition])).
% 0.15/0.49 fof(f667,plain,(
% 0.15/0.49 sQ21_spl|~sQ11_spl|~sQ8_spl),
% 0.15/0.49 inference(split_clause,[status(thm)],[f659,f664,f576,f528])).
% 0.15/0.49 fof(f675,plain,(
% 0.15/0.49 ![X0]: (~ssItem(X0)|~ssList(nil)|~ssList(sK49_skl)|~memberP(sK49_skl,X0)|memberP(nil,X0)|memberP(sK49_skl,X0))),
% 0.15/0.49 inference(paramodulation,[status(thm)],[f652,f270])).
% 0.15/0.49 fof(f676,plain,(
% 0.15/0.49 ~ssList(sK49_skl)|~ssList(nil)|frontsegP(app(nil,sK49_skl),nil)|~ssList(sK49_skl)),
% 0.15/0.49 inference(paramodulation,[status(thm)],[f652,f465])).
% 0.15/0.49 fof(f677,definition,(
% 0.15/0.49 ![X0]: (sQ23_spl <=> (~ssItem(X0)|~memberP(sK49_skl,X0)|memberP(nil,X0)|memberP(sK49_skl,X0)))),
% 0.15/0.49 introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition])).
% 0.15/0.49 fof(f680,definition,(
% 0.15/0.49 sQ24_spl <=> (ssList(sK49_skl))),
% 0.15/0.49 introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition])).
% 0.15/0.49 fof(f682,plain,(
% 0.15/0.49 ~ssList(sK49_skl)|sQ24_spl),
% 0.15/0.49 inference(component_clause,[status(thm)],[f680])).
% 0.15/0.49 fof(f683,plain,(
% 0.15/0.49 sQ23_spl|~sQ11_spl|~sQ24_spl),
% 0.15/0.49 inference(split_clause,[status(thm)],[f675,f677,f576,f680])).
% 0.15/0.49 fof(f684,definition,(
% 0.15/0.49 sQ25_spl <=> (frontsegP(app(nil,sK49_skl),nil))),
% 0.15/0.49 introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition])).
% 0.15/0.49 fof(f685,plain,(
% 0.15/0.49 frontsegP(app(nil,sK49_skl),nil)|~sQ25_spl),
% 0.15/0.49 inference(component_clause,[status(thm)],[f684])).
% 0.15/0.49 fof(f687,plain,(
% 0.15/0.49 ~sQ24_spl|~sQ11_spl|sQ25_spl),
% 0.15/0.49 inference(split_clause,[status(thm)],[f676,f680,f576,f684])).
% 0.15/0.49 fof(f688,plain,(
% 0.15/0.49 $false|sQ24_spl),
% 0.15/0.49 inference(forward_subsumption_resolution,[status(thm)],[f682,f421])).
% 0.15/0.49 fof(f689,plain,(
% 0.15/0.49 sQ24_spl),
% 0.15/0.49 inference(contradiction_clause,[status(thm)],[f688])).
% 0.15/0.49 fof(f690,plain,(
% 0.15/0.49 frontsegP(sK49_skl,nil)|~sQ25_spl),
% 0.15/0.49 inference(forward_demodulation,[status(thm)],[f652,f685])).
% 0.15/0.49 fof(f691,plain,(
% 0.15/0.49 ~ssList(sK49_skl)|~ssList(nil)|app(nil,sK5_skl(nil,sK49_skl))=sK49_skl|~sQ25_spl),
% 0.15/0.49 inference(resolution,[status(thm)],[f690,f123])).
% 0.15/0.49 fof(f692,definition,(
% 0.15/0.49 sQ26_spl <=> (app(nil,sK5_skl(nil,sK49_skl))=sK49_skl)),
% 0.15/0.49 introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition])).
% 0.15/0.49 fof(f695,plain,(
% 0.15/0.49 ~sQ24_spl|~sQ11_spl|sQ26_spl|~sQ25_spl),
% 0.15/0.49 inference(split_clause,[status(thm)],[f691,f680,f576,f692,f684])).
% 0.15/0.49 fof(f696,plain,(
% 0.15/0.49 app(sK49_skl,nil)=sK49_skl),
% 0.15/0.49 inference(resolution,[status(thm)],[f389,f421])).
% 0.15/0.49 fof(f699,plain,(
% 0.15/0.49 app(sK50_skl,nil)=sK50_skl),
% 0.15/0.49 inference(resolution,[status(thm)],[f389,f422])).
% 0.15/0.49 fof(f705,plain,(
% 0.15/0.49 ~ssList(sK49_skl)|~ssList(sK49_skl)|frontsegP(app(sK49_skl,nil),sK49_skl)|~ssList(nil)),
% 0.15/0.49 inference(paramodulation,[status(thm)],[f696,f465])).
% 0.15/0.49 fof(f707,definition,(
% 0.15/0.49 sQ27_spl <=> (frontsegP(app(sK49_skl,nil),sK49_skl))),
% 0.15/0.49 introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition])).
% 0.15/0.49 fof(f708,plain,(
% 0.15/0.49 frontsegP(app(sK49_skl,nil),sK49_skl)|~sQ27_spl),
% 0.15/0.49 inference(component_clause,[status(thm)],[f707])).
% 0.15/0.49 fof(f710,plain,(
% 0.15/0.49 ~sQ24_spl|sQ27_spl|~sQ11_spl),
% 0.15/0.49 inference(split_clause,[status(thm)],[f705,f680,f707,f576])).
% 0.15/0.49 fof(f711,plain,(
% 0.15/0.49 frontsegP(sK49_skl,sK49_skl)|~sQ27_spl),
% 0.15/0.49 inference(forward_demodulation,[status(thm)],[f696,f708])).
% 0.15/0.49 fof(f712,plain,(
% 0.15/0.49 ~ssList(sK49_skl)|~ssList(sK49_skl)|app(sK49_skl,sK5_skl(sK49_skl,sK49_skl))=sK49_skl|~sQ27_spl),
% 0.15/0.49 inference(resolution,[status(thm)],[f711,f123])).
% 0.15/0.49 fof(f713,definition,(
% 0.15/0.49 sQ28_spl <=> (app(sK49_skl,sK5_skl(sK49_skl,sK49_skl))=sK49_skl)),
% 0.15/0.49 introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition])).
% 0.15/0.49 fof(f716,plain,(
% 0.15/0.49 ~sQ24_spl|sQ28_spl|~sQ27_spl),
% 0.15/0.49 inference(split_clause,[status(thm)],[f712,f680,f713,f707])).
% 0.15/0.49 fof(f718,plain,(
% 0.15/0.49 ~ssList(sK50_skl)|~ssList(sK50_skl)|frontsegP(app(sK50_skl,nil),sK50_skl)|~ssList(nil)),
% 0.15/0.49 inference(paramodulation,[status(thm)],[f699,f465])).
% 0.15/0.49 fof(f720,definition,(
% 0.15/0.49 sQ29_spl <=> (frontsegP(app(sK50_skl,nil),sK50_skl))),
% 0.15/0.49 introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition])).
% 0.15/0.49 fof(f721,plain,(
% 0.15/0.49 frontsegP(app(sK50_skl,nil),sK50_skl)|~sQ29_spl),
% 0.15/0.49 inference(component_clause,[status(thm)],[f720])).
% 0.15/0.49 fof(f723,plain,(
% 0.15/0.49 ~sQ8_spl|sQ29_spl|~sQ11_spl),
% 0.15/0.49 inference(split_clause,[status(thm)],[f718,f528,f720,f576])).
% 0.15/0.49 fof(f724,plain,(
% 0.15/0.49 frontsegP(sK50_skl,sK50_skl)|~sQ29_spl),
% 0.15/0.49 inference(forward_demodulation,[status(thm)],[f699,f721])).
% 0.15/0.49 fof(f725,plain,(
% 0.15/0.49 ![X0]: (~ssList(X0)|~ssList(nil)|app(sK6_skl(nil,X0),nil)=X0|~ssList(X0))),
% 0.15/0.49 inference(resolution,[status(thm)],[f129,f309])).
% 0.15/0.49 fof(f727,definition,(
% 0.15/0.49 ![X0]: (sQ30_spl <=> (~ssList(X0)|app(sK6_skl(nil,X0),nil)=X0|~ssList(X0)))),
% 0.15/0.49 introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition])).
% 0.15/0.49 fof(f730,plain,(
% 0.15/0.49 sQ30_spl|~sQ11_spl),
% 0.15/0.49 inference(split_clause,[status(thm)],[f725,f727,f576])).
% 0.15/0.49 fof(f733,plain,(
% 0.15/0.49 ~ssList(sK50_skl)|~ssList(nil)|rearsegP(app(sK50_skl,nil),nil)|~ssList(sK50_skl)),
% 0.15/0.49 inference(paramodulation,[status(thm)],[f699,f466])).
% 0.15/0.49 fof(f734,plain,(
% 0.15/0.49 ~ssList(sK49_skl)|~ssList(nil)|rearsegP(app(sK49_skl,nil),nil)|~ssList(sK49_skl)),
% 0.15/0.49 inference(paramodulation,[status(thm)],[f696,f466])).
% 0.15/0.49 fof(f735,plain,(
% 0.15/0.49 ~ssList(sK49_skl)|~ssList(sK49_skl)|rearsegP(app(nil,sK49_skl),sK49_skl)|~ssList(nil)),
% 0.15/0.49 inference(paramodulation,[status(thm)],[f652,f466])).
% 0.15/0.49 fof(f736,plain,(
% 0.15/0.49 ~ssList(nil)|~ssList(nil)|rearsegP(app(nil,nil),nil)|~ssList(nil)),
% 0.15/0.49 inference(paramodulation,[status(thm)],[f606,f466])).
% 0.15/0.49 fof(f737,plain,(
% 0.15/0.49 ~ssList(sK50_skl)|~ssList(sK50_skl)|rearsegP(app(nil,sK50_skl),sK50_skl)|~ssList(nil)),
% 0.15/0.49 inference(paramodulation,[status(thm)],[f602,f466])).
% 0.15/0.49 fof(f738,definition,(
% 0.15/0.49 sQ31_spl <=> (rearsegP(app(sK50_skl,nil),nil))),
% 0.15/0.49 introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition])).
% 0.15/0.49 fof(f739,plain,(
% 0.15/0.49 rearsegP(app(sK50_skl,nil),nil)|~sQ31_spl),
% 0.15/0.49 inference(component_clause,[status(thm)],[f738])).
% 0.15/0.49 fof(f741,plain,(
% 0.15/0.49 ~sQ8_spl|~sQ11_spl|sQ31_spl),
% 0.15/0.49 inference(split_clause,[status(thm)],[f733,f528,f576,f738])).
% 0.15/0.49 fof(f742,definition,(
% 0.15/0.49 sQ32_spl <=> (rearsegP(app(sK49_skl,nil),nil))),
% 0.15/0.49 introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition])).
% 0.15/0.49 fof(f743,plain,(
% 0.15/0.49 rearsegP(app(sK49_skl,nil),nil)|~sQ32_spl),
% 0.15/0.49 inference(component_clause,[status(thm)],[f742])).
% 0.15/0.49 fof(f745,plain,(
% 0.15/0.49 ~sQ24_spl|~sQ11_spl|sQ32_spl),
% 0.15/0.49 inference(split_clause,[status(thm)],[f734,f680,f576,f742])).
% 0.15/0.49 fof(f746,definition,(
% 0.15/0.49 sQ33_spl <=> (rearsegP(app(nil,sK49_skl),sK49_skl))),
% 0.15/0.49 introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition])).
% 0.15/0.49 fof(f747,plain,(
% 0.15/0.49 rearsegP(app(nil,sK49_skl),sK49_skl)|~sQ33_spl),
% 0.15/0.49 inference(component_clause,[status(thm)],[f746])).
% 0.15/0.49 fof(f749,plain,(
% 0.15/0.49 ~sQ24_spl|sQ33_spl|~sQ11_spl),
% 0.15/0.49 inference(split_clause,[status(thm)],[f735,f680,f746,f576])).
% 0.15/0.49 fof(f750,definition,(
% 0.15/0.49 sQ34_spl <=> (rearsegP(app(nil,nil),nil))),
% 0.15/0.49 introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition])).
% 0.15/0.49 fof(f751,plain,(
% 0.15/0.49 rearsegP(app(nil,nil),nil)|~sQ34_spl),
% 0.15/0.49 inference(component_clause,[status(thm)],[f750])).
% 0.15/0.49 fof(f753,plain,(
% 0.15/0.49 ~sQ11_spl|sQ34_spl),
% 0.15/0.49 inference(split_clause,[status(thm)],[f736,f576,f750])).
% 0.15/0.49 fof(f754,definition,(
% 0.15/0.49 sQ35_spl <=> (rearsegP(app(nil,sK50_skl),sK50_skl))),
% 0.15/0.49 introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition])).
% 0.15/0.49 fof(f755,plain,(
% 0.15/0.49 rearsegP(app(nil,sK50_skl),sK50_skl)|~sQ35_spl),
% 0.15/0.49 inference(component_clause,[status(thm)],[f754])).
% 0.15/0.49 fof(f757,plain,(
% 0.15/0.49 ~sQ8_spl|sQ35_spl|~sQ11_spl),
% 0.15/0.49 inference(split_clause,[status(thm)],[f737,f528,f754,f576])).
% 0.15/0.49 fof(f758,plain,(
% 0.15/0.49 rearsegP(sK50_skl,nil)|~sQ31_spl),
% 0.15/0.49 inference(forward_demodulation,[status(thm)],[f699,f739])).
% 0.15/0.49 fof(f759,plain,(
% 0.15/0.49 rearsegP(sK50_skl,sK50_skl)|~sQ35_spl),
% 0.15/0.49 inference(forward_demodulation,[status(thm)],[f602,f755])).
% 0.15/0.49 fof(f760,plain,(
% 0.15/0.49 rearsegP(sK49_skl,nil)|~sQ32_spl),
% 0.15/0.49 inference(forward_demodulation,[status(thm)],[f696,f743])).
% 0.15/0.49 fof(f761,plain,(
% 0.15/0.49 rearsegP(sK49_skl,sK49_skl)|~sQ33_spl),
% 0.15/0.49 inference(forward_demodulation,[status(thm)],[f652,f747])).
% 0.15/0.49 fof(f762,plain,(
% 0.15/0.49 rearsegP(nil,nil)|~sQ34_spl),
% 0.15/0.49 inference(forward_demodulation,[status(thm)],[f606,f751])).
% 0.15/0.49 fof(f763,plain,(
% 0.15/0.49 ![X0]: (~ssList(X0)|~ssList(nil)|ssList(sK7_skl(nil,X0))|~ssList(X0))),
% 0.15/0.49 inference(resolution,[status(thm)],[f134,f323])).
% 0.15/0.49 fof(f765,definition,(
% 0.15/0.49 ![X0]: (sQ36_spl <=> (~ssList(X0)|ssList(sK7_skl(nil,X0))|~ssList(X0)))),
% 0.15/0.49 introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition])).
% 0.15/0.49 fof(f768,plain,(
% 0.15/0.49 sQ36_spl|~sQ11_spl),
% 0.15/0.49 inference(split_clause,[status(thm)],[f763,f765,f576])).
% 0.15/0.49 fof(f771,plain,(
% 0.15/0.49 ~ssList(sK50_skl)|~ssList(sK50_skl)|app(sK50_skl,sK5_skl(sK50_skl,sK50_skl))=sK50_skl|~sQ29_spl),
% 0.15/0.49 inference(resolution,[status(thm)],[f724,f123])).
% 0.15/0.49 fof(f772,definition,(
% 0.15/0.49 sQ37_spl <=> (app(sK50_skl,sK5_skl(sK50_skl,sK50_skl))=sK50_skl)),
% 0.15/0.49 introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition])).
% 0.15/0.49 fof(f775,plain,(
% 0.15/0.49 ~sQ8_spl|sQ37_spl|~sQ29_spl),
% 0.15/0.49 inference(split_clause,[status(thm)],[f771,f528,f772,f720])).
% 0.15/0.49 fof(f776,plain,(
% 0.15/0.49 ~ssList(sK50_skl)|~ssList(nil)|app(sK6_skl(nil,sK50_skl),nil)=sK50_skl|~sQ31_spl),
% 0.15/0.49 inference(resolution,[status(thm)],[f758,f129])).
% 0.15/0.49 fof(f777,definition,(
% 0.15/0.49 sQ38_spl <=> (app(sK6_skl(nil,sK50_skl),nil)=sK50_skl)),
% 0.15/0.49 introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition])).
% 0.15/0.49 fof(f780,plain,(
% 0.15/0.49 ~sQ8_spl|~sQ11_spl|sQ38_spl|~sQ31_spl),
% 0.15/0.49 inference(split_clause,[status(thm)],[f776,f528,f576,f777,f738])).
% 0.15/0.49 fof(f781,plain,(
% 0.15/0.49 ~ssList(sK50_skl)|~ssList(sK50_skl)|app(sK6_skl(sK50_skl,sK50_skl),sK50_skl)=sK50_skl|~sQ35_spl),
% 0.15/0.49 inference(resolution,[status(thm)],[f759,f129])).
% 0.15/0.49 fof(f782,definition,(
% 0.15/0.49 sQ39_spl <=> (app(sK6_skl(sK50_skl,sK50_skl),sK50_skl)=sK50_skl)),
% 0.15/0.49 introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition])).
% 0.15/0.49 fof(f785,plain,(
% 0.15/0.49 ~sQ8_spl|sQ39_spl|~sQ35_spl),
% 0.15/0.49 inference(split_clause,[status(thm)],[f781,f528,f782,f754])).
% 0.15/0.49 fof(f786,plain,(
% 0.15/0.49 cons(sK52_skl,nil)=sK49_skl|~sQ2_spl),
% 0.15/0.49 inference(resolution,[status(thm)],[f436,f451])).
% 0.15/0.49 fof(f787,plain,(
% 0.15/0.49 $false|sQ6_spl|~sQ2_spl),
% 0.15/0.49 inference(forward_subsumption_resolution,[status(thm)],[f786,f523])).
% 0.15/0.49 fof(f788,plain,(
% 0.15/0.49 sQ6_spl|~sQ2_spl),
% 0.15/0.49 inference(contradiction_clause,[status(thm)],[f787])).
% 0.15/0.49 fof(f803,definition,(
% 0.15/0.49 sQ40_spl <=> (app(sK6_skl(nil,nil),nil)=nil)),
% 0.15/0.49 introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition])).
% 0.15/0.49 fof(f815,plain,(
% 0.15/0.49 ~ssList(sK49_skl)|~ssList(sK49_skl)|app(sK6_skl(sK49_skl,sK49_skl),sK49_skl)=sK49_skl|~sQ33_spl),
% 0.15/0.49 inference(resolution,[status(thm)],[f761,f129])).
% 0.15/0.49 fof(f816,definition,(
% 0.15/0.49 sQ42_spl <=> (app(sK6_skl(sK49_skl,sK49_skl),sK49_skl)=sK49_skl)),
% 0.15/0.49 introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition])).
% 0.15/0.49 fof(f819,plain,(
% 0.15/0.49 ~sQ24_spl|sQ42_spl|~sQ33_spl),
% 0.15/0.49 inference(split_clause,[status(thm)],[f815,f680,f816,f746])).
% 0.15/0.49 fof(f820,plain,(
% 0.15/0.49 ~ssList(nil)|~ssList(nil)|app(sK6_skl(nil,nil),nil)=nil|~sQ34_spl),
% 0.15/0.49 inference(resolution,[status(thm)],[f762,f129])).
% 0.15/0.49 fof(f821,plain,(
% 0.15/0.49 ~sQ11_spl|sQ40_spl|~sQ34_spl),
% 0.15/0.49 inference(split_clause,[status(thm)],[f820,f576,f803,f750])).
% 0.15/0.49 fof(f829,plain,(
% 0.15/0.49 ~ssList(sK49_skl)|~ssList(nil)|app(sK6_skl(nil,sK49_skl),nil)=sK49_skl|~sQ32_spl),
% 0.15/0.49 inference(resolution,[status(thm)],[f760,f129])).
% 0.15/0.49 fof(f830,definition,(
% 0.15/0.49 sQ43_spl <=> (app(sK6_skl(nil,sK49_skl),nil)=sK49_skl)),
% 0.15/0.49 introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition])).
% 0.15/0.49 fof(f833,plain,(
% 0.15/0.49 ~sQ24_spl|~sQ11_spl|sQ43_spl|~sQ32_spl),
% 0.15/0.49 inference(split_clause,[status(thm)],[f829,f680,f576,f830,f742])).
% 0.15/0.49 fof(f859,plain,(
% 0.15/0.49 ![X0]: (~ssList(X0)|~ssList(nil)|ssList(sK8_skl(nil,X0))|~ssList(X0))),
% 0.15/0.49 inference(resolution,[status(thm)],[f135,f323])).
% 0.15/0.49 fof(f861,definition,(
% 0.15/0.49 ![X0]: (sQ47_spl <=> (~ssList(X0)|ssList(sK8_skl(nil,X0))|~ssList(X0)))),
% 0.15/0.49 introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition])).
% 0.15/0.49 fof(f864,plain,(
% 0.15/0.49 sQ47_spl|~sQ11_spl),
% 0.15/0.49 inference(split_clause,[status(thm)],[f859,f861,f576])).
% 0.15/0.49 fof(f867,plain,(
% 0.15/0.49 ![X0]: (~ssList(X0)|~ssList(nil)|app(app(sK7_skl(nil,X0),nil),sK8_skl(nil,X0))=X0|~ssList(X0))),
% 0.15/0.49 inference(resolution,[status(thm)],[f136,f323])).
% 0.15/0.49 fof(f869,definition,(
% 0.15/0.49 ![X0]: (sQ48_spl <=> (~ssList(X0)|app(app(sK7_skl(nil,X0),nil),sK8_skl(nil,X0))=X0|~ssList(X0)))),
% 0.15/0.49 introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition])).
% 0.15/0.49 fof(f872,plain,(
% 0.15/0.49 sQ48_spl|~sQ11_spl),
% 0.15/0.49 inference(split_clause,[status(thm)],[f867,f869,f576])).
% 0.15/0.49 fof(f875,plain,(
% 0.15/0.49 ![X0]: (~ssList(app(sK50_skl,X0))|~ssList(nil)|segmentP(app(app(sK50_skl,nil),X0),nil)|~ssList(sK50_skl)|~ssList(X0))),
% 0.15/0.49 inference(paramodulation,[status(thm)],[f699,f467])).
% 0.15/0.49 fof(f876,plain,(
% 0.15/0.49 ![X0]: (~ssList(app(nil,X0))|~ssList(nil)|segmentP(app(app(nil,nil),X0),nil)|~ssList(nil)|~ssList(X0))),
% 0.15/0.49 inference(paramodulation,[status(thm)],[f606,f467])).
% 0.15/0.50 fof(f877,plain,(
% 0.15/0.50 ![X0]: (~ssList(app(sK50_skl,X0))|~ssList(sK50_skl)|segmentP(app(app(nil,sK50_skl),X0),sK50_skl)|~ssList(nil)|~ssList(X0))),
% 0.15/0.50 inference(paramodulation,[status(thm)],[f602,f467])).
% 0.15/0.50 fof(f878,definition,(
% 0.15/0.50 ![X0]: (sQ49_spl <=> (~ssList(app(sK50_skl,X0))|segmentP(app(app(sK50_skl,nil),X0),nil)|~ssList(X0)))),
% 0.15/0.50 introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition])).
% 0.15/0.50 fof(f881,plain,(
% 0.15/0.50 sQ49_spl|~sQ11_spl|~sQ8_spl),
% 0.15/0.50 inference(split_clause,[status(thm)],[f875,f878,f576,f528])).
% 0.15/0.50 fof(f882,definition,(
% 0.15/0.50 ![X0]: (sQ50_spl <=> (~ssList(app(nil,X0))|segmentP(app(app(nil,nil),X0),nil)|~ssList(X0)))),
% 0.15/0.50 introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition])).
% 0.15/0.50 fof(f885,plain,(
% 0.15/0.50 sQ50_spl|~sQ11_spl),
% 0.15/0.50 inference(split_clause,[status(thm)],[f876,f882,f576])).
% 0.15/0.50 fof(f886,definition,(
% 0.15/0.50 ![X0]: (sQ51_spl <=> (~ssList(app(sK50_skl,X0))|segmentP(app(app(nil,sK50_skl),X0),sK50_skl)|~ssList(X0)))),
% 0.15/0.50 introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition])).
% 0.15/0.50 fof(f889,plain,(
% 0.15/0.50 sQ51_spl|~sQ8_spl|~sQ11_spl),
% 0.15/0.50 inference(split_clause,[status(thm)],[f877,f886,f528,f576])).
% 0.15/0.50 fof(f910,plain,(
% 0.15/0.50 ![X0]: (~ssList(app(sK49_skl,X0))|~ssList(nil)|segmentP(app(app(sK49_skl,nil),X0),nil)|~ssList(sK49_skl)|~ssList(X0))),
% 0.15/0.50 inference(paramodulation,[status(thm)],[f696,f467])).
% 0.15/0.50 fof(f914,definition,(
% 0.15/0.50 ![X0]: (sQ54_spl <=> (~ssList(app(sK49_skl,X0))|segmentP(app(app(sK49_skl,nil),X0),nil)|~ssList(X0)))),
% 0.15/0.50 introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition])).
% 0.15/0.50 fof(f917,plain,(
% 0.15/0.50 sQ54_spl|~sQ11_spl|~sQ24_spl),
% 0.15/0.50 inference(split_clause,[status(thm)],[f910,f914,f576,f680])).
% 0.15/0.50 fof(f922,plain,(
% 0.15/0.50 ![X0]: (~ssList(app(sK49_skl,X0))|~ssList(sK49_skl)|segmentP(app(app(nil,sK49_skl),X0),sK49_skl)|~ssList(nil)|~ssList(X0))),
% 0.15/0.50 inference(paramodulation,[status(thm)],[f652,f467])).
% 0.15/0.50 fof(f926,definition,(
% 0.15/0.50 ![X0]: (sQ55_spl <=> (~ssList(app(sK49_skl,X0))|segmentP(app(app(nil,sK49_skl),X0),sK49_skl)|~ssList(X0)))),
% 0.15/0.50 introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition])).
% 0.15/0.50 fof(f929,plain,(
% 0.15/0.50 sQ55_spl|~sQ24_spl|~sQ11_spl),
% 0.15/0.50 inference(split_clause,[status(thm)],[f922,f926,f680,f576])).
% 0.15/0.50 fof(f934,plain,(
% 0.15/0.50 ![X0]: (~ssItem(X0)|sK52_skl=X0|~memberP(sK50_skl,X0)|~leq(sK52_skl,X0)|~sQ2_spl)),
% 0.15/0.50 inference(resolution,[status(thm)],[f451,f438])).
% 0.15/0.50 fof(f1137,plain,(
% 0.15/0.50 ~ssItem(sK52_skl)|~cons(sK52_skl,nil)=sK49_skl|memberP(sK50_skl,sK51_skl(sK52_skl))|~sQ2_spl),
% 0.15/0.50 inference(resolution,[status(thm)],[f540,f515])).
% 0.15/0.50 fof(f1138,definition,(
% 0.15/0.50 sQ72_spl <=> (memberP(sK50_skl,sK51_skl(sK52_skl)))),
% 0.15/0.50 introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition])).
% 0.15/0.50 fof(f1139,plain,(
% 0.15/0.50 memberP(sK50_skl,sK51_skl(sK52_skl))|~sQ72_spl),
% 0.15/0.50 inference(component_clause,[status(thm)],[f1138])).
% 0.15/0.50 fof(f1141,plain,(
% 0.15/0.50 ~sQ5_spl|~sQ6_spl|sQ72_spl|~sQ2_spl),
% 0.15/0.50 inference(split_clause,[status(thm)],[f1137,f518,f521,f1138,f450])).
% 0.15/0.50 fof(f1267,plain,(
% 0.15/0.50 ![X0]: (~ssItem(X0)|~cons(X0,nil)=sK49_skl|~X0=sK51_skl(X0)|~memberP(sK50_skl,X0))),
% 0.15/0.50 inference(forward_demodulation,[status(thm)],[f424,f649])).
% 0.15/0.50 fof(f1269,plain,(
% 0.15/0.50 ~ssItem(sK52_skl)|~cons(sK52_skl,nil)=sK49_skl|~sK52_skl=sK51_skl(sK52_skl)|~sQ2_spl),
% 0.15/0.50 inference(resolution,[status(thm)],[f1267,f515])).
% 0.15/0.50 fof(f1274,plain,(
% 0.15/0.50 ~sQ5_spl|~sQ6_spl|~sQ18_spl|~sQ2_spl),
% 0.15/0.50 inference(split_clause,[status(thm)],[f1269,f518,f521,f645,f450])).
% 0.15/0.50 fof(f1289,plain,(
% 0.15/0.50 ![X0]: (~ssItem(X0)|~cons(X0,nil)=sK49_skl|leq(X0,sK51_skl(X0))|~memberP(sK50_skl,X0))),
% 0.15/0.50 inference(forward_demodulation,[status(thm)],[f424,f650])).
% 0.15/0.50 fof(f1436,plain,(
% 0.15/0.50 ![X0]: (~ssList(app(sK50_skl,X0))|~ssList(sK5_skl(nil,sK50_skl))|segmentP(app(app(nil,sK5_skl(nil,sK50_skl)),X0),sK5_skl(nil,sK50_skl))|~ssList(nil)|~ssList(X0)|~sQ17_spl)),
% 0.15/0.50 inference(paramodulation,[status(thm)],[f632,f467])).
% 0.15/0.50 fof(f1437,plain,(
% 0.15/0.50 ~ssList(sK50_skl)|~ssList(sK5_skl(nil,sK50_skl))|rearsegP(app(nil,sK5_skl(nil,sK50_skl)),sK5_skl(nil,sK50_skl))|~ssList(nil)|~sQ17_spl),
% 0.15/0.50 inference(paramodulation,[status(thm)],[f632,f466])).
% 0.15/0.50 fof(f1438,plain,(
% 0.15/0.50 ![X0]: (~ssItem(X0)|~ssList(nil)|~ssList(sK5_skl(nil,sK50_skl))|~memberP(sK50_skl,X0)|memberP(nil,X0)|memberP(sK5_skl(nil,sK50_skl),X0)|~sQ17_spl)),
% 0.15/0.50 inference(paramodulation,[status(thm)],[f632,f270])).
% 0.15/0.50 fof(f1439,plain,(
% 0.15/0.50 ~ssList(sK50_skl)|~ssList(nil)|frontsegP(app(nil,sK5_skl(nil,sK50_skl)),nil)|~ssList(sK5_skl(nil,sK50_skl))|~sQ17_spl),
% 0.15/0.50 inference(paramodulation,[status(thm)],[f632,f465])).
% 0.15/0.50 fof(f1440,definition,(
% 0.15/0.50 ![X0]: (sQ109_spl <=> (~ssList(app(sK50_skl,X0))|segmentP(app(app(nil,sK5_skl(nil,sK50_skl)),X0),sK5_skl(nil,sK50_skl))|~ssList(X0)))),
% 0.15/0.50 introduced(definition,[new_symbols(definition,[sQ109_spl])],[split_symbol_definition])).
% 0.15/0.50 fof(f1443,definition,(
% 0.15/0.50 sQ110_spl <=> (ssList(sK5_skl(nil,sK50_skl)))),
% 0.15/0.50 introduced(definition,[new_symbols(definition,[sQ110_spl])],[split_symbol_definition])).
% 0.15/0.50 fof(f1444,plain,(
% 0.15/0.50 ssList(sK5_skl(nil,sK50_skl))|~sQ110_spl),
% 0.15/0.50 inference(component_clause,[status(thm)],[f1443])).
% 0.15/0.50 fof(f1445,plain,(
% 0.15/0.50 ~ssList(sK5_skl(nil,sK50_skl))|sQ110_spl),
% 0.15/0.50 inference(component_clause,[status(thm)],[f1443])).
% 0.15/0.50 fof(f1446,plain,(
% 0.15/0.50 sQ109_spl|~sQ110_spl|~sQ11_spl|~sQ17_spl),
% 0.15/0.50 inference(split_clause,[status(thm)],[f1436,f1440,f1443,f576,f631])).
% 0.15/0.50 fof(f1447,definition,(
% 0.15/0.50 sQ111_spl <=> (rearsegP(app(nil,sK5_skl(nil,sK50_skl)),sK5_skl(nil,sK50_skl)))),
% 0.15/0.50 introduced(definition,[new_symbols(definition,[sQ111_spl])],[split_symbol_definition])).
% 0.15/0.50 fof(f1450,plain,(
% 0.15/0.50 ~sQ8_spl|~sQ110_spl|sQ111_spl|~sQ11_spl|~sQ17_spl),
% 0.15/0.50 inference(split_clause,[status(thm)],[f1437,f528,f1443,f1447,f576,f631])).
% 0.15/0.50 fof(f1451,definition,(
% 0.15/0.50 ![X0]: (sQ112_spl <=> (~ssItem(X0)|~memberP(sK50_skl,X0)|memberP(nil,X0)|memberP(sK5_skl(nil,sK50_skl),X0)))),
% 0.15/0.50 introduced(definition,[new_symbols(definition,[sQ112_spl])],[split_symbol_definition])).
% 0.15/0.50 fof(f1454,plain,(
% 0.15/0.50 sQ112_spl|~sQ11_spl|~sQ110_spl|~sQ17_spl),
% 0.15/0.50 inference(split_clause,[status(thm)],[f1438,f1451,f576,f1443,f631])).
% 0.15/0.50 fof(f1455,definition,(
% 0.15/0.50 sQ113_spl <=> (frontsegP(app(nil,sK5_skl(nil,sK50_skl)),nil))),
% 0.15/0.50 introduced(definition,[new_symbols(definition,[sQ113_spl])],[split_symbol_definition])).
% 0.15/0.50 fof(f1458,plain,(
% 0.15/0.50 ~sQ8_spl|~sQ11_spl|sQ113_spl|~sQ110_spl|~sQ17_spl),
% 0.15/0.50 inference(split_clause,[status(thm)],[f1439,f528,f576,f1455,f1443,f631])).
% 0.15/0.50 fof(f1459,plain,(
% 0.15/0.50 ~ssList(sK50_skl)|~ssList(nil)|~frontsegP(sK50_skl,nil)|sQ110_spl),
% 0.15/0.50 inference(resolution,[status(thm)],[f1445,f122])).
% 0.15/0.50 fof(f1460,definition,(
% 0.15/0.50 sQ114_spl <=> (frontsegP(sK50_skl,nil))),
% 0.15/0.50 introduced(definition,[new_symbols(definition,[sQ114_spl])],[split_symbol_definition])).
% 0.15/0.50 fof(f1462,plain,(
% 0.15/0.50 ~frontsegP(sK50_skl,nil)|sQ114_spl),
% 0.15/0.50 inference(component_clause,[status(thm)],[f1460])).
% 0.15/0.50 fof(f1463,plain,(
% 0.15/0.50 ~sQ8_spl|~sQ11_spl|~sQ114_spl|sQ110_spl),
% 0.15/0.50 inference(split_clause,[status(thm)],[f1459,f528,f576,f1460,f1443])).
% 0.15/0.50 fof(f1464,plain,(
% 0.15/0.50 $false|~sQ16_spl|sQ114_spl),
% 0.15/0.50 inference(forward_subsumption_resolution,[status(thm)],[f1462,f627])).
% 0.15/0.50 fof(f1465,plain,(
% 0.15/0.50 ~sQ16_spl|sQ114_spl),
% 0.15/0.50 inference(contradiction_clause,[status(thm)],[f1464])).
% 0.15/0.50 fof(f1472,plain,(
% 0.15/0.50 cyclefreeP(sK5_skl(nil,sK50_skl))|app(app(sK11_skl(sK5_skl(nil,sK50_skl)),cons(sK9_skl(sK5_skl(nil,sK50_skl)),sK12_skl(sK5_skl(nil,sK50_skl)))),cons(sK10_skl(sK5_skl(nil,sK50_skl)),sK13_skl(sK5_skl(nil,sK50_skl))))=sK5_skl(nil,sK50_skl)|~sQ110_spl),
% 0.15/0.50 inference(resolution,[status(thm)],[f1444,f147])).
% 0.15/0.50 fof(f1481,definition,(
% 0.15/0.50 sQ115_spl <=> (cyclefreeP(sK5_skl(nil,sK50_skl)))),
% 0.15/0.50 introduced(definition,[new_symbols(definition,[sQ115_spl])],[split_symbol_definition])).
% 0.15/0.50 fof(f1484,definition,(
% 0.15/0.50 sQ116_spl <=> (app(app(sK11_skl(sK5_skl(nil,sK50_skl)),cons(sK9_skl(sK5_skl(nil,sK50_skl)),sK12_skl(sK5_skl(nil,sK50_skl)))),cons(sK10_skl(sK5_skl(nil,sK50_skl)),sK13_skl(sK5_skl(nil,sK50_skl))))=sK5_skl(nil,sK50_skl))),
% 0.15/0.50 introduced(definition,[new_symbols(definition,[sQ116_spl])],[split_symbol_definition])).
% 0.15/0.50 fof(f1487,plain,(
% 0.15/0.50 sQ115_spl|sQ116_spl|~sQ110_spl),
% 0.15/0.50 inference(split_clause,[status(thm)],[f1472,f1481,f1484,f1443])).
% 0.15/0.50 fof(f1489,plain,(
% 0.15/0.50 ~ssItem(sK51_skl(sK52_skl))|sK52_skl=sK51_skl(sK52_skl)|~leq(sK52_skl,sK51_skl(sK52_skl))|~sQ2_spl|~sQ72_spl),
% 0.15/0.50 inference(resolution,[status(thm)],[f934,f1139])).
% 0.15/0.50 fof(f1491,plain,(
% 0.15/0.50 ~sQ7_spl|sQ18_spl|~sQ13_spl|~sQ2_spl|~sQ72_spl),
% 0.15/0.50 inference(split_clause,[status(thm)],[f1489,f524,f645,f589,f450,f1138])).
% 0.15/0.50 fof(f1504,plain,(
% 0.15/0.50 ~ssItem(sK52_skl)|~cons(sK52_skl,nil)=sK49_skl|~memberP(sK50_skl,sK52_skl)|sQ13_spl),
% 0.15/0.50 inference(resolution,[status(thm)],[f591,f1289])).
% 0.15/0.50 fof(f1506,definition,(
% 0.15/0.50 sQ119_spl <=> (memberP(sK50_skl,sK52_skl))),
% 0.15/0.50 introduced(definition,[new_symbols(definition,[sQ119_spl])],[split_symbol_definition])).
% 0.15/0.50 fof(f1508,plain,(
% 0.15/0.50 ~memberP(sK50_skl,sK52_skl)|sQ119_spl),
% 0.15/0.50 inference(component_clause,[status(thm)],[f1506])).
% 0.15/0.50 fof(f1509,plain,(
% 0.15/0.50 ~sQ5_spl|~sQ6_spl|~sQ119_spl|sQ13_spl),
% 0.15/0.50 inference(split_clause,[status(thm)],[f1504,f518,f521,f1506,f589])).
% 0.15/0.50 fof(f1514,plain,(
% 0.15/0.50 $false|~sQ2_spl|sQ119_spl),
% 0.15/0.50 inference(forward_subsumption_resolution,[status(thm)],[f1508,f515])).
% 0.15/0.50 fof(f1515,plain,(
% 0.15/0.50 ~sQ2_spl|sQ119_spl),
% 0.15/0.50 inference(contradiction_clause,[status(thm)],[f1514])).
% 0.15/0.50 fof(f1516,plain,(
% 0.15/0.50 $false),
% 0.15/0.50 inference(sat_refutation,[status(thm)],[f449,f456,f460,f527,f536,f543,f545,f564,f579,f612,f615,f622,f626,f634,f657,f663,f667,f683,f687,f689,f695,f710,f716,f723,f730,f741,f745,f749,f753,f757,f768,f775,f780,f785,f788,f819,f821,f833,f864,f872,f881,f885,f889,f917,f929,f1141,f1274,f1446,f1450,f1454,f1458,f1463,f1465,f1487,f1491,f1509,f1515])).
% 0.15/0.50 % SZS output end CNFRefutation for theBenchmark.p
% 0.50/0.51 % Elapsed time: 0.132274 seconds
% 0.50/0.51 % CPU time: 0.642243 seconds
% 0.50/0.51 % Total memory used: 119.755 MB
% 0.50/0.51 % Net memory used: 119.040 MB
%------------------------------------------------------------------------------