%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SWC018+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 : n018.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 02:41:20 PM UTC 2026
% Result : Theorem 0.10s 0.44s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC018+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
% 0.10/0.37 % Computer : n018.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 07:51:29 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.39 % Drodi V4.1.1
% 0.10/0.44 % Refutation found
% 0.10/0.44 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.44 % SZS output start CNFRefutation for theBenchmark
% 0.10/0.44 fof(f2,axiom,(
% 0.10/0.44 (? [U] :( ssItem(U)& (? [V] :( ssItem(V)& U != V ) )) )),
% 0.10/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.44 fof(f4,axiom,(
% 0.10/0.44 (! [U] :( ssList(U)=> ( singletonP(U)<=> (? [V] :( ssItem(V)& cons(V,nil) = U ) )) ) )),
% 0.10/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.44 fof(f5,axiom,(
% 0.10/0.44 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> ( frontsegP(U,V)<=> (? [W] :( ssList(W)& app(V,W) = U ) )) ) )) )),
% 0.10/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.44 fof(f6,axiom,(
% 0.10/0.44 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> ( rearsegP(U,V)<=> (? [W] :( ssList(W)& app(W,V) = U ) )) ) )) )),
% 0.10/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.44 fof(f7,axiom,(
% 0.10/0.44 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> ( segmentP(U,V)<=> (? [W] :( ssList(W)& (? [X] :( ssList(X)& app(app(W,V),X) = U ) )) )) ) )) )),
% 0.10/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.44 fof(f15,axiom,(
% 0.10/0.44 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> ( neq(U,V)<=> U != V ) ) )) )),
% 0.10/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.44 fof(f16,axiom,(
% 0.10/0.44 (! [U] :( ssList(U)=> (! [V] :( ssItem(V)=> ssList(cons(V,U)) ) )) )),
% 0.10/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.44 fof(f17,axiom,(
% 0.10/0.44 ssList(nil) ),
% 0.10/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.44 fof(f28,axiom,(
% 0.10/0.44 (! [U] :( ssList(U)=> app(nil,U) = U ) )),
% 0.10/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.44 fof(f40,axiom,(
% 0.10/0.44 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> ( ( frontsegP(U,V)& frontsegP(V,W) )=> frontsegP(U,W) ) ) )) )) )),
% 0.10/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.44 fof(f41,axiom,(
% 0.10/0.44 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> ( ( frontsegP(U,V)& frontsegP(V,U) )=> U = V ) ) )) )),
% 0.10/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.44 fof(f42,axiom,(
% 0.10/0.44 (! [U] :( ssList(U)=> frontsegP(U,U) ) )),
% 0.10/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.44 fof(f43,axiom,(
% 0.10/0.44 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> ( frontsegP(U,V)=> frontsegP(app(U,W),V) ) ) )) )) )),
% 0.10/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.44 fof(f44,axiom,(
% 0.10/0.44 (! [U] :( ssItem(U)=> (! [V] :( ssItem(V)=> (! [W] :( ssList(W)=> (! [X] :( ssList(X)=> ( frontsegP(cons(U,W),cons(V,X))<=> ( U = V& frontsegP(W,X) ) ) ) )) )) )) )),
% 0.10/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.44 fof(f45,axiom,(
% 0.10/0.44 (! [U] :( ssList(U)=> frontsegP(U,nil) ) )),
% 0.10/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.44 fof(f46,axiom,(
% 0.10/0.44 (! [U] :( ssList(U)=> ( frontsegP(nil,U)<=> nil = U ) ) )),
% 0.10/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.44 fof(f51,axiom,(
% 0.10/0.44 (! [U] :( ssList(U)=> rearsegP(U,nil) ) )),
% 0.10/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.44 fof(f57,axiom,(
% 0.10/0.44 (! [U] :( ssList(U)=> segmentP(U,nil) ) )),
% 0.10/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.44 fof(f84,axiom,(
% 0.10/0.44 (! [U] :( ssList(U)=> app(U,nil) = U ) )),
% 0.10/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.44 fof(f96,conjecture,(
% 0.10/0.44 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> (! [X] :( ssList(X)=> ( V != X| U != W| (! [Y] :( ssList(Y)=> ( app(W,Y) != X| ~ equalelemsP(W)| (? [Z] :( ssItem(Z)& (? [X1] :( ssList(X1)& app(cons(Z,nil),X1) = Y& (? [X2] :( ssList(X2)& app(X2,cons(Z,nil)) = W ) )) )) )) ))| ( nil != X& nil = W )| ( ( nil != V| nil = U )& ( ~ neq(V,nil)| (? [X3] :( ssList(X3)& neq(X3,nil)& frontsegP(V,X3)& frontsegP(U,X3) ) )) ) ) ) )) )) )) )),
% 0.10/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.44 fof(f97,negated_conjecture,(
% 0.10/0.44 ~((! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> (! [X] :( ssList(X)=> ( V != X| U != W| (! [Y] :( ssList(Y)=> ( app(W,Y) != X| ~ equalelemsP(W)| (? [Z] :( ssItem(Z)& (? [X1] :( ssList(X1)& app(cons(Z,nil),X1) = Y& (? [X2] :( ssList(X2)& app(X2,cons(Z,nil)) = W ) )) )) )) ))| ( nil != X& nil = W )| ( ( nil != V| nil = U )& ( ~ neq(V,nil)| (? [X3] :( ssList(X3)& neq(X3,nil)& frontsegP(V,X3)& frontsegP(U,X3) ) )) ) ) ) )) )) )) ))),
% 0.10/0.45 inference(negated_conjecture,[status(cth)],[f96])).
% 0.10/0.45 fof(f102,plain,(
% 0.10/0.45 (ssItem(sK0_skl)&(ssItem(sK1_skl)&~sK0_skl=sK1_skl))),
% 0.10/0.45 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(U,sK0_skl),skolemize(V,sK1_skl)],[f2])).
% 0.10/0.45 fof(f104,plain,(
% 0.10/0.45 ssItem(sK1_skl)),
% 0.10/0.45 inference(cnf_transformation,[status(thm)],[f102])).
% 0.10/0.45 fof(f113,plain,(
% 0.10/0.45 ![U]: (~ssList(U)|(singletonP(U)<=>(?[V]: (ssItem(V)&cons(V,nil)=U))))),
% 0.10/0.45 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 0.10/0.45 fof(f114,plain,(
% 0.10/0.45 ![U]: (~ssList(U)|((~singletonP(U)|(?[V]: (ssItem(V)&cons(V,nil)=U)))&(singletonP(U)|(![V]: (~ssItem(V)|~cons(V,nil)=U)))))),
% 0.10/0.45 inference(NNF_transformation,[status(thm)],[f113])).
% 0.10/0.45 fof(f115,plain,(
% 0.10/0.45 ![U]: (~ssList(U)|((~singletonP(U)|(ssItem(sK4_skl(U))&cons(sK4_skl(U),nil)=U))&(singletonP(U)|(![V]: (~ssItem(V)|~cons(V,nil)=U)))))),
% 0.10/0.45 inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(V,sK4_skl(U))],[f114])).
% 0.10/0.45 fof(f118,plain,(
% 0.10/0.45 ![X0,X1]: (~ssList(X0)|singletonP(X0)|~ssItem(X1)|~cons(X1,nil)=X0)),
% 0.10/0.45 inference(cnf_transformation,[status(thm)],[f115])).
% 0.10/0.45 fof(f119,plain,(
% 0.10/0.45 ![U]: (~ssList(U)|(![V]: (~ssList(V)|(frontsegP(U,V)<=>(?[W]: (ssList(W)&app(V,W)=U))))))),
% 0.10/0.45 inference(pre_NNF_transformation,[status(thm)],[f5])).
% 0.10/0.45 fof(f120,plain,(
% 0.10/0.45 ![U]: (~ssList(U)|(![V]: (~ssList(V)|((~frontsegP(U,V)|(?[W]: (ssList(W)&app(V,W)=U)))&(frontsegP(U,V)|(![W]: (~ssList(W)|~app(V,W)=U)))))))),
% 0.10/0.45 inference(NNF_transformation,[status(thm)],[f119])).
% 0.10/0.45 fof(f121,plain,(
% 0.10/0.45 ![U]: (~ssList(U)|(![V]: (~ssList(V)|((~frontsegP(U,V)|(ssList(sK5_skl(V,U))&app(V,sK5_skl(V,U))=U))&(frontsegP(U,V)|(![W]: (~ssList(W)|~app(V,W)=U)))))))),
% 0.10/0.45 inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(W,sK5_skl(V,U))],[f120])).
% 0.10/0.45 fof(f123,plain,(
% 0.10/0.45 ![X0,X1]: (~ssList(X0)|~ssList(X1)|~frontsegP(X0,X1)|app(X1,sK5_skl(X1,X0))=X0)),
% 0.10/0.45 inference(cnf_transformation,[status(thm)],[f121])).
% 0.10/0.45 fof(f124,plain,(
% 0.10/0.45 ![X0,X1,X2]: (~ssList(X0)|~ssList(X1)|frontsegP(X0,X1)|~ssList(X2)|~app(X1,X2)=X0)),
% 0.10/0.45 inference(cnf_transformation,[status(thm)],[f121])).
% 0.10/0.45 fof(f125,plain,(
% 0.10/0.45 ![U]: (~ssList(U)|(![V]: (~ssList(V)|(rearsegP(U,V)<=>(?[W]: (ssList(W)&app(W,V)=U))))))),
% 0.10/0.45 inference(pre_NNF_transformation,[status(thm)],[f6])).
% 0.10/0.45 fof(f126,plain,(
% 0.10/0.45 ![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)))))))),
% 0.10/0.45 inference(NNF_transformation,[status(thm)],[f125])).
% 0.10/0.45 fof(f127,plain,(
% 0.10/0.45 ![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)))))))),
% 0.10/0.45 inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl]),skolemize(W,sK6_skl(V,U))],[f126])).
% 0.10/0.45 fof(f129,plain,(
% 0.10/0.45 ![X0,X1]: (~ssList(X0)|~ssList(X1)|~rearsegP(X0,X1)|app(sK6_skl(X1,X0),X1)=X0)),
% 0.10/0.45 inference(cnf_transformation,[status(thm)],[f127])).
% 0.10/0.45 fof(f130,plain,(
% 0.10/0.45 ![X0,X1,X2]: (~ssList(X0)|~ssList(X1)|rearsegP(X0,X1)|~ssList(X2)|~app(X2,X1)=X0)),
% 0.10/0.45 inference(cnf_transformation,[status(thm)],[f127])).
% 0.10/0.45 fof(f131,plain,(
% 0.10/0.45 ![U]: (~ssList(U)|(![V]: (~ssList(V)|(segmentP(U,V)<=>(?[W]: (ssList(W)&(?[X]: (ssList(X)&app(app(W,V),X)=U))))))))),
% 0.10/0.45 inference(pre_NNF_transformation,[status(thm)],[f7])).
% 0.10/0.45 fof(f132,plain,(
% 0.10/0.45 ![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)))))))))),
% 0.10/0.45 inference(NNF_transformation,[status(thm)],[f131])).
% 0.10/0.45 fof(f133,plain,(
% 0.10/0.45 ![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)))))))))),
% 0.10/0.45 inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl,sK8_skl]),skolemize(W,sK7_skl(V,U)),skolemize(X,sK8_skl(V,U))],[f132])).
% 0.10/0.45 fof(f136,plain,(
% 0.10/0.45 ![X0,X1]: (~ssList(X0)|~ssList(X1)|~segmentP(X0,X1)|app(app(sK7_skl(X1,X0),X1),sK8_skl(X1,X0))=X0)),
% 0.10/0.45 inference(cnf_transformation,[status(thm)],[f133])).
% 0.10/0.45 fof(f137,plain,(
% 0.10/0.45 ![X0,X1,X2,X3]: (~ssList(X0)|~ssList(X1)|segmentP(X0,X1)|~ssList(X2)|~ssList(X3)|~app(app(X2,X1),X3)=X0)),
% 0.10/0.45 inference(cnf_transformation,[status(thm)],[f133])).
% 0.10/0.45 fof(f217,plain,(
% 0.10/0.45 ![U]: (~ssList(U)|(![V]: (~ssList(V)|(neq(U,V)<=>~U=V))))),
% 0.10/0.45 inference(pre_NNF_transformation,[status(thm)],[f15])).
% 0.10/0.45 fof(f218,plain,(
% 0.10/0.45 ![U]: (~ssList(U)|(![V]: (~ssList(V)|((~neq(U,V)|~U=V)&(neq(U,V)|U=V)))))),
% 0.10/0.45 inference(NNF_transformation,[status(thm)],[f217])).
% 0.10/0.45 fof(f219,plain,(
% 0.10/0.45 ![X0,X1]: (~ssList(X0)|~ssList(X1)|~neq(X0,X1)|~X0=X1)),
% 0.10/0.45 inference(cnf_transformation,[status(thm)],[f218])).
% 0.10/0.45 fof(f220,plain,(
% 0.10/0.45 ![X0,X1]: (~ssList(X0)|~ssList(X1)|neq(X0,X1)|X0=X1)),
% 0.10/0.45 inference(cnf_transformation,[status(thm)],[f218])).
% 0.10/0.45 fof(f221,plain,(
% 0.10/0.45 ![U]: (~ssList(U)|(![V]: (~ssItem(V)|ssList(cons(V,U)))))),
% 0.10/0.45 inference(pre_NNF_transformation,[status(thm)],[f16])).
% 0.10/0.45 fof(f222,plain,(
% 0.10/0.45 ![X0,X1]: (~ssList(X0)|~ssItem(X1)|ssList(cons(X1,X0)))),
% 0.10/0.45 inference(cnf_transformation,[status(thm)],[f221])).
% 0.10/0.45 fof(f223,plain,(
% 0.10/0.45 ssList(nil)),
% 0.10/0.45 inference(cnf_transformation,[status(thm)],[f17])).
% 0.10/0.45 fof(f248,plain,(
% 0.10/0.45 ![U]: (~ssList(U)|app(nil,U)=U)),
% 0.10/0.45 inference(pre_NNF_transformation,[status(thm)],[f28])).
% 0.10/0.45 fof(f249,plain,(
% 0.10/0.45 ![X0]: (~ssList(X0)|app(nil,X0)=X0)),
% 0.10/0.45 inference(cnf_transformation,[status(thm)],[f248])).
% 0.10/0.45 fof(f281,plain,(
% 0.10/0.45 ![U]: (~ssList(U)|(![V]: (~ssList(V)|(![W]: (~ssList(W)|((~frontsegP(U,V)|~frontsegP(V,W))|frontsegP(U,W)))))))),
% 0.10/0.45 inference(pre_NNF_transformation,[status(thm)],[f40])).
% 0.10/0.45 fof(f282,plain,(
% 0.10/0.45 ![X0,X1,X2]: (~ssList(X0)|~ssList(X1)|~ssList(X2)|~frontsegP(X0,X1)|~frontsegP(X1,X2)|frontsegP(X0,X2))),
% 0.10/0.45 inference(cnf_transformation,[status(thm)],[f281])).
% 0.10/0.45 fof(f283,plain,(
% 0.10/0.45 ![U]: (~ssList(U)|(![V]: (~ssList(V)|((~frontsegP(U,V)|~frontsegP(V,U))|U=V))))),
% 0.10/0.45 inference(pre_NNF_transformation,[status(thm)],[f41])).
% 0.10/0.45 fof(f284,plain,(
% 0.10/0.45 ![X0,X1]: (~ssList(X0)|~ssList(X1)|~frontsegP(X0,X1)|~frontsegP(X1,X0)|X0=X1)),
% 0.10/0.45 inference(cnf_transformation,[status(thm)],[f283])).
% 0.10/0.45 fof(f285,plain,(
% 0.10/0.45 ![U]: (~ssList(U)|frontsegP(U,U))),
% 0.10/0.45 inference(pre_NNF_transformation,[status(thm)],[f42])).
% 0.10/0.45 fof(f286,plain,(
% 0.10/0.45 ![X0]: (~ssList(X0)|frontsegP(X0,X0))),
% 0.10/0.45 inference(cnf_transformation,[status(thm)],[f285])).
% 0.10/0.45 fof(f287,plain,(
% 0.10/0.45 ![U]: (~ssList(U)|(![V]: (~ssList(V)|(![W]: (~ssList(W)|(~frontsegP(U,V)|frontsegP(app(U,W),V)))))))),
% 0.10/0.45 inference(pre_NNF_transformation,[status(thm)],[f43])).
% 0.10/0.45 fof(f288,plain,(
% 0.10/0.45 ![X0,X1,X2]: (~ssList(X0)|~ssList(X1)|~ssList(X2)|~frontsegP(X0,X1)|frontsegP(app(X0,X2),X1))),
% 0.10/0.45 inference(cnf_transformation,[status(thm)],[f287])).
% 0.10/0.45 fof(f289,plain,(
% 0.10/0.45 ![U]: (~ssItem(U)|(![V]: (~ssItem(V)|(![W]: (~ssList(W)|(![X]: (~ssList(X)|(frontsegP(cons(U,W),cons(V,X))<=>(U=V&frontsegP(W,X))))))))))),
% 0.10/0.45 inference(pre_NNF_transformation,[status(thm)],[f44])).
% 0.10/0.45 fof(f290,plain,(
% 0.10/0.45 ![U]: (~ssItem(U)|(![V]: (~ssItem(V)|(![W]: (~ssList(W)|(![X]: (~ssList(X)|((~frontsegP(cons(U,W),cons(V,X))|(U=V&frontsegP(W,X)))&(frontsegP(cons(U,W),cons(V,X))|(~U=V|~frontsegP(W,X)))))))))))),
% 0.10/0.45 inference(NNF_transformation,[status(thm)],[f289])).
% 0.10/0.45 fof(f292,plain,(
% 0.10/0.45 ![X0,X1,X2,X3]: (~ssItem(X0)|~ssItem(X1)|~ssList(X2)|~ssList(X3)|~frontsegP(cons(X0,X2),cons(X1,X3))|frontsegP(X2,X3))),
% 0.10/0.45 inference(cnf_transformation,[status(thm)],[f290])).
% 0.10/0.45 fof(f293,plain,(
% 0.10/0.45 ![X0,X1,X2,X3]: (~ssItem(X0)|~ssItem(X1)|~ssList(X2)|~ssList(X3)|frontsegP(cons(X0,X2),cons(X1,X3))|~X0=X1|~frontsegP(X2,X3))),
% 0.10/0.45 inference(cnf_transformation,[status(thm)],[f290])).
% 0.10/0.45 fof(f294,plain,(
% 0.10/0.45 ![U]: (~ssList(U)|frontsegP(U,nil))),
% 0.10/0.45 inference(pre_NNF_transformation,[status(thm)],[f45])).
% 0.10/0.45 fof(f295,plain,(
% 0.10/0.45 ![X0]: (~ssList(X0)|frontsegP(X0,nil))),
% 0.10/0.45 inference(cnf_transformation,[status(thm)],[f294])).
% 0.10/0.45 fof(f296,plain,(
% 0.10/0.45 ![U]: (~ssList(U)|(frontsegP(nil,U)<=>nil=U))),
% 0.10/0.45 inference(pre_NNF_transformation,[status(thm)],[f46])).
% 0.10/0.45 fof(f297,plain,(
% 0.10/0.45 ![U]: (~ssList(U)|((~frontsegP(nil,U)|nil=U)&(frontsegP(nil,U)|~nil=U)))),
% 0.10/0.45 inference(NNF_transformation,[status(thm)],[f296])).
% 0.10/0.45 fof(f298,plain,(
% 0.10/0.45 ![X0]: (~ssList(X0)|~frontsegP(nil,X0)|nil=X0)),
% 0.10/0.45 inference(cnf_transformation,[status(thm)],[f297])).
% 0.10/0.45 fof(f308,plain,(
% 0.10/0.45 ![U]: (~ssList(U)|rearsegP(U,nil))),
% 0.10/0.45 inference(pre_NNF_transformation,[status(thm)],[f51])).
% 0.10/0.45 fof(f309,plain,(
% 0.10/0.45 ![X0]: (~ssList(X0)|rearsegP(X0,nil))),
% 0.10/0.45 inference(cnf_transformation,[status(thm)],[f308])).
% 0.10/0.45 fof(f322,plain,(
% 0.10/0.45 ![U]: (~ssList(U)|segmentP(U,nil))),
% 0.10/0.45 inference(pre_NNF_transformation,[status(thm)],[f57])).
% 0.10/0.45 fof(f323,plain,(
% 0.10/0.45 ![X0]: (~ssList(X0)|segmentP(X0,nil))),
% 0.10/0.45 inference(cnf_transformation,[status(thm)],[f322])).
% 0.10/0.45 fof(f388,plain,(
% 0.10/0.45 ![U]: (~ssList(U)|app(U,nil)=U)),
% 0.10/0.45 inference(pre_NNF_transformation,[status(thm)],[f84])).
% 0.10/0.45 fof(f389,plain,(
% 0.10/0.45 ![X0]: (~ssList(X0)|app(X0,nil)=X0)),
% 0.10/0.45 inference(cnf_transformation,[status(thm)],[f388])).
% 0.10/0.45 fof(f415,plain,(
% 0.10/0.45 (?[U]: (ssList(U)&(?[V]: (ssList(V)&(?[W]: (ssList(W)&(?[X]: (ssList(X)&((((V=X&U=W)&(?[Y]: (ssList(Y)&((app(W,Y)=X&equalelemsP(W))&(![Z]: (~ssItem(Z)|(![X1]: ((~ssList(X1)|~app(cons(Z,nil),X1)=Y)|(![X2]: (~ssList(X2)|~app(X2,cons(Z,nil))=W))))))))))&(nil=X|~nil=W))&((nil=V&~nil=U)|(neq(V,nil)&(![X3]: (((~ssList(X3)|~neq(X3,nil))|~frontsegP(V,X3))|~frontsegP(U,X3))))))))))))))),
% 0.10/0.45 inference(pre_NNF_transformation,[status(thm)],[f97])).
% 0.10/0.45 fof(f416,definition,(
% 0.10/0.45 ![U,V]: (sP0_prd(V,U)<=>(nil=V&~nil=U))),
% 0.10/0.45 introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 0.10/0.45 fof(f417,plain,(
% 0.10/0.45 ?[U]: (ssList(U)&(?[V]: (ssList(V)&(?[W]: (ssList(W)&(?[X]: (ssList(X)&((((V=X&U=W)&(?[Y]: (ssList(Y)&((app(W,Y)=X&equalelemsP(W))&(![Z]: (~ssItem(Z)|(![X1]: ((~ssList(X1)|~app(cons(Z,nil),X1)=Y)|(![X2]: (~ssList(X2)|~app(X2,cons(Z,nil))=W))))))))))&(nil=X|~nil=W))&(sP0_prd(V,U)|(neq(V,nil)&(![X3]: (((~ssList(X3)|~neq(X3,nil))|~frontsegP(V,X3))|~frontsegP(U,X3)))))))))))))),
% 0.10/0.45 inference(formula_renaming,[status(thm)],[f415,f416])).
% 0.10/0.45 fof(f418,plain,(
% 0.10/0.45 ?[U]: (ssList(U)&(?[V]: (ssList(V)&(?[W]: (ssList(W)&(?[X]: (ssList(X)&((((V=X&U=W)&(?[Y]: (ssList(Y)&((app(W,Y)=X&equalelemsP(W))&(![Z]: (~ssItem(Z)|((![X1]: (~ssList(X1)|~app(cons(Z,nil),X1)=Y))|(![X2]: (~ssList(X2)|~app(X2,cons(Z,nil))=W)))))))))&(nil=X|~nil=W))&(sP0_prd(V,U)|(neq(V,nil)&(![X3]: (((~ssList(X3)|~neq(X3,nil))|~frontsegP(V,X3))|~frontsegP(U,X3)))))))))))))),
% 0.10/0.45 inference(miniscoping,[status(thm)],[f417])).
% 0.10/0.45 fof(f419,plain,(
% 0.10/0.45 (ssList(sK47_skl)&(ssList(sK48_skl)&(ssList(sK49_skl)&(ssList(sK50_skl)&((((sK48_skl=sK50_skl&sK47_skl=sK49_skl)&(ssList(sK51_skl)&((app(sK49_skl,sK51_skl)=sK50_skl&equalelemsP(sK49_skl))&(![Z]: (~ssItem(Z)|((![X1]: (~ssList(X1)|~app(cons(Z,nil),X1)=sK51_skl))|(![X2]: (~ssList(X2)|~app(X2,cons(Z,nil))=sK49_skl))))))))&(nil=sK50_skl|~nil=sK49_skl))&(sP0_prd(sK48_skl,sK47_skl)|(neq(sK48_skl,nil)&(![X3]: (((~ssList(X3)|~neq(X3,nil))|~frontsegP(sK48_skl,X3))|~frontsegP(sK47_skl,X3))))))))))),
% 0.10/0.45 inference(skolemize,[status(esa),new_symbols(skolem,[sK47_skl,sK48_skl,sK49_skl,sK50_skl,sK51_skl]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl),skolemize(Y,sK51_skl)],[f418])).
% 0.10/0.45 fof(f420,plain,(
% 0.10/0.45 ssList(sK47_skl)),
% 0.10/0.45 inference(cnf_transformation,[status(thm)],[f419])).
% 0.10/0.45 fof(f423,plain,(
% 0.10/0.45 ssList(sK50_skl)),
% 0.10/0.45 inference(cnf_transformation,[status(thm)],[f419])).
% 0.10/0.45 fof(f424,plain,(
% 0.10/0.45 sK48_skl=sK50_skl),
% 0.10/0.45 inference(cnf_transformation,[status(thm)],[f419])).
% 0.10/0.45 fof(f425,plain,(
% 0.10/0.45 sK47_skl=sK49_skl),
% 0.10/0.45 inference(cnf_transformation,[status(thm)],[f419])).
% 0.10/0.45 fof(f426,plain,(
% 0.10/0.45 ssList(sK51_skl)),
% 0.10/0.45 inference(cnf_transformation,[status(thm)],[f419])).
% 0.10/0.45 fof(f427,plain,(
% 0.10/0.45 app(sK49_skl,sK51_skl)=sK50_skl),
% 0.10/0.45 inference(cnf_transformation,[status(thm)],[f419])).
% 0.10/0.45 fof(f430,plain,(
% 0.10/0.45 nil=sK50_skl|~nil=sK49_skl),
% 0.10/0.45 inference(cnf_transformation,[status(thm)],[f419])).
% 0.10/0.45 fof(f431,plain,(
% 0.10/0.45 sP0_prd(sK48_skl,sK47_skl)|neq(sK48_skl,nil)),
% 0.10/0.45 inference(cnf_transformation,[status(thm)],[f419])).
% 0.10/0.45 fof(f432,plain,(
% 0.10/0.45 ![X0]: (sP0_prd(sK48_skl,sK47_skl)|~ssList(X0)|~neq(X0,nil)|~frontsegP(sK48_skl,X0)|~frontsegP(sK47_skl,X0))),
% 0.10/0.45 inference(cnf_transformation,[status(thm)],[f419])).
% 0.10/0.45 fof(f433,plain,(
% 0.10/0.45 ![U,V]: ((~sP0_prd(V,U)|(nil=V&~nil=U))&(sP0_prd(V,U)|(~nil=V|nil=U)))),
% 0.10/0.45 inference(NNF_transformation,[status(thm)],[f416])).
% 0.10/0.45 fof(f434,plain,(
% 0.10/0.45 (![U,V]: (~sP0_prd(V,U)|(nil=V&~nil=U)))&(![U,V]: (sP0_prd(V,U)|(~nil=V|nil=U)))),
% 0.10/0.45 inference(miniscoping,[status(thm)],[f433])).
% 0.10/0.45 fof(f435,plain,(
% 0.10/0.45 ![X0,X1]: (~sP0_prd(X0,X1)|nil=X0)),
% 0.10/0.45 inference(cnf_transformation,[status(thm)],[f434])).
% 0.10/0.45 fof(f436,plain,(
% 0.10/0.45 ![X0,X1]: (~sP0_prd(X0,X1)|~nil=X1)),
% 0.10/0.45 inference(cnf_transformation,[status(thm)],[f434])).
% 0.10/0.45 fof(f438,definition,(
% 0.10/0.45 sQ0_spl <=> (nil=sK50_skl)),
% 0.10/0.45 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.10/0.45 fof(f439,plain,(
% 0.10/0.45 nil=sK50_skl|~sQ0_spl),
% 0.10/0.45 inference(component_clause,[status(thm)],[f438])).
% 0.10/0.45 fof(f441,definition,(
% 0.10/0.45 sQ1_spl <=> (nil=sK49_skl)),
% 0.10/0.45 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.10/0.45 fof(f443,plain,(
% 0.10/0.45 ~nil=sK49_skl|sQ1_spl),
% 0.10/0.45 inference(component_clause,[status(thm)],[f441])).
% 0.10/0.45 fof(f444,plain,(
% 0.10/0.45 sQ0_spl|~sQ1_spl),
% 0.10/0.45 inference(split_clause,[status(thm)],[f430,f438,f441])).
% 0.10/0.45 fof(f445,definition,(
% 0.10/0.45 sQ2_spl <=> (sP0_prd(sK48_skl,sK47_skl))),
% 0.10/0.45 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.10/0.45 fof(f446,plain,(
% 0.10/0.45 sP0_prd(sK48_skl,sK47_skl)|~sQ2_spl),
% 0.10/0.45 inference(component_clause,[status(thm)],[f445])).
% 0.10/0.45 fof(f448,definition,(
% 0.10/0.45 sQ3_spl <=> (neq(sK48_skl,nil))),
% 0.10/0.45 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.10/0.45 fof(f449,plain,(
% 0.10/0.45 neq(sK48_skl,nil)|~sQ3_spl),
% 0.10/0.45 inference(component_clause,[status(thm)],[f448])).
% 0.10/0.45 fof(f451,plain,(
% 0.10/0.45 sQ2_spl|sQ3_spl),
% 0.10/0.45 inference(split_clause,[status(thm)],[f431,f445,f448])).
% 0.10/0.45 fof(f452,definition,(
% 0.10/0.45 ![X0]: (sQ4_spl <=> (~ssList(X0)|~neq(X0,nil)|~frontsegP(sK48_skl,X0)|~frontsegP(sK47_skl,X0)))),
% 0.10/0.45 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 0.10/0.45 fof(f453,plain,(
% 0.10/0.45 ![X0]: (~ssList(X0)|~neq(X0,nil)|~frontsegP(sK48_skl,X0)|~frontsegP(sK47_skl,X0)|~sQ4_spl)),
% 0.10/0.45 inference(component_clause,[status(thm)],[f452])).
% 0.10/0.45 fof(f455,plain,(
% 0.10/0.45 sQ2_spl|sQ4_spl),
% 0.10/0.45 inference(split_clause,[status(thm)],[f432,f445,f452])).
% 0.10/0.45 fof(f459,plain,(
% 0.10/0.45 ![X0]: (~ssList(cons(X0,nil))|singletonP(cons(X0,nil))|~ssItem(X0))),
% 0.10/0.45 inference(destructive_equality_resolution,[status(thm)],[f118])).
% 0.10/0.45 fof(f460,plain,(
% 0.10/0.45 ![X0,X1]: (~ssList(app(X0,X1))|~ssList(X0)|frontsegP(app(X0,X1),X0)|~ssList(X1))),
% 0.10/0.45 inference(destructive_equality_resolution,[status(thm)],[f124])).
% 0.10/0.45 fof(f461,plain,(
% 0.10/0.45 ![X0,X1]: (~ssList(app(X0,X1))|~ssList(X1)|rearsegP(app(X0,X1),X1)|~ssList(X0))),
% 0.10/0.45 inference(destructive_equality_resolution,[status(thm)],[f130])).
% 0.10/0.45 fof(f462,plain,(
% 0.10/0.45 ![X0,X1,X2]: (~ssList(app(app(X0,X1),X2))|~ssList(X1)|segmentP(app(app(X0,X1),X2),X1)|~ssList(X0)|~ssList(X2))),
% 0.10/0.45 inference(destructive_equality_resolution,[status(thm)],[f137])).
% 0.10/0.45 fof(f471,plain,(
% 0.10/0.45 ![X1]: (~ssList(X1)|~ssList(X1)|~neq(X1,X1))),
% 0.10/0.45 inference(destructive_equality_resolution,[status(thm)],[f219])).
% 0.10/0.45 fof(f472,plain,(
% 0.10/0.45 ![X0]: (~ssList(X0)|~neq(X0,X0))),
% 0.10/0.45 inference(duplicate_literals_removal,[status(thm)],[f471])).
% 0.10/0.45 fof(f475,plain,(
% 0.10/0.45 ![X1,X2,X3]: (~ssItem(X1)|~ssItem(X1)|~ssList(X2)|~ssList(X3)|frontsegP(cons(X1,X2),cons(X1,X3))|~frontsegP(X2,X3))),
% 0.10/0.45 inference(destructive_equality_resolution,[status(thm)],[f293])).
% 0.10/0.45 fof(f476,plain,(
% 0.10/0.45 ![X0,X1,X2]: (~ssItem(X0)|~ssList(X1)|~ssList(X2)|frontsegP(cons(X0,X1),cons(X0,X2))|~frontsegP(X1,X2))),
% 0.10/0.45 inference(duplicate_literals_removal,[status(thm)],[f475])).
% 0.10/0.45 fof(f486,plain,(
% 0.10/0.45 ![X0]: (~sP0_prd(X0,nil))),
% 0.10/0.45 inference(destructive_equality_resolution,[status(thm)],[f436])).
% 0.10/0.45 fof(f495,plain,(
% 0.10/0.45 sK48_skl=nil|~sQ0_spl),
% 0.10/0.45 inference(backward_demodulation,[status(thm)],[f439,f424])).
% 0.10/0.45 fof(f497,plain,(
% 0.10/0.45 app(sK47_skl,sK51_skl)=sK50_skl),
% 0.10/0.45 inference(forward_demodulation,[status(thm)],[f425,f427])).
% 0.10/0.45 fof(f502,definition,(
% 0.10/0.45 sQ5_spl <=> (ssList(nil))),
% 0.10/0.45 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 0.10/0.45 fof(f504,plain,(
% 0.10/0.45 ~ssList(nil)|sQ5_spl),
% 0.10/0.45 inference(component_clause,[status(thm)],[f502])).
% 0.10/0.45 fof(f505,definition,(
% 0.10/0.45 sQ6_spl <=> (ssList(sK47_skl))),
% 0.10/0.45 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.10/0.45 fof(f507,plain,(
% 0.10/0.45 ~ssList(sK47_skl)|sQ6_spl),
% 0.10/0.45 inference(component_clause,[status(thm)],[f505])).
% 0.10/0.45 fof(f508,definition,(
% 0.10/0.45 sQ7_spl <=> (frontsegP(app(sK47_skl,sK51_skl),sK47_skl))),
% 0.10/0.45 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 0.10/0.45 fof(f509,plain,(
% 0.10/0.45 frontsegP(app(sK47_skl,sK51_skl),sK47_skl)|~sQ7_spl),
% 0.10/0.45 inference(component_clause,[status(thm)],[f508])).
% 0.10/0.45 fof(f511,definition,(
% 0.10/0.45 sQ8_spl <=> (ssList(sK51_skl))),
% 0.10/0.45 introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition])).
% 0.10/0.45 fof(f513,plain,(
% 0.10/0.45 ~ssList(sK51_skl)|sQ8_spl),
% 0.10/0.45 inference(component_clause,[status(thm)],[f511])).
% 0.10/0.45 fof(f515,plain,(
% 0.10/0.45 ~nil=sK47_skl|sQ1_spl),
% 0.10/0.45 inference(forward_demodulation,[status(thm)],[f425,f443])).
% 0.10/0.45 fof(f516,plain,(
% 0.10/0.45 $false|sQ8_spl),
% 0.10/0.45 inference(forward_subsumption_resolution,[status(thm)],[f513,f426])).
% 0.10/0.45 fof(f517,plain,(
% 0.10/0.45 sQ8_spl),
% 0.10/0.45 inference(contradiction_clause,[status(thm)],[f516])).
% 0.10/0.45 fof(f518,plain,(
% 0.10/0.45 sP0_prd(sK50_skl,sK47_skl)|~sQ2_spl),
% 0.10/0.45 inference(forward_demodulation,[status(thm)],[f424,f446])).
% 0.10/0.45 fof(f519,plain,(
% 0.10/0.45 nil=sK50_skl|~sQ2_spl),
% 0.10/0.45 inference(resolution,[status(thm)],[f518,f435])).
% 0.10/0.45 fof(f520,plain,(
% 0.10/0.45 sP0_prd(nil,sK47_skl)|~sQ2_spl),
% 0.10/0.45 inference(backward_demodulation,[status(thm)],[f519,f518])).
% 0.10/0.45 fof(f529,definition,(
% 0.10/0.45 sQ10_spl <=> (nil=nil)),
% 0.10/0.45 introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition])).
% 0.10/0.45 fof(f565,plain,(
% 0.10/0.45 app(sK47_skl,sK51_skl)=nil|~sQ2_spl),
% 0.10/0.45 inference(forward_demodulation,[status(thm)],[f519,f497])).
% 0.10/0.45 fof(f585,plain,(
% 0.10/0.45 ![X0]: (singletonP(cons(X0,nil))|~ssItem(X0)|~ssList(nil)|~ssItem(X0))),
% 0.10/0.45 inference(resolution,[status(thm)],[f459,f222])).
% 0.10/0.45 fof(f586,definition,(
% 0.10/0.45 ![X0]: (sQ19_spl <=> (singletonP(cons(X0,nil))|~ssItem(X0)|~ssItem(X0)))),
% 0.10/0.45 introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition])).
% 0.10/0.45 fof(f589,plain,(
% 0.10/0.45 sQ19_spl|~sQ5_spl),
% 0.10/0.45 inference(split_clause,[status(thm)],[f585,f586,f502])).
% 0.10/0.45 fof(f590,plain,(
% 0.10/0.45 $false|sQ5_spl),
% 0.10/0.45 inference(forward_subsumption_resolution,[status(thm)],[f504,f223])).
% 0.10/0.45 fof(f591,plain,(
% 0.10/0.45 sQ5_spl),
% 0.10/0.45 inference(contradiction_clause,[status(thm)],[f590])).
% 0.10/0.45 fof(f592,plain,(
% 0.10/0.45 $false|sQ6_spl),
% 0.10/0.45 inference(forward_subsumption_resolution,[status(thm)],[f507,f420])).
% 0.10/0.45 fof(f593,plain,(
% 0.10/0.45 sQ6_spl),
% 0.10/0.45 inference(contradiction_clause,[status(thm)],[f592])).
% 0.10/0.45 fof(f595,plain,(
% 0.10/0.45 frontsegP(nil,sK47_skl)|~sQ2_spl|~sQ7_spl),
% 0.10/0.45 inference(forward_demodulation,[status(thm)],[f565,f509])).
% 0.10/0.45 fof(f596,plain,(
% 0.10/0.45 ![X0]: (~ssList(X0)|~ssList(nil)|app(nil,sK5_skl(nil,X0))=X0|~ssList(X0))),
% 0.10/0.45 inference(resolution,[status(thm)],[f123,f295])).
% 0.10/0.45 fof(f598,definition,(
% 0.10/0.45 ![X0]: (sQ20_spl <=> (~ssList(X0)|app(nil,sK5_skl(nil,X0))=X0|~ssList(X0)))),
% 0.10/0.45 introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition])).
% 0.10/0.45 fof(f601,plain,(
% 0.10/0.45 sQ20_spl|~sQ5_spl),
% 0.10/0.45 inference(split_clause,[status(thm)],[f596,f598,f502])).
% 0.10/0.45 fof(f614,plain,(
% 0.10/0.45 neq(nil,nil)|~sQ0_spl|~sQ3_spl),
% 0.10/0.45 inference(forward_demodulation,[status(thm)],[f495,f449])).
% 0.10/0.45 fof(f615,plain,(
% 0.10/0.45 ~ssList(nil)|~sQ0_spl|~sQ3_spl),
% 0.10/0.45 inference(resolution,[status(thm)],[f614,f472])).
% 0.10/0.45 fof(f616,plain,(
% 0.10/0.45 ~sQ5_spl|~sQ0_spl|~sQ3_spl),
% 0.10/0.45 inference(split_clause,[status(thm)],[f615,f502,f438,f448])).
% 0.10/0.45 fof(f624,plain,(
% 0.10/0.45 ~ssList(sK50_skl)|~ssList(sK47_skl)|frontsegP(app(sK47_skl,sK51_skl),sK47_skl)|~ssList(sK51_skl)),
% 0.10/0.45 inference(paramodulation,[status(thm)],[f497,f460])).
% 0.10/0.45 fof(f625,definition,(
% 0.10/0.45 sQ22_spl <=> (ssList(sK50_skl))),
% 0.10/0.45 introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition])).
% 0.10/0.45 fof(f627,plain,(
% 0.10/0.45 ~ssList(sK50_skl)|sQ22_spl),
% 0.10/0.45 inference(component_clause,[status(thm)],[f625])).
% 0.10/0.45 fof(f628,plain,(
% 0.10/0.45 ~sQ22_spl|~sQ6_spl|sQ7_spl|~sQ8_spl),
% 0.10/0.45 inference(split_clause,[status(thm)],[f624,f625,f505,f508,f511])).
% 0.10/0.45 fof(f629,plain,(
% 0.10/0.45 app(nil,sK50_skl)=sK50_skl),
% 0.10/0.45 inference(resolution,[status(thm)],[f249,f423])).
% 0.10/0.45 fof(f634,plain,(
% 0.10/0.45 app(nil,sK51_skl)=sK51_skl),
% 0.10/0.45 inference(resolution,[status(thm)],[f249,f426])).
% 0.10/0.45 fof(f635,plain,(
% 0.10/0.45 app(nil,nil)=nil),
% 0.10/0.45 inference(resolution,[status(thm)],[f249,f223])).
% 0.10/0.45 fof(f636,plain,(
% 0.10/0.45 app(nil,sK47_skl)=sK47_skl),
% 0.10/0.45 inference(resolution,[status(thm)],[f249,f420])).
% 0.10/0.45 fof(f637,plain,(
% 0.10/0.45 ~ssList(sK50_skl)|~ssList(nil)|frontsegP(app(nil,sK50_skl),nil)|~ssList(sK50_skl)),
% 0.10/0.45 inference(paramodulation,[status(thm)],[f629,f460])).
% 0.10/0.45 fof(f638,definition,(
% 0.10/0.45 sQ23_spl <=> (frontsegP(app(nil,sK50_skl),nil))),
% 0.10/0.45 introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition])).
% 0.10/0.45 fof(f639,plain,(
% 0.10/0.45 frontsegP(app(nil,sK50_skl),nil)|~sQ23_spl),
% 0.10/0.45 inference(component_clause,[status(thm)],[f638])).
% 0.10/0.45 fof(f641,plain,(
% 0.10/0.45 ~sQ22_spl|~sQ5_spl|sQ23_spl),
% 0.10/0.45 inference(split_clause,[status(thm)],[f637,f625,f502,f638])).
% 0.10/0.45 fof(f642,plain,(
% 0.10/0.45 $false|sQ22_spl),
% 0.10/0.45 inference(forward_subsumption_resolution,[status(thm)],[f627,f423])).
% 0.10/0.45 fof(f643,plain,(
% 0.10/0.45 sQ22_spl),
% 0.10/0.45 inference(contradiction_clause,[status(thm)],[f642])).
% 0.10/0.45 fof(f644,plain,(
% 0.10/0.45 frontsegP(sK50_skl,nil)|~sQ23_spl),
% 0.10/0.45 inference(forward_demodulation,[status(thm)],[f629,f639])).
% 0.10/0.45 fof(f645,plain,(
% 0.10/0.45 ~ssList(sK50_skl)|~ssList(nil)|app(nil,sK5_skl(nil,sK50_skl))=sK50_skl|~sQ23_spl),
% 0.10/0.45 inference(resolution,[status(thm)],[f644,f123])).
% 0.10/0.45 fof(f646,definition,(
% 0.10/0.45 sQ24_spl <=> (app(nil,sK5_skl(nil,sK50_skl))=sK50_skl)),
% 0.10/0.45 introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition])).
% 0.10/0.45 fof(f649,plain,(
% 0.10/0.45 ~sQ22_spl|~sQ5_spl|sQ24_spl|~sQ23_spl),
% 0.10/0.45 inference(split_clause,[status(thm)],[f645,f625,f502,f646,f638])).
% 0.10/0.45 fof(f650,plain,(
% 0.10/0.45 ~ssList(sK51_skl)|~ssList(nil)|frontsegP(app(nil,sK51_skl),nil)|~ssList(sK51_skl)),
% 0.10/0.45 inference(paramodulation,[status(thm)],[f634,f460])).
% 0.10/0.45 fof(f651,definition,(
% 0.10/0.45 sQ25_spl <=> (frontsegP(app(nil,sK51_skl),nil))),
% 0.10/0.45 introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition])).
% 0.10/0.45 fof(f652,plain,(
% 0.10/0.45 frontsegP(app(nil,sK51_skl),nil)|~sQ25_spl),
% 0.10/0.45 inference(component_clause,[status(thm)],[f651])).
% 0.10/0.45 fof(f654,plain,(
% 0.10/0.45 ~sQ8_spl|~sQ5_spl|sQ25_spl),
% 0.10/0.45 inference(split_clause,[status(thm)],[f650,f511,f502,f651])).
% 0.10/0.45 fof(f655,plain,(
% 0.10/0.45 frontsegP(sK51_skl,nil)|~sQ25_spl),
% 0.10/0.45 inference(forward_demodulation,[status(thm)],[f634,f652])).
% 0.10/0.45 fof(f657,plain,(
% 0.10/0.45 ![X0]: (~ssList(X0)|~ssList(nil)|app(sK6_skl(nil,X0),nil)=X0|~ssList(X0))),
% 0.10/0.45 inference(resolution,[status(thm)],[f129,f309])).
% 0.10/0.45 fof(f659,definition,(
% 0.10/0.45 ![X0]: (sQ26_spl <=> (~ssList(X0)|app(sK6_skl(nil,X0),nil)=X0|~ssList(X0)))),
% 0.10/0.45 introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition])).
% 0.10/0.45 fof(f662,plain,(
% 0.10/0.45 sQ26_spl|~sQ5_spl),
% 0.10/0.45 inference(split_clause,[status(thm)],[f657,f659,f502])).
% 0.10/0.45 fof(f665,plain,(
% 0.10/0.45 ~ssList(sK51_skl)|~ssList(sK51_skl)|rearsegP(app(nil,sK51_skl),sK51_skl)|~ssList(nil)),
% 0.10/0.45 inference(paramodulation,[status(thm)],[f634,f461])).
% 0.10/0.45 fof(f666,plain,(
% 0.10/0.45 ~ssList(sK50_skl)|~ssList(sK50_skl)|rearsegP(app(nil,sK50_skl),sK50_skl)|~ssList(nil)),
% 0.10/0.45 inference(paramodulation,[status(thm)],[f629,f461])).
% 0.10/0.45 fof(f667,plain,(
% 0.10/0.45 ~ssList(sK50_skl)|~ssList(sK51_skl)|rearsegP(app(sK47_skl,sK51_skl),sK51_skl)|~ssList(sK47_skl)),
% 0.10/0.45 inference(paramodulation,[status(thm)],[f497,f461])).
% 0.10/0.45 fof(f668,definition,(
% 0.10/0.45 sQ27_spl <=> (rearsegP(app(nil,sK51_skl),sK51_skl))),
% 0.10/0.45 introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition])).
% 0.10/0.45 fof(f669,plain,(
% 0.10/0.45 rearsegP(app(nil,sK51_skl),sK51_skl)|~sQ27_spl),
% 0.10/0.45 inference(component_clause,[status(thm)],[f668])).
% 0.10/0.45 fof(f671,plain,(
% 0.10/0.45 ~sQ8_spl|sQ27_spl|~sQ5_spl),
% 0.10/0.45 inference(split_clause,[status(thm)],[f665,f511,f668,f502])).
% 0.10/0.45 fof(f672,definition,(
% 0.10/0.45 sQ28_spl <=> (rearsegP(app(nil,sK50_skl),sK50_skl))),
% 0.10/0.45 introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition])).
% 0.10/0.45 fof(f673,plain,(
% 0.10/0.45 rearsegP(app(nil,sK50_skl),sK50_skl)|~sQ28_spl),
% 0.10/0.45 inference(component_clause,[status(thm)],[f672])).
% 0.10/0.45 fof(f675,plain,(
% 0.10/0.45 ~sQ22_spl|sQ28_spl|~sQ5_spl),
% 0.10/0.45 inference(split_clause,[status(thm)],[f666,f625,f672,f502])).
% 0.10/0.45 fof(f676,definition,(
% 0.10/0.45 sQ29_spl <=> (rearsegP(app(sK47_skl,sK51_skl),sK51_skl))),
% 0.10/0.45 introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition])).
% 0.10/0.45 fof(f677,plain,(
% 0.10/0.45 rearsegP(app(sK47_skl,sK51_skl),sK51_skl)|~sQ29_spl),
% 0.10/0.45 inference(component_clause,[status(thm)],[f676])).
% 0.10/0.45 fof(f679,plain,(
% 0.10/0.45 ~sQ22_spl|~sQ8_spl|sQ29_spl|~sQ6_spl),
% 0.10/0.45 inference(split_clause,[status(thm)],[f667,f625,f511,f676,f505])).
% 0.10/0.45 fof(f680,plain,(
% 0.10/0.45 rearsegP(sK51_skl,sK51_skl)|~sQ27_spl),
% 0.10/0.45 inference(forward_demodulation,[status(thm)],[f634,f669])).
% 0.10/0.45 fof(f681,plain,(
% 0.10/0.45 rearsegP(sK50_skl,sK51_skl)|~sQ29_spl),
% 0.10/0.45 inference(forward_demodulation,[status(thm)],[f497,f677])).
% 0.10/0.45 fof(f682,plain,(
% 0.10/0.45 rearsegP(sK50_skl,sK50_skl)|~sQ28_spl),
% 0.10/0.45 inference(forward_demodulation,[status(thm)],[f629,f673])).
% 0.10/0.45 fof(f683,plain,(
% 0.10/0.45 ~ssList(sK51_skl)|~ssList(nil)|app(nil,sK5_skl(nil,sK51_skl))=sK51_skl|~sQ25_spl),
% 0.10/0.45 inference(resolution,[status(thm)],[f655,f123])).
% 0.10/0.45 fof(f684,definition,(
% 0.10/0.45 sQ30_spl <=> (app(nil,sK5_skl(nil,sK51_skl))=sK51_skl)),
% 0.10/0.45 introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition])).
% 0.10/0.45 fof(f687,plain,(
% 0.10/0.45 ~sQ8_spl|~sQ5_spl|sQ30_spl|~sQ25_spl),
% 0.10/0.45 inference(split_clause,[status(thm)],[f683,f511,f502,f684,f651])).
% 0.10/0.45 fof(f688,plain,(
% 0.10/0.45 ~ssList(sK51_skl)|~ssList(sK51_skl)|app(sK6_skl(sK51_skl,sK51_skl),sK51_skl)=sK51_skl|~sQ27_spl),
% 0.10/0.45 inference(resolution,[status(thm)],[f680,f129])).
% 0.10/0.45 fof(f689,definition,(
% 0.10/0.45 sQ31_spl <=> (app(sK6_skl(sK51_skl,sK51_skl),sK51_skl)=sK51_skl)),
% 0.10/0.45 introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition])).
% 0.10/0.45 fof(f692,plain,(
% 0.10/0.45 ~sQ8_spl|sQ31_spl|~sQ27_spl),
% 0.10/0.45 inference(split_clause,[status(thm)],[f688,f511,f689,f668])).
% 0.10/0.45 fof(f693,plain,(
% 0.10/0.45 ~ssList(sK50_skl)|~ssList(sK51_skl)|app(sK6_skl(sK51_skl,sK50_skl),sK51_skl)=sK50_skl|~sQ29_spl),
% 0.10/0.45 inference(resolution,[status(thm)],[f681,f129])).
% 0.10/0.45 fof(f694,definition,(
% 0.10/0.45 sQ32_spl <=> (app(sK6_skl(sK51_skl,sK50_skl),sK51_skl)=sK50_skl)),
% 0.10/0.45 introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition])).
% 0.10/0.45 fof(f697,plain,(
% 0.10/0.45 ~sQ22_spl|~sQ8_spl|sQ32_spl|~sQ29_spl),
% 0.10/0.45 inference(split_clause,[status(thm)],[f693,f625,f511,f694,f676])).
% 0.10/0.45 fof(f698,plain,(
% 0.10/0.45 ![X0]: (~ssList(X0)|~neq(X0,nil)|~frontsegP(sK50_skl,X0)|~frontsegP(sK47_skl,X0)|~sQ4_spl)),
% 0.10/0.45 inference(forward_demodulation,[status(thm)],[f424,f453])).
% 0.10/0.45 fof(f700,plain,(
% 0.10/0.45 ~ssList(sK47_skl)|~neq(sK47_skl,nil)|~frontsegP(sK50_skl,sK47_skl)|~ssList(sK47_skl)|~sQ4_spl),
% 0.10/0.45 inference(resolution,[status(thm)],[f698,f286])).
% 0.10/0.45 fof(f704,definition,(
% 0.10/0.45 sQ34_spl <=> (frontsegP(sK50_skl,nil))),
% 0.10/0.45 introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition])).
% 0.10/0.45 fof(f706,plain,(
% 0.10/0.45 ~frontsegP(sK50_skl,nil)|sQ34_spl),
% 0.10/0.45 inference(component_clause,[status(thm)],[f704])).
% 0.10/0.45 fof(f708,definition,(
% 0.10/0.45 sQ35_spl <=> (neq(sK47_skl,nil))),
% 0.10/0.45 introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition])).
% 0.10/0.45 fof(f710,plain,(
% 0.10/0.45 ~neq(sK47_skl,nil)|sQ35_spl),
% 0.10/0.45 inference(component_clause,[status(thm)],[f708])).
% 0.10/0.45 fof(f711,definition,(
% 0.10/0.45 sQ36_spl <=> (frontsegP(sK50_skl,sK47_skl))),
% 0.10/0.45 introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition])).
% 0.10/0.45 fof(f713,plain,(
% 0.10/0.45 ~frontsegP(sK50_skl,sK47_skl)|sQ36_spl),
% 0.10/0.45 inference(component_clause,[status(thm)],[f711])).
% 0.10/0.45 fof(f714,plain,(
% 0.10/0.45 ~sQ6_spl|~sQ35_spl|~sQ36_spl|~sQ4_spl),
% 0.10/0.45 inference(split_clause,[status(thm)],[f700,f505,f708,f711,f452])).
% 0.10/0.45 fof(f715,plain,(
% 0.10/0.45 ~ssList(sK50_skl)|~ssList(sK50_skl)|app(sK6_skl(sK50_skl,sK50_skl),sK50_skl)=sK50_skl|~sQ28_spl),
% 0.10/0.45 inference(resolution,[status(thm)],[f682,f129])).
% 0.10/0.45 fof(f716,definition,(
% 0.10/0.45 sQ37_spl <=> (app(sK6_skl(sK50_skl,sK50_skl),sK50_skl)=sK50_skl)),
% 0.10/0.45 introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition])).
% 0.10/0.45 fof(f719,plain,(
% 0.10/0.45 ~sQ22_spl|sQ37_spl|~sQ28_spl),
% 0.10/0.45 inference(split_clause,[status(thm)],[f715,f625,f716,f672])).
% 0.10/0.45 fof(f722,plain,(
% 0.10/0.45 $false|~sQ23_spl|sQ34_spl),
% 0.10/0.45 inference(forward_subsumption_resolution,[status(thm)],[f706,f644])).
% 0.10/0.45 fof(f723,plain,(
% 0.10/0.45 ~sQ23_spl|sQ34_spl),
% 0.10/0.45 inference(contradiction_clause,[status(thm)],[f722])).
% 0.10/0.45 fof(f745,definition,(
% 0.10/0.45 sQ38_spl <=> (app(sK6_skl(nil,nil),nil)=nil)),
% 0.10/0.45 introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition])).
% 0.10/0.45 fof(f750,plain,(
% 0.10/0.45 ~ssList(sK47_skl)|~ssList(nil)|sK47_skl=nil|sQ35_spl),
% 0.10/0.45 inference(resolution,[status(thm)],[f710,f220])).
% 0.10/0.45 fof(f751,definition,(
% 0.10/0.45 sQ39_spl <=> (sK47_skl=nil)),
% 0.10/0.45 introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition])).
% 0.10/0.45 fof(f752,plain,(
% 0.10/0.45 sK47_skl=nil|~sQ39_spl),
% 0.10/0.45 inference(component_clause,[status(thm)],[f751])).
% 0.10/0.45 fof(f754,plain,(
% 0.10/0.45 ~sQ6_spl|~sQ5_spl|sQ39_spl|sQ35_spl),
% 0.10/0.45 inference(split_clause,[status(thm)],[f750,f505,f502,f751,f708])).
% 0.10/0.45 fof(f755,plain,(
% 0.10/0.45 $false|sQ1_spl|~sQ39_spl),
% 0.10/0.45 inference(forward_subsumption_resolution,[status(thm)],[f752,f515])).
% 0.10/0.45 fof(f756,plain,(
% 0.10/0.45 sQ1_spl|~sQ39_spl),
% 0.10/0.45 inference(contradiction_clause,[status(thm)],[f755])).
% 0.10/0.45 fof(f759,plain,(
% 0.10/0.45 ![X0]: (~ssList(X0)|~ssList(nil)|app(app(sK7_skl(nil,X0),nil),sK8_skl(nil,X0))=X0|~ssList(X0))),
% 0.10/0.45 inference(resolution,[status(thm)],[f136,f323])).
% 0.10/0.45 fof(f761,definition,(
% 0.10/0.45 ![X0]: (sQ40_spl <=> (~ssList(X0)|app(app(sK7_skl(nil,X0),nil),sK8_skl(nil,X0))=X0|~ssList(X0)))),
% 0.10/0.45 introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition])).
% 0.10/0.45 fof(f764,plain,(
% 0.10/0.45 sQ40_spl|~sQ5_spl),
% 0.10/0.45 inference(split_clause,[status(thm)],[f759,f761,f502])).
% 0.10/0.45 fof(f779,plain,(
% 0.10/0.45 ~ssList(nil)|~ssList(nil)|rearsegP(app(nil,nil),nil)|~ssList(nil)),
% 0.10/0.45 inference(paramodulation,[status(thm)],[f635,f461])).
% 0.10/0.45 fof(f780,plain,(
% 0.10/0.45 ~ssList(nil)|~ssList(nil)|frontsegP(app(nil,nil),nil)|~ssList(nil)),
% 0.10/0.45 inference(paramodulation,[status(thm)],[f635,f460])).
% 0.10/0.45 fof(f781,definition,(
% 0.10/0.45 sQ41_spl <=> (rearsegP(app(nil,nil),nil))),
% 0.10/0.45 introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition])).
% 0.10/0.45 fof(f782,plain,(
% 0.10/0.45 rearsegP(app(nil,nil),nil)|~sQ41_spl),
% 0.10/0.45 inference(component_clause,[status(thm)],[f781])).
% 0.10/0.45 fof(f784,plain,(
% 0.10/0.45 ~sQ5_spl|sQ41_spl),
% 0.10/0.45 inference(split_clause,[status(thm)],[f779,f502,f781])).
% 0.10/0.45 fof(f785,definition,(
% 0.10/0.45 sQ42_spl <=> (frontsegP(app(nil,nil),nil))),
% 0.10/0.45 introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition])).
% 0.10/0.45 fof(f786,plain,(
% 0.10/0.45 frontsegP(app(nil,nil),nil)|~sQ42_spl),
% 0.10/0.45 inference(component_clause,[status(thm)],[f785])).
% 0.10/0.45 fof(f788,plain,(
% 0.10/0.45 ~sQ5_spl|sQ42_spl),
% 0.10/0.45 inference(split_clause,[status(thm)],[f780,f502,f785])).
% 0.10/0.45 fof(f789,plain,(
% 0.10/0.45 rearsegP(nil,nil)|~sQ41_spl),
% 0.10/0.45 inference(forward_demodulation,[status(thm)],[f635,f782])).
% 0.10/0.45 fof(f790,plain,(
% 0.10/0.45 frontsegP(nil,nil)|~sQ42_spl),
% 0.10/0.45 inference(forward_demodulation,[status(thm)],[f635,f786])).
% 0.10/0.45 fof(f807,plain,(
% 0.10/0.45 ~ssList(nil)|~ssList(nil)|app(sK6_skl(nil,nil),nil)=nil|~sQ41_spl),
% 0.10/0.45 inference(resolution,[status(thm)],[f789,f129])).
% 0.10/0.45 fof(f808,plain,(
% 0.10/0.45 ~sQ5_spl|sQ38_spl|~sQ41_spl),
% 0.10/0.45 inference(split_clause,[status(thm)],[f807,f502,f745,f781])).
% 0.10/0.45 fof(f821,plain,(
% 0.10/0.45 ![X0]: (~ssList(app(nil,X0))|~ssList(nil)|segmentP(app(app(nil,nil),X0),nil)|~ssList(nil)|~ssList(X0))),
% 0.10/0.45 inference(paramodulation,[status(thm)],[f635,f462])).
% 0.10/0.45 fof(f822,plain,(
% 0.10/0.45 ![X0]: (~ssList(app(sK51_skl,X0))|~ssList(sK51_skl)|segmentP(app(app(nil,sK51_skl),X0),sK51_skl)|~ssList(nil)|~ssList(X0))),
% 0.10/0.45 inference(paramodulation,[status(thm)],[f634,f462])).
% 0.10/0.45 fof(f825,definition,(
% 0.10/0.45 ![X0]: (sQ43_spl <=> (~ssList(app(nil,X0))|segmentP(app(app(nil,nil),X0),nil)|~ssList(X0)))),
% 0.10/0.45 introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition])).
% 0.10/0.45 fof(f828,plain,(
% 0.10/0.45 sQ43_spl|~sQ5_spl),
% 0.10/0.45 inference(split_clause,[status(thm)],[f821,f825,f502])).
% 0.10/0.45 fof(f829,definition,(
% 0.10/0.45 ![X0]: (sQ44_spl <=> (~ssList(app(sK51_skl,X0))|segmentP(app(app(nil,sK51_skl),X0),sK51_skl)|~ssList(X0)))),
% 0.10/0.45 introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition])).
% 0.10/0.45 fof(f832,plain,(
% 0.10/0.45 sQ44_spl|~sQ8_spl|~sQ5_spl),
% 0.10/0.45 inference(split_clause,[status(thm)],[f822,f829,f511,f502])).
% 0.10/0.45 fof(f848,definition,(
% 0.10/0.45 sQ46_spl <=> (app(nil,sK5_skl(nil,nil))=nil)),
% 0.10/0.45 introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition])).
% 0.10/0.45 fof(f870,plain,(
% 0.10/0.45 sP0_prd(nil,nil)|~sQ39_spl|~sQ2_spl),
% 0.10/0.45 inference(forward_demodulation,[status(thm)],[f752,f520])).
% 0.10/0.45 fof(f871,plain,(
% 0.10/0.45 $false|~sQ39_spl|~sQ2_spl),
% 0.10/0.45 inference(forward_subsumption_resolution,[status(thm)],[f870,f486])).
% 0.10/0.45 fof(f872,plain,(
% 0.10/0.45 ~sQ39_spl|~sQ2_spl),
% 0.10/0.45 inference(contradiction_clause,[status(thm)],[f871])).
% 0.10/0.45 fof(f879,plain,(
% 0.10/0.45 ![X0]: (~ssList(nil)|~ssList(X0)|~frontsegP(nil,X0)|nil=X0|~ssList(X0))),
% 0.10/0.45 inference(resolution,[status(thm)],[f284,f295])).
% 0.10/0.45 fof(f886,definition,(
% 0.10/0.45 ![X0]: (sQ49_spl <=> (~ssList(X0)|~frontsegP(nil,X0)|nil=X0|~ssList(X0)))),
% 0.10/0.45 introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition])).
% 0.10/0.45 fof(f889,plain,(
% 0.10/0.45 ~sQ5_spl|sQ49_spl),
% 0.10/0.45 inference(split_clause,[status(thm)],[f879,f502,f886])).
% 0.10/0.45 fof(f897,plain,(
% 0.10/0.45 ~ssList(sK47_skl)|~ssList(nil)|~frontsegP(sK47_skl,nil)|sK47_skl=nil|~sQ2_spl|~sQ7_spl),
% 0.10/0.45 inference(resolution,[status(thm)],[f595,f284])).
% 0.10/0.45 fof(f899,definition,(
% 0.10/0.45 sQ50_spl <=> (frontsegP(sK47_skl,nil))),
% 0.10/0.45 introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition])).
% 0.10/0.45 fof(f900,plain,(
% 0.10/0.45 frontsegP(sK47_skl,nil)|~sQ50_spl),
% 0.10/0.45 inference(component_clause,[status(thm)],[f899])).
% 0.10/0.45 fof(f901,plain,(
% 0.10/0.45 ~frontsegP(sK47_skl,nil)|sQ50_spl),
% 0.10/0.45 inference(component_clause,[status(thm)],[f899])).
% 0.10/0.45 fof(f902,plain,(
% 0.10/0.45 ~sQ6_spl|~sQ5_spl|~sQ50_spl|sQ39_spl|~sQ2_spl|~sQ7_spl),
% 0.10/0.45 inference(split_clause,[status(thm)],[f897,f505,f502,f899,f751,f445,f508])).
% 0.10/0.45 fof(f937,plain,(
% 0.10/0.45 ~ssList(sK47_skl)|sQ50_spl),
% 0.10/0.45 inference(resolution,[status(thm)],[f901,f295])).
% 0.10/0.45 fof(f939,plain,(
% 0.10/0.45 ~sQ6_spl|sQ50_spl),
% 0.10/0.45 inference(split_clause,[status(thm)],[f937,f505,f899])).
% 0.10/0.45 fof(f946,plain,(
% 0.10/0.45 ![X0]: (~ssList(nil)|~ssList(X0)|~ssList(nil)|~frontsegP(nil,X0)|frontsegP(nil,X0))),
% 0.10/0.45 inference(paramodulation,[status(thm)],[f635,f288])).
% 0.10/0.45 fof(f951,definition,(
% 0.10/0.45 ![X0]: (sQ55_spl <=> (~ssList(X0)|~frontsegP(nil,X0)|frontsegP(nil,X0)))),
% 0.10/0.45 introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition])).
% 0.10/0.45 fof(f954,plain,(
% 0.10/0.45 ~sQ5_spl|sQ55_spl),
% 0.10/0.45 inference(split_clause,[status(thm)],[f946,f502,f951])).
% 0.10/0.45 fof(f974,plain,(
% 0.10/0.45 ~ssList(nil)|~ssList(nil)|app(nil,sK5_skl(nil,nil))=nil|~sQ42_spl),
% 0.10/0.45 inference(resolution,[status(thm)],[f790,f123])).
% 0.10/0.45 fof(f976,plain,(
% 0.10/0.45 ~sQ5_spl|sQ46_spl|~sQ42_spl),
% 0.10/0.45 inference(split_clause,[status(thm)],[f974,f502,f848,f785])).
% 0.10/0.45 fof(f1044,plain,(
% 0.10/0.45 ~ssList(sK47_skl)|~ssList(nil)|app(nil,sK5_skl(nil,sK47_skl))=sK47_skl|~sQ50_spl),
% 0.10/0.45 inference(resolution,[status(thm)],[f900,f123])).
% 0.10/0.45 fof(f1049,definition,(
% 0.10/0.45 sQ69_spl <=> (app(nil,sK5_skl(nil,sK47_skl))=sK47_skl)),
% 0.10/0.45 introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition])).
% 0.10/0.45 fof(f1052,plain,(
% 0.10/0.45 ~sQ6_spl|~sQ5_spl|sQ69_spl|~sQ50_spl),
% 0.10/0.45 inference(split_clause,[status(thm)],[f1044,f505,f502,f1049,f899])).
% 0.10/0.45 fof(f1064,plain,(
% 0.10/0.45 ![X0,X1,X2]: (~ssItem(X0)|~ssList(X1)|~ssList(X2)|~frontsegP(X1,X2)|~ssItem(X0)|~ssItem(X0)|~ssList(X1)|~ssList(X2)|frontsegP(X1,X2))),
% 0.10/0.45 inference(resolution,[status(thm)],[f476,f292])).
% 0.10/0.45 fof(f1068,definition,(
% 0.10/0.45 ![X0]: (sQ71_spl <=> (~ssItem(X0)|~ssItem(X0)|~ssItem(X0)))),
% 0.10/0.45 introduced(definition,[new_symbols(definition,[sQ71_spl])],[split_symbol_definition])).
% 0.10/0.45 fof(f1069,plain,(
% 0.10/0.45 ![X0]: (~ssItem(X0)|~ssItem(X0)|~ssItem(X0)|~sQ71_spl)),
% 0.10/0.45 inference(component_clause,[status(thm)],[f1068])).
% 0.10/0.45 fof(f1071,definition,(
% 0.10/0.45 ![X1,X2]: (sQ72_spl <=> (~ssList(X1)|~ssList(X2)|~frontsegP(X1,X2)|~ssList(X1)|~ssList(X2)|frontsegP(X1,X2)))),
% 0.10/0.45 introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition])).
% 0.10/0.45 fof(f1074,plain,(
% 0.10/0.45 sQ71_spl|sQ72_spl),
% 0.10/0.45 inference(split_clause,[status(thm)],[f1064,f1068,f1071])).
% 0.10/0.45 fof(f1084,plain,(
% 0.10/0.45 ![X0]: (~ssItem(X0)|~sQ71_spl)),
% 0.10/0.45 inference(duplicate_literals_removal,[status(thm)],[f1069])).
% 0.10/0.45 fof(f1088,plain,(
% 0.10/0.45 $false|~sQ71_spl),
% 0.10/0.45 inference(backward_subsumption_resolution,[status(thm)],[f104,f1084])).
% 0.10/0.45 fof(f1090,plain,(
% 0.10/0.45 ~sQ71_spl),
% 0.10/0.45 inference(contradiction_clause,[status(thm)],[f1088])).
% 0.10/0.45 fof(f1106,plain,(
% 0.10/0.45 ![X0]: (~ssList(nil)|~ssList(X0)|~ssList(sK47_skl)|~frontsegP(nil,X0)|frontsegP(sK47_skl,X0))),
% 0.10/0.45 inference(paramodulation,[status(thm)],[f636,f288])).
% 0.10/0.45 fof(f1107,plain,(
% 0.10/0.45 ![X0]: (~ssList(app(sK47_skl,X0))|~ssList(sK47_skl)|segmentP(app(app(nil,sK47_skl),X0),sK47_skl)|~ssList(nil)|~ssList(X0))),
% 0.10/0.45 inference(paramodulation,[status(thm)],[f636,f462])).
% 0.10/0.45 fof(f1109,definition,(
% 0.10/0.45 ![X0]: (sQ76_spl <=> (~ssList(X0)|~frontsegP(nil,X0)|frontsegP(sK47_skl,X0)))),
% 0.10/0.45 introduced(definition,[new_symbols(definition,[sQ76_spl])],[split_symbol_definition])).
% 0.10/0.45 fof(f1112,plain,(
% 0.10/0.45 ~sQ5_spl|sQ76_spl|~sQ6_spl),
% 0.10/0.45 inference(split_clause,[status(thm)],[f1106,f502,f1109,f505])).
% 0.10/0.45 fof(f1113,definition,(
% 0.10/0.45 ![X0]: (sQ77_spl <=> (~ssList(app(sK47_skl,X0))|segmentP(app(app(nil,sK47_skl),X0),sK47_skl)|~ssList(X0)))),
% 0.10/0.45 introduced(definition,[new_symbols(definition,[sQ77_spl])],[split_symbol_definition])).
% 0.10/0.45 fof(f1116,plain,(
% 0.10/0.45 sQ77_spl|~sQ6_spl|~sQ5_spl),
% 0.10/0.45 inference(split_clause,[status(thm)],[f1107,f1113,f505,f502])).
% 0.10/0.45 fof(f1119,plain,(
% 0.10/0.45 ![X0]: (~ssList(nil)|~ssList(X0)|~ssList(sK50_skl)|~frontsegP(nil,X0)|frontsegP(sK50_skl,X0))),
% 0.10/0.45 inference(paramodulation,[status(thm)],[f629,f288])).
% 0.10/0.45 fof(f1120,plain,(
% 0.10/0.45 ![X0]: (~ssList(app(sK50_skl,X0))|~ssList(sK50_skl)|segmentP(app(app(nil,sK50_skl),X0),sK50_skl)|~ssList(nil)|~ssList(X0))),
% 0.10/0.45 inference(paramodulation,[status(thm)],[f629,f462])).
% 0.10/0.45 fof(f1122,definition,(
% 0.10/0.45 ![X0]: (sQ78_spl <=> (~ssList(X0)|~frontsegP(nil,X0)|frontsegP(sK50_skl,X0)))),
% 0.10/0.45 introduced(definition,[new_symbols(definition,[sQ78_spl])],[split_symbol_definition])).
% 0.10/0.45 fof(f1125,plain,(
% 0.10/0.45 ~sQ5_spl|sQ78_spl|~sQ22_spl),
% 0.10/0.45 inference(split_clause,[status(thm)],[f1119,f502,f1122,f625])).
% 0.10/0.45 fof(f1126,definition,(
% 0.10/0.45 ![X0]: (sQ79_spl <=> (~ssList(app(sK50_skl,X0))|segmentP(app(app(nil,sK50_skl),X0),sK50_skl)|~ssList(X0)))),
% 0.10/0.45 introduced(definition,[new_symbols(definition,[sQ79_spl])],[split_symbol_definition])).
% 0.10/0.45 fof(f1129,plain,(
% 0.10/0.45 sQ79_spl|~sQ22_spl|~sQ5_spl),
% 0.10/0.45 inference(split_clause,[status(thm)],[f1120,f1126,f625,f502])).
% 0.10/0.45 fof(f1132,plain,(
% 0.10/0.45 ![X0]: (~ssList(sK47_skl)|~ssList(X0)|~ssList(sK51_skl)|~frontsegP(sK47_skl,X0)|frontsegP(sK50_skl,X0))),
% 0.10/0.45 inference(paramodulation,[status(thm)],[f497,f288])).
% 0.10/0.45 fof(f1133,plain,(
% 0.10/0.45 ![X0]: (~ssList(app(sK50_skl,X0))|~ssList(sK51_skl)|segmentP(app(app(sK47_skl,sK51_skl),X0),sK51_skl)|~ssList(sK47_skl)|~ssList(X0))),
% 0.10/0.45 inference(paramodulation,[status(thm)],[f497,f462])).
% 0.10/0.45 fof(f1135,definition,(
% 0.10/0.45 ![X0]: (sQ80_spl <=> (~ssList(X0)|~frontsegP(sK47_skl,X0)|frontsegP(sK50_skl,X0)))),
% 0.10/0.46 introduced(definition,[new_symbols(definition,[sQ80_spl])],[split_symbol_definition])).
% 0.10/0.46 fof(f1138,plain,(
% 0.10/0.46 ~sQ6_spl|sQ80_spl|~sQ8_spl),
% 0.10/0.46 inference(split_clause,[status(thm)],[f1132,f505,f1135,f511])).
% 0.10/0.46 fof(f1139,definition,(
% 0.10/0.46 ![X0]: (sQ81_spl <=> (~ssList(app(sK50_skl,X0))|segmentP(app(app(sK47_skl,sK51_skl),X0),sK51_skl)|~ssList(X0)))),
% 0.10/0.46 introduced(definition,[new_symbols(definition,[sQ81_spl])],[split_symbol_definition])).
% 0.10/0.46 fof(f1142,plain,(
% 0.10/0.46 sQ81_spl|~sQ8_spl|~sQ6_spl),
% 0.10/0.46 inference(split_clause,[status(thm)],[f1133,f1139,f511,f505])).
% 0.10/0.46 fof(f1146,plain,(
% 0.10/0.46 ![X0]: (~ssList(nil)|~ssList(X0)|~ssList(sK51_skl)|~frontsegP(nil,X0)|frontsegP(sK51_skl,X0))),
% 0.10/0.46 inference(paramodulation,[status(thm)],[f634,f288])).
% 0.10/0.46 fof(f1149,definition,(
% 0.10/0.46 ![X0]: (sQ82_spl <=> (~ssList(X0)|~frontsegP(nil,X0)|frontsegP(sK51_skl,X0)))),
% 0.10/0.46 introduced(definition,[new_symbols(definition,[sQ82_spl])],[split_symbol_definition])).
% 0.10/0.46 fof(f1152,plain,(
% 0.10/0.46 ~sQ5_spl|sQ82_spl|~sQ8_spl),
% 0.10/0.46 inference(split_clause,[status(thm)],[f1146,f502,f1149,f511])).
% 0.10/0.46 fof(f1156,plain,(
% 0.10/0.46 ~ssList(nil)|nil=nil|~ssList(nil)),
% 0.10/0.46 inference(resolution,[status(thm)],[f298,f295])).
% 0.10/0.46 fof(f1157,plain,(
% 0.10/0.46 ![X0,X1]: (~ssList(X0)|nil=X0|~ssList(nil)|~ssList(X1)|~ssList(X0)|~frontsegP(nil,X1)|~frontsegP(X1,X0))),
% 0.10/0.46 inference(resolution,[status(thm)],[f298,f282])).
% 0.10/0.46 fof(f1160,plain,(
% 0.10/0.46 ~sQ5_spl|sQ10_spl),
% 0.10/0.46 inference(split_clause,[status(thm)],[f1156,f502,f529])).
% 0.10/0.46 fof(f1161,definition,(
% 0.10/0.46 ![X0,X1]: (sQ83_spl <=> (~ssList(X0)|nil=X0|~ssList(X1)|~ssList(X0)|~frontsegP(nil,X1)|~frontsegP(X1,X0)))),
% 0.10/0.46 introduced(definition,[new_symbols(definition,[sQ83_spl])],[split_symbol_definition])).
% 0.10/0.46 fof(f1164,plain,(
% 0.10/0.46 sQ83_spl|~sQ5_spl),
% 0.10/0.46 inference(split_clause,[status(thm)],[f1157,f1161,f502])).
% 0.10/0.46 fof(f1168,plain,(
% 0.10/0.46 app(sK51_skl,nil)=sK51_skl),
% 0.10/0.46 inference(resolution,[status(thm)],[f389,f426])).
% 0.10/0.46 fof(f1169,plain,(
% 0.10/0.46 app(sK50_skl,nil)=sK50_skl),
% 0.10/0.46 inference(resolution,[status(thm)],[f389,f423])).
% 0.10/0.46 fof(f1172,plain,(
% 0.10/0.46 app(sK47_skl,nil)=sK47_skl),
% 0.10/0.46 inference(resolution,[status(thm)],[f389,f420])).
% 0.10/0.46 fof(f1179,plain,(
% 0.10/0.46 ![X0]: (~ssList(sK51_skl)|~ssList(X0)|~ssList(nil)|~frontsegP(sK51_skl,X0)|frontsegP(sK51_skl,X0))),
% 0.10/0.46 inference(paramodulation,[status(thm)],[f1168,f288])).
% 0.10/0.46 fof(f1180,plain,(
% 0.10/0.46 ![X0]: (~ssList(app(sK51_skl,X0))|~ssList(nil)|segmentP(app(app(sK51_skl,nil),X0),nil)|~ssList(sK51_skl)|~ssList(X0))),
% 0.10/0.46 inference(paramodulation,[status(thm)],[f1168,f462])).
% 0.10/0.46 fof(f1182,definition,(
% 0.10/0.46 ![X0]: (sQ84_spl <=> (~ssList(X0)|~frontsegP(sK51_skl,X0)|frontsegP(sK51_skl,X0)))),
% 0.10/0.46 introduced(definition,[new_symbols(definition,[sQ84_spl])],[split_symbol_definition])).
% 0.10/0.46 fof(f1185,plain,(
% 0.10/0.46 ~sQ8_spl|sQ84_spl|~sQ5_spl),
% 0.10/0.46 inference(split_clause,[status(thm)],[f1179,f511,f1182,f502])).
% 0.10/0.46 fof(f1186,definition,(
% 0.10/0.46 ![X0]: (sQ85_spl <=> (~ssList(app(sK51_skl,X0))|segmentP(app(app(sK51_skl,nil),X0),nil)|~ssList(X0)))),
% 0.10/0.46 introduced(definition,[new_symbols(definition,[sQ85_spl])],[split_symbol_definition])).
% 0.10/0.46 fof(f1189,plain,(
% 0.10/0.46 sQ85_spl|~sQ5_spl|~sQ8_spl),
% 0.10/0.46 inference(split_clause,[status(thm)],[f1180,f1186,f502,f511])).
% 0.10/0.46 fof(f1192,plain,(
% 0.10/0.46 ![X0]: (~ssList(sK50_skl)|~ssList(X0)|~ssList(nil)|~frontsegP(sK50_skl,X0)|frontsegP(sK50_skl,X0))),
% 0.10/0.46 inference(paramodulation,[status(thm)],[f1169,f288])).
% 0.10/0.46 fof(f1193,plain,(
% 0.10/0.46 ![X0]: (~ssList(app(sK50_skl,X0))|~ssList(nil)|segmentP(app(app(sK50_skl,nil),X0),nil)|~ssList(sK50_skl)|~ssList(X0))),
% 0.10/0.46 inference(paramodulation,[status(thm)],[f1169,f462])).
% 0.10/0.46 fof(f1195,definition,(
% 0.10/0.46 ![X0]: (sQ86_spl <=> (~ssList(X0)|~frontsegP(sK50_skl,X0)|frontsegP(sK50_skl,X0)))),
% 0.10/0.46 introduced(definition,[new_symbols(definition,[sQ86_spl])],[split_symbol_definition])).
% 0.10/0.46 fof(f1198,plain,(
% 0.10/0.46 ~sQ22_spl|sQ86_spl|~sQ5_spl),
% 0.10/0.46 inference(split_clause,[status(thm)],[f1192,f625,f1195,f502])).
% 0.10/0.46 fof(f1199,definition,(
% 0.10/0.46 ![X0]: (sQ87_spl <=> (~ssList(app(sK50_skl,X0))|segmentP(app(app(sK50_skl,nil),X0),nil)|~ssList(X0)))),
% 0.10/0.46 introduced(definition,[new_symbols(definition,[sQ87_spl])],[split_symbol_definition])).
% 0.10/0.46 fof(f1202,plain,(
% 0.10/0.46 sQ87_spl|~sQ5_spl|~sQ22_spl),
% 0.10/0.46 inference(split_clause,[status(thm)],[f1193,f1199,f502,f625])).
% 0.10/0.46 fof(f1205,plain,(
% 0.10/0.46 ![X0]: (~ssList(sK47_skl)|~ssList(X0)|~ssList(nil)|~frontsegP(sK47_skl,X0)|frontsegP(sK47_skl,X0))),
% 0.10/0.46 inference(paramodulation,[status(thm)],[f1172,f288])).
% 0.10/0.46 fof(f1206,plain,(
% 0.10/0.46 ![X0]: (~ssList(app(sK47_skl,X0))|~ssList(nil)|segmentP(app(app(sK47_skl,nil),X0),nil)|~ssList(sK47_skl)|~ssList(X0))),
% 0.10/0.46 inference(paramodulation,[status(thm)],[f1172,f462])).
% 0.10/0.46 fof(f1208,definition,(
% 0.10/0.46 ![X0]: (sQ88_spl <=> (~ssList(X0)|~frontsegP(sK47_skl,X0)|frontsegP(sK47_skl,X0)))),
% 0.10/0.46 introduced(definition,[new_symbols(definition,[sQ88_spl])],[split_symbol_definition])).
% 0.10/0.46 fof(f1211,plain,(
% 0.10/0.46 ~sQ6_spl|sQ88_spl|~sQ5_spl),
% 0.10/0.46 inference(split_clause,[status(thm)],[f1205,f505,f1208,f502])).
% 0.10/0.46 fof(f1212,definition,(
% 0.10/0.46 ![X0]: (sQ89_spl <=> (~ssList(app(sK47_skl,X0))|segmentP(app(app(sK47_skl,nil),X0),nil)|~ssList(X0)))),
% 0.10/0.46 introduced(definition,[new_symbols(definition,[sQ89_spl])],[split_symbol_definition])).
% 0.10/0.46 fof(f1215,plain,(
% 0.10/0.46 sQ89_spl|~sQ5_spl|~sQ6_spl),
% 0.10/0.46 inference(split_clause,[status(thm)],[f1206,f1212,f502,f505])).
% 0.10/0.46 fof(f1238,plain,(
% 0.10/0.46 frontsegP(sK50_skl,sK47_skl)|~sQ7_spl),
% 0.10/0.46 inference(forward_demodulation,[status(thm)],[f497,f509])).
% 0.10/0.46 fof(f1239,plain,(
% 0.10/0.46 $false|sQ36_spl|~sQ7_spl),
% 0.10/0.46 inference(forward_subsumption_resolution,[status(thm)],[f1238,f713])).
% 0.10/0.46 fof(f1240,plain,(
% 0.10/0.46 sQ36_spl|~sQ7_spl),
% 0.10/0.46 inference(contradiction_clause,[status(thm)],[f1239])).
% 0.10/0.46 fof(f1241,plain,(
% 0.10/0.46 $false),
% 0.10/0.46 inference(sat_refutation,[status(thm)],[f444,f451,f455,f517,f589,f591,f593,f601,f616,f628,f641,f643,f649,f654,f662,f671,f675,f679,f687,f692,f697,f714,f719,f723,f754,f756,f764,f784,f788,f808,f828,f832,f872,f889,f902,f939,f954,f976,f1052,f1074,f1090,f1112,f1116,f1125,f1129,f1138,f1142,f1152,f1160,f1164,f1185,f1189,f1198,f1202,f1211,f1215,f1240])).
% 0.10/0.46 % SZS output end CNFRefutation for theBenchmark.p
% 0.10/0.47 % Elapsed time: 0.082406 seconds
% 0.10/0.47 % CPU time: 0.366888 seconds
% 0.10/0.47 % Total memory used: 90.276 MB
% 0.10/0.47 % Net memory used: 89.941 MB
%------------------------------------------------------------------------------