TSTP Solution File: SWC067+1 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SWC067+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed May 31 12:39:07 EDT 2023
% Result : Theorem 0.13s 0.37s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC067+1 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n029.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue May 30 11:37:52 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % Drodi V3.5.1
% 0.13/0.37 % Refutation found
% 0.13/0.37 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.37 % SZS output start CNFRefutation for theBenchmark
% 0.13/0.37 fof(f1,axiom,(
% 0.13/0.37 (! [U] :( ssItem(U)=> (! [V] :( ssItem(V)=> ( neq(U,V)<=> U != V ) ) )) )),
% 0.13/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.37 fof(f2,axiom,(
% 0.13/0.37 (? [U] :( ssItem(U)& (? [V] :( ssItem(V)& U != V ) )) )),
% 0.13/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.37 fof(f4,axiom,(
% 0.13/0.37 (! [U] :( ssList(U)=> ( singletonP(U)<=> (? [V] :( ssItem(V)& cons(V,nil) = U ) )) ) )),
% 0.13/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.37 fof(f5,axiom,(
% 0.13/0.37 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> ( frontsegP(U,V)<=> (? [W] :( ssList(W)& app(V,W) = U ) )) ) )) )),
% 0.13/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.37 fof(f7,axiom,(
% 0.13/0.37 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> ( segmentP(U,V)<=> (? [W] :( ssList(W)& (? [X] :( ssList(X)& app(app(W,V),X) = U ) )) )) ) )) )),
% 0.13/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.37 fof(f15,axiom,(
% 0.13/0.37 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> ( neq(U,V)<=> U != V ) ) )) )),
% 0.13/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.37 fof(f16,axiom,(
% 0.13/0.37 (! [U] :( ssList(U)=> (! [V] :( ssItem(V)=> ssList(cons(V,U)) ) )) )),
% 0.13/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.37 fof(f17,axiom,(
% 0.13/0.37 ssList(nil) ),
% 0.13/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.37 fof(f28,axiom,(
% 0.13/0.37 (! [U] :( ssList(U)=> app(nil,U) = U ) )),
% 0.13/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.37 fof(f45,axiom,(
% 0.13/0.37 (! [U] :( ssList(U)=> frontsegP(U,nil) ) )),
% 0.13/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.37 fof(f55,axiom,(
% 0.13/0.37 (! [U] :( ssList(U)=> segmentP(U,U) ) )),
% 0.13/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.37 fof(f57,axiom,(
% 0.13/0.37 (! [U] :( ssList(U)=> segmentP(U,nil) ) )),
% 0.13/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.37 fof(f58,axiom,(
% 0.13/0.37 (! [U] :( ssList(U)=> ( segmentP(nil,U)<=> nil = U ) ) )),
% 0.13/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.37 fof(f84,axiom,(
% 0.13/0.37 (! [U] :( ssList(U)=> app(U,nil) = U ) )),
% 0.13/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.37 fof(f96,conjecture,(
% 0.13/0.37 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> (! [X] :( ssList(X)=> ( V != X| U != W| (! [Y] :( ssList(Y)=> (! [Z] :( ssList(Z)=> ( app(app(Y,W),Z) != X| ~ strictorderedP(W)| (? [X1] :( ssItem(X1)& (? [X2] :( ssList(X2)& app(X2,cons(X1,nil)) = Y& (? [X3] :( ssItem(X3)& (? [X4] :( ssList(X4)& app(cons(X3,nil),X4) = W& lt(X1,X3) ) )) )) )))| (? [X5] :( ssItem(X5)& (? [X6] :( ssList(X6)& app(cons(X5,nil),X6) = Z& (? [X7] :( ssItem(X7)& (? [X8] :( ssList(X8)& app(X8,cons(X7,nil)) = W& lt(X7,X5) ) )) )) )) )) ) )))| ( nil != X& nil = W )| ( ( nil != V| nil = U )& ( ~ neq(V,nil)| (? [X9] :( ssList(X9)& neq(X9,nil)& segmentP(V,X9)& segmentP(U,X9) ) )) ) ) ) )) )) )) )),
% 0.13/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.37 fof(f97,negated_conjecture,(
% 0.13/0.37 ~((! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> (! [X] :( ssList(X)=> ( V != X| U != W| (! [Y] :( ssList(Y)=> (! [Z] :( ssList(Z)=> ( app(app(Y,W),Z) != X| ~ strictorderedP(W)| (? [X1] :( ssItem(X1)& (? [X2] :( ssList(X2)& app(X2,cons(X1,nil)) = Y& (? [X3] :( ssItem(X3)& (? [X4] :( ssList(X4)& app(cons(X3,nil),X4) = W& lt(X1,X3) ) )) )) )))| (? [X5] :( ssItem(X5)& (? [X6] :( ssList(X6)& app(cons(X5,nil),X6) = Z& (? [X7] :( ssItem(X7)& (? [X8] :( ssList(X8)& app(X8,cons(X7,nil)) = W& lt(X7,X5) ) )) )) )) )) ) )))| ( nil != X& nil = W )| ( ( nil != V| nil = U )& ( ~ neq(V,nil)| (? [X9] :( ssList(X9)& neq(X9,nil)& segmentP(V,X9)& segmentP(U,X9) ) )) ) ) ) )) )) )) ))),
% 0.13/0.37 inference(negated_conjecture,[status(cth)],[f96])).
% 0.13/0.37 fof(f98,plain,(
% 0.13/0.37 ![U]: (~ssItem(U)|(![V]: (~ssItem(V)|(neq(U,V)<=>~U=V))))),
% 0.13/0.37 inference(pre_NNF_transformation,[status(esa)],[f1])).
% 0.13/0.37 fof(f99,plain,(
% 0.13/0.37 ![U]: (~ssItem(U)|(![V]: (~ssItem(V)|((~neq(U,V)|~U=V)&(neq(U,V)|U=V)))))),
% 0.13/0.37 inference(NNF_transformation,[status(esa)],[f98])).
% 0.13/0.37 fof(f100,plain,(
% 0.13/0.37 ![X0,X1]: (~ssItem(X0)|~ssItem(X1)|~neq(X0,X1)|~X0=X1)),
% 0.13/0.37 inference(cnf_transformation,[status(esa)],[f99])).
% 0.13/0.37 fof(f101,plain,(
% 0.13/0.37 ![X0,X1]: (~ssItem(X0)|~ssItem(X1)|neq(X0,X1)|X0=X1)),
% 0.13/0.37 inference(cnf_transformation,[status(esa)],[f99])).
% 0.13/0.37 fof(f102,plain,(
% 0.13/0.37 (ssItem(sk0_0)&(ssItem(sk0_1)&~sk0_0=sk0_1))),
% 0.13/0.37 inference(skolemization,[status(esa)],[f2])).
% 0.13/0.37 fof(f103,plain,(
% 0.13/0.37 ssItem(sk0_0)),
% 0.13/0.37 inference(cnf_transformation,[status(esa)],[f102])).
% 0.13/0.37 fof(f113,plain,(
% 0.13/0.37 ![U]: (~ssList(U)|(singletonP(U)<=>(?[V]: (ssItem(V)&cons(V,nil)=U))))),
% 0.13/0.37 inference(pre_NNF_transformation,[status(esa)],[f4])).
% 0.13/0.37 fof(f114,plain,(
% 0.13/0.37 ![U]: (~ssList(U)|((~singletonP(U)|(?[V]: (ssItem(V)&cons(V,nil)=U)))&(singletonP(U)|(![V]: (~ssItem(V)|~cons(V,nil)=U)))))),
% 0.13/0.37 inference(NNF_transformation,[status(esa)],[f113])).
% 0.13/0.37 fof(f115,plain,(
% 0.13/0.37 ![U]: (~ssList(U)|((~singletonP(U)|(ssItem(sk0_4(U))&cons(sk0_4(U),nil)=U))&(singletonP(U)|(![V]: (~ssItem(V)|~cons(V,nil)=U)))))),
% 0.13/0.37 inference(skolemization,[status(esa)],[f114])).
% 0.13/0.37 fof(f118,plain,(
% 0.13/0.37 ![X0,X1]: (~ssList(X0)|singletonP(X0)|~ssItem(X1)|~cons(X1,nil)=X0)),
% 0.13/0.37 inference(cnf_transformation,[status(esa)],[f115])).
% 0.13/0.37 fof(f119,plain,(
% 0.13/0.37 ![U]: (~ssList(U)|(![V]: (~ssList(V)|(frontsegP(U,V)<=>(?[W]: (ssList(W)&app(V,W)=U))))))),
% 0.13/0.37 inference(pre_NNF_transformation,[status(esa)],[f5])).
% 0.13/0.37 fof(f120,plain,(
% 0.13/0.37 ![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)))))))),
% 0.13/0.37 inference(NNF_transformation,[status(esa)],[f119])).
% 0.13/0.37 fof(f121,plain,(
% 0.13/0.37 ![U]: (~ssList(U)|(![V]: (~ssList(V)|((~frontsegP(U,V)|(ssList(sk0_5(V,U))&app(V,sk0_5(V,U))=U))&(frontsegP(U,V)|(![W]: (~ssList(W)|~app(V,W)=U)))))))),
% 0.13/0.37 inference(skolemization,[status(esa)],[f120])).
% 0.13/0.37 fof(f122,plain,(
% 0.13/0.37 ![X0,X1]: (~ssList(X0)|~ssList(X1)|~frontsegP(X0,X1)|ssList(sk0_5(X1,X0)))),
% 0.13/0.37 inference(cnf_transformation,[status(esa)],[f121])).
% 0.13/0.37 fof(f123,plain,(
% 0.13/0.37 ![X0,X1]: (~ssList(X0)|~ssList(X1)|~frontsegP(X0,X1)|app(X1,sk0_5(X1,X0))=X0)),
% 0.13/0.37 inference(cnf_transformation,[status(esa)],[f121])).
% 0.13/0.37 fof(f131,plain,(
% 0.13/0.37 ![U]: (~ssList(U)|(![V]: (~ssList(V)|(segmentP(U,V)<=>(?[W]: (ssList(W)&(?[X]: (ssList(X)&app(app(W,V),X)=U))))))))),
% 0.13/0.37 inference(pre_NNF_transformation,[status(esa)],[f7])).
% 0.13/0.37 fof(f132,plain,(
% 0.13/0.37 ![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)))))))))),
% 0.13/0.37 inference(NNF_transformation,[status(esa)],[f131])).
% 0.13/0.37 fof(f133,plain,(
% 0.13/0.37 ![U]: (~ssList(U)|(![V]: (~ssList(V)|((~segmentP(U,V)|(ssList(sk0_7(V,U))&(ssList(sk0_8(V,U))&app(app(sk0_7(V,U),V),sk0_8(V,U))=U)))&(segmentP(U,V)|(![W]: (~ssList(W)|(![X]: (~ssList(X)|~app(app(W,V),X)=U)))))))))),
% 0.13/0.37 inference(skolemization,[status(esa)],[f132])).
% 0.13/0.37 fof(f137,plain,(
% 0.13/0.37 ![X0,X1,X2,X3]: (~ssList(X0)|~ssList(X1)|segmentP(X0,X1)|~ssList(X2)|~ssList(X3)|~app(app(X2,X1),X3)=X0)),
% 0.13/0.37 inference(cnf_transformation,[status(esa)],[f133])).
% 0.13/0.37 fof(f217,plain,(
% 0.13/0.37 ![U]: (~ssList(U)|(![V]: (~ssList(V)|(neq(U,V)<=>~U=V))))),
% 0.13/0.37 inference(pre_NNF_transformation,[status(esa)],[f15])).
% 0.13/0.37 fof(f218,plain,(
% 0.13/0.37 ![U]: (~ssList(U)|(![V]: (~ssList(V)|((~neq(U,V)|~U=V)&(neq(U,V)|U=V)))))),
% 0.13/0.37 inference(NNF_transformation,[status(esa)],[f217])).
% 0.13/0.37 fof(f220,plain,(
% 0.13/0.37 ![X0,X1]: (~ssList(X0)|~ssList(X1)|neq(X0,X1)|X0=X1)),
% 0.13/0.37 inference(cnf_transformation,[status(esa)],[f218])).
% 0.13/0.37 fof(f221,plain,(
% 0.13/0.37 ![U]: (~ssList(U)|(![V]: (~ssItem(V)|ssList(cons(V,U)))))),
% 0.13/0.37 inference(pre_NNF_transformation,[status(esa)],[f16])).
% 0.13/0.37 fof(f222,plain,(
% 0.13/0.37 ![X0,X1]: (~ssList(X0)|~ssItem(X1)|ssList(cons(X1,X0)))),
% 0.13/0.37 inference(cnf_transformation,[status(esa)],[f221])).
% 0.13/0.37 fof(f223,plain,(
% 0.13/0.37 ssList(nil)),
% 0.13/0.37 inference(cnf_transformation,[status(esa)],[f17])).
% 0.13/0.37 fof(f248,plain,(
% 0.13/0.37 ![U]: (~ssList(U)|app(nil,U)=U)),
% 0.13/0.37 inference(pre_NNF_transformation,[status(esa)],[f28])).
% 0.13/0.37 fof(f249,plain,(
% 0.13/0.37 ![X0]: (~ssList(X0)|app(nil,X0)=X0)),
% 0.13/0.37 inference(cnf_transformation,[status(esa)],[f248])).
% 0.13/0.37 fof(f294,plain,(
% 0.13/0.37 ![U]: (~ssList(U)|frontsegP(U,nil))),
% 0.13/0.37 inference(pre_NNF_transformation,[status(esa)],[f45])).
% 0.13/0.37 fof(f295,plain,(
% 0.13/0.37 ![X0]: (~ssList(X0)|frontsegP(X0,nil))),
% 0.13/0.37 inference(cnf_transformation,[status(esa)],[f294])).
% 0.13/0.37 fof(f318,plain,(
% 0.13/0.37 ![U]: (~ssList(U)|segmentP(U,U))),
% 0.13/0.37 inference(pre_NNF_transformation,[status(esa)],[f55])).
% 0.13/0.37 fof(f319,plain,(
% 0.13/0.37 ![X0]: (~ssList(X0)|segmentP(X0,X0))),
% 0.13/0.37 inference(cnf_transformation,[status(esa)],[f318])).
% 0.13/0.37 fof(f322,plain,(
% 0.13/0.37 ![U]: (~ssList(U)|segmentP(U,nil))),
% 0.13/0.37 inference(pre_NNF_transformation,[status(esa)],[f57])).
% 0.13/0.37 fof(f323,plain,(
% 0.13/0.37 ![X0]: (~ssList(X0)|segmentP(X0,nil))),
% 0.13/0.37 inference(cnf_transformation,[status(esa)],[f322])).
% 0.13/0.37 fof(f324,plain,(
% 0.13/0.37 ![U]: (~ssList(U)|(segmentP(nil,U)<=>nil=U))),
% 0.13/0.37 inference(pre_NNF_transformation,[status(esa)],[f58])).
% 0.13/0.37 fof(f325,plain,(
% 0.13/0.37 ![U]: (~ssList(U)|((~segmentP(nil,U)|nil=U)&(segmentP(nil,U)|~nil=U)))),
% 0.13/0.37 inference(NNF_transformation,[status(esa)],[f324])).
% 0.13/0.37 fof(f326,plain,(
% 0.13/0.37 ![X0]: (~ssList(X0)|~segmentP(nil,X0)|nil=X0)),
% 0.13/0.37 inference(cnf_transformation,[status(esa)],[f325])).
% 0.13/0.37 fof(f388,plain,(
% 0.13/0.37 ![U]: (~ssList(U)|app(U,nil)=U)),
% 0.13/0.37 inference(pre_NNF_transformation,[status(esa)],[f84])).
% 0.13/0.37 fof(f389,plain,(
% 0.13/0.37 ![X0]: (~ssList(X0)|app(X0,nil)=X0)),
% 0.13/0.37 inference(cnf_transformation,[status(esa)],[f388])).
% 0.13/0.37 fof(f415,plain,(
% 0.13/0.37 (?[U]: (ssList(U)&(?[V]: (ssList(V)&(?[W]: (ssList(W)&(?[X]: (ssList(X)&((((V=X&U=W)&(?[Y]: (ssList(Y)&(?[Z]: (ssList(Z)&(((app(app(Y,W),Z)=X&strictorderedP(W))&(![X1]: (~ssItem(X1)|(![X2]: ((~ssList(X2)|~app(X2,cons(X1,nil))=Y)|(![X3]: (~ssItem(X3)|(![X4]: ((~ssList(X4)|~app(cons(X3,nil),X4)=W)|~lt(X1,X3))))))))))&(![X5]: (~ssItem(X5)|(![X6]: ((~ssList(X6)|~app(cons(X5,nil),X6)=Z)|(![X7]: (~ssItem(X7)|(![X8]: ((~ssList(X8)|~app(X8,cons(X7,nil))=W)|~lt(X7,X5)))))))))))))))&(nil=X|~nil=W))&((nil=V&~nil=U)|(neq(V,nil)&(![X9]: (((~ssList(X9)|~neq(X9,nil))|~segmentP(V,X9))|~segmentP(U,X9))))))))))))))),
% 0.13/0.37 inference(pre_NNF_transformation,[status(esa)],[f97])).
% 0.13/0.37 fof(f416,plain,(
% 0.13/0.37 ![U,V]: (pd0_0(V,U)=>(nil=V&~nil=U))),
% 0.13/0.37 introduced(predicate_definition,[f415])).
% 0.13/0.37 fof(f417,plain,(
% 0.13/0.37 ?[U]: (ssList(U)&(?[V]: (ssList(V)&(?[W]: (ssList(W)&(?[X]: (ssList(X)&((((V=X&U=W)&(?[Y]: (ssList(Y)&(?[Z]: (ssList(Z)&(((app(app(Y,W),Z)=X&strictorderedP(W))&(![X1]: (~ssItem(X1)|(![X2]: ((~ssList(X2)|~app(X2,cons(X1,nil))=Y)|(![X3]: (~ssItem(X3)|(![X4]: ((~ssList(X4)|~app(cons(X3,nil),X4)=W)|~lt(X1,X3))))))))))&(![X5]: (~ssItem(X5)|(![X6]: ((~ssList(X6)|~app(cons(X5,nil),X6)=Z)|(![X7]: (~ssItem(X7)|(![X8]: ((~ssList(X8)|~app(X8,cons(X7,nil))=W)|~lt(X7,X5)))))))))))))))&(nil=X|~nil=W))&(pd0_0(V,U)|(neq(V,nil)&(![X9]: (((~ssList(X9)|~neq(X9,nil))|~segmentP(V,X9))|~segmentP(U,X9)))))))))))))),
% 0.13/0.37 inference(formula_renaming,[status(thm)],[f415,f416])).
% 0.13/0.37 fof(f418,plain,(
% 0.13/0.37 ?[U]: (ssList(U)&(?[V]: (ssList(V)&(?[W]: (ssList(W)&(?[X]: (ssList(X)&((((V=X&U=W)&(?[Y]: (ssList(Y)&(?[Z]: (ssList(Z)&(((app(app(Y,W),Z)=X&strictorderedP(W))&(![X1]: (~ssItem(X1)|((![X2]: (~ssList(X2)|~app(X2,cons(X1,nil))=Y))|(![X3]: (~ssItem(X3)|((![X4]: (~ssList(X4)|~app(cons(X3,nil),X4)=W))|~lt(X1,X3))))))))&(![X5]: (~ssItem(X5)|((![X6]: (~ssList(X6)|~app(cons(X5,nil),X6)=Z))|(![X7]: (~ssItem(X7)|((![X8]: (~ssList(X8)|~app(X8,cons(X7,nil))=W))|~lt(X7,X5)))))))))))))&(nil=X|~nil=W))&(pd0_0(V,U)|(neq(V,nil)&(![X9]: (((~ssList(X9)|~neq(X9,nil))|~segmentP(V,X9))|~segmentP(U,X9)))))))))))))),
% 0.13/0.37 inference(miniscoping,[status(esa)],[f417])).
% 0.13/0.37 fof(f419,plain,(
% 0.13/0.37 (ssList(sk0_47)&(ssList(sk0_48)&(ssList(sk0_49)&(ssList(sk0_50)&((((sk0_48=sk0_50&sk0_47=sk0_49)&(ssList(sk0_51)&(ssList(sk0_52)&(((app(app(sk0_51,sk0_49),sk0_52)=sk0_50&strictorderedP(sk0_49))&(![X1]: (~ssItem(X1)|((![X2]: (~ssList(X2)|~app(X2,cons(X1,nil))=sk0_51))|(![X3]: (~ssItem(X3)|((![X4]: (~ssList(X4)|~app(cons(X3,nil),X4)=sk0_49))|~lt(X1,X3))))))))&(![X5]: (~ssItem(X5)|((![X6]: (~ssList(X6)|~app(cons(X5,nil),X6)=sk0_52))|(![X7]: (~ssItem(X7)|((![X8]: (~ssList(X8)|~app(X8,cons(X7,nil))=sk0_49))|~lt(X7,X5)))))))))))&(nil=sk0_50|~nil=sk0_49))&(pd0_0(sk0_48,sk0_47)|(neq(sk0_48,nil)&(![X9]: (((~ssList(X9)|~neq(X9,nil))|~segmentP(sk0_48,X9))|~segmentP(sk0_47,X9))))))))))),
% 0.13/0.37 inference(skolemization,[status(esa)],[f418])).
% 0.13/0.37 fof(f420,plain,(
% 0.13/0.37 ssList(sk0_47)),
% 0.13/0.37 inference(cnf_transformation,[status(esa)],[f419])).
% 0.13/0.37 fof(f421,plain,(
% 0.13/0.37 ssList(sk0_48)),
% 0.13/0.37 inference(cnf_transformation,[status(esa)],[f419])).
% 0.13/0.37 fof(f424,plain,(
% 0.13/0.37 sk0_48=sk0_50),
% 0.13/0.37 inference(cnf_transformation,[status(esa)],[f419])).
% 0.13/0.37 fof(f425,plain,(
% 0.13/0.37 sk0_47=sk0_49),
% 0.13/0.37 inference(cnf_transformation,[status(esa)],[f419])).
% 0.13/0.37 fof(f426,plain,(
% 0.13/0.37 ssList(sk0_51)),
% 0.13/0.37 inference(cnf_transformation,[status(esa)],[f419])).
% 0.13/0.37 fof(f427,plain,(
% 0.13/0.37 ssList(sk0_52)),
% 0.13/0.37 inference(cnf_transformation,[status(esa)],[f419])).
% 0.13/0.37 fof(f428,plain,(
% 0.13/0.37 app(app(sk0_51,sk0_49),sk0_52)=sk0_50),
% 0.13/0.37 inference(cnf_transformation,[status(esa)],[f419])).
% 0.13/0.37 fof(f432,plain,(
% 0.13/0.37 nil=sk0_50|~nil=sk0_49),
% 0.13/0.37 inference(cnf_transformation,[status(esa)],[f419])).
% 0.13/0.37 fof(f433,plain,(
% 0.13/0.37 pd0_0(sk0_48,sk0_47)|neq(sk0_48,nil)),
% 0.13/0.37 inference(cnf_transformation,[status(esa)],[f419])).
% 0.13/0.37 fof(f434,plain,(
% 0.13/0.37 ![X0]: (pd0_0(sk0_48,sk0_47)|~ssList(X0)|~neq(X0,nil)|~segmentP(sk0_48,X0)|~segmentP(sk0_47,X0))),
% 0.13/0.37 inference(cnf_transformation,[status(esa)],[f419])).
% 0.13/0.37 fof(f435,plain,(
% 0.13/0.37 ![U,V]: (~pd0_0(V,U)|(nil=V&~nil=U))),
% 0.13/0.37 inference(pre_NNF_transformation,[status(esa)],[f416])).
% 0.13/0.37 fof(f436,plain,(
% 0.13/0.37 ![X0,X1]: (~pd0_0(X0,X1)|nil=X0)),
% 0.13/0.37 inference(cnf_transformation,[status(esa)],[f435])).
% 0.13/0.37 fof(f437,plain,(
% 0.13/0.37 ![X0,X1]: (~pd0_0(X0,X1)|~nil=X1)),
% 0.13/0.37 inference(cnf_transformation,[status(esa)],[f435])).
% 0.13/0.37 fof(f438,plain,(
% 0.13/0.37 spl0_0 <=> nil=sk0_50),
% 0.13/0.37 introduced(split_symbol_definition)).
% 0.13/0.37 fof(f439,plain,(
% 0.13/0.37 nil=sk0_50|~spl0_0),
% 0.13/0.37 inference(component_clause,[status(thm)],[f438])).
% 0.13/0.37 fof(f441,plain,(
% 0.13/0.37 spl0_1 <=> nil=sk0_49),
% 0.13/0.37 introduced(split_symbol_definition)).
% 0.13/0.37 fof(f443,plain,(
% 0.13/0.37 ~nil=sk0_49|spl0_1),
% 0.13/0.37 inference(component_clause,[status(thm)],[f441])).
% 0.13/0.37 fof(f444,plain,(
% 0.13/0.37 spl0_0|~spl0_1),
% 0.13/0.37 inference(split_clause,[status(thm)],[f432,f438,f441])).
% 0.13/0.37 fof(f445,plain,(
% 0.13/0.37 spl0_2 <=> pd0_0(sk0_48,sk0_47)),
% 0.13/0.37 introduced(split_symbol_definition)).
% 0.13/0.37 fof(f446,plain,(
% 0.13/0.37 pd0_0(sk0_48,sk0_47)|~spl0_2),
% 0.13/0.37 inference(component_clause,[status(thm)],[f445])).
% 0.13/0.37 fof(f448,plain,(
% 0.13/0.37 spl0_3 <=> neq(sk0_48,nil)),
% 0.13/0.37 introduced(split_symbol_definition)).
% 0.13/0.37 fof(f451,plain,(
% 0.13/0.37 spl0_2|spl0_3),
% 0.13/0.37 inference(split_clause,[status(thm)],[f433,f445,f448])).
% 0.13/0.37 fof(f452,plain,(
% 0.13/0.37 spl0_4 <=> ~ssList(X0)|~neq(X0,nil)|~segmentP(sk0_48,X0)|~segmentP(sk0_47,X0)),
% 0.13/0.37 introduced(split_symbol_definition)).
% 0.13/0.37 fof(f453,plain,(
% 0.13/0.37 ![X0]: (~ssList(X0)|~neq(X0,nil)|~segmentP(sk0_48,X0)|~segmentP(sk0_47,X0)|~spl0_4)),
% 0.13/0.37 inference(component_clause,[status(thm)],[f452])).
% 0.13/0.37 fof(f455,plain,(
% 0.13/0.37 spl0_2|spl0_4),
% 0.13/0.37 inference(split_clause,[status(thm)],[f434,f445,f452])).
% 0.13/0.37 fof(f456,plain,(
% 0.13/0.37 ![X1]: (~ssItem(X1)|~ssItem(X1)|~neq(X1,X1))),
% 0.13/0.37 inference(destructive_equality_resolution,[status(esa)],[f100])).
% 0.13/0.37 fof(f457,plain,(
% 0.13/0.37 ![X0]: (~ssItem(X0)|~neq(X0,X0))),
% 0.13/0.37 inference(duplicate_literals_removal,[status(esa)],[f456])).
% 0.13/0.37 fof(f459,plain,(
% 0.13/0.37 ![X0]: (~ssList(cons(X0,nil))|singletonP(cons(X0,nil))|~ssItem(X0))),
% 0.13/0.37 inference(destructive_equality_resolution,[status(esa)],[f118])).
% 0.13/0.37 fof(f462,plain,(
% 0.13/0.37 ![X0,X1,X2]: (~ssList(app(app(X0,X1),X2))|~ssList(X1)|segmentP(app(app(X0,X1),X2),X1)|~ssList(X0)|~ssList(X2))),
% 0.13/0.37 inference(destructive_equality_resolution,[status(esa)],[f137])).
% 0.13/0.37 fof(f486,plain,(
% 0.13/0.37 ![X0]: (~pd0_0(X0,nil))),
% 0.13/0.37 inference(destructive_equality_resolution,[status(esa)],[f437])).
% 0.13/0.37 fof(f490,plain,(
% 0.13/0.37 ![X0]: (~ssItem(X0)|neq(X0,sk0_0)|X0=sk0_0)),
% 0.13/0.37 inference(resolution,[status(thm)],[f103,f101])).
% 0.13/0.37 fof(f492,plain,(
% 0.13/0.37 ~neq(sk0_0,sk0_0)),
% 0.13/0.37 inference(resolution,[status(thm)],[f103,f457])).
% 0.13/0.37 fof(f496,plain,(
% 0.13/0.37 ~nil=sk0_47|spl0_1),
% 0.13/0.37 inference(forward_demodulation,[status(thm)],[f425,f443])).
% 0.13/0.37 fof(f497,plain,(
% 0.13/0.37 nil=sk0_48|~spl0_2),
% 0.13/0.37 inference(resolution,[status(thm)],[f436,f446])).
% 0.13/0.37 fof(f498,plain,(
% 0.13/0.37 pd0_0(nil,sk0_47)|~spl0_2),
% 0.13/0.37 inference(backward_demodulation,[status(thm)],[f497,f446])).
% 0.13/0.37 fof(f499,plain,(
% 0.13/0.37 nil=sk0_50|~spl0_2),
% 0.13/0.37 inference(backward_demodulation,[status(thm)],[f497,f424])).
% 0.13/0.37 fof(f501,plain,(
% 0.13/0.37 app(app(sk0_51,sk0_47),sk0_52)=sk0_50),
% 0.13/0.37 inference(forward_demodulation,[status(thm)],[f425,f428])).
% 0.13/0.37 fof(f503,plain,(
% 0.13/0.37 spl0_5 <=> ssList(nil)),
% 0.13/0.37 introduced(split_symbol_definition)).
% 0.13/0.37 fof(f505,plain,(
% 0.13/0.37 ~ssList(nil)|spl0_5),
% 0.13/0.37 inference(component_clause,[status(thm)],[f503])).
% 0.13/0.37 fof(f506,plain,(
% 0.13/0.37 spl0_6 <=> ssList(sk0_47)),
% 0.13/0.37 introduced(split_symbol_definition)).
% 0.13/0.37 fof(f508,plain,(
% 0.13/0.37 ~ssList(sk0_47)|spl0_6),
% 0.13/0.37 inference(component_clause,[status(thm)],[f506])).
% 0.13/0.37 fof(f509,plain,(
% 0.13/0.37 spl0_7 <=> segmentP(app(app(sk0_51,sk0_47),sk0_52),sk0_47)),
% 0.13/0.37 introduced(split_symbol_definition)).
% 0.13/0.37 fof(f510,plain,(
% 0.13/0.37 segmentP(app(app(sk0_51,sk0_47),sk0_52),sk0_47)|~spl0_7),
% 0.13/0.37 inference(component_clause,[status(thm)],[f509])).
% 0.13/0.37 fof(f512,plain,(
% 0.13/0.37 spl0_8 <=> ssList(sk0_51)),
% 0.13/0.37 introduced(split_symbol_definition)).
% 0.13/0.37 fof(f514,plain,(
% 0.13/0.37 ~ssList(sk0_51)|spl0_8),
% 0.13/0.37 inference(component_clause,[status(thm)],[f512])).
% 0.13/0.37 fof(f515,plain,(
% 0.13/0.37 spl0_9 <=> ssList(sk0_52)),
% 0.13/0.37 introduced(split_symbol_definition)).
% 0.13/0.37 fof(f517,plain,(
% 0.13/0.37 ~ssList(sk0_52)|spl0_9),
% 0.13/0.37 inference(component_clause,[status(thm)],[f515])).
% 0.13/0.37 fof(f528,plain,(
% 0.13/0.37 $false|spl0_8),
% 0.13/0.37 inference(forward_subsumption_resolution,[status(thm)],[f514,f426])).
% 0.13/0.37 fof(f529,plain,(
% 0.13/0.37 spl0_8),
% 0.13/0.37 inference(contradiction_clause,[status(thm)],[f528])).
% 0.13/0.37 fof(f530,plain,(
% 0.13/0.37 $false|spl0_6),
% 0.13/0.37 inference(forward_subsumption_resolution,[status(thm)],[f508,f420])).
% 0.13/0.37 fof(f531,plain,(
% 0.13/0.37 spl0_6),
% 0.13/0.37 inference(contradiction_clause,[status(thm)],[f530])).
% 0.13/0.37 fof(f532,plain,(
% 0.13/0.37 $false|spl0_5),
% 0.13/0.37 inference(forward_subsumption_resolution,[status(thm)],[f505,f223])).
% 0.13/0.37 fof(f533,plain,(
% 0.13/0.37 spl0_5),
% 0.13/0.37 inference(contradiction_clause,[status(thm)],[f532])).
% 0.13/0.37 fof(f534,plain,(
% 0.13/0.37 $false|spl0_9),
% 0.13/0.37 inference(forward_subsumption_resolution,[status(thm)],[f517,f427])).
% 0.13/0.37 fof(f535,plain,(
% 0.13/0.37 spl0_9),
% 0.13/0.37 inference(contradiction_clause,[status(thm)],[f534])).
% 0.13/0.37 fof(f536,plain,(
% 0.13/0.37 spl0_12 <=> ssList(sk0_48)),
% 0.13/0.37 introduced(split_symbol_definition)).
% 0.13/0.37 fof(f538,plain,(
% 0.13/0.37 ~ssList(sk0_48)|spl0_12),
% 0.13/0.37 inference(component_clause,[status(thm)],[f536])).
% 0.13/0.37 fof(f539,plain,(
% 0.13/0.37 spl0_13 <=> segmentP(sk0_47,sk0_48)),
% 0.13/0.37 introduced(split_symbol_definition)).
% 0.13/0.37 fof(f541,plain,(
% 0.13/0.37 ~segmentP(sk0_47,sk0_48)|spl0_13),
% 0.13/0.37 inference(component_clause,[status(thm)],[f539])).
% 0.13/0.37 fof(f542,plain,(
% 0.13/0.37 ~ssList(sk0_48)|~neq(sk0_48,nil)|~segmentP(sk0_47,sk0_48)|~ssList(sk0_48)|~spl0_4),
% 0.13/0.37 inference(resolution,[status(thm)],[f453,f319])).
% 0.13/0.37 fof(f543,plain,(
% 0.13/0.37 ~spl0_12|~spl0_3|~spl0_13|~spl0_4),
% 0.13/0.37 inference(split_clause,[status(thm)],[f542,f536,f448,f539,f452])).
% 0.13/0.37 fof(f544,plain,(
% 0.13/0.37 spl0_14 <=> neq(sk0_47,nil)),
% 0.13/0.37 introduced(split_symbol_definition)).
% 0.13/0.37 fof(f546,plain,(
% 0.13/0.37 ~neq(sk0_47,nil)|spl0_14),
% 0.13/0.37 inference(component_clause,[status(thm)],[f544])).
% 0.13/0.37 fof(f561,plain,(
% 0.13/0.37 $false|spl0_12),
% 0.13/0.37 inference(forward_subsumption_resolution,[status(thm)],[f421,f538])).
% 0.13/0.37 fof(f562,plain,(
% 0.13/0.37 spl0_12),
% 0.13/0.37 inference(contradiction_clause,[status(thm)],[f561])).
% 0.13/0.37 fof(f563,plain,(
% 0.13/0.37 app(app(sk0_51,sk0_47),sk0_52)=sk0_48),
% 0.13/0.37 inference(forward_demodulation,[status(thm)],[f424,f501])).
% 0.13/0.37 fof(f564,plain,(
% 0.13/0.37 ~ssList(sk0_48)|~ssList(sk0_47)|segmentP(app(app(sk0_51,sk0_47),sk0_52),sk0_47)|~ssList(sk0_51)|~ssList(sk0_52)),
% 0.13/0.37 inference(paramodulation,[status(thm)],[f563,f462])).
% 0.13/0.37 fof(f565,plain,(
% 0.13/0.37 ~spl0_12|~spl0_6|spl0_7|~spl0_8|~spl0_9),
% 0.13/0.37 inference(split_clause,[status(thm)],[f564,f536,f506,f509,f512,f515])).
% 0.13/0.37 fof(f571,plain,(
% 0.13/0.37 segmentP(sk0_48,sk0_47)|~spl0_7),
% 0.13/0.37 inference(forward_demodulation,[status(thm)],[f563,f510])).
% 0.13/0.37 fof(f572,plain,(
% 0.13/0.37 spl0_17 <=> segmentP(sk0_47,sk0_47)),
% 0.13/0.37 introduced(split_symbol_definition)).
% 0.13/0.37 fof(f574,plain,(
% 0.13/0.37 ~segmentP(sk0_47,sk0_47)|spl0_17),
% 0.13/0.37 inference(component_clause,[status(thm)],[f572])).
% 0.13/0.37 fof(f575,plain,(
% 0.13/0.37 ~ssList(sk0_47)|~neq(sk0_47,nil)|~segmentP(sk0_47,sk0_47)|~spl0_7|~spl0_4),
% 0.13/0.37 inference(resolution,[status(thm)],[f571,f453])).
% 0.13/0.37 fof(f576,plain,(
% 0.13/0.37 ~spl0_6|~spl0_14|~spl0_17|~spl0_7|~spl0_4),
% 0.13/0.37 inference(split_clause,[status(thm)],[f575,f506,f544,f572,f509,f452])).
% 0.13/0.37 fof(f579,plain,(
% 0.13/0.37 spl0_18 <=> sk0_47=nil),
% 0.13/0.37 introduced(split_symbol_definition)).
% 0.13/0.37 fof(f580,plain,(
% 0.13/0.37 sk0_47=nil|~spl0_18),
% 0.13/0.37 inference(component_clause,[status(thm)],[f579])).
% 0.13/0.37 fof(f582,plain,(
% 0.13/0.37 ~ssList(sk0_47)|~ssList(nil)|sk0_47=nil|spl0_14),
% 0.13/0.37 inference(resolution,[status(thm)],[f220,f546])).
% 0.13/0.37 fof(f583,plain,(
% 0.13/0.37 ~spl0_6|~spl0_5|spl0_18|spl0_14),
% 0.13/0.37 inference(split_clause,[status(thm)],[f582,f506,f503,f579,f544])).
% 0.13/0.37 fof(f595,plain,(
% 0.13/0.37 spl0_22 <=> sk0_0=sk0_0),
% 0.13/0.37 introduced(split_symbol_definition)).
% 0.13/0.37 fof(f600,plain,(
% 0.13/0.37 $false|spl0_1|~spl0_18),
% 0.13/0.37 inference(forward_subsumption_resolution,[status(thm)],[f580,f496])).
% 0.13/0.37 fof(f601,plain,(
% 0.13/0.37 spl0_1|~spl0_18),
% 0.13/0.37 inference(contradiction_clause,[status(thm)],[f600])).
% 0.13/0.37 fof(f602,plain,(
% 0.13/0.37 nil=sk0_48|~spl0_0),
% 0.13/0.37 inference(forward_demodulation,[status(thm)],[f424,f439])).
% 0.13/0.37 fof(f604,plain,(
% 0.13/0.37 segmentP(nil,sk0_47)|~spl0_0|~spl0_7),
% 0.13/0.37 inference(backward_demodulation,[status(thm)],[f602,f571])).
% 0.13/0.37 fof(f606,plain,(
% 0.13/0.37 ~segmentP(sk0_47,nil)|~spl0_0|spl0_13),
% 0.13/0.37 inference(backward_demodulation,[status(thm)],[f602,f541])).
% 0.13/0.37 fof(f614,plain,(
% 0.13/0.37 app(nil,sk0_52)=sk0_52),
% 0.13/0.37 inference(resolution,[status(thm)],[f249,f427])).
% 0.13/0.37 fof(f615,plain,(
% 0.13/0.37 app(nil,sk0_51)=sk0_51),
% 0.13/0.37 inference(resolution,[status(thm)],[f249,f426])).
% 0.13/0.37 fof(f616,plain,(
% 0.13/0.37 app(nil,nil)=nil),
% 0.13/0.37 inference(resolution,[status(thm)],[f249,f223])).
% 0.13/0.37 fof(f617,plain,(
% 0.13/0.37 app(nil,sk0_47)=sk0_47),
% 0.13/0.37 inference(resolution,[status(thm)],[f249,f420])).
% 0.13/0.37 fof(f618,plain,(
% 0.13/0.37 spl0_23 <=> ~ssList(app(sk0_52,X0))|segmentP(app(app(nil,sk0_52),X0),sk0_52)|~ssList(X0)),
% 0.13/0.37 introduced(split_symbol_definition)).
% 0.13/0.37 fof(f621,plain,(
% 0.13/0.37 ![X0]: (~ssList(app(sk0_52,X0))|~ssList(sk0_52)|segmentP(app(app(nil,sk0_52),X0),sk0_52)|~ssList(nil)|~ssList(X0))),
% 0.13/0.37 inference(paramodulation,[status(thm)],[f614,f462])).
% 0.13/0.37 fof(f622,plain,(
% 0.13/0.37 spl0_23|~spl0_9|~spl0_5),
% 0.13/0.37 inference(split_clause,[status(thm)],[f621,f618,f515,f503])).
% 0.13/0.37 fof(f624,plain,(
% 0.13/0.37 spl0_24 <=> ~ssList(app(sk0_51,X0))|segmentP(app(app(nil,sk0_51),X0),sk0_51)|~ssList(X0)),
% 0.13/0.37 introduced(split_symbol_definition)).
% 0.13/0.37 fof(f627,plain,(
% 0.13/0.37 ![X0]: (~ssList(app(sk0_51,X0))|~ssList(sk0_51)|segmentP(app(app(nil,sk0_51),X0),sk0_51)|~ssList(nil)|~ssList(X0))),
% 0.13/0.37 inference(paramodulation,[status(thm)],[f615,f462])).
% 0.13/0.37 fof(f628,plain,(
% 0.13/0.37 spl0_24|~spl0_8|~spl0_5),
% 0.13/0.37 inference(split_clause,[status(thm)],[f627,f624,f512,f503])).
% 0.13/0.37 fof(f630,plain,(
% 0.13/0.37 spl0_25 <=> ~ssList(app(sk0_47,X0))|segmentP(app(app(nil,sk0_47),X0),sk0_47)|~ssList(X0)),
% 0.13/0.37 introduced(split_symbol_definition)).
% 0.13/0.37 fof(f633,plain,(
% 0.13/0.37 ![X0]: (~ssList(app(sk0_47,X0))|~ssList(sk0_47)|segmentP(app(app(nil,sk0_47),X0),sk0_47)|~ssList(nil)|~ssList(X0))),
% 0.13/0.37 inference(paramodulation,[status(thm)],[f617,f462])).
% 0.13/0.37 fof(f634,plain,(
% 0.13/0.37 spl0_25|~spl0_6|~spl0_5),
% 0.13/0.37 inference(split_clause,[status(thm)],[f633,f630,f506,f503])).
% 0.13/0.37 fof(f637,plain,(
% 0.13/0.37 spl0_26 <=> ~ssList(app(nil,X0))|segmentP(app(app(nil,nil),X0),nil)|~ssList(X0)),
% 0.13/0.37 introduced(split_symbol_definition)).
% 0.13/0.37 fof(f640,plain,(
% 0.13/0.37 ![X0]: (~ssList(app(nil,X0))|~ssList(nil)|segmentP(app(app(nil,nil),X0),nil)|~ssList(nil)|~ssList(X0))),
% 0.13/0.37 inference(paramodulation,[status(thm)],[f616,f462])).
% 0.13/0.37 fof(f641,plain,(
% 0.13/0.37 spl0_26|~spl0_5),
% 0.13/0.37 inference(split_clause,[status(thm)],[f640,f637,f503])).
% 0.13/0.37 fof(f646,plain,(
% 0.13/0.37 app(sk0_52,nil)=sk0_52),
% 0.13/0.37 inference(resolution,[status(thm)],[f389,f427])).
% 0.13/0.37 fof(f647,plain,(
% 0.13/0.37 app(sk0_51,nil)=sk0_51),
% 0.13/0.37 inference(resolution,[status(thm)],[f389,f426])).
% 0.13/0.37 fof(f649,plain,(
% 0.13/0.37 app(sk0_47,nil)=sk0_47),
% 0.13/0.37 inference(resolution,[status(thm)],[f389,f420])).
% 0.13/0.37 fof(f650,plain,(
% 0.13/0.37 spl0_27 <=> ~ssList(app(sk0_52,X0))|segmentP(app(app(sk0_52,nil),X0),nil)|~ssList(X0)),
% 0.13/0.37 introduced(split_symbol_definition)).
% 0.13/0.37 fof(f653,plain,(
% 0.13/0.37 ![X0]: (~ssList(app(sk0_52,X0))|~ssList(nil)|segmentP(app(app(sk0_52,nil),X0),nil)|~ssList(sk0_52)|~ssList(X0))),
% 0.13/0.37 inference(paramodulation,[status(thm)],[f646,f462])).
% 0.13/0.37 fof(f654,plain,(
% 0.13/0.37 spl0_27|~spl0_5|~spl0_9),
% 0.13/0.37 inference(split_clause,[status(thm)],[f653,f650,f503,f515])).
% 0.13/0.37 fof(f656,plain,(
% 0.13/0.37 spl0_28 <=> ~ssList(app(sk0_51,X0))|segmentP(app(app(sk0_51,nil),X0),nil)|~ssList(X0)),
% 0.13/0.37 introduced(split_symbol_definition)).
% 0.13/0.37 fof(f659,plain,(
% 0.13/0.37 ![X0]: (~ssList(app(sk0_51,X0))|~ssList(nil)|segmentP(app(app(sk0_51,nil),X0),nil)|~ssList(sk0_51)|~ssList(X0))),
% 0.13/0.37 inference(paramodulation,[status(thm)],[f647,f462])).
% 0.13/0.37 fof(f660,plain,(
% 0.13/0.37 spl0_28|~spl0_5|~spl0_8),
% 0.13/0.37 inference(split_clause,[status(thm)],[f659,f656,f503,f512])).
% 0.13/0.37 fof(f662,plain,(
% 0.13/0.37 spl0_29 <=> ~ssList(app(sk0_47,X0))|segmentP(app(app(sk0_47,nil),X0),nil)|~ssList(X0)),
% 0.13/0.37 introduced(split_symbol_definition)).
% 0.13/0.37 fof(f665,plain,(
% 0.13/0.37 ![X0]: (~ssList(app(sk0_47,X0))|~ssList(nil)|segmentP(app(app(sk0_47,nil),X0),nil)|~ssList(sk0_47)|~ssList(X0))),
% 0.13/0.37 inference(paramodulation,[status(thm)],[f649,f462])).
% 0.13/0.37 fof(f666,plain,(
% 0.13/0.37 spl0_29|~spl0_5|~spl0_6),
% 0.13/0.37 inference(split_clause,[status(thm)],[f665,f662,f503,f506])).
% 0.13/0.37 fof(f711,plain,(
% 0.13/0.37 segmentP(nil,nil)|~spl0_18|~spl0_0|~spl0_7),
% 0.13/0.37 inference(forward_demodulation,[status(thm)],[f580,f604])).
% 0.13/0.37 fof(f720,plain,(
% 0.13/0.37 ~segmentP(nil,nil)|~spl0_18|~spl0_0|spl0_13),
% 0.13/0.37 inference(forward_demodulation,[status(thm)],[f580,f606])).
% 0.13/0.37 fof(f721,plain,(
% 0.13/0.37 $false|~spl0_7|~spl0_18|~spl0_0|spl0_13),
% 0.13/0.37 inference(forward_subsumption_resolution,[status(thm)],[f720,f711])).
% 0.13/0.37 fof(f722,plain,(
% 0.13/0.37 ~spl0_7|~spl0_18|~spl0_0|spl0_13),
% 0.13/0.37 inference(contradiction_clause,[status(thm)],[f721])).
% 0.13/0.37 fof(f727,plain,(
% 0.13/0.37 ~ssList(sk0_47)|spl0_17),
% 0.13/0.37 inference(resolution,[status(thm)],[f574,f319])).
% 0.13/0.37 fof(f728,plain,(
% 0.13/0.37 ~spl0_6|spl0_17),
% 0.13/0.37 inference(split_clause,[status(thm)],[f727,f506,f572])).
% 0.13/0.37 fof(f744,plain,(
% 0.13/0.37 spl0_31 <=> nil=nil),
% 0.13/0.37 introduced(split_symbol_definition)).
% 0.13/0.37 fof(f763,plain,(
% 0.13/0.37 ~ssList(sk0_47)|nil=sk0_47|~spl0_0|~spl0_7),
% 0.13/0.37 inference(resolution,[status(thm)],[f326,f604])).
% 0.13/0.37 fof(f764,plain,(
% 0.13/0.37 ~spl0_6|spl0_18|~spl0_0|~spl0_7),
% 0.13/0.37 inference(split_clause,[status(thm)],[f763,f506,f579,f438,f509])).
% 0.13/0.37 fof(f765,plain,(
% 0.13/0.37 ~ssList(nil)|nil=nil|~ssList(nil)),
% 0.13/0.37 inference(resolution,[status(thm)],[f326,f323])).
% 0.13/0.37 fof(f766,plain,(
% 0.13/0.37 ~spl0_5|spl0_31),
% 0.13/0.37 inference(split_clause,[status(thm)],[f765,f503,f744])).
% 0.13/0.37 fof(f769,plain,(
% 0.13/0.37 spl0_0|~spl0_2),
% 0.13/0.37 inference(split_clause,[status(thm)],[f499,f438,f445])).
% 0.13/0.37 fof(f774,plain,(
% 0.13/0.37 spl0_32 <=> ssItem(sk0_0)),
% 0.13/0.37 introduced(split_symbol_definition)).
% 0.13/0.37 fof(f776,plain,(
% 0.13/0.37 ~ssItem(sk0_0)|spl0_32),
% 0.13/0.37 inference(component_clause,[status(thm)],[f774])).
% 0.13/0.37 fof(f777,plain,(
% 0.13/0.37 ~ssItem(sk0_0)|sk0_0=sk0_0),
% 0.13/0.37 inference(resolution,[status(thm)],[f490,f492])).
% 0.13/0.37 fof(f778,plain,(
% 0.13/0.37 ~spl0_32|spl0_22),
% 0.13/0.37 inference(split_clause,[status(thm)],[f777,f774,f595])).
% 0.13/0.37 fof(f781,plain,(
% 0.13/0.37 $false|spl0_32),
% 0.13/0.37 inference(forward_subsumption_resolution,[status(thm)],[f776,f103])).
% 0.13/0.37 fof(f782,plain,(
% 0.13/0.37 spl0_32),
% 0.13/0.37 inference(contradiction_clause,[status(thm)],[f781])).
% 0.13/0.37 fof(f806,plain,(
% 0.13/0.37 spl0_33 <=> singletonP(cons(X0,nil))|~ssItem(X0)|~ssItem(X0)),
% 0.13/0.37 introduced(split_symbol_definition)).
% 0.13/0.37 fof(f809,plain,(
% 0.13/0.37 ![X0]: (singletonP(cons(X0,nil))|~ssItem(X0)|~ssList(nil)|~ssItem(X0))),
% 0.13/0.37 inference(resolution,[status(thm)],[f459,f222])).
% 0.13/0.37 fof(f810,plain,(
% 0.13/0.37 spl0_33|~spl0_5),
% 0.13/0.37 inference(split_clause,[status(thm)],[f809,f806,f503])).
% 0.13/0.37 fof(f812,plain,(
% 0.13/0.37 spl0_34 <=> ~ssList(X0)|ssList(sk0_5(nil,X0))|~ssList(X0)),
% 0.13/0.37 introduced(split_symbol_definition)).
% 0.13/0.37 fof(f815,plain,(
% 0.13/0.37 ![X0]: (~ssList(X0)|~ssList(nil)|ssList(sk0_5(nil,X0))|~ssList(X0))),
% 0.13/0.37 inference(resolution,[status(thm)],[f122,f295])).
% 0.13/0.37 fof(f816,plain,(
% 0.13/0.37 spl0_34|~spl0_5),
% 0.13/0.37 inference(split_clause,[status(thm)],[f815,f812,f503])).
% 0.13/0.37 fof(f820,plain,(
% 0.13/0.37 spl0_35 <=> ~ssList(X0)|app(nil,sk0_5(nil,X0))=X0|~ssList(X0)),
% 0.13/0.37 introduced(split_symbol_definition)).
% 0.13/0.37 fof(f823,plain,(
% 0.13/0.37 ![X0]: (~ssList(X0)|~ssList(nil)|app(nil,sk0_5(nil,X0))=X0|~ssList(X0))),
% 0.13/0.37 inference(resolution,[status(thm)],[f123,f295])).
% 0.13/0.37 fof(f824,plain,(
% 0.13/0.37 spl0_35|~spl0_5),
% 0.13/0.37 inference(split_clause,[status(thm)],[f823,f820,f503])).
% 0.13/0.37 fof(f849,plain,(
% 0.13/0.37 pd0_0(nil,nil)|~spl0_18|~spl0_2),
% 0.13/0.37 inference(backward_demodulation,[status(thm)],[f580,f498])).
% 0.13/0.37 fof(f850,plain,(
% 0.13/0.37 $false|~spl0_18|~spl0_2),
% 0.13/0.37 inference(forward_subsumption_resolution,[status(thm)],[f849,f486])).
% 0.13/0.37 fof(f851,plain,(
% 0.13/0.37 ~spl0_18|~spl0_2),
% 0.13/0.37 inference(contradiction_clause,[status(thm)],[f850])).
% 0.13/0.37 fof(f852,plain,(
% 0.13/0.37 $false),
% 0.13/0.37 inference(sat_refutation,[status(thm)],[f444,f451,f455,f529,f531,f533,f535,f543,f562,f565,f576,f583,f601,f622,f628,f634,f641,f654,f660,f666,f722,f728,f764,f766,f769,f778,f782,f810,f816,f824,f851])).
% 0.13/0.37 % SZS output end CNFRefutation for theBenchmark.p
% 0.13/0.38 % Elapsed time: 0.037789 seconds
% 0.13/0.38 % CPU time: 0.103295 seconds
% 0.13/0.38 % Memory used: 16.525 MB
%------------------------------------------------------------------------------