TSTP Solution File: SWC100+1 by Drodi---3.5.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SWC100+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n009.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 12:39:14 EDT 2023
% Result : Theorem 0.08s 0.31s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09 % Problem : SWC100+1 : TPTP v8.1.2. Released v2.4.0.
% 0.02/0.09 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.08/0.29 % Computer : n009.cluster.edu
% 0.08/0.29 % Model : x86_64 x86_64
% 0.08/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.29 % Memory : 8042.1875MB
% 0.08/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.29 % CPULimit : 300
% 0.08/0.29 % WCLimit : 300
% 0.08/0.29 % DateTime : Tue May 30 11:19:46 EDT 2023
% 0.08/0.29 % CPUTime :
% 0.08/0.30 % Drodi V3.5.1
% 0.08/0.31 % Refutation found
% 0.08/0.31 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/0.31 % SZS output start CNFRefutation for theBenchmark
% 0.08/0.31 fof(f3,axiom,(
% 0.08/0.31 (! [U] :( ssList(U)=> (! [V] :( ssItem(V)=> ( memberP(U,V)<=> (? [W] :( ssList(W)& (? [X] :( ssList(X)& app(W,cons(V,X)) = U ) )) )) ) )) )),
% 0.08/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.31 fof(f4,axiom,(
% 0.08/0.31 (! [U] :( ssList(U)=> ( singletonP(U)<=> (? [V] :( ssItem(V)& cons(V,nil) = U ) )) ) )),
% 0.08/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.31 fof(f5,axiom,(
% 0.08/0.31 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> ( frontsegP(U,V)<=> (? [W] :( ssList(W)& app(V,W) = U ) )) ) )) )),
% 0.08/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.31 fof(f15,axiom,(
% 0.08/0.31 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> ( neq(U,V)<=> U != V ) ) )) )),
% 0.08/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.31 fof(f16,axiom,(
% 0.08/0.31 (! [U] :( ssList(U)=> (! [V] :( ssItem(V)=> ssList(cons(V,U)) ) )) )),
% 0.08/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.31 fof(f17,axiom,(
% 0.08/0.31 ssList(nil) ),
% 0.08/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.31 fof(f19,axiom,(
% 0.08/0.31 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssItem(W)=> (! [X] :( ssItem(X)=> ( cons(W,U) = cons(X,V)=> ( W = X& V = U ) ) ) )) )) )) )),
% 0.08/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.31 fof(f26,axiom,(
% 0.08/0.31 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> ssList(app(U,V)) ) )) )),
% 0.08/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.31 fof(f40,axiom,(
% 0.08/0.31 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> ( ( frontsegP(U,V)& frontsegP(V,W) )=> frontsegP(U,W) ) ) )) )) )),
% 0.08/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.31 fof(f45,axiom,(
% 0.08/0.31 (! [U] :( ssList(U)=> frontsegP(U,nil) ) )),
% 0.08/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.31 fof(f46,axiom,(
% 0.08/0.31 (! [U] :( ssList(U)=> ( frontsegP(nil,U)<=> nil = U ) ) )),
% 0.08/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.31 fof(f83,axiom,(
% 0.08/0.31 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> ( nil = app(U,V)<=> ( nil = V& nil = U ) ) ) )) )),
% 0.08/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.31 fof(f96,conjecture,(
% 0.08/0.31 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> (! [X] :( ssList(X)=> ( V != X| U != W| (! [Y] :( ssList(Y)=> ( app(W,Y) != X| ~ strictorderedP(W)| (? [Z] :( ssItem(Z)& (? [X1] :( ssList(X1)& app(cons(Z,nil),X1) = Y& (? [X2] :( ssItem(X2)& (? [X3] :( ssList(X3)& app(X3,cons(X2,nil)) = W& lt(X2,Z) ) )) )) )) )) ))| ( nil != X& nil = W )| ( ( nil != V| nil = U )& ( ~ neq(V,nil)| ( neq(U,nil)& frontsegP(V,U) ) ) ) ) ) )) )) )) )),
% 0.08/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.31 fof(f97,negated_conjecture,(
% 0.08/0.31 ~((! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> (! [X] :( ssList(X)=> ( V != X| U != W| (! [Y] :( ssList(Y)=> ( app(W,Y) != X| ~ strictorderedP(W)| (? [Z] :( ssItem(Z)& (? [X1] :( ssList(X1)& app(cons(Z,nil),X1) = Y& (? [X2] :( ssItem(X2)& (? [X3] :( ssList(X3)& app(X3,cons(X2,nil)) = W& lt(X2,Z) ) )) )) )) )) ))| ( nil != X& nil = W )| ( ( nil != V| nil = U )& ( ~ neq(V,nil)| ( neq(U,nil)& frontsegP(V,U) ) ) ) ) ) )) )) )) ))),
% 0.08/0.31 inference(negated_conjecture,[status(cth)],[f96])).
% 0.08/0.31 fof(f106,plain,(
% 0.08/0.31 ![U]: (~ssList(U)|(![V]: (~ssItem(V)|(memberP(U,V)<=>(?[W]: (ssList(W)&(?[X]: (ssList(X)&app(W,cons(V,X))=U))))))))),
% 0.08/0.31 inference(pre_NNF_transformation,[status(esa)],[f3])).
% 0.08/0.31 fof(f107,plain,(
% 0.08/0.31 ![U]: (~ssList(U)|(![V]: (~ssItem(V)|((~memberP(U,V)|(?[W]: (ssList(W)&(?[X]: (ssList(X)&app(W,cons(V,X))=U)))))&(memberP(U,V)|(![W]: (~ssList(W)|(![X]: (~ssList(X)|~app(W,cons(V,X))=U)))))))))),
% 0.08/0.31 inference(NNF_transformation,[status(esa)],[f106])).
% 0.08/0.31 fof(f108,plain,(
% 0.08/0.31 ![U]: (~ssList(U)|(![V]: (~ssItem(V)|((~memberP(U,V)|(ssList(sk0_2(V,U))&(ssList(sk0_3(V,U))&app(sk0_2(V,U),cons(V,sk0_3(V,U)))=U)))&(memberP(U,V)|(![W]: (~ssList(W)|(![X]: (~ssList(X)|~app(W,cons(V,X))=U)))))))))),
% 0.08/0.31 inference(skolemization,[status(esa)],[f107])).
% 0.08/0.31 fof(f111,plain,(
% 0.08/0.31 ![X0,X1]: (~ssList(X0)|~ssItem(X1)|~memberP(X0,X1)|app(sk0_2(X1,X0),cons(X1,sk0_3(X1,X0)))=X0)),
% 0.08/0.31 inference(cnf_transformation,[status(esa)],[f108])).
% 0.08/0.31 fof(f113,plain,(
% 0.08/0.31 ![U]: (~ssList(U)|(singletonP(U)<=>(?[V]: (ssItem(V)&cons(V,nil)=U))))),
% 0.08/0.31 inference(pre_NNF_transformation,[status(esa)],[f4])).
% 0.08/0.31 fof(f114,plain,(
% 0.08/0.31 ![U]: (~ssList(U)|((~singletonP(U)|(?[V]: (ssItem(V)&cons(V,nil)=U)))&(singletonP(U)|(![V]: (~ssItem(V)|~cons(V,nil)=U)))))),
% 0.08/0.31 inference(NNF_transformation,[status(esa)],[f113])).
% 0.08/0.31 fof(f115,plain,(
% 0.08/0.31 ![U]: (~ssList(U)|((~singletonP(U)|(ssItem(sk0_4(U))&cons(sk0_4(U),nil)=U))&(singletonP(U)|(![V]: (~ssItem(V)|~cons(V,nil)=U)))))),
% 0.08/0.31 inference(skolemization,[status(esa)],[f114])).
% 0.08/0.31 fof(f117,plain,(
% 0.08/0.31 ![X0]: (~ssList(X0)|~singletonP(X0)|cons(sk0_4(X0),nil)=X0)),
% 0.08/0.31 inference(cnf_transformation,[status(esa)],[f115])).
% 0.08/0.31 fof(f118,plain,(
% 0.08/0.31 ![X0,X1]: (~ssList(X0)|singletonP(X0)|~ssItem(X1)|~cons(X1,nil)=X0)),
% 0.08/0.31 inference(cnf_transformation,[status(esa)],[f115])).
% 0.08/0.31 fof(f119,plain,(
% 0.08/0.31 ![U]: (~ssList(U)|(![V]: (~ssList(V)|(frontsegP(U,V)<=>(?[W]: (ssList(W)&app(V,W)=U))))))),
% 0.08/0.31 inference(pre_NNF_transformation,[status(esa)],[f5])).
% 0.08/0.31 fof(f120,plain,(
% 0.08/0.31 ![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)))))))),
% 0.08/0.31 inference(NNF_transformation,[status(esa)],[f119])).
% 0.08/0.31 fof(f121,plain,(
% 0.08/0.31 ![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)))))))),
% 0.08/0.31 inference(skolemization,[status(esa)],[f120])).
% 0.08/0.31 fof(f124,plain,(
% 0.08/0.31 ![X0,X1,X2]: (~ssList(X0)|~ssList(X1)|frontsegP(X0,X1)|~ssList(X2)|~app(X1,X2)=X0)),
% 0.08/0.31 inference(cnf_transformation,[status(esa)],[f121])).
% 0.08/0.31 fof(f217,plain,(
% 0.08/0.31 ![U]: (~ssList(U)|(![V]: (~ssList(V)|(neq(U,V)<=>~U=V))))),
% 0.08/0.31 inference(pre_NNF_transformation,[status(esa)],[f15])).
% 0.08/0.31 fof(f218,plain,(
% 0.08/0.31 ![U]: (~ssList(U)|(![V]: (~ssList(V)|((~neq(U,V)|~U=V)&(neq(U,V)|U=V)))))),
% 0.08/0.31 inference(NNF_transformation,[status(esa)],[f217])).
% 0.08/0.31 fof(f220,plain,(
% 0.08/0.31 ![X0,X1]: (~ssList(X0)|~ssList(X1)|neq(X0,X1)|X0=X1)),
% 0.08/0.31 inference(cnf_transformation,[status(esa)],[f218])).
% 0.08/0.31 fof(f221,plain,(
% 0.08/0.31 ![U]: (~ssList(U)|(![V]: (~ssItem(V)|ssList(cons(V,U)))))),
% 0.08/0.31 inference(pre_NNF_transformation,[status(esa)],[f16])).
% 0.08/0.31 fof(f222,plain,(
% 0.08/0.31 ![X0,X1]: (~ssList(X0)|~ssItem(X1)|ssList(cons(X1,X0)))),
% 0.08/0.31 inference(cnf_transformation,[status(esa)],[f221])).
% 0.08/0.31 fof(f223,plain,(
% 0.08/0.31 ssList(nil)),
% 0.08/0.31 inference(cnf_transformation,[status(esa)],[f17])).
% 0.08/0.31 fof(f226,plain,(
% 0.08/0.31 ![U]: (~ssList(U)|(![V]: (~ssList(V)|(![W]: (~ssItem(W)|(![X]: (~ssItem(X)|(~cons(W,U)=cons(X,V)|(W=X&V=U)))))))))),
% 0.08/0.31 inference(pre_NNF_transformation,[status(esa)],[f19])).
% 0.08/0.31 fof(f227,plain,(
% 0.08/0.31 ![X0,X1,X2,X3]: (~ssList(X0)|~ssList(X1)|~ssItem(X2)|~ssItem(X3)|~cons(X2,X0)=cons(X3,X1)|X2=X3)),
% 0.08/0.31 inference(cnf_transformation,[status(esa)],[f226])).
% 0.08/0.31 fof(f244,plain,(
% 0.08/0.31 ![U]: (~ssList(U)|(![V]: (~ssList(V)|ssList(app(U,V)))))),
% 0.08/0.31 inference(pre_NNF_transformation,[status(esa)],[f26])).
% 0.08/0.31 fof(f245,plain,(
% 0.08/0.31 ![X0,X1]: (~ssList(X0)|~ssList(X1)|ssList(app(X0,X1)))),
% 0.08/0.31 inference(cnf_transformation,[status(esa)],[f244])).
% 0.08/0.31 fof(f281,plain,(
% 0.08/0.31 ![U]: (~ssList(U)|(![V]: (~ssList(V)|(![W]: (~ssList(W)|((~frontsegP(U,V)|~frontsegP(V,W))|frontsegP(U,W)))))))),
% 0.08/0.31 inference(pre_NNF_transformation,[status(esa)],[f40])).
% 0.08/0.31 fof(f282,plain,(
% 0.08/0.31 ![X0,X1,X2]: (~ssList(X0)|~ssList(X1)|~ssList(X2)|~frontsegP(X0,X1)|~frontsegP(X1,X2)|frontsegP(X0,X2))),
% 0.08/0.31 inference(cnf_transformation,[status(esa)],[f281])).
% 0.08/0.31 fof(f294,plain,(
% 0.08/0.31 ![U]: (~ssList(U)|frontsegP(U,nil))),
% 0.08/0.31 inference(pre_NNF_transformation,[status(esa)],[f45])).
% 0.08/0.31 fof(f295,plain,(
% 0.08/0.31 ![X0]: (~ssList(X0)|frontsegP(X0,nil))),
% 0.08/0.31 inference(cnf_transformation,[status(esa)],[f294])).
% 0.08/0.31 fof(f296,plain,(
% 0.08/0.31 ![U]: (~ssList(U)|(frontsegP(nil,U)<=>nil=U))),
% 0.08/0.31 inference(pre_NNF_transformation,[status(esa)],[f46])).
% 0.08/0.31 fof(f297,plain,(
% 0.08/0.31 ![U]: (~ssList(U)|((~frontsegP(nil,U)|nil=U)&(frontsegP(nil,U)|~nil=U)))),
% 0.08/0.31 inference(NNF_transformation,[status(esa)],[f296])).
% 0.08/0.31 fof(f298,plain,(
% 0.08/0.31 ![X0]: (~ssList(X0)|~frontsegP(nil,X0)|nil=X0)),
% 0.08/0.31 inference(cnf_transformation,[status(esa)],[f297])).
% 0.08/0.31 fof(f383,plain,(
% 0.08/0.31 ![U]: (~ssList(U)|(![V]: (~ssList(V)|(nil=app(U,V)<=>(nil=V&nil=U)))))),
% 0.08/0.31 inference(pre_NNF_transformation,[status(esa)],[f83])).
% 0.08/0.31 fof(f384,plain,(
% 0.08/0.31 ![U]: (~ssList(U)|(![V]: (~ssList(V)|((~nil=app(U,V)|(nil=V&nil=U))&(nil=app(U,V)|(~nil=V|~nil=U))))))),
% 0.08/0.31 inference(NNF_transformation,[status(esa)],[f383])).
% 0.08/0.31 fof(f385,plain,(
% 0.08/0.31 ![X0,X1]: (~ssList(X0)|~ssList(X1)|~nil=app(X0,X1)|nil=X1)),
% 0.08/0.31 inference(cnf_transformation,[status(esa)],[f384])).
% 0.08/0.31 fof(f415,plain,(
% 0.08/0.31 (?[U]: (ssList(U)&(?[V]: (ssList(V)&(?[W]: (ssList(W)&(?[X]: (ssList(X)&((((V=X&U=W)&(?[Y]: (ssList(Y)&((app(W,Y)=X&strictorderedP(W))&(![Z]: (~ssItem(Z)|(![X1]: ((~ssList(X1)|~app(cons(Z,nil),X1)=Y)|(![X2]: (~ssItem(X2)|(![X3]: ((~ssList(X3)|~app(X3,cons(X2,nil))=W)|~lt(X2,Z)))))))))))))&(nil=X|~nil=W))&((nil=V&~nil=U)|(neq(V,nil)&(~neq(U,nil)|~frontsegP(V,U)))))))))))))),
% 0.08/0.31 inference(pre_NNF_transformation,[status(esa)],[f97])).
% 0.08/0.31 fof(f416,plain,(
% 0.08/0.31 ![U,V]: (pd0_0(V,U)=>(nil=V&~nil=U))),
% 0.08/0.31 introduced(predicate_definition,[f415])).
% 0.08/0.31 fof(f417,plain,(
% 0.08/0.31 ?[U]: (ssList(U)&(?[V]: (ssList(V)&(?[W]: (ssList(W)&(?[X]: (ssList(X)&((((V=X&U=W)&(?[Y]: (ssList(Y)&((app(W,Y)=X&strictorderedP(W))&(![Z]: (~ssItem(Z)|(![X1]: ((~ssList(X1)|~app(cons(Z,nil),X1)=Y)|(![X2]: (~ssItem(X2)|(![X3]: ((~ssList(X3)|~app(X3,cons(X2,nil))=W)|~lt(X2,Z)))))))))))))&(nil=X|~nil=W))&(pd0_0(V,U)|(neq(V,nil)&(~neq(U,nil)|~frontsegP(V,U))))))))))))),
% 0.08/0.31 inference(formula_renaming,[status(thm)],[f415,f416])).
% 0.08/0.31 fof(f418,plain,(
% 0.08/0.31 ?[U]: (ssList(U)&(?[V]: (ssList(V)&(?[W]: (ssList(W)&(?[X]: (ssList(X)&((((V=X&U=W)&(?[Y]: (ssList(Y)&((app(W,Y)=X&strictorderedP(W))&(![Z]: (~ssItem(Z)|((![X1]: (~ssList(X1)|~app(cons(Z,nil),X1)=Y))|(![X2]: (~ssItem(X2)|((![X3]: (~ssList(X3)|~app(X3,cons(X2,nil))=W))|~lt(X2,Z)))))))))))&(nil=X|~nil=W))&(pd0_0(V,U)|(neq(V,nil)&(~neq(U,nil)|~frontsegP(V,U))))))))))))),
% 0.08/0.31 inference(miniscoping,[status(esa)],[f417])).
% 0.08/0.31 fof(f419,plain,(
% 0.08/0.31 (ssList(sk0_47)&(ssList(sk0_48)&(ssList(sk0_49)&(ssList(sk0_50)&((((sk0_48=sk0_50&sk0_47=sk0_49)&(ssList(sk0_51)&((app(sk0_49,sk0_51)=sk0_50&strictorderedP(sk0_49))&(![Z]: (~ssItem(Z)|((![X1]: (~ssList(X1)|~app(cons(Z,nil),X1)=sk0_51))|(![X2]: (~ssItem(X2)|((![X3]: (~ssList(X3)|~app(X3,cons(X2,nil))=sk0_49))|~lt(X2,Z))))))))))&(nil=sk0_50|~nil=sk0_49))&(pd0_0(sk0_48,sk0_47)|(neq(sk0_48,nil)&(~neq(sk0_47,nil)|~frontsegP(sk0_48,sk0_47)))))))))),
% 0.08/0.31 inference(skolemization,[status(esa)],[f418])).
% 0.08/0.31 fof(f420,plain,(
% 0.08/0.31 ssList(sk0_47)),
% 0.08/0.31 inference(cnf_transformation,[status(esa)],[f419])).
% 0.08/0.31 fof(f421,plain,(
% 0.08/0.31 ssList(sk0_48)),
% 0.08/0.31 inference(cnf_transformation,[status(esa)],[f419])).
% 0.08/0.31 fof(f424,plain,(
% 0.08/0.31 sk0_48=sk0_50),
% 0.08/0.31 inference(cnf_transformation,[status(esa)],[f419])).
% 0.08/0.31 fof(f425,plain,(
% 0.08/0.31 sk0_47=sk0_49),
% 0.08/0.31 inference(cnf_transformation,[status(esa)],[f419])).
% 0.08/0.31 fof(f426,plain,(
% 0.08/0.31 ssList(sk0_51)),
% 0.08/0.31 inference(cnf_transformation,[status(esa)],[f419])).
% 0.08/0.31 fof(f427,plain,(
% 0.08/0.31 app(sk0_49,sk0_51)=sk0_50),
% 0.08/0.31 inference(cnf_transformation,[status(esa)],[f419])).
% 0.08/0.31 fof(f430,plain,(
% 0.08/0.31 nil=sk0_50|~nil=sk0_49),
% 0.08/0.31 inference(cnf_transformation,[status(esa)],[f419])).
% 0.08/0.31 fof(f431,plain,(
% 0.08/0.31 pd0_0(sk0_48,sk0_47)|neq(sk0_48,nil)),
% 0.08/0.31 inference(cnf_transformation,[status(esa)],[f419])).
% 0.08/0.31 fof(f432,plain,(
% 0.08/0.31 pd0_0(sk0_48,sk0_47)|~neq(sk0_47,nil)|~frontsegP(sk0_48,sk0_47)),
% 0.08/0.31 inference(cnf_transformation,[status(esa)],[f419])).
% 0.08/0.31 fof(f433,plain,(
% 0.08/0.31 ![U,V]: (~pd0_0(V,U)|(nil=V&~nil=U))),
% 0.08/0.31 inference(pre_NNF_transformation,[status(esa)],[f416])).
% 0.08/0.31 fof(f434,plain,(
% 0.08/0.31 ![X0,X1]: (~pd0_0(X0,X1)|nil=X0)),
% 0.08/0.31 inference(cnf_transformation,[status(esa)],[f433])).
% 0.08/0.31 fof(f435,plain,(
% 0.08/0.31 ![X0,X1]: (~pd0_0(X0,X1)|~nil=X1)),
% 0.08/0.31 inference(cnf_transformation,[status(esa)],[f433])).
% 0.08/0.31 fof(f436,plain,(
% 0.08/0.31 spl0_0 <=> nil=sk0_50),
% 0.08/0.31 introduced(split_symbol_definition)).
% 0.08/0.31 fof(f437,plain,(
% 0.08/0.31 nil=sk0_50|~spl0_0),
% 0.08/0.31 inference(component_clause,[status(thm)],[f436])).
% 0.08/0.31 fof(f439,plain,(
% 0.08/0.31 spl0_1 <=> nil=sk0_49),
% 0.08/0.31 introduced(split_symbol_definition)).
% 0.08/0.31 fof(f440,plain,(
% 0.08/0.31 nil=sk0_49|~spl0_1),
% 0.08/0.31 inference(component_clause,[status(thm)],[f439])).
% 0.08/0.31 fof(f441,plain,(
% 0.08/0.31 ~nil=sk0_49|spl0_1),
% 0.08/0.31 inference(component_clause,[status(thm)],[f439])).
% 0.08/0.31 fof(f442,plain,(
% 0.08/0.31 spl0_0|~spl0_1),
% 0.08/0.31 inference(split_clause,[status(thm)],[f430,f436,f439])).
% 0.08/0.31 fof(f443,plain,(
% 0.08/0.31 spl0_2 <=> pd0_0(sk0_48,sk0_47)),
% 0.08/0.31 introduced(split_symbol_definition)).
% 0.08/0.31 fof(f444,plain,(
% 0.08/0.31 pd0_0(sk0_48,sk0_47)|~spl0_2),
% 0.08/0.31 inference(component_clause,[status(thm)],[f443])).
% 0.08/0.31 fof(f446,plain,(
% 0.08/0.31 spl0_3 <=> neq(sk0_48,nil)),
% 0.08/0.31 introduced(split_symbol_definition)).
% 0.08/0.31 fof(f447,plain,(
% 0.08/0.31 neq(sk0_48,nil)|~spl0_3),
% 0.08/0.31 inference(component_clause,[status(thm)],[f446])).
% 0.08/0.31 fof(f449,plain,(
% 0.08/0.31 spl0_2|spl0_3),
% 0.08/0.31 inference(split_clause,[status(thm)],[f431,f443,f446])).
% 0.08/0.31 fof(f450,plain,(
% 0.08/0.31 spl0_4 <=> neq(sk0_47,nil)),
% 0.08/0.31 introduced(split_symbol_definition)).
% 0.08/0.31 fof(f452,plain,(
% 0.08/0.31 ~neq(sk0_47,nil)|spl0_4),
% 0.08/0.31 inference(component_clause,[status(thm)],[f450])).
% 0.08/0.31 fof(f453,plain,(
% 0.08/0.31 spl0_5 <=> frontsegP(sk0_48,sk0_47)),
% 0.08/0.31 introduced(split_symbol_definition)).
% 0.08/0.31 fof(f454,plain,(
% 0.08/0.31 frontsegP(sk0_48,sk0_47)|~spl0_5),
% 0.08/0.31 inference(component_clause,[status(thm)],[f453])).
% 0.08/0.31 fof(f456,plain,(
% 0.08/0.31 spl0_2|~spl0_4|~spl0_5),
% 0.08/0.31 inference(split_clause,[status(thm)],[f432,f443,f450,f453])).
% 0.08/0.31 fof(f460,plain,(
% 0.08/0.31 ![X0]: (~ssList(cons(X0,nil))|singletonP(cons(X0,nil))|~ssItem(X0))),
% 0.08/0.31 inference(destructive_equality_resolution,[status(esa)],[f118])).
% 0.08/0.31 fof(f461,plain,(
% 0.08/0.31 ![X0,X1]: (~ssList(app(X0,X1))|~ssList(X0)|frontsegP(app(X0,X1),X0)|~ssList(X1))),
% 0.08/0.31 inference(destructive_equality_resolution,[status(esa)],[f124])).
% 0.08/0.31 fof(f487,plain,(
% 0.08/0.31 ![X0]: (~pd0_0(X0,nil))),
% 0.08/0.31 inference(destructive_equality_resolution,[status(esa)],[f435])).
% 0.08/0.31 fof(f491,plain,(
% 0.08/0.31 ~nil=sk0_47|spl0_1),
% 0.08/0.31 inference(forward_demodulation,[status(thm)],[f425,f441])).
% 0.08/0.31 fof(f492,plain,(
% 0.08/0.31 nil=sk0_48|~spl0_2),
% 0.08/0.31 inference(resolution,[status(thm)],[f444,f434])).
% 0.08/0.31 fof(f493,plain,(
% 0.08/0.31 pd0_0(nil,sk0_47)|~spl0_2),
% 0.08/0.31 inference(backward_demodulation,[status(thm)],[f492,f444])).
% 0.08/0.31 fof(f496,plain,(
% 0.08/0.31 app(sk0_47,sk0_51)=sk0_50),
% 0.08/0.31 inference(forward_demodulation,[status(thm)],[f425,f427])).
% 0.08/0.31 fof(f498,plain,(
% 0.08/0.31 spl0_6 <=> ssList(app(sk0_47,sk0_51))),
% 0.08/0.31 introduced(split_symbol_definition)).
% 0.08/0.31 fof(f500,plain,(
% 0.08/0.31 ~ssList(app(sk0_47,sk0_51))|spl0_6),
% 0.08/0.31 inference(component_clause,[status(thm)],[f498])).
% 0.08/0.31 fof(f501,plain,(
% 0.08/0.31 spl0_7 <=> ssList(sk0_47)),
% 0.08/0.31 introduced(split_symbol_definition)).
% 0.08/0.31 fof(f503,plain,(
% 0.08/0.31 ~ssList(sk0_47)|spl0_7),
% 0.08/0.31 inference(component_clause,[status(thm)],[f501])).
% 0.08/0.31 fof(f507,plain,(
% 0.08/0.31 spl0_9 <=> ssList(sk0_51)),
% 0.08/0.31 introduced(split_symbol_definition)).
% 0.08/0.31 fof(f509,plain,(
% 0.08/0.31 ~ssList(sk0_51)|spl0_9),
% 0.08/0.31 inference(component_clause,[status(thm)],[f507])).
% 0.08/0.31 fof(f512,plain,(
% 0.08/0.31 $false|spl0_9),
% 0.08/0.31 inference(forward_subsumption_resolution,[status(thm)],[f509,f426])).
% 0.08/0.31 fof(f513,plain,(
% 0.08/0.31 spl0_9),
% 0.08/0.31 inference(contradiction_clause,[status(thm)],[f512])).
% 0.08/0.31 fof(f514,plain,(
% 0.08/0.31 $false|spl0_7),
% 0.08/0.31 inference(forward_subsumption_resolution,[status(thm)],[f503,f420])).
% 0.08/0.31 fof(f515,plain,(
% 0.08/0.31 spl0_7),
% 0.08/0.31 inference(contradiction_clause,[status(thm)],[f514])).
% 0.08/0.31 fof(f525,plain,(
% 0.08/0.31 spl0_12 <=> sk0_47=nil),
% 0.08/0.31 introduced(split_symbol_definition)).
% 0.08/0.31 fof(f526,plain,(
% 0.08/0.31 sk0_47=nil|~spl0_12),
% 0.08/0.31 inference(component_clause,[status(thm)],[f525])).
% 0.08/0.31 fof(f530,plain,(
% 0.08/0.31 app(sk0_47,sk0_51)=sk0_48),
% 0.08/0.31 inference(forward_demodulation,[status(thm)],[f424,f496])).
% 0.08/0.31 fof(f531,plain,(
% 0.08/0.31 ~ssList(app(sk0_47,sk0_51))|~ssList(sk0_47)|frontsegP(sk0_48,sk0_47)|~ssList(sk0_51)),
% 0.08/0.31 inference(paramodulation,[status(thm)],[f530,f461])).
% 0.08/0.31 fof(f532,plain,(
% 0.08/0.31 ~spl0_6|~spl0_7|spl0_5|~spl0_9),
% 0.08/0.31 inference(split_clause,[status(thm)],[f531,f498,f501,f453,f507])).
% 0.08/0.31 fof(f533,plain,(
% 0.08/0.31 ~ssList(sk0_48)|spl0_6),
% 0.08/0.31 inference(forward_demodulation,[status(thm)],[f530,f500])).
% 0.08/0.31 fof(f534,plain,(
% 0.08/0.31 $false|spl0_6),
% 0.08/0.31 inference(forward_subsumption_resolution,[status(thm)],[f533,f421])).
% 0.08/0.31 fof(f535,plain,(
% 0.08/0.31 spl0_6),
% 0.08/0.31 inference(contradiction_clause,[status(thm)],[f534])).
% 0.08/0.31 fof(f542,plain,(
% 0.08/0.31 frontsegP(nil,sk0_47)|~spl0_2|~spl0_5),
% 0.08/0.31 inference(forward_demodulation,[status(thm)],[f492,f454])).
% 0.08/0.31 fof(f546,plain,(
% 0.08/0.31 ~ssList(sk0_47)|nil=sk0_47|~spl0_2|~spl0_5),
% 0.08/0.31 inference(resolution,[status(thm)],[f298,f542])).
% 0.08/0.31 fof(f547,plain,(
% 0.08/0.31 ~spl0_7|spl0_12|~spl0_2|~spl0_5),
% 0.08/0.31 inference(split_clause,[status(thm)],[f546,f501,f525,f443,f453])).
% 0.08/0.31 fof(f548,plain,(
% 0.08/0.31 spl0_13 <=> ssList(nil)),
% 0.08/0.31 introduced(split_symbol_definition)).
% 0.08/0.31 fof(f550,plain,(
% 0.08/0.31 ~ssList(nil)|spl0_13),
% 0.08/0.31 inference(component_clause,[status(thm)],[f548])).
% 0.08/0.31 fof(f551,plain,(
% 0.08/0.31 spl0_14 <=> nil=nil),
% 0.08/0.31 introduced(split_symbol_definition)).
% 0.08/0.31 fof(f554,plain,(
% 0.08/0.31 ~ssList(nil)|nil=nil|~ssList(nil)),
% 0.08/0.31 inference(resolution,[status(thm)],[f298,f295])).
% 0.08/0.31 fof(f555,plain,(
% 0.08/0.31 ~spl0_13|spl0_14),
% 0.08/0.31 inference(split_clause,[status(thm)],[f554,f548,f551])).
% 0.08/0.31 fof(f558,plain,(
% 0.08/0.31 $false|spl0_13),
% 0.08/0.31 inference(forward_subsumption_resolution,[status(thm)],[f550,f223])).
% 0.08/0.31 fof(f559,plain,(
% 0.08/0.31 spl0_13),
% 0.08/0.31 inference(contradiction_clause,[status(thm)],[f558])).
% 0.08/0.31 fof(f560,plain,(
% 0.08/0.31 $false|spl0_1|~spl0_12),
% 0.08/0.31 inference(forward_subsumption_resolution,[status(thm)],[f526,f491])).
% 0.08/0.31 fof(f561,plain,(
% 0.08/0.31 spl0_1|~spl0_12),
% 0.08/0.31 inference(contradiction_clause,[status(thm)],[f560])).
% 0.08/0.31 fof(f562,plain,(
% 0.08/0.31 nil=sk0_47|~spl0_1),
% 0.08/0.31 inference(forward_demodulation,[status(thm)],[f425,f440])).
% 0.08/0.31 fof(f565,plain,(
% 0.08/0.31 pd0_0(nil,nil)|~spl0_12|~spl0_2),
% 0.08/0.31 inference(backward_demodulation,[status(thm)],[f526,f493])).
% 0.08/0.31 fof(f566,plain,(
% 0.08/0.31 $false|~spl0_12|~spl0_2),
% 0.08/0.31 inference(forward_subsumption_resolution,[status(thm)],[f565,f487])).
% 0.08/0.31 fof(f567,plain,(
% 0.08/0.31 ~spl0_12|~spl0_2),
% 0.08/0.31 inference(contradiction_clause,[status(thm)],[f566])).
% 0.08/0.31 fof(f569,plain,(
% 0.08/0.31 sk0_48=nil|~spl0_0),
% 0.08/0.31 inference(forward_demodulation,[status(thm)],[f437,f424])).
% 0.08/0.31 fof(f572,plain,(
% 0.08/0.31 neq(nil,nil)|~spl0_0|~spl0_3),
% 0.08/0.31 inference(backward_demodulation,[status(thm)],[f569,f447])).
% 0.08/0.31 fof(f604,plain,(
% 0.08/0.31 spl0_18 <=> ~ssList(sk0_2(X0,nil))|~ssList(cons(X0,sk0_3(X0,nil)))|nil=cons(X0,sk0_3(X0,nil))|~ssItem(X0)|~memberP(nil,X0)),
% 0.08/0.31 introduced(split_symbol_definition)).
% 0.08/0.31 fof(f607,plain,(
% 0.08/0.31 ![X0]: (~ssList(sk0_2(X0,nil))|~ssList(cons(X0,sk0_3(X0,nil)))|nil=cons(X0,sk0_3(X0,nil))|~ssList(nil)|~ssItem(X0)|~memberP(nil,X0))),
% 0.08/0.31 inference(resolution,[status(thm)],[f385,f111])).
% 0.08/0.31 fof(f608,plain,(
% 0.08/0.31 spl0_18|~spl0_13),
% 0.08/0.31 inference(split_clause,[status(thm)],[f607,f604,f548])).
% 0.08/0.31 fof(f613,plain,(
% 0.08/0.31 spl0_19 <=> ~ssList(X0)|~ssList(X0)),
% 0.08/0.31 introduced(split_symbol_definition)).
% 0.08/0.31 fof(f614,plain,(
% 0.08/0.31 ![X0]: (~ssList(X0)|~ssList(X0)|~spl0_19)),
% 0.08/0.31 inference(component_clause,[status(thm)],[f613])).
% 0.08/0.31 fof(f616,plain,(
% 0.08/0.31 spl0_20 <=> ~ssItem(X1)|~ssItem(X1)|X1=X1),
% 0.08/0.31 introduced(split_symbol_definition)).
% 0.08/0.31 fof(f619,plain,(
% 0.08/0.31 ![X0,X1]: (~ssList(X0)|~ssList(X0)|~ssItem(X1)|~ssItem(X1)|X1=X1)),
% 0.08/0.31 inference(equality_resolution,[status(esa)],[f227])).
% 0.08/0.31 fof(f620,plain,(
% 0.08/0.31 spl0_19|spl0_20),
% 0.08/0.31 inference(split_clause,[status(thm)],[f619,f613,f616])).
% 0.08/0.31 fof(f621,plain,(
% 0.08/0.31 ![X0]: (~ssList(X0)|~spl0_19)),
% 0.08/0.31 inference(duplicate_literals_removal,[status(esa)],[f614])).
% 0.08/0.31 fof(f622,plain,(
% 0.08/0.31 spl0_21 <=> ~ssList(cons(X0,X1))|~singletonP(cons(X0,X1))|~ssList(X1)|~ssItem(sk0_4(cons(X0,X1)))|~ssItem(X0)|sk0_4(cons(X0,X1))=X0),
% 0.08/0.31 introduced(split_symbol_definition)).
% 0.08/0.31 fof(f625,plain,(
% 0.08/0.31 ![X0,X1]: (~ssList(cons(X0,X1))|~singletonP(cons(X0,X1))|~ssList(nil)|~ssList(X1)|~ssItem(sk0_4(cons(X0,X1)))|~ssItem(X0)|sk0_4(cons(X0,X1))=X0)),
% 0.08/0.31 inference(resolution,[status(thm)],[f117,f227])).
% 0.08/0.31 fof(f626,plain,(
% 0.08/0.31 spl0_21|~spl0_13),
% 0.08/0.31 inference(split_clause,[status(thm)],[f625,f622,f548])).
% 0.08/0.31 fof(f640,plain,(
% 0.08/0.31 spl0_24 <=> singletonP(cons(X0,nil))|~ssItem(X0)|~ssItem(X0)),
% 0.08/0.31 introduced(split_symbol_definition)).
% 0.08/0.31 fof(f643,plain,(
% 0.08/0.31 ![X0]: (singletonP(cons(X0,nil))|~ssItem(X0)|~ssList(nil)|~ssItem(X0))),
% 0.08/0.31 inference(resolution,[status(thm)],[f460,f222])).
% 0.08/0.31 fof(f644,plain,(
% 0.08/0.31 spl0_24|~spl0_13),
% 0.08/0.31 inference(split_clause,[status(thm)],[f643,f640,f548])).
% 0.08/0.31 fof(f650,plain,(
% 0.08/0.31 ~neq(nil,nil)|~spl0_1|spl0_4),
% 0.08/0.31 inference(forward_demodulation,[status(thm)],[f562,f452])).
% 0.08/0.31 fof(f658,plain,(
% 0.08/0.31 $false|~spl0_1|spl0_4|~spl0_0|~spl0_3),
% 0.08/0.31 inference(forward_subsumption_resolution,[status(thm)],[f572,f650])).
% 0.08/0.31 fof(f659,plain,(
% 0.08/0.31 ~spl0_1|spl0_4|~spl0_0|~spl0_3),
% 0.08/0.31 inference(contradiction_clause,[status(thm)],[f658])).
% 0.08/0.31 fof(f660,plain,(
% 0.08/0.31 $false|~spl0_19),
% 0.08/0.31 inference(backward_subsumption_resolution,[status(thm)],[f223,f621])).
% 0.08/0.31 fof(f661,plain,(
% 0.08/0.31 ~spl0_19),
% 0.08/0.31 inference(contradiction_clause,[status(thm)],[f660])).
% 0.08/0.31 fof(f677,plain,(
% 0.08/0.31 spl0_27 <=> ssList(sk0_48)),
% 0.13/0.53 introduced(split_symbol_definition)).
% 0.13/0.53 fof(f680,plain,(
% 0.13/0.53 ~ssList(sk0_47)|~ssList(sk0_51)|ssList(sk0_48)),
% 0.13/0.53 inference(paramodulation,[status(thm)],[f530,f245])).
% 0.13/0.53 fof(f681,plain,(
% 0.13/0.53 ~spl0_7|~spl0_9|spl0_27),
% 0.13/0.53 inference(split_clause,[status(thm)],[f680,f501,f507,f677])).
% 0.13/0.53 fof(f682,plain,(
% 0.13/0.53 spl0_28 <=> ~ssList(X0)|~frontsegP(X0,sk0_48)|frontsegP(X0,sk0_47)),
% 0.13/0.53 introduced(split_symbol_definition)).
% 0.13/0.53 fof(f685,plain,(
% 0.13/0.53 ![X0]: (~ssList(X0)|~ssList(sk0_48)|~ssList(sk0_47)|~frontsegP(X0,sk0_48)|frontsegP(X0,sk0_47)|~spl0_5)),
% 0.13/0.53 inference(resolution,[status(thm)],[f282,f454])).
% 0.13/0.53 fof(f686,plain,(
% 0.13/0.53 spl0_28|~spl0_27|~spl0_7|~spl0_5),
% 0.13/0.53 inference(split_clause,[status(thm)],[f685,f682,f677,f501,f453])).
% 0.13/0.53 fof(f687,plain,(
% 0.13/0.53 spl0_29 <=> ~ssList(X0)|~ssList(X1)|~frontsegP(X0,X1)|frontsegP(X0,nil)|~ssList(X1)),
% 0.13/0.53 introduced(split_symbol_definition)).
% 0.13/0.53 fof(f690,plain,(
% 0.13/0.53 ![X0,X1]: (~ssList(X0)|~ssList(X1)|~ssList(nil)|~frontsegP(X0,X1)|frontsegP(X0,nil)|~ssList(X1))),
% 0.13/0.53 inference(resolution,[status(thm)],[f282,f295])).
% 0.13/0.53 fof(f691,plain,(
% 0.13/0.53 spl0_29|~spl0_13),
% 0.13/0.53 inference(split_clause,[status(thm)],[f690,f687,f548])).
% 0.13/0.53 fof(f693,plain,(
% 0.13/0.53 ~ssList(sk0_47)|~ssList(nil)|sk0_47=nil|spl0_4),
% 0.13/0.53 inference(resolution,[status(thm)],[f220,f452])).
% 0.13/0.53 fof(f694,plain,(
% 0.13/0.53 ~spl0_7|~spl0_13|spl0_12|spl0_4),
% 0.13/0.53 inference(split_clause,[status(thm)],[f693,f501,f548,f525,f450])).
% 0.13/0.53 fof(f695,plain,(
% 0.13/0.53 $false),
% 0.13/0.53 inference(sat_refutation,[status(thm)],[f442,f449,f456,f513,f515,f532,f535,f547,f555,f559,f561,f567,f608,f620,f626,f644,f659,f661,f681,f686,f691,f694])).
% 0.13/0.53 % SZS output end CNFRefutation for theBenchmark.p
% 0.13/0.53 % Elapsed time: 0.022433 seconds
% 0.13/0.53 % CPU time: 0.023669 seconds
% 0.13/0.53 % Memory used: 4.203 MB
%------------------------------------------------------------------------------