%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SWC016+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 0.15s 5.61s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC016+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.57 % Computer : n016.cluster.edu
% 0.09/5.57 % Model : x86_64 x86_64
% 0.09/5.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.57 % Memory : 8046.5625MB
% 0.09/5.57 % OS : Linux 6.8.0-71-generic
% 0.09/5.57 % CPULimit : 300
% 0.09/5.57 % WCLimit : 300
% 0.09/5.57 % DateTime : Mon Sep 21 07:54:16 UTC 2026
% 0.09/5.58 % CPUTime :
% 0.09/5.59 % Drodi V4.1.1
% 0.15/5.61 % Refutation found
% 0.15/5.61 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/5.61 % SZS output start CNFRefutation for theBenchmark
% 0.15/5.61 fof(f2,axiom,(
% 0.15/5.61 (? [U] :( ssItem(U)& (? [V] :( ssItem(V)& U != V ) )) )),
% 0.15/5.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/5.61 fof(f4,axiom,(
% 0.15/5.61 (! [U] :( ssList(U)=> ( singletonP(U)<=> (? [V] :( ssItem(V)& cons(V,nil) = U ) )) ) )),
% 0.15/5.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/5.61 fof(f5,axiom,(
% 0.15/5.61 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> ( frontsegP(U,V)<=> (? [W] :( ssList(W)& app(V,W) = U ) )) ) )) )),
% 0.15/5.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/5.61 fof(f17,axiom,(
% 0.15/5.61 ssList(nil) ),
% 0.15/5.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/5.61 fof(f40,axiom,(
% 0.15/5.61 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> ( ( frontsegP(U,V)& frontsegP(V,W) )=> frontsegP(U,W) ) ) )) )) )),
% 0.15/5.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/5.61 fof(f42,axiom,(
% 0.15/5.61 (! [U] :( ssList(U)=> frontsegP(U,U) ) )),
% 0.15/5.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/5.61 fof(f96,conjecture,(
% 0.15/5.61 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> (! [X] :( ssList(X)=> ( V != X| U != W| ( nil != W& nil = X )| ( (! [Y] :( ssList(Y)=> ( ~ neq(Y,nil)| ~ frontsegP(X,Y)| ~ frontsegP(W,Y) ) ))& neq(X,nil) )| ( ( nil != V| nil = U )& ( ~ neq(V,nil)| (? [Z] :( ssList(Z)& neq(Z,nil)& frontsegP(V,Z)& frontsegP(U,Z) ) )) ) ) ) )) )) )) )),
% 0.15/5.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/5.61 fof(f97,negated_conjecture,(
% 0.15/5.61 ~((! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> (! [X] :( ssList(X)=> ( V != X| U != W| ( nil != W& nil = X )| ( (! [Y] :( ssList(Y)=> ( ~ neq(Y,nil)| ~ frontsegP(X,Y)| ~ frontsegP(W,Y) ) ))& neq(X,nil) )| ( ( nil != V| nil = U )& ( ~ neq(V,nil)| (? [Z] :( ssList(Z)& neq(Z,nil)& frontsegP(V,Z)& frontsegP(U,Z) ) )) ) ) ) )) )) )) ))),
% 0.15/5.61 inference(negated_conjecture,[status(cth)],[f96])).
% 0.15/5.61 fof(f102,plain,(
% 0.15/5.61 (ssItem(sK0_skl)&(ssItem(sK1_skl)&~sK0_skl=sK1_skl))),
% 0.15/5.61 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(U,sK0_skl),skolemize(V,sK1_skl)],[f2])).
% 0.15/5.61 fof(f105,plain,(
% 0.15/5.61 ~sK0_skl=sK1_skl),
% 0.15/5.61 inference(cnf_transformation,[status(thm)],[f102])).
% 0.15/5.61 fof(f113,plain,(
% 0.15/5.61 ![U]: (~ssList(U)|(singletonP(U)<=>(?[V]: (ssItem(V)&cons(V,nil)=U))))),
% 0.15/5.61 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 0.15/5.61 fof(f114,plain,(
% 0.15/5.61 ![U]: (~ssList(U)|((~singletonP(U)|(?[V]: (ssItem(V)&cons(V,nil)=U)))&(singletonP(U)|(![V]: (~ssItem(V)|~cons(V,nil)=U)))))),
% 0.15/5.61 inference(NNF_transformation,[status(thm)],[f113])).
% 0.15/5.61 fof(f115,plain,(
% 0.15/5.61 ![U]: (~ssList(U)|((~singletonP(U)|(ssItem(sK4_skl(U))&cons(sK4_skl(U),nil)=U))&(singletonP(U)|(![V]: (~ssItem(V)|~cons(V,nil)=U)))))),
% 0.15/5.61 inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(V,sK4_skl(U))],[f114])).
% 0.15/5.61 fof(f116,plain,(
% 0.15/5.61 ![X0]: (~ssList(X0)|~singletonP(X0)|ssItem(sK4_skl(X0)))),
% 0.15/5.61 inference(cnf_transformation,[status(thm)],[f115])).
% 0.15/5.61 fof(f119,plain,(
% 0.15/5.61 ![U]: (~ssList(U)|(![V]: (~ssList(V)|(frontsegP(U,V)<=>(?[W]: (ssList(W)&app(V,W)=U))))))),
% 0.15/5.61 inference(pre_NNF_transformation,[status(thm)],[f5])).
% 0.15/5.61 fof(f120,plain,(
% 0.15/5.61 ![U]: (~ssList(U)|(![V]: (~ssList(V)|((~frontsegP(U,V)|(?[W]: (ssList(W)&app(V,W)=U)))&(frontsegP(U,V)|(![W]: (~ssList(W)|~app(V,W)=U)))))))),
% 0.15/5.61 inference(NNF_transformation,[status(thm)],[f119])).
% 0.15/5.61 fof(f121,plain,(
% 0.15/5.61 ![U]: (~ssList(U)|(![V]: (~ssList(V)|((~frontsegP(U,V)|(ssList(sK5_skl(V,U))&app(V,sK5_skl(V,U))=U))&(frontsegP(U,V)|(![W]: (~ssList(W)|~app(V,W)=U)))))))),
% 0.15/5.61 inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(W,sK5_skl(V,U))],[f120])).
% 0.15/5.61 fof(f122,plain,(
% 0.15/5.61 ![X0,X1]: (~ssList(X0)|~ssList(X1)|~frontsegP(X0,X1)|ssList(sK5_skl(X1,X0)))),
% 0.15/5.61 inference(cnf_transformation,[status(thm)],[f121])).
% 0.15/5.61 fof(f123,plain,(
% 0.15/5.61 ![X0,X1]: (~ssList(X0)|~ssList(X1)|~frontsegP(X0,X1)|app(X1,sK5_skl(X1,X0))=X0)),
% 0.15/5.61 inference(cnf_transformation,[status(thm)],[f121])).
% 0.15/5.61 fof(f223,plain,(
% 0.15/5.61 ssList(nil)),
% 0.15/5.61 inference(cnf_transformation,[status(thm)],[f17])).
% 0.15/5.61 fof(f281,plain,(
% 0.15/5.61 ![U]: (~ssList(U)|(![V]: (~ssList(V)|(![W]: (~ssList(W)|((~frontsegP(U,V)|~frontsegP(V,W))|frontsegP(U,W)))))))),
% 0.15/5.61 inference(pre_NNF_transformation,[status(thm)],[f40])).
% 0.15/5.61 fof(f282,plain,(
% 0.15/5.61 ![X0,X1,X2]: (~ssList(X0)|~ssList(X1)|~ssList(X2)|~frontsegP(X0,X1)|~frontsegP(X1,X2)|frontsegP(X0,X2))),
% 0.15/5.61 inference(cnf_transformation,[status(thm)],[f281])).
% 0.15/5.61 fof(f285,plain,(
% 0.15/5.61 ![U]: (~ssList(U)|frontsegP(U,U))),
% 0.15/5.61 inference(pre_NNF_transformation,[status(thm)],[f42])).
% 0.15/5.61 fof(f286,plain,(
% 0.15/5.61 ![X0]: (~ssList(X0)|frontsegP(X0,X0))),
% 0.15/5.61 inference(cnf_transformation,[status(thm)],[f285])).
% 0.15/5.61 fof(f415,plain,(
% 0.15/5.61 (?[U]: (ssList(U)&(?[V]: (ssList(V)&(?[W]: (ssList(W)&(?[X]: (ssList(X)&((((V=X&U=W)&(nil=W|~nil=X))&((?[Y]: (ssList(Y)&((neq(Y,nil)&frontsegP(X,Y))&frontsegP(W,Y))))|~neq(X,nil)))&((nil=V&~nil=U)|(neq(V,nil)&(![Z]: (((~ssList(Z)|~neq(Z,nil))|~frontsegP(V,Z))|~frontsegP(U,Z))))))))))))))),
% 0.15/5.61 inference(pre_NNF_transformation,[status(thm)],[f97])).
% 0.15/5.61 fof(f416,definition,(
% 0.15/5.61 ![U,V]: (sP0_prd(V,U)<=>(nil=V&~nil=U))),
% 0.15/5.61 introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 0.15/5.61 fof(f417,plain,(
% 0.15/5.61 ?[U]: (ssList(U)&(?[V]: (ssList(V)&(?[W]: (ssList(W)&(?[X]: (ssList(X)&((((V=X&U=W)&(nil=W|~nil=X))&((?[Y]: (ssList(Y)&((neq(Y,nil)&frontsegP(X,Y))&frontsegP(W,Y))))|~neq(X,nil)))&(sP0_prd(V,U)|(neq(V,nil)&(![Z]: (((~ssList(Z)|~neq(Z,nil))|~frontsegP(V,Z))|~frontsegP(U,Z)))))))))))))),
% 0.15/5.61 inference(formula_renaming,[status(thm)],[f415,f416])).
% 0.15/5.61 fof(f418,plain,(
% 0.15/5.61 (ssList(sK47_skl)&(ssList(sK48_skl)&(ssList(sK49_skl)&(ssList(sK50_skl)&((((sK48_skl=sK50_skl&sK47_skl=sK49_skl)&(nil=sK49_skl|~nil=sK50_skl))&((ssList(sK51_skl)&((neq(sK51_skl,nil)&frontsegP(sK50_skl,sK51_skl))&frontsegP(sK49_skl,sK51_skl)))|~neq(sK50_skl,nil)))&(sP0_prd(sK48_skl,sK47_skl)|(neq(sK48_skl,nil)&(![Z]: (((~ssList(Z)|~neq(Z,nil))|~frontsegP(sK48_skl,Z))|~frontsegP(sK47_skl,Z))))))))))),
% 0.15/5.61 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)],[f417])).
% 0.15/5.61 fof(f421,plain,(
% 0.15/5.61 ssList(sK49_skl)),
% 0.15/5.61 inference(cnf_transformation,[status(thm)],[f418])).
% 0.15/5.61 fof(f422,plain,(
% 0.15/5.61 ssList(sK50_skl)),
% 0.15/5.61 inference(cnf_transformation,[status(thm)],[f418])).
% 0.15/5.61 fof(f423,plain,(
% 0.15/5.61 sK48_skl=sK50_skl),
% 0.15/5.61 inference(cnf_transformation,[status(thm)],[f418])).
% 0.15/5.61 fof(f424,plain,(
% 0.15/5.61 sK47_skl=sK49_skl),
% 0.15/5.61 inference(cnf_transformation,[status(thm)],[f418])).
% 0.15/5.61 fof(f425,plain,(
% 0.15/5.61 nil=sK49_skl|~nil=sK50_skl),
% 0.15/5.61 inference(cnf_transformation,[status(thm)],[f418])).
% 0.15/5.61 fof(f426,plain,(
% 0.15/5.61 ssList(sK51_skl)|~neq(sK50_skl,nil)),
% 0.15/5.61 inference(cnf_transformation,[status(thm)],[f418])).
% 0.15/5.61 fof(f427,plain,(
% 0.15/5.61 neq(sK51_skl,nil)|~neq(sK50_skl,nil)),
% 0.15/5.61 inference(cnf_transformation,[status(thm)],[f418])).
% 0.15/5.61 fof(f428,plain,(
% 0.15/5.61 frontsegP(sK50_skl,sK51_skl)|~neq(sK50_skl,nil)),
% 0.15/5.61 inference(cnf_transformation,[status(thm)],[f418])).
% 0.15/5.61 fof(f429,plain,(
% 0.15/5.61 frontsegP(sK49_skl,sK51_skl)|~neq(sK50_skl,nil)),
% 0.15/5.61 inference(cnf_transformation,[status(thm)],[f418])).
% 0.15/5.61 fof(f430,plain,(
% 0.15/5.61 sP0_prd(sK48_skl,sK47_skl)|neq(sK48_skl,nil)),
% 0.15/5.61 inference(cnf_transformation,[status(thm)],[f418])).
% 0.15/5.61 fof(f431,plain,(
% 0.15/5.61 ![X0]: (sP0_prd(sK48_skl,sK47_skl)|~ssList(X0)|~neq(X0,nil)|~frontsegP(sK48_skl,X0)|~frontsegP(sK47_skl,X0))),
% 0.15/5.61 inference(cnf_transformation,[status(thm)],[f418])).
% 0.15/5.61 fof(f432,plain,(
% 0.15/5.61 ![U,V]: ((~sP0_prd(V,U)|(nil=V&~nil=U))&(sP0_prd(V,U)|(~nil=V|nil=U)))),
% 0.15/5.61 inference(NNF_transformation,[status(thm)],[f416])).
% 0.15/5.61 fof(f433,plain,(
% 0.15/5.61 (![U,V]: (~sP0_prd(V,U)|(nil=V&~nil=U)))&(![U,V]: (sP0_prd(V,U)|(~nil=V|nil=U)))),
% 0.15/5.61 inference(miniscoping,[status(thm)],[f432])).
% 0.15/5.61 fof(f434,plain,(
% 0.15/5.61 ![X0,X1]: (~sP0_prd(X0,X1)|nil=X0)),
% 0.15/5.61 inference(cnf_transformation,[status(thm)],[f433])).
% 0.15/5.61 fof(f435,plain,(
% 0.15/5.61 ![X0,X1]: (~sP0_prd(X0,X1)|~nil=X1)),
% 0.15/5.61 inference(cnf_transformation,[status(thm)],[f433])).
% 0.15/5.61 fof(f436,plain,(
% 0.15/5.61 ![X0,X1]: (sP0_prd(X0,X1)|~nil=X0|nil=X1)),
% 0.15/5.61 inference(cnf_transformation,[status(thm)],[f433])).
% 0.15/5.61 fof(f437,definition,(
% 0.15/5.61 sQ0_spl <=> (nil=sK49_skl)),
% 0.15/5.61 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.15/5.61 fof(f438,plain,(
% 0.15/5.61 nil=sK49_skl|~sQ0_spl),
% 0.15/5.61 inference(component_clause,[status(thm)],[f437])).
% 0.15/5.61 fof(f440,definition,(
% 0.15/5.61 sQ1_spl <=> (nil=sK50_skl)),
% 0.15/5.61 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.15/5.61 fof(f442,plain,(
% 0.15/5.61 ~nil=sK50_skl|sQ1_spl),
% 0.15/5.61 inference(component_clause,[status(thm)],[f440])).
% 0.15/5.61 fof(f443,plain,(
% 0.15/5.61 sQ0_spl|~sQ1_spl),
% 0.15/5.61 inference(split_clause,[status(thm)],[f425,f437,f440])).
% 0.15/5.61 fof(f444,definition,(
% 0.15/5.61 sQ2_spl <=> (ssList(sK51_skl))),
% 0.15/5.61 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.15/5.61 fof(f445,plain,(
% 0.15/5.61 ssList(sK51_skl)|~sQ2_spl),
% 0.15/5.61 inference(component_clause,[status(thm)],[f444])).
% 0.15/5.61 fof(f447,definition,(
% 0.15/5.61 sQ3_spl <=> (neq(sK50_skl,nil))),
% 0.15/5.61 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.15/5.61 fof(f449,plain,(
% 0.15/5.61 ~neq(sK50_skl,nil)|sQ3_spl),
% 0.15/5.61 inference(component_clause,[status(thm)],[f447])).
% 0.15/5.61 fof(f450,plain,(
% 0.15/5.61 sQ2_spl|~sQ3_spl),
% 0.15/5.61 inference(split_clause,[status(thm)],[f426,f444,f447])).
% 0.15/5.61 fof(f451,definition,(
% 0.15/5.61 sQ4_spl <=> (neq(sK51_skl,nil))),
% 0.15/5.61 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 0.15/5.61 fof(f452,plain,(
% 0.15/5.61 neq(sK51_skl,nil)|~sQ4_spl),
% 0.15/5.61 inference(component_clause,[status(thm)],[f451])).
% 0.15/5.61 fof(f454,plain,(
% 0.15/5.61 sQ4_spl|~sQ3_spl),
% 0.15/5.61 inference(split_clause,[status(thm)],[f427,f451,f447])).
% 0.15/5.61 fof(f455,definition,(
% 0.15/5.61 sQ5_spl <=> (frontsegP(sK50_skl,sK51_skl))),
% 0.15/5.61 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 0.15/5.61 fof(f458,plain,(
% 0.15/5.61 sQ5_spl|~sQ3_spl),
% 0.15/5.61 inference(split_clause,[status(thm)],[f428,f455,f447])).
% 0.15/5.61 fof(f459,definition,(
% 0.15/5.61 sQ6_spl <=> (frontsegP(sK49_skl,sK51_skl))),
% 0.15/5.61 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.15/5.61 fof(f460,plain,(
% 0.15/5.61 frontsegP(sK49_skl,sK51_skl)|~sQ6_spl),
% 0.15/5.61 inference(component_clause,[status(thm)],[f459])).
% 0.15/5.61 fof(f462,plain,(
% 0.15/5.61 sQ6_spl|~sQ3_spl),
% 0.15/5.61 inference(split_clause,[status(thm)],[f429,f459,f447])).
% 0.15/5.61 fof(f463,definition,(
% 0.15/5.61 sQ7_spl <=> (sP0_prd(sK48_skl,sK47_skl))),
% 0.15/5.61 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 0.15/5.61 fof(f464,plain,(
% 0.15/5.61 sP0_prd(sK48_skl,sK47_skl)|~sQ7_spl),
% 0.15/5.61 inference(component_clause,[status(thm)],[f463])).
% 0.15/5.61 fof(f466,definition,(
% 0.15/5.61 sQ8_spl <=> (neq(sK48_skl,nil))),
% 0.15/5.61 introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition])).
% 0.15/5.61 fof(f467,plain,(
% 0.15/5.61 neq(sK48_skl,nil)|~sQ8_spl),
% 0.15/5.61 inference(component_clause,[status(thm)],[f466])).
% 0.15/5.61 fof(f469,plain,(
% 0.15/5.61 sQ7_spl|sQ8_spl),
% 0.15/5.61 inference(split_clause,[status(thm)],[f430,f463,f466])).
% 0.15/5.61 fof(f470,definition,(
% 0.15/5.61 ![X0]: (sQ9_spl <=> (~ssList(X0)|~neq(X0,nil)|~frontsegP(sK48_skl,X0)|~frontsegP(sK47_skl,X0)))),
% 0.15/5.61 introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition])).
% 0.15/5.61 fof(f471,plain,(
% 0.15/5.61 ![X0]: (~ssList(X0)|~neq(X0,nil)|~frontsegP(sK48_skl,X0)|~frontsegP(sK47_skl,X0)|~sQ9_spl)),
% 0.15/5.61 inference(component_clause,[status(thm)],[f470])).
% 0.15/5.61 fof(f473,plain,(
% 0.15/5.61 sQ7_spl|sQ9_spl),
% 0.15/5.61 inference(split_clause,[status(thm)],[f431,f463,f470])).
% 0.15/5.61 fof(f504,plain,(
% 0.15/5.61 ![X0]: (~sP0_prd(X0,nil))),
% 0.15/5.61 inference(destructive_equality_resolution,[status(thm)],[f435])).
% 0.15/5.61 fof(f505,plain,(
% 0.15/5.61 ![X0]: (sP0_prd(nil,X0)|nil=X0)),
% 0.15/5.61 inference(destructive_equality_resolution,[status(thm)],[f436])).
% 0.15/5.61 fof(f509,plain,(
% 0.15/5.61 ![X0]: (~sP0_prd(X0,sK49_skl)|~sQ0_spl)),
% 0.15/5.61 inference(forward_demodulation,[status(thm)],[f438,f504])).
% 0.15/5.61 fof(f511,plain,(
% 0.15/5.61 sP0_prd(sK50_skl,sK47_skl)|~sQ7_spl),
% 0.15/5.61 inference(forward_demodulation,[status(thm)],[f423,f464])).
% 0.15/5.61 fof(f512,plain,(
% 0.15/5.61 sP0_prd(sK50_skl,sK49_skl)|~sQ7_spl),
% 0.15/5.61 inference(forward_demodulation,[status(thm)],[f424,f511])).
% 0.15/5.61 fof(f513,plain,(
% 0.15/5.61 $false|~sQ0_spl|~sQ7_spl),
% 0.15/5.61 inference(forward_subsumption_resolution,[status(thm)],[f512,f509])).
% 0.15/5.61 fof(f514,plain,(
% 0.15/5.61 ~sQ0_spl|~sQ7_spl),
% 0.15/5.61 inference(contradiction_clause,[status(thm)],[f513])).
% 0.15/5.61 fof(f515,plain,(
% 0.15/5.61 neq(sK50_skl,nil)|~sQ8_spl),
% 0.15/5.61 inference(forward_demodulation,[status(thm)],[f423,f467])).
% 0.15/5.61 fof(f516,plain,(
% 0.15/5.61 ![X0]: (~ssList(X0)|~neq(X0,nil)|~frontsegP(sK50_skl,X0)|~frontsegP(sK47_skl,X0)|~sQ9_spl)),
% 0.15/5.61 inference(forward_demodulation,[status(thm)],[f423,f471])).
% 0.15/5.61 fof(f517,plain,(
% 0.15/5.61 ![X0]: (~ssList(X0)|~neq(X0,nil)|~frontsegP(sK50_skl,X0)|~frontsegP(sK49_skl,X0)|~sQ9_spl)),
% 0.15/5.61 inference(forward_demodulation,[status(thm)],[f424,f516])).
% 0.15/5.61 fof(f522,plain,(
% 0.15/5.61 $false|~sQ8_spl|sQ3_spl),
% 0.15/5.61 inference(forward_subsumption_resolution,[status(thm)],[f449,f515])).
% 0.15/5.61 fof(f523,plain,(
% 0.15/5.61 ~sQ8_spl|sQ3_spl),
% 0.15/5.61 inference(contradiction_clause,[status(thm)],[f522])).
% 0.15/5.61 fof(f524,plain,(
% 0.15/5.61 nil=sK50_skl|~sQ7_spl),
% 0.15/5.61 inference(resolution,[status(thm)],[f434,f512])).
% 0.15/5.61 fof(f525,plain,(
% 0.15/5.61 $false|sQ1_spl|~sQ7_spl),
% 0.15/5.61 inference(forward_subsumption_resolution,[status(thm)],[f524,f442])).
% 0.15/5.61 fof(f526,plain,(
% 0.15/5.61 sQ1_spl|~sQ7_spl),
% 0.15/5.61 inference(contradiction_clause,[status(thm)],[f525])).
% 0.15/5.61 fof(f528,plain,(
% 0.15/5.61 ![X0]: (nil=X0|nil=nil)),
% 0.15/5.61 inference(resolution,[status(thm)],[f505,f434])).
% 0.15/5.61 fof(f529,definition,(
% 0.15/5.61 ![X0]: (sQ10_spl <=> (nil=X0))),
% 0.15/5.61 introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition])).
% 0.15/5.61 fof(f530,plain,(
% 0.15/5.61 ![X0]: (nil=X0|~sQ10_spl)),
% 0.15/5.61 inference(component_clause,[status(thm)],[f529])).
% 0.15/5.61 fof(f532,definition,(
% 0.15/5.61 sQ11_spl <=> (nil=nil)),
% 0.15/5.61 introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition])).
% 0.15/5.61 fof(f535,plain,(
% 0.15/5.61 sQ10_spl|sQ11_spl),
% 0.15/5.61 inference(split_clause,[status(thm)],[f528,f529,f532])).
% 0.15/5.61 fof(f536,plain,(
% 0.15/5.61 ![X0,X1]: (X0=X1|~sQ10_spl)),
% 0.15/5.61 inference(paramodulation,[status(thm)],[f530,f530])).
% 0.15/5.61 fof(f549,plain,(
% 0.15/5.61 $false|~sQ10_spl),
% 0.15/5.61 inference(backward_subsumption_resolution,[status(thm)],[f105,f536])).
% 0.15/5.61 fof(f550,plain,(
% 0.15/5.61 ~sQ10_spl),
% 0.15/5.61 inference(contradiction_clause,[status(thm)],[f549])).
% 0.15/5.61 fof(f565,plain,(
% 0.15/5.61 frontsegP(sK51_skl,sK51_skl)|~sQ2_spl),
% 0.15/5.61 inference(resolution,[status(thm)],[f286,f445])).
% 0.15/5.61 fof(f566,plain,(
% 0.15/5.61 frontsegP(sK50_skl,sK50_skl)),
% 0.15/5.61 inference(resolution,[status(thm)],[f286,f422])).
% 0.15/5.61 fof(f567,plain,(
% 0.15/5.61 frontsegP(sK49_skl,sK49_skl)),
% 0.15/5.61 inference(resolution,[status(thm)],[f286,f421])).
% 0.15/5.61 fof(f568,plain,(
% 0.15/5.61 ~singletonP(sK51_skl)|ssItem(sK4_skl(sK51_skl))|~sQ2_spl),
% 0.15/5.61 inference(resolution,[status(thm)],[f116,f445])).
% 0.15/5.61 fof(f571,definition,(
% 0.15/5.61 sQ12_spl <=> (singletonP(sK51_skl))),
% 0.15/5.61 introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition])).
% 0.15/5.61 fof(f574,definition,(
% 0.15/5.61 sQ13_spl <=> (ssItem(sK4_skl(sK51_skl)))),
% 0.15/5.61 introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition])).
% 0.15/5.61 fof(f577,plain,(
% 0.15/5.61 ~sQ12_spl|sQ13_spl|~sQ2_spl),
% 0.15/5.61 inference(split_clause,[status(thm)],[f568,f571,f574,f444])).
% 0.15/5.61 fof(f624,definition,(
% 0.15/5.61 sQ23_spl <=> (ssList(sK50_skl))),
% 0.15/5.61 introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition])).
% 0.15/5.61 fof(f626,plain,(
% 0.15/5.61 ~ssList(sK50_skl)|sQ23_spl),
% 0.15/5.61 inference(component_clause,[status(thm)],[f624])).
% 0.15/5.61 fof(f635,plain,(
% 0.15/5.61 frontsegP(nil,nil)),
% 0.15/5.61 inference(resolution,[status(thm)],[f223,f286])).
% 0.15/5.61 fof(f647,plain,(
% 0.15/5.61 ![X0]: (~ssList(X0)|~ssList(nil)|~ssList(nil)|~frontsegP(X0,nil)|frontsegP(X0,nil))),
% 0.15/5.61 inference(resolution,[status(thm)],[f282,f635])).
% 0.15/5.61 fof(f648,plain,(
% 0.15/5.61 ![X0]: (~ssList(X0)|~ssList(sK51_skl)|~ssList(sK51_skl)|~frontsegP(X0,sK51_skl)|frontsegP(X0,sK51_skl)|~sQ2_spl)),
% 0.15/5.61 inference(resolution,[status(thm)],[f282,f565])).
% 0.15/5.61 fof(f649,plain,(
% 0.15/5.61 ![X0]: (~ssList(X0)|~ssList(sK49_skl)|~ssList(sK49_skl)|~frontsegP(X0,sK49_skl)|frontsegP(X0,sK49_skl))),
% 0.15/5.61 inference(resolution,[status(thm)],[f282,f567])).
% 0.15/5.61 fof(f650,plain,(
% 0.15/5.61 ![X0]: (~ssList(X0)|~ssList(sK49_skl)|~ssList(sK51_skl)|~frontsegP(X0,sK49_skl)|frontsegP(X0,sK51_skl)|~sQ6_spl)),
% 0.15/5.61 inference(resolution,[status(thm)],[f282,f460])).
% 0.15/5.61 fof(f651,plain,(
% 0.15/5.61 ![X0]: (~ssList(X0)|~ssList(sK50_skl)|~ssList(sK50_skl)|~frontsegP(X0,sK50_skl)|frontsegP(X0,sK50_skl))),
% 0.15/5.61 inference(resolution,[status(thm)],[f282,f566])).
% 0.15/5.61 fof(f655,definition,(
% 0.15/5.61 ![X0]: (sQ28_spl <=> (~ssList(X0)|~frontsegP(X0,nil)|frontsegP(X0,nil)))),
% 0.15/5.61 introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition])).
% 0.15/5.61 fof(f658,definition,(
% 0.15/5.61 sQ29_spl <=> (ssList(nil))),
% 0.15/5.61 introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition])).
% 0.15/5.61 fof(f660,plain,(
% 0.15/5.61 ~ssList(nil)|sQ29_spl),
% 0.15/5.61 inference(component_clause,[status(thm)],[f658])).
% 0.15/5.61 fof(f661,plain,(
% 0.15/5.61 sQ28_spl|~sQ29_spl),
% 0.15/5.61 inference(split_clause,[status(thm)],[f647,f655,f658])).
% 0.15/5.61 fof(f662,definition,(
% 0.15/5.61 ![X0]: (sQ30_spl <=> (~ssList(X0)|~frontsegP(X0,sK51_skl)|frontsegP(X0,sK51_skl)))),
% 0.15/5.61 introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition])).
% 0.15/5.61 fof(f665,plain,(
% 0.15/5.61 sQ30_spl|~sQ2_spl),
% 0.15/5.61 inference(split_clause,[status(thm)],[f648,f662,f444])).
% 0.15/5.61 fof(f666,definition,(
% 0.15/5.61 ![X0]: (sQ31_spl <=> (~ssList(X0)|~frontsegP(X0,sK49_skl)|frontsegP(X0,sK49_skl)))),
% 0.15/5.61 introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition])).
% 0.15/5.61 fof(f669,definition,(
% 0.15/5.61 sQ32_spl <=> (ssList(sK49_skl))),
% 0.15/5.61 introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition])).
% 0.15/5.61 fof(f671,plain,(
% 0.15/5.61 ~ssList(sK49_skl)|sQ32_spl),
% 0.15/5.61 inference(component_clause,[status(thm)],[f669])).
% 0.15/5.61 fof(f672,plain,(
% 0.15/5.61 sQ31_spl|~sQ32_spl),
% 0.15/5.61 inference(split_clause,[status(thm)],[f649,f666,f669])).
% 0.15/5.61 fof(f673,definition,(
% 0.15/5.61 ![X0]: (sQ33_spl <=> (~ssList(X0)|~frontsegP(X0,sK49_skl)|frontsegP(X0,sK51_skl)))),
% 0.15/5.61 introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition])).
% 0.15/5.61 fof(f676,plain,(
% 0.15/5.61 sQ33_spl|~sQ32_spl|~sQ2_spl|~sQ6_spl),
% 0.15/5.61 inference(split_clause,[status(thm)],[f650,f673,f669,f444,f459])).
% 0.15/5.61 fof(f677,definition,(
% 0.15/5.61 ![X0]: (sQ34_spl <=> (~ssList(X0)|~frontsegP(X0,sK50_skl)|frontsegP(X0,sK50_skl)))),
% 0.15/5.61 introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition])).
% 0.15/5.61 fof(f680,plain,(
% 0.15/5.61 sQ34_spl|~sQ23_spl),
% 0.15/5.61 inference(split_clause,[status(thm)],[f651,f677,f624])).
% 0.15/5.61 fof(f687,plain,(
% 0.15/5.61 $false|sQ23_spl),
% 0.15/5.61 inference(forward_subsumption_resolution,[status(thm)],[f626,f422])).
% 0.15/5.61 fof(f688,plain,(
% 0.15/5.61 sQ23_spl),
% 0.15/5.61 inference(contradiction_clause,[status(thm)],[f687])).
% 0.15/5.61 fof(f689,plain,(
% 0.15/5.61 $false|sQ32_spl),
% 0.15/5.61 inference(forward_subsumption_resolution,[status(thm)],[f671,f421])).
% 0.15/5.61 fof(f690,plain,(
% 0.15/5.61 sQ32_spl),
% 0.15/5.61 inference(contradiction_clause,[status(thm)],[f689])).
% 0.15/5.61 fof(f699,plain,(
% 0.15/5.61 ~ssList(nil)|~ssList(nil)|ssList(sK5_skl(nil,nil))),
% 0.15/5.61 inference(resolution,[status(thm)],[f122,f635])).
% 0.15/5.61 fof(f700,plain,(
% 0.15/5.61 ~ssList(sK51_skl)|~ssList(sK51_skl)|ssList(sK5_skl(sK51_skl,sK51_skl))|~sQ2_spl),
% 0.15/5.61 inference(resolution,[status(thm)],[f122,f565])).
% 0.15/5.61 fof(f701,plain,(
% 0.15/5.61 ~ssList(sK49_skl)|~ssList(sK49_skl)|ssList(sK5_skl(sK49_skl,sK49_skl))),
% 0.15/5.61 inference(resolution,[status(thm)],[f122,f567])).
% 0.15/5.61 fof(f702,plain,(
% 0.15/5.61 ~ssList(sK49_skl)|~ssList(sK51_skl)|ssList(sK5_skl(sK51_skl,sK49_skl))|~sQ6_spl),
% 0.15/5.61 inference(resolution,[status(thm)],[f122,f460])).
% 0.15/5.61 fof(f703,plain,(
% 0.15/5.61 ~ssList(sK50_skl)|~ssList(sK50_skl)|ssList(sK5_skl(sK50_skl,sK50_skl))),
% 0.15/5.61 inference(resolution,[status(thm)],[f122,f566])).
% 0.15/5.61 fof(f706,definition,(
% 0.15/5.61 sQ36_spl <=> (ssList(sK5_skl(nil,nil)))),
% 0.15/5.61 introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition])).
% 0.15/5.61 fof(f709,plain,(
% 0.15/5.61 ~sQ29_spl|sQ36_spl),
% 0.15/5.61 inference(split_clause,[status(thm)],[f699,f658,f706])).
% 0.15/5.61 fof(f710,definition,(
% 0.15/5.61 sQ37_spl <=> (ssList(sK5_skl(sK51_skl,sK51_skl)))),
% 0.15/5.61 introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition])).
% 0.15/5.61 fof(f713,plain,(
% 0.15/5.61 ~sQ2_spl|sQ37_spl),
% 0.15/5.61 inference(split_clause,[status(thm)],[f700,f444,f710])).
% 0.15/5.61 fof(f714,definition,(
% 0.15/5.61 sQ38_spl <=> (ssList(sK5_skl(sK49_skl,sK49_skl)))),
% 0.15/5.61 introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition])).
% 0.15/5.61 fof(f717,plain,(
% 0.15/5.61 ~sQ32_spl|sQ38_spl),
% 0.15/5.61 inference(split_clause,[status(thm)],[f701,f669,f714])).
% 0.15/5.61 fof(f718,definition,(
% 0.15/5.61 sQ39_spl <=> (ssList(sK5_skl(sK51_skl,sK49_skl)))),
% 0.15/5.61 introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition])).
% 0.15/5.61 fof(f721,plain,(
% 0.15/5.61 ~sQ32_spl|~sQ2_spl|sQ39_spl|~sQ6_spl),
% 0.15/5.61 inference(split_clause,[status(thm)],[f702,f669,f444,f718,f459])).
% 0.15/5.61 fof(f722,definition,(
% 0.15/5.61 sQ40_spl <=> (ssList(sK5_skl(sK50_skl,sK50_skl)))),
% 0.15/5.61 introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition])).
% 0.15/5.61 fof(f725,plain,(
% 0.15/5.61 ~sQ23_spl|sQ40_spl),
% 0.15/5.61 inference(split_clause,[status(thm)],[f703,f624,f722])).
% 0.15/5.61 fof(f731,plain,(
% 0.15/5.61 $false|sQ29_spl),
% 0.15/5.61 inference(forward_subsumption_resolution,[status(thm)],[f660,f223])).
% 0.15/5.61 fof(f732,plain,(
% 0.15/5.61 sQ29_spl),
% 0.15/5.61 inference(contradiction_clause,[status(thm)],[f731])).
% 0.15/5.61 fof(f733,plain,(
% 0.15/5.61 ~ssList(nil)|~ssList(nil)|app(nil,sK5_skl(nil,nil))=nil),
% 0.15/5.61 inference(resolution,[status(thm)],[f123,f635])).
% 0.15/5.61 fof(f734,plain,(
% 0.15/5.61 ~ssList(sK51_skl)|~ssList(sK51_skl)|app(sK51_skl,sK5_skl(sK51_skl,sK51_skl))=sK51_skl|~sQ2_spl),
% 0.15/5.61 inference(resolution,[status(thm)],[f123,f565])).
% 0.15/5.61 fof(f735,plain,(
% 0.15/5.61 ~ssList(sK49_skl)|~ssList(sK49_skl)|app(sK49_skl,sK5_skl(sK49_skl,sK49_skl))=sK49_skl),
% 0.15/5.61 inference(resolution,[status(thm)],[f123,f567])).
% 0.15/5.61 fof(f736,plain,(
% 0.15/5.61 ~ssList(sK49_skl)|~ssList(sK51_skl)|app(sK51_skl,sK5_skl(sK51_skl,sK49_skl))=sK49_skl|~sQ6_spl),
% 0.15/5.61 inference(resolution,[status(thm)],[f123,f460])).
% 0.15/5.61 fof(f737,plain,(
% 0.15/5.61 ~ssList(sK50_skl)|~ssList(sK50_skl)|app(sK50_skl,sK5_skl(sK50_skl,sK50_skl))=sK50_skl),
% 0.15/5.61 inference(resolution,[status(thm)],[f123,f566])).
% 0.15/5.61 fof(f740,definition,(
% 0.15/5.61 sQ42_spl <=> (app(nil,sK5_skl(nil,nil))=nil)),
% 0.15/5.61 introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition])).
% 0.15/5.61 fof(f743,plain,(
% 0.15/5.61 ~sQ29_spl|sQ42_spl),
% 0.15/5.61 inference(split_clause,[status(thm)],[f733,f658,f740])).
% 0.15/5.61 fof(f744,definition,(
% 0.15/5.61 sQ43_spl <=> (app(sK51_skl,sK5_skl(sK51_skl,sK51_skl))=sK51_skl)),
% 0.15/5.61 introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition])).
% 0.15/5.61 fof(f747,plain,(
% 0.15/5.61 ~sQ2_spl|sQ43_spl),
% 0.15/5.61 inference(split_clause,[status(thm)],[f734,f444,f744])).
% 0.15/5.61 fof(f748,definition,(
% 0.15/5.61 sQ44_spl <=> (app(sK49_skl,sK5_skl(sK49_skl,sK49_skl))=sK49_skl)),
% 0.15/5.61 introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition])).
% 0.15/5.61 fof(f751,plain,(
% 0.15/5.61 ~sQ32_spl|sQ44_spl),
% 0.15/5.61 inference(split_clause,[status(thm)],[f735,f669,f748])).
% 0.15/5.61 fof(f752,definition,(
% 0.15/5.61 sQ45_spl <=> (app(sK51_skl,sK5_skl(sK51_skl,sK49_skl))=sK49_skl)),
% 0.15/5.61 introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition])).
% 0.15/5.61 fof(f755,plain,(
% 0.15/5.61 ~sQ32_spl|~sQ2_spl|sQ45_spl|~sQ6_spl),
% 0.15/5.61 inference(split_clause,[status(thm)],[f736,f669,f444,f752,f459])).
% 0.15/5.61 fof(f756,definition,(
% 0.15/5.61 sQ46_spl <=> (app(sK50_skl,sK5_skl(sK50_skl,sK50_skl))=sK50_skl)),
% 0.15/5.61 introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition])).
% 0.15/5.61 fof(f759,plain,(
% 0.15/5.61 ~sQ23_spl|sQ46_spl),
% 0.15/5.61 inference(split_clause,[status(thm)],[f737,f624,f756])).
% 0.15/5.61 fof(f768,plain,(
% 0.15/5.61 ~ssList(sK51_skl)|~frontsegP(sK50_skl,sK51_skl)|~frontsegP(sK49_skl,sK51_skl)|~sQ9_spl|~sQ4_spl),
% 0.15/5.61 inference(resolution,[status(thm)],[f517,f452])).
% 0.15/5.61 fof(f770,plain,(
% 0.15/5.61 ~sQ2_spl|~sQ5_spl|~sQ6_spl|~sQ9_spl|~sQ4_spl),
% 0.15/5.61 inference(split_clause,[status(thm)],[f768,f444,f455,f459,f470,f451])).
% 0.15/5.61 fof(f772,plain,(
% 0.15/5.61 $false),
% 0.15/5.61 inference(sat_refutation,[status(thm)],[f443,f450,f454,f458,f462,f469,f473,f514,f523,f526,f535,f550,f577,f661,f665,f672,f676,f680,f688,f690,f709,f713,f717,f721,f725,f732,f743,f747,f751,f755,f759,f770])).
% 0.15/5.61 % SZS output end CNFRefutation for theBenchmark.p
% 0.15/5.64 % Elapsed time: 0.055730 seconds
% 0.15/5.64 % CPU time: 0.156176 seconds
% 0.15/5.64 % Total memory used: 62.693 MB
% 0.15/5.64 % Net memory used: 62.605 MB
%------------------------------------------------------------------------------