%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SWC054+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 02:41:27 PM UTC 2026
% Result : Theorem 0.11s 0.41s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC054+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n017.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 21 07:47:12 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.38 % Drodi V4.1.1
% 0.11/0.41 % Refutation found
% 0.11/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.41 % SZS output start CNFRefutation for theBenchmark
% 0.11/0.41 fof(f2,axiom,(
% 0.11/0.41 (? [U] :( ssItem(U)& (? [V] :( ssItem(V)& U != V ) )) )),
% 0.11/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.41 fof(f4,axiom,(
% 0.11/0.41 (! [U] :( ssList(U)=> ( singletonP(U)<=> (? [V] :( ssItem(V)& cons(V,nil) = U ) )) ) )),
% 0.11/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.41 fof(f5,axiom,(
% 0.11/0.41 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> ( frontsegP(U,V)<=> (? [W] :( ssList(W)& app(V,W) = U ) )) ) )) )),
% 0.11/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.41 fof(f17,axiom,(
% 0.11/0.41 ssList(nil) ),
% 0.11/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.41 fof(f42,axiom,(
% 0.11/0.41 (! [U] :( ssList(U)=> frontsegP(U,U) ) )),
% 0.11/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.41 fof(f53,axiom,(
% 0.11/0.41 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> ( ( segmentP(U,V)& segmentP(V,W) )=> segmentP(U,W) ) ) )) )) )),
% 0.11/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.41 fof(f55,axiom,(
% 0.11/0.41 (! [U] :( ssList(U)=> segmentP(U,U) ) )),
% 0.11/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.41 fof(f96,conjecture,(
% 0.11/0.41 (! [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)| ~ segmentP(X,Y)| ~ segmentP(W,Y) ))& neq(X,nil) )| ( ( nil != V| nil = U )& ( ~ neq(V,nil)| (? [Z] :( ssList(Z)& neq(Z,nil)& segmentP(V,Z)& segmentP(U,Z) ) )) ) ) )) )) )) )),
% 0.11/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.41 fof(f97,negated_conjecture,(
% 0.11/0.41 ~((! [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)| ~ segmentP(X,Y)| ~ segmentP(W,Y) ))& neq(X,nil) )| ( ( nil != V| nil = U )& ( ~ neq(V,nil)| (? [Z] :( ssList(Z)& neq(Z,nil)& segmentP(V,Z)& segmentP(U,Z) ) )) ) ) )) )) )) ))),
% 0.11/0.41 inference(negated_conjecture,[status(cth)],[f96])).
% 0.11/0.41 fof(f102,plain,(
% 0.11/0.41 (ssItem(sK0_skl)&(ssItem(sK1_skl)&~sK0_skl=sK1_skl))),
% 0.11/0.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(U,sK0_skl),skolemize(V,sK1_skl)],[f2])).
% 0.11/0.41 fof(f105,plain,(
% 0.11/0.41 ~sK0_skl=sK1_skl),
% 0.11/0.41 inference(cnf_transformation,[status(thm)],[f102])).
% 0.11/0.41 fof(f113,plain,(
% 0.11/0.41 ![U]: (~ssList(U)|(singletonP(U)<=>(?[V]: (ssItem(V)&cons(V,nil)=U))))),
% 0.11/0.41 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 0.11/0.41 fof(f114,plain,(
% 0.11/0.41 ![U]: (~ssList(U)|((~singletonP(U)|(?[V]: (ssItem(V)&cons(V,nil)=U)))&(singletonP(U)|(![V]: (~ssItem(V)|~cons(V,nil)=U)))))),
% 0.11/0.41 inference(NNF_transformation,[status(thm)],[f113])).
% 0.11/0.41 fof(f115,plain,(
% 0.11/0.41 ![U]: (~ssList(U)|((~singletonP(U)|(ssItem(sK4_skl(U))&cons(sK4_skl(U),nil)=U))&(singletonP(U)|(![V]: (~ssItem(V)|~cons(V,nil)=U)))))),
% 0.11/0.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(V,sK4_skl(U))],[f114])).
% 0.11/0.41 fof(f116,plain,(
% 0.11/0.41 ![X0]: (~ssList(X0)|~singletonP(X0)|ssItem(sK4_skl(X0)))),
% 0.11/0.41 inference(cnf_transformation,[status(thm)],[f115])).
% 0.11/0.41 fof(f119,plain,(
% 0.11/0.41 ![U]: (~ssList(U)|(![V]: (~ssList(V)|(frontsegP(U,V)<=>(?[W]: (ssList(W)&app(V,W)=U))))))),
% 0.11/0.41 inference(pre_NNF_transformation,[status(thm)],[f5])).
% 0.11/0.41 fof(f120,plain,(
% 0.11/0.41 ![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)))))))),
% 0.11/0.41 inference(NNF_transformation,[status(thm)],[f119])).
% 0.11/0.41 fof(f121,plain,(
% 0.11/0.41 ![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)))))))),
% 0.11/0.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(W,sK5_skl(V,U))],[f120])).
% 0.11/0.41 fof(f122,plain,(
% 0.11/0.41 ![X0,X1]: (~ssList(X0)|~ssList(X1)|~frontsegP(X0,X1)|ssList(sK5_skl(X1,X0)))),
% 0.11/0.41 inference(cnf_transformation,[status(thm)],[f121])).
% 0.11/0.41 fof(f123,plain,(
% 0.11/0.41 ![X0,X1]: (~ssList(X0)|~ssList(X1)|~frontsegP(X0,X1)|app(X1,sK5_skl(X1,X0))=X0)),
% 0.11/0.41 inference(cnf_transformation,[status(thm)],[f121])).
% 0.11/0.41 fof(f223,plain,(
% 0.11/0.41 ssList(nil)),
% 0.11/0.41 inference(cnf_transformation,[status(thm)],[f17])).
% 0.11/0.41 fof(f285,plain,(
% 0.11/0.41 ![U]: (~ssList(U)|frontsegP(U,U))),
% 0.11/0.41 inference(pre_NNF_transformation,[status(thm)],[f42])).
% 0.11/0.41 fof(f286,plain,(
% 0.11/0.41 ![X0]: (~ssList(X0)|frontsegP(X0,X0))),
% 0.11/0.41 inference(cnf_transformation,[status(thm)],[f285])).
% 0.11/0.41 fof(f314,plain,(
% 0.11/0.41 ![U]: (~ssList(U)|(![V]: (~ssList(V)|(![W]: (~ssList(W)|((~segmentP(U,V)|~segmentP(V,W))|segmentP(U,W)))))))),
% 0.11/0.41 inference(pre_NNF_transformation,[status(thm)],[f53])).
% 0.11/0.41 fof(f315,plain,(
% 0.11/0.41 ![X0,X1,X2]: (~ssList(X0)|~ssList(X1)|~ssList(X2)|~segmentP(X0,X1)|~segmentP(X1,X2)|segmentP(X0,X2))),
% 0.11/0.41 inference(cnf_transformation,[status(thm)],[f314])).
% 0.11/0.41 fof(f318,plain,(
% 0.11/0.41 ![U]: (~ssList(U)|segmentP(U,U))),
% 0.11/0.41 inference(pre_NNF_transformation,[status(thm)],[f55])).
% 0.11/0.41 fof(f319,plain,(
% 0.11/0.41 ![X0]: (~ssList(X0)|segmentP(X0,X0))),
% 0.11/0.41 inference(cnf_transformation,[status(thm)],[f318])).
% 0.11/0.41 fof(f415,plain,(
% 0.11/0.41 (?[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))&segmentP(X,Y))&segmentP(W,Y)))|~neq(X,nil)))&((nil=V&~nil=U)|(neq(V,nil)&(![Z]: (((~ssList(Z)|~neq(Z,nil))|~segmentP(V,Z))|~segmentP(U,Z)))))))))))))),
% 0.11/0.41 inference(pre_NNF_transformation,[status(thm)],[f97])).
% 0.11/0.41 fof(f416,definition,(
% 0.11/0.41 ![U,V]: (sP0_prd(V,U)<=>(nil=V&~nil=U))),
% 0.11/0.41 introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 0.11/0.41 fof(f417,plain,(
% 0.11/0.41 ?[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))&segmentP(X,Y))&segmentP(W,Y)))|~neq(X,nil)))&(sP0_prd(V,U)|(neq(V,nil)&(![Z]: (((~ssList(Z)|~neq(Z,nil))|~segmentP(V,Z))|~segmentP(U,Z))))))))))))),
% 0.11/0.41 inference(formula_renaming,[status(thm)],[f415,f416])).
% 0.11/0.41 fof(f418,plain,(
% 0.11/0.41 ?[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))&segmentP(X,Y))&segmentP(W,Y)))|~neq(X,nil))))&(sP0_prd(V,U)|(neq(V,nil)&(![Z]: (((~ssList(Z)|~neq(Z,nil))|~segmentP(V,Z))|~segmentP(U,Z)))))))))))),
% 0.11/0.41 inference(miniscoping,[status(thm)],[f417])).
% 0.11/0.41 fof(f419,plain,(
% 0.11/0.41 (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))&segmentP(sK50_skl,sK51_skl))&segmentP(sK49_skl,sK51_skl))|~neq(sK50_skl,nil)))&(sP0_prd(sK48_skl,sK47_skl)|(neq(sK48_skl,nil)&(![Z]: (((~ssList(Z)|~neq(Z,nil))|~segmentP(sK48_skl,Z))|~segmentP(sK47_skl,Z)))))))))),
% 0.11/0.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK47_skl,sK48_skl,sK49_skl,sK50_skl,sK51_skl]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl),skolemize(Y,sK51_skl)],[f418])).
% 0.11/0.41 fof(f422,plain,(
% 0.11/0.41 ssList(sK49_skl)),
% 0.11/0.41 inference(cnf_transformation,[status(thm)],[f419])).
% 0.11/0.41 fof(f423,plain,(
% 0.11/0.41 ssList(sK50_skl)),
% 0.11/0.41 inference(cnf_transformation,[status(thm)],[f419])).
% 0.11/0.41 fof(f424,plain,(
% 0.11/0.41 sK48_skl=sK50_skl),
% 0.11/0.41 inference(cnf_transformation,[status(thm)],[f419])).
% 0.11/0.41 fof(f425,plain,(
% 0.11/0.41 sK47_skl=sK49_skl),
% 0.11/0.41 inference(cnf_transformation,[status(thm)],[f419])).
% 0.11/0.41 fof(f426,plain,(
% 0.11/0.41 nil=sK49_skl|~nil=sK50_skl),
% 0.11/0.41 inference(cnf_transformation,[status(thm)],[f419])).
% 0.11/0.41 fof(f427,plain,(
% 0.11/0.41 ssList(sK51_skl)|~neq(sK50_skl,nil)),
% 0.11/0.41 inference(cnf_transformation,[status(thm)],[f419])).
% 0.11/0.41 fof(f428,plain,(
% 0.11/0.41 neq(sK51_skl,nil)|~neq(sK50_skl,nil)),
% 0.11/0.41 inference(cnf_transformation,[status(thm)],[f419])).
% 0.11/0.41 fof(f429,plain,(
% 0.11/0.41 segmentP(sK50_skl,sK51_skl)|~neq(sK50_skl,nil)),
% 0.11/0.41 inference(cnf_transformation,[status(thm)],[f419])).
% 0.11/0.41 fof(f430,plain,(
% 0.11/0.41 segmentP(sK49_skl,sK51_skl)|~neq(sK50_skl,nil)),
% 0.11/0.41 inference(cnf_transformation,[status(thm)],[f419])).
% 0.11/0.41 fof(f431,plain,(
% 0.11/0.41 sP0_prd(sK48_skl,sK47_skl)|neq(sK48_skl,nil)),
% 0.11/0.41 inference(cnf_transformation,[status(thm)],[f419])).
% 0.11/0.41 fof(f432,plain,(
% 0.11/0.41 ![X0]: (sP0_prd(sK48_skl,sK47_skl)|~ssList(X0)|~neq(X0,nil)|~segmentP(sK48_skl,X0)|~segmentP(sK47_skl,X0))),
% 0.11/0.41 inference(cnf_transformation,[status(thm)],[f419])).
% 0.11/0.41 fof(f433,plain,(
% 0.11/0.41 ![U,V]: ((~sP0_prd(V,U)|(nil=V&~nil=U))&(sP0_prd(V,U)|(~nil=V|nil=U)))),
% 0.11/0.41 inference(NNF_transformation,[status(thm)],[f416])).
% 0.11/0.41 fof(f434,plain,(
% 0.11/0.41 (![U,V]: (~sP0_prd(V,U)|(nil=V&~nil=U)))&(![U,V]: (sP0_prd(V,U)|(~nil=V|nil=U)))),
% 0.11/0.41 inference(miniscoping,[status(thm)],[f433])).
% 0.11/0.41 fof(f435,plain,(
% 0.11/0.41 ![X0,X1]: (~sP0_prd(X0,X1)|nil=X0)),
% 0.11/0.41 inference(cnf_transformation,[status(thm)],[f434])).
% 0.11/0.41 fof(f436,plain,(
% 0.11/0.41 ![X0,X1]: (~sP0_prd(X0,X1)|~nil=X1)),
% 0.11/0.41 inference(cnf_transformation,[status(thm)],[f434])).
% 0.11/0.41 fof(f437,plain,(
% 0.11/0.41 ![X0,X1]: (sP0_prd(X0,X1)|~nil=X0|nil=X1)),
% 0.11/0.41 inference(cnf_transformation,[status(thm)],[f434])).
% 0.11/0.41 fof(f438,definition,(
% 0.11/0.41 sQ0_spl <=> (nil=sK49_skl)),
% 0.11/0.41 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.11/0.41 fof(f439,plain,(
% 0.11/0.41 nil=sK49_skl|~sQ0_spl),
% 0.11/0.41 inference(component_clause,[status(thm)],[f438])).
% 0.11/0.41 fof(f441,definition,(
% 0.11/0.41 sQ1_spl <=> (nil=sK50_skl)),
% 0.11/0.41 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.11/0.41 fof(f443,plain,(
% 0.11/0.41 ~nil=sK50_skl|sQ1_spl),
% 0.11/0.41 inference(component_clause,[status(thm)],[f441])).
% 0.11/0.41 fof(f444,plain,(
% 0.11/0.41 sQ0_spl|~sQ1_spl),
% 0.11/0.41 inference(split_clause,[status(thm)],[f426,f438,f441])).
% 0.11/0.41 fof(f445,definition,(
% 0.11/0.41 sQ2_spl <=> (ssList(sK51_skl))),
% 0.11/0.41 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.11/0.41 fof(f446,plain,(
% 0.11/0.41 ssList(sK51_skl)|~sQ2_spl),
% 0.11/0.41 inference(component_clause,[status(thm)],[f445])).
% 0.11/0.41 fof(f448,definition,(
% 0.11/0.41 sQ3_spl <=> (neq(sK50_skl,nil))),
% 0.11/0.41 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.11/0.41 fof(f450,plain,(
% 0.11/0.41 ~neq(sK50_skl,nil)|sQ3_spl),
% 0.11/0.41 inference(component_clause,[status(thm)],[f448])).
% 0.11/0.41 fof(f451,plain,(
% 0.11/0.41 sQ2_spl|~sQ3_spl),
% 0.11/0.41 inference(split_clause,[status(thm)],[f427,f445,f448])).
% 0.11/0.41 fof(f452,definition,(
% 0.11/0.41 sQ4_spl <=> (neq(sK51_skl,nil))),
% 0.11/0.41 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 0.11/0.41 fof(f453,plain,(
% 0.11/0.41 neq(sK51_skl,nil)|~sQ4_spl),
% 0.11/0.41 inference(component_clause,[status(thm)],[f452])).
% 0.11/0.41 fof(f455,plain,(
% 0.11/0.41 sQ4_spl|~sQ3_spl),
% 0.11/0.41 inference(split_clause,[status(thm)],[f428,f452,f448])).
% 0.11/0.41 fof(f456,definition,(
% 0.11/0.41 sQ5_spl <=> (segmentP(sK50_skl,sK51_skl))),
% 0.11/0.41 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 0.11/0.41 fof(f459,plain,(
% 0.11/0.41 sQ5_spl|~sQ3_spl),
% 0.11/0.41 inference(split_clause,[status(thm)],[f429,f456,f448])).
% 0.11/0.41 fof(f460,definition,(
% 0.11/0.41 sQ6_spl <=> (segmentP(sK49_skl,sK51_skl))),
% 0.11/0.41 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.11/0.41 fof(f461,plain,(
% 0.11/0.41 segmentP(sK49_skl,sK51_skl)|~sQ6_spl),
% 0.11/0.41 inference(component_clause,[status(thm)],[f460])).
% 0.11/0.41 fof(f463,plain,(
% 0.11/0.41 sQ6_spl|~sQ3_spl),
% 0.11/0.41 inference(split_clause,[status(thm)],[f430,f460,f448])).
% 0.11/0.41 fof(f464,definition,(
% 0.11/0.41 sQ7_spl <=> (sP0_prd(sK48_skl,sK47_skl))),
% 0.11/0.41 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 0.11/0.41 fof(f465,plain,(
% 0.11/0.41 sP0_prd(sK48_skl,sK47_skl)|~sQ7_spl),
% 0.11/0.41 inference(component_clause,[status(thm)],[f464])).
% 0.11/0.41 fof(f467,definition,(
% 0.11/0.41 sQ8_spl <=> (neq(sK48_skl,nil))),
% 0.11/0.41 introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition])).
% 0.11/0.41 fof(f468,plain,(
% 0.11/0.41 neq(sK48_skl,nil)|~sQ8_spl),
% 0.11/0.41 inference(component_clause,[status(thm)],[f467])).
% 0.11/0.41 fof(f470,plain,(
% 0.11/0.41 sQ7_spl|sQ8_spl),
% 0.11/0.41 inference(split_clause,[status(thm)],[f431,f464,f467])).
% 0.11/0.41 fof(f471,definition,(
% 0.11/0.41 ![X0]: (sQ9_spl <=> (~ssList(X0)|~neq(X0,nil)|~segmentP(sK48_skl,X0)|~segmentP(sK47_skl,X0)))),
% 0.11/0.41 introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition])).
% 0.11/0.41 fof(f472,plain,(
% 0.11/0.41 ![X0]: (~ssList(X0)|~neq(X0,nil)|~segmentP(sK48_skl,X0)|~segmentP(sK47_skl,X0)|~sQ9_spl)),
% 0.11/0.41 inference(component_clause,[status(thm)],[f471])).
% 0.11/0.41 fof(f474,plain,(
% 0.11/0.41 sQ7_spl|sQ9_spl),
% 0.11/0.41 inference(split_clause,[status(thm)],[f432,f464,f471])).
% 0.11/0.41 fof(f505,plain,(
% 0.11/0.41 ![X0]: (~sP0_prd(X0,nil))),
% 0.11/0.41 inference(destructive_equality_resolution,[status(thm)],[f436])).
% 0.11/0.41 fof(f506,plain,(
% 0.11/0.41 ![X0]: (sP0_prd(nil,X0)|nil=X0)),
% 0.11/0.41 inference(destructive_equality_resolution,[status(thm)],[f437])).
% 0.11/0.41 fof(f510,plain,(
% 0.11/0.41 ![X0]: (~sP0_prd(X0,sK49_skl)|~sQ0_spl)),
% 0.11/0.41 inference(forward_demodulation,[status(thm)],[f439,f505])).
% 0.11/0.41 fof(f512,plain,(
% 0.11/0.41 sP0_prd(sK50_skl,sK47_skl)|~sQ7_spl),
% 0.11/0.41 inference(forward_demodulation,[status(thm)],[f424,f465])).
% 0.11/0.41 fof(f513,plain,(
% 0.11/0.41 sP0_prd(sK50_skl,sK49_skl)|~sQ7_spl),
% 0.11/0.41 inference(forward_demodulation,[status(thm)],[f425,f512])).
% 0.11/0.41 fof(f514,plain,(
% 0.11/0.41 $false|~sQ0_spl|~sQ7_spl),
% 0.11/0.41 inference(forward_subsumption_resolution,[status(thm)],[f513,f510])).
% 0.11/0.41 fof(f515,plain,(
% 0.11/0.41 ~sQ0_spl|~sQ7_spl),
% 0.11/0.41 inference(contradiction_clause,[status(thm)],[f514])).
% 0.11/0.41 fof(f516,plain,(
% 0.11/0.41 neq(sK50_skl,nil)|~sQ8_spl),
% 0.11/0.41 inference(forward_demodulation,[status(thm)],[f424,f468])).
% 0.11/0.41 fof(f517,plain,(
% 0.11/0.41 ![X0]: (~ssList(X0)|~neq(X0,nil)|~segmentP(sK50_skl,X0)|~segmentP(sK47_skl,X0)|~sQ9_spl)),
% 0.11/0.41 inference(forward_demodulation,[status(thm)],[f424,f472])).
% 0.11/0.41 fof(f518,plain,(
% 0.11/0.41 ![X0]: (~ssList(X0)|~neq(X0,nil)|~segmentP(sK50_skl,X0)|~segmentP(sK49_skl,X0)|~sQ9_spl)),
% 0.11/0.41 inference(forward_demodulation,[status(thm)],[f425,f517])).
% 0.11/0.41 fof(f523,plain,(
% 0.11/0.41 $false|~sQ8_spl|sQ3_spl),
% 0.11/0.41 inference(forward_subsumption_resolution,[status(thm)],[f450,f516])).
% 0.11/0.41 fof(f524,plain,(
% 0.11/0.41 ~sQ8_spl|sQ3_spl),
% 0.11/0.41 inference(contradiction_clause,[status(thm)],[f523])).
% 0.11/0.41 fof(f525,plain,(
% 0.11/0.41 nil=sK50_skl|~sQ7_spl),
% 0.11/0.41 inference(resolution,[status(thm)],[f435,f513])).
% 0.11/0.41 fof(f526,plain,(
% 0.11/0.41 $false|sQ1_spl|~sQ7_spl),
% 0.11/0.41 inference(forward_subsumption_resolution,[status(thm)],[f525,f443])).
% 0.11/0.41 fof(f527,plain,(
% 0.11/0.41 sQ1_spl|~sQ7_spl),
% 0.11/0.41 inference(contradiction_clause,[status(thm)],[f526])).
% 0.11/0.41 fof(f529,plain,(
% 0.11/0.41 ![X0]: (nil=X0|nil=nil)),
% 0.11/0.41 inference(resolution,[status(thm)],[f506,f435])).
% 0.11/0.41 fof(f530,definition,(
% 0.11/0.41 ![X0]: (sQ10_spl <=> (nil=X0))),
% 0.11/0.41 introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition])).
% 0.11/0.41 fof(f531,plain,(
% 0.11/0.41 ![X0]: (nil=X0|~sQ10_spl)),
% 0.11/0.41 inference(component_clause,[status(thm)],[f530])).
% 0.11/0.41 fof(f533,definition,(
% 0.11/0.41 sQ11_spl <=> (nil=nil)),
% 0.11/0.41 introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition])).
% 0.11/0.41 fof(f536,plain,(
% 0.11/0.41 sQ10_spl|sQ11_spl),
% 0.11/0.41 inference(split_clause,[status(thm)],[f529,f530,f533])).
% 0.11/0.41 fof(f537,plain,(
% 0.11/0.41 ![X0,X1]: (X0=X1|~sQ10_spl)),
% 0.11/0.41 inference(paramodulation,[status(thm)],[f531,f531])).
% 0.11/0.41 fof(f550,plain,(
% 0.11/0.41 $false|~sQ10_spl),
% 0.11/0.41 inference(backward_subsumption_resolution,[status(thm)],[f105,f537])).
% 0.11/0.41 fof(f551,plain,(
% 0.11/0.41 ~sQ10_spl),
% 0.11/0.41 inference(contradiction_clause,[status(thm)],[f550])).
% 0.11/0.41 fof(f566,plain,(
% 0.11/0.41 frontsegP(sK51_skl,sK51_skl)|~sQ2_spl),
% 0.11/0.41 inference(resolution,[status(thm)],[f286,f446])).
% 0.11/0.41 fof(f567,plain,(
% 0.11/0.41 frontsegP(sK50_skl,sK50_skl)),
% 0.11/0.41 inference(resolution,[status(thm)],[f286,f423])).
% 0.11/0.41 fof(f568,plain,(
% 0.11/0.41 frontsegP(sK49_skl,sK49_skl)),
% 0.11/0.41 inference(resolution,[status(thm)],[f286,f422])).
% 0.11/0.41 fof(f569,plain,(
% 0.11/0.41 ~singletonP(sK51_skl)|ssItem(sK4_skl(sK51_skl))|~sQ2_spl),
% 0.11/0.41 inference(resolution,[status(thm)],[f116,f446])).
% 0.11/0.41 fof(f572,definition,(
% 0.11/0.41 sQ12_spl <=> (singletonP(sK51_skl))),
% 0.11/0.41 introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition])).
% 0.11/0.41 fof(f575,definition,(
% 0.11/0.41 sQ13_spl <=> (ssItem(sK4_skl(sK51_skl)))),
% 0.11/0.41 introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition])).
% 0.11/0.41 fof(f578,plain,(
% 0.11/0.41 ~sQ12_spl|sQ13_spl|~sQ2_spl),
% 0.11/0.41 inference(split_clause,[status(thm)],[f569,f572,f575,f445])).
% 0.11/0.41 fof(f625,definition,(
% 0.11/0.41 sQ23_spl <=> (ssList(sK50_skl))),
% 0.11/0.41 introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition])).
% 0.11/0.41 fof(f627,plain,(
% 0.11/0.41 ~ssList(sK50_skl)|sQ23_spl),
% 0.11/0.41 inference(component_clause,[status(thm)],[f625])).
% 0.11/0.41 fof(f636,plain,(
% 0.11/0.41 frontsegP(nil,nil)),
% 0.11/0.41 inference(resolution,[status(thm)],[f223,f286])).
% 0.11/0.41 fof(f648,plain,(
% 0.11/0.41 ![X0]: (~ssList(X0)|~ssList(sK49_skl)|~ssList(sK51_skl)|~segmentP(X0,sK49_skl)|segmentP(X0,sK51_skl)|~sQ6_spl)),
% 0.11/0.41 inference(resolution,[status(thm)],[f315,f461])).
% 0.11/0.41 fof(f652,definition,(
% 0.11/0.41 ![X0]: (sQ28_spl <=> (~ssList(X0)|~segmentP(X0,sK49_skl)|segmentP(X0,sK51_skl)))),
% 0.11/0.41 introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition])).
% 0.11/0.41 fof(f655,definition,(
% 0.11/0.41 sQ29_spl <=> (ssList(sK49_skl))),
% 0.11/0.41 introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition])).
% 0.11/0.41 fof(f657,plain,(
% 0.11/0.41 ~ssList(sK49_skl)|sQ29_spl),
% 0.11/0.41 inference(component_clause,[status(thm)],[f655])).
% 0.11/0.41 fof(f658,plain,(
% 0.11/0.41 sQ28_spl|~sQ29_spl|~sQ2_spl|~sQ6_spl),
% 0.11/0.41 inference(split_clause,[status(thm)],[f648,f652,f655,f445,f460])).
% 0.11/0.41 fof(f665,plain,(
% 0.11/0.41 $false|sQ23_spl),
% 0.11/0.41 inference(forward_subsumption_resolution,[status(thm)],[f627,f423])).
% 0.11/0.41 fof(f666,plain,(
% 0.11/0.41 sQ23_spl),
% 0.11/0.41 inference(contradiction_clause,[status(thm)],[f665])).
% 0.11/0.41 fof(f671,plain,(
% 0.11/0.41 segmentP(nil,nil)),
% 0.11/0.41 inference(resolution,[status(thm)],[f319,f223])).
% 0.11/0.41 fof(f672,plain,(
% 0.11/0.41 segmentP(sK51_skl,sK51_skl)|~sQ2_spl),
% 0.11/0.41 inference(resolution,[status(thm)],[f319,f446])).
% 0.11/0.41 fof(f673,plain,(
% 0.11/0.41 segmentP(sK50_skl,sK50_skl)),
% 0.11/0.41 inference(resolution,[status(thm)],[f319,f423])).
% 0.11/0.41 fof(f674,plain,(
% 0.11/0.41 segmentP(sK49_skl,sK49_skl)),
% 0.11/0.41 inference(resolution,[status(thm)],[f319,f422])).
% 0.11/0.41 fof(f675,plain,(
% 0.11/0.41 ![X0]: (~ssList(X0)|~ssList(nil)|~ssList(nil)|~segmentP(X0,nil)|segmentP(X0,nil))),
% 0.11/0.41 inference(resolution,[status(thm)],[f671,f315])).
% 0.11/0.41 fof(f676,definition,(
% 0.11/0.41 ![X0]: (sQ31_spl <=> (~ssList(X0)|~segmentP(X0,nil)|segmentP(X0,nil)))),
% 0.11/0.41 introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition])).
% 0.11/0.41 fof(f679,definition,(
% 0.11/0.41 sQ32_spl <=> (ssList(nil))),
% 0.11/0.41 introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition])).
% 0.11/0.41 fof(f681,plain,(
% 0.11/0.41 ~ssList(nil)|sQ32_spl),
% 0.11/0.41 inference(component_clause,[status(thm)],[f679])).
% 0.11/0.41 fof(f682,plain,(
% 0.11/0.41 sQ31_spl|~sQ32_spl),
% 0.11/0.41 inference(split_clause,[status(thm)],[f675,f676,f679])).
% 0.11/0.41 fof(f683,plain,(
% 0.11/0.41 ~ssList(nil)|~ssList(nil)|ssList(sK5_skl(nil,nil))),
% 0.11/0.41 inference(resolution,[status(thm)],[f122,f636])).
% 0.11/0.41 fof(f684,plain,(
% 0.11/0.41 ~ssList(sK49_skl)|~ssList(sK49_skl)|ssList(sK5_skl(sK49_skl,sK49_skl))),
% 0.11/0.41 inference(resolution,[status(thm)],[f122,f568])).
% 0.11/0.41 fof(f685,plain,(
% 0.11/0.41 ~ssList(sK50_skl)|~ssList(sK50_skl)|ssList(sK5_skl(sK50_skl,sK50_skl))),
% 0.11/0.41 inference(resolution,[status(thm)],[f122,f567])).
% 0.11/0.41 fof(f686,plain,(
% 0.11/0.41 ~ssList(sK51_skl)|~ssList(sK51_skl)|ssList(sK5_skl(sK51_skl,sK51_skl))|~sQ2_spl),
% 0.11/0.41 inference(resolution,[status(thm)],[f122,f566])).
% 0.11/0.41 fof(f687,definition,(
% 0.11/0.41 sQ33_spl <=> (ssList(sK5_skl(nil,nil)))),
% 0.11/0.41 introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition])).
% 0.11/0.41 fof(f690,plain,(
% 0.11/0.41 ~sQ32_spl|sQ33_spl),
% 0.11/0.41 inference(split_clause,[status(thm)],[f683,f679,f687])).
% 0.11/0.41 fof(f691,definition,(
% 0.11/0.41 sQ34_spl <=> (ssList(sK5_skl(sK49_skl,sK49_skl)))),
% 0.11/0.41 introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition])).
% 0.11/0.41 fof(f694,plain,(
% 0.11/0.41 ~sQ29_spl|sQ34_spl),
% 0.11/0.41 inference(split_clause,[status(thm)],[f684,f655,f691])).
% 0.11/0.41 fof(f695,definition,(
% 0.11/0.41 sQ35_spl <=> (ssList(sK5_skl(sK50_skl,sK50_skl)))),
% 0.11/0.41 introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition])).
% 0.11/0.41 fof(f698,plain,(
% 0.11/0.41 ~sQ23_spl|sQ35_spl),
% 0.11/0.41 inference(split_clause,[status(thm)],[f685,f625,f695])).
% 0.11/0.41 fof(f699,definition,(
% 0.11/0.41 sQ36_spl <=> (ssList(sK5_skl(sK51_skl,sK51_skl)))),
% 0.11/0.41 introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition])).
% 0.11/0.41 fof(f702,plain,(
% 0.11/0.41 ~sQ2_spl|sQ36_spl),
% 0.11/0.41 inference(split_clause,[status(thm)],[f686,f445,f699])).
% 0.11/0.41 fof(f703,plain,(
% 0.11/0.41 $false|sQ29_spl),
% 0.11/0.41 inference(forward_subsumption_resolution,[status(thm)],[f657,f422])).
% 0.11/0.41 fof(f704,plain,(
% 0.11/0.41 sQ29_spl),
% 0.11/0.41 inference(contradiction_clause,[status(thm)],[f703])).
% 0.11/0.41 fof(f705,plain,(
% 0.11/0.41 $false|sQ32_spl),
% 0.11/0.41 inference(forward_subsumption_resolution,[status(thm)],[f681,f223])).
% 0.11/0.41 fof(f706,plain,(
% 0.11/0.41 sQ32_spl),
% 0.11/0.41 inference(contradiction_clause,[status(thm)],[f705])).
% 0.11/0.41 fof(f707,plain,(
% 0.11/0.41 ~ssList(nil)|~ssList(nil)|app(nil,sK5_skl(nil,nil))=nil),
% 0.11/0.41 inference(resolution,[status(thm)],[f123,f636])).
% 0.11/0.41 fof(f708,plain,(
% 0.11/0.41 ~ssList(sK49_skl)|~ssList(sK49_skl)|app(sK49_skl,sK5_skl(sK49_skl,sK49_skl))=sK49_skl),
% 0.11/0.41 inference(resolution,[status(thm)],[f123,f568])).
% 0.11/0.41 fof(f709,plain,(
% 0.11/0.41 ~ssList(sK50_skl)|~ssList(sK50_skl)|app(sK50_skl,sK5_skl(sK50_skl,sK50_skl))=sK50_skl),
% 0.11/0.41 inference(resolution,[status(thm)],[f123,f567])).
% 0.11/0.41 fof(f710,plain,(
% 0.11/0.41 ~ssList(sK51_skl)|~ssList(sK51_skl)|app(sK51_skl,sK5_skl(sK51_skl,sK51_skl))=sK51_skl|~sQ2_spl),
% 0.11/0.41 inference(resolution,[status(thm)],[f123,f566])).
% 0.11/0.41 fof(f711,definition,(
% 0.11/0.41 sQ37_spl <=> (app(nil,sK5_skl(nil,nil))=nil)),
% 0.11/0.41 introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition])).
% 0.11/0.41 fof(f714,plain,(
% 0.11/0.41 ~sQ32_spl|sQ37_spl),
% 0.11/0.41 inference(split_clause,[status(thm)],[f707,f679,f711])).
% 0.11/0.41 fof(f715,definition,(
% 0.11/0.41 sQ38_spl <=> (app(sK49_skl,sK5_skl(sK49_skl,sK49_skl))=sK49_skl)),
% 0.11/0.41 introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition])).
% 0.11/0.41 fof(f718,plain,(
% 0.11/0.41 ~sQ29_spl|sQ38_spl),
% 0.11/0.41 inference(split_clause,[status(thm)],[f708,f655,f715])).
% 0.11/0.41 fof(f719,definition,(
% 0.11/0.41 sQ39_spl <=> (app(sK50_skl,sK5_skl(sK50_skl,sK50_skl))=sK50_skl)),
% 0.11/0.41 introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition])).
% 0.11/0.41 fof(f722,plain,(
% 0.11/0.41 ~sQ23_spl|sQ39_spl),
% 0.11/0.41 inference(split_clause,[status(thm)],[f709,f625,f719])).
% 0.11/0.41 fof(f723,definition,(
% 0.11/0.41 sQ40_spl <=> (app(sK51_skl,sK5_skl(sK51_skl,sK51_skl))=sK51_skl)),
% 0.11/0.41 introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition])).
% 0.11/0.41 fof(f726,plain,(
% 0.11/0.41 ~sQ2_spl|sQ40_spl),
% 0.11/0.41 inference(split_clause,[status(thm)],[f710,f445,f723])).
% 0.11/0.41 fof(f727,plain,(
% 0.11/0.41 ![X0]: (~ssList(X0)|~ssList(sK51_skl)|~ssList(sK51_skl)|~segmentP(X0,sK51_skl)|segmentP(X0,sK51_skl)|~sQ2_spl)),
% 0.11/0.41 inference(resolution,[status(thm)],[f672,f315])).
% 0.11/0.41 fof(f728,definition,(
% 0.11/0.41 ![X0]: (sQ41_spl <=> (~ssList(X0)|~segmentP(X0,sK51_skl)|segmentP(X0,sK51_skl)))),
% 0.11/0.41 introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition])).
% 0.11/0.41 fof(f731,plain,(
% 0.11/0.41 sQ41_spl|~sQ2_spl),
% 0.11/0.41 inference(split_clause,[status(thm)],[f727,f728,f445])).
% 0.11/0.41 fof(f732,plain,(
% 0.11/0.41 ![X0]: (~ssList(X0)|~ssList(sK50_skl)|~ssList(sK50_skl)|~segmentP(X0,sK50_skl)|segmentP(X0,sK50_skl))),
% 0.11/0.41 inference(resolution,[status(thm)],[f673,f315])).
% 0.11/0.41 fof(f733,definition,(
% 0.11/0.41 ![X0]: (sQ42_spl <=> (~ssList(X0)|~segmentP(X0,sK50_skl)|segmentP(X0,sK50_skl)))),
% 0.11/0.41 introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition])).
% 0.11/0.41 fof(f736,plain,(
% 0.11/0.41 sQ42_spl|~sQ23_spl),
% 0.11/0.41 inference(split_clause,[status(thm)],[f732,f733,f625])).
% 0.11/0.41 fof(f737,plain,(
% 0.11/0.41 ![X0]: (~ssList(X0)|~ssList(sK49_skl)|~ssList(sK49_skl)|~segmentP(X0,sK49_skl)|segmentP(X0,sK49_skl))),
% 0.11/0.41 inference(resolution,[status(thm)],[f674,f315])).
% 0.11/0.41 fof(f738,definition,(
% 0.11/0.41 ![X0]: (sQ43_spl <=> (~ssList(X0)|~segmentP(X0,sK49_skl)|segmentP(X0,sK49_skl)))),
% 0.11/0.41 introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition])).
% 0.11/0.41 fof(f741,plain,(
% 0.11/0.41 sQ43_spl|~sQ29_spl),
% 0.11/0.41 inference(split_clause,[status(thm)],[f737,f738,f655])).
% 0.11/0.41 fof(f745,plain,(
% 0.11/0.41 ~ssList(sK51_skl)|~segmentP(sK50_skl,sK51_skl)|~segmentP(sK49_skl,sK51_skl)|~sQ9_spl|~sQ4_spl),
% 0.11/0.41 inference(resolution,[status(thm)],[f518,f453])).
% 0.11/0.41 fof(f747,plain,(
% 0.11/0.41 ~sQ2_spl|~sQ5_spl|~sQ6_spl|~sQ9_spl|~sQ4_spl),
% 0.11/0.41 inference(split_clause,[status(thm)],[f745,f445,f456,f460,f471,f452])).
% 0.11/0.41 fof(f749,plain,(
% 0.11/0.41 $false),
% 0.11/0.41 inference(sat_refutation,[status(thm)],[f444,f451,f455,f459,f463,f470,f474,f515,f524,f527,f536,f551,f578,f658,f666,f682,f690,f694,f698,f702,f704,f706,f714,f718,f722,f726,f731,f736,f741,f747])).
% 0.11/0.41 % SZS output end CNFRefutation for theBenchmark.p
% 0.11/0.44 % Elapsed time: 0.068569 seconds
% 0.11/0.44 % CPU time: 0.184542 seconds
% 0.11/0.44 % Total memory used: 110.832 MB
% 0.11/0.44 % Net memory used: 110.705 MB
%------------------------------------------------------------------------------