%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SWC200+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 : n001.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 02:41:50 PM UTC 2026
% Result : Theorem 0.18s 0.53s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC200+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.43 % Computer : n001.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Mon Sep 21 08:09:44 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.46 % Drodi V4.1.1
% 0.18/0.53 % Refutation found
% 0.18/0.53 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.18/0.53 % SZS output start CNFRefutation for theBenchmark
% 0.18/0.53 fof(f2,axiom,(
% 0.18/0.53 (? [U] :( ssItem(U)& (? [V] :( ssItem(V)& U != V ) )) )),
% 0.18/0.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.18/0.53 fof(f3,axiom,(
% 0.18/0.53 (! [U] :( ssList(U)=> (! [V] :( ssItem(V)=> ( memberP(U,V)<=> (? [W] :( ssList(W)& (? [X] :( ssList(X)& app(W,cons(V,X)) = U ) )) )) ) )) )),
% 0.18/0.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.18/0.53 fof(f4,axiom,(
% 0.18/0.53 (! [U] :( ssList(U)=> ( singletonP(U)<=> (? [V] :( ssItem(V)& cons(V,nil) = U ) )) ) )),
% 0.18/0.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.18/0.53 fof(f17,axiom,(
% 0.18/0.53 ssList(nil) ),
% 0.18/0.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.18/0.53 fof(f37,axiom,(
% 0.18/0.53 (! [U] :( ssItem(U)=> (! [V] :( ssItem(V)=> (! [W] :( ssList(W)=> ( memberP(cons(V,W),U)<=> ( U = V| memberP(W,U) ) ) ) )) )) )),
% 0.18/0.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.18/0.53 fof(f38,axiom,(
% 0.18/0.53 (! [U] :( ssItem(U)=> ~ memberP(nil,U) ) )),
% 0.18/0.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.18/0.53 fof(f96,conjecture,(
% 0.18/0.53 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> (! [X] :( ssList(X)=> ( V != X| U != W| ~ singletonP(W)| (? [Y] :( ssItem(Y)& (! [Z] :( ssItem(Z)=> ( ~ memberP(U,Z)| Y = Z ) ) )) )) ) )) )) )) )),
% 0.18/0.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.18/0.53 fof(f97,negated_conjecture,(
% 0.18/0.53 ~((! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> (! [X] :( ssList(X)=> ( V != X| U != W| ~ singletonP(W)| (? [Y] :( ssItem(Y)& (! [Z] :( ssItem(Z)=> ( ~ memberP(U,Z)| Y = Z ) ) )) )) ) )) )) )) ))),
% 0.18/0.53 inference(negated_conjecture,[status(cth)],[f96])).
% 0.18/0.53 fof(f102,plain,(
% 0.18/0.53 (ssItem(sK0_skl)&(ssItem(sK1_skl)&~sK0_skl=sK1_skl))),
% 0.18/0.53 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(U,sK0_skl),skolemize(V,sK1_skl)],[f2])).
% 0.18/0.53 fof(f103,plain,(
% 0.18/0.53 ssItem(sK0_skl)),
% 0.18/0.53 inference(cnf_transformation,[status(thm)],[f102])).
% 0.18/0.53 fof(f104,plain,(
% 0.18/0.53 ssItem(sK1_skl)),
% 0.18/0.53 inference(cnf_transformation,[status(thm)],[f102])).
% 0.18/0.53 fof(f106,plain,(
% 0.18/0.53 ![U]: (~ssList(U)|(![V]: (~ssItem(V)|(memberP(U,V)<=>(?[W]: (ssList(W)&(?[X]: (ssList(X)&app(W,cons(V,X))=U))))))))),
% 0.18/0.53 inference(pre_NNF_transformation,[status(thm)],[f3])).
% 0.18/0.53 fof(f107,plain,(
% 0.18/0.53 ![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)))))))))),
% 0.18/0.53 inference(NNF_transformation,[status(thm)],[f106])).
% 0.18/0.53 fof(f108,plain,(
% 0.18/0.53 ![U]: (~ssList(U)|(![V]: (~ssItem(V)|((~memberP(U,V)|(ssList(sK2_skl(V,U))&(ssList(sK3_skl(V,U))&app(sK2_skl(V,U),cons(V,sK3_skl(V,U)))=U)))&(memberP(U,V)|(![W]: (~ssList(W)|(![X]: (~ssList(X)|~app(W,cons(V,X))=U)))))))))),
% 0.18/0.53 inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(W,sK2_skl(V,U)),skolemize(X,sK3_skl(V,U))],[f107])).
% 0.18/0.53 fof(f109,plain,(
% 0.18/0.53 ![X0,X1]: (~ssList(X0)|~ssItem(X1)|~memberP(X0,X1)|ssList(sK2_skl(X1,X0)))),
% 0.18/0.53 inference(cnf_transformation,[status(thm)],[f108])).
% 0.18/0.53 fof(f110,plain,(
% 0.18/0.53 ![X0,X1]: (~ssList(X0)|~ssItem(X1)|~memberP(X0,X1)|ssList(sK3_skl(X1,X0)))),
% 0.18/0.53 inference(cnf_transformation,[status(thm)],[f108])).
% 0.18/0.53 fof(f111,plain,(
% 0.18/0.53 ![X0,X1]: (~ssList(X0)|~ssItem(X1)|~memberP(X0,X1)|app(sK2_skl(X1,X0),cons(X1,sK3_skl(X1,X0)))=X0)),
% 0.18/0.53 inference(cnf_transformation,[status(thm)],[f108])).
% 0.18/0.53 fof(f112,plain,(
% 0.18/0.53 ![X0,X1,X2,X3]: (~ssList(X0)|~ssItem(X1)|memberP(X0,X1)|~ssList(X2)|~ssList(X3)|~app(X2,cons(X1,X3))=X0)),
% 0.18/0.53 inference(cnf_transformation,[status(thm)],[f108])).
% 0.18/0.53 fof(f113,plain,(
% 0.18/0.53 ![U]: (~ssList(U)|(singletonP(U)<=>(?[V]: (ssItem(V)&cons(V,nil)=U))))),
% 0.18/0.53 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 0.18/0.53 fof(f114,plain,(
% 0.18/0.53 ![U]: (~ssList(U)|((~singletonP(U)|(?[V]: (ssItem(V)&cons(V,nil)=U)))&(singletonP(U)|(![V]: (~ssItem(V)|~cons(V,nil)=U)))))),
% 0.18/0.53 inference(NNF_transformation,[status(thm)],[f113])).
% 0.18/0.53 fof(f115,plain,(
% 0.18/0.53 ![U]: (~ssList(U)|((~singletonP(U)|(ssItem(sK4_skl(U))&cons(sK4_skl(U),nil)=U))&(singletonP(U)|(![V]: (~ssItem(V)|~cons(V,nil)=U)))))),
% 0.18/0.53 inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(V,sK4_skl(U))],[f114])).
% 0.18/0.53 fof(f116,plain,(
% 0.18/0.53 ![X0]: (~ssList(X0)|~singletonP(X0)|ssItem(sK4_skl(X0)))),
% 0.18/0.53 inference(cnf_transformation,[status(thm)],[f115])).
% 0.18/0.53 fof(f117,plain,(
% 0.18/0.53 ![X0]: (~ssList(X0)|~singletonP(X0)|cons(sK4_skl(X0),nil)=X0)),
% 0.18/0.53 inference(cnf_transformation,[status(thm)],[f115])).
% 0.18/0.53 fof(f223,plain,(
% 0.18/0.53 ssList(nil)),
% 0.18/0.53 inference(cnf_transformation,[status(thm)],[f17])).
% 0.18/0.53 fof(f273,plain,(
% 0.18/0.53 ![U]: (~ssItem(U)|(![V]: (~ssItem(V)|(![W]: (~ssList(W)|(memberP(cons(V,W),U)<=>(U=V|memberP(W,U))))))))),
% 0.18/0.53 inference(pre_NNF_transformation,[status(thm)],[f37])).
% 0.18/0.53 fof(f274,plain,(
% 0.18/0.53 ![U]: (~ssItem(U)|(![V]: (~ssItem(V)|(![W]: (~ssList(W)|((~memberP(cons(V,W),U)|(U=V|memberP(W,U)))&(memberP(cons(V,W),U)|(~U=V&~memberP(W,U)))))))))),
% 0.18/0.53 inference(NNF_transformation,[status(thm)],[f273])).
% 0.18/0.53 fof(f275,plain,(
% 0.18/0.53 ![X0,X1,X2]: (~ssItem(X0)|~ssItem(X1)|~ssList(X2)|~memberP(cons(X1,X2),X0)|X0=X1|memberP(X2,X0))),
% 0.18/0.53 inference(cnf_transformation,[status(thm)],[f274])).
% 0.18/0.53 fof(f278,plain,(
% 0.18/0.53 ![U]: (~ssItem(U)|~memberP(nil,U))),
% 0.18/0.53 inference(pre_NNF_transformation,[status(thm)],[f38])).
% 0.18/0.53 fof(f279,plain,(
% 0.18/0.53 ![X0]: (~ssItem(X0)|~memberP(nil,X0))),
% 0.18/0.53 inference(cnf_transformation,[status(thm)],[f278])).
% 0.18/0.53 fof(f415,plain,(
% 0.18/0.53 (?[U]: (ssList(U)&(?[V]: (ssList(V)&(?[W]: (ssList(W)&(?[X]: (ssList(X)&(((V=X&U=W)&singletonP(W))&(![Y]: (~ssItem(Y)|(?[Z]: (ssItem(Z)&(memberP(U,Z)&~Y=Z))))))))))))))),
% 0.18/0.53 inference(pre_NNF_transformation,[status(thm)],[f97])).
% 0.18/0.53 fof(f416,plain,(
% 0.18/0.53 (ssList(sK47_skl)&(ssList(sK48_skl)&(ssList(sK49_skl)&(ssList(sK50_skl)&(((sK48_skl=sK50_skl&sK47_skl=sK49_skl)&singletonP(sK49_skl))&(![Y]: (~ssItem(Y)|(ssItem(sK51_skl(Y))&(memberP(sK47_skl,sK51_skl(Y))&~Y=sK51_skl(Y))))))))))),
% 0.18/0.53 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(Z,sK51_skl(Y))],[f415])).
% 0.18/0.53 fof(f417,plain,(
% 0.18/0.53 ssList(sK47_skl)),
% 0.18/0.53 inference(cnf_transformation,[status(thm)],[f416])).
% 0.18/0.53 fof(f418,plain,(
% 0.18/0.53 ssList(sK48_skl)),
% 0.18/0.53 inference(cnf_transformation,[status(thm)],[f416])).
% 0.18/0.53 fof(f422,plain,(
% 0.18/0.53 sK47_skl=sK49_skl),
% 0.18/0.53 inference(cnf_transformation,[status(thm)],[f416])).
% 0.18/0.53 fof(f423,plain,(
% 0.18/0.53 singletonP(sK49_skl)),
% 0.18/0.53 inference(cnf_transformation,[status(thm)],[f416])).
% 0.18/0.53 fof(f424,plain,(
% 0.18/0.53 ![X0]: (~ssItem(X0)|ssItem(sK51_skl(X0)))),
% 0.18/0.53 inference(cnf_transformation,[status(thm)],[f416])).
% 0.18/0.53 fof(f425,plain,(
% 0.18/0.53 ![X0]: (~ssItem(X0)|memberP(sK47_skl,sK51_skl(X0)))),
% 0.18/0.53 inference(cnf_transformation,[status(thm)],[f416])).
% 0.18/0.53 fof(f426,plain,(
% 0.18/0.53 ![X0]: (~ssItem(X0)|~X0=sK51_skl(X0))),
% 0.18/0.53 inference(cnf_transformation,[status(thm)],[f416])).
% 0.18/0.53 fof(f429,plain,(
% 0.18/0.53 ![X0,X1,X2]: (~ssList(app(X0,cons(X1,X2)))|~ssItem(X1)|memberP(app(X0,cons(X1,X2)),X1)|~ssList(X0)|~ssList(X2))),
% 0.18/0.53 inference(destructive_equality_resolution,[status(thm)],[f112])).
% 0.18/0.53 fof(f459,plain,(
% 0.18/0.53 singletonP(sK47_skl)),
% 0.18/0.53 inference(forward_demodulation,[status(thm)],[f422,f423])).
% 0.18/0.53 fof(f473,plain,(
% 0.18/0.53 ![X0]: (~ssList(sK47_skl)|~ssItem(sK51_skl(X0))|app(sK2_skl(sK51_skl(X0),sK47_skl),cons(sK51_skl(X0),sK3_skl(sK51_skl(X0),sK47_skl)))=sK47_skl|~ssItem(X0))),
% 0.18/0.53 inference(resolution,[status(thm)],[f111,f425])).
% 0.18/0.53 fof(f475,definition,(
% 0.18/0.53 sQ0_spl <=> (ssList(sK47_skl))),
% 0.18/0.53 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.18/0.53 fof(f477,plain,(
% 0.18/0.53 ~ssList(sK47_skl)|sQ0_spl),
% 0.18/0.53 inference(component_clause,[status(thm)],[f475])).
% 0.18/0.53 fof(f478,definition,(
% 0.18/0.53 ![X0]: (sQ1_spl <=> (~ssItem(sK51_skl(X0))|app(sK2_skl(sK51_skl(X0),sK47_skl),cons(sK51_skl(X0),sK3_skl(sK51_skl(X0),sK47_skl)))=sK47_skl|~ssItem(X0)))),
% 0.18/0.53 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.18/0.53 fof(f479,plain,(
% 0.18/0.53 ![X0]: (~ssItem(sK51_skl(X0))|app(sK2_skl(sK51_skl(X0),sK47_skl),cons(sK51_skl(X0),sK3_skl(sK51_skl(X0),sK47_skl)))=sK47_skl|~ssItem(X0)|~sQ1_spl)),
% 0.18/0.53 inference(component_clause,[status(thm)],[f478])).
% 0.18/0.53 fof(f481,plain,(
% 0.18/0.53 ~sQ0_spl|sQ1_spl),
% 0.18/0.53 inference(split_clause,[status(thm)],[f473,f475,f478])).
% 0.18/0.53 fof(f482,plain,(
% 0.18/0.53 $false|sQ0_spl),
% 0.18/0.53 inference(forward_subsumption_resolution,[status(thm)],[f477,f417])).
% 0.18/0.53 fof(f483,plain,(
% 0.18/0.53 sQ0_spl),
% 0.18/0.53 inference(contradiction_clause,[status(thm)],[f482])).
% 0.18/0.53 fof(f484,plain,(
% 0.18/0.53 ![X0]: (app(sK2_skl(sK51_skl(X0),sK47_skl),cons(sK51_skl(X0),sK3_skl(sK51_skl(X0),sK47_skl)))=sK47_skl|~ssItem(X0)|~sQ1_spl)),
% 0.18/0.53 inference(forward_subsumption_resolution,[status(thm)],[f479,f424])).
% 0.18/0.53 fof(f485,plain,(
% 0.18/0.53 ~ssList(sK47_skl)|ssItem(sK4_skl(sK47_skl))),
% 0.18/0.53 inference(resolution,[status(thm)],[f116,f459])).
% 0.18/0.53 fof(f486,definition,(
% 0.18/0.53 sQ2_spl <=> (ssItem(sK4_skl(sK47_skl)))),
% 0.18/0.53 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.18/0.53 fof(f487,plain,(
% 0.18/0.53 ssItem(sK4_skl(sK47_skl))|~sQ2_spl),
% 0.18/0.53 inference(component_clause,[status(thm)],[f486])).
% 0.18/0.53 fof(f489,plain,(
% 0.18/0.53 ~sQ0_spl|sQ2_spl),
% 0.18/0.53 inference(split_clause,[status(thm)],[f485,f475,f486])).
% 0.18/0.53 fof(f492,plain,(
% 0.18/0.53 ~sK4_skl(sK47_skl)=sK51_skl(sK4_skl(sK47_skl))|~sQ2_spl),
% 0.18/0.53 inference(resolution,[status(thm)],[f487,f426])).
% 0.18/0.53 fof(f493,plain,(
% 0.18/0.53 app(sK2_skl(sK51_skl(sK4_skl(sK47_skl)),sK47_skl),cons(sK51_skl(sK4_skl(sK47_skl)),sK3_skl(sK51_skl(sK4_skl(sK47_skl)),sK47_skl)))=sK47_skl|~sQ1_spl|~sQ2_spl),
% 0.18/0.53 inference(resolution,[status(thm)],[f484,f487])).
% 0.18/0.53 fof(f518,definition,(
% 0.18/0.53 sQ4_spl <=> (ssList(nil))),
% 0.18/0.53 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 0.18/0.53 fof(f520,plain,(
% 0.18/0.53 ~ssList(nil)|sQ4_spl),
% 0.18/0.53 inference(component_clause,[status(thm)],[f518])).
% 0.18/0.53 fof(f527,plain,(
% 0.18/0.53 $false|sQ4_spl),
% 0.18/0.53 inference(forward_subsumption_resolution,[status(thm)],[f520,f223])).
% 0.18/0.53 fof(f528,plain,(
% 0.18/0.53 sQ4_spl),
% 0.18/0.53 inference(contradiction_clause,[status(thm)],[f527])).
% 0.18/0.53 fof(f535,definition,(
% 0.18/0.53 sQ7_spl <=> (ssList(sK48_skl))),
% 0.18/0.53 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 0.18/0.53 fof(f537,plain,(
% 0.18/0.53 ~ssList(sK48_skl)|sQ7_spl),
% 0.18/0.53 inference(component_clause,[status(thm)],[f535])).
% 0.18/0.53 fof(f547,plain,(
% 0.18/0.53 $false|sQ7_spl),
% 0.18/0.53 inference(forward_subsumption_resolution,[status(thm)],[f537,f418])).
% 0.18/0.53 fof(f548,plain,(
% 0.18/0.53 sQ7_spl),
% 0.18/0.53 inference(contradiction_clause,[status(thm)],[f547])).
% 0.18/0.53 fof(f569,plain,(
% 0.18/0.53 ~ssList(sK47_skl)|cons(sK4_skl(sK47_skl),nil)=sK47_skl),
% 0.18/0.53 inference(resolution,[status(thm)],[f117,f459])).
% 0.18/0.53 fof(f570,definition,(
% 0.18/0.53 sQ13_spl <=> (cons(sK4_skl(sK47_skl),nil)=sK47_skl)),
% 0.18/0.53 introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition])).
% 0.18/0.53 fof(f571,plain,(
% 0.18/0.53 cons(sK4_skl(sK47_skl),nil)=sK47_skl|~sQ13_spl),
% 0.18/0.53 inference(component_clause,[status(thm)],[f570])).
% 0.18/0.53 fof(f573,plain,(
% 0.18/0.53 ~sQ0_spl|sQ13_spl),
% 0.18/0.53 inference(split_clause,[status(thm)],[f569,f475,f570])).
% 0.18/0.53 fof(f597,plain,(
% 0.18/0.53 ![X0]: (~ssItem(X0)|~ssItem(sK4_skl(sK47_skl))|~ssList(nil)|~memberP(sK47_skl,X0)|X0=sK4_skl(sK47_skl)|memberP(nil,X0)|~sQ13_spl)),
% 0.18/0.53 inference(paramodulation,[status(thm)],[f571,f275])).
% 0.18/0.53 fof(f604,definition,(
% 0.18/0.53 ![X0]: (sQ16_spl <=> (~ssItem(X0)|~memberP(sK47_skl,X0)|X0=sK4_skl(sK47_skl)|memberP(nil,X0)))),
% 0.18/0.53 introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition])).
% 0.18/0.53 fof(f605,plain,(
% 0.18/0.53 ![X0]: (~ssItem(X0)|~memberP(sK47_skl,X0)|X0=sK4_skl(sK47_skl)|memberP(nil,X0)|~sQ16_spl)),
% 0.18/0.53 inference(component_clause,[status(thm)],[f604])).
% 0.18/0.53 fof(f607,plain,(
% 0.18/0.53 sQ16_spl|~sQ2_spl|~sQ4_spl|~sQ13_spl),
% 0.18/0.53 inference(split_clause,[status(thm)],[f597,f604,f486,f518,f570])).
% 0.18/0.53 fof(f617,plain,(
% 0.18/0.53 ![X0]: (~ssItem(X0)|~memberP(sK47_skl,X0)|X0=sK4_skl(sK47_skl)|~sQ16_spl)),
% 0.18/0.53 inference(forward_subsumption_resolution,[status(thm)],[f605,f279])).
% 0.18/0.53 fof(f619,plain,(
% 0.18/0.53 ~ssList(sK47_skl)|~ssItem(sK51_skl(sK4_skl(sK47_skl)))|memberP(app(sK2_skl(sK51_skl(sK4_skl(sK47_skl)),sK47_skl),cons(sK51_skl(sK4_skl(sK47_skl)),sK3_skl(sK51_skl(sK4_skl(sK47_skl)),sK47_skl))),sK51_skl(sK4_skl(sK47_skl)))|~ssList(sK2_skl(sK51_skl(sK4_skl(sK47_skl)),sK47_skl))|~ssList(sK3_skl(sK51_skl(sK4_skl(sK47_skl)),sK47_skl))|~sQ1_spl|~sQ2_spl),
% 0.18/0.53 inference(paramodulation,[status(thm)],[f493,f429])).
% 0.18/0.53 fof(f623,definition,(
% 0.18/0.53 sQ19_spl <=> (ssItem(sK51_skl(sK4_skl(sK47_skl))))),
% 0.18/0.53 introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition])).
% 0.18/0.53 fof(f625,plain,(
% 0.18/0.53 ~ssItem(sK51_skl(sK4_skl(sK47_skl)))|sQ19_spl),
% 0.18/0.53 inference(component_clause,[status(thm)],[f623])).
% 0.18/0.53 fof(f626,definition,(
% 0.18/0.53 sQ20_spl <=> (memberP(app(sK2_skl(sK51_skl(sK4_skl(sK47_skl)),sK47_skl),cons(sK51_skl(sK4_skl(sK47_skl)),sK3_skl(sK51_skl(sK4_skl(sK47_skl)),sK47_skl))),sK51_skl(sK4_skl(sK47_skl))))),
% 0.18/0.53 introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition])).
% 0.18/0.53 fof(f627,plain,(
% 0.18/0.53 memberP(app(sK2_skl(sK51_skl(sK4_skl(sK47_skl)),sK47_skl),cons(sK51_skl(sK4_skl(sK47_skl)),sK3_skl(sK51_skl(sK4_skl(sK47_skl)),sK47_skl))),sK51_skl(sK4_skl(sK47_skl)))|~sQ20_spl),
% 0.18/0.53 inference(component_clause,[status(thm)],[f626])).
% 0.18/0.53 fof(f629,definition,(
% 0.18/0.53 sQ21_spl <=> (ssList(sK2_skl(sK51_skl(sK4_skl(sK47_skl)),sK47_skl)))),
% 0.18/0.53 introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition])).
% 0.18/0.53 fof(f631,plain,(
% 0.18/0.53 ~ssList(sK2_skl(sK51_skl(sK4_skl(sK47_skl)),sK47_skl))|sQ21_spl),
% 0.18/0.53 inference(component_clause,[status(thm)],[f629])).
% 0.18/0.53 fof(f632,definition,(
% 0.18/0.53 sQ22_spl <=> (ssList(sK3_skl(sK51_skl(sK4_skl(sK47_skl)),sK47_skl)))),
% 0.18/0.53 introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition])).
% 0.18/0.53 fof(f634,plain,(
% 0.18/0.53 ~ssList(sK3_skl(sK51_skl(sK4_skl(sK47_skl)),sK47_skl))|sQ22_spl),
% 0.18/0.53 inference(component_clause,[status(thm)],[f632])).
% 0.18/0.53 fof(f635,plain,(
% 0.18/0.53 ~sQ0_spl|~sQ19_spl|sQ20_spl|~sQ21_spl|~sQ22_spl|~sQ1_spl|~sQ2_spl),
% 0.18/0.53 inference(split_clause,[status(thm)],[f619,f475,f623,f626,f629,f632,f478,f486])).
% 0.18/0.53 fof(f656,plain,(
% 0.18/0.53 ~ssList(sK47_skl)|~ssItem(sK51_skl(sK4_skl(sK47_skl)))|~memberP(sK47_skl,sK51_skl(sK4_skl(sK47_skl)))|sQ21_spl),
% 0.18/0.53 inference(resolution,[status(thm)],[f631,f109])).
% 0.18/0.53 fof(f657,definition,(
% 0.18/0.53 sQ28_spl <=> (memberP(sK47_skl,sK51_skl(sK4_skl(sK47_skl))))),
% 0.18/0.53 introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition])).
% 0.18/0.53 fof(f659,plain,(
% 0.18/0.53 ~memberP(sK47_skl,sK51_skl(sK4_skl(sK47_skl)))|sQ28_spl),
% 0.18/0.53 inference(component_clause,[status(thm)],[f657])).
% 0.18/0.53 fof(f660,plain,(
% 0.18/0.53 ~sQ0_spl|~sQ19_spl|~sQ28_spl|sQ21_spl),
% 0.18/0.53 inference(split_clause,[status(thm)],[f656,f475,f623,f657,f629])).
% 0.18/0.53 fof(f661,plain,(
% 0.18/0.53 ~ssItem(sK4_skl(sK47_skl))|sQ19_spl),
% 0.18/0.53 inference(resolution,[status(thm)],[f625,f424])).
% 0.18/0.53 fof(f662,plain,(
% 0.18/0.53 $false|~sQ2_spl|sQ19_spl),
% 0.18/0.53 inference(forward_subsumption_resolution,[status(thm)],[f661,f487])).
% 0.18/0.53 fof(f663,plain,(
% 0.18/0.53 ~sQ2_spl|sQ19_spl),
% 0.18/0.53 inference(contradiction_clause,[status(thm)],[f662])).
% 0.18/0.53 fof(f664,plain,(
% 0.18/0.53 memberP(sK47_skl,sK51_skl(sK4_skl(sK47_skl)))|~sQ1_spl|~sQ2_spl|~sQ20_spl),
% 0.18/0.53 inference(forward_demodulation,[status(thm)],[f493,f627])).
% 0.18/0.53 fof(f772,plain,(
% 0.18/0.53 ~ssList(sK47_skl)|~ssItem(sK51_skl(sK4_skl(sK47_skl)))|~memberP(sK47_skl,sK51_skl(sK4_skl(sK47_skl)))|sQ22_spl),
% 0.18/0.53 inference(resolution,[status(thm)],[f634,f110])).
% 0.18/0.53 fof(f773,plain,(
% 0.18/0.53 ~sQ0_spl|~sQ19_spl|~sQ28_spl|sQ22_spl),
% 0.18/0.53 inference(split_clause,[status(thm)],[f772,f475,f623,f657,f632])).
% 0.18/0.53 fof(f774,plain,(
% 0.18/0.53 ~ssItem(sK4_skl(sK47_skl))|sQ28_spl),
% 0.18/0.53 inference(resolution,[status(thm)],[f659,f425])).
% 0.18/0.53 fof(f775,plain,(
% 0.18/0.53 $false|~sQ2_spl|sQ28_spl),
% 0.18/0.53 inference(forward_subsumption_resolution,[status(thm)],[f774,f487])).
% 0.18/0.53 fof(f776,plain,(
% 0.18/0.53 ~sQ2_spl|sQ28_spl),
% 0.18/0.53 inference(contradiction_clause,[status(thm)],[f775])).
% 0.18/0.53 fof(f877,definition,(
% 0.18/0.53 sQ59_spl <=> (ssItem(sK51_skl(sK1_skl)))),
% 0.18/0.53 introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition])).
% 0.18/0.53 fof(f879,plain,(
% 0.18/0.53 ~ssItem(sK51_skl(sK1_skl))|sQ59_spl),
% 0.18/0.53 inference(component_clause,[status(thm)],[f877])).
% 0.18/0.53 fof(f919,definition,(
% 0.18/0.53 sQ70_spl <=> (memberP(sK47_skl,sK51_skl(sK1_skl)))),
% 0.18/0.53 introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition])).
% 0.18/0.53 fof(f921,plain,(
% 0.18/0.53 ~memberP(sK47_skl,sK51_skl(sK1_skl))|sQ70_spl),
% 0.18/0.53 inference(component_clause,[status(thm)],[f919])).
% 0.18/0.53 fof(f923,plain,(
% 0.18/0.53 ~ssItem(sK1_skl)|sQ59_spl),
% 0.18/0.53 inference(resolution,[status(thm)],[f879,f424])).
% 0.18/0.53 fof(f924,plain,(
% 0.18/0.53 $false|sQ59_spl),
% 0.18/0.53 inference(forward_subsumption_resolution,[status(thm)],[f923,f104])).
% 0.18/0.53 fof(f925,plain,(
% 0.18/0.53 sQ59_spl),
% 0.18/0.53 inference(contradiction_clause,[status(thm)],[f924])).
% 0.18/0.53 fof(f954,definition,(
% 0.18/0.53 sQ73_spl <=> (ssItem(sK51_skl(sK0_skl)))),
% 0.18/0.55 introduced(definition,[new_symbols(definition,[sQ73_spl])],[split_symbol_definition])).
% 0.18/0.55 fof(f956,plain,(
% 0.18/0.55 ~ssItem(sK51_skl(sK0_skl))|sQ73_spl),
% 0.18/0.55 inference(component_clause,[status(thm)],[f954])).
% 0.18/0.55 fof(f999,plain,(
% 0.18/0.55 ~ssItem(sK1_skl)|sQ70_spl),
% 0.18/0.55 inference(resolution,[status(thm)],[f921,f425])).
% 0.18/0.55 fof(f1000,plain,(
% 0.18/0.55 $false|sQ70_spl),
% 0.18/0.55 inference(forward_subsumption_resolution,[status(thm)],[f999,f104])).
% 0.18/0.55 fof(f1001,plain,(
% 0.18/0.55 sQ70_spl),
% 0.18/0.55 inference(contradiction_clause,[status(thm)],[f1000])).
% 0.18/0.55 fof(f1009,plain,(
% 0.18/0.55 ~ssItem(sK0_skl)|sQ73_spl),
% 0.18/0.55 inference(resolution,[status(thm)],[f956,f424])).
% 0.18/0.55 fof(f1010,plain,(
% 0.18/0.55 $false|sQ73_spl),
% 0.18/0.55 inference(forward_subsumption_resolution,[status(thm)],[f1009,f103])).
% 0.18/0.55 fof(f1011,plain,(
% 0.18/0.55 sQ73_spl),
% 0.18/0.55 inference(contradiction_clause,[status(thm)],[f1010])).
% 0.18/0.55 fof(f1086,plain,(
% 0.18/0.55 ~ssItem(sK51_skl(sK4_skl(sK47_skl)))|sK51_skl(sK4_skl(sK47_skl))=sK4_skl(sK47_skl)|~sQ16_spl|~sQ1_spl|~sQ2_spl|~sQ20_spl),
% 0.18/0.55 inference(resolution,[status(thm)],[f617,f664])).
% 0.18/0.55 fof(f1096,definition,(
% 0.18/0.55 sQ97_spl <=> (sK51_skl(sK4_skl(sK47_skl))=sK4_skl(sK47_skl))),
% 0.18/0.55 introduced(definition,[new_symbols(definition,[sQ97_spl])],[split_symbol_definition])).
% 0.18/0.55 fof(f1097,plain,(
% 0.18/0.55 sK51_skl(sK4_skl(sK47_skl))=sK4_skl(sK47_skl)|~sQ97_spl),
% 0.18/0.55 inference(component_clause,[status(thm)],[f1096])).
% 0.18/0.55 fof(f1099,plain,(
% 0.18/0.55 ~sQ19_spl|sQ97_spl|~sQ16_spl|~sQ1_spl|~sQ2_spl|~sQ20_spl),
% 0.18/0.55 inference(split_clause,[status(thm)],[f1086,f623,f1096,f604,f478,f486,f626])).
% 0.18/0.55 fof(f1101,plain,(
% 0.18/0.55 $false|~sQ2_spl|~sQ97_spl),
% 0.18/0.55 inference(forward_subsumption_resolution,[status(thm)],[f1097,f492])).
% 0.18/0.55 fof(f1102,plain,(
% 0.18/0.55 ~sQ2_spl|~sQ97_spl),
% 0.18/0.55 inference(contradiction_clause,[status(thm)],[f1101])).
% 0.18/0.55 fof(f1103,plain,(
% 0.18/0.55 $false),
% 0.18/0.55 inference(sat_refutation,[status(thm)],[f481,f483,f489,f528,f548,f573,f607,f635,f660,f663,f773,f776,f925,f1001,f1011,f1099,f1102])).
% 0.18/0.55 % SZS output end CNFRefutation for theBenchmark.p
% 0.25/0.56 % Elapsed time: 0.113810 seconds
% 0.25/0.56 % CPU time: 0.577379 seconds
% 0.25/0.56 % Total memory used: 108.544 MB
% 0.25/0.56 % Net memory used: 108.104 MB
%------------------------------------------------------------------------------