%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SWC384+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 : n018.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 02:42:19 PM UTC 2026
% Result : Theorem 0.09s 0.47s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC384+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
% 0.09/0.36 % Computer : n018.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 08:22:29 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.39 % Drodi V4.1.1
% 0.09/0.47 % Refutation found
% 0.09/0.47 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.47 % SZS output start CNFRefutation for theBenchmark
% 0.09/0.47 fof(f4,axiom,(
% 0.09/0.47 (! [U] :( ssList(U)=> ( singletonP(U)<=> (? [V] :( ssItem(V)& cons(V,nil) = U ) )) ) )),
% 0.09/0.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.47 fof(f7,axiom,(
% 0.09/0.47 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> ( segmentP(U,V)<=> (? [W] :( ssList(W)& (? [X] :( ssList(X)& app(app(W,V),X) = U ) )) )) ) )) )),
% 0.09/0.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.47 fof(f15,axiom,(
% 0.09/0.47 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> ( neq(U,V)<=> U != V ) ) )) )),
% 0.09/0.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.47 fof(f17,axiom,(
% 0.09/0.47 ssList(nil) ),
% 0.09/0.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.47 fof(f96,conjecture,(
% 0.09/0.47 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> (! [X] :( ssList(X)=> ( V != X| U != W| ~ neq(V,nil)| ( (! [Y] :( ssItem(Y)=> (! [Z] :( ssList(Z)=> (! [X1] :( ssList(X1)=> ( cons(Y,nil) != W| app(app(Z,W),X1) != X| (? [X2] :( ssItem(X2)& memberP(Z,X2)& lt(Y,X2) ))| (? [X3] :( ssItem(X3)& memberP(X1,X3)& lt(X3,Y) ) )) ) )) )))& ( nil != X| nil != W ) )| ( singletonP(U)& segmentP(V,U) ) ) ) )) )) )) )),
% 0.09/0.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.47 fof(f97,negated_conjecture,(
% 0.09/0.47 ~((! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> (! [X] :( ssList(X)=> ( V != X| U != W| ~ neq(V,nil)| ( (! [Y] :( ssItem(Y)=> (! [Z] :( ssList(Z)=> (! [X1] :( ssList(X1)=> ( cons(Y,nil) != W| app(app(Z,W),X1) != X| (? [X2] :( ssItem(X2)& memberP(Z,X2)& lt(Y,X2) ))| (? [X3] :( ssItem(X3)& memberP(X1,X3)& lt(X3,Y) ) )) ) )) )))& ( nil != X| nil != W ) )| ( singletonP(U)& segmentP(V,U) ) ) ) )) )) )) ))),
% 0.09/0.47 inference(negated_conjecture,[status(cth)],[f96])).
% 0.09/0.47 fof(f113,plain,(
% 0.09/0.47 ![U]: (~ssList(U)|(singletonP(U)<=>(?[V]: (ssItem(V)&cons(V,nil)=U))))),
% 0.09/0.47 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 0.09/0.47 fof(f114,plain,(
% 0.09/0.47 ![U]: (~ssList(U)|((~singletonP(U)|(?[V]: (ssItem(V)&cons(V,nil)=U)))&(singletonP(U)|(![V]: (~ssItem(V)|~cons(V,nil)=U)))))),
% 0.09/0.47 inference(NNF_transformation,[status(thm)],[f113])).
% 0.09/0.47 fof(f115,plain,(
% 0.09/0.47 ![U]: (~ssList(U)|((~singletonP(U)|(ssItem(sK4_skl(U))&cons(sK4_skl(U),nil)=U))&(singletonP(U)|(![V]: (~ssItem(V)|~cons(V,nil)=U)))))),
% 0.09/0.47 inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(V,sK4_skl(U))],[f114])).
% 0.09/0.47 fof(f118,plain,(
% 0.09/0.47 ![X0,X1]: (~ssList(X0)|singletonP(X0)|~ssItem(X1)|~cons(X1,nil)=X0)),
% 0.09/0.47 inference(cnf_transformation,[status(thm)],[f115])).
% 0.09/0.47 fof(f131,plain,(
% 0.09/0.47 ![U]: (~ssList(U)|(![V]: (~ssList(V)|(segmentP(U,V)<=>(?[W]: (ssList(W)&(?[X]: (ssList(X)&app(app(W,V),X)=U))))))))),
% 0.09/0.47 inference(pre_NNF_transformation,[status(thm)],[f7])).
% 0.09/0.47 fof(f132,plain,(
% 0.09/0.47 ![U]: (~ssList(U)|(![V]: (~ssList(V)|((~segmentP(U,V)|(?[W]: (ssList(W)&(?[X]: (ssList(X)&app(app(W,V),X)=U)))))&(segmentP(U,V)|(![W]: (~ssList(W)|(![X]: (~ssList(X)|~app(app(W,V),X)=U)))))))))),
% 0.09/0.47 inference(NNF_transformation,[status(thm)],[f131])).
% 0.09/0.47 fof(f133,plain,(
% 0.09/0.47 ![U]: (~ssList(U)|(![V]: (~ssList(V)|((~segmentP(U,V)|(ssList(sK7_skl(V,U))&(ssList(sK8_skl(V,U))&app(app(sK7_skl(V,U),V),sK8_skl(V,U))=U)))&(segmentP(U,V)|(![W]: (~ssList(W)|(![X]: (~ssList(X)|~app(app(W,V),X)=U)))))))))),
% 0.09/0.47 inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl,sK8_skl]),skolemize(W,sK7_skl(V,U)),skolemize(X,sK8_skl(V,U))],[f132])).
% 0.09/0.47 fof(f137,plain,(
% 0.09/0.47 ![X0,X1,X2,X3]: (~ssList(X0)|~ssList(X1)|segmentP(X0,X1)|~ssList(X2)|~ssList(X3)|~app(app(X2,X1),X3)=X0)),
% 0.09/0.47 inference(cnf_transformation,[status(thm)],[f133])).
% 0.09/0.47 fof(f217,plain,(
% 0.09/0.47 ![U]: (~ssList(U)|(![V]: (~ssList(V)|(neq(U,V)<=>~U=V))))),
% 0.09/0.47 inference(pre_NNF_transformation,[status(thm)],[f15])).
% 0.09/0.47 fof(f218,plain,(
% 0.09/0.47 ![U]: (~ssList(U)|(![V]: (~ssList(V)|((~neq(U,V)|~U=V)&(neq(U,V)|U=V)))))),
% 0.09/0.47 inference(NNF_transformation,[status(thm)],[f217])).
% 0.09/0.47 fof(f219,plain,(
% 0.09/0.47 ![X0,X1]: (~ssList(X0)|~ssList(X1)|~neq(X0,X1)|~X0=X1)),
% 0.09/0.47 inference(cnf_transformation,[status(thm)],[f218])).
% 0.09/0.47 fof(f223,plain,(
% 0.09/0.47 ssList(nil)),
% 0.09/0.47 inference(cnf_transformation,[status(thm)],[f17])).
% 0.09/0.47 fof(f415,plain,(
% 0.09/0.47 (?[U]: (ssList(U)&(?[V]: (ssList(V)&(?[W]: (ssList(W)&(?[X]: (ssList(X)&((((V=X&U=W)&neq(V,nil))&((?[Y]: (ssItem(Y)&(?[Z]: (ssList(Z)&(?[X1]: (ssList(X1)&(((cons(Y,nil)=W&app(app(Z,W),X1)=X)&(![X2]: ((~ssItem(X2)|~memberP(Z,X2))|~lt(Y,X2))))&(![X3]: ((~ssItem(X3)|~memberP(X1,X3))|~lt(X3,Y))))))))))|(nil=X&nil=W)))&(~singletonP(U)|~segmentP(V,U)))))))))))),
% 0.09/0.47 inference(pre_NNF_transformation,[status(thm)],[f97])).
% 0.09/0.47 fof(f416,definition,(
% 0.09/0.47 ![W,X,Y]: (sP0_prd(Y,X,W)<=>(ssItem(Y)&(?[Z]: (ssList(Z)&(?[X1]: (ssList(X1)&(((cons(Y,nil)=W&app(app(Z,W),X1)=X)&(![X2]: ((~ssItem(X2)|~memberP(Z,X2))|~lt(Y,X2))))&(![X3]: ((~ssItem(X3)|~memberP(X1,X3))|~lt(X3,Y))))))))))),
% 0.09/0.47 introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 0.09/0.47 fof(f417,plain,(
% 0.09/0.47 ?[U]: (ssList(U)&(?[V]: (ssList(V)&(?[W]: (ssList(W)&(?[X]: (ssList(X)&((((V=X&U=W)&neq(V,nil))&((?[Y]: sP0_prd(Y,X,W))|(nil=X&nil=W)))&(~singletonP(U)|~segmentP(V,U))))))))))),
% 0.09/0.47 inference(formula_renaming,[status(thm)],[f415,f416])).
% 0.09/0.47 fof(f418,plain,(
% 0.09/0.47 (ssList(sK47_skl)&(ssList(sK48_skl)&(ssList(sK49_skl)&(ssList(sK50_skl)&((((sK48_skl=sK50_skl&sK47_skl=sK49_skl)&neq(sK48_skl,nil))&(sP0_prd(sK51_skl,sK50_skl,sK49_skl)|(nil=sK50_skl&nil=sK49_skl)))&(~singletonP(sK47_skl)|~segmentP(sK48_skl,sK47_skl)))))))),
% 0.09/0.47 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])).
% 0.09/0.47 fof(f419,plain,(
% 0.09/0.47 ssList(sK47_skl)),
% 0.09/0.47 inference(cnf_transformation,[status(thm)],[f418])).
% 0.09/0.47 fof(f420,plain,(
% 0.09/0.47 ssList(sK48_skl)),
% 0.09/0.47 inference(cnf_transformation,[status(thm)],[f418])).
% 0.09/0.47 fof(f423,plain,(
% 0.09/0.47 sK48_skl=sK50_skl),
% 0.09/0.47 inference(cnf_transformation,[status(thm)],[f418])).
% 0.09/0.47 fof(f424,plain,(
% 0.09/0.47 sK47_skl=sK49_skl),
% 0.09/0.47 inference(cnf_transformation,[status(thm)],[f418])).
% 0.09/0.47 fof(f425,plain,(
% 0.09/0.47 neq(sK48_skl,nil)),
% 0.09/0.47 inference(cnf_transformation,[status(thm)],[f418])).
% 0.09/0.47 fof(f426,plain,(
% 0.09/0.47 sP0_prd(sK51_skl,sK50_skl,sK49_skl)|nil=sK50_skl),
% 0.09/0.47 inference(cnf_transformation,[status(thm)],[f418])).
% 0.09/0.47 fof(f428,plain,(
% 0.09/0.47 ~singletonP(sK47_skl)|~segmentP(sK48_skl,sK47_skl)),
% 0.09/0.47 inference(cnf_transformation,[status(thm)],[f418])).
% 0.09/0.47 fof(f429,definition,(
% 0.09/0.47 ![Y,Z,X2]: (sP1_prd(X2,Z,Y)<=>((~ssItem(X2)|~memberP(Z,X2))|~lt(Y,X2)))),
% 0.09/0.47 introduced(definition,[new_symbols(definition,[sP1_prd])],[])).
% 0.09/0.47 fof(f430,plain,(
% 0.09/0.47 ![W,X,Y]: (sP0_prd(Y,X,W)<=>(ssItem(Y)&(?[Z]: (ssList(Z)&(?[X1]: (ssList(X1)&(((cons(Y,nil)=W&app(app(Z,W),X1)=X)&(![X2]: sP1_prd(X2,Z,Y)))&(![X3]: ((~ssItem(X3)|~memberP(X1,X3))|~lt(X3,Y))))))))))),
% 0.09/0.47 inference(formula_renaming,[status(thm)],[f416,f429])).
% 0.09/0.47 fof(f431,plain,(
% 0.09/0.47 ![W,X,Y]: ((~sP0_prd(Y,X,W)|(ssItem(Y)&(?[Z]: (ssList(Z)&(?[X1]: (ssList(X1)&(((cons(Y,nil)=W&app(app(Z,W),X1)=X)&(![X2]: sP1_prd(X2,Z,Y)))&(![X3]: ((~ssItem(X3)|~memberP(X1,X3))|~lt(X3,Y))))))))))&(sP0_prd(Y,X,W)|(~ssItem(Y)|(![Z]: (~ssList(Z)|(![X1]: (~ssList(X1)|(((~cons(Y,nil)=W|~app(app(Z,W),X1)=X)|(?[X2]: ~sP1_prd(X2,Z,Y)))|(?[X3]: ((ssItem(X3)&memberP(X1,X3))<(X3,Y)))))))))))),
% 0.09/0.47 inference(NNF_transformation,[status(thm)],[f430])).
% 0.09/0.47 fof(f432,plain,(
% 0.09/0.47 (![W,X,Y]: (~sP0_prd(Y,X,W)|(ssItem(Y)&(?[Z]: (ssList(Z)&(?[X1]: (ssList(X1)&(((cons(Y,nil)=W&app(app(Z,W),X1)=X)&(![X2]: sP1_prd(X2,Z,Y)))&(![X3]: ((~ssItem(X3)|~memberP(X1,X3))|~lt(X3,Y)))))))))))&(![W,X,Y]: (sP0_prd(Y,X,W)|(~ssItem(Y)|(![Z]: (~ssList(Z)|(![X1]: (~ssList(X1)|(((~cons(Y,nil)=W|~app(app(Z,W),X1)=X)|(?[X2]: ~sP1_prd(X2,Z,Y)))|(?[X3]: ((ssItem(X3)&memberP(X1,X3))<(X3,Y)))))))))))),
% 0.09/0.47 inference(miniscoping,[status(thm)],[f431])).
% 0.09/0.47 fof(f433,plain,(
% 0.09/0.47 (![W,X,Y]: (~sP0_prd(Y,X,W)|(ssItem(Y)&(ssList(sK52_skl(Y,X,W))&(ssList(sK53_skl(Y,X,W))&(((cons(Y,nil)=W&app(app(sK52_skl(Y,X,W),W),sK53_skl(Y,X,W))=X)&(![X2]: sP1_prd(X2,sK52_skl(Y,X,W),Y)))&(![X3]: ((~ssItem(X3)|~memberP(sK53_skl(Y,X,W),X3))|~lt(X3,Y)))))))))&(![W,X,Y]: (sP0_prd(Y,X,W)|(~ssItem(Y)|(![Z]: (~ssList(Z)|(![X1]: (~ssList(X1)|(((~cons(Y,nil)=W|~app(app(Z,W),X1)=X)|~sP1_prd(sK54_skl(X1,Z,Y,X,W),Z,Y))|((ssItem(sK55_skl(X1,Z,Y,X,W))&memberP(X1,sK55_skl(X1,Z,Y,X,W)))<(sK55_skl(X1,Z,Y,X,W),Y))))))))))),
% 0.09/0.47 inference(skolemize,[status(esa),new_symbols(skolem,[sK52_skl,sK53_skl,sK54_skl,sK55_skl]),skolemize(Z,sK52_skl(Y,X,W)),skolemize(X1,sK53_skl(Y,X,W)),skolemize(X2,sK54_skl(X1,Z,Y,X,W)),skolemize(X3,sK55_skl(X1,Z,Y,X,W))],[f432])).
% 0.09/0.47 fof(f434,plain,(
% 0.09/0.47 ![X0,X1,X2]: (~sP0_prd(X0,X1,X2)|ssItem(X0))),
% 0.09/0.47 inference(cnf_transformation,[status(thm)],[f433])).
% 0.09/0.47 fof(f435,plain,(
% 0.09/0.47 ![X0,X1,X2]: (~sP0_prd(X0,X1,X2)|ssList(sK52_skl(X0,X1,X2)))),
% 0.09/0.47 inference(cnf_transformation,[status(thm)],[f433])).
% 0.09/0.47 fof(f436,plain,(
% 0.09/0.47 ![X0,X1,X2]: (~sP0_prd(X0,X1,X2)|ssList(sK53_skl(X0,X1,X2)))),
% 0.09/0.47 inference(cnf_transformation,[status(thm)],[f433])).
% 0.09/0.47 fof(f437,plain,(
% 0.09/0.47 ![X0,X1,X2]: (~sP0_prd(X0,X1,X2)|cons(X0,nil)=X2)),
% 0.09/0.47 inference(cnf_transformation,[status(thm)],[f433])).
% 0.09/0.47 fof(f438,plain,(
% 0.09/0.47 ![X0,X1,X2]: (~sP0_prd(X0,X1,X2)|app(app(sK52_skl(X0,X1,X2),X2),sK53_skl(X0,X1,X2))=X1)),
% 0.09/0.47 inference(cnf_transformation,[status(thm)],[f433])).
% 0.09/0.47 fof(f450,definition,(
% 0.09/0.47 sQ0_spl <=> (sP0_prd(sK51_skl,sK50_skl,sK49_skl))),
% 0.09/0.47 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.09/0.47 fof(f451,plain,(
% 0.09/0.47 sP0_prd(sK51_skl,sK50_skl,sK49_skl)|~sQ0_spl),
% 0.09/0.47 inference(component_clause,[status(thm)],[f450])).
% 0.09/0.47 fof(f453,definition,(
% 0.09/0.47 sQ1_spl <=> (nil=sK50_skl)),
% 0.09/0.47 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.09/0.47 fof(f454,plain,(
% 0.09/0.47 nil=sK50_skl|~sQ1_spl),
% 0.09/0.47 inference(component_clause,[status(thm)],[f453])).
% 0.09/0.47 fof(f456,plain,(
% 0.09/0.47 sQ0_spl|sQ1_spl),
% 0.09/0.47 inference(split_clause,[status(thm)],[f426,f450,f453])).
% 0.09/0.47 fof(f461,definition,(
% 0.09/0.47 sQ3_spl <=> (singletonP(sK47_skl))),
% 0.09/0.47 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.09/0.47 fof(f463,plain,(
% 0.09/0.47 ~singletonP(sK47_skl)|sQ3_spl),
% 0.09/0.47 inference(component_clause,[status(thm)],[f461])).
% 0.09/0.47 fof(f464,definition,(
% 0.09/0.47 sQ4_spl <=> (segmentP(sK48_skl,sK47_skl))),
% 0.09/0.47 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 0.09/0.47 fof(f466,plain,(
% 0.09/0.47 ~segmentP(sK48_skl,sK47_skl)|sQ4_spl),
% 0.09/0.47 inference(component_clause,[status(thm)],[f464])).
% 0.09/0.47 fof(f467,plain,(
% 0.09/0.47 ~sQ3_spl|~sQ4_spl),
% 0.09/0.47 inference(split_clause,[status(thm)],[f428,f461,f464])).
% 0.09/0.47 fof(f471,plain,(
% 0.09/0.47 ![X0]: (~ssList(cons(X0,nil))|singletonP(cons(X0,nil))|~ssItem(X0))),
% 0.09/0.47 inference(destructive_equality_resolution,[status(thm)],[f118])).
% 0.09/0.47 fof(f474,plain,(
% 0.09/0.47 ![X0,X1,X2]: (~ssList(app(app(X0,X1),X2))|~ssList(X1)|segmentP(app(app(X0,X1),X2),X1)|~ssList(X0)|~ssList(X2))),
% 0.09/0.47 inference(destructive_equality_resolution,[status(thm)],[f137])).
% 0.09/0.47 fof(f483,plain,(
% 0.09/0.47 ![X1]: (~ssList(X1)|~ssList(X1)|~neq(X1,X1))),
% 0.09/0.47 inference(destructive_equality_resolution,[status(thm)],[f219])).
% 0.09/0.47 fof(f484,plain,(
% 0.09/0.47 ![X0]: (~ssList(X0)|~neq(X0,X0))),
% 0.09/0.47 inference(duplicate_literals_removal,[status(thm)],[f483])).
% 0.09/0.47 fof(f507,plain,(
% 0.09/0.47 sP0_prd(sK51_skl,sK48_skl,sK49_skl)|~sQ0_spl),
% 0.09/0.47 inference(forward_demodulation,[status(thm)],[f423,f451])).
% 0.09/0.47 fof(f508,plain,(
% 0.09/0.47 sP0_prd(sK51_skl,sK48_skl,sK47_skl)|~sQ0_spl),
% 0.09/0.47 inference(forward_demodulation,[status(thm)],[f424,f507])).
% 0.09/0.47 fof(f509,plain,(
% 0.09/0.47 ssItem(sK51_skl)|~sQ0_spl),
% 0.09/0.47 inference(resolution,[status(thm)],[f508,f434])).
% 0.09/0.47 fof(f512,plain,(
% 0.09/0.47 cons(sK51_skl,nil)=sK47_skl|~sQ0_spl),
% 0.09/0.47 inference(resolution,[status(thm)],[f437,f508])).
% 0.09/0.47 fof(f513,plain,(
% 0.09/0.47 ~ssList(sK47_skl)|singletonP(cons(sK51_skl,nil))|~ssItem(sK51_skl)|~sQ0_spl),
% 0.09/0.47 inference(paramodulation,[status(thm)],[f512,f471])).
% 0.09/0.47 fof(f515,definition,(
% 0.09/0.47 sQ5_spl <=> (ssList(sK47_skl))),
% 0.09/0.47 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 0.09/0.47 fof(f517,plain,(
% 0.09/0.47 ~ssList(sK47_skl)|sQ5_spl),
% 0.09/0.47 inference(component_clause,[status(thm)],[f515])).
% 0.09/0.47 fof(f518,definition,(
% 0.09/0.47 sQ6_spl <=> (singletonP(cons(sK51_skl,nil)))),
% 0.09/0.47 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.09/0.47 fof(f519,plain,(
% 0.09/0.47 singletonP(cons(sK51_skl,nil))|~sQ6_spl),
% 0.09/0.47 inference(component_clause,[status(thm)],[f518])).
% 0.09/0.47 fof(f521,definition,(
% 0.09/0.47 sQ7_spl <=> (ssItem(sK51_skl))),
% 0.09/0.47 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 0.09/0.47 fof(f523,plain,(
% 0.09/0.47 ~ssItem(sK51_skl)|sQ7_spl),
% 0.09/0.47 inference(component_clause,[status(thm)],[f521])).
% 0.09/0.47 fof(f524,plain,(
% 0.09/0.47 ~sQ5_spl|sQ6_spl|~sQ7_spl|~sQ0_spl),
% 0.09/0.47 inference(split_clause,[status(thm)],[f513,f515,f518,f521,f450])).
% 0.09/0.47 fof(f532,plain,(
% 0.09/0.47 sK48_skl=nil|~sQ1_spl),
% 0.09/0.47 inference(backward_demodulation,[status(thm)],[f454,f423])).
% 0.09/0.47 fof(f534,plain,(
% 0.09/0.47 neq(nil,nil)|~sQ1_spl),
% 0.09/0.47 inference(backward_demodulation,[status(thm)],[f532,f425])).
% 0.09/0.47 fof(f555,plain,(
% 0.09/0.47 ~ssList(nil)|~sQ1_spl),
% 0.09/0.47 inference(resolution,[status(thm)],[f534,f484])).
% 0.09/0.47 fof(f556,plain,(
% 0.09/0.47 $false|~sQ1_spl),
% 0.09/0.47 inference(forward_subsumption_resolution,[status(thm)],[f555,f223])).
% 0.09/0.47 fof(f557,plain,(
% 0.09/0.47 ~sQ1_spl),
% 0.09/0.47 inference(contradiction_clause,[status(thm)],[f556])).
% 0.09/0.47 fof(f558,plain,(
% 0.09/0.47 $false|sQ7_spl|~sQ0_spl),
% 0.09/0.47 inference(forward_subsumption_resolution,[status(thm)],[f509,f523])).
% 0.09/0.47 fof(f559,plain,(
% 0.09/0.47 sQ7_spl|~sQ0_spl),
% 0.09/0.47 inference(contradiction_clause,[status(thm)],[f558])).
% 0.09/0.47 fof(f571,plain,(
% 0.09/0.47 $false|sQ5_spl),
% 0.09/0.47 inference(forward_subsumption_resolution,[status(thm)],[f517,f419])).
% 0.09/0.47 fof(f572,plain,(
% 0.09/0.47 sQ5_spl),
% 0.09/0.47 inference(contradiction_clause,[status(thm)],[f571])).
% 0.09/0.47 fof(f583,plain,(
% 0.09/0.47 app(app(sK52_skl(sK51_skl,sK48_skl,sK47_skl),sK47_skl),sK53_skl(sK51_skl,sK48_skl,sK47_skl))=sK48_skl|~sQ0_spl),
% 0.09/0.47 inference(resolution,[status(thm)],[f508,f438])).
% 0.09/0.47 fof(f601,plain,(
% 0.09/0.47 singletonP(sK47_skl)|~sQ0_spl|~sQ6_spl),
% 0.09/0.47 inference(forward_demodulation,[status(thm)],[f512,f519])).
% 0.09/0.47 fof(f602,plain,(
% 0.09/0.47 $false|sQ3_spl|~sQ0_spl|~sQ6_spl),
% 0.09/0.47 inference(forward_subsumption_resolution,[status(thm)],[f601,f463])).
% 0.09/0.47 fof(f603,plain,(
% 0.09/0.47 sQ3_spl|~sQ0_spl|~sQ6_spl),
% 0.09/0.47 inference(contradiction_clause,[status(thm)],[f602])).
% 0.09/0.47 fof(f639,definition,(
% 0.09/0.47 sQ21_spl <=> (ssList(sK48_skl))),
% 0.09/0.47 introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition])).
% 0.09/0.47 fof(f641,plain,(
% 0.09/0.47 ~ssList(sK48_skl)|sQ21_spl),
% 0.09/0.47 inference(component_clause,[status(thm)],[f639])).
% 0.09/0.47 fof(f654,plain,(
% 0.09/0.47 $false|sQ21_spl),
% 0.09/0.47 inference(forward_subsumption_resolution,[status(thm)],[f641,f420])).
% 0.09/0.47 fof(f655,plain,(
% 0.09/0.47 sQ21_spl),
% 0.09/0.47 inference(contradiction_clause,[status(thm)],[f654])).
% 0.09/0.47 fof(f1818,plain,(
% 0.09/0.47 ~ssList(sK48_skl)|~ssList(sK47_skl)|segmentP(app(app(sK52_skl(sK51_skl,sK48_skl,sK47_skl),sK47_skl),sK53_skl(sK51_skl,sK48_skl,sK47_skl)),sK47_skl)|~ssList(sK52_skl(sK51_skl,sK48_skl,sK47_skl))|~ssList(sK53_skl(sK51_skl,sK48_skl,sK47_skl))|~sQ0_spl),
% 0.09/0.47 inference(paramodulation,[status(thm)],[f583,f474])).
% 0.09/0.47 fof(f1821,definition,(
% 0.09/0.47 sQ134_spl <=> (segmentP(app(app(sK52_skl(sK51_skl,sK48_skl,sK47_skl),sK47_skl),sK53_skl(sK51_skl,sK48_skl,sK47_skl)),sK47_skl))),
% 0.09/0.47 introduced(definition,[new_symbols(definition,[sQ134_spl])],[split_symbol_definition])).
% 0.09/0.47 fof(f1822,plain,(
% 0.09/0.47 segmentP(app(app(sK52_skl(sK51_skl,sK48_skl,sK47_skl),sK47_skl),sK53_skl(sK51_skl,sK48_skl,sK47_skl)),sK47_skl)|~sQ134_spl),
% 0.09/0.47 inference(component_clause,[status(thm)],[f1821])).
% 0.09/0.47 fof(f1824,definition,(
% 0.09/0.47 sQ135_spl <=> (ssList(sK52_skl(sK51_skl,sK48_skl,sK47_skl)))),
% 0.09/0.47 introduced(definition,[new_symbols(definition,[sQ135_spl])],[split_symbol_definition])).
% 0.09/0.47 fof(f1826,plain,(
% 0.09/0.47 ~ssList(sK52_skl(sK51_skl,sK48_skl,sK47_skl))|sQ135_spl),
% 0.09/0.47 inference(component_clause,[status(thm)],[f1824])).
% 0.09/0.47 fof(f1827,definition,(
% 0.09/0.47 sQ136_spl <=> (ssList(sK53_skl(sK51_skl,sK48_skl,sK47_skl)))),
% 0.09/0.47 introduced(definition,[new_symbols(definition,[sQ136_spl])],[split_symbol_definition])).
% 0.09/0.47 fof(f1829,plain,(
% 0.09/0.47 ~ssList(sK53_skl(sK51_skl,sK48_skl,sK47_skl))|sQ136_spl),
% 0.09/0.47 inference(component_clause,[status(thm)],[f1827])).
% 0.09/0.47 fof(f1830,plain,(
% 0.09/0.47 ~sQ21_spl|~sQ5_spl|sQ134_spl|~sQ135_spl|~sQ136_spl|~sQ0_spl),
% 0.09/0.47 inference(split_clause,[status(thm)],[f1818,f639,f515,f1821,f1824,f1827,f450])).
% 0.09/0.47 fof(f1842,plain,(
% 0.09/0.47 ~sP0_prd(sK51_skl,sK48_skl,sK47_skl)|sQ136_spl),
% 0.09/0.47 inference(resolution,[status(thm)],[f1829,f436])).
% 0.09/0.47 fof(f1843,plain,(
% 0.09/0.47 $false|~sQ0_spl|sQ136_spl),
% 0.09/0.47 inference(forward_subsumption_resolution,[status(thm)],[f1842,f508])).
% 0.09/0.47 fof(f1844,plain,(
% 0.09/0.47 ~sQ0_spl|sQ136_spl),
% 0.09/0.47 inference(contradiction_clause,[status(thm)],[f1843])).
% 0.09/0.47 fof(f1845,plain,(
% 0.09/0.47 segmentP(sK48_skl,sK47_skl)|~sQ0_spl|~sQ134_spl),
% 0.09/0.47 inference(forward_demodulation,[status(thm)],[f583,f1822])).
% 0.09/0.48 fof(f1846,plain,(
% 0.09/0.48 $false|sQ4_spl|~sQ0_spl|~sQ134_spl),
% 0.09/0.48 inference(forward_subsumption_resolution,[status(thm)],[f1845,f466])).
% 0.09/0.48 fof(f1847,plain,(
% 0.09/0.48 sQ4_spl|~sQ0_spl|~sQ134_spl),
% 0.09/0.48 inference(contradiction_clause,[status(thm)],[f1846])).
% 0.09/0.48 fof(f1883,plain,(
% 0.09/0.48 ~sP0_prd(sK51_skl,sK48_skl,sK47_skl)|sQ135_spl),
% 0.09/0.48 inference(resolution,[status(thm)],[f1826,f435])).
% 0.09/0.48 fof(f1884,plain,(
% 0.09/0.48 $false|~sQ0_spl|sQ135_spl),
% 0.09/0.48 inference(forward_subsumption_resolution,[status(thm)],[f1883,f508])).
% 0.09/0.48 fof(f1885,plain,(
% 0.09/0.48 ~sQ0_spl|sQ135_spl),
% 0.09/0.48 inference(contradiction_clause,[status(thm)],[f1884])).
% 0.09/0.48 fof(f1886,plain,(
% 0.09/0.48 $false),
% 0.09/0.48 inference(sat_refutation,[status(thm)],[f456,f467,f524,f557,f559,f572,f603,f655,f1830,f1844,f1847,f1885])).
% 0.09/0.48 % SZS output end CNFRefutation for theBenchmark.p
% 0.09/0.49 % Elapsed time: 0.115880 seconds
% 0.09/0.49 % CPU time: 0.551672 seconds
% 0.09/0.49 % Total memory used: 118.087 MB
% 0.09/0.49 % Net memory used: 117.510 MB
%------------------------------------------------------------------------------