%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SWC218+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 02:41:53 PM UTC 2026
% Result : Theorem 0.21s 1.31s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC218+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
% 0.17/0.66 % Computer : n016.cluster.edu
% 0.17/0.66 % Model : x86_64 x86_64
% 0.17/0.66 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.66 % Memory : 8046.5625MB
% 0.17/0.66 % OS : Linux 6.8.0-71-generic
% 0.17/0.66 % CPULimit : 300
% 0.17/0.66 % WCLimit : 300
% 0.17/0.66 % DateTime : Mon Sep 21 08:10:09 UTC 2026
% 0.17/0.67 % CPUTime :
% 0.17/0.69 % Drodi V4.1.1
% 0.21/1.31 % Refutation found
% 0.21/1.31 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.21/1.31 % SZS output start CNFRefutation for theBenchmark
% 0.21/1.31 fof(f4,axiom,(
% 0.21/1.31 (! [U] :( ssList(U)=> ( singletonP(U)<=> (? [V] :( ssItem(V)& cons(V,nil) = U ) )) ) )),
% 0.21/1.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.21/1.31 fof(f7,axiom,(
% 0.21/1.31 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> ( segmentP(U,V)<=> (? [W] :( ssList(W)& (? [X] :( ssList(X)& app(app(W,V),X) = U ) )) )) ) )) )),
% 0.21/1.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.21/1.31 fof(f15,axiom,(
% 0.21/1.31 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> ( neq(U,V)<=> U != V ) ) )) )),
% 0.21/1.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.21/1.31 fof(f16,axiom,(
% 0.21/1.31 (! [U] :( ssList(U)=> (! [V] :( ssItem(V)=> ssList(cons(V,U)) ) )) )),
% 0.21/1.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.21/1.31 fof(f17,axiom,(
% 0.21/1.31 ssList(nil) ),
% 0.21/1.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.21/1.31 fof(f39,axiom,(
% 0.21/1.31 ~ singletonP(nil) ),
% 0.21/1.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.21/1.31 fof(f58,axiom,(
% 0.21/1.31 (! [U] :( ssList(U)=> ( segmentP(nil,U)<=> nil = U ) ) )),
% 0.21/1.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.21/1.31 fof(f96,conjecture,(
% 0.21/1.31 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> (! [X] :( ssList(X)=> ( V != X| U != W| (! [Y] :( ssList(Y)=> (! [Z] :( ssList(Z)=> ( app(Y,Z) != X| (! [X1] :( ssItem(X1)=> app(app(Y,cons(X1,nil)),Z) != W ) )) ) )))| neq(U,nil) ) ) )) )) )) )),
% 0.21/1.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.21/1.31 fof(f97,negated_conjecture,(
% 0.21/1.31 ~((! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> (! [X] :( ssList(X)=> ( V != X| U != W| (! [Y] :( ssList(Y)=> (! [Z] :( ssList(Z)=> ( app(Y,Z) != X| (! [X1] :( ssItem(X1)=> app(app(Y,cons(X1,nil)),Z) != W ) )) ) )))| neq(U,nil) ) ) )) )) )) ))),
% 0.21/1.31 inference(negated_conjecture,[status(cth)],[f96])).
% 0.21/1.31 fof(f113,plain,(
% 0.21/1.31 ![U]: (~ssList(U)|(singletonP(U)<=>(?[V]: (ssItem(V)&cons(V,nil)=U))))),
% 0.21/1.31 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 0.21/1.31 fof(f114,plain,(
% 0.21/1.31 ![U]: (~ssList(U)|((~singletonP(U)|(?[V]: (ssItem(V)&cons(V,nil)=U)))&(singletonP(U)|(![V]: (~ssItem(V)|~cons(V,nil)=U)))))),
% 0.21/1.31 inference(NNF_transformation,[status(thm)],[f113])).
% 0.21/1.31 fof(f115,plain,(
% 0.21/1.31 ![U]: (~ssList(U)|((~singletonP(U)|(ssItem(sK4_skl(U))&cons(sK4_skl(U),nil)=U))&(singletonP(U)|(![V]: (~ssItem(V)|~cons(V,nil)=U)))))),
% 0.21/1.31 inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(V,sK4_skl(U))],[f114])).
% 0.21/1.31 fof(f118,plain,(
% 0.21/1.31 ![X0,X1]: (~ssList(X0)|singletonP(X0)|~ssItem(X1)|~cons(X1,nil)=X0)),
% 0.21/1.31 inference(cnf_transformation,[status(thm)],[f115])).
% 0.21/1.31 fof(f131,plain,(
% 0.21/1.31 ![U]: (~ssList(U)|(![V]: (~ssList(V)|(segmentP(U,V)<=>(?[W]: (ssList(W)&(?[X]: (ssList(X)&app(app(W,V),X)=U))))))))),
% 0.21/1.31 inference(pre_NNF_transformation,[status(thm)],[f7])).
% 0.21/1.31 fof(f132,plain,(
% 0.21/1.31 ![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)))))))))),
% 0.21/1.31 inference(NNF_transformation,[status(thm)],[f131])).
% 0.21/1.31 fof(f133,plain,(
% 0.21/1.31 ![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)))))))))),
% 0.21/1.31 inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl,sK8_skl]),skolemize(W,sK7_skl(V,U)),skolemize(X,sK8_skl(V,U))],[f132])).
% 0.21/1.31 fof(f137,plain,(
% 0.21/1.31 ![X0,X1,X2,X3]: (~ssList(X0)|~ssList(X1)|segmentP(X0,X1)|~ssList(X2)|~ssList(X3)|~app(app(X2,X1),X3)=X0)),
% 0.21/1.31 inference(cnf_transformation,[status(thm)],[f133])).
% 0.21/1.31 fof(f217,plain,(
% 0.21/1.31 ![U]: (~ssList(U)|(![V]: (~ssList(V)|(neq(U,V)<=>~U=V))))),
% 0.21/1.31 inference(pre_NNF_transformation,[status(thm)],[f15])).
% 0.21/1.31 fof(f218,plain,(
% 0.21/1.31 ![U]: (~ssList(U)|(![V]: (~ssList(V)|((~neq(U,V)|~U=V)&(neq(U,V)|U=V)))))),
% 0.21/1.31 inference(NNF_transformation,[status(thm)],[f217])).
% 0.21/1.31 fof(f220,plain,(
% 0.21/1.31 ![X0,X1]: (~ssList(X0)|~ssList(X1)|neq(X0,X1)|X0=X1)),
% 0.21/1.31 inference(cnf_transformation,[status(thm)],[f218])).
% 0.21/1.31 fof(f221,plain,(
% 0.21/1.31 ![U]: (~ssList(U)|(![V]: (~ssItem(V)|ssList(cons(V,U)))))),
% 0.21/1.31 inference(pre_NNF_transformation,[status(thm)],[f16])).
% 0.21/1.31 fof(f222,plain,(
% 0.21/1.31 ![X0,X1]: (~ssList(X0)|~ssItem(X1)|ssList(cons(X1,X0)))),
% 0.21/1.31 inference(cnf_transformation,[status(thm)],[f221])).
% 0.21/1.31 fof(f223,plain,(
% 0.21/1.31 ssList(nil)),
% 0.21/1.31 inference(cnf_transformation,[status(thm)],[f17])).
% 0.21/1.31 fof(f280,plain,(
% 0.21/1.31 ~singletonP(nil)),
% 0.21/1.31 inference(cnf_transformation,[status(thm)],[f39])).
% 0.21/1.31 fof(f324,plain,(
% 0.21/1.31 ![U]: (~ssList(U)|(segmentP(nil,U)<=>nil=U))),
% 0.21/1.31 inference(pre_NNF_transformation,[status(thm)],[f58])).
% 0.21/1.31 fof(f325,plain,(
% 0.21/1.31 ![U]: (~ssList(U)|((~segmentP(nil,U)|nil=U)&(segmentP(nil,U)|~nil=U)))),
% 0.21/1.31 inference(NNF_transformation,[status(thm)],[f324])).
% 0.21/1.31 fof(f326,plain,(
% 0.21/1.31 ![X0]: (~ssList(X0)|~segmentP(nil,X0)|nil=X0)),
% 0.21/1.31 inference(cnf_transformation,[status(thm)],[f325])).
% 0.21/1.31 fof(f415,plain,(
% 0.21/1.31 (?[U]: (ssList(U)&(?[V]: (ssList(V)&(?[W]: (ssList(W)&(?[X]: (ssList(X)&(((V=X&U=W)&(?[Y]: (ssList(Y)&(?[Z]: (ssList(Z)&(app(Y,Z)=X&(?[X1]: (ssItem(X1)&app(app(Y,cons(X1,nil)),Z)=W))))))))&~neq(U,nil))))))))))),
% 0.21/1.31 inference(pre_NNF_transformation,[status(thm)],[f97])).
% 0.21/1.31 fof(f416,plain,(
% 0.21/1.31 (ssList(sK47_skl)&(ssList(sK48_skl)&(ssList(sK49_skl)&(ssList(sK50_skl)&(((sK48_skl=sK50_skl&sK47_skl=sK49_skl)&(ssList(sK51_skl)&(ssList(sK52_skl)&(app(sK51_skl,sK52_skl)=sK50_skl&(ssItem(sK53_skl)&app(app(sK51_skl,cons(sK53_skl,nil)),sK52_skl)=sK49_skl)))))&~neq(sK47_skl,nil))))))),
% 0.21/1.31 inference(skolemize,[status(esa),new_symbols(skolem,[sK47_skl,sK48_skl,sK49_skl,sK50_skl,sK51_skl,sK52_skl,sK53_skl]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl),skolemize(Y,sK51_skl),skolemize(Z,sK52_skl),skolemize(X1,sK53_skl)],[f415])).
% 0.21/1.31 fof(f419,plain,(
% 0.21/1.31 ssList(sK49_skl)),
% 0.21/1.31 inference(cnf_transformation,[status(thm)],[f416])).
% 0.21/1.31 fof(f422,plain,(
% 0.21/1.31 sK47_skl=sK49_skl),
% 0.21/1.31 inference(cnf_transformation,[status(thm)],[f416])).
% 0.21/1.31 fof(f423,plain,(
% 0.21/1.31 ssList(sK51_skl)),
% 0.21/1.31 inference(cnf_transformation,[status(thm)],[f416])).
% 0.21/1.31 fof(f424,plain,(
% 0.21/1.31 ssList(sK52_skl)),
% 0.21/1.31 inference(cnf_transformation,[status(thm)],[f416])).
% 0.21/1.31 fof(f426,plain,(
% 0.21/1.31 ssItem(sK53_skl)),
% 0.21/1.31 inference(cnf_transformation,[status(thm)],[f416])).
% 0.21/1.31 fof(f427,plain,(
% 0.21/1.31 app(app(sK51_skl,cons(sK53_skl,nil)),sK52_skl)=sK49_skl),
% 0.21/1.31 inference(cnf_transformation,[status(thm)],[f416])).
% 0.21/1.31 fof(f428,plain,(
% 0.21/1.31 ~neq(sK47_skl,nil)),
% 0.21/1.31 inference(cnf_transformation,[status(thm)],[f416])).
% 0.21/1.31 fof(f432,plain,(
% 0.21/1.31 ![X0]: (~ssList(cons(X0,nil))|singletonP(cons(X0,nil))|~ssItem(X0))),
% 0.21/1.31 inference(destructive_equality_resolution,[status(thm)],[f118])).
% 0.21/1.31 fof(f435,plain,(
% 0.21/1.31 ![X0,X1,X2]: (~ssList(app(app(X0,X1),X2))|~ssList(X1)|segmentP(app(app(X0,X1),X2),X1)|~ssList(X0)|~ssList(X2))),
% 0.21/1.31 inference(destructive_equality_resolution,[status(thm)],[f137])).
% 0.21/1.31 fof(f461,plain,(
% 0.21/1.31 ~neq(sK49_skl,nil)),
% 0.21/1.31 inference(forward_demodulation,[status(thm)],[f422,f428])).
% 0.21/1.31 fof(f467,plain,(
% 0.21/1.31 ![X0]: (~ssList(X0)|neq(sK49_skl,X0)|sK49_skl=X0)),
% 0.21/1.31 inference(resolution,[status(thm)],[f220,f419])).
% 0.21/1.31 fof(f488,plain,(
% 0.21/1.31 ![X0]: (~ssItem(X0)|ssList(cons(X0,nil)))),
% 0.21/1.31 inference(resolution,[status(thm)],[f222,f223])).
% 0.21/1.31 fof(f688,plain,(
% 0.21/1.31 ![X0]: (singletonP(cons(X0,nil))|~ssItem(X0))),
% 0.21/1.31 inference(backward_subsumption_resolution,[status(thm)],[f432,f488])).
% 0.21/1.31 fof(f691,plain,(
% 0.21/1.31 ssList(cons(sK53_skl,nil))),
% 0.21/1.31 inference(resolution,[status(thm)],[f488,f426])).
% 0.21/1.31 fof(f1285,plain,(
% 0.21/1.31 neq(sK49_skl,nil)|sK49_skl=nil),
% 0.21/1.31 inference(resolution,[status(thm)],[f467,f223])).
% 0.21/1.31 fof(f1288,plain,(
% 0.21/1.31 sK49_skl=nil),
% 0.21/1.31 inference(forward_subsumption_resolution,[status(thm)],[f1285,f461])).
% 0.21/1.31 fof(f1301,plain,(
% 0.21/1.31 app(app(sK51_skl,cons(sK53_skl,nil)),sK52_skl)=nil),
% 0.21/1.31 inference(backward_demodulation,[status(thm)],[f1288,f427])).
% 0.21/1.31 fof(f1514,plain,(
% 0.21/1.31 ~ssList(nil)|~ssList(cons(sK53_skl,nil))|segmentP(app(app(sK51_skl,cons(sK53_skl,nil)),sK52_skl),cons(sK53_skl,nil))|~ssList(sK51_skl)|~ssList(sK52_skl)),
% 0.21/1.31 inference(paramodulation,[status(thm)],[f1301,f435])).
% 0.21/1.31 fof(f1520,plain,(
% 0.21/1.31 ~ssList(nil)|~ssList(cons(sK53_skl,nil))|segmentP(nil,cons(sK53_skl,nil))|~ssList(sK51_skl)|~ssList(sK52_skl)),
% 0.21/1.31 inference(forward_demodulation,[status(thm)],[f1301,f1514])).
% 0.21/1.31 fof(f1521,plain,(
% 0.21/1.32 ~ssList(cons(sK53_skl,nil))|segmentP(nil,cons(sK53_skl,nil))|~ssList(sK51_skl)|~ssList(sK52_skl)),
% 0.21/1.32 inference(forward_subsumption_resolution,[status(thm)],[f1520,f223])).
% 0.21/1.32 fof(f1655,plain,(
% 0.21/1.32 singletonP(cons(sK53_skl,nil))),
% 0.21/1.32 inference(resolution,[status(thm)],[f688,f426])).
% 0.21/1.32 fof(f10726,plain,(
% 0.21/1.32 segmentP(nil,cons(sK53_skl,nil))|~ssList(sK51_skl)|~ssList(sK52_skl)),
% 0.21/1.32 inference(forward_subsumption_resolution,[status(thm)],[f1521,f691])).
% 0.21/1.32 fof(f10727,plain,(
% 0.21/1.32 segmentP(nil,cons(sK53_skl,nil))|~ssList(sK52_skl)),
% 0.21/1.32 inference(resolution,[status(thm)],[f10726,f423])).
% 0.21/1.32 fof(f10728,plain,(
% 0.21/1.32 segmentP(nil,cons(sK53_skl,nil))),
% 0.21/1.32 inference(forward_subsumption_resolution,[status(thm)],[f10727,f424])).
% 0.21/1.32 fof(f13788,plain,(
% 0.21/1.32 ~ssList(cons(sK53_skl,nil))|nil=cons(sK53_skl,nil)),
% 0.21/1.32 inference(resolution,[status(thm)],[f326,f10728])).
% 0.21/1.32 fof(f13790,plain,(
% 0.21/1.32 nil=cons(sK53_skl,nil)),
% 0.21/1.32 inference(forward_subsumption_resolution,[status(thm)],[f13788,f691])).
% 0.21/1.32 fof(f13799,plain,(
% 0.21/1.32 singletonP(nil)),
% 0.21/1.32 inference(backward_demodulation,[status(thm)],[f13790,f1655])).
% 0.21/1.32 fof(f13841,plain,(
% 0.21/1.32 $false),
% 0.21/1.32 inference(forward_subsumption_resolution,[status(thm)],[f13799,f280])).
% 0.21/1.32 % SZS output end CNFRefutation for theBenchmark.p
% 4.01/1.36 % Elapsed time: 0.678791 seconds
% 4.01/1.36 % CPU time: 4.828289 seconds
% 4.01/1.36 % Total memory used: 156.535 MB
% 4.01/1.36 % Net memory used: 153.220 MB
%------------------------------------------------------------------------------