%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SWC182+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 : n009.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 02:41:48 PM UTC 2026
% Result : Theorem 9.46s 1.62s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC182+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
% 0.10/0.36 % Computer : n009.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 08:02:28 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 9.46/1.62 % Refutation found
% 9.46/1.62 % SZS status Theorem for theBenchmark: Theorem is valid
% 9.46/1.62 % SZS output start CNFRefutation for theBenchmark
% 9.46/1.62 fof(f4,axiom,(
% 9.46/1.62 (! [U] :( ssList(U)=> ( singletonP(U)<=> (? [V] :( ssItem(V)& cons(V,nil) = U ) )) ) )),
% 9.46/1.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 9.46/1.62 fof(f7,axiom,(
% 9.46/1.62 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> ( segmentP(U,V)<=> (? [W] :( ssList(W)& (? [X] :( ssList(X)& app(app(W,V),X) = U ) )) )) ) )) )),
% 9.46/1.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 9.46/1.62 fof(f16,axiom,(
% 9.46/1.62 (! [U] :( ssList(U)=> (! [V] :( ssItem(V)=> ssList(cons(V,U)) ) )) )),
% 9.46/1.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 9.46/1.62 fof(f17,axiom,(
% 9.46/1.62 ssList(nil) ),
% 9.46/1.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 9.46/1.62 fof(f39,axiom,(
% 9.46/1.62 ~ singletonP(nil) ),
% 9.46/1.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 9.46/1.62 fof(f58,axiom,(
% 9.46/1.62 (! [U] :( ssList(U)=> ( segmentP(nil,U)<=> nil = U ) ) )),
% 9.46/1.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 9.46/1.62 fof(f96,conjecture,(
% 9.46/1.62 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> (! [X] :( ssList(X)=> ( nil != W| V != X| U != W| (! [Y] :( ssItem(Y)=> (! [Z] :( ssList(Z)=> (! [X1] :( ssList(X1)=> ( app(app(Z,cons(Y,nil)),X1) != U| ( ~ memberP(Z,Y)& ~ memberP(X1,Y) ) ) ) )) )) )) ) )) )) )) )),
% 9.46/1.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 9.46/1.62 fof(f97,negated_conjecture,(
% 9.46/1.62 ~((! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> (! [X] :( ssList(X)=> ( nil != W| V != X| U != W| (! [Y] :( ssItem(Y)=> (! [Z] :( ssList(Z)=> (! [X1] :( ssList(X1)=> ( app(app(Z,cons(Y,nil)),X1) != U| ( ~ memberP(Z,Y)& ~ memberP(X1,Y) ) ) ) )) )) )) ) )) )) )) ))),
% 9.46/1.62 inference(negated_conjecture,[status(cth)],[f96])).
% 9.46/1.62 fof(f113,plain,(
% 9.46/1.62 ![U]: (~ssList(U)|(singletonP(U)<=>(?[V]: (ssItem(V)&cons(V,nil)=U))))),
% 9.46/1.62 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 9.46/1.62 fof(f114,plain,(
% 9.46/1.62 ![U]: (~ssList(U)|((~singletonP(U)|(?[V]: (ssItem(V)&cons(V,nil)=U)))&(singletonP(U)|(![V]: (~ssItem(V)|~cons(V,nil)=U)))))),
% 9.46/1.62 inference(NNF_transformation,[status(thm)],[f113])).
% 9.46/1.62 fof(f115,plain,(
% 9.46/1.62 ![U]: (~ssList(U)|((~singletonP(U)|(ssItem(sK4_skl(U))&cons(sK4_skl(U),nil)=U))&(singletonP(U)|(![V]: (~ssItem(V)|~cons(V,nil)=U)))))),
% 9.46/1.62 inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(V,sK4_skl(U))],[f114])).
% 9.46/1.62 fof(f118,plain,(
% 9.46/1.62 ![X0,X1]: (~ssList(X0)|singletonP(X0)|~ssItem(X1)|~cons(X1,nil)=X0)),
% 9.46/1.62 inference(cnf_transformation,[status(thm)],[f115])).
% 9.46/1.62 fof(f131,plain,(
% 9.46/1.62 ![U]: (~ssList(U)|(![V]: (~ssList(V)|(segmentP(U,V)<=>(?[W]: (ssList(W)&(?[X]: (ssList(X)&app(app(W,V),X)=U))))))))),
% 9.46/1.62 inference(pre_NNF_transformation,[status(thm)],[f7])).
% 9.46/1.62 fof(f132,plain,(
% 9.46/1.62 ![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)))))))))),
% 9.46/1.62 inference(NNF_transformation,[status(thm)],[f131])).
% 9.46/1.62 fof(f133,plain,(
% 9.46/1.62 ![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)))))))))),
% 9.46/1.62 inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl,sK8_skl]),skolemize(W,sK7_skl(V,U)),skolemize(X,sK8_skl(V,U))],[f132])).
% 9.46/1.62 fof(f137,plain,(
% 9.46/1.62 ![X0,X1,X2,X3]: (~ssList(X0)|~ssList(X1)|segmentP(X0,X1)|~ssList(X2)|~ssList(X3)|~app(app(X2,X1),X3)=X0)),
% 9.46/1.62 inference(cnf_transformation,[status(thm)],[f133])).
% 9.46/1.62 fof(f221,plain,(
% 9.46/1.62 ![U]: (~ssList(U)|(![V]: (~ssItem(V)|ssList(cons(V,U)))))),
% 9.46/1.62 inference(pre_NNF_transformation,[status(thm)],[f16])).
% 9.46/1.62 fof(f222,plain,(
% 9.46/1.62 ![X0,X1]: (~ssList(X0)|~ssItem(X1)|ssList(cons(X1,X0)))),
% 9.46/1.62 inference(cnf_transformation,[status(thm)],[f221])).
% 9.46/1.62 fof(f223,plain,(
% 9.46/1.62 ssList(nil)),
% 9.46/1.62 inference(cnf_transformation,[status(thm)],[f17])).
% 9.46/1.62 fof(f280,plain,(
% 9.46/1.62 ~singletonP(nil)),
% 9.46/1.62 inference(cnf_transformation,[status(thm)],[f39])).
% 9.46/1.62 fof(f324,plain,(
% 9.46/1.62 ![U]: (~ssList(U)|(segmentP(nil,U)<=>nil=U))),
% 9.46/1.62 inference(pre_NNF_transformation,[status(thm)],[f58])).
% 9.46/1.62 fof(f325,plain,(
% 9.46/1.62 ![U]: (~ssList(U)|((~segmentP(nil,U)|nil=U)&(segmentP(nil,U)|~nil=U)))),
% 9.46/1.62 inference(NNF_transformation,[status(thm)],[f324])).
% 9.46/1.62 fof(f326,plain,(
% 9.46/1.62 ![X0]: (~ssList(X0)|~segmentP(nil,X0)|nil=X0)),
% 9.46/1.62 inference(cnf_transformation,[status(thm)],[f325])).
% 9.46/1.62 fof(f415,plain,(
% 9.46/1.62 (?[U]: (ssList(U)&(?[V]: (ssList(V)&(?[W]: (ssList(W)&(?[X]: (ssList(X)&(((nil=W&V=X)&U=W)&(?[Y]: (ssItem(Y)&(?[Z]: (ssList(Z)&(?[X1]: (ssList(X1)&(app(app(Z,cons(Y,nil)),X1)=U&(memberP(Z,Y)|memberP(X1,Y))))))))))))))))))),
% 9.46/1.62 inference(pre_NNF_transformation,[status(thm)],[f97])).
% 9.46/1.62 fof(f416,plain,(
% 9.46/1.62 (ssList(sK47_skl)&(ssList(sK48_skl)&(ssList(sK49_skl)&(ssList(sK50_skl)&(((nil=sK49_skl&sK48_skl=sK50_skl)&sK47_skl=sK49_skl)&(ssItem(sK51_skl)&(ssList(sK52_skl)&(ssList(sK53_skl)&(app(app(sK52_skl,cons(sK51_skl,nil)),sK53_skl)=sK47_skl&(memberP(sK52_skl,sK51_skl)|memberP(sK53_skl,sK51_skl)))))))))))),
% 9.46/1.62 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])).
% 9.46/1.62 fof(f421,plain,(
% 9.46/1.62 nil=sK49_skl),
% 9.46/1.62 inference(cnf_transformation,[status(thm)],[f416])).
% 9.46/1.62 fof(f423,plain,(
% 9.46/1.62 sK47_skl=sK49_skl),
% 9.46/1.62 inference(cnf_transformation,[status(thm)],[f416])).
% 9.46/1.62 fof(f424,plain,(
% 9.46/1.62 ssItem(sK51_skl)),
% 9.46/1.62 inference(cnf_transformation,[status(thm)],[f416])).
% 9.46/1.62 fof(f425,plain,(
% 9.46/1.62 ssList(sK52_skl)),
% 9.46/1.62 inference(cnf_transformation,[status(thm)],[f416])).
% 9.46/1.62 fof(f426,plain,(
% 9.46/1.62 ssList(sK53_skl)),
% 9.46/1.62 inference(cnf_transformation,[status(thm)],[f416])).
% 9.46/1.62 fof(f427,plain,(
% 9.46/1.62 app(app(sK52_skl,cons(sK51_skl,nil)),sK53_skl)=sK47_skl),
% 9.46/1.62 inference(cnf_transformation,[status(thm)],[f416])).
% 9.46/1.62 fof(f432,plain,(
% 9.46/1.62 ![X0]: (~ssList(cons(X0,nil))|singletonP(cons(X0,nil))|~ssItem(X0))),
% 9.46/1.62 inference(destructive_equality_resolution,[status(thm)],[f118])).
% 9.46/1.62 fof(f435,plain,(
% 9.46/1.62 ![X0,X1,X2]: (~ssList(app(app(X0,X1),X2))|~ssList(X1)|segmentP(app(app(X0,X1),X2),X1)|~ssList(X0)|~ssList(X2))),
% 9.46/1.62 inference(destructive_equality_resolution,[status(thm)],[f137])).
% 9.46/1.62 fof(f462,plain,(
% 9.46/1.62 sK47_skl=nil),
% 9.46/1.62 inference(forward_demodulation,[status(thm)],[f421,f423])).
% 9.46/1.62 fof(f465,plain,(
% 9.46/1.62 ![X0]: (~ssItem(X0)|ssList(cons(X0,nil)))),
% 9.46/1.62 inference(resolution,[status(thm)],[f222,f223])).
% 9.46/1.62 fof(f476,plain,(
% 9.46/1.62 app(app(sK52_skl,cons(sK51_skl,nil)),sK53_skl)=nil),
% 9.46/1.62 inference(forward_demodulation,[status(thm)],[f462,f427])).
% 9.46/1.62 fof(f555,plain,(
% 9.46/1.62 ssList(cons(sK51_skl,nil))),
% 9.46/1.62 inference(resolution,[status(thm)],[f465,f424])).
% 9.46/1.62 fof(f607,plain,(
% 9.46/1.62 ![X0]: (singletonP(cons(X0,nil))|~ssItem(X0))),
% 9.46/1.62 inference(forward_subsumption_resolution,[status(thm)],[f432,f465])).
% 9.46/1.62 fof(f610,plain,(
% 9.46/1.62 singletonP(cons(sK51_skl,nil))),
% 9.46/1.62 inference(resolution,[status(thm)],[f607,f424])).
% 9.46/1.62 fof(f1237,plain,(
% 9.46/1.62 ~ssList(nil)|~ssList(cons(sK51_skl,nil))|segmentP(app(app(sK52_skl,cons(sK51_skl,nil)),sK53_skl),cons(sK51_skl,nil))|~ssList(sK52_skl)|~ssList(sK53_skl)),
% 9.46/1.62 inference(paramodulation,[status(thm)],[f476,f435])).
% 9.46/1.62 fof(f1246,plain,(
% 9.46/1.62 ~ssList(nil)|~ssList(cons(sK51_skl,nil))|segmentP(nil,cons(sK51_skl,nil))|~ssList(sK52_skl)|~ssList(sK53_skl)),
% 9.46/1.62 inference(forward_demodulation,[status(thm)],[f476,f1237])).
% 9.46/1.62 fof(f1247,plain,(
% 9.46/1.62 ~ssList(cons(sK51_skl,nil))|segmentP(nil,cons(sK51_skl,nil))|~ssList(sK52_skl)|~ssList(sK53_skl)),
% 9.46/1.62 inference(forward_subsumption_resolution,[status(thm)],[f1246,f223])).
% 9.46/1.62 fof(f10940,plain,(
% 9.46/1.62 segmentP(nil,cons(sK51_skl,nil))|~ssList(sK52_skl)|~ssList(sK53_skl)),
% 9.46/1.62 inference(forward_subsumption_resolution,[status(thm)],[f1247,f555])).
% 9.46/1.62 fof(f10941,plain,(
% 9.46/1.62 segmentP(nil,cons(sK51_skl,nil))|~ssList(sK53_skl)),
% 9.46/1.62 inference(resolution,[status(thm)],[f10940,f425])).
% 9.46/1.62 fof(f10942,plain,(
% 9.46/1.62 segmentP(nil,cons(sK51_skl,nil))),
% 9.46/1.62 inference(forward_subsumption_resolution,[status(thm)],[f10941,f426])).
% 9.46/1.62 fof(f14321,plain,(
% 9.46/1.62 ~ssList(cons(sK51_skl,nil))|nil=cons(sK51_skl,nil)),
% 9.46/1.62 inference(resolution,[status(thm)],[f326,f10942])).
% 9.46/1.62 fof(f14323,plain,(
% 9.46/1.62 nil=cons(sK51_skl,nil)),
% 9.46/1.62 inference(forward_subsumption_resolution,[status(thm)],[f14321,f555])).
% 9.46/1.62 fof(f14337,plain,(
% 9.46/1.64 singletonP(nil)),
% 9.46/1.64 inference(backward_demodulation,[status(thm)],[f14323,f610])).
% 9.46/1.64 fof(f14365,plain,(
% 9.46/1.64 $false),
% 9.46/1.64 inference(forward_subsumption_resolution,[status(thm)],[f14337,f280])).
% 9.46/1.64 % SZS output end CNFRefutation for theBenchmark.p
% 9.46/1.66 % Elapsed time: 1.284031 seconds
% 9.46/1.66 % CPU time: 9.824779 seconds
% 9.46/1.66 % Total memory used: 207.408 MB
% 9.46/1.66 % Net memory used: 200.258 MB
%------------------------------------------------------------------------------