%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SWC046+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 : 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 02:41:26 PM UTC 2026
% Result : Theorem 10.07s 1.76s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC046+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
% 0.09/0.37 % Computer : n001.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 07:56:59 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.39 % Drodi V4.1.1
% 10.07/1.76 % Refutation found
% 10.07/1.76 % SZS status Theorem for theBenchmark: Theorem is valid
% 10.07/1.76 % SZS output start CNFRefutation for theBenchmark
% 10.07/1.76 fof(f37,axiom,(
% 10.07/1.76 (! [U] :( ssItem(U)=> (! [V] :( ssItem(V)=> (! [W] :( ssList(W)=> ( memberP(cons(V,W),U)<=> ( U = V| memberP(W,U) ) ) ) )) )) )),
% 10.07/1.76 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.07/1.76 fof(f38,axiom,(
% 10.07/1.76 (! [U] :( ssItem(U)=> ~ memberP(nil,U) ) )),
% 10.07/1.76 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.07/1.76 fof(f75,axiom,(
% 10.07/1.76 (! [U] :( ssList(U)=> ( nil != U=> (? [V] :( ssItem(V)& hd(U) = V ) )) ) )),
% 10.07/1.76 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.07/1.76 fof(f76,axiom,(
% 10.07/1.76 (! [U] :( ssList(U)=> ( nil != U=> (? [V] :( ssList(V)& tl(U) = V ) )) ) )),
% 10.07/1.76 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.07/1.76 fof(f78,axiom,(
% 10.07/1.76 (! [U] :( ssList(U)=> ( nil != U=> cons(hd(U),tl(U)) = U ) ) )),
% 10.07/1.76 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.07/1.76 fof(f96,conjecture,(
% 10.07/1.76 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> (! [X] :( ssList(X)=> ( nil != V| V != X| U != W| nil = U| (? [Y] :( ssItem(Y)& ( ( ~ memberP(W,Y)& (! [Z] :( ssList(Z)=> ~ segmentP(X,app(app(cons(Y,nil),Z),cons(Y,nil))) ))& memberP(X,Y) )| ( memberP(W,Y)& ( ~ memberP(X,Y)| (? [Z] :( ssList(Z)& segmentP(X,app(app(cons(Y,nil),Z),cons(Y,nil))) ) )) ) ) ) )) ) )) )) )) )),
% 10.07/1.76 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.07/1.76 fof(f97,negated_conjecture,(
% 10.07/1.76 ~((! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> (! [X] :( ssList(X)=> ( nil != V| V != X| U != W| nil = U| (? [Y] :( ssItem(Y)& ( ( ~ memberP(W,Y)& (! [Z] :( ssList(Z)=> ~ segmentP(X,app(app(cons(Y,nil),Z),cons(Y,nil))) ))& memberP(X,Y) )| ( memberP(W,Y)& ( ~ memberP(X,Y)| (? [Z] :( ssList(Z)& segmentP(X,app(app(cons(Y,nil),Z),cons(Y,nil))) ) )) ) ) ) )) ) )) )) )) ))),
% 10.07/1.76 inference(negated_conjecture,[status(cth)],[f96])).
% 10.07/1.76 fof(f273,plain,(
% 10.07/1.76 ![U]: (~ssItem(U)|(![V]: (~ssItem(V)|(![W]: (~ssList(W)|(memberP(cons(V,W),U)<=>(U=V|memberP(W,U))))))))),
% 10.07/1.76 inference(pre_NNF_transformation,[status(thm)],[f37])).
% 10.07/1.76 fof(f274,plain,(
% 10.07/1.76 ![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)))))))))),
% 10.07/1.76 inference(NNF_transformation,[status(thm)],[f273])).
% 10.07/1.76 fof(f276,plain,(
% 10.07/1.76 ![X0,X1,X2]: (~ssItem(X0)|~ssItem(X1)|~ssList(X2)|memberP(cons(X1,X2),X0)|~X0=X1)),
% 10.07/1.76 inference(cnf_transformation,[status(thm)],[f274])).
% 10.07/1.76 fof(f278,plain,(
% 10.07/1.76 ![U]: (~ssItem(U)|~memberP(nil,U))),
% 10.07/1.76 inference(pre_NNF_transformation,[status(thm)],[f38])).
% 10.07/1.76 fof(f279,plain,(
% 10.07/1.76 ![X0]: (~ssItem(X0)|~memberP(nil,X0))),
% 10.07/1.76 inference(cnf_transformation,[status(thm)],[f278])).
% 10.07/1.76 fof(f363,plain,(
% 10.07/1.76 ![U]: (~ssList(U)|(nil=U|(?[V]: (ssItem(V)&hd(U)=V))))),
% 10.07/1.76 inference(pre_NNF_transformation,[status(thm)],[f75])).
% 10.07/1.76 fof(f364,plain,(
% 10.07/1.76 ![U]: (~ssList(U)|(nil=U|(ssItem(sK45_skl(U))&hd(U)=sK45_skl(U))))),
% 10.07/1.76 inference(skolemize,[status(esa),new_symbols(skolem,[sK45_skl]),skolemize(V,sK45_skl(U))],[f363])).
% 10.07/1.76 fof(f365,plain,(
% 10.07/1.76 ![X0]: (~ssList(X0)|nil=X0|ssItem(sK45_skl(X0)))),
% 10.07/1.76 inference(cnf_transformation,[status(thm)],[f364])).
% 10.07/1.76 fof(f366,plain,(
% 10.07/1.76 ![X0]: (~ssList(X0)|nil=X0|hd(X0)=sK45_skl(X0))),
% 10.07/1.76 inference(cnf_transformation,[status(thm)],[f364])).
% 10.07/1.76 fof(f367,plain,(
% 10.07/1.76 ![U]: (~ssList(U)|(nil=U|(?[V]: (ssList(V)&tl(U)=V))))),
% 10.07/1.76 inference(pre_NNF_transformation,[status(thm)],[f76])).
% 10.07/1.76 fof(f368,plain,(
% 10.07/1.76 ![U]: (~ssList(U)|(nil=U|(ssList(sK46_skl(U))&tl(U)=sK46_skl(U))))),
% 10.07/1.76 inference(skolemize,[status(esa),new_symbols(skolem,[sK46_skl]),skolemize(V,sK46_skl(U))],[f367])).
% 10.07/1.76 fof(f369,plain,(
% 10.07/1.76 ![X0]: (~ssList(X0)|nil=X0|ssList(sK46_skl(X0)))),
% 10.07/1.76 inference(cnf_transformation,[status(thm)],[f368])).
% 10.07/1.76 fof(f370,plain,(
% 10.07/1.76 ![X0]: (~ssList(X0)|nil=X0|tl(X0)=sK46_skl(X0))),
% 10.07/1.76 inference(cnf_transformation,[status(thm)],[f368])).
% 10.07/1.76 fof(f373,plain,(
% 10.07/1.76 ![U]: (~ssList(U)|(nil=U|cons(hd(U),tl(U))=U))),
% 10.07/1.76 inference(pre_NNF_transformation,[status(thm)],[f78])).
% 10.07/1.76 fof(f374,plain,(
% 10.07/1.76 ![X0]: (~ssList(X0)|nil=X0|cons(hd(X0),tl(X0))=X0)),
% 10.07/1.76 inference(cnf_transformation,[status(thm)],[f373])).
% 10.07/1.76 fof(f415,plain,(
% 10.07/1.76 (?[U]: (ssList(U)&(?[V]: (ssList(V)&(?[W]: (ssList(W)&(?[X]: (ssList(X)&((((nil=V&V=X)&U=W)&~nil=U)&(![Y]: (~ssItem(Y)|(((memberP(W,Y)|(?[Z]: (ssList(Z)&segmentP(X,app(app(cons(Y,nil),Z),cons(Y,nil))))))|~memberP(X,Y))&(~memberP(W,Y)|(memberP(X,Y)&(![Z]: (~ssList(Z)|~segmentP(X,app(app(cons(Y,nil),Z),cons(Y,nil)))))))))))))))))))),
% 10.07/1.76 inference(pre_NNF_transformation,[status(thm)],[f97])).
% 10.07/1.76 fof(f416,plain,(
% 10.07/1.76 (ssList(sK47_skl)&(ssList(sK48_skl)&(ssList(sK49_skl)&(ssList(sK50_skl)&((((nil=sK48_skl&sK48_skl=sK50_skl)&sK47_skl=sK49_skl)&~nil=sK47_skl)&(![Y]: (~ssItem(Y)|(((memberP(sK49_skl,Y)|(ssList(sK51_skl(Y))&segmentP(sK50_skl,app(app(cons(Y,nil),sK51_skl(Y)),cons(Y,nil)))))|~memberP(sK50_skl,Y))&(~memberP(sK49_skl,Y)|(memberP(sK50_skl,Y)&(![Z]: (~ssList(Z)|~segmentP(sK50_skl,app(app(cons(Y,nil),Z),cons(Y,nil)))))))))))))))),
% 10.07/1.76 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])).
% 10.07/1.76 fof(f419,plain,(
% 10.07/1.76 ssList(sK49_skl)),
% 10.07/1.76 inference(cnf_transformation,[status(thm)],[f416])).
% 10.07/1.76 fof(f421,plain,(
% 10.07/1.76 nil=sK48_skl),
% 10.07/1.76 inference(cnf_transformation,[status(thm)],[f416])).
% 10.07/1.76 fof(f422,plain,(
% 10.07/1.76 sK48_skl=sK50_skl),
% 10.07/1.76 inference(cnf_transformation,[status(thm)],[f416])).
% 10.07/1.76 fof(f423,plain,(
% 10.07/1.76 sK47_skl=sK49_skl),
% 10.07/1.76 inference(cnf_transformation,[status(thm)],[f416])).
% 10.07/1.76 fof(f424,plain,(
% 10.07/1.76 ~nil=sK47_skl),
% 10.07/1.76 inference(cnf_transformation,[status(thm)],[f416])).
% 10.07/1.76 fof(f427,plain,(
% 10.07/1.76 ![X0]: (~ssItem(X0)|~memberP(sK49_skl,X0)|memberP(sK50_skl,X0))),
% 10.07/1.76 inference(cnf_transformation,[status(thm)],[f416])).
% 10.07/1.76 fof(f448,plain,(
% 10.07/1.76 ![X1,X2]: (~ssItem(X1)|~ssItem(X1)|~ssList(X2)|memberP(cons(X1,X2),X1))),
% 10.07/1.76 inference(destructive_equality_resolution,[status(thm)],[f276])).
% 10.07/1.76 fof(f449,plain,(
% 10.07/1.76 ![X0,X1]: (~ssItem(X0)|~ssList(X1)|memberP(cons(X0,X1),X0))),
% 10.07/1.76 inference(duplicate_literals_removal,[status(thm)],[f448])).
% 10.07/1.76 fof(f467,plain,(
% 10.07/1.76 ![X0]: (~ssList(X0)|sK48_skl=X0|cons(hd(X0),tl(X0))=X0)),
% 10.07/1.76 inference(backward_demodulation,[status(thm)],[f421,f374])).
% 10.07/1.76 fof(f469,plain,(
% 10.07/1.76 ![X0]: (~ssList(X0)|sK48_skl=X0|tl(X0)=sK46_skl(X0))),
% 10.07/1.76 inference(backward_demodulation,[status(thm)],[f421,f370])).
% 10.07/1.76 fof(f470,plain,(
% 10.07/1.76 ![X0]: (~ssList(X0)|sK48_skl=X0|ssList(sK46_skl(X0)))),
% 10.07/1.76 inference(backward_demodulation,[status(thm)],[f421,f369])).
% 10.07/1.76 fof(f471,plain,(
% 10.07/1.76 ![X0]: (~ssList(X0)|sK48_skl=X0|hd(X0)=sK45_skl(X0))),
% 10.07/1.76 inference(backward_demodulation,[status(thm)],[f421,f366])).
% 10.07/1.76 fof(f472,plain,(
% 10.07/1.76 ![X0]: (~ssList(X0)|sK48_skl=X0|ssItem(sK45_skl(X0)))),
% 10.07/1.76 inference(backward_demodulation,[status(thm)],[f421,f365])).
% 10.07/1.76 fof(f500,plain,(
% 10.07/1.76 ![X0]: (~ssItem(X0)|~memberP(sK48_skl,X0))),
% 10.07/1.76 inference(backward_demodulation,[status(thm)],[f421,f279])).
% 10.07/1.76 fof(f514,plain,(
% 10.07/1.76 ~sK48_skl=sK47_skl),
% 10.07/1.76 inference(forward_demodulation,[status(thm)],[f421,f424])).
% 10.07/1.76 fof(f515,plain,(
% 10.07/1.76 ~sK50_skl=sK47_skl),
% 10.07/1.76 inference(forward_demodulation,[status(thm)],[f422,f514])).
% 10.07/1.76 fof(f516,plain,(
% 10.07/1.76 ~sK50_skl=sK49_skl),
% 10.07/1.76 inference(forward_demodulation,[status(thm)],[f423,f515])).
% 10.07/1.76 fof(f535,plain,(
% 10.07/1.76 ![X0]: (~ssList(X0)|sK50_skl=X0|cons(hd(X0),tl(X0))=X0)),
% 10.07/1.76 inference(forward_demodulation,[status(thm)],[f422,f467])).
% 10.07/1.76 fof(f539,plain,(
% 10.07/1.76 ![X0]: (~ssList(X0)|sK50_skl=X0|tl(X0)=sK46_skl(X0))),
% 10.07/1.76 inference(forward_demodulation,[status(thm)],[f422,f469])).
% 10.07/1.76 fof(f540,plain,(
% 10.07/1.76 ![X0]: (~ssList(X0)|sK50_skl=X0|ssList(sK46_skl(X0)))),
% 10.07/1.76 inference(forward_demodulation,[status(thm)],[f422,f470])).
% 10.07/1.76 fof(f541,plain,(
% 10.07/1.76 ![X0]: (~ssList(X0)|sK50_skl=X0|hd(X0)=sK45_skl(X0))),
% 10.07/1.76 inference(forward_demodulation,[status(thm)],[f422,f471])).
% 10.07/1.76 fof(f542,plain,(
% 10.07/1.76 ![X0]: (~ssList(X0)|sK50_skl=X0|ssItem(sK45_skl(X0)))),
% 10.07/1.76 inference(forward_demodulation,[status(thm)],[f422,f472])).
% 10.07/1.76 fof(f576,plain,(
% 10.07/1.76 ![X0]: (~ssItem(X0)|~memberP(sK49_skl,X0))),
% 10.07/1.76 inference(backward_subsumption_resolution,[status(thm)],[f427,f577])).
% 10.07/1.76 fof(f577,plain,(
% 10.07/1.76 ![X0]: (~ssItem(X0)|~memberP(sK50_skl,X0))),
% 10.07/1.76 inference(forward_demodulation,[status(thm)],[f422,f500])).
% 10.07/1.76 fof(f825,plain,(
% 10.07/1.76 sK50_skl=sK49_skl|tl(sK49_skl)=sK46_skl(sK49_skl)),
% 10.07/1.77 inference(resolution,[status(thm)],[f539,f419])).
% 10.07/1.77 fof(f827,plain,(
% 10.07/1.77 tl(sK49_skl)=sK46_skl(sK49_skl)),
% 10.07/1.77 inference(forward_subsumption_resolution,[status(thm)],[f825,f516])).
% 10.07/1.77 fof(f885,plain,(
% 10.07/1.77 sK50_skl=sK49_skl|hd(sK49_skl)=sK45_skl(sK49_skl)),
% 10.07/1.77 inference(resolution,[status(thm)],[f541,f419])).
% 10.07/1.77 fof(f887,plain,(
% 10.07/1.77 hd(sK49_skl)=sK45_skl(sK49_skl)),
% 10.07/1.77 inference(forward_subsumption_resolution,[status(thm)],[f885,f516])).
% 10.07/1.77 fof(f1889,plain,(
% 10.07/1.77 sK50_skl=sK49_skl|cons(hd(sK49_skl),tl(sK49_skl))=sK49_skl),
% 10.07/1.77 inference(resolution,[status(thm)],[f535,f419])).
% 10.07/1.77 fof(f1904,plain,(
% 10.07/1.77 sK50_skl=sK49_skl|cons(sK45_skl(sK49_skl),tl(sK49_skl))=sK49_skl),
% 10.07/1.77 inference(forward_demodulation,[status(thm)],[f887,f1889])).
% 10.07/1.77 fof(f1905,plain,(
% 10.07/1.77 sK50_skl=sK49_skl|cons(sK45_skl(sK49_skl),sK46_skl(sK49_skl))=sK49_skl),
% 10.07/1.77 inference(forward_demodulation,[status(thm)],[f827,f1904])).
% 10.07/1.77 fof(f1906,plain,(
% 10.07/1.77 cons(sK45_skl(sK49_skl),sK46_skl(sK49_skl))=sK49_skl),
% 10.07/1.77 inference(forward_subsumption_resolution,[status(thm)],[f1905,f516])).
% 10.07/1.77 fof(f1910,plain,(
% 10.07/1.77 ~ssItem(sK45_skl(sK49_skl))|~ssList(sK46_skl(sK49_skl))|memberP(sK49_skl,sK45_skl(sK49_skl))),
% 10.07/1.77 inference(paramodulation,[status(thm)],[f1906,f449])).
% 10.07/1.77 fof(f1915,plain,(
% 10.07/1.77 ~ssItem(sK45_skl(sK49_skl))|~ssList(sK46_skl(sK49_skl))),
% 10.07/1.77 inference(forward_subsumption_resolution,[status(thm)],[f1910,f576])).
% 10.07/1.77 fof(f1918,plain,(
% 10.07/1.77 ~ssList(sK46_skl(sK49_skl))|~ssList(sK49_skl)|sK50_skl=sK49_skl),
% 10.07/1.77 inference(resolution,[status(thm)],[f1915,f542])).
% 10.07/1.77 fof(f1919,plain,(
% 10.07/1.77 ~ssList(sK49_skl)|sK50_skl=sK49_skl),
% 10.07/1.77 inference(forward_subsumption_resolution,[status(thm)],[f1918,f540])).
% 10.07/1.77 fof(f1920,plain,(
% 10.07/1.77 sK50_skl=sK49_skl),
% 10.07/1.77 inference(resolution,[status(thm)],[f1919,f419])).
% 10.07/1.77 fof(f1921,plain,(
% 10.07/1.77 $false),
% 10.07/1.77 inference(forward_subsumption_resolution,[status(thm)],[f1920,f516])).
% 10.07/1.77 % SZS output end CNFRefutation for theBenchmark.p
% 10.07/1.80 % Elapsed time: 1.411212 seconds
% 10.07/1.80 % CPU time: 10.793883 seconds
% 10.07/1.80 % Total memory used: 223.767 MB
% 10.07/1.80 % Net memory used: 216.036 MB
%------------------------------------------------------------------------------