%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SWC118+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 : n017.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 02:41:38 PM UTC 2026
% Result : Theorem 0.14s 0.41s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC118+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
% 0.09/0.35 % Computer : n017.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 07:52:41 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.14/0.41 % Refutation found
% 0.14/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.41 % SZS output start CNFRefutation for theBenchmark
% 0.14/0.41 fof(f7,axiom,(
% 0.14/0.41 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> ( segmentP(U,V)<=> (? [W] :( ssList(W)& (? [X] :( ssList(X)& app(app(W,V),X) = U ) )) )) ) )) )),
% 0.14/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.41 fof(f15,axiom,(
% 0.14/0.41 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> ( neq(U,V)<=> U != V ) ) )) )),
% 0.14/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.41 fof(f17,axiom,(
% 0.14/0.41 ssList(nil) ),
% 0.14/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.41 fof(f96,conjecture,(
% 0.14/0.41 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> (! [X] :( ssList(X)=> ( V != X| U != W| (! [Y] :( ssList(Y)=> (! [Z] :( ssList(Z)=> ( app(app(Y,W),Z) != X| ~ totalorderedP(W)| (? [X1] :( ssItem(X1)& (? [X2] :( ssList(X2)& app(X2,cons(X1,nil)) = Y& (? [X3] :( ssItem(X3)& (? [X4] :( ssList(X4)& app(cons(X3,nil),X4) = W& leq(X1,X3) ) )) )) )))| (? [X5] :( ssItem(X5)& (? [X6] :( ssList(X6)& app(cons(X5,nil),X6) = Z& (? [X7] :( ssItem(X7)& (? [X8] :( ssList(X8)& app(X8,cons(X7,nil)) = W& leq(X7,X5) ) )) )) )) )) ) )))| ( nil != X& nil = W )| ( nil = V& nil = U )| ( neq(U,nil)& segmentP(V,U) ) ) ) )) )) )) )),
% 0.14/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.41 fof(f97,negated_conjecture,(
% 0.14/0.41 ~((! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> (! [X] :( ssList(X)=> ( V != X| U != W| (! [Y] :( ssList(Y)=> (! [Z] :( ssList(Z)=> ( app(app(Y,W),Z) != X| ~ totalorderedP(W)| (? [X1] :( ssItem(X1)& (? [X2] :( ssList(X2)& app(X2,cons(X1,nil)) = Y& (? [X3] :( ssItem(X3)& (? [X4] :( ssList(X4)& app(cons(X3,nil),X4) = W& leq(X1,X3) ) )) )) )))| (? [X5] :( ssItem(X5)& (? [X6] :( ssList(X6)& app(cons(X5,nil),X6) = Z& (? [X7] :( ssItem(X7)& (? [X8] :( ssList(X8)& app(X8,cons(X7,nil)) = W& leq(X7,X5) ) )) )) )) )) ) )))| ( nil != X& nil = W )| ( nil = V& nil = U )| ( neq(U,nil)& segmentP(V,U) ) ) ) )) )) )) ))),
% 0.14/0.41 inference(negated_conjecture,[status(cth)],[f96])).
% 0.14/0.41 fof(f131,plain,(
% 0.14/0.41 ![U]: (~ssList(U)|(![V]: (~ssList(V)|(segmentP(U,V)<=>(?[W]: (ssList(W)&(?[X]: (ssList(X)&app(app(W,V),X)=U))))))))),
% 0.14/0.41 inference(pre_NNF_transformation,[status(thm)],[f7])).
% 0.14/0.41 fof(f132,plain,(
% 0.14/0.41 ![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)))))))))),
% 0.14/0.41 inference(NNF_transformation,[status(thm)],[f131])).
% 0.14/0.41 fof(f133,plain,(
% 0.14/0.41 ![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)))))))))),
% 0.14/0.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl,sK8_skl]),skolemize(W,sK7_skl(V,U)),skolemize(X,sK8_skl(V,U))],[f132])).
% 0.14/0.41 fof(f137,plain,(
% 0.14/0.41 ![X0,X1,X2,X3]: (~ssList(X0)|~ssList(X1)|segmentP(X0,X1)|~ssList(X2)|~ssList(X3)|~app(app(X2,X1),X3)=X0)),
% 0.14/0.41 inference(cnf_transformation,[status(thm)],[f133])).
% 0.14/0.41 fof(f217,plain,(
% 0.14/0.41 ![U]: (~ssList(U)|(![V]: (~ssList(V)|(neq(U,V)<=>~U=V))))),
% 0.14/0.41 inference(pre_NNF_transformation,[status(thm)],[f15])).
% 0.14/0.41 fof(f218,plain,(
% 0.14/0.41 ![U]: (~ssList(U)|(![V]: (~ssList(V)|((~neq(U,V)|~U=V)&(neq(U,V)|U=V)))))),
% 0.14/0.41 inference(NNF_transformation,[status(thm)],[f217])).
% 0.14/0.41 fof(f220,plain,(
% 0.14/0.41 ![X0,X1]: (~ssList(X0)|~ssList(X1)|neq(X0,X1)|X0=X1)),
% 0.14/0.41 inference(cnf_transformation,[status(thm)],[f218])).
% 0.14/0.41 fof(f223,plain,(
% 0.14/0.41 ssList(nil)),
% 0.14/0.41 inference(cnf_transformation,[status(thm)],[f17])).
% 0.14/0.41 fof(f415,plain,(
% 0.14/0.41 (?[U]: (ssList(U)&(?[V]: (ssList(V)&(?[W]: (ssList(W)&(?[X]: (ssList(X)&(((((V=X&U=W)&(?[Y]: (ssList(Y)&(?[Z]: (ssList(Z)&(((app(app(Y,W),Z)=X&totalorderedP(W))&(![X1]: (~ssItem(X1)|(![X2]: ((~ssList(X2)|~app(X2,cons(X1,nil))=Y)|(![X3]: (~ssItem(X3)|(![X4]: ((~ssList(X4)|~app(cons(X3,nil),X4)=W)|~leq(X1,X3))))))))))&(![X5]: (~ssItem(X5)|(![X6]: ((~ssList(X6)|~app(cons(X5,nil),X6)=Z)|(![X7]: (~ssItem(X7)|(![X8]: ((~ssList(X8)|~app(X8,cons(X7,nil))=W)|~leq(X7,X5)))))))))))))))&(nil=X|~nil=W))&(~nil=V|~nil=U))&(~neq(U,nil)|~segmentP(V,U)))))))))))),
% 0.14/0.41 inference(pre_NNF_transformation,[status(thm)],[f97])).
% 0.14/0.41 fof(f416,plain,(
% 0.14/0.41 ?[U]: (ssList(U)&(?[V]: (ssList(V)&(?[W]: (ssList(W)&(?[X]: (ssList(X)&(((((V=X&U=W)&(?[Y]: (ssList(Y)&(?[Z]: (ssList(Z)&(((app(app(Y,W),Z)=X&totalorderedP(W))&(![X1]: (~ssItem(X1)|((![X2]: (~ssList(X2)|~app(X2,cons(X1,nil))=Y))|(![X3]: (~ssItem(X3)|((![X4]: (~ssList(X4)|~app(cons(X3,nil),X4)=W))|~leq(X1,X3))))))))&(![X5]: (~ssItem(X5)|((![X6]: (~ssList(X6)|~app(cons(X5,nil),X6)=Z))|(![X7]: (~ssItem(X7)|((![X8]: (~ssList(X8)|~app(X8,cons(X7,nil))=W))|~leq(X7,X5)))))))))))))&(nil=X|~nil=W))&(~nil=V|~nil=U))&(~neq(U,nil)|~segmentP(V,U))))))))))),
% 0.14/0.41 inference(miniscoping,[status(thm)],[f415])).
% 0.14/0.41 fof(f417,plain,(
% 0.14/0.41 (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(app(sK51_skl,sK49_skl),sK52_skl)=sK50_skl&totalorderedP(sK49_skl))&(![X1]: (~ssItem(X1)|((![X2]: (~ssList(X2)|~app(X2,cons(X1,nil))=sK51_skl))|(![X3]: (~ssItem(X3)|((![X4]: (~ssList(X4)|~app(cons(X3,nil),X4)=sK49_skl))|~leq(X1,X3))))))))&(![X5]: (~ssItem(X5)|((![X6]: (~ssList(X6)|~app(cons(X5,nil),X6)=sK52_skl))|(![X7]: (~ssItem(X7)|((![X8]: (~ssList(X8)|~app(X8,cons(X7,nil))=sK49_skl))|~leq(X7,X5)))))))))))&(nil=sK50_skl|~nil=sK49_skl))&(~nil=sK48_skl|~nil=sK47_skl))&(~neq(sK47_skl,nil)|~segmentP(sK48_skl,sK47_skl)))))))),
% 0.14/0.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK47_skl,sK48_skl,sK49_skl,sK50_skl,sK51_skl,sK52_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)],[f416])).
% 0.14/0.41 fof(f418,plain,(
% 0.14/0.41 ssList(sK47_skl)),
% 0.14/0.41 inference(cnf_transformation,[status(thm)],[f417])).
% 0.14/0.41 fof(f419,plain,(
% 0.14/0.41 ssList(sK48_skl)),
% 0.14/0.41 inference(cnf_transformation,[status(thm)],[f417])).
% 0.14/0.41 fof(f422,plain,(
% 0.14/0.41 sK48_skl=sK50_skl),
% 0.14/0.41 inference(cnf_transformation,[status(thm)],[f417])).
% 0.14/0.41 fof(f423,plain,(
% 0.14/0.41 sK47_skl=sK49_skl),
% 0.14/0.41 inference(cnf_transformation,[status(thm)],[f417])).
% 0.14/0.41 fof(f424,plain,(
% 0.14/0.41 ssList(sK51_skl)),
% 0.14/0.41 inference(cnf_transformation,[status(thm)],[f417])).
% 0.14/0.41 fof(f425,plain,(
% 0.14/0.41 ssList(sK52_skl)),
% 0.14/0.41 inference(cnf_transformation,[status(thm)],[f417])).
% 0.14/0.41 fof(f426,plain,(
% 0.14/0.41 app(app(sK51_skl,sK49_skl),sK52_skl)=sK50_skl),
% 0.14/0.41 inference(cnf_transformation,[status(thm)],[f417])).
% 0.14/0.41 fof(f430,plain,(
% 0.14/0.41 nil=sK50_skl|~nil=sK49_skl),
% 0.14/0.41 inference(cnf_transformation,[status(thm)],[f417])).
% 0.14/0.41 fof(f431,plain,(
% 0.14/0.41 ~nil=sK48_skl|~nil=sK47_skl),
% 0.14/0.41 inference(cnf_transformation,[status(thm)],[f417])).
% 0.14/0.41 fof(f432,plain,(
% 0.14/0.41 ~neq(sK47_skl,nil)|~segmentP(sK48_skl,sK47_skl)),
% 0.14/0.41 inference(cnf_transformation,[status(thm)],[f417])).
% 0.14/0.41 fof(f439,plain,(
% 0.14/0.41 ![X0,X1,X2]: (~ssList(app(app(X0,X1),X2))|~ssList(X1)|segmentP(app(app(X0,X1),X2),X1)|~ssList(X0)|~ssList(X2))),
% 0.14/0.41 inference(destructive_equality_resolution,[status(thm)],[f137])).
% 0.14/0.41 fof(f476,plain,(
% 0.14/0.41 app(app(sK51_skl,sK47_skl),sK52_skl)=sK50_skl),
% 0.14/0.41 inference(forward_demodulation,[status(thm)],[f423,f426])).
% 0.14/0.41 fof(f477,plain,(
% 0.14/0.41 app(app(sK51_skl,sK47_skl),sK52_skl)=sK48_skl),
% 0.14/0.41 inference(forward_demodulation,[status(thm)],[f422,f476])).
% 0.14/0.41 fof(f478,plain,(
% 0.14/0.41 ~ssList(sK48_skl)|~ssList(sK47_skl)|segmentP(app(app(sK51_skl,sK47_skl),sK52_skl),sK47_skl)|~ssList(sK51_skl)|~ssList(sK52_skl)),
% 0.14/0.41 inference(paramodulation,[status(thm)],[f477,f439])).
% 0.14/0.41 fof(f481,plain,(
% 0.14/0.41 ~ssList(sK48_skl)|~ssList(sK47_skl)|segmentP(sK48_skl,sK47_skl)|~ssList(sK51_skl)|~ssList(sK52_skl)),
% 0.14/0.41 inference(forward_demodulation,[status(thm)],[f477,f478])).
% 0.14/0.41 fof(f482,plain,(
% 0.14/0.41 ~ssList(sK47_skl)|segmentP(sK48_skl,sK47_skl)|~ssList(sK51_skl)|~ssList(sK52_skl)),
% 0.14/0.41 inference(forward_subsumption_resolution,[status(thm)],[f481,f419])).
% 0.14/0.41 fof(f516,plain,(
% 0.14/0.41 nil=sK48_skl|~nil=sK49_skl),
% 0.14/0.41 inference(forward_demodulation,[status(thm)],[f422,f430])).
% 0.14/0.41 fof(f517,plain,(
% 0.14/0.41 nil=sK48_skl|~nil=sK47_skl),
% 0.14/0.41 inference(forward_demodulation,[status(thm)],[f423,f516])).
% 0.14/0.41 fof(f519,plain,(
% 0.14/0.41 ~nil=sK47_skl),
% 0.14/0.41 inference(forward_subsumption_resolution,[status(thm)],[f431,f517])).
% 0.14/0.41 fof(f573,plain,(
% 0.14/0.41 segmentP(sK48_skl,sK47_skl)|~ssList(sK51_skl)|~ssList(sK52_skl)),
% 0.14/0.41 inference(forward_subsumption_resolution,[status(thm)],[f482,f418])).
% 0.14/0.41 fof(f574,plain,(
% 0.14/0.41 segmentP(sK48_skl,sK47_skl)|~ssList(sK51_skl)),
% 0.14/0.41 inference(resolution,[status(thm)],[f573,f425])).
% 0.14/0.41 fof(f575,plain,(
% 0.14/0.41 segmentP(sK48_skl,sK47_skl)),
% 0.14/0.41 inference(forward_subsumption_resolution,[status(thm)],[f574,f424])).
% 0.14/0.41 fof(f576,plain,(
% 0.14/0.41 ~neq(sK47_skl,nil)),
% 0.14/0.41 inference(backward_subsumption_resolution,[status(thm)],[f432,f575])).
% 0.14/0.41 fof(f579,plain,(
% 0.14/0.41 ~ssList(sK47_skl)|~ssList(nil)|sK47_skl=nil),
% 0.14/0.41 inference(resolution,[status(thm)],[f576,f220])).
% 0.14/0.41 fof(f580,plain,(
% 0.14/0.41 ~ssList(nil)|sK47_skl=nil),
% 0.14/0.41 inference(forward_subsumption_resolution,[status(thm)],[f579,f418])).
% 0.14/0.41 fof(f700,plain,(
% 0.14/0.41 ~sK47_skl=sK47_skl),
% 0.14/0.41 inference(backward_demodulation,[status(thm)],[f714,f519])).
% 0.14/0.41 fof(f714,plain,(
% 0.14/0.41 sK47_skl=nil),
% 0.14/0.41 inference(forward_subsumption_resolution,[status(thm)],[f580,f223])).
% 0.14/0.41 fof(f719,plain,(
% 0.14/0.41 $false),
% 0.14/0.41 inference(trivial_equality_resolution,[status(thm)],[f700])).
% 0.14/0.41 % SZS output end CNFRefutation for theBenchmark.p
% 0.14/0.44 % Elapsed time: 0.073979 seconds
% 0.14/0.44 % CPU time: 0.243443 seconds
% 0.14/0.44 % Total memory used: 112.472 MB
% 0.14/0.44 % Net memory used: 112.195 MB
%------------------------------------------------------------------------------