%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SWC332+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 : 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 02:42:11 PM UTC 2026
% Result : Theorem 0.23s 5.51s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC332+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.07 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/5.45 % Computer : n016.cluster.edu
% 0.18/5.45 % Model : x86_64 x86_64
% 0.18/5.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/5.45 % Memory : 8046.5625MB
% 0.18/5.45 % OS : Linux 6.8.0-71-generic
% 0.18/5.45 % CPULimit : 300
% 0.18/5.45 % WCLimit : 300
% 0.18/5.45 % DateTime : Mon Sep 21 08:20:58 UTC 2026
% 0.18/5.46 % CPUTime :
% 0.18/5.48 % Drodi V4.1.1
% 0.23/5.51 % Refutation found
% 0.23/5.51 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.23/5.51 % SZS output start CNFRefutation for theBenchmark
% 0.23/5.51 fof(f4,axiom,(
% 0.23/5.51 (! [U] :( ssList(U)=> ( singletonP(U)<=> (? [V] :( ssItem(V)& cons(V,nil) = U ) )) ) )),
% 0.23/5.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.23/5.51 fof(f15,axiom,(
% 0.23/5.51 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> ( neq(U,V)<=> U != V ) ) )) )),
% 0.23/5.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.23/5.51 fof(f17,axiom,(
% 0.23/5.51 ssList(nil) ),
% 0.23/5.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.23/5.51 fof(f58,axiom,(
% 0.23/5.51 (! [U] :( ssList(U)=> ( segmentP(nil,U)<=> nil = U ) ) )),
% 0.23/5.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.23/5.51 fof(f73,axiom,(
% 0.23/5.51 (! [U] :( ssItem(U)=> equalelemsP(cons(U,nil)) ) )),
% 0.23/5.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.23/5.51 fof(f74,axiom,(
% 0.23/5.51 equalelemsP(nil) ),
% 0.23/5.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.23/5.51 fof(f96,conjecture,(
% 0.23/5.51 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> (! [X] :( ssList(X)=> ( V != X| U != W| ~ segmentP(X,W)| ( ~ singletonP(W)& neq(X,nil) )| ( segmentP(V,U)& equalelemsP(U) ) ) ) )) )) )) )),
% 0.23/5.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.23/5.51 fof(f97,negated_conjecture,(
% 0.23/5.51 ~((! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> (! [X] :( ssList(X)=> ( V != X| U != W| ~ segmentP(X,W)| ( ~ singletonP(W)& neq(X,nil) )| ( segmentP(V,U)& equalelemsP(U) ) ) ) )) )) )) ))),
% 0.23/5.51 inference(negated_conjecture,[status(cth)],[f96])).
% 0.23/5.51 fof(f113,plain,(
% 0.23/5.51 ![U]: (~ssList(U)|(singletonP(U)<=>(?[V]: (ssItem(V)&cons(V,nil)=U))))),
% 0.23/5.51 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 0.23/5.51 fof(f114,plain,(
% 0.23/5.51 ![U]: (~ssList(U)|((~singletonP(U)|(?[V]: (ssItem(V)&cons(V,nil)=U)))&(singletonP(U)|(![V]: (~ssItem(V)|~cons(V,nil)=U)))))),
% 0.23/5.51 inference(NNF_transformation,[status(thm)],[f113])).
% 0.23/5.51 fof(f115,plain,(
% 0.23/5.51 ![U]: (~ssList(U)|((~singletonP(U)|(ssItem(sK4_skl(U))&cons(sK4_skl(U),nil)=U))&(singletonP(U)|(![V]: (~ssItem(V)|~cons(V,nil)=U)))))),
% 0.23/5.51 inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(V,sK4_skl(U))],[f114])).
% 0.23/5.51 fof(f116,plain,(
% 0.23/5.51 ![X0]: (~ssList(X0)|~singletonP(X0)|ssItem(sK4_skl(X0)))),
% 0.23/5.51 inference(cnf_transformation,[status(thm)],[f115])).
% 0.23/5.51 fof(f117,plain,(
% 0.23/5.51 ![X0]: (~ssList(X0)|~singletonP(X0)|cons(sK4_skl(X0),nil)=X0)),
% 0.23/5.51 inference(cnf_transformation,[status(thm)],[f115])).
% 0.23/5.51 fof(f217,plain,(
% 0.23/5.51 ![U]: (~ssList(U)|(![V]: (~ssList(V)|(neq(U,V)<=>~U=V))))),
% 0.23/5.51 inference(pre_NNF_transformation,[status(thm)],[f15])).
% 0.23/5.51 fof(f218,plain,(
% 0.23/5.51 ![U]: (~ssList(U)|(![V]: (~ssList(V)|((~neq(U,V)|~U=V)&(neq(U,V)|U=V)))))),
% 0.23/5.51 inference(NNF_transformation,[status(thm)],[f217])).
% 0.23/5.51 fof(f220,plain,(
% 0.23/5.51 ![X0,X1]: (~ssList(X0)|~ssList(X1)|neq(X0,X1)|X0=X1)),
% 0.23/5.51 inference(cnf_transformation,[status(thm)],[f218])).
% 0.23/5.51 fof(f223,plain,(
% 0.23/5.51 ssList(nil)),
% 0.23/5.51 inference(cnf_transformation,[status(thm)],[f17])).
% 0.23/5.51 fof(f324,plain,(
% 0.23/5.51 ![U]: (~ssList(U)|(segmentP(nil,U)<=>nil=U))),
% 0.23/5.51 inference(pre_NNF_transformation,[status(thm)],[f58])).
% 0.23/5.51 fof(f325,plain,(
% 0.23/5.51 ![U]: (~ssList(U)|((~segmentP(nil,U)|nil=U)&(segmentP(nil,U)|~nil=U)))),
% 0.23/5.51 inference(NNF_transformation,[status(thm)],[f324])).
% 0.23/5.51 fof(f326,plain,(
% 0.23/5.51 ![X0]: (~ssList(X0)|~segmentP(nil,X0)|nil=X0)),
% 0.23/5.51 inference(cnf_transformation,[status(thm)],[f325])).
% 0.23/5.51 fof(f360,plain,(
% 0.23/5.51 ![U]: (~ssItem(U)|equalelemsP(cons(U,nil)))),
% 0.23/5.51 inference(pre_NNF_transformation,[status(thm)],[f73])).
% 0.23/5.51 fof(f361,plain,(
% 0.23/5.51 ![X0]: (~ssItem(X0)|equalelemsP(cons(X0,nil)))),
% 0.23/5.51 inference(cnf_transformation,[status(thm)],[f360])).
% 0.23/5.51 fof(f362,plain,(
% 0.23/5.51 equalelemsP(nil)),
% 0.23/5.51 inference(cnf_transformation,[status(thm)],[f74])).
% 0.23/5.51 fof(f415,plain,(
% 0.23/5.51 (?[U]: (ssList(U)&(?[V]: (ssList(V)&(?[W]: (ssList(W)&(?[X]: (ssList(X)&((((V=X&U=W)&segmentP(X,W))&(singletonP(W)|~neq(X,nil)))&(~segmentP(V,U)|~equalelemsP(U)))))))))))),
% 0.23/5.51 inference(pre_NNF_transformation,[status(thm)],[f97])).
% 0.23/5.51 fof(f416,plain,(
% 0.23/5.51 (ssList(sK47_skl)&(ssList(sK48_skl)&(ssList(sK49_skl)&(ssList(sK50_skl)&((((sK48_skl=sK50_skl&sK47_skl=sK49_skl)&segmentP(sK50_skl,sK49_skl))&(singletonP(sK49_skl)|~neq(sK50_skl,nil)))&(~segmentP(sK48_skl,sK47_skl)|~equalelemsP(sK47_skl)))))))),
% 0.23/5.52 inference(skolemize,[status(esa),new_symbols(skolem,[sK47_skl,sK48_skl,sK49_skl,sK50_skl]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl)],[f415])).
% 0.23/5.52 fof(f417,plain,(
% 0.23/5.52 ssList(sK47_skl)),
% 0.23/5.52 inference(cnf_transformation,[status(thm)],[f416])).
% 0.23/5.52 fof(f418,plain,(
% 0.23/5.52 ssList(sK48_skl)),
% 0.23/5.52 inference(cnf_transformation,[status(thm)],[f416])).
% 0.23/5.52 fof(f421,plain,(
% 0.23/5.52 sK48_skl=sK50_skl),
% 0.23/5.52 inference(cnf_transformation,[status(thm)],[f416])).
% 0.23/5.52 fof(f422,plain,(
% 0.23/5.52 sK47_skl=sK49_skl),
% 0.23/5.52 inference(cnf_transformation,[status(thm)],[f416])).
% 0.23/5.52 fof(f423,plain,(
% 0.23/5.52 segmentP(sK50_skl,sK49_skl)),
% 0.23/5.52 inference(cnf_transformation,[status(thm)],[f416])).
% 0.23/5.52 fof(f424,plain,(
% 0.23/5.52 singletonP(sK49_skl)|~neq(sK50_skl,nil)),
% 0.23/5.52 inference(cnf_transformation,[status(thm)],[f416])).
% 0.23/5.52 fof(f425,plain,(
% 0.23/5.52 ~segmentP(sK48_skl,sK47_skl)|~equalelemsP(sK47_skl)),
% 0.23/5.52 inference(cnf_transformation,[status(thm)],[f416])).
% 0.23/5.52 fof(f466,plain,(
% 0.23/5.52 segmentP(sK48_skl,sK49_skl)),
% 0.23/5.52 inference(forward_demodulation,[status(thm)],[f421,f423])).
% 0.23/5.52 fof(f467,plain,(
% 0.23/5.52 segmentP(sK48_skl,sK47_skl)),
% 0.23/5.52 inference(forward_demodulation,[status(thm)],[f422,f466])).
% 0.23/5.52 fof(f471,plain,(
% 0.23/5.52 singletonP(sK47_skl)|~neq(sK50_skl,nil)),
% 0.23/5.52 inference(forward_demodulation,[status(thm)],[f422,f424])).
% 0.23/5.52 fof(f472,plain,(
% 0.23/5.52 singletonP(sK47_skl)|~neq(sK48_skl,nil)),
% 0.23/5.52 inference(forward_demodulation,[status(thm)],[f421,f471])).
% 0.23/5.52 fof(f473,plain,(
% 0.23/5.52 singletonP(sK47_skl)|~ssList(sK48_skl)|~ssList(nil)|sK48_skl=nil),
% 0.23/5.52 inference(resolution,[status(thm)],[f472,f220])).
% 0.23/5.52 fof(f474,plain,(
% 0.23/5.52 singletonP(sK47_skl)|~ssList(nil)|sK48_skl=nil),
% 0.23/5.52 inference(forward_subsumption_resolution,[status(thm)],[f473,f418])).
% 0.23/5.52 fof(f475,plain,(
% 0.23/5.52 ~equalelemsP(sK47_skl)),
% 0.23/5.52 inference(forward_subsumption_resolution,[status(thm)],[f425,f467])).
% 0.23/5.52 fof(f476,plain,(
% 0.23/5.52 singletonP(sK47_skl)|sK48_skl=nil),
% 0.23/5.52 inference(forward_subsumption_resolution,[status(thm)],[f474,f223])).
% 0.23/5.52 fof(f477,plain,(
% 0.23/5.52 sK48_skl=nil|~ssList(sK47_skl)|cons(sK4_skl(sK47_skl),nil)=sK47_skl),
% 0.23/5.52 inference(resolution,[status(thm)],[f476,f117])).
% 0.23/5.52 fof(f478,plain,(
% 0.23/5.52 sK48_skl=nil|~ssList(sK47_skl)|ssItem(sK4_skl(sK47_skl))),
% 0.23/5.52 inference(resolution,[status(thm)],[f476,f116])).
% 0.23/5.52 fof(f479,plain,(
% 0.23/5.52 sK48_skl=nil|cons(sK4_skl(sK47_skl),nil)=sK47_skl),
% 0.23/5.52 inference(forward_subsumption_resolution,[status(thm)],[f477,f417])).
% 0.23/5.52 fof(f480,plain,(
% 0.23/5.52 sK48_skl=nil|ssItem(sK4_skl(sK47_skl))),
% 0.23/5.52 inference(forward_subsumption_resolution,[status(thm)],[f478,f417])).
% 0.23/5.52 fof(f545,plain,(
% 0.23/5.52 ~ssItem(sK4_skl(sK47_skl))|equalelemsP(sK47_skl)|sK48_skl=nil),
% 0.23/5.52 inference(paramodulation,[status(thm)],[f479,f361])).
% 0.23/5.52 fof(f551,plain,(
% 0.23/5.52 equalelemsP(sK47_skl)|sK48_skl=nil),
% 0.23/5.52 inference(forward_subsumption_resolution,[status(thm)],[f545,f480])).
% 0.23/5.52 fof(f567,plain,(
% 0.23/5.52 ![X0]: (~ssList(X0)|~segmentP(nil,X0)|sK48_skl=X0)),
% 0.23/5.52 inference(backward_demodulation,[status(thm)],[f584,f326])).
% 0.23/5.52 fof(f579,plain,(
% 0.23/5.52 equalelemsP(sK48_skl)),
% 0.23/5.52 inference(backward_demodulation,[status(thm)],[f584,f362])).
% 0.23/5.52 fof(f584,plain,(
% 0.23/5.52 sK48_skl=nil),
% 0.23/5.52 inference(forward_subsumption_resolution,[status(thm)],[f551,f475])).
% 0.23/5.52 fof(f585,plain,(
% 0.23/5.52 ![X0]: (~ssList(X0)|~segmentP(sK48_skl,X0)|sK48_skl=X0)),
% 0.23/5.52 inference(forward_demodulation,[status(thm)],[f584,f567])).
% 0.23/5.52 fof(f587,plain,(
% 0.23/5.52 ~ssList(sK47_skl)|sK48_skl=sK47_skl),
% 0.23/5.52 inference(resolution,[status(thm)],[f585,f467])).
% 0.23/5.52 fof(f590,plain,(
% 0.23/5.52 sK48_skl=sK47_skl),
% 0.23/5.52 inference(forward_subsumption_resolution,[status(thm)],[f587,f417])).
% 0.23/5.52 fof(f624,plain,(
% 0.23/5.52 equalelemsP(sK47_skl)),
% 0.23/5.52 inference(backward_demodulation,[status(thm)],[f590,f579])).
% 0.23/5.52 fof(f648,plain,(
% 0.23/5.52 $false),
% 0.23/5.52 inference(forward_subsumption_resolution,[status(thm)],[f624,f475])).
% 0.23/5.52 % SZS output end CNFRefutation for theBenchmark.p
% 0.23/5.53 % Elapsed time: 0.068341 seconds
% 0.23/5.53 % CPU time: 0.215751 seconds
% 0.23/5.53 % Total memory used: 49.012 MB
% 0.23/5.53 % Net memory used: 48.896 MB
%------------------------------------------------------------------------------