%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SWC323+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 : n005.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 02:42:09 PM UTC 2026
% Result : Theorem 0.08s 0.47s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC323+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n005.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 08:15:34 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.38 % Drodi V4.1.1
% 0.08/0.47 % Refutation found
% 0.08/0.47 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/0.47 % SZS output start CNFRefutation for theBenchmark
% 0.08/0.47 fof(f15,axiom,(
% 0.08/0.47 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> ( neq(U,V)<=> U != V ) ) )) )),
% 0.08/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.47 fof(f16,axiom,(
% 0.08/0.47 (! [U] :( ssList(U)=> (! [V] :( ssItem(V)=> ssList(cons(V,U)) ) )) )),
% 0.08/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.47 fof(f17,axiom,(
% 0.08/0.47 ssList(nil) ),
% 0.08/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.47 fof(f28,axiom,(
% 0.08/0.47 (! [U] :( ssList(U)=> app(nil,U) = U ) )),
% 0.08/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.47 fof(f96,conjecture,(
% 0.08/0.47 (! [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) = V& app(Z,Y) = U ) )))| ( nil != W& nil = X )| ( (! [X1] :( ssItem(X1)=> (! [X2] :( ssList(X2)=> ( app(cons(X1,nil),X2) != X| app(X2,cons(X1,nil)) != W ) ) )))& neq(X,nil) ) ) ) )) )) )) )),
% 0.08/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.47 fof(f97,negated_conjecture,(
% 0.08/0.47 ~((! [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) = V& app(Z,Y) = U ) )))| ( nil != W& nil = X )| ( (! [X1] :( ssItem(X1)=> (! [X2] :( ssList(X2)=> ( app(cons(X1,nil),X2) != X| app(X2,cons(X1,nil)) != W ) ) )))& neq(X,nil) ) ) ) )) )) )) ))),
% 0.08/0.47 inference(negated_conjecture,[status(cth)],[f96])).
% 0.08/0.47 fof(f217,plain,(
% 0.08/0.47 ![U]: (~ssList(U)|(![V]: (~ssList(V)|(neq(U,V)<=>~U=V))))),
% 0.08/0.47 inference(pre_NNF_transformation,[status(thm)],[f15])).
% 0.08/0.47 fof(f218,plain,(
% 0.08/0.47 ![U]: (~ssList(U)|(![V]: (~ssList(V)|((~neq(U,V)|~U=V)&(neq(U,V)|U=V)))))),
% 0.08/0.47 inference(NNF_transformation,[status(thm)],[f217])).
% 0.08/0.47 fof(f220,plain,(
% 0.08/0.47 ![X0,X1]: (~ssList(X0)|~ssList(X1)|neq(X0,X1)|X0=X1)),
% 0.08/0.47 inference(cnf_transformation,[status(thm)],[f218])).
% 0.08/0.47 fof(f221,plain,(
% 0.08/0.47 ![U]: (~ssList(U)|(![V]: (~ssItem(V)|ssList(cons(V,U)))))),
% 0.08/0.47 inference(pre_NNF_transformation,[status(thm)],[f16])).
% 0.08/0.47 fof(f222,plain,(
% 0.08/0.47 ![X0,X1]: (~ssList(X0)|~ssItem(X1)|ssList(cons(X1,X0)))),
% 0.08/0.47 inference(cnf_transformation,[status(thm)],[f221])).
% 0.08/0.47 fof(f223,plain,(
% 0.08/0.47 ssList(nil)),
% 0.08/0.47 inference(cnf_transformation,[status(thm)],[f17])).
% 0.08/0.47 fof(f248,plain,(
% 0.08/0.47 ![U]: (~ssList(U)|app(nil,U)=U)),
% 0.08/0.47 inference(pre_NNF_transformation,[status(thm)],[f28])).
% 0.08/0.47 fof(f249,plain,(
% 0.08/0.47 ![X0]: (~ssList(X0)|app(nil,X0)=X0)),
% 0.08/0.47 inference(cnf_transformation,[status(thm)],[f248])).
% 0.08/0.47 fof(f415,plain,(
% 0.08/0.47 (?[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)=V)|~app(Z,Y)=U)))))&(nil=W|~nil=X))&((?[X1]: (ssItem(X1)&(?[X2]: (ssList(X2)&(app(cons(X1,nil),X2)=X&app(X2,cons(X1,nil))=W)))))|~neq(X,nil)))))))))))),
% 0.08/0.47 inference(pre_NNF_transformation,[status(thm)],[f97])).
% 0.08/0.47 fof(f416,plain,(
% 0.08/0.47 (ssList(sK47_skl)&(ssList(sK48_skl)&(ssList(sK49_skl)&(ssList(sK50_skl)&((((sK48_skl=sK50_skl&sK47_skl=sK49_skl)&(![Y]: (~ssList(Y)|(![Z]: ((~ssList(Z)|~app(Y,Z)=sK48_skl)|~app(Z,Y)=sK47_skl)))))&(nil=sK49_skl|~nil=sK50_skl))&((ssItem(sK51_skl)&(ssList(sK52_skl)&(app(cons(sK51_skl,nil),sK52_skl)=sK50_skl&app(sK52_skl,cons(sK51_skl,nil))=sK49_skl)))|~neq(sK50_skl,nil)))))))),
% 0.08/0.47 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(X1,sK51_skl),skolemize(X2,sK52_skl)],[f415])).
% 0.08/0.47 fof(f420,plain,(
% 0.08/0.47 ssList(sK50_skl)),
% 0.08/0.47 inference(cnf_transformation,[status(thm)],[f416])).
% 0.08/0.47 fof(f421,plain,(
% 0.08/0.47 sK48_skl=sK50_skl),
% 0.08/0.47 inference(cnf_transformation,[status(thm)],[f416])).
% 0.08/0.47 fof(f422,plain,(
% 0.08/0.47 sK47_skl=sK49_skl),
% 0.08/0.47 inference(cnf_transformation,[status(thm)],[f416])).
% 0.08/0.47 fof(f423,plain,(
% 0.08/0.47 ![X0,X1]: (~ssList(X0)|~ssList(X1)|~app(X0,X1)=sK48_skl|~app(X1,X0)=sK47_skl)),
% 0.08/0.47 inference(cnf_transformation,[status(thm)],[f416])).
% 0.08/0.47 fof(f424,plain,(
% 0.08/0.47 nil=sK49_skl|~nil=sK50_skl),
% 0.08/0.47 inference(cnf_transformation,[status(thm)],[f416])).
% 0.08/0.47 fof(f425,plain,(
% 0.08/0.47 ssItem(sK51_skl)|~neq(sK50_skl,nil)),
% 0.08/0.49 inference(cnf_transformation,[status(thm)],[f416])).
% 0.08/0.49 fof(f426,plain,(
% 0.08/0.49 ssList(sK52_skl)|~neq(sK50_skl,nil)),
% 0.08/0.49 inference(cnf_transformation,[status(thm)],[f416])).
% 0.08/0.49 fof(f427,plain,(
% 0.08/0.49 app(cons(sK51_skl,nil),sK52_skl)=sK50_skl|~neq(sK50_skl,nil)),
% 0.08/0.49 inference(cnf_transformation,[status(thm)],[f416])).
% 0.08/0.49 fof(f428,plain,(
% 0.08/0.49 app(sK52_skl,cons(sK51_skl,nil))=sK49_skl|~neq(sK50_skl,nil)),
% 0.08/0.49 inference(cnf_transformation,[status(thm)],[f416])).
% 0.08/0.49 fof(f461,plain,(
% 0.08/0.49 app(nil,nil)=nil),
% 0.08/0.49 inference(resolution,[status(thm)],[f249,f223])).
% 0.08/0.49 fof(f465,plain,(
% 0.08/0.49 ![X0]: (~ssList(X0)|neq(sK50_skl,X0)|sK50_skl=X0)),
% 0.08/0.49 inference(resolution,[status(thm)],[f220,f420])).
% 0.08/0.49 fof(f471,plain,(
% 0.08/0.49 neq(sK50_skl,nil)|sK50_skl=nil),
% 0.08/0.49 inference(resolution,[status(thm)],[f465,f223])).
% 0.08/0.49 fof(f474,plain,(
% 0.08/0.49 ![X0,X1]: (~ssList(X0)|~ssList(X1)|~app(X0,X1)=sK50_skl|~app(X1,X0)=sK47_skl)),
% 0.08/0.49 inference(forward_demodulation,[status(thm)],[f421,f423])).
% 0.08/0.49 fof(f475,plain,(
% 0.08/0.49 ![X0,X1]: (~ssList(X0)|~ssList(X1)|~app(X0,X1)=sK50_skl|~app(X1,X0)=sK49_skl)),
% 0.08/0.49 inference(forward_demodulation,[status(thm)],[f422,f474])).
% 0.08/0.49 fof(f479,plain,(
% 0.08/0.49 ~ssList(nil)|~ssList(nil)|~app(nil,nil)=sK50_skl|~nil=sK49_skl),
% 0.08/0.49 inference(paramodulation,[status(thm)],[f461,f475])).
% 0.08/0.49 fof(f484,plain,(
% 0.08/0.49 ~ssList(nil)|~ssList(nil)|~nil=sK50_skl|~nil=sK49_skl),
% 0.08/0.49 inference(forward_demodulation,[status(thm)],[f461,f479])).
% 0.08/0.49 fof(f485,plain,(
% 0.08/0.49 ~ssList(nil)|~nil=sK50_skl|~nil=sK49_skl),
% 0.08/0.49 inference(duplicate_literals_removal,[status(thm)],[f484])).
% 0.08/0.49 fof(f486,plain,(
% 0.08/0.49 ~nil=sK50_skl|~nil=sK49_skl),
% 0.08/0.49 inference(forward_subsumption_resolution,[status(thm)],[f485,f223])).
% 0.08/0.49 fof(f487,plain,(
% 0.08/0.49 ~nil=sK50_skl),
% 0.08/0.49 inference(forward_subsumption_resolution,[status(thm)],[f486,f424])).
% 0.08/0.49 fof(f503,plain,(
% 0.08/0.49 ssList(sK52_skl)),
% 0.08/0.49 inference(backward_subsumption_resolution,[status(thm)],[f426,f505])).
% 0.08/0.49 fof(f504,plain,(
% 0.08/0.49 ssItem(sK51_skl)),
% 0.08/0.49 inference(backward_subsumption_resolution,[status(thm)],[f425,f505])).
% 0.08/0.49 fof(f505,plain,(
% 0.08/0.49 neq(sK50_skl,nil)),
% 0.08/0.49 inference(forward_subsumption_resolution,[status(thm)],[f471,f487])).
% 0.08/0.49 fof(f506,plain,(
% 0.08/0.49 ![X0]: (~ssItem(X0)|ssList(cons(X0,nil)))),
% 0.08/0.49 inference(resolution,[status(thm)],[f222,f223])).
% 0.08/0.49 fof(f537,plain,(
% 0.08/0.49 app(cons(sK51_skl,nil),sK52_skl)=sK50_skl),
% 0.08/0.49 inference(forward_subsumption_resolution,[status(thm)],[f427,f505])).
% 0.08/0.49 fof(f540,plain,(
% 0.08/0.49 ssList(cons(sK51_skl,nil))),
% 0.08/0.49 inference(resolution,[status(thm)],[f506,f504])).
% 0.08/0.49 fof(f653,plain,(
% 0.08/0.49 app(sK52_skl,cons(sK51_skl,nil))=sK49_skl),
% 0.08/0.49 inference(forward_subsumption_resolution,[status(thm)],[f428,f505])).
% 0.08/0.49 fof(f654,plain,(
% 0.08/0.49 ~ssList(cons(sK51_skl,nil))|~ssList(sK52_skl)|~app(cons(sK51_skl,nil),sK52_skl)=sK50_skl),
% 0.08/0.49 inference(resolution,[status(thm)],[f653,f475])).
% 0.08/0.49 fof(f657,plain,(
% 0.08/0.49 ~ssList(cons(sK51_skl,nil))|~ssList(sK52_skl)|~sK50_skl=sK50_skl),
% 0.08/0.49 inference(forward_demodulation,[status(thm)],[f537,f654])).
% 0.08/0.49 fof(f658,plain,(
% 0.08/0.49 ~ssList(cons(sK51_skl,nil))|~ssList(sK52_skl)),
% 0.08/0.49 inference(trivial_equality_resolution,[status(thm)],[f657])).
% 0.08/0.49 fof(f659,plain,(
% 0.08/0.49 ~ssList(sK52_skl)),
% 0.08/0.49 inference(forward_subsumption_resolution,[status(thm)],[f658,f540])).
% 0.08/0.49 fof(f665,plain,(
% 0.08/0.49 $false),
% 0.08/0.49 inference(forward_subsumption_resolution,[status(thm)],[f659,f503])).
% 0.08/0.49 % SZS output end CNFRefutation for theBenchmark.p
% 0.08/0.50 % Elapsed time: 0.125188 seconds
% 0.08/0.50 % CPU time: 0.683747 seconds
% 0.08/0.50 % Total memory used: 118.233 MB
% 0.08/0.50 % Net memory used: 117.491 MB
%------------------------------------------------------------------------------