%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SWC325+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 02:42:09 PM UTC 2026
% Result : Theorem 0.26s 0.88s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWC325+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.43 % Computer : n009.cluster.edu
% 0.19/0.43 % Model : x86_64 x86_64
% 0.19/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.43 % Memory : 8046.5625MB
% 0.19/0.43 % OS : Linux 6.8.0-71-generic
% 0.19/0.43 % CPULimit : 300
% 0.19/0.43 % WCLimit : 300
% 0.19/0.43 % DateTime : Mon Sep 21 08:15:28 UTC 2026
% 0.19/0.44 % CPUTime :
% 0.19/0.47 % Drodi V4.1.1
% 0.26/0.88 % Refutation found
% 0.26/0.88 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.26/0.88 % SZS output start CNFRefutation for theBenchmark
% 0.26/0.88 fof(f15,axiom,(
% 0.26/0.88 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> ( neq(U,V)<=> U != V ) ) )) )),
% 0.26/0.88 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.26/0.88 fof(f16,axiom,(
% 0.26/0.88 (! [U] :( ssList(U)=> (! [V] :( ssItem(V)=> ssList(cons(V,U)) ) )) )),
% 0.26/0.88 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.26/0.88 fof(f17,axiom,(
% 0.26/0.88 ssList(nil) ),
% 0.26/0.88 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.26/0.88 fof(f84,axiom,(
% 0.26/0.88 (! [U] :( ssList(U)=> app(U,nil) = U ) )),
% 0.26/0.88 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.26/0.88 fof(f96,conjecture,(
% 0.26/0.88 (! [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) != W| app(X2,cons(X1,nil)) != X ) ) )))& neq(X,nil) ) ) ) )) )) )) )),
% 0.26/0.88 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.26/0.88 fof(f97,negated_conjecture,(
% 0.26/0.88 ~((! [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) != W| app(X2,cons(X1,nil)) != X ) ) )))& neq(X,nil) ) ) ) )) )) )) ))),
% 0.26/0.88 inference(negated_conjecture,[status(cth)],[f96])).
% 0.26/0.88 fof(f217,plain,(
% 0.26/0.88 ![U]: (~ssList(U)|(![V]: (~ssList(V)|(neq(U,V)<=>~U=V))))),
% 0.26/0.88 inference(pre_NNF_transformation,[status(thm)],[f15])).
% 0.26/0.88 fof(f218,plain,(
% 0.26/0.88 ![U]: (~ssList(U)|(![V]: (~ssList(V)|((~neq(U,V)|~U=V)&(neq(U,V)|U=V)))))),
% 0.26/0.88 inference(NNF_transformation,[status(thm)],[f217])).
% 0.26/0.88 fof(f220,plain,(
% 0.26/0.88 ![X0,X1]: (~ssList(X0)|~ssList(X1)|neq(X0,X1)|X0=X1)),
% 0.26/0.88 inference(cnf_transformation,[status(thm)],[f218])).
% 0.26/0.88 fof(f221,plain,(
% 0.26/0.88 ![U]: (~ssList(U)|(![V]: (~ssItem(V)|ssList(cons(V,U)))))),
% 0.26/0.88 inference(pre_NNF_transformation,[status(thm)],[f16])).
% 0.26/0.88 fof(f222,plain,(
% 0.26/0.88 ![X0,X1]: (~ssList(X0)|~ssItem(X1)|ssList(cons(X1,X0)))),
% 0.26/0.88 inference(cnf_transformation,[status(thm)],[f221])).
% 0.26/0.88 fof(f223,plain,(
% 0.26/0.88 ssList(nil)),
% 0.26/0.88 inference(cnf_transformation,[status(thm)],[f17])).
% 0.26/0.88 fof(f388,plain,(
% 0.26/0.88 ![U]: (~ssList(U)|app(U,nil)=U)),
% 0.26/0.88 inference(pre_NNF_transformation,[status(thm)],[f84])).
% 0.26/0.88 fof(f389,plain,(
% 0.26/0.88 ![X0]: (~ssList(X0)|app(X0,nil)=X0)),
% 0.26/0.88 inference(cnf_transformation,[status(thm)],[f388])).
% 0.26/0.88 fof(f415,plain,(
% 0.26/0.88 (?[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)=W&app(X2,cons(X1,nil))=X)))))|~neq(X,nil)))))))))))),
% 0.26/0.88 inference(pre_NNF_transformation,[status(thm)],[f97])).
% 0.26/0.88 fof(f416,plain,(
% 0.26/0.88 (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)=sK49_skl&app(sK52_skl,cons(sK51_skl,nil))=sK50_skl)))|~neq(sK50_skl,nil)))))))),
% 0.26/0.88 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])).
% 0.26/0.88 fof(f418,plain,(
% 0.26/0.88 ssList(sK48_skl)),
% 0.26/0.88 inference(cnf_transformation,[status(thm)],[f416])).
% 0.26/0.88 fof(f421,plain,(
% 0.26/0.88 sK48_skl=sK50_skl),
% 0.26/0.88 inference(cnf_transformation,[status(thm)],[f416])).
% 0.26/0.88 fof(f422,plain,(
% 0.26/0.88 sK47_skl=sK49_skl),
% 0.26/0.88 inference(cnf_transformation,[status(thm)],[f416])).
% 0.26/0.88 fof(f423,plain,(
% 0.26/0.88 ![X0,X1]: (~ssList(X0)|~ssList(X1)|~app(X0,X1)=sK48_skl|~app(X1,X0)=sK47_skl)),
% 0.26/0.88 inference(cnf_transformation,[status(thm)],[f416])).
% 0.26/0.88 fof(f424,plain,(
% 0.26/0.88 nil=sK49_skl|~nil=sK50_skl),
% 0.26/0.88 inference(cnf_transformation,[status(thm)],[f416])).
% 0.26/0.88 fof(f425,plain,(
% 0.26/0.88 ssItem(sK51_skl)|~neq(sK50_skl,nil)),
% 0.26/0.89 inference(cnf_transformation,[status(thm)],[f416])).
% 0.26/0.89 fof(f426,plain,(
% 0.26/0.89 ssList(sK52_skl)|~neq(sK50_skl,nil)),
% 0.26/0.89 inference(cnf_transformation,[status(thm)],[f416])).
% 0.26/0.89 fof(f427,plain,(
% 0.26/0.89 app(cons(sK51_skl,nil),sK52_skl)=sK49_skl|~neq(sK50_skl,nil)),
% 0.26/0.89 inference(cnf_transformation,[status(thm)],[f416])).
% 0.26/0.89 fof(f428,plain,(
% 0.26/0.89 app(sK52_skl,cons(sK51_skl,nil))=sK50_skl|~neq(sK50_skl,nil)),
% 0.26/0.89 inference(cnf_transformation,[status(thm)],[f416])).
% 0.26/0.89 fof(f463,plain,(
% 0.26/0.89 nil=sK47_skl|~nil=sK50_skl),
% 0.26/0.89 inference(forward_demodulation,[status(thm)],[f422,f424])).
% 0.26/0.89 fof(f464,plain,(
% 0.26/0.89 nil=sK47_skl|~nil=sK48_skl),
% 0.26/0.89 inference(forward_demodulation,[status(thm)],[f421,f463])).
% 0.26/0.89 fof(f465,plain,(
% 0.26/0.89 ssItem(sK51_skl)|~neq(sK48_skl,nil)),
% 0.26/0.89 inference(forward_demodulation,[status(thm)],[f421,f425])).
% 0.26/0.89 fof(f466,plain,(
% 0.26/0.89 ssList(sK52_skl)|~neq(sK48_skl,nil)),
% 0.26/0.89 inference(forward_demodulation,[status(thm)],[f421,f426])).
% 0.26/0.89 fof(f467,plain,(
% 0.26/0.89 app(cons(sK51_skl,nil),sK52_skl)=sK47_skl|~neq(sK50_skl,nil)),
% 0.26/0.89 inference(forward_demodulation,[status(thm)],[f422,f427])).
% 0.26/0.89 fof(f468,plain,(
% 0.26/0.89 app(cons(sK51_skl,nil),sK52_skl)=sK47_skl|~neq(sK48_skl,nil)),
% 0.26/0.89 inference(forward_demodulation,[status(thm)],[f421,f467])).
% 0.26/0.89 fof(f469,plain,(
% 0.26/0.89 app(sK52_skl,cons(sK51_skl,nil))=sK48_skl|~neq(sK50_skl,nil)),
% 0.26/0.89 inference(forward_demodulation,[status(thm)],[f421,f428])).
% 0.26/0.89 fof(f470,plain,(
% 0.26/0.89 app(sK52_skl,cons(sK51_skl,nil))=sK48_skl|~neq(sK48_skl,nil)),
% 0.26/0.89 inference(forward_demodulation,[status(thm)],[f421,f469])).
% 0.26/0.89 fof(f504,plain,(
% 0.26/0.89 ![X0]: (~ssItem(X0)|ssList(cons(X0,nil)))),
% 0.26/0.89 inference(resolution,[status(thm)],[f223,f222])).
% 0.26/0.89 fof(f507,plain,(
% 0.26/0.89 ![X0]: (~ssList(X0)|neq(X0,nil)|X0=nil)),
% 0.26/0.89 inference(resolution,[status(thm)],[f223,f220])).
% 0.26/0.89 fof(f508,plain,(
% 0.26/0.89 app(nil,nil)=nil),
% 0.26/0.89 inference(resolution,[status(thm)],[f223,f389])).
% 0.26/0.89 fof(f512,plain,(
% 0.26/0.89 ~ssList(nil)|~ssList(nil)|~nil=sK48_skl|~app(nil,nil)=sK47_skl),
% 0.26/0.89 inference(paramodulation,[status(thm)],[f508,f423])).
% 0.26/0.89 fof(f513,plain,(
% 0.26/0.89 ~ssList(nil)|~ssList(nil)|~nil=sK48_skl|~nil=sK47_skl),
% 0.26/0.89 inference(forward_demodulation,[status(thm)],[f508,f512])).
% 0.26/0.89 fof(f514,plain,(
% 0.26/0.89 ~ssList(nil)|~nil=sK48_skl|~nil=sK47_skl),
% 0.26/0.89 inference(duplicate_literals_removal,[status(thm)],[f513])).
% 0.26/0.89 fof(f515,plain,(
% 0.26/0.89 ~nil=sK48_skl),
% 0.26/0.89 inference(backward_subsumption_resolution,[status(thm)],[f464,f516])).
% 0.26/0.89 fof(f516,plain,(
% 0.26/0.89 ~nil=sK48_skl|~nil=sK47_skl),
% 0.26/0.89 inference(forward_subsumption_resolution,[status(thm)],[f514,f223])).
% 0.26/0.89 fof(f535,plain,(
% 0.26/0.89 neq(sK48_skl,nil)|sK48_skl=nil),
% 0.26/0.89 inference(resolution,[status(thm)],[f507,f418])).
% 0.26/0.89 fof(f537,plain,(
% 0.26/0.89 app(sK52_skl,cons(sK51_skl,nil))=sK48_skl),
% 0.26/0.89 inference(backward_subsumption_resolution,[status(thm)],[f470,f541])).
% 0.26/0.89 fof(f538,plain,(
% 0.26/0.89 app(cons(sK51_skl,nil),sK52_skl)=sK47_skl),
% 0.26/0.89 inference(backward_subsumption_resolution,[status(thm)],[f468,f541])).
% 0.26/0.89 fof(f539,plain,(
% 0.26/0.89 ssList(sK52_skl)),
% 0.26/0.89 inference(backward_subsumption_resolution,[status(thm)],[f466,f541])).
% 0.26/0.89 fof(f540,plain,(
% 0.26/0.89 ssItem(sK51_skl)),
% 0.26/0.89 inference(backward_subsumption_resolution,[status(thm)],[f465,f541])).
% 0.26/0.89 fof(f541,plain,(
% 0.26/0.89 neq(sK48_skl,nil)),
% 0.26/0.89 inference(forward_subsumption_resolution,[status(thm)],[f535,f515])).
% 0.26/0.89 fof(f549,plain,(
% 0.26/0.89 ssList(cons(sK51_skl,nil))),
% 0.26/0.89 inference(resolution,[status(thm)],[f540,f504])).
% 0.26/0.89 fof(f593,plain,(
% 0.26/0.89 ~ssList(sK52_skl)|~ssList(cons(sK51_skl,nil))|~app(cons(sK51_skl,nil),sK52_skl)=sK47_skl),
% 0.26/0.89 inference(resolution,[status(thm)],[f537,f423])).
% 0.26/0.89 fof(f596,plain,(
% 0.26/0.89 ~ssList(sK52_skl)|~ssList(cons(sK51_skl,nil))|~sK47_skl=sK47_skl),
% 0.26/0.89 inference(forward_demodulation,[status(thm)],[f538,f593])).
% 0.26/0.89 fof(f597,plain,(
% 0.26/0.89 ~ssList(sK52_skl)|~ssList(cons(sK51_skl,nil))),
% 0.26/0.89 inference(trivial_equality_resolution,[status(thm)],[f596])).
% 0.26/0.89 fof(f599,plain,(
% 0.26/0.89 ~ssList(cons(sK51_skl,nil))),
% 0.26/0.89 inference(forward_subsumption_resolution,[status(thm)],[f597,f539])).
% 0.26/0.89 fof(f600,plain,(
% 0.26/0.89 $false),
% 0.26/0.89 inference(backward_subsumption_resolution,[status(thm)],[f549,f599])).
% 0.26/0.89 % SZS output end CNFRefutation for theBenchmark.p
% 0.26/0.91 % Elapsed time: 0.455722 seconds
% 0.26/0.91 % CPU time: 2.873414 seconds
% 0.26/0.91 % Total memory used: 133.398 MB
% 0.26/0.91 % Net memory used: 131.445 MB
%------------------------------------------------------------------------------