%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SWC213+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 02:41:53 PM UTC 2026
% Result : Theorem 0.12s 0.41s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC213+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n001.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Mon Sep 21 08:10:43 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.12/0.37 % Drodi V4.1.1
% 0.12/0.41 % Refutation found
% 0.12/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.41 % SZS output start CNFRefutation for theBenchmark
% 0.12/0.41 fof(f15,axiom,(
% 0.12/0.41 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> ( neq(U,V)<=> U != V ) ) )) )),
% 0.12/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.41 fof(f17,axiom,(
% 0.12/0.41 ssList(nil) ),
% 0.12/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.41 fof(f96,conjecture,(
% 0.12/0.41 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> (! [X] :( ssList(X)=> ( V != X| U != W| ~ neq(V,nil)| (! [Y] :( ssList(Y)=> (! [Z] :( ssList(Z)=> ( app(app(Y,W),Z) != X| ~ equalelemsP(W)| (? [X1] :( ssItem(X1)& (? [X2] :( ssList(X2)& app(X2,cons(X1,nil)) = Y& (? [X3] :( ssList(X3)& app(cons(X1,nil),X3) = W ) )) )))| (? [X4] :( ssItem(X4)& (? [X5] :( ssList(X5)& app(cons(X4,nil),X5) = Z& (? [X6] :( ssList(X6)& app(X6,cons(X4,nil)) = W ) )) )) )) ) )))| neq(U,nil)| ( nil != X& nil = W ) ) ) )) )) )) )),
% 0.12/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.41 fof(f97,negated_conjecture,(
% 0.12/0.41 ~((! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> (! [X] :( ssList(X)=> ( V != X| U != W| ~ neq(V,nil)| (! [Y] :( ssList(Y)=> (! [Z] :( ssList(Z)=> ( app(app(Y,W),Z) != X| ~ equalelemsP(W)| (? [X1] :( ssItem(X1)& (? [X2] :( ssList(X2)& app(X2,cons(X1,nil)) = Y& (? [X3] :( ssList(X3)& app(cons(X1,nil),X3) = W ) )) )))| (? [X4] :( ssItem(X4)& (? [X5] :( ssList(X5)& app(cons(X4,nil),X5) = Z& (? [X6] :( ssList(X6)& app(X6,cons(X4,nil)) = W ) )) )) )) ) )))| neq(U,nil)| ( nil != X& nil = W ) ) ) )) )) )) ))),
% 0.12/0.41 inference(negated_conjecture,[status(cth)],[f96])).
% 0.12/0.41 fof(f217,plain,(
% 0.12/0.41 ![U]: (~ssList(U)|(![V]: (~ssList(V)|(neq(U,V)<=>~U=V))))),
% 0.12/0.41 inference(pre_NNF_transformation,[status(thm)],[f15])).
% 0.12/0.41 fof(f218,plain,(
% 0.12/0.41 ![U]: (~ssList(U)|(![V]: (~ssList(V)|((~neq(U,V)|~U=V)&(neq(U,V)|U=V)))))),
% 0.12/0.41 inference(NNF_transformation,[status(thm)],[f217])).
% 0.12/0.41 fof(f219,plain,(
% 0.12/0.41 ![X0,X1]: (~ssList(X0)|~ssList(X1)|~neq(X0,X1)|~X0=X1)),
% 0.12/0.41 inference(cnf_transformation,[status(thm)],[f218])).
% 0.12/0.41 fof(f220,plain,(
% 0.12/0.41 ![X0,X1]: (~ssList(X0)|~ssList(X1)|neq(X0,X1)|X0=X1)),
% 0.12/0.41 inference(cnf_transformation,[status(thm)],[f218])).
% 0.12/0.41 fof(f223,plain,(
% 0.12/0.41 ssList(nil)),
% 0.12/0.41 inference(cnf_transformation,[status(thm)],[f17])).
% 0.12/0.41 fof(f415,plain,(
% 0.12/0.41 (?[U]: (ssList(U)&(?[V]: (ssList(V)&(?[W]: (ssList(W)&(?[X]: (ssList(X)&(((((V=X&U=W)&neq(V,nil))&(?[Y]: (ssList(Y)&(?[Z]: (ssList(Z)&(((app(app(Y,W),Z)=X&equalelemsP(W))&(![X1]: (~ssItem(X1)|(![X2]: ((~ssList(X2)|~app(X2,cons(X1,nil))=Y)|(![X3]: (~ssList(X3)|~app(cons(X1,nil),X3)=W)))))))&(![X4]: (~ssItem(X4)|(![X5]: ((~ssList(X5)|~app(cons(X4,nil),X5)=Z)|(![X6]: (~ssList(X6)|~app(X6,cons(X4,nil))=W))))))))))))&~neq(U,nil))&(nil=X|~nil=W))))))))))),
% 0.12/0.41 inference(pre_NNF_transformation,[status(thm)],[f97])).
% 0.12/0.41 fof(f416,plain,(
% 0.12/0.41 ?[U]: (ssList(U)&(?[V]: (ssList(V)&(?[W]: (ssList(W)&(?[X]: (ssList(X)&(((((V=X&U=W)&neq(V,nil))&(?[Y]: (ssList(Y)&(?[Z]: (ssList(Z)&(((app(app(Y,W),Z)=X&equalelemsP(W))&(![X1]: (~ssItem(X1)|((![X2]: (~ssList(X2)|~app(X2,cons(X1,nil))=Y))|(![X3]: (~ssList(X3)|~app(cons(X1,nil),X3)=W))))))&(![X4]: (~ssItem(X4)|((![X5]: (~ssList(X5)|~app(cons(X4,nil),X5)=Z))|(![X6]: (~ssList(X6)|~app(X6,cons(X4,nil))=W)))))))))))&~neq(U,nil))&(nil=X|~nil=W)))))))))),
% 0.12/0.41 inference(miniscoping,[status(thm)],[f415])).
% 0.12/0.41 fof(f417,plain,(
% 0.12/0.41 (ssList(sK47_skl)&(ssList(sK48_skl)&(ssList(sK49_skl)&(ssList(sK50_skl)&(((((sK48_skl=sK50_skl&sK47_skl=sK49_skl)&neq(sK48_skl,nil))&(ssList(sK51_skl)&(ssList(sK52_skl)&(((app(app(sK51_skl,sK49_skl),sK52_skl)=sK50_skl&equalelemsP(sK49_skl))&(![X1]: (~ssItem(X1)|((![X2]: (~ssList(X2)|~app(X2,cons(X1,nil))=sK51_skl))|(![X3]: (~ssList(X3)|~app(cons(X1,nil),X3)=sK49_skl))))))&(![X4]: (~ssItem(X4)|((![X5]: (~ssList(X5)|~app(cons(X4,nil),X5)=sK52_skl))|(![X6]: (~ssList(X6)|~app(X6,cons(X4,nil))=sK49_skl)))))))))&~neq(sK47_skl,nil))&(nil=sK50_skl|~nil=sK49_skl))))))),
% 0.12/0.41 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])).
% 0.12/0.42 fof(f418,plain,(
% 0.12/0.42 ssList(sK47_skl)),
% 0.12/0.42 inference(cnf_transformation,[status(thm)],[f417])).
% 0.12/0.42 fof(f422,plain,(
% 0.12/0.42 sK48_skl=sK50_skl),
% 0.12/0.42 inference(cnf_transformation,[status(thm)],[f417])).
% 0.12/0.42 fof(f423,plain,(
% 0.12/0.42 sK47_skl=sK49_skl),
% 0.12/0.42 inference(cnf_transformation,[status(thm)],[f417])).
% 0.12/0.42 fof(f424,plain,(
% 0.12/0.42 neq(sK48_skl,nil)),
% 0.12/0.42 inference(cnf_transformation,[status(thm)],[f417])).
% 0.12/0.42 fof(f431,plain,(
% 0.12/0.42 ~neq(sK47_skl,nil)),
% 0.12/0.42 inference(cnf_transformation,[status(thm)],[f417])).
% 0.12/0.42 fof(f432,plain,(
% 0.12/0.42 nil=sK50_skl|~nil=sK49_skl),
% 0.12/0.42 inference(cnf_transformation,[status(thm)],[f417])).
% 0.12/0.42 fof(f433,definition,(
% 0.12/0.42 sQ0_spl <=> (nil=sK50_skl)),
% 0.12/0.42 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.12/0.42 fof(f434,plain,(
% 0.12/0.42 nil=sK50_skl|~sQ0_spl),
% 0.12/0.42 inference(component_clause,[status(thm)],[f433])).
% 0.12/0.42 fof(f436,definition,(
% 0.12/0.42 sQ1_spl <=> (nil=sK49_skl)),
% 0.12/0.42 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.12/0.42 fof(f438,plain,(
% 0.12/0.42 ~nil=sK49_skl|sQ1_spl),
% 0.12/0.42 inference(component_clause,[status(thm)],[f436])).
% 0.12/0.42 fof(f439,plain,(
% 0.12/0.42 sQ0_spl|~sQ1_spl),
% 0.12/0.42 inference(split_clause,[status(thm)],[f432,f433,f436])).
% 0.12/0.42 fof(f455,plain,(
% 0.12/0.42 ![X1]: (~ssList(X1)|~ssList(X1)|~neq(X1,X1))),
% 0.12/0.42 inference(destructive_equality_resolution,[status(thm)],[f219])).
% 0.12/0.42 fof(f456,plain,(
% 0.12/0.42 ![X0]: (~ssList(X0)|~neq(X0,X0))),
% 0.12/0.42 inference(duplicate_literals_removal,[status(thm)],[f455])).
% 0.12/0.42 fof(f477,plain,(
% 0.12/0.42 sK48_skl=nil|~sQ0_spl),
% 0.12/0.42 inference(backward_demodulation,[status(thm)],[f434,f422])).
% 0.12/0.42 fof(f479,plain,(
% 0.12/0.42 neq(nil,nil)|~sQ0_spl),
% 0.12/0.42 inference(forward_demodulation,[status(thm)],[f477,f424])).
% 0.12/0.42 fof(f480,plain,(
% 0.12/0.42 ~ssList(nil)|~sQ0_spl),
% 0.12/0.42 inference(resolution,[status(thm)],[f456,f479])).
% 0.12/0.42 fof(f481,plain,(
% 0.12/0.42 $false|~sQ0_spl),
% 0.12/0.42 inference(forward_subsumption_resolution,[status(thm)],[f480,f223])).
% 0.12/0.42 fof(f482,plain,(
% 0.12/0.42 ~sQ0_spl),
% 0.12/0.42 inference(contradiction_clause,[status(thm)],[f481])).
% 0.12/0.42 fof(f483,plain,(
% 0.12/0.42 ~nil=sK47_skl|sQ1_spl),
% 0.12/0.42 inference(forward_demodulation,[status(thm)],[f423,f438])).
% 0.12/0.42 fof(f486,plain,(
% 0.12/0.43 ~ssList(sK47_skl)|~ssList(nil)|sK47_skl=nil),
% 0.12/0.43 inference(resolution,[status(thm)],[f220,f431])).
% 0.12/0.43 fof(f502,definition,(
% 0.12/0.43 sQ6_spl <=> (ssList(sK47_skl))),
% 0.12/0.43 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.12/0.43 fof(f504,plain,(
% 0.12/0.43 ~ssList(sK47_skl)|sQ6_spl),
% 0.12/0.43 inference(component_clause,[status(thm)],[f502])).
% 0.12/0.43 fof(f505,definition,(
% 0.12/0.43 sQ7_spl <=> (ssList(nil))),
% 0.12/0.43 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 0.12/0.43 fof(f507,plain,(
% 0.12/0.43 ~ssList(nil)|sQ7_spl),
% 0.12/0.43 inference(component_clause,[status(thm)],[f505])).
% 0.12/0.43 fof(f508,definition,(
% 0.12/0.43 sQ8_spl <=> (sK47_skl=nil)),
% 0.12/0.43 introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition])).
% 0.12/0.43 fof(f509,plain,(
% 0.12/0.43 sK47_skl=nil|~sQ8_spl),
% 0.12/0.43 inference(component_clause,[status(thm)],[f508])).
% 0.12/0.43 fof(f511,plain,(
% 0.12/0.43 ~sQ6_spl|~sQ7_spl|sQ8_spl),
% 0.12/0.43 inference(split_clause,[status(thm)],[f486,f502,f505,f508])).
% 0.12/0.43 fof(f512,plain,(
% 0.12/0.43 $false|sQ1_spl|~sQ8_spl),
% 0.12/0.43 inference(forward_subsumption_resolution,[status(thm)],[f509,f483])).
% 0.12/0.43 fof(f513,plain,(
% 0.12/0.43 sQ1_spl|~sQ8_spl),
% 0.12/0.43 inference(contradiction_clause,[status(thm)],[f512])).
% 0.12/0.43 fof(f514,plain,(
% 0.12/0.43 $false|sQ6_spl),
% 0.12/0.43 inference(forward_subsumption_resolution,[status(thm)],[f504,f418])).
% 0.12/0.43 fof(f515,plain,(
% 0.12/0.43 sQ6_spl),
% 0.12/0.43 inference(contradiction_clause,[status(thm)],[f514])).
% 0.12/0.43 fof(f516,plain,(
% 0.12/0.43 $false|sQ7_spl),
% 0.12/0.43 inference(forward_subsumption_resolution,[status(thm)],[f507,f223])).
% 0.12/0.43 fof(f517,plain,(
% 0.12/0.43 sQ7_spl),
% 0.12/0.43 inference(contradiction_clause,[status(thm)],[f516])).
% 0.12/0.43 fof(f518,plain,(
% 0.12/0.43 $false),
% 0.12/0.43 inference(sat_refutation,[status(thm)],[f439,f482,f511,f513,f515,f517])).
% 0.12/0.43 % SZS output end CNFRefutation for theBenchmark.p
% 0.12/0.44 % Elapsed time: 0.072644 seconds
% 0.12/0.44 % CPU time: 0.269089 seconds
% 0.12/0.44 % Total memory used: 112.826 MB
% 0.12/0.44 % Net memory used: 112.525 MB
%------------------------------------------------------------------------------