%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SWC104+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 : 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 02:41:35 PM UTC 2026
% Result : Theorem 0.09s 0.40s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC104+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
% 0.09/0.35 % Computer : n009.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 07:56:12 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.40 % Refutation found
% 0.09/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.40 % SZS output start CNFRefutation for theBenchmark
% 0.09/0.40 fof(f5,axiom,(
% 0.09/0.40 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> ( frontsegP(U,V)<=> (? [W] :( ssList(W)& app(V,W) = U ) )) ) )) )),
% 0.09/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.40 fof(f15,axiom,(
% 0.09/0.40 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> ( neq(U,V)<=> U != V ) ) )) )),
% 0.09/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.40 fof(f17,axiom,(
% 0.09/0.40 ssList(nil) ),
% 0.09/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.40 fof(f96,conjecture,(
% 0.09/0.40 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> (! [X] :( ssList(X)=> ( V != X| U != W| ~ neq(V,nil)| (! [Y] :( ssList(Y)=> ( app(W,Y) != X| ~ totalorderedP(W)| (? [Z] :( ssItem(Z)& (? [X1] :( ssList(X1)& app(cons(Z,nil),X1) = Y& (? [X2] :( ssItem(X2)& (? [X3] :( ssList(X3)& app(X3,cons(X2,nil)) = W& leq(X2,Z) ) )) )) )) )) ))| ( nil != X& nil = W )| ( neq(U,nil)& frontsegP(V,U) ) ) ) )) )) )) )),
% 0.09/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.40 fof(f97,negated_conjecture,(
% 0.09/0.40 ~((! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> (! [X] :( ssList(X)=> ( V != X| U != W| ~ neq(V,nil)| (! [Y] :( ssList(Y)=> ( app(W,Y) != X| ~ totalorderedP(W)| (? [Z] :( ssItem(Z)& (? [X1] :( ssList(X1)& app(cons(Z,nil),X1) = Y& (? [X2] :( ssItem(X2)& (? [X3] :( ssList(X3)& app(X3,cons(X2,nil)) = W& leq(X2,Z) ) )) )) )) )) ))| ( nil != X& nil = W )| ( neq(U,nil)& frontsegP(V,U) ) ) ) )) )) )) ))),
% 0.09/0.40 inference(negated_conjecture,[status(cth)],[f96])).
% 0.09/0.40 fof(f119,plain,(
% 0.09/0.40 ![U]: (~ssList(U)|(![V]: (~ssList(V)|(frontsegP(U,V)<=>(?[W]: (ssList(W)&app(V,W)=U))))))),
% 0.09/0.40 inference(pre_NNF_transformation,[status(thm)],[f5])).
% 0.09/0.40 fof(f120,plain,(
% 0.09/0.40 ![U]: (~ssList(U)|(![V]: (~ssList(V)|((~frontsegP(U,V)|(?[W]: (ssList(W)&app(V,W)=U)))&(frontsegP(U,V)|(![W]: (~ssList(W)|~app(V,W)=U)))))))),
% 0.09/0.40 inference(NNF_transformation,[status(thm)],[f119])).
% 0.09/0.40 fof(f121,plain,(
% 0.09/0.40 ![U]: (~ssList(U)|(![V]: (~ssList(V)|((~frontsegP(U,V)|(ssList(sK5_skl(V,U))&app(V,sK5_skl(V,U))=U))&(frontsegP(U,V)|(![W]: (~ssList(W)|~app(V,W)=U)))))))),
% 0.09/0.40 inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(W,sK5_skl(V,U))],[f120])).
% 0.09/0.40 fof(f124,plain,(
% 0.09/0.40 ![X0,X1,X2]: (~ssList(X0)|~ssList(X1)|frontsegP(X0,X1)|~ssList(X2)|~app(X1,X2)=X0)),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f121])).
% 0.09/0.40 fof(f217,plain,(
% 0.09/0.40 ![U]: (~ssList(U)|(![V]: (~ssList(V)|(neq(U,V)<=>~U=V))))),
% 0.09/0.40 inference(pre_NNF_transformation,[status(thm)],[f15])).
% 0.09/0.40 fof(f218,plain,(
% 0.09/0.40 ![U]: (~ssList(U)|(![V]: (~ssList(V)|((~neq(U,V)|~U=V)&(neq(U,V)|U=V)))))),
% 0.09/0.40 inference(NNF_transformation,[status(thm)],[f217])).
% 0.09/0.40 fof(f219,plain,(
% 0.09/0.40 ![X0,X1]: (~ssList(X0)|~ssList(X1)|~neq(X0,X1)|~X0=X1)),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f218])).
% 0.09/0.40 fof(f220,plain,(
% 0.09/0.40 ![X0,X1]: (~ssList(X0)|~ssList(X1)|neq(X0,X1)|X0=X1)),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f218])).
% 0.09/0.40 fof(f223,plain,(
% 0.09/0.40 ssList(nil)),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f17])).
% 0.09/0.40 fof(f415,plain,(
% 0.09/0.40 (?[U]: (ssList(U)&(?[V]: (ssList(V)&(?[W]: (ssList(W)&(?[X]: (ssList(X)&(((((V=X&U=W)&neq(V,nil))&(?[Y]: (ssList(Y)&((app(W,Y)=X&totalorderedP(W))&(![Z]: (~ssItem(Z)|(![X1]: ((~ssList(X1)|~app(cons(Z,nil),X1)=Y)|(![X2]: (~ssItem(X2)|(![X3]: ((~ssList(X3)|~app(X3,cons(X2,nil))=W)|~leq(X2,Z)))))))))))))&(nil=X|~nil=W))&(~neq(U,nil)|~frontsegP(V,U)))))))))))),
% 0.09/0.40 inference(pre_NNF_transformation,[status(thm)],[f97])).
% 0.09/0.40 fof(f416,plain,(
% 0.09/0.40 ?[U]: (ssList(U)&(?[V]: (ssList(V)&(?[W]: (ssList(W)&(?[X]: (ssList(X)&(((((V=X&U=W)&neq(V,nil))&(?[Y]: (ssList(Y)&((app(W,Y)=X&totalorderedP(W))&(![Z]: (~ssItem(Z)|((![X1]: (~ssList(X1)|~app(cons(Z,nil),X1)=Y))|(![X2]: (~ssItem(X2)|((![X3]: (~ssList(X3)|~app(X3,cons(X2,nil))=W))|~leq(X2,Z)))))))))))&(nil=X|~nil=W))&(~neq(U,nil)|~frontsegP(V,U))))))))))),
% 0.09/0.40 inference(miniscoping,[status(thm)],[f415])).
% 0.09/0.40 fof(f417,plain,(
% 0.09/0.40 (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)&((app(sK49_skl,sK51_skl)=sK50_skl&totalorderedP(sK49_skl))&(![Z]: (~ssItem(Z)|((![X1]: (~ssList(X1)|~app(cons(Z,nil),X1)=sK51_skl))|(![X2]: (~ssItem(X2)|((![X3]: (~ssList(X3)|~app(X3,cons(X2,nil))=sK49_skl))|~leq(X2,Z))))))))))&(nil=sK50_skl|~nil=sK49_skl))&(~neq(sK47_skl,nil)|~frontsegP(sK48_skl,sK47_skl)))))))),
% 0.09/0.40 inference(skolemize,[status(esa),new_symbols(skolem,[sK47_skl,sK48_skl,sK49_skl,sK50_skl,sK51_skl]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl),skolemize(Y,sK51_skl)],[f416])).
% 0.09/0.40 fof(f418,plain,(
% 0.09/0.40 ssList(sK47_skl)),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f417])).
% 0.09/0.40 fof(f419,plain,(
% 0.09/0.40 ssList(sK48_skl)),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f417])).
% 0.09/0.40 fof(f422,plain,(
% 0.09/0.40 sK48_skl=sK50_skl),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f417])).
% 0.09/0.40 fof(f423,plain,(
% 0.09/0.40 sK47_skl=sK49_skl),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f417])).
% 0.09/0.40 fof(f424,plain,(
% 0.09/0.40 neq(sK48_skl,nil)),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f417])).
% 0.09/0.40 fof(f425,plain,(
% 0.09/0.40 ssList(sK51_skl)),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f417])).
% 0.09/0.40 fof(f426,plain,(
% 0.09/0.40 app(sK49_skl,sK51_skl)=sK50_skl),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f417])).
% 0.09/0.40 fof(f429,plain,(
% 0.09/0.40 nil=sK50_skl|~nil=sK49_skl),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f417])).
% 0.09/0.40 fof(f430,plain,(
% 0.09/0.40 ~neq(sK47_skl,nil)|~frontsegP(sK48_skl,sK47_skl)),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f417])).
% 0.09/0.40 fof(f431,definition,(
% 0.09/0.40 sQ0_spl <=> (nil=sK50_skl)),
% 0.09/0.40 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.09/0.40 fof(f432,plain,(
% 0.09/0.40 nil=sK50_skl|~sQ0_spl),
% 0.09/0.40 inference(component_clause,[status(thm)],[f431])).
% 0.09/0.40 fof(f434,definition,(
% 0.09/0.40 sQ1_spl <=> (nil=sK49_skl)),
% 0.09/0.40 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.09/0.40 fof(f436,plain,(
% 0.09/0.40 ~nil=sK49_skl|sQ1_spl),
% 0.09/0.40 inference(component_clause,[status(thm)],[f434])).
% 0.09/0.40 fof(f437,plain,(
% 0.09/0.40 sQ0_spl|~sQ1_spl),
% 0.09/0.40 inference(split_clause,[status(thm)],[f429,f431,f434])).
% 0.09/0.40 fof(f438,definition,(
% 0.09/0.40 sQ2_spl <=> (neq(sK47_skl,nil))),
% 0.09/0.40 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.09/0.40 fof(f440,plain,(
% 0.09/0.40 ~neq(sK47_skl,nil)|sQ2_spl),
% 0.09/0.40 inference(component_clause,[status(thm)],[f438])).
% 0.09/0.40 fof(f441,definition,(
% 0.09/0.40 sQ3_spl <=> (frontsegP(sK48_skl,sK47_skl))),
% 0.09/0.40 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.09/0.40 fof(f443,plain,(
% 0.09/0.40 ~frontsegP(sK48_skl,sK47_skl)|sQ3_spl),
% 0.09/0.40 inference(component_clause,[status(thm)],[f441])).
% 0.09/0.40 fof(f444,plain,(
% 0.09/0.40 ~sQ2_spl|~sQ3_spl),
% 0.09/0.40 inference(split_clause,[status(thm)],[f430,f438,f441])).
% 0.09/0.40 fof(f449,plain,(
% 0.09/0.40 ![X0,X1]: (~ssList(app(X0,X1))|~ssList(X0)|frontsegP(app(X0,X1),X0)|~ssList(X1))),
% 0.09/0.40 inference(destructive_equality_resolution,[status(thm)],[f124])).
% 0.09/0.40 fof(f460,plain,(
% 0.09/0.40 ![X1]: (~ssList(X1)|~ssList(X1)|~neq(X1,X1))),
% 0.09/0.40 inference(destructive_equality_resolution,[status(thm)],[f219])).
% 0.09/0.40 fof(f461,plain,(
% 0.09/0.40 ![X0]: (~ssList(X0)|~neq(X0,X0))),
% 0.09/0.40 inference(duplicate_literals_removal,[status(thm)],[f460])).
% 0.09/0.40 fof(f482,plain,(
% 0.09/0.40 sK48_skl=nil|~sQ0_spl),
% 0.09/0.40 inference(backward_demodulation,[status(thm)],[f432,f422])).
% 0.09/0.40 fof(f484,plain,(
% 0.09/0.40 neq(nil,nil)|~sQ0_spl),
% 0.09/0.40 inference(forward_demodulation,[status(thm)],[f482,f424])).
% 0.09/0.40 fof(f485,plain,(
% 0.09/0.40 app(sK47_skl,sK51_skl)=sK50_skl),
% 0.09/0.40 inference(forward_demodulation,[status(thm)],[f423,f426])).
% 0.09/0.40 fof(f487,plain,(
% 0.09/0.40 ~ssList(nil)|~sQ0_spl),
% 0.09/0.40 inference(resolution,[status(thm)],[f461,f484])).
% 0.09/0.40 fof(f488,plain,(
% 0.09/0.40 $false|~sQ0_spl),
% 0.09/0.40 inference(forward_subsumption_resolution,[status(thm)],[f487,f223])).
% 0.09/0.40 fof(f489,plain,(
% 0.09/0.40 ~sQ0_spl),
% 0.09/0.40 inference(contradiction_clause,[status(thm)],[f488])).
% 0.09/0.40 fof(f490,plain,(
% 0.09/0.40 ~nil=sK47_skl|sQ1_spl),
% 0.09/0.40 inference(forward_demodulation,[status(thm)],[f423,f436])).
% 0.09/0.40 fof(f492,plain,(
% 0.09/0.40 app(sK47_skl,sK51_skl)=sK48_skl),
% 0.09/0.40 inference(forward_demodulation,[status(thm)],[f422,f485])).
% 0.09/0.40 fof(f493,plain,(
% 0.09/0.40 ~ssList(sK48_skl)|~ssList(sK47_skl)|frontsegP(app(sK47_skl,sK51_skl),sK47_skl)|~ssList(sK51_skl)),
% 0.09/0.40 inference(paramodulation,[status(thm)],[f492,f449])).
% 0.09/0.40 fof(f494,definition,(
% 0.09/0.40 sQ4_spl <=> (ssList(sK48_skl))),
% 0.09/0.40 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f496,plain,(
% 0.09/0.41 ~ssList(sK48_skl)|sQ4_spl),
% 0.09/0.41 inference(component_clause,[status(thm)],[f494])).
% 0.09/0.41 fof(f497,definition,(
% 0.09/0.41 sQ5_spl <=> (ssList(sK47_skl))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f499,plain,(
% 0.09/0.41 ~ssList(sK47_skl)|sQ5_spl),
% 0.09/0.41 inference(component_clause,[status(thm)],[f497])).
% 0.09/0.41 fof(f500,definition,(
% 0.09/0.41 sQ6_spl <=> (frontsegP(app(sK47_skl,sK51_skl),sK47_skl))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f501,plain,(
% 0.09/0.41 frontsegP(app(sK47_skl,sK51_skl),sK47_skl)|~sQ6_spl),
% 0.09/0.41 inference(component_clause,[status(thm)],[f500])).
% 0.09/0.41 fof(f503,definition,(
% 0.09/0.41 sQ7_spl <=> (ssList(sK51_skl))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f505,plain,(
% 0.09/0.41 ~ssList(sK51_skl)|sQ7_spl),
% 0.09/0.41 inference(component_clause,[status(thm)],[f503])).
% 0.09/0.41 fof(f506,plain,(
% 0.09/0.41 ~sQ4_spl|~sQ5_spl|sQ6_spl|~sQ7_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f493,f494,f497,f500,f503])).
% 0.09/0.41 fof(f507,plain,(
% 0.09/0.41 $false|sQ7_spl),
% 0.09/0.41 inference(forward_subsumption_resolution,[status(thm)],[f505,f425])).
% 0.09/0.41 fof(f508,plain,(
% 0.09/0.41 sQ7_spl),
% 0.09/0.41 inference(contradiction_clause,[status(thm)],[f507])).
% 0.09/0.41 fof(f509,plain,(
% 0.09/0.41 frontsegP(sK48_skl,sK47_skl)|~sQ6_spl),
% 0.09/0.41 inference(forward_demodulation,[status(thm)],[f492,f501])).
% 0.09/0.41 fof(f536,definition,(
% 0.09/0.41 sQ12_spl <=> (ssList(nil))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f538,plain,(
% 0.09/0.41 ~ssList(nil)|sQ12_spl),
% 0.09/0.41 inference(component_clause,[status(thm)],[f536])).
% 0.09/0.41 fof(f543,plain,(
% 0.09/0.41 $false|sQ4_spl),
% 0.09/0.41 inference(forward_subsumption_resolution,[status(thm)],[f496,f419])).
% 0.09/0.41 fof(f544,plain,(
% 0.09/0.41 sQ4_spl),
% 0.09/0.41 inference(contradiction_clause,[status(thm)],[f543])).
% 0.09/0.41 fof(f545,plain,(
% 0.09/0.41 $false|sQ5_spl),
% 0.09/0.41 inference(forward_subsumption_resolution,[status(thm)],[f499,f418])).
% 0.09/0.41 fof(f546,plain,(
% 0.09/0.41 sQ5_spl),
% 0.09/0.41 inference(contradiction_clause,[status(thm)],[f545])).
% 0.09/0.41 fof(f547,plain,(
% 0.09/0.41 $false|sQ12_spl),
% 0.09/0.41 inference(forward_subsumption_resolution,[status(thm)],[f538,f223])).
% 0.09/0.41 fof(f548,plain,(
% 0.09/0.41 sQ12_spl),
% 0.09/0.41 inference(contradiction_clause,[status(thm)],[f547])).
% 0.09/0.41 fof(f558,plain,(
% 0.09/0.41 ~ssList(sK47_skl)|~ssList(nil)|sK47_skl=nil|sQ2_spl),
% 0.09/0.41 inference(resolution,[status(thm)],[f220,f440])).
% 0.09/0.41 fof(f574,definition,(
% 0.09/0.41 sQ19_spl <=> (sK47_skl=nil)),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f575,plain,(
% 0.09/0.41 sK47_skl=nil|~sQ19_spl),
% 0.09/0.41 inference(component_clause,[status(thm)],[f574])).
% 0.09/0.41 fof(f577,plain,(
% 0.09/0.41 ~sQ5_spl|~sQ12_spl|sQ19_spl|sQ2_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f558,f497,f536,f574,f438])).
% 0.09/0.41 fof(f578,plain,(
% 0.09/0.41 $false|sQ1_spl|~sQ19_spl),
% 0.09/0.41 inference(forward_subsumption_resolution,[status(thm)],[f575,f490])).
% 0.09/0.41 fof(f579,plain,(
% 0.09/0.41 sQ1_spl|~sQ19_spl),
% 0.09/0.41 inference(contradiction_clause,[status(thm)],[f578])).
% 0.09/0.41 fof(f580,plain,(
% 0.09/0.41 $false|~sQ6_spl|sQ3_spl),
% 0.09/0.41 inference(forward_subsumption_resolution,[status(thm)],[f443,f509])).
% 0.09/0.41 fof(f581,plain,(
% 0.09/0.41 ~sQ6_spl|sQ3_spl),
% 0.09/0.41 inference(contradiction_clause,[status(thm)],[f580])).
% 0.09/0.41 fof(f582,plain,(
% 0.09/0.41 $false),
% 0.09/0.41 inference(sat_refutation,[status(thm)],[f437,f444,f489,f506,f508,f544,f546,f548,f577,f579,f581])).
% 0.09/0.41 % SZS output end CNFRefutation for theBenchmark.p
% 0.09/0.44 % Elapsed time: 0.065578 seconds
% 0.09/0.44 % CPU time: 0.218633 seconds
% 0.09/0.44 % Total memory used: 80.613 MB
% 0.09/0.44 % Net memory used: 80.420 MB
%------------------------------------------------------------------------------