%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SWC351+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 : n014.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 02:42:14 PM UTC 2026
% Result : Theorem 0.08s 0.38s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC351+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n014.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Mon Sep 21 08:18:05 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 0.08/0.38 % Refutation found
% 0.08/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/0.38 % SZS output start CNFRefutation for theBenchmark
% 0.08/0.38 fof(f5,axiom,(
% 0.08/0.38 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> ( frontsegP(U,V)<=> (? [W] :( ssList(W)& app(V,W) = U ) )) ) )) )),
% 0.08/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.38 fof(f96,conjecture,(
% 0.08/0.38 (! [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| ~ strictorderedP(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& lt(X2,Z) ) )) )) )) )) ))| frontsegP(V,U)| ( nil != X& nil = W ) ) ) )) )) )) )),
% 0.08/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.38 fof(f97,negated_conjecture,(
% 0.08/0.38 ~((! [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| ~ strictorderedP(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& lt(X2,Z) ) )) )) )) )) ))| frontsegP(V,U)| ( nil != X& nil = W ) ) ) )) )) )) ))),
% 0.08/0.38 inference(negated_conjecture,[status(cth)],[f96])).
% 0.08/0.38 fof(f119,plain,(
% 0.08/0.38 ![U]: (~ssList(U)|(![V]: (~ssList(V)|(frontsegP(U,V)<=>(?[W]: (ssList(W)&app(V,W)=U))))))),
% 0.08/0.38 inference(pre_NNF_transformation,[status(thm)],[f5])).
% 0.08/0.38 fof(f120,plain,(
% 0.08/0.38 ![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)))))))),
% 0.08/0.38 inference(NNF_transformation,[status(thm)],[f119])).
% 0.08/0.38 fof(f121,plain,(
% 0.08/0.38 ![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)))))))),
% 0.08/0.38 inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(W,sK5_skl(V,U))],[f120])).
% 0.08/0.38 fof(f124,plain,(
% 0.08/0.38 ![X0,X1,X2]: (~ssList(X0)|~ssList(X1)|frontsegP(X0,X1)|~ssList(X2)|~app(X1,X2)=X0)),
% 0.08/0.38 inference(cnf_transformation,[status(thm)],[f121])).
% 0.08/0.38 fof(f415,plain,(
% 0.08/0.38 (?[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&strictorderedP(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)|~lt(X2,Z)))))))))))))&~frontsegP(V,U))&(nil=X|~nil=W))))))))))),
% 0.08/0.38 inference(pre_NNF_transformation,[status(thm)],[f97])).
% 0.08/0.38 fof(f416,plain,(
% 0.08/0.38 ?[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&strictorderedP(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))|~lt(X2,Z)))))))))))&~frontsegP(V,U))&(nil=X|~nil=W)))))))))),
% 0.08/0.38 inference(miniscoping,[status(thm)],[f415])).
% 0.08/0.38 fof(f417,plain,(
% 0.08/0.38 (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&strictorderedP(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))|~lt(X2,Z))))))))))&~frontsegP(sK48_skl,sK47_skl))&(nil=sK50_skl|~nil=sK49_skl))))))),
% 0.08/0.38 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])).
% 0.08/0.38 fof(f420,plain,(
% 0.08/0.38 ssList(sK49_skl)),
% 0.08/0.38 inference(cnf_transformation,[status(thm)],[f417])).
% 0.08/0.38 fof(f421,plain,(
% 0.08/0.38 ssList(sK50_skl)),
% 0.08/0.38 inference(cnf_transformation,[status(thm)],[f417])).
% 0.08/0.38 fof(f422,plain,(
% 0.08/0.38 sK48_skl=sK50_skl),
% 0.08/0.38 inference(cnf_transformation,[status(thm)],[f417])).
% 0.08/0.38 fof(f423,plain,(
% 0.08/0.38 sK47_skl=sK49_skl),
% 0.08/0.38 inference(cnf_transformation,[status(thm)],[f417])).
% 0.08/0.38 fof(f425,plain,(
% 0.08/0.38 ssList(sK51_skl)),
% 0.08/0.38 inference(cnf_transformation,[status(thm)],[f417])).
% 0.12/0.38 fof(f426,plain,(
% 0.12/0.38 app(sK49_skl,sK51_skl)=sK50_skl),
% 0.12/0.38 inference(cnf_transformation,[status(thm)],[f417])).
% 0.12/0.38 fof(f429,plain,(
% 0.12/0.38 ~frontsegP(sK48_skl,sK47_skl)),
% 0.12/0.38 inference(cnf_transformation,[status(thm)],[f417])).
% 0.12/0.38 fof(f442,plain,(
% 0.12/0.38 ![X0,X1]: (~ssList(app(X0,X1))|~ssList(X0)|frontsegP(app(X0,X1),X0)|~ssList(X1))),
% 0.12/0.38 inference(destructive_equality_resolution,[status(thm)],[f124])).
% 0.12/0.38 fof(f474,plain,(
% 0.12/0.38 ~frontsegP(sK50_skl,sK47_skl)),
% 0.12/0.38 inference(forward_demodulation,[status(thm)],[f422,f429])).
% 0.12/0.38 fof(f475,plain,(
% 0.12/0.38 ~frontsegP(sK50_skl,sK49_skl)),
% 0.12/0.38 inference(forward_demodulation,[status(thm)],[f423,f474])).
% 0.12/0.38 fof(f489,plain,(
% 0.12/0.38 ~ssList(sK50_skl)|~ssList(sK49_skl)|frontsegP(app(sK49_skl,sK51_skl),sK49_skl)|~ssList(sK51_skl)),
% 0.12/0.38 inference(paramodulation,[status(thm)],[f426,f442])).
% 0.12/0.38 fof(f490,definition,(
% 0.12/0.38 sQ2_spl <=> (ssList(sK50_skl))),
% 0.12/0.38 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.12/0.38 fof(f492,plain,(
% 0.12/0.38 ~ssList(sK50_skl)|sQ2_spl),
% 0.12/0.38 inference(component_clause,[status(thm)],[f490])).
% 0.12/0.38 fof(f493,definition,(
% 0.12/0.38 sQ3_spl <=> (ssList(sK49_skl))),
% 0.12/0.38 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.12/0.38 fof(f495,plain,(
% 0.12/0.38 ~ssList(sK49_skl)|sQ3_spl),
% 0.12/0.38 inference(component_clause,[status(thm)],[f493])).
% 0.12/0.38 fof(f496,definition,(
% 0.12/0.38 sQ4_spl <=> (frontsegP(app(sK49_skl,sK51_skl),sK49_skl))),
% 0.12/0.38 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 0.12/0.38 fof(f497,plain,(
% 0.12/0.38 frontsegP(app(sK49_skl,sK51_skl),sK49_skl)|~sQ4_spl),
% 0.12/0.38 inference(component_clause,[status(thm)],[f496])).
% 0.12/0.38 fof(f499,definition,(
% 0.12/0.38 sQ5_spl <=> (ssList(sK51_skl))),
% 0.12/0.38 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 0.12/0.38 fof(f501,plain,(
% 0.12/0.38 ~ssList(sK51_skl)|sQ5_spl),
% 0.12/0.38 inference(component_clause,[status(thm)],[f499])).
% 0.12/0.38 fof(f502,plain,(
% 0.12/0.38 ~sQ2_spl|~sQ3_spl|sQ4_spl|~sQ5_spl),
% 0.12/0.38 inference(split_clause,[status(thm)],[f489,f490,f493,f496,f499])).
% 0.12/0.38 fof(f503,plain,(
% 0.12/0.38 $false|sQ5_spl),
% 0.12/0.38 inference(forward_subsumption_resolution,[status(thm)],[f501,f425])).
% 0.12/0.38 fof(f504,plain,(
% 0.12/0.38 sQ5_spl),
% 0.12/0.38 inference(contradiction_clause,[status(thm)],[f503])).
% 0.12/0.38 fof(f505,plain,(
% 0.12/0.38 frontsegP(sK50_skl,sK49_skl)|~sQ4_spl),
% 0.12/0.38 inference(forward_demodulation,[status(thm)],[f426,f497])).
% 0.12/0.38 fof(f506,plain,(
% 0.12/0.38 $false|~sQ4_spl),
% 0.12/0.38 inference(forward_subsumption_resolution,[status(thm)],[f505,f475])).
% 0.12/0.38 fof(f507,plain,(
% 0.12/0.38 ~sQ4_spl),
% 0.12/0.38 inference(contradiction_clause,[status(thm)],[f506])).
% 0.12/0.38 fof(f508,plain,(
% 0.12/0.38 $false|sQ2_spl),
% 0.12/0.38 inference(forward_subsumption_resolution,[status(thm)],[f492,f421])).
% 0.12/0.38 fof(f509,plain,(
% 0.12/0.38 sQ2_spl),
% 0.12/0.38 inference(contradiction_clause,[status(thm)],[f508])).
% 0.12/0.38 fof(f511,plain,(
% 0.12/0.38 $false|sQ3_spl),
% 0.12/0.38 inference(forward_subsumption_resolution,[status(thm)],[f495,f420])).
% 0.12/0.38 fof(f512,plain,(
% 0.12/0.38 sQ3_spl),
% 0.12/0.38 inference(contradiction_clause,[status(thm)],[f511])).
% 0.12/0.38 fof(f513,plain,(
% 0.12/0.38 $false),
% 0.12/0.38 inference(sat_refutation,[status(thm)],[f502,f504,f507,f509,f512])).
% 0.12/0.38 % SZS output end CNFRefutation for theBenchmark.p
% 0.12/0.44 % Elapsed time: 0.087523 seconds
% 0.12/0.44 % CPU time: 0.173217 seconds
% 0.12/0.44 % Total memory used: 62.138 MB
% 0.12/0.44 % Net memory used: 62.050 MB
%------------------------------------------------------------------------------