%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SWC339+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 : n008.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 02:42:12 PM UTC 2026
% Result : Theorem 0.19s 0.49s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWC339+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n008.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Mon Sep 21 08:17:54 UTC 2026
% 0.19/0.44 % CPUTime :
% 0.19/0.47 % Drodi V4.1.1
% 0.19/0.49 % Refutation found
% 0.19/0.49 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/0.49 % SZS output start CNFRefutation for theBenchmark
% 0.19/0.49 fof(f7,axiom,(
% 0.19/0.49 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> ( segmentP(U,V)<=> (? [W] :( ssList(W)& (? [X] :( ssList(X)& app(app(W,V),X) = U ) )) )) ) )) )),
% 0.19/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.49 fof(f96,conjecture,(
% 0.19/0.49 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> (! [X] :( ssList(X)=> ( V != X| U != W| (! [Y] :( ssList(Y)=> (! [Z] :( ssList(Z)=> ( app(app(Y,W),Z) != X| ~ totalorderedP(W)| (? [X1] :( ssItem(X1)& (? [X2] :( ssList(X2)& app(X2,cons(X1,nil)) = Y& (? [X3] :( ssItem(X3)& (? [X4] :( ssList(X4)& app(cons(X3,nil),X4) = W& leq(X1,X3) ) )) )) )))| (? [X5] :( ssItem(X5)& (? [X6] :( ssList(X6)& app(cons(X5,nil),X6) = Z& (? [X7] :( ssItem(X7)& (? [X8] :( ssList(X8)& app(X8,cons(X7,nil)) = W& leq(X7,X5) ) )) )) )) )) ) )))| ( nil != X& nil = W )| ( segmentP(V,U)& totalorderedP(U) ) ) ) )) )) )) )),
% 0.19/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.49 fof(f97,negated_conjecture,(
% 0.19/0.49 ~((! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> (! [X] :( ssList(X)=> ( V != X| U != W| (! [Y] :( ssList(Y)=> (! [Z] :( ssList(Z)=> ( app(app(Y,W),Z) != X| ~ totalorderedP(W)| (? [X1] :( ssItem(X1)& (? [X2] :( ssList(X2)& app(X2,cons(X1,nil)) = Y& (? [X3] :( ssItem(X3)& (? [X4] :( ssList(X4)& app(cons(X3,nil),X4) = W& leq(X1,X3) ) )) )) )))| (? [X5] :( ssItem(X5)& (? [X6] :( ssList(X6)& app(cons(X5,nil),X6) = Z& (? [X7] :( ssItem(X7)& (? [X8] :( ssList(X8)& app(X8,cons(X7,nil)) = W& leq(X7,X5) ) )) )) )) )) ) )))| ( nil != X& nil = W )| ( segmentP(V,U)& totalorderedP(U) ) ) ) )) )) )) ))),
% 0.19/0.49 inference(negated_conjecture,[status(cth)],[f96])).
% 0.19/0.49 fof(f131,plain,(
% 0.19/0.49 ![U]: (~ssList(U)|(![V]: (~ssList(V)|(segmentP(U,V)<=>(?[W]: (ssList(W)&(?[X]: (ssList(X)&app(app(W,V),X)=U))))))))),
% 0.19/0.49 inference(pre_NNF_transformation,[status(thm)],[f7])).
% 0.19/0.49 fof(f132,plain,(
% 0.19/0.49 ![U]: (~ssList(U)|(![V]: (~ssList(V)|((~segmentP(U,V)|(?[W]: (ssList(W)&(?[X]: (ssList(X)&app(app(W,V),X)=U)))))&(segmentP(U,V)|(![W]: (~ssList(W)|(![X]: (~ssList(X)|~app(app(W,V),X)=U)))))))))),
% 0.19/0.49 inference(NNF_transformation,[status(thm)],[f131])).
% 0.19/0.49 fof(f133,plain,(
% 0.19/0.49 ![U]: (~ssList(U)|(![V]: (~ssList(V)|((~segmentP(U,V)|(ssList(sK7_skl(V,U))&(ssList(sK8_skl(V,U))&app(app(sK7_skl(V,U),V),sK8_skl(V,U))=U)))&(segmentP(U,V)|(![W]: (~ssList(W)|(![X]: (~ssList(X)|~app(app(W,V),X)=U)))))))))),
% 0.19/0.49 inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl,sK8_skl]),skolemize(W,sK7_skl(V,U)),skolemize(X,sK8_skl(V,U))],[f132])).
% 0.19/0.49 fof(f137,plain,(
% 0.19/0.49 ![X0,X1,X2,X3]: (~ssList(X0)|~ssList(X1)|segmentP(X0,X1)|~ssList(X2)|~ssList(X3)|~app(app(X2,X1),X3)=X0)),
% 0.19/0.49 inference(cnf_transformation,[status(thm)],[f133])).
% 0.19/0.49 fof(f415,plain,(
% 0.19/0.49 (?[U]: (ssList(U)&(?[V]: (ssList(V)&(?[W]: (ssList(W)&(?[X]: (ssList(X)&((((V=X&U=W)&(?[Y]: (ssList(Y)&(?[Z]: (ssList(Z)&(((app(app(Y,W),Z)=X&totalorderedP(W))&(![X1]: (~ssItem(X1)|(![X2]: ((~ssList(X2)|~app(X2,cons(X1,nil))=Y)|(![X3]: (~ssItem(X3)|(![X4]: ((~ssList(X4)|~app(cons(X3,nil),X4)=W)|~leq(X1,X3))))))))))&(![X5]: (~ssItem(X5)|(![X6]: ((~ssList(X6)|~app(cons(X5,nil),X6)=Z)|(![X7]: (~ssItem(X7)|(![X8]: ((~ssList(X8)|~app(X8,cons(X7,nil))=W)|~leq(X7,X5)))))))))))))))&(nil=X|~nil=W))&(~segmentP(V,U)|~totalorderedP(U)))))))))))),
% 0.19/0.49 inference(pre_NNF_transformation,[status(thm)],[f97])).
% 0.19/0.49 fof(f416,plain,(
% 0.19/0.49 ?[U]: (ssList(U)&(?[V]: (ssList(V)&(?[W]: (ssList(W)&(?[X]: (ssList(X)&((((V=X&U=W)&(?[Y]: (ssList(Y)&(?[Z]: (ssList(Z)&(((app(app(Y,W),Z)=X&totalorderedP(W))&(![X1]: (~ssItem(X1)|((![X2]: (~ssList(X2)|~app(X2,cons(X1,nil))=Y))|(![X3]: (~ssItem(X3)|((![X4]: (~ssList(X4)|~app(cons(X3,nil),X4)=W))|~leq(X1,X3))))))))&(![X5]: (~ssItem(X5)|((![X6]: (~ssList(X6)|~app(cons(X5,nil),X6)=Z))|(![X7]: (~ssItem(X7)|((![X8]: (~ssList(X8)|~app(X8,cons(X7,nil))=W))|~leq(X7,X5)))))))))))))&(nil=X|~nil=W))&(~segmentP(V,U)|~totalorderedP(U))))))))))),
% 0.19/0.49 inference(miniscoping,[status(thm)],[f415])).
% 0.19/0.49 fof(f417,plain,(
% 0.19/0.49 (ssList(sK47_skl)&(ssList(sK48_skl)&(ssList(sK49_skl)&(ssList(sK50_skl)&((((sK48_skl=sK50_skl&sK47_skl=sK49_skl)&(ssList(sK51_skl)&(ssList(sK52_skl)&(((app(app(sK51_skl,sK49_skl),sK52_skl)=sK50_skl&totalorderedP(sK49_skl))&(![X1]: (~ssItem(X1)|((![X2]: (~ssList(X2)|~app(X2,cons(X1,nil))=sK51_skl))|(![X3]: (~ssItem(X3)|((![X4]: (~ssList(X4)|~app(cons(X3,nil),X4)=sK49_skl))|~leq(X1,X3))))))))&(![X5]: (~ssItem(X5)|((![X6]: (~ssList(X6)|~app(cons(X5,nil),X6)=sK52_skl))|(![X7]: (~ssItem(X7)|((![X8]: (~ssList(X8)|~app(X8,cons(X7,nil))=sK49_skl))|~leq(X7,X5)))))))))))&(nil=sK50_skl|~nil=sK49_skl))&(~segmentP(sK48_skl,sK47_skl)|~totalorderedP(sK47_skl)))))))),
% 0.19/0.49 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])).
% 0.19/0.49 fof(f420,plain,(
% 0.19/0.49 ssList(sK49_skl)),
% 0.19/0.49 inference(cnf_transformation,[status(thm)],[f417])).
% 0.19/0.49 fof(f421,plain,(
% 0.19/0.49 ssList(sK50_skl)),
% 0.19/0.49 inference(cnf_transformation,[status(thm)],[f417])).
% 0.19/0.49 fof(f422,plain,(
% 0.19/0.49 sK48_skl=sK50_skl),
% 0.19/0.49 inference(cnf_transformation,[status(thm)],[f417])).
% 0.19/0.49 fof(f423,plain,(
% 0.19/0.49 sK47_skl=sK49_skl),
% 0.19/0.49 inference(cnf_transformation,[status(thm)],[f417])).
% 0.19/0.49 fof(f424,plain,(
% 0.19/0.49 ssList(sK51_skl)),
% 0.19/0.49 inference(cnf_transformation,[status(thm)],[f417])).
% 0.19/0.49 fof(f425,plain,(
% 0.19/0.49 ssList(sK52_skl)),
% 0.19/0.49 inference(cnf_transformation,[status(thm)],[f417])).
% 0.19/0.49 fof(f426,plain,(
% 0.19/0.49 app(app(sK51_skl,sK49_skl),sK52_skl)=sK50_skl),
% 0.19/0.49 inference(cnf_transformation,[status(thm)],[f417])).
% 0.19/0.49 fof(f427,plain,(
% 0.19/0.49 totalorderedP(sK49_skl)),
% 0.19/0.49 inference(cnf_transformation,[status(thm)],[f417])).
% 0.19/0.49 fof(f431,plain,(
% 0.19/0.49 ~segmentP(sK48_skl,sK47_skl)|~totalorderedP(sK47_skl)),
% 0.19/0.49 inference(cnf_transformation,[status(thm)],[f417])).
% 0.19/0.49 fof(f439,definition,(
% 0.19/0.49 sQ2_spl <=> (segmentP(sK48_skl,sK47_skl))),
% 0.19/0.49 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.19/0.49 fof(f441,plain,(
% 0.19/0.49 ~segmentP(sK48_skl,sK47_skl)|sQ2_spl),
% 0.19/0.49 inference(component_clause,[status(thm)],[f439])).
% 0.19/0.49 fof(f442,definition,(
% 0.19/0.49 sQ3_spl <=> (totalorderedP(sK47_skl))),
% 0.19/0.49 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.19/0.49 fof(f444,plain,(
% 0.19/0.49 ~totalorderedP(sK47_skl)|sQ3_spl),
% 0.19/0.49 inference(component_clause,[status(thm)],[f442])).
% 0.19/0.49 fof(f445,plain,(
% 0.19/0.49 ~sQ2_spl|~sQ3_spl),
% 0.19/0.49 inference(split_clause,[status(thm)],[f431,f439,f442])).
% 0.19/0.49 fof(f452,plain,(
% 0.19/0.49 ![X0,X1,X2]: (~ssList(app(app(X0,X1),X2))|~ssList(X1)|segmentP(app(app(X0,X1),X2),X1)|~ssList(X0)|~ssList(X2))),
% 0.19/0.49 inference(destructive_equality_resolution,[status(thm)],[f137])).
% 0.19/0.49 fof(f480,plain,(
% 0.19/0.49 ~segmentP(sK50_skl,sK47_skl)|sQ2_spl),
% 0.19/0.49 inference(forward_demodulation,[status(thm)],[f422,f441])).
% 0.19/0.49 fof(f481,plain,(
% 0.19/0.49 ~segmentP(sK50_skl,sK49_skl)|sQ2_spl),
% 0.19/0.49 inference(forward_demodulation,[status(thm)],[f423,f480])).
% 0.19/0.49 fof(f497,plain,(
% 0.19/0.49 ~ssList(sK50_skl)|~ssList(sK49_skl)|segmentP(app(app(sK51_skl,sK49_skl),sK52_skl),sK49_skl)|~ssList(sK51_skl)|~ssList(sK52_skl)),
% 0.19/0.49 inference(paramodulation,[status(thm)],[f426,f452])).
% 0.19/0.49 fof(f499,definition,(
% 0.19/0.49 sQ4_spl <=> (ssList(sK50_skl))),
% 0.19/0.49 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 0.19/0.49 fof(f501,plain,(
% 0.19/0.49 ~ssList(sK50_skl)|sQ4_spl),
% 0.19/0.49 inference(component_clause,[status(thm)],[f499])).
% 0.19/0.49 fof(f502,definition,(
% 0.19/0.49 sQ5_spl <=> (ssList(sK49_skl))),
% 0.19/0.49 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 0.19/0.49 fof(f504,plain,(
% 0.19/0.49 ~ssList(sK49_skl)|sQ5_spl),
% 0.19/0.49 inference(component_clause,[status(thm)],[f502])).
% 0.19/0.49 fof(f505,definition,(
% 0.19/0.49 sQ6_spl <=> (segmentP(app(app(sK51_skl,sK49_skl),sK52_skl),sK49_skl))),
% 0.19/0.49 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.19/0.49 fof(f506,plain,(
% 0.19/0.49 segmentP(app(app(sK51_skl,sK49_skl),sK52_skl),sK49_skl)|~sQ6_spl),
% 0.19/0.49 inference(component_clause,[status(thm)],[f505])).
% 0.19/0.49 fof(f508,definition,(
% 0.19/0.49 sQ7_spl <=> (ssList(sK51_skl))),
% 0.19/0.49 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 0.19/0.49 fof(f510,plain,(
% 0.19/0.49 ~ssList(sK51_skl)|sQ7_spl),
% 0.19/0.49 inference(component_clause,[status(thm)],[f508])).
% 0.19/0.49 fof(f511,definition,(
% 0.19/0.49 sQ8_spl <=> (ssList(sK52_skl))),
% 0.19/0.49 introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition])).
% 0.19/0.49 fof(f513,plain,(
% 0.19/0.49 ~ssList(sK52_skl)|sQ8_spl),
% 0.19/0.49 inference(component_clause,[status(thm)],[f511])).
% 0.19/0.49 fof(f514,plain,(
% 0.19/0.49 ~sQ4_spl|~sQ5_spl|sQ6_spl|~sQ7_spl|~sQ8_spl),
% 0.19/0.49 inference(split_clause,[status(thm)],[f497,f499,f502,f505,f508,f511])).
% 0.19/0.49 fof(f522,plain,(
% 0.19/0.49 $false|sQ8_spl),
% 0.19/0.49 inference(forward_subsumption_resolution,[status(thm)],[f513,f425])).
% 0.19/0.49 fof(f523,plain,(
% 0.19/0.49 sQ8_spl),
% 0.19/0.49 inference(contradiction_clause,[status(thm)],[f522])).
% 0.19/0.49 fof(f525,plain,(
% 0.19/0.49 $false|sQ7_spl),
% 0.19/0.49 inference(forward_subsumption_resolution,[status(thm)],[f510,f424])).
% 0.19/0.49 fof(f526,plain,(
% 0.19/0.49 sQ7_spl),
% 0.19/0.49 inference(contradiction_clause,[status(thm)],[f525])).
% 0.19/0.49 fof(f527,plain,(
% 0.19/0.49 segmentP(sK50_skl,sK49_skl)|~sQ6_spl),
% 0.19/0.49 inference(forward_demodulation,[status(thm)],[f426,f506])).
% 0.19/0.49 fof(f528,plain,(
% 0.19/0.49 $false|sQ2_spl|~sQ6_spl),
% 0.19/0.49 inference(forward_subsumption_resolution,[status(thm)],[f527,f481])).
% 0.19/0.49 fof(f529,plain,(
% 0.19/0.49 sQ2_spl|~sQ6_spl),
% 0.19/0.49 inference(contradiction_clause,[status(thm)],[f528])).
% 0.19/0.49 fof(f530,plain,(
% 0.19/0.49 ~totalorderedP(sK49_skl)|sQ3_spl),
% 0.19/0.49 inference(forward_demodulation,[status(thm)],[f423,f444])).
% 0.19/0.49 fof(f531,plain,(
% 0.19/0.49 $false|sQ3_spl),
% 0.19/0.49 inference(forward_subsumption_resolution,[status(thm)],[f530,f427])).
% 0.19/0.49 fof(f532,plain,(
% 0.19/0.49 sQ3_spl),
% 0.19/0.49 inference(contradiction_clause,[status(thm)],[f531])).
% 0.19/0.49 fof(f533,plain,(
% 0.19/0.49 $false|sQ4_spl),
% 0.19/0.49 inference(forward_subsumption_resolution,[status(thm)],[f501,f421])).
% 0.19/0.49 fof(f534,plain,(
% 0.19/0.49 sQ4_spl),
% 0.19/0.49 inference(contradiction_clause,[status(thm)],[f533])).
% 0.19/0.49 fof(f537,plain,(
% 0.19/0.49 $false|sQ5_spl),
% 0.19/0.49 inference(forward_subsumption_resolution,[status(thm)],[f504,f420])).
% 0.19/0.49 fof(f538,plain,(
% 0.19/0.49 sQ5_spl),
% 0.19/0.49 inference(contradiction_clause,[status(thm)],[f537])).
% 0.19/0.49 fof(f539,plain,(
% 0.19/0.49 $false),
% 0.19/0.49 inference(sat_refutation,[status(thm)],[f445,f514,f523,f526,f529,f532,f534,f538])).
% 0.19/0.49 % SZS output end CNFRefutation for theBenchmark.p
% 0.27/0.53 % Elapsed time: 0.073066 seconds
% 0.27/0.53 % CPU time: 0.182021 seconds
% 0.27/0.53 % Total memory used: 59.046 MB
% 0.27/0.53 % Net memory used: 58.965 MB
%------------------------------------------------------------------------------