%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SWC258+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 : 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 02:41:59 PM UTC 2026
% Result : Theorem 0.08s 0.43s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC258+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
% 0.08/0.36 % Computer : n001.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 08:14:45 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.38 % Drodi V4.1.1
% 0.08/0.43 % Refutation found
% 0.08/0.43 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/0.43 % SZS output start CNFRefutation for theBenchmark
% 0.08/0.43 fof(f65,axiom,(
% 0.08/0.43 (! [U] :( ssItem(U)=> totalorderedP(cons(U,nil)) ) )),
% 0.08/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.43 fof(f66,axiom,(
% 0.08/0.43 totalorderedP(nil) ),
% 0.08/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.43 fof(f96,conjecture,(
% 0.08/0.43 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> (! [X] :( ssList(X)=> ( V != X| U != W| totalorderedP(U)| ( (! [Y] :( ssItem(Y)=> ( cons(Y,nil) != W| ~ memberP(X,Y)| (? [Z] :( ssItem(Z)& Y != Z& memberP(X,Z)& leq(Z,Y) ) )) ))& ( nil != X| nil != W ) ) ) ) )) )) )) )),
% 0.08/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.43 fof(f97,negated_conjecture,(
% 0.08/0.43 ~((! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> (! [X] :( ssList(X)=> ( V != X| U != W| totalorderedP(U)| ( (! [Y] :( ssItem(Y)=> ( cons(Y,nil) != W| ~ memberP(X,Y)| (? [Z] :( ssItem(Z)& Y != Z& memberP(X,Z)& leq(Z,Y) ) )) ))& ( nil != X| nil != W ) ) ) ) )) )) )) ))),
% 0.08/0.43 inference(negated_conjecture,[status(cth)],[f96])).
% 0.08/0.43 fof(f337,plain,(
% 0.08/0.43 ![U]: (~ssItem(U)|totalorderedP(cons(U,nil)))),
% 0.08/0.43 inference(pre_NNF_transformation,[status(thm)],[f65])).
% 0.08/0.43 fof(f338,plain,(
% 0.08/0.43 ![X0]: (~ssItem(X0)|totalorderedP(cons(X0,nil)))),
% 0.08/0.43 inference(cnf_transformation,[status(thm)],[f337])).
% 0.08/0.43 fof(f339,plain,(
% 0.08/0.43 totalorderedP(nil)),
% 0.08/0.43 inference(cnf_transformation,[status(thm)],[f66])).
% 0.08/0.43 fof(f415,plain,(
% 0.08/0.43 (?[U]: (ssList(U)&(?[V]: (ssList(V)&(?[W]: (ssList(W)&(?[X]: (ssList(X)&(((V=X&U=W)&~totalorderedP(U))&((?[Y]: (ssItem(Y)&((cons(Y,nil)=W&memberP(X,Y))&(![Z]: (((~ssItem(Z)|Y=Z)|~memberP(X,Z))|~leq(Z,Y))))))|(nil=X&nil=W)))))))))))),
% 0.08/0.43 inference(pre_NNF_transformation,[status(thm)],[f97])).
% 0.08/0.43 fof(f416,definition,(
% 0.08/0.43 ![W,X,Y]: (sP0_prd(Y,X,W)<=>(ssItem(Y)&((cons(Y,nil)=W&memberP(X,Y))&(![Z]: (((~ssItem(Z)|Y=Z)|~memberP(X,Z))|~leq(Z,Y))))))),
% 0.08/0.43 introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 0.08/0.43 fof(f417,plain,(
% 0.08/0.43 ?[U]: (ssList(U)&(?[V]: (ssList(V)&(?[W]: (ssList(W)&(?[X]: (ssList(X)&(((V=X&U=W)&~totalorderedP(U))&((?[Y]: sP0_prd(Y,X,W))|(nil=X&nil=W))))))))))),
% 0.08/0.43 inference(formula_renaming,[status(thm)],[f415,f416])).
% 0.08/0.43 fof(f418,plain,(
% 0.08/0.43 (ssList(sK47_skl)&(ssList(sK48_skl)&(ssList(sK49_skl)&(ssList(sK50_skl)&(((sK48_skl=sK50_skl&sK47_skl=sK49_skl)&~totalorderedP(sK47_skl))&(sP0_prd(sK51_skl,sK50_skl,sK49_skl)|(nil=sK50_skl&nil=sK49_skl)))))))),
% 0.08/0.43 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)],[f417])).
% 0.08/0.43 fof(f423,plain,(
% 0.08/0.43 sK48_skl=sK50_skl),
% 0.08/0.43 inference(cnf_transformation,[status(thm)],[f418])).
% 0.08/0.43 fof(f424,plain,(
% 0.08/0.43 sK47_skl=sK49_skl),
% 0.08/0.43 inference(cnf_transformation,[status(thm)],[f418])).
% 0.08/0.43 fof(f425,plain,(
% 0.08/0.43 ~totalorderedP(sK47_skl)),
% 0.08/0.43 inference(cnf_transformation,[status(thm)],[f418])).
% 0.08/0.43 fof(f427,plain,(
% 0.08/0.43 sP0_prd(sK51_skl,sK50_skl,sK49_skl)|nil=sK49_skl),
% 0.08/0.43 inference(cnf_transformation,[status(thm)],[f418])).
% 0.08/0.43 fof(f428,plain,(
% 0.08/0.43 ![W,X,Y]: ((~sP0_prd(Y,X,W)|(ssItem(Y)&((cons(Y,nil)=W&memberP(X,Y))&(![Z]: (((~ssItem(Z)|Y=Z)|~memberP(X,Z))|~leq(Z,Y))))))&(sP0_prd(Y,X,W)|(~ssItem(Y)|((~cons(Y,nil)=W|~memberP(X,Y))|(?[Z]: (((ssItem(Z)&~Y=Z)&memberP(X,Z))&leq(Z,Y)))))))),
% 0.08/0.43 inference(NNF_transformation,[status(thm)],[f416])).
% 0.08/0.43 fof(f429,plain,(
% 0.08/0.43 (![W,X,Y]: (~sP0_prd(Y,X,W)|(ssItem(Y)&((cons(Y,nil)=W&memberP(X,Y))&(![Z]: (((~ssItem(Z)|Y=Z)|~memberP(X,Z))|~leq(Z,Y)))))))&(![W,X,Y]: (sP0_prd(Y,X,W)|(~ssItem(Y)|((~cons(Y,nil)=W|~memberP(X,Y))|(?[Z]: (((ssItem(Z)&~Y=Z)&memberP(X,Z))&leq(Z,Y)))))))),
% 0.08/0.43 inference(miniscoping,[status(thm)],[f428])).
% 0.08/0.43 fof(f430,plain,(
% 0.08/0.43 (![W,X,Y]: (~sP0_prd(Y,X,W)|(ssItem(Y)&((cons(Y,nil)=W&memberP(X,Y))&(![Z]: (((~ssItem(Z)|Y=Z)|~memberP(X,Z))|~leq(Z,Y)))))))&(![W,X,Y]: (sP0_prd(Y,X,W)|(~ssItem(Y)|((~cons(Y,nil)=W|~memberP(X,Y))|(((ssItem(sK52_skl(Y,X,W))&~Y=sK52_skl(Y,X,W))&memberP(X,sK52_skl(Y,X,W)))&leq(sK52_skl(Y,X,W),Y))))))),
% 0.08/0.43 inference(skolemize,[status(esa),new_symbols(skolem,[sK52_skl]),skolemize(Z,sK52_skl(Y,X,W))],[f429])).
% 0.08/0.43 fof(f431,plain,(
% 0.08/0.43 ![X0,X1,X2]: (~sP0_prd(X0,X1,X2)|ssItem(X0))),
% 0.08/0.43 inference(cnf_transformation,[status(thm)],[f430])).
% 0.08/0.43 fof(f432,plain,(
% 0.08/0.43 ![X0,X1,X2]: (~sP0_prd(X0,X1,X2)|cons(X0,nil)=X2)),
% 0.08/0.43 inference(cnf_transformation,[status(thm)],[f430])).
% 0.08/0.43 fof(f439,definition,(
% 0.08/0.43 sQ0_spl <=> (sP0_prd(sK51_skl,sK50_skl,sK49_skl))),
% 0.08/0.43 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.08/0.43 fof(f440,plain,(
% 0.08/0.43 sP0_prd(sK51_skl,sK50_skl,sK49_skl)|~sQ0_spl),
% 0.08/0.43 inference(component_clause,[status(thm)],[f439])).
% 0.08/0.43 fof(f446,definition,(
% 0.08/0.43 sQ2_spl <=> (nil=sK49_skl)),
% 0.08/0.43 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.08/0.43 fof(f447,plain,(
% 0.08/0.43 nil=sK49_skl|~sQ2_spl),
% 0.08/0.43 inference(component_clause,[status(thm)],[f446])).
% 0.08/0.43 fof(f449,plain,(
% 0.08/0.43 sQ0_spl|sQ2_spl),
% 0.08/0.43 inference(split_clause,[status(thm)],[f427,f439,f446])).
% 0.08/0.43 fof(f489,plain,(
% 0.08/0.43 sP0_prd(sK51_skl,sK48_skl,sK49_skl)|~sQ0_spl),
% 0.08/0.43 inference(forward_demodulation,[status(thm)],[f423,f440])).
% 0.08/0.43 fof(f490,plain,(
% 0.08/0.43 sP0_prd(sK51_skl,sK48_skl,sK47_skl)|~sQ0_spl),
% 0.08/0.43 inference(forward_demodulation,[status(thm)],[f424,f489])).
% 0.08/0.43 fof(f491,plain,(
% 0.08/0.43 ssItem(sK51_skl)|~sQ0_spl),
% 0.08/0.43 inference(resolution,[status(thm)],[f490,f431])).
% 0.08/0.43 fof(f493,plain,(
% 0.08/0.43 cons(sK51_skl,nil)=sK47_skl|~sQ0_spl),
% 0.08/0.43 inference(resolution,[status(thm)],[f432,f490])).
% 0.08/0.43 fof(f500,definition,(
% 0.08/0.43 sQ4_spl <=> (ssItem(sK51_skl))),
% 0.08/0.43 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 0.08/0.43 fof(f502,plain,(
% 0.08/0.43 ~ssItem(sK51_skl)|sQ4_spl),
% 0.08/0.43 inference(component_clause,[status(thm)],[f500])).
% 0.08/0.43 fof(f517,plain,(
% 0.08/0.43 $false|~sQ0_spl|sQ4_spl),
% 0.08/0.43 inference(forward_subsumption_resolution,[status(thm)],[f502,f491])).
% 0.08/0.43 fof(f518,plain,(
% 0.08/0.43 ~sQ0_spl|sQ4_spl),
% 0.08/0.43 inference(contradiction_clause,[status(thm)],[f517])).
% 0.08/0.43 fof(f524,plain,(
% 0.08/0.43 sK47_skl=nil|~sQ2_spl),
% 0.08/0.43 inference(backward_demodulation,[status(thm)],[f447,f424])).
% 0.08/0.43 fof(f526,plain,(
% 0.08/0.43 ~totalorderedP(nil)|~sQ2_spl),
% 0.08/0.43 inference(backward_demodulation,[status(thm)],[f524,f425])).
% 0.08/0.43 fof(f528,plain,(
% 0.08/0.43 $false|~sQ2_spl),
% 0.08/0.43 inference(forward_subsumption_resolution,[status(thm)],[f526,f339])).
% 0.08/0.43 fof(f529,plain,(
% 0.08/0.43 ~sQ2_spl),
% 0.08/0.43 inference(contradiction_clause,[status(thm)],[f528])).
% 0.08/0.43 fof(f752,plain,(
% 0.08/0.43 ~ssItem(sK51_skl)|totalorderedP(sK47_skl)|~sQ0_spl),
% 0.08/0.43 inference(paramodulation,[status(thm)],[f493,f338])).
% 0.08/0.43 fof(f753,definition,(
% 0.08/0.43 sQ38_spl <=> (totalorderedP(sK47_skl))),
% 0.08/0.43 introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition])).
% 0.08/0.43 fof(f754,plain,(
% 0.08/0.43 totalorderedP(sK47_skl)|~sQ38_spl),
% 0.08/0.43 inference(component_clause,[status(thm)],[f753])).
% 0.08/0.43 fof(f756,plain,(
% 0.08/0.43 ~sQ4_spl|sQ38_spl|~sQ0_spl),
% 0.08/0.43 inference(split_clause,[status(thm)],[f752,f500,f753,f439])).
% 0.08/0.43 fof(f757,plain,(
% 0.08/0.43 $false|~sQ38_spl),
% 0.08/0.43 inference(forward_subsumption_resolution,[status(thm)],[f754,f425])).
% 0.08/0.43 fof(f758,plain,(
% 0.08/0.43 ~sQ38_spl),
% 0.08/0.43 inference(contradiction_clause,[status(thm)],[f757])).
% 0.08/0.43 fof(f759,plain,(
% 0.08/0.43 $false),
% 0.08/0.43 inference(sat_refutation,[status(thm)],[f449,f518,f529,f756,f758])).
% 0.08/0.43 % SZS output end CNFRefutation for theBenchmark.p
% 0.08/0.45 % Elapsed time: 0.080924 seconds
% 0.08/0.45 % CPU time: 0.293209 seconds
% 0.08/0.45 % Total memory used: 113.094 MB
% 0.08/0.45 % Net memory used: 112.798 MB
%------------------------------------------------------------------------------