%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SWC027+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 : n015.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 02:41:22 PM UTC 2026
% Result : Theorem 0.14s 0.42s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC027+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
% 0.10/0.36 % Computer : n015.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 07:53:07 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.14/0.38 % Drodi V4.1.1
% 0.14/0.42 % Refutation found
% 0.14/0.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.42 % SZS output start CNFRefutation for theBenchmark
% 0.14/0.42 fof(f17,axiom,(
% 0.14/0.42 ssList(nil) ),
% 0.14/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.42 fof(f18,axiom,(
% 0.14/0.42 (! [U] :( ssList(U)=> (! [V] :( ssItem(V)=> cons(V,U) != U ) )) )),
% 0.14/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.42 fof(f38,axiom,(
% 0.14/0.42 (! [U] :( ssItem(U)=> ~ memberP(nil,U) ) )),
% 0.14/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.42 fof(f96,conjecture,(
% 0.14/0.42 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> (! [X] :( ssList(X)=> ( V != X| U != W| ( (! [Y] :( ssItem(Y)=> ( cons(Y,nil) != W| ~ memberP(X,Y)| (? [Z] :( ssItem(Z)& Y != Z& memberP(X,Z)& leq(Y,Z) ) )) ))& ( nil != X| nil != W ) )| ( ( nil != V| nil = U )& ( nil != U| nil = V ) ) ) ) )) )) )) )),
% 0.14/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.42 fof(f97,negated_conjecture,(
% 0.14/0.42 ~((! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> (! [X] :( ssList(X)=> ( V != X| U != W| ( (! [Y] :( ssItem(Y)=> ( cons(Y,nil) != W| ~ memberP(X,Y)| (? [Z] :( ssItem(Z)& Y != Z& memberP(X,Z)& leq(Y,Z) ) )) ))& ( nil != X| nil != W ) )| ( ( nil != V| nil = U )& ( nil != U| nil = V ) ) ) ) )) )) )) ))),
% 0.14/0.42 inference(negated_conjecture,[status(cth)],[f96])).
% 0.14/0.42 fof(f223,plain,(
% 0.14/0.42 ssList(nil)),
% 0.14/0.42 inference(cnf_transformation,[status(thm)],[f17])).
% 0.14/0.42 fof(f224,plain,(
% 0.14/0.42 ![U]: (~ssList(U)|(![V]: (~ssItem(V)|~cons(V,U)=U)))),
% 0.14/0.42 inference(pre_NNF_transformation,[status(thm)],[f18])).
% 0.14/0.42 fof(f225,plain,(
% 0.14/0.42 ![X0,X1]: (~ssList(X0)|~ssItem(X1)|~cons(X1,X0)=X0)),
% 0.14/0.42 inference(cnf_transformation,[status(thm)],[f224])).
% 0.14/0.42 fof(f278,plain,(
% 0.14/0.42 ![U]: (~ssItem(U)|~memberP(nil,U))),
% 0.14/0.42 inference(pre_NNF_transformation,[status(thm)],[f38])).
% 0.14/0.42 fof(f279,plain,(
% 0.14/0.42 ![X0]: (~ssItem(X0)|~memberP(nil,X0))),
% 0.14/0.42 inference(cnf_transformation,[status(thm)],[f278])).
% 0.14/0.42 fof(f415,plain,(
% 0.14/0.42 (?[U]: (ssList(U)&(?[V]: (ssList(V)&(?[W]: (ssList(W)&(?[X]: (ssList(X)&(((V=X&U=W)&((?[Y]: (ssItem(Y)&((cons(Y,nil)=W&memberP(X,Y))&(![Z]: (((~ssItem(Z)|Y=Z)|~memberP(X,Z))|~leq(Y,Z))))))|(nil=X&nil=W)))&((nil=V&~nil=U)|(nil=U&~nil=V)))))))))))),
% 0.14/0.42 inference(pre_NNF_transformation,[status(thm)],[f97])).
% 0.14/0.42 fof(f416,definition,(
% 0.14/0.42 ![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(Y,Z))))))),
% 0.14/0.42 introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 0.14/0.42 fof(f417,definition,(
% 0.14/0.42 ![U,V]: (sP1_prd(V,U)<=>(nil=V&~nil=U))),
% 0.14/0.42 introduced(definition,[new_symbols(definition,[sP1_prd])],[])).
% 0.14/0.42 fof(f418,plain,(
% 0.14/0.42 ?[U]: (ssList(U)&(?[V]: (ssList(V)&(?[W]: (ssList(W)&(?[X]: (ssList(X)&(((V=X&U=W)&((?[Y]: sP0_prd(Y,X,W))|(nil=X&nil=W)))&(sP1_prd(V,U)|(nil=U&~nil=V))))))))))),
% 0.14/0.42 inference(formula_renaming,[status(thm)],[f415,f417,f416])).
% 0.14/0.42 fof(f419,plain,(
% 0.14/0.42 (ssList(sK47_skl)&(ssList(sK48_skl)&(ssList(sK49_skl)&(ssList(sK50_skl)&(((sK48_skl=sK50_skl&sK47_skl=sK49_skl)&(sP0_prd(sK51_skl,sK50_skl,sK49_skl)|(nil=sK50_skl&nil=sK49_skl)))&(sP1_prd(sK48_skl,sK47_skl)|(nil=sK47_skl&~nil=sK48_skl)))))))),
% 0.14/0.42 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)],[f418])).
% 0.14/0.42 fof(f424,plain,(
% 0.14/0.42 sK48_skl=sK50_skl),
% 0.14/0.42 inference(cnf_transformation,[status(thm)],[f419])).
% 0.14/0.42 fof(f425,plain,(
% 0.14/0.42 sK47_skl=sK49_skl),
% 0.14/0.42 inference(cnf_transformation,[status(thm)],[f419])).
% 0.14/0.42 fof(f426,plain,(
% 0.14/0.42 sP0_prd(sK51_skl,sK50_skl,sK49_skl)|nil=sK50_skl),
% 0.14/0.42 inference(cnf_transformation,[status(thm)],[f419])).
% 0.14/0.42 fof(f427,plain,(
% 0.14/0.42 sP0_prd(sK51_skl,sK50_skl,sK49_skl)|nil=sK49_skl),
% 0.14/0.42 inference(cnf_transformation,[status(thm)],[f419])).
% 0.14/0.42 fof(f428,plain,(
% 0.14/0.42 sP1_prd(sK48_skl,sK47_skl)|nil=sK47_skl),
% 0.14/0.42 inference(cnf_transformation,[status(thm)],[f419])).
% 0.14/0.42 fof(f429,plain,(
% 0.14/0.42 sP1_prd(sK48_skl,sK47_skl)|~nil=sK48_skl),
% 0.14/0.42 inference(cnf_transformation,[status(thm)],[f419])).
% 0.14/0.42 fof(f430,plain,(
% 0.14/0.42 ![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(Y,Z))))))&(sP0_prd(Y,X,W)|(~ssItem(Y)|((~cons(Y,nil)=W|~memberP(X,Y))|(?[Z]: (((ssItem(Z)&~Y=Z)&memberP(X,Z))&leq(Y,Z)))))))),
% 0.14/0.42 inference(NNF_transformation,[status(thm)],[f416])).
% 0.14/0.42 fof(f431,plain,(
% 0.14/0.42 (![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(Y,Z)))))))&(![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(Y,Z)))))))),
% 0.14/0.42 inference(miniscoping,[status(thm)],[f430])).
% 0.14/0.42 fof(f432,plain,(
% 0.14/0.42 (![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(Y,Z)))))))&(![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(Y,sK52_skl(Y,X,W)))))))),
% 0.14/0.42 inference(skolemize,[status(esa),new_symbols(skolem,[sK52_skl]),skolemize(Z,sK52_skl(Y,X,W))],[f431])).
% 0.14/0.42 fof(f433,plain,(
% 0.14/0.42 ![X0,X1,X2]: (~sP0_prd(X0,X1,X2)|ssItem(X0))),
% 0.14/0.42 inference(cnf_transformation,[status(thm)],[f432])).
% 0.14/0.42 fof(f434,plain,(
% 0.14/0.42 ![X0,X1,X2]: (~sP0_prd(X0,X1,X2)|cons(X0,nil)=X2)),
% 0.14/0.42 inference(cnf_transformation,[status(thm)],[f432])).
% 0.14/0.42 fof(f435,plain,(
% 0.14/0.42 ![X0,X1,X2]: (~sP0_prd(X0,X1,X2)|memberP(X1,X0))),
% 0.14/0.42 inference(cnf_transformation,[status(thm)],[f432])).
% 0.14/0.42 fof(f441,plain,(
% 0.14/0.42 ![U,V]: ((~sP1_prd(V,U)|(nil=V&~nil=U))&(sP1_prd(V,U)|(~nil=V|nil=U)))),
% 0.14/0.42 inference(NNF_transformation,[status(thm)],[f417])).
% 0.14/0.42 fof(f442,plain,(
% 0.14/0.42 (![U,V]: (~sP1_prd(V,U)|(nil=V&~nil=U)))&(![U,V]: (sP1_prd(V,U)|(~nil=V|nil=U)))),
% 0.14/0.42 inference(miniscoping,[status(thm)],[f441])).
% 0.14/0.42 fof(f443,plain,(
% 0.14/0.42 ![X0,X1]: (~sP1_prd(X0,X1)|nil=X0)),
% 0.14/0.42 inference(cnf_transformation,[status(thm)],[f442])).
% 0.14/0.42 fof(f444,plain,(
% 0.14/0.42 ![X0,X1]: (~sP1_prd(X0,X1)|~nil=X1)),
% 0.14/0.42 inference(cnf_transformation,[status(thm)],[f442])).
% 0.14/0.42 fof(f480,plain,(
% 0.14/0.42 sP0_prd(sK51_skl,sK48_skl,sK49_skl)|nil=sK50_skl),
% 0.14/0.42 inference(forward_demodulation,[status(thm)],[f424,f426])).
% 0.14/0.42 fof(f481,plain,(
% 0.14/0.42 sP0_prd(sK51_skl,sK48_skl,sK47_skl)|nil=sK50_skl),
% 0.14/0.42 inference(forward_demodulation,[status(thm)],[f425,f480])).
% 0.14/0.42 fof(f482,plain,(
% 0.14/0.42 sP0_prd(sK51_skl,sK48_skl,sK47_skl)|nil=sK48_skl),
% 0.14/0.42 inference(forward_demodulation,[status(thm)],[f424,f481])).
% 0.14/0.42 fof(f483,plain,(
% 0.14/0.42 sP0_prd(sK51_skl,sK48_skl,sK49_skl)|nil=sK49_skl),
% 0.14/0.42 inference(forward_demodulation,[status(thm)],[f424,f427])).
% 0.14/0.42 fof(f484,plain,(
% 0.14/0.42 sP0_prd(sK51_skl,sK48_skl,sK47_skl)|nil=sK49_skl),
% 0.14/0.42 inference(forward_demodulation,[status(thm)],[f425,f483])).
% 0.14/0.42 fof(f485,plain,(
% 0.14/0.42 sP0_prd(sK51_skl,sK48_skl,sK47_skl)|nil=sK47_skl),
% 0.14/0.42 inference(forward_demodulation,[status(thm)],[f425,f484])).
% 0.14/0.42 fof(f490,plain,(
% 0.14/0.42 ![X0]: (~sP1_prd(X0,nil))),
% 0.14/0.42 inference(destructive_equality_resolution,[status(thm)],[f444])).
% 0.14/0.42 fof(f495,plain,(
% 0.14/0.42 nil=sK48_skl|ssItem(sK51_skl)),
% 0.14/0.42 inference(resolution,[status(thm)],[f482,f433])).
% 0.14/0.42 fof(f504,plain,(
% 0.14/0.42 ![X0]: (nil=sK48_skl|~ssList(X0)|~cons(sK51_skl,X0)=X0)),
% 0.14/0.42 inference(resolution,[status(thm)],[f495,f225])).
% 0.14/0.42 fof(f507,plain,(
% 0.14/0.42 nil=sK47_skl|memberP(sK48_skl,sK51_skl)),
% 0.14/0.42 inference(resolution,[status(thm)],[f485,f435])).
% 0.14/0.42 fof(f508,plain,(
% 0.14/0.42 nil=sK47_skl|ssItem(sK51_skl)),
% 0.14/0.42 inference(resolution,[status(thm)],[f485,f433])).
% 0.14/0.42 fof(f530,plain,(
% 0.14/0.42 nil=sK47_skl|nil=sK48_skl),
% 0.14/0.42 inference(resolution,[status(thm)],[f428,f443])).
% 0.14/0.42 fof(f578,plain,(
% 0.14/0.42 cons(sK51_skl,nil)=sK47_skl|nil=sK48_skl),
% 0.14/0.42 inference(resolution,[status(thm)],[f434,f482])).
% 0.14/0.42 fof(f583,plain,(
% 0.14/0.42 nil=sK47_skl|memberP(nil,sK51_skl)|nil=sK47_skl),
% 0.14/0.42 inference(paramodulation,[status(thm)],[f530,f507])).
% 0.14/0.42 fof(f585,plain,(
% 0.14/0.42 nil=sK47_skl|memberP(nil,sK51_skl)),
% 0.14/0.42 inference(duplicate_literals_removal,[status(thm)],[f583])).
% 0.14/0.42 fof(f633,plain,(
% 0.14/0.42 nil=sK47_skl|~ssItem(sK51_skl)),
% 0.14/0.42 inference(resolution,[status(thm)],[f585,f279])).
% 0.14/0.42 fof(f644,plain,(
% 0.14/0.42 sP1_prd(sK48_skl,nil)|~nil=sK48_skl),
% 0.14/0.42 inference(backward_demodulation,[status(thm)],[f663,f429])).
% 0.14/0.42 fof(f654,plain,(
% 0.14/0.42 cons(sK51_skl,nil)=nil|nil=sK48_skl),
% 0.14/0.42 inference(backward_demodulation,[status(thm)],[f663,f578])).
% 0.14/0.42 fof(f663,plain,(
% 0.14/0.42 nil=sK47_skl),
% 0.14/0.42 inference(forward_subsumption_resolution,[status(thm)],[f633,f508])).
% 0.14/0.42 fof(f674,plain,(
% 0.14/0.42 ![X0]: (~ssList(X0)|~cons(sK51_skl,X0)=X0)),
% 0.14/0.42 inference(backward_subsumption_resolution,[status(thm)],[f504,f676])).
% 0.14/0.42 fof(f676,plain,(
% 0.14/0.42 ~nil=sK48_skl),
% 0.14/0.42 inference(forward_subsumption_resolution,[status(thm)],[f644,f490])).
% 0.14/0.42 fof(f679,plain,(
% 0.14/0.42 cons(sK51_skl,nil)=nil),
% 0.14/0.42 inference(forward_subsumption_resolution,[status(thm)],[f654,f676])).
% 0.14/0.42 fof(f719,plain,(
% 0.14/0.42 ~cons(sK51_skl,nil)=nil),
% 0.14/0.42 inference(resolution,[status(thm)],[f674,f223])).
% 0.14/0.42 fof(f721,plain,(
% 0.14/0.42 ~nil=nil),
% 0.14/0.42 inference(forward_demodulation,[status(thm)],[f679,f719])).
% 0.14/0.42 fof(f722,plain,(
% 0.14/0.42 $false),
% 0.14/0.42 inference(trivial_equality_resolution,[status(thm)],[f721])).
% 0.14/0.42 % SZS output end CNFRefutation for theBenchmark.p
% 0.14/0.45 % Elapsed time: 0.073559 seconds
% 0.14/0.45 % CPU time: 0.345670 seconds
% 0.14/0.45 % Total memory used: 69.313 MB
% 0.14/0.45 % Net memory used: 68.996 MB
%------------------------------------------------------------------------------