%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SWC381+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 : 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 02:42:19 PM UTC 2026
% Result : Theorem 0.12s 0.41s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC381+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
% 0.10/0.34 % Computer : n001.cluster.edu
% 0.10/0.34 % Model : x86_64 x86_64
% 0.10/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.34 % Memory : 8046.5625MB
% 0.10/0.34 % OS : Linux 6.8.0-71-generic
% 0.10/0.34 % CPULimit : 300
% 0.10/0.34 % WCLimit : 300
% 0.10/0.34 % DateTime : Mon Sep 21 08:25:28 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.36 % Drodi V4.1.1
% 0.12/0.41 % Refutation found
% 0.12/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.41 % SZS output start CNFRefutation for theBenchmark
% 0.12/0.41 fof(f96,conjecture,(
% 0.12/0.41 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> (! [X] :( ssList(X)=> ( V != X| U != W| ( ( ~ neq(V,nil)| (? [Y] :( ssItem(Y)& cons(Y,nil) = U& memberP(V,Y) ))| (! [Z] :( ssItem(Z)=> ( cons(Z,nil) != W| ~ memberP(X,Z) ) ) ))& ( ~ neq(V,nil)| neq(X,nil) ) ) ) ) )) )) )) )),
% 0.12/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.41 fof(f97,negated_conjecture,(
% 0.12/0.41 ~((! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> (! [X] :( ssList(X)=> ( V != X| U != W| ( ( ~ neq(V,nil)| (? [Y] :( ssItem(Y)& cons(Y,nil) = U& memberP(V,Y) ))| (! [Z] :( ssItem(Z)=> ( cons(Z,nil) != W| ~ memberP(X,Z) ) ) ))& ( ~ neq(V,nil)| neq(X,nil) ) ) ) ) )) )) )) ))),
% 0.12/0.41 inference(negated_conjecture,[status(cth)],[f96])).
% 0.12/0.41 fof(f415,plain,(
% 0.12/0.41 (?[U]: (ssList(U)&(?[V]: (ssList(V)&(?[W]: (ssList(W)&(?[X]: (ssList(X)&((V=X&U=W)&(((neq(V,nil)&(![Y]: ((~ssItem(Y)|~cons(Y,nil)=U)|~memberP(V,Y))))&(?[Z]: (ssItem(Z)&(cons(Z,nil)=W&memberP(X,Z)))))|(neq(V,nil)&~neq(X,nil))))))))))))),
% 0.12/0.41 inference(pre_NNF_transformation,[status(thm)],[f97])).
% 0.12/0.41 fof(f416,definition,(
% 0.12/0.41 ![U,V,W,X]: (sP0_prd(X,W,V,U)<=>((neq(V,nil)&(![Y]: ((~ssItem(Y)|~cons(Y,nil)=U)|~memberP(V,Y))))&(?[Z]: (ssItem(Z)&(cons(Z,nil)=W&memberP(X,Z))))))),
% 0.12/0.41 introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 0.12/0.41 fof(f417,plain,(
% 0.12/0.41 ?[U]: (ssList(U)&(?[V]: (ssList(V)&(?[W]: (ssList(W)&(?[X]: (ssList(X)&((V=X&U=W)&(sP0_prd(X,W,V,U)|(neq(V,nil)&~neq(X,nil)))))))))))),
% 0.12/0.41 inference(formula_renaming,[status(thm)],[f415,f416])).
% 0.12/0.41 fof(f418,plain,(
% 0.12/0.41 (ssList(sK47_skl)&(ssList(sK48_skl)&(ssList(sK49_skl)&(ssList(sK50_skl)&((sK48_skl=sK50_skl&sK47_skl=sK49_skl)&(sP0_prd(sK50_skl,sK49_skl,sK48_skl,sK47_skl)|(neq(sK48_skl,nil)&~neq(sK50_skl,nil))))))))),
% 0.12/0.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK47_skl,sK48_skl,sK49_skl,sK50_skl]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl)],[f417])).
% 0.12/0.41 fof(f423,plain,(
% 0.12/0.41 sK48_skl=sK50_skl),
% 0.12/0.41 inference(cnf_transformation,[status(thm)],[f418])).
% 0.12/0.41 fof(f424,plain,(
% 0.12/0.41 sK47_skl=sK49_skl),
% 0.12/0.41 inference(cnf_transformation,[status(thm)],[f418])).
% 0.12/0.41 fof(f425,plain,(
% 0.12/0.41 sP0_prd(sK50_skl,sK49_skl,sK48_skl,sK47_skl)|neq(sK48_skl,nil)),
% 0.12/0.41 inference(cnf_transformation,[status(thm)],[f418])).
% 0.12/0.41 fof(f426,plain,(
% 0.12/0.41 sP0_prd(sK50_skl,sK49_skl,sK48_skl,sK47_skl)|~neq(sK50_skl,nil)),
% 0.12/0.41 inference(cnf_transformation,[status(thm)],[f418])).
% 0.12/0.41 fof(f427,plain,(
% 0.12/0.41 ![U,V,W,X]: ((~sP0_prd(X,W,V,U)|((neq(V,nil)&(![Y]: ((~ssItem(Y)|~cons(Y,nil)=U)|~memberP(V,Y))))&(?[Z]: (ssItem(Z)&(cons(Z,nil)=W&memberP(X,Z))))))&(sP0_prd(X,W,V,U)|((~neq(V,nil)|(?[Y]: ((ssItem(Y)&cons(Y,nil)=U)&memberP(V,Y))))|(![Z]: (~ssItem(Z)|(~cons(Z,nil)=W|~memberP(X,Z)))))))),
% 0.12/0.41 inference(NNF_transformation,[status(thm)],[f416])).
% 0.12/0.41 fof(f428,plain,(
% 0.12/0.41 (![U,V,W,X]: (~sP0_prd(X,W,V,U)|((neq(V,nil)&(![Y]: ((~ssItem(Y)|~cons(Y,nil)=U)|~memberP(V,Y))))&(?[Z]: (ssItem(Z)&(cons(Z,nil)=W&memberP(X,Z)))))))&(![U,V,W,X]: (sP0_prd(X,W,V,U)|((~neq(V,nil)|(?[Y]: ((ssItem(Y)&cons(Y,nil)=U)&memberP(V,Y))))|(![Z]: (~ssItem(Z)|(~cons(Z,nil)=W|~memberP(X,Z)))))))),
% 0.12/0.41 inference(miniscoping,[status(thm)],[f427])).
% 0.12/0.41 fof(f429,plain,(
% 0.12/0.41 (![U,V,W,X]: (~sP0_prd(X,W,V,U)|((neq(V,nil)&(![Y]: ((~ssItem(Y)|~cons(Y,nil)=U)|~memberP(V,Y))))&(ssItem(sK51_skl(X,W,V,U))&(cons(sK51_skl(X,W,V,U),nil)=W&memberP(X,sK51_skl(X,W,V,U)))))))&(![U,V,W,X]: (sP0_prd(X,W,V,U)|((~neq(V,nil)|((ssItem(sK52_skl(X,W,V,U))&cons(sK52_skl(X,W,V,U),nil)=U)&memberP(V,sK52_skl(X,W,V,U))))|(![Z]: (~ssItem(Z)|(~cons(Z,nil)=W|~memberP(X,Z)))))))),
% 0.12/0.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK51_skl,sK52_skl]),skolemize(Z,sK51_skl(X,W,V,U)),skolemize(Y,sK52_skl(X,W,V,U))],[f428])).
% 0.12/0.41 fof(f431,plain,(
% 0.12/0.41 ![X0,X1,X2,X3,X4]: (~sP0_prd(X0,X1,X2,X3)|~ssItem(X4)|~cons(X4,nil)=X3|~memberP(X2,X4))),
% 0.12/0.41 inference(cnf_transformation,[status(thm)],[f429])).
% 0.12/0.41 fof(f432,plain,(
% 0.12/0.41 ![X0,X1,X2,X3]: (~sP0_prd(X0,X1,X2,X3)|ssItem(sK51_skl(X0,X1,X2,X3)))),
% 0.12/0.41 inference(cnf_transformation,[status(thm)],[f429])).
% 0.12/0.42 fof(f433,plain,(
% 0.12/0.42 ![X0,X1,X2,X3]: (~sP0_prd(X0,X1,X2,X3)|cons(sK51_skl(X0,X1,X2,X3),nil)=X1)),
% 0.12/0.42 inference(cnf_transformation,[status(thm)],[f429])).
% 0.12/0.42 fof(f434,plain,(
% 0.12/0.42 ![X0,X1,X2,X3]: (~sP0_prd(X0,X1,X2,X3)|memberP(X0,sK51_skl(X0,X1,X2,X3)))),
% 0.12/0.42 inference(cnf_transformation,[status(thm)],[f429])).
% 0.12/0.42 fof(f472,plain,(
% 0.12/0.42 sP0_prd(sK48_skl,sK49_skl,sK48_skl,sK47_skl)|neq(sK48_skl,nil)),
% 0.12/0.42 inference(forward_demodulation,[status(thm)],[f423,f425])).
% 0.12/0.42 fof(f473,plain,(
% 0.12/0.42 sP0_prd(sK48_skl,sK47_skl,sK48_skl,sK47_skl)|neq(sK48_skl,nil)),
% 0.12/0.42 inference(forward_demodulation,[status(thm)],[f424,f472])).
% 0.12/0.42 fof(f474,plain,(
% 0.12/0.42 sP0_prd(sK48_skl,sK49_skl,sK48_skl,sK47_skl)|~neq(sK50_skl,nil)),
% 0.12/0.42 inference(forward_demodulation,[status(thm)],[f423,f426])).
% 0.12/0.42 fof(f475,plain,(
% 0.12/0.42 sP0_prd(sK48_skl,sK47_skl,sK48_skl,sK47_skl)|~neq(sK50_skl,nil)),
% 0.12/0.42 inference(forward_demodulation,[status(thm)],[f424,f474])).
% 0.12/0.42 fof(f476,plain,(
% 0.12/0.42 sP0_prd(sK48_skl,sK47_skl,sK48_skl,sK47_skl)|~neq(sK48_skl,nil)),
% 0.12/0.42 inference(forward_demodulation,[status(thm)],[f423,f475])).
% 0.12/0.42 fof(f477,plain,(
% 0.12/0.42 sP0_prd(sK48_skl,sK47_skl,sK48_skl,sK47_skl)),
% 0.12/0.42 inference(forward_subsumption_resolution,[status(thm)],[f476,f473])).
% 0.12/0.42 fof(f478,plain,(
% 0.12/0.42 ![X0,X1,X2,X3]: (~sP0_prd(X0,X1,X2,cons(X3,nil))|~ssItem(X3)|~memberP(X2,X3))),
% 0.12/0.42 inference(destructive_equality_resolution,[status(thm)],[f431])).
% 0.12/0.42 fof(f493,plain,(
% 0.12/0.42 ssItem(sK51_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl))),
% 0.12/0.42 inference(resolution,[status(thm)],[f432,f477])).
% 0.12/0.42 fof(f496,plain,(
% 0.12/0.42 cons(sK51_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl),nil)=sK47_skl),
% 0.12/0.42 inference(resolution,[status(thm)],[f433,f477])).
% 0.12/0.42 fof(f521,plain,(
% 0.12/0.42 memberP(sK48_skl,sK51_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl))),
% 0.12/0.42 inference(resolution,[status(thm)],[f434,f477])).
% 0.12/0.42 fof(f559,plain,(
% 0.12/0.42 ![X0,X1]: (~sP0_prd(X0,X1,sK48_skl,cons(sK51_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl),nil))|~ssItem(sK51_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl)))),
% 0.12/0.42 inference(resolution,[status(thm)],[f521,f478])).
% 0.12/0.42 fof(f561,plain,(
% 0.12/0.42 ![X0,X1]: (~sP0_prd(X0,X1,sK48_skl,sK47_skl)|~ssItem(sK51_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl)))),
% 0.12/0.42 inference(forward_demodulation,[status(thm)],[f496,f559])).
% 0.12/0.42 fof(f563,plain,(
% 0.12/0.42 ![X0,X1]: (~sP0_prd(X0,X1,sK48_skl,sK47_skl))),
% 0.12/0.42 inference(forward_subsumption_resolution,[status(thm)],[f561,f493])).
% 0.12/0.42 fof(f564,plain,(
% 0.12/0.42 $false),
% 0.12/0.42 inference(backward_subsumption_resolution,[status(thm)],[f477,f563])).
% 0.12/0.42 % SZS output end CNFRefutation for theBenchmark.p
% 0.12/0.44 % Elapsed time: 0.086390 seconds
% 0.12/0.44 % CPU time: 0.369452 seconds
% 0.12/0.44 % Total memory used: 114.387 MB
% 0.12/0.44 % Net memory used: 114.035 MB
%------------------------------------------------------------------------------