%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SWC415+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 : n026.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 02:42:25 PM UTC 2026
% Result : Theorem 0.17s 1.02s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC415+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.59 % Computer : n026.cluster.edu
% 0.11/0.59 % Model : x86_64 x86_64
% 0.11/0.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.59 % Memory : 8046.5625MB
% 0.11/0.59 % OS : Linux 6.8.0-71-generic
% 0.11/0.59 % CPULimit : 300
% 0.11/0.59 % WCLimit : 300
% 0.11/0.59 % DateTime : Mon Sep 21 08:25:37 UTC 2026
% 0.11/0.59 % CPUTime :
% 0.11/0.61 % Drodi V4.1.1
% 0.17/1.02 % Refutation found
% 0.17/1.02 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/1.02 % SZS output start CNFRefutation for theBenchmark
% 0.17/1.02 fof(f15,axiom,(
% 0.17/1.02 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> ( neq(U,V)<=> U != V ) ) )) )),
% 0.17/1.02 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/1.02 fof(f17,axiom,(
% 0.17/1.02 ssList(nil) ),
% 0.17/1.02 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/1.02 fof(f24,axiom,(
% 0.17/1.02 (! [U] :( ssList(U)=> ( nil != U=> ssList(tl(U)) ) ) )),
% 0.17/1.02 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/1.02 fof(f96,conjecture,(
% 0.17/1.02 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> (! [X] :( ssList(X)=> ( V != X| U != W| ( ( ~ neq(V,nil)| (? [Y] :( ssList(Y)& W != Y& tl(X) = Y& neq(nil,X) ))| (? [Z] :( ssList(Z)& tl(V) = Z& U = Z& neq(nil,V) ) ))& ( ~ neq(V,nil)| neq(X,nil) ) ) ) ) )) )) )) )),
% 0.17/1.02 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/1.02 fof(f97,negated_conjecture,(
% 0.17/1.02 ~((! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> (! [X] :( ssList(X)=> ( V != X| U != W| ( ( ~ neq(V,nil)| (? [Y] :( ssList(Y)& W != Y& tl(X) = Y& neq(nil,X) ))| (? [Z] :( ssList(Z)& tl(V) = Z& U = Z& neq(nil,V) ) ))& ( ~ neq(V,nil)| neq(X,nil) ) ) ) ) )) )) )) ))),
% 0.17/1.02 inference(negated_conjecture,[status(cth)],[f96])).
% 0.17/1.02 fof(f217,plain,(
% 0.17/1.02 ![U]: (~ssList(U)|(![V]: (~ssList(V)|(neq(U,V)<=>~U=V))))),
% 0.17/1.02 inference(pre_NNF_transformation,[status(thm)],[f15])).
% 0.17/1.02 fof(f218,plain,(
% 0.17/1.02 ![U]: (~ssList(U)|(![V]: (~ssList(V)|((~neq(U,V)|~U=V)&(neq(U,V)|U=V)))))),
% 0.17/1.02 inference(NNF_transformation,[status(thm)],[f217])).
% 0.17/1.02 fof(f219,plain,(
% 0.17/1.02 ![X0,X1]: (~ssList(X0)|~ssList(X1)|~neq(X0,X1)|~X0=X1)),
% 0.17/1.02 inference(cnf_transformation,[status(thm)],[f218])).
% 0.17/1.02 fof(f220,plain,(
% 0.17/1.02 ![X0,X1]: (~ssList(X0)|~ssList(X1)|neq(X0,X1)|X0=X1)),
% 0.17/1.02 inference(cnf_transformation,[status(thm)],[f218])).
% 0.17/1.02 fof(f223,plain,(
% 0.17/1.02 ssList(nil)),
% 0.17/1.02 inference(cnf_transformation,[status(thm)],[f17])).
% 0.17/1.02 fof(f240,plain,(
% 0.17/1.02 ![U]: (~ssList(U)|(nil=U|ssList(tl(U))))),
% 0.17/1.02 inference(pre_NNF_transformation,[status(thm)],[f24])).
% 0.17/1.02 fof(f241,plain,(
% 0.17/1.02 ![X0]: (~ssList(X0)|nil=X0|ssList(tl(X0)))),
% 0.17/1.02 inference(cnf_transformation,[status(thm)],[f240])).
% 0.17/1.02 fof(f415,plain,(
% 0.17/1.02 (?[U]: (ssList(U)&(?[V]: (ssList(V)&(?[W]: (ssList(W)&(?[X]: (ssList(X)&((V=X&U=W)&(((neq(V,nil)&(![Y]: (((~ssList(Y)|W=Y)|~tl(X)=Y)|~neq(nil,X))))&(![Z]: (((~ssList(Z)|~tl(V)=Z)|~U=Z)|~neq(nil,V))))|(neq(V,nil)&~neq(X,nil))))))))))))),
% 0.17/1.02 inference(pre_NNF_transformation,[status(thm)],[f97])).
% 0.17/1.02 fof(f416,definition,(
% 0.17/1.02 ![U,V,W,X]: (sP0_prd(X,W,V,U)<=>((neq(V,nil)&(![Y]: (((~ssList(Y)|W=Y)|~tl(X)=Y)|~neq(nil,X))))&(![Z]: (((~ssList(Z)|~tl(V)=Z)|~U=Z)|~neq(nil,V)))))),
% 0.17/1.02 introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 0.17/1.02 fof(f417,plain,(
% 0.17/1.02 ?[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)))))))))))),
% 0.17/1.02 inference(formula_renaming,[status(thm)],[f415,f416])).
% 0.17/1.02 fof(f418,plain,(
% 0.17/1.02 (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))))))))),
% 0.17/1.02 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])).
% 0.17/1.02 fof(f420,plain,(
% 0.17/1.02 ssList(sK48_skl)),
% 0.17/1.02 inference(cnf_transformation,[status(thm)],[f418])).
% 0.17/1.02 fof(f423,plain,(
% 0.17/1.02 sK48_skl=sK50_skl),
% 0.17/1.02 inference(cnf_transformation,[status(thm)],[f418])).
% 0.17/1.02 fof(f424,plain,(
% 0.17/1.02 sK47_skl=sK49_skl),
% 0.17/1.02 inference(cnf_transformation,[status(thm)],[f418])).
% 0.17/1.02 fof(f425,plain,(
% 0.17/1.02 sP0_prd(sK50_skl,sK49_skl,sK48_skl,sK47_skl)|neq(sK48_skl,nil)),
% 0.17/1.02 inference(cnf_transformation,[status(thm)],[f418])).
% 0.17/1.02 fof(f426,plain,(
% 0.17/1.02 sP0_prd(sK50_skl,sK49_skl,sK48_skl,sK47_skl)|~neq(sK50_skl,nil)),
% 0.17/1.02 inference(cnf_transformation,[status(thm)],[f418])).
% 0.17/1.02 fof(f427,definition,(
% 0.17/1.02 ![W,X,Y]: (sP1_prd(Y,X,W)<=>(((~ssList(Y)|W=Y)|~tl(X)=Y)|~neq(nil,X)))),
% 0.17/1.02 introduced(definition,[new_symbols(definition,[sP1_prd])],[])).
% 0.17/1.02 fof(f428,plain,(
% 0.17/1.02 ![U,V,W,X]: (sP0_prd(X,W,V,U)<=>((neq(V,nil)&(![Y]: sP1_prd(Y,X,W)))&(![Z]: (((~ssList(Z)|~tl(V)=Z)|~U=Z)|~neq(nil,V)))))),
% 0.17/1.02 inference(formula_renaming,[status(thm)],[f416,f427])).
% 0.17/1.02 fof(f429,plain,(
% 0.17/1.02 ![U,V,W,X]: ((~sP0_prd(X,W,V,U)|((neq(V,nil)&(![Y]: sP1_prd(Y,X,W)))&(![Z]: (((~ssList(Z)|~tl(V)=Z)|~U=Z)|~neq(nil,V)))))&(sP0_prd(X,W,V,U)|((~neq(V,nil)|(?[Y]: ~sP1_prd(Y,X,W)))|(?[Z]: (((ssList(Z)&tl(V)=Z)&U=Z)&neq(nil,V))))))),
% 0.17/1.02 inference(NNF_transformation,[status(thm)],[f428])).
% 0.17/1.02 fof(f430,plain,(
% 0.17/1.02 (![U,V,W,X]: (~sP0_prd(X,W,V,U)|((neq(V,nil)&(![Y]: sP1_prd(Y,X,W)))&((![Z]: ((~ssList(Z)|~tl(V)=Z)|~U=Z))|~neq(nil,V)))))&(![U,V,W,X]: (sP0_prd(X,W,V,U)|((~neq(V,nil)|(?[Y]: ~sP1_prd(Y,X,W)))|((?[Z]: ((ssList(Z)&tl(V)=Z)&U=Z))&neq(nil,V)))))),
% 0.17/1.02 inference(miniscoping,[status(thm)],[f429])).
% 0.17/1.02 fof(f431,plain,(
% 0.17/1.02 (![U,V,W,X]: (~sP0_prd(X,W,V,U)|((neq(V,nil)&(![Y]: sP1_prd(Y,X,W)))&((![Z]: ((~ssList(Z)|~tl(V)=Z)|~U=Z))|~neq(nil,V)))))&(![U,V,W,X]: (sP0_prd(X,W,V,U)|((~neq(V,nil)|~sP1_prd(sK51_skl(X,W,V,U),X,W))|(((ssList(sK52_skl(X,W,V,U))&tl(V)=sK52_skl(X,W,V,U))&U=sK52_skl(X,W,V,U))&neq(nil,V)))))),
% 0.17/1.02 inference(skolemize,[status(esa),new_symbols(skolem,[sK51_skl,sK52_skl]),skolemize(Y,sK51_skl(X,W,V,U)),skolemize(Z,sK52_skl(X,W,V,U))],[f430])).
% 0.17/1.02 fof(f432,plain,(
% 0.17/1.02 ![X0,X1,X2,X3]: (~sP0_prd(X0,X1,X2,X3)|neq(X2,nil))),
% 0.17/1.02 inference(cnf_transformation,[status(thm)],[f431])).
% 0.17/1.02 fof(f433,plain,(
% 0.17/1.02 ![X0,X1,X2,X3,X4]: (~sP0_prd(X0,X1,X2,X3)|sP1_prd(X4,X0,X1))),
% 0.17/1.02 inference(cnf_transformation,[status(thm)],[f431])).
% 0.17/1.02 fof(f434,plain,(
% 0.17/1.02 ![X0,X1,X2,X3,X4]: (~sP0_prd(X0,X1,X2,X3)|~ssList(X4)|~tl(X2)=X4|~X3=X4|~neq(nil,X2))),
% 0.17/1.02 inference(cnf_transformation,[status(thm)],[f431])).
% 0.17/1.02 fof(f439,plain,(
% 0.17/1.02 ![W,X,Y]: ((~sP1_prd(Y,X,W)|(((~ssList(Y)|W=Y)|~tl(X)=Y)|~neq(nil,X)))&(sP1_prd(Y,X,W)|(((ssList(Y)&~W=Y)&tl(X)=Y)&neq(nil,X))))),
% 0.17/1.02 inference(NNF_transformation,[status(thm)],[f427])).
% 0.17/1.02 fof(f440,plain,(
% 0.17/1.02 (![W,X,Y]: (~sP1_prd(Y,X,W)|(((~ssList(Y)|W=Y)|~tl(X)=Y)|~neq(nil,X))))&(![W,X,Y]: (sP1_prd(Y,X,W)|(((ssList(Y)&~W=Y)&tl(X)=Y)&neq(nil,X))))),
% 0.17/1.02 inference(miniscoping,[status(thm)],[f439])).
% 0.17/1.02 fof(f441,plain,(
% 0.17/1.02 ![X0,X1,X2]: (~sP1_prd(X0,X1,X2)|~ssList(X0)|X2=X0|~tl(X1)=X0|~neq(nil,X1))),
% 0.17/1.02 inference(cnf_transformation,[status(thm)],[f440])).
% 0.17/1.02 fof(f461,plain,(
% 0.17/1.02 ![X1]: (~ssList(X1)|~ssList(X1)|~neq(X1,X1))),
% 0.17/1.02 inference(destructive_equality_resolution,[status(thm)],[f219])).
% 0.17/1.02 fof(f462,plain,(
% 0.17/1.02 ![X0]: (~ssList(X0)|~neq(X0,X0))),
% 0.17/1.02 inference(duplicate_literals_removal,[status(thm)],[f461])).
% 0.17/1.02 fof(f476,plain,(
% 0.17/1.02 ![X0,X1,X2]: (~sP0_prd(X0,X1,X2,tl(X2))|~ssList(tl(X2))|~neq(nil,X2))),
% 0.17/1.02 inference(destructive_equality_resolution,[status(thm)],[f434])).
% 0.17/1.02 fof(f477,plain,(
% 0.17/1.02 ![X0,X1]: (~sP1_prd(tl(X0),X0,X1)|~ssList(tl(X0))|X1=tl(X0)|~neq(nil,X0))),
% 0.17/1.02 inference(destructive_equality_resolution,[status(thm)],[f441])).
% 0.17/1.02 fof(f481,plain,(
% 0.17/1.02 sP0_prd(sK48_skl,sK49_skl,sK48_skl,sK47_skl)|~neq(sK50_skl,nil)),
% 0.17/1.02 inference(forward_demodulation,[status(thm)],[f423,f426])).
% 0.17/1.02 fof(f482,plain,(
% 0.17/1.02 sP0_prd(sK48_skl,sK47_skl,sK48_skl,sK47_skl)|~neq(sK50_skl,nil)),
% 0.17/1.02 inference(forward_demodulation,[status(thm)],[f424,f481])).
% 0.17/1.02 fof(f483,plain,(
% 0.17/1.02 sP0_prd(sK48_skl,sK47_skl,sK48_skl,sK47_skl)|~neq(sK48_skl,nil)),
% 0.17/1.02 inference(forward_demodulation,[status(thm)],[f423,f482])).
% 0.17/1.02 fof(f488,plain,(
% 0.17/1.02 sP0_prd(sK48_skl,sK49_skl,sK48_skl,sK47_skl)|neq(sK48_skl,nil)),
% 0.17/1.02 inference(forward_demodulation,[status(thm)],[f423,f425])).
% 0.17/1.02 fof(f489,plain,(
% 0.17/1.02 sP0_prd(sK48_skl,sK47_skl,sK48_skl,sK47_skl)|neq(sK48_skl,nil)),
% 0.17/1.02 inference(forward_demodulation,[status(thm)],[f424,f488])).
% 0.17/1.02 fof(f490,plain,(
% 0.17/1.02 sP0_prd(sK48_skl,sK47_skl,sK48_skl,sK47_skl)),
% 0.17/1.02 inference(backward_subsumption_resolution,[status(thm)],[f483,f491])).
% 0.17/1.02 fof(f491,plain,(
% 0.17/1.02 neq(sK48_skl,nil)),
% 0.17/1.02 inference(forward_subsumption_resolution,[status(thm)],[f489,f432])).
% 0.17/1.02 fof(f526,plain,(
% 0.17/1.02 nil=sK48_skl|ssList(tl(sK48_skl))),
% 0.17/1.02 inference(resolution,[status(thm)],[f241,f420])).
% 0.17/1.02 fof(f541,plain,(
% 0.17/1.02 ![X0]: (~ssList(X0)|neq(nil,X0)|nil=X0)),
% 0.17/1.02 inference(resolution,[status(thm)],[f220,f223])).
% 0.17/1.02 fof(f548,plain,(
% 0.17/1.02 neq(nil,sK48_skl)|nil=sK48_skl),
% 0.17/1.02 inference(resolution,[status(thm)],[f541,f420])).
% 0.17/1.02 fof(f1598,plain,(
% 0.17/1.03 ![X0]: (sP1_prd(X0,sK48_skl,sK47_skl))),
% 0.17/1.03 inference(resolution,[status(thm)],[f490,f433])).
% 0.17/1.03 fof(f1604,plain,(
% 0.17/1.03 ~ssList(tl(sK48_skl))|sK47_skl=tl(sK48_skl)|~neq(nil,sK48_skl)),
% 0.17/1.03 inference(resolution,[status(thm)],[f477,f1598])).
% 0.17/1.03 fof(f1610,plain,(
% 0.17/1.03 ~ssList(tl(sK48_skl))|sK47_skl=tl(sK48_skl)|nil=sK48_skl),
% 0.17/1.03 inference(resolution,[status(thm)],[f1604,f548])).
% 0.17/1.03 fof(f1611,plain,(
% 0.17/1.03 sK47_skl=tl(sK48_skl)|nil=sK48_skl),
% 0.17/1.03 inference(forward_subsumption_resolution,[status(thm)],[f1610,f526])).
% 0.17/1.03 fof(f2071,plain,(
% 0.17/1.03 ![X0,X1]: (~sP0_prd(X0,X1,sK48_skl,sK47_skl)|~ssList(tl(sK48_skl))|~neq(nil,sK48_skl)|nil=sK48_skl)),
% 0.17/1.03 inference(paramodulation,[status(thm)],[f1611,f476])).
% 0.17/1.03 fof(f2083,plain,(
% 0.17/1.03 ![X0,X1]: (~sP0_prd(X0,X1,sK48_skl,sK47_skl)|~neq(nil,sK48_skl)|nil=sK48_skl)),
% 0.17/1.03 inference(forward_subsumption_resolution,[status(thm)],[f2071,f526])).
% 0.17/1.03 fof(f4184,plain,(
% 0.17/1.03 ![X0,X1]: (~sP0_prd(X0,X1,sK48_skl,sK47_skl)|nil=sK48_skl)),
% 0.17/1.03 inference(forward_subsumption_resolution,[status(thm)],[f2083,f548])).
% 0.17/1.03 fof(f4185,plain,(
% 0.17/1.03 nil=sK48_skl),
% 0.17/1.03 inference(resolution,[status(thm)],[f4184,f490])).
% 0.17/1.03 fof(f4281,plain,(
% 0.17/1.03 neq(nil,nil)),
% 0.17/1.03 inference(backward_demodulation,[status(thm)],[f4185,f491])).
% 0.17/1.03 fof(f4420,plain,(
% 0.17/1.03 ~ssList(nil)),
% 0.17/1.03 inference(resolution,[status(thm)],[f4281,f462])).
% 0.17/1.03 fof(f4422,plain,(
% 0.17/1.03 $false),
% 0.17/1.03 inference(forward_subsumption_resolution,[status(thm)],[f4420,f223])).
% 0.17/1.03 % SZS output end CNFRefutation for theBenchmark.p
% 0.17/1.03 % Elapsed time: 0.429107 seconds
% 0.17/1.03 % CPU time: 3.216522 seconds
% 0.17/1.03 % Total memory used: 160.640 MB
% 0.17/1.03 % Net memory used: 156.908 MB
%------------------------------------------------------------------------------