%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SWC025+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 : n011.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 43.70s 5.98s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC025+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
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Mon Sep 21 07:49:40 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.13/0.36 % Drodi V4.1.1
% 43.70/5.98 % Refutation found
% 43.70/5.98 % SZS status Theorem for theBenchmark: Theorem is valid
% 43.70/5.98 % SZS output start CNFRefutation for theBenchmark
% 43.70/5.98 fof(f20,axiom,(
% 43.70/5.98 (! [U] :( ssList(U)=> ( nil = U| (? [V] :( ssList(V)& (? [W] :( ssItem(W)& cons(W,V) = U ) )) )) ) )),
% 43.70/5.98 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 43.70/5.98 fof(f22,axiom,(
% 43.70/5.98 (! [U] :( ssList(U)=> ( nil != U=> ssItem(hd(U)) ) ) )),
% 43.70/5.98 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 43.70/5.98 fof(f24,axiom,(
% 43.70/5.98 (! [U] :( ssList(U)=> ( nil != U=> ssList(tl(U)) ) ) )),
% 43.70/5.98 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 43.70/5.98 fof(f37,axiom,(
% 43.70/5.98 (! [U] :( ssItem(U)=> (! [V] :( ssItem(V)=> (! [W] :( ssList(W)=> ( memberP(cons(V,W),U)<=> ( U = V| memberP(W,U) ) ) ) )) )) )),
% 43.70/5.98 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 43.70/5.98 fof(f38,axiom,(
% 43.70/5.98 (! [U] :( ssItem(U)=> ~ memberP(nil,U) ) )),
% 43.70/5.98 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 43.70/5.98 fof(f78,axiom,(
% 43.70/5.98 (! [U] :( ssList(U)=> ( nil != U=> cons(hd(U),tl(U)) = U ) ) )),
% 43.70/5.98 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 43.70/5.98 fof(f96,conjecture,(
% 43.70/5.98 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> (! [X] :( ssList(X)=> ( V != X| U != W| ~ duplicatefreeP(W)| (? [Y] :( ssItem(Y)& ( ( ~ memberP(X,Y)& memberP(W,Y) )| ( ~ memberP(W,Y)& memberP(X,Y) ) ) ))| ( ( nil != V| nil = U )& ( nil != U| nil = V ) ) ) ) )) )) )) )),
% 43.70/5.98 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 43.70/5.98 fof(f97,negated_conjecture,(
% 43.70/5.98 ~((! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> (! [X] :( ssList(X)=> ( V != X| U != W| ~ duplicatefreeP(W)| (? [Y] :( ssItem(Y)& ( ( ~ memberP(X,Y)& memberP(W,Y) )| ( ~ memberP(W,Y)& memberP(X,Y) ) ) ))| ( ( nil != V| nil = U )& ( nil != U| nil = V ) ) ) ) )) )) )) ))),
% 43.70/5.98 inference(negated_conjecture,[status(cth)],[f96])).
% 43.70/5.98 fof(f229,plain,(
% 43.70/5.98 ![U]: (~ssList(U)|(nil=U|(?[V]: (ssList(V)&(?[W]: (ssItem(W)&cons(W,V)=U))))))),
% 43.70/5.98 inference(pre_NNF_transformation,[status(thm)],[f20])).
% 43.70/5.98 fof(f230,plain,(
% 43.70/5.98 ![U]: (~ssList(U)|(nil=U|(ssList(sK43_skl(U))&(ssItem(sK44_skl(U))&cons(sK44_skl(U),sK43_skl(U))=U))))),
% 43.70/5.98 inference(skolemize,[status(esa),new_symbols(skolem,[sK43_skl,sK44_skl]),skolemize(V,sK43_skl(U)),skolemize(W,sK44_skl(U))],[f229])).
% 43.70/5.98 fof(f231,plain,(
% 43.70/5.98 ![X0]: (~ssList(X0)|nil=X0|ssList(sK43_skl(X0)))),
% 43.70/5.98 inference(cnf_transformation,[status(thm)],[f230])).
% 43.70/5.98 fof(f232,plain,(
% 43.70/5.98 ![X0]: (~ssList(X0)|nil=X0|ssItem(sK44_skl(X0)))),
% 43.70/5.98 inference(cnf_transformation,[status(thm)],[f230])).
% 43.70/5.98 fof(f233,plain,(
% 43.70/5.98 ![X0]: (~ssList(X0)|nil=X0|cons(sK44_skl(X0),sK43_skl(X0))=X0)),
% 43.70/5.98 inference(cnf_transformation,[status(thm)],[f230])).
% 43.70/5.98 fof(f236,plain,(
% 43.70/5.98 ![U]: (~ssList(U)|(nil=U|ssItem(hd(U))))),
% 43.70/5.98 inference(pre_NNF_transformation,[status(thm)],[f22])).
% 43.70/5.98 fof(f237,plain,(
% 43.70/5.98 ![X0]: (~ssList(X0)|nil=X0|ssItem(hd(X0)))),
% 43.70/5.98 inference(cnf_transformation,[status(thm)],[f236])).
% 43.70/5.98 fof(f240,plain,(
% 43.70/5.98 ![U]: (~ssList(U)|(nil=U|ssList(tl(U))))),
% 43.70/5.98 inference(pre_NNF_transformation,[status(thm)],[f24])).
% 43.70/5.98 fof(f241,plain,(
% 43.70/5.98 ![X0]: (~ssList(X0)|nil=X0|ssList(tl(X0)))),
% 43.70/5.98 inference(cnf_transformation,[status(thm)],[f240])).
% 43.70/5.98 fof(f273,plain,(
% 43.70/5.98 ![U]: (~ssItem(U)|(![V]: (~ssItem(V)|(![W]: (~ssList(W)|(memberP(cons(V,W),U)<=>(U=V|memberP(W,U))))))))),
% 43.70/5.98 inference(pre_NNF_transformation,[status(thm)],[f37])).
% 43.70/5.98 fof(f274,plain,(
% 43.70/5.98 ![U]: (~ssItem(U)|(![V]: (~ssItem(V)|(![W]: (~ssList(W)|((~memberP(cons(V,W),U)|(U=V|memberP(W,U)))&(memberP(cons(V,W),U)|(~U=V&~memberP(W,U)))))))))),
% 43.70/5.98 inference(NNF_transformation,[status(thm)],[f273])).
% 43.70/5.98 fof(f276,plain,(
% 43.70/5.98 ![X0,X1,X2]: (~ssItem(X0)|~ssItem(X1)|~ssList(X2)|memberP(cons(X1,X2),X0)|~X0=X1)),
% 43.70/5.98 inference(cnf_transformation,[status(thm)],[f274])).
% 43.70/5.98 fof(f278,plain,(
% 43.70/5.98 ![U]: (~ssItem(U)|~memberP(nil,U))),
% 43.70/5.98 inference(pre_NNF_transformation,[status(thm)],[f38])).
% 43.70/5.98 fof(f279,plain,(
% 43.70/5.98 ![X0]: (~ssItem(X0)|~memberP(nil,X0))),
% 43.70/5.98 inference(cnf_transformation,[status(thm)],[f278])).
% 43.70/5.98 fof(f373,plain,(
% 43.70/5.98 ![U]: (~ssList(U)|(nil=U|cons(hd(U),tl(U))=U))),
% 43.70/5.98 inference(pre_NNF_transformation,[status(thm)],[f78])).
% 43.70/5.98 fof(f374,plain,(
% 43.70/5.98 ![X0]: (~ssList(X0)|nil=X0|cons(hd(X0),tl(X0))=X0)),
% 43.70/5.98 inference(cnf_transformation,[status(thm)],[f373])).
% 43.70/5.98 fof(f415,plain,(
% 43.70/5.98 (?[U]: (ssList(U)&(?[V]: (ssList(V)&(?[W]: (ssList(W)&(?[X]: (ssList(X)&((((V=X&U=W)&duplicatefreeP(W))&(![Y]: (~ssItem(Y)|((memberP(X,Y)|~memberP(W,Y))&(memberP(W,Y)|~memberP(X,Y))))))&((nil=V&~nil=U)|(nil=U&~nil=V)))))))))))),
% 43.70/5.98 inference(pre_NNF_transformation,[status(thm)],[f97])).
% 43.70/5.98 fof(f416,definition,(
% 43.70/5.98 ![U,V]: (sP0_prd(V,U)<=>(nil=V&~nil=U))),
% 43.70/5.98 introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 43.70/5.98 fof(f417,plain,(
% 43.70/5.98 ?[U]: (ssList(U)&(?[V]: (ssList(V)&(?[W]: (ssList(W)&(?[X]: (ssList(X)&((((V=X&U=W)&duplicatefreeP(W))&(![Y]: (~ssItem(Y)|((memberP(X,Y)|~memberP(W,Y))&(memberP(W,Y)|~memberP(X,Y))))))&(sP0_prd(V,U)|(nil=U&~nil=V))))))))))),
% 43.70/5.98 inference(formula_renaming,[status(thm)],[f415,f416])).
% 43.70/5.98 fof(f418,plain,(
% 43.70/5.98 (ssList(sK47_skl)&(ssList(sK48_skl)&(ssList(sK49_skl)&(ssList(sK50_skl)&((((sK48_skl=sK50_skl&sK47_skl=sK49_skl)&duplicatefreeP(sK49_skl))&(![Y]: (~ssItem(Y)|((memberP(sK50_skl,Y)|~memberP(sK49_skl,Y))&(memberP(sK49_skl,Y)|~memberP(sK50_skl,Y))))))&(sP0_prd(sK48_skl,sK47_skl)|(nil=sK47_skl&~nil=sK48_skl)))))))),
% 43.70/5.98 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])).
% 43.70/5.98 fof(f419,plain,(
% 43.70/5.98 ssList(sK47_skl)),
% 43.70/5.98 inference(cnf_transformation,[status(thm)],[f418])).
% 43.70/5.98 fof(f420,plain,(
% 43.70/5.98 ssList(sK48_skl)),
% 43.70/5.98 inference(cnf_transformation,[status(thm)],[f418])).
% 43.70/5.98 fof(f423,plain,(
% 43.70/5.98 sK48_skl=sK50_skl),
% 43.70/5.98 inference(cnf_transformation,[status(thm)],[f418])).
% 43.70/5.98 fof(f424,plain,(
% 43.70/5.98 sK47_skl=sK49_skl),
% 43.70/5.98 inference(cnf_transformation,[status(thm)],[f418])).
% 43.70/5.98 fof(f426,plain,(
% 43.70/5.98 ![X0]: (~ssItem(X0)|memberP(sK50_skl,X0)|~memberP(sK49_skl,X0))),
% 43.70/5.98 inference(cnf_transformation,[status(thm)],[f418])).
% 43.70/5.98 fof(f427,plain,(
% 43.70/5.98 ![X0]: (~ssItem(X0)|memberP(sK49_skl,X0)|~memberP(sK50_skl,X0))),
% 43.70/5.98 inference(cnf_transformation,[status(thm)],[f418])).
% 43.70/5.98 fof(f428,plain,(
% 43.70/5.98 sP0_prd(sK48_skl,sK47_skl)|nil=sK47_skl),
% 43.70/5.98 inference(cnf_transformation,[status(thm)],[f418])).
% 43.70/5.98 fof(f429,plain,(
% 43.70/5.98 sP0_prd(sK48_skl,sK47_skl)|~nil=sK48_skl),
% 43.70/5.98 inference(cnf_transformation,[status(thm)],[f418])).
% 43.70/5.98 fof(f430,plain,(
% 43.70/5.98 ![U,V]: ((~sP0_prd(V,U)|(nil=V&~nil=U))&(sP0_prd(V,U)|(~nil=V|nil=U)))),
% 43.70/5.98 inference(NNF_transformation,[status(thm)],[f416])).
% 43.70/5.98 fof(f431,plain,(
% 43.70/5.98 (![U,V]: (~sP0_prd(V,U)|(nil=V&~nil=U)))&(![U,V]: (sP0_prd(V,U)|(~nil=V|nil=U)))),
% 43.70/5.98 inference(miniscoping,[status(thm)],[f430])).
% 43.70/5.98 fof(f432,plain,(
% 43.70/5.98 ![X0,X1]: (~sP0_prd(X0,X1)|nil=X0)),
% 43.70/5.98 inference(cnf_transformation,[status(thm)],[f431])).
% 43.70/5.98 fof(f433,plain,(
% 43.70/5.98 ![X0,X1]: (~sP0_prd(X0,X1)|~nil=X1)),
% 43.70/5.98 inference(cnf_transformation,[status(thm)],[f431])).
% 43.70/5.98 fof(f454,plain,(
% 43.70/5.98 ![X1,X2]: (~ssItem(X1)|~ssItem(X1)|~ssList(X2)|memberP(cons(X1,X2),X1))),
% 43.70/5.98 inference(destructive_equality_resolution,[status(thm)],[f276])).
% 43.70/5.98 fof(f455,plain,(
% 43.70/5.98 ![X0,X1]: (~ssItem(X0)|~ssList(X1)|memberP(cons(X0,X1),X0))),
% 43.70/5.98 inference(duplicate_literals_removal,[status(thm)],[f454])).
% 43.70/5.98 fof(f470,plain,(
% 43.70/5.98 ![X0]: (~ssItem(X0)|memberP(sK48_skl,X0)|~memberP(sK49_skl,X0))),
% 43.70/5.98 inference(forward_demodulation,[status(thm)],[f423,f426])).
% 43.70/5.98 fof(f471,plain,(
% 43.70/5.98 ![X0]: (~ssItem(X0)|memberP(sK48_skl,X0)|~memberP(sK47_skl,X0))),
% 43.70/5.98 inference(forward_demodulation,[status(thm)],[f424,f470])).
% 43.70/5.98 fof(f472,plain,(
% 43.70/5.98 ![X0]: (~ssItem(X0)|memberP(sK47_skl,X0)|~memberP(sK50_skl,X0))),
% 43.70/5.98 inference(forward_demodulation,[status(thm)],[f424,f427])).
% 43.70/5.98 fof(f473,plain,(
% 43.70/5.98 ![X0]: (~ssItem(X0)|memberP(sK47_skl,X0)|~memberP(sK48_skl,X0))),
% 43.70/5.98 inference(forward_demodulation,[status(thm)],[f423,f472])).
% 43.70/5.98 fof(f474,plain,(
% 43.70/5.98 ![X0]: (~sP0_prd(X0,nil))),
% 43.70/5.98 inference(destructive_equality_resolution,[status(thm)],[f433])).
% 43.70/5.98 fof(f479,plain,(
% 43.70/5.98 nil=sK47_skl|nil=sK48_skl),
% 43.70/5.98 inference(resolution,[status(thm)],[f428,f432])).
% 43.70/5.98 fof(f485,plain,(
% 43.70/5.98 ![X0]: (~ssItem(X0)|memberP(nil,X0)|~memberP(sK47_skl,X0)|nil=sK47_skl)),
% 43.70/5.98 inference(paramodulation,[status(thm)],[f479,f471])).
% 43.70/5.98 fof(f488,plain,(
% 43.70/5.98 ![X0]: (~ssItem(X0)|~memberP(sK47_skl,X0)|nil=sK47_skl)),
% 43.70/5.98 inference(forward_subsumption_resolution,[status(thm)],[f485,f279])).
% 43.70/6.01 fof(f1583,plain,(
% 43.70/6.01 nil=sK47_skl|cons(sK44_skl(sK47_skl),sK43_skl(sK47_skl))=sK47_skl),
% 43.70/6.01 inference(resolution,[status(thm)],[f233,f419])).
% 43.70/6.01 fof(f1885,plain,(
% 43.70/6.01 ~ssItem(sK44_skl(sK47_skl))|~ssList(sK43_skl(sK47_skl))|memberP(sK47_skl,sK44_skl(sK47_skl))|nil=sK47_skl),
% 43.70/6.01 inference(paramodulation,[status(thm)],[f1583,f455])).
% 43.70/6.01 fof(f1890,plain,(
% 43.70/6.01 ~ssItem(sK44_skl(sK47_skl))|~ssList(sK43_skl(sK47_skl))|nil=sK47_skl),
% 43.70/6.01 inference(forward_subsumption_resolution,[status(thm)],[f1885,f488])).
% 43.70/6.01 fof(f3029,plain,(
% 43.70/6.01 nil=sK48_skl|cons(hd(sK48_skl),tl(sK48_skl))=sK48_skl),
% 43.70/6.01 inference(resolution,[status(thm)],[f374,f420])).
% 43.70/6.01 fof(f3229,plain,(
% 43.70/6.01 ~ssItem(hd(sK48_skl))|~ssList(tl(sK48_skl))|memberP(sK48_skl,hd(sK48_skl))|nil=sK48_skl),
% 43.70/6.01 inference(paramodulation,[status(thm)],[f3029,f455])).
% 43.70/6.01 fof(f3838,plain,(
% 43.70/6.01 ~ssItem(sK44_skl(sK47_skl))|nil=sK47_skl|~ssList(sK47_skl)|nil=sK47_skl),
% 43.70/6.01 inference(resolution,[status(thm)],[f1890,f231])).
% 43.70/6.01 fof(f3839,plain,(
% 43.70/6.01 ~ssItem(sK44_skl(sK47_skl))|nil=sK47_skl|~ssList(sK47_skl)),
% 43.70/6.01 inference(duplicate_literals_removal,[status(thm)],[f3838])).
% 43.70/6.01 fof(f3840,plain,(
% 43.70/6.01 nil=sK47_skl|~ssList(sK47_skl)),
% 43.70/6.01 inference(forward_subsumption_resolution,[status(thm)],[f3839,f232])).
% 43.70/6.01 fof(f3845,plain,(
% 43.70/6.01 nil=sK47_skl),
% 43.70/6.01 inference(resolution,[status(thm)],[f3840,f419])).
% 43.70/6.01 fof(f3943,plain,(
% 43.70/6.01 ![X0]: (~ssItem(X0)|memberP(nil,X0)|~memberP(sK48_skl,X0))),
% 43.70/6.01 inference(backward_demodulation,[status(thm)],[f3845,f473])).
% 43.70/6.01 fof(f3944,plain,(
% 43.70/6.01 sP0_prd(sK48_skl,nil)|~nil=sK48_skl),
% 43.70/6.01 inference(backward_demodulation,[status(thm)],[f3845,f429])).
% 43.70/6.01 fof(f4503,plain,(
% 43.70/6.01 ~ssItem(hd(sK48_skl))|~ssList(tl(sK48_skl))|nil=sK48_skl),
% 43.70/6.01 inference(backward_subsumption_resolution,[status(thm)],[f3229,f4511])).
% 43.70/6.01 fof(f4511,plain,(
% 43.70/6.01 ![X0]: (~ssItem(X0)|~memberP(sK48_skl,X0))),
% 43.70/6.01 inference(forward_subsumption_resolution,[status(thm)],[f3943,f279])).
% 43.70/6.01 fof(f4606,plain,(
% 43.70/6.01 ~nil=sK48_skl),
% 43.70/6.01 inference(forward_subsumption_resolution,[status(thm)],[f3944,f474])).
% 43.70/6.01 fof(f4930,plain,(
% 43.70/6.01 ~ssItem(hd(sK48_skl))|~ssList(tl(sK48_skl))),
% 43.70/6.01 inference(forward_subsumption_resolution,[status(thm)],[f4503,f4606])).
% 43.70/6.01 fof(f5249,plain,(
% 43.70/6.01 ~ssItem(hd(sK48_skl))|~ssList(sK48_skl)|nil=sK48_skl),
% 43.70/6.01 inference(resolution,[status(thm)],[f4930,f241])).
% 43.70/6.01 fof(f5250,plain,(
% 43.70/6.01 ~ssList(sK48_skl)|nil=sK48_skl),
% 43.70/6.01 inference(forward_subsumption_resolution,[status(thm)],[f5249,f237])).
% 43.70/6.01 fof(f5251,plain,(
% 43.70/6.01 nil=sK48_skl),
% 43.70/6.01 inference(resolution,[status(thm)],[f5250,f420])).
% 43.70/6.01 fof(f5252,plain,(
% 43.70/6.01 $false),
% 43.70/6.01 inference(forward_subsumption_resolution,[status(thm)],[f5251,f4606])).
% 43.70/6.01 % SZS output end CNFRefutation for theBenchmark.p
% 29.52/6.03 % Elapsed time: 5.679109 seconds
% 29.52/6.03 % CPU time: 44.651349 seconds
% 29.52/6.03 % Total memory used: 426.357 MB
% 29.52/6.03 % Net memory used: 403.951 MB
%------------------------------------------------------------------------------