%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SWC252+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 02:41:58 PM UTC 2026
% Result : Theorem 3.82s 1.14s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC252+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
% 0.13/0.59 % Computer : n001.cluster.edu
% 0.13/0.59 % Model : x86_64 x86_64
% 0.13/0.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.59 % Memory : 8046.5625MB
% 0.13/0.59 % OS : Linux 6.8.0-71-generic
% 0.13/0.59 % CPULimit : 300
% 0.13/0.59 % WCLimit : 300
% 0.13/0.59 % DateTime : Mon Sep 21 08:14:30 UTC 2026
% 0.13/0.59 % CPUTime :
% 0.13/0.61 % Drodi V4.1.1
% 3.82/1.14 % Refutation found
% 3.82/1.14 % SZS status Theorem for theBenchmark: Theorem is valid
% 3.82/1.14 % SZS output start CNFRefutation for theBenchmark
% 3.82/1.14 fof(f17,axiom,(
% 3.82/1.14 ssList(nil) ),
% 3.82/1.14 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.82/1.14 fof(f28,axiom,(
% 3.82/1.14 (! [U] :( ssList(U)=> app(nil,U) = U ) )),
% 3.82/1.14 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.82/1.14 fof(f84,axiom,(
% 3.82/1.14 (! [U] :( ssList(U)=> app(U,nil) = U ) )),
% 3.82/1.14 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.82/1.14 fof(f93,axiom,(
% 3.82/1.14 (! [U] :( ssItem(U)=> (! [V] :( ssItem(V)=> ( lt(U,V)<=> ( U != V& leq(U,V) ) ) ) )) )),
% 3.82/1.14 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.82/1.14 fof(f96,conjecture,(
% 3.82/1.14 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> (! [X] :( ssList(X)=> ( V != X| U != W| nil = U| (? [Y] :( ssItem(Y)& (? [Z] :( ssList(Z)& (? [X1] :( ssList(X1)& app(app(Z,cons(Y,nil)),X1) = U& (! [X2] :( ssItem(X2)=> ( ~ memberP(Z,X2)| ~ memberP(X1,X2)| ~ lt(Y,X2)| leq(Y,X2) ) ) )) )) )))| ( (! [X3] :( ssItem(X3)=> ( cons(X3,nil) != W| ~ memberP(X,X3) ) ))& ( nil != X| nil != W ) ) ) ) )) )) )) )),
% 3.82/1.14 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.82/1.14 fof(f97,negated_conjecture,(
% 3.82/1.14 ~((! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> (! [X] :( ssList(X)=> ( V != X| U != W| nil = U| (? [Y] :( ssItem(Y)& (? [Z] :( ssList(Z)& (? [X1] :( ssList(X1)& app(app(Z,cons(Y,nil)),X1) = U& (! [X2] :( ssItem(X2)=> ( ~ memberP(Z,X2)| ~ memberP(X1,X2)| ~ lt(Y,X2)| leq(Y,X2) ) ) )) )) )))| ( (! [X3] :( ssItem(X3)=> ( cons(X3,nil) != W| ~ memberP(X,X3) ) ))& ( nil != X| nil != W ) ) ) ) )) )) )) ))),
% 3.82/1.14 inference(negated_conjecture,[status(cth)],[f96])).
% 3.82/1.14 fof(f223,plain,(
% 3.82/1.14 ssList(nil)),
% 3.82/1.14 inference(cnf_transformation,[status(thm)],[f17])).
% 3.82/1.14 fof(f248,plain,(
% 3.82/1.14 ![U]: (~ssList(U)|app(nil,U)=U)),
% 3.82/1.14 inference(pre_NNF_transformation,[status(thm)],[f28])).
% 3.82/1.14 fof(f249,plain,(
% 3.82/1.14 ![X0]: (~ssList(X0)|app(nil,X0)=X0)),
% 3.82/1.14 inference(cnf_transformation,[status(thm)],[f248])).
% 3.82/1.14 fof(f388,plain,(
% 3.82/1.14 ![U]: (~ssList(U)|app(U,nil)=U)),
% 3.82/1.14 inference(pre_NNF_transformation,[status(thm)],[f84])).
% 3.82/1.14 fof(f389,plain,(
% 3.82/1.14 ![X0]: (~ssList(X0)|app(X0,nil)=X0)),
% 3.82/1.14 inference(cnf_transformation,[status(thm)],[f388])).
% 3.82/1.14 fof(f406,plain,(
% 3.82/1.14 ![U]: (~ssItem(U)|(![V]: (~ssItem(V)|(lt(U,V)<=>(~U=V&leq(U,V))))))),
% 3.82/1.14 inference(pre_NNF_transformation,[status(thm)],[f93])).
% 3.82/1.14 fof(f407,plain,(
% 3.82/1.14 ![U]: (~ssItem(U)|(![V]: (~ssItem(V)|((~lt(U,V)|(~U=V&leq(U,V)))&(lt(U,V)|(U=V|~leq(U,V)))))))),
% 3.82/1.14 inference(NNF_transformation,[status(thm)],[f406])).
% 3.82/1.14 fof(f409,plain,(
% 3.82/1.14 ![X0,X1]: (~ssItem(X0)|~ssItem(X1)|~lt(X0,X1)|leq(X0,X1))),
% 3.82/1.14 inference(cnf_transformation,[status(thm)],[f407])).
% 3.82/1.14 fof(f415,plain,(
% 3.82/1.14 (?[U]: (ssList(U)&(?[V]: (ssList(V)&(?[W]: (ssList(W)&(?[X]: (ssList(X)&((((V=X&U=W)&~nil=U)&(![Y]: (~ssItem(Y)|(![Z]: (~ssList(Z)|(![X1]: ((~ssList(X1)|~app(app(Z,cons(Y,nil)),X1)=U)|(?[X2]: (ssItem(X2)&(((memberP(Z,X2)&memberP(X1,X2))<(Y,X2))&~leq(Y,X2)))))))))))&((?[X3]: (ssItem(X3)&(cons(X3,nil)=W&memberP(X,X3))))|(nil=X&nil=W)))))))))))),
% 3.82/1.14 inference(pre_NNF_transformation,[status(thm)],[f97])).
% 3.82/1.14 fof(f416,definition,(
% 3.82/1.14 ![W,X,X3]: (sP0_prd(X3,X,W)<=>(ssItem(X3)&(cons(X3,nil)=W&memberP(X,X3))))),
% 3.82/1.14 introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 3.82/1.14 fof(f417,plain,(
% 3.82/1.14 ?[U]: (ssList(U)&(?[V]: (ssList(V)&(?[W]: (ssList(W)&(?[X]: (ssList(X)&((((V=X&U=W)&~nil=U)&(![Y]: (~ssItem(Y)|(![Z]: (~ssList(Z)|(![X1]: ((~ssList(X1)|~app(app(Z,cons(Y,nil)),X1)=U)|(?[X2]: (ssItem(X2)&(((memberP(Z,X2)&memberP(X1,X2))<(Y,X2))&~leq(Y,X2)))))))))))&((?[X3]: sP0_prd(X3,X,W))|(nil=X&nil=W))))))))))),
% 3.82/1.14 inference(formula_renaming,[status(thm)],[f415,f416])).
% 3.82/1.14 fof(f418,plain,(
% 3.82/1.14 (ssList(sK47_skl)&(ssList(sK48_skl)&(ssList(sK49_skl)&(ssList(sK50_skl)&((((sK48_skl=sK50_skl&sK47_skl=sK49_skl)&~nil=sK47_skl)&(![Y]: (~ssItem(Y)|(![Z]: (~ssList(Z)|(![X1]: ((~ssList(X1)|~app(app(Z,cons(Y,nil)),X1)=sK47_skl)|(ssItem(sK51_skl(X1,Z,Y))&(((memberP(Z,sK51_skl(X1,Z,Y))&memberP(X1,sK51_skl(X1,Z,Y)))<(Y,sK51_skl(X1,Z,Y)))&~leq(Y,sK51_skl(X1,Z,Y)))))))))))&(sP0_prd(sK52_skl,sK50_skl,sK49_skl)|(nil=sK50_skl&nil=sK49_skl)))))))),
% 3.82/1.14 inference(skolemize,[status(esa),new_symbols(skolem,[sK47_skl,sK48_skl,sK49_skl,sK50_skl,sK51_skl,sK52_skl]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl),skolemize(X2,sK51_skl(X1,Z,Y)),skolemize(X3,sK52_skl)],[f417])).
% 3.82/1.15 fof(f421,plain,(
% 3.82/1.15 ssList(sK49_skl)),
% 3.82/1.15 inference(cnf_transformation,[status(thm)],[f418])).
% 3.82/1.15 fof(f423,plain,(
% 3.82/1.15 sK48_skl=sK50_skl),
% 3.82/1.15 inference(cnf_transformation,[status(thm)],[f418])).
% 3.82/1.15 fof(f424,plain,(
% 3.82/1.15 sK47_skl=sK49_skl),
% 3.82/1.15 inference(cnf_transformation,[status(thm)],[f418])).
% 3.82/1.15 fof(f425,plain,(
% 3.82/1.15 ~nil=sK47_skl),
% 3.82/1.15 inference(cnf_transformation,[status(thm)],[f418])).
% 3.82/1.15 fof(f426,plain,(
% 3.82/1.15 ![X0,X1,X2]: (~ssItem(X0)|~ssList(X1)|~ssList(X2)|~app(app(X1,cons(X0,nil)),X2)=sK47_skl|ssItem(sK51_skl(X2,X1,X0)))),
% 3.82/1.15 inference(cnf_transformation,[status(thm)],[f418])).
% 3.82/1.15 fof(f429,plain,(
% 3.82/1.15 ![X0,X1,X2]: (~ssItem(X0)|~ssList(X1)|~ssList(X2)|~app(app(X1,cons(X0,nil)),X2)=sK47_skl|lt(X0,sK51_skl(X2,X1,X0)))),
% 3.82/1.15 inference(cnf_transformation,[status(thm)],[f418])).
% 3.82/1.15 fof(f430,plain,(
% 3.82/1.15 ![X0,X1,X2]: (~ssItem(X0)|~ssList(X1)|~ssList(X2)|~app(app(X1,cons(X0,nil)),X2)=sK47_skl|~leq(X0,sK51_skl(X2,X1,X0)))),
% 3.82/1.15 inference(cnf_transformation,[status(thm)],[f418])).
% 3.82/1.15 fof(f432,plain,(
% 3.82/1.15 sP0_prd(sK52_skl,sK50_skl,sK49_skl)|nil=sK49_skl),
% 3.82/1.15 inference(cnf_transformation,[status(thm)],[f418])).
% 3.82/1.15 fof(f433,plain,(
% 3.82/1.15 ![W,X,X3]: ((~sP0_prd(X3,X,W)|(ssItem(X3)&(cons(X3,nil)=W&memberP(X,X3))))&(sP0_prd(X3,X,W)|(~ssItem(X3)|(~cons(X3,nil)=W|~memberP(X,X3)))))),
% 3.82/1.15 inference(NNF_transformation,[status(thm)],[f416])).
% 3.82/1.15 fof(f434,plain,(
% 3.82/1.15 (![W,X,X3]: (~sP0_prd(X3,X,W)|(ssItem(X3)&(cons(X3,nil)=W&memberP(X,X3)))))&(![W,X,X3]: (sP0_prd(X3,X,W)|(~ssItem(X3)|(~cons(X3,nil)=W|~memberP(X,X3)))))),
% 3.82/1.15 inference(miniscoping,[status(thm)],[f433])).
% 3.82/1.15 fof(f435,plain,(
% 3.82/1.15 ![X0,X1,X2]: (~sP0_prd(X0,X1,X2)|ssItem(X0))),
% 3.82/1.15 inference(cnf_transformation,[status(thm)],[f434])).
% 3.82/1.15 fof(f436,plain,(
% 3.82/1.15 ![X0,X1,X2]: (~sP0_prd(X0,X1,X2)|cons(X0,nil)=X2)),
% 3.82/1.15 inference(cnf_transformation,[status(thm)],[f434])).
% 3.82/1.15 fof(f473,plain,(
% 3.82/1.15 ~nil=sK49_skl),
% 3.82/1.15 inference(forward_demodulation,[status(thm)],[f424,f425])).
% 3.82/1.15 fof(f474,plain,(
% 3.82/1.15 ![X0,X1,X2]: (~ssItem(X0)|~ssList(X1)|~ssList(X2)|~app(app(X1,cons(X0,nil)),X2)=sK49_skl|ssItem(sK51_skl(X2,X1,X0)))),
% 3.82/1.15 inference(forward_demodulation,[status(thm)],[f424,f426])).
% 3.82/1.15 fof(f477,plain,(
% 3.82/1.15 ![X0,X1,X2]: (~ssItem(X0)|~ssList(X1)|~ssList(X2)|~app(app(X1,cons(X0,nil)),X2)=sK49_skl|lt(X0,sK51_skl(X2,X1,X0)))),
% 3.82/1.15 inference(forward_demodulation,[status(thm)],[f424,f429])).
% 3.82/1.15 fof(f478,plain,(
% 3.82/1.15 ![X0,X1,X2]: (~ssItem(X0)|~ssList(X1)|~ssList(X2)|~app(app(X1,cons(X0,nil)),X2)=sK49_skl|~leq(X0,sK51_skl(X2,X1,X0)))),
% 3.82/1.15 inference(forward_demodulation,[status(thm)],[f424,f430])).
% 3.82/1.15 fof(f481,plain,(
% 3.82/1.15 sP0_prd(sK52_skl,sK48_skl,sK49_skl)|nil=sK49_skl),
% 3.82/1.15 inference(forward_demodulation,[status(thm)],[f423,f432])).
% 3.82/1.15 fof(f482,plain,(
% 3.82/1.15 sP0_prd(sK52_skl,sK48_skl,sK49_skl)),
% 3.82/1.15 inference(forward_subsumption_resolution,[status(thm)],[f481,f473])).
% 3.82/1.15 fof(f484,plain,(
% 3.82/1.15 app(nil,sK49_skl)=sK49_skl),
% 3.82/1.15 inference(resolution,[status(thm)],[f249,f421])).
% 3.82/1.15 fof(f486,plain,(
% 3.82/1.15 app(sK49_skl,nil)=sK49_skl),
% 3.82/1.15 inference(resolution,[status(thm)],[f389,f421])).
% 3.82/1.15 fof(f500,plain,(
% 3.82/1.15 cons(sK52_skl,nil)=sK49_skl),
% 3.82/1.15 inference(resolution,[status(thm)],[f482,f436])).
% 3.82/1.15 fof(f502,plain,(
% 3.82/1.15 ssItem(sK52_skl)),
% 3.82/1.15 inference(resolution,[status(thm)],[f482,f435])).
% 3.82/1.15 fof(f915,plain,(
% 3.82/1.15 ![X0,X1,X2]: (~ssItem(X0)|~ssItem(sK51_skl(X1,X2,X0))|leq(X0,sK51_skl(X1,X2,X0))|~ssItem(X0)|~ssList(X2)|~ssList(X1)|~app(app(X2,cons(X0,nil)),X1)=sK49_skl)),
% 3.82/1.15 inference(resolution,[status(thm)],[f409,f477])).
% 3.82/1.15 fof(f916,plain,(
% 3.82/1.15 ![X0,X1,X2]: (~ssItem(X0)|~ssItem(sK51_skl(X1,X2,X0))|leq(X0,sK51_skl(X1,X2,X0))|~ssList(X2)|~ssList(X1)|~app(app(X2,cons(X0,nil)),X1)=sK49_skl)),
% 3.82/1.15 inference(duplicate_literals_removal,[status(thm)],[f915])).
% 3.82/1.15 fof(f917,plain,(
% 3.82/1.15 ![X0,X1,X2]: (~ssItem(X0)|~ssList(X1)|~ssList(X2)|~app(app(X1,cons(X0,nil)),X2)=sK49_skl)),
% 3.82/1.15 inference(backward_subsumption_resolution,[status(thm)],[f478,f918])).
% 3.82/1.15 fof(f918,plain,(
% 3.82/1.15 ![X0,X1,X2]: (~ssItem(X0)|leq(X0,sK51_skl(X1,X2,X0))|~ssList(X2)|~ssList(X1)|~app(app(X2,cons(X0,nil)),X1)=sK49_skl)),
% 3.82/1.16 inference(forward_subsumption_resolution,[status(thm)],[f916,f474])).
% 3.82/1.16 fof(f1014,plain,(
% 3.82/1.16 ![X0,X1]: (~ssList(X0)|~ssList(X1)|~app(app(X0,cons(sK52_skl,nil)),X1)=sK49_skl)),
% 3.82/1.16 inference(resolution,[status(thm)],[f917,f502])).
% 3.82/1.16 fof(f1017,plain,(
% 3.82/1.16 ![X0,X1]: (~ssList(X0)|~ssList(X1)|~app(app(X0,sK49_skl),X1)=sK49_skl)),
% 3.82/1.16 inference(forward_demodulation,[status(thm)],[f500,f1014])).
% 3.82/1.16 fof(f1130,plain,(
% 3.82/1.16 ![X0]: (~ssList(X0)|~app(app(X0,sK49_skl),nil)=sK49_skl)),
% 3.82/1.16 inference(resolution,[status(thm)],[f1017,f223])).
% 3.82/1.16 fof(f1136,plain,(
% 3.82/1.16 ~app(app(nil,sK49_skl),nil)=sK49_skl),
% 3.82/1.16 inference(resolution,[status(thm)],[f1130,f223])).
% 3.82/1.16 fof(f1139,plain,(
% 3.82/1.16 ~app(sK49_skl,nil)=sK49_skl),
% 3.82/1.16 inference(forward_demodulation,[status(thm)],[f484,f1136])).
% 3.82/1.16 fof(f1140,plain,(
% 3.82/1.16 ~sK49_skl=sK49_skl),
% 3.82/1.16 inference(forward_demodulation,[status(thm)],[f486,f1139])).
% 3.82/1.16 fof(f1141,plain,(
% 3.82/1.16 $false),
% 3.82/1.16 inference(trivial_equality_resolution,[status(thm)],[f1140])).
% 3.82/1.16 % SZS output end CNFRefutation for theBenchmark.p
% 3.82/1.17 % Elapsed time: 0.566642 seconds
% 3.82/1.17 % CPU time: 4.148672 seconds
% 3.82/1.17 % Total memory used: 161.819 MB
% 3.82/1.17 % Net memory used: 157.930 MB
%------------------------------------------------------------------------------