%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SWC239+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 : n010.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 02:41:56 PM UTC 2026
% Result : Theorem 3.88s 0.98s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC239+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n010.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 21 08:07:54 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.37 % Drodi V4.1.1
% 3.88/0.98 % Refutation found
% 3.88/0.98 % SZS status Theorem for theBenchmark: Theorem is valid
% 3.88/0.98 % SZS output start CNFRefutation for theBenchmark
% 3.88/0.98 fof(f17,axiom,(
% 3.88/0.98 ssList(nil) ),
% 3.88/0.98 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 3.88/0.98 fof(f28,axiom,(
% 3.88/0.98 (! [U] :( ssList(U)=> app(nil,U) = U ) )),
% 3.88/0.98 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 3.88/0.98 fof(f38,axiom,(
% 3.88/0.98 (! [U] :( ssItem(U)=> ~ memberP(nil,U) ) )),
% 3.88/0.98 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 3.88/0.98 fof(f84,axiom,(
% 3.88/0.98 (! [U] :( ssList(U)=> app(U,nil) = U ) )),
% 3.88/0.98 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 3.88/0.98 fof(f96,conjecture,(
% 3.88/0.98 (! [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)| (? [X4] :( ssItem(X4)& X3 != X4& memberP(X,X4)& leq(X3,X4) ) )) ))& ( nil != X| nil != W ) ) ) ) )) )) )) )),
% 3.88/0.98 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 3.88/0.98 fof(f97,negated_conjecture,(
% 3.88/0.98 ~((! [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)| (? [X4] :( ssItem(X4)& X3 != X4& memberP(X,X4)& leq(X3,X4) ) )) ))& ( nil != X| nil != W ) ) ) ) )) )) )) ))),
% 3.88/0.98 inference(negated_conjecture,[status(cth)],[f96])).
% 3.88/0.98 fof(f223,plain,(
% 3.88/0.98 ssList(nil)),
% 3.88/0.98 inference(cnf_transformation,[status(thm)],[f17])).
% 3.88/0.98 fof(f248,plain,(
% 3.88/0.98 ![U]: (~ssList(U)|app(nil,U)=U)),
% 3.88/0.98 inference(pre_NNF_transformation,[status(thm)],[f28])).
% 3.88/0.98 fof(f249,plain,(
% 3.88/0.98 ![X0]: (~ssList(X0)|app(nil,X0)=X0)),
% 3.88/0.98 inference(cnf_transformation,[status(thm)],[f248])).
% 3.88/0.98 fof(f278,plain,(
% 3.88/0.98 ![U]: (~ssItem(U)|~memberP(nil,U))),
% 3.88/0.98 inference(pre_NNF_transformation,[status(thm)],[f38])).
% 3.88/0.98 fof(f279,plain,(
% 3.88/0.98 ![X0]: (~ssItem(X0)|~memberP(nil,X0))),
% 3.88/0.98 inference(cnf_transformation,[status(thm)],[f278])).
% 3.88/0.98 fof(f388,plain,(
% 3.88/0.98 ![U]: (~ssList(U)|app(U,nil)=U)),
% 3.88/0.98 inference(pre_NNF_transformation,[status(thm)],[f84])).
% 3.88/0.98 fof(f389,plain,(
% 3.88/0.98 ![X0]: (~ssList(X0)|app(X0,nil)=X0)),
% 3.88/0.98 inference(cnf_transformation,[status(thm)],[f388])).
% 3.88/0.98 fof(f415,plain,(
% 3.88/0.98 (?[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))&(![X4]: (((~ssItem(X4)|X3=X4)|~memberP(X,X4))|~leq(X3,X4))))))|(nil=X&nil=W)))))))))))),
% 3.88/0.98 inference(pre_NNF_transformation,[status(thm)],[f97])).
% 3.88/0.98 fof(f416,definition,(
% 3.88/0.98 ![W,X,X3]: (sP0_prd(X3,X,W)<=>(ssItem(X3)&((cons(X3,nil)=W&memberP(X,X3))&(![X4]: (((~ssItem(X4)|X3=X4)|~memberP(X,X4))|~leq(X3,X4))))))),
% 3.88/0.98 introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 3.88/0.98 fof(f417,plain,(
% 3.88/0.98 ?[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))))))))))),
% 3.88/0.98 inference(formula_renaming,[status(thm)],[f415,f416])).
% 3.88/0.98 fof(f418,plain,(
% 3.88/0.98 (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)))))))),
% 3.88/0.98 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])).
% 3.88/0.98 fof(f419,plain,(
% 3.88/0.98 ssList(sK47_skl)),
% 3.88/0.98 inference(cnf_transformation,[status(thm)],[f418])).
% 3.88/0.98 fof(f423,plain,(
% 3.88/0.98 sK48_skl=sK50_skl),
% 3.88/0.98 inference(cnf_transformation,[status(thm)],[f418])).
% 3.88/0.98 fof(f424,plain,(
% 3.88/0.98 sK47_skl=sK49_skl),
% 3.88/0.98 inference(cnf_transformation,[status(thm)],[f418])).
% 3.88/0.98 fof(f425,plain,(
% 3.88/0.98 ~nil=sK47_skl),
% 3.88/0.98 inference(cnf_transformation,[status(thm)],[f418])).
% 3.88/0.98 fof(f426,plain,(
% 3.88/0.98 ![X0,X1,X2]: (~ssItem(X0)|~ssList(X1)|~ssList(X2)|~app(app(X1,cons(X0,nil)),X2)=sK47_skl|ssItem(sK51_skl(X2,X1,X0)))),
% 3.88/0.98 inference(cnf_transformation,[status(thm)],[f418])).
% 3.88/0.98 fof(f427,plain,(
% 3.88/0.98 ![X0,X1,X2]: (~ssItem(X0)|~ssList(X1)|~ssList(X2)|~app(app(X1,cons(X0,nil)),X2)=sK47_skl|memberP(X1,sK51_skl(X2,X1,X0)))),
% 3.88/0.98 inference(cnf_transformation,[status(thm)],[f418])).
% 3.88/0.98 fof(f432,plain,(
% 3.88/0.98 sP0_prd(sK52_skl,sK50_skl,sK49_skl)|nil=sK49_skl),
% 3.88/0.98 inference(cnf_transformation,[status(thm)],[f418])).
% 3.88/0.98 fof(f433,plain,(
% 3.88/0.98 ![W,X,X3]: ((~sP0_prd(X3,X,W)|(ssItem(X3)&((cons(X3,nil)=W&memberP(X,X3))&(![X4]: (((~ssItem(X4)|X3=X4)|~memberP(X,X4))|~leq(X3,X4))))))&(sP0_prd(X3,X,W)|(~ssItem(X3)|((~cons(X3,nil)=W|~memberP(X,X3))|(?[X4]: (((ssItem(X4)&~X3=X4)&memberP(X,X4))&leq(X3,X4)))))))),
% 3.88/0.98 inference(NNF_transformation,[status(thm)],[f416])).
% 3.88/0.98 fof(f434,plain,(
% 3.88/0.98 (![W,X,X3]: (~sP0_prd(X3,X,W)|(ssItem(X3)&((cons(X3,nil)=W&memberP(X,X3))&(![X4]: (((~ssItem(X4)|X3=X4)|~memberP(X,X4))|~leq(X3,X4)))))))&(![W,X,X3]: (sP0_prd(X3,X,W)|(~ssItem(X3)|((~cons(X3,nil)=W|~memberP(X,X3))|(?[X4]: (((ssItem(X4)&~X3=X4)&memberP(X,X4))&leq(X3,X4)))))))),
% 3.88/0.98 inference(miniscoping,[status(thm)],[f433])).
% 3.88/0.98 fof(f435,plain,(
% 3.88/0.98 (![W,X,X3]: (~sP0_prd(X3,X,W)|(ssItem(X3)&((cons(X3,nil)=W&memberP(X,X3))&(![X4]: (((~ssItem(X4)|X3=X4)|~memberP(X,X4))|~leq(X3,X4)))))))&(![W,X,X3]: (sP0_prd(X3,X,W)|(~ssItem(X3)|((~cons(X3,nil)=W|~memberP(X,X3))|(((ssItem(sK53_skl(X3,X,W))&~X3=sK53_skl(X3,X,W))&memberP(X,sK53_skl(X3,X,W)))&leq(X3,sK53_skl(X3,X,W)))))))),
% 3.88/0.98 inference(skolemize,[status(esa),new_symbols(skolem,[sK53_skl]),skolemize(X4,sK53_skl(X3,X,W))],[f434])).
% 3.88/0.98 fof(f436,plain,(
% 3.88/0.98 ![X0,X1,X2]: (~sP0_prd(X0,X1,X2)|ssItem(X0))),
% 3.88/0.98 inference(cnf_transformation,[status(thm)],[f435])).
% 3.88/0.98 fof(f437,plain,(
% 3.88/0.98 ![X0,X1,X2]: (~sP0_prd(X0,X1,X2)|cons(X0,nil)=X2)),
% 3.88/0.98 inference(cnf_transformation,[status(thm)],[f435])).
% 3.88/0.98 fof(f506,plain,(
% 3.88/0.98 ![X0,X1]: (~ssItem(sK51_skl(X0,nil,X1))|~ssItem(X1)|~ssList(nil)|~ssList(X0)|~app(app(nil,cons(X1,nil)),X0)=sK47_skl)),
% 3.88/0.98 inference(resolution,[status(thm)],[f279,f427])).
% 3.88/0.98 fof(f507,plain,(
% 3.88/0.98 ![X0,X1]: (~ssItem(X0)|~ssList(nil)|~ssList(X1)|~app(app(nil,cons(X0,nil)),X1)=sK47_skl)),
% 3.88/0.98 inference(forward_subsumption_resolution,[status(thm)],[f506,f426])).
% 3.88/0.98 fof(f516,plain,(
% 3.88/0.98 app(nil,sK47_skl)=sK47_skl),
% 3.88/0.98 inference(resolution,[status(thm)],[f249,f419])).
% 3.88/0.98 fof(f626,plain,(
% 3.88/0.98 app(sK47_skl,nil)=sK47_skl),
% 3.88/0.98 inference(resolution,[status(thm)],[f389,f419])).
% 3.88/0.98 fof(f720,plain,(
% 3.88/0.98 sP0_prd(sK52_skl,sK48_skl,sK49_skl)|nil=sK49_skl),
% 3.88/0.98 inference(forward_demodulation,[status(thm)],[f423,f432])).
% 3.88/0.98 fof(f721,plain,(
% 3.88/0.98 sP0_prd(sK52_skl,sK48_skl,sK47_skl)|nil=sK49_skl),
% 3.88/0.98 inference(forward_demodulation,[status(thm)],[f424,f720])).
% 3.88/0.98 fof(f722,plain,(
% 3.88/0.98 sP0_prd(sK52_skl,sK48_skl,sK47_skl)|nil=sK47_skl),
% 3.88/0.98 inference(forward_demodulation,[status(thm)],[f424,f721])).
% 3.88/0.98 fof(f723,plain,(
% 3.88/0.98 sP0_prd(sK52_skl,sK48_skl,sK47_skl)),
% 3.88/0.98 inference(forward_subsumption_resolution,[status(thm)],[f722,f425])).
% 3.88/0.98 fof(f724,plain,(
% 3.88/0.98 ssItem(sK52_skl)),
% 3.88/0.98 inference(resolution,[status(thm)],[f723,f436])).
% 3.88/0.98 fof(f725,plain,(
% 3.88/0.98 cons(sK52_skl,nil)=sK47_skl),
% 3.88/0.98 inference(resolution,[status(thm)],[f437,f723])).
% 3.88/0.98 fof(f1352,plain,(
% 3.88/0.98 ![X0,X1]: (~ssItem(X0)|~ssList(X1)|~app(app(nil,cons(X0,nil)),X1)=sK47_skl)),
% 3.88/0.98 inference(forward_subsumption_resolution,[status(thm)],[f507,f223])).
% 3.88/0.98 fof(f1362,plain,(
% 3.88/0.98 ![X0]: (~ssList(X0)|~app(app(nil,cons(sK52_skl,nil)),X0)=sK47_skl)),
% 3.88/0.98 inference(resolution,[status(thm)],[f1352,f724])).
% 3.88/0.99 fof(f1367,plain,(
% 3.88/0.99 ![X0]: (~ssList(X0)|~app(app(nil,sK47_skl),X0)=sK47_skl)),
% 3.88/0.99 inference(forward_demodulation,[status(thm)],[f725,f1362])).
% 3.88/0.99 fof(f1368,plain,(
% 3.88/0.99 ![X0]: (~ssList(X0)|~app(sK47_skl,X0)=sK47_skl)),
% 3.88/0.99 inference(forward_demodulation,[status(thm)],[f516,f1367])).
% 3.88/0.99 fof(f2570,plain,(
% 3.88/0.99 ~app(sK47_skl,nil)=sK47_skl),
% 3.88/0.99 inference(resolution,[status(thm)],[f1368,f223])).
% 3.88/0.99 fof(f2573,plain,(
% 3.88/0.99 ~sK47_skl=sK47_skl),
% 3.88/0.99 inference(forward_demodulation,[status(thm)],[f626,f2570])).
% 3.88/0.99 fof(f2574,plain,(
% 3.88/0.99 $false),
% 3.88/0.99 inference(trivial_equality_resolution,[status(thm)],[f2573])).
% 3.88/0.99 % SZS output end CNFRefutation for theBenchmark.p
% 3.88/1.00 % Elapsed time: 0.631880 seconds
% 3.88/1.00 % CPU time: 4.655923 seconds
% 3.88/1.00 % Total memory used: 166.594 MB
% 3.88/1.00 % Net memory used: 162.545 MB
%------------------------------------------------------------------------------