%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GRP001+6 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 12:35:24 PM UTC 2026
% Result : Theorem 1.26s 0.58s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP001+6 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n019.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 20 19:52:49 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 1.26/0.58 % Refutation found
% 1.26/0.58 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.26/0.58 % SZS output start CNFRefutation for theBenchmark
% 1.26/0.58 fof(f1,conjecture,(
% 1.26/0.58 (! [E] :( ( (! [X,Y] :(? [Z] : product(X,Y,Z)))& (! [X,Y,Z,U,V,W] :( ( product(X,Y,U)& product(Y,Z,V)& product(U,Z,W) )=> product(X,V,W) ))& (! [X,Y,Z,U,V,W] :( ( product(X,Y,U)& product(Y,Z,V)& product(X,V,W) )=> product(U,Z,W) ))& (! [X] : product(X,E,X))& (! [X] : product(E,X,X))& (! [X] : product(X,inverse(X),E))& (! [X] : product(inverse(X),X,E) ))=> ( (! [X] : product(X,X,E))=> (! [U,V,W] :( product(U,V,W)=> product(V,U,W) ) )) ) )),
% 1.26/0.58 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.26/0.58 fof(f2,negated_conjecture,(
% 1.26/0.58 ~((! [E] :( ( (! [X,Y] :(? [Z] : product(X,Y,Z)))& (! [X,Y,Z,U,V,W] :( ( product(X,Y,U)& product(Y,Z,V)& product(U,Z,W) )=> product(X,V,W) ))& (! [X,Y,Z,U,V,W] :( ( product(X,Y,U)& product(Y,Z,V)& product(X,V,W) )=> product(U,Z,W) ))& (! [X] : product(X,E,X))& (! [X] : product(E,X,X))& (! [X] : product(X,inverse(X),E))& (! [X] : product(inverse(X),X,E) ))=> ( (! [X] : product(X,X,E))=> (! [U,V,W] :( product(U,V,W)=> product(V,U,W) ) )) ) ))),
% 1.26/0.58 inference(negated_conjecture,[status(cth)],[f1])).
% 1.26/0.58 fof(f3,plain,(
% 1.26/0.58 (?[E]: ((((((((![X,Y]: ?[Z]: product(X,Y,Z))&(![X,Y,Z,U,V,W]: (((~product(X,Y,U)|~product(Y,Z,V))|~product(U,Z,W))|product(X,V,W))))&(![X,Y,Z,U,V,W]: (((~product(X,Y,U)|~product(Y,Z,V))|~product(X,V,W))|product(U,Z,W))))&(![X]: product(X,E,X)))&(![X]: product(E,X,X)))&(![X]: product(X,inverse(X),E)))&(![X]: product(inverse(X),X,E)))&((![X]: product(X,X,E))&(?[U,V,W]: (product(U,V,W)&~product(V,U,W))))))),
% 1.26/0.58 inference(pre_NNF_transformation,[status(thm)],[f2])).
% 1.26/0.58 fof(f4,plain,(
% 1.26/0.58 ?[E]: ((((((((![X,Y]: ?[Z]: product(X,Y,Z))&(![X,V,W]: ((![Z,U]: ((![Y]: (~product(X,Y,U)|~product(Y,Z,V)))|~product(U,Z,W)))|product(X,V,W))))&(![Z,U,W]: ((![X,V]: ((![Y]: (~product(X,Y,U)|~product(Y,Z,V)))|~product(X,V,W)))|product(U,Z,W))))&(![X]: product(X,E,X)))&(![X]: product(E,X,X)))&(![X]: product(X,inverse(X),E)))&(![X]: product(inverse(X),X,E)))&((![X]: product(X,X,E))&(?[U,V,W]: (product(U,V,W)&~product(V,U,W)))))),
% 1.26/0.58 inference(miniscoping,[status(thm)],[f3])).
% 1.26/0.58 fof(f5,plain,(
% 1.26/0.58 ((((((((![X,Y]: product(X,Y,sK1_skl(Y,X)))&(![X,V,W]: ((![Z,U]: ((![Y]: (~product(X,Y,U)|~product(Y,Z,V)))|~product(U,Z,W)))|product(X,V,W))))&(![Z,U,W]: ((![X,V]: ((![Y]: (~product(X,Y,U)|~product(Y,Z,V)))|~product(X,V,W)))|product(U,Z,W))))&(![X]: product(X,sK0_skl,X)))&(![X]: product(sK0_skl,X,X)))&(![X]: product(X,inverse(X),sK0_skl)))&(![X]: product(inverse(X),X,sK0_skl)))&((![X]: product(X,X,sK0_skl))&(product(sK2_skl,sK3_skl,sK4_skl)&~product(sK3_skl,sK2_skl,sK4_skl))))),
% 1.26/0.58 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl,sK4_skl]),skolemize(E,sK0_skl),skolemize(Z,sK1_skl(Y,X)),skolemize(U,sK2_skl),skolemize(V,sK3_skl),skolemize(W,sK4_skl)],[f4])).
% 1.26/0.58 fof(f6,plain,(
% 1.26/0.58 ![X0,X1]: (product(X0,X1,sK1_skl(X1,X0)))),
% 1.26/0.58 inference(cnf_transformation,[status(thm)],[f5])).
% 1.26/0.58 fof(f7,plain,(
% 1.26/0.58 ![X0,X1,X2,X3,X4,X5]: (~product(X0,X1,X2)|~product(X1,X3,X4)|~product(X2,X3,X5)|product(X0,X4,X5))),
% 1.26/0.58 inference(cnf_transformation,[status(thm)],[f5])).
% 1.26/0.58 fof(f8,plain,(
% 1.26/0.58 ![X0,X1,X2,X3,X4,X5]: (~product(X0,X1,X2)|~product(X1,X3,X4)|~product(X0,X4,X5)|product(X2,X3,X5))),
% 1.26/0.58 inference(cnf_transformation,[status(thm)],[f5])).
% 1.26/0.58 fof(f9,plain,(
% 1.26/0.58 ![X0]: (product(X0,sK0_skl,X0))),
% 1.26/0.58 inference(cnf_transformation,[status(thm)],[f5])).
% 1.26/0.58 fof(f10,plain,(
% 1.26/0.58 ![X0]: (product(sK0_skl,X0,X0))),
% 1.26/0.58 inference(cnf_transformation,[status(thm)],[f5])).
% 1.26/0.58 fof(f13,plain,(
% 1.26/0.58 ![X0]: (product(X0,X0,sK0_skl))),
% 1.26/0.58 inference(cnf_transformation,[status(thm)],[f5])).
% 1.26/0.58 fof(f14,plain,(
% 1.26/0.58 product(sK2_skl,sK3_skl,sK4_skl)),
% 1.26/0.58 inference(cnf_transformation,[status(thm)],[f5])).
% 1.26/0.58 fof(f15,plain,(
% 1.26/0.58 ~product(sK3_skl,sK2_skl,sK4_skl)),
% 1.26/0.58 inference(cnf_transformation,[status(thm)],[f5])).
% 1.26/0.58 fof(f16,plain,(
% 1.26/0.58 ![X0,X1,X2]: (~product(sK3_skl,X0,X1)|~product(X0,X2,sK2_skl)|~product(X1,X2,sK4_skl))),
% 1.26/0.58 inference(resolution,[status(thm)],[f15,f7])).
% 1.26/0.58 fof(f18,plain,(
% 1.26/0.58 ![X0]: (~product(sK3_skl,sK2_skl,X0)|~product(X0,sK0_skl,sK4_skl))),
% 1.26/0.58 inference(resolution,[status(thm)],[f16,f9])).
% 1.26/0.58 fof(f21,plain,(
% 1.26/0.58 ~product(sK1_skl(sK2_skl,sK3_skl),sK0_skl,sK4_skl)),
% 1.26/0.58 inference(resolution,[status(thm)],[f18,f6])).
% 1.26/0.58 fof(f23,plain,(
% 1.26/0.58 ![X0,X1,X2]: (~product(sK1_skl(sK2_skl,sK3_skl),X0,X1)|~product(X0,X2,sK0_skl)|~product(X1,X2,sK4_skl))),
% 1.26/0.58 inference(resolution,[status(thm)],[f21,f7])).
% 1.26/0.58 fof(f39,plain,(
% 1.26/0.58 ![X0]: (~product(sK1_skl(sK2_skl,sK3_skl),X0,sK0_skl)|~product(X0,sK4_skl,sK0_skl))),
% 1.26/0.58 inference(resolution,[status(thm)],[f23,f10])).
% 1.26/0.58 fof(f54,plain,(
% 1.26/0.58 ~product(sK1_skl(sK2_skl,sK3_skl),sK4_skl,sK0_skl)),
% 1.26/0.58 inference(resolution,[status(thm)],[f39,f13])).
% 1.26/0.58 fof(f57,plain,(
% 1.26/0.58 ![X0,X1,X2]: (~product(X0,X1,sK1_skl(sK2_skl,sK3_skl))|~product(X1,sK4_skl,X2)|~product(X0,X2,sK0_skl))),
% 1.26/0.58 inference(resolution,[status(thm)],[f54,f8])).
% 1.26/0.58 fof(f77,plain,(
% 1.26/0.58 ![X0]: (~product(sK2_skl,sK4_skl,X0)|~product(sK3_skl,X0,sK0_skl))),
% 1.26/0.58 inference(resolution,[status(thm)],[f57,f6])).
% 1.26/0.58 fof(f81,plain,(
% 1.26/0.58 ![X0,X1,X2,X3]: (~product(sK3_skl,X0,sK0_skl)|~product(X1,X2,sK2_skl)|~product(X2,sK4_skl,X3)|~product(X1,X3,X0))),
% 1.26/0.58 inference(resolution,[status(thm)],[f77,f8])).
% 1.26/0.58 fof(f485,plain,(
% 1.26/0.58 ![X0,X1,X2]: (~product(X0,X1,sK2_skl)|~product(X1,sK4_skl,X2)|~product(X0,X2,sK3_skl))),
% 1.26/0.58 inference(resolution,[status(thm)],[f81,f13])).
% 1.26/0.58 fof(f488,plain,(
% 1.26/0.58 ![X0]: (~product(sK2_skl,sK4_skl,X0)|~product(sK0_skl,X0,sK3_skl))),
% 1.26/0.58 inference(resolution,[status(thm)],[f485,f10])).
% 1.26/0.58 fof(f500,plain,(
% 1.26/0.58 ~product(sK2_skl,sK4_skl,sK3_skl)),
% 1.26/0.58 inference(resolution,[status(thm)],[f488,f10])).
% 1.26/0.58 fof(f504,plain,(
% 1.26/0.58 ![X0,X1,X2]: (~product(sK2_skl,X0,X1)|~product(X0,X2,sK4_skl)|~product(X1,X2,sK3_skl))),
% 1.26/0.58 inference(resolution,[status(thm)],[f500,f7])).
% 1.26/0.58 fof(f507,plain,(
% 1.26/0.58 ![X0]: (~product(sK2_skl,X0,sK0_skl)|~product(X0,sK3_skl,sK4_skl))),
% 1.26/0.58 inference(resolution,[status(thm)],[f504,f10])).
% 1.26/0.58 fof(f511,plain,(
% 1.26/0.58 ~product(sK2_skl,sK2_skl,sK0_skl)),
% 1.26/0.58 inference(resolution,[status(thm)],[f507,f14])).
% 1.26/0.58 fof(f514,plain,(
% 1.26/0.58 $false),
% 1.26/0.58 inference(forward_subsumption_resolution,[status(thm)],[f511,f13])).
% 1.26/0.58 % SZS output end CNFRefutation for theBenchmark.p
% 1.26/0.61 % Elapsed time: 0.243204 seconds
% 1.26/0.61 % CPU time: 1.623672 seconds
% 1.26/0.61 % Total memory used: 68.625 MB
% 1.26/0.61 % Net memory used: 64.908 MB
%------------------------------------------------------------------------------