%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GRP012+5 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 12:35:26 PM UTC 2026
% Result : Theorem 274.44s 40.12s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP012+5 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.36 % Computer : n018.cluster.edu
% 0.10/5.36 % Model : x86_64 x86_64
% 0.10/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.36 % Memory : 8046.5625MB
% 0.10/5.36 % OS : Linux 6.8.0-71-generic
% 0.10/5.36 % CPULimit : 300
% 0.10/5.36 % WCLimit : 300
% 0.10/5.36 % DateTime : Sun Sep 20 19:55:49 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.38 % Drodi V4.1.1
% 274.44/40.12 % Refutation found
% 274.44/40.12 % SZS status Theorem for theBenchmark: Theorem is valid
% 274.44/40.12 % SZS output start CNFRefutation for theBenchmark
% 274.44/40.12 fof(f1,conjecture,(
% 274.44/40.12 (! [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) ))=> (! [U,V,W,X] :( ( product(inverse(U),inverse(V),W)& product(V,U,X) )=> product(inverse(W),inverse(X),E) ) )) )),
% 274.44/40.12 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 274.44/40.12 fof(f2,negated_conjecture,(
% 274.44/40.12 ~((! [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) ))=> (! [U,V,W,X] :( ( product(inverse(U),inverse(V),W)& product(V,U,X) )=> product(inverse(W),inverse(X),E) ) )) ))),
% 274.44/40.12 inference(negated_conjecture,[status(cth)],[f1])).
% 274.44/40.12 fof(f3,plain,(
% 274.44/40.12 (?[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)))&(?[U,V,W,X]: ((product(inverse(U),inverse(V),W)&product(V,U,X))&~product(inverse(W),inverse(X),E)))))),
% 274.44/40.12 inference(pre_NNF_transformation,[status(thm)],[f2])).
% 274.44/40.12 fof(f4,plain,(
% 274.44/40.12 ?[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)))&(?[W,X]: ((?[U,V]: (product(inverse(U),inverse(V),W)&product(V,U,X)))&~product(inverse(W),inverse(X),E))))),
% 274.44/40.12 inference(miniscoping,[status(thm)],[f3])).
% 274.44/40.12 fof(f5,plain,(
% 274.44/40.12 ((((((((![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)))&((product(inverse(sK4_skl),inverse(sK5_skl),sK2_skl)&product(sK5_skl,sK4_skl,sK3_skl))&~product(inverse(sK2_skl),inverse(sK3_skl),sK0_skl)))),
% 274.44/40.12 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl,sK4_skl,sK5_skl]),skolemize(E,sK0_skl),skolemize(Z,sK1_skl(Y,X)),skolemize(W,sK2_skl),skolemize(X,sK3_skl),skolemize(U,sK4_skl),skolemize(V,sK5_skl)],[f4])).
% 274.44/40.12 fof(f6,plain,(
% 274.44/40.12 ![X0,X1]: (product(X0,X1,sK1_skl(X1,X0)))),
% 274.44/40.12 inference(cnf_transformation,[status(thm)],[f5])).
% 274.44/40.12 fof(f7,plain,(
% 274.44/40.12 ![X0,X1,X2,X3,X4,X5]: (~product(X0,X1,X2)|~product(X1,X3,X4)|~product(X2,X3,X5)|product(X0,X4,X5))),
% 274.44/40.12 inference(cnf_transformation,[status(thm)],[f5])).
% 274.44/40.12 fof(f8,plain,(
% 274.44/40.12 ![X0,X1,X2,X3,X4,X5]: (~product(X0,X1,X2)|~product(X1,X3,X4)|~product(X0,X4,X5)|product(X2,X3,X5))),
% 274.44/40.12 inference(cnf_transformation,[status(thm)],[f5])).
% 274.44/40.12 fof(f9,plain,(
% 274.44/40.12 ![X0]: (product(X0,sK0_skl,X0))),
% 274.44/40.12 inference(cnf_transformation,[status(thm)],[f5])).
% 274.44/40.12 fof(f10,plain,(
% 274.44/40.12 ![X0]: (product(sK0_skl,X0,X0))),
% 274.44/40.12 inference(cnf_transformation,[status(thm)],[f5])).
% 274.44/40.12 fof(f11,plain,(
% 274.44/40.12 ![X0]: (product(X0,inverse(X0),sK0_skl))),
% 274.44/40.12 inference(cnf_transformation,[status(thm)],[f5])).
% 274.44/40.12 fof(f12,plain,(
% 274.44/40.12 ![X0]: (product(inverse(X0),X0,sK0_skl))),
% 274.44/40.12 inference(cnf_transformation,[status(thm)],[f5])).
% 274.44/40.12 fof(f13,plain,(
% 274.44/40.12 product(inverse(sK4_skl),inverse(sK5_skl),sK2_skl)),
% 274.44/40.12 inference(cnf_transformation,[status(thm)],[f5])).
% 274.44/40.12 fof(f14,plain,(
% 274.44/40.15 product(sK5_skl,sK4_skl,sK3_skl)),
% 274.44/40.15 inference(cnf_transformation,[status(thm)],[f5])).
% 274.44/40.15 fof(f15,plain,(
% 274.44/40.15 ~product(inverse(sK2_skl),inverse(sK3_skl),sK0_skl)),
% 274.44/40.15 inference(cnf_transformation,[status(thm)],[f5])).
% 274.44/40.15 fof(f17,plain,(
% 274.44/40.15 ![X0,X1,X2]: (~product(X0,X1,inverse(sK2_skl))|~product(X1,inverse(sK3_skl),X2)|~product(X0,X2,sK0_skl))),
% 274.44/40.15 inference(resolution,[status(thm)],[f8,f15])).
% 274.44/40.15 fof(f29,plain,(
% 274.44/40.15 ![X0]: (~product(sK0_skl,inverse(sK3_skl),X0)|~product(inverse(sK2_skl),X0,sK0_skl))),
% 274.44/40.15 inference(resolution,[status(thm)],[f17,f9])).
% 274.44/40.15 fof(f42,plain,(
% 274.44/40.15 ~product(sK0_skl,inverse(sK3_skl),sK2_skl)),
% 274.44/40.15 inference(resolution,[status(thm)],[f29,f12])).
% 274.44/40.15 fof(f46,plain,(
% 274.44/40.15 ![X0,X1,X2]: (~product(X0,X1,sK0_skl)|~product(X1,inverse(sK3_skl),X2)|~product(X0,X2,sK2_skl))),
% 274.44/40.15 inference(resolution,[status(thm)],[f42,f8])).
% 274.44/40.15 fof(f56,plain,(
% 274.44/40.15 ![X0]: (~product(sK2_skl,X0,sK0_skl)|~product(X0,inverse(sK3_skl),sK0_skl))),
% 274.44/40.15 inference(resolution,[status(thm)],[f46,f9])).
% 274.44/40.15 fof(f62,plain,(
% 274.44/40.15 ![X0,X1,X2,X3]: (~product(X0,inverse(sK3_skl),sK0_skl)|~product(X1,X2,sK2_skl)|~product(X2,X0,X3)|~product(X1,X3,sK0_skl))),
% 274.44/40.15 inference(resolution,[status(thm)],[f56,f8])).
% 274.44/40.15 fof(f528,plain,(
% 274.44/40.15 ![X0,X1,X2]: (~product(X0,X1,sK2_skl)|~product(X1,sK3_skl,X2)|~product(X0,X2,sK0_skl))),
% 274.44/40.15 inference(resolution,[status(thm)],[f62,f11])).
% 274.44/40.15 fof(f536,plain,(
% 274.44/40.15 ![X0]: (~product(X0,sK0_skl,sK2_skl)|~product(X0,sK3_skl,sK0_skl))),
% 274.44/40.15 inference(resolution,[status(thm)],[f528,f10])).
% 274.44/40.15 fof(f542,plain,(
% 274.44/40.15 ![X0,X1,X2,X3]: (~product(X0,sK0_skl,sK2_skl)|~product(X0,X1,X2)|~product(X1,X3,sK3_skl)|~product(X2,X3,sK0_skl))),
% 274.44/40.15 inference(resolution,[status(thm)],[f536,f7])).
% 274.44/40.15 fof(f741,plain,(
% 274.44/40.15 ![X0,X1,X2]: (~product(sK2_skl,X0,X1)|~product(X0,X2,sK3_skl)|~product(X1,X2,sK0_skl))),
% 274.44/40.15 inference(resolution,[status(thm)],[f542,f9])).
% 274.44/40.15 fof(f746,plain,(
% 274.44/40.15 ![X0,X1]: (~product(X0,X1,sK3_skl)|~product(sK1_skl(X0,sK2_skl),X1,sK0_skl))),
% 274.44/40.15 inference(resolution,[status(thm)],[f741,f6])).
% 274.44/40.15 fof(f758,plain,(
% 274.44/40.15 ![X0]: (~product(X0,inverse(sK1_skl(X0,sK2_skl)),sK3_skl))),
% 274.44/40.15 inference(resolution,[status(thm)],[f746,f11])).
% 274.44/40.15 fof(f761,plain,(
% 274.44/40.15 ![X0,X1,X2,X3]: (~product(X0,X1,X2)|~product(X1,inverse(sK1_skl(X2,sK2_skl)),X3)|~product(X0,X3,sK3_skl))),
% 274.44/40.15 inference(resolution,[status(thm)],[f758,f8])).
% 274.44/40.15 fof(f765,plain,(
% 274.44/40.15 ![X0,X1]: (~product(sK3_skl,X0,X1)|~product(X0,inverse(sK1_skl(X1,sK2_skl)),sK0_skl))),
% 274.44/40.15 inference(resolution,[status(thm)],[f761,f9])).
% 274.44/40.15 fof(f777,plain,(
% 274.44/40.15 ![X0]: (~product(sK3_skl,sK1_skl(X0,sK2_skl),X0))),
% 274.44/40.15 inference(resolution,[status(thm)],[f765,f11])).
% 274.44/40.15 fof(f781,plain,(
% 274.44/40.15 ![X0,X1,X2,X3]: (~product(sK3_skl,X0,X1)|~product(X0,X2,sK1_skl(X3,sK2_skl))|~product(X1,X2,X3))),
% 274.44/40.15 inference(resolution,[status(thm)],[f777,f7])).
% 274.44/40.15 fof(f810,plain,(
% 274.44/40.15 ![X0,X1]: (~product(sK0_skl,X0,sK1_skl(X1,sK2_skl))|~product(sK3_skl,X0,X1))),
% 274.44/40.15 inference(resolution,[status(thm)],[f781,f9])).
% 274.44/40.15 fof(f815,plain,(
% 274.44/40.15 ![X0,X1,X2,X3,X4]: (~product(sK3_skl,X0,X1)|~product(X2,X3,sK0_skl)|~product(X3,X0,X4)|~product(X2,X4,sK1_skl(X1,sK2_skl)))),
% 274.44/40.15 inference(resolution,[status(thm)],[f810,f8])).
% 274.44/40.15 fof(f8023,plain,(
% 274.44/40.15 ![X0,X1,X2,X3]: (~product(X0,X1,sK0_skl)|~product(X1,X2,X3)|~product(X0,X3,sK1_skl(sK1_skl(X2,sK3_skl),sK2_skl)))),
% 274.44/40.15 inference(resolution,[status(thm)],[f815,f6])).
% 274.44/40.15 fof(f8041,plain,(
% 274.44/40.15 ![X0,X1]: (~product(sK2_skl,X0,sK0_skl)|~product(X0,X1,sK1_skl(X1,sK3_skl)))),
% 274.44/40.15 inference(resolution,[status(thm)],[f8023,f6])).
% 274.44/40.15 fof(f8044,plain,(
% 274.44/40.15 ![X0]: (~product(inverse(sK2_skl),X0,sK1_skl(X0,sK3_skl)))),
% 274.44/40.15 inference(resolution,[status(thm)],[f8041,f11])).
% 274.44/40.15 fof(f8048,plain,(
% 274.44/40.15 ![X0,X1,X2,X3]: (~product(inverse(sK2_skl),X0,X1)|~product(X0,X2,X3)|~product(X1,X2,sK1_skl(X3,sK3_skl)))),
% 274.44/40.15 inference(resolution,[status(thm)],[f8044,f7])).
% 274.44/40.15 fof(f8072,plain,(
% 274.44/40.15 ![X0,X1]: (~product(inverse(sK2_skl),X0,sK3_skl)|~product(X0,X1,X1))),
% 274.44/40.15 inference(resolution,[status(thm)],[f8048,f6])).
% 274.44/40.15 fof(f8076,plain,(
% 274.44/40.15 ![X0,X1,X2,X3,X4]: (~product(X0,X1,X1)|~product(inverse(sK2_skl),X2,X3)|~product(X2,X4,X0)|~product(X3,X4,sK3_skl))),
% 274.44/40.15 inference(resolution,[status(thm)],[f8072,f7])).
% 274.44/40.15 fof(f8098,plain,(
% 274.44/40.15 ![X0,X1,X2]: (~product(X0,X1,X1)|~product(inverse(sK2_skl),X2,sK0_skl)|~product(X2,sK3_skl,X0))),
% 166.05/40.23 inference(resolution,[status(thm)],[f8076,f10])).
% 166.05/40.23 fof(f8108,plain,(
% 166.05/40.23 ![X0,X1]: (~product(X0,X1,X1)|~product(sK2_skl,sK3_skl,X0))),
% 166.05/40.23 inference(resolution,[status(thm)],[f8098,f12])).
% 166.05/40.23 fof(f8114,plain,(
% 166.05/40.23 ![X0,X1,X2,X3,X4]: (~product(X0,X1,X1)|~product(sK2_skl,X2,X3)|~product(X2,X4,sK3_skl)|~product(X3,X4,X0))),
% 166.05/40.23 inference(resolution,[status(thm)],[f8108,f7])).
% 166.05/40.23 fof(f8223,plain,(
% 166.05/40.23 ![X0,X1,X2,X3]: (~product(X0,X1,X1)|~product(X2,X3,sK3_skl)|~product(sK1_skl(X2,sK2_skl),X3,X0))),
% 166.05/40.23 inference(resolution,[status(thm)],[f8114,f6])).
% 166.05/40.23 fof(f8235,plain,(
% 166.05/40.23 ![X0,X1]: (~product(X0,X1,X1)|~product(sK1_skl(sK5_skl,sK2_skl),sK4_skl,X0))),
% 166.05/40.23 inference(resolution,[status(thm)],[f8223,f14])).
% 166.05/40.23 fof(f8240,plain,(
% 166.05/40.23 ![X0]: (~product(sK1_skl(sK4_skl,sK1_skl(sK5_skl,sK2_skl)),X0,X0))),
% 166.05/40.23 inference(resolution,[status(thm)],[f8235,f6])).
% 166.05/40.23 fof(f8243,plain,(
% 166.05/40.23 ![X0,X1,X2,X3]: (~product(X0,X1,sK1_skl(sK4_skl,sK1_skl(sK5_skl,sK2_skl)))|~product(X1,X2,X3)|~product(X0,X3,X2))),
% 166.05/40.23 inference(resolution,[status(thm)],[f8240,f8])).
% 166.05/40.23 fof(f8688,plain,(
% 166.05/40.23 ![X0,X1]: (~product(sK4_skl,X0,X1)|~product(sK1_skl(sK5_skl,sK2_skl),X1,X0))),
% 166.05/40.23 inference(resolution,[status(thm)],[f8243,f6])).
% 166.05/40.23 fof(f8692,plain,(
% 166.05/40.23 ~product(sK4_skl,sK1_skl(sK5_skl,sK2_skl),sK0_skl)),
% 166.05/40.23 inference(resolution,[status(thm)],[f8688,f9])).
% 166.05/40.23 fof(f8696,plain,(
% 166.05/40.23 ![X0,X1,X2]: (~product(X0,X1,sK4_skl)|~product(X1,sK1_skl(sK5_skl,sK2_skl),X2)|~product(X0,X2,sK0_skl))),
% 166.05/40.23 inference(resolution,[status(thm)],[f8692,f8])).
% 166.05/40.23 fof(f8714,plain,(
% 166.05/40.23 ![X0]: (~product(sK0_skl,sK1_skl(sK5_skl,sK2_skl),X0)|~product(sK4_skl,X0,sK0_skl))),
% 166.05/40.23 inference(resolution,[status(thm)],[f8696,f9])).
% 166.05/40.23 fof(f8722,plain,(
% 166.05/40.23 ~product(sK0_skl,sK1_skl(sK5_skl,sK2_skl),inverse(sK4_skl))),
% 166.05/40.23 inference(resolution,[status(thm)],[f8714,f11])).
% 166.05/40.23 fof(f8730,plain,(
% 166.05/40.23 ![X0,X1,X2]: (~product(sK0_skl,X0,X1)|~product(X0,X2,sK1_skl(sK5_skl,sK2_skl))|~product(X1,X2,inverse(sK4_skl)))),
% 166.05/40.23 inference(resolution,[status(thm)],[f8722,f7])).
% 166.05/40.23 fof(f9194,plain,(
% 166.05/40.23 ![X0]: (~product(sK0_skl,X0,inverse(sK4_skl))|~product(X0,sK0_skl,sK1_skl(sK5_skl,sK2_skl)))),
% 166.05/40.23 inference(resolution,[status(thm)],[f8730,f9])).
% 166.05/40.23 fof(f9199,plain,(
% 166.05/40.23 ~product(inverse(sK4_skl),sK0_skl,sK1_skl(sK5_skl,sK2_skl))),
% 166.05/40.23 inference(resolution,[status(thm)],[f9194,f10])).
% 166.05/40.23 fof(f9203,plain,(
% 166.05/40.23 ![X0,X1,X2]: (~product(inverse(sK4_skl),X0,X1)|~product(X0,X2,sK0_skl)|~product(X1,X2,sK1_skl(sK5_skl,sK2_skl)))),
% 166.05/40.23 inference(resolution,[status(thm)],[f9199,f7])).
% 166.05/40.23 fof(f9311,plain,(
% 166.05/40.23 ![X0]: (~product(inverse(sK4_skl),X0,sK2_skl)|~product(X0,sK5_skl,sK0_skl))),
% 166.05/40.23 inference(resolution,[status(thm)],[f9203,f6])).
% 166.05/40.23 fof(f9314,plain,(
% 166.05/40.23 ~product(inverse(sK5_skl),sK5_skl,sK0_skl)),
% 166.05/40.23 inference(resolution,[status(thm)],[f9311,f13])).
% 166.05/40.23 fof(f9317,plain,(
% 166.05/40.23 $false),
% 166.05/40.23 inference(forward_subsumption_resolution,[status(thm)],[f9314,f12])).
% 166.05/40.23 % SZS output end CNFRefutation for theBenchmark.p
% 24.78/40.29 % Elapsed time: 34.892604 seconds
% 24.78/40.29 % CPU time: 275.968410 seconds
% 24.78/40.29 % Total memory used: 479.075 MB
% 24.78/40.29 % Net memory used: 317.024 MB
%------------------------------------------------------------------------------