%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : ALG211+1 : 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 : n013.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 11:49:49 AM UTC 2026
% Result : Theorem 0.15s 0.40s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG211+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n013.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 13:01:21 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.15/0.40 % Refutation found
% 0.15/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.40 % SZS output start CNFRefutation for theBenchmark
% 0.15/0.40 fof(f1,axiom,(
% 0.15/0.40 (! [B,V] :( basis_of(B,V)=> ( lin_ind_subset(B,V)& a_subset_of(B,vec_to_class(V)) ) ) )),
% 0.15/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.40 fof(f2,axiom,(
% 0.15/0.40 (! [S,T,V] :( ( lin_ind_subset(S,V)& basis_of(T,V) )=> (? [U] :( a_subset_of(U,T)& basis_of(union(S,U),V) ) )) )),
% 0.15/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.40 fof(f3,axiom,(
% 0.15/0.40 (! [A] :( a_vector_space(A)=> (? [B] : basis_of(B,A) )) )),
% 0.15/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.40 fof(f4,axiom,(
% 0.15/0.40 (! [A,B] :( a_vector_subspace_of(A,B)=> a_vector_space(A) ) )),
% 0.15/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.40 fof(f5,axiom,(
% 0.15/0.40 (! [W,V,E] :( ( a_vector_subspace_of(W,V)& a_subset_of(E,vec_to_class(W)) )=> ( lin_ind_subset(E,W)<=> lin_ind_subset(E,V) ) ) )),
% 0.15/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.40 fof(f6,conjecture,(
% 0.15/0.40 (! [W,V] :( ( a_vector_subspace_of(W,V)& a_vector_space(V) )=> (? [E,F] :( basis_of(union(E,F),V)& basis_of(E,W) ) )) )),
% 0.15/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.40 fof(f7,negated_conjecture,(
% 0.15/0.40 ~((! [W,V] :( ( a_vector_subspace_of(W,V)& a_vector_space(V) )=> (? [E,F] :( basis_of(union(E,F),V)& basis_of(E,W) ) )) ))),
% 0.15/0.40 inference(negated_conjecture,[status(cth)],[f6])).
% 0.15/0.40 fof(f8,plain,(
% 0.15/0.40 ![B,V]: (~basis_of(B,V)|(lin_ind_subset(B,V)&a_subset_of(B,vec_to_class(V))))),
% 0.15/0.40 inference(pre_NNF_transformation,[status(thm)],[f1])).
% 0.15/0.40 fof(f9,plain,(
% 0.15/0.40 ![X0,X1]: (~basis_of(X0,X1)|lin_ind_subset(X0,X1))),
% 0.15/0.40 inference(cnf_transformation,[status(thm)],[f8])).
% 0.15/0.40 fof(f10,plain,(
% 0.15/0.40 ![X0,X1]: (~basis_of(X0,X1)|a_subset_of(X0,vec_to_class(X1)))),
% 0.15/0.40 inference(cnf_transformation,[status(thm)],[f8])).
% 0.15/0.40 fof(f11,plain,(
% 0.15/0.40 ![S,T,V]: ((~lin_ind_subset(S,V)|~basis_of(T,V))|(?[U]: (a_subset_of(U,T)&basis_of(union(S,U),V))))),
% 0.15/0.40 inference(pre_NNF_transformation,[status(thm)],[f2])).
% 0.15/0.40 fof(f12,plain,(
% 0.15/0.40 ![S,T,V]: ((~lin_ind_subset(S,V)|~basis_of(T,V))|(a_subset_of(sK0_skl(V,T,S),T)&basis_of(union(S,sK0_skl(V,T,S)),V)))),
% 0.15/0.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(U,sK0_skl(V,T,S))],[f11])).
% 0.15/0.41 fof(f14,plain,(
% 0.15/0.41 ![X0,X1,X2]: (~lin_ind_subset(X0,X1)|~basis_of(X2,X1)|basis_of(union(X0,sK0_skl(X1,X2,X0)),X1))),
% 0.15/0.41 inference(cnf_transformation,[status(thm)],[f12])).
% 0.15/0.41 fof(f15,plain,(
% 0.15/0.41 ![A]: (~a_vector_space(A)|(?[B]: basis_of(B,A)))),
% 0.15/0.41 inference(pre_NNF_transformation,[status(thm)],[f3])).
% 0.15/0.41 fof(f16,plain,(
% 0.15/0.41 ![A]: (~a_vector_space(A)|basis_of(sK1_skl(A),A))),
% 0.15/0.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(B,sK1_skl(A))],[f15])).
% 0.15/0.41 fof(f17,plain,(
% 0.15/0.41 ![X0]: (~a_vector_space(X0)|basis_of(sK1_skl(X0),X0))),
% 0.15/0.41 inference(cnf_transformation,[status(thm)],[f16])).
% 0.15/0.41 fof(f18,plain,(
% 0.15/0.41 ![A,B]: (~a_vector_subspace_of(A,B)|a_vector_space(A))),
% 0.15/0.41 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 0.15/0.41 fof(f19,plain,(
% 0.15/0.41 ![A]: ((![B]: ~a_vector_subspace_of(A,B))|a_vector_space(A))),
% 0.15/0.41 inference(miniscoping,[status(thm)],[f18])).
% 0.15/0.41 fof(f20,plain,(
% 0.15/0.41 ![X0,X1]: (~a_vector_subspace_of(X0,X1)|a_vector_space(X0))),
% 0.15/0.41 inference(cnf_transformation,[status(thm)],[f19])).
% 0.15/0.41 fof(f21,plain,(
% 0.15/0.41 ![W,V,E]: ((~a_vector_subspace_of(W,V)|~a_subset_of(E,vec_to_class(W)))|(lin_ind_subset(E,W)<=>lin_ind_subset(E,V)))),
% 0.15/0.41 inference(pre_NNF_transformation,[status(thm)],[f5])).
% 0.15/0.41 fof(f22,plain,(
% 0.15/0.41 ![W,V,E]: ((~a_vector_subspace_of(W,V)|~a_subset_of(E,vec_to_class(W)))|((~lin_ind_subset(E,W)|lin_ind_subset(E,V))&(lin_ind_subset(E,W)|~lin_ind_subset(E,V))))),
% 0.15/0.41 inference(NNF_transformation,[status(thm)],[f21])).
% 0.15/0.41 fof(f23,plain,(
% 0.15/0.41 ![X0,X1,X2]: (~a_vector_subspace_of(X0,X1)|~a_subset_of(X2,vec_to_class(X0))|~lin_ind_subset(X2,X0)|lin_ind_subset(X2,X1))),
% 0.15/0.41 inference(cnf_transformation,[status(thm)],[f22])).
% 0.15/0.41 fof(f25,plain,(
% 0.15/0.41 (?[W,V]: ((a_vector_subspace_of(W,V)&a_vector_space(V))&(![E,F]: (~basis_of(union(E,F),V)|~basis_of(E,W)))))),
% 0.15/0.41 inference(pre_NNF_transformation,[status(thm)],[f7])).
% 0.15/0.41 fof(f26,plain,(
% 0.15/0.41 ?[W,V]: ((a_vector_subspace_of(W,V)&a_vector_space(V))&(![E]: ((![F]: ~basis_of(union(E,F),V))|~basis_of(E,W))))),
% 0.15/0.41 inference(miniscoping,[status(thm)],[f25])).
% 0.15/0.41 fof(f27,plain,(
% 0.15/0.41 ((a_vector_subspace_of(sK2_skl,sK3_skl)&a_vector_space(sK3_skl))&(![E]: ((![F]: ~basis_of(union(E,F),sK3_skl))|~basis_of(E,sK2_skl))))),
% 0.15/0.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(W,sK2_skl),skolemize(V,sK3_skl)],[f26])).
% 0.15/0.41 fof(f28,plain,(
% 0.15/0.41 a_vector_subspace_of(sK2_skl,sK3_skl)),
% 0.15/0.41 inference(cnf_transformation,[status(thm)],[f27])).
% 0.15/0.41 fof(f29,plain,(
% 0.15/0.41 a_vector_space(sK3_skl)),
% 0.15/0.41 inference(cnf_transformation,[status(thm)],[f27])).
% 0.15/0.41 fof(f30,plain,(
% 0.15/0.41 ![X0,X1]: (~basis_of(union(X0,X1),sK3_skl)|~basis_of(X0,sK2_skl))),
% 0.15/0.41 inference(cnf_transformation,[status(thm)],[f27])).
% 0.15/0.41 fof(f31,plain,(
% 0.15/0.41 a_vector_space(sK2_skl)),
% 0.15/0.41 inference(resolution,[status(thm)],[f20,f28])).
% 0.15/0.41 fof(f32,plain,(
% 0.15/0.41 ![X0]: (~a_vector_space(X0)|lin_ind_subset(sK1_skl(X0),X0))),
% 0.15/0.41 inference(resolution,[status(thm)],[f17,f9])).
% 0.15/0.41 fof(f33,plain,(
% 0.15/0.41 ![X0,X1]: (~a_vector_space(X0)|~basis_of(X1,X0)|basis_of(union(sK1_skl(X0),sK0_skl(X0,X1,sK1_skl(X0))),X0))),
% 0.15/0.41 inference(resolution,[status(thm)],[f32,f14])).
% 0.15/0.41 fof(f34,plain,(
% 0.15/0.41 ![X0]: (~a_vector_space(X0)|basis_of(union(sK1_skl(X0),sK0_skl(X0,sK1_skl(X0),sK1_skl(X0))),X0)|~a_vector_space(X0))),
% 0.15/0.41 inference(resolution,[status(thm)],[f33,f17])).
% 0.15/0.41 fof(f35,plain,(
% 0.15/0.41 ![X0]: (~a_vector_space(X0)|basis_of(union(sK1_skl(X0),sK0_skl(X0,sK1_skl(X0),sK1_skl(X0))),X0))),
% 0.15/0.41 inference(duplicate_literals_removal,[status(thm)],[f34])).
% 0.15/0.41 fof(f36,plain,(
% 0.15/0.41 basis_of(union(sK1_skl(sK2_skl),sK0_skl(sK2_skl,sK1_skl(sK2_skl),sK1_skl(sK2_skl))),sK2_skl)),
% 0.15/0.41 inference(resolution,[status(thm)],[f35,f31])).
% 0.15/0.41 fof(f37,plain,(
% 0.15/0.41 basis_of(union(sK1_skl(sK3_skl),sK0_skl(sK3_skl,sK1_skl(sK3_skl),sK1_skl(sK3_skl))),sK3_skl)),
% 0.15/0.41 inference(resolution,[status(thm)],[f35,f29])).
% 0.15/0.41 fof(f38,plain,(
% 0.15/0.41 ~a_vector_space(sK2_skl)|basis_of(union(sK1_skl(sK2_skl),sK0_skl(sK2_skl,union(sK1_skl(sK2_skl),sK0_skl(sK2_skl,sK1_skl(sK2_skl),sK1_skl(sK2_skl))),sK1_skl(sK2_skl))),sK2_skl)),
% 0.15/0.41 inference(resolution,[status(thm)],[f36,f33])).
% 0.15/0.41 fof(f40,plain,(
% 0.15/0.41 basis_of(union(sK1_skl(sK2_skl),sK0_skl(sK2_skl,union(sK1_skl(sK2_skl),sK0_skl(sK2_skl,sK1_skl(sK2_skl),sK1_skl(sK2_skl))),sK1_skl(sK2_skl))),sK2_skl)),
% 0.15/0.41 inference(forward_subsumption_resolution,[status(thm)],[f38,f31])).
% 0.15/0.41 fof(f49,plain,(
% 0.15/0.41 ![X0]: (~a_subset_of(X0,vec_to_class(sK2_skl))|~lin_ind_subset(X0,sK2_skl)|lin_ind_subset(X0,sK3_skl))),
% 0.15/0.41 inference(resolution,[status(thm)],[f23,f28])).
% 0.15/0.41 fof(f51,plain,(
% 0.15/0.41 ![X0]: (~lin_ind_subset(X0,sK2_skl)|lin_ind_subset(X0,sK3_skl)|~basis_of(X0,sK2_skl))),
% 0.15/0.41 inference(resolution,[status(thm)],[f49,f10])).
% 0.15/0.41 fof(f52,plain,(
% 0.15/0.41 ![X0]: (lin_ind_subset(X0,sK3_skl)|~basis_of(X0,sK2_skl))),
% 0.15/0.41 inference(forward_subsumption_resolution,[status(thm)],[f51,f9])).
% 0.15/0.41 fof(f53,plain,(
% 0.15/0.41 ![X0,X1]: (~basis_of(X0,sK2_skl)|~basis_of(X1,sK3_skl)|basis_of(union(X0,sK0_skl(sK3_skl,X1,X0)),sK3_skl))),
% 0.15/0.41 inference(resolution,[status(thm)],[f52,f14])).
% 0.15/0.41 fof(f54,plain,(
% 0.15/0.41 ![X0,X1]: (~basis_of(X0,sK2_skl)|~basis_of(X1,sK3_skl))),
% 0.15/0.41 inference(forward_subsumption_resolution,[status(thm)],[f53,f30])).
% 0.15/0.41 fof(f55,plain,(
% 0.15/0.41 ![X0]: (~basis_of(X0,sK2_skl))),
% 0.15/0.41 inference(resolution,[status(thm)],[f54,f37])).
% 0.15/0.41 fof(f59,plain,(
% 0.15/0.41 $false),
% 0.15/0.41 inference(backward_subsumption_resolution,[status(thm)],[f40,f55])).
% 0.15/0.41 % SZS output end CNFRefutation for theBenchmark.p
% 0.15/0.44 % Elapsed time: 0.057496 seconds
% 0.15/0.44 % CPU time: 0.158107 seconds
% 0.15/0.44 % Total memory used: 55.792 MB
% 0.15/0.44 % Net memory used: 55.379 MB
%------------------------------------------------------------------------------