%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ALG211+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n006.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 11:48:57 AM UTC 2026
% Result : Theorem 0.10s 0.40s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 44 ( 8 unt; 0 def)
% Number of atoms : 114 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 120 ( 50 ~; 43 |; 18 &)
% ( 2 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-3 aty)
% Number of variables : 81 ( 69 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B,V] :
( basis_of(B,V)
=> ( a_subset_of(B,vec_to_class(V))
& lin_ind_subset(B,V) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [S,T,V] :
( ( basis_of(T,V)
& lin_ind_subset(S,V) )
=> ? [U] :
( basis_of(union(S,U),V)
& a_subset_of(U,T) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A] :
( a_vector_space(A)
=> ? [B] : basis_of(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B] :
( a_vector_subspace_of(A,B)
=> a_vector_space(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [W,V,E] :
( ( a_subset_of(E,vec_to_class(W))
& a_vector_subspace_of(W,V) )
=> ( lin_ind_subset(E,W)
<=> lin_ind_subset(E,V) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,conjecture,
! [W,V] :
( ( a_vector_space(V)
& a_vector_subspace_of(W,V) )
=> ? [E,F] :
( basis_of(E,W)
& basis_of(union(E,F),V) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
~ ! [W,V] :
( ( a_vector_space(V)
& a_vector_subspace_of(W,V) )
=> ? [E,F] :
( basis_of(E,W)
& basis_of(union(E,F),V) ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f8,plain,
! [B,V] :
( ( a_subset_of(B,vec_to_class(V))
& lin_ind_subset(B,V) )
| ~ basis_of(B,V) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f9,plain,
! [X0,X1] :
( lin_ind_subset(X0,X1)
| ~ basis_of(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f10,plain,
! [X0,X1] :
( a_subset_of(X0,vec_to_class(X1))
| ~ basis_of(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f11,plain,
! [S,T,V] :
( ? [U] :
( basis_of(union(S,U),V)
& a_subset_of(U,T) )
| ~ basis_of(T,V)
| ~ lin_ind_subset(S,V) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f12,plain,
! [S,T,V] :
( ( basis_of(union(S,sK0_skl(V,T,S)),V)
& a_subset_of(sK0_skl(V,T,S),T) )
| ~ basis_of(T,V)
| ~ lin_ind_subset(S,V) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(U,sK0_skl(V,T,S))],[f11]) ).
fof(f14,plain,
! [X0,X1,X2] :
( basis_of(union(X0,sK0_skl(X1,X2,X0)),X1)
| ~ basis_of(X2,X1)
| ~ lin_ind_subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f15,plain,
! [A] :
( ? [B] : basis_of(B,A)
| ~ a_vector_space(A) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f16,plain,
! [A] :
( basis_of(sK1_skl(A),A)
| ~ a_vector_space(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(B,sK1_skl(A))],[f15]) ).
fof(f17,plain,
! [X0] :
( basis_of(sK1_skl(X0),X0)
| ~ a_vector_space(X0) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f18,plain,
! [A,B] :
( a_vector_space(A)
| ~ a_vector_subspace_of(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f19,plain,
! [A] :
( a_vector_space(A)
| ! [B] : ~ a_vector_subspace_of(A,B) ),
inference(miniscoping,[status(thm)],[f18]) ).
fof(f20,plain,
! [X0,X1] :
( a_vector_space(X0)
| ~ a_vector_subspace_of(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f21,plain,
! [W,V,E] :
( ( lin_ind_subset(E,W)
<=> lin_ind_subset(E,V) )
| ~ a_subset_of(E,vec_to_class(W))
| ~ a_vector_subspace_of(W,V) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f22,plain,
! [W,V,E] :
( ( ( ~ lin_ind_subset(E,V)
| lin_ind_subset(E,W) )
& ( lin_ind_subset(E,V)
| ~ lin_ind_subset(E,W) ) )
| ~ a_subset_of(E,vec_to_class(W))
| ~ a_vector_subspace_of(W,V) ),
inference(NNF_transformation,[status(thm)],[f21]) ).
fof(f23,plain,
! [X0,X1,X2] :
( lin_ind_subset(X2,X1)
| ~ lin_ind_subset(X2,X0)
| ~ a_subset_of(X2,vec_to_class(X0))
| ~ a_vector_subspace_of(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f25,plain,
? [W,V] :
( ! [E,F] :
( ~ basis_of(E,W)
| ~ basis_of(union(E,F),V) )
& a_vector_space(V)
& a_vector_subspace_of(W,V) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f26,plain,
? [W,V] :
( ! [E] :
( ~ basis_of(E,W)
| ! [F] : ~ basis_of(union(E,F),V) )
& a_vector_space(V)
& a_vector_subspace_of(W,V) ),
inference(miniscoping,[status(thm)],[f25]) ).
fof(f27,plain,
( ! [E] :
( ~ basis_of(E,sK2_skl)
| ! [F] : ~ basis_of(union(E,F),sK3_skl) )
& a_vector_space(sK3_skl)
& a_vector_subspace_of(sK2_skl,sK3_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(W,sK2_skl),skolemize(V,sK3_skl)],[f26]) ).
fof(f28,plain,
a_vector_subspace_of(sK2_skl,sK3_skl),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f29,plain,
a_vector_space(sK3_skl),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f30,plain,
! [X0,X1] :
( ~ basis_of(X0,sK2_skl)
| ~ basis_of(union(X0,X1),sK3_skl) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f31,plain,
a_vector_space(sK2_skl),
inference(resolution,[status(thm)],[f20,f28]) ).
fof(f32,plain,
! [X0] :
( lin_ind_subset(sK1_skl(X0),X0)
| ~ a_vector_space(X0) ),
inference(resolution,[status(thm)],[f17,f9]) ).
fof(f33,plain,
! [X0,X1] :
( basis_of(union(sK1_skl(X0),sK0_skl(X0,X1,sK1_skl(X0))),X0)
| ~ basis_of(X1,X0)
| ~ a_vector_space(X0) ),
inference(resolution,[status(thm)],[f32,f14]) ).
fof(f34,plain,
! [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) ),
inference(resolution,[status(thm)],[f33,f17]) ).
fof(f35,plain,
! [X0] :
( basis_of(union(sK1_skl(X0),sK0_skl(X0,sK1_skl(X0),sK1_skl(X0))),X0)
| ~ a_vector_space(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f34]) ).
fof(f36,plain,
basis_of(union(sK1_skl(sK2_skl),sK0_skl(sK2_skl,sK1_skl(sK2_skl),sK1_skl(sK2_skl))),sK2_skl),
inference(resolution,[status(thm)],[f35,f31]) ).
fof(f37,plain,
basis_of(union(sK1_skl(sK3_skl),sK0_skl(sK3_skl,sK1_skl(sK3_skl),sK1_skl(sK3_skl))),sK3_skl),
inference(resolution,[status(thm)],[f35,f29]) ).
fof(f38,plain,
( 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)
| ~ a_vector_space(sK2_skl) ),
inference(resolution,[status(thm)],[f36,f33]) ).
fof(f40,plain,
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),
inference(forward_subsumption_resolution,[status(thm)],[f38,f31]) ).
fof(f49,plain,
! [X0] :
( lin_ind_subset(X0,sK3_skl)
| ~ lin_ind_subset(X0,sK2_skl)
| ~ a_subset_of(X0,vec_to_class(sK2_skl)) ),
inference(resolution,[status(thm)],[f23,f28]) ).
fof(f51,plain,
! [X0] :
( ~ basis_of(X0,sK2_skl)
| lin_ind_subset(X0,sK3_skl)
| ~ lin_ind_subset(X0,sK2_skl) ),
inference(resolution,[status(thm)],[f49,f10]) ).
fof(f52,plain,
! [X0] :
( ~ basis_of(X0,sK2_skl)
| lin_ind_subset(X0,sK3_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f51,f9]) ).
fof(f53,plain,
! [X0,X1] :
( basis_of(union(X0,sK0_skl(sK3_skl,X1,X0)),sK3_skl)
| ~ basis_of(X1,sK3_skl)
| ~ basis_of(X0,sK2_skl) ),
inference(resolution,[status(thm)],[f52,f14]) ).
fof(f54,plain,
! [X0,X1] :
( ~ basis_of(X1,sK3_skl)
| ~ basis_of(X0,sK2_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f53,f30]) ).
fof(f55,plain,
! [X0] : ~ basis_of(X0,sK2_skl),
inference(resolution,[status(thm)],[f54,f37]) ).
fof(f59,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f40,f55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG211+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n006.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 13:01:43 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.39 % Drodi V4.1.1
% 0.10/0.40 % Refutation found
% 0.10/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.43 % Elapsed time: 0.049474 seconds
% 0.10/0.43 % CPU time: 0.114707 seconds
% 0.10/0.43 % Total memory used: 33.185 MB
% 0.10/0.43 % Net memory used: 32.957 MB
%------------------------------------------------------------------------------