%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : ALG211+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Jul 24 09:45:58 AM UTC 2025
% Result : Theorem 0.12s 0.35s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of formulae : 31 ( 5 unt; 0 def)
% Number of atoms : 72 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 69 ( 28 ~; 25 |; 8 &)
% ( 1 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 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 : 36 ( 2 sgn 15 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(bg_2_4_3,plain,
! [W,V] :
( ( a_vector_subspace_of(W,V)
& a_vector_space(V) )
=> ? [E,F] :
( basis_of(union(E,F),V)
& basis_of(E,W) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bg_2_4_3) ).
fof(bg_2_4_3_negated,plain,
~ ! [W,V] :
( ( a_vector_subspace_of(W,V)
& a_vector_space(V) )
=> ? [E,F] :
( basis_of(union(E,F),V)
& basis_of(E,W) ) ),
inference(negate_conjecture,[status(cth)],[bg_2_4_3]) ).
cnf(8,plain,
a_vector_subspace_of(sK3,sK4),
inference(cnf,[status(esa)],[bg_2_4_3_negated]) ).
cnf(l0,plain,
a_vector_subspace_of(sK3,sK4),
inference(instantiation,[status(thm)],[8]) ).
fof(bg_2_4_2,plain,
! [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) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bg_2_4_2) ).
cnf(6,plain,
( ~ a_subset_of(X0,vec_to_class(X1))
| ~ lin_ind_subset(X0,X1)
| ~ a_vector_subspace_of(X1,X2)
| lin_ind_subset(X0,X2) ),
inference(cnf,[status(esa)],[bg_2_4_2]) ).
cnf(l1,plain,
( ~ a_subset_of(sK2(sK3),vec_to_class(sK3))
| ~ lin_ind_subset(sK2(sK3),sK3)
| ~ a_vector_subspace_of(sK3,sK4)
| lin_ind_subset(sK2(sK3),sK4) ),
inference(instantiation,[status(thm)],[6]) ).
fof(basis_of,plain,
! [B,V] :
( basis_of(B,V)
=> ( lin_ind_subset(B,V)
& a_subset_of(B,vec_to_class(V)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',basis_of) ).
cnf(1,plain,
( ~ basis_of(X0,X1)
| a_subset_of(X0,vec_to_class(X1)) ),
inference(cnf,[status(esa)],[basis_of]) ).
cnf(l2,plain,
( ~ basis_of(sK2(sK3),sK3)
| a_subset_of(sK2(sK3),vec_to_class(sK3)) ),
inference(instantiation,[status(thm)],[1]) ).
fof(bg_2_2_5,plain,
! [S,T,V] :
( ( lin_ind_subset(S,V)
& basis_of(T,V) )
=> ? [U] :
( a_subset_of(U,T)
& basis_of(union(S,U),V) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bg_2_2_5) ).
cnf(3,plain,
( ~ basis_of(X0,X1)
| ~ lin_ind_subset(X2,X1)
| basis_of(union(X2,sK1(X2,X0,X1)),X1) ),
inference(cnf,[status(esa)],[bg_2_2_5]) ).
cnf(l4,plain,
( ~ basis_of(sK2(sK4),sK4)
| ~ lin_ind_subset(sK2(sK3),sK4)
| basis_of(union(sK2(sK3),sK1(sK2(sK3),sK2(sK4),sK4)),sK4) ),
inference(instantiation,[status(thm)],[3]) ).
cnf(10,plain,
( ~ basis_of(X0,sK3)
| ~ basis_of(union(X0,X1),sK4) ),
inference(cnf,[status(esa)],[bg_2_4_3_negated]) ).
cnf(l8,plain,
( ~ basis_of(sK2(sK3),sK3)
| ~ basis_of(union(sK2(sK3),sK1(sK2(sK3),sK2(sK4),sK4)),sK4) ),
inference(instantiation,[status(thm)],[10]) ).
fof(bg_remark_63_a,plain,
! [A] :
( a_vector_space(A)
=> ? [B] : basis_of(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bg_remark_63_a) ).
cnf(4,plain,
( ~ a_vector_space(X0)
| basis_of(sK2(X0),X0) ),
inference(cnf,[status(esa)],[bg_remark_63_a]) ).
cnf(l10,plain,
( ~ a_vector_space(sK4)
| basis_of(sK2(sK4),sK4) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l33,plain,
( ~ a_vector_space(sK3)
| basis_of(sK2(sK3),sK3) ),
inference(instantiation,[status(thm)],[4]) ).
fof(bg_2_4_a,plain,
! [A,B] :
( a_vector_subspace_of(A,B)
=> a_vector_space(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bg_2_4_a) ).
cnf(5,plain,
( ~ a_vector_subspace_of(X0,X1)
| a_vector_space(X0) ),
inference(cnf,[status(esa)],[bg_2_4_a]) ).
cnf(l34,plain,
( ~ a_vector_subspace_of(sK3,sK4)
| a_vector_space(sK3) ),
inference(instantiation,[status(thm)],[5]) ).
cnf(l6,plain,
( ~ a_vector_space(sK3)
| basis_of(sK2(sK3),sK3) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(0,plain,
( ~ basis_of(X0,X1)
| lin_ind_subset(X0,X1) ),
inference(cnf,[status(esa)],[basis_of]) ).
cnf(l3,plain,
( ~ basis_of(sK2(sK3),sK3)
| lin_ind_subset(sK2(sK3),sK3) ),
inference(instantiation,[status(thm)],[0]) ).
cnf(l5,plain,
( ~ a_vector_space(sK3)
| basis_of(sK2(sK3),sK3) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l21,plain,
( ~ a_vector_subspace_of(sK3,sK4)
| a_vector_space(sK3) ),
inference(instantiation,[status(thm)],[5]) ).
cnf(l11,plain,
( ~ a_vector_subspace_of(sK3,sK4)
| a_vector_space(sK3) ),
inference(instantiation,[status(thm)],[5]) ).
cnf(9,plain,
a_vector_space(sK4),
inference(cnf,[status(esa)],[bg_2_4_3_negated]) ).
cnf(l17,plain,
a_vector_space(sK4),
inference(instantiation,[status(thm)],[9]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l2,l4,l8,l10,l33,l34,l6,l3,l5,l21,l11,l17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : ALG211+1 : TPTP v9.0.0. Released v3.1.0.
% 0.06/0.12 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n017.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sun Jul 20 02:44:49 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.34 % launching worker at depth: 2
% 0.12/0.34 % launching worker at depth: 6
% 0.12/0.34 % launching worker at depth: 4
% 0.12/0.34 % launching worker at depth: 1
% 0.12/0.34 % launching worker at depth: 3
% 0.12/0.34 % launching worker at depth: 5
% 0.12/0.34 % launching worker at depth: 7
% 0.12/0.34 % launching worker at depth: 8
% 0.12/0.34 % launching worker at depth: 9
% 0.12/0.34 % launching worker at depth: 10
% 0.12/0.34 % launching worker at depth: 11
% 0.12/0.35 % SZS status Theorem for theBenchmark
% 0.12/0.35 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------