%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : ALG211+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 08:11:48 AM UTC 2026
% Result : Theorem 0.12s 0.38s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 61 ( 20 unt; 0 def)
% Number of atoms : 145 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 142 ( 58 ~; 49 |; 27 &)
% ( 1 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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 : 87 ( 2 sgn 55 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(basis_of,axiom,
! [B,V] :
( basis_of(B,V)
=> ( a_subset_of(B,vec_to_class(V))
& lin_ind_subset(B,V) ) ),
file('theBenchmark.p',basis_of) ).
fof(bg_2_2_5,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('theBenchmark.p',bg_2_2_5) ).
fof(bg_remark_63_a,axiom,
! [A] :
( a_vector_space(A)
=> ? [B] : basis_of(B,A) ),
file('theBenchmark.p',bg_remark_63_a) ).
fof(bg_2_4_a,axiom,
! [A,B] :
( a_vector_subspace_of(A,B)
=> a_vector_space(A) ),
file('theBenchmark.p',bg_2_4_a) ).
fof(bg_2_4_2,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('theBenchmark.p',bg_2_4_2) ).
fof(bg_2_4_3,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('theBenchmark.p',bg_2_4_3) ).
fof(f_1_1,plain,
! [B,V] :
( ( a_subset_of(B,vec_to_class(V))
& lin_ind_subset(B,V) )
| ~ basis_of(B,V) ),
inference(fof_nnf,[status(thm)],[basis_of]) ).
fof(f_1_2,plain,
! [U_1,U_0] :
( ( a_subset_of(U_1,vec_to_class(U_0))
& lin_ind_subset(U_1,U_0) )
| ~ basis_of(U_1,U_0) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
cnf(f_1_3,plain,
( lin_ind_subset(U_1,U_0)
| ~ basis_of(U_1,U_0) ),
inference(clausify,[status(thm)],[f_1_2]) ).
cnf(f_1_4,plain,
( a_subset_of(U_1,vec_to_class(U_0))
| ~ basis_of(U_1,U_0) ),
inference(clausify,[status(thm)],[f_1_2]) ).
fof(f_2_1,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(fof_nnf,[status(thm)],[bg_2_2_5]) ).
fof(f_2_2,plain,
! [U_5,U_4,U_3] :
( ? [U_2] :
( basis_of(union(U_5,U_2),U_3)
& a_subset_of(U_2,U_4) )
| ~ basis_of(U_4,U_3)
| ~ lin_ind_subset(U_5,U_3) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
! [U_5,U_4,U_3] :
( ( basis_of(union(U_5,sK1(U_5,U_4,U_3)),U_3)
& a_subset_of(sK1(U_5,U_4,U_3),U_4) )
| ~ basis_of(U_4,U_3)
| ~ lin_ind_subset(U_5,U_3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_2,sK1(U_5,U_4,U_3))],[f_2_2]) ).
cnf(f_2_5,plain,
( basis_of(union(U_5,sK1(U_5,U_4,U_3)),U_3)
| ~ basis_of(U_4,U_3)
| ~ lin_ind_subset(U_5,U_3) ),
inference(clausify,[status(thm)],[f_2_3]) ).
fof(f_3_1,plain,
! [A] :
( ? [B] : basis_of(B,A)
| ~ a_vector_space(A) ),
inference(fof_nnf,[status(thm)],[bg_remark_63_a]) ).
fof(f_3_2,plain,
! [U_7] :
( ? [U_6] : basis_of(U_6,U_7)
| ~ a_vector_space(U_7) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
! [U_7] :
( basis_of(sK2(U_7),U_7)
| ~ a_vector_space(U_7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_6,sK2(U_7))],[f_3_2]) ).
cnf(f_3_4,plain,
( basis_of(sK2(U_7),U_7)
| ~ a_vector_space(U_7) ),
inference(clausify,[status(thm)],[f_3_3]) ).
fof(f_4_1,plain,
! [A,B] :
( a_vector_space(A)
| ~ a_vector_subspace_of(A,B) ),
inference(fof_nnf,[status(thm)],[bg_2_4_a]) ).
fof(f_4_2,plain,
! [U_9,U_8] :
( a_vector_space(U_9)
| ~ a_vector_subspace_of(U_9,U_8) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
! [U_9] :
( ! [U_8] : ~ a_vector_subspace_of(U_9,U_8)
| a_vector_space(U_9) ),
inference(miniscope,[status(thm)],[f_4_2]) ).
cnf(f_4_4,plain,
( ~ a_vector_subspace_of(U_9,U_8)
| a_vector_space(U_9) ),
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_5_1,plain,
! [W,V,E] :
( ( ( lin_ind_subset(E,W)
| ~ lin_ind_subset(E,V) )
& ( 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(fof_nnf,[status(thm)],[bg_2_4_2]) ).
fof(f_5_2,plain,
! [U_12,U_11,U_10] :
( ( ( lin_ind_subset(U_10,U_12)
| ~ lin_ind_subset(U_10,U_11) )
& ( lin_ind_subset(U_10,U_11)
| ~ lin_ind_subset(U_10,U_12) ) )
| ~ a_subset_of(U_10,vec_to_class(U_12))
| ~ a_vector_subspace_of(U_12,U_11) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
( lin_ind_subset(U_10,U_11)
| ~ lin_ind_subset(U_10,U_12)
| ~ a_subset_of(U_10,vec_to_class(U_12))
| ~ a_vector_subspace_of(U_12,U_11) ),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_1,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(negate,[status(cth)],[bg_2_4_3]) ).
fof(f_6_2,negated_conjecture,
? [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(fof_nnf,[status(thm)],[f_6_1]) ).
fof(f_6_3,negated_conjecture,
? [U_16,U_15] :
( ! [U_14,U_13] :
( ~ basis_of(U_14,U_16)
| ~ basis_of(union(U_14,U_13),U_15) )
& a_vector_space(U_15)
& a_vector_subspace_of(U_16,U_15) ),
inference(variable_rename,[status(thm)],[f_6_2]) ).
fof(f_6_4,negated_conjecture,
? [U_16,U_15] :
( ! [U_14] :
( ! [U_13] : ~ basis_of(union(U_14,U_13),U_15)
| ~ basis_of(U_14,U_16) )
& a_vector_space(U_15)
& a_vector_subspace_of(U_16,U_15) ),
inference(miniscope,[status(thm)],[f_6_3]) ).
fof(f_6_5,negated_conjecture,
? [U_15] :
( ! [U_14] :
( ! [U_13] : ~ basis_of(union(U_14,U_13),U_15)
| ~ basis_of(U_14,sK3) )
& a_vector_space(U_15)
& a_vector_subspace_of(sK3,U_15) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_16,sK3)],[f_6_4]) ).
fof(f_6_6,negated_conjecture,
( ! [U_14] :
( ! [U_13] : ~ basis_of(union(U_14,U_13),sK4)
| ~ basis_of(U_14,sK3) )
& a_vector_space(sK4)
& a_vector_subspace_of(sK3,sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_15,sK4)],[f_6_5]) ).
fof(f_6_7,negated_conjecture,
( ! [U_13,U_14] :
( ~ basis_of(union(U_14,U_13),sK4)
| ~ basis_of(U_14,sK3) )
& a_vector_space(sK4)
& a_vector_subspace_of(sK3,sK4) ),
inference(definitional_conversion,[status(esa)],[f_6_6]) ).
cnf(f_6_8,negated_conjecture,
a_vector_subspace_of(sK3,sK4),
inference(clausify,[status(thm)],[f_6_7]) ).
cnf(f_6_9,negated_conjecture,
a_vector_space(sK4),
inference(clausify,[status(thm)],[f_6_7]) ).
cnf(f_6_10,negated_conjecture,
( ~ basis_of(union(U_14,U_13),sK4)
| ~ basis_of(U_14,sK3) ),
inference(clausify,[status(thm)],[f_6_7]) ).
cnf(t1,plain,
( ~ basis_of(union(sK2(sK3),sK1(sK2(sK3),sK2(sK4),sK4)),sK4)
| ~ basis_of(sK2(sK3),sK3) ),
inference(start,[status(thm),parent(0:0)],[f_6_10]) ).
cnf(t2,plain,
( ~ a_vector_space(sK3)
| basis_of(sK2(sK3),sK3) ),
inference(extension,[status(thm),parent(t1:1)],[f_3_4]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ a_vector_subspace_of(sK3,sK4)
| a_vector_space(sK3) ),
inference(extension,[status(thm),parent(t2:2)],[f_4_4]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
a_vector_subspace_of(sK3,sK4),
inference(extension,[status(thm),parent(t4:2)],[f_6_8]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(l1,lemma,
basis_of(sK2(sK3),sK3),
inference(lemma,[status(cth),parent(t1:1),below(0:0)],[t1:1]) ).
cnf(t8,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(extension,[status(thm),parent(t1:2)],[f_2_5]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t1:2]) ).
cnf(t10,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(extension,[status(thm),parent(t8:2)],[f_5_3]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
a_vector_subspace_of(sK3,sK4),
inference(extension,[status(thm),parent(t10:2)],[f_6_8]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
( ~ basis_of(sK2(sK3),sK3)
| lin_ind_subset(sK2(sK3),sK3) ),
inference(extension,[status(thm),parent(t10:3)],[f_1_3]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t10:3]) ).
cnf(t16,plain,
basis_of(sK2(sK3),sK3),
inference(lemma_extension,[status(thm),parent(t14:2)],[l1:1]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(t18,plain,
( ~ basis_of(sK2(sK3),sK3)
| a_subset_of(sK2(sK3),vec_to_class(sK3)) ),
inference(extension,[status(thm),parent(t10:4)],[f_1_4]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t10:4]) ).
cnf(t20,plain,
basis_of(sK2(sK3),sK3),
inference(lemma_extension,[status(thm),parent(t18:2)],[l1:1]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t18:2]) ).
cnf(t22,plain,
( ~ a_vector_space(sK4)
| basis_of(sK2(sK4),sK4) ),
inference(extension,[status(thm),parent(t8:3)],[f_3_4]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t8:3]) ).
cnf(t24,plain,
a_vector_space(sK4),
inference(extension,[status(thm),parent(t22:2)],[f_6_9]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t22:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG211+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.03 This is a FOF_THM_RFO_NEQ problem
% 0.00/0.03 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n011.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 20 09:44:40 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.12/0.38 % SZS status Theorem for theBenchmark
% 0.12/0.38 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------