%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : ALG211+1 : TPTP v9.2.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n029.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 : Tue May 5 04:08:15 PM UTC 2026
% Result : Theorem 1.25s 1.72s
% Output : CNFRefutation 1.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 29 ( 5 unt; 0 def)
% Number of atoms : 81 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 89 ( 37 ~; 31 |; 13 &)
% ( 1 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 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 : 58 ( 6 sgn 28 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(bg_2_4_3,conjecture,
! [X7,X2] :
( ( a_vector_subspace_of(X7,X2)
& a_vector_space(X2) )
=> ? [X8,X9] :
( basis_of(union(X8,X9),X2)
& basis_of(X8,X7) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bg_2_4_3) ).
fof(bg_2_4_2,axiom,
! [X7,X2,X8] :
( ( a_vector_subspace_of(X7,X2)
& a_subset_of(X8,vec_to_class(X7)) )
=> ( lin_ind_subset(X8,X7)
<=> lin_ind_subset(X8,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bg_2_4_2) ).
fof(basis_of,axiom,
! [X1,X2] :
( basis_of(X1,X2)
=> ( lin_ind_subset(X1,X2)
& a_subset_of(X1,vec_to_class(X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',basis_of) ).
fof(bg_2_2_5,axiom,
! [X3,X4,X2] :
( ( lin_ind_subset(X3,X2)
& basis_of(X4,X2) )
=> ? [X5] :
( a_subset_of(X5,X4)
& basis_of(union(X3,X5),X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bg_2_2_5) ).
fof(bg_2_4_a,axiom,
! [X6,X1] :
( a_vector_subspace_of(X6,X1)
=> a_vector_space(X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bg_2_4_a) ).
fof(bg_remark_63_a,axiom,
! [X6] :
( a_vector_space(X6)
=> ? [X1] : basis_of(X1,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bg_remark_63_a) ).
fof(c_0_6,negated_conjecture,
~ ! [X7,X2] :
( ( a_vector_subspace_of(X7,X2)
& a_vector_space(X2) )
=> ? [X8,X9] :
( basis_of(union(X8,X9),X2)
& basis_of(X8,X7) ) ),
inference(assume_negation,[status(cth)],[bg_2_4_3]) ).
fof(c_0_7,plain,
! [X37,X38,X39] :
( ( ~ lin_ind_subset(X39,X37)
| lin_ind_subset(X39,X38)
| ~ a_vector_subspace_of(X37,X38)
| ~ a_subset_of(X39,vec_to_class(X37)) )
& ( ~ lin_ind_subset(X39,X38)
| lin_ind_subset(X39,X37)
| ~ a_vector_subspace_of(X37,X38)
| ~ a_subset_of(X39,vec_to_class(X37)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[bg_2_4_2])])]) ).
fof(c_0_8,plain,
! [X27,X28] :
( ( lin_ind_subset(X27,X28)
| ~ basis_of(X27,X28) )
& ( a_subset_of(X27,vec_to_class(X28))
| ~ basis_of(X27,X28) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[basis_of])])]) ).
fof(c_0_9,negated_conjecture,
! [X42,X43] :
( a_vector_subspace_of(esk3_0,esk4_0)
& a_vector_space(esk4_0)
& ( ~ basis_of(union(X42,X43),esk4_0)
| ~ basis_of(X42,esk3_0) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).
fof(c_0_10,plain,
! [X29,X30,X31] :
( ( a_subset_of(esk1_3(X29,X30,X31),X30)
| ~ lin_ind_subset(X29,X31)
| ~ basis_of(X30,X31) )
& ( basis_of(union(X29,esk1_3(X29,X30,X31)),X31)
| ~ lin_ind_subset(X29,X31)
| ~ basis_of(X30,X31) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[bg_2_2_5])])])]) ).
cnf(c_0_11,plain,
( lin_ind_subset(X1,X3)
| ~ lin_ind_subset(X1,X2)
| ~ a_vector_subspace_of(X2,X3)
| ~ a_subset_of(X1,vec_to_class(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
( a_subset_of(X1,vec_to_class(X2))
| ~ basis_of(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
( lin_ind_subset(X1,X2)
| ~ basis_of(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,negated_conjecture,
( ~ basis_of(union(X1,X2),esk4_0)
| ~ basis_of(X1,esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( basis_of(union(X1,esk1_3(X1,X2,X3)),X3)
| ~ lin_ind_subset(X1,X3)
| ~ basis_of(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
( lin_ind_subset(X1,X2)
| ~ a_vector_subspace_of(X3,X2)
| ~ basis_of(X1,X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]) ).
cnf(c_0_17,negated_conjecture,
a_vector_subspace_of(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_18,plain,
! [X35,X36] :
( ~ a_vector_subspace_of(X35,X36)
| a_vector_space(X35) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[bg_2_4_a])]) ).
cnf(c_0_19,negated_conjecture,
( ~ lin_ind_subset(X1,esk4_0)
| ~ basis_of(X1,esk3_0)
| ~ basis_of(X2,esk4_0) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_20,negated_conjecture,
( lin_ind_subset(X1,esk4_0)
| ~ basis_of(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
fof(c_0_21,plain,
! [X33] :
( ~ a_vector_space(X33)
| basis_of(esk2_1(X33),X33) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[bg_remark_63_a])])]) ).
cnf(c_0_22,plain,
( a_vector_space(X1)
| ~ a_vector_subspace_of(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_23,negated_conjecture,
( ~ basis_of(X1,esk3_0)
| ~ basis_of(X2,esk4_0) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,plain,
( basis_of(esk2_1(X1),X1)
| ~ a_vector_space(X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_25,negated_conjecture,
a_vector_space(esk3_0),
inference(spm,[status(thm)],[c_0_22,c_0_17]) ).
cnf(c_0_26,negated_conjecture,
~ basis_of(X1,esk4_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25])]) ).
cnf(c_0_27,negated_conjecture,
a_vector_space(esk4_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_28,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_24]),c_0_27])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : ALG211+1 : TPTP v9.2.1. Released v3.1.0.
% 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n029.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue May 5 10:24:29 EDT 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 1.25/1.72 % Version : CSE_E---1.7
% 1.25/1.72 % Problem : theBenchmark.p
% 1.25/1.72 % SZS status Theorem for theBenchmark.p
% 1.25/1.72 % SZS output start CNFRefutation
% See solution above
% 1.25/1.72 % Total time : 1.372s
%------------------------------------------------------------------------------