TSTP Solution File: ALG211+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : ALG211+1 : TPTP v5.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art06.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 2018MB
% OS : Linux 2.6.26.8-57.fc8
% CPULimit : 300s
% DateTime : Sat Dec 25 04:16:58 EST 2010
% Result : Theorem 0.16s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of formulae : 56 ( 10 unt; 0 def)
% Number of atoms : 156 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 179 ( 79 ~; 64 |; 26 &)
% ( 3 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-3 aty)
% Number of variables : 101 ( 5 sgn 59 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] :
( basis_of(X1,X2)
=> ( lin_ind_subset(X1,X2)
& a_subset_of(X1,vec_to_class(X2)) ) ),
file('/tmp/tmpy3eEz9/sel_ALG211+1.p_1',basis_of) ).
fof(2,axiom,
! [X3,X2,X4] :
( ( a_vector_subspace_of(X3,X2)
& a_subset_of(X4,vec_to_class(X3)) )
=> ( lin_ind_subset(X4,X3)
<=> lin_ind_subset(X4,X2) ) ),
file('/tmp/tmpy3eEz9/sel_ALG211+1.p_1',bg_2_4_2) ).
fof(3,conjecture,
! [X3,X2] :
( ( a_vector_subspace_of(X3,X2)
& a_vector_space(X2) )
=> ? [X4,X5] :
( basis_of(union(X4,X5),X2)
& basis_of(X4,X3) ) ),
file('/tmp/tmpy3eEz9/sel_ALG211+1.p_1',bg_2_4_3) ).
fof(4,axiom,
! [X6] :
( a_vector_space(X6)
=> ? [X1] : basis_of(X1,X6) ),
file('/tmp/tmpy3eEz9/sel_ALG211+1.p_1',bg_remark_63_a) ).
fof(5,axiom,
! [X6,X1] :
( a_vector_subspace_of(X6,X1)
=> a_vector_space(X6) ),
file('/tmp/tmpy3eEz9/sel_ALG211+1.p_1',bg_2_4_a) ).
fof(6,axiom,
! [X7,X8,X2] :
( ( lin_ind_subset(X7,X2)
& basis_of(X8,X2) )
=> ? [X9] :
( a_subset_of(X9,X8)
& basis_of(union(X7,X9),X2) ) ),
file('/tmp/tmpy3eEz9/sel_ALG211+1.p_1',bg_2_2_5) ).
fof(7,negated_conjecture,
~ ! [X3,X2] :
( ( a_vector_subspace_of(X3,X2)
& a_vector_space(X2) )
=> ? [X4,X5] :
( basis_of(union(X4,X5),X2)
& basis_of(X4,X3) ) ),
inference(assume_negation,[status(cth)],[3]) ).
fof(8,plain,
! [X1,X2] :
( ~ basis_of(X1,X2)
| ( lin_ind_subset(X1,X2)
& a_subset_of(X1,vec_to_class(X2)) ) ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(9,plain,
! [X3,X4] :
( ~ basis_of(X3,X4)
| ( lin_ind_subset(X3,X4)
& a_subset_of(X3,vec_to_class(X4)) ) ),
inference(variable_rename,[status(thm)],[8]) ).
fof(10,plain,
! [X3,X4] :
( ( lin_ind_subset(X3,X4)
| ~ basis_of(X3,X4) )
& ( a_subset_of(X3,vec_to_class(X4))
| ~ basis_of(X3,X4) ) ),
inference(distribute,[status(thm)],[9]) ).
cnf(11,plain,
( a_subset_of(X1,vec_to_class(X2))
| ~ basis_of(X1,X2) ),
inference(split_conjunct,[status(thm)],[10]) ).
cnf(12,plain,
( lin_ind_subset(X1,X2)
| ~ basis_of(X1,X2) ),
inference(split_conjunct,[status(thm)],[10]) ).
fof(13,plain,
! [X3,X2,X4] :
( ~ a_vector_subspace_of(X3,X2)
| ~ a_subset_of(X4,vec_to_class(X3))
| ( ( ~ lin_ind_subset(X4,X3)
| lin_ind_subset(X4,X2) )
& ( ~ lin_ind_subset(X4,X2)
| lin_ind_subset(X4,X3) ) ) ),
inference(fof_nnf,[status(thm)],[2]) ).
fof(14,plain,
! [X5,X6,X7] :
( ~ a_vector_subspace_of(X5,X6)
| ~ a_subset_of(X7,vec_to_class(X5))
| ( ( ~ lin_ind_subset(X7,X5)
| lin_ind_subset(X7,X6) )
& ( ~ lin_ind_subset(X7,X6)
| lin_ind_subset(X7,X5) ) ) ),
inference(variable_rename,[status(thm)],[13]) ).
fof(15,plain,
! [X5,X6,X7] :
( ( ~ lin_ind_subset(X7,X5)
| lin_ind_subset(X7,X6)
| ~ a_vector_subspace_of(X5,X6)
| ~ a_subset_of(X7,vec_to_class(X5)) )
& ( ~ lin_ind_subset(X7,X6)
| lin_ind_subset(X7,X5)
| ~ a_vector_subspace_of(X5,X6)
| ~ a_subset_of(X7,vec_to_class(X5)) ) ),
inference(distribute,[status(thm)],[14]) ).
cnf(17,plain,
( lin_ind_subset(X1,X3)
| ~ a_subset_of(X1,vec_to_class(X2))
| ~ a_vector_subspace_of(X2,X3)
| ~ lin_ind_subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[15]) ).
fof(18,negated_conjecture,
? [X3,X2] :
( a_vector_subspace_of(X3,X2)
& a_vector_space(X2)
& ! [X4,X5] :
( ~ basis_of(union(X4,X5),X2)
| ~ basis_of(X4,X3) ) ),
inference(fof_nnf,[status(thm)],[7]) ).
fof(19,negated_conjecture,
? [X6,X7] :
( a_vector_subspace_of(X6,X7)
& a_vector_space(X7)
& ! [X8,X9] :
( ~ basis_of(union(X8,X9),X7)
| ~ basis_of(X8,X6) ) ),
inference(variable_rename,[status(thm)],[18]) ).
fof(20,negated_conjecture,
( a_vector_subspace_of(esk1_0,esk2_0)
& a_vector_space(esk2_0)
& ! [X8,X9] :
( ~ basis_of(union(X8,X9),esk2_0)
| ~ basis_of(X8,esk1_0) ) ),
inference(skolemize,[status(esa)],[19]) ).
fof(21,negated_conjecture,
! [X8,X9] :
( ( ~ basis_of(union(X8,X9),esk2_0)
| ~ basis_of(X8,esk1_0) )
& a_vector_subspace_of(esk1_0,esk2_0)
& a_vector_space(esk2_0) ),
inference(shift_quantors,[status(thm)],[20]) ).
cnf(22,negated_conjecture,
a_vector_space(esk2_0),
inference(split_conjunct,[status(thm)],[21]) ).
cnf(23,negated_conjecture,
a_vector_subspace_of(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[21]) ).
cnf(24,negated_conjecture,
( ~ basis_of(X1,esk1_0)
| ~ basis_of(union(X1,X2),esk2_0) ),
inference(split_conjunct,[status(thm)],[21]) ).
fof(25,plain,
! [X6] :
( ~ a_vector_space(X6)
| ? [X1] : basis_of(X1,X6) ),
inference(fof_nnf,[status(thm)],[4]) ).
fof(26,plain,
! [X7] :
( ~ a_vector_space(X7)
| ? [X8] : basis_of(X8,X7) ),
inference(variable_rename,[status(thm)],[25]) ).
fof(27,plain,
! [X7] :
( ~ a_vector_space(X7)
| basis_of(esk3_1(X7),X7) ),
inference(skolemize,[status(esa)],[26]) ).
cnf(28,plain,
( basis_of(esk3_1(X1),X1)
| ~ a_vector_space(X1) ),
inference(split_conjunct,[status(thm)],[27]) ).
fof(29,plain,
! [X6,X1] :
( ~ a_vector_subspace_of(X6,X1)
| a_vector_space(X6) ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(30,plain,
! [X7,X8] :
( ~ a_vector_subspace_of(X7,X8)
| a_vector_space(X7) ),
inference(variable_rename,[status(thm)],[29]) ).
cnf(31,plain,
( a_vector_space(X1)
| ~ a_vector_subspace_of(X1,X2) ),
inference(split_conjunct,[status(thm)],[30]) ).
fof(32,plain,
! [X7,X8,X2] :
( ~ lin_ind_subset(X7,X2)
| ~ basis_of(X8,X2)
| ? [X9] :
( a_subset_of(X9,X8)
& basis_of(union(X7,X9),X2) ) ),
inference(fof_nnf,[status(thm)],[6]) ).
fof(33,plain,
! [X10,X11,X12] :
( ~ lin_ind_subset(X10,X12)
| ~ basis_of(X11,X12)
| ? [X13] :
( a_subset_of(X13,X11)
& basis_of(union(X10,X13),X12) ) ),
inference(variable_rename,[status(thm)],[32]) ).
fof(34,plain,
! [X10,X11,X12] :
( ~ lin_ind_subset(X10,X12)
| ~ basis_of(X11,X12)
| ( a_subset_of(esk4_3(X10,X11,X12),X11)
& basis_of(union(X10,esk4_3(X10,X11,X12)),X12) ) ),
inference(skolemize,[status(esa)],[33]) ).
fof(35,plain,
! [X10,X11,X12] :
( ( a_subset_of(esk4_3(X10,X11,X12),X11)
| ~ lin_ind_subset(X10,X12)
| ~ basis_of(X11,X12) )
& ( basis_of(union(X10,esk4_3(X10,X11,X12)),X12)
| ~ lin_ind_subset(X10,X12)
| ~ basis_of(X11,X12) ) ),
inference(distribute,[status(thm)],[34]) ).
cnf(36,plain,
( basis_of(union(X3,esk4_3(X3,X1,X2)),X2)
| ~ basis_of(X1,X2)
| ~ lin_ind_subset(X3,X2) ),
inference(split_conjunct,[status(thm)],[35]) ).
cnf(38,negated_conjecture,
a_vector_space(esk1_0),
inference(spm,[status(thm)],[31,23,theory(equality)]) ).
cnf(39,negated_conjecture,
( ~ basis_of(X1,esk1_0)
| ~ lin_ind_subset(X1,esk2_0)
| ~ basis_of(X2,esk2_0) ),
inference(spm,[status(thm)],[24,36,theory(equality)]) ).
cnf(40,plain,
( lin_ind_subset(X1,X2)
| ~ a_vector_subspace_of(X3,X2)
| ~ lin_ind_subset(X1,X3)
| ~ basis_of(X1,X3) ),
inference(spm,[status(thm)],[17,11,theory(equality)]) ).
fof(44,plain,
( ~ epred1_0
<=> ! [X1] :
( ~ basis_of(X1,esk1_0)
| ~ lin_ind_subset(X1,esk2_0) ) ),
introduced(definition),
[split] ).
cnf(45,plain,
( epred1_0
| ~ basis_of(X1,esk1_0)
| ~ lin_ind_subset(X1,esk2_0) ),
inference(split_equiv,[status(thm)],[44]) ).
fof(46,plain,
( ~ epred2_0
<=> ! [X2] : ~ basis_of(X2,esk2_0) ),
introduced(definition),
[split] ).
cnf(47,plain,
( epred2_0
| ~ basis_of(X2,esk2_0) ),
inference(split_equiv,[status(thm)],[46]) ).
cnf(48,negated_conjecture,
( ~ epred2_0
| ~ epred1_0 ),
inference(apply_def,[status(esa)],[inference(apply_def,[status(esa)],[39,44,theory(equality)]),46,theory(equality)]),
[split] ).
cnf(49,negated_conjecture,
( epred2_0
| ~ a_vector_space(esk2_0) ),
inference(spm,[status(thm)],[47,28,theory(equality)]) ).
cnf(51,negated_conjecture,
( epred2_0
| $false ),
inference(rw,[status(thm)],[49,22,theory(equality)]) ).
cnf(52,negated_conjecture,
epred2_0,
inference(cn,[status(thm)],[51,theory(equality)]) ).
cnf(54,negated_conjecture,
( $false
| ~ epred1_0 ),
inference(rw,[status(thm)],[48,52,theory(equality)]) ).
cnf(55,negated_conjecture,
~ epred1_0,
inference(cn,[status(thm)],[54,theory(equality)]) ).
cnf(56,plain,
( lin_ind_subset(X1,X2)
| ~ a_vector_subspace_of(X3,X2)
| ~ basis_of(X1,X3) ),
inference(csr,[status(thm)],[40,12]) ).
cnf(57,negated_conjecture,
( lin_ind_subset(X1,esk2_0)
| ~ basis_of(X1,esk1_0) ),
inference(spm,[status(thm)],[56,23,theory(equality)]) ).
cnf(58,negated_conjecture,
( ~ basis_of(X1,esk1_0)
| ~ lin_ind_subset(X1,esk2_0) ),
inference(sr,[status(thm)],[45,55,theory(equality)]) ).
cnf(64,negated_conjecture,
~ basis_of(X1,esk1_0),
inference(csr,[status(thm)],[57,58]) ).
cnf(65,negated_conjecture,
~ a_vector_space(esk1_0),
inference(spm,[status(thm)],[64,28,theory(equality)]) ).
cnf(67,negated_conjecture,
$false,
inference(rw,[status(thm)],[65,38,theory(equality)]) ).
cnf(68,negated_conjecture,
$false,
inference(cn,[status(thm)],[67,theory(equality)]) ).
cnf(69,negated_conjecture,
$false,
68,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/ALG/ALG211+1.p
% --creating new selector for []
% -running prover on /tmp/tmpy3eEz9/sel_ALG211+1.p_1 with time limit 29
% -prover status Theorem
% Problem ALG211+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/ALG/ALG211+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/ALG/ALG211+1.p
% Solved 1 out of 1.
% # Problem is unsatisfiable (or provable), constructing proof object
% # SZS status Theorem
% # SZS output start CNFRefutation.
% See solution above
% # SZS output end CNFRefutation
%
%------------------------------------------------------------------------------