TSTP Solution File: ALG211+1 by ET---2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : ALG211+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n024.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 : 600s
% DateTime : Thu Jul 14 16:50:24 EDT 2022
% Result : Theorem 0.22s 1.40s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 28 ( 5 unt; 0 def)
% Number of atoms : 78 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 84 ( 34 ~; 29 |; 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 : 56 ( 5 sgn 28 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
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/solver/bin/../tmp/theBenchmark.p.mepo_128.in',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/solver/bin/../tmp/theBenchmark.p.mepo_128.in',basis_of) ).
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/solver/bin/../tmp/theBenchmark.p.mepo_128.in',bg_2_4_3) ).
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/solver/bin/../tmp/theBenchmark.p.mepo_128.in',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/solver/bin/../tmp/theBenchmark.p.mepo_128.in',bg_2_4_a) ).
fof(bg_remark_63_a,axiom,
! [X6] :
( a_vector_space(X6)
=> ? [X1] : basis_of(X1,X6) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',bg_remark_63_a) ).
fof(c_0_6,plain,
! [X9,X10,X11] :
( ( ~ lin_ind_subset(X11,X9)
| lin_ind_subset(X11,X10)
| ~ a_vector_subspace_of(X9,X10)
| ~ a_subset_of(X11,vec_to_class(X9)) )
& ( ~ lin_ind_subset(X11,X10)
| lin_ind_subset(X11,X9)
| ~ a_vector_subspace_of(X9,X10)
| ~ a_subset_of(X11,vec_to_class(X9)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[bg_2_4_2])])]) ).
fof(c_0_7,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)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[basis_of])])]) ).
fof(c_0_8,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]) ).
cnf(c_0_9,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)],[c_0_6]) ).
cnf(c_0_10,plain,
( a_subset_of(X1,vec_to_class(X2))
| ~ basis_of(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
( lin_ind_subset(X1,X2)
| ~ basis_of(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_12,negated_conjecture,
! [X12,X13] :
( a_vector_subspace_of(esk3_0,esk4_0)
& a_vector_space(esk4_0)
& ( ~ basis_of(union(X12,X13),esk4_0)
| ~ basis_of(X12,esk3_0) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])])])]) ).
fof(c_0_13,plain,
! [X6,X7,X8] :
( ( a_subset_of(esk1_3(X6,X7,X8),X7)
| ~ lin_ind_subset(X6,X8)
| ~ basis_of(X7,X8) )
& ( basis_of(union(X6,esk1_3(X6,X7,X8)),X8)
| ~ lin_ind_subset(X6,X8)
| ~ basis_of(X7,X8) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[bg_2_2_5])])])])])]) ).
cnf(c_0_14,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_9,c_0_10]),c_0_11]) ).
cnf(c_0_15,negated_conjecture,
a_vector_subspace_of(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_16,plain,
! [X7,X8] :
( ~ a_vector_subspace_of(X7,X8)
| a_vector_space(X7) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[bg_2_4_a])])])]) ).
cnf(c_0_17,negated_conjecture,
( ~ basis_of(X1,esk3_0)
| ~ basis_of(union(X1,X2),esk4_0) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,plain,
( basis_of(union(X3,esk1_3(X3,X1,X2)),X2)
| ~ basis_of(X1,X2)
| ~ lin_ind_subset(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,negated_conjecture,
( lin_ind_subset(X1,esk4_0)
| ~ basis_of(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
fof(c_0_20,plain,
! [X7] :
( ~ a_vector_space(X7)
| basis_of(esk2_1(X7),X7) ),
inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[bg_remark_63_a])])])])]) ).
cnf(c_0_21,plain,
( a_vector_space(X1)
| ~ a_vector_subspace_of(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,negated_conjecture,
( ~ basis_of(X1,esk3_0)
| ~ basis_of(X2,esk4_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]) ).
cnf(c_0_23,plain,
( basis_of(esk2_1(X1),X1)
| ~ a_vector_space(X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_24,negated_conjecture,
a_vector_space(esk3_0),
inference(spm,[status(thm)],[c_0_21,c_0_15]) ).
cnf(c_0_25,negated_conjecture,
~ basis_of(X1,esk4_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24])]) ).
cnf(c_0_26,negated_conjecture,
a_vector_space(esk4_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_27,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_23]),c_0_26])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : ALG211+1 : TPTP v8.1.0. Released v3.1.0.
% 0.10/0.12 % Command : run_ET %s %d
% 0.12/0.33 % Computer : n024.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 : 600
% 0.12/0.33 % DateTime : Wed Jun 8 06:39:34 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.22/1.40 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.22/1.40 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.22/1.40 # Preprocessing time : 0.014 s
% 0.22/1.40
% 0.22/1.40 # Failure: Out of unprocessed clauses!
% 0.22/1.40 # OLD status GaveUp
% 0.22/1.40 # Parsed axioms : 6
% 0.22/1.40 # Removed by relevancy pruning/SinE : 2
% 0.22/1.40 # Initial clauses : 7
% 0.22/1.40 # Removed in clause preprocessing : 0
% 0.22/1.40 # Initial clauses in saturation : 7
% 0.22/1.40 # Processed clauses : 9
% 0.22/1.40 # ...of these trivial : 0
% 0.22/1.40 # ...subsumed : 0
% 0.22/1.40 # ...remaining for further processing : 9
% 0.22/1.40 # Other redundant clauses eliminated : 0
% 0.22/1.40 # Clauses deleted for lack of memory : 0
% 0.22/1.40 # Backward-subsumed : 0
% 0.22/1.40 # Backward-rewritten : 0
% 0.22/1.40 # Generated clauses : 2
% 0.22/1.40 # ...of the previous two non-trivial : 2
% 0.22/1.40 # Contextual simplify-reflections : 0
% 0.22/1.40 # Paramodulations : 2
% 0.22/1.40 # Factorizations : 0
% 0.22/1.40 # Equation resolutions : 0
% 0.22/1.40 # Current number of processed clauses : 9
% 0.22/1.40 # Positive orientable unit clauses : 3
% 0.22/1.40 # Positive unorientable unit clauses: 0
% 0.22/1.40 # Negative unit clauses : 0
% 0.22/1.40 # Non-unit-clauses : 6
% 0.22/1.40 # Current number of unprocessed clauses: 0
% 0.22/1.40 # ...number of literals in the above : 0
% 0.22/1.40 # Current number of archived formulas : 0
% 0.22/1.40 # Current number of archived clauses : 0
% 0.22/1.40 # Clause-clause subsumption calls (NU) : 1
% 0.22/1.40 # Rec. Clause-clause subsumption calls : 0
% 0.22/1.40 # Non-unit clause-clause subsumptions : 0
% 0.22/1.40 # Unit Clause-clause subsumption calls : 0
% 0.22/1.40 # Rewrite failures with RHS unbound : 0
% 0.22/1.40 # BW rewrite match attempts : 0
% 0.22/1.40 # BW rewrite match successes : 0
% 0.22/1.40 # Condensation attempts : 0
% 0.22/1.40 # Condensation successes : 0
% 0.22/1.40 # Termbank termtop insertions : 477
% 0.22/1.40
% 0.22/1.40 # -------------------------------------------------
% 0.22/1.40 # User time : 0.014 s
% 0.22/1.40 # System time : 0.001 s
% 0.22/1.40 # Total time : 0.015 s
% 0.22/1.40 # Maximum resident set size: 2776 pages
% 0.22/1.40 # Running protocol protocol_eprover_f171197f65f27d1ba69648a20c844832c84a5dd7 for 23 seconds:
% 0.22/1.40 # Preprocessing time : 0.014 s
% 0.22/1.40
% 0.22/1.40 # Proof found!
% 0.22/1.40 # SZS status Theorem
% 0.22/1.40 # SZS output start CNFRefutation
% See solution above
% 0.22/1.40 # Proof object total steps : 28
% 0.22/1.40 # Proof object clause steps : 15
% 0.22/1.40 # Proof object formula steps : 13
% 0.22/1.40 # Proof object conjectures : 11
% 0.22/1.40 # Proof object clause conjectures : 8
% 0.22/1.40 # Proof object formula conjectures : 3
% 0.22/1.40 # Proof object initial clauses used : 9
% 0.22/1.40 # Proof object initial formulas used : 6
% 0.22/1.40 # Proof object generating inferences : 6
% 0.22/1.40 # Proof object simplifying inferences : 6
% 0.22/1.40 # Training examples: 0 positive, 0 negative
% 0.22/1.40 # Parsed axioms : 6
% 0.22/1.40 # Removed by relevancy pruning/SinE : 0
% 0.22/1.40 # Initial clauses : 11
% 0.22/1.40 # Removed in clause preprocessing : 0
% 0.22/1.40 # Initial clauses in saturation : 11
% 0.22/1.40 # Processed clauses : 17
% 0.22/1.40 # ...of these trivial : 0
% 0.22/1.40 # ...subsumed : 1
% 0.22/1.40 # ...remaining for further processing : 16
% 0.22/1.40 # Other redundant clauses eliminated : 0
% 0.22/1.40 # Clauses deleted for lack of memory : 0
% 0.22/1.40 # Backward-subsumed : 1
% 0.22/1.40 # Backward-rewritten : 0
% 0.22/1.40 # Generated clauses : 11
% 0.22/1.40 # ...of the previous two non-trivial : 9
% 0.22/1.40 # Contextual simplify-reflections : 4
% 0.22/1.40 # Paramodulations : 11
% 0.22/1.40 # Factorizations : 0
% 0.22/1.40 # Equation resolutions : 0
% 0.22/1.40 # Current number of processed clauses : 15
% 0.22/1.40 # Positive orientable unit clauses : 3
% 0.22/1.40 # Positive unorientable unit clauses: 0
% 0.22/1.40 # Negative unit clauses : 1
% 0.22/1.40 # Non-unit-clauses : 11
% 0.22/1.40 # Current number of unprocessed clauses: 3
% 0.22/1.40 # ...number of literals in the above : 13
% 0.22/1.40 # Current number of archived formulas : 0
% 0.22/1.40 # Current number of archived clauses : 1
% 0.22/1.40 # Clause-clause subsumption calls (NU) : 17
% 0.22/1.40 # Rec. Clause-clause subsumption calls : 15
% 0.22/1.40 # Non-unit clause-clause subsumptions : 6
% 0.22/1.40 # Unit Clause-clause subsumption calls : 8
% 0.22/1.40 # Rewrite failures with RHS unbound : 0
% 0.22/1.40 # BW rewrite match attempts : 0
% 0.22/1.40 # BW rewrite match successes : 0
% 0.22/1.40 # Condensation attempts : 0
% 0.22/1.40 # Condensation successes : 0
% 0.22/1.40 # Termbank termtop insertions : 807
% 0.22/1.40
% 0.22/1.40 # -------------------------------------------------
% 0.22/1.40 # User time : 0.014 s
% 0.22/1.40 # System time : 0.001 s
% 0.22/1.40 # Total time : 0.015 s
% 0.22/1.40 # Maximum resident set size: 2780 pages
%------------------------------------------------------------------------------