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
%------------------------------------------------------------------------------