TSTP Solution File: SET679+3 by ET---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : SET679+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_ET %s %d

% Computer : n019.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 : Tue Jul 19 00:53:06 EDT 2022

% Result   : Theorem 0.22s 1.41s
% Output   : CNFRefutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   27 (   9 unt;   0 def)
%            Number of atoms       :   79 (   6 equ)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives :   93 (  41   ~;  32   |;   8   &)
%                                         (   3 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   32 (   3 sgn  18   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(prove_relset_1_46,conjecture,
    ! [X1] :
      ( ( ~ empty(X1)
        & ilf_type(X1,set_type) )
     => not_equal(identity_relation_of(X1),empty_set) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',prove_relset_1_46) ).

fof(p7,axiom,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ! [X2] :
          ( ilf_type(X2,set_type)
         => ( not_equal(X1,X2)
          <=> X1 != X2 ) ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',p7) ).

fof(p22,axiom,
    ! [X1] : ilf_type(X1,set_type),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',p22) ).

fof(p1,axiom,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ! [X2] :
          ( ilf_type(X2,set_type)
         => ( member(X2,X1)
          <=> member(ordered_pair(X2,X2),identity_relation_of(X1)) ) ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',p1) ).

fof(p2,axiom,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ~ member(X1,empty_set) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',p2) ).

fof(p8,axiom,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ( empty(X1)
      <=> ! [X2] :
            ( ilf_type(X2,set_type)
           => ~ member(X2,X1) ) ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',p8) ).

fof(c_0_6,negated_conjecture,
    ~ ! [X1] :
        ( ( ~ empty(X1)
          & ilf_type(X1,set_type) )
       => not_equal(identity_relation_of(X1),empty_set) ),
    inference(assume_negation,[status(cth)],[prove_relset_1_46]) ).

fof(c_0_7,plain,
    ! [X3,X4] :
      ( ( ~ not_equal(X3,X4)
        | X3 != X4
        | ~ ilf_type(X4,set_type)
        | ~ ilf_type(X3,set_type) )
      & ( X3 = X4
        | not_equal(X3,X4)
        | ~ ilf_type(X4,set_type)
        | ~ ilf_type(X3,set_type) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p7])])])])])]) ).

fof(c_0_8,plain,
    ! [X2] : ilf_type(X2,set_type),
    inference(variable_rename,[status(thm)],[p22]) ).

fof(c_0_9,plain,
    ! [X3,X4] :
      ( ( ~ member(X4,X3)
        | member(ordered_pair(X4,X4),identity_relation_of(X3))
        | ~ ilf_type(X4,set_type)
        | ~ ilf_type(X3,set_type) )
      & ( ~ member(ordered_pair(X4,X4),identity_relation_of(X3))
        | member(X4,X3)
        | ~ ilf_type(X4,set_type)
        | ~ ilf_type(X3,set_type) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p1])])])])])]) ).

fof(c_0_10,negated_conjecture,
    ( ~ empty(esk1_0)
    & ilf_type(esk1_0,set_type)
    & ~ not_equal(identity_relation_of(esk1_0),empty_set) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_6])])])]) ).

cnf(c_0_11,plain,
    ( not_equal(X1,X2)
    | X1 = X2
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_12,plain,
    ilf_type(X1,set_type),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

fof(c_0_13,plain,
    ! [X2] :
      ( ~ ilf_type(X2,set_type)
      | ~ member(X2,empty_set) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[p2])])]) ).

cnf(c_0_14,plain,
    ( member(ordered_pair(X2,X2),identity_relation_of(X1))
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type)
    | ~ member(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_15,negated_conjecture,
    ~ not_equal(identity_relation_of(esk1_0),empty_set),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_16,plain,
    ( X1 = X2
    | not_equal(X1,X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_12]),c_0_12])]) ).

cnf(c_0_17,plain,
    ( ~ member(X1,empty_set)
    | ~ ilf_type(X1,set_type) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

fof(c_0_18,plain,
    ! [X3,X4] :
      ( ( ~ empty(X3)
        | ~ ilf_type(X4,set_type)
        | ~ member(X4,X3)
        | ~ ilf_type(X3,set_type) )
      & ( ilf_type(esk2_1(X3),set_type)
        | empty(X3)
        | ~ ilf_type(X3,set_type) )
      & ( member(esk2_1(X3),X3)
        | empty(X3)
        | ~ ilf_type(X3,set_type) ) ),
    inference(distribute,[status(thm)],[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)],[inference(fof_simplification,[status(thm)],[p8])])])])])])])]) ).

cnf(c_0_19,plain,
    ( member(ordered_pair(X1,X1),identity_relation_of(X2))
    | ~ member(X1,X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_12]),c_0_12])]) ).

cnf(c_0_20,negated_conjecture,
    identity_relation_of(esk1_0) = empty_set,
    inference(spm,[status(thm)],[c_0_15,c_0_16]) ).

cnf(c_0_21,plain,
    ~ member(X1,empty_set),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_12])]) ).

cnf(c_0_22,plain,
    ( empty(X1)
    | member(esk2_1(X1),X1)
    | ~ ilf_type(X1,set_type) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_23,negated_conjecture,
    ~ member(X1,esk1_0),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]) ).

cnf(c_0_24,plain,
    ( empty(X1)
    | member(esk2_1(X1),X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_12])]) ).

cnf(c_0_25,negated_conjecture,
    ~ empty(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_26,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SET679+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.13  % Command  : run_ET %s %d
% 0.13/0.33  % Computer : n019.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Sun Jul 10 16:14:53 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.22/1.41  # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.22/1.41  # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.22/1.41  # Preprocessing time       : 0.017 s
% 0.22/1.41  
% 0.22/1.41  # Proof found!
% 0.22/1.41  # SZS status Theorem
% 0.22/1.41  # SZS output start CNFRefutation
% See solution above
% 0.22/1.41  # Proof object total steps             : 27
% 0.22/1.41  # Proof object clause steps            : 14
% 0.22/1.41  # Proof object formula steps           : 13
% 0.22/1.41  # Proof object conjectures             : 8
% 0.22/1.41  # Proof object clause conjectures      : 5
% 0.22/1.41  # Proof object formula conjectures     : 3
% 0.22/1.41  # Proof object initial clauses used    : 7
% 0.22/1.41  # Proof object initial formulas used   : 6
% 0.22/1.41  # Proof object generating inferences   : 3
% 0.22/1.41  # Proof object simplifying inferences  : 12
% 0.22/1.41  # Training examples: 0 positive, 0 negative
% 0.22/1.41  # Parsed axioms                        : 24
% 0.22/1.41  # Removed by relevancy pruning/SinE    : 9
% 0.22/1.41  # Initial clauses                      : 34
% 0.22/1.41  # Removed in clause preprocessing      : 3
% 0.22/1.41  # Initial clauses in saturation        : 31
% 0.22/1.41  # Processed clauses                    : 41
% 0.22/1.41  # ...of these trivial                  : 8
% 0.22/1.41  # ...subsumed                          : 2
% 0.22/1.41  # ...remaining for further processing  : 31
% 0.22/1.41  # Other redundant clauses eliminated   : 2
% 0.22/1.41  # Clauses deleted for lack of memory   : 0
% 0.22/1.41  # Backward-subsumed                    : 1
% 0.22/1.41  # Backward-rewritten                   : 2
% 0.22/1.41  # Generated clauses                    : 33
% 0.22/1.41  # ...of the previous two non-trivial   : 25
% 0.22/1.41  # Contextual simplify-reflections      : 0
% 0.22/1.41  # Paramodulations                      : 29
% 0.22/1.41  # Factorizations                       : 2
% 0.22/1.41  # Equation resolutions                 : 2
% 0.22/1.41  # Current number of processed clauses  : 26
% 0.22/1.41  #    Positive orientable unit clauses  : 7
% 0.22/1.41  #    Positive unorientable unit clauses: 0
% 0.22/1.41  #    Negative unit clauses             : 4
% 0.22/1.41  #    Non-unit-clauses                  : 15
% 0.22/1.41  # Current number of unprocessed clauses: 15
% 0.22/1.41  # ...number of literals in the above   : 36
% 0.22/1.41  # Current number of archived formulas  : 0
% 0.22/1.41  # Current number of archived clauses   : 3
% 0.22/1.41  # Clause-clause subsumption calls (NU) : 28
% 0.22/1.41  # Rec. Clause-clause subsumption calls : 26
% 0.22/1.41  # Non-unit clause-clause subsumptions  : 2
% 0.22/1.41  # Unit Clause-clause subsumption calls : 25
% 0.22/1.41  # Rewrite failures with RHS unbound    : 0
% 0.22/1.41  # BW rewrite match attempts            : 2
% 0.22/1.41  # BW rewrite match successes           : 2
% 0.22/1.41  # Condensation attempts                : 0
% 0.22/1.41  # Condensation successes               : 0
% 0.22/1.41  # Termbank termtop insertions          : 2730
% 0.22/1.41  
% 0.22/1.41  # -------------------------------------------------
% 0.22/1.41  # User time                : 0.016 s
% 0.22/1.41  # System time              : 0.002 s
% 0.22/1.41  # Total time               : 0.018 s
% 0.22/1.41  # Maximum resident set size: 2744 pages
%------------------------------------------------------------------------------