TSTP Solution File: NUM414+1 by ET---2.0

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%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : NUM414+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_ET %s %d

% Computer : n013.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 : Mon Jul 18 09:32:11 EDT 2022

% Result   : Theorem 0.24s 1.42s
% Output   : CNFRefutation 0.24s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   23 (   7 unt;   0 def)
%            Number of atoms       :   72 (   8 equ)
%            Maximal formula atoms :    8 (   3 avg)
%            Number of connectives :   84 (  35   ~;  27   |;  14   &)
%                                         (   2 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :    2 (   2 usr;   2 con; 0-0 aty)
%            Number of variables   :   25 (   2 sgn  18   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(t50_ordinal1,conjecture,
    ! [X1] :
      ( ordinal(X1)
     => ! [X2] :
          ( ordinal(X2)
         => ~ ( ~ proper_subset(X1,X2)
              & X1 != X2
              & ~ proper_subset(X2,X1) ) ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',t50_ordinal1) ).

fof(connectedness_r1_ordinal1,axiom,
    ! [X1,X2] :
      ( ( ordinal(X1)
        & ordinal(X2) )
     => ( ordinal_subset(X1,X2)
        | ordinal_subset(X2,X1) ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',connectedness_r1_ordinal1) ).

fof(redefinition_r1_ordinal1,axiom,
    ! [X1,X2] :
      ( ( ordinal(X1)
        & ordinal(X2) )
     => ( ordinal_subset(X1,X2)
      <=> subset(X1,X2) ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',redefinition_r1_ordinal1) ).

fof(d8_xboole_0,axiom,
    ! [X1,X2] :
      ( proper_subset(X1,X2)
    <=> ( subset(X1,X2)
        & X1 != X2 ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',d8_xboole_0) ).

fof(c_0_4,negated_conjecture,
    ~ ! [X1] :
        ( ordinal(X1)
       => ! [X2] :
            ( ordinal(X2)
           => ~ ( ~ proper_subset(X1,X2)
                & X1 != X2
                & ~ proper_subset(X2,X1) ) ) ),
    inference(assume_negation,[status(cth)],[t50_ordinal1]) ).

fof(c_0_5,plain,
    ! [X3,X4] :
      ( ~ ordinal(X3)
      | ~ ordinal(X4)
      | ordinal_subset(X3,X4)
      | ordinal_subset(X4,X3) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[connectedness_r1_ordinal1])]) ).

fof(c_0_6,negated_conjecture,
    ( ordinal(esk1_0)
    & ordinal(esk2_0)
    & ~ proper_subset(esk1_0,esk2_0)
    & esk1_0 != esk2_0
    & ~ proper_subset(esk2_0,esk1_0) ),
    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)],[c_0_4])])])])])]) ).

cnf(c_0_7,plain,
    ( ordinal_subset(X1,X2)
    | ordinal_subset(X2,X1)
    | ~ ordinal(X1)
    | ~ ordinal(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_8,negated_conjecture,
    ordinal(esk2_0),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

fof(c_0_9,plain,
    ! [X3,X4] :
      ( ( ~ ordinal_subset(X3,X4)
        | subset(X3,X4)
        | ~ ordinal(X3)
        | ~ ordinal(X4) )
      & ( ~ subset(X3,X4)
        | ordinal_subset(X3,X4)
        | ~ ordinal(X3)
        | ~ ordinal(X4) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_r1_ordinal1])])]) ).

cnf(c_0_10,negated_conjecture,
    ( ordinal_subset(esk2_0,X1)
    | ordinal_subset(X1,esk2_0)
    | ~ ordinal(X1) ),
    inference(spm,[status(thm)],[c_0_7,c_0_8]) ).

cnf(c_0_11,negated_conjecture,
    ordinal(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_12,plain,
    ( subset(X2,X1)
    | ~ ordinal(X1)
    | ~ ordinal(X2)
    | ~ ordinal_subset(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_13,negated_conjecture,
    ( ordinal_subset(esk1_0,esk2_0)
    | ordinal_subset(esk2_0,esk1_0) ),
    inference(spm,[status(thm)],[c_0_10,c_0_11]) ).

fof(c_0_14,plain,
    ! [X3,X4,X3,X4] :
      ( ( subset(X3,X4)
        | ~ proper_subset(X3,X4) )
      & ( X3 != X4
        | ~ proper_subset(X3,X4) )
      & ( ~ subset(X3,X4)
        | X3 = X4
        | proper_subset(X3,X4) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d8_xboole_0])])])])]) ).

cnf(c_0_15,negated_conjecture,
    ( subset(esk2_0,esk1_0)
    | ordinal_subset(esk1_0,esk2_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_8]),c_0_11])]) ).

cnf(c_0_16,plain,
    ( proper_subset(X1,X2)
    | X1 = X2
    | ~ subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_17,negated_conjecture,
    ( subset(esk2_0,esk1_0)
    | subset(esk1_0,esk2_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_15]),c_0_11]),c_0_8])]) ).

cnf(c_0_18,negated_conjecture,
    esk1_0 != esk2_0,
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_19,negated_conjecture,
    ~ proper_subset(esk2_0,esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_20,negated_conjecture,
    subset(esk1_0,esk2_0),
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]),c_0_19]) ).

cnf(c_0_21,negated_conjecture,
    ~ proper_subset(esk1_0,esk2_0),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_22,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_20]),c_0_18]),c_0_21]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : NUM414+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13  % Command  : run_ET %s %d
% 0.13/0.34  % Computer : n013.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Tue Jul  5 18:38:14 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.24/1.42  # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.24/1.42  # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.24/1.42  # Preprocessing time       : 0.016 s
% 0.24/1.42  
% 0.24/1.42  # Proof found!
% 0.24/1.42  # SZS status Theorem
% 0.24/1.42  # SZS output start CNFRefutation
% See solution above
% 0.24/1.42  # Proof object total steps             : 23
% 0.24/1.42  # Proof object clause steps            : 14
% 0.24/1.42  # Proof object formula steps           : 9
% 0.24/1.42  # Proof object conjectures             : 14
% 0.24/1.42  # Proof object clause conjectures      : 11
% 0.24/1.42  # Proof object formula conjectures     : 3
% 0.24/1.42  # Proof object initial clauses used    : 8
% 0.24/1.42  # Proof object initial formulas used   : 4
% 0.24/1.42  # Proof object generating inferences   : 6
% 0.24/1.42  # Proof object simplifying inferences  : 10
% 0.24/1.42  # Training examples: 0 positive, 0 negative
% 0.24/1.42  # Parsed axioms                        : 42
% 0.24/1.42  # Removed by relevancy pruning/SinE    : 20
% 0.24/1.42  # Initial clauses                      : 32
% 0.24/1.42  # Removed in clause preprocessing      : 0
% 0.24/1.42  # Initial clauses in saturation        : 32
% 0.24/1.42  # Processed clauses                    : 48
% 0.24/1.42  # ...of these trivial                  : 0
% 0.24/1.42  # ...subsumed                          : 2
% 0.24/1.42  # ...remaining for further processing  : 46
% 0.24/1.42  # Other redundant clauses eliminated   : 1
% 0.24/1.42  # Clauses deleted for lack of memory   : 0
% 0.24/1.42  # Backward-subsumed                    : 1
% 0.24/1.42  # Backward-rewritten                   : 4
% 0.24/1.42  # Generated clauses                    : 35
% 0.24/1.42  # ...of the previous two non-trivial   : 27
% 0.24/1.42  # Contextual simplify-reflections      : 0
% 0.24/1.42  # Paramodulations                      : 34
% 0.24/1.42  # Factorizations                       : 0
% 0.24/1.42  # Equation resolutions                 : 1
% 0.24/1.42  # Current number of processed clauses  : 40
% 0.24/1.42  #    Positive orientable unit clauses  : 12
% 0.24/1.42  #    Positive unorientable unit clauses: 0
% 0.24/1.42  #    Negative unit clauses             : 6
% 0.24/1.42  #    Non-unit-clauses                  : 22
% 0.24/1.42  # Current number of unprocessed clauses: 8
% 0.24/1.42  # ...number of literals in the above   : 19
% 0.24/1.42  # Current number of archived formulas  : 0
% 0.24/1.42  # Current number of archived clauses   : 5
% 0.24/1.42  # Clause-clause subsumption calls (NU) : 36
% 0.24/1.42  # Rec. Clause-clause subsumption calls : 29
% 0.24/1.42  # Non-unit clause-clause subsumptions  : 2
% 0.24/1.42  # Unit Clause-clause subsumption calls : 11
% 0.24/1.42  # Rewrite failures with RHS unbound    : 0
% 0.24/1.42  # BW rewrite match attempts            : 4
% 0.24/1.42  # BW rewrite match successes           : 2
% 0.24/1.42  # Condensation attempts                : 0
% 0.24/1.42  # Condensation successes               : 0
% 0.24/1.42  # Termbank termtop insertions          : 2080
% 0.24/1.42  
% 0.24/1.42  # -------------------------------------------------
% 0.24/1.42  # User time                : 0.014 s
% 0.24/1.42  # System time              : 0.004 s
% 0.24/1.42  # Total time               : 0.018 s
% 0.24/1.42  # Maximum resident set size: 2984 pages
%------------------------------------------------------------------------------