TSTP Solution File: NUM477+1 by ET---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : NUM477+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_ET %s %d

% Computer : n027.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 09:32:51 EDT 2022

% Result   : Theorem 0.22s 1.40s
% Output   : CNFRefutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   37 (  11 unt;   0 def)
%            Number of atoms       :  130 (  21 equ)
%            Maximal formula atoms :   13 (   3 avg)
%            Number of connectives :  158 (  65   ~;  68   |;  16   &)
%                                         (   1 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   49 (   0 sgn  25   !;   1   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(mLETran,axiom,
    ! [X1,X2,X3] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2)
        & aNaturalNumber0(X3) )
     => ( ( sdtlseqdt0(X1,X2)
          & sdtlseqdt0(X2,X3) )
       => sdtlseqdt0(X1,X3) ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mLETran) ).

fof(mMonMul2,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => ( X1 != sz00
       => sdtlseqdt0(X2,sdtasdt0(X2,X1)) ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mMonMul2) ).

fof(mSortsB_02,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => aNaturalNumber0(sdtasdt0(X1,X2)) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mSortsB_02) ).

fof(mLETotal,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => ( sdtlseqdt0(X1,X2)
        | ( X2 != X1
          & sdtlseqdt0(X2,X1) ) ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mLETotal) ).

fof(mDefDiv,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => ( doDivides0(X1,X2)
      <=> ? [X3] :
            ( aNaturalNumber0(X3)
            & X2 = sdtasdt0(X1,X3) ) ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mDefDiv) ).

fof(m__1494,hypothesis,
    ( aNaturalNumber0(xm)
    & aNaturalNumber0(xn) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',m__1494) ).

fof(m__,conjecture,
    sdtlseqdt0(xm,xn),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',m__) ).

fof(m_MulZero,axiom,
    ! [X1] :
      ( aNaturalNumber0(X1)
     => ( sdtasdt0(X1,sz00) = sz00
        & sz00 = sdtasdt0(sz00,X1) ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',m_MulZero) ).

fof(m__1494_04,hypothesis,
    ( doDivides0(xm,xn)
    & xn != sz00 ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',m__1494_04) ).

fof(c_0_9,plain,
    ! [X4,X5,X6] :
      ( ~ aNaturalNumber0(X4)
      | ~ aNaturalNumber0(X5)
      | ~ aNaturalNumber0(X6)
      | ~ sdtlseqdt0(X4,X5)
      | ~ sdtlseqdt0(X5,X6)
      | sdtlseqdt0(X4,X6) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETran])]) ).

fof(c_0_10,plain,
    ! [X3,X4] :
      ( ~ aNaturalNumber0(X3)
      | ~ aNaturalNumber0(X4)
      | X3 = sz00
      | sdtlseqdt0(X4,sdtasdt0(X4,X3)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMonMul2])]) ).

fof(c_0_11,plain,
    ! [X3,X4] :
      ( ~ aNaturalNumber0(X3)
      | ~ aNaturalNumber0(X4)
      | aNaturalNumber0(sdtasdt0(X3,X4)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])]) ).

fof(c_0_12,plain,
    ! [X3,X4] :
      ( ( X4 != X3
        | sdtlseqdt0(X3,X4)
        | ~ aNaturalNumber0(X3)
        | ~ aNaturalNumber0(X4) )
      & ( sdtlseqdt0(X4,X3)
        | sdtlseqdt0(X3,X4)
        | ~ aNaturalNumber0(X3)
        | ~ aNaturalNumber0(X4) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETotal])])]) ).

cnf(c_0_13,plain,
    ( sdtlseqdt0(X1,X2)
    | ~ sdtlseqdt0(X3,X2)
    | ~ sdtlseqdt0(X1,X3)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X3)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_14,plain,
    ( sdtlseqdt0(X1,sdtasdt0(X1,X2))
    | X2 = sz00
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_15,plain,
    ( aNaturalNumber0(sdtasdt0(X1,X2))
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

fof(c_0_16,plain,
    ! [X4,X5,X7] :
      ( ( aNaturalNumber0(esk1_2(X4,X5))
        | ~ doDivides0(X4,X5)
        | ~ aNaturalNumber0(X4)
        | ~ aNaturalNumber0(X5) )
      & ( X5 = sdtasdt0(X4,esk1_2(X4,X5))
        | ~ doDivides0(X4,X5)
        | ~ aNaturalNumber0(X4)
        | ~ aNaturalNumber0(X5) )
      & ( ~ aNaturalNumber0(X7)
        | X5 != sdtasdt0(X4,X7)
        | doDivides0(X4,X5)
        | ~ aNaturalNumber0(X4)
        | ~ aNaturalNumber0(X5) ) ),
    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)],[mDefDiv])])])])])])]) ).

cnf(c_0_17,plain,
    ( sdtlseqdt0(X2,X1)
    | sdtlseqdt0(X1,X2)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_18,hypothesis,
    aNaturalNumber0(xm),
    inference(split_conjunct,[status(thm)],[m__1494]) ).

cnf(c_0_19,plain,
    ( X1 = sz00
    | sdtlseqdt0(X2,sdtasdt0(X3,X1))
    | ~ sdtlseqdt0(X2,X3)
    | ~ aNaturalNumber0(X3)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).

cnf(c_0_20,plain,
    ( X1 = sdtasdt0(X2,esk1_2(X2,X1))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ doDivides0(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_21,plain,
    ( aNaturalNumber0(esk1_2(X2,X1))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ doDivides0(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_22,hypothesis,
    ( sdtlseqdt0(xm,X1)
    | sdtlseqdt0(X1,xm)
    | ~ aNaturalNumber0(X1) ),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_23,plain,
    ( esk1_2(X1,X2) = sz00
    | sdtlseqdt0(X3,X2)
    | ~ doDivides0(X1,X2)
    | ~ sdtlseqdt0(X3,X1)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X3)
    | ~ aNaturalNumber0(X2) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]) ).

cnf(c_0_24,hypothesis,
    sdtlseqdt0(xm,xm),
    inference(spm,[status(thm)],[c_0_22,c_0_18]) ).

fof(c_0_25,negated_conjecture,
    ~ sdtlseqdt0(xm,xn),
    inference(assume_negation,[status(cth)],[m__]) ).

cnf(c_0_26,hypothesis,
    ( esk1_2(xm,X1) = sz00
    | sdtlseqdt0(xm,X1)
    | ~ doDivides0(xm,X1)
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_18])]) ).

fof(c_0_27,negated_conjecture,
    ~ sdtlseqdt0(xm,xn),
    inference(fof_simplification,[status(thm)],[c_0_25]) ).

fof(c_0_28,plain,
    ! [X2] :
      ( ( sdtasdt0(X2,sz00) = sz00
        | ~ aNaturalNumber0(X2) )
      & ( sz00 = sdtasdt0(sz00,X2)
        | ~ aNaturalNumber0(X2) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulZero])])]) ).

cnf(c_0_29,hypothesis,
    ( sdtasdt0(xm,sz00) = X1
    | sdtlseqdt0(xm,X1)
    | ~ doDivides0(xm,X1)
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_26]),c_0_18])]) ).

cnf(c_0_30,hypothesis,
    doDivides0(xm,xn),
    inference(split_conjunct,[status(thm)],[m__1494_04]) ).

cnf(c_0_31,hypothesis,
    aNaturalNumber0(xn),
    inference(split_conjunct,[status(thm)],[m__1494]) ).

cnf(c_0_32,negated_conjecture,
    ~ sdtlseqdt0(xm,xn),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_33,plain,
    ( sdtasdt0(X1,sz00) = sz00
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_28]) ).

cnf(c_0_34,hypothesis,
    sdtasdt0(xm,sz00) = xn,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31])]),c_0_32]) ).

cnf(c_0_35,hypothesis,
    xn != sz00,
    inference(split_conjunct,[status(thm)],[m__1494_04]) ).

cnf(c_0_36,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_18])]),c_0_35]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : NUM477+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12  % Command  : run_ET %s %d
% 0.12/0.33  % Computer : n027.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 : Tue Jul  5 15:14:57 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       : 0.018 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             : 37
% 0.22/1.40  # Proof object clause steps            : 20
% 0.22/1.40  # Proof object formula steps           : 17
% 0.22/1.40  # Proof object conjectures             : 4
% 0.22/1.40  # Proof object clause conjectures      : 1
% 0.22/1.40  # Proof object formula conjectures     : 3
% 0.22/1.40  # Proof object initial clauses used    : 12
% 0.22/1.40  # Proof object initial formulas used   : 9
% 0.22/1.40  # Proof object generating inferences   : 8
% 0.22/1.40  # Proof object simplifying inferences  : 12
% 0.22/1.40  # Training examples: 0 positive, 0 negative
% 0.22/1.40  # Parsed axioms                        : 37
% 0.22/1.40  # Removed by relevancy pruning/SinE    : 7
% 0.22/1.40  # Initial clauses                      : 49
% 0.22/1.40  # Removed in clause preprocessing      : 1
% 0.22/1.40  # Initial clauses in saturation        : 48
% 0.22/1.40  # Processed clauses                    : 1447
% 0.22/1.40  # ...of these trivial                  : 6
% 0.22/1.40  # ...subsumed                          : 955
% 0.22/1.40  # ...remaining for further processing  : 486
% 0.22/1.40  # Other redundant clauses eliminated   : 11
% 0.22/1.40  # Clauses deleted for lack of memory   : 0
% 0.22/1.40  # Backward-subsumed                    : 31
% 0.22/1.40  # Backward-rewritten                   : 13
% 0.22/1.40  # Generated clauses                    : 10213
% 0.22/1.40  # ...of the previous two non-trivial   : 9440
% 0.22/1.40  # Contextual simplify-reflections      : 348
% 0.22/1.40  # Paramodulations                      : 10165
% 0.22/1.40  # Factorizations                       : 0
% 0.22/1.40  # Equation resolutions                 : 48
% 0.22/1.40  # Current number of processed clauses  : 441
% 0.22/1.40  #    Positive orientable unit clauses  : 17
% 0.22/1.40  #    Positive unorientable unit clauses: 0
% 0.22/1.40  #    Negative unit clauses             : 15
% 0.22/1.40  #    Non-unit-clauses                  : 409
% 0.22/1.40  # Current number of unprocessed clauses: 7837
% 0.22/1.40  # ...number of literals in the above   : 52236
% 0.22/1.40  # Current number of archived formulas  : 0
% 0.22/1.40  # Current number of archived clauses   : 44
% 0.22/1.40  # Clause-clause subsumption calls (NU) : 31453
% 0.22/1.40  # Rec. Clause-clause subsumption calls : 10079
% 0.22/1.40  # Non-unit clause-clause subsumptions  : 1056
% 0.22/1.40  # Unit Clause-clause subsumption calls : 571
% 0.22/1.40  # Rewrite failures with RHS unbound    : 0
% 0.22/1.40  # BW rewrite match attempts            : 8
% 0.22/1.40  # BW rewrite match successes           : 8
% 0.22/1.40  # Condensation attempts                : 0
% 0.22/1.40  # Condensation successes               : 0
% 0.22/1.40  # Termbank termtop insertions          : 199850
% 0.22/1.40  
% 0.22/1.40  # -------------------------------------------------
% 0.22/1.40  # User time                : 0.228 s
% 0.22/1.40  # System time              : 0.007 s
% 0.22/1.40  # Total time               : 0.235 s
% 0.22/1.40  # Maximum resident set size: 11264 pages
%------------------------------------------------------------------------------