TSTP Solution File: NUM501+3 by ET---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : NUM501+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_ET %s %d

% Computer : n021.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 09:33:08 EDT 2022

% Result   : Theorem 0.35s 23.54s
% Output   : CNFRefutation 0.35s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   39 (  13 unt;   0 def)
%            Number of atoms       :  155 (  51 equ)
%            Maximal formula atoms :   16 (   3 avg)
%            Number of connectives :  181 (  65   ~;  62   |;  47   &)
%                                         (   1 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   9 con; 0-2 aty)
%            Number of variables   :   51 (   0 sgn  26   !;   7   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(mMulAsso,axiom,
    ! [X1,X2,X3] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2)
        & aNaturalNumber0(X3) )
     => sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3)) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',mMulAsso) ).

fof(m__2342,hypothesis,
    ( aNaturalNumber0(xr)
    & ? [X1] :
        ( aNaturalNumber0(X1)
        & xk = sdtasdt0(xr,X1) )
    & doDivides0(xr,xk)
    & xr != sz00
    & xr != sz10
    & ! [X1] :
        ( ( aNaturalNumber0(X1)
          & ( ? [X2] :
                ( aNaturalNumber0(X2)
                & xr = sdtasdt0(X1,X2) )
            | doDivides0(X1,xr) ) )
       => ( X1 = sz10
          | X1 = xr ) )
    & isPrime0(xr) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',m__2342) ).

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',mDefDiv) ).

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

fof(m__,conjecture,
    ( ? [X1] :
        ( aNaturalNumber0(X1)
        & sdtasdt0(xn,xm) = sdtasdt0(xr,X1) )
    | doDivides0(xr,sdtasdt0(xn,xm)) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',m__) ).

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

fof(m__1860,hypothesis,
    ( xp != sz00
    & xp != sz10
    & ! [X1] :
        ( ( aNaturalNumber0(X1)
          & ( ? [X2] :
                ( aNaturalNumber0(X2)
                & xp = sdtasdt0(X1,X2) )
            | doDivides0(X1,xp) ) )
       => ( X1 = sz10
          | X1 = xp ) )
    & isPrime0(xp)
    & ? [X1] :
        ( aNaturalNumber0(X1)
        & sdtasdt0(xn,xm) = sdtasdt0(xp,X1) )
    & doDivides0(xp,sdtasdt0(xn,xm)) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',m__1860) ).

fof(m__2306,hypothesis,
    ( aNaturalNumber0(xk)
    & sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
    & xk = sdtsldt0(sdtasdt0(xn,xm),xp) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',m__2306) ).

fof(m__1837,hypothesis,
    ( aNaturalNumber0(xn)
    & aNaturalNumber0(xm)
    & aNaturalNumber0(xp) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',m__1837) ).

fof(c_0_9,plain,
    ! [X4,X5,X6] :
      ( ~ aNaturalNumber0(X4)
      | ~ aNaturalNumber0(X5)
      | ~ aNaturalNumber0(X6)
      | sdtasdt0(sdtasdt0(X4,X5),X6) = sdtasdt0(X4,sdtasdt0(X5,X6)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])]) ).

fof(c_0_10,hypothesis,
    ! [X4,X5] :
      ( aNaturalNumber0(xr)
      & aNaturalNumber0(esk8_0)
      & xk = sdtasdt0(xr,esk8_0)
      & doDivides0(xr,xk)
      & xr != sz00
      & xr != sz10
      & ( ~ aNaturalNumber0(X5)
        | xr != sdtasdt0(X4,X5)
        | ~ aNaturalNumber0(X4)
        | X4 = sz10
        | X4 = xr )
      & ( ~ doDivides0(X4,xr)
        | ~ aNaturalNumber0(X4)
        | X4 = sz10
        | X4 = xr )
      & isPrime0(xr) ),
    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)],[m__2342])])])])])])]) ).

fof(c_0_11,plain,
    ! [X4,X5,X7] :
      ( ( aNaturalNumber0(esk9_2(X4,X5))
        | ~ doDivides0(X4,X5)
        | ~ aNaturalNumber0(X4)
        | ~ aNaturalNumber0(X5) )
      & ( X5 = sdtasdt0(X4,esk9_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_12,plain,
    ( sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
    | ~ aNaturalNumber0(X3)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_13,hypothesis,
    xk = sdtasdt0(xr,esk8_0),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_14,hypothesis,
    aNaturalNumber0(esk8_0),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_15,hypothesis,
    aNaturalNumber0(xr),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_16,plain,
    ( doDivides0(X2,X1)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | X1 != sdtasdt0(X2,X3)
    | ~ aNaturalNumber0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_17,hypothesis,
    ( sdtasdt0(xr,sdtasdt0(esk8_0,X1)) = sdtasdt0(xk,X1)
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]),c_0_15])]) ).

fof(c_0_18,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_19,negated_conjecture,
    ~ ( ? [X1] :
          ( aNaturalNumber0(X1)
          & sdtasdt0(xn,xm) = sdtasdt0(xr,X1) )
      | doDivides0(xr,sdtasdt0(xn,xm)) ),
    inference(assume_negation,[status(cth)],[m__]) ).

cnf(c_0_20,hypothesis,
    ( doDivides0(xr,X1)
    | X1 != sdtasdt0(xk,X2)
    | ~ aNaturalNumber0(sdtasdt0(esk8_0,X2))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_15])]) ).

cnf(c_0_21,plain,
    ( aNaturalNumber0(sdtasdt0(X1,X2))
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

fof(c_0_22,plain,
    ! [X3,X4] :
      ( ~ aNaturalNumber0(X3)
      | ~ aNaturalNumber0(X4)
      | sdtasdt0(X3,X4) = sdtasdt0(X4,X3) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])]) ).

fof(c_0_23,hypothesis,
    ! [X3,X4] :
      ( xp != sz00
      & xp != sz10
      & ( ~ aNaturalNumber0(X4)
        | xp != sdtasdt0(X3,X4)
        | ~ aNaturalNumber0(X3)
        | X3 = sz10
        | X3 = xp )
      & ( ~ doDivides0(X3,xp)
        | ~ aNaturalNumber0(X3)
        | X3 = sz10
        | X3 = xp )
      & isPrime0(xp)
      & aNaturalNumber0(esk5_0)
      & sdtasdt0(xn,xm) = sdtasdt0(xp,esk5_0)
      & doDivides0(xp,sdtasdt0(xn,xm)) ),
    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)],[m__1860])])])])])])]) ).

fof(c_0_24,negated_conjecture,
    ! [X2] :
      ( ( ~ aNaturalNumber0(X2)
        | sdtasdt0(xn,xm) != sdtasdt0(xr,X2) )
      & ~ doDivides0(xr,sdtasdt0(xn,xm)) ),
    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)],[c_0_19])])])])]) ).

cnf(c_0_25,hypothesis,
    ( doDivides0(xr,X1)
    | X1 != sdtasdt0(xk,X2)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_14])]) ).

cnf(c_0_26,plain,
    ( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

cnf(c_0_27,hypothesis,
    aNaturalNumber0(xk),
    inference(split_conjunct,[status(thm)],[m__2306]) ).

cnf(c_0_28,hypothesis,
    sdtasdt0(xn,xm) = sdtasdt0(xp,esk5_0),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

cnf(c_0_29,hypothesis,
    sdtasdt0(xn,xm) = sdtasdt0(xp,xk),
    inference(split_conjunct,[status(thm)],[m__2306]) ).

cnf(c_0_30,negated_conjecture,
    ~ doDivides0(xr,sdtasdt0(xn,xm)),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_31,hypothesis,
    ( doDivides0(xr,X1)
    | X1 != sdtasdt0(X2,xk)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27])]) ).

cnf(c_0_32,hypothesis,
    sdtasdt0(xp,esk5_0) = sdtasdt0(xp,xk),
    inference(rw,[status(thm)],[c_0_28,c_0_29]) ).

cnf(c_0_33,hypothesis,
    aNaturalNumber0(esk5_0),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

cnf(c_0_34,hypothesis,
    aNaturalNumber0(xp),
    inference(split_conjunct,[status(thm)],[m__1837]) ).

cnf(c_0_35,negated_conjecture,
    ~ doDivides0(xr,sdtasdt0(xp,xk)),
    inference(rw,[status(thm)],[c_0_30,c_0_29]) ).

cnf(c_0_36,hypothesis,
    ( doDivides0(xr,sdtasdt0(X1,xk))
    | ~ aNaturalNumber0(sdtasdt0(X1,xk))
    | ~ aNaturalNumber0(X1) ),
    inference(er,[status(thm)],[c_0_31]) ).

cnf(c_0_37,hypothesis,
    aNaturalNumber0(sdtasdt0(xp,xk)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_32]),c_0_33]),c_0_34])]) ).

cnf(c_0_38,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]),c_0_34])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : NUM501+3 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13  % Command  : run_ET %s %d
% 0.13/0.34  % Computer : n021.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 : Fri Jul  8 00:36:50 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.35/23.41  eprover: CPU time limit exceeded, terminating
% 0.35/23.41  eprover: CPU time limit exceeded, terminating
% 0.35/23.42  eprover: CPU time limit exceeded, terminating
% 0.35/23.43  eprover: CPU time limit exceeded, terminating
% 0.35/23.54  # Running protocol protocol_eprover_63dc1b1eb7d762c2f3686774d32795976f981b97 for 23 seconds:
% 0.35/23.54  
% 0.35/23.54  # Failure: Resource limit exceeded (time)
% 0.35/23.54  # OLD status Res
% 0.35/23.54  # Preprocessing time       : 0.026 s
% 0.35/23.54  # Running protocol protocol_eprover_f6eb5f7f05126ea361481ae651a4823314e3d740 for 23 seconds:
% 0.35/23.54  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,02,20000,1.0)
% 0.35/23.54  # Preprocessing time       : 0.015 s
% 0.35/23.54  
% 0.35/23.54  # Proof found!
% 0.35/23.54  # SZS status Theorem
% 0.35/23.54  # SZS output start CNFRefutation
% See solution above
% 0.35/23.54  # Proof object total steps             : 39
% 0.35/23.54  # Proof object clause steps            : 22
% 0.35/23.54  # Proof object formula steps           : 17
% 0.35/23.54  # Proof object conjectures             : 6
% 0.35/23.54  # Proof object clause conjectures      : 3
% 0.35/23.54  # Proof object formula conjectures     : 3
% 0.35/23.54  # Proof object initial clauses used    : 13
% 0.35/23.54  # Proof object initial formulas used   : 9
% 0.35/23.54  # Proof object generating inferences   : 7
% 0.35/23.54  # Proof object simplifying inferences  : 17
% 0.35/23.54  # Training examples: 0 positive, 0 negative
% 0.35/23.54  # Parsed axioms                        : 49
% 0.35/23.54  # Removed by relevancy pruning/SinE    : 1
% 0.35/23.54  # Initial clauses                      : 234
% 0.35/23.54  # Removed in clause preprocessing      : 3
% 0.35/23.54  # Initial clauses in saturation        : 231
% 0.35/23.54  # Processed clauses                    : 361
% 0.35/23.54  # ...of these trivial                  : 12
% 0.35/23.54  # ...subsumed                          : 68
% 0.35/23.54  # ...remaining for further processing  : 281
% 0.35/23.54  # Other redundant clauses eliminated   : 31
% 0.35/23.54  # Clauses deleted for lack of memory   : 0
% 0.35/23.54  # Backward-subsumed                    : 1
% 0.35/23.54  # Backward-rewritten                   : 4
% 0.35/23.54  # Generated clauses                    : 3721
% 0.35/23.54  # ...of the previous two non-trivial   : 3579
% 0.35/23.54  # Contextual simplify-reflections      : 8
% 0.35/23.54  # Paramodulations                      : 3670
% 0.35/23.54  # Factorizations                       : 0
% 0.35/23.54  # Equation resolutions                 : 51
% 0.35/23.54  # Current number of processed clauses  : 275
% 0.35/23.54  #    Positive orientable unit clauses  : 45
% 0.35/23.54  #    Positive unorientable unit clauses: 0
% 0.35/23.54  #    Negative unit clauses             : 12
% 0.35/23.54  #    Non-unit-clauses                  : 218
% 0.35/23.54  # Current number of unprocessed clauses: 3409
% 0.35/23.54  # ...number of literals in the above   : 33539
% 0.35/23.54  # Current number of archived formulas  : 0
% 0.35/23.54  # Current number of archived clauses   : 5
% 0.35/23.54  # Clause-clause subsumption calls (NU) : 25087
% 0.35/23.54  # Rec. Clause-clause subsumption calls : 972
% 0.35/23.54  # Non-unit clause-clause subsumptions  : 56
% 0.35/23.54  # Unit Clause-clause subsumption calls : 2084
% 0.35/23.54  # Rewrite failures with RHS unbound    : 0
% 0.35/23.54  # BW rewrite match attempts            : 2
% 0.35/23.54  # BW rewrite match successes           : 2
% 0.35/23.54  # Condensation attempts                : 0
% 0.35/23.54  # Condensation successes               : 0
% 0.35/23.54  # Termbank termtop insertions          : 139044
% 0.35/23.54  
% 0.35/23.54  # -------------------------------------------------
% 0.35/23.54  # User time                : 0.095 s
% 0.35/23.54  # System time              : 0.006 s
% 0.35/23.54  # Total time               : 0.101 s
% 0.35/23.54  # Maximum resident set size: 7392 pages
%------------------------------------------------------------------------------