TSTP Solution File: NUM523+1 by ET---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : NUM523+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_ET %s %d

% Computer : n007.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 09:33:22 EDT 2022

% Result   : Theorem 0.23s 1.42s
% Output   : CNFRefutation 0.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   27 (  10 unt;   0 def)
%            Number of atoms       :   86 (   9 equ)
%            Maximal formula atoms :   13 (   3 avg)
%            Number of connectives :  104 (  45   ~;  39   |;  15   &)
%                                         (   1 <=>;   4  =>;   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    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :   27 (   0 sgn  15   !;   1   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(m__,conjecture,
    ( doDivides0(xp,sdtasdt0(xn,xn))
    & doDivides0(xp,xn) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',m__) ).

fof(mPDP,axiom,
    ! [X1,X2,X3] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2)
        & aNaturalNumber0(X3) )
     => ( ( isPrime0(X3)
          & doDivides0(X3,sdtasdt0(X1,X2)) )
       => ( doDivides0(X3,X1)
          | doDivides0(X3,X2) ) ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mPDP) ).

fof(m__3014,hypothesis,
    sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',m__3014) ).

fof(m__2987,hypothesis,
    ( aNaturalNumber0(xn)
    & aNaturalNumber0(xm)
    & aNaturalNumber0(xp)
    & xn != sz00
    & xm != sz00
    & xp != sz00 ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',m__2987) ).

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(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(m__3025,hypothesis,
    isPrime0(xp),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',m__3025) ).

fof(c_0_7,negated_conjecture,
    ~ ( doDivides0(xp,sdtasdt0(xn,xn))
      & doDivides0(xp,xn) ),
    inference(assume_negation,[status(cth)],[m__]) ).

fof(c_0_8,plain,
    ! [X4,X5,X6] :
      ( ~ aNaturalNumber0(X4)
      | ~ aNaturalNumber0(X5)
      | ~ aNaturalNumber0(X6)
      | ~ isPrime0(X6)
      | ~ doDivides0(X6,sdtasdt0(X4,X5))
      | doDivides0(X6,X4)
      | doDivides0(X6,X5) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mPDP])]) ).

fof(c_0_9,negated_conjecture,
    ( ~ doDivides0(xp,sdtasdt0(xn,xn))
    | ~ doDivides0(xp,xn) ),
    inference(fof_nnf,[status(thm)],[c_0_7]) ).

cnf(c_0_10,plain,
    ( doDivides0(X1,X2)
    | doDivides0(X1,X3)
    | ~ doDivides0(X1,sdtasdt0(X3,X2))
    | ~ isPrime0(X1)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_11,hypothesis,
    sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
    inference(split_conjunct,[status(thm)],[m__3014]) ).

cnf(c_0_12,hypothesis,
    aNaturalNumber0(xn),
    inference(split_conjunct,[status(thm)],[m__2987]) ).

cnf(c_0_13,negated_conjecture,
    ( ~ doDivides0(xp,xn)
    | ~ doDivides0(xp,sdtasdt0(xn,xn)) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

fof(c_0_14,plain,
    ! [X4,X5,X7] :
      ( ( aNaturalNumber0(esk3_2(X4,X5))
        | ~ doDivides0(X4,X5)
        | ~ aNaturalNumber0(X4)
        | ~ aNaturalNumber0(X5) )
      & ( X5 = sdtasdt0(X4,esk3_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])])])])])])]) ).

fof(c_0_15,plain,
    ! [X3,X4] :
      ( ~ aNaturalNumber0(X3)
      | ~ aNaturalNumber0(X4)
      | aNaturalNumber0(sdtasdt0(X3,X4)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])]) ).

cnf(c_0_16,hypothesis,
    ( doDivides0(X1,xn)
    | ~ isPrime0(X1)
    | ~ doDivides0(X1,sdtasdt0(xp,sdtasdt0(xm,xm)))
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12])]) ).

cnf(c_0_17,hypothesis,
    isPrime0(xp),
    inference(split_conjunct,[status(thm)],[m__3025]) ).

cnf(c_0_18,hypothesis,
    aNaturalNumber0(xp),
    inference(split_conjunct,[status(thm)],[m__2987]) ).

cnf(c_0_19,negated_conjecture,
    ( ~ doDivides0(xp,sdtasdt0(xp,sdtasdt0(xm,xm)))
    | ~ doDivides0(xp,xn) ),
    inference(rw,[status(thm)],[c_0_13,c_0_11]) ).

cnf(c_0_20,plain,
    ( doDivides0(X2,X1)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | X1 != sdtasdt0(X2,X3)
    | ~ aNaturalNumber0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_21,plain,
    ( aNaturalNumber0(sdtasdt0(X1,X2))
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_22,hypothesis,
    ~ doDivides0(xp,sdtasdt0(xp,sdtasdt0(xm,xm))),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18])]),c_0_19]) ).

cnf(c_0_23,plain,
    ( doDivides0(X1,sdtasdt0(X1,X2))
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_20]),c_0_21]) ).

cnf(c_0_24,hypothesis,
    ~ aNaturalNumber0(sdtasdt0(xm,xm)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_18])]) ).

cnf(c_0_25,hypothesis,
    aNaturalNumber0(xm),
    inference(split_conjunct,[status(thm)],[m__2987]) ).

cnf(c_0_26,hypothesis,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_21]),c_0_25])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : NUM523+1 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13  % Command  : run_ET %s %d
% 0.12/0.34  % Computer : n007.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Wed Jul  6 14:50:28 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.23/1.42  # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.23/1.42  # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.23/1.42  # Preprocessing time       : 0.019 s
% 0.23/1.42  
% 0.23/1.42  # Proof found!
% 0.23/1.42  # SZS status Theorem
% 0.23/1.42  # SZS output start CNFRefutation
% See solution above
% 0.23/1.42  # Proof object total steps             : 27
% 0.23/1.42  # Proof object clause steps            : 15
% 0.23/1.42  # Proof object formula steps           : 12
% 0.23/1.42  # Proof object conjectures             : 5
% 0.23/1.42  # Proof object clause conjectures      : 2
% 0.23/1.42  # Proof object formula conjectures     : 3
% 0.23/1.42  # Proof object initial clauses used    : 9
% 0.23/1.42  # Proof object initial formulas used   : 7
% 0.23/1.42  # Proof object generating inferences   : 5
% 0.23/1.42  # Proof object simplifying inferences  : 11
% 0.23/1.42  # Training examples: 0 positive, 0 negative
% 0.23/1.42  # Parsed axioms                        : 44
% 0.23/1.42  # Removed by relevancy pruning/SinE    : 3
% 0.23/1.42  # Initial clauses                      : 74
% 0.23/1.42  # Removed in clause preprocessing      : 3
% 0.23/1.42  # Initial clauses in saturation        : 71
% 0.23/1.42  # Processed clauses                    : 1991
% 0.23/1.42  # ...of these trivial                  : 197
% 0.23/1.42  # ...subsumed                          : 985
% 0.23/1.42  # ...remaining for further processing  : 809
% 0.23/1.42  # Other redundant clauses eliminated   : 29
% 0.23/1.42  # Clauses deleted for lack of memory   : 0
% 0.23/1.42  # Backward-subsumed                    : 36
% 0.23/1.42  # Backward-rewritten                   : 88
% 0.23/1.42  # Generated clauses                    : 24010
% 0.23/1.42  # ...of the previous two non-trivial   : 21383
% 0.23/1.42  # Contextual simplify-reflections      : 194
% 0.23/1.42  # Paramodulations                      : 23960
% 0.23/1.42  # Factorizations                       : 1
% 0.23/1.42  # Equation resolutions                 : 48
% 0.23/1.42  # Current number of processed clauses  : 683
% 0.23/1.42  #    Positive orientable unit clauses  : 219
% 0.23/1.42  #    Positive unorientable unit clauses: 0
% 0.23/1.42  #    Negative unit clauses             : 56
% 0.23/1.42  #    Non-unit-clauses                  : 408
% 0.23/1.42  # Current number of unprocessed clauses: 16693
% 0.23/1.42  # ...number of literals in the above   : 80597
% 0.23/1.42  # Current number of archived formulas  : 0
% 0.23/1.42  # Current number of archived clauses   : 125
% 0.23/1.42  # Clause-clause subsumption calls (NU) : 23051
% 0.23/1.42  # Rec. Clause-clause subsumption calls : 7237
% 0.23/1.42  # Non-unit clause-clause subsumptions  : 806
% 0.23/1.42  # Unit Clause-clause subsumption calls : 2628
% 0.23/1.42  # Rewrite failures with RHS unbound    : 0
% 0.23/1.42  # BW rewrite match attempts            : 101
% 0.23/1.42  # BW rewrite match successes           : 44
% 0.23/1.42  # Condensation attempts                : 0
% 0.23/1.42  # Condensation successes               : 0
% 0.23/1.42  # Termbank termtop insertions          : 500068
% 0.23/1.42  
% 0.23/1.42  # -------------------------------------------------
% 0.23/1.42  # User time                : 0.365 s
% 0.23/1.42  # System time              : 0.018 s
% 0.23/1.42  # Total time               : 0.383 s
% 0.23/1.42  # Maximum resident set size: 20016 pages
% 0.23/23.41  eprover: CPU time limit exceeded, terminating
% 0.23/23.43  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.43  eprover: No such file or directory
% 0.23/23.43  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.43  eprover: No such file or directory
% 0.23/23.43  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.43  eprover: No such file or directory
% 0.23/23.44  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.44  eprover: No such file or directory
% 0.23/23.44  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.44  eprover: No such file or directory
% 0.23/23.44  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.44  eprover: No such file or directory
% 0.23/23.45  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.45  eprover: No such file or directory
% 0.23/23.45  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.45  eprover: No such file or directory
% 0.23/23.45  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.45  eprover: No such file or directory
% 0.23/23.46  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.46  eprover: No such file or directory
% 0.23/23.46  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.23/23.46  eprover: No such file or directory
%------------------------------------------------------------------------------