TSTP Solution File: NUM501+3 by E---3.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1
% Problem  : NUM501+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n028.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 : 2400s
% WCLimit  : 300s
% DateTime : Tue Oct 10 18:56:03 EDT 2023

% Result   : Theorem 0.16s 0.50s
% Output   : CNFRefutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   35 (  11 unt;   0 def)
%            Number of atoms       :  150 (  42 equ)
%            Maximal formula atoms :   16 (   4 avg)
%            Number of connectives :  176 (  61   ~;  59   |;  48   &)
%                                         (   1 <=>;   7  =>;   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   :   48 (   0 sgn;  26   !;   7   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(mDefDiv,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => ( doDivides0(X1,X2)
      <=> ? [X3] :
            ( aNaturalNumber0(X3)
            & X2 = sdtasdt0(X1,X3) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.cvKI9dJWOO/E---3.1_13634.p',mDefDiv) ).

fof(mSortsB_02,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => aNaturalNumber0(sdtasdt0(X1,X2)) ),
    file('/export/starexec/sandbox/tmp/tmp.cvKI9dJWOO/E---3.1_13634.p',mSortsB_02) ).

fof(mMulComm,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
    file('/export/starexec/sandbox/tmp/tmp.cvKI9dJWOO/E---3.1_13634.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/tmp/tmp.cvKI9dJWOO/E---3.1_13634.p',m__1860) ).

fof(m__,conjecture,
    ( ? [X1] :
        ( aNaturalNumber0(X1)
        & sdtasdt0(xn,xm) = sdtasdt0(xr,X1) )
    | doDivides0(xr,sdtasdt0(xn,xm)) ),
    file('/export/starexec/sandbox/tmp/tmp.cvKI9dJWOO/E---3.1_13634.p',m__) ).

fof(mDivTrans,axiom,
    ! [X1,X2,X3] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2)
        & aNaturalNumber0(X3) )
     => ( ( doDivides0(X1,X2)
          & doDivides0(X2,X3) )
       => doDivides0(X1,X3) ) ),
    file('/export/starexec/sandbox/tmp/tmp.cvKI9dJWOO/E---3.1_13634.p',mDivTrans) ).

fof(m__2306,hypothesis,
    ( aNaturalNumber0(xk)
    & sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
    & xk = sdtsldt0(sdtasdt0(xn,xm),xp) ),
    file('/export/starexec/sandbox/tmp/tmp.cvKI9dJWOO/E---3.1_13634.p',m__2306) ).

fof(m__1837,hypothesis,
    ( aNaturalNumber0(xn)
    & aNaturalNumber0(xm)
    & aNaturalNumber0(xp) ),
    file('/export/starexec/sandbox/tmp/tmp.cvKI9dJWOO/E---3.1_13634.p',m__1837) ).

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/tmp/tmp.cvKI9dJWOO/E---3.1_13634.p',m__2342) ).

fof(c_0_9,plain,
    ! [X62,X63,X65] :
      ( ( aNaturalNumber0(esk2_2(X62,X63))
        | ~ doDivides0(X62,X63)
        | ~ aNaturalNumber0(X62)
        | ~ aNaturalNumber0(X63) )
      & ( X63 = sdtasdt0(X62,esk2_2(X62,X63))
        | ~ doDivides0(X62,X63)
        | ~ aNaturalNumber0(X62)
        | ~ aNaturalNumber0(X63) )
      & ( ~ aNaturalNumber0(X65)
        | X63 != sdtasdt0(X62,X65)
        | doDivides0(X62,X63)
        | ~ aNaturalNumber0(X62)
        | ~ aNaturalNumber0(X63) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefDiv])])])])]) ).

fof(c_0_10,plain,
    ! [X8,X9] :
      ( ~ aNaturalNumber0(X8)
      | ~ aNaturalNumber0(X9)
      | aNaturalNumber0(sdtasdt0(X8,X9)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])]) ).

cnf(c_0_11,plain,
    ( doDivides0(X3,X2)
    | ~ aNaturalNumber0(X1)
    | X2 != sdtasdt0(X3,X1)
    | ~ aNaturalNumber0(X3)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_12,plain,
    ( aNaturalNumber0(sdtasdt0(X1,X2))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

fof(c_0_13,plain,
    ! [X16,X17] :
      ( ~ aNaturalNumber0(X16)
      | ~ aNaturalNumber0(X17)
      | sdtasdt0(X16,X17) = sdtasdt0(X17,X16) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])]) ).

cnf(c_0_14,plain,
    ( doDivides0(X1,sdtasdt0(X1,X2))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_11]),c_0_12]) ).

cnf(c_0_15,plain,
    ( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

fof(c_0_16,hypothesis,
    ! [X96,X97] :
      ( xp != sz00
      & xp != sz10
      & ( ~ aNaturalNumber0(X97)
        | xp != sdtasdt0(X96,X97)
        | ~ aNaturalNumber0(X96)
        | X96 = sz10
        | X96 = xp )
      & ( ~ doDivides0(X96,xp)
        | ~ aNaturalNumber0(X96)
        | X96 = sz10
        | X96 = xp )
      & isPrime0(xp)
      & aNaturalNumber0(esk9_0)
      & sdtasdt0(xn,xm) = sdtasdt0(xp,esk9_0)
      & doDivides0(xp,sdtasdt0(xn,xm)) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__1860])])])])]) ).

fof(c_0_17,negated_conjecture,
    ~ ( ? [X1] :
          ( aNaturalNumber0(X1)
          & sdtasdt0(xn,xm) = sdtasdt0(xr,X1) )
      | doDivides0(xr,sdtasdt0(xn,xm)) ),
    inference(assume_negation,[status(cth)],[m__]) ).

fof(c_0_18,plain,
    ! [X69,X70,X71] :
      ( ~ aNaturalNumber0(X69)
      | ~ aNaturalNumber0(X70)
      | ~ aNaturalNumber0(X71)
      | ~ doDivides0(X69,X70)
      | ~ doDivides0(X70,X71)
      | doDivides0(X69,X71) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivTrans])]) ).

cnf(c_0_19,plain,
    ( doDivides0(X1,sdtasdt0(X2,X1))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_20,hypothesis,
    sdtasdt0(xn,xm) = sdtasdt0(xp,xk),
    inference(split_conjunct,[status(thm)],[m__2306]) ).

cnf(c_0_21,hypothesis,
    aNaturalNumber0(xk),
    inference(split_conjunct,[status(thm)],[m__2306]) ).

cnf(c_0_22,hypothesis,
    aNaturalNumber0(xp),
    inference(split_conjunct,[status(thm)],[m__1837]) ).

cnf(c_0_23,hypothesis,
    sdtasdt0(xn,xm) = sdtasdt0(xp,esk9_0),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_24,hypothesis,
    aNaturalNumber0(esk9_0),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

fof(c_0_25,negated_conjecture,
    ! [X106] :
      ( ( ~ aNaturalNumber0(X106)
        | sdtasdt0(xn,xm) != sdtasdt0(xr,X106) )
      & ~ doDivides0(xr,sdtasdt0(xn,xm)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])]) ).

cnf(c_0_26,plain,
    ( doDivides0(X1,X3)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X3)
    | ~ doDivides0(X1,X2)
    | ~ doDivides0(X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_27,hypothesis,
    doDivides0(xk,sdtasdt0(xn,xm)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]),c_0_22])]) ).

cnf(c_0_28,hypothesis,
    aNaturalNumber0(sdtasdt0(xn,xm)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_23]),c_0_24]),c_0_22])]) ).

fof(c_0_29,hypothesis,
    ! [X104,X105] :
      ( aNaturalNumber0(xr)
      & aNaturalNumber0(esk12_0)
      & xk = sdtasdt0(xr,esk12_0)
      & doDivides0(xr,xk)
      & xr != sz00
      & xr != sz10
      & ( ~ aNaturalNumber0(X105)
        | xr != sdtasdt0(X104,X105)
        | ~ aNaturalNumber0(X104)
        | X104 = sz10
        | X104 = xr )
      & ( ~ doDivides0(X104,xr)
        | ~ aNaturalNumber0(X104)
        | X104 = sz10
        | X104 = xr )
      & isPrime0(xr) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__2342])])])])]) ).

cnf(c_0_30,negated_conjecture,
    ~ doDivides0(xr,sdtasdt0(xn,xm)),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_31,hypothesis,
    ( doDivides0(X1,sdtasdt0(xn,xm))
    | ~ doDivides0(X1,xk)
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]),c_0_21])]) ).

cnf(c_0_32,hypothesis,
    doDivides0(xr,xk),
    inference(split_conjunct,[status(thm)],[c_0_29]) ).

cnf(c_0_33,hypothesis,
    aNaturalNumber0(xr),
    inference(split_conjunct,[status(thm)],[c_0_29]) ).

cnf(c_0_34,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]),c_0_33])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.10  % Problem    : NUM501+3 : TPTP v8.1.2. Released v4.0.0.
% 0.08/0.11  % Command    : run_E %s %d THM
% 0.11/0.31  % Computer : n028.cluster.edu
% 0.11/0.31  % Model    : x86_64 x86_64
% 0.11/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31  % Memory   : 8042.1875MB
% 0.11/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31  % CPULimit   : 2400
% 0.11/0.31  % WCLimit    : 300
% 0.11/0.31  % DateTime   : Mon Oct  2 15:17:36 EDT 2023
% 0.16/0.31  % CPUTime    : 
% 0.16/0.42  Running first-order theorem proving
% 0.16/0.42  Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.cvKI9dJWOO/E---3.1_13634.p
% 0.16/0.50  # Version: 3.1pre001
% 0.16/0.50  # Preprocessing class: FSLSSMSSSSSNFFN.
% 0.16/0.50  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.50  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.16/0.50  # Starting new_bool_3 with 300s (1) cores
% 0.16/0.50  # Starting new_bool_1 with 300s (1) cores
% 0.16/0.50  # Starting sh5l with 300s (1) cores
% 0.16/0.50  # G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 13712 completed with status 0
% 0.16/0.50  # Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.16/0.50  # Preprocessing class: FSLSSMSSSSSNFFN.
% 0.16/0.50  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.50  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.16/0.50  # No SInE strategy applied
% 0.16/0.50  # Search class: FGHSF-FSLM32-SFFFFFNN
% 0.16/0.50  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.16/0.50  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2m with 811s (1) cores
% 0.16/0.50  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.16/0.50  # Starting new_bool_3 with 136s (1) cores
% 0.16/0.50  # Starting U----_116_C05_02_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN1 with 136s (1) cores
% 0.16/0.50  # Starting G-N--_023_B07_F1_SP_PI_Q7_CS_SP_CO_S5PRR_S0Y1 with 136s (1) cores
% 0.16/0.50  # U----_116_C05_02_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN1 with pid 13721 completed with status 0
% 0.16/0.50  # Result found by U----_116_C05_02_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN1
% 0.16/0.50  # Preprocessing class: FSLSSMSSSSSNFFN.
% 0.16/0.50  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.50  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.16/0.50  # No SInE strategy applied
% 0.16/0.50  # Search class: FGHSF-FSLM32-SFFFFFNN
% 0.16/0.50  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.16/0.50  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2m with 811s (1) cores
% 0.16/0.50  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.16/0.50  # Starting new_bool_3 with 136s (1) cores
% 0.16/0.50  # Starting U----_116_C05_02_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN1 with 136s (1) cores
% 0.16/0.50  # Preprocessing time       : 0.004 s
% 0.16/0.50  # Presaturation interreduction done
% 0.16/0.50  
% 0.16/0.50  # Proof found!
% 0.16/0.50  # SZS status Theorem
% 0.16/0.50  # SZS output start CNFRefutation
% See solution above
% 0.16/0.50  # Parsed axioms                        : 49
% 0.16/0.50  # Removed by relevancy pruning/SinE    : 0
% 0.16/0.50  # Initial clauses                      : 237
% 0.16/0.50  # Removed in clause preprocessing      : 3
% 0.16/0.50  # Initial clauses in saturation        : 234
% 0.16/0.50  # Processed clauses                    : 724
% 0.16/0.50  # ...of these trivial                  : 10
% 0.16/0.50  # ...subsumed                          : 143
% 0.16/0.50  # ...remaining for further processing  : 571
% 0.16/0.50  # Other redundant clauses eliminated   : 11
% 0.16/0.50  # Clauses deleted for lack of memory   : 0
% 0.16/0.50  # Backward-subsumed                    : 17
% 0.16/0.50  # Backward-rewritten                   : 7
% 0.16/0.50  # Generated clauses                    : 918
% 0.16/0.50  # ...of the previous two non-redundant : 807
% 0.16/0.50  # ...aggressively subsumed             : 0
% 0.16/0.50  # Contextual simplify-reflections      : 6
% 0.16/0.50  # Paramodulations                      : 905
% 0.16/0.50  # Factorizations                       : 2
% 0.16/0.50  # NegExts                              : 0
% 0.16/0.50  # Equation resolutions                 : 11
% 0.16/0.50  # Total rewrite steps                  : 400
% 0.16/0.50  # Propositional unsat checks           : 0
% 0.16/0.50  #    Propositional check models        : 0
% 0.16/0.50  #    Propositional check unsatisfiable : 0
% 0.16/0.50  #    Propositional clauses             : 0
% 0.16/0.50  #    Propositional clauses after purity: 0
% 0.16/0.50  #    Propositional unsat core size     : 0
% 0.16/0.50  #    Propositional preprocessing time  : 0.000
% 0.16/0.50  #    Propositional encoding time       : 0.000
% 0.16/0.50  #    Propositional solver time         : 0.000
% 0.16/0.50  #    Success case prop preproc time    : 0.000
% 0.16/0.50  #    Success case prop encoding time   : 0.000
% 0.16/0.50  #    Success case prop solver time     : 0.000
% 0.16/0.50  # Current number of processed clauses  : 309
% 0.16/0.50  #    Positive orientable unit clauses  : 85
% 0.16/0.50  #    Positive unorientable unit clauses: 0
% 0.16/0.50  #    Negative unit clauses             : 19
% 0.16/0.50  #    Non-unit-clauses                  : 205
% 0.16/0.50  # Current number of unprocessed clauses: 511
% 0.16/0.50  # ...number of literals in the above   : 2880
% 0.16/0.50  # Current number of archived formulas  : 0
% 0.16/0.50  # Current number of archived clauses   : 251
% 0.16/0.50  # Clause-clause subsumption calls (NU) : 29588
% 0.16/0.50  # Rec. Clause-clause subsumption calls : 4655
% 0.16/0.50  # Non-unit clause-clause subsumptions  : 140
% 0.16/0.50  # Unit Clause-clause subsumption calls : 1394
% 0.16/0.50  # Rewrite failures with RHS unbound    : 0
% 0.16/0.50  # BW rewrite match attempts            : 15
% 0.16/0.50  # BW rewrite match successes           : 15
% 0.16/0.50  # Condensation attempts                : 0
% 0.16/0.50  # Condensation successes               : 0
% 0.16/0.50  # Termbank termtop insertions          : 31091
% 0.16/0.50  
% 0.16/0.50  # -------------------------------------------------
% 0.16/0.50  # User time                : 0.065 s
% 0.16/0.50  # System time              : 0.005 s
% 0.16/0.50  # Total time               : 0.070 s
% 0.16/0.50  # Maximum resident set size: 2408 pages
% 0.16/0.50  
% 0.16/0.50  # -------------------------------------------------
% 0.16/0.50  # User time                : 0.297 s
% 0.16/0.50  # System time              : 0.015 s
% 0.16/0.50  # Total time               : 0.311 s
% 0.16/0.50  # Maximum resident set size: 1744 pages
% 0.16/0.50  % E---3.1 exiting
% 0.16/0.50  % E---3.1 exiting
%------------------------------------------------------------------------------