TSTP Solution File: NUM498+3 by E---3.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1
% Problem  : NUM498+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

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

% Result   : Theorem 0.64s 0.59s
% Output   : CNFRefutation 0.64s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   45 (  19 unt;   0 def)
%            Number of atoms       :  144 (  81 equ)
%            Maximal formula atoms :   15 (   3 avg)
%            Number of connectives :  148 (  49   ~;  46   |;  46   &)
%                                         (   0 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   9 con; 0-2 aty)
%            Number of variables   :   30 (   0 sgn;  13   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(m__,conjecture,
    ( ( xk = sz00
      | xk = sz10 )
   => ( ? [X1] :
          ( aNaturalNumber0(X1)
          & xn = sdtasdt0(xp,X1) )
      | doDivides0(xp,xn)
      | ? [X1] :
          ( aNaturalNumber0(X1)
          & xm = sdtasdt0(xp,X1) )
      | doDivides0(xp,xm) ) ),
    file('/export/starexec/sandbox/tmp/tmp.nDR6XcSoPD/E---3.1_29637.p',m__) ).

fof(m_MulZero,axiom,
    ! [X1] :
      ( aNaturalNumber0(X1)
     => ( sdtasdt0(X1,sz00) = sz00
        & sz00 = sdtasdt0(sz00,X1) ) ),
    file('/export/starexec/sandbox/tmp/tmp.nDR6XcSoPD/E---3.1_29637.p',m_MulZero) ).

fof(mZeroMul,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => ( sdtasdt0(X1,X2) = sz00
       => ( X1 = sz00
          | X2 = sz00 ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.nDR6XcSoPD/E---3.1_29637.p',mZeroMul) ).

fof(mSortsC,axiom,
    aNaturalNumber0(sz00),
    file('/export/starexec/sandbox/tmp/tmp.nDR6XcSoPD/E---3.1_29637.p',mSortsC) ).

fof(m__1837,hypothesis,
    ( aNaturalNumber0(xn)
    & aNaturalNumber0(xm)
    & aNaturalNumber0(xp) ),
    file('/export/starexec/sandbox/tmp/tmp.nDR6XcSoPD/E---3.1_29637.p',m__1837) ).

fof(m__2306,hypothesis,
    ( aNaturalNumber0(xk)
    & sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
    & xk = sdtsldt0(sdtasdt0(xn,xm),xp) ),
    file('/export/starexec/sandbox/tmp/tmp.nDR6XcSoPD/E---3.1_29637.p',m__2306) ).

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.nDR6XcSoPD/E---3.1_29637.p',m__1860) ).

fof(m__2287,hypothesis,
    ( xn != xp
    & ? [X1] :
        ( aNaturalNumber0(X1)
        & sdtpldt0(xn,X1) = xp )
    & sdtlseqdt0(xn,xp)
    & xm != xp
    & ? [X1] :
        ( aNaturalNumber0(X1)
        & sdtpldt0(xm,X1) = xp )
    & sdtlseqdt0(xm,xp) ),
    file('/export/starexec/sandbox/tmp/tmp.nDR6XcSoPD/E---3.1_29637.p',m__2287) ).

fof(m_MulUnit,axiom,
    ! [X1] :
      ( aNaturalNumber0(X1)
     => ( sdtasdt0(X1,sz10) = X1
        & X1 = sdtasdt0(sz10,X1) ) ),
    file('/export/starexec/sandbox/tmp/tmp.nDR6XcSoPD/E---3.1_29637.p',m_MulUnit) ).

fof(c_0_9,negated_conjecture,
    ~ ( ( xk = sz00
        | xk = sz10 )
     => ( ? [X1] :
            ( aNaturalNumber0(X1)
            & xn = sdtasdt0(xp,X1) )
        | doDivides0(xp,xn)
        | ? [X1] :
            ( aNaturalNumber0(X1)
            & xm = sdtasdt0(xp,X1) )
        | doDivides0(xp,xm) ) ),
    inference(assume_negation,[status(cth)],[m__]) ).

fof(c_0_10,negated_conjecture,
    ! [X21,X22] :
      ( ( xk = sz00
        | xk = sz10 )
      & ( ~ aNaturalNumber0(X21)
        | xn != sdtasdt0(xp,X21) )
      & ~ doDivides0(xp,xn)
      & ( ~ aNaturalNumber0(X22)
        | xm != sdtasdt0(xp,X22) )
      & ~ doDivides0(xp,xm) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).

fof(c_0_11,plain,
    ! [X45] :
      ( ( sdtasdt0(X45,sz00) = sz00
        | ~ aNaturalNumber0(X45) )
      & ( sz00 = sdtasdt0(sz00,X45)
        | ~ aNaturalNumber0(X45) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulZero])])]) ).

fof(c_0_12,plain,
    ! [X52,X53] :
      ( ~ aNaturalNumber0(X52)
      | ~ aNaturalNumber0(X53)
      | sdtasdt0(X52,X53) != sz00
      | X52 = sz00
      | X53 = sz00 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroMul])]) ).

cnf(c_0_13,negated_conjecture,
    ( ~ aNaturalNumber0(X1)
    | xm != sdtasdt0(xp,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_14,plain,
    ( sdtasdt0(X1,sz00) = sz00
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_15,plain,
    aNaturalNumber0(sz00),
    inference(split_conjunct,[status(thm)],[mSortsC]) ).

cnf(c_0_16,hypothesis,
    aNaturalNumber0(xp),
    inference(split_conjunct,[status(thm)],[m__1837]) ).

cnf(c_0_17,negated_conjecture,
    ( ~ aNaturalNumber0(X1)
    | xn != sdtasdt0(xp,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_18,plain,
    ( X1 = sz00
    | X2 = sz00
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | sdtasdt0(X1,X2) != sz00 ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_19,hypothesis,
    sdtasdt0(xn,xm) = sdtasdt0(xp,xk),
    inference(split_conjunct,[status(thm)],[m__2306]) ).

cnf(c_0_20,hypothesis,
    aNaturalNumber0(xm),
    inference(split_conjunct,[status(thm)],[m__1837]) ).

cnf(c_0_21,hypothesis,
    aNaturalNumber0(xn),
    inference(split_conjunct,[status(thm)],[m__1837]) ).

cnf(c_0_22,negated_conjecture,
    xm != sz00,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]),c_0_16])]) ).

cnf(c_0_23,negated_conjecture,
    xn != sz00,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_14]),c_0_15]),c_0_16])]) ).

fof(c_0_24,hypothesis,
    ! [X14,X15] :
      ( xp != sz00
      & xp != sz10
      & ( ~ aNaturalNumber0(X15)
        | xp != sdtasdt0(X14,X15)
        | ~ aNaturalNumber0(X14)
        | X14 = sz10
        | X14 = xp )
      & ( ~ doDivides0(X14,xp)
        | ~ aNaturalNumber0(X14)
        | X14 = sz10
        | X14 = 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(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__1860])])])])]) ).

fof(c_0_25,hypothesis,
    ( xn != xp
    & aNaturalNumber0(esk6_0)
    & sdtpldt0(xn,esk6_0) = xp
    & sdtlseqdt0(xn,xp)
    & xm != xp
    & aNaturalNumber0(esk7_0)
    & sdtpldt0(xm,esk7_0) = xp
    & sdtlseqdt0(xm,xp) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__2287])]) ).

cnf(c_0_26,hypothesis,
    sdtasdt0(xp,xk) != sz00,
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]),c_0_21])]),c_0_22]),c_0_23]) ).

cnf(c_0_27,negated_conjecture,
    ( xk = sz00
    | xk = sz10 ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_28,hypothesis,
    ( X2 = sz10
    | X2 = xp
    | ~ aNaturalNumber0(X1)
    | xp != sdtasdt0(X2,X1)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_29,hypothesis,
    xn != xp,
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_30,negated_conjecture,
    ( xk = sz10
    | sdtasdt0(xp,sz00) != sz00 ),
    inference(spm,[status(thm)],[c_0_26,c_0_27]) ).

cnf(c_0_31,hypothesis,
    ( xn = sz10
    | sdtasdt0(xp,xk) != xp ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_19]),c_0_21]),c_0_20])]),c_0_29]) ).

cnf(c_0_32,negated_conjecture,
    xk = sz10,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_14]),c_0_16])]) ).

fof(c_0_33,plain,
    ! [X86] :
      ( ( sdtasdt0(X86,sz10) = X86
        | ~ aNaturalNumber0(X86) )
      & ( X86 = sdtasdt0(sz10,X86)
        | ~ aNaturalNumber0(X86) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulUnit])])]) ).

cnf(c_0_34,hypothesis,
    sdtasdt0(xn,xm) = sdtasdt0(xp,esk5_0),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_35,hypothesis,
    ( xn = sz10
    | sdtasdt0(xp,sz10) != xp ),
    inference(rw,[status(thm)],[c_0_31,c_0_32]) ).

cnf(c_0_36,plain,
    ( sdtasdt0(X1,sz10) = X1
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_33]) ).

cnf(c_0_37,hypothesis,
    sdtasdt0(xp,esk5_0) = sdtasdt0(xp,xk),
    inference(rw,[status(thm)],[c_0_34,c_0_19]) ).

cnf(c_0_38,hypothesis,
    aNaturalNumber0(esk5_0),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_39,hypothesis,
    xn = sz10,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_16])]) ).

cnf(c_0_40,hypothesis,
    sdtasdt0(xp,xk) != xm,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_37]),c_0_38])]) ).

cnf(c_0_41,plain,
    ( X1 = sdtasdt0(sz10,X1)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_33]) ).

cnf(c_0_42,hypothesis,
    sdtasdt0(sz10,xm) = sdtasdt0(xp,sz10),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_32]),c_0_39]) ).

cnf(c_0_43,hypothesis,
    sdtasdt0(xp,sz10) != xm,
    inference(rw,[status(thm)],[c_0_40,c_0_32]) ).

cnf(c_0_44,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_20])]),c_0_43]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.15  % Problem    : NUM498+3 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.16  % Command    : run_E %s %d THM
% 0.14/0.37  % Computer : n027.cluster.edu
% 0.14/0.37  % Model    : x86_64 x86_64
% 0.14/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37  % Memory   : 8042.1875MB
% 0.14/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37  % CPULimit   : 2400
% 0.14/0.37  % WCLimit    : 300
% 0.14/0.37  % DateTime   : Mon Oct  2 13:54:00 EDT 2023
% 0.14/0.37  % CPUTime    : 
% 0.22/0.52  Running first-order theorem proving
% 0.22/0.52  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.nDR6XcSoPD/E---3.1_29637.p
% 0.64/0.59  # Version: 3.1pre001
% 0.64/0.59  # Preprocessing class: FSLSSMSSSSSNFFN.
% 0.64/0.59  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.64/0.59  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.64/0.59  # Starting new_bool_3 with 300s (1) cores
% 0.64/0.59  # Starting new_bool_1 with 300s (1) cores
% 0.64/0.59  # Starting sh5l with 300s (1) cores
% 0.64/0.59  # new_bool_1 with pid 29717 completed with status 0
% 0.64/0.59  # Result found by new_bool_1
% 0.64/0.59  # Preprocessing class: FSLSSMSSSSSNFFN.
% 0.64/0.59  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.64/0.59  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.64/0.59  # Starting new_bool_3 with 300s (1) cores
% 0.64/0.59  # Starting new_bool_1 with 300s (1) cores
% 0.64/0.59  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.64/0.59  # Search class: FGHSF-FSLM32-SFFFFFNN
% 0.64/0.59  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.64/0.59  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2m with 163s (1) cores
% 0.64/0.59  # G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2m with pid 29719 completed with status 0
% 0.64/0.59  # Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2m
% 0.64/0.59  # Preprocessing class: FSLSSMSSSSSNFFN.
% 0.64/0.59  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.64/0.59  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.64/0.59  # Starting new_bool_3 with 300s (1) cores
% 0.64/0.59  # Starting new_bool_1 with 300s (1) cores
% 0.64/0.59  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.64/0.59  # Search class: FGHSF-FSLM32-SFFFFFNN
% 0.64/0.59  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.64/0.59  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2m with 163s (1) cores
% 0.64/0.59  # Preprocessing time       : 0.004 s
% 0.64/0.59  # Presaturation interreduction done
% 0.64/0.59  
% 0.64/0.59  # Proof found!
% 0.64/0.59  # SZS status Theorem
% 0.64/0.59  # SZS output start CNFRefutation
% See solution above
% 0.64/0.59  # Parsed axioms                        : 46
% 0.64/0.59  # Removed by relevancy pruning/SinE    : 1
% 0.64/0.59  # Initial clauses                      : 224
% 0.64/0.59  # Removed in clause preprocessing      : 3
% 0.64/0.59  # Initial clauses in saturation        : 221
% 0.64/0.59  # Processed clauses                    : 335
% 0.64/0.59  # ...of these trivial                  : 1
% 0.64/0.59  # ...subsumed                          : 27
% 0.64/0.59  # ...remaining for further processing  : 307
% 0.64/0.59  # Other redundant clauses eliminated   : 8
% 0.64/0.59  # Clauses deleted for lack of memory   : 0
% 0.64/0.59  # Backward-subsumed                    : 0
% 0.64/0.59  # Backward-rewritten                   : 30
% 0.64/0.59  # Generated clauses                    : 74
% 0.64/0.59  # ...of the previous two non-redundant : 72
% 0.64/0.59  # ...aggressively subsumed             : 0
% 0.64/0.59  # Contextual simplify-reflections      : 4
% 0.64/0.59  # Paramodulations                      : 65
% 0.64/0.59  # Factorizations                       : 1
% 0.64/0.59  # NegExts                              : 0
% 0.64/0.59  # Equation resolutions                 : 8
% 0.64/0.59  # Total rewrite steps                  : 128
% 0.64/0.59  # Propositional unsat checks           : 0
% 0.64/0.59  #    Propositional check models        : 0
% 0.64/0.59  #    Propositional check unsatisfiable : 0
% 0.64/0.59  #    Propositional clauses             : 0
% 0.64/0.59  #    Propositional clauses after purity: 0
% 0.64/0.59  #    Propositional unsat core size     : 0
% 0.64/0.59  #    Propositional preprocessing time  : 0.000
% 0.64/0.59  #    Propositional encoding time       : 0.000
% 0.64/0.59  #    Propositional solver time         : 0.000
% 0.64/0.59  #    Success case prop preproc time    : 0.000
% 0.64/0.59  #    Success case prop encoding time   : 0.000
% 0.64/0.59  #    Success case prop solver time     : 0.000
% 0.64/0.59  # Current number of processed clauses  : 53
% 0.64/0.59  #    Positive orientable unit clauses  : 17
% 0.64/0.59  #    Positive unorientable unit clauses: 0
% 0.64/0.59  #    Negative unit clauses             : 13
% 0.64/0.59  #    Non-unit-clauses                  : 23
% 0.64/0.59  # Current number of unprocessed clauses: 173
% 0.64/0.59  # ...number of literals in the above   : 1478
% 0.64/0.59  # Current number of archived formulas  : 0
% 0.64/0.59  # Current number of archived clauses   : 246
% 0.64/0.59  # Clause-clause subsumption calls (NU) : 25930
% 0.64/0.59  # Rec. Clause-clause subsumption calls : 172
% 0.64/0.59  # Non-unit clause-clause subsumptions  : 9
% 0.64/0.59  # Unit Clause-clause subsumption calls : 140
% 0.64/0.59  # Rewrite failures with RHS unbound    : 0
% 0.64/0.59  # BW rewrite match attempts            : 2
% 0.64/0.59  # BW rewrite match successes           : 2
% 0.64/0.59  # Condensation attempts                : 0
% 0.64/0.59  # Condensation successes               : 0
% 0.64/0.59  # Termbank termtop insertions          : 20499
% 0.64/0.59  
% 0.64/0.59  # -------------------------------------------------
% 0.64/0.59  # User time                : 0.051 s
% 0.64/0.59  # System time              : 0.005 s
% 0.64/0.59  # Total time               : 0.056 s
% 0.64/0.59  # Maximum resident set size: 2296 pages
% 0.64/0.59  
% 0.64/0.59  # -------------------------------------------------
% 0.64/0.59  # User time                : 0.052 s
% 0.64/0.59  # System time              : 0.008 s
% 0.64/0.59  # Total time               : 0.060 s
% 0.64/0.59  # Maximum resident set size: 1740 pages
% 0.64/0.59  % E---3.1 exiting
% 0.64/0.59  % E---3.1 exiting
%------------------------------------------------------------------------------