TSTP Solution File: NUM504+3 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : NUM504+3 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n008.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  : 300s
% DateTime : Tue May 21 01:14:21 EDT 2024

% Result   : ContradictoryAxioms 0.18s 0.54s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   30 (  14 unt;   0 def)
%            Number of atoms       :  120 (  45 equ)
%            Maximal formula atoms :   16 (   4 avg)
%            Number of connectives :  121 (  31   ~;  23   |;  62   &)
%                                         (   0 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   15 (  15 usr;  12 con; 0-2 aty)
%            Number of variables   :   26 (   0 sgn  12   !;  10   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(m__2414,hypothesis,
    ( sdtasdt0(xn,xm) != sdtasdt0(xp,xm)
    & ? [X1] :
        ( aNaturalNumber0(X1)
        & sdtpldt0(sdtasdt0(xn,xm),X1) = sdtasdt0(xp,xm) )
    & sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
    & sdtasdt0(xp,xm) != sdtasdt0(xp,xk)
    & ? [X1] :
        ( aNaturalNumber0(X1)
        & sdtpldt0(sdtasdt0(xp,xm),X1) = sdtasdt0(xp,xk) )
    & sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2414) ).

fof(m__2362,hypothesis,
    ( ? [X1] :
        ( aNaturalNumber0(X1)
        & sdtpldt0(xr,X1) = xk )
    & ? [X1] :
        ( aNaturalNumber0(X1)
        & sdtasdt0(xn,xm) = sdtasdt0(xr,X1) )
    & doDivides0(xr,sdtasdt0(xn,xm)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2362) ).

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/benchmark/theBenchmark.p',m__2342) ).

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

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

fof(mLEAsym,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => ( ( sdtlseqdt0(X1,X2)
          & sdtlseqdt0(X2,X1) )
       => X1 = X2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLEAsym) ).

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

fof(c_0_7,hypothesis,
    ( sdtasdt0(xn,xm) != sdtasdt0(xp,xm)
    & ? [X1] :
        ( aNaturalNumber0(X1)
        & sdtpldt0(sdtasdt0(xn,xm),X1) = sdtasdt0(xp,xm) )
    & sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
    & sdtasdt0(xp,xm) != sdtasdt0(xp,xk)
    & ? [X1] :
        ( aNaturalNumber0(X1)
        & sdtpldt0(sdtasdt0(xp,xm),X1) = sdtasdt0(xp,xk) )
    & sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)) ),
    inference(fof_simplification,[status(thm)],[m__2414]) ).

fof(c_0_8,hypothesis,
    ( aNaturalNumber0(esk9_0)
    & sdtpldt0(xr,esk9_0) = xk
    & aNaturalNumber0(esk10_0)
    & sdtasdt0(xn,xm) = sdtasdt0(xr,esk10_0)
    & doDivides0(xr,sdtasdt0(xn,xm)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__2362])]) ).

fof(c_0_9,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) ),
    inference(fof_simplification,[status(thm)],[m__2342]) ).

fof(c_0_10,hypothesis,
    ( sdtasdt0(xn,xm) != sdtasdt0(xp,xm)
    & aNaturalNumber0(esk12_0)
    & sdtpldt0(sdtasdt0(xn,xm),esk12_0) = sdtasdt0(xp,xm)
    & sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
    & sdtasdt0(xp,xm) != sdtasdt0(xp,xk)
    & aNaturalNumber0(esk13_0)
    & sdtpldt0(sdtasdt0(xp,xm),esk13_0) = sdtasdt0(xp,xk)
    & sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)) ),
    inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_7])])]) ).

fof(c_0_11,plain,
    ! [X45,X46] :
      ( ~ aNaturalNumber0(X45)
      | ~ aNaturalNumber0(X46)
      | aNaturalNumber0(sdtasdt0(X45,X46)) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])])]) ).

cnf(c_0_12,hypothesis,
    sdtasdt0(xn,xm) = sdtasdt0(xr,esk10_0),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_13,hypothesis,
    sdtasdt0(xn,xm) = sdtasdt0(xp,xk),
    inference(split_conjunct,[status(thm)],[m__2306]) ).

fof(c_0_14,hypothesis,
    ! [X22,X23] :
      ( aNaturalNumber0(xr)
      & aNaturalNumber0(esk8_0)
      & xk = sdtasdt0(xr,esk8_0)
      & doDivides0(xr,xk)
      & xr != sz00
      & xr != sz10
      & ( ~ aNaturalNumber0(X23)
        | xr != sdtasdt0(X22,X23)
        | ~ aNaturalNumber0(X22)
        | X22 = sz10
        | X22 = xr )
      & ( ~ doDivides0(X22,xr)
        | ~ aNaturalNumber0(X22)
        | X22 = sz10
        | X22 = xr )
      & isPrime0(xr) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])])])])]) ).

fof(c_0_15,plain,
    ! [X98,X99] :
      ( ~ aNaturalNumber0(X98)
      | ~ aNaturalNumber0(X99)
      | ~ sdtlseqdt0(X98,X99)
      | ~ sdtlseqdt0(X99,X98)
      | X98 = X99 ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLEAsym])])]) ).

cnf(c_0_16,hypothesis,
    sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_17,plain,
    ( aNaturalNumber0(sdtasdt0(X1,X2))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_18,hypothesis,
    sdtasdt0(xr,esk10_0) = sdtasdt0(xp,xk),
    inference(rw,[status(thm)],[c_0_12,c_0_13]) ).

cnf(c_0_19,hypothesis,
    aNaturalNumber0(esk10_0),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_20,hypothesis,
    aNaturalNumber0(xr),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_21,plain,
    ( X1 = X2
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ sdtlseqdt0(X1,X2)
    | ~ sdtlseqdt0(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_22,hypothesis,
    sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_23,hypothesis,
    sdtlseqdt0(sdtasdt0(xp,xk),sdtasdt0(xp,xm)),
    inference(rw,[status(thm)],[c_0_16,c_0_13]) ).

cnf(c_0_24,hypothesis,
    aNaturalNumber0(sdtasdt0(xp,xk)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]),c_0_20])]) ).

cnf(c_0_25,hypothesis,
    sdtasdt0(xp,xm) != sdtasdt0(xp,xk),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_26,hypothesis,
    ~ aNaturalNumber0(sdtasdt0(xp,xm)),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]),c_0_24])]),c_0_25]) ).

cnf(c_0_27,hypothesis,
    aNaturalNumber0(xm),
    inference(split_conjunct,[status(thm)],[m__1837]) ).

cnf(c_0_28,hypothesis,
    aNaturalNumber0(xp),
    inference(split_conjunct,[status(thm)],[m__1837]) ).

cnf(c_0_29,hypothesis,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_17]),c_0_27]),c_0_28])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10  % Problem    : NUM504+3 : TPTP v8.2.0. Released v4.0.0.
% 0.03/0.11  % Command    : run_E %s %d THM
% 0.11/0.33  % Computer : n008.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit   : 300
% 0.11/0.33  % WCLimit    : 300
% 0.11/0.33  % DateTime   : Mon May 20 03:49:22 EDT 2024
% 0.11/0.33  % CPUTime    : 
% 0.18/0.46  Running first-order theorem proving
% 0.18/0.46  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/benchmark/theBenchmark.p
% 0.18/0.54  # Version: 3.1.0
% 0.18/0.54  # Preprocessing class: FSLSSMSSSSSNFFN.
% 0.18/0.54  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.54  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.18/0.54  # Starting new_bool_3 with 300s (1) cores
% 0.18/0.54  # Starting new_bool_1 with 300s (1) cores
% 0.18/0.54  # Starting sh5l with 300s (1) cores
% 0.18/0.54  # sh5l with pid 10241 completed with status 8
% 0.18/0.54  # new_bool_1 with pid 10240 completed with status 0
% 0.18/0.54  # Result found by new_bool_1
% 0.18/0.54  # Preprocessing class: FSLSSMSSSSSNFFN.
% 0.18/0.54  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.54  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.18/0.54  # Starting new_bool_3 with 300s (1) cores
% 0.18/0.54  # Starting new_bool_1 with 300s (1) cores
% 0.18/0.54  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.18/0.54  # Search class: FGHSF-FSLM32-SFFFFFNN
% 0.18/0.54  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.18/0.54  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2m with 163s (1) cores
% 0.18/0.54  # G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2m with pid 10255 completed with status 0
% 0.18/0.54  # Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2m
% 0.18/0.54  # Preprocessing class: FSLSSMSSSSSNFFN.
% 0.18/0.54  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.54  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.18/0.54  # Starting new_bool_3 with 300s (1) cores
% 0.18/0.54  # Starting new_bool_1 with 300s (1) cores
% 0.18/0.54  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.18/0.54  # Search class: FGHSF-FSLM32-SFFFFFNN
% 0.18/0.54  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.18/0.54  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2m with 163s (1) cores
% 0.18/0.54  # Preprocessing time       : 0.004 s
% 0.18/0.54  # Presaturation interreduction done
% 0.18/0.54  
% 0.18/0.54  # Proof found!
% 0.18/0.54  # SZS status ContradictoryAxioms
% 0.18/0.54  # SZS output start CNFRefutation
% See solution above
% 0.18/0.54  # Parsed axioms                        : 52
% 0.18/0.54  # Removed by relevancy pruning/SinE    : 1
% 0.18/0.54  # Initial clauses                      : 249
% 0.18/0.54  # Removed in clause preprocessing      : 4
% 0.18/0.54  # Initial clauses in saturation        : 245
% 0.18/0.54  # Processed clauses                    : 338
% 0.18/0.54  # ...of these trivial                  : 2
% 0.18/0.54  # ...subsumed                          : 20
% 0.18/0.54  # ...remaining for further processing  : 316
% 0.18/0.54  # Other redundant clauses eliminated   : 8
% 0.18/0.54  # Clauses deleted for lack of memory   : 0
% 0.18/0.54  # Backward-subsumed                    : 0
% 0.18/0.54  # Backward-rewritten                   : 1
% 0.18/0.54  # Generated clauses                    : 48
% 0.18/0.54  # ...of the previous two non-redundant : 35
% 0.18/0.54  # ...aggressively subsumed             : 0
% 0.18/0.54  # Contextual simplify-reflections      : 4
% 0.18/0.54  # Paramodulations                      : 40
% 0.18/0.54  # Factorizations                       : 0
% 0.18/0.54  # NegExts                              : 0
% 0.18/0.54  # Equation resolutions                 : 8
% 0.18/0.54  # Disequality decompositions           : 0
% 0.18/0.54  # Total rewrite steps                  : 81
% 0.18/0.54  # ...of those cached                   : 62
% 0.18/0.54  # Propositional unsat checks           : 0
% 0.18/0.54  #    Propositional check models        : 0
% 0.18/0.54  #    Propositional check unsatisfiable : 0
% 0.18/0.54  #    Propositional clauses             : 0
% 0.18/0.54  #    Propositional clauses after purity: 0
% 0.18/0.54  #    Propositional unsat core size     : 0
% 0.18/0.54  #    Propositional preprocessing time  : 0.000
% 0.18/0.54  #    Propositional encoding time       : 0.000
% 0.18/0.54  #    Propositional solver time         : 0.000
% 0.18/0.54  #    Success case prop preproc time    : 0.000
% 0.18/0.54  #    Success case prop encoding time   : 0.000
% 0.18/0.54  #    Success case prop solver time     : 0.000
% 0.18/0.54  # Current number of processed clauses  : 70
% 0.18/0.54  #    Positive orientable unit clauses  : 38
% 0.18/0.54  #    Positive unorientable unit clauses: 0
% 0.18/0.54  #    Negative unit clauses             : 17
% 0.18/0.54  #    Non-unit-clauses                  : 15
% 0.18/0.54  # Current number of unprocessed clauses: 179
% 0.18/0.54  # ...number of literals in the above   : 1525
% 0.18/0.54  # Current number of archived formulas  : 0
% 0.18/0.54  # Current number of archived clauses   : 238
% 0.18/0.54  # Clause-clause subsumption calls (NU) : 31136
% 0.18/0.54  # Rec. Clause-clause subsumption calls : 144
% 0.18/0.54  # Non-unit clause-clause subsumptions  : 9
% 0.18/0.54  # Unit Clause-clause subsumption calls : 104
% 0.18/0.54  # Rewrite failures with RHS unbound    : 0
% 0.18/0.54  # BW rewrite match attempts            : 1
% 0.18/0.54  # BW rewrite match successes           : 1
% 0.18/0.54  # Condensation attempts                : 0
% 0.18/0.54  # Condensation successes               : 0
% 0.18/0.54  # Termbank termtop insertions          : 22171
% 0.18/0.54  # Search garbage collected termcells   : 2377
% 0.18/0.54  
% 0.18/0.54  # -------------------------------------------------
% 0.18/0.54  # User time                : 0.061 s
% 0.18/0.54  # System time              : 0.004 s
% 0.18/0.54  # Total time               : 0.065 s
% 0.18/0.54  # Maximum resident set size: 2340 pages
% 0.18/0.54  
% 0.18/0.54  # -------------------------------------------------
% 0.18/0.54  # User time                : 0.073 s
% 0.18/0.54  # System time              : 0.013 s
% 0.18/0.54  # Total time               : 0.086 s
% 0.18/0.54  # Maximum resident set size: 1760 pages
% 0.18/0.54  % E---3.1 exiting
% 0.18/0.54  % E exiting
%------------------------------------------------------------------------------