TSTP Solution File: NUM016^5 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : NUM016^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n019.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 : Sat May  4 08:47:29 EDT 2024

% Result   : Theorem 0.21s 0.51s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   23 (   5 unt;   6 typ;   0 def)
%            Number of atoms       :   91 (   0 equ;   0 cnn)
%            Maximal formula atoms :   22 (   5 avg)
%            Number of connectives :  307 (  46   ~;  41   |;  33   &; 187   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   33 (   9 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    7 (   7   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   6 usr;   2 con; 0-2 aty)
%            Number of variables   :   60 (   0   ^  60   !;   0   ?;  60   :)

% Comments : 
%------------------------------------------------------------------------------
thf(decl_22,type,
    a: $i ).

thf(decl_23,type,
    factorial_plus_one: $i > $i ).

thf(decl_24,type,
    less: $i > $i > $o ).

thf(decl_25,type,
    prime: $i > $o ).

thf(decl_26,type,
    prime_divisor: $i > $i ).

thf(decl_27,type,
    divides: $i > $i > $o ).

thf(cNUM016_1,conjecture,
    ~ ( ! [X1: $i] :
          ~ ( less @ X1 @ X1 )
      & ! [X1: $i,X2: $i] :
          ( ~ ( less @ X1 @ X2 )
          | ~ ( less @ X2 @ X1 ) )
      & ! [X1: $i] : ( divides @ X1 @ X1 )
      & ! [X1: $i,X2: $i,X3: $i] :
          ( ~ ( divides @ X1 @ X2 )
          | ~ ( divides @ X2 @ X3 )
          | ( divides @ X1 @ X3 ) )
      & ! [X1: $i,X2: $i] :
          ( ~ ( divides @ X1 @ X2 )
          | ~ ( less @ X2 @ X1 ) )
      & ! [X1: $i] : ( less @ X1 @ ( factorial_plus_one @ X1 ) )
      & ! [X1: $i,X2: $i] :
          ( ~ ( divides @ X1 @ ( factorial_plus_one @ X2 ) )
          | ( less @ X2 @ X1 ) )
      & ! [X1: $i] :
          ( ( prime @ X1 )
          | ( divides @ ( prime_divisor @ X1 ) @ X1 ) )
      & ! [X1: $i] :
          ( ( prime @ X1 )
          | ( prime @ ( prime_divisor @ X1 ) ) )
      & ! [X1: $i] :
          ( ( prime @ X1 )
          | ( less @ ( prime_divisor @ X1 ) @ X1 ) )
      & ( prime @ a )
      & ! [X1: $i] :
          ( ~ ( prime @ X1 )
          | ~ ( less @ a @ X1 )
          | ( less @ ( factorial_plus_one @ a ) @ X1 ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.ayQQfYkDVv/E---3.1_21029.p',cNUM016_1) ).

thf(c_0_1,negated_conjecture,
    ~ ~ ( ! [X1: $i] :
            ~ ( less @ X1 @ X1 )
        & ! [X1: $i,X2: $i] :
            ( ~ ( less @ X1 @ X2 )
            | ~ ( less @ X2 @ X1 ) )
        & ! [X1: $i] : ( divides @ X1 @ X1 )
        & ! [X1: $i,X2: $i,X3: $i] :
            ( ~ ( divides @ X1 @ X2 )
            | ~ ( divides @ X2 @ X3 )
            | ( divides @ X1 @ X3 ) )
        & ! [X1: $i,X2: $i] :
            ( ~ ( divides @ X1 @ X2 )
            | ~ ( less @ X2 @ X1 ) )
        & ! [X1: $i] : ( less @ X1 @ ( factorial_plus_one @ X1 ) )
        & ! [X1: $i,X2: $i] :
            ( ~ ( divides @ X1 @ ( factorial_plus_one @ X2 ) )
            | ( less @ X2 @ X1 ) )
        & ! [X1: $i] :
            ( ( prime @ X1 )
            | ( divides @ ( prime_divisor @ X1 ) @ X1 ) )
        & ! [X1: $i] :
            ( ( prime @ X1 )
            | ( prime @ ( prime_divisor @ X1 ) ) )
        & ! [X1: $i] :
            ( ( prime @ X1 )
            | ( less @ ( prime_divisor @ X1 ) @ X1 ) )
        & ( prime @ a )
        & ! [X1: $i] :
            ( ~ ( prime @ X1 )
            | ~ ( less @ a @ X1 )
            | ( less @ ( factorial_plus_one @ a ) @ X1 ) ) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[cNUM016_1])]) ).

thf(c_0_2,negated_conjecture,
    ! [X20: $i,X21: $i,X22: $i,X23: $i,X24: $i,X25: $i,X26: $i,X27: $i,X28: $i,X29: $i,X30: $i,X31: $i,X32: $i,X33: $i,X34: $i,X35: $i] :
      ( ~ ( less @ X20 @ X20 )
      & ( ~ ( less @ X21 @ X22 )
        | ~ ( less @ X22 @ X21 ) )
      & ( divides @ X23 @ X23 )
      & ( ~ ( divides @ X24 @ X25 )
        | ~ ( divides @ X25 @ X26 )
        | ( divides @ X24 @ X26 ) )
      & ( ~ ( divides @ X27 @ X28 )
        | ~ ( less @ X28 @ X27 ) )
      & ( less @ X29 @ ( factorial_plus_one @ X29 ) )
      & ( ~ ( divides @ X30 @ ( factorial_plus_one @ X31 ) )
        | ( less @ X31 @ X30 ) )
      & ( ( prime @ X32 )
        | ( divides @ ( prime_divisor @ X32 ) @ X32 ) )
      & ( ( prime @ X33 )
        | ( prime @ ( prime_divisor @ X33 ) ) )
      & ( ( prime @ X34 )
        | ( less @ ( prime_divisor @ X34 ) @ X34 ) )
      & ( prime @ a )
      & ( ~ ( prime @ X35 )
        | ~ ( less @ a @ X35 )
        | ( less @ ( factorial_plus_one @ a ) @ X35 ) ) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1])])])]) ).

thf(c_0_3,negated_conjecture,
    ! [X2: $i,X1: $i] :
      ( ~ ( less @ X1 @ X2 )
      | ~ ( less @ X2 @ X1 ) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

thf(c_0_4,negated_conjecture,
    ! [X1: $i] :
      ( ( less @ ( factorial_plus_one @ a ) @ X1 )
      | ~ ( prime @ X1 )
      | ~ ( less @ a @ X1 ) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

thf(c_0_5,negated_conjecture,
    ! [X1: $i] :
      ~ ( less @ X1 @ X1 ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

thf(c_0_6,negated_conjecture,
    ! [X1: $i] : ( less @ X1 @ ( factorial_plus_one @ X1 ) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

thf(c_0_7,negated_conjecture,
    ! [X1: $i] :
      ( ~ ( less @ X1 @ ( factorial_plus_one @ a ) )
      | ~ ( less @ a @ X1 )
      | ~ ( prime @ X1 ) ),
    inference(spm,[status(thm)],[c_0_3,c_0_4]) ).

thf(c_0_8,negated_conjecture,
    ! [X1: $i] :
      ( ( prime @ X1 )
      | ( less @ ( prime_divisor @ X1 ) @ X1 ) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

thf(c_0_9,negated_conjecture,
    ~ ( prime @ ( factorial_plus_one @ a ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_4]),c_0_6])]) ).

thf(c_0_10,negated_conjecture,
    ! [X1: $i,X2: $i] :
      ( ( less @ X2 @ X1 )
      | ~ ( divides @ X1 @ ( factorial_plus_one @ X2 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

thf(c_0_11,negated_conjecture,
    ! [X1: $i] :
      ( ( prime @ X1 )
      | ( divides @ ( prime_divisor @ X1 ) @ X1 ) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

thf(c_0_12,negated_conjecture,
    ( ~ ( less @ a @ ( prime_divisor @ ( factorial_plus_one @ a ) ) )
    | ~ ( prime @ ( prime_divisor @ ( factorial_plus_one @ a ) ) ) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_9]) ).

thf(c_0_13,negated_conjecture,
    ! [X1: $i] :
      ( ( less @ X1 @ ( prime_divisor @ ( factorial_plus_one @ X1 ) ) )
      | ( prime @ ( factorial_plus_one @ X1 ) ) ),
    inference(spm,[status(thm)],[c_0_10,c_0_11]) ).

thf(c_0_14,negated_conjecture,
    ~ ( prime @ ( prime_divisor @ ( factorial_plus_one @ a ) ) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_9]) ).

thf(c_0_15,negated_conjecture,
    ! [X1: $i] :
      ( ( prime @ X1 )
      | ( prime @ ( prime_divisor @ X1 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

thf(c_0_16,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_9]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem    : NUM016^5 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.14  % Command    : run_E %s %d THM
% 0.14/0.35  % Computer : n019.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Fri May  3 09:15:14 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.21/0.49  Running higher-order theorem proving
% 0.21/0.49  Running: /export/starexec/sandbox/solver/bin/eprover-ho --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.ayQQfYkDVv/E---3.1_21029.p
% 0.21/0.51  # Version: 3.1.0-ho
% 0.21/0.51  # Preprocessing class: HSMSSMSSSSSNFFN.
% 0.21/0.51  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.51  # Starting new_ho_10 with 1500s (5) cores
% 0.21/0.51  # Starting new_bool_1 with 300s (1) cores
% 0.21/0.51  # Starting full_lambda_5 with 300s (1) cores
% 0.21/0.51  # Starting new_ho_10_unif with 300s (1) cores
% 0.21/0.51  # full_lambda_5 with pid 21176 completed with status 0
% 0.21/0.51  # Result found by full_lambda_5
% 0.21/0.51  # Preprocessing class: HSMSSMSSSSSNFFN.
% 0.21/0.51  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.51  # Starting new_ho_10 with 1500s (5) cores
% 0.21/0.51  # Starting new_bool_1 with 300s (1) cores
% 0.21/0.51  # Starting full_lambda_5 with 300s (1) cores
% 0.21/0.51  # No SInE strategy applied
% 0.21/0.51  # Search class: HGHNS-FFSF11-SFFFFFNN
% 0.21/0.51  # partial match(1): HGHNF-FFSF11-SFFFFFNN
% 0.21/0.51  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.51  # Starting new_ho_10 with 163s (1) cores
% 0.21/0.51  # new_ho_10 with pid 21178 completed with status 0
% 0.21/0.51  # Result found by new_ho_10
% 0.21/0.51  # Preprocessing class: HSMSSMSSSSSNFFN.
% 0.21/0.51  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.51  # Starting new_ho_10 with 1500s (5) cores
% 0.21/0.51  # Starting new_bool_1 with 300s (1) cores
% 0.21/0.51  # Starting full_lambda_5 with 300s (1) cores
% 0.21/0.51  # No SInE strategy applied
% 0.21/0.51  # Search class: HGHNS-FFSF11-SFFFFFNN
% 0.21/0.51  # partial match(1): HGHNF-FFSF11-SFFFFFNN
% 0.21/0.51  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.51  # Starting new_ho_10 with 163s (1) cores
% 0.21/0.51  # Preprocessing time       : 0.001 s
% 0.21/0.51  # Presaturation interreduction done
% 0.21/0.51  
% 0.21/0.51  # Proof found!
% 0.21/0.51  # SZS status Theorem
% 0.21/0.51  # SZS output start CNFRefutation
% See solution above
% 0.21/0.51  # Parsed axioms                        : 7
% 0.21/0.51  # Removed by relevancy pruning/SinE    : 0
% 0.21/0.51  # Initial clauses                      : 18
% 0.21/0.51  # Removed in clause preprocessing      : 6
% 0.21/0.51  # Initial clauses in saturation        : 12
% 0.21/0.51  # Processed clauses                    : 38
% 0.21/0.51  # ...of these trivial                  : 0
% 0.21/0.51  # ...subsumed                          : 6
% 0.21/0.51  # ...remaining for further processing  : 32
% 0.21/0.51  # Other redundant clauses eliminated   : 0
% 0.21/0.51  # Clauses deleted for lack of memory   : 0
% 0.21/0.51  # Backward-subsumed                    : 1
% 0.21/0.51  # Backward-rewritten                   : 0
% 0.21/0.51  # Generated clauses                    : 20
% 0.21/0.51  # ...of the previous two non-redundant : 17
% 0.21/0.51  # ...aggressively subsumed             : 0
% 0.21/0.51  # Contextual simplify-reflections      : 0
% 0.21/0.51  # Paramodulations                      : 20
% 0.21/0.51  # Factorizations                       : 0
% 0.21/0.51  # NegExts                              : 0
% 0.21/0.51  # Equation resolutions                 : 0
% 0.21/0.51  # Disequality decompositions           : 0
% 0.21/0.51  # Total rewrite steps                  : 5
% 0.21/0.51  # ...of those cached                   : 2
% 0.21/0.51  # Propositional unsat checks           : 0
% 0.21/0.51  #    Propositional check models        : 0
% 0.21/0.51  #    Propositional check unsatisfiable : 0
% 0.21/0.51  #    Propositional clauses             : 0
% 0.21/0.51  #    Propositional clauses after purity: 0
% 0.21/0.51  #    Propositional unsat core size     : 0
% 0.21/0.51  #    Propositional preprocessing time  : 0.000
% 0.21/0.51  #    Propositional encoding time       : 0.000
% 0.21/0.51  #    Propositional solver time         : 0.000
% 0.21/0.51  #    Success case prop preproc time    : 0.000
% 0.21/0.51  #    Success case prop encoding time   : 0.000
% 0.21/0.51  #    Success case prop solver time     : 0.000
% 0.21/0.51  # Current number of processed clauses  : 19
% 0.21/0.51  #    Positive orientable unit clauses  : 3
% 0.21/0.51  #    Positive unorientable unit clauses: 0
% 0.21/0.51  #    Negative unit clauses             : 4
% 0.21/0.51  #    Non-unit-clauses                  : 12
% 0.21/0.51  # Current number of unprocessed clauses: 3
% 0.21/0.51  # ...number of literals in the above   : 7
% 0.21/0.51  # Current number of archived formulas  : 0
% 0.21/0.51  # Current number of archived clauses   : 13
% 0.21/0.51  # Clause-clause subsumption calls (NU) : 14
% 0.21/0.51  # Rec. Clause-clause subsumption calls : 13
% 0.21/0.51  # Non-unit clause-clause subsumptions  : 2
% 0.21/0.51  # Unit Clause-clause subsumption calls : 5
% 0.21/0.51  # Rewrite failures with RHS unbound    : 0
% 0.21/0.51  # BW rewrite match attempts            : 0
% 0.21/0.51  # BW rewrite match successes           : 0
% 0.21/0.51  # Condensation attempts                : 38
% 0.21/0.51  # Condensation successes               : 0
% 0.21/0.51  # Termbank termtop insertions          : 1251
% 0.21/0.51  # Search garbage collected termcells   : 183
% 0.21/0.51  
% 0.21/0.51  # -------------------------------------------------
% 0.21/0.51  # User time                : 0.005 s
% 0.21/0.51  # System time              : 0.001 s
% 0.21/0.51  # Total time               : 0.006 s
% 0.21/0.51  # Maximum resident set size: 1704 pages
% 0.21/0.51  
% 0.21/0.51  # -------------------------------------------------
% 0.21/0.51  # User time                : 0.007 s
% 0.21/0.51  # System time              : 0.003 s
% 0.21/0.51  # Total time               : 0.010 s
% 0.21/0.51  # Maximum resident set size: 1704 pages
% 0.21/0.51  % E---3.1 exiting
% 0.21/0.51  % E exiting
%------------------------------------------------------------------------------