TSTP Solution File: NUM636^1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : NUM636^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n011.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 08:55:51 EDT 2024

% Result   : Theorem 0.17s 0.45s
% Output   : CNFRefutation 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   38 (  16 unt;   8 typ;   0 def)
%            Number of atoms       :   57 (  27 equ;   0 cnn)
%            Maximal formula atoms :    6 (   1 avg)
%            Number of connectives :  174 (  33   ~;  18   |;   1   &; 115   @)
%                                         (   0 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :   12 (  12   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   46 (   7   ^  39   !;   0   ?;  46   :)

% Comments : 
%------------------------------------------------------------------------------
thf(decl_sort1,type,
    nat: $tType ).

thf(decl_sort2,type,
    set: $tType ).

thf(decl_22,type,
    x: nat ).

thf(decl_23,type,
    suc: nat > nat ).

thf(decl_24,type,
    esti: nat > set > $o ).

thf(decl_25,type,
    setof: ( nat > $o ) > set ).

thf(decl_26,type,
    n_1: nat ).

thf(decl_27,type,
    esk1_1: set > nat ).

thf(ax3,axiom,
    ! [X4: nat] :
      ( ( suc @ X4 )
     != n_1 ),
    file('/export/starexec/sandbox2/tmp/tmp.n4KXk9dlN3/E---3.1_14593.p',ax3) ).

thf(estii,axiom,
    ! [X1: nat > $o,X2: nat] :
      ( ( X1 @ X2 )
     => ( esti @ X2 @ ( setof @ X1 ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.n4KXk9dlN3/E---3.1_14593.p',estii) ).

thf(satz2,conjecture,
    ( ( suc @ x )
   != x ),
    file('/export/starexec/sandbox2/tmp/tmp.n4KXk9dlN3/E---3.1_14593.p',satz2) ).

thf(satz1,axiom,
    ! [X4: nat,X5: nat] :
      ( ( X4 != X5 )
     => ( ( suc @ X4 )
       != ( suc @ X5 ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.n4KXk9dlN3/E---3.1_14593.p',satz1) ).

thf(estie,axiom,
    ! [X1: nat > $o,X2: nat] :
      ( ( esti @ X2 @ ( setof @ X1 ) )
     => ( X1 @ X2 ) ),
    file('/export/starexec/sandbox2/tmp/tmp.n4KXk9dlN3/E---3.1_14593.p',estie) ).

thf(ax5,axiom,
    ! [X3: set] :
      ( ( esti @ n_1 @ X3 )
     => ( ! [X4: nat] :
            ( ( esti @ X4 @ X3 )
           => ( esti @ ( suc @ X4 ) @ X3 ) )
       => ! [X4: nat] : ( esti @ X4 @ X3 ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.n4KXk9dlN3/E---3.1_14593.p',ax5) ).

thf(c_0_6,plain,
    ! [X4: nat] :
      ( ( suc @ X4 )
     != n_1 ),
    inference(fof_simplification,[status(thm)],[ax3]) ).

thf(c_0_7,plain,
    ! [X24: nat > $o,X25: nat] :
      ( ~ ( X24 @ X25 )
      | ( esti @ X25 @ ( setof @ X24 ) ) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[estii])])]) ).

thf(c_0_8,negated_conjecture,
    ( ( suc @ x )
    = x ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[satz2])]) ).

thf(c_0_9,plain,
    ! [X4: nat,X5: nat] :
      ( ( X4 != X5 )
     => ( ( suc @ X4 )
       != ( suc @ X5 ) ) ),
    inference(fof_simplification,[status(thm)],[satz1]) ).

thf(c_0_10,plain,
    ! [X22: nat > $o,X23: nat] :
      ( ~ ( esti @ X23 @ ( setof @ X22 ) )
      | ( X22 @ X23 ) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[estie])])]) ).

thf(c_0_11,plain,
    ! [X16: set,X18: nat] :
      ( ( ( esti @ ( esk1_1 @ X16 ) @ X16 )
        | ( esti @ X18 @ X16 )
        | ~ ( esti @ n_1 @ X16 ) )
      & ( ~ ( esti @ ( suc @ ( esk1_1 @ X16 ) ) @ X16 )
        | ( esti @ X18 @ X16 )
        | ~ ( esti @ n_1 @ X16 ) ) ),
    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)],[ax5])])])])])]) ).

thf(c_0_12,plain,
    ! [X19: nat] :
      ( ( suc @ X19 )
     != n_1 ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_6])]) ).

thf(c_0_13,plain,
    ! [X1: nat > $o,X2: nat] :
      ( ( esti @ X2 @ ( setof @ X1 ) )
      | ~ ( X1 @ X2 ) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

thf(c_0_14,negated_conjecture,
    ( ( suc @ x )
    = x ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

thf(c_0_15,plain,
    ! [X20: nat,X21: nat] :
      ( ( X20 = X21 )
      | ( ( suc @ X20 )
       != ( suc @ X21 ) ) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).

thf(c_0_16,plain,
    ! [X2: nat,X1: nat > $o] :
      ( ( X1 @ X2 )
      | ~ ( esti @ X2 @ ( setof @ X1 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

thf(c_0_17,plain,
    ! [X2: nat,X3: set] :
      ( ( esti @ ( esk1_1 @ X3 ) @ X3 )
      | ( esti @ X2 @ X3 )
      | ~ ( esti @ n_1 @ X3 ) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

thf(c_0_18,plain,
    ! [X2: nat] :
      ( ( suc @ X2 )
     != n_1 ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

thf(c_0_19,plain,
    ! [X2: nat] :
      ( ( esti @ X2
        @ ( setof
          @ ^ [Z0: nat] :
              ( Z0
             != ( suc @ Z0 ) ) ) )
      | ( X2
        = ( suc @ X2 ) ) ),
    inference(trigger,[status(thm)],[inference(cn,[status(thm)],[]),c_0_13,c_0_14]) ).

thf(c_0_20,plain,
    ! [X2: nat,X4: nat] :
      ( ( X2 = X4 )
      | ( ( suc @ X2 )
       != ( suc @ X4 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

thf(c_0_21,plain,
    ! [X2: nat] :
      ( ( X2
       != ( suc @ X2 ) )
      | ~ ( esti @ X2
          @ ( setof
            @ ^ [Z0: nat] :
                ( Z0
               != ( suc @ Z0 ) ) ) ) ),
    inference(trigger,[status(thm)],[inference(cn,[status(thm)],[]),c_0_16,c_0_14]) ).

thf(c_0_22,plain,
    ! [X3: set] :
      ( ( esti @ ( esk1_1 @ X3 ) @ X3 )
      | ~ ( esti @ n_1 @ X3 ) ),
    inference(condense,[status(thm)],[c_0_17]) ).

thf(c_0_23,plain,
    ( esti @ n_1
    @ ( setof
      @ ^ [Z0: nat] :
          ( Z0
         != ( suc @ Z0 ) ) ) ),
    inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19])]) ).

thf(c_0_24,plain,
    ! [X2: nat,X3: set] :
      ( ( esti @ X2 @ X3 )
      | ~ ( esti @ ( suc @ ( esk1_1 @ X3 ) ) @ X3 )
      | ~ ( esti @ n_1 @ X3 ) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

thf(c_0_25,plain,
    ! [X2: nat] :
      ( ( ( suc @ X2 )
        = X2 )
      | ( esti @ ( suc @ X2 )
        @ ( setof
          @ ^ [Z0: nat] :
              ( Z0
             != ( suc @ Z0 ) ) ) ) ),
    inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_19])]) ).

thf(c_0_26,plain,
    ( ( suc
      @ ( esk1_1
        @ ( setof
          @ ^ [Z0: nat] :
              ( Z0
             != ( suc @ Z0 ) ) ) ) )
   != ( esk1_1
      @ ( setof
        @ ^ [Z0: nat] :
            ( Z0
           != ( suc @ Z0 ) ) ) ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23])]) ).

thf(c_0_27,plain,
    ! [X2: nat] :
      ( esti @ X2
      @ ( setof
        @ ^ [Z0: nat] :
            ( Z0
           != ( suc @ Z0 ) ) ) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_23])]),c_0_26]) ).

thf(c_0_28,plain,
    ! [X2: nat] :
      ( ( suc @ X2 )
     != X2 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_27])]) ).

thf(c_0_29,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[c_0_14,c_0_28]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem    : NUM636^1 : TPTP v8.1.2. Released v3.7.0.
% 0.03/0.12  % Command    : run_E %s %d THM
% 0.11/0.32  % Computer : n011.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit   : 300
% 0.11/0.32  % WCLimit    : 300
% 0.11/0.32  % DateTime   : Fri May  3 09:33:48 EDT 2024
% 0.11/0.32  % CPUTime    : 
% 0.17/0.43  Running higher-order theorem proving
% 0.17/0.43  Running: /export/starexec/sandbox2/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/sandbox2/tmp/tmp.n4KXk9dlN3/E---3.1_14593.p
% 0.17/0.45  # Version: 3.1.0-ho
% 0.17/0.45  # Preprocessing class: HSSSSMSSSSSNSFA.
% 0.17/0.45  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.45  # Starting new_ho_14 with 1500s (5) cores
% 0.17/0.45  # Starting full_lambda_8 with 300s (1) cores
% 0.17/0.45  # Starting new_ho_13 with 300s (1) cores
% 0.17/0.45  # Starting ho_unfolding_3 with 300s (1) cores
% 0.17/0.45  # new_ho_14 with pid 14673 completed with status 0
% 0.17/0.45  # Result found by new_ho_14
% 0.17/0.45  # Preprocessing class: HSSSSMSSSSSNSFA.
% 0.17/0.45  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.45  # Starting new_ho_14 with 1500s (5) cores
% 0.17/0.45  # SinE strategy is gf500_gu_R04_F100_L20000
% 0.17/0.45  # Search class: HGHSF-FFSF11-MSFFFSBN
% 0.17/0.45  # partial match(2): HGUSF-FFSF11-SSFFFSBN
% 0.17/0.45  # Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.17/0.45  # Starting new_ho_14 with 901s (1) cores
% 0.17/0.45  # Starting new_ho_13 with 151s (1) cores
% 0.17/0.45  # Starting ho_unfolding_6 with 151s (1) cores
% 0.17/0.45  # Starting sh4l with 151s (1) cores
% 0.17/0.45  # Starting full_lambda_8 with 146s (1) cores
% 0.17/0.45  # full_lambda_8 with pid 14684 completed with status 0
% 0.17/0.45  # Result found by full_lambda_8
% 0.17/0.45  # Preprocessing class: HSSSSMSSSSSNSFA.
% 0.17/0.45  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.45  # Starting new_ho_14 with 1500s (5) cores
% 0.17/0.45  # SinE strategy is gf500_gu_R04_F100_L20000
% 0.17/0.45  # Search class: HGHSF-FFSF11-MSFFFSBN
% 0.17/0.45  # partial match(2): HGUSF-FFSF11-SSFFFSBN
% 0.17/0.45  # Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.17/0.45  # Starting new_ho_14 with 901s (1) cores
% 0.17/0.45  # Starting new_ho_13 with 151s (1) cores
% 0.17/0.45  # Starting ho_unfolding_6 with 151s (1) cores
% 0.17/0.45  # Starting sh4l with 151s (1) cores
% 0.17/0.45  # Starting full_lambda_8 with 146s (1) cores
% 0.17/0.45  # Preprocessing time       : 0.001 s
% 0.17/0.45  # Presaturation interreduction done
% 0.17/0.45  
% 0.17/0.45  # Proof found!
% 0.17/0.45  # SZS status Theorem
% 0.17/0.45  # SZS output start CNFRefutation
% See solution above
% 0.17/0.45  # Parsed axioms                        : 13
% 0.17/0.45  # Removed by relevancy pruning/SinE    : 7
% 0.17/0.45  # Initial clauses                      : 7
% 0.17/0.45  # Removed in clause preprocessing      : 0
% 0.17/0.45  # Initial clauses in saturation        : 9
% 0.17/0.45  # Processed clauses                    : 35
% 0.17/0.45  # ...of these trivial                  : 0
% 0.17/0.45  # ...subsumed                          : 7
% 0.17/0.45  # ...remaining for further processing  : 28
% 0.17/0.45  # Other redundant clauses eliminated   : 3
% 0.17/0.45  # Clauses deleted for lack of memory   : 0
% 0.17/0.45  # Backward-subsumed                    : 2
% 0.17/0.45  # Backward-rewritten                   : 4
% 0.17/0.45  # Generated clauses                    : 30
% 0.17/0.45  # ...of the previous two non-redundant : 22
% 0.17/0.45  # ...aggressively subsumed             : 0
% 0.17/0.45  # Contextual simplify-reflections      : 0
% 0.17/0.45  # Paramodulations                      : 24
% 0.17/0.45  # Factorizations                       : 0
% 0.17/0.45  # NegExts                              : 0
% 0.17/0.45  # Equation resolutions                 : 4
% 0.17/0.45  # Disequality decompositions           : 0
% 0.17/0.45  # Total rewrite steps                  : 8
% 0.17/0.45  # ...of those cached                   : 3
% 0.17/0.45  # Propositional unsat checks           : 0
% 0.17/0.45  #    Propositional check models        : 0
% 0.17/0.45  #    Propositional check unsatisfiable : 0
% 0.17/0.45  #    Propositional clauses             : 0
% 0.17/0.45  #    Propositional clauses after purity: 0
% 0.17/0.45  #    Propositional unsat core size     : 0
% 0.17/0.45  #    Propositional preprocessing time  : 0.000
% 0.17/0.45  #    Propositional encoding time       : 0.000
% 0.17/0.45  #    Propositional solver time         : 0.000
% 0.17/0.45  #    Success case prop preproc time    : 0.000
% 0.17/0.45  #    Success case prop encoding time   : 0.000
% 0.17/0.45  #    Success case prop solver time     : 0.000
% 0.17/0.45  # Current number of processed clauses  : 12
% 0.17/0.45  #    Positive orientable unit clauses  : 3
% 0.17/0.45  #    Positive unorientable unit clauses: 0
% 0.17/0.45  #    Negative unit clauses             : 3
% 0.17/0.45  #    Non-unit-clauses                  : 6
% 0.17/0.45  # Current number of unprocessed clauses: 5
% 0.17/0.45  # ...number of literals in the above   : 11
% 0.17/0.45  # Current number of archived formulas  : 0
% 0.17/0.45  # Current number of archived clauses   : 16
% 0.17/0.45  # Clause-clause subsumption calls (NU) : 7
% 0.17/0.45  # Rec. Clause-clause subsumption calls : 7
% 0.17/0.45  # Non-unit clause-clause subsumptions  : 4
% 0.17/0.45  # Unit Clause-clause subsumption calls : 8
% 0.17/0.45  # Rewrite failures with RHS unbound    : 0
% 0.17/0.45  # BW rewrite match attempts            : 4
% 0.17/0.45  # BW rewrite match successes           : 4
% 0.17/0.45  # Condensation attempts                : 35
% 0.17/0.45  # Condensation successes               : 1
% 0.17/0.45  # Termbank termtop insertions          : 936
% 0.17/0.45  # Search garbage collected termcells   : 150
% 0.17/0.45  
% 0.17/0.45  # -------------------------------------------------
% 0.17/0.45  # User time                : 0.005 s
% 0.17/0.45  # System time              : 0.001 s
% 0.17/0.45  # Total time               : 0.006 s
% 0.17/0.45  # Maximum resident set size: 1864 pages
% 0.17/0.45  
% 0.17/0.45  # -------------------------------------------------
% 0.17/0.45  # User time                : 0.016 s
% 0.17/0.45  # System time              : 0.006 s
% 0.17/0.45  # Total time               : 0.023 s
% 0.17/0.45  # Maximum resident set size: 1728 pages
% 0.17/0.45  % E---3.1 exiting
% 0.17/0.45  % E exiting
%------------------------------------------------------------------------------