TSTP Solution File: NUN025^3 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : NUN025^3 : TPTP v8.2.0. Released v6.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n022.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 02:15:23 EDT 2024

% Result   : Theorem 0.20s 0.51s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   28 (   8 unt;   5 typ;   0 def)
%            Number of atoms       :  140 (  85 equ;   0 cnn)
%            Maximal formula atoms :   24 (   6 avg)
%            Number of connectives :  392 (  56   ~;  49   |;  30   &; 247   @)
%                                         (   1 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   21 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    9 (   9   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   5 usr;   4 con; 0-3 aty)
%            Number of variables   :   56 (   0   ^  54   !;   2   ?;  56   :)

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

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

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

thf(decl_25,type,
    h: $i > $i ).

thf(decl_26,type,
    epred1_0: $o ).

thf(n10,conjecture,
    ( ( ! [X1: $o,X2: $i,X3: $i] :
          ( X1
         => ( ( ite @ X1 @ X2 @ X3 )
            = X2 ) )
      & ! [X1: $o,X2: $i,X3: $i] :
          ( ~ X1
         => ( ( ite @ X1 @ X2 @ X3 )
            = X3 ) )
      & ! [X4: $i] :
          ( ( s @ X4 )
         != zero )
      & ! [X4: $i] :
          ( ( s @ X4 )
         != X4 )
      & ! [X4: $i] :
          ( ( h @ X4 )
          = ( ite @ ( X4 = zero ) @ ( s @ zero )
            @ ( ite
              @ ( X4
                = ( s @ zero ) )
              @ zero
              @ ( s @ zero ) ) ) ) )
   => ? [X5: $i > $i] :
        ( ( ( X5 @ zero )
          = ( s @ zero ) )
        & ( ( X5 @ ( s @ zero ) )
          = zero )
        & ( ( X5 @ ( s @ ( s @ zero ) ) )
          = ( s @ zero ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',n10) ).

thf(c_0_1,plain,
    ( epred1_0
  <=> ( ! [X1: $o,X2: $i,X3: $i] :
          ( X1
         => ( ( ite @ X1 @ X2 @ X3 )
            = X2 ) )
      & ! [X1: $o,X2: $i,X3: $i] :
          ( ~ X1
         => ( ( ite @ X1 @ X2 @ X3 )
            = X3 ) )
      & ! [X4: $i] :
          ( ( s @ X4 )
         != zero )
      & ! [X4: $i] :
          ( ( s @ X4 )
         != X4 )
      & ! [X4: $i] :
          ( ( ( X4 != zero )
            | ( ( ( X4
                 != ( s @ zero ) )
                | ( ( h @ X4 )
                  = ( ite @ $true @ ( s @ zero ) @ ( ite @ $true @ zero @ ( s @ zero ) ) ) ) )
              & ( ( X4
                  = ( s @ zero ) )
                | ( ( h @ X4 )
                  = ( ite @ $true @ ( s @ zero ) @ ( ite @ $false @ zero @ ( s @ zero ) ) ) ) ) ) )
          & ( ( X4 = zero )
            | ( ( ( X4
                 != ( s @ zero ) )
                | ( ( h @ X4 )
                  = ( ite @ $false @ ( s @ zero ) @ ( ite @ $true @ zero @ ( s @ zero ) ) ) ) )
              & ( ( X4
                  = ( s @ zero ) )
                | ( ( h @ X4 )
                  = ( ite @ $false @ ( s @ zero ) @ ( ite @ $false @ zero @ ( s @ zero ) ) ) ) ) ) ) ) ) ),
    introduced(definition) ).

thf(c_0_2,plain,
    ( epred1_0
   => ( ! [X1: $o,X2: $i,X3: $i] :
          ( X1
         => ( ( ite @ X1 @ X2 @ X3 )
            = X2 ) )
      & ! [X1: $o,X2: $i,X3: $i] :
          ( ~ X1
         => ( ( ite @ X1 @ X2 @ X3 )
            = X3 ) )
      & ! [X4: $i] :
          ( ( s @ X4 )
         != zero )
      & ! [X4: $i] :
          ( ( s @ X4 )
         != X4 )
      & ! [X4: $i] :
          ( ( ( X4 != zero )
            | ( ( ( X4
                 != ( s @ zero ) )
                | ( ( h @ X4 )
                  = ( ite @ $true @ ( s @ zero ) @ ( ite @ $true @ zero @ ( s @ zero ) ) ) ) )
              & ( ( X4
                  = ( s @ zero ) )
                | ( ( h @ X4 )
                  = ( ite @ $true @ ( s @ zero ) @ ( ite @ $false @ zero @ ( s @ zero ) ) ) ) ) ) )
          & ( ( X4 = zero )
            | ( ( ( X4
                 != ( s @ zero ) )
                | ( ( h @ X4 )
                  = ( ite @ $false @ ( s @ zero ) @ ( ite @ $true @ zero @ ( s @ zero ) ) ) ) )
              & ( ( X4
                  = ( s @ zero ) )
                | ( ( h @ X4 )
                  = ( ite @ $false @ ( s @ zero ) @ ( ite @ $false @ zero @ ( s @ zero ) ) ) ) ) ) ) ) ) ),
    inference(split_equiv,[status(thm)],[c_0_1]) ).

thf(c_0_3,negated_conjecture,
    ~ ( epred1_0
     => ? [X5: $i > $i] :
          ( ( ( X5 @ zero )
            = ( s @ zero ) )
          & ( ( X5 @ ( s @ zero ) )
            = zero )
          & ( ( X5 @ ( s @ ( s @ zero ) ) )
            = ( s @ zero ) ) ) ),
    inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(assume_negation,[status(cth)],[n10])])]),c_0_1]) ).

thf(c_0_4,plain,
    ! [X17: $o,X18: $i,X19: $i,X20: $o,X21: $i,X22: $i,X23: $i,X24: $i,X25: $i] :
      ( ( ~ X17
        | ( ( ite @ X17 @ X18 @ X19 )
          = X18 )
        | ~ epred1_0 )
      & ( X20
        | ( ( ite @ X20 @ X21 @ X22 )
          = X22 )
        | ~ epred1_0 )
      & ( ( ( s @ X23 )
         != zero )
        | ~ epred1_0 )
      & ( ( ( s @ X24 )
         != X24 )
        | ~ epred1_0 )
      & ( ( X25
         != ( s @ zero ) )
        | ( ( h @ X25 )
          = ( ite @ $true @ ( s @ zero ) @ ( ite @ $true @ zero @ ( s @ zero ) ) ) )
        | ( X25 != zero )
        | ~ epred1_0 )
      & ( ( X25
          = ( s @ zero ) )
        | ( ( h @ X25 )
          = ( ite @ $true @ ( s @ zero ) @ ( ite @ $false @ zero @ ( s @ zero ) ) ) )
        | ( X25 != zero )
        | ~ epred1_0 )
      & ( ( X25
         != ( s @ zero ) )
        | ( ( h @ X25 )
          = ( ite @ $false @ ( s @ zero ) @ ( ite @ $true @ zero @ ( s @ zero ) ) ) )
        | ( X25 = zero )
        | ~ epred1_0 )
      & ( ( X25
          = ( s @ zero ) )
        | ( ( h @ X25 )
          = ( ite @ $false @ ( s @ zero ) @ ( ite @ $false @ zero @ ( s @ zero ) ) ) )
        | ( X25 = zero )
        | ~ epred1_0 ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2])])])])]) ).

thf(c_0_5,negated_conjecture,
    ! [X16: $i > $i] :
      ( epred1_0
      & ( ( ( X16 @ zero )
         != ( s @ zero ) )
        | ( ( X16 @ ( s @ zero ) )
         != zero )
        | ( ( X16 @ ( s @ ( s @ zero ) ) )
         != ( s @ zero ) ) ) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])])]) ).

thf(c_0_6,plain,
    ! [X2: $i,X3: $i] :
      ( ( ( ite @ ~ $true @ X2 @ X3 )
        = X3 )
      | ~ epred1_0 ),
    inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_4])])]) ).

thf(c_0_7,negated_conjecture,
    epred1_0,
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

thf(c_0_8,plain,
    ! [X3: $i,X2: $i] :
      ( ( ( ite @ $true @ X2 @ X3 )
        = X2 )
      | ~ epred1_0 ),
    inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_4])])]) ).

thf(c_0_9,plain,
    ! [X2: $i] :
      ( ( ( s @ X2 )
       != X2 )
      | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

thf(c_0_10,plain,
    ! [X2: $i] :
      ( ( X2
        = ( s @ zero ) )
      | ( ( h @ X2 )
        = ( ite @ ~ $true @ ( s @ zero ) @ ( ite @ ~ $true @ zero @ ( s @ zero ) ) ) )
      | ( X2 = zero )
      | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

thf(c_0_11,plain,
    ! [X2: $i,X3: $i] :
      ( ( ite @ ~ $true @ X2 @ X3 )
      = X3 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_6,c_0_7])]) ).

thf(c_0_12,plain,
    ! [X2: $i] :
      ( ( ( s @ X2 )
       != zero )
      | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

thf(c_0_13,plain,
    ! [X2: $i] :
      ( ( X2
        = ( s @ zero ) )
      | ( ( h @ X2 )
        = ( ite @ $true @ ( s @ zero ) @ ( ite @ ~ $true @ zero @ ( s @ zero ) ) ) )
      | ( X2 != zero )
      | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

thf(c_0_14,plain,
    ! [X3: $i,X2: $i] :
      ( ( ite @ $true @ X2 @ X3 )
      = X2 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_8,c_0_7])]) ).

thf(c_0_15,plain,
    ! [X2: $i] :
      ( ( s @ X2 )
     != X2 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_7])]) ).

thf(c_0_16,plain,
    ! [X2: $i] :
      ( ( ( h @ X2 )
        = ( ite @ ~ $true @ ( s @ zero ) @ ( ite @ $true @ zero @ ( s @ zero ) ) ) )
      | ( X2 = zero )
      | ( X2
       != ( s @ zero ) )
      | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

thf(c_0_17,negated_conjecture,
    ! [X5: $i > $i] :
      ( ( ( X5 @ zero )
       != ( s @ zero ) )
      | ( ( X5 @ ( s @ zero ) )
       != zero )
      | ( ( X5 @ ( s @ ( s @ zero ) ) )
       != ( s @ zero ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

thf(c_0_18,plain,
    ! [X2: $i] :
      ( ( ( h @ X2 )
        = ( s @ zero ) )
      | ( X2
        = ( s @ zero ) )
      | ( X2 = zero ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_11]),c_0_11]),c_0_7])]) ).

thf(c_0_19,plain,
    ! [X2: $i] :
      ( ( s @ X2 )
     != zero ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_7])]) ).

thf(c_0_20,plain,
    ( ( h @ zero )
    = ( s @ zero ) ),
    inference(sr,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_11]),c_0_14]),c_0_7])])]),c_0_15]) ).

thf(c_0_21,plain,
    ( ( h @ ( s @ zero ) )
    = zero ),
    inference(sr,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_14]),c_0_11]),c_0_7])])]),c_0_15]) ).

thf(c_0_22,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_15]),c_0_19]),c_0_20]),c_0_21])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : NUN025^3 : TPTP v8.2.0. Released v6.4.0.
% 0.07/0.13  % Command    : run_E %s %d THM
% 0.13/0.35  % Computer : n022.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Sat May 18 15:05:23 EDT 2024
% 0.13/0.35  % CPUTime    : 
% 0.20/0.50  Running higher-order theorem proving
% 0.20/0.50  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/benchmark/theBenchmark.p
% 0.20/0.51  # Version: 3.1.0-ho
% 0.20/0.51  # Preprocessing class: HSSSSMSSSSSNSSA.
% 0.20/0.51  # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.51  # Starting post_as_ho12 with 300s (1) cores
% 0.20/0.51  # Starting new_bool_9 with 300s (1) cores
% 0.20/0.51  # Starting post_as_ho1 with 300s (1) cores
% 0.20/0.51  # Starting post_as_ho4 with 300s (1) cores
% 0.20/0.51  # Starting post_as_ho2 with 300s (1) cores
% 0.20/0.51  # Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.20/0.51  # Starting full_lambda_10 with 300s (1) cores
% 0.20/0.51  # Starting new_ho_8 with 300s (1) cores
% 0.20/0.51  # post_as_ho12 with pid 22344 completed with status 0
% 0.20/0.51  # Result found by post_as_ho12
% 0.20/0.51  # Preprocessing class: HSSSSMSSSSSNSSA.
% 0.20/0.51  # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.51  # Starting post_as_ho12 with 300s (1) cores
% 0.20/0.51  # No SInE strategy applied
% 0.20/0.51  # Search class: HGHSF-FFSF31-MSSFFSNN
% 0.20/0.51  # partial match(2): HGHPS-FFSF31-MSSFFSNN
% 0.20/0.51  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.51  # Starting new_ho_10 with 163s (1) cores
% 0.20/0.51  # new_ho_10 with pid 22353 completed with status 0
% 0.20/0.51  # Result found by new_ho_10
% 0.20/0.51  # Preprocessing class: HSSSSMSSSSSNSSA.
% 0.20/0.51  # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.51  # Starting post_as_ho12 with 300s (1) cores
% 0.20/0.51  # No SInE strategy applied
% 0.20/0.51  # Search class: HGHSF-FFSF31-MSSFFSNN
% 0.20/0.51  # partial match(2): HGHPS-FFSF31-MSSFFSNN
% 0.20/0.51  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.51  # Starting new_ho_10 with 163s (1) cores
% 0.20/0.51  # Preprocessing time       : 0.001 s
% 0.20/0.51  # Presaturation interreduction done
% 0.20/0.51  
% 0.20/0.51  # Proof found!
% 0.20/0.51  # SZS status Theorem
% 0.20/0.51  # SZS output start CNFRefutation
% See solution above
% 0.20/0.51  # Parsed axioms                        : 5
% 0.20/0.51  # Removed by relevancy pruning/SinE    : 0
% 0.20/0.51  # Initial clauses                      : 14
% 0.20/0.51  # Removed in clause preprocessing      : 4
% 0.20/0.51  # Initial clauses in saturation        : 10
% 0.20/0.51  # Processed clauses                    : 24
% 0.20/0.51  # ...of these trivial                  : 0
% 0.20/0.51  # ...subsumed                          : 2
% 0.20/0.51  # ...remaining for further processing  : 21
% 0.20/0.51  # Other redundant clauses eliminated   : 4
% 0.20/0.51  # Clauses deleted for lack of memory   : 0
% 0.20/0.51  # Backward-subsumed                    : 0
% 0.20/0.51  # Backward-rewritten                   : 0
% 0.20/0.51  # Generated clauses                    : 7
% 0.20/0.51  # ...of the previous two non-redundant : 6
% 0.20/0.51  # ...aggressively subsumed             : 0
% 0.20/0.51  # Contextual simplify-reflections      : 0
% 0.20/0.51  # Paramodulations                      : 3
% 0.20/0.51  # Factorizations                       : 0
% 0.20/0.51  # NegExts                              : 0
% 0.20/0.51  # Equation resolutions                 : 4
% 0.20/0.51  # Disequality decompositions           : 0
% 0.20/0.51  # Total rewrite steps                  : 22
% 0.20/0.51  # ...of those cached                   : 9
% 0.20/0.51  # Propositional unsat checks           : 0
% 0.20/0.51  #    Propositional check models        : 0
% 0.20/0.51  #    Propositional check unsatisfiable : 0
% 0.20/0.51  #    Propositional clauses             : 0
% 0.20/0.51  #    Propositional clauses after purity: 0
% 0.20/0.51  #    Propositional unsat core size     : 0
% 0.20/0.51  #    Propositional preprocessing time  : 0.000
% 0.20/0.51  #    Propositional encoding time       : 0.000
% 0.20/0.51  #    Propositional solver time         : 0.000
% 0.20/0.51  #    Success case prop preproc time    : 0.000
% 0.20/0.51  #    Success case prop encoding time   : 0.000
% 0.20/0.51  #    Success case prop solver time     : 0.000
% 0.20/0.51  # Current number of processed clauses  : 9
% 0.20/0.51  #    Positive orientable unit clauses  : 5
% 0.20/0.51  #    Positive unorientable unit clauses: 0
% 0.20/0.51  #    Negative unit clauses             : 2
% 0.20/0.51  #    Non-unit-clauses                  : 2
% 0.20/0.51  # Current number of unprocessed clauses: 1
% 0.20/0.51  # ...number of literals in the above   : 2
% 0.20/0.51  # Current number of archived formulas  : 0
% 0.20/0.51  # Current number of archived clauses   : 9
% 0.20/0.51  # Clause-clause subsumption calls (NU) : 0
% 0.20/0.51  # Rec. Clause-clause subsumption calls : 0
% 0.20/0.51  # Non-unit clause-clause subsumptions  : 0
% 0.20/0.51  # Unit Clause-clause subsumption calls : 4
% 0.20/0.51  # Rewrite failures with RHS unbound    : 0
% 0.20/0.51  # BW rewrite match attempts            : 0
% 0.20/0.51  # BW rewrite match successes           : 0
% 0.20/0.51  # Condensation attempts                : 24
% 0.20/0.51  # Condensation successes               : 0
% 0.20/0.51  # Termbank termtop insertions          : 1238
% 0.20/0.51  # Search garbage collected termcells   : 202
% 0.20/0.51  
% 0.20/0.51  # -------------------------------------------------
% 0.20/0.51  # User time                : 0.004 s
% 0.20/0.51  # System time              : 0.002 s
% 0.20/0.51  # Total time               : 0.006 s
% 0.20/0.51  # Maximum resident set size: 1776 pages
% 0.20/0.51  
% 0.20/0.51  # -------------------------------------------------
% 0.20/0.51  # User time                : 0.005 s
% 0.20/0.51  # System time              : 0.004 s
% 0.20/0.51  # Total time               : 0.009 s
% 0.20/0.51  # Maximum resident set size: 1720 pages
% 0.20/0.51  % E---3.1 exiting
% 0.20/0.51  % E exiting
%------------------------------------------------------------------------------