TSTP Solution File: SEU997^5 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SEU997^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n028.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 03:31:02 EDT 2024

% Result   : Theorem 0.20s 0.53s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   32 (  20 unt;   9 typ;   0 def)
%            Number of atoms       :   83 (  82 equ;   0 cnn)
%            Maximal formula atoms :   21 (   3 avg)
%            Number of connectives :  349 (   3   ~;   0   |;  56   &; 286   @)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   49 (   6 avg)
%            Number of types       :    1 (   1 usr)
%            Number of type conns  :   13 (  13   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   8 usr;   6 con; 0-2 aty)
%            Number of variables   :  110 (   0   ^ 108   !;   2   ?; 110   :)

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

thf(decl_22,type,
    esk1_0: a > a > a ).

thf(decl_23,type,
    esk2_0: a > a > a ).

thf(decl_24,type,
    esk3_0: a ).

thf(decl_25,type,
    esk4_0: a ).

thf(decl_26,type,
    esk5_1: a > a ).

thf(decl_27,type,
    esk6_0: a ).

thf(decl_28,type,
    esk7_0: a ).

thf(decl_29,type,
    esk8_0: a ).

thf(cCD_LATTICE_THM_pme,conjecture,
    ! [X1: a > a > a,X2: a > a > a,X3: a,X4: a] :
      ( ( ! [X5: a] :
            ( ( X1 @ X5 @ X5 )
            = X5 )
        & ! [X5: a] :
            ( ( X2 @ X5 @ X5 )
            = X5 )
        & ! [X5: a,X6: a,X7: a] :
            ( ( X1 @ ( X1 @ X5 @ X6 ) @ X7 )
            = ( X1 @ X5 @ ( X1 @ X6 @ X7 ) ) )
        & ! [X5: a,X6: a,X7: a] :
            ( ( X2 @ ( X2 @ X5 @ X6 ) @ X7 )
            = ( X2 @ X5 @ ( X2 @ X6 @ X7 ) ) )
        & ! [X5: a,X6: a] :
            ( ( X1 @ X5 @ X6 )
            = ( X1 @ X6 @ X5 ) )
        & ! [X5: a,X6: a] :
            ( ( X2 @ X5 @ X6 )
            = ( X2 @ X6 @ X5 ) )
        & ! [X5: a,X6: a] :
            ( ( X1 @ ( X2 @ X5 @ X6 ) @ X6 )
            = X6 )
        & ! [X5: a,X6: a] :
            ( ( X2 @ ( X1 @ X5 @ X6 ) @ X6 )
            = X6 )
        & ! [X5: a,X6: a,X7: a] :
            ( ( X2 @ X5 @ ( X1 @ X6 @ X7 ) )
            = ( X1 @ ( X2 @ X5 @ X6 ) @ ( X2 @ X5 @ X7 ) ) )
        & ! [X5: a,X6: a,X7: a] :
            ( ( X1 @ X5 @ ( X2 @ X6 @ X7 ) )
            = ( X2 @ ( X1 @ X5 @ X6 ) @ ( X1 @ X5 @ X7 ) ) )
        & ! [X5: a] :
            ( ( X2 @ X3 @ X5 )
            = X5 )
        & ! [X5: a] :
            ( ( X1 @ X3 @ X5 )
            = X3 )
        & ! [X5: a] :
            ( ( X2 @ X4 @ X5 )
            = X4 )
        & ! [X5: a] :
            ( ( X1 @ X4 @ X5 )
            = X5 )
        & ! [X5: a] :
          ? [X6: a] :
            ( ( ( X1 @ X5 @ X6 )
              = X3 )
            & ( ( X2 @ X5 @ X6 )
              = X4 ) ) )
     => ! [X5: a,X6: a,X7: a] :
          ( ( ( ( X1 @ X5 @ X6 )
              = X3 )
            & ( ( X2 @ X5 @ X6 )
              = X4 )
            & ( ( X1 @ X5 @ X7 )
              = X3 )
            & ( ( X2 @ X5 @ X7 )
              = X4 ) )
         => ( X6 = X7 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cCD_LATTICE_THM_pme) ).

thf(c_0_1,negated_conjecture,
    ~ ! [X1: a > a > a,X2: a > a > a,X3: a,X4: a] :
        ( ( ! [X5: a] :
              ( ( X1 @ X5 @ X5 )
              = X5 )
          & ! [X5: a] :
              ( ( X2 @ X5 @ X5 )
              = X5 )
          & ! [X5: a,X6: a,X7: a] :
              ( ( X1 @ ( X1 @ X5 @ X6 ) @ X7 )
              = ( X1 @ X5 @ ( X1 @ X6 @ X7 ) ) )
          & ! [X5: a,X6: a,X7: a] :
              ( ( X2 @ ( X2 @ X5 @ X6 ) @ X7 )
              = ( X2 @ X5 @ ( X2 @ X6 @ X7 ) ) )
          & ! [X5: a,X6: a] :
              ( ( X1 @ X5 @ X6 )
              = ( X1 @ X6 @ X5 ) )
          & ! [X5: a,X6: a] :
              ( ( X2 @ X5 @ X6 )
              = ( X2 @ X6 @ X5 ) )
          & ! [X5: a,X6: a] :
              ( ( X1 @ ( X2 @ X5 @ X6 ) @ X6 )
              = X6 )
          & ! [X5: a,X6: a] :
              ( ( X2 @ ( X1 @ X5 @ X6 ) @ X6 )
              = X6 )
          & ! [X5: a,X6: a,X7: a] :
              ( ( X2 @ X5 @ ( X1 @ X6 @ X7 ) )
              = ( X1 @ ( X2 @ X5 @ X6 ) @ ( X2 @ X5 @ X7 ) ) )
          & ! [X5: a,X6: a,X7: a] :
              ( ( X1 @ X5 @ ( X2 @ X6 @ X7 ) )
              = ( X2 @ ( X1 @ X5 @ X6 ) @ ( X1 @ X5 @ X7 ) ) )
          & ! [X5: a] :
              ( ( X2 @ X3 @ X5 )
              = X5 )
          & ! [X5: a] :
              ( ( X1 @ X3 @ X5 )
              = X3 )
          & ! [X5: a] :
              ( ( X2 @ X4 @ X5 )
              = X4 )
          & ! [X5: a] :
              ( ( X1 @ X4 @ X5 )
              = X5 )
          & ! [X5: a] :
            ? [X6: a] :
              ( ( ( X1 @ X5 @ X6 )
                = X3 )
              & ( ( X2 @ X5 @ X6 )
                = X4 ) ) )
       => ! [X5: a,X6: a,X7: a] :
            ( ( ( ( X1 @ X5 @ X6 )
                = X3 )
              & ( ( X2 @ X5 @ X6 )
                = X4 )
              & ( ( X1 @ X5 @ X7 )
                = X3 )
              & ( ( X2 @ X5 @ X7 )
                = X4 ) )
           => ( X6 = X7 ) ) ),
    inference(assume_negation,[status(cth)],[cCD_LATTICE_THM_pme]) ).

thf(c_0_2,negated_conjecture,
    ! [X47: a,X48: a,X49: a,X50: a,X51: a,X52: a,X53: a,X54: a,X55: a,X56: a,X57: a,X58: a,X59: a,X60: a,X61: a,X62: a,X63: a,X64: a,X65: a,X66: a,X67: a,X68: a,X69: a,X70: a,X71: a,X72: a,X73: a] :
      ( ( ( esk1_0 @ X47 @ X47 )
        = X47 )
      & ( ( esk2_0 @ X48 @ X48 )
        = X48 )
      & ( ( esk1_0 @ ( esk1_0 @ X49 @ X50 ) @ X51 )
        = ( esk1_0 @ X49 @ ( esk1_0 @ X50 @ X51 ) ) )
      & ( ( esk2_0 @ ( esk2_0 @ X52 @ X53 ) @ X54 )
        = ( esk2_0 @ X52 @ ( esk2_0 @ X53 @ X54 ) ) )
      & ( ( esk1_0 @ X55 @ X56 )
        = ( esk1_0 @ X56 @ X55 ) )
      & ( ( esk2_0 @ X57 @ X58 )
        = ( esk2_0 @ X58 @ X57 ) )
      & ( ( esk1_0 @ ( esk2_0 @ X59 @ X60 ) @ X60 )
        = X60 )
      & ( ( esk2_0 @ ( esk1_0 @ X61 @ X62 ) @ X62 )
        = X62 )
      & ( ( esk2_0 @ X63 @ ( esk1_0 @ X64 @ X65 ) )
        = ( esk1_0 @ ( esk2_0 @ X63 @ X64 ) @ ( esk2_0 @ X63 @ X65 ) ) )
      & ( ( esk1_0 @ X66 @ ( esk2_0 @ X67 @ X68 ) )
        = ( esk2_0 @ ( esk1_0 @ X66 @ X67 ) @ ( esk1_0 @ X66 @ X68 ) ) )
      & ( ( esk2_0 @ esk3_0 @ X69 )
        = X69 )
      & ( ( esk1_0 @ esk3_0 @ X70 )
        = esk3_0 )
      & ( ( esk2_0 @ esk4_0 @ X71 )
        = esk4_0 )
      & ( ( esk1_0 @ esk4_0 @ X72 )
        = X72 )
      & ( ( esk1_0 @ X73 @ ( esk5_1 @ X73 ) )
        = esk3_0 )
      & ( ( esk2_0 @ X73 @ ( esk5_1 @ X73 ) )
        = esk4_0 )
      & ( ( esk1_0 @ esk6_0 @ esk7_0 )
        = esk3_0 )
      & ( ( esk2_0 @ esk6_0 @ esk7_0 )
        = esk4_0 )
      & ( ( esk1_0 @ esk6_0 @ esk8_0 )
        = esk3_0 )
      & ( ( esk2_0 @ esk6_0 @ esk8_0 )
        = esk4_0 )
      & ( esk7_0 != esk8_0 ) ),
    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_1])])])])]) ).

thf(c_0_3,negated_conjecture,
    ( ( esk2_0 @ esk6_0 @ esk8_0 )
    = esk4_0 ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

thf(c_0_4,negated_conjecture,
    ! [X4: a,X3: a] :
      ( ( esk2_0 @ X3 @ X4 )
      = ( esk2_0 @ X4 @ X3 ) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

thf(c_0_5,negated_conjecture,
    ! [X3: a] :
      ( ( esk1_0 @ esk4_0 @ X3 )
      = X3 ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

thf(c_0_6,negated_conjecture,
    ! [X4: a,X3: a] :
      ( ( esk1_0 @ X3 @ X4 )
      = ( esk1_0 @ X4 @ X3 ) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

thf(c_0_7,negated_conjecture,
    ( ( esk2_0 @ esk6_0 @ esk7_0 )
    = esk4_0 ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

thf(c_0_8,negated_conjecture,
    ! [X3: a,X4: a,X5: a] :
      ( ( esk2_0 @ X3 @ ( esk1_0 @ X4 @ X5 ) )
      = ( esk1_0 @ ( esk2_0 @ X3 @ X4 ) @ ( esk2_0 @ X3 @ X5 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

thf(c_0_9,negated_conjecture,
    ( ( esk2_0 @ esk8_0 @ esk6_0 )
    = esk4_0 ),
    inference(rw,[status(thm)],[c_0_3,c_0_4]) ).

thf(c_0_10,negated_conjecture,
    ! [X3: a] :
      ( ( esk1_0 @ X3 @ esk4_0 )
      = X3 ),
    inference(spm,[status(thm)],[c_0_5,c_0_6]) ).

thf(c_0_11,negated_conjecture,
    ( ( esk1_0 @ esk6_0 @ esk7_0 )
    = esk3_0 ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

thf(c_0_12,negated_conjecture,
    ! [X3: a] :
      ( ( esk2_0 @ esk3_0 @ X3 )
      = X3 ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

thf(c_0_13,negated_conjecture,
    ( ( esk2_0 @ esk7_0 @ esk6_0 )
    = esk4_0 ),
    inference(rw,[status(thm)],[c_0_7,c_0_4]) ).

thf(c_0_14,negated_conjecture,
    ( ( esk1_0 @ esk6_0 @ esk8_0 )
    = esk3_0 ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

thf(c_0_15,negated_conjecture,
    ! [X3: a] :
      ( ( esk2_0 @ esk8_0 @ ( esk1_0 @ X3 @ esk6_0 ) )
      = ( esk2_0 @ esk8_0 @ X3 ) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_10]) ).

thf(c_0_16,negated_conjecture,
    ( ( esk1_0 @ esk7_0 @ esk6_0 )
    = esk3_0 ),
    inference(rw,[status(thm)],[c_0_11,c_0_6]) ).

thf(c_0_17,negated_conjecture,
    ! [X3: a] :
      ( ( esk2_0 @ X3 @ esk3_0 )
      = X3 ),
    inference(spm,[status(thm)],[c_0_12,c_0_4]) ).

thf(c_0_18,negated_conjecture,
    ! [X3: a] :
      ( ( esk2_0 @ esk7_0 @ ( esk1_0 @ X3 @ esk6_0 ) )
      = ( esk2_0 @ esk7_0 @ X3 ) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_13]),c_0_10]) ).

thf(c_0_19,negated_conjecture,
    ( ( esk1_0 @ esk8_0 @ esk6_0 )
    = esk3_0 ),
    inference(rw,[status(thm)],[c_0_14,c_0_6]) ).

thf(c_0_20,negated_conjecture,
    ( ( esk2_0 @ esk7_0 @ esk8_0 )
    = esk8_0 ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]),c_0_4]) ).

thf(c_0_21,negated_conjecture,
    esk7_0 != esk8_0,
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem    : SEU997^5 : TPTP v8.2.0. Released v4.0.0.
% 0.03/0.14  % Command    : run_E %s %d THM
% 0.13/0.35  % Computer : n028.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   : Sun May 19 18:13:08 EDT 2024
% 0.13/0.35  % CPUTime    : 
% 0.20/0.51  Running higher-order theorem proving
% 0.20/0.51  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/benchmark/theBenchmark.p
% 0.20/0.53  # Version: 3.1.0-ho
% 0.20/0.53  # Preprocessing class: HSMSSMSSSSSNSSA.
% 0.20/0.53  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.53  # Starting post_as_ho1 with 1500s (5) cores
% 0.20/0.53  # Starting post_as_ho12 with 300s (1) cores
% 0.20/0.53  # Starting new_ho_3 with 300s (1) cores
% 0.20/0.53  # Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.20/0.53  # post_as_ho1 with pid 5866 completed with status 0
% 0.20/0.53  # Result found by post_as_ho1
% 0.20/0.53  # Preprocessing class: HSMSSMSSSSSNSSA.
% 0.20/0.53  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.53  # Starting post_as_ho1 with 1500s (5) cores
% 0.20/0.53  # No SInE strategy applied
% 0.20/0.53  # Search class: HUUPM-FFSS11-SSSFFFNN
% 0.20/0.53  # partial match(3): HUUPF-FFSF11-SSSFFMNN
% 0.20/0.53  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.20/0.53  # Starting post_as_ho12 with 811s (1) cores
% 0.20/0.53  # Starting post_as_ho1 with 151s (1) cores
% 0.20/0.53  # Starting new_ho_4 with 136s (1) cores
% 0.20/0.53  # Starting post_as_ho5 with 136s (1) cores
% 0.20/0.53  # Starting post_as_ho4 with 136s (1) cores
% 0.20/0.53  # post_as_ho5 with pid 5877 completed with status 0
% 0.20/0.53  # Result found by post_as_ho5
% 0.20/0.53  # Preprocessing class: HSMSSMSSSSSNSSA.
% 0.20/0.53  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.53  # Starting post_as_ho1 with 1500s (5) cores
% 0.20/0.53  # No SInE strategy applied
% 0.20/0.53  # Search class: HUUPM-FFSS11-SSSFFFNN
% 0.20/0.53  # partial match(3): HUUPF-FFSF11-SSSFFMNN
% 0.20/0.53  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.20/0.53  # Starting post_as_ho12 with 811s (1) cores
% 0.20/0.53  # Starting post_as_ho1 with 151s (1) cores
% 0.20/0.53  # Starting new_ho_4 with 136s (1) cores
% 0.20/0.53  # Starting post_as_ho5 with 136s (1) cores
% 0.20/0.53  # Preprocessing time       : 0.001 s
% 0.20/0.53  # Presaturation interreduction done
% 0.20/0.53  
% 0.20/0.53  # Proof found!
% 0.20/0.53  # SZS status Theorem
% 0.20/0.53  # SZS output start CNFRefutation
% See solution above
% 0.20/0.53  # Parsed axioms                        : 2
% 0.20/0.53  # Removed by relevancy pruning/SinE    : 0
% 0.20/0.53  # Initial clauses                      : 22
% 0.20/0.53  # Removed in clause preprocessing      : 1
% 0.20/0.53  # Initial clauses in saturation        : 21
% 0.20/0.53  # Processed clauses                    : 127
% 0.20/0.53  # ...of these trivial                  : 27
% 0.20/0.53  # ...subsumed                          : 9
% 0.20/0.53  # ...remaining for further processing  : 91
% 0.20/0.53  # Other redundant clauses eliminated   : 0
% 0.20/0.53  # Clauses deleted for lack of memory   : 0
% 0.20/0.53  # Backward-subsumed                    : 0
% 0.20/0.53  # Backward-rewritten                   : 10
% 0.20/0.53  # Generated clauses                    : 946
% 0.20/0.53  # ...of the previous two non-redundant : 489
% 0.20/0.53  # ...aggressively subsumed             : 0
% 0.20/0.53  # Contextual simplify-reflections      : 0
% 0.20/0.53  # Paramodulations                      : 946
% 0.20/0.53  # Factorizations                       : 0
% 0.20/0.53  # NegExts                              : 0
% 0.20/0.53  # Equation resolutions                 : 0
% 0.20/0.53  # Disequality decompositions           : 0
% 0.20/0.53  # Total rewrite steps                  : 1000
% 0.20/0.53  # ...of those cached                   : 676
% 0.20/0.53  # Propositional unsat checks           : 0
% 0.20/0.53  #    Propositional check models        : 0
% 0.20/0.53  #    Propositional check unsatisfiable : 0
% 0.20/0.53  #    Propositional clauses             : 0
% 0.20/0.53  #    Propositional clauses after purity: 0
% 0.20/0.53  #    Propositional unsat core size     : 0
% 0.20/0.53  #    Propositional preprocessing time  : 0.000
% 0.20/0.53  #    Propositional encoding time       : 0.000
% 0.20/0.53  #    Propositional solver time         : 0.000
% 0.20/0.53  #    Success case prop preproc time    : 0.000
% 0.20/0.53  #    Success case prop encoding time   : 0.000
% 0.20/0.53  #    Success case prop solver time     : 0.000
% 0.20/0.53  # Current number of processed clauses  : 60
% 0.20/0.53  #    Positive orientable unit clauses  : 55
% 0.20/0.53  #    Positive unorientable unit clauses: 4
% 0.20/0.53  #    Negative unit clauses             : 1
% 0.20/0.53  #    Non-unit-clauses                  : 0
% 0.20/0.53  # Current number of unprocessed clauses: 400
% 0.20/0.53  # ...number of literals in the above   : 400
% 0.20/0.53  # Current number of archived formulas  : 0
% 0.20/0.53  # Current number of archived clauses   : 31
% 0.20/0.53  # Clause-clause subsumption calls (NU) : 0
% 0.20/0.53  # Rec. Clause-clause subsumption calls : 0
% 0.20/0.53  # Non-unit clause-clause subsumptions  : 0
% 0.20/0.53  # Unit Clause-clause subsumption calls : 4
% 0.20/0.53  # Rewrite failures with RHS unbound    : 0
% 0.20/0.53  # BW rewrite match attempts            : 122
% 0.20/0.53  # BW rewrite match successes           : 92
% 0.20/0.53  # Condensation attempts                : 0
% 0.20/0.53  # Condensation successes               : 0
% 0.20/0.53  # Termbank termtop insertions          : 14226
% 0.20/0.53  # Search garbage collected termcells   : 663
% 0.20/0.53  
% 0.20/0.53  # -------------------------------------------------
% 0.20/0.53  # User time                : 0.018 s
% 0.20/0.53  # System time              : 0.002 s
% 0.20/0.53  # Total time               : 0.019 s
% 0.20/0.53  # Maximum resident set size: 1876 pages
% 0.20/0.53  
% 0.20/0.53  # -------------------------------------------------
% 0.20/0.53  # User time                : 0.079 s
% 0.20/0.53  # System time              : 0.012 s
% 0.20/0.53  # Total time               : 0.091 s
% 0.20/0.53  # Maximum resident set size: 1724 pages
% 0.20/0.53  % E---3.1 exiting
% 0.20/0.53  % E exiting
%------------------------------------------------------------------------------