TSTP Solution File: PUZ031^5 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : PUZ031^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n007.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 02:24:46 EDT 2024

% Result   : Theorem 0.19s 0.51s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   19
% Syntax   : Number of formulae    :   60 (  12 unt;  18 typ;   0 def)
%            Number of atoms       :  290 (   0 equ;   0 cnn)
%            Maximal formula atoms :   63 (   6 avg)
%            Number of connectives :  819 ( 185   ~; 173   |;  75   &; 386   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   66 (   9 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   14 (  14   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   19 (  18 usr;   7 con; 0-2 aty)
%            Number of variables   :  150 (   0   ^ 150   !;   0   ?; 150   :)

% Comments : 
%------------------------------------------------------------------------------
thf(decl_22,type,
    eats: $i > $i > $o ).

thf(decl_23,type,
    grain: $i > $o ).

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

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

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

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

thf(decl_28,type,
    caterpillar: $i > $o ).

thf(decl_29,type,
    cf: $i > $i ).

thf(decl_30,type,
    bird: $i > $o ).

thf(decl_31,type,
    wolf: $i > $o ).

thf(decl_32,type,
    fox: $i > $o ).

thf(decl_33,type,
    msmaller: $i > $i > $o ).

thf(decl_34,type,
    a_grain: $i ).

thf(decl_35,type,
    a_snail: $i ).

thf(decl_36,type,
    a_caterpillar: $i ).

thf(decl_37,type,
    a_bird: $i ).

thf(decl_38,type,
    a_fox: $i ).

thf(decl_39,type,
    a_wolf: $i ).

thf(cPUZ031_1,conjecture,
    ~ ( ! [X1: $i] :
          ( ( animal @ X1 )
          | ~ ( wolf @ X1 ) )
      & ! [X1: $i] :
          ( ( animal @ X1 )
          | ~ ( fox @ X1 ) )
      & ! [X1: $i] :
          ( ( animal @ X1 )
          | ~ ( bird @ X1 ) )
      & ! [X1: $i] :
          ( ( animal @ X1 )
          | ~ ( caterpillar @ X1 ) )
      & ! [X1: $i] :
          ( ( animal @ X1 )
          | ~ ( snail @ X1 ) )
      & ( wolf @ a_wolf )
      & ( fox @ a_fox )
      & ( bird @ a_bird )
      & ( caterpillar @ a_caterpillar )
      & ( snail @ a_snail )
      & ( grain @ a_grain )
      & ! [X1: $i] :
          ( ( plant @ X1 )
          | ~ ( grain @ X1 ) )
      & ! [X2: $i,X3: $i,X4: $i,X5: $i] :
          ( ( eats @ X2 @ X3 )
          | ( eats @ X2 @ X4 )
          | ~ ( animal @ X2 )
          | ~ ( plant @ X3 )
          | ~ ( animal @ X4 )
          | ~ ( plant @ X5 )
          | ~ ( msmaller @ X4 @ X2 )
          | ~ ( eats @ X4 @ X5 ) )
      & ! [X6: $i,X7: $i] :
          ( ( msmaller @ X6 @ X7 )
          | ~ ( caterpillar @ X6 )
          | ~ ( bird @ X7 ) )
      & ! [X4: $i,X7: $i] :
          ( ( msmaller @ X4 @ X7 )
          | ~ ( snail @ X4 )
          | ~ ( bird @ X7 ) )
      & ! [X7: $i,X8: $i] :
          ( ( msmaller @ X7 @ X8 )
          | ~ ( bird @ X7 )
          | ~ ( fox @ X8 ) )
      & ! [X8: $i,X9: $i] :
          ( ( msmaller @ X8 @ X9 )
          | ~ ( fox @ X8 )
          | ~ ( wolf @ X9 ) )
      & ! [X8: $i,X9: $i] :
          ( ~ ( wolf @ X9 )
          | ~ ( fox @ X8 )
          | ~ ( eats @ X9 @ X8 ) )
      & ! [X9: $i,X10: $i] :
          ( ~ ( wolf @ X9 )
          | ~ ( grain @ X10 )
          | ~ ( eats @ X9 @ X10 ) )
      & ! [X7: $i,X6: $i] :
          ( ( eats @ X7 @ X6 )
          | ~ ( bird @ X7 )
          | ~ ( caterpillar @ X6 ) )
      & ! [X7: $i,X4: $i] :
          ( ~ ( bird @ X7 )
          | ~ ( snail @ X4 )
          | ~ ( eats @ X7 @ X4 ) )
      & ! [X6: $i] :
          ( ( plant @ ( cf @ X6 ) )
          | ~ ( caterpillar @ X6 ) )
      & ! [X6: $i] :
          ( ( eats @ X6 @ ( cf @ X6 ) )
          | ~ ( caterpillar @ X6 ) )
      & ! [X4: $i] :
          ( ( plant @ ( sf @ X4 ) )
          | ~ ( snail @ X4 ) )
      & ! [X4: $i] :
          ( ( eats @ X4 @ ( sf @ X4 ) )
          | ~ ( snail @ X4 ) )
      & ! [X2: $i,X11: $i,X10: $i] :
          ( ~ ( animal @ X2 )
          | ~ ( animal @ X11 )
          | ~ ( grain @ X10 )
          | ~ ( eats @ X2 @ X11 )
          | ~ ( eats @ X11 @ X10 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cPUZ031_1) ).

thf(c_0_1,negated_conjecture,
    ~ ~ ( ! [X1: $i] :
            ( ( animal @ X1 )
            | ~ ( wolf @ X1 ) )
        & ! [X1: $i] :
            ( ( animal @ X1 )
            | ~ ( fox @ X1 ) )
        & ! [X1: $i] :
            ( ( animal @ X1 )
            | ~ ( bird @ X1 ) )
        & ! [X1: $i] :
            ( ( animal @ X1 )
            | ~ ( caterpillar @ X1 ) )
        & ! [X1: $i] :
            ( ( animal @ X1 )
            | ~ ( snail @ X1 ) )
        & ( wolf @ a_wolf )
        & ( fox @ a_fox )
        & ( bird @ a_bird )
        & ( caterpillar @ a_caterpillar )
        & ( snail @ a_snail )
        & ( grain @ a_grain )
        & ! [X1: $i] :
            ( ( plant @ X1 )
            | ~ ( grain @ X1 ) )
        & ! [X2: $i,X3: $i,X4: $i,X5: $i] :
            ( ( eats @ X2 @ X3 )
            | ( eats @ X2 @ X4 )
            | ~ ( animal @ X2 )
            | ~ ( plant @ X3 )
            | ~ ( animal @ X4 )
            | ~ ( plant @ X5 )
            | ~ ( msmaller @ X4 @ X2 )
            | ~ ( eats @ X4 @ X5 ) )
        & ! [X6: $i,X7: $i] :
            ( ( msmaller @ X6 @ X7 )
            | ~ ( caterpillar @ X6 )
            | ~ ( bird @ X7 ) )
        & ! [X4: $i,X7: $i] :
            ( ( msmaller @ X4 @ X7 )
            | ~ ( snail @ X4 )
            | ~ ( bird @ X7 ) )
        & ! [X7: $i,X8: $i] :
            ( ( msmaller @ X7 @ X8 )
            | ~ ( bird @ X7 )
            | ~ ( fox @ X8 ) )
        & ! [X8: $i,X9: $i] :
            ( ( msmaller @ X8 @ X9 )
            | ~ ( fox @ X8 )
            | ~ ( wolf @ X9 ) )
        & ! [X8: $i,X9: $i] :
            ( ~ ( wolf @ X9 )
            | ~ ( fox @ X8 )
            | ~ ( eats @ X9 @ X8 ) )
        & ! [X9: $i,X10: $i] :
            ( ~ ( wolf @ X9 )
            | ~ ( grain @ X10 )
            | ~ ( eats @ X9 @ X10 ) )
        & ! [X7: $i,X6: $i] :
            ( ( eats @ X7 @ X6 )
            | ~ ( bird @ X7 )
            | ~ ( caterpillar @ X6 ) )
        & ! [X7: $i,X4: $i] :
            ( ~ ( bird @ X7 )
            | ~ ( snail @ X4 )
            | ~ ( eats @ X7 @ X4 ) )
        & ! [X6: $i] :
            ( ( plant @ ( cf @ X6 ) )
            | ~ ( caterpillar @ X6 ) )
        & ! [X6: $i] :
            ( ( eats @ X6 @ ( cf @ X6 ) )
            | ~ ( caterpillar @ X6 ) )
        & ! [X4: $i] :
            ( ( plant @ ( sf @ X4 ) )
            | ~ ( snail @ X4 ) )
        & ! [X4: $i] :
            ( ( eats @ X4 @ ( sf @ X4 ) )
            | ~ ( snail @ X4 ) )
        & ! [X2: $i,X11: $i,X10: $i] :
            ( ~ ( animal @ X2 )
            | ~ ( animal @ X11 )
            | ~ ( grain @ X10 )
            | ~ ( eats @ X2 @ X11 )
            | ~ ( eats @ X11 @ X10 ) ) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[cPUZ031_1])]) ).

thf(c_0_2,negated_conjecture,
    ! [X45: $i,X46: $i,X47: $i,X48: $i,X49: $i,X50: $i,X51: $i,X52: $i,X53: $i,X54: $i,X55: $i,X56: $i,X57: $i,X58: $i,X59: $i,X60: $i,X61: $i,X62: $i,X63: $i,X64: $i,X65: $i,X66: $i,X67: $i,X68: $i,X69: $i,X70: $i,X71: $i,X72: $i,X73: $i,X74: $i,X75: $i,X76: $i,X77: $i] :
      ( ( ( animal @ X45 )
        | ~ ( wolf @ X45 ) )
      & ( ( animal @ X46 )
        | ~ ( fox @ X46 ) )
      & ( ( animal @ X47 )
        | ~ ( bird @ X47 ) )
      & ( ( animal @ X48 )
        | ~ ( caterpillar @ X48 ) )
      & ( ( animal @ X49 )
        | ~ ( snail @ X49 ) )
      & ( wolf @ a_wolf )
      & ( fox @ a_fox )
      & ( bird @ a_bird )
      & ( caterpillar @ a_caterpillar )
      & ( snail @ a_snail )
      & ( grain @ a_grain )
      & ( ( plant @ X50 )
        | ~ ( grain @ X50 ) )
      & ( ( eats @ X51 @ X52 )
        | ( eats @ X51 @ X53 )
        | ~ ( animal @ X51 )
        | ~ ( plant @ X52 )
        | ~ ( animal @ X53 )
        | ~ ( plant @ X54 )
        | ~ ( msmaller @ X53 @ X51 )
        | ~ ( eats @ X53 @ X54 ) )
      & ( ( msmaller @ X55 @ X56 )
        | ~ ( caterpillar @ X55 )
        | ~ ( bird @ X56 ) )
      & ( ( msmaller @ X57 @ X58 )
        | ~ ( snail @ X57 )
        | ~ ( bird @ X58 ) )
      & ( ( msmaller @ X59 @ X60 )
        | ~ ( bird @ X59 )
        | ~ ( fox @ X60 ) )
      & ( ( msmaller @ X61 @ X62 )
        | ~ ( fox @ X61 )
        | ~ ( wolf @ X62 ) )
      & ( ~ ( wolf @ X64 )
        | ~ ( fox @ X63 )
        | ~ ( eats @ X64 @ X63 ) )
      & ( ~ ( wolf @ X65 )
        | ~ ( grain @ X66 )
        | ~ ( eats @ X65 @ X66 ) )
      & ( ( eats @ X67 @ X68 )
        | ~ ( bird @ X67 )
        | ~ ( caterpillar @ X68 ) )
      & ( ~ ( bird @ X69 )
        | ~ ( snail @ X70 )
        | ~ ( eats @ X69 @ X70 ) )
      & ( ( plant @ ( cf @ X71 ) )
        | ~ ( caterpillar @ X71 ) )
      & ( ( eats @ X72 @ ( cf @ X72 ) )
        | ~ ( caterpillar @ X72 ) )
      & ( ( plant @ ( sf @ X73 ) )
        | ~ ( snail @ X73 ) )
      & ( ( eats @ X74 @ ( sf @ X74 ) )
        | ~ ( snail @ X74 ) )
      & ( ~ ( animal @ X75 )
        | ~ ( animal @ X76 )
        | ~ ( grain @ X77 )
        | ~ ( eats @ X75 @ X76 )
        | ~ ( eats @ X76 @ X77 ) ) ),
    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,
    ! [X1: $i,X2: $i,X3: $i,X4: $i] :
      ( ( eats @ X1 @ X2 )
      | ( eats @ X1 @ X3 )
      | ~ ( animal @ X1 )
      | ~ ( plant @ X2 )
      | ~ ( animal @ X3 )
      | ~ ( plant @ X4 )
      | ~ ( msmaller @ X3 @ X1 )
      | ~ ( eats @ X3 @ X4 ) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

thf(c_0_4,negated_conjecture,
    ! [X1: $i,X2: $i] :
      ( ( msmaller @ X1 @ X2 )
      | ~ ( snail @ X1 )
      | ~ ( bird @ X2 ) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

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

thf(c_0_6,negated_conjecture,
    ! [X1: $i] :
      ( ( animal @ X1 )
      | ~ ( snail @ X1 ) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

thf(c_0_7,negated_conjecture,
    ! [X1: $i,X2: $i] :
      ( ~ ( bird @ X1 )
      | ~ ( snail @ X2 )
      | ~ ( eats @ X1 @ X2 ) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

thf(c_0_8,negated_conjecture,
    ! [X4: $i,X3: $i,X2: $i,X1: $i] :
      ( ( eats @ X1 @ X2 )
      | ~ ( eats @ X3 @ X4 )
      | ~ ( plant @ X4 )
      | ~ ( plant @ X2 )
      | ~ ( snail @ X3 )
      | ~ ( bird @ X1 ) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_4]),c_0_5]),c_0_6]),c_0_7]) ).

thf(c_0_9,negated_conjecture,
    ! [X1: $i] :
      ( ( eats @ X1 @ ( sf @ X1 ) )
      | ~ ( snail @ X1 ) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

thf(c_0_10,negated_conjecture,
    ! [X1: $i] :
      ( ( plant @ ( sf @ X1 ) )
      | ~ ( snail @ X1 ) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

thf(c_0_11,negated_conjecture,
    ! [X1: $i] :
      ( ( plant @ X1 )
      | ~ ( grain @ X1 ) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

thf(c_0_12,negated_conjecture,
    grain @ a_grain,
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

thf(c_0_13,negated_conjecture,
    ! [X3: $i,X2: $i,X1: $i] :
      ( ( eats @ X1 @ X2 )
      | ~ ( plant @ X2 )
      | ~ ( snail @ X3 )
      | ~ ( bird @ X1 ) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_10]) ).

thf(c_0_14,negated_conjecture,
    plant @ a_grain,
    inference(spm,[status(thm)],[c_0_11,c_0_12]) ).

thf(c_0_15,negated_conjecture,
    ! [X2: $i,X1: $i] :
      ( ( eats @ X1 @ a_grain )
      | ~ ( snail @ X2 )
      | ~ ( bird @ X1 ) ),
    inference(spm,[status(thm)],[c_0_13,c_0_14]) ).

thf(c_0_16,negated_conjecture,
    snail @ a_snail,
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

thf(c_0_17,negated_conjecture,
    ! [X1: $i,X2: $i] :
      ( ( msmaller @ X1 @ X2 )
      | ~ ( bird @ X1 )
      | ~ ( fox @ X2 ) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

thf(c_0_18,negated_conjecture,
    ! [X1: $i] :
      ( ( animal @ X1 )
      | ~ ( fox @ X1 ) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

thf(c_0_19,negated_conjecture,
    ! [X1: $i] :
      ( ( eats @ X1 @ a_grain )
      | ~ ( bird @ X1 ) ),
    inference(spm,[status(thm)],[c_0_15,c_0_16]) ).

thf(c_0_20,negated_conjecture,
    bird @ a_bird,
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

thf(c_0_21,negated_conjecture,
    ! [X4: $i,X3: $i,X2: $i,X1: $i] :
      ( ( eats @ X1 @ X2 )
      | ( eats @ X1 @ X3 )
      | ~ ( eats @ X3 @ X4 )
      | ~ ( plant @ X4 )
      | ~ ( plant @ X2 )
      | ~ ( bird @ X3 )
      | ~ ( fox @ X1 ) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_17]),c_0_18]),c_0_5]) ).

thf(c_0_22,negated_conjecture,
    eats @ a_bird @ a_grain,
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

thf(c_0_23,negated_conjecture,
    ! [X2: $i,X1: $i] :
      ( ( eats @ X1 @ a_bird )
      | ( eats @ X1 @ X2 )
      | ~ ( plant @ X2 )
      | ~ ( fox @ X1 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_14]),c_0_20])]) ).

thf(c_0_24,negated_conjecture,
    ! [X1: $i,X2: $i,X3: $i] :
      ( ~ ( animal @ X1 )
      | ~ ( animal @ X2 )
      | ~ ( grain @ X3 )
      | ~ ( eats @ X1 @ X2 )
      | ~ ( eats @ X2 @ X3 ) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

thf(c_0_25,negated_conjecture,
    animal @ a_bird,
    inference(spm,[status(thm)],[c_0_5,c_0_20]) ).

thf(c_0_26,negated_conjecture,
    ! [X1: $i] :
      ( ( eats @ X1 @ a_grain )
      | ( eats @ X1 @ a_bird )
      | ~ ( fox @ X1 ) ),
    inference(spm,[status(thm)],[c_0_23,c_0_14]) ).

thf(c_0_27,negated_conjecture,
    fox @ a_fox,
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

thf(c_0_28,negated_conjecture,
    ! [X1: $i,X2: $i] :
      ( ( msmaller @ X1 @ X2 )
      | ~ ( fox @ X1 )
      | ~ ( wolf @ X2 ) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

thf(c_0_29,negated_conjecture,
    ! [X1: $i] :
      ( ( animal @ X1 )
      | ~ ( wolf @ X1 ) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

thf(c_0_30,negated_conjecture,
    ! [X1: $i,X2: $i] :
      ( ~ ( wolf @ X1 )
      | ~ ( fox @ X2 )
      | ~ ( eats @ X1 @ X2 ) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

thf(c_0_31,negated_conjecture,
    ! [X1: $i] :
      ( ~ ( eats @ X1 @ a_bird )
      | ~ ( animal @ X1 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_22]),c_0_12]),c_0_25])]) ).

thf(c_0_32,negated_conjecture,
    ( ( eats @ a_fox @ a_bird )
    | ( eats @ a_fox @ a_grain ) ),
    inference(spm,[status(thm)],[c_0_26,c_0_27]) ).

thf(c_0_33,negated_conjecture,
    animal @ a_fox,
    inference(spm,[status(thm)],[c_0_18,c_0_27]) ).

thf(c_0_34,negated_conjecture,
    ! [X1: $i,X2: $i,X4: $i,X3: $i] :
      ( ( eats @ X1 @ X2 )
      | ~ ( eats @ X3 @ X4 )
      | ~ ( plant @ X4 )
      | ~ ( plant @ X2 )
      | ~ ( wolf @ X1 )
      | ~ ( fox @ X3 ) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_28]),c_0_29]),c_0_18]),c_0_30]) ).

thf(c_0_35,negated_conjecture,
    eats @ a_fox @ a_grain,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33])]) ).

thf(c_0_36,negated_conjecture,
    ! [X2: $i,X1: $i] :
      ( ( eats @ X1 @ X2 )
      | ~ ( plant @ X2 )
      | ~ ( wolf @ X1 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_14]),c_0_27])]) ).

thf(c_0_37,negated_conjecture,
    ! [X1: $i] :
      ( ( eats @ X1 @ a_grain )
      | ~ ( wolf @ X1 ) ),
    inference(spm,[status(thm)],[c_0_36,c_0_14]) ).

thf(c_0_38,negated_conjecture,
    wolf @ a_wolf,
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

thf(c_0_39,negated_conjecture,
    ! [X1: $i,X2: $i] :
      ( ~ ( wolf @ X1 )
      | ~ ( grain @ X2 )
      | ~ ( eats @ X1 @ X2 ) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

thf(c_0_40,negated_conjecture,
    eats @ a_wolf @ a_grain,
    inference(spm,[status(thm)],[c_0_37,c_0_38]) ).

thf(c_0_41,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_12]),c_0_38])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : PUZ031^5 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.14  % Command    : run_E %s %d THM
% 0.13/0.35  % Computer : n007.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 11:01:23 EDT 2024
% 0.13/0.35  % CPUTime    : 
% 0.19/0.49  Running higher-order theorem proving
% 0.19/0.49  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
% 0.19/0.51  # Version: 3.1.0-ho
% 0.19/0.51  # Preprocessing class: HSMSSMSSSSSNFFN.
% 0.19/0.51  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.51  # Starting new_ho_10 with 1500s (5) cores
% 0.19/0.51  # Starting new_bool_1 with 300s (1) cores
% 0.19/0.51  # Starting full_lambda_5 with 300s (1) cores
% 0.19/0.51  # Starting new_ho_10_unif with 300s (1) cores
% 0.19/0.51  # new_ho_10 with pid 10731 completed with status 0
% 0.19/0.51  # Result found by new_ho_10
% 0.19/0.51  # Preprocessing class: HSMSSMSSSSSNFFN.
% 0.19/0.51  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.51  # Starting new_ho_10 with 1500s (5) cores
% 0.19/0.51  # No SInE strategy applied
% 0.19/0.51  # Search class: HGHNF-FFSM11-SFFFFFNN
% 0.19/0.51  # partial match(1): HGHNF-FFSF11-SFFFFFNN
% 0.19/0.51  # Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.19/0.51  # Starting new_ho_10 with 901s (1) cores
% 0.19/0.51  # Starting sh5l with 151s (1) cores
% 0.19/0.51  # Starting ehoh_best_sine_rwall with 151s (1) cores
% 0.19/0.51  # Starting lpo1_def_fix with 151s (1) cores
% 0.19/0.51  # Starting ehoh_best8_lambda with 146s (1) cores
% 0.19/0.51  # lpo1_def_fix with pid 10741 completed with status 0
% 0.19/0.51  # Result found by lpo1_def_fix
% 0.19/0.51  # Preprocessing class: HSMSSMSSSSSNFFN.
% 0.19/0.51  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.51  # Starting new_ho_10 with 1500s (5) cores
% 0.19/0.51  # No SInE strategy applied
% 0.19/0.51  # Search class: HGHNF-FFSM11-SFFFFFNN
% 0.19/0.51  # partial match(1): HGHNF-FFSF11-SFFFFFNN
% 0.19/0.51  # Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.19/0.51  # Starting new_ho_10 with 901s (1) cores
% 0.19/0.51  # Starting sh5l with 151s (1) cores
% 0.19/0.51  # Starting ehoh_best_sine_rwall with 151s (1) cores
% 0.19/0.51  # Starting lpo1_def_fix with 151s (1) cores
% 0.19/0.51  # Preprocessing time       : 0.001 s
% 0.19/0.51  # Presaturation interreduction done
% 0.19/0.51  
% 0.19/0.51  # Proof found!
% 0.19/0.51  # SZS status Theorem
% 0.19/0.51  # SZS output start CNFRefutation
% See solution above
% 0.19/0.51  # Parsed axioms                        : 19
% 0.19/0.51  # Removed by relevancy pruning/SinE    : 0
% 0.19/0.51  # Initial clauses                      : 44
% 0.19/0.51  # Removed in clause preprocessing      : 18
% 0.19/0.51  # Initial clauses in saturation        : 26
% 0.19/0.51  # Processed clauses                    : 122
% 0.19/0.51  # ...of these trivial                  : 0
% 0.19/0.51  # ...subsumed                          : 13
% 0.19/0.51  # ...remaining for further processing  : 109
% 0.19/0.51  # Other redundant clauses eliminated   : 0
% 0.19/0.51  # Clauses deleted for lack of memory   : 0
% 0.19/0.51  # Backward-subsumed                    : 15
% 0.19/0.51  # Backward-rewritten                   : 3
% 0.19/0.51  # Generated clauses                    : 96
% 0.19/0.51  # ...of the previous two non-redundant : 91
% 0.19/0.51  # ...aggressively subsumed             : 0
% 0.19/0.51  # Contextual simplify-reflections      : 13
% 0.19/0.51  # Paramodulations                      : 96
% 0.19/0.51  # Factorizations                       : 0
% 0.19/0.51  # NegExts                              : 0
% 0.19/0.51  # Equation resolutions                 : 0
% 0.19/0.51  # Disequality decompositions           : 0
% 0.19/0.51  # Total rewrite steps                  : 30
% 0.19/0.51  # ...of those cached                   : 21
% 0.19/0.51  # Propositional unsat checks           : 0
% 0.19/0.51  #    Propositional check models        : 0
% 0.19/0.51  #    Propositional check unsatisfiable : 0
% 0.19/0.51  #    Propositional clauses             : 0
% 0.19/0.51  #    Propositional clauses after purity: 0
% 0.19/0.51  #    Propositional unsat core size     : 0
% 0.19/0.51  #    Propositional preprocessing time  : 0.000
% 0.19/0.51  #    Propositional encoding time       : 0.000
% 0.19/0.51  #    Propositional solver time         : 0.000
% 0.19/0.51  #    Success case prop preproc time    : 0.000
% 0.19/0.51  #    Success case prop encoding time   : 0.000
% 0.19/0.51  #    Success case prop solver time     : 0.000
% 0.19/0.51  # Current number of processed clauses  : 65
% 0.19/0.51  #    Positive orientable unit clauses  : 16
% 0.19/0.51  #    Positive unorientable unit clauses: 0
% 0.19/0.51  #    Negative unit clauses             : 4
% 0.19/0.51  #    Non-unit-clauses                  : 45
% 0.19/0.51  # Current number of unprocessed clauses: 17
% 0.19/0.51  # ...number of literals in the above   : 85
% 0.19/0.51  # Current number of archived formulas  : 0
% 0.19/0.51  # Current number of archived clauses   : 44
% 0.19/0.51  # Clause-clause subsumption calls (NU) : 341
% 0.19/0.51  # Rec. Clause-clause subsumption calls : 143
% 0.19/0.51  # Non-unit clause-clause subsumptions  : 32
% 0.19/0.51  # Unit Clause-clause subsumption calls : 111
% 0.19/0.51  # Rewrite failures with RHS unbound    : 0
% 0.19/0.51  # BW rewrite match attempts            : 2
% 0.19/0.51  # BW rewrite match successes           : 2
% 0.19/0.51  # Condensation attempts                : 0
% 0.19/0.51  # Condensation successes               : 0
% 0.19/0.51  # Termbank termtop insertions          : 4368
% 0.19/0.51  # Search garbage collected termcells   : 500
% 0.19/0.51  
% 0.19/0.51  # -------------------------------------------------
% 0.19/0.51  # User time                : 0.012 s
% 0.19/0.51  # System time              : 0.001 s
% 0.19/0.51  # Total time               : 0.013 s
% 0.19/0.51  # Maximum resident set size: 1928 pages
% 0.19/0.51  
% 0.19/0.51  # -------------------------------------------------
% 0.19/0.51  # User time                : 0.049 s
% 0.19/0.51  # System time              : 0.007 s
% 0.19/0.51  # Total time               : 0.056 s
% 0.19/0.51  # Maximum resident set size: 1756 pages
% 0.19/0.51  % E---3.1 exiting
% 0.19/0.51  % E exiting
%------------------------------------------------------------------------------