TSTP Solution File: ALG272^5 by E---3.1.00

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%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : ALG272^5 : TPTP v8.2.0. Bugfixed v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n002.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 : Mon May 20 18:05:59 EDT 2024

% Result   : Theorem 0.38s 0.56s
% Output   : CNFRefutation 0.38s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :   30
% Syntax   : Number of formulae    :   64 (  27 unt;  22 typ;   0 def)
%            Number of atoms       :  165 ( 140 equ;   0 cnn)
%            Maximal formula atoms :   38 (   3 avg)
%            Number of connectives :  569 (  35   ~;  48   |;  41   &; 443   @)
%                                         (   2 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   29 (   4 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   67 (  67   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   23 (  21 usr;  12 con; 0-2 aty)
%            Number of variables   :  137 (  30   ^  97   !;  10   ?; 137   :)

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

thf(decl_22,type,
    cGROUP1: ( g > g > g ) > g > $o ).

thf(decl_23,type,
    cGROUP2: ( g > g > g ) > g > $o ).

thf(decl_24,type,
    cGRP_ASSOC: ( g > g > g ) > $o ).

thf(decl_25,type,
    cGRP_INVERSE: ( g > g > g ) > g > $o ).

thf(decl_26,type,
    cGRP_LEFT_INVERSE: ( g > g > g ) > g > $o ).

thf(decl_27,type,
    cGRP_LEFT_UNIT: ( g > g > g ) > g > $o ).

thf(decl_28,type,
    cGRP_UNIT: ( g > g > g ) > g > $o ).

thf(decl_29,type,
    esk1_0: g > g > g ).

thf(decl_30,type,
    esk2_0: g ).

thf(decl_31,type,
    esk3_0: g ).

thf(decl_32,type,
    esk4_0: g ).

thf(decl_33,type,
    esk5_0: g ).

thf(decl_34,type,
    esk6_0: g ).

thf(decl_35,type,
    esk7_0: g ).

thf(decl_36,type,
    esk8_0: g ).

thf(decl_37,type,
    esk9_0: g ).

thf(decl_38,type,
    esk10_0: g ).

thf(decl_39,type,
    esk11_0: g ).

thf(decl_40,type,
    esk12_0: g ).

thf(decl_41,type,
    esk13_1: g > g ).

thf(decl_42,type,
    esk14_1: g > g ).

thf(cGROUP1_def,axiom,
    ( cGROUP1
    = ( ^ [X1: g > g > g,X5: g] :
          ( ( cGRP_ASSOC @ X1 )
          & ( cGRP_UNIT @ X1 @ X5 )
          & ( cGRP_INVERSE @ X1 @ X5 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cGROUP1_def) ).

thf(cGRP_ASSOC_def,axiom,
    ( cGRP_ASSOC
    = ( ^ [X1: g > g > g] :
        ! [X2: g,X3: g,X4: g] :
          ( ( X1 @ ( X1 @ X2 @ X3 ) @ X4 )
          = ( X1 @ X2 @ ( X1 @ X3 @ X4 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cGRP_ASSOC_def) ).

thf(cGRP_INVERSE_def,axiom,
    ( cGRP_INVERSE
    = ( ^ [X1: g > g > g,X5: g] :
        ! [X2: g] :
        ? [X3: g] :
          ( ( ( X1 @ X2 @ X3 )
            = X5 )
          & ( ( X1 @ X3 @ X2 )
            = X5 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cGRP_INVERSE_def) ).

thf(cGRP_UNIT_def,axiom,
    ( cGRP_UNIT
    = ( ^ [X1: g > g > g,X5: g] :
        ! [X2: g] :
          ( ( ( X1 @ X5 @ X2 )
            = X2 )
          & ( ( X1 @ X2 @ X5 )
            = X2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cGRP_UNIT_def) ).

thf(cGROUP2_def,axiom,
    ( cGROUP2
    = ( ^ [X1: g > g > g,X5: g] :
          ( ( cGRP_ASSOC @ X1 )
          & ( cGRP_LEFT_UNIT @ X1 @ X5 )
          & ( cGRP_LEFT_INVERSE @ X1 @ X5 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cGROUP2_def) ).

thf(cGRP_LEFT_INVERSE_def,axiom,
    ( cGRP_LEFT_INVERSE
    = ( ^ [X1: g > g > g,X5: g] :
        ! [X2: g] :
        ? [X3: g] :
          ( ( X1 @ X3 @ X2 )
          = X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cGRP_LEFT_INVERSE_def) ).

thf(cGRP_LEFT_UNIT_def,axiom,
    ( cGRP_LEFT_UNIT
    = ( ^ [X1: g > g > g,X5: g] :
        ! [X2: g] :
          ( ( X1 @ X5 @ X2 )
          = X2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cGRP_LEFT_UNIT_def) ).

thf(cEQUIV_01_02,conjecture,
    ! [X1: g > g > g,X5: g] :
      ( ( cGROUP1 @ X1 @ X5 )
    <=> ( cGROUP2 @ X1 @ X5 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cEQUIV_01_02) ).

thf(c_0_8,plain,
    ( cGROUP1
    = ( ^ [Z0: g > g > g,Z1: g] :
          ( ! [X8: g,X9: g,X10: g] :
              ( ( Z0 @ ( Z0 @ X8 @ X9 ) @ X10 )
              = ( Z0 @ X8 @ ( Z0 @ X9 @ X10 ) ) )
          & ! [X11: g] :
              ( ( ( Z0 @ Z1 @ X11 )
                = X11 )
              & ( ( Z0 @ X11 @ Z1 )
                = X11 ) )
          & ! [X12: g] :
            ? [X13: g] :
              ( ( ( Z0 @ X12 @ X13 )
                = Z1 )
              & ( ( Z0 @ X13 @ X12 )
                = Z1 ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[cGROUP1_def]) ).

thf(c_0_9,plain,
    ( cGRP_ASSOC
    = ( ^ [Z0: g > g > g] :
        ! [X2: g,X3: g,X4: g] :
          ( ( Z0 @ ( Z0 @ X2 @ X3 ) @ X4 )
          = ( Z0 @ X2 @ ( Z0 @ X3 @ X4 ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[cGRP_ASSOC_def]) ).

thf(c_0_10,plain,
    ( cGRP_INVERSE
    = ( ^ [Z0: g > g > g,Z1: g] :
        ! [X2: g] :
        ? [X3: g] :
          ( ( ( Z0 @ X2 @ X3 )
            = Z1 )
          & ( ( Z0 @ X3 @ X2 )
            = Z1 ) ) ) ),
    inference(fof_simplification,[status(thm)],[cGRP_INVERSE_def]) ).

thf(c_0_11,plain,
    ( cGRP_UNIT
    = ( ^ [Z0: g > g > g,Z1: g] :
        ! [X2: g] :
          ( ( ( Z0 @ Z1 @ X2 )
            = X2 )
          & ( ( Z0 @ X2 @ Z1 )
            = X2 ) ) ) ),
    inference(fof_simplification,[status(thm)],[cGRP_UNIT_def]) ).

thf(c_0_12,plain,
    ( cGROUP2
    = ( ^ [Z0: g > g > g,Z1: g] :
          ( ! [X14: g,X15: g,X16: g] :
              ( ( Z0 @ ( Z0 @ X14 @ X15 ) @ X16 )
              = ( Z0 @ X14 @ ( Z0 @ X15 @ X16 ) ) )
          & ! [X17: g] :
              ( ( Z0 @ Z1 @ X17 )
              = X17 )
          & ! [X18: g] :
            ? [X19: g] :
              ( ( Z0 @ X19 @ X18 )
              = Z1 ) ) ) ),
    inference(fof_simplification,[status(thm)],[cGROUP2_def]) ).

thf(c_0_13,plain,
    ( cGRP_LEFT_INVERSE
    = ( ^ [Z0: g > g > g,Z1: g] :
        ! [X2: g] :
        ? [X3: g] :
          ( ( Z0 @ X3 @ X2 )
          = Z1 ) ) ),
    inference(fof_simplification,[status(thm)],[cGRP_LEFT_INVERSE_def]) ).

thf(c_0_14,plain,
    ( cGRP_LEFT_UNIT
    = ( ^ [Z0: g > g > g,Z1: g] :
        ! [X2: g] :
          ( ( Z0 @ Z1 @ X2 )
          = X2 ) ) ),
    inference(fof_simplification,[status(thm)],[cGRP_LEFT_UNIT_def]) ).

thf(c_0_15,plain,
    ( cGROUP1
    = ( ^ [Z0: g > g > g,Z1: g] :
          ( ! [X8: g,X9: g,X10: g] :
              ( ( Z0 @ ( Z0 @ X8 @ X9 ) @ X10 )
              = ( Z0 @ X8 @ ( Z0 @ X9 @ X10 ) ) )
          & ! [X11: g] :
              ( ( ( Z0 @ Z1 @ X11 )
                = X11 )
              & ( ( Z0 @ X11 @ Z1 )
                = X11 ) )
          & ! [X12: g] :
            ? [X13: g] :
              ( ( ( Z0 @ X12 @ X13 )
                = Z1 )
              & ( ( Z0 @ X13 @ X12 )
                = Z1 ) ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_8,c_0_9]),c_0_10]),c_0_11]) ).

thf(c_0_16,plain,
    ( cGROUP2
    = ( ^ [Z0: g > g > g,Z1: g] :
          ( ! [X14: g,X15: g,X16: g] :
              ( ( Z0 @ ( Z0 @ X14 @ X15 ) @ X16 )
              = ( Z0 @ X14 @ ( Z0 @ X15 @ X16 ) ) )
          & ! [X17: g] :
              ( ( Z0 @ Z1 @ X17 )
              = X17 )
          & ! [X18: g] :
            ? [X19: g] :
              ( ( Z0 @ X19 @ X18 )
              = Z1 ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_12,c_0_9]),c_0_13]),c_0_14]) ).

thf(c_0_17,negated_conjecture,
    ~ ! [X1: g > g > g,X5: g] :
        ( ( ! [X20: g,X21: g,X22: g] :
              ( ( X1 @ ( X1 @ X20 @ X21 ) @ X22 )
              = ( X1 @ X20 @ ( X1 @ X21 @ X22 ) ) )
          & ! [X23: g] :
              ( ( ( X1 @ X5 @ X23 )
                = X23 )
              & ( ( X1 @ X23 @ X5 )
                = X23 ) )
          & ! [X24: g] :
            ? [X25: g] :
              ( ( ( X1 @ X24 @ X25 )
                = X5 )
              & ( ( X1 @ X25 @ X24 )
                = X5 ) ) )
      <=> ( ! [X26: g,X27: g,X28: g] :
              ( ( X1 @ ( X1 @ X26 @ X27 ) @ X28 )
              = ( X1 @ X26 @ ( X1 @ X27 @ X28 ) ) )
          & ! [X29: g] :
              ( ( X1 @ X5 @ X29 )
              = X29 )
          & ! [X30: g] :
            ? [X31: g] :
              ( ( X1 @ X31 @ X30 )
              = X5 ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[cEQUIV_01_02]),c_0_15]),c_0_16]) ).

thf(c_0_18,negated_conjecture,
    ! [X39: g,X45: g,X46: g,X47: g,X48: g,X49: g,X50: g,X52: g,X53: g,X54: g,X55: g,X56: g] :
      ( ( ( ( esk1_0 @ ( esk1_0 @ esk3_0 @ esk4_0 ) @ esk5_0 )
         != ( esk1_0 @ esk3_0 @ ( esk1_0 @ esk4_0 @ esk5_0 ) ) )
        | ( ( esk1_0 @ esk2_0 @ esk6_0 )
         != esk6_0 )
        | ( ( esk1_0 @ esk6_0 @ esk2_0 )
         != esk6_0 )
        | ( ( esk1_0 @ esk7_0 @ X39 )
         != esk2_0 )
        | ( ( esk1_0 @ X39 @ esk7_0 )
         != esk2_0 )
        | ( ( esk1_0 @ ( esk1_0 @ esk8_0 @ esk9_0 ) @ esk10_0 )
         != ( esk1_0 @ esk8_0 @ ( esk1_0 @ esk9_0 @ esk10_0 ) ) )
        | ( ( esk1_0 @ esk2_0 @ esk11_0 )
         != esk11_0 )
        | ( ( esk1_0 @ X45 @ esk12_0 )
         != esk2_0 ) )
      & ( ( ( esk1_0 @ ( esk1_0 @ X52 @ X53 ) @ X54 )
          = ( esk1_0 @ X52 @ ( esk1_0 @ X53 @ X54 ) ) )
        | ( ( esk1_0 @ ( esk1_0 @ X46 @ X47 ) @ X48 )
          = ( esk1_0 @ X46 @ ( esk1_0 @ X47 @ X48 ) ) ) )
      & ( ( ( esk1_0 @ esk2_0 @ X55 )
          = X55 )
        | ( ( esk1_0 @ ( esk1_0 @ X46 @ X47 ) @ X48 )
          = ( esk1_0 @ X46 @ ( esk1_0 @ X47 @ X48 ) ) ) )
      & ( ( ( esk1_0 @ ( esk14_1 @ X56 ) @ X56 )
          = esk2_0 )
        | ( ( esk1_0 @ ( esk1_0 @ X46 @ X47 ) @ X48 )
          = ( esk1_0 @ X46 @ ( esk1_0 @ X47 @ X48 ) ) ) )
      & ( ( ( esk1_0 @ ( esk1_0 @ X52 @ X53 ) @ X54 )
          = ( esk1_0 @ X52 @ ( esk1_0 @ X53 @ X54 ) ) )
        | ( ( esk1_0 @ esk2_0 @ X49 )
          = X49 ) )
      & ( ( ( esk1_0 @ esk2_0 @ X55 )
          = X55 )
        | ( ( esk1_0 @ esk2_0 @ X49 )
          = X49 ) )
      & ( ( ( esk1_0 @ ( esk14_1 @ X56 ) @ X56 )
          = esk2_0 )
        | ( ( esk1_0 @ esk2_0 @ X49 )
          = X49 ) )
      & ( ( ( esk1_0 @ ( esk1_0 @ X52 @ X53 ) @ X54 )
          = ( esk1_0 @ X52 @ ( esk1_0 @ X53 @ X54 ) ) )
        | ( ( esk1_0 @ X49 @ esk2_0 )
          = X49 ) )
      & ( ( ( esk1_0 @ esk2_0 @ X55 )
          = X55 )
        | ( ( esk1_0 @ X49 @ esk2_0 )
          = X49 ) )
      & ( ( ( esk1_0 @ ( esk14_1 @ X56 ) @ X56 )
          = esk2_0 )
        | ( ( esk1_0 @ X49 @ esk2_0 )
          = X49 ) )
      & ( ( ( esk1_0 @ ( esk1_0 @ X52 @ X53 ) @ X54 )
          = ( esk1_0 @ X52 @ ( esk1_0 @ X53 @ X54 ) ) )
        | ( ( esk1_0 @ X50 @ ( esk13_1 @ X50 ) )
          = esk2_0 ) )
      & ( ( ( esk1_0 @ esk2_0 @ X55 )
          = X55 )
        | ( ( esk1_0 @ X50 @ ( esk13_1 @ X50 ) )
          = esk2_0 ) )
      & ( ( ( esk1_0 @ ( esk14_1 @ X56 ) @ X56 )
          = esk2_0 )
        | ( ( esk1_0 @ X50 @ ( esk13_1 @ X50 ) )
          = esk2_0 ) )
      & ( ( ( esk1_0 @ ( esk1_0 @ X52 @ X53 ) @ X54 )
          = ( esk1_0 @ X52 @ ( esk1_0 @ X53 @ X54 ) ) )
        | ( ( esk1_0 @ ( esk13_1 @ X50 ) @ X50 )
          = esk2_0 ) )
      & ( ( ( esk1_0 @ esk2_0 @ X55 )
          = X55 )
        | ( ( esk1_0 @ ( esk13_1 @ X50 ) @ X50 )
          = esk2_0 ) )
      & ( ( ( esk1_0 @ ( esk14_1 @ X56 ) @ X56 )
          = esk2_0 )
        | ( ( esk1_0 @ ( esk13_1 @ X50 ) @ X50 )
          = esk2_0 ) ) ),
    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)],[c_0_17])])])])])]) ).

thf(c_0_19,negated_conjecture,
    ! [X2: g,X3: g] :
      ( ( ( esk1_0 @ esk2_0 @ X2 )
        = X2 )
      | ( ( esk1_0 @ esk2_0 @ X3 )
        = X3 ) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

thf(c_0_20,negated_conjecture,
    ! [X2: g,X3: g] :
      ( ( ( esk1_0 @ ( esk1_0 @ esk3_0 @ esk4_0 ) @ esk5_0 )
       != ( esk1_0 @ esk3_0 @ ( esk1_0 @ esk4_0 @ esk5_0 ) ) )
      | ( ( esk1_0 @ esk2_0 @ esk6_0 )
       != esk6_0 )
      | ( ( esk1_0 @ esk6_0 @ esk2_0 )
       != esk6_0 )
      | ( ( esk1_0 @ esk7_0 @ X2 )
       != esk2_0 )
      | ( ( esk1_0 @ X2 @ esk7_0 )
       != esk2_0 )
      | ( ( esk1_0 @ ( esk1_0 @ esk8_0 @ esk9_0 ) @ esk10_0 )
       != ( esk1_0 @ esk8_0 @ ( esk1_0 @ esk9_0 @ esk10_0 ) ) )
      | ( ( esk1_0 @ esk2_0 @ esk11_0 )
       != esk11_0 )
      | ( ( esk1_0 @ X3 @ esk12_0 )
       != esk2_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

thf(c_0_21,negated_conjecture,
    ! [X2: g] :
      ( ( esk1_0 @ esk2_0 @ X2 )
      = X2 ),
    inference(ef,[status(thm)],[c_0_19]) ).

thf(c_0_22,negated_conjecture,
    ! [X2: g,X3: g,X4: g,X5: g,X7: g,X8: g] :
      ( ( ( esk1_0 @ ( esk1_0 @ X2 @ X3 ) @ X4 )
        = ( esk1_0 @ X2 @ ( esk1_0 @ X3 @ X4 ) ) )
      | ( ( esk1_0 @ ( esk1_0 @ X5 @ X7 ) @ X8 )
        = ( esk1_0 @ X5 @ ( esk1_0 @ X7 @ X8 ) ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

thf(c_0_23,negated_conjecture,
    ! [X2: g,X3: g] :
      ( ( ( esk1_0 @ ( esk1_0 @ esk3_0 @ esk4_0 ) @ esk5_0 )
       != ( esk1_0 @ esk3_0 @ ( esk1_0 @ esk4_0 @ esk5_0 ) ) )
      | ( ( esk1_0 @ ( esk1_0 @ esk8_0 @ esk9_0 ) @ esk10_0 )
       != ( esk1_0 @ esk8_0 @ ( esk1_0 @ esk9_0 @ esk10_0 ) ) )
      | ( ( esk1_0 @ esk6_0 @ esk2_0 )
       != esk6_0 )
      | ( ( esk1_0 @ X2 @ esk12_0 )
       != esk2_0 )
      | ( ( esk1_0 @ X3 @ esk7_0 )
       != esk2_0 )
      | ( ( esk1_0 @ esk7_0 @ X3 )
       != esk2_0 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_21]),c_0_21])]) ).

thf(c_0_24,negated_conjecture,
    ! [X2: g,X3: g,X4: g] :
      ( ( esk1_0 @ ( esk1_0 @ X2 @ X3 ) @ X4 )
      = ( esk1_0 @ X2 @ ( esk1_0 @ X3 @ X4 ) ) ),
    inference(ef,[status(thm)],[c_0_22]) ).

thf(c_0_25,negated_conjecture,
    ! [X2: g,X3: g] :
      ( ( ( esk1_0 @ esk6_0 @ esk2_0 )
       != esk6_0 )
      | ( ( esk1_0 @ X2 @ esk12_0 )
       != esk2_0 )
      | ( ( esk1_0 @ X3 @ esk7_0 )
       != esk2_0 )
      | ( ( esk1_0 @ esk7_0 @ X3 )
       != esk2_0 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_24]),c_0_24])]) ).

thf(c_0_26,negated_conjecture,
    ! [X2: g,X3: g] :
      ( ( ( esk1_0 @ ( esk14_1 @ X2 ) @ X2 )
        = esk2_0 )
      | ( ( esk1_0 @ ( esk13_1 @ X3 ) @ X3 )
        = esk2_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

thf(c_0_27,negated_conjecture,
    ! [X2: g,X3: g] :
      ( ( ( esk1_0 @ ( esk14_1 @ X2 ) @ X2 )
        = esk2_0 )
      | ( ( esk1_0 @ X3 @ esk2_0 )
        = X3 ) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

thf(c_0_28,negated_conjecture,
    ! [X2: g,X3: g] :
      ( ( ( esk1_0 @ ( esk14_1 @ X2 ) @ X2 )
        = esk2_0 )
      | ( ( esk1_0 @ X3 @ esk7_0 )
       != esk2_0 )
      | ( ( esk1_0 @ esk7_0 @ X3 )
       != esk2_0 ) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]) ).

thf(c_0_29,negated_conjecture,
    ! [X2: g,X3: g] :
      ( ( ( esk1_0 @ ( esk14_1 @ X2 ) @ X2 )
        = esk2_0 )
      | ( ( esk1_0 @ X3 @ ( esk13_1 @ X3 ) )
        = esk2_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

thf(c_0_30,negated_conjecture,
    ! [X2: g,X3: g] :
      ( ( ( esk1_0 @ ( esk14_1 @ X2 ) @ X2 )
        = esk2_0 )
      | ( ( esk1_0 @ ( esk14_1 @ X3 ) @ X3 )
        = esk2_0 ) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_26]),c_0_29]) ).

thf(c_0_31,negated_conjecture,
    ! [X2: g] :
      ( ( esk1_0 @ ( esk14_1 @ X2 ) @ X2 )
      = esk2_0 ),
    inference(ef,[status(thm)],[c_0_30]) ).

thf(c_0_32,negated_conjecture,
    ! [X2: g,X3: g] :
      ( ( esk1_0 @ ( esk14_1 @ X2 ) @ ( esk1_0 @ X2 @ X3 ) )
      = X3 ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_31]),c_0_21]) ).

thf(c_0_33,negated_conjecture,
    ! [X2: g] :
      ( ( esk1_0 @ ( esk14_1 @ ( esk14_1 @ X2 ) ) @ esk2_0 )
      = X2 ),
    inference(spm,[status(thm)],[c_0_32,c_0_31]) ).

thf(c_0_34,negated_conjecture,
    ! [X2: g] :
      ( ( esk1_0 @ ( esk14_1 @ ( esk14_1 @ ( esk14_1 @ X2 ) ) ) @ X2 )
      = esk2_0 ),
    inference(spm,[status(thm)],[c_0_32,c_0_33]) ).

thf(c_0_35,negated_conjecture,
    ! [X2: g] :
      ( ( ( esk1_0 @ esk6_0 @ esk2_0 )
       != esk6_0 )
      | ( ( esk1_0 @ X2 @ esk7_0 )
       != esk2_0 )
      | ( ( esk1_0 @ esk7_0 @ X2 )
       != esk2_0 ) ),
    inference(spm,[status(thm)],[c_0_25,c_0_31]) ).

thf(c_0_36,negated_conjecture,
    ! [X2: g] :
      ( ( esk14_1 @ ( esk14_1 @ X2 ) )
      = X2 ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_34]),c_0_33]) ).

thf(c_0_37,negated_conjecture,
    ( ( ( esk1_0 @ esk7_0 @ ( esk14_1 @ esk7_0 ) )
     != esk2_0 )
    | ( ( esk1_0 @ esk6_0 @ esk2_0 )
     != esk6_0 ) ),
    inference(spm,[status(thm)],[c_0_35,c_0_31]) ).

thf(c_0_38,negated_conjecture,
    ! [X2: g] :
      ( ( esk1_0 @ X2 @ esk2_0 )
      = X2 ),
    inference(rw,[status(thm)],[c_0_33,c_0_36]) ).

thf(c_0_39,negated_conjecture,
    ( ( esk1_0 @ esk7_0 @ ( esk14_1 @ esk7_0 ) )
   != esk2_0 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_38])]) ).

thf(c_0_40,negated_conjecture,
    ! [X2: g] :
      ( ( esk1_0 @ X2 @ ( esk14_1 @ X2 ) )
      = esk2_0 ),
    inference(spm,[status(thm)],[c_0_31,c_0_36]) ).

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.14  % Problem    : ALG272^5 : TPTP v8.2.0. Bugfixed v5.3.0.
% 0.03/0.15  % Command    : run_E %s %d THM
% 0.15/0.37  % Computer : n002.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit   : 300
% 0.15/0.37  % WCLimit    : 300
% 0.15/0.37  % DateTime   : Sat May 18 22:36:38 EDT 2024
% 0.15/0.37  % CPUTime    : 
% 0.23/0.53  Running higher-order theorem proving
% 0.23/0.53  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
% 0.38/0.56  # Version: 3.1.0-ho
% 0.38/0.56  # Preprocessing class: HSSSSMSSSLSNHSN.
% 0.38/0.56  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.38/0.56  # Starting ho_unfolding_3 with 1500s (5) cores
% 0.38/0.56  # Starting lpo8_lambda_fix with 300s (1) cores
% 0.38/0.56  # Starting lpo8_s with 300s (1) cores
% 0.38/0.56  # Starting new_bool_11 with 300s (1) cores
% 0.38/0.56  # ho_unfolding_3 with pid 32224 completed with status 0
% 0.38/0.56  # Result found by ho_unfolding_3
% 0.38/0.56  # Preprocessing class: HSSSSMSSSLSNHSN.
% 0.38/0.56  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.38/0.56  # Starting ho_unfolding_3 with 1500s (5) cores
% 0.38/0.56  # No SInE strategy applied
% 0.38/0.56  # Search class: HGHPF-FFMF11-SHSFMFNN
% 0.38/0.56  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.38/0.56  # Starting new_ho_10 with 811s (1) cores
% 0.38/0.56  # Starting ho_unfolding_3 with 151s (1) cores
% 0.38/0.56  # Starting new_bool_1 with 136s (1) cores
% 0.38/0.56  # Starting lpo1_def_fix with 136s (1) cores
% 0.38/0.56  # Starting ehoh_best8_lambda with 136s (1) cores
% 0.38/0.56  # lpo1_def_fix with pid 32234 completed with status 0
% 0.38/0.56  # Result found by lpo1_def_fix
% 0.38/0.56  # Preprocessing class: HSSSSMSSSLSNHSN.
% 0.38/0.56  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.38/0.56  # Starting ho_unfolding_3 with 1500s (5) cores
% 0.38/0.56  # No SInE strategy applied
% 0.38/0.56  # Search class: HGHPF-FFMF11-SHSFMFNN
% 0.38/0.56  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.38/0.56  # Starting new_ho_10 with 811s (1) cores
% 0.38/0.56  # Starting ho_unfolding_3 with 151s (1) cores
% 0.38/0.56  # Starting new_bool_1 with 136s (1) cores
% 0.38/0.56  # Starting lpo1_def_fix with 136s (1) cores
% 0.38/0.56  # Preprocessing time       : 0.001 s
% 0.38/0.56  # Presaturation interreduction done
% 0.38/0.56  
% 0.38/0.56  # Proof found!
% 0.38/0.56  # SZS status Theorem
% 0.38/0.56  # SZS output start CNFRefutation
% See solution above
% 0.38/0.56  # Parsed axioms                        : 16
% 0.38/0.56  # Removed by relevancy pruning/SinE    : 0
% 0.38/0.56  # Initial clauses                      : 24
% 0.38/0.56  # Removed in clause preprocessing      : 8
% 0.38/0.56  # Initial clauses in saturation        : 16
% 0.38/0.56  # Processed clauses                    : 161
% 0.38/0.56  # ...of these trivial                  : 2
% 0.38/0.56  # ...subsumed                          : 68
% 0.38/0.56  # ...remaining for further processing  : 91
% 0.38/0.56  # Other redundant clauses eliminated   : 1
% 0.38/0.56  # Clauses deleted for lack of memory   : 0
% 0.38/0.56  # Backward-subsumed                    : 41
% 0.38/0.56  # Backward-rewritten                   : 25
% 0.38/0.56  # Generated clauses                    : 486
% 0.38/0.56  # ...of the previous two non-redundant : 406
% 0.38/0.56  # ...aggressively subsumed             : 0
% 0.38/0.56  # Contextual simplify-reflections      : 8
% 0.38/0.56  # Paramodulations                      : 473
% 0.38/0.56  # Factorizations                       : 12
% 0.38/0.56  # NegExts                              : 0
% 0.38/0.56  # Equation resolutions                 : 1
% 0.38/0.56  # Disequality decompositions           : 0
% 0.38/0.56  # Total rewrite steps                  : 256
% 0.38/0.56  # ...of those cached                   : 202
% 0.38/0.56  # Propositional unsat checks           : 0
% 0.38/0.56  #    Propositional check models        : 0
% 0.38/0.56  #    Propositional check unsatisfiable : 0
% 0.38/0.56  #    Propositional clauses             : 0
% 0.38/0.56  #    Propositional clauses after purity: 0
% 0.38/0.56  #    Propositional unsat core size     : 0
% 0.38/0.56  #    Propositional preprocessing time  : 0.000
% 0.38/0.56  #    Propositional encoding time       : 0.000
% 0.38/0.56  #    Propositional solver time         : 0.000
% 0.38/0.56  #    Success case prop preproc time    : 0.000
% 0.38/0.56  #    Success case prop encoding time   : 0.000
% 0.38/0.56  #    Success case prop solver time     : 0.000
% 0.38/0.56  # Current number of processed clauses  : 10
% 0.38/0.56  #    Positive orientable unit clauses  : 8
% 0.38/0.56  #    Positive unorientable unit clauses: 0
% 0.38/0.56  #    Negative unit clauses             : 1
% 0.38/0.56  #    Non-unit-clauses                  : 1
% 0.38/0.56  # Current number of unprocessed clauses: 35
% 0.38/0.56  # ...number of literals in the above   : 86
% 0.38/0.56  # Current number of archived formulas  : 0
% 0.38/0.56  # Current number of archived clauses   : 81
% 0.38/0.56  # Clause-clause subsumption calls (NU) : 456
% 0.38/0.56  # Rec. Clause-clause subsumption calls : 237
% 0.38/0.56  # Non-unit clause-clause subsumptions  : 97
% 0.38/0.56  # Unit Clause-clause subsumption calls : 19
% 0.38/0.56  # Rewrite failures with RHS unbound    : 0
% 0.38/0.56  # BW rewrite match attempts            : 27
% 0.38/0.56  # BW rewrite match successes           : 21
% 0.38/0.56  # Condensation attempts                : 0
% 0.38/0.56  # Condensation successes               : 0
% 0.38/0.56  # Termbank termtop insertions          : 8989
% 0.38/0.56  # Search garbage collected termcells   : 470
% 0.38/0.56  
% 0.38/0.56  # -------------------------------------------------
% 0.38/0.56  # User time                : 0.020 s
% 0.38/0.56  # System time              : 0.008 s
% 0.38/0.56  # Total time               : 0.028 s
% 0.38/0.56  # Maximum resident set size: 1860 pages
% 0.38/0.56  
% 0.38/0.56  # -------------------------------------------------
% 0.38/0.56  # User time                : 0.117 s
% 0.38/0.56  # System time              : 0.014 s
% 0.38/0.56  # Total time               : 0.131 s
% 0.38/0.56  # Maximum resident set size: 1728 pages
% 0.38/0.56  % E---3.1 exiting
% 0.38/0.57  % E exiting
%------------------------------------------------------------------------------