TSTP Solution File: SYO269^5 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SYO269^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n020.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 08:45:19 EDT 2024

% Result   : Theorem 0.19s 0.49s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   42 (  16 unt;   8 typ;   0 def)
%            Number of atoms       :   85 (  58 equ;   0 cnn)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  641 (  57   ~;  66   |;  18   &; 496   @)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   26 (   8 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  216 ( 216   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   11 (   8 usr;   2 con; 0-3 aty)
%            Number of variables   :  177 (  90   ^  83   !;   4   ?; 177   :)

% Comments : 
%------------------------------------------------------------------------------
thf(decl_22,type,
    epred1_0: $i > $o ).

thf(decl_23,type,
    esk1_2: ( ( $i > $i ) > $i > $o ) > ( ( $i > $i ) > $i > $o ) > $i ).

thf(decl_24,type,
    esk2_2: ( ( $i > $i ) > $i > $o ) > ( ( $i > $i ) > $i > $o ) > $i > $i ).

thf(decl_25,type,
    esk3_2: ( ( $i > $i ) > $i > $o ) > ( ( $i > $i ) > $i > $o ) > $i > $i ).

thf(decl_26,type,
    esk4_2: ( ( $i > $i ) > $i > $o ) > ( ( $i > $i ) > $i > $o ) > $i ).

thf(decl_27,type,
    esk5_2: ( ( $i > $i ) > $i > $o ) > ( ( $i > $i ) > $i > $o ) > $i ).

thf(decl_28,type,
    esk6_2: ( ( $i > $i ) > $i > $o ) > ( ( $i > $i ) > $i > $o ) > $i > $i ).

thf(decl_29,type,
    esk7_0: $i > $i ).

thf(cTHM112D,conjecture,
    ! [X1: $i > $o] :
    ? [X2: ( $i > $i ) > $i > $o,X3: ( $i > $i ) > $i > $o] :
      ( ! [X4: $i] :
          ( ( X2
            @ ^ [X5: $i] : X5
            @ X4 )
          | ( X3
            @ ^ [X5: $i] : X5
            @ X4 ) )
      & ! [X6: $i > $i,X7: $i > $i] :
          ( ( ! [X4: $i] :
                ( ( X2 @ X6 @ X4 )
                | ( X3 @ X6 @ X4 ) )
            & ! [X4: $i] :
                ( ( X2 @ X6 @ X4 )
                | ( X3 @ X6 @ X4 ) )
            & ! [X4: $i] :
                ( ( X2 @ X7 @ X4 )
                | ( X3 @ X7 @ X4 ) ) )
         => ( ! [X4: $i] :
                ( ( X2
                  @ ^ [X5: $i] : ( X6 @ ( X7 @ X5 ) )
                  @ X4 )
                | ( X3
                  @ ^ [X5: $i] : ( X6 @ ( X7 @ X5 ) )
                  @ X4 ) )
            & ! [X8: $i] :
                ( ( X1 @ X8 )
               => ( X1 @ ( X6 @ X8 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM112D) ).

thf(c_0_1,negated_conjecture,
    ~ ! [X1: $i > $o] :
      ? [X2: ( $i > $i ) > $i > $o,X3: ( $i > $i ) > $i > $o] :
        ( ! [X4: $i] :
            ( ( X2
              @ ^ [Z0: $i] : Z0
              @ X4 )
            | ( X3
              @ ^ [Z0: $i] : Z0
              @ X4 ) )
        & ! [X6: $i > $i,X7: $i > $i] :
            ( ( ! [X4: $i] :
                  ( ( X2 @ X6 @ X4 )
                  | ( X3 @ X6 @ X4 ) )
              & ! [X4: $i] :
                  ( ( X2 @ X7 @ X4 )
                  | ( X3 @ X7 @ X4 ) ) )
           => ( ! [X4: $i] :
                  ( ( X2
                    @ ^ [Z0: $i] : ( X6 @ ( X7 @ Z0 ) )
                    @ X4 )
                  | ( X3
                    @ ^ [Z0: $i] : ( X6 @ ( X7 @ Z0 ) )
                    @ X4 ) )
              & ! [X8: $i] :
                  ( ( X1 @ X8 )
                 => ( X1 @ ( X6 @ X8 ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[cTHM112D])])]) ).

thf(c_0_2,negated_conjecture,
    ! [X21: ( $i > $i ) > $i > $o,X22: ( $i > $i ) > $i > $o,X26: $i,X27: $i] :
      ( ( ( X21 @ ( esk2_2 @ X21 @ X22 ) @ X26 )
        | ( X22 @ ( esk2_2 @ X21 @ X22 ) @ X26 )
        | ~ ( X21
            @ ^ [Z0: $i] : Z0
            @ ( esk1_2 @ X21 @ X22 ) ) )
      & ( ( X21 @ ( esk3_2 @ X21 @ X22 ) @ X27 )
        | ( X22 @ ( esk3_2 @ X21 @ X22 ) @ X27 )
        | ~ ( X21
            @ ^ [Z0: $i] : Z0
            @ ( esk1_2 @ X21 @ X22 ) ) )
      & ( ( epred1_0 @ ( esk5_2 @ X21 @ X22 ) )
        | ~ ( X21
            @ ^ [Z0: $i] : ( esk2_2 @ X21 @ X22 @ ( esk3_2 @ X21 @ X22 @ Z0 ) )
            @ ( esk4_2 @ X21 @ X22 ) )
        | ~ ( X21
            @ ^ [Z0: $i] : Z0
            @ ( esk1_2 @ X21 @ X22 ) ) )
      & ( ~ ( epred1_0 @ ( esk2_2 @ X21 @ X22 @ ( esk5_2 @ X21 @ X22 ) ) )
        | ~ ( X21
            @ ^ [Z0: $i] : ( esk2_2 @ X21 @ X22 @ ( esk3_2 @ X21 @ X22 @ Z0 ) )
            @ ( esk4_2 @ X21 @ X22 ) )
        | ~ ( X21
            @ ^ [Z0: $i] : Z0
            @ ( esk1_2 @ X21 @ X22 ) ) )
      & ( ( epred1_0 @ ( esk5_2 @ X21 @ X22 ) )
        | ~ ( X22
            @ ^ [Z0: $i] : ( esk2_2 @ X21 @ X22 @ ( esk3_2 @ X21 @ X22 @ Z0 ) )
            @ ( esk4_2 @ X21 @ X22 ) )
        | ~ ( X21
            @ ^ [Z0: $i] : Z0
            @ ( esk1_2 @ X21 @ X22 ) ) )
      & ( ~ ( epred1_0 @ ( esk2_2 @ X21 @ X22 @ ( esk5_2 @ X21 @ X22 ) ) )
        | ~ ( X22
            @ ^ [Z0: $i] : ( esk2_2 @ X21 @ X22 @ ( esk3_2 @ X21 @ X22 @ Z0 ) )
            @ ( esk4_2 @ X21 @ X22 ) )
        | ~ ( X21
            @ ^ [Z0: $i] : Z0
            @ ( esk1_2 @ X21 @ X22 ) ) )
      & ( ( X21 @ ( esk2_2 @ X21 @ X22 ) @ X26 )
        | ( X22 @ ( esk2_2 @ X21 @ X22 ) @ X26 )
        | ~ ( X22
            @ ^ [Z0: $i] : Z0
            @ ( esk1_2 @ X21 @ X22 ) ) )
      & ( ( X21 @ ( esk3_2 @ X21 @ X22 ) @ X27 )
        | ( X22 @ ( esk3_2 @ X21 @ X22 ) @ X27 )
        | ~ ( X22
            @ ^ [Z0: $i] : Z0
            @ ( esk1_2 @ X21 @ X22 ) ) )
      & ( ( epred1_0 @ ( esk5_2 @ X21 @ X22 ) )
        | ~ ( X21
            @ ^ [Z0: $i] : ( esk2_2 @ X21 @ X22 @ ( esk3_2 @ X21 @ X22 @ Z0 ) )
            @ ( esk4_2 @ X21 @ X22 ) )
        | ~ ( X22
            @ ^ [Z0: $i] : Z0
            @ ( esk1_2 @ X21 @ X22 ) ) )
      & ( ~ ( epred1_0 @ ( esk2_2 @ X21 @ X22 @ ( esk5_2 @ X21 @ X22 ) ) )
        | ~ ( X21
            @ ^ [Z0: $i] : ( esk2_2 @ X21 @ X22 @ ( esk3_2 @ X21 @ X22 @ Z0 ) )
            @ ( esk4_2 @ X21 @ X22 ) )
        | ~ ( X22
            @ ^ [Z0: $i] : Z0
            @ ( esk1_2 @ X21 @ X22 ) ) )
      & ( ( epred1_0 @ ( esk5_2 @ X21 @ X22 ) )
        | ~ ( X22
            @ ^ [Z0: $i] : ( esk2_2 @ X21 @ X22 @ ( esk3_2 @ X21 @ X22 @ Z0 ) )
            @ ( esk4_2 @ X21 @ X22 ) )
        | ~ ( X22
            @ ^ [Z0: $i] : Z0
            @ ( esk1_2 @ X21 @ X22 ) ) )
      & ( ~ ( epred1_0 @ ( esk2_2 @ X21 @ X22 @ ( esk5_2 @ X21 @ X22 ) ) )
        | ~ ( X22
            @ ^ [Z0: $i] : ( esk2_2 @ X21 @ X22 @ ( esk3_2 @ X21 @ X22 @ Z0 ) )
            @ ( esk4_2 @ X21 @ X22 ) )
        | ~ ( X22
            @ ^ [Z0: $i] : Z0
            @ ( esk1_2 @ X21 @ X22 ) ) ) ),
    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_1])])])])])]) ).

thf(c_0_3,plain,
    ! [X31: $i] :
      ( ( esk7_0 @ X31 )
      = X31 ),
    introduced(definition) ).

thf(c_0_4,negated_conjecture,
    ! [X2: ( $i > $i ) > $i > $o,X4: $i,X3: ( $i > $i ) > $i > $o] :
      ( ( X2 @ ( esk2_2 @ X2 @ X3 ) @ X4 )
      | ( X3 @ ( esk2_2 @ X2 @ X3 ) @ X4 )
      | ( ( X3 @ esk7_0 @ ( esk1_2 @ X2 @ X3 ) )
       != $true ) ),
    inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_2]),c_0_3]) ).

thf(c_0_5,negated_conjecture,
    ! [X2: ( $i > $i ) > $i > $o,X4: $i,X3: ( $i > $i ) > $i > $o] :
      ( ( X2 @ ( esk2_2 @ X2 @ X3 ) @ X4 )
      | ( X3 @ ( esk2_2 @ X2 @ X3 ) @ X4 )
      | ~ ( X3 @ esk7_0 @ ( esk1_2 @ X2 @ X3 ) ) ),
    inference(cn,[status(thm)],[c_0_4]) ).

thf(c_0_6,plain,
    ! [X53: $i] :
      ( ( esk7_0 @ X53 )
      = X53 ),
    inference(variable_rename,[status(thm)],]) ).

thf(c_0_7,plain,
    ! [X50: $i,X51: ( $i > $i ) > $i > $o,X52: ( $i > $i ) > $i > $o] :
      ( ( esk6_2 @ X52 @ X51 @ X50 )
      = ( esk2_2 @ X51 @ X52 @ ( esk3_2 @ X51 @ X52 @ X50 ) ) ),
    inference(variable_rename,[status(thm)],]) ).

thf(c_0_8,negated_conjecture,
    ! [X2: ( $i > $i ) > $i > $o,X4: $i] :
      ( ( ( esk2_2 @ X2
          @ ^ [Z0: $i > $i,Z1: $i] : ( Z0 = esk7_0 ) )
        = esk7_0 )
      | ( X2
        @ ( esk2_2 @ X2
          @ ^ [Z0: $i > $i,Z1: $i] : ( Z0 = esk7_0 ) )
        @ X4 ) ),
    inference(eliminate_leibniz_eq,[status(thm)],[inference(cn,[status(thm)],[]),c_0_5]) ).

thf(c_0_9,plain,
    ! [X4: $i] :
      ( ( esk7_0 @ X4 )
      = X4 ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

thf(c_0_10,negated_conjecture,
    ! [X2: ( $i > $i ) > $i > $o,X4: $i,X3: ( $i > $i ) > $i > $o] :
      ( ( X2 @ ( esk3_2 @ X2 @ X3 ) @ X4 )
      | ( X3 @ ( esk3_2 @ X2 @ X3 ) @ X4 )
      | ( ( X2 @ esk7_0 @ ( esk1_2 @ X2 @ X3 ) )
       != $true ) ),
    inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_2]),c_0_3]) ).

thf(c_0_11,plain,
    ! [X2: ( $i > $i ) > $i > $o,X3: ( $i > $i ) > $i > $o,X4: $i] :
      ( ( esk6_2 @ X2 @ X3 @ X4 )
      = ( esk2_2 @ X3 @ X2 @ ( esk3_2 @ X3 @ X2 @ X4 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

thf(c_0_12,negated_conjecture,
    ! [X2: ( $i > $i ) > $i > $o,X4: $i,X5: $i] :
      ( ( ( esk2_2 @ X2
          @ ^ [Z0: $i > $i,Z1: $i] : ( Z0 = esk7_0 )
          @ X4 )
        = X4 )
      | ( X2
        @ ( esk2_2 @ X2
          @ ^ [Z0: $i > $i,Z1: $i] : ( Z0 = esk7_0 ) )
        @ X5 ) ),
    inference(rw,[status(thm)],[inference(arg_cong,[status(thm)],[c_0_8]),c_0_9]) ).

thf(c_0_13,plain,
    ! [X30: $i,X2: ( $i > $i ) > $i > $o,X3: ( $i > $i ) > $i > $o] :
      ( ( esk6_2 @ X3 @ X2 @ X30 )
      = ( esk2_2 @ X2 @ X3 @ ( esk3_2 @ X2 @ X3 @ X30 ) ) ),
    introduced(definition) ).

thf(c_0_14,negated_conjecture,
    ! [X2: ( $i > $i ) > $i > $o,X4: $i,X3: ( $i > $i ) > $i > $o] :
      ( ( X2 @ ( esk3_2 @ X2 @ X3 ) @ X4 )
      | ( X3 @ ( esk3_2 @ X2 @ X3 ) @ X4 )
      | ~ ( X2 @ esk7_0 @ ( esk1_2 @ X2 @ X3 ) ) ),
    inference(cn,[status(thm)],[c_0_10]) ).

thf(c_0_15,plain,
    ! [X2: ( $i > $i ) > $i > $o,X4: $i,X5: $i] :
      ( ( ( esk3_2 @ X2
          @ ^ [Z0: $i > $i,Z1: $i] : ( Z0 = esk7_0 )
          @ X4 )
        = ( esk6_2
          @ ^ [Z0: $i > $i,Z1: $i] : ( Z0 = esk7_0 )
          @ X2
          @ X4 ) )
      | ( X2
        @ ( esk2_2 @ X2
          @ ^ [Z0: $i > $i,Z1: $i] : ( Z0 = esk7_0 ) )
        @ X5 ) ),
    inference(spm,[status(thm)],[c_0_11,c_0_12]) ).

thf(c_0_16,negated_conjecture,
    ! [X2: ( $i > $i ) > $i > $o,X3: ( $i > $i ) > $i > $o] :
      ( ~ ( epred1_0 @ ( esk2_2 @ X2 @ X3 @ ( esk5_2 @ X2 @ X3 ) ) )
      | ( ( X3 @ ( esk6_2 @ X3 @ X2 ) @ ( esk4_2 @ X2 @ X3 ) )
       != $true )
      | ( ( X3 @ esk7_0 @ ( esk1_2 @ X2 @ X3 ) )
       != $true ) ),
    inference(lift_lambdas,[status(thm)],[inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_2]),c_0_3]),c_0_13]) ).

thf(c_0_17,negated_conjecture,
    ! [X2: ( $i > $i ) > $i > $o,X3: ( $i > $i ) > $i > $o] :
      ( ( epred1_0 @ ( esk5_2 @ X2 @ X3 ) )
      | ( ( X3 @ ( esk6_2 @ X3 @ X2 ) @ ( esk4_2 @ X2 @ X3 ) )
       != $true )
      | ( ( X2 @ esk7_0 @ ( esk1_2 @ X2 @ X3 ) )
       != $true ) ),
    inference(lift_lambdas,[status(thm)],[inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_2]),c_0_3]),c_0_13]) ).

thf(c_0_18,negated_conjecture,
    ! [X2: ( $i > $i ) > $i > $o,X4: $i] :
      ( ( ( esk1_2
          @ ^ [Z0: $i > $i,Z1: $i] : ( Z1 != X4 )
          @ X2 )
        = X4 )
      | ( X2
        @ ( esk3_2
          @ ^ [Z0: $i > $i,Z1: $i] : ( Z1 != X4 )
          @ X2 )
        @ X4 ) ),
    inference(eliminate_leibniz_eq,[status(thm)],[inference(cn,[status(thm)],[]),c_0_14]) ).

thf(c_0_19,plain,
    ! [X2: ( $i > $i ) > $i > $o,X4: $i] :
      ( ( ( esk3_2 @ X2
          @ ^ [Z0: $i > $i,Z1: $i] : ( Z0 = esk7_0 ) )
        = ( esk6_2
          @ ^ [Z0: $i > $i,Z1: $i] : ( Z0 = esk7_0 )
          @ X2 ) )
      | ( X2
        @ ( esk2_2 @ X2
          @ ^ [Z0: $i > $i,Z1: $i] : ( Z0 = esk7_0 ) )
        @ X4 ) ),
    inference(pos_ext,[status(thm)],[c_0_15]) ).

thf(c_0_20,negated_conjecture,
    ! [X2: ( $i > $i ) > $i > $o,X3: ( $i > $i ) > $i > $o] :
      ( ~ ( epred1_0 @ ( esk2_2 @ X2 @ X3 @ ( esk5_2 @ X2 @ X3 ) ) )
      | ~ ( X3 @ ( esk6_2 @ X3 @ X2 ) @ ( esk4_2 @ X2 @ X3 ) )
      | ~ ( X3 @ esk7_0 @ ( esk1_2 @ X2 @ X3 ) ) ),
    inference(cn,[status(thm)],[c_0_16]) ).

thf(c_0_21,negated_conjecture,
    ! [X2: ( $i > $i ) > $i > $o,X3: ( $i > $i ) > $i > $o] :
      ( ( epred1_0 @ ( esk5_2 @ X2 @ X3 ) )
      | ~ ( X3 @ ( esk6_2 @ X3 @ X2 ) @ ( esk4_2 @ X2 @ X3 ) )
      | ~ ( X2 @ esk7_0 @ ( esk1_2 @ X2 @ X3 ) ) ),
    inference(cn,[status(thm)],[c_0_17]) ).

thf(c_0_22,negated_conjecture,
    ! [X4: $i] :
      ( ( ( esk6_2
          @ ^ [Z0: $i > $i,Z1: $i] : ( Z0 = esk7_0 )
          @ ^ [Z0: $i > $i,Z1: $i] : ( Z1 != X4 ) )
        = esk7_0 )
      | ( ( esk1_2
          @ ^ [Z0: $i > $i,Z1: $i] : ( Z1 != X4 )
          @ ^ [Z0: $i > $i,Z1: $i] : ( Z0 = esk7_0 ) )
        = X4 ) ),
    inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19])])]) ).

thf(c_0_23,negated_conjecture,
    ! [X2: ( $i > $i ) > $i > $o,X4: $i,X3: ( $i > $i ) > $i > $o] :
      ( ( X2 @ ( esk3_2 @ X2 @ X3 ) @ X4 )
      | ( X3 @ ( esk3_2 @ X2 @ X3 ) @ X4 )
      | ( ( X3 @ esk7_0 @ ( esk1_2 @ X2 @ X3 ) )
       != $true ) ),
    inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_2]),c_0_3]) ).

thf(c_0_24,negated_conjecture,
    ! [X4: $i,X2: ( $i > $i ) > $i > $o] :
      ( ( X2
        @ ( esk2_2 @ X2
          @ ^ [Z0: $i > $i,Z1: $i] : ( Z0 = esk7_0 ) )
        @ X4 )
      | ( ( esk6_2
          @ ^ [Z0: $i > $i,Z1: $i] : ( Z0 = esk7_0 )
          @ X2 )
       != esk7_0 )
      | ~ ( epred1_0
          @ ( esk5_2 @ X2
            @ ^ [Z0: $i > $i,Z1: $i] : ( Z0 = esk7_0 ) ) ) ),
    inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_12])])]) ).

thf(c_0_25,negated_conjecture,
    ! [X4: $i] :
      ( ( ( esk1_2
          @ ^ [Z0: $i > $i,Z1: $i] : ( Z1 != X4 )
          @ ^ [Z0: $i > $i,Z1: $i] : ( Z0 = esk7_0 ) )
        = X4 )
      | ( epred1_0
        @ ( esk5_2
          @ ^ [Z0: $i > $i,Z1: $i] : ( Z1 != X4 )
          @ ^ [Z0: $i > $i,Z1: $i] : ( Z0 = esk7_0 ) ) ) ),
    inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22])])]) ).

thf(c_0_26,negated_conjecture,
    ! [X2: ( $i > $i ) > $i > $o,X4: $i,X3: ( $i > $i ) > $i > $o] :
      ( ( X2 @ ( esk3_2 @ X2 @ X3 ) @ X4 )
      | ( X3 @ ( esk3_2 @ X2 @ X3 ) @ X4 )
      | ~ ( X3 @ esk7_0 @ ( esk1_2 @ X2 @ X3 ) ) ),
    inference(cn,[status(thm)],[c_0_23]) ).

thf(c_0_27,negated_conjecture,
    ! [X4: $i] :
      ( ( esk1_2
        @ ^ [Z0: $i > $i,Z1: $i] : ( Z1 != X4 )
        @ ^ [Z0: $i > $i,Z1: $i] : ( Z0 = esk7_0 ) )
      = X4 ),
    inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25])])]),c_0_22]) ).

thf(c_0_28,negated_conjecture,
    ! [X2: ( $i > $i ) > $i > $o,X3: ( $i > $i ) > $i > $o] :
      ( ( epred1_0 @ ( esk5_2 @ X2 @ X3 ) )
      | ( ( X3 @ ( esk6_2 @ X3 @ X2 ) @ ( esk4_2 @ X2 @ X3 ) )
       != $true )
      | ( ( X3 @ esk7_0 @ ( esk1_2 @ X2 @ X3 ) )
       != $true ) ),
    inference(lift_lambdas,[status(thm)],[inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_2]),c_0_3]),c_0_13]) ).

thf(c_0_29,negated_conjecture,
    ! [X4: $i] :
      ( ( esk3_2
        @ ^ [Z0: $i > $i,Z1: $i] : ( Z1 != X4 )
        @ ^ [Z0: $i > $i,Z1: $i] : ( Z0 = esk7_0 ) )
      = esk7_0 ),
    inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27])])])]) ).

thf(c_0_30,negated_conjecture,
    ! [X2: ( $i > $i ) > $i > $o,X3: ( $i > $i ) > $i > $o] :
      ( ( epred1_0 @ ( esk5_2 @ X2 @ X3 ) )
      | ~ ( X3 @ ( esk6_2 @ X3 @ X2 ) @ ( esk4_2 @ X2 @ X3 ) )
      | ~ ( X3 @ esk7_0 @ ( esk1_2 @ X2 @ X3 ) ) ),
    inference(cn,[status(thm)],[c_0_28]) ).

thf(c_0_31,plain,
    ! [X4: $i] :
      ( ( esk6_2
        @ ^ [Z0: $i > $i,Z1: $i] : ( Z0 = esk7_0 )
        @ ^ [Z0: $i > $i,Z1: $i] : ( Z1 != X4 ) )
      = esk7_0 ),
    inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_29])])]) ).

thf(c_0_32,negated_conjecture,
    ! [X4: $i] :
      ( epred1_0
      @ ( esk5_2
        @ ^ [Z0: $i > $i,Z1: $i] : ( Z1 != X4 )
        @ ^ [Z0: $i > $i,Z1: $i] : ( Z0 = esk7_0 ) ) ),
    inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31])])]) ).

thf(c_0_33,negated_conjecture,
    $false,
    inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_32])]),c_0_31])])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SYO269^5 : TPTP v8.2.0. Released v4.0.0.
% 0.03/0.13  % Command    : run_E %s %d THM
% 0.13/0.33  % Computer : n020.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Mon May 20 09:24:23 EDT 2024
% 0.13/0.34  % CPUTime    : 
% 0.19/0.46  Running higher-order theorem proving
% 0.19/0.46  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
% 0.19/0.49  # Version: 3.1.0-ho
% 0.19/0.49  # Preprocessing class: HSSSSMSSSSMNHHA.
% 0.19/0.49  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.49  # Starting post_as_ho5 with 1500s (5) cores
% 0.19/0.49  # Starting sh2lt with 300s (1) cores
% 0.19/0.49  # Starting ehoh_best8_lambda with 300s (1) cores
% 0.19/0.49  # Starting post_as_ho10 with 300s (1) cores
% 0.19/0.49  # sh2lt with pid 5182 completed with status 0
% 0.19/0.49  # Result found by sh2lt
% 0.19/0.49  # Preprocessing class: HSSSSMSSSSMNHHA.
% 0.19/0.49  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.49  # Starting post_as_ho5 with 1500s (5) cores
% 0.19/0.49  # Starting sh2lt with 300s (1) cores
% 0.19/0.49  # SinE strategy is GSinE(CountFormulas,hypos,5,,4,20000,1.0,true)
% 0.19/0.49  # Search class: HGHSS-FFMF22-SHHFFSBN
% 0.19/0.49  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.19/0.49  # Starting lpo8_lambda_fix with 163s (1) cores
% 0.19/0.49  # lpo8_lambda_fix with pid 5192 completed with status 0
% 0.19/0.49  # Result found by lpo8_lambda_fix
% 0.19/0.49  # Preprocessing class: HSSSSMSSSSMNHHA.
% 0.19/0.49  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.49  # Starting post_as_ho5 with 1500s (5) cores
% 0.19/0.49  # Starting sh2lt with 300s (1) cores
% 0.19/0.49  # SinE strategy is GSinE(CountFormulas,hypos,5,,4,20000,1.0,true)
% 0.19/0.49  # Search class: HGHSS-FFMF22-SHHFFSBN
% 0.19/0.49  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.19/0.49  # Starting lpo8_lambda_fix with 163s (1) cores
% 0.19/0.49  # Preprocessing time       : 0.001 s
% 0.19/0.49  # Presaturation interreduction done
% 0.19/0.49  
% 0.19/0.49  # Proof found!
% 0.19/0.49  # SZS status Theorem
% 0.19/0.49  # SZS output start CNFRefutation
% See solution above
% 0.19/0.49  # Parsed axioms                        : 1
% 0.19/0.49  # Removed by relevancy pruning/SinE    : 0
% 0.19/0.49  # Initial clauses                      : 14
% 0.19/0.49  # Removed in clause preprocessing      : 0
% 0.19/0.49  # Initial clauses in saturation        : 14
% 0.19/0.49  # Processed clauses                    : 89
% 0.19/0.49  # ...of these trivial                  : 1
% 0.19/0.49  # ...subsumed                          : 17
% 0.19/0.49  # ...remaining for further processing  : 71
% 0.19/0.49  # Other redundant clauses eliminated   : 26
% 0.19/0.49  # Clauses deleted for lack of memory   : 0
% 0.19/0.49  # Backward-subsumed                    : 0
% 0.19/0.49  # Backward-rewritten                   : 2
% 0.19/0.49  # Generated clauses                    : 164
% 0.19/0.49  # ...of the previous two non-redundant : 102
% 0.19/0.49  # ...aggressively subsumed             : 0
% 0.19/0.49  # Contextual simplify-reflections      : 1
% 0.19/0.49  # Paramodulations                      : 81
% 0.19/0.49  # Factorizations                       : 0
% 0.19/0.49  # NegExts                              : 12
% 0.19/0.49  # Equation resolutions                 : 31
% 0.19/0.49  # Disequality decompositions           : 0
% 0.19/0.49  # Total rewrite steps                  : 22
% 0.19/0.49  # ...of those cached                   : 5
% 0.19/0.49  # Propositional unsat checks           : 0
% 0.19/0.49  #    Propositional check models        : 0
% 0.19/0.49  #    Propositional check unsatisfiable : 0
% 0.19/0.49  #    Propositional clauses             : 0
% 0.19/0.49  #    Propositional clauses after purity: 0
% 0.19/0.49  #    Propositional unsat core size     : 0
% 0.19/0.49  #    Propositional preprocessing time  : 0.000
% 0.19/0.49  #    Propositional encoding time       : 0.000
% 0.19/0.49  #    Propositional solver time         : 0.000
% 0.19/0.49  #    Success case prop preproc time    : 0.000
% 0.19/0.49  #    Success case prop encoding time   : 0.000
% 0.19/0.49  #    Success case prop solver time     : 0.000
% 0.19/0.49  # Current number of processed clauses  : 51
% 0.19/0.49  #    Positive orientable unit clauses  : 7
% 0.19/0.49  #    Positive unorientable unit clauses: 0
% 0.19/0.49  #    Negative unit clauses             : 0
% 0.19/0.49  #    Non-unit-clauses                  : 44
% 0.19/0.49  # Current number of unprocessed clauses: 41
% 0.19/0.49  # ...number of literals in the above   : 110
% 0.19/0.49  # Current number of archived formulas  : 0
% 0.19/0.49  # Current number of archived clauses   : 20
% 0.19/0.49  # Clause-clause subsumption calls (NU) : 418
% 0.19/0.49  # Rec. Clause-clause subsumption calls : 301
% 0.19/0.49  # Non-unit clause-clause subsumptions  : 18
% 0.19/0.49  # Unit Clause-clause subsumption calls : 89
% 0.19/0.49  # Rewrite failures with RHS unbound    : 0
% 0.19/0.49  # BW rewrite match attempts            : 4
% 0.19/0.49  # BW rewrite match successes           : 1
% 0.19/0.49  # Condensation attempts                : 89
% 0.19/0.49  # Condensation successes               : 0
% 0.19/0.49  # Termbank termtop insertions          : 15560
% 0.19/0.49  # Search garbage collected termcells   : 347
% 0.19/0.49  
% 0.19/0.49  # -------------------------------------------------
% 0.19/0.49  # User time                : 0.015 s
% 0.19/0.49  # System time              : 0.003 s
% 0.19/0.49  # Total time               : 0.018 s
% 0.19/0.49  # Maximum resident set size: 1936 pages
% 0.19/0.49  
% 0.19/0.49  # -------------------------------------------------
% 0.19/0.49  # User time                : 0.016 s
% 0.19/0.49  # System time              : 0.005 s
% 0.19/0.49  # Total time               : 0.021 s
% 0.19/0.49  # Maximum resident set size: 1720 pages
% 0.19/0.49  % E---3.1 exiting
% 0.19/0.49  % E exiting
%------------------------------------------------------------------------------