TSTP Solution File: SYO330^5 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SYO330^5 : 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 08:45:38 EDT 2024

% Result   : Theorem 0.70s 0.58s
% Output   : CNFRefutation 0.70s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   61 (  15 unt;   8 typ;   0 def)
%            Number of atoms       :  167 (   0 equ;   0 cnn)
%            Maximal formula atoms :   26 (   3 avg)
%            Number of connectives :  694 ( 105   ~; 126   |;  43   &; 401   @)
%                                         (   4 <=>;  15  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   26 (   8 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   43 (  43   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   8 usr;   5 con; 0-2 aty)
%            Number of variables   :  111 (  18   ^  93   !;   0   ?; 111   :)

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

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

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

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

thf(decl_26,type,
    c0: $i ).

thf(decl_27,type,
    epred1_0: $o ).

thf(decl_28,type,
    esk1_0: $i ).

thf(decl_29,type,
    esk2_2: ( $i > $o ) > ( $i > $o ) > $i ).

thf(cEVEN_ODD_4,conjecture,
    ( ( ( cEVEN @ c0 )
      & ! [X1: $i] :
          ( ( cEVEN @ X1 )
         => ( cEVEN @ ( cS @ ( cS @ X1 ) ) ) )
      & ( cODD @ ( cS @ c0 ) )
      & ! [X1: $i] :
          ( ( cODD @ X1 )
         => ( cODD @ ( cS @ ( cS @ X1 ) ) ) )
      & ! [X2: $i > $o,X3: $i > $o] :
          ( ( ( X2 @ c0 )
            & ( X3 @ c0 )
            & ! [X4: $i] :
                ( ( ( X2 @ X4 )
                  & ( X3 @ X4 ) )
               => ( ( X2 @ ( cS @ X4 ) )
                  & ( X3 @ ( cS @ X4 ) ) ) ) )
         => ! [X4: $i] :
              ( ( X2 @ X4 )
              & ( X3 @ X4 ) ) )
      & ! [X1: $i] :
          ( ( cNUMBER @ X1 )
        <=> ( ( cEVEN @ X1 )
            | ( cODD @ X1 ) ) ) )
   => ! [X1: $i] : ( cNUMBER @ X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cEVEN_ODD_4) ).

thf(c_0_1,plain,
    ( epred1_0
  <=> ( ( cEVEN @ c0 )
      & ! [X1: $i] :
          ( ( cEVEN @ X1 )
         => ( cEVEN @ ( cS @ ( cS @ X1 ) ) ) )
      & ( cODD @ ( cS @ c0 ) )
      & ! [X1: $i] :
          ( ( cODD @ X1 )
         => ( cODD @ ( cS @ ( cS @ X1 ) ) ) )
      & ! [X2: $i > $o,X3: $i > $o] :
          ( ( ( X2 @ c0 )
            & ( X3 @ c0 )
            & ! [X4: $i] :
                ( ( ( X2 @ X4 )
                  & ( X3 @ X4 ) )
               => ( ( X2 @ ( cS @ X4 ) )
                  & ( X3 @ ( cS @ X4 ) ) ) ) )
         => ! [X4: $i] :
              ( ( X2 @ X4 )
              & ( X3 @ X4 ) ) )
      & ! [X1: $i] :
          ( ( cNUMBER @ X1 )
        <=> ( ( cEVEN @ X1 )
            | ( cODD @ X1 ) ) ) ) ),
    introduced(definition) ).

thf(c_0_2,plain,
    ( epred1_0
   => ( ( cEVEN @ c0 )
      & ! [X1: $i] :
          ( ( cEVEN @ X1 )
         => ( cEVEN @ ( cS @ ( cS @ X1 ) ) ) )
      & ( cODD @ ( cS @ c0 ) )
      & ! [X1: $i] :
          ( ( cODD @ X1 )
         => ( cODD @ ( cS @ ( cS @ X1 ) ) ) )
      & ! [X2: $i > $o,X3: $i > $o] :
          ( ( ( X2 @ c0 )
            & ( X3 @ c0 )
            & ! [X4: $i] :
                ( ( ( X2 @ X4 )
                  & ( X3 @ X4 ) )
               => ( ( X2 @ ( cS @ X4 ) )
                  & ( X3 @ ( cS @ X4 ) ) ) ) )
         => ! [X4: $i] :
              ( ( X2 @ X4 )
              & ( X3 @ X4 ) ) )
      & ! [X1: $i] :
          ( ( cNUMBER @ X1 )
        <=> ( ( cEVEN @ X1 )
            | ( cODD @ X1 ) ) ) ) ),
    inference(split_equiv,[status(thm)],[c_0_1]) ).

thf(c_0_3,negated_conjecture,
    ~ ( epred1_0
     => ! [X1: $i] : ( cNUMBER @ X1 ) ),
    inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[cEVEN_ODD_4]),c_0_1]) ).

thf(c_0_4,plain,
    ! [X14: $i,X15: $i,X16: $i > $o,X17: $i > $o,X19: $i,X20: $i,X21: $i] :
      ( ( ( cEVEN @ c0 )
        | ~ epred1_0 )
      & ( ~ ( cEVEN @ X14 )
        | ( cEVEN @ ( cS @ ( cS @ X14 ) ) )
        | ~ epred1_0 )
      & ( ( cODD @ ( cS @ c0 ) )
        | ~ epred1_0 )
      & ( ~ ( cODD @ X15 )
        | ( cODD @ ( cS @ ( cS @ X15 ) ) )
        | ~ epred1_0 )
      & ( ( X16 @ X19 )
        | ( X16 @ ( esk2_2 @ X16 @ X17 ) )
        | ~ ( X16 @ c0 )
        | ~ ( X17 @ c0 )
        | ~ epred1_0 )
      & ( ( X17 @ X20 )
        | ( X16 @ ( esk2_2 @ X16 @ X17 ) )
        | ~ ( X16 @ c0 )
        | ~ ( X17 @ c0 )
        | ~ epred1_0 )
      & ( ( X16 @ X19 )
        | ( X17 @ ( esk2_2 @ X16 @ X17 ) )
        | ~ ( X16 @ c0 )
        | ~ ( X17 @ c0 )
        | ~ epred1_0 )
      & ( ( X17 @ X20 )
        | ( X17 @ ( esk2_2 @ X16 @ X17 ) )
        | ~ ( X16 @ c0 )
        | ~ ( X17 @ c0 )
        | ~ epred1_0 )
      & ( ( X16 @ X19 )
        | ~ ( X16 @ ( cS @ ( esk2_2 @ X16 @ X17 ) ) )
        | ~ ( X17 @ ( cS @ ( esk2_2 @ X16 @ X17 ) ) )
        | ~ ( X16 @ c0 )
        | ~ ( X17 @ c0 )
        | ~ epred1_0 )
      & ( ( X17 @ X20 )
        | ~ ( X16 @ ( cS @ ( esk2_2 @ X16 @ X17 ) ) )
        | ~ ( X17 @ ( cS @ ( esk2_2 @ X16 @ X17 ) ) )
        | ~ ( X16 @ c0 )
        | ~ ( X17 @ c0 )
        | ~ epred1_0 )
      & ( ~ ( cNUMBER @ X21 )
        | ( cEVEN @ X21 )
        | ( cODD @ X21 )
        | ~ epred1_0 )
      & ( ~ ( cEVEN @ X21 )
        | ( cNUMBER @ X21 )
        | ~ epred1_0 )
      & ( ~ ( cODD @ X21 )
        | ( cNUMBER @ X21 )
        | ~ epred1_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(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2])])])])])])]) ).

thf(c_0_5,negated_conjecture,
    ( epred1_0
    & ~ ( cNUMBER @ esk1_0 ) ),
    inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])])]) ).

thf(c_0_6,plain,
    ! [X1: $i,X3: $i > $o,X2: $i > $o] :
      ( ( X2 @ X1 )
      | ( X2 @ ( esk2_2 @ X3 @ X2 ) )
      | ~ ( X3 @ c0 )
      | ~ ( X2 @ c0 )
      | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

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

thf(c_0_8,plain,
    ! [X1: $i] :
      ( ( cNUMBER @ X1 )
      | ~ ( cEVEN @ X1 )
      | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

thf(c_0_9,plain,
    ! [X1: $i,X3: $i > $o,X2: $i > $o] :
      ( ( X2 @ ( esk2_2 @ X3 @ X2 ) )
      | ( X2 @ X1 )
      | ~ ( X3 @ c0 )
      | ~ ( X2 @ c0 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_6,c_0_7])]) ).

thf(c_0_10,plain,
    ! [X1: $i] :
      ( ( cNUMBER @ X1 )
      | ~ ( cEVEN @ X1 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_8,c_0_7])]) ).

thf(c_0_11,plain,
    ( ( cEVEN @ c0 )
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

thf(c_0_12,plain,
    ! [X1: $i,X3: $i > $o,X2: $i > $o] :
      ( ( X2 @ X1 )
      | ( X3 @ ( esk2_2 @ X3 @ X2 ) )
      | ~ ( X3 @ c0 )
      | ~ ( X2 @ c0 )
      | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

thf(c_0_13,plain,
    ! [X1: $i] :
      ( ( cNUMBER @ X1 )
      | ~ ( cODD @ X1 )
      | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

thf(c_0_14,plain,
    ! [X1: $i,X22: $i > $i,X2: $i > $o] :
      ( ( X2
        @ ( esk2_2
          @ ^ [Z0: $i] : ( cNUMBER @ ( X22 @ Z0 ) )
          @ X2 ) )
      | ( X2 @ X1 )
      | ~ ( cEVEN @ ( X22 @ c0 ) )
      | ~ ( X2 @ c0 ) ),
    inference(spm,[status(thm)],[c_0_9,c_0_10]) ).

thf(c_0_15,plain,
    cEVEN @ c0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_7])]) ).

thf(c_0_16,plain,
    ! [X1: $i,X2: $i > $o,X3: $i > $o] :
      ( ( X2 @ ( esk2_2 @ X2 @ X3 ) )
      | ( X3 @ X1 )
      | ~ ( X2 @ c0 )
      | ~ ( X3 @ c0 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_7])]) ).

thf(c_0_17,plain,
    ! [X1: $i] :
      ( ( cNUMBER @ X1 )
      | ~ ( cODD @ X1 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_7])]) ).

thf(c_0_18,plain,
    ( ( cODD @ ( cS @ c0 ) )
    | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

thf(c_0_19,plain,
    ! [X1: $i,X2: $i > $o] :
      ( ( X2 @ ( esk2_2 @ cNUMBER @ X2 ) )
      | ( X2 @ X1 )
      | ~ ( X2 @ c0 ) ),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

thf(c_0_20,plain,
    ! [X1: $i,X22: $i > $i,X2: $i > $o] :
      ( ( cNUMBER
        @ ( X22
          @ ( esk2_2
            @ ^ [Z0: $i] : ( cNUMBER @ ( X22 @ Z0 ) )
            @ X2 ) ) )
      | ( X2 @ X1 )
      | ~ ( cODD @ ( X22 @ c0 ) )
      | ~ ( X2 @ c0 ) ),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

thf(c_0_21,plain,
    cODD @ ( cS @ c0 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_7])]) ).

thf(c_0_22,plain,
    ! [X1: $i,X22: $i > $i] :
      ( ( cNUMBER
        @ ( X22
          @ ( esk2_2 @ cNUMBER
            @ ^ [Z0: $i] : ( cNUMBER @ ( X22 @ Z0 ) ) ) ) )
      | ( cNUMBER @ ( X22 @ X1 ) )
      | ~ ( cEVEN @ ( X22 @ c0 ) ) ),
    inference(spm,[status(thm)],[c_0_19,c_0_10]) ).

thf(c_0_23,plain,
    ! [X1: $i,X2: $i > $o] :
      ( ( cNUMBER
        @ ( cS
          @ ( esk2_2
            @ ^ [Z0: $i] : ( cNUMBER @ ( cS @ Z0 ) )
            @ X2 ) ) )
      | ( X2 @ X1 )
      | ~ ( X2 @ c0 ) ),
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

thf(c_0_24,plain,
    cNUMBER @ c0,
    inference(spm,[status(thm)],[c_0_22,c_0_15]) ).

thf(c_0_25,plain,
    ! [X1: $i,X2: $i > $o,X3: $i > $o] :
      ( ( X2 @ X1 )
      | ~ ( X2 @ ( cS @ ( esk2_2 @ X2 @ X3 ) ) )
      | ~ ( X3 @ ( cS @ ( esk2_2 @ X2 @ X3 ) ) )
      | ~ ( X2 @ c0 )
      | ~ ( X3 @ c0 )
      | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

thf(c_0_26,plain,
    ! [X1: $i] :
      ( ( cNUMBER
        @ ( cS
          @ ( esk2_2
            @ ^ [Z0: $i] : ( cNUMBER @ ( cS @ Z0 ) )
            @ cNUMBER ) ) )
      | ( cNUMBER @ X1 ) ),
    inference(spm,[status(thm)],[c_0_23,c_0_24]) ).

thf(c_0_27,plain,
    ! [X1: $i,X22: $i > $i,X2: $i > $o] :
      ( ( X2
        @ ( esk2_2
          @ ^ [Z0: $i] : ( cNUMBER @ ( X22 @ Z0 ) )
          @ X2 ) )
      | ( X2 @ X1 )
      | ~ ( cODD @ ( X22 @ c0 ) )
      | ~ ( X2 @ c0 ) ),
    inference(spm,[status(thm)],[c_0_9,c_0_17]) ).

thf(c_0_28,plain,
    ! [X1: $i,X3: $i > $o,X2: $i > $o] :
      ( ( X2 @ X1 )
      | ~ ( X3 @ ( cS @ ( esk2_2 @ X2 @ X3 ) ) )
      | ~ ( X2 @ ( cS @ ( esk2_2 @ X2 @ X3 ) ) )
      | ~ ( X3 @ c0 )
      | ~ ( X2 @ c0 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_7])]) ).

thf(c_0_29,plain,
    ( cNUMBER
    @ ( cS
      @ ( esk2_2
        @ ^ [Z0: $i] : ( cNUMBER @ ( cS @ Z0 ) )
        @ cNUMBER ) ) ),
    inference(ef,[status(thm)],[c_0_26]) ).

thf(c_0_30,plain,
    ! [X1: $i,X2: $i > $o] :
      ( ( X2
        @ ( esk2_2
          @ ^ [Z0: $i] : ( cNUMBER @ ( cS @ Z0 ) )
          @ X2 ) )
      | ( X2 @ X1 )
      | ~ ( X2 @ c0 ) ),
    inference(spm,[status(thm)],[c_0_27,c_0_21]) ).

thf(c_0_31,plain,
    ! [X1: $i] :
      ( ( cNUMBER @ ( cS @ X1 ) )
      | ~ ( cNUMBER
          @ ( cS
            @ ( cS
              @ ( esk2_2
                @ ^ [Z0: $i] : ( cNUMBER @ ( cS @ Z0 ) )
                @ cNUMBER ) ) ) )
      | ~ ( cNUMBER @ ( cS @ c0 ) ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_24])]) ).

thf(c_0_32,plain,
    ! [X1: $i] :
      ( ( cODD @ ( cS @ ( cS @ X1 ) ) )
      | ~ ( cODD @ X1 )
      | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

thf(c_0_33,plain,
    ! [X1: $i] :
      ( ( cEVEN @ X1 )
      | ( cODD @ X1 )
      | ~ ( cNUMBER @ X1 )
      | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

thf(c_0_34,plain,
    ! [X1: $i] :
      ( ( cNUMBER
        @ ( esk2_2
          @ ^ [Z0: $i] : ( cNUMBER @ ( cS @ Z0 ) )
          @ cNUMBER ) )
      | ( cNUMBER @ X1 ) ),
    inference(spm,[status(thm)],[c_0_30,c_0_24]) ).

thf(c_0_35,plain,
    ! [X1: $i] :
      ( ( cEVEN @ ( cS @ ( cS @ X1 ) ) )
      | ~ ( cEVEN @ X1 )
      | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

thf(c_0_36,plain,
    ! [X1: $i] :
      ( ( cNUMBER @ ( cS @ X1 ) )
      | ~ ( cODD
          @ ( cS
            @ ( cS
              @ ( esk2_2
                @ ^ [Z0: $i] : ( cNUMBER @ ( cS @ Z0 ) )
                @ cNUMBER ) ) ) )
      | ~ ( cNUMBER @ ( cS @ c0 ) ) ),
    inference(spm,[status(thm)],[c_0_31,c_0_17]) ).

thf(c_0_37,plain,
    ! [X1: $i] :
      ( ( cODD @ ( cS @ ( cS @ X1 ) ) )
      | ~ ( cODD @ X1 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_7])]) ).

thf(c_0_38,plain,
    ! [X1: $i] :
      ( ( cEVEN @ X1 )
      | ( cODD @ X1 )
      | ~ ( cNUMBER @ X1 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_7])]) ).

thf(c_0_39,plain,
    ( cNUMBER
    @ ( esk2_2
      @ ^ [Z0: $i] : ( cNUMBER @ ( cS @ Z0 ) )
      @ cNUMBER ) ),
    inference(ef,[status(thm)],[c_0_34]) ).

thf(c_0_40,plain,
    ! [X1: $i] :
      ( ( cNUMBER @ ( cS @ X1 ) )
      | ~ ( cEVEN
          @ ( cS
            @ ( cS
              @ ( esk2_2
                @ ^ [Z0: $i] : ( cNUMBER @ ( cS @ Z0 ) )
                @ cNUMBER ) ) ) )
      | ~ ( cNUMBER @ ( cS @ c0 ) ) ),
    inference(spm,[status(thm)],[c_0_31,c_0_10]) ).

thf(c_0_41,plain,
    ! [X1: $i] :
      ( ( cEVEN @ ( cS @ ( cS @ X1 ) ) )
      | ~ ( cEVEN @ X1 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_7])]) ).

thf(c_0_42,plain,
    ! [X1: $i,X3: $i > $o,X2: $i > $o] :
      ( ( X2 @ X1 )
      | ~ ( X3 @ ( cS @ ( esk2_2 @ X3 @ X2 ) ) )
      | ~ ( X2 @ ( cS @ ( esk2_2 @ X3 @ X2 ) ) )
      | ~ ( X3 @ c0 )
      | ~ ( X2 @ c0 )
      | ~ epred1_0 ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

thf(c_0_43,plain,
    ! [X1: $i] :
      ( ( cNUMBER @ ( cS @ X1 ) )
      | ~ ( cODD
          @ ( esk2_2
            @ ^ [Z0: $i] : ( cNUMBER @ ( cS @ Z0 ) )
            @ cNUMBER ) )
      | ~ ( cNUMBER @ ( cS @ c0 ) ) ),
    inference(spm,[status(thm)],[c_0_36,c_0_37]) ).

thf(c_0_44,plain,
    ( ( cEVEN
      @ ( esk2_2
        @ ^ [Z0: $i] : ( cNUMBER @ ( cS @ Z0 ) )
        @ cNUMBER ) )
    | ( cODD
      @ ( esk2_2
        @ ^ [Z0: $i] : ( cNUMBER @ ( cS @ Z0 ) )
        @ cNUMBER ) ) ),
    inference(spm,[status(thm)],[c_0_38,c_0_39]) ).

thf(c_0_45,plain,
    ! [X1: $i] :
      ( ( cNUMBER @ ( cS @ X1 ) )
      | ~ ( cEVEN
          @ ( esk2_2
            @ ^ [Z0: $i] : ( cNUMBER @ ( cS @ Z0 ) )
            @ cNUMBER ) )
      | ~ ( cNUMBER @ ( cS @ c0 ) ) ),
    inference(spm,[status(thm)],[c_0_40,c_0_41]) ).

thf(c_0_46,plain,
    ! [X1: $i,X3: $i > $o,X2: $i > $o] :
      ( ( X2 @ X1 )
      | ~ ( X3 @ ( cS @ ( esk2_2 @ X3 @ X2 ) ) )
      | ~ ( X2 @ ( cS @ ( esk2_2 @ X3 @ X2 ) ) )
      | ~ ( X3 @ c0 )
      | ~ ( X2 @ c0 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_7])]) ).

thf(c_0_47,plain,
    ! [X1: $i] :
      ( ( cNUMBER @ ( cS @ X1 ) )
      | ~ ( cNUMBER @ ( cS @ c0 ) ) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]) ).

thf(c_0_48,plain,
    ! [X1: $i,X2: $i > $o] :
      ( ( X2 @ X1 )
      | ~ ( X2
          @ ( cS
            @ ( esk2_2
              @ ^ [Z0: $i] : $true
              @ X2 ) ) )
      | ~ ( X2 @ c0 ) ),
    inference(primitive_enumeration,[status(thm)],[c_0_46]) ).

thf(c_0_49,plain,
    ! [X1: $i] : ( cNUMBER @ ( cS @ X1 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_17]),c_0_21])]) ).

thf(c_0_50,negated_conjecture,
    ~ ( cNUMBER @ esk1_0 ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

thf(c_0_51,plain,
    ! [X1: $i] : ( cNUMBER @ X1 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_24])]) ).

thf(c_0_52,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_51])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14  % Problem    : SYO330^5 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.15  % Command    : run_E %s %d THM
% 0.16/0.36  % Computer : n028.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit   : 300
% 0.16/0.36  % WCLimit    : 300
% 0.16/0.36  % DateTime   : Mon May 20 09:05:22 EDT 2024
% 0.16/0.36  % CPUTime    : 
% 0.22/0.46  Running higher-order theorem proving
% 0.22/0.46  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
% 0.70/0.58  # Version: 3.1.0-ho
% 0.70/0.58  # Preprocessing class: HSMSSMSSSSSNSSA.
% 0.70/0.58  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.70/0.58  # Starting post_as_ho1 with 1500s (5) cores
% 0.70/0.58  # Starting post_as_ho12 with 300s (1) cores
% 0.70/0.58  # Starting new_ho_3 with 300s (1) cores
% 0.70/0.58  # Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.70/0.58  # post_as_ho12 with pid 27851 completed with status 0
% 0.70/0.58  # Result found by post_as_ho12
% 0.70/0.58  # Preprocessing class: HSMSSMSSSSSNSSA.
% 0.70/0.58  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.70/0.58  # Starting post_as_ho1 with 1500s (5) cores
% 0.70/0.58  # Starting post_as_ho12 with 300s (1) cores
% 0.70/0.58  # No SInE strategy applied
% 0.70/0.58  # Search class: HGUNF-FFSF21-SSSFFSBN
% 0.70/0.58  # partial match(1): HGUSF-FFSF21-SSSFFSBN
% 0.70/0.58  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.70/0.58  # Starting post_as_ho12 with 181s (1) cores
% 0.70/0.58  # post_as_ho12 with pid 27855 completed with status 0
% 0.70/0.58  # Result found by post_as_ho12
% 0.70/0.58  # Preprocessing class: HSMSSMSSSSSNSSA.
% 0.70/0.58  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.70/0.58  # Starting post_as_ho1 with 1500s (5) cores
% 0.70/0.58  # Starting post_as_ho12 with 300s (1) cores
% 0.70/0.58  # No SInE strategy applied
% 0.70/0.58  # Search class: HGUNF-FFSF21-SSSFFSBN
% 0.70/0.58  # partial match(1): HGUSF-FFSF21-SSSFFSBN
% 0.70/0.58  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.70/0.58  # Starting post_as_ho12 with 181s (1) cores
% 0.70/0.58  # Preprocessing time       : 0.001 s
% 0.70/0.58  # Presaturation interreduction done
% 0.70/0.58  
% 0.70/0.58  # Proof found!
% 0.70/0.58  # SZS status Theorem
% 0.70/0.58  # SZS output start CNFRefutation
% See solution above
% 0.70/0.58  # Parsed axioms                        : 6
% 0.70/0.58  # Removed by relevancy pruning/SinE    : 0
% 0.70/0.58  # Initial clauses                      : 20
% 0.70/0.58  # Removed in clause preprocessing      : 5
% 0.70/0.58  # Initial clauses in saturation        : 15
% 0.70/0.58  # Processed clauses                    : 416
% 0.70/0.58  # ...of these trivial                  : 9
% 0.70/0.58  # ...subsumed                          : 119
% 0.70/0.58  # ...remaining for further processing  : 288
% 0.70/0.58  # Other redundant clauses eliminated   : 48
% 0.70/0.58  # Clauses deleted for lack of memory   : 0
% 0.70/0.58  # Backward-subsumed                    : 79
% 0.70/0.58  # Backward-rewritten                   : 100
% 0.70/0.58  # Generated clauses                    : 3377
% 0.70/0.58  # ...of the previous two non-redundant : 2655
% 0.70/0.58  # ...aggressively subsumed             : 0
% 0.70/0.58  # Contextual simplify-reflections      : 4
% 0.70/0.58  # Paramodulations                      : 3105
% 0.70/0.58  # Factorizations                       : 78
% 0.70/0.58  # NegExts                              : 0
% 0.70/0.58  # Equation resolutions                 : 141
% 0.70/0.58  # Disequality decompositions           : 0
% 0.70/0.58  # Total rewrite steps                  : 839
% 0.70/0.58  # ...of those cached                   : 750
% 0.70/0.58  # Propositional unsat checks           : 0
% 0.70/0.58  #    Propositional check models        : 0
% 0.70/0.58  #    Propositional check unsatisfiable : 0
% 0.70/0.58  #    Propositional clauses             : 0
% 0.70/0.58  #    Propositional clauses after purity: 0
% 0.70/0.58  #    Propositional unsat core size     : 0
% 0.70/0.58  #    Propositional preprocessing time  : 0.000
% 0.70/0.58  #    Propositional encoding time       : 0.000
% 0.70/0.58  #    Propositional solver time         : 0.000
% 0.70/0.58  #    Success case prop preproc time    : 0.000
% 0.70/0.58  #    Success case prop encoding time   : 0.000
% 0.70/0.58  #    Success case prop solver time     : 0.000
% 0.70/0.58  # Current number of processed clauses  : 94
% 0.70/0.58  #    Positive orientable unit clauses  : 18
% 0.70/0.58  #    Positive unorientable unit clauses: 0
% 0.70/0.58  #    Negative unit clauses             : 2
% 0.70/0.58  #    Non-unit-clauses                  : 74
% 0.70/0.58  # Current number of unprocessed clauses: 1573
% 0.70/0.58  # ...number of literals in the above   : 5608
% 0.70/0.58  # Current number of archived formulas  : 0
% 0.70/0.58  # Current number of archived clauses   : 194
% 0.70/0.58  # Clause-clause subsumption calls (NU) : 2837
% 0.70/0.58  # Rec. Clause-clause subsumption calls : 2294
% 0.70/0.58  # Non-unit clause-clause subsumptions  : 160
% 0.70/0.58  # Unit Clause-clause subsumption calls : 163
% 0.70/0.58  # Rewrite failures with RHS unbound    : 0
% 0.70/0.58  # BW rewrite match attempts            : 149
% 0.70/0.58  # BW rewrite match successes           : 86
% 0.70/0.58  # Condensation attempts                : 0
% 0.70/0.58  # Condensation successes               : 0
% 0.70/0.58  # Termbank termtop insertions          : 270309
% 0.70/0.58  # Search garbage collected termcells   : 316
% 0.70/0.58  
% 0.70/0.58  # -------------------------------------------------
% 0.70/0.58  # User time                : 0.097 s
% 0.70/0.58  # System time              : 0.009 s
% 0.70/0.58  # Total time               : 0.106 s
% 0.70/0.58  # Maximum resident set size: 1720 pages
% 0.70/0.58  
% 0.70/0.58  # -------------------------------------------------
% 0.70/0.58  # User time                : 0.097 s
% 0.70/0.58  # System time              : 0.012 s
% 0.70/0.58  # Total time               : 0.109 s
% 0.70/0.58  # Maximum resident set size: 1708 pages
% 0.70/0.58  % E---3.1 exiting
% 0.70/0.59  % E exiting
%------------------------------------------------------------------------------