TSTP Solution File: SWV019-1 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SWV019-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n016.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  : 600s
% DateTime : Wed Jul 20 19:53:13 EDT 2022

% Result   : Unsatisfiable 0.19s 0.39s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   21
% Syntax   : Number of formulae    :   81 (  45 unt;  10 typ;   0 def)
%            Number of atoms       :  427 ( 131 equ;   0 cnn)
%            Maximal formula atoms :    7 (   6 avg)
%            Number of connectives :  674 (  78   ~; 132   |;   0   &; 464   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    7 (   7   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   13 (  10 usr;   8 con; 0-2 aty)
%            Number of variables   :   58 (   0   ^  58   !;   0   ?;  58   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_an_index,type,
    an_index: $i ).

thf(tp_array,type,
    array: $i ).

thf(tp_array_value_at,type,
    array_value_at: $i > $i > $i ).

thf(tp_in_array_bounds,type,
    in_array_bounds: $i > $i > $o ).

thf(tp_index_of_maximal,type,
    index_of_maximal: $i ).

thf(tp_less_than,type,
    less_than: $i > $i > $o ).

thf(tp_lower_bound,type,
    lower_bound: $i ).

thf(tp_maximal_value,type,
    maximal_value: $i ).

thf(tp_successor,type,
    successor: $i > $i ).

thf(tp_upper_bound,type,
    upper_bound: $i ).

thf(1,axiom,
    ~ ( less_than @ index_of_maximal @ lower_bound ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',maximal_above_lower_bound) ).

thf(2,axiom,
    ~ ( less_than @ upper_bound @ an_index ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',somewhere_below_upper_bound) ).

thf(3,axiom,
    ~ ( less_than @ an_index @ lower_bound ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',somewhere_above_lower_bound) ).

thf(4,axiom,
    less_than @ index_of_maximal @ an_index,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',maximal_before_somewhere) ).

thf(5,axiom,
    ( ~ ( in_array_bounds @ array @ index_of_maximal )
    | ( maximal_value
      = ( array_value_at @ array @ index_of_maximal ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',this_is_maximal) ).

thf(6,axiom,
    ! [X: $i] : ( less_than @ X @ ( successor @ X ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_greater) ).

thf(7,axiom,
    ! [X: $i,Y: $i,Z: $i] :
      ( ~ ( less_than @ X @ Y )
      | ~ ( less_than @ Y @ Z )
      | ( less_than @ X @ Z ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_less) ).

thf(8,axiom,
    ! [X: $i,Y: $i] :
      ( ~ ( less_than @ ( successor @ X ) @ ( successor @ Y ) )
      | ( less_than @ X @ Y ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',predecessor_less) ).

thf(9,axiom,
    ! [X1: $i] :
      ( ( less_than @ X1 @ lower_bound )
      | ( less_than @ upper_bound @ X1 )
      | ( in_array_bounds @ array @ X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',in_bounds) ).

thf(10,conjecture,
    $false,
    file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).

thf(11,negated_conjecture,
    $false = $false,
    inference(negate_conjecture,[status(cth)],[10]) ).

thf(12,negated_conjecture,
    ( ~ ( in_array_bounds @ array @ an_index )
    | ( less_than @ ( successor @ an_index ) @ lower_bound )
    | ( less_than @ ( successor @ upper_bound ) @ ( successor @ an_index ) )
    | ( less_than @ index_of_maximal @ lower_bound )
    | ~ ( less_than @ index_of_maximal @ ( successor @ an_index ) )
    | ~ ( in_array_bounds @ array @ index_of_maximal )
    | ( maximal_value
     != ( array_value_at @ array @ index_of_maximal ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).

thf(13,plain,
    $false = $false,
    inference(unfold_def,[status(thm)],[11]) ).

thf(14,plain,
    ( ( ~ ( less_than @ index_of_maximal @ lower_bound ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(15,plain,
    ( ( ~ ( less_than @ upper_bound @ an_index ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(16,plain,
    ( ( ~ ( less_than @ an_index @ lower_bound ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3]) ).

thf(17,plain,
    ( ( less_than @ index_of_maximal @ an_index )
    = $true ),
    inference(unfold_def,[status(thm)],[4]) ).

thf(18,plain,
    ( ( ~ ( in_array_bounds @ array @ index_of_maximal )
      | ( maximal_value
        = ( array_value_at @ array @ index_of_maximal ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5]) ).

thf(19,plain,
    ( ( ! [X: $i] : ( less_than @ X @ ( successor @ X ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6]) ).

thf(20,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ~ ( less_than @ X @ Y )
          | ~ ( less_than @ Y @ Z )
          | ( less_than @ X @ Z ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7]) ).

thf(21,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( less_than @ ( successor @ X ) @ ( successor @ Y ) )
          | ( less_than @ X @ Y ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8]) ).

thf(22,plain,
    ( ( ! [X1: $i] :
          ( ( less_than @ X1 @ lower_bound )
          | ( less_than @ upper_bound @ X1 )
          | ( in_array_bounds @ array @ X1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9]) ).

thf(23,plain,
    ( ( ~ ( in_array_bounds @ array @ an_index )
      | ( less_than @ ( successor @ an_index ) @ lower_bound )
      | ( less_than @ ( successor @ upper_bound ) @ ( successor @ an_index ) )
      | ( less_than @ index_of_maximal @ lower_bound )
      | ~ ( less_than @ index_of_maximal @ ( successor @ an_index ) )
      | ~ ( in_array_bounds @ array @ index_of_maximal )
      | ( maximal_value
       != ( array_value_at @ array @ index_of_maximal ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[12]) ).

thf(24,plain,
    ( ( ~ $false )
    = $true ),
    inference(polarity_switch,[status(thm)],[13]) ).

thf(25,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( less_than @ X @ Y )
          | ! [Z: $i] :
              ( ~ ( less_than @ Y @ Z )
              | ( less_than @ X @ Z ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[20]) ).

thf(26,plain,
    ( ( ! [X1: $i] :
          ( ( less_than @ X1 @ lower_bound )
          | ( in_array_bounds @ array @ X1 )
          | ( less_than @ upper_bound @ X1 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[22]) ).

thf(27,plain,
    ( ( ~ ( in_array_bounds @ array @ an_index )
      | ( less_than @ ( successor @ an_index ) @ lower_bound )
      | ( less_than @ ( successor @ upper_bound ) @ ( successor @ an_index ) )
      | ( less_than @ index_of_maximal @ lower_bound )
      | ~ ( less_than @ index_of_maximal @ ( successor @ an_index ) )
      | ~ ( in_array_bounds @ array @ index_of_maximal )
      | ( maximal_value
       != ( array_value_at @ array @ index_of_maximal ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[23]) ).

thf(28,plain,
    ( ( ~ ( in_array_bounds @ array @ an_index )
      | ( less_than @ ( successor @ an_index ) @ lower_bound )
      | ( less_than @ ( successor @ upper_bound ) @ ( successor @ an_index ) )
      | ( less_than @ index_of_maximal @ lower_bound )
      | ~ ( less_than @ index_of_maximal @ ( successor @ an_index ) )
      | ~ ( in_array_bounds @ array @ index_of_maximal )
      | ( maximal_value
       != ( array_value_at @ array @ index_of_maximal ) ) )
    = $true ),
    inference(copy,[status(thm)],[27]) ).

thf(29,plain,
    ( ( ! [X1: $i] :
          ( ( less_than @ X1 @ lower_bound )
          | ( in_array_bounds @ array @ X1 )
          | ( less_than @ upper_bound @ X1 ) ) )
    = $true ),
    inference(copy,[status(thm)],[26]) ).

thf(30,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( less_than @ ( successor @ X ) @ ( successor @ Y ) )
          | ( less_than @ X @ Y ) ) )
    = $true ),
    inference(copy,[status(thm)],[21]) ).

thf(31,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( less_than @ X @ Y )
          | ! [Z: $i] :
              ( ~ ( less_than @ Y @ Z )
              | ( less_than @ X @ Z ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[25]) ).

thf(32,plain,
    ( ( ! [X: $i] : ( less_than @ X @ ( successor @ X ) ) )
    = $true ),
    inference(copy,[status(thm)],[19]) ).

thf(33,plain,
    ( ( ~ ( in_array_bounds @ array @ index_of_maximal )
      | ( maximal_value
        = ( array_value_at @ array @ index_of_maximal ) ) )
    = $true ),
    inference(copy,[status(thm)],[18]) ).

thf(34,plain,
    ( ( less_than @ index_of_maximal @ an_index )
    = $true ),
    inference(copy,[status(thm)],[17]) ).

thf(35,plain,
    ( ( ~ ( less_than @ an_index @ lower_bound ) )
    = $true ),
    inference(copy,[status(thm)],[16]) ).

thf(36,plain,
    ( ( ~ ( less_than @ upper_bound @ an_index ) )
    = $true ),
    inference(copy,[status(thm)],[15]) ).

thf(37,plain,
    ( ( ~ ( less_than @ index_of_maximal @ lower_bound ) )
    = $true ),
    inference(copy,[status(thm)],[14]) ).

thf(38,plain,
    ( ( ~ $false )
    = $true ),
    inference(copy,[status(thm)],[24]) ).

thf(39,plain,
    ( ( ( ~ ( in_array_bounds @ array @ an_index ) )
      = $true )
    | ( ( ( less_than @ ( successor @ an_index ) @ lower_bound )
        | ( less_than @ ( successor @ upper_bound ) @ ( successor @ an_index ) )
        | ( less_than @ index_of_maximal @ lower_bound )
        | ~ ( less_than @ index_of_maximal @ ( successor @ an_index ) )
        | ~ ( in_array_bounds @ array @ index_of_maximal )
        | ( maximal_value
         != ( array_value_at @ array @ index_of_maximal ) ) )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[28]) ).

thf(40,plain,
    ! [SV1: $i] :
      ( ( ( less_than @ SV1 @ lower_bound )
        | ( in_array_bounds @ array @ SV1 )
        | ( less_than @ upper_bound @ SV1 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[29]) ).

thf(41,plain,
    ! [SV2: $i] :
      ( ( ! [SY7: $i] :
            ( ~ ( less_than @ ( successor @ SV2 ) @ ( successor @ SY7 ) )
            | ( less_than @ SV2 @ SY7 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[30]) ).

thf(42,plain,
    ! [SV3: $i] :
      ( ( ! [SY8: $i] :
            ( ~ ( less_than @ SV3 @ SY8 )
            | ! [SY9: $i] :
                ( ~ ( less_than @ SY8 @ SY9 )
                | ( less_than @ SV3 @ SY9 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[31]) ).

thf(43,plain,
    ! [SV4: $i] :
      ( ( less_than @ SV4 @ ( successor @ SV4 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[32]) ).

thf(44,plain,
    ( ( ( ~ ( in_array_bounds @ array @ index_of_maximal ) )
      = $true )
    | ( ( maximal_value
        = ( array_value_at @ array @ index_of_maximal ) )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[33]) ).

thf(45,plain,
    ( ( less_than @ an_index @ lower_bound )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[35]) ).

thf(46,plain,
    ( ( less_than @ upper_bound @ an_index )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[36]) ).

thf(47,plain,
    ( ( less_than @ index_of_maximal @ lower_bound )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[37]) ).

thf(48,plain,
    $false = $false,
    inference(extcnf_not_pos,[status(thm)],[38]) ).

thf(49,plain,
    ( ( ( in_array_bounds @ array @ an_index )
      = $false )
    | ( ( ( less_than @ ( successor @ an_index ) @ lower_bound )
        | ( less_than @ ( successor @ upper_bound ) @ ( successor @ an_index ) )
        | ( less_than @ index_of_maximal @ lower_bound )
        | ~ ( less_than @ index_of_maximal @ ( successor @ an_index ) )
        | ~ ( in_array_bounds @ array @ index_of_maximal )
        | ( maximal_value
         != ( array_value_at @ array @ index_of_maximal ) ) )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[39]) ).

thf(50,plain,
    ! [SV1: $i] :
      ( ( ( less_than @ SV1 @ lower_bound )
        = $true )
      | ( ( ( in_array_bounds @ array @ SV1 )
          | ( less_than @ upper_bound @ SV1 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[40]) ).

thf(51,plain,
    ! [SV5: $i,SV2: $i] :
      ( ( ~ ( less_than @ ( successor @ SV2 ) @ ( successor @ SV5 ) )
        | ( less_than @ SV2 @ SV5 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[41]) ).

thf(52,plain,
    ! [SV6: $i,SV3: $i] :
      ( ( ~ ( less_than @ SV3 @ SV6 )
        | ! [SY10: $i] :
            ( ~ ( less_than @ SV6 @ SY10 )
            | ( less_than @ SV3 @ SY10 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[42]) ).

thf(53,plain,
    ( ( ( in_array_bounds @ array @ index_of_maximal )
      = $false )
    | ( ( maximal_value
        = ( array_value_at @ array @ index_of_maximal ) )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[44]) ).

thf(54,plain,
    ( ( ( less_than @ ( successor @ an_index ) @ lower_bound )
      = $true )
    | ( ( ( less_than @ ( successor @ upper_bound ) @ ( successor @ an_index ) )
        | ( less_than @ index_of_maximal @ lower_bound )
        | ~ ( less_than @ index_of_maximal @ ( successor @ an_index ) )
        | ~ ( in_array_bounds @ array @ index_of_maximal )
        | ( maximal_value
         != ( array_value_at @ array @ index_of_maximal ) ) )
      = $true )
    | ( ( in_array_bounds @ array @ an_index )
      = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[49]) ).

thf(55,plain,
    ! [SV1: $i] :
      ( ( ( in_array_bounds @ array @ SV1 )
        = $true )
      | ( ( less_than @ upper_bound @ SV1 )
        = $true )
      | ( ( less_than @ SV1 @ lower_bound )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[50]) ).

thf(56,plain,
    ! [SV5: $i,SV2: $i] :
      ( ( ( ~ ( less_than @ ( successor @ SV2 ) @ ( successor @ SV5 ) ) )
        = $true )
      | ( ( less_than @ SV2 @ SV5 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[51]) ).

thf(57,plain,
    ! [SV6: $i,SV3: $i] :
      ( ( ( ~ ( less_than @ SV3 @ SV6 ) )
        = $true )
      | ( ( ! [SY10: $i] :
              ( ~ ( less_than @ SV6 @ SY10 )
              | ( less_than @ SV3 @ SY10 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[52]) ).

thf(58,plain,
    ( ( ( less_than @ ( successor @ upper_bound ) @ ( successor @ an_index ) )
      = $true )
    | ( ( ( less_than @ index_of_maximal @ lower_bound )
        | ~ ( less_than @ index_of_maximal @ ( successor @ an_index ) )
        | ~ ( in_array_bounds @ array @ index_of_maximal )
        | ( maximal_value
         != ( array_value_at @ array @ index_of_maximal ) ) )
      = $true )
    | ( ( less_than @ ( successor @ an_index ) @ lower_bound )
      = $true )
    | ( ( in_array_bounds @ array @ an_index )
      = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[54]) ).

thf(59,plain,
    ! [SV5: $i,SV2: $i] :
      ( ( ( less_than @ ( successor @ SV2 ) @ ( successor @ SV5 ) )
        = $false )
      | ( ( less_than @ SV2 @ SV5 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[56]) ).

thf(60,plain,
    ! [SV6: $i,SV3: $i] :
      ( ( ( less_than @ SV3 @ SV6 )
        = $false )
      | ( ( ! [SY10: $i] :
              ( ~ ( less_than @ SV6 @ SY10 )
              | ( less_than @ SV3 @ SY10 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[57]) ).

thf(61,plain,
    ( ( ( less_than @ index_of_maximal @ lower_bound )
      = $true )
    | ( ( ~ ( less_than @ index_of_maximal @ ( successor @ an_index ) )
        | ~ ( in_array_bounds @ array @ index_of_maximal )
        | ( maximal_value
         != ( array_value_at @ array @ index_of_maximal ) ) )
      = $true )
    | ( ( less_than @ ( successor @ upper_bound ) @ ( successor @ an_index ) )
      = $true )
    | ( ( less_than @ ( successor @ an_index ) @ lower_bound )
      = $true )
    | ( ( in_array_bounds @ array @ an_index )
      = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[58]) ).

thf(62,plain,
    ! [SV3: $i,SV7: $i,SV6: $i] :
      ( ( ( ~ ( less_than @ SV6 @ SV7 )
          | ( less_than @ SV3 @ SV7 ) )
        = $true )
      | ( ( less_than @ SV3 @ SV6 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[60]) ).

thf(63,plain,
    ( ( ( ~ ( less_than @ index_of_maximal @ ( successor @ an_index ) ) )
      = $true )
    | ( ( ~ ( in_array_bounds @ array @ index_of_maximal )
        | ( maximal_value
         != ( array_value_at @ array @ index_of_maximal ) ) )
      = $true )
    | ( ( less_than @ index_of_maximal @ lower_bound )
      = $true )
    | ( ( less_than @ ( successor @ upper_bound ) @ ( successor @ an_index ) )
      = $true )
    | ( ( less_than @ ( successor @ an_index ) @ lower_bound )
      = $true )
    | ( ( in_array_bounds @ array @ an_index )
      = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[61]) ).

thf(64,plain,
    ! [SV3: $i,SV7: $i,SV6: $i] :
      ( ( ( ~ ( less_than @ SV6 @ SV7 ) )
        = $true )
      | ( ( less_than @ SV3 @ SV7 )
        = $true )
      | ( ( less_than @ SV3 @ SV6 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[62]) ).

thf(65,plain,
    ( ( ( less_than @ index_of_maximal @ ( successor @ an_index ) )
      = $false )
    | ( ( ~ ( in_array_bounds @ array @ index_of_maximal )
        | ( maximal_value
         != ( array_value_at @ array @ index_of_maximal ) ) )
      = $true )
    | ( ( less_than @ index_of_maximal @ lower_bound )
      = $true )
    | ( ( less_than @ ( successor @ upper_bound ) @ ( successor @ an_index ) )
      = $true )
    | ( ( less_than @ ( successor @ an_index ) @ lower_bound )
      = $true )
    | ( ( in_array_bounds @ array @ an_index )
      = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[63]) ).

thf(66,plain,
    ! [SV3: $i,SV7: $i,SV6: $i] :
      ( ( ( less_than @ SV6 @ SV7 )
        = $false )
      | ( ( less_than @ SV3 @ SV7 )
        = $true )
      | ( ( less_than @ SV3 @ SV6 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[64]) ).

thf(67,plain,
    ( ( ( ~ ( in_array_bounds @ array @ index_of_maximal ) )
      = $true )
    | ( ( ( maximal_value
         != ( array_value_at @ array @ index_of_maximal ) ) )
      = $true )
    | ( ( less_than @ index_of_maximal @ ( successor @ an_index ) )
      = $false )
    | ( ( less_than @ index_of_maximal @ lower_bound )
      = $true )
    | ( ( less_than @ ( successor @ upper_bound ) @ ( successor @ an_index ) )
      = $true )
    | ( ( less_than @ ( successor @ an_index ) @ lower_bound )
      = $true )
    | ( ( in_array_bounds @ array @ an_index )
      = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[65]) ).

thf(68,plain,
    ( ( ( in_array_bounds @ array @ index_of_maximal )
      = $false )
    | ( ( ( maximal_value
         != ( array_value_at @ array @ index_of_maximal ) ) )
      = $true )
    | ( ( less_than @ index_of_maximal @ ( successor @ an_index ) )
      = $false )
    | ( ( less_than @ index_of_maximal @ lower_bound )
      = $true )
    | ( ( less_than @ ( successor @ upper_bound ) @ ( successor @ an_index ) )
      = $true )
    | ( ( less_than @ ( successor @ an_index ) @ lower_bound )
      = $true )
    | ( ( in_array_bounds @ array @ an_index )
      = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[67]) ).

thf(69,plain,
    ( ( ( maximal_value
        = ( array_value_at @ array @ index_of_maximal ) )
      = $false )
    | ( ( in_array_bounds @ array @ index_of_maximal )
      = $false )
    | ( ( less_than @ index_of_maximal @ ( successor @ an_index ) )
      = $false )
    | ( ( less_than @ index_of_maximal @ lower_bound )
      = $true )
    | ( ( less_than @ ( successor @ upper_bound ) @ ( successor @ an_index ) )
      = $true )
    | ( ( less_than @ ( successor @ an_index ) @ lower_bound )
      = $true )
    | ( ( in_array_bounds @ array @ an_index )
      = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[68]) ).

thf(70,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[34,69,66,59,55,53,48,47,46,45,43]) ).

thf(71,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[70]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SWV019-1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.34  % Computer : n016.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Tue Jun 14 22:45:31 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.35  
% 0.12/0.35   No.of.Axioms: 10
% 0.12/0.35  
% 0.12/0.35   Length.of.Defs: 0
% 0.12/0.35  
% 0.12/0.35   Contains.Choice.Funs: false
% 0.12/0.35  (rf:0,axioms:10,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:12,loop_count:0,foatp_calls:0,translation:fof_full)..
% 0.19/0.39  
% 0.19/0.39  ********************************
% 0.19/0.39  *   All subproblems solved!    *
% 0.19/0.39  ********************************
% 0.19/0.39  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:10,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:70,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.19/0.39  
% 0.19/0.39  %**** Beginning of derivation protocol ****
% 0.19/0.39  % SZS output start CNFRefutation
% See solution above
% 0.19/0.39  
% 0.19/0.39  %**** End of derivation protocol ****
% 0.19/0.39  %**** no. of clauses in derivation: 71 ****
% 0.19/0.39  %**** clause counter: 70 ****
% 0.19/0.39  
% 0.19/0.39  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:10,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:70,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------