TSTP Solution File: CSR138^1 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : CSR138^1 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% 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  : 600s
% DateTime : Fri Jul 15 21:37:27 EDT 2022

% Result   : Theorem 0.19s 0.43s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   37
%            Number of leaves      :   23
% Syntax   : Number of formulae    :  236 (  39 unt;  13 typ;   0 def)
%            Number of atoms       : 2535 (1127 equ;   0 cnn)
%            Maximal formula atoms :    6 (  11 avg)
%            Number of connectives : 2548 ( 234   ~; 846   |;  12   &;1456   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   9 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :  764 ( 764   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   15 (  12 usr;  12 con; 0-2 aty)
%            Number of variables   : 1262 ( 206   ^1036   !;  20   ?;1262   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_num,type,
    num: $tType ).

thf(tp_lAnna_THFTYPE_i,type,
    lAnna_THFTYPE_i: $i ).

thf(tp_lBen_THFTYPE_i,type,
    lBen_THFTYPE_i: $i ).

thf(tp_lBill_THFTYPE_i,type,
    lBill_THFTYPE_i: $i ).

thf(tp_lBob_THFTYPE_i,type,
    lBob_THFTYPE_i: $i ).

thf(tp_lMary_THFTYPE_i,type,
    lMary_THFTYPE_i: $i ).

thf(tp_lSue_THFTYPE_i,type,
    lSue_THFTYPE_i: $i ).

thf(tp_likes_THFTYPE_IiioI,type,
    likes_THFTYPE_IiioI: $i > $i > $o ).

thf(tp_parent_THFTYPE_IiioI,type,
    parent_THFTYPE_IiioI: $i > $i > $o ).

thf(tp_sK1_X,type,
    sK1_X: $i ).

thf(tp_sK2_SY11,type,
    sK2_SY11: $i ).

thf(tp_sK3_X,type,
    sK3_X: $i ).

thf(tp_sK4_SY12,type,
    sK4_SY12: $i ).

thf(1,axiom,
    parent_THFTYPE_IiioI @ lMary_THFTYPE_i @ lAnna_THFTYPE_i,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_008) ).

thf(2,axiom,
    parent_THFTYPE_IiioI @ lSue_THFTYPE_i @ lAnna_THFTYPE_i,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_007) ).

thf(3,axiom,
    likes_THFTYPE_IiioI @ lBob_THFTYPE_i @ lBill_THFTYPE_i,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_006) ).

thf(4,axiom,
    parent_THFTYPE_IiioI @ lSue_THFTYPE_i @ lBen_THFTYPE_i,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_005) ).

thf(5,axiom,
    parent_THFTYPE_IiioI @ lMary_THFTYPE_i @ lBen_THFTYPE_i,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_004) ).

thf(6,axiom,
    ? [X: $i,Y: $i] :
      ~ ( likes_THFTYPE_IiioI @ X @ Y ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_003) ).

thf(7,axiom,
    ? [X: $i,Y: $i] :
      ~ ( parent_THFTYPE_IiioI @ X @ Y ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_002) ).

thf(8,axiom,
    likes_THFTYPE_IiioI @ lMary_THFTYPE_i @ lBill_THFTYPE_i,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_001) ).

thf(9,axiom,
    likes_THFTYPE_IiioI @ lSue_THFTYPE_i @ lBill_THFTYPE_i,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax) ).

thf(10,conjecture,
    ? [Q: $i > $i > $o,R: $i > $i > $o,Y: $i] :
      ( ( R @ Y @ lBill_THFTYPE_i )
      & ( Q @ Y @ lAnna_THFTYPE_i )
      & ( R
       != ( ^ [Z: $i,W: $i] : $true ) )
      & ( Q
       != ( ^ [Z: $i,W: $i] : $true ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).

thf(11,negated_conjecture,
    ( ( ? [Q: $i > $i > $o,R: $i > $i > $o,Y: $i] :
          ( ( R @ Y @ lBill_THFTYPE_i )
          & ( Q @ Y @ lAnna_THFTYPE_i )
          & ( R
           != ( ^ [Z: $i,W: $i] : $true ) )
          & ( Q
           != ( ^ [Z: $i,W: $i] : $true ) ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[10]) ).

thf(12,plain,
    ( ( ? [Q: $i > $i > $o,R: $i > $i > $o,Y: $i] :
          ( ( R @ Y @ lBill_THFTYPE_i )
          & ( Q @ Y @ lAnna_THFTYPE_i )
          & ( R
           != ( ^ [Z: $i,W: $i] : $true ) )
          & ( Q
           != ( ^ [Z: $i,W: $i] : $true ) ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[11]) ).

thf(13,plain,
    ( ( parent_THFTYPE_IiioI @ lMary_THFTYPE_i @ lAnna_THFTYPE_i )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(14,plain,
    ( ( parent_THFTYPE_IiioI @ lSue_THFTYPE_i @ lAnna_THFTYPE_i )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(15,plain,
    ( ( likes_THFTYPE_IiioI @ lBob_THFTYPE_i @ lBill_THFTYPE_i )
    = $true ),
    inference(unfold_def,[status(thm)],[3]) ).

thf(16,plain,
    ( ( parent_THFTYPE_IiioI @ lSue_THFTYPE_i @ lBen_THFTYPE_i )
    = $true ),
    inference(unfold_def,[status(thm)],[4]) ).

thf(17,plain,
    ( ( parent_THFTYPE_IiioI @ lMary_THFTYPE_i @ lBen_THFTYPE_i )
    = $true ),
    inference(unfold_def,[status(thm)],[5]) ).

thf(18,plain,
    ( ( ? [X: $i,Y: $i] :
          ~ ( likes_THFTYPE_IiioI @ X @ Y ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6]) ).

thf(19,plain,
    ( ( ? [X: $i,Y: $i] :
          ~ ( parent_THFTYPE_IiioI @ X @ Y ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7]) ).

thf(20,plain,
    ( ( likes_THFTYPE_IiioI @ lMary_THFTYPE_i @ lBill_THFTYPE_i )
    = $true ),
    inference(unfold_def,[status(thm)],[8]) ).

thf(21,plain,
    ( ( likes_THFTYPE_IiioI @ lSue_THFTYPE_i @ lBill_THFTYPE_i )
    = $true ),
    inference(unfold_def,[status(thm)],[9]) ).

thf(22,plain,
    ( ( ~ ? [Q: $i > $i > $o,R: $i > $i > $o,Y: $i] :
            ( ( R @ Y @ lBill_THFTYPE_i )
            & ( Q @ Y @ lAnna_THFTYPE_i )
            & ( R
             != ( ^ [Z: $i,W: $i] : $true ) )
            & ( Q
             != ( ^ [Z: $i,W: $i] : $true ) ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[12]) ).

thf(23,plain,
    ( ( ! [Q: $i > $i > $o] :
          ( ! [R: $i > $i > $o] :
              ( ! [Y: $i] :
                  ( ~ ( Q @ Y @ lAnna_THFTYPE_i )
                  | ~ ( R @ Y @ lBill_THFTYPE_i ) )
              | ( R
                = ( ^ [Z: $i,W: $i] : $true ) ) )
          | ( Q
            = ( ^ [Z: $i,W: $i] : $true ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[22]) ).

thf(24,plain,
    ( ( ~ ( likes_THFTYPE_IiioI @ sK1_X @ sK2_SY11 ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[18]) ).

thf(25,plain,
    ( ( ~ ( parent_THFTYPE_IiioI @ sK3_X @ sK4_SY12 ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[19]) ).

thf(26,plain,
    ( ( likes_THFTYPE_IiioI @ lSue_THFTYPE_i @ lBill_THFTYPE_i )
    = $true ),
    inference(copy,[status(thm)],[21]) ).

thf(27,plain,
    ( ( likes_THFTYPE_IiioI @ lMary_THFTYPE_i @ lBill_THFTYPE_i )
    = $true ),
    inference(copy,[status(thm)],[20]) ).

thf(28,plain,
    ( ( ~ ( parent_THFTYPE_IiioI @ sK3_X @ sK4_SY12 ) )
    = $true ),
    inference(copy,[status(thm)],[25]) ).

thf(29,plain,
    ( ( ~ ( likes_THFTYPE_IiioI @ sK1_X @ sK2_SY11 ) )
    = $true ),
    inference(copy,[status(thm)],[24]) ).

thf(30,plain,
    ( ( parent_THFTYPE_IiioI @ lMary_THFTYPE_i @ lBen_THFTYPE_i )
    = $true ),
    inference(copy,[status(thm)],[17]) ).

thf(31,plain,
    ( ( parent_THFTYPE_IiioI @ lSue_THFTYPE_i @ lBen_THFTYPE_i )
    = $true ),
    inference(copy,[status(thm)],[16]) ).

thf(32,plain,
    ( ( likes_THFTYPE_IiioI @ lBob_THFTYPE_i @ lBill_THFTYPE_i )
    = $true ),
    inference(copy,[status(thm)],[15]) ).

thf(33,plain,
    ( ( parent_THFTYPE_IiioI @ lSue_THFTYPE_i @ lAnna_THFTYPE_i )
    = $true ),
    inference(copy,[status(thm)],[14]) ).

thf(34,plain,
    ( ( parent_THFTYPE_IiioI @ lMary_THFTYPE_i @ lAnna_THFTYPE_i )
    = $true ),
    inference(copy,[status(thm)],[13]) ).

thf(35,plain,
    ( ( ! [Q: $i > $i > $o] :
          ( ! [R: $i > $i > $o] :
              ( ! [Y: $i] :
                  ( ~ ( Q @ Y @ lAnna_THFTYPE_i )
                  | ~ ( R @ Y @ lBill_THFTYPE_i ) )
              | ( R
                = ( ^ [Z: $i,W: $i] : $true ) ) )
          | ( Q
            = ( ^ [Z: $i,W: $i] : $true ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[23]) ).

thf(36,plain,
    ( ( parent_THFTYPE_IiioI @ sK3_X @ sK4_SY12 )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[28]) ).

thf(37,plain,
    ( ( likes_THFTYPE_IiioI @ sK1_X @ sK2_SY11 )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[29]) ).

thf(38,plain,
    ! [SV1: $i > $i > $o] :
      ( ( ! [SY13: $i > $i > $o] :
            ( ! [SY14: $i] :
                ( ~ ( SV1 @ SY14 @ lAnna_THFTYPE_i )
                | ~ ( SY13 @ SY14 @ lBill_THFTYPE_i ) )
            | ( SY13
              = ( ^ [Z: $i,W: $i] : $true ) ) )
        | ( SV1
          = ( ^ [Z: $i,W: $i] : $true ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[35]) ).

thf(39,plain,
    ! [SV1: $i > $i > $o] :
      ( ( ( ! [SY13: $i > $i > $o] :
              ( ! [SY14: $i] :
                  ( ~ ( SV1 @ SY14 @ lAnna_THFTYPE_i )
                  | ~ ( SY13 @ SY14 @ lBill_THFTYPE_i ) )
              | ( SY13
                = ( ^ [Z: $i,W: $i] : $true ) ) ) )
        = $true )
      | ( ( SV1
          = ( ^ [Z: $i,W: $i] : $true ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[38]) ).

thf(40,plain,
    ! [SV2: $i > $i > $o,SV1: $i > $i > $o] :
      ( ( ( ! [SY19: $i] :
              ( ~ ( SV1 @ SY19 @ lAnna_THFTYPE_i )
              | ~ ( SV2 @ SY19 @ lBill_THFTYPE_i ) )
          | ( SV2
            = ( ^ [Z: $i,W: $i] : $true ) ) )
        = $true )
      | ( ( SV1
          = ( ^ [Z: $i,W: $i] : $true ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[39]) ).

thf(41,plain,
    ! [SV2: $i > $i > $o,SV1: $i > $i > $o] :
      ( ( ( ! [SY19: $i] :
              ( ~ ( SV1 @ SY19 @ lAnna_THFTYPE_i )
              | ~ ( SV2 @ SY19 @ lBill_THFTYPE_i ) ) )
        = $true )
      | ( ( SV2
          = ( ^ [Z: $i,W: $i] : $true ) )
        = $true )
      | ( ( SV1
          = ( ^ [Z: $i,W: $i] : $true ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[40]) ).

thf(42,plain,
    ! [SV2: $i > $i > $o,SV3: $i,SV1: $i > $i > $o] :
      ( ( ( ~ ( SV1 @ SV3 @ lAnna_THFTYPE_i )
          | ~ ( SV2 @ SV3 @ lBill_THFTYPE_i ) )
        = $true )
      | ( ( SV2
          = ( ^ [Z: $i,W: $i] : $true ) )
        = $true )
      | ( ( SV1
          = ( ^ [Z: $i,W: $i] : $true ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[41]) ).

thf(43,plain,
    ! [SV2: $i > $i > $o,SV3: $i,SV1: $i > $i > $o] :
      ( ( ( ~ ( SV1 @ SV3 @ lAnna_THFTYPE_i ) )
        = $true )
      | ( ( ~ ( SV2 @ SV3 @ lBill_THFTYPE_i ) )
        = $true )
      | ( ( SV2
          = ( ^ [Z: $i,W: $i] : $true ) )
        = $true )
      | ( ( SV1
          = ( ^ [Z: $i,W: $i] : $true ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[42]) ).

thf(44,plain,
    ! [SV2: $i > $i > $o,SV3: $i,SV1: $i > $i > $o] :
      ( ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( ~ ( SV2 @ SV3 @ lBill_THFTYPE_i ) )
        = $true )
      | ( ( SV2
          = ( ^ [Z: $i,W: $i] : $true ) )
        = $true )
      | ( ( SV1
          = ( ^ [Z: $i,W: $i] : $true ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[43]) ).

thf(45,plain,
    ! [SV1: $i > $i > $o,SV3: $i,SV2: $i > $i > $o] :
      ( ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2
          = ( ^ [Z: $i,W: $i] : $true ) )
        = $true )
      | ( ( SV1
          = ( ^ [Z: $i,W: $i] : $true ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[44]) ).

thf(46,plain,
    ! [SV3: $i,SV1: $i > $i > $o,SV2: $i > $i > $o] :
      ( ( ( ! [SV4: $i] :
              ( ( SV2 @ SV4 )
              = ( ^ [W: $i] : $true ) ) )
        = $true )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1
          = ( ^ [Z: $i,W: $i] : $true ) )
        = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[45]) ).

thf(47,plain,
    ! [SV3: $i,SV1: $i > $i > $o,SV2: $i > $i > $o] :
      ( ( ( SV2
          = ( ^ [Z: $i,W: $i] : $true ) )
        = $true )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1
          = ( ^ [Z: $i,W: $i] : $true ) )
        = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[45]) ).

thf(48,plain,
    ! [SV3: $i,SV1: $i > $i > $o,SV5: $i,SV2: $i > $i > $o] :
      ( ( ( ( SV2 @ SV5 )
          = ( ^ [W: $i] : $true ) )
        = $true )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1
          = ( ^ [Z: $i,W: $i] : $true ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[46]) ).

thf(49,plain,
    ! [SV3: $i,SV2: $i > $i > $o,SV1: $i > $i > $o] :
      ( ( ( ! [SV6: $i] :
              ( ( SV1 @ SV6 )
              = ( ^ [W: $i] : $true ) ) )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2
          = ( ^ [Z: $i,W: $i] : $true ) )
        = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[47]) ).

thf(50,plain,
    ! [SV3: $i,SV2: $i > $i > $o,SV1: $i > $i > $o] :
      ( ( ( SV1
          = ( ^ [Z: $i,W: $i] : $true ) )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2
          = ( ^ [Z: $i,W: $i] : $true ) )
        = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[47]) ).

thf(51,plain,
    ! [SV3: $i,SV1: $i > $i > $o,SV5: $i,SV2: $i > $i > $o] :
      ( ( ( ! [SV7: $i] :
              ( ( SV2 @ SV5 @ SV7 )
              = $true ) )
        = $true )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1
          = ( ^ [Z: $i,W: $i] : $true ) )
        = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[48]) ).

thf(52,plain,
    ! [SV3: $i,SV1: $i > $i > $o,SV5: $i,SV2: $i > $i > $o] :
      ( ( ( ( SV2 @ SV5 )
          = ( ^ [W: $i] : $true ) )
        = $true )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1
          = ( ^ [Z: $i,W: $i] : $true ) )
        = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[48]) ).

thf(53,plain,
    ! [SV3: $i,SV2: $i > $i > $o,SV8: $i,SV1: $i > $i > $o] :
      ( ( ( ( SV1 @ SV8 )
          = ( ^ [W: $i] : $true ) )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2
          = ( ^ [Z: $i,W: $i] : $true ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[49]) ).

thf(54,plain,
    ! [SV3: $i,SV1: $i > $i > $o,SV9: $i,SV5: $i,SV2: $i > $i > $o] :
      ( ( ( ( SV2 @ SV5 @ SV9 )
          = $true )
        = $true )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1
          = ( ^ [Z: $i,W: $i] : $true ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[51]) ).

thf(55,plain,
    ! [SV5: $i,SV3: $i,SV2: $i > $i > $o,SV1: $i > $i > $o] :
      ( ( ( ! [SV10: $i] :
              ( ( SV1 @ SV10 )
              = ( ^ [W: $i] : $true ) ) )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( ( SV2 @ SV5 )
          = ( ^ [W: $i] : $true ) )
        = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[52]) ).

thf(56,plain,
    ! [SV5: $i,SV3: $i,SV2: $i > $i > $o,SV1: $i > $i > $o] :
      ( ( ( SV1
          = ( ^ [Z: $i,W: $i] : $true ) )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( ( SV2 @ SV5 )
          = ( ^ [W: $i] : $true ) )
        = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[52]) ).

thf(57,plain,
    ! [SV3: $i,SV2: $i > $i > $o,SV8: $i,SV1: $i > $i > $o] :
      ( ( ( ! [SV11: $i] :
              ( ( SV1 @ SV8 @ SV11 )
              = $true ) )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2
          = ( ^ [Z: $i,W: $i] : $true ) )
        = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[53]) ).

thf(58,plain,
    ! [SV3: $i,SV2: $i > $i > $o,SV8: $i,SV1: $i > $i > $o] :
      ( ( ( ( SV1 @ SV8 )
          = ( ^ [W: $i] : $true ) )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2
          = ( ^ [Z: $i,W: $i] : $true ) )
        = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[53]) ).

thf(59,plain,
    ! [SV3: $i,SV1: $i > $i > $o,SV9: $i,SV5: $i,SV2: $i > $i > $o] :
      ( ( ( ~ ( ( SV2 @ SV5 @ SV9 )
              | $true )
          | ~ ( ~ ( SV2 @ SV5 @ SV9 )
              | ~ $true ) )
        = $true )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1
          = ( ^ [Z: $i,W: $i] : $true ) )
        = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[54]) ).

thf(60,plain,
    ! [SV3: $i,SV1: $i > $i > $o,SV9: $i,SV5: $i,SV2: $i > $i > $o] :
      ( ( ( ( SV2 @ SV5 @ SV9 )
          = $true )
        = $true )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1
          = ( ^ [Z: $i,W: $i] : $true ) )
        = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[54]) ).

thf(61,plain,
    ! [SV5: $i,SV3: $i,SV2: $i > $i > $o,SV12: $i,SV1: $i > $i > $o] :
      ( ( ( ( SV1 @ SV12 )
          = ( ^ [W: $i] : $true ) )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( ( SV2 @ SV5 )
          = ( ^ [W: $i] : $true ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[55]) ).

thf(62,plain,
    ! [SV3: $i,SV2: $i > $i > $o,SV13: $i,SV8: $i,SV1: $i > $i > $o] :
      ( ( ( ( SV1 @ SV8 @ SV13 )
          = $true )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2
          = ( ^ [Z: $i,W: $i] : $true ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[57]) ).

thf(63,plain,
    ! [SV3: $i,SV1: $i > $i > $o,SV9: $i,SV5: $i,SV2: $i > $i > $o] :
      ( ( ( ~ ( ( SV2 @ SV5 @ SV9 )
              | $true ) )
        = $true )
      | ( ( ~ ( ~ ( SV2 @ SV5 @ SV9 )
              | ~ $true ) )
        = $true )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1
          = ( ^ [Z: $i,W: $i] : $true ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[59]) ).

thf(64,plain,
    ! [SV9: $i,SV5: $i,SV3: $i,SV2: $i > $i > $o,SV1: $i > $i > $o] :
      ( ( ( ! [SV14: $i] :
              ( ( SV1 @ SV14 )
              = ( ^ [W: $i] : $true ) ) )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( ( SV2 @ SV5 @ SV9 )
          = $true )
        = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[60]) ).

thf(65,plain,
    ! [SV9: $i,SV5: $i,SV3: $i,SV2: $i > $i > $o,SV1: $i > $i > $o] :
      ( ( ( SV1
          = ( ^ [Z: $i,W: $i] : $true ) )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( ( SV2 @ SV5 @ SV9 )
          = $true )
        = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[60]) ).

thf(66,plain,
    ! [SV5: $i,SV3: $i,SV2: $i > $i > $o,SV12: $i,SV1: $i > $i > $o] :
      ( ( ( ! [SV15: $i] :
              ( ( SV1 @ SV12 @ SV15 )
              = $true ) )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( ( SV2 @ SV5 )
          = ( ^ [W: $i] : $true ) )
        = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[61]) ).

thf(67,plain,
    ! [SV5: $i,SV3: $i,SV2: $i > $i > $o,SV12: $i,SV1: $i > $i > $o] :
      ( ( ( ( SV1 @ SV12 )
          = ( ^ [W: $i] : $true ) )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( ( SV2 @ SV5 )
          = ( ^ [W: $i] : $true ) )
        = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[61]) ).

thf(68,plain,
    ! [SV3: $i,SV2: $i > $i > $o,SV13: $i,SV8: $i,SV1: $i > $i > $o] :
      ( ( ( ~ ( ( SV1 @ SV8 @ SV13 )
              | $true )
          | ~ ( ~ ( SV1 @ SV8 @ SV13 )
              | ~ $true ) )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2
          = ( ^ [Z: $i,W: $i] : $true ) )
        = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[62]) ).

thf(69,plain,
    ! [SV3: $i,SV2: $i > $i > $o,SV13: $i,SV8: $i,SV1: $i > $i > $o] :
      ( ( ( ( SV1 @ SV8 @ SV13 )
          = $true )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2
          = ( ^ [Z: $i,W: $i] : $true ) )
        = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[62]) ).

thf(70,plain,
    ! [SV3: $i,SV1: $i > $i > $o,SV9: $i,SV5: $i,SV2: $i > $i > $o] :
      ( ( ( ( SV2 @ SV5 @ SV9 )
          | $true )
        = $false )
      | ( ( ~ ( ~ ( SV2 @ SV5 @ SV9 )
              | ~ $true ) )
        = $true )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1
          = ( ^ [Z: $i,W: $i] : $true ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[63]) ).

thf(71,plain,
    ! [SV9: $i,SV5: $i,SV3: $i,SV2: $i > $i > $o,SV16: $i,SV1: $i > $i > $o] :
      ( ( ( ( SV1 @ SV16 )
          = ( ^ [W: $i] : $true ) )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( ( SV2 @ SV5 @ SV9 )
          = $true )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[64]) ).

thf(72,plain,
    ! [SV5: $i,SV3: $i,SV2: $i > $i > $o,SV17: $i,SV12: $i,SV1: $i > $i > $o] :
      ( ( ( ( SV1 @ SV12 @ SV17 )
          = $true )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( ( SV2 @ SV5 )
          = ( ^ [W: $i] : $true ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[66]) ).

thf(73,plain,
    ! [SV3: $i,SV2: $i > $i > $o,SV13: $i,SV8: $i,SV1: $i > $i > $o] :
      ( ( ( ~ ( ( SV1 @ SV8 @ SV13 )
              | $true ) )
        = $true )
      | ( ( ~ ( ~ ( SV1 @ SV8 @ SV13 )
              | ~ $true ) )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2
          = ( ^ [Z: $i,W: $i] : $true ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[68]) ).

thf(74,plain,
    ! [SV3: $i,SV1: $i > $i > $o,SV9: $i,SV5: $i,SV2: $i > $i > $o] :
      ( ( ( SV2 @ SV5 @ SV9 )
        = $false )
      | ( ( ~ ( ~ ( SV2 @ SV5 @ SV9 )
              | ~ $true ) )
        = $true )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1
          = ( ^ [Z: $i,W: $i] : $true ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[70]) ).

thf(75,plain,
    ! [SV3: $i,SV1: $i > $i > $o,SV9: $i,SV5: $i,SV2: $i > $i > $o] :
      ( ( $true = $false )
      | ( ( ~ ( ~ ( SV2 @ SV5 @ SV9 )
              | ~ $true ) )
        = $true )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1
          = ( ^ [Z: $i,W: $i] : $true ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[70]) ).

thf(76,plain,
    ! [SV9: $i,SV5: $i,SV3: $i,SV2: $i > $i > $o,SV16: $i,SV1: $i > $i > $o] :
      ( ( ( ! [SV18: $i] :
              ( ( SV1 @ SV16 @ SV18 )
              = $true ) )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( ( SV2 @ SV5 @ SV9 )
          = $true )
        = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[71]) ).

thf(77,plain,
    ! [SV9: $i,SV5: $i,SV3: $i,SV2: $i > $i > $o,SV16: $i,SV1: $i > $i > $o] :
      ( ( ( ( SV1 @ SV16 )
          = ( ^ [W: $i] : $true ) )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( ( SV2 @ SV5 @ SV9 )
          = $true )
        = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[71]) ).

thf(78,plain,
    ! [SV5: $i,SV3: $i,SV2: $i > $i > $o,SV17: $i,SV12: $i,SV1: $i > $i > $o] :
      ( ( ( ~ ( ( SV1 @ SV12 @ SV17 )
              | $true )
          | ~ ( ~ ( SV1 @ SV12 @ SV17 )
              | ~ $true ) )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( ( SV2 @ SV5 )
          = ( ^ [W: $i] : $true ) )
        = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[72]) ).

thf(79,plain,
    ! [SV5: $i,SV3: $i,SV2: $i > $i > $o,SV17: $i,SV12: $i,SV1: $i > $i > $o] :
      ( ( ( ( SV1 @ SV12 @ SV17 )
          = $true )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( ( SV2 @ SV5 )
          = ( ^ [W: $i] : $true ) )
        = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[72]) ).

thf(80,plain,
    ! [SV3: $i,SV2: $i > $i > $o,SV13: $i,SV8: $i,SV1: $i > $i > $o] :
      ( ( ( ( SV1 @ SV8 @ SV13 )
          | $true )
        = $false )
      | ( ( ~ ( ~ ( SV1 @ SV8 @ SV13 )
              | ~ $true ) )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2
          = ( ^ [Z: $i,W: $i] : $true ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[73]) ).

thf(81,plain,
    ! [SV3: $i,SV1: $i > $i > $o,SV9: $i,SV5: $i,SV2: $i > $i > $o] :
      ( ( ( ~ ( SV2 @ SV5 @ SV9 )
          | ~ $true )
        = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1
          = ( ^ [Z: $i,W: $i] : $true ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[74]) ).

thf(82,plain,
    ! [SV3: $i,SV1: $i > $i > $o,SV9: $i,SV5: $i,SV2: $i > $i > $o] :
      ( ( ( ~ ( SV2 @ SV5 @ SV9 )
          | ~ $true )
        = $false )
      | ( $true = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1
          = ( ^ [Z: $i,W: $i] : $true ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[75]) ).

thf(83,plain,
    ! [SV9: $i,SV5: $i,SV3: $i,SV2: $i > $i > $o,SV19: $i,SV16: $i,SV1: $i > $i > $o] :
      ( ( ( ( SV1 @ SV16 @ SV19 )
          = $true )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( ( SV2 @ SV5 @ SV9 )
          = $true )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[76]) ).

thf(84,plain,
    ! [SV5: $i,SV3: $i,SV2: $i > $i > $o,SV17: $i,SV12: $i,SV1: $i > $i > $o] :
      ( ( ( ~ ( ( SV1 @ SV12 @ SV17 )
              | $true ) )
        = $true )
      | ( ( ~ ( ~ ( SV1 @ SV12 @ SV17 )
              | ~ $true ) )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( ( SV2 @ SV5 )
          = ( ^ [W: $i] : $true ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[78]) ).

thf(85,plain,
    ! [SV3: $i,SV2: $i > $i > $o,SV13: $i,SV8: $i,SV1: $i > $i > $o] :
      ( ( ( SV1 @ SV8 @ SV13 )
        = $false )
      | ( ( ~ ( ~ ( SV1 @ SV8 @ SV13 )
              | ~ $true ) )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2
          = ( ^ [Z: $i,W: $i] : $true ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[80]) ).

thf(86,plain,
    ! [SV3: $i,SV2: $i > $i > $o,SV13: $i,SV8: $i,SV1: $i > $i > $o] :
      ( ( $true = $false )
      | ( ( ~ ( ~ ( SV1 @ SV8 @ SV13 )
              | ~ $true ) )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2
          = ( ^ [Z: $i,W: $i] : $true ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[80]) ).

thf(87,plain,
    ! [SV3: $i,SV1: $i > $i > $o,SV9: $i,SV5: $i,SV2: $i > $i > $o] :
      ( ( ( ~ ( SV2 @ SV5 @ SV9 ) )
        = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1
          = ( ^ [Z: $i,W: $i] : $true ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[81]) ).

thf(88,plain,
    ! [SV3: $i,SV1: $i > $i > $o,SV9: $i,SV5: $i,SV2: $i > $i > $o] :
      ( ( ( ~ $true )
        = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1
          = ( ^ [Z: $i,W: $i] : $true ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[81]) ).

thf(89,plain,
    ! [SV3: $i,SV1: $i > $i > $o,SV9: $i,SV5: $i,SV2: $i > $i > $o] :
      ( ( ( ~ ( SV2 @ SV5 @ SV9 ) )
        = $false )
      | ( $true = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1
          = ( ^ [Z: $i,W: $i] : $true ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[82]) ).

thf(90,plain,
    ! [SV2: $i > $i > $o,SV3: $i,SV1: $i > $i > $o] :
      ( ( ( ~ $true )
        = $false )
      | ( $true = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1
          = ( ^ [Z: $i,W: $i] : $true ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[82]) ).

thf(91,plain,
    ! [SV9: $i,SV5: $i,SV3: $i,SV2: $i > $i > $o,SV19: $i,SV16: $i,SV1: $i > $i > $o] :
      ( ( ( ~ ( ( SV1 @ SV16 @ SV19 )
              | $true )
          | ~ ( ~ ( SV1 @ SV16 @ SV19 )
              | ~ $true ) )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( ( SV2 @ SV5 @ SV9 )
          = $true )
        = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[83]) ).

thf(92,plain,
    ! [SV9: $i,SV5: $i,SV3: $i,SV2: $i > $i > $o,SV19: $i,SV16: $i,SV1: $i > $i > $o] :
      ( ( ( ( SV1 @ SV16 @ SV19 )
          = $true )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( ( SV2 @ SV5 @ SV9 )
          = $true )
        = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[83]) ).

thf(93,plain,
    ! [SV5: $i,SV3: $i,SV2: $i > $i > $o,SV17: $i,SV12: $i,SV1: $i > $i > $o] :
      ( ( ( ( SV1 @ SV12 @ SV17 )
          | $true )
        = $false )
      | ( ( ~ ( ~ ( SV1 @ SV12 @ SV17 )
              | ~ $true ) )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( ( SV2 @ SV5 )
          = ( ^ [W: $i] : $true ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[84]) ).

thf(94,plain,
    ! [SV3: $i,SV2: $i > $i > $o,SV13: $i,SV8: $i,SV1: $i > $i > $o] :
      ( ( ( ~ ( SV1 @ SV8 @ SV13 )
          | ~ $true )
        = $false )
      | ( ( SV1 @ SV8 @ SV13 )
        = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2
          = ( ^ [Z: $i,W: $i] : $true ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[85]) ).

thf(95,plain,
    ! [SV3: $i,SV2: $i > $i > $o,SV13: $i,SV8: $i,SV1: $i > $i > $o] :
      ( ( ( ~ ( SV1 @ SV8 @ SV13 )
          | ~ $true )
        = $false )
      | ( $true = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2
          = ( ^ [Z: $i,W: $i] : $true ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[86]) ).

thf(96,plain,
    ! [SV3: $i,SV1: $i > $i > $o,SV9: $i,SV5: $i,SV2: $i > $i > $o] :
      ( ( ( SV2 @ SV5 @ SV9 )
        = $true )
      | ( ( SV2 @ SV5 @ SV9 )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1
          = ( ^ [Z: $i,W: $i] : $true ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[87]) ).

thf(97,plain,
    ! [SV3: $i,SV1: $i > $i > $o,SV9: $i,SV5: $i,SV2: $i > $i > $o] :
      ( ( $true = $true )
      | ( ( SV2 @ SV5 @ SV9 )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1
          = ( ^ [Z: $i,W: $i] : $true ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[88]) ).

thf(98,plain,
    ! [SV3: $i,SV1: $i > $i > $o,SV9: $i,SV5: $i,SV2: $i > $i > $o] :
      ( ( ( SV2 @ SV5 @ SV9 )
        = $true )
      | ( $true = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1
          = ( ^ [Z: $i,W: $i] : $true ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[89]) ).

thf(99,plain,
    ! [SV2: $i > $i > $o,SV3: $i,SV1: $i > $i > $o] :
      ( ( $true = $true )
      | ( $true = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1
          = ( ^ [Z: $i,W: $i] : $true ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[90]) ).

thf(100,plain,
    ! [SV9: $i,SV5: $i,SV3: $i,SV2: $i > $i > $o,SV19: $i,SV16: $i,SV1: $i > $i > $o] :
      ( ( ( ~ ( ( SV1 @ SV16 @ SV19 )
              | $true ) )
        = $true )
      | ( ( ~ ( ~ ( SV1 @ SV16 @ SV19 )
              | ~ $true ) )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( ( SV2 @ SV5 @ SV9 )
          = $true )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[91]) ).

thf(101,plain,
    ! [SV5: $i,SV3: $i,SV2: $i > $i > $o,SV17: $i,SV12: $i,SV1: $i > $i > $o] :
      ( ( ( SV1 @ SV12 @ SV17 )
        = $false )
      | ( ( ~ ( ~ ( SV1 @ SV12 @ SV17 )
              | ~ $true ) )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( ( SV2 @ SV5 )
          = ( ^ [W: $i] : $true ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[93]) ).

thf(102,plain,
    ! [SV5: $i,SV3: $i,SV2: $i > $i > $o,SV17: $i,SV12: $i,SV1: $i > $i > $o] :
      ( ( $true = $false )
      | ( ( ~ ( ~ ( SV1 @ SV12 @ SV17 )
              | ~ $true ) )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( ( SV2 @ SV5 )
          = ( ^ [W: $i] : $true ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[93]) ).

thf(103,plain,
    ! [SV3: $i,SV2: $i > $i > $o,SV13: $i,SV8: $i,SV1: $i > $i > $o] :
      ( ( ( ~ ( SV1 @ SV8 @ SV13 ) )
        = $false )
      | ( ( SV1 @ SV8 @ SV13 )
        = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2
          = ( ^ [Z: $i,W: $i] : $true ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[94]) ).

thf(104,plain,
    ! [SV3: $i,SV2: $i > $i > $o,SV13: $i,SV8: $i,SV1: $i > $i > $o] :
      ( ( ( ~ $true )
        = $false )
      | ( ( SV1 @ SV8 @ SV13 )
        = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2
          = ( ^ [Z: $i,W: $i] : $true ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[94]) ).

thf(105,plain,
    ! [SV3: $i,SV2: $i > $i > $o,SV13: $i,SV8: $i,SV1: $i > $i > $o] :
      ( ( ( ~ ( SV1 @ SV8 @ SV13 ) )
        = $false )
      | ( $true = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2
          = ( ^ [Z: $i,W: $i] : $true ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[95]) ).

thf(106,plain,
    ! [SV1: $i > $i > $o,SV3: $i,SV2: $i > $i > $o] :
      ( ( ( ~ $true )
        = $false )
      | ( $true = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2
          = ( ^ [Z: $i,W: $i] : $true ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[95]) ).

thf(107,plain,
    ! [SV9: $i,SV5: $i,SV3: $i,SV2: $i > $i > $o,SV1: $i > $i > $o] :
      ( ( ( ! [SV20: $i] :
              ( ( SV1 @ SV20 )
              = ( ^ [W: $i] : $true ) ) )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[96]) ).

thf(108,plain,
    ! [SV9: $i,SV5: $i,SV3: $i,SV2: $i > $i > $o,SV1: $i > $i > $o] :
      ( ( ( SV1
          = ( ^ [Z: $i,W: $i] : $true ) )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[96]) ).

thf(109,plain,
    ! [SV9: $i,SV5: $i,SV3: $i,SV2: $i > $i > $o,SV1: $i > $i > $o] :
      ( ( ( ! [SV21: $i] :
              ( ( SV1 @ SV21 )
              = ( ^ [W: $i] : $true ) ) )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $false )
      | ( $true = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[97]) ).

thf(110,plain,
    ! [SV9: $i,SV5: $i,SV3: $i,SV2: $i > $i > $o,SV1: $i > $i > $o] :
      ( ( ( SV1
          = ( ^ [Z: $i,W: $i] : $true ) )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $false )
      | ( $true = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[97]) ).

thf(111,plain,
    ! [SV9: $i,SV5: $i,SV3: $i,SV2: $i > $i > $o,SV1: $i > $i > $o] :
      ( ( ( ! [SV22: $i] :
              ( ( SV1 @ SV22 )
              = ( ^ [W: $i] : $true ) ) )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( $true = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[98]) ).

thf(112,plain,
    ! [SV9: $i,SV5: $i,SV3: $i,SV2: $i > $i > $o,SV1: $i > $i > $o] :
      ( ( ( SV1
          = ( ^ [Z: $i,W: $i] : $true ) )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( $true = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[98]) ).

thf(113,plain,
    ! [SV3: $i,SV2: $i > $i > $o,SV1: $i > $i > $o] :
      ( ( ( ! [SV23: $i] :
              ( ( SV1 @ SV23 )
              = ( ^ [W: $i] : $true ) ) )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( $true = $false )
      | ( $true = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[99]) ).

thf(114,plain,
    ! [SV3: $i,SV2: $i > $i > $o,SV1: $i > $i > $o] :
      ( ( ( SV1
          = ( ^ [Z: $i,W: $i] : $true ) )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( $true = $false )
      | ( $true = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[99]) ).

thf(115,plain,
    ! [SV9: $i,SV5: $i,SV3: $i,SV2: $i > $i > $o,SV19: $i,SV16: $i,SV1: $i > $i > $o] :
      ( ( ( ( SV1 @ SV16 @ SV19 )
          | $true )
        = $false )
      | ( ( ~ ( ~ ( SV1 @ SV16 @ SV19 )
              | ~ $true ) )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( ( SV2 @ SV5 @ SV9 )
          = $true )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[100]) ).

thf(116,plain,
    ! [SV5: $i,SV3: $i,SV2: $i > $i > $o,SV17: $i,SV12: $i,SV1: $i > $i > $o] :
      ( ( ( ~ ( SV1 @ SV12 @ SV17 )
          | ~ $true )
        = $false )
      | ( ( SV1 @ SV12 @ SV17 )
        = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( ( SV2 @ SV5 )
          = ( ^ [W: $i] : $true ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[101]) ).

thf(117,plain,
    ! [SV5: $i,SV3: $i,SV2: $i > $i > $o,SV17: $i,SV12: $i,SV1: $i > $i > $o] :
      ( ( ( ~ ( SV1 @ SV12 @ SV17 )
          | ~ $true )
        = $false )
      | ( $true = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( ( SV2 @ SV5 )
          = ( ^ [W: $i] : $true ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[102]) ).

thf(118,plain,
    ! [SV3: $i,SV2: $i > $i > $o,SV13: $i,SV8: $i,SV1: $i > $i > $o] :
      ( ( ( SV1 @ SV8 @ SV13 )
        = $true )
      | ( ( SV1 @ SV8 @ SV13 )
        = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2
          = ( ^ [Z: $i,W: $i] : $true ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[103]) ).

thf(119,plain,
    ! [SV3: $i,SV2: $i > $i > $o,SV13: $i,SV8: $i,SV1: $i > $i > $o] :
      ( ( $true = $true )
      | ( ( SV1 @ SV8 @ SV13 )
        = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2
          = ( ^ [Z: $i,W: $i] : $true ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[104]) ).

thf(120,plain,
    ! [SV3: $i,SV2: $i > $i > $o,SV13: $i,SV8: $i,SV1: $i > $i > $o] :
      ( ( ( SV1 @ SV8 @ SV13 )
        = $true )
      | ( $true = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2
          = ( ^ [Z: $i,W: $i] : $true ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[105]) ).

thf(121,plain,
    ! [SV1: $i > $i > $o,SV3: $i,SV2: $i > $i > $o] :
      ( ( $true = $true )
      | ( $true = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2
          = ( ^ [Z: $i,W: $i] : $true ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[106]) ).

thf(122,plain,
    ! [SV9: $i,SV5: $i,SV3: $i,SV2: $i > $i > $o,SV24: $i,SV1: $i > $i > $o] :
      ( ( ( ( SV1 @ SV24 )
          = ( ^ [W: $i] : $true ) )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[107]) ).

thf(123,plain,
    ! [SV9: $i,SV5: $i,SV3: $i,SV2: $i > $i > $o,SV25: $i,SV1: $i > $i > $o] :
      ( ( ( ( SV1 @ SV25 )
          = ( ^ [W: $i] : $true ) )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $false )
      | ( $true = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[109]) ).

thf(124,plain,
    ! [SV9: $i,SV5: $i,SV3: $i,SV2: $i > $i > $o,SV26: $i,SV1: $i > $i > $o] :
      ( ( ( ( SV1 @ SV26 )
          = ( ^ [W: $i] : $true ) )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( $true = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[111]) ).

thf(125,plain,
    ! [SV3: $i,SV2: $i > $i > $o,SV27: $i,SV1: $i > $i > $o] :
      ( ( ( ( SV1 @ SV27 )
          = ( ^ [W: $i] : $true ) )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( $true = $false )
      | ( $true = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[113]) ).

thf(126,plain,
    ! [SV9: $i,SV5: $i,SV3: $i,SV2: $i > $i > $o,SV19: $i,SV16: $i,SV1: $i > $i > $o] :
      ( ( ( SV1 @ SV16 @ SV19 )
        = $false )
      | ( ( ~ ( ~ ( SV1 @ SV16 @ SV19 )
              | ~ $true ) )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( ( SV2 @ SV5 @ SV9 )
          = $true )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[115]) ).

thf(127,plain,
    ! [SV9: $i,SV5: $i,SV3: $i,SV2: $i > $i > $o,SV19: $i,SV16: $i,SV1: $i > $i > $o] :
      ( ( $true = $false )
      | ( ( ~ ( ~ ( SV1 @ SV16 @ SV19 )
              | ~ $true ) )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( ( SV2 @ SV5 @ SV9 )
          = $true )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[115]) ).

thf(128,plain,
    ! [SV5: $i,SV3: $i,SV2: $i > $i > $o,SV17: $i,SV12: $i,SV1: $i > $i > $o] :
      ( ( ( ~ ( SV1 @ SV12 @ SV17 ) )
        = $false )
      | ( ( SV1 @ SV12 @ SV17 )
        = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( ( SV2 @ SV5 )
          = ( ^ [W: $i] : $true ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[116]) ).

thf(129,plain,
    ! [SV5: $i,SV3: $i,SV2: $i > $i > $o,SV17: $i,SV12: $i,SV1: $i > $i > $o] :
      ( ( ( ~ $true )
        = $false )
      | ( ( SV1 @ SV12 @ SV17 )
        = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( ( SV2 @ SV5 )
          = ( ^ [W: $i] : $true ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[116]) ).

thf(130,plain,
    ! [SV5: $i,SV3: $i,SV2: $i > $i > $o,SV17: $i,SV12: $i,SV1: $i > $i > $o] :
      ( ( ( ~ ( SV1 @ SV12 @ SV17 ) )
        = $false )
      | ( $true = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( ( SV2 @ SV5 )
          = ( ^ [W: $i] : $true ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[117]) ).

thf(131,plain,
    ! [SV5: $i,SV1: $i > $i > $o,SV3: $i,SV2: $i > $i > $o] :
      ( ( ( ~ $true )
        = $false )
      | ( $true = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( ( SV2 @ SV5 )
          = ( ^ [W: $i] : $true ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[117]) ).

thf(132,plain,
    ! [SV9: $i,SV5: $i,SV3: $i,SV2: $i > $i > $o,SV24: $i,SV1: $i > $i > $o] :
      ( ( ( ! [SV28: $i] :
              ( ( SV1 @ SV24 @ SV28 )
              = $true ) )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[122]) ).

thf(133,plain,
    ! [SV9: $i,SV5: $i,SV3: $i,SV2: $i > $i > $o,SV24: $i,SV1: $i > $i > $o] :
      ( ( ( ( SV1 @ SV24 )
          = ( ^ [W: $i] : $true ) )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[122]) ).

thf(134,plain,
    ! [SV9: $i,SV5: $i,SV3: $i,SV2: $i > $i > $o,SV25: $i,SV1: $i > $i > $o] :
      ( ( ( ! [SV29: $i] :
              ( ( SV1 @ SV25 @ SV29 )
              = $true ) )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $false )
      | ( $true = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[123]) ).

thf(135,plain,
    ! [SV9: $i,SV5: $i,SV3: $i,SV2: $i > $i > $o,SV25: $i,SV1: $i > $i > $o] :
      ( ( ( ( SV1 @ SV25 )
          = ( ^ [W: $i] : $true ) )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $false )
      | ( $true = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[123]) ).

thf(136,plain,
    ! [SV9: $i,SV5: $i,SV3: $i,SV2: $i > $i > $o,SV26: $i,SV1: $i > $i > $o] :
      ( ( ( ! [SV30: $i] :
              ( ( SV1 @ SV26 @ SV30 )
              = $true ) )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( $true = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[124]) ).

thf(137,plain,
    ! [SV9: $i,SV5: $i,SV3: $i,SV2: $i > $i > $o,SV26: $i,SV1: $i > $i > $o] :
      ( ( ( ( SV1 @ SV26 )
          = ( ^ [W: $i] : $true ) )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( $true = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[124]) ).

thf(138,plain,
    ! [SV3: $i,SV2: $i > $i > $o,SV27: $i,SV1: $i > $i > $o] :
      ( ( ( ! [SV31: $i] :
              ( ( SV1 @ SV27 @ SV31 )
              = $true ) )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( $true = $false )
      | ( $true = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[125]) ).

thf(139,plain,
    ! [SV3: $i,SV2: $i > $i > $o,SV27: $i,SV1: $i > $i > $o] :
      ( ( ( ( SV1 @ SV27 )
          = ( ^ [W: $i] : $true ) )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( $true = $false )
      | ( $true = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[125]) ).

thf(140,plain,
    ! [SV9: $i,SV5: $i,SV3: $i,SV2: $i > $i > $o,SV19: $i,SV16: $i,SV1: $i > $i > $o] :
      ( ( ( ~ ( SV1 @ SV16 @ SV19 )
          | ~ $true )
        = $false )
      | ( ( SV1 @ SV16 @ SV19 )
        = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( ( SV2 @ SV5 @ SV9 )
          = $true )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[126]) ).

thf(141,plain,
    ! [SV9: $i,SV5: $i,SV3: $i,SV2: $i > $i > $o,SV19: $i,SV16: $i,SV1: $i > $i > $o] :
      ( ( ( ~ ( SV1 @ SV16 @ SV19 )
          | ~ $true )
        = $false )
      | ( $true = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( ( SV2 @ SV5 @ SV9 )
          = $true )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[127]) ).

thf(142,plain,
    ! [SV5: $i,SV3: $i,SV2: $i > $i > $o,SV17: $i,SV12: $i,SV1: $i > $i > $o] :
      ( ( ( SV1 @ SV12 @ SV17 )
        = $true )
      | ( ( SV1 @ SV12 @ SV17 )
        = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( ( SV2 @ SV5 )
          = ( ^ [W: $i] : $true ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[128]) ).

thf(143,plain,
    ! [SV5: $i,SV3: $i,SV2: $i > $i > $o,SV17: $i,SV12: $i,SV1: $i > $i > $o] :
      ( ( $true = $true )
      | ( ( SV1 @ SV12 @ SV17 )
        = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( ( SV2 @ SV5 )
          = ( ^ [W: $i] : $true ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[129]) ).

thf(144,plain,
    ! [SV5: $i,SV3: $i,SV2: $i > $i > $o,SV17: $i,SV12: $i,SV1: $i > $i > $o] :
      ( ( ( SV1 @ SV12 @ SV17 )
        = $true )
      | ( $true = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( ( SV2 @ SV5 )
          = ( ^ [W: $i] : $true ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[130]) ).

thf(145,plain,
    ! [SV5: $i,SV1: $i > $i > $o,SV3: $i,SV2: $i > $i > $o] :
      ( ( $true = $true )
      | ( $true = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( ( SV2 @ SV5 )
          = ( ^ [W: $i] : $true ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[131]) ).

thf(146,plain,
    ! [SV9: $i,SV5: $i,SV3: $i,SV2: $i > $i > $o,SV32: $i,SV24: $i,SV1: $i > $i > $o] :
      ( ( ( ( SV1 @ SV24 @ SV32 )
          = $true )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[132]) ).

thf(147,plain,
    ! [SV9: $i,SV5: $i,SV3: $i,SV2: $i > $i > $o,SV33: $i,SV25: $i,SV1: $i > $i > $o] :
      ( ( ( ( SV1 @ SV25 @ SV33 )
          = $true )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $false )
      | ( $true = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[134]) ).

thf(148,plain,
    ! [SV9: $i,SV5: $i,SV3: $i,SV2: $i > $i > $o,SV34: $i,SV26: $i,SV1: $i > $i > $o] :
      ( ( ( ( SV1 @ SV26 @ SV34 )
          = $true )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( $true = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[136]) ).

thf(149,plain,
    ! [SV3: $i,SV2: $i > $i > $o,SV35: $i,SV27: $i,SV1: $i > $i > $o] :
      ( ( ( ( SV1 @ SV27 @ SV35 )
          = $true )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( $true = $false )
      | ( $true = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[138]) ).

thf(150,plain,
    ! [SV9: $i,SV5: $i,SV3: $i,SV2: $i > $i > $o,SV19: $i,SV16: $i,SV1: $i > $i > $o] :
      ( ( ( ~ ( SV1 @ SV16 @ SV19 ) )
        = $false )
      | ( ( SV1 @ SV16 @ SV19 )
        = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( ( SV2 @ SV5 @ SV9 )
          = $true )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[140]) ).

thf(151,plain,
    ! [SV9: $i,SV5: $i,SV3: $i,SV2: $i > $i > $o,SV19: $i,SV16: $i,SV1: $i > $i > $o] :
      ( ( ( ~ $true )
        = $false )
      | ( ( SV1 @ SV16 @ SV19 )
        = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( ( SV2 @ SV5 @ SV9 )
          = $true )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[140]) ).

thf(152,plain,
    ! [SV9: $i,SV5: $i,SV3: $i,SV2: $i > $i > $o,SV19: $i,SV16: $i,SV1: $i > $i > $o] :
      ( ( ( ~ ( SV1 @ SV16 @ SV19 ) )
        = $false )
      | ( $true = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( ( SV2 @ SV5 @ SV9 )
          = $true )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[141]) ).

thf(153,plain,
    ! [SV9: $i,SV5: $i,SV1: $i > $i > $o,SV3: $i,SV2: $i > $i > $o] :
      ( ( ( ~ $true )
        = $false )
      | ( $true = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( ( SV2 @ SV5 @ SV9 )
          = $true )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[141]) ).

thf(154,plain,
    ! [SV9: $i,SV5: $i,SV3: $i,SV2: $i > $i > $o,SV32: $i,SV24: $i,SV1: $i > $i > $o] :
      ( ( ( ~ ( ( SV1 @ SV24 @ SV32 )
              | $true )
          | ~ ( ~ ( SV1 @ SV24 @ SV32 )
              | ~ $true ) )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[146]) ).

thf(155,plain,
    ! [SV9: $i,SV5: $i,SV3: $i,SV2: $i > $i > $o,SV32: $i,SV24: $i,SV1: $i > $i > $o] :
      ( ( ( ( SV1 @ SV24 @ SV32 )
          = $true )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[146]) ).

thf(156,plain,
    ! [SV9: $i,SV5: $i,SV3: $i,SV2: $i > $i > $o,SV33: $i,SV25: $i,SV1: $i > $i > $o] :
      ( ( ( ~ ( ( SV1 @ SV25 @ SV33 )
              | $true )
          | ~ ( ~ ( SV1 @ SV25 @ SV33 )
              | ~ $true ) )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $false )
      | ( $true = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[147]) ).

thf(157,plain,
    ! [SV9: $i,SV5: $i,SV3: $i,SV2: $i > $i > $o,SV33: $i,SV25: $i,SV1: $i > $i > $o] :
      ( ( ( ( SV1 @ SV25 @ SV33 )
          = $true )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $false )
      | ( $true = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[147]) ).

thf(158,plain,
    ! [SV9: $i,SV5: $i,SV3: $i,SV2: $i > $i > $o,SV34: $i,SV26: $i,SV1: $i > $i > $o] :
      ( ( ( ~ ( ( SV1 @ SV26 @ SV34 )
              | $true )
          | ~ ( ~ ( SV1 @ SV26 @ SV34 )
              | ~ $true ) )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( $true = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[148]) ).

thf(159,plain,
    ! [SV9: $i,SV5: $i,SV3: $i,SV2: $i > $i > $o,SV34: $i,SV26: $i,SV1: $i > $i > $o] :
      ( ( ( ( SV1 @ SV26 @ SV34 )
          = $true )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( $true = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[148]) ).

thf(160,plain,
    ! [SV3: $i,SV2: $i > $i > $o,SV35: $i,SV27: $i,SV1: $i > $i > $o] :
      ( ( ( ~ ( ( SV1 @ SV27 @ SV35 )
              | $true )
          | ~ ( ~ ( SV1 @ SV27 @ SV35 )
              | ~ $true ) )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( $true = $false )
      | ( $true = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[149]) ).

thf(161,plain,
    ! [SV3: $i,SV2: $i > $i > $o,SV35: $i,SV27: $i,SV1: $i > $i > $o] :
      ( ( ( ( SV1 @ SV27 @ SV35 )
          = $true )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( $true = $false )
      | ( $true = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[149]) ).

thf(162,plain,
    ! [SV9: $i,SV5: $i,SV3: $i,SV2: $i > $i > $o,SV19: $i,SV16: $i,SV1: $i > $i > $o] :
      ( ( ( SV1 @ SV16 @ SV19 )
        = $true )
      | ( ( SV1 @ SV16 @ SV19 )
        = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( ( SV2 @ SV5 @ SV9 )
          = $true )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[150]) ).

thf(163,plain,
    ! [SV9: $i,SV5: $i,SV3: $i,SV2: $i > $i > $o,SV19: $i,SV16: $i,SV1: $i > $i > $o] :
      ( ( $true = $true )
      | ( ( SV1 @ SV16 @ SV19 )
        = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( ( SV2 @ SV5 @ SV9 )
          = $true )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[151]) ).

thf(164,plain,
    ! [SV9: $i,SV5: $i,SV3: $i,SV2: $i > $i > $o,SV19: $i,SV16: $i,SV1: $i > $i > $o] :
      ( ( ( SV1 @ SV16 @ SV19 )
        = $true )
      | ( $true = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( ( SV2 @ SV5 @ SV9 )
          = $true )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[152]) ).

thf(165,plain,
    ! [SV9: $i,SV5: $i,SV1: $i > $i > $o,SV3: $i,SV2: $i > $i > $o] :
      ( ( $true = $true )
      | ( $true = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( ( SV2 @ SV5 @ SV9 )
          = $true )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[153]) ).

thf(166,plain,
    ! [SV9: $i,SV5: $i,SV3: $i,SV2: $i > $i > $o,SV32: $i,SV24: $i,SV1: $i > $i > $o] :
      ( ( ( ~ ( ( SV1 @ SV24 @ SV32 )
              | $true ) )
        = $true )
      | ( ( ~ ( ~ ( SV1 @ SV24 @ SV32 )
              | ~ $true ) )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[154]) ).

thf(167,plain,
    ! [SV9: $i,SV5: $i,SV3: $i,SV2: $i > $i > $o,SV33: $i,SV25: $i,SV1: $i > $i > $o] :
      ( ( ( ~ ( ( SV1 @ SV25 @ SV33 )
              | $true ) )
        = $true )
      | ( ( ~ ( ~ ( SV1 @ SV25 @ SV33 )
              | ~ $true ) )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $false )
      | ( $true = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[156]) ).

thf(168,plain,
    ! [SV9: $i,SV5: $i,SV3: $i,SV2: $i > $i > $o,SV34: $i,SV26: $i,SV1: $i > $i > $o] :
      ( ( ( ~ ( ( SV1 @ SV26 @ SV34 )
              | $true ) )
        = $true )
      | ( ( ~ ( ~ ( SV1 @ SV26 @ SV34 )
              | ~ $true ) )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( $true = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[158]) ).

thf(169,plain,
    ! [SV3: $i,SV2: $i > $i > $o,SV35: $i,SV27: $i,SV1: $i > $i > $o] :
      ( ( ( ~ ( ( SV1 @ SV27 @ SV35 )
              | $true ) )
        = $true )
      | ( ( ~ ( ~ ( SV1 @ SV27 @ SV35 )
              | ~ $true ) )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( $true = $false )
      | ( $true = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[160]) ).

thf(170,plain,
    ! [SV9: $i,SV5: $i,SV3: $i,SV2: $i > $i > $o,SV32: $i,SV24: $i,SV1: $i > $i > $o] :
      ( ( ( ( SV1 @ SV24 @ SV32 )
          | $true )
        = $false )
      | ( ( ~ ( ~ ( SV1 @ SV24 @ SV32 )
              | ~ $true ) )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[166]) ).

thf(171,plain,
    ! [SV9: $i,SV5: $i,SV3: $i,SV2: $i > $i > $o,SV33: $i,SV25: $i,SV1: $i > $i > $o] :
      ( ( ( ( SV1 @ SV25 @ SV33 )
          | $true )
        = $false )
      | ( ( ~ ( ~ ( SV1 @ SV25 @ SV33 )
              | ~ $true ) )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $false )
      | ( $true = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[167]) ).

thf(172,plain,
    ! [SV9: $i,SV5: $i,SV3: $i,SV2: $i > $i > $o,SV34: $i,SV26: $i,SV1: $i > $i > $o] :
      ( ( ( ( SV1 @ SV26 @ SV34 )
          | $true )
        = $false )
      | ( ( ~ ( ~ ( SV1 @ SV26 @ SV34 )
              | ~ $true ) )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( $true = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[168]) ).

thf(173,plain,
    ! [SV3: $i,SV2: $i > $i > $o,SV35: $i,SV27: $i,SV1: $i > $i > $o] :
      ( ( ( ( SV1 @ SV27 @ SV35 )
          | $true )
        = $false )
      | ( ( ~ ( ~ ( SV1 @ SV27 @ SV35 )
              | ~ $true ) )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( $true = $false )
      | ( $true = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[169]) ).

thf(174,plain,
    ! [SV9: $i,SV5: $i,SV3: $i,SV2: $i > $i > $o,SV32: $i,SV24: $i,SV1: $i > $i > $o] :
      ( ( ( SV1 @ SV24 @ SV32 )
        = $false )
      | ( ( ~ ( ~ ( SV1 @ SV24 @ SV32 )
              | ~ $true ) )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[170]) ).

thf(175,plain,
    ! [SV9: $i,SV5: $i,SV3: $i,SV2: $i > $i > $o,SV32: $i,SV24: $i,SV1: $i > $i > $o] :
      ( ( $true = $false )
      | ( ( ~ ( ~ ( SV1 @ SV24 @ SV32 )
              | ~ $true ) )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[170]) ).

thf(176,plain,
    ! [SV9: $i,SV5: $i,SV3: $i,SV2: $i > $i > $o,SV33: $i,SV25: $i,SV1: $i > $i > $o] :
      ( ( ( SV1 @ SV25 @ SV33 )
        = $false )
      | ( ( ~ ( ~ ( SV1 @ SV25 @ SV33 )
              | ~ $true ) )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $false )
      | ( $true = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[171]) ).

thf(177,plain,
    ! [SV9: $i,SV5: $i,SV3: $i,SV2: $i > $i > $o,SV33: $i,SV25: $i,SV1: $i > $i > $o] :
      ( ( $true = $false )
      | ( ( ~ ( ~ ( SV1 @ SV25 @ SV33 )
              | ~ $true ) )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $false )
      | ( $true = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[171]) ).

thf(178,plain,
    ! [SV9: $i,SV5: $i,SV3: $i,SV2: $i > $i > $o,SV34: $i,SV26: $i,SV1: $i > $i > $o] :
      ( ( ( SV1 @ SV26 @ SV34 )
        = $false )
      | ( ( ~ ( ~ ( SV1 @ SV26 @ SV34 )
              | ~ $true ) )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( $true = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[172]) ).

thf(179,plain,
    ! [SV9: $i,SV5: $i,SV3: $i,SV2: $i > $i > $o,SV34: $i,SV26: $i,SV1: $i > $i > $o] :
      ( ( $true = $false )
      | ( ( ~ ( ~ ( SV1 @ SV26 @ SV34 )
              | ~ $true ) )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( $true = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[172]) ).

thf(180,plain,
    ! [SV3: $i,SV2: $i > $i > $o,SV35: $i,SV27: $i,SV1: $i > $i > $o] :
      ( ( ( SV1 @ SV27 @ SV35 )
        = $false )
      | ( ( ~ ( ~ ( SV1 @ SV27 @ SV35 )
              | ~ $true ) )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( $true = $false )
      | ( $true = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[173]) ).

thf(181,plain,
    ! [SV3: $i,SV2: $i > $i > $o,SV35: $i,SV27: $i,SV1: $i > $i > $o] :
      ( ( $true = $false )
      | ( ( ~ ( ~ ( SV1 @ SV27 @ SV35 )
              | ~ $true ) )
        = $true )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( $true = $false )
      | ( $true = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[173]) ).

thf(182,plain,
    ! [SV9: $i,SV5: $i,SV3: $i,SV2: $i > $i > $o,SV32: $i,SV24: $i,SV1: $i > $i > $o] :
      ( ( ( ~ ( SV1 @ SV24 @ SV32 )
          | ~ $true )
        = $false )
      | ( ( SV1 @ SV24 @ SV32 )
        = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[174]) ).

thf(183,plain,
    ! [SV9: $i,SV5: $i,SV3: $i,SV2: $i > $i > $o,SV32: $i,SV24: $i,SV1: $i > $i > $o] :
      ( ( ( ~ ( SV1 @ SV24 @ SV32 )
          | ~ $true )
        = $false )
      | ( $true = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[175]) ).

thf(184,plain,
    ! [SV9: $i,SV5: $i,SV3: $i,SV2: $i > $i > $o,SV33: $i,SV25: $i,SV1: $i > $i > $o] :
      ( ( ( ~ ( SV1 @ SV25 @ SV33 )
          | ~ $true )
        = $false )
      | ( ( SV1 @ SV25 @ SV33 )
        = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $false )
      | ( $true = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[176]) ).

thf(185,plain,
    ! [SV9: $i,SV5: $i,SV3: $i,SV2: $i > $i > $o,SV33: $i,SV25: $i,SV1: $i > $i > $o] :
      ( ( ( ~ ( SV1 @ SV25 @ SV33 )
          | ~ $true )
        = $false )
      | ( $true = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $false )
      | ( $true = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[177]) ).

thf(186,plain,
    ! [SV9: $i,SV5: $i,SV3: $i,SV2: $i > $i > $o,SV34: $i,SV26: $i,SV1: $i > $i > $o] :
      ( ( ( ~ ( SV1 @ SV26 @ SV34 )
          | ~ $true )
        = $false )
      | ( ( SV1 @ SV26 @ SV34 )
        = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( $true = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[178]) ).

thf(187,plain,
    ! [SV9: $i,SV5: $i,SV3: $i,SV2: $i > $i > $o,SV34: $i,SV26: $i,SV1: $i > $i > $o] :
      ( ( ( ~ ( SV1 @ SV26 @ SV34 )
          | ~ $true )
        = $false )
      | ( $true = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( $true = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[179]) ).

thf(188,plain,
    ! [SV3: $i,SV2: $i > $i > $o,SV35: $i,SV27: $i,SV1: $i > $i > $o] :
      ( ( ( ~ ( SV1 @ SV27 @ SV35 )
          | ~ $true )
        = $false )
      | ( ( SV1 @ SV27 @ SV35 )
        = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( $true = $false )
      | ( $true = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[180]) ).

thf(189,plain,
    ! [SV3: $i,SV2: $i > $i > $o,SV35: $i,SV27: $i,SV1: $i > $i > $o] :
      ( ( ( ~ ( SV1 @ SV27 @ SV35 )
          | ~ $true )
        = $false )
      | ( $true = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( $true = $false )
      | ( $true = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[181]) ).

thf(190,plain,
    ! [SV9: $i,SV5: $i,SV3: $i,SV2: $i > $i > $o,SV32: $i,SV24: $i,SV1: $i > $i > $o] :
      ( ( ( ~ ( SV1 @ SV24 @ SV32 ) )
        = $false )
      | ( ( SV1 @ SV24 @ SV32 )
        = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[182]) ).

thf(191,plain,
    ! [SV9: $i,SV5: $i,SV3: $i,SV2: $i > $i > $o,SV32: $i,SV24: $i,SV1: $i > $i > $o] :
      ( ( ( ~ $true )
        = $false )
      | ( ( SV1 @ SV24 @ SV32 )
        = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[182]) ).

thf(192,plain,
    ! [SV9: $i,SV5: $i,SV3: $i,SV2: $i > $i > $o,SV32: $i,SV24: $i,SV1: $i > $i > $o] :
      ( ( ( ~ ( SV1 @ SV24 @ SV32 ) )
        = $false )
      | ( $true = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[183]) ).

thf(193,plain,
    ! [SV9: $i,SV5: $i,SV1: $i > $i > $o,SV3: $i,SV2: $i > $i > $o] :
      ( ( ( ~ $true )
        = $false )
      | ( $true = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[183]) ).

thf(194,plain,
    ! [SV9: $i,SV5: $i,SV3: $i,SV2: $i > $i > $o,SV33: $i,SV25: $i,SV1: $i > $i > $o] :
      ( ( ( ~ ( SV1 @ SV25 @ SV33 ) )
        = $false )
      | ( ( SV1 @ SV25 @ SV33 )
        = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $false )
      | ( $true = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[184]) ).

thf(195,plain,
    ! [SV9: $i,SV5: $i,SV3: $i,SV2: $i > $i > $o,SV33: $i,SV25: $i,SV1: $i > $i > $o] :
      ( ( ( ~ $true )
        = $false )
      | ( ( SV1 @ SV25 @ SV33 )
        = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $false )
      | ( $true = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[184]) ).

thf(196,plain,
    ! [SV9: $i,SV5: $i,SV3: $i,SV2: $i > $i > $o,SV33: $i,SV25: $i,SV1: $i > $i > $o] :
      ( ( ( ~ ( SV1 @ SV25 @ SV33 ) )
        = $false )
      | ( $true = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $false )
      | ( $true = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[185]) ).

thf(197,plain,
    ! [SV9: $i,SV5: $i,SV1: $i > $i > $o,SV3: $i,SV2: $i > $i > $o] :
      ( ( ( ~ $true )
        = $false )
      | ( $true = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $false )
      | ( $true = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[185]) ).

thf(198,plain,
    ! [SV9: $i,SV5: $i,SV3: $i,SV2: $i > $i > $o,SV34: $i,SV26: $i,SV1: $i > $i > $o] :
      ( ( ( ~ ( SV1 @ SV26 @ SV34 ) )
        = $false )
      | ( ( SV1 @ SV26 @ SV34 )
        = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( $true = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[186]) ).

thf(199,plain,
    ! [SV9: $i,SV5: $i,SV3: $i,SV2: $i > $i > $o,SV34: $i,SV26: $i,SV1: $i > $i > $o] :
      ( ( ( ~ $true )
        = $false )
      | ( ( SV1 @ SV26 @ SV34 )
        = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( $true = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[186]) ).

thf(200,plain,
    ! [SV9: $i,SV5: $i,SV3: $i,SV2: $i > $i > $o,SV34: $i,SV26: $i,SV1: $i > $i > $o] :
      ( ( ( ~ ( SV1 @ SV26 @ SV34 ) )
        = $false )
      | ( $true = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( $true = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[187]) ).

thf(201,plain,
    ! [SV9: $i,SV5: $i,SV1: $i > $i > $o,SV3: $i,SV2: $i > $i > $o] :
      ( ( ( ~ $true )
        = $false )
      | ( $true = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( $true = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[187]) ).

thf(202,plain,
    ! [SV3: $i,SV2: $i > $i > $o,SV35: $i,SV27: $i,SV1: $i > $i > $o] :
      ( ( ( ~ ( SV1 @ SV27 @ SV35 ) )
        = $false )
      | ( ( SV1 @ SV27 @ SV35 )
        = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( $true = $false )
      | ( $true = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[188]) ).

thf(203,plain,
    ! [SV3: $i,SV2: $i > $i > $o,SV35: $i,SV27: $i,SV1: $i > $i > $o] :
      ( ( ( ~ $true )
        = $false )
      | ( ( SV1 @ SV27 @ SV35 )
        = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( $true = $false )
      | ( $true = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[188]) ).

thf(204,plain,
    ! [SV3: $i,SV2: $i > $i > $o,SV35: $i,SV27: $i,SV1: $i > $i > $o] :
      ( ( ( ~ ( SV1 @ SV27 @ SV35 ) )
        = $false )
      | ( $true = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( $true = $false )
      | ( $true = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[189]) ).

thf(205,plain,
    ! [SV1: $i > $i > $o,SV3: $i,SV2: $i > $i > $o] :
      ( ( ( ~ $true )
        = $false )
      | ( $true = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( $true = $false )
      | ( $true = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[189]) ).

thf(206,plain,
    ! [SV9: $i,SV5: $i,SV3: $i,SV2: $i > $i > $o,SV32: $i,SV24: $i,SV1: $i > $i > $o] :
      ( ( ( SV1 @ SV24 @ SV32 )
        = $true )
      | ( ( SV1 @ SV24 @ SV32 )
        = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[190]) ).

thf(207,plain,
    ! [SV9: $i,SV5: $i,SV3: $i,SV2: $i > $i > $o,SV32: $i,SV24: $i,SV1: $i > $i > $o] :
      ( ( $true = $true )
      | ( ( SV1 @ SV24 @ SV32 )
        = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[191]) ).

thf(208,plain,
    ! [SV9: $i,SV5: $i,SV3: $i,SV2: $i > $i > $o,SV32: $i,SV24: $i,SV1: $i > $i > $o] :
      ( ( ( SV1 @ SV24 @ SV32 )
        = $true )
      | ( $true = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[192]) ).

thf(209,plain,
    ! [SV9: $i,SV5: $i,SV1: $i > $i > $o,SV3: $i,SV2: $i > $i > $o] :
      ( ( $true = $true )
      | ( $true = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[193]) ).

thf(210,plain,
    ! [SV9: $i,SV5: $i,SV3: $i,SV2: $i > $i > $o,SV33: $i,SV25: $i,SV1: $i > $i > $o] :
      ( ( ( SV1 @ SV25 @ SV33 )
        = $true )
      | ( ( SV1 @ SV25 @ SV33 )
        = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $false )
      | ( $true = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[194]) ).

thf(211,plain,
    ! [SV9: $i,SV5: $i,SV3: $i,SV2: $i > $i > $o,SV33: $i,SV25: $i,SV1: $i > $i > $o] :
      ( ( $true = $true )
      | ( ( SV1 @ SV25 @ SV33 )
        = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $false )
      | ( $true = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[195]) ).

thf(212,plain,
    ! [SV9: $i,SV5: $i,SV3: $i,SV2: $i > $i > $o,SV33: $i,SV25: $i,SV1: $i > $i > $o] :
      ( ( ( SV1 @ SV25 @ SV33 )
        = $true )
      | ( $true = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $false )
      | ( $true = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[196]) ).

thf(213,plain,
    ! [SV9: $i,SV5: $i,SV1: $i > $i > $o,SV3: $i,SV2: $i > $i > $o] :
      ( ( $true = $true )
      | ( $true = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $false )
      | ( $true = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[197]) ).

thf(214,plain,
    ! [SV9: $i,SV5: $i,SV3: $i,SV2: $i > $i > $o,SV34: $i,SV26: $i,SV1: $i > $i > $o] :
      ( ( ( SV1 @ SV26 @ SV34 )
        = $true )
      | ( ( SV1 @ SV26 @ SV34 )
        = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( $true = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[198]) ).

thf(215,plain,
    ! [SV9: $i,SV5: $i,SV3: $i,SV2: $i > $i > $o,SV34: $i,SV26: $i,SV1: $i > $i > $o] :
      ( ( $true = $true )
      | ( ( SV1 @ SV26 @ SV34 )
        = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( $true = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[199]) ).

thf(216,plain,
    ! [SV9: $i,SV5: $i,SV3: $i,SV2: $i > $i > $o,SV34: $i,SV26: $i,SV1: $i > $i > $o] :
      ( ( ( SV1 @ SV26 @ SV34 )
        = $true )
      | ( $true = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( $true = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[200]) ).

thf(217,plain,
    ! [SV9: $i,SV5: $i,SV1: $i > $i > $o,SV3: $i,SV2: $i > $i > $o] :
      ( ( $true = $true )
      | ( $true = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( $true = $false )
      | ( ( SV2 @ SV5 @ SV9 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[201]) ).

thf(218,plain,
    ! [SV3: $i,SV2: $i > $i > $o,SV35: $i,SV27: $i,SV1: $i > $i > $o] :
      ( ( ( SV1 @ SV27 @ SV35 )
        = $true )
      | ( ( SV1 @ SV27 @ SV35 )
        = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( $true = $false )
      | ( $true = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[202]) ).

thf(219,plain,
    ! [SV3: $i,SV2: $i > $i > $o,SV35: $i,SV27: $i,SV1: $i > $i > $o] :
      ( ( $true = $true )
      | ( ( SV1 @ SV27 @ SV35 )
        = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( $true = $false )
      | ( $true = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[203]) ).

thf(220,plain,
    ! [SV3: $i,SV2: $i > $i > $o,SV35: $i,SV27: $i,SV1: $i > $i > $o] :
      ( ( ( SV1 @ SV27 @ SV35 )
        = $true )
      | ( $true = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( $true = $false )
      | ( $true = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[204]) ).

thf(221,plain,
    ! [SV1: $i > $i > $o,SV3: $i,SV2: $i > $i > $o] :
      ( ( $true = $true )
      | ( $true = $false )
      | ( ( SV2 @ SV3 @ lBill_THFTYPE_i )
        = $false )
      | ( ( SV1 @ SV3 @ lAnna_THFTYPE_i )
        = $false )
      | ( $true = $false )
      | ( $true = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[205]) ).

thf(222,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[26,221,220,219,218,217,216,215,214,213,212,211,210,209,208,207,206,165,164,163,162,161,159,157,155,145,144,143,142,139,137,135,133,121,120,119,118,114,112,110,108,92,79,77,69,67,65,58,56,50,37,36,34,33,32,31,30,27]) ).

thf(223,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[222]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : CSR138^1 : TPTP v8.1.0. Released v4.1.0.
% 0.06/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34  % Computer : n020.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Sat Jun 11 12:28:50 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  
% 0.13/0.34   No.of.Axioms: 9
% 0.13/0.34  
% 0.13/0.34   Length.of.Defs: 0
% 0.13/0.34  
% 0.13/0.34   Contains.Choice.Funs: false
% 0.13/0.35  (rf:0,axioms:9,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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:11,loop_count:0,foatp_calls:0,translation:fof_full)....
% 0.19/0.43  
% 0.19/0.43  ********************************
% 0.19/0.43  *   All subproblems solved!    *
% 0.19/0.43  ********************************
% 0.19/0.43  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:9,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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:222,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.19/0.47  
% 0.19/0.47  %**** Beginning of derivation protocol ****
% 0.19/0.47  % SZS output start CNFRefutation
% See solution above
% 0.19/0.47  
% 0.19/0.47  %**** End of derivation protocol ****
% 0.19/0.47  %**** no. of clauses in derivation: 223 ****
% 0.19/0.47  %**** clause counter: 222 ****
% 0.19/0.47  
% 0.19/0.47  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:9,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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:222,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------