TSTP Solution File: SYO277^5 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SYO277^5 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n013.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 : Thu Jul 21 17:33:08 EDT 2022

% Result   : Theorem 0.36s 0.55s
% Output   : CNFRefutation 0.36s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   29
%            Number of leaves      :    6
% Syntax   : Number of formulae    :  109 (  44 unt;   5 typ;   0 def)
%            Number of atoms       :  454 ( 212 equ;   0 cnn)
%            Maximal formula atoms :    3 (   4 avg)
%            Number of connectives : 1879 ( 712   ~; 131   |;   8   &;1001   @)
%                                         (   5 <=>;  22  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  166 ( 166   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :  435 ( 320   ^ 115   !;   0   ?; 435   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_sK1_X,type,
    sK1_X: $i ).

thf(tp_sK2_SY5,type,
    sK2_SY5: $i ).

thf(tp_sK3_SY10,type,
    sK3_SY10: $i > $i > $o ).

thf(tp_sK4_SY9,type,
    sK4_SY9: $i > $o ).

thf(tp_sK5_Z,type,
    sK5_Z: ( $i > $i > $o ) > $i ).

thf(1,conjecture,
    ! [X: $i,Y: $i] :
      ( ! [Xq: $i > $o] :
          ( ( Xq @ X )
         => ( Xq @ Y ) )
    <=> ! [R: $i > $i > $o] :
          ( ! [Z: $i] : ( R @ Z @ Z )
         => ( R @ X @ Y ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM47D) ).

thf(2,negated_conjecture,
    ( ( ! [X: $i,Y: $i] :
          ( ! [Xq: $i > $o] :
              ( ( Xq @ X )
             => ( Xq @ Y ) )
        <=> ! [R: $i > $i > $o] :
              ( ! [Z: $i] : ( R @ Z @ Z )
             => ( R @ X @ Y ) ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ! [Xq: $i > $o] :
              ( ( Xq @ X )
             => ( Xq @ Y ) )
        <=> ! [R: $i > $i > $o] :
              ( ! [Z: $i] : ( R @ Z @ Z )
             => ( R @ X @ Y ) ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(4,plain,
    ( ( ! [SY5: $i] :
          ( ! [SY6: $i > $o] :
              ( ( SY6 @ sK1_X )
             => ( SY6 @ SY5 ) )
        <=> ! [SY7: $i > $i > $o] :
              ( ! [Z: $i] : ( SY7 @ Z @ Z )
             => ( SY7 @ sK1_X @ SY5 ) ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[3]) ).

thf(5,plain,
    ( ( ! [SY9: $i > $o] :
          ( ( SY9 @ sK1_X )
         => ( SY9 @ sK2_SY5 ) )
    <=> ! [SY10: $i > $i > $o] :
          ( ! [Z: $i] : ( SY10 @ Z @ Z )
         => ( SY10 @ sK1_X @ sK2_SY5 ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[4]) ).

thf(6,plain,
    ( ( ! [SY9: $i > $o] :
          ( ( SY9 @ sK1_X )
         => ( SY9 @ sK2_SY5 ) )
     => ! [SY10: $i > $i > $o] :
          ( ! [Z: $i] : ( SY10 @ Z @ Z )
         => ( SY10 @ sK1_X @ sK2_SY5 ) ) )
    = $false ),
    inference(split_conjecture,[split_conjecture(split,[])],[5]) ).

thf(7,plain,
    ( ( ! [SY10: $i > $i > $o] :
          ( ! [Z: $i] : ( SY10 @ Z @ Z )
         => ( SY10 @ sK1_X @ sK2_SY5 ) )
     => ! [SY9: $i > $o] :
          ( ( SY9 @ sK1_X )
         => ( SY9 @ sK2_SY5 ) ) )
    = $false ),
    inference(split_conjecture,[split_conjecture(split,[])],[5]) ).

thf(8,plain,
    ( ( ~ ( ! [SY9: $i > $o] :
              ( ( SY9 @ sK1_X )
             => ( SY9 @ sK2_SY5 ) )
         => ! [SY10: $i > $i > $o] :
              ( ! [Z: $i] : ( SY10 @ Z @ Z )
             => ( SY10 @ sK1_X @ sK2_SY5 ) ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[6]) ).

thf(9,plain,
    ( ( ~ ( ! [SY10: $i > $i > $o] :
              ( ! [Z: $i] : ( SY10 @ Z @ Z )
             => ( SY10 @ sK1_X @ sK2_SY5 ) )
         => ! [SY9: $i > $o] :
              ( ( SY9 @ sK1_X )
             => ( SY9 @ sK2_SY5 ) ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[7]) ).

thf(10,plain,
    ( ( ! [SY9: $i > $o] :
          ( ~ ( SY9 @ sK1_X )
          | ( SY9 @ sK2_SY5 ) )
      & ! [SY12: $i] : ( sK3_SY10 @ SY12 @ SY12 )
      & ~ ( sK3_SY10 @ sK1_X @ sK2_SY5 ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[8]) ).

thf(11,plain,
    ( ( ! [SY10: $i > $i > $o] :
          ( ~ ( SY10 @ ( sK5_Z @ SY10 ) @ ( sK5_Z @ SY10 ) )
          | ( SY10 @ sK1_X @ sK2_SY5 ) )
      & ( sK4_SY9 @ sK1_X )
      & ~ ( sK4_SY9 @ sK2_SY5 ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[9]) ).

thf(12,plain,
    ( ( ! [SY9: $i > $o] :
          ( ~ ( SY9 @ sK1_X )
          | ( SY9 @ sK2_SY5 ) )
      & ! [SY12: $i] : ( sK3_SY10 @ SY12 @ SY12 )
      & ~ ( sK3_SY10 @ sK1_X @ sK2_SY5 ) )
    = $true ),
    inference(copy,[status(thm)],[10]) ).

thf(13,plain,
    ( ( ~ ( ~ ! [SX0: $i > $o] :
                ( ~ ( SX0 @ sK1_X )
                | ( SX0 @ sK2_SY5 ) )
          | ~ ~ ( ~ ! [SX0: $i] : ( sK3_SY10 @ SX0 @ SX0 )
                | ~ ~ ( sK3_SY10 @ sK1_X @ sK2_SY5 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[12]) ).

thf(14,plain,
    ( ( ~ ! [SX0: $i > $o] :
            ( ~ ( SX0 @ sK1_X )
            | ( SX0 @ sK2_SY5 ) )
      | ~ ~ ( ~ ! [SX0: $i] : ( sK3_SY10 @ SX0 @ SX0 )
            | ~ ~ ( sK3_SY10 @ sK1_X @ sK2_SY5 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[13]) ).

thf(15,plain,
    ( ( ~ ! [SX0: $i > $o] :
            ( ~ ( SX0 @ sK1_X )
            | ( SX0 @ sK2_SY5 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[14]) ).

thf(16,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] : ( sK3_SY10 @ SX0 @ SX0 )
            | ~ ~ ( sK3_SY10 @ sK1_X @ sK2_SY5 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[14]) ).

thf(17,plain,
    ( ( ! [SX0: $i > $o] :
          ( ~ ( SX0 @ sK1_X )
          | ( SX0 @ sK2_SY5 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[15]) ).

thf(18,plain,
    ( ( ~ ( ~ ! [SX0: $i] : ( sK3_SY10 @ SX0 @ SX0 )
          | ~ ~ ( sK3_SY10 @ sK1_X @ sK2_SY5 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[16]) ).

thf(19,plain,
    ! [SV1: $i > $o] :
      ( ( ~ ( SV1 @ sK1_X )
        | ( SV1 @ sK2_SY5 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[17]) ).

thf(20,plain,
    ( ( ~ ! [SX0: $i] : ( sK3_SY10 @ SX0 @ SX0 )
      | ~ ~ ( sK3_SY10 @ sK1_X @ sK2_SY5 ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[18]) ).

thf(21,plain,
    ! [SV1: $i > $o] :
      ( ( ( ~ ( SV1 @ sK1_X ) )
        = $true )
      | ( ( SV1 @ sK2_SY5 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[19]) ).

thf(22,plain,
    ( ( ~ ! [SX0: $i] : ( sK3_SY10 @ SX0 @ SX0 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[20]) ).

thf(23,plain,
    ( ( ~ ~ ( sK3_SY10 @ sK1_X @ sK2_SY5 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[20]) ).

thf(24,plain,
    ! [SV1: $i > $o] :
      ( ( ( SV1 @ sK1_X )
        = $false )
      | ( ( SV1 @ sK2_SY5 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[21]) ).

thf(25,plain,
    ( ( ! [SX0: $i] : ( sK3_SY10 @ SX0 @ SX0 ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[22]) ).

thf(26,plain,
    ( ( ~ ( sK3_SY10 @ sK1_X @ sK2_SY5 ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[23]) ).

thf(27,plain,
    ! [SV2: $i] :
      ( ( sK3_SY10 @ SV2 @ SV2 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[25]) ).

thf(28,plain,
    ( ( sK3_SY10 @ sK1_X @ sK2_SY5 )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[26]) ).

thf(29,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[24,28,27]) ).

thf(30,plain,
    ( ( ! [SY10: $i > $i > $o] :
          ( ~ ( SY10 @ ( sK5_Z @ SY10 ) @ ( sK5_Z @ SY10 ) )
          | ( SY10 @ sK1_X @ sK2_SY5 ) )
      & ( sK4_SY9 @ sK1_X )
      & ~ ( sK4_SY9 @ sK2_SY5 ) )
    = $true ),
    inference(copy,[status(thm)],[11]) ).

thf(31,plain,
    ( ( ~ ( ~ ! [SX0: $i > $i > $o] :
                ( ~ ( SX0 @ ( sK5_Z @ SX0 ) @ ( sK5_Z @ SX0 ) )
                | ( SX0 @ sK1_X @ sK2_SY5 ) )
          | ~ ~ ( ~ ( sK4_SY9 @ sK1_X )
                | ~ ~ ( sK4_SY9 @ sK2_SY5 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[30]) ).

thf(32,plain,
    ( ( ~ ! [SX0: $i > $i > $o] :
            ( ~ ( SX0 @ ( sK5_Z @ SX0 ) @ ( sK5_Z @ SX0 ) )
            | ( SX0 @ sK1_X @ sK2_SY5 ) )
      | ~ ~ ( ~ ( sK4_SY9 @ sK1_X )
            | ~ ~ ( sK4_SY9 @ sK2_SY5 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[31]) ).

thf(33,plain,
    ( ( ~ ! [SX0: $i > $i > $o] :
            ( ~ ( SX0 @ ( sK5_Z @ SX0 ) @ ( sK5_Z @ SX0 ) )
            | ( SX0 @ sK1_X @ sK2_SY5 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[32]) ).

thf(34,plain,
    ( ( ~ ~ ( ~ ( sK4_SY9 @ sK1_X )
            | ~ ~ ( sK4_SY9 @ sK2_SY5 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[32]) ).

thf(35,plain,
    ( ( ! [SX0: $i > $i > $o] :
          ( ~ ( SX0 @ ( sK5_Z @ SX0 ) @ ( sK5_Z @ SX0 ) )
          | ( SX0 @ sK1_X @ sK2_SY5 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[33]) ).

thf(36,plain,
    ( ( ~ ( ~ ( sK4_SY9 @ sK1_X )
          | ~ ~ ( sK4_SY9 @ sK2_SY5 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[34]) ).

thf(37,plain,
    ! [SV3: $i > $i > $o] :
      ( ( ~ ( SV3 @ ( sK5_Z @ SV3 ) @ ( sK5_Z @ SV3 ) )
        | ( SV3 @ sK1_X @ sK2_SY5 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[35]) ).

thf(38,plain,
    ( ( ~ ( sK4_SY9 @ sK1_X )
      | ~ ~ ( sK4_SY9 @ sK2_SY5 ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[36]) ).

thf(39,plain,
    ! [SV3: $i > $i > $o] :
      ( ( ( ~ ( SV3 @ ( sK5_Z @ SV3 ) @ ( sK5_Z @ SV3 ) ) )
        = $true )
      | ( ( SV3 @ sK1_X @ sK2_SY5 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[37]) ).

thf(40,plain,
    ( ( ~ ( sK4_SY9 @ sK1_X ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[38]) ).

thf(41,plain,
    ( ( ~ ~ ( sK4_SY9 @ sK2_SY5 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[38]) ).

thf(42,plain,
    ! [SV3: $i > $i > $o] :
      ( ( ( SV3 @ ( sK5_Z @ SV3 ) @ ( sK5_Z @ SV3 ) )
        = $false )
      | ( ( SV3 @ sK1_X @ sK2_SY5 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[39]) ).

thf(43,plain,
    ( ( sK4_SY9 @ sK1_X )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[40]) ).

thf(44,plain,
    ( ( ~ ( sK4_SY9 @ sK2_SY5 ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[41]) ).

thf(45,plain,
    ( ( sK4_SY9 @ sK2_SY5 )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[44]) ).

thf(46,plain,
    ( ( ( ( sK5_Z
          @ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) )
        = ( sK5_Z
          @ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) ) )
      = $false )
    | ( ( sK1_X = sK2_SY5 )
      = $true ) ),
    inference(replace_andrewsEQ,[status(thm)],[42:[bind(SV3,$thf( ^ [SV5: $i] : ^ [SV4: $i] : ( SV5 = SV4 ) ))]]) ).

thf(47,plain,
    ( ( sK1_X = sK2_SY5 )
    = $true ),
    inference(sim,[status(thm)],[46]) ).

thf(50,plain,
    ! [SV8: $i > $i > $o] :
      ( ( ( ~ ( SV8
              @ ( sK5_Z
                @ ^ [SX0: $i,SX1: $i] :
                    ~ ( SV8 @ SX0 @ SX1 ) )
              @ ( sK5_Z
                @ ^ [SX0: $i,SX1: $i] :
                    ~ ( SV8 @ SX0 @ SX1 ) ) ) )
        = $false )
      | ( ( ~ ( SV8 @ sK1_X @ sK2_SY5 ) )
        = $true ) ),
    inference(prim_subst,[status(thm)],[42:[bind(SV3,$thf( ^ [SV6: $i] : ^ [SV7: $i] : ~ ( SV8 @ SV6 @ SV7 ) ))]]) ).

thf(52,plain,
    ( ( ( ( sK5_Z
          @ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) )
        = ( sK5_Z
          @ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) ) )
      = $false )
    | ( ( sK1_X = sK2_SY5 )
      = $true ) ),
    inference(prim_subst,[status(thm)],[42:[bind(SV3,$thf( ^ [SV14: $i] : ^ [SV13: $i] : ( SV14 = SV13 ) ))]]) ).

thf(53,plain,
    ! [SV3: $i > $i > $o] :
      ( ( ( SV3 @ ( sK5_Z @ SV3 ) @ ( sK5_Z @ SV3 ) )
        = $false )
      | ( ( ( SV3 @ ( sK5_Z @ SV3 ) @ ( sK5_Z @ SV3 ) )
          = ( ~ ( SV3 @ sK1_X @ sK2_SY5 ) ) )
        = $false ) ),
    inference(fac_restr,[status(thm)],[42]) ).

thf(54,plain,
    ! [SV3: $i > $i > $o] :
      ( ( ( ~ ( ( SV3 @ ( sK5_Z @ SV3 ) @ ( sK5_Z @ SV3 ) )
              | ~ ( SV3 @ sK1_X @ sK2_SY5 ) )
          | ~ ( ~ ( SV3 @ ( sK5_Z @ SV3 ) @ ( sK5_Z @ SV3 ) )
              | ~ ~ ( SV3 @ sK1_X @ sK2_SY5 ) ) )
        = $false )
      | ( ( SV3 @ ( sK5_Z @ SV3 ) @ ( sK5_Z @ SV3 ) )
        = $false ) ),
    inference(extcnf_equal_neg,[status(thm)],[53]) ).

thf(55,plain,
    ! [SV3: $i > $i > $o] :
      ( ( ( ( SV3 @ ( sK5_Z @ SV3 ) @ ( sK5_Z @ SV3 ) )
          = ( ~ ( SV3 @ sK1_X @ sK2_SY5 ) ) )
        = $false )
      | ( ( SV3 @ ( sK5_Z @ SV3 ) @ ( sK5_Z @ SV3 ) )
        = $false ) ),
    inference(extcnf_equal_neg,[status(thm)],[53]) ).

thf(57,plain,
    ! [SV3: $i > $i > $o] :
      ( ( ( ~ ( ~ ( SV3 @ ( sK5_Z @ SV3 ) @ ( sK5_Z @ SV3 ) )
              | ~ ~ ( SV3 @ sK1_X @ sK2_SY5 ) ) )
        = $false )
      | ( ( SV3 @ ( sK5_Z @ SV3 ) @ ( sK5_Z @ SV3 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[54]) ).

thf(59,plain,
    ! [SV3: $i > $i > $o] :
      ( ( ( ~ ( SV3 @ ( sK5_Z @ SV3 ) @ ( sK5_Z @ SV3 ) )
          | ~ ~ ( SV3 @ sK1_X @ sK2_SY5 ) )
        = $true )
      | ( ( SV3 @ ( sK5_Z @ SV3 ) @ ( sK5_Z @ SV3 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[57]) ).

thf(61,plain,
    ! [SV3: $i > $i > $o] :
      ( ( ( ~ ( SV3 @ ( sK5_Z @ SV3 ) @ ( sK5_Z @ SV3 ) ) )
        = $true )
      | ( ( ~ ~ ( SV3 @ sK1_X @ sK2_SY5 ) )
        = $true )
      | ( ( SV3 @ ( sK5_Z @ SV3 ) @ ( sK5_Z @ SV3 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[59]) ).

thf(63,plain,
    ! [SV3: $i > $i > $o] :
      ( ( ( SV3 @ ( sK5_Z @ SV3 ) @ ( sK5_Z @ SV3 ) )
        = $false )
      | ( ( ~ ~ ( SV3 @ sK1_X @ sK2_SY5 ) )
        = $true )
      | ( ( SV3 @ ( sK5_Z @ SV3 ) @ ( sK5_Z @ SV3 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[61]) ).

thf(64,plain,
    ! [SV3: $i > $i > $o] :
      ( ( ( ~ ( SV3 @ sK1_X @ sK2_SY5 ) )
        = $false )
      | ( ( SV3 @ ( sK5_Z @ SV3 ) @ ( sK5_Z @ SV3 ) )
        = $false )
      | ( ( SV3 @ ( sK5_Z @ SV3 ) @ ( sK5_Z @ SV3 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[63]) ).

thf(65,plain,
    ! [SV3: $i > $i > $o] :
      ( ( ( SV3 @ sK1_X @ sK2_SY5 )
        = $true )
      | ( ( SV3 @ ( sK5_Z @ SV3 ) @ ( sK5_Z @ SV3 ) )
        = $false )
      | ( ( SV3 @ ( sK5_Z @ SV3 ) @ ( sK5_Z @ SV3 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[64]) ).

thf(67,plain,
    ! [SV39: $i > $i > $o] :
      ( ( ( ~ ~ ~ ~ ~ ( SV39
                      @ ( sK5_Z
                        @ ^ [SX0: $i,SX1: $i] :
                            ~ ~ ~ ~ ~ ( SV39 @ SX0 @ SX1 ) )
                      @ ( sK5_Z
                        @ ^ [SX0: $i,SX1: $i] :
                            ~ ~ ~ ~ ~ ( SV39 @ SX0 @ SX1 ) ) ) )
        = $false )
      | ( ( ~ ( SV39
              @ ( sK5_Z
                @ ^ [SX0: $i,SX1: $i] :
                    ~ ~ ~ ~ ~ ( SV39 @ SX0 @ SX1 ) )
              @ ( sK5_Z
                @ ^ [SX0: $i,SX1: $i] :
                    ~ ~ ~ ~ ~ ( SV39 @ SX0 @ SX1 ) ) ) )
        = $false )
      | ( ( ~ ~ ( SV39 @ sK1_X @ sK2_SY5 ) )
        = $false ) ),
    inference(extuni,[status(esa)],[55:[bind(SV3,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ~ ( ~ ( ~ ( ~ ( ~ ( SV39 @ SX0 @ SX1 ) ) ) ) ) ))]]) ).

thf(68,plain,
    ! [SV34: $i > $i > $o] :
      ( ( ( ~ ~ ~ ~ ( SV34
                    @ ( sK5_Z
                      @ ^ [SX0: $i,SX1: $i] :
                          ~ ~ ~ ~ ( SV34 @ SX0 @ SX1 ) )
                    @ ( sK5_Z
                      @ ^ [SX0: $i,SX1: $i] :
                          ~ ~ ~ ~ ( SV34 @ SX0 @ SX1 ) ) ) )
        = $false )
      | ( ( ~ ( SV34
              @ ( sK5_Z
                @ ^ [SX0: $i,SX1: $i] :
                    ~ ~ ~ ~ ( SV34 @ SX0 @ SX1 ) )
              @ ( sK5_Z
                @ ^ [SX0: $i,SX1: $i] :
                    ~ ~ ~ ~ ( SV34 @ SX0 @ SX1 ) ) ) )
        = $true )
      | ( ( ~ ~ ( SV34 @ sK1_X @ sK2_SY5 ) )
        = $true ) ),
    inference(extuni,[status(esa)],[55:[bind(SV3,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ~ ( ~ ( ~ ( ~ ( SV34 @ SX0 @ SX1 ) ) ) ) ))]]) ).

thf(71,plain,
    ! [SV29: $i > $i > $o] :
      ( ( ( ~ ~ ~ ( SV29
                  @ ( sK5_Z
                    @ ^ [SX0: $i,SX1: $i] :
                        ~ ~ ~ ( SV29 @ SX0 @ SX1 ) )
                  @ ( sK5_Z
                    @ ^ [SX0: $i,SX1: $i] :
                        ~ ~ ~ ( SV29 @ SX0 @ SX1 ) ) ) )
        = $false )
      | ( ( ~ ( SV29
              @ ( sK5_Z
                @ ^ [SX0: $i,SX1: $i] :
                    ~ ~ ~ ( SV29 @ SX0 @ SX1 ) )
              @ ( sK5_Z
                @ ^ [SX0: $i,SX1: $i] :
                    ~ ~ ~ ( SV29 @ SX0 @ SX1 ) ) ) )
        = $false )
      | ( ( ~ ~ ( SV29 @ sK1_X @ sK2_SY5 ) )
        = $false ) ),
    inference(extuni,[status(esa)],[55:[bind(SV3,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ~ ( ~ ( ~ ( SV29 @ SX0 @ SX1 ) ) ) ))]]) ).

thf(72,plain,
    ! [SV24: $i > $i > $o] :
      ( ( ( ~ ~ ( SV24
                @ ( sK5_Z
                  @ ^ [SX0: $i,SX1: $i] :
                      ~ ~ ( SV24 @ SX0 @ SX1 ) )
                @ ( sK5_Z
                  @ ^ [SX0: $i,SX1: $i] :
                      ~ ~ ( SV24 @ SX0 @ SX1 ) ) ) )
        = $false )
      | ( ( ~ ( SV24
              @ ( sK5_Z
                @ ^ [SX0: $i,SX1: $i] :
                    ~ ~ ( SV24 @ SX0 @ SX1 ) )
              @ ( sK5_Z
                @ ^ [SX0: $i,SX1: $i] :
                    ~ ~ ( SV24 @ SX0 @ SX1 ) ) ) )
        = $true )
      | ( ( ~ ~ ( SV24 @ sK1_X @ sK2_SY5 ) )
        = $true ) ),
    inference(extuni,[status(esa)],[55:[bind(SV3,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ~ ( ~ ( SV24 @ SX0 @ SX1 ) ) ))]]) ).

thf(75,plain,
    ! [SV19: $i > $i > $o] :
      ( ( ( ~ ( SV19
              @ ( sK5_Z
                @ ^ [SX0: $i,SX1: $i] :
                    ~ ( SV19 @ SX0 @ SX1 ) )
              @ ( sK5_Z
                @ ^ [SX0: $i,SX1: $i] :
                    ~ ( SV19 @ SX0 @ SX1 ) ) ) )
        = $false )
      | ( ( ~ ( SV19
              @ ( sK5_Z
                @ ^ [SX0: $i,SX1: $i] :
                    ~ ( SV19 @ SX0 @ SX1 ) )
              @ ( sK5_Z
                @ ^ [SX0: $i,SX1: $i] :
                    ~ ( SV19 @ SX0 @ SX1 ) ) ) )
        = $false )
      | ( ( ~ ~ ( SV19 @ sK1_X @ sK2_SY5 ) )
        = $false ) ),
    inference(extuni,[status(esa)],[55:[bind(SV3,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ~ ( SV19 @ SX0 @ SX1 ) ))]]) ).

thf(76,plain,
    ! [SV19: $i > $i > $o] :
      ( ( ( SV19
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ( SV19 @ SX0 @ SX1 ) )
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ( SV19 @ SX0 @ SX1 ) ) )
        = $true )
      | ( ( ~ ( SV19
              @ ( sK5_Z
                @ ^ [SX0: $i,SX1: $i] :
                    ~ ( SV19 @ SX0 @ SX1 ) )
              @ ( sK5_Z
                @ ^ [SX0: $i,SX1: $i] :
                    ~ ( SV19 @ SX0 @ SX1 ) ) ) )
        = $false )
      | ( ( ~ ~ ( SV19 @ sK1_X @ sK2_SY5 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[75]) ).

thf(79,plain,
    ! [SV24: $i > $i > $o] :
      ( ( ( ~ ( SV24
              @ ( sK5_Z
                @ ^ [SX0: $i,SX1: $i] :
                    ~ ~ ( SV24 @ SX0 @ SX1 ) )
              @ ( sK5_Z
                @ ^ [SX0: $i,SX1: $i] :
                    ~ ~ ( SV24 @ SX0 @ SX1 ) ) ) )
        = $true )
      | ( ( ~ ( SV24
              @ ( sK5_Z
                @ ^ [SX0: $i,SX1: $i] :
                    ~ ~ ( SV24 @ SX0 @ SX1 ) )
              @ ( sK5_Z
                @ ^ [SX0: $i,SX1: $i] :
                    ~ ~ ( SV24 @ SX0 @ SX1 ) ) ) )
        = $true )
      | ( ( ~ ~ ( SV24 @ sK1_X @ sK2_SY5 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[72]) ).

thf(80,plain,
    ! [SV29: $i > $i > $o] :
      ( ( ( ~ ~ ( SV29
                @ ( sK5_Z
                  @ ^ [SX0: $i,SX1: $i] :
                      ~ ~ ~ ( SV29 @ SX0 @ SX1 ) )
                @ ( sK5_Z
                  @ ^ [SX0: $i,SX1: $i] :
                      ~ ~ ~ ( SV29 @ SX0 @ SX1 ) ) ) )
        = $true )
      | ( ( ~ ( SV29
              @ ( sK5_Z
                @ ^ [SX0: $i,SX1: $i] :
                    ~ ~ ~ ( SV29 @ SX0 @ SX1 ) )
              @ ( sK5_Z
                @ ^ [SX0: $i,SX1: $i] :
                    ~ ~ ~ ( SV29 @ SX0 @ SX1 ) ) ) )
        = $false )
      | ( ( ~ ~ ( SV29 @ sK1_X @ sK2_SY5 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[71]) ).

thf(83,plain,
    ! [SV34: $i > $i > $o] :
      ( ( ( ~ ~ ~ ( SV34
                  @ ( sK5_Z
                    @ ^ [SX0: $i,SX1: $i] :
                        ~ ~ ~ ~ ( SV34 @ SX0 @ SX1 ) )
                  @ ( sK5_Z
                    @ ^ [SX0: $i,SX1: $i] :
                        ~ ~ ~ ~ ( SV34 @ SX0 @ SX1 ) ) ) )
        = $true )
      | ( ( ~ ( SV34
              @ ( sK5_Z
                @ ^ [SX0: $i,SX1: $i] :
                    ~ ~ ~ ~ ( SV34 @ SX0 @ SX1 ) )
              @ ( sK5_Z
                @ ^ [SX0: $i,SX1: $i] :
                    ~ ~ ~ ~ ( SV34 @ SX0 @ SX1 ) ) ) )
        = $true )
      | ( ( ~ ~ ( SV34 @ sK1_X @ sK2_SY5 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[68]) ).

thf(84,plain,
    ! [SV39: $i > $i > $o] :
      ( ( ( ~ ~ ~ ~ ( SV39
                    @ ( sK5_Z
                      @ ^ [SX0: $i,SX1: $i] :
                          ~ ~ ~ ~ ~ ( SV39 @ SX0 @ SX1 ) )
                    @ ( sK5_Z
                      @ ^ [SX0: $i,SX1: $i] :
                          ~ ~ ~ ~ ~ ( SV39 @ SX0 @ SX1 ) ) ) )
        = $true )
      | ( ( ~ ( SV39
              @ ( sK5_Z
                @ ^ [SX0: $i,SX1: $i] :
                    ~ ~ ~ ~ ~ ( SV39 @ SX0 @ SX1 ) )
              @ ( sK5_Z
                @ ^ [SX0: $i,SX1: $i] :
                    ~ ~ ~ ~ ~ ( SV39 @ SX0 @ SX1 ) ) ) )
        = $false )
      | ( ( ~ ~ ( SV39 @ sK1_X @ sK2_SY5 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[67]) ).

thf(86,plain,
    ! [SV19: $i > $i > $o] :
      ( ( ( SV19
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ( SV19 @ SX0 @ SX1 ) )
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ( SV19 @ SX0 @ SX1 ) ) )
        = $true )
      | ( ( SV19
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ( SV19 @ SX0 @ SX1 ) )
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ( SV19 @ SX0 @ SX1 ) ) )
        = $true )
      | ( ( ~ ~ ( SV19 @ sK1_X @ sK2_SY5 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[76]) ).

thf(89,plain,
    ! [SV24: $i > $i > $o] :
      ( ( ( SV24
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ~ ( SV24 @ SX0 @ SX1 ) )
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ~ ( SV24 @ SX0 @ SX1 ) ) )
        = $false )
      | ( ( ~ ( SV24
              @ ( sK5_Z
                @ ^ [SX0: $i,SX1: $i] :
                    ~ ~ ( SV24 @ SX0 @ SX1 ) )
              @ ( sK5_Z
                @ ^ [SX0: $i,SX1: $i] :
                    ~ ~ ( SV24 @ SX0 @ SX1 ) ) ) )
        = $true )
      | ( ( ~ ~ ( SV24 @ sK1_X @ sK2_SY5 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[79]) ).

thf(90,plain,
    ! [SV29: $i > $i > $o] :
      ( ( ( ~ ( SV29
              @ ( sK5_Z
                @ ^ [SX0: $i,SX1: $i] :
                    ~ ~ ~ ( SV29 @ SX0 @ SX1 ) )
              @ ( sK5_Z
                @ ^ [SX0: $i,SX1: $i] :
                    ~ ~ ~ ( SV29 @ SX0 @ SX1 ) ) ) )
        = $false )
      | ( ( ~ ( SV29
              @ ( sK5_Z
                @ ^ [SX0: $i,SX1: $i] :
                    ~ ~ ~ ( SV29 @ SX0 @ SX1 ) )
              @ ( sK5_Z
                @ ^ [SX0: $i,SX1: $i] :
                    ~ ~ ~ ( SV29 @ SX0 @ SX1 ) ) ) )
        = $false )
      | ( ( ~ ~ ( SV29 @ sK1_X @ sK2_SY5 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[80]) ).

thf(93,plain,
    ! [SV34: $i > $i > $o] :
      ( ( ( ~ ~ ( SV34
                @ ( sK5_Z
                  @ ^ [SX0: $i,SX1: $i] :
                      ~ ~ ~ ~ ( SV34 @ SX0 @ SX1 ) )
                @ ( sK5_Z
                  @ ^ [SX0: $i,SX1: $i] :
                      ~ ~ ~ ~ ( SV34 @ SX0 @ SX1 ) ) ) )
        = $false )
      | ( ( ~ ( SV34
              @ ( sK5_Z
                @ ^ [SX0: $i,SX1: $i] :
                    ~ ~ ~ ~ ( SV34 @ SX0 @ SX1 ) )
              @ ( sK5_Z
                @ ^ [SX0: $i,SX1: $i] :
                    ~ ~ ~ ~ ( SV34 @ SX0 @ SX1 ) ) ) )
        = $true )
      | ( ( ~ ~ ( SV34 @ sK1_X @ sK2_SY5 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[83]) ).

thf(94,plain,
    ! [SV39: $i > $i > $o] :
      ( ( ( ~ ~ ~ ( SV39
                  @ ( sK5_Z
                    @ ^ [SX0: $i,SX1: $i] :
                        ~ ~ ~ ~ ~ ( SV39 @ SX0 @ SX1 ) )
                  @ ( sK5_Z
                    @ ^ [SX0: $i,SX1: $i] :
                        ~ ~ ~ ~ ~ ( SV39 @ SX0 @ SX1 ) ) ) )
        = $false )
      | ( ( ~ ( SV39
              @ ( sK5_Z
                @ ^ [SX0: $i,SX1: $i] :
                    ~ ~ ~ ~ ~ ( SV39 @ SX0 @ SX1 ) )
              @ ( sK5_Z
                @ ^ [SX0: $i,SX1: $i] :
                    ~ ~ ~ ~ ~ ( SV39 @ SX0 @ SX1 ) ) ) )
        = $false )
      | ( ( ~ ~ ( SV39 @ sK1_X @ sK2_SY5 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[84]) ).

thf(96,plain,
    ! [SV19: $i > $i > $o] :
      ( ( ( ~ ( SV19 @ sK1_X @ sK2_SY5 ) )
        = $true )
      | ( ( SV19
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ( SV19 @ SX0 @ SX1 ) )
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ( SV19 @ SX0 @ SX1 ) ) )
        = $true )
      | ( ( SV19
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ( SV19 @ SX0 @ SX1 ) )
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ( SV19 @ SX0 @ SX1 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[86]) ).

thf(99,plain,
    ! [SV24: $i > $i > $o] :
      ( ( ( SV24
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ~ ( SV24 @ SX0 @ SX1 ) )
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ~ ( SV24 @ SX0 @ SX1 ) ) )
        = $false )
      | ( ( SV24
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ~ ( SV24 @ SX0 @ SX1 ) )
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ~ ( SV24 @ SX0 @ SX1 ) ) )
        = $false )
      | ( ( ~ ~ ( SV24 @ sK1_X @ sK2_SY5 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[89]) ).

thf(100,plain,
    ! [SV29: $i > $i > $o] :
      ( ( ( SV29
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ~ ~ ( SV29 @ SX0 @ SX1 ) )
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ~ ~ ( SV29 @ SX0 @ SX1 ) ) )
        = $true )
      | ( ( ~ ( SV29
              @ ( sK5_Z
                @ ^ [SX0: $i,SX1: $i] :
                    ~ ~ ~ ( SV29 @ SX0 @ SX1 ) )
              @ ( sK5_Z
                @ ^ [SX0: $i,SX1: $i] :
                    ~ ~ ~ ( SV29 @ SX0 @ SX1 ) ) ) )
        = $false )
      | ( ( ~ ~ ( SV29 @ sK1_X @ sK2_SY5 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[90]) ).

thf(103,plain,
    ! [SV34: $i > $i > $o] :
      ( ( ( ~ ( SV34
              @ ( sK5_Z
                @ ^ [SX0: $i,SX1: $i] :
                    ~ ~ ~ ~ ( SV34 @ SX0 @ SX1 ) )
              @ ( sK5_Z
                @ ^ [SX0: $i,SX1: $i] :
                    ~ ~ ~ ~ ( SV34 @ SX0 @ SX1 ) ) ) )
        = $true )
      | ( ( ~ ( SV34
              @ ( sK5_Z
                @ ^ [SX0: $i,SX1: $i] :
                    ~ ~ ~ ~ ( SV34 @ SX0 @ SX1 ) )
              @ ( sK5_Z
                @ ^ [SX0: $i,SX1: $i] :
                    ~ ~ ~ ~ ( SV34 @ SX0 @ SX1 ) ) ) )
        = $true )
      | ( ( ~ ~ ( SV34 @ sK1_X @ sK2_SY5 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[93]) ).

thf(104,plain,
    ! [SV39: $i > $i > $o] :
      ( ( ( ~ ~ ( SV39
                @ ( sK5_Z
                  @ ^ [SX0: $i,SX1: $i] :
                      ~ ~ ~ ~ ~ ( SV39 @ SX0 @ SX1 ) )
                @ ( sK5_Z
                  @ ^ [SX0: $i,SX1: $i] :
                      ~ ~ ~ ~ ~ ( SV39 @ SX0 @ SX1 ) ) ) )
        = $true )
      | ( ( ~ ( SV39
              @ ( sK5_Z
                @ ^ [SX0: $i,SX1: $i] :
                    ~ ~ ~ ~ ~ ( SV39 @ SX0 @ SX1 ) )
              @ ( sK5_Z
                @ ^ [SX0: $i,SX1: $i] :
                    ~ ~ ~ ~ ~ ( SV39 @ SX0 @ SX1 ) ) ) )
        = $false )
      | ( ( ~ ~ ( SV39 @ sK1_X @ sK2_SY5 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[94]) ).

thf(106,plain,
    ! [SV19: $i > $i > $o] :
      ( ( ( SV19 @ sK1_X @ sK2_SY5 )
        = $false )
      | ( ( SV19
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ( SV19 @ SX0 @ SX1 ) )
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ( SV19 @ SX0 @ SX1 ) ) )
        = $true )
      | ( ( SV19
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ( SV19 @ SX0 @ SX1 ) )
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ( SV19 @ SX0 @ SX1 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[96]) ).

thf(109,plain,
    ! [SV24: $i > $i > $o] :
      ( ( ( ~ ( SV24 @ sK1_X @ sK2_SY5 ) )
        = $false )
      | ( ( SV24
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ~ ( SV24 @ SX0 @ SX1 ) )
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ~ ( SV24 @ SX0 @ SX1 ) ) )
        = $false )
      | ( ( SV24
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ~ ( SV24 @ SX0 @ SX1 ) )
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ~ ( SV24 @ SX0 @ SX1 ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[99]) ).

thf(110,plain,
    ! [SV29: $i > $i > $o] :
      ( ( ( SV29
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ~ ~ ( SV29 @ SX0 @ SX1 ) )
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ~ ~ ( SV29 @ SX0 @ SX1 ) ) )
        = $true )
      | ( ( SV29
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ~ ~ ( SV29 @ SX0 @ SX1 ) )
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ~ ~ ( SV29 @ SX0 @ SX1 ) ) )
        = $true )
      | ( ( ~ ~ ( SV29 @ sK1_X @ sK2_SY5 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[100]) ).

thf(113,plain,
    ! [SV34: $i > $i > $o] :
      ( ( ( SV34
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ~ ~ ~ ( SV34 @ SX0 @ SX1 ) )
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ~ ~ ~ ( SV34 @ SX0 @ SX1 ) ) )
        = $false )
      | ( ( ~ ( SV34
              @ ( sK5_Z
                @ ^ [SX0: $i,SX1: $i] :
                    ~ ~ ~ ~ ( SV34 @ SX0 @ SX1 ) )
              @ ( sK5_Z
                @ ^ [SX0: $i,SX1: $i] :
                    ~ ~ ~ ~ ( SV34 @ SX0 @ SX1 ) ) ) )
        = $true )
      | ( ( ~ ~ ( SV34 @ sK1_X @ sK2_SY5 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[103]) ).

thf(114,plain,
    ! [SV39: $i > $i > $o] :
      ( ( ( ~ ( SV39
              @ ( sK5_Z
                @ ^ [SX0: $i,SX1: $i] :
                    ~ ~ ~ ~ ~ ( SV39 @ SX0 @ SX1 ) )
              @ ( sK5_Z
                @ ^ [SX0: $i,SX1: $i] :
                    ~ ~ ~ ~ ~ ( SV39 @ SX0 @ SX1 ) ) ) )
        = $false )
      | ( ( ~ ( SV39
              @ ( sK5_Z
                @ ^ [SX0: $i,SX1: $i] :
                    ~ ~ ~ ~ ~ ( SV39 @ SX0 @ SX1 ) )
              @ ( sK5_Z
                @ ^ [SX0: $i,SX1: $i] :
                    ~ ~ ~ ~ ~ ( SV39 @ SX0 @ SX1 ) ) ) )
        = $false )
      | ( ( ~ ~ ( SV39 @ sK1_X @ sK2_SY5 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[104]) ).

thf(117,plain,
    ! [SV24: $i > $i > $o] :
      ( ( ( SV24 @ sK1_X @ sK2_SY5 )
        = $true )
      | ( ( SV24
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ~ ( SV24 @ SX0 @ SX1 ) )
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ~ ( SV24 @ SX0 @ SX1 ) ) )
        = $false )
      | ( ( SV24
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ~ ( SV24 @ SX0 @ SX1 ) )
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ~ ( SV24 @ SX0 @ SX1 ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[109]) ).

thf(118,plain,
    ! [SV29: $i > $i > $o] :
      ( ( ( ~ ( SV29 @ sK1_X @ sK2_SY5 ) )
        = $true )
      | ( ( SV29
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ~ ~ ( SV29 @ SX0 @ SX1 ) )
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ~ ~ ( SV29 @ SX0 @ SX1 ) ) )
        = $true )
      | ( ( SV29
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ~ ~ ( SV29 @ SX0 @ SX1 ) )
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ~ ~ ( SV29 @ SX0 @ SX1 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[110]) ).

thf(121,plain,
    ! [SV34: $i > $i > $o] :
      ( ( ( SV34
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ~ ~ ~ ( SV34 @ SX0 @ SX1 ) )
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ~ ~ ~ ( SV34 @ SX0 @ SX1 ) ) )
        = $false )
      | ( ( SV34
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ~ ~ ~ ( SV34 @ SX0 @ SX1 ) )
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ~ ~ ~ ( SV34 @ SX0 @ SX1 ) ) )
        = $false )
      | ( ( ~ ~ ( SV34 @ sK1_X @ sK2_SY5 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[113]) ).

thf(122,plain,
    ! [SV39: $i > $i > $o] :
      ( ( ( SV39
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ~ ~ ~ ~ ( SV39 @ SX0 @ SX1 ) )
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ~ ~ ~ ~ ( SV39 @ SX0 @ SX1 ) ) )
        = $true )
      | ( ( ~ ( SV39
              @ ( sK5_Z
                @ ^ [SX0: $i,SX1: $i] :
                    ~ ~ ~ ~ ~ ( SV39 @ SX0 @ SX1 ) )
              @ ( sK5_Z
                @ ^ [SX0: $i,SX1: $i] :
                    ~ ~ ~ ~ ~ ( SV39 @ SX0 @ SX1 ) ) ) )
        = $false )
      | ( ( ~ ~ ( SV39 @ sK1_X @ sK2_SY5 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[114]) ).

thf(124,plain,
    ! [SV29: $i > $i > $o] :
      ( ( ( SV29 @ sK1_X @ sK2_SY5 )
        = $false )
      | ( ( SV29
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ~ ~ ( SV29 @ SX0 @ SX1 ) )
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ~ ~ ( SV29 @ SX0 @ SX1 ) ) )
        = $true )
      | ( ( SV29
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ~ ~ ( SV29 @ SX0 @ SX1 ) )
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ~ ~ ( SV29 @ SX0 @ SX1 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[118]) ).

thf(127,plain,
    ! [SV34: $i > $i > $o] :
      ( ( ( ~ ( SV34 @ sK1_X @ sK2_SY5 ) )
        = $false )
      | ( ( SV34
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ~ ~ ~ ( SV34 @ SX0 @ SX1 ) )
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ~ ~ ~ ( SV34 @ SX0 @ SX1 ) ) )
        = $false )
      | ( ( SV34
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ~ ~ ~ ( SV34 @ SX0 @ SX1 ) )
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ~ ~ ~ ( SV34 @ SX0 @ SX1 ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[121]) ).

thf(128,plain,
    ! [SV39: $i > $i > $o] :
      ( ( ( SV39
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ~ ~ ~ ~ ( SV39 @ SX0 @ SX1 ) )
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ~ ~ ~ ~ ( SV39 @ SX0 @ SX1 ) ) )
        = $true )
      | ( ( SV39
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ~ ~ ~ ~ ( SV39 @ SX0 @ SX1 ) )
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ~ ~ ~ ~ ( SV39 @ SX0 @ SX1 ) ) )
        = $true )
      | ( ( ~ ~ ( SV39 @ sK1_X @ sK2_SY5 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[122]) ).

thf(131,plain,
    ! [SV34: $i > $i > $o] :
      ( ( ( SV34 @ sK1_X @ sK2_SY5 )
        = $true )
      | ( ( SV34
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ~ ~ ~ ( SV34 @ SX0 @ SX1 ) )
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ~ ~ ~ ( SV34 @ SX0 @ SX1 ) ) )
        = $false )
      | ( ( SV34
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ~ ~ ~ ( SV34 @ SX0 @ SX1 ) )
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ~ ~ ~ ( SV34 @ SX0 @ SX1 ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[127]) ).

thf(132,plain,
    ! [SV39: $i > $i > $o] :
      ( ( ( ~ ( SV39 @ sK1_X @ sK2_SY5 ) )
        = $true )
      | ( ( SV39
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ~ ~ ~ ~ ( SV39 @ SX0 @ SX1 ) )
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ~ ~ ~ ~ ( SV39 @ SX0 @ SX1 ) ) )
        = $true )
      | ( ( SV39
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ~ ~ ~ ~ ( SV39 @ SX0 @ SX1 ) )
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ~ ~ ~ ~ ( SV39 @ SX0 @ SX1 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[128]) ).

thf(134,plain,
    ! [SV39: $i > $i > $o] :
      ( ( ( SV39 @ sK1_X @ sK2_SY5 )
        = $false )
      | ( ( SV39
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ~ ~ ~ ~ ( SV39 @ SX0 @ SX1 ) )
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ~ ~ ~ ~ ( SV39 @ SX0 @ SX1 ) ) )
        = $true )
      | ( ( SV39
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ~ ~ ~ ~ ( SV39 @ SX0 @ SX1 ) )
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ~ ~ ~ ~ ( SV39 @ SX0 @ SX1 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[132]) ).

thf(136,plain,
    ! [SV8: $i > $i > $o] :
      ( ( ( SV8
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ( SV8 @ SX0 @ SX1 ) )
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ( SV8 @ SX0 @ SX1 ) ) )
        = $true )
      | ( ( ~ ( SV8 @ sK1_X @ sK2_SY5 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[50]) ).

thf(138,plain,
    ! [SV8: $i > $i > $o] :
      ( ( ( SV8 @ sK1_X @ sK2_SY5 )
        = $false )
      | ( ( SV8
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ( SV8 @ SX0 @ SX1 ) )
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ( SV8 @ SX0 @ SX1 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[136]) ).

thf(140,plain,
    ( ( sK1_X = sK2_SY5 )
    = $true ),
    inference(extuni,[status(esa)],[52]) ).

thf(141,plain,
    ! [SV3: $i > $i > $o] :
      ( ( ( SV3 @ sK1_X @ sK2_SY5 )
        = $true )
      | ( ( SV3 @ ( sK5_Z @ SV3 ) @ ( sK5_Z @ SV3 ) )
        = $false ) ),
    inference(sim,[status(thm)],[65]) ).

thf(142,plain,
    ! [SV19: $i > $i > $o] :
      ( ( ( SV19 @ sK1_X @ sK2_SY5 )
        = $false )
      | ( ( SV19
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ( SV19 @ SX0 @ SX1 ) )
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ( SV19 @ SX0 @ SX1 ) ) )
        = $true ) ),
    inference(sim,[status(thm)],[106]) ).

thf(143,plain,
    ! [SV24: $i > $i > $o] :
      ( ( ( SV24 @ sK1_X @ sK2_SY5 )
        = $true )
      | ( ( SV24
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ~ ( SV24 @ SX0 @ SX1 ) )
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ~ ( SV24 @ SX0 @ SX1 ) ) )
        = $false ) ),
    inference(sim,[status(thm)],[117]) ).

thf(144,plain,
    ! [SV29: $i > $i > $o] :
      ( ( ( SV29 @ sK1_X @ sK2_SY5 )
        = $false )
      | ( ( SV29
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ~ ~ ( SV29 @ SX0 @ SX1 ) )
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ~ ~ ( SV29 @ SX0 @ SX1 ) ) )
        = $true ) ),
    inference(sim,[status(thm)],[124]) ).

thf(145,plain,
    ! [SV34: $i > $i > $o] :
      ( ( ( SV34 @ sK1_X @ sK2_SY5 )
        = $true )
      | ( ( SV34
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ~ ~ ~ ( SV34 @ SX0 @ SX1 ) )
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ~ ~ ~ ( SV34 @ SX0 @ SX1 ) ) )
        = $false ) ),
    inference(sim,[status(thm)],[131]) ).

thf(146,plain,
    ! [SV39: $i > $i > $o] :
      ( ( ( SV39 @ sK1_X @ sK2_SY5 )
        = $false )
      | ( ( SV39
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ~ ~ ~ ~ ( SV39 @ SX0 @ SX1 ) )
          @ ( sK5_Z
            @ ^ [SX0: $i,SX1: $i] :
                ~ ~ ~ ~ ~ ( SV39 @ SX0 @ SX1 ) ) )
        = $true ) ),
    inference(sim,[status(thm)],[134]) ).

thf(147,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[42,146,145,144,143,142,141,140,138,47,45,43]) ).

thf(148,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[147,29]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SYO277^5 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.34  % Computer : n013.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 600
% 0.14/0.34  % DateTime : Sat Jul  9 02:17:59 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 0.14/0.35  
% 0.14/0.35   No.of.Axioms: 0
% 0.14/0.35  
% 0.14/0.35   Length.of.Defs: 0
% 0.14/0.35  
% 0.14/0.35   Contains.Choice.Funs: false
% 0.14/0.35  (rf:0,axioms:0,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:2,loop_count:0,foatp_calls:0,translation:fof_full)...
% 0.36/0.55  
% 0.36/0.55  ********************************
% 0.36/0.55  *   All subproblems solved!    *
% 0.36/0.55  ********************************
% 0.36/0.55  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:0,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:147,loop_count:0,foatp_calls:2,translation:fof_full)
% 0.36/0.55  
% 0.36/0.55  %**** Beginning of derivation protocol ****
% 0.36/0.55  % SZS output start CNFRefutation
% See solution above
% 0.36/0.55  
% 0.36/0.55  %**** End of derivation protocol ****
% 0.36/0.55  %**** no. of clauses in derivation: 104 ****
% 0.36/0.55  %**** clause counter: 147 ****
% 0.36/0.55  
% 0.36/0.55  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:0,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:147,loop_count:0,foatp_calls:2,translation:fof_full)
%------------------------------------------------------------------------------