TSTP Solution File: LCL736^5 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : LCL736^5 : 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 : n010.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 : Sun Jul 17 12:26:20 EDT 2022

% Result   : Theorem 0.19s 0.55s
% Output   : CNFRefutation 0.38s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   22
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   69 (  25 unt;   8 typ;   0 def)
%            Number of atoms       :  320 ( 108 equ;   0 cnn)
%            Maximal formula atoms :    3 (   5 avg)
%            Number of connectives : 1358 ( 127   ~;  91   |;   4   &;1124   @)
%                                         (   0 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   4 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :  514 ( 514   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   7 usr;   2 con; 0-3 aty)
%            Number of variables   :  442 ( 186   ^ 230   !;  26   ?; 442   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_b,type,
    b: $tType ).

thf(tp_sK1_Xp,type,
    sK1_Xp: ( ( b > $o ) > b ) > b > $o ).

thf(tp_sK2_SY11,type,
    sK2_SY11: ( ( b > $o ) > b ) > b ).

thf(tp_sK3_Xf,type,
    sK3_Xf: ( ( b > $o ) > b > b > $o ) > ( ( b > $o ) > b > b > $o ) > ( b > $o ) > b ).

thf(tp_sK4_SY14,type,
    sK4_SY14: ( b > $o ) > ( ( b > $o ) > b > b > $o ) > ( ( b > $o ) > b > b > $o ) > b ).

thf(tp_sK5_SY13,type,
    sK5_SY13: ( b > $o ) > ( ( b > $o ) > b > b > $o ) > ( ( b > $o ) > b > b > $o ) > b ).

thf(tp_sK6_Xx,type,
    sK6_Xx: ( ( b > $o ) > b > b > $o ) > ( ( b > $o ) > b > b > $o ) > b > $o ).

thf(tp_sK7_Eigen,type,
    sK7_Eigen: ( b > $o ) > b ).

thf(1,conjecture,
    ( ! [Xr_41: ( b > $o ) > b > b > $o,Xr_42: ( b > $o ) > b > b > $o] :
        ( ! [Xx: b > $o] :
          ? [Xy: b,Xw_11: b] :
            ( ( Xr_41 @ Xx @ Xy @ Xw_11 )
            | ( Xr_42 @ Xx @ Xy @ Xw_11 ) )
       => ? [Xf: ( b > $o ) > b] :
          ! [Xx: b > $o] :
          ? [Xw_11: b] :
            ( ( Xr_41 @ Xx @ ( Xf @ Xx ) @ Xw_11 )
            | ( Xr_42 @ Xx @ ( Xf @ Xx ) @ Xw_11 ) ) )
   => ? [Xj: ( b > $o ) > b] :
      ! [Xp: b > $o] :
        ( ? [Xz: b] : ( Xp @ Xz )
       => ( Xp @ ( Xj @ Xp ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cX5310D) ).

thf(2,negated_conjecture,
    ( ( ! [Xr_41: ( b > $o ) > b > b > $o,Xr_42: ( b > $o ) > b > b > $o] :
          ( ! [Xx: b > $o] :
            ? [Xy: b,Xw_11: b] :
              ( ( Xr_41 @ Xx @ Xy @ Xw_11 )
              | ( Xr_42 @ Xx @ Xy @ Xw_11 ) )
         => ? [Xf: ( b > $o ) > b] :
            ! [Xx: b > $o] :
            ? [Xw_11: b] :
              ( ( Xr_41 @ Xx @ ( Xf @ Xx ) @ Xw_11 )
              | ( Xr_42 @ Xx @ ( Xf @ Xx ) @ Xw_11 ) ) )
     => ? [Xj: ( b > $o ) > b] :
        ! [Xp: b > $o] :
          ( ? [Xz: b] : ( Xp @ Xz )
         => ( Xp @ ( Xj @ Xp ) ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ( ( ! [Xr_41: ( b > $o ) > b > b > $o,Xr_42: ( b > $o ) > b > b > $o] :
          ( ! [Xx: b > $o] :
            ? [Xy: b,Xw_11: b] :
              ( ( Xr_41 @ Xx @ Xy @ Xw_11 )
              | ( Xr_42 @ Xx @ Xy @ Xw_11 ) )
         => ? [Xf: ( b > $o ) > b] :
            ! [Xx: b > $o] :
            ? [Xw_11: b] :
              ( ( Xr_41 @ Xx @ ( Xf @ Xx ) @ Xw_11 )
              | ( Xr_42 @ Xx @ ( Xf @ Xx ) @ Xw_11 ) ) )
     => ? [Xj: ( b > $o ) > b] :
        ! [Xp: b > $o] :
          ( ? [Xz: b] : ( Xp @ Xz )
         => ( Xp @ ( Xj @ Xp ) ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(4,plain,
    ( ( ! [Xr_41: ( b > $o ) > b > b > $o,Xr_42: ( b > $o ) > b > b > $o] :
          ( ! [Xx: b > $o] :
            ? [Xy: b,Xw_11: b] :
              ( ( Xr_41 @ Xx @ Xy @ Xw_11 )
              | ( Xr_42 @ Xx @ Xy @ Xw_11 ) )
         => ? [Xf: ( b > $o ) > b] :
            ! [Xx: b > $o] :
            ? [Xw_11: b] :
              ( ( Xr_41 @ Xx @ ( Xf @ Xx ) @ Xw_11 )
              | ( Xr_42 @ Xx @ ( Xf @ Xx ) @ Xw_11 ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(5,plain,
    ( ( ? [Xj: ( b > $o ) > b] :
        ! [Xp: b > $o] :
          ( ? [Xz: b] : ( Xp @ Xz )
         => ( Xp @ ( Xj @ Xp ) ) ) )
    = $false ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(6,plain,
    ( ( ~ ? [Xj: ( b > $o ) > b] :
          ! [Xp: b > $o] :
            ( ? [Xz: b] : ( Xp @ Xz )
           => ( Xp @ ( Xj @ Xp ) ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[5]) ).

thf(7,plain,
    ( ( ! [Xj: ( b > $o ) > b] :
          ( ( sK1_Xp @ Xj @ ( sK2_SY11 @ Xj ) )
          & ~ ( sK1_Xp @ Xj @ ( Xj @ ( sK1_Xp @ Xj ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[6]) ).

thf(8,plain,
    ( ( ! [Xr_41: ( b > $o ) > b > b > $o,Xr_42: ( b > $o ) > b > b > $o] :
          ( ( ! [SY15: b,SY16: b] :
                ~ ( Xr_41 @ ( sK6_Xx @ Xr_42 @ Xr_41 ) @ SY15 @ SY16 )
            & ! [SY17: b,SY18: b] :
                ~ ( Xr_42 @ ( sK6_Xx @ Xr_42 @ Xr_41 ) @ SY17 @ SY18 ) )
          | ! [SY12: b > $o] :
              ( ( Xr_41 @ SY12 @ ( sK3_Xf @ Xr_42 @ Xr_41 @ SY12 ) @ ( sK5_SY13 @ SY12 @ Xr_42 @ Xr_41 ) )
              | ( Xr_42 @ SY12 @ ( sK3_Xf @ Xr_42 @ Xr_41 @ SY12 ) @ ( sK4_SY14 @ SY12 @ Xr_42 @ Xr_41 ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[4]) ).

thf(9,plain,
    ( ( ! [Xr_41: ( b > $o ) > b > b > $o,Xr_42: ( b > $o ) > b > b > $o] :
          ( ( ! [SY15: b,SY16: b] :
                ~ ( Xr_41 @ ( sK6_Xx @ Xr_42 @ Xr_41 ) @ SY15 @ SY16 )
            & ! [SY17: b,SY18: b] :
                ~ ( Xr_42 @ ( sK6_Xx @ Xr_42 @ Xr_41 ) @ SY17 @ SY18 ) )
          | ! [SY12: b > $o] :
              ( ( Xr_41 @ SY12 @ ( sK3_Xf @ Xr_42 @ Xr_41 @ SY12 ) @ ( sK5_SY13 @ SY12 @ Xr_42 @ Xr_41 ) )
              | ( Xr_42 @ SY12 @ ( sK3_Xf @ Xr_42 @ Xr_41 @ SY12 ) @ ( sK4_SY14 @ SY12 @ Xr_42 @ Xr_41 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[8]) ).

thf(10,plain,
    ( ( ! [Xj: ( b > $o ) > b] :
          ( ( sK1_Xp @ Xj @ ( sK2_SY11 @ Xj ) )
          & ~ ( sK1_Xp @ Xj @ ( Xj @ ( sK1_Xp @ Xj ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[7]) ).

thf(11,plain,
    ( ( ! [SX0: ( b > $o ) > b > b > $o,SX1: ( b > $o ) > b > b > $o] :
          ( ~ ( ~ ! [SX2: b,SX3: b] :
                    ~ ( SX0 @ ( sK6_Xx @ SX1 @ SX0 ) @ SX2 @ SX3 )
              | ~ ! [SX2: b,SX3: b] :
                    ~ ( SX1 @ ( sK6_Xx @ SX1 @ SX0 ) @ SX2 @ SX3 ) )
          | ! [SX2: b > $o] :
              ( ( SX0 @ SX2 @ ( sK3_Xf @ SX1 @ SX0 @ SX2 ) @ ( sK5_SY13 @ SX2 @ SX1 @ SX0 ) )
              | ( SX1 @ SX2 @ ( sK3_Xf @ SX1 @ SX0 @ SX2 ) @ ( sK4_SY14 @ SX2 @ SX1 @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9]) ).

thf(12,plain,
    ( ( ! [SX0: ( b > $o ) > b] :
          ~ ( ~ ( sK1_Xp @ SX0 @ ( sK2_SY11 @ SX0 ) )
            | ~ ~ ( sK1_Xp @ SX0 @ ( SX0 @ ( sK1_Xp @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10]) ).

thf(13,plain,
    ! [SV1: ( b > $o ) > b > b > $o] :
      ( ( ! [SY19: ( b > $o ) > b > b > $o] :
            ( ~ ( ~ ! [SY20: b,SY21: b] :
                      ~ ( SV1 @ ( sK6_Xx @ SY19 @ SV1 ) @ SY20 @ SY21 )
                | ~ ! [SY22: b,SY23: b] :
                      ~ ( SY19 @ ( sK6_Xx @ SY19 @ SV1 ) @ SY22 @ SY23 ) )
            | ! [SY24: b > $o] :
                ( ( SV1 @ SY24 @ ( sK3_Xf @ SY19 @ SV1 @ SY24 ) @ ( sK5_SY13 @ SY24 @ SY19 @ SV1 ) )
                | ( SY19 @ SY24 @ ( sK3_Xf @ SY19 @ SV1 @ SY24 ) @ ( sK4_SY14 @ SY24 @ SY19 @ SV1 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11]) ).

thf(14,plain,
    ! [SV2: ( b > $o ) > b] :
      ( ( ~ ( ~ ( sK1_Xp @ SV2 @ ( sK2_SY11 @ SV2 ) )
            | ~ ~ ( sK1_Xp @ SV2 @ ( SV2 @ ( sK1_Xp @ SV2 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[12]) ).

thf(15,plain,
    ! [SV3: ( b > $o ) > b > b > $o,SV1: ( b > $o ) > b > b > $o] :
      ( ( ~ ( ~ ! [SY25: b,SY26: b] :
                  ~ ( SV1 @ ( sK6_Xx @ SV3 @ SV1 ) @ SY25 @ SY26 )
            | ~ ! [SY27: b,SY28: b] :
                  ~ ( SV3 @ ( sK6_Xx @ SV3 @ SV1 ) @ SY27 @ SY28 ) )
        | ! [SY29: b > $o] :
            ( ( SV1 @ SY29 @ ( sK3_Xf @ SV3 @ SV1 @ SY29 ) @ ( sK5_SY13 @ SY29 @ SV3 @ SV1 ) )
            | ( SV3 @ SY29 @ ( sK3_Xf @ SV3 @ SV1 @ SY29 ) @ ( sK4_SY14 @ SY29 @ SV3 @ SV1 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[13]) ).

thf(16,plain,
    ! [SV2: ( b > $o ) > b] :
      ( ( ~ ( sK1_Xp @ SV2 @ ( sK2_SY11 @ SV2 ) )
        | ~ ~ ( sK1_Xp @ SV2 @ ( SV2 @ ( sK1_Xp @ SV2 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[14]) ).

thf(17,plain,
    ! [SV3: ( b > $o ) > b > b > $o,SV1: ( b > $o ) > b > b > $o] :
      ( ( ( ~ ( ~ ! [SY25: b,SY26: b] :
                    ~ ( SV1 @ ( sK6_Xx @ SV3 @ SV1 ) @ SY25 @ SY26 )
              | ~ ! [SY27: b,SY28: b] :
                    ~ ( SV3 @ ( sK6_Xx @ SV3 @ SV1 ) @ SY27 @ SY28 ) ) )
        = $true )
      | ( ( ! [SY29: b > $o] :
              ( ( SV1 @ SY29 @ ( sK3_Xf @ SV3 @ SV1 @ SY29 ) @ ( sK5_SY13 @ SY29 @ SV3 @ SV1 ) )
              | ( SV3 @ SY29 @ ( sK3_Xf @ SV3 @ SV1 @ SY29 ) @ ( sK4_SY14 @ SY29 @ SV3 @ SV1 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[15]) ).

thf(18,plain,
    ! [SV2: ( b > $o ) > b] :
      ( ( ~ ( sK1_Xp @ SV2 @ ( sK2_SY11 @ SV2 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[16]) ).

thf(19,plain,
    ! [SV2: ( b > $o ) > b] :
      ( ( ~ ~ ( sK1_Xp @ SV2 @ ( SV2 @ ( sK1_Xp @ SV2 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[16]) ).

thf(20,plain,
    ! [SV3: ( b > $o ) > b > b > $o,SV1: ( b > $o ) > b > b > $o] :
      ( ( ( ~ ! [SY25: b,SY26: b] :
                ~ ( SV1 @ ( sK6_Xx @ SV3 @ SV1 ) @ SY25 @ SY26 )
          | ~ ! [SY27: b,SY28: b] :
                ~ ( SV3 @ ( sK6_Xx @ SV3 @ SV1 ) @ SY27 @ SY28 ) )
        = $false )
      | ( ( ! [SY29: b > $o] :
              ( ( SV1 @ SY29 @ ( sK3_Xf @ SV3 @ SV1 @ SY29 ) @ ( sK5_SY13 @ SY29 @ SV3 @ SV1 ) )
              | ( SV3 @ SY29 @ ( sK3_Xf @ SV3 @ SV1 @ SY29 ) @ ( sK4_SY14 @ SY29 @ SV3 @ SV1 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[17]) ).

thf(21,plain,
    ! [SV2: ( b > $o ) > b] :
      ( ( sK1_Xp @ SV2 @ ( sK2_SY11 @ SV2 ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[18]) ).

thf(22,plain,
    ! [SV2: ( b > $o ) > b] :
      ( ( ~ ( sK1_Xp @ SV2 @ ( SV2 @ ( sK1_Xp @ SV2 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[19]) ).

thf(23,plain,
    ! [SV3: ( b > $o ) > b > b > $o,SV1: ( b > $o ) > b > b > $o] :
      ( ( ( ~ ! [SY25: b,SY26: b] :
                ~ ( SV1 @ ( sK6_Xx @ SV3 @ SV1 ) @ SY25 @ SY26 ) )
        = $false )
      | ( ( ! [SY29: b > $o] :
              ( ( SV1 @ SY29 @ ( sK3_Xf @ SV3 @ SV1 @ SY29 ) @ ( sK5_SY13 @ SY29 @ SV3 @ SV1 ) )
              | ( SV3 @ SY29 @ ( sK3_Xf @ SV3 @ SV1 @ SY29 ) @ ( sK4_SY14 @ SY29 @ SV3 @ SV1 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[20]) ).

thf(24,plain,
    ! [SV1: ( b > $o ) > b > b > $o,SV3: ( b > $o ) > b > b > $o] :
      ( ( ( ~ ! [SY27: b,SY28: b] :
                ~ ( SV3 @ ( sK6_Xx @ SV3 @ SV1 ) @ SY27 @ SY28 ) )
        = $false )
      | ( ( ! [SY29: b > $o] :
              ( ( SV1 @ SY29 @ ( sK3_Xf @ SV3 @ SV1 @ SY29 ) @ ( sK5_SY13 @ SY29 @ SV3 @ SV1 ) )
              | ( SV3 @ SY29 @ ( sK3_Xf @ SV3 @ SV1 @ SY29 ) @ ( sK4_SY14 @ SY29 @ SV3 @ SV1 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[20]) ).

thf(25,plain,
    ! [SV2: ( b > $o ) > b] :
      ( ( sK1_Xp @ SV2 @ ( SV2 @ ( sK1_Xp @ SV2 ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[22]) ).

thf(26,plain,
    ! [SV3: ( b > $o ) > b > b > $o,SV1: ( b > $o ) > b > b > $o] :
      ( ( ( ! [SY25: b,SY26: b] :
              ~ ( SV1 @ ( sK6_Xx @ SV3 @ SV1 ) @ SY25 @ SY26 ) )
        = $true )
      | ( ( ! [SY29: b > $o] :
              ( ( SV1 @ SY29 @ ( sK3_Xf @ SV3 @ SV1 @ SY29 ) @ ( sK5_SY13 @ SY29 @ SV3 @ SV1 ) )
              | ( SV3 @ SY29 @ ( sK3_Xf @ SV3 @ SV1 @ SY29 ) @ ( sK4_SY14 @ SY29 @ SV3 @ SV1 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[23]) ).

thf(27,plain,
    ! [SV1: ( b > $o ) > b > b > $o,SV3: ( b > $o ) > b > b > $o] :
      ( ( ( ! [SY27: b,SY28: b] :
              ~ ( SV3 @ ( sK6_Xx @ SV3 @ SV1 ) @ SY27 @ SY28 ) )
        = $true )
      | ( ( ! [SY29: b > $o] :
              ( ( SV1 @ SY29 @ ( sK3_Xf @ SV3 @ SV1 @ SY29 ) @ ( sK5_SY13 @ SY29 @ SV3 @ SV1 ) )
              | ( SV3 @ SY29 @ ( sK3_Xf @ SV3 @ SV1 @ SY29 ) @ ( sK4_SY14 @ SY29 @ SV3 @ SV1 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[24]) ).

thf(28,plain,
    ! [SV4: b,SV3: ( b > $o ) > b > b > $o,SV1: ( b > $o ) > b > b > $o] :
      ( ( ( ! [SY30: b] :
              ~ ( SV1 @ ( sK6_Xx @ SV3 @ SV1 ) @ SV4 @ SY30 ) )
        = $true )
      | ( ( ! [SY29: b > $o] :
              ( ( SV1 @ SY29 @ ( sK3_Xf @ SV3 @ SV1 @ SY29 ) @ ( sK5_SY13 @ SY29 @ SV3 @ SV1 ) )
              | ( SV3 @ SY29 @ ( sK3_Xf @ SV3 @ SV1 @ SY29 ) @ ( sK4_SY14 @ SY29 @ SV3 @ SV1 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[26]) ).

thf(29,plain,
    ! [SV5: b,SV1: ( b > $o ) > b > b > $o,SV3: ( b > $o ) > b > b > $o] :
      ( ( ( ! [SY31: b] :
              ~ ( SV3 @ ( sK6_Xx @ SV3 @ SV1 ) @ SV5 @ SY31 ) )
        = $true )
      | ( ( ! [SY29: b > $o] :
              ( ( SV1 @ SY29 @ ( sK3_Xf @ SV3 @ SV1 @ SY29 ) @ ( sK5_SY13 @ SY29 @ SV3 @ SV1 ) )
              | ( SV3 @ SY29 @ ( sK3_Xf @ SV3 @ SV1 @ SY29 ) @ ( sK4_SY14 @ SY29 @ SV3 @ SV1 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[27]) ).

thf(30,plain,
    ! [SV6: b,SV4: b,SV3: ( b > $o ) > b > b > $o,SV1: ( b > $o ) > b > b > $o] :
      ( ( ( ~ ( SV1 @ ( sK6_Xx @ SV3 @ SV1 ) @ SV4 @ SV6 ) )
        = $true )
      | ( ( ! [SY29: b > $o] :
              ( ( SV1 @ SY29 @ ( sK3_Xf @ SV3 @ SV1 @ SY29 ) @ ( sK5_SY13 @ SY29 @ SV3 @ SV1 ) )
              | ( SV3 @ SY29 @ ( sK3_Xf @ SV3 @ SV1 @ SY29 ) @ ( sK4_SY14 @ SY29 @ SV3 @ SV1 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[28]) ).

thf(31,plain,
    ! [SV7: b,SV5: b,SV1: ( b > $o ) > b > b > $o,SV3: ( b > $o ) > b > b > $o] :
      ( ( ( ~ ( SV3 @ ( sK6_Xx @ SV3 @ SV1 ) @ SV5 @ SV7 ) )
        = $true )
      | ( ( ! [SY29: b > $o] :
              ( ( SV1 @ SY29 @ ( sK3_Xf @ SV3 @ SV1 @ SY29 ) @ ( sK5_SY13 @ SY29 @ SV3 @ SV1 ) )
              | ( SV3 @ SY29 @ ( sK3_Xf @ SV3 @ SV1 @ SY29 ) @ ( sK4_SY14 @ SY29 @ SV3 @ SV1 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[29]) ).

thf(32,plain,
    ! [SV6: b,SV4: b,SV3: ( b > $o ) > b > b > $o,SV1: ( b > $o ) > b > b > $o] :
      ( ( ( SV1 @ ( sK6_Xx @ SV3 @ SV1 ) @ SV4 @ SV6 )
        = $false )
      | ( ( ! [SY29: b > $o] :
              ( ( SV1 @ SY29 @ ( sK3_Xf @ SV3 @ SV1 @ SY29 ) @ ( sK5_SY13 @ SY29 @ SV3 @ SV1 ) )
              | ( SV3 @ SY29 @ ( sK3_Xf @ SV3 @ SV1 @ SY29 ) @ ( sK4_SY14 @ SY29 @ SV3 @ SV1 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[30]) ).

thf(33,plain,
    ! [SV7: b,SV5: b,SV1: ( b > $o ) > b > b > $o,SV3: ( b > $o ) > b > b > $o] :
      ( ( ( SV3 @ ( sK6_Xx @ SV3 @ SV1 ) @ SV5 @ SV7 )
        = $false )
      | ( ( ! [SY29: b > $o] :
              ( ( SV1 @ SY29 @ ( sK3_Xf @ SV3 @ SV1 @ SY29 ) @ ( sK5_SY13 @ SY29 @ SV3 @ SV1 ) )
              | ( SV3 @ SY29 @ ( sK3_Xf @ SV3 @ SV1 @ SY29 ) @ ( sK4_SY14 @ SY29 @ SV3 @ SV1 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[31]) ).

thf(34,plain,
    ! [SV6: b,SV4: b,SV3: ( b > $o ) > b > b > $o,SV8: b > $o,SV1: ( b > $o ) > b > b > $o] :
      ( ( ( ( SV1 @ SV8 @ ( sK3_Xf @ SV3 @ SV1 @ SV8 ) @ ( sK5_SY13 @ SV8 @ SV3 @ SV1 ) )
          | ( SV3 @ SV8 @ ( sK3_Xf @ SV3 @ SV1 @ SV8 ) @ ( sK4_SY14 @ SV8 @ SV3 @ SV1 ) ) )
        = $true )
      | ( ( SV1 @ ( sK6_Xx @ SV3 @ SV1 ) @ SV4 @ SV6 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[32]) ).

thf(35,plain,
    ! [SV7: b,SV5: b,SV3: ( b > $o ) > b > b > $o,SV9: b > $o,SV1: ( b > $o ) > b > b > $o] :
      ( ( ( ( SV1 @ SV9 @ ( sK3_Xf @ SV3 @ SV1 @ SV9 ) @ ( sK5_SY13 @ SV9 @ SV3 @ SV1 ) )
          | ( SV3 @ SV9 @ ( sK3_Xf @ SV3 @ SV1 @ SV9 ) @ ( sK4_SY14 @ SV9 @ SV3 @ SV1 ) ) )
        = $true )
      | ( ( SV3 @ ( sK6_Xx @ SV3 @ SV1 ) @ SV5 @ SV7 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[33]) ).

thf(36,plain,
    ! [SV6: b,SV4: b,SV3: ( b > $o ) > b > b > $o,SV8: b > $o,SV1: ( b > $o ) > b > b > $o] :
      ( ( ( SV1 @ SV8 @ ( sK3_Xf @ SV3 @ SV1 @ SV8 ) @ ( sK5_SY13 @ SV8 @ SV3 @ SV1 ) )
        = $true )
      | ( ( SV3 @ SV8 @ ( sK3_Xf @ SV3 @ SV1 @ SV8 ) @ ( sK4_SY14 @ SV8 @ SV3 @ SV1 ) )
        = $true )
      | ( ( SV1 @ ( sK6_Xx @ SV3 @ SV1 ) @ SV4 @ SV6 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[34]) ).

thf(37,plain,
    ! [SV7: b,SV5: b,SV3: ( b > $o ) > b > b > $o,SV9: b > $o,SV1: ( b > $o ) > b > b > $o] :
      ( ( ( SV1 @ SV9 @ ( sK3_Xf @ SV3 @ SV1 @ SV9 ) @ ( sK5_SY13 @ SV9 @ SV3 @ SV1 ) )
        = $true )
      | ( ( SV3 @ SV9 @ ( sK3_Xf @ SV3 @ SV1 @ SV9 ) @ ( sK4_SY14 @ SV9 @ SV3 @ SV1 ) )
        = $true )
      | ( ( SV3 @ ( sK6_Xx @ SV3 @ SV1 ) @ SV5 @ SV7 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[35]) ).

thf(38,plain,
    ( ( sK1_Xp @ sK7_Eigen @ ( sK7_Eigen @ ( sK1_Xp @ sK7_Eigen ) ) )
    = $false ),
    inference(instantiate,[status(thm)],[25:[bind(SV2,$thf( sK7_Eigen ))]]) ).

thf(39,plain,
    ! [SV2: ( b > $o ) > b] :
      ( ( ~ ~ ! [SV10: b] :
                ~ ( sK1_Xp @ SV2 @ SV10 )
        | ( sK1_Xp @ SV2 @ ( sK7_Eigen @ ( sK1_Xp @ SV2 ) ) ) )
      = $true ),
    inference(choice,[status(thm)],[25]) ).

thf(40,plain,
    ! [SV11: ( b > $o ) > b] :
      ( ( ~ ~ ! [SX0: b] :
                ~ ( sK1_Xp @ SV11 @ SX0 )
        | ( sK1_Xp @ SV11 @ ( sK7_Eigen @ ( sK1_Xp @ SV11 ) ) ) )
      = $true ),
    inference(rename,[status(thm)],[39]) ).

thf(41,plain,
    ! [SV11: ( b > $o ) > b] :
      ( ( ( ~ ~ ! [SX0: b] :
                  ~ ( sK1_Xp @ SV11 @ SX0 ) )
        = $true )
      | ( ( sK1_Xp @ SV11 @ ( sK7_Eigen @ ( sK1_Xp @ SV11 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[40]) ).

thf(42,plain,
    ! [SV11: ( b > $o ) > b] :
      ( ( ( ~ ! [SX0: b] :
                ~ ( sK1_Xp @ SV11 @ SX0 ) )
        = $false )
      | ( ( sK1_Xp @ SV11 @ ( sK7_Eigen @ ( sK1_Xp @ SV11 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[41]) ).

thf(43,plain,
    ! [SV11: ( b > $o ) > b] :
      ( ( ( ! [SX0: b] :
              ~ ( sK1_Xp @ SV11 @ SX0 ) )
        = $true )
      | ( ( sK1_Xp @ SV11 @ ( sK7_Eigen @ ( sK1_Xp @ SV11 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[42]) ).

thf(44,plain,
    ! [SV12: b,SV11: ( b > $o ) > b] :
      ( ( ( ~ ( sK1_Xp @ SV11 @ SV12 ) )
        = $true )
      | ( ( sK1_Xp @ SV11 @ ( sK7_Eigen @ ( sK1_Xp @ SV11 ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[43]) ).

thf(45,plain,
    ! [SV12: b,SV11: ( b > $o ) > b] :
      ( ( ( sK1_Xp @ SV11 @ SV12 )
        = $false )
      | ( ( sK1_Xp @ SV11 @ ( sK7_Eigen @ ( sK1_Xp @ SV11 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[44]) ).

thf(47,plain,
    ! [SV6: b,SV4: b,SV8: b > $o,SV1: ( b > $o ) > b > b > $o] :
      ( ( ( SV1 @ SV8
          @ ( sK3_Xf
            @ ^ [SX0: b > $o,SX1: b,SX2: b] : $false
            @ SV1
            @ SV8 )
          @ ( sK5_SY13 @ SV8
            @ ^ [SX0: b > $o,SX1: b,SX2: b] : $false
            @ SV1 ) )
        = $true )
      | ( $false = $true )
      | ( ( SV1
          @ ( sK6_Xx
            @ ^ [SX0: b > $o,SX1: b,SX2: b] : $false
            @ SV1 )
          @ SV4
          @ SV6 )
        = $false ) ),
    inference(prim_subst,[status(thm)],[36:[bind(SV3,$thf( ^ [SV17: b > $o] : ^ [SV18: b] : ^ [SV19: b] : $false ))]]) ).

thf(48,plain,
    ! [SV6: b,SV4: b,SV16: ( b > $o ) > b > b > $o,SV8: b > $o,SV1: ( b > $o ) > b > b > $o] :
      ( ( ( SV1 @ SV8
          @ ( sK3_Xf
            @ ^ [SX0: b > $o,SX1: b,SX2: b] :
                ~ ( SV16 @ SX0 @ SX1 @ SX2 )
            @ SV1
            @ SV8 )
          @ ( sK5_SY13 @ SV8
            @ ^ [SX0: b > $o,SX1: b,SX2: b] :
                ~ ( SV16 @ SX0 @ SX1 @ SX2 )
            @ SV1 ) )
        = $true )
      | ( ( ~ ( SV16 @ SV8
              @ ( sK3_Xf
                @ ^ [SX0: b > $o,SX1: b,SX2: b] :
                    ~ ( SV16 @ SX0 @ SX1 @ SX2 )
                @ SV1
                @ SV8 )
              @ ( sK4_SY14 @ SV8
                @ ^ [SX0: b > $o,SX1: b,SX2: b] :
                    ~ ( SV16 @ SX0 @ SX1 @ SX2 )
                @ SV1 ) ) )
        = $true )
      | ( ( SV1
          @ ( sK6_Xx
            @ ^ [SX0: b > $o,SX1: b,SX2: b] :
                ~ ( SV16 @ SX0 @ SX1 @ SX2 )
            @ SV1 )
          @ SV4
          @ SV6 )
        = $false ) ),
    inference(prim_subst,[status(thm)],[36:[bind(SV3,$thf( ^ [SV13: b > $o] : ^ [SV14: b] : ^ [SV15: b] : ~ ( SV16 @ SV13 @ SV14 @ SV15 ) ))]]) ).

thf(51,plain,
    ! [SV6: b,SV4: b,SV3: ( b > $o ) > b > b > $o,SV8: b > $o,SV26: ( b > $o ) > b > b > $o] :
      ( ( ( ~ ( SV26 @ SV8
              @ ( sK3_Xf @ SV3
                @ ^ [SX0: b > $o,SX1: b,SX2: b] :
                    ~ ( SV26 @ SX0 @ SX1 @ SX2 )
                @ SV8 )
              @ ( sK5_SY13 @ SV8 @ SV3
                @ ^ [SX0: b > $o,SX1: b,SX2: b] :
                    ~ ( SV26 @ SX0 @ SX1 @ SX2 ) ) ) )
        = $true )
      | ( ( SV3 @ SV8
          @ ( sK3_Xf @ SV3
            @ ^ [SX0: b > $o,SX1: b,SX2: b] :
                ~ ( SV26 @ SX0 @ SX1 @ SX2 )
            @ SV8 )
          @ ( sK4_SY14 @ SV8 @ SV3
            @ ^ [SX0: b > $o,SX1: b,SX2: b] :
                ~ ( SV26 @ SX0 @ SX1 @ SX2 ) ) )
        = $true )
      | ( ( ~ ( SV26
              @ ( sK6_Xx @ SV3
                @ ^ [SX0: b > $o,SX1: b,SX2: b] :
                    ~ ( SV26 @ SX0 @ SX1 @ SX2 ) )
              @ SV4
              @ SV6 ) )
        = $false ) ),
    inference(prim_subst,[status(thm)],[36:[bind(SV1,$thf( ^ [SV23: b > $o] : ^ [SV24: b] : ^ [SV25: b] : ~ ( SV26 @ SV23 @ SV24 @ SV25 ) ))]]) ).

thf(54,plain,
    ! [SV7: b,SV5: b,SV16: ( b > $o ) > b > b > $o,SV9: b > $o,SV1: ( b > $o ) > b > b > $o] :
      ( ( ( SV1 @ SV9
          @ ( sK3_Xf
            @ ^ [SX0: b > $o,SX1: b,SX2: b] :
                ~ ( SV16 @ SX0 @ SX1 @ SX2 )
            @ SV1
            @ SV9 )
          @ ( sK5_SY13 @ SV9
            @ ^ [SX0: b > $o,SX1: b,SX2: b] :
                ~ ( SV16 @ SX0 @ SX1 @ SX2 )
            @ SV1 ) )
        = $true )
      | ( ( ~ ( SV16 @ SV9
              @ ( sK3_Xf
                @ ^ [SX0: b > $o,SX1: b,SX2: b] :
                    ~ ( SV16 @ SX0 @ SX1 @ SX2 )
                @ SV1
                @ SV9 )
              @ ( sK4_SY14 @ SV9
                @ ^ [SX0: b > $o,SX1: b,SX2: b] :
                    ~ ( SV16 @ SX0 @ SX1 @ SX2 )
                @ SV1 ) ) )
        = $true )
      | ( ( ~ ( SV16
              @ ( sK6_Xx
                @ ^ [SX0: b > $o,SX1: b,SX2: b] :
                    ~ ( SV16 @ SX0 @ SX1 @ SX2 )
                @ SV1 )
              @ SV5
              @ SV7 ) )
        = $false ) ),
    inference(prim_subst,[status(thm)],[37:[bind(SV3,$thf( ^ [SV13: b > $o] : ^ [SV14: b] : ^ [SV15: b] : ~ ( SV16 @ SV13 @ SV14 @ SV15 ) ))]]) ).

thf(56,plain,
    ! [SV7: b,SV5: b,SV9: b > $o,SV3: ( b > $o ) > b > b > $o] :
      ( ( $false = $true )
      | ( ( SV3 @ SV9
          @ ( sK3_Xf @ SV3
            @ ^ [SX0: b > $o,SX1: b,SX2: b] : $false
            @ SV9 )
          @ ( sK4_SY14 @ SV9 @ SV3
            @ ^ [SX0: b > $o,SX1: b,SX2: b] : $false ) )
        = $true )
      | ( ( SV3
          @ ( sK6_Xx @ SV3
            @ ^ [SX0: b > $o,SX1: b,SX2: b] : $false )
          @ SV5
          @ SV7 )
        = $false ) ),
    inference(prim_subst,[status(thm)],[37:[bind(SV1,$thf( ^ [SV27: b > $o] : ^ [SV28: b] : ^ [SV29: b] : $false ))]]) ).

thf(57,plain,
    ! [SV7: b,SV5: b,SV3: ( b > $o ) > b > b > $o,SV9: b > $o,SV26: ( b > $o ) > b > b > $o] :
      ( ( ( ~ ( SV26 @ SV9
              @ ( sK3_Xf @ SV3
                @ ^ [SX0: b > $o,SX1: b,SX2: b] :
                    ~ ( SV26 @ SX0 @ SX1 @ SX2 )
                @ SV9 )
              @ ( sK5_SY13 @ SV9 @ SV3
                @ ^ [SX0: b > $o,SX1: b,SX2: b] :
                    ~ ( SV26 @ SX0 @ SX1 @ SX2 ) ) ) )
        = $true )
      | ( ( SV3 @ SV9
          @ ( sK3_Xf @ SV3
            @ ^ [SX0: b > $o,SX1: b,SX2: b] :
                ~ ( SV26 @ SX0 @ SX1 @ SX2 )
            @ SV9 )
          @ ( sK4_SY14 @ SV9 @ SV3
            @ ^ [SX0: b > $o,SX1: b,SX2: b] :
                ~ ( SV26 @ SX0 @ SX1 @ SX2 ) ) )
        = $true )
      | ( ( SV3
          @ ( sK6_Xx @ SV3
            @ ^ [SX0: b > $o,SX1: b,SX2: b] :
                ~ ( SV26 @ SX0 @ SX1 @ SX2 ) )
          @ SV5
          @ SV7 )
        = $false ) ),
    inference(prim_subst,[status(thm)],[37:[bind(SV1,$thf( ^ [SV23: b > $o] : ^ [SV24: b] : ^ [SV25: b] : ~ ( SV26 @ SV23 @ SV24 @ SV25 ) ))]]) ).

thf(58,plain,
    ! [SV6: b,SV4: b,SV1: ( b > $o ) > b > b > $o,SV8: b > $o,SV16: ( b > $o ) > b > b > $o] :
      ( ( ( SV16 @ SV8
          @ ( sK3_Xf
            @ ^ [SX0: b > $o,SX1: b,SX2: b] :
                ~ ( SV16 @ SX0 @ SX1 @ SX2 )
            @ SV1
            @ SV8 )
          @ ( sK4_SY14 @ SV8
            @ ^ [SX0: b > $o,SX1: b,SX2: b] :
                ~ ( SV16 @ SX0 @ SX1 @ SX2 )
            @ SV1 ) )
        = $false )
      | ( ( SV1 @ SV8
          @ ( sK3_Xf
            @ ^ [SX0: b > $o,SX1: b,SX2: b] :
                ~ ( SV16 @ SX0 @ SX1 @ SX2 )
            @ SV1
            @ SV8 )
          @ ( sK5_SY13 @ SV8
            @ ^ [SX0: b > $o,SX1: b,SX2: b] :
                ~ ( SV16 @ SX0 @ SX1 @ SX2 )
            @ SV1 ) )
        = $true )
      | ( ( SV1
          @ ( sK6_Xx
            @ ^ [SX0: b > $o,SX1: b,SX2: b] :
                ~ ( SV16 @ SX0 @ SX1 @ SX2 )
            @ SV1 )
          @ SV4
          @ SV6 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[48]) ).

thf(59,plain,
    ! [SV6: b,SV4: b,SV3: ( b > $o ) > b > b > $o,SV8: b > $o,SV26: ( b > $o ) > b > b > $o] :
      ( ( ( SV26 @ SV8
          @ ( sK3_Xf @ SV3
            @ ^ [SX0: b > $o,SX1: b,SX2: b] :
                ~ ( SV26 @ SX0 @ SX1 @ SX2 )
            @ SV8 )
          @ ( sK5_SY13 @ SV8 @ SV3
            @ ^ [SX0: b > $o,SX1: b,SX2: b] :
                ~ ( SV26 @ SX0 @ SX1 @ SX2 ) ) )
        = $false )
      | ( ( SV3 @ SV8
          @ ( sK3_Xf @ SV3
            @ ^ [SX0: b > $o,SX1: b,SX2: b] :
                ~ ( SV26 @ SX0 @ SX1 @ SX2 )
            @ SV8 )
          @ ( sK4_SY14 @ SV8 @ SV3
            @ ^ [SX0: b > $o,SX1: b,SX2: b] :
                ~ ( SV26 @ SX0 @ SX1 @ SX2 ) ) )
        = $true )
      | ( ( ~ ( SV26
              @ ( sK6_Xx @ SV3
                @ ^ [SX0: b > $o,SX1: b,SX2: b] :
                    ~ ( SV26 @ SX0 @ SX1 @ SX2 ) )
              @ SV4
              @ SV6 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[51]) ).

thf(60,plain,
    ! [SV7: b,SV5: b,SV1: ( b > $o ) > b > b > $o,SV9: b > $o,SV16: ( b > $o ) > b > b > $o] :
      ( ( ( SV16 @ SV9
          @ ( sK3_Xf
            @ ^ [SX0: b > $o,SX1: b,SX2: b] :
                ~ ( SV16 @ SX0 @ SX1 @ SX2 )
            @ SV1
            @ SV9 )
          @ ( sK4_SY14 @ SV9
            @ ^ [SX0: b > $o,SX1: b,SX2: b] :
                ~ ( SV16 @ SX0 @ SX1 @ SX2 )
            @ SV1 ) )
        = $false )
      | ( ( SV1 @ SV9
          @ ( sK3_Xf
            @ ^ [SX0: b > $o,SX1: b,SX2: b] :
                ~ ( SV16 @ SX0 @ SX1 @ SX2 )
            @ SV1
            @ SV9 )
          @ ( sK5_SY13 @ SV9
            @ ^ [SX0: b > $o,SX1: b,SX2: b] :
                ~ ( SV16 @ SX0 @ SX1 @ SX2 )
            @ SV1 ) )
        = $true )
      | ( ( ~ ( SV16
              @ ( sK6_Xx
                @ ^ [SX0: b > $o,SX1: b,SX2: b] :
                    ~ ( SV16 @ SX0 @ SX1 @ SX2 )
                @ SV1 )
              @ SV5
              @ SV7 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[54]) ).

thf(61,plain,
    ! [SV7: b,SV5: b,SV3: ( b > $o ) > b > b > $o,SV9: b > $o,SV26: ( b > $o ) > b > b > $o] :
      ( ( ( SV26 @ SV9
          @ ( sK3_Xf @ SV3
            @ ^ [SX0: b > $o,SX1: b,SX2: b] :
                ~ ( SV26 @ SX0 @ SX1 @ SX2 )
            @ SV9 )
          @ ( sK5_SY13 @ SV9 @ SV3
            @ ^ [SX0: b > $o,SX1: b,SX2: b] :
                ~ ( SV26 @ SX0 @ SX1 @ SX2 ) ) )
        = $false )
      | ( ( SV3 @ SV9
          @ ( sK3_Xf @ SV3
            @ ^ [SX0: b > $o,SX1: b,SX2: b] :
                ~ ( SV26 @ SX0 @ SX1 @ SX2 )
            @ SV9 )
          @ ( sK4_SY14 @ SV9 @ SV3
            @ ^ [SX0: b > $o,SX1: b,SX2: b] :
                ~ ( SV26 @ SX0 @ SX1 @ SX2 ) ) )
        = $true )
      | ( ( SV3
          @ ( sK6_Xx @ SV3
            @ ^ [SX0: b > $o,SX1: b,SX2: b] :
                ~ ( SV26 @ SX0 @ SX1 @ SX2 ) )
          @ SV5
          @ SV7 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[57]) ).

thf(62,plain,
    ! [SV8: b > $o,SV6: b,SV4: b,SV3: ( b > $o ) > b > b > $o,SV26: ( b > $o ) > b > b > $o] :
      ( ( ( SV26
          @ ( sK6_Xx @ SV3
            @ ^ [SX0: b > $o,SX1: b,SX2: b] :
                ~ ( SV26 @ SX0 @ SX1 @ SX2 ) )
          @ SV4
          @ SV6 )
        = $true )
      | ( ( SV3 @ SV8
          @ ( sK3_Xf @ SV3
            @ ^ [SX0: b > $o,SX1: b,SX2: b] :
                ~ ( SV26 @ SX0 @ SX1 @ SX2 )
            @ SV8 )
          @ ( sK4_SY14 @ SV8 @ SV3
            @ ^ [SX0: b > $o,SX1: b,SX2: b] :
                ~ ( SV26 @ SX0 @ SX1 @ SX2 ) ) )
        = $true )
      | ( ( SV26 @ SV8
          @ ( sK3_Xf @ SV3
            @ ^ [SX0: b > $o,SX1: b,SX2: b] :
                ~ ( SV26 @ SX0 @ SX1 @ SX2 )
            @ SV8 )
          @ ( sK5_SY13 @ SV8 @ SV3
            @ ^ [SX0: b > $o,SX1: b,SX2: b] :
                ~ ( SV26 @ SX0 @ SX1 @ SX2 ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[59]) ).

thf(63,plain,
    ! [SV9: b > $o,SV7: b,SV5: b,SV1: ( b > $o ) > b > b > $o,SV16: ( b > $o ) > b > b > $o] :
      ( ( ( SV16
          @ ( sK6_Xx
            @ ^ [SX0: b > $o,SX1: b,SX2: b] :
                ~ ( SV16 @ SX0 @ SX1 @ SX2 )
            @ SV1 )
          @ SV5
          @ SV7 )
        = $true )
      | ( ( SV1 @ SV9
          @ ( sK3_Xf
            @ ^ [SX0: b > $o,SX1: b,SX2: b] :
                ~ ( SV16 @ SX0 @ SX1 @ SX2 )
            @ SV1
            @ SV9 )
          @ ( sK5_SY13 @ SV9
            @ ^ [SX0: b > $o,SX1: b,SX2: b] :
                ~ ( SV16 @ SX0 @ SX1 @ SX2 )
            @ SV1 ) )
        = $true )
      | ( ( SV16 @ SV9
          @ ( sK3_Xf
            @ ^ [SX0: b > $o,SX1: b,SX2: b] :
                ~ ( SV16 @ SX0 @ SX1 @ SX2 )
            @ SV1
            @ SV9 )
          @ ( sK4_SY14 @ SV9
            @ ^ [SX0: b > $o,SX1: b,SX2: b] :
                ~ ( SV16 @ SX0 @ SX1 @ SX2 )
            @ SV1 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[60]) ).

thf(64,plain,
    ! [SV6: b,SV4: b,SV8: b > $o,SV1: ( b > $o ) > b > b > $o] :
      ( ( ( SV1 @ SV8
          @ ( sK3_Xf
            @ ^ [SX0: b > $o,SX1: b,SX2: b] : $false
            @ SV1
            @ SV8 )
          @ ( sK5_SY13 @ SV8
            @ ^ [SX0: b > $o,SX1: b,SX2: b] : $false
            @ SV1 ) )
        = $true )
      | ( ( SV1
          @ ( sK6_Xx
            @ ^ [SX0: b > $o,SX1: b,SX2: b] : $false
            @ SV1 )
          @ SV4
          @ SV6 )
        = $false ) ),
    inference(sim,[status(thm)],[47]) ).

thf(65,plain,
    ! [SV7: b,SV5: b,SV9: b > $o,SV3: ( b > $o ) > b > b > $o] :
      ( ( ( SV3 @ SV9
          @ ( sK3_Xf @ SV3
            @ ^ [SX0: b > $o,SX1: b,SX2: b] : $false
            @ SV9 )
          @ ( sK4_SY14 @ SV9 @ SV3
            @ ^ [SX0: b > $o,SX1: b,SX2: b] : $false ) )
        = $true )
      | ( ( SV3
          @ ( sK6_Xx @ SV3
            @ ^ [SX0: b > $o,SX1: b,SX2: b] : $false )
          @ SV5
          @ SV7 )
        = $false ) ),
    inference(sim,[status(thm)],[56]) ).

thf(66,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[21,65,64,63,62,61,58,45,38,37,36,25]) ).

thf(67,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[66]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : LCL736^5 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34  % Computer : n010.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 : Mon Jul  4 12:31:17 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  
% 0.13/0.34   No.of.Axioms: 0
% 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: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)...
% 0.19/0.39  
% 0.19/0.39   *** Modified list of choice operators: sK7_Eigen ***
% 0.19/0.40  .
% 0.19/0.55  
% 0.19/0.55  ********************************
% 0.19/0.55  *   All subproblems solved!    *
% 0.19/0.55  ********************************
% 0.19/0.55  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:1,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:66,loop_count:0,foatp_calls:2,translation:fof_full)
% 0.38/0.56  
% 0.38/0.56  %**** Beginning of derivation protocol ****
% 0.38/0.56  % SZS output start CNFRefutation
% See solution above
% 0.38/0.56  
% 0.38/0.56  %**** End of derivation protocol ****
% 0.38/0.56  %**** no. of clauses in derivation: 61 ****
% 0.38/0.56  %**** clause counter: 66 ****
% 0.38/0.56  
% 0.38/0.56  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:1,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:66,loop_count:0,foatp_calls:2,translation:fof_full)
%------------------------------------------------------------------------------