TSTP Solution File: SYO359^5 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SYO359^5 : 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 : n027.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 17:33:33 EDT 2022

% Result   : Theorem 0.22s 0.46s
% Output   : CNFRefutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   32
%            Number of leaves      :   17
% Syntax   : Number of formulae    :  143 (  28 unt;  16 typ;   0 def)
%            Number of atoms       : 1263 ( 391 equ;   0 cnn)
%            Maximal formula atoms :    7 (   9 avg)
%            Number of connectives :  908 ( 150   ~; 324   |;   6   &; 404   @)
%                                         (   8 <=>;  16  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :   44 (  44   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   17 (  14 usr;   7 con; 0-2 aty)
%            Number of variables   :  110 (   0   ^ 110   !;   0   ?; 110   :)

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

thf(tp_gtype,type,
    gtype: $tType ).

thf(tp_f,type,
    f: b > $o ).

thf(tp_g,type,
    g: b > $o ).

thf(tp_h,type,
    h: ( b > $o ) > gtype ).

thf(tp_sK10_E,type,
    sK10_E: b > b ).

thf(tp_sK11_E,type,
    sK11_E: b > b ).

thf(tp_sK1_Xx,type,
    sK1_Xx: b ).

thf(tp_sK2_REN,type,
    sK2_REN: $o ).

thf(tp_sK3_SV14,type,
    sK3_SV14: b ).

thf(tp_sK4_E,type,
    sK4_E: b ).

thf(tp_sK5_E,type,
    sK5_E: b ).

thf(tp_sK6_SV18,type,
    sK6_SV18: b > b ).

thf(tp_sK7_SV19,type,
    sK7_SV19: b > b ).

thf(tp_sK8_SV20,type,
    sK8_SV20: b > b ).

thf(tp_sK9_SV21,type,
    sK9_SV21: b > b ).

thf(1,conjecture,
    ( ( ! [Xx: b] :
          ( ( f @ Xx )
        <=> ( g @ Xx ) )
     => ! [Xq: ( b > $o ) > $o] :
          ( ( Xq @ f )
         => ( Xq @ g ) ) )
   => ( ! [Xx: b] :
          ( ( f @ Xx )
        <=> ( g @ Xx ) )
     => ( ( h @ f )
        = ( h @ g ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cEXT1) ).

thf(2,negated_conjecture,
    ( ( ( ! [Xx: b] :
            ( ( f @ Xx )
          <=> ( g @ Xx ) )
       => ! [Xq: ( b > $o ) > $o] :
            ( ( Xq @ f )
           => ( Xq @ g ) ) )
     => ( ! [Xx: b] :
            ( ( f @ Xx )
          <=> ( g @ Xx ) )
       => ( ( h @ f )
          = ( h @ g ) ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ( ( ( ! [Xx: b] :
            ( ( f @ Xx )
          <=> ( g @ Xx ) )
       => ! [Xq: ( b > $o ) > $o] :
            ( ( Xq @ f )
           => ( Xq @ g ) ) )
     => ( ! [Xx: b] :
            ( ( f @ Xx )
          <=> ( g @ Xx ) )
       => ( ( h @ f )
          = ( h @ g ) ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(4,plain,
    ( ( ! [Xx: b] :
          ( ( f @ Xx )
        <=> ( g @ Xx ) )
     => ! [Xq: ( b > $o ) > $o] :
          ( ( Xq @ f )
         => ( Xq @ g ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(5,plain,
    ( ( ! [Xx: b] :
          ( ( f @ Xx )
        <=> ( g @ Xx ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(6,plain,
    ( ( ( h @ f )
      = ( h @ g ) )
    = $false ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(7,plain,
    ( ( ( ( h @ f )
       != ( h @ g ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[6]) ).

thf(8,plain,
    ( ( ( sK2_REN
        | ! [Xq: ( b > $o ) > $o] :
            ( ~ ( Xq @ f )
            | ( Xq @ g ) ) )
      & ( sK2_REN
       => ( ( ~ ( f @ sK1_Xx )
            | ~ ( g @ sK1_Xx ) )
          & ( ( f @ sK1_Xx )
            | ( g @ sK1_Xx ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[4]) ).

thf(9,plain,
    ( ( ! [Xx: b] :
          ( ~ ( f @ Xx )
          | ( g @ Xx ) )
      & ! [Xx: b] :
          ( ~ ( g @ Xx )
          | ( f @ Xx ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5]) ).

thf(10,plain,
    ( ( ! [Xx: b] :
          ( ~ ( f @ Xx )
          | ( g @ Xx ) )
      & ! [Xx: b] :
          ( ~ ( g @ Xx )
          | ( f @ Xx ) ) )
    = $true ),
    inference(copy,[status(thm)],[9]) ).

thf(11,plain,
    ( ( ( sK2_REN
        | ! [Xq: ( b > $o ) > $o] :
            ( ~ ( Xq @ f )
            | ( Xq @ g ) ) )
      & ( sK2_REN
       => ( ( ~ ( f @ sK1_Xx )
            | ~ ( g @ sK1_Xx ) )
          & ( ( f @ sK1_Xx )
            | ( g @ sK1_Xx ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[8]) ).

thf(12,plain,
    ( ( ( ( h @ f )
       != ( h @ g ) ) )
    = $true ),
    inference(copy,[status(thm)],[7]) ).

thf(13,plain,
    ( ( ~ ( ~ ( sK2_REN
              | ! [SX0: ( b > $o ) > $o] :
                  ( ~ ( SX0 @ f )
                  | ( SX0 @ g ) ) )
          | ~ ( ~ sK2_REN
              | ~ ( ~ ( ~ ( f @ sK1_Xx )
                      | ~ ( g @ sK1_Xx ) )
                  | ~ ( ( f @ sK1_Xx )
                      | ( g @ sK1_Xx ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11]) ).

thf(14,plain,
    ( ( ~ ( ~ ! [SX0: b] :
                ( ~ ( f @ SX0 )
                | ( g @ SX0 ) )
          | ~ ! [SX0: b] :
                ( ~ ( g @ SX0 )
                | ( f @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10]) ).

thf(15,plain,
    ( ( ( h @ f )
      = ( h @ g ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[12]) ).

thf(16,plain,
    ( ( ~ ( sK2_REN
          | ! [SX0: ( b > $o ) > $o] :
              ( ~ ( SX0 @ f )
              | ( SX0 @ g ) ) )
      | ~ ( ~ sK2_REN
          | ~ ( ~ ( ~ ( f @ sK1_Xx )
                  | ~ ( g @ sK1_Xx ) )
              | ~ ( ( f @ sK1_Xx )
                  | ( g @ sK1_Xx ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[13]) ).

thf(17,plain,
    ( ( ~ ! [SX0: b] :
            ( ~ ( f @ SX0 )
            | ( g @ SX0 ) )
      | ~ ! [SX0: b] :
            ( ~ ( g @ SX0 )
            | ( f @ SX0 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[14]) ).

thf(18,plain,
    ( ( ~ ( sK2_REN
          | ! [SX0: ( b > $o ) > $o] :
              ( ~ ( SX0 @ f )
              | ( SX0 @ g ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[16]) ).

thf(19,plain,
    ( ( ~ ( ~ sK2_REN
          | ~ ( ~ ( ~ ( f @ sK1_Xx )
                  | ~ ( g @ sK1_Xx ) )
              | ~ ( ( f @ sK1_Xx )
                  | ( g @ sK1_Xx ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[16]) ).

thf(20,plain,
    ( ( ~ ! [SX0: b] :
            ( ~ ( f @ SX0 )
            | ( g @ SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[17]) ).

thf(21,plain,
    ( ( ~ ! [SX0: b] :
            ( ~ ( g @ SX0 )
            | ( f @ SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[17]) ).

thf(22,plain,
    ( ( sK2_REN
      | ! [SX0: ( b > $o ) > $o] :
          ( ~ ( SX0 @ f )
          | ( SX0 @ g ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[18]) ).

thf(23,plain,
    ( ( ~ sK2_REN
      | ~ ( ~ ( ~ ( f @ sK1_Xx )
              | ~ ( g @ sK1_Xx ) )
          | ~ ( ( f @ sK1_Xx )
              | ( g @ sK1_Xx ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[19]) ).

thf(24,plain,
    ( ( ! [SX0: b] :
          ( ~ ( f @ SX0 )
          | ( g @ SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[20]) ).

thf(25,plain,
    ( ( ! [SX0: b] :
          ( ~ ( g @ SX0 )
          | ( f @ SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[21]) ).

thf(26,plain,
    ( ( sK2_REN = $true )
    | ( ( ! [SX0: ( b > $o ) > $o] :
            ( ~ ( SX0 @ f )
            | ( SX0 @ g ) ) )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[22]) ).

thf(27,plain,
    ( ( ( ~ sK2_REN )
      = $true )
    | ( ( ~ ( ~ ( ~ ( f @ sK1_Xx )
                | ~ ( g @ sK1_Xx ) )
            | ~ ( ( f @ sK1_Xx )
                | ( g @ sK1_Xx ) ) ) )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[23]) ).

thf(28,plain,
    ! [SV1: b] :
      ( ( ~ ( f @ SV1 )
        | ( g @ SV1 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[24]) ).

thf(29,plain,
    ! [SV2: b] :
      ( ( ~ ( g @ SV2 )
        | ( f @ SV2 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[25]) ).

thf(30,plain,
    ! [SV3: ( b > $o ) > $o] :
      ( ( ( ~ ( SV3 @ f )
          | ( SV3 @ g ) )
        = $true )
      | ( sK2_REN = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[26]) ).

thf(31,plain,
    ( ( sK2_REN = $false )
    | ( ( ~ ( ~ ( ~ ( f @ sK1_Xx )
                | ~ ( g @ sK1_Xx ) )
            | ~ ( ( f @ sK1_Xx )
                | ( g @ sK1_Xx ) ) ) )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[27]) ).

thf(32,plain,
    ! [SV1: b] :
      ( ( ( ~ ( f @ SV1 ) )
        = $true )
      | ( ( g @ SV1 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[28]) ).

thf(33,plain,
    ! [SV2: b] :
      ( ( ( ~ ( g @ SV2 ) )
        = $true )
      | ( ( f @ SV2 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[29]) ).

thf(34,plain,
    ! [SV3: ( b > $o ) > $o] :
      ( ( ( ~ ( SV3 @ f ) )
        = $true )
      | ( ( SV3 @ g )
        = $true )
      | ( sK2_REN = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[30]) ).

thf(35,plain,
    ( ( ( ~ ( ~ ( f @ sK1_Xx )
            | ~ ( g @ sK1_Xx ) )
        | ~ ( ( f @ sK1_Xx )
            | ( g @ sK1_Xx ) ) )
      = $false )
    | ( sK2_REN = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[31]) ).

thf(36,plain,
    ! [SV1: b] :
      ( ( ( f @ SV1 )
        = $false )
      | ( ( g @ SV1 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[32]) ).

thf(37,plain,
    ! [SV2: b] :
      ( ( ( g @ SV2 )
        = $false )
      | ( ( f @ SV2 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[33]) ).

thf(38,plain,
    ! [SV3: ( b > $o ) > $o] :
      ( ( ( SV3 @ f )
        = $false )
      | ( ( SV3 @ g )
        = $true )
      | ( sK2_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[34]) ).

thf(39,plain,
    ( ( ( ~ ( ~ ( f @ sK1_Xx )
            | ~ ( g @ sK1_Xx ) ) )
      = $false )
    | ( sK2_REN = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[35]) ).

thf(40,plain,
    ( ( ( ~ ( ( f @ sK1_Xx )
            | ( g @ sK1_Xx ) ) )
      = $false )
    | ( sK2_REN = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[35]) ).

thf(41,plain,
    ( ( ( ~ ( f @ sK1_Xx )
        | ~ ( g @ sK1_Xx ) )
      = $true )
    | ( sK2_REN = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[39]) ).

thf(42,plain,
    ( ( ( ( f @ sK1_Xx )
        | ( g @ sK1_Xx ) )
      = $true )
    | ( sK2_REN = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[40]) ).

thf(43,plain,
    ( ( ( ~ ( f @ sK1_Xx ) )
      = $true )
    | ( ( ~ ( g @ sK1_Xx ) )
      = $true )
    | ( sK2_REN = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[41]) ).

thf(44,plain,
    ( ( ( f @ sK1_Xx )
      = $true )
    | ( ( g @ sK1_Xx )
      = $true )
    | ( sK2_REN = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[42]) ).

thf(45,plain,
    ( ( ( f @ sK1_Xx )
      = $false )
    | ( ( ~ ( g @ sK1_Xx ) )
      = $true )
    | ( sK2_REN = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[43]) ).

thf(46,plain,
    ( ( ( g @ sK1_Xx )
      = $false )
    | ( ( f @ sK1_Xx )
      = $false )
    | ( sK2_REN = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[45]) ).

thf(47,plain,
    ( ( ( f = f )
      = $false )
    | ( ( g = f )
      = $true )
    | ( sK2_REN = $true ) ),
    inference(replace_leibnizEQ,[status(thm)],[38:[bind(SV3,$thf( ^ [SV4: b > $o] : ( SV4 = f ) ))]]) ).

thf(48,plain,
    ( ( ( g = f )
      = $true )
    | ( sK2_REN = $true ) ),
    inference(sim,[status(thm)],[47]) ).

thf(51,plain,
    ! [SV6: ( b > $o ) > $o] :
      ( ( ( ~ ( SV6 @ f ) )
        = $false )
      | ( ( ~ ( SV6 @ g ) )
        = $true )
      | ( sK2_REN = $true ) ),
    inference(prim_subst,[status(thm)],[38:[bind(SV3,$thf( ^ [SV5: b > $o] : ~ ( SV6 @ SV5 ) ))]]) ).

thf(53,plain,
    ( ( ( f = f )
      = $false )
    | ( ( g = f )
      = $true )
    | ( sK2_REN = $true ) ),
    inference(prim_subst,[status(thm)],[38:[bind(SV3,$thf( ^ [SV10: b > $o] : ( SV10 = f ) ))]]) ).

thf(54,plain,
    ( ( sK2_REN = $true )
    | ( ( ( g = f )
        = sK2_REN )
      = $false ) ),
    inference(fac_restr,[status(thm)],[48]) ).

thf(55,plain,
    ! [SV11: b] :
      ( ( sK2_REN = $true )
      | ( ( ( g @ SV11 )
          = ( f @ SV11 ) )
        = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[48]) ).

thf(56,plain,
    ! [SV11: b] :
      ( ( ( g @ SV11 )
        = $true )
      | ( ( f @ SV11 )
        = $false )
      | ( sK2_REN = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[55]) ).

thf(57,plain,
    ! [SV11: b] :
      ( ( ( g @ SV11 )
        = $false )
      | ( ( f @ SV11 )
        = $true )
      | ( sK2_REN = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[55]) ).

thf(58,plain,
    ( ( ( ~ ( ( g = f )
            | sK2_REN )
        | ~ ( ( g != f )
            | ~ sK2_REN ) )
      = $false )
    | ( sK2_REN = $true ) ),
    inference(extcnf_equal_neg,[status(thm)],[54]) ).

thf(60,plain,
    ( ( ( ~ ( ( g = f )
            | sK2_REN ) )
      = $false )
    | ( sK2_REN = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[58]) ).

thf(62,plain,
    ( ( ( ( g = f )
        | sK2_REN )
      = $true )
    | ( sK2_REN = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[60]) ).

thf(64,plain,
    ( ( ( g = f )
      = $true )
    | ( sK2_REN = $true )
    | ( sK2_REN = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[62]) ).

thf(66,plain,
    ( ( ( ! [SV12: b] :
            ( ( g @ SV12 )
            = ( f @ SV12 ) ) )
      = $true )
    | ( sK2_REN = $true )
    | ( sK2_REN = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[64]) ).

thf(67,plain,
    ( ( ( g = f )
      = $true )
    | ( sK2_REN = $true )
    | ( sK2_REN = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[64]) ).

thf(69,plain,
    ! [SV13: b] :
      ( ( ( ( g @ SV13 )
          = ( f @ SV13 ) )
        = $true )
      | ( sK2_REN = $true )
      | ( sK2_REN = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[66]) ).

thf(72,plain,
    ! [SV13: b] :
      ( ( ( ~ ( ( g @ SV13 )
              | ( f @ SV13 ) )
          | ~ ( ~ ( g @ SV13 )
              | ~ ( f @ SV13 ) ) )
        = $true )
      | ( sK2_REN = $true )
      | ( sK2_REN = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[69]) ).

thf(73,plain,
    ! [SV13: b] :
      ( ( ( ( g @ SV13 )
          = ( f @ SV13 ) )
        = $true )
      | ( sK2_REN = $true )
      | ( sK2_REN = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[69]) ).

thf(76,plain,
    ! [SV13: b] :
      ( ( ( ~ ( ( g @ SV13 )
              | ( f @ SV13 ) ) )
        = $true )
      | ( ( ~ ( ~ ( g @ SV13 )
              | ~ ( f @ SV13 ) ) )
        = $true )
      | ( sK2_REN = $true )
      | ( sK2_REN = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[72]) ).

thf(79,plain,
    ! [SV13: b] :
      ( ( ( ( g @ SV13 )
          | ( f @ SV13 ) )
        = $false )
      | ( ( ~ ( ~ ( g @ SV13 )
              | ~ ( f @ SV13 ) ) )
        = $true )
      | ( sK2_REN = $true )
      | ( sK2_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[76]) ).

thf(83,plain,
    ! [SV13: b] :
      ( ( ( g @ SV13 )
        = $false )
      | ( ( ~ ( ~ ( g @ SV13 )
              | ~ ( f @ SV13 ) ) )
        = $true )
      | ( sK2_REN = $true )
      | ( sK2_REN = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[79]) ).

thf(84,plain,
    ! [SV13: b] :
      ( ( ( f @ SV13 )
        = $false )
      | ( ( ~ ( ~ ( g @ SV13 )
              | ~ ( f @ SV13 ) ) )
        = $true )
      | ( sK2_REN = $true )
      | ( sK2_REN = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[79]) ).

thf(87,plain,
    ! [SV13: b] :
      ( ( ( ~ ( g @ SV13 )
          | ~ ( f @ SV13 ) )
        = $false )
      | ( ( g @ SV13 )
        = $false )
      | ( sK2_REN = $true )
      | ( sK2_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[83]) ).

thf(88,plain,
    ! [SV13: b] :
      ( ( ( ~ ( g @ SV13 )
          | ~ ( f @ SV13 ) )
        = $false )
      | ( ( f @ SV13 )
        = $false )
      | ( sK2_REN = $true )
      | ( sK2_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[84]) ).

thf(92,plain,
    ! [SV13: b] :
      ( ( ( ~ ( f @ SV13 ) )
        = $false )
      | ( ( g @ SV13 )
        = $false )
      | ( sK2_REN = $true )
      | ( sK2_REN = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[87]) ).

thf(93,plain,
    ! [SV13: b] :
      ( ( ( ~ ( g @ SV13 ) )
        = $false )
      | ( ( f @ SV13 )
        = $false )
      | ( sK2_REN = $true )
      | ( sK2_REN = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[88]) ).

thf(98,plain,
    ! [SV13: b] :
      ( ( ( f @ SV13 )
        = $true )
      | ( ( g @ SV13 )
        = $false )
      | ( sK2_REN = $true )
      | ( sK2_REN = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[92]) ).

thf(99,plain,
    ! [SV13: b] :
      ( ( ( g @ SV13 )
        = $true )
      | ( ( f @ SV13 )
        = $false )
      | ( sK2_REN = $true )
      | ( sK2_REN = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[93]) ).

thf(103,plain,
    ! [SV15: b] :
      ( ( sK2_REN = $true )
      | ( sK2_REN = $true )
      | ( ( ( g @ SV15 )
          = ( f @ SV15 ) )
        = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[67]) ).

thf(104,plain,
    ! [SV13: b] :
      ( ( sK2_REN = $true )
      | ( sK2_REN = $true )
      | ( ( g @ SV13 )
        = $true )
      | ( ( f @ SV13 )
        = $false ) ),
    inference(extcnf_equal_pos,[status(thm)],[73]) ).

thf(105,plain,
    ! [SV13: b] :
      ( ( sK2_REN = $true )
      | ( sK2_REN = $true )
      | ( ( g @ SV13 )
        = $false )
      | ( ( f @ SV13 )
        = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[73]) ).

thf(106,plain,
    ! [SV15: b] :
      ( ( ( g @ SV15 )
        = $true )
      | ( ( f @ SV15 )
        = $false )
      | ( sK2_REN = $true )
      | ( sK2_REN = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[103]) ).

thf(107,plain,
    ! [SV15: b] :
      ( ( ( g @ SV15 )
        = $false )
      | ( ( f @ SV15 )
        = $true )
      | ( sK2_REN = $true )
      | ( sK2_REN = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[103]) ).

thf(110,plain,
    ( ( ( f @ sK5_E )
      = $true )
    | ( ( g @ sK5_E )
      = $true ) ),
    inference(extuni,[status(esa)],[15]) ).

thf(111,plain,
    ( ( ( f @ sK5_E )
      = $false )
    | ( ( g @ sK5_E )
      = $false ) ),
    inference(extuni,[status(esa)],[15]) ).

thf(113,plain,
    ! [SV17: b] :
      ( ( sK2_REN = $true )
      | ( ( ( g @ SV17 )
          = ( f @ SV17 ) )
        = $true )
      | ( ( f = f )
        = $false ) ),
    inference(extcnf_equal_pos,[status(thm)],[53]) ).

thf(116,plain,
    ! [SV17: b] :
      ( ( ( f = f )
        = $false )
      | ( ( g @ SV17 )
        = $true )
      | ( ( f @ SV17 )
        = $false )
      | ( sK2_REN = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[113]) ).

thf(117,plain,
    ! [SV17: b] :
      ( ( ( f = f )
        = $false )
      | ( ( g @ SV17 )
        = $false )
      | ( ( f @ SV17 )
        = $true )
      | ( sK2_REN = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[113]) ).

thf(118,plain,
    ! [SV6: ( b > $o ) > $o] :
      ( ( ( SV6 @ f )
        = $true )
      | ( ( ~ ( SV6 @ g ) )
        = $true )
      | ( sK2_REN = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[51]) ).

thf(123,plain,
    ! [SV17: b] :
      ( ( ( ! [SV20: b] :
              ( ( f @ SV20 )
              = ( f @ SV20 ) ) )
        = $false )
      | ( ( g @ SV17 )
        = $false )
      | ( ( f @ SV17 )
        = $true )
      | ( sK2_REN = $true ) ),
    inference(extcnf_equal_neg,[status(thm)],[117]) ).

thf(124,plain,
    ! [SV17: b] :
      ( ( ( f = f )
        = $false )
      | ( ( g @ SV17 )
        = $false )
      | ( ( f @ SV17 )
        = $true )
      | ( sK2_REN = $true ) ),
    inference(extcnf_equal_neg,[status(thm)],[117]) ).

thf(125,plain,
    ! [SV17: b] :
      ( ( ( ! [SV21: b] :
              ( ( f @ SV21 )
              = ( f @ SV21 ) ) )
        = $false )
      | ( ( g @ SV17 )
        = $true )
      | ( ( f @ SV17 )
        = $false )
      | ( sK2_REN = $true ) ),
    inference(extcnf_equal_neg,[status(thm)],[116]) ).

thf(126,plain,
    ! [SV17: b] :
      ( ( ( f = f )
        = $false )
      | ( ( g @ SV17 )
        = $true )
      | ( ( f @ SV17 )
        = $false )
      | ( sK2_REN = $true ) ),
    inference(extcnf_equal_neg,[status(thm)],[116]) ).

thf(127,plain,
    ! [SV6: ( b > $o ) > $o] :
      ( ( ( SV6 @ g )
        = $false )
      | ( ( SV6 @ f )
        = $true )
      | ( sK2_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[118]) ).

thf(130,plain,
    ! [SV17: b] :
      ( ( ( ( f @ ( sK8_SV20 @ SV17 ) )
          = ( f @ ( sK8_SV20 @ SV17 ) ) )
        = $false )
      | ( ( g @ SV17 )
        = $false )
      | ( ( f @ SV17 )
        = $true )
      | ( sK2_REN = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[123]) ).

thf(131,plain,
    ! [SV17: b] :
      ( ( ( ( f @ ( sK9_SV21 @ SV17 ) )
          = ( f @ ( sK9_SV21 @ SV17 ) ) )
        = $false )
      | ( ( g @ SV17 )
        = $true )
      | ( ( f @ SV17 )
        = $false )
      | ( sK2_REN = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[125]) ).

thf(136,plain,
    ! [SV17: b] :
      ( ( ( ~ ( ( f @ ( sK8_SV20 @ SV17 ) )
              | ( f @ ( sK8_SV20 @ SV17 ) ) )
          | ~ ( ~ ( f @ ( sK8_SV20 @ SV17 ) )
              | ~ ( f @ ( sK8_SV20 @ SV17 ) ) ) )
        = $false )
      | ( ( g @ SV17 )
        = $false )
      | ( ( f @ SV17 )
        = $true )
      | ( sK2_REN = $true ) ),
    inference(extcnf_equal_neg,[status(thm)],[130]) ).

thf(137,plain,
    ! [SV17: b] :
      ( ( ( ( f @ ( sK8_SV20 @ SV17 ) )
          = ( f @ ( sK8_SV20 @ SV17 ) ) )
        = $false )
      | ( ( g @ SV17 )
        = $false )
      | ( ( f @ SV17 )
        = $true )
      | ( sK2_REN = $true ) ),
    inference(extcnf_equal_neg,[status(thm)],[130]) ).

thf(138,plain,
    ! [SV17: b] :
      ( ( ( ~ ( ( f @ ( sK9_SV21 @ SV17 ) )
              | ( f @ ( sK9_SV21 @ SV17 ) ) )
          | ~ ( ~ ( f @ ( sK9_SV21 @ SV17 ) )
              | ~ ( f @ ( sK9_SV21 @ SV17 ) ) ) )
        = $false )
      | ( ( g @ SV17 )
        = $true )
      | ( ( f @ SV17 )
        = $false )
      | ( sK2_REN = $true ) ),
    inference(extcnf_equal_neg,[status(thm)],[131]) ).

thf(139,plain,
    ! [SV17: b] :
      ( ( ( ( f @ ( sK9_SV21 @ SV17 ) )
          = ( f @ ( sK9_SV21 @ SV17 ) ) )
        = $false )
      | ( ( g @ SV17 )
        = $true )
      | ( ( f @ SV17 )
        = $false )
      | ( sK2_REN = $true ) ),
    inference(extcnf_equal_neg,[status(thm)],[131]) ).

thf(144,plain,
    ! [SV17: b] :
      ( ( ( ~ ( ( f @ ( sK8_SV20 @ SV17 ) )
              | ( f @ ( sK8_SV20 @ SV17 ) ) ) )
        = $false )
      | ( ( g @ SV17 )
        = $false )
      | ( ( f @ SV17 )
        = $true )
      | ( sK2_REN = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[136]) ).

thf(145,plain,
    ! [SV17: b] :
      ( ( ( ~ ( ~ ( f @ ( sK8_SV20 @ SV17 ) )
              | ~ ( f @ ( sK8_SV20 @ SV17 ) ) ) )
        = $false )
      | ( ( g @ SV17 )
        = $false )
      | ( ( f @ SV17 )
        = $true )
      | ( sK2_REN = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[136]) ).

thf(146,plain,
    ! [SV17: b] :
      ( ( ( ~ ( ( f @ ( sK9_SV21 @ SV17 ) )
              | ( f @ ( sK9_SV21 @ SV17 ) ) ) )
        = $false )
      | ( ( g @ SV17 )
        = $true )
      | ( ( f @ SV17 )
        = $false )
      | ( sK2_REN = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[138]) ).

thf(147,plain,
    ! [SV17: b] :
      ( ( ( ~ ( ~ ( f @ ( sK9_SV21 @ SV17 ) )
              | ~ ( f @ ( sK9_SV21 @ SV17 ) ) ) )
        = $false )
      | ( ( g @ SV17 )
        = $true )
      | ( ( f @ SV17 )
        = $false )
      | ( sK2_REN = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[138]) ).

thf(152,plain,
    ! [SV17: b] :
      ( ( ( ( f @ ( sK8_SV20 @ SV17 ) )
          | ( f @ ( sK8_SV20 @ SV17 ) ) )
        = $true )
      | ( ( g @ SV17 )
        = $false )
      | ( ( f @ SV17 )
        = $true )
      | ( sK2_REN = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[144]) ).

thf(153,plain,
    ! [SV17: b] :
      ( ( ( ~ ( f @ ( sK8_SV20 @ SV17 ) )
          | ~ ( f @ ( sK8_SV20 @ SV17 ) ) )
        = $true )
      | ( ( g @ SV17 )
        = $false )
      | ( ( f @ SV17 )
        = $true )
      | ( sK2_REN = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[145]) ).

thf(154,plain,
    ! [SV17: b] :
      ( ( ( ( f @ ( sK9_SV21 @ SV17 ) )
          | ( f @ ( sK9_SV21 @ SV17 ) ) )
        = $true )
      | ( ( g @ SV17 )
        = $true )
      | ( ( f @ SV17 )
        = $false )
      | ( sK2_REN = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[146]) ).

thf(155,plain,
    ! [SV17: b] :
      ( ( ( ~ ( f @ ( sK9_SV21 @ SV17 ) )
          | ~ ( f @ ( sK9_SV21 @ SV17 ) ) )
        = $true )
      | ( ( g @ SV17 )
        = $true )
      | ( ( f @ SV17 )
        = $false )
      | ( sK2_REN = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[147]) ).

thf(160,plain,
    ! [SV17: b] :
      ( ( ( f @ ( sK8_SV20 @ SV17 ) )
        = $true )
      | ( ( f @ ( sK8_SV20 @ SV17 ) )
        = $true )
      | ( ( g @ SV17 )
        = $false )
      | ( ( f @ SV17 )
        = $true )
      | ( sK2_REN = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[152]) ).

thf(161,plain,
    ! [SV17: b] :
      ( ( ( ~ ( f @ ( sK8_SV20 @ SV17 ) ) )
        = $true )
      | ( ( ~ ( f @ ( sK8_SV20 @ SV17 ) ) )
        = $true )
      | ( ( g @ SV17 )
        = $false )
      | ( ( f @ SV17 )
        = $true )
      | ( sK2_REN = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[153]) ).

thf(162,plain,
    ! [SV17: b] :
      ( ( ( f @ ( sK9_SV21 @ SV17 ) )
        = $true )
      | ( ( f @ ( sK9_SV21 @ SV17 ) )
        = $true )
      | ( ( g @ SV17 )
        = $true )
      | ( ( f @ SV17 )
        = $false )
      | ( sK2_REN = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[154]) ).

thf(163,plain,
    ! [SV17: b] :
      ( ( ( ~ ( f @ ( sK9_SV21 @ SV17 ) ) )
        = $true )
      | ( ( ~ ( f @ ( sK9_SV21 @ SV17 ) ) )
        = $true )
      | ( ( g @ SV17 )
        = $true )
      | ( ( f @ SV17 )
        = $false )
      | ( sK2_REN = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[155]) ).

thf(166,plain,
    ! [SV17: b] :
      ( ( ( f @ ( sK8_SV20 @ SV17 ) )
        = $false )
      | ( ( ~ ( f @ ( sK8_SV20 @ SV17 ) ) )
        = $true )
      | ( ( g @ SV17 )
        = $false )
      | ( ( f @ SV17 )
        = $true )
      | ( sK2_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[161]) ).

thf(167,plain,
    ! [SV17: b] :
      ( ( ( f @ ( sK9_SV21 @ SV17 ) )
        = $false )
      | ( ( ~ ( f @ ( sK9_SV21 @ SV17 ) ) )
        = $true )
      | ( ( g @ SV17 )
        = $true )
      | ( ( f @ SV17 )
        = $false )
      | ( sK2_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[163]) ).

thf(170,plain,
    ! [SV17: b] :
      ( ( ( f @ ( sK8_SV20 @ SV17 ) )
        = $false )
      | ( ( f @ ( sK8_SV20 @ SV17 ) )
        = $false )
      | ( ( g @ SV17 )
        = $false )
      | ( ( f @ SV17 )
        = $true )
      | ( sK2_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[166]) ).

thf(171,plain,
    ! [SV17: b] :
      ( ( ( f @ ( sK9_SV21 @ SV17 ) )
        = $false )
      | ( ( f @ ( sK9_SV21 @ SV17 ) )
        = $false )
      | ( ( g @ SV17 )
        = $true )
      | ( ( f @ SV17 )
        = $false )
      | ( sK2_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[167]) ).

thf(176,plain,
    ! [SV17: b] :
      ( ( sK2_REN = $true )
      | ( ( f @ SV17 )
        = $true )
      | ( ( g @ SV17 )
        = $false ) ),
    inference(extuni,[status(esa)],[137]) ).

thf(177,plain,
    ! [SV17: b] :
      ( ( sK2_REN = $true )
      | ( ( f @ SV17 )
        = $true )
      | ( ( g @ SV17 )
        = $false ) ),
    inference(extuni,[status(esa)],[124]) ).

thf(178,plain,
    ! [SV17: b] :
      ( ( sK2_REN = $true )
      | ( ( f @ SV17 )
        = $false )
      | ( ( g @ SV17 )
        = $true ) ),
    inference(extuni,[status(esa)],[139]) ).

thf(179,plain,
    ! [SV17: b] :
      ( ( sK2_REN = $true )
      | ( ( f @ SV17 )
        = $false )
      | ( ( g @ SV17 )
        = $true ) ),
    inference(extuni,[status(esa)],[126]) ).

thf(180,plain,
    ! [SV13: b] :
      ( ( ( f @ SV13 )
        = $true )
      | ( ( g @ SV13 )
        = $false )
      | ( sK2_REN = $true ) ),
    inference(sim,[status(thm)],[98]) ).

thf(181,plain,
    ! [SV13: b] :
      ( ( ( g @ SV13 )
        = $true )
      | ( ( f @ SV13 )
        = $false )
      | ( sK2_REN = $true ) ),
    inference(sim,[status(thm)],[99]) ).

thf(182,plain,
    ! [SV13: b] :
      ( ( sK2_REN = $true )
      | ( ( g @ SV13 )
        = $false )
      | ( ( f @ SV13 )
        = $true ) ),
    inference(sim,[status(thm)],[105]) ).

thf(183,plain,
    ! [SV13: b] :
      ( ( sK2_REN = $true )
      | ( ( g @ SV13 )
        = $true )
      | ( ( f @ SV13 )
        = $false ) ),
    inference(sim,[status(thm)],[104]) ).

thf(184,plain,
    ! [SV15: b] :
      ( ( ( g @ SV15 )
        = $false )
      | ( ( f @ SV15 )
        = $true )
      | ( sK2_REN = $true ) ),
    inference(sim,[status(thm)],[107]) ).

thf(185,plain,
    ! [SV15: b] :
      ( ( ( g @ SV15 )
        = $true )
      | ( ( f @ SV15 )
        = $false )
      | ( sK2_REN = $true ) ),
    inference(sim,[status(thm)],[106]) ).

thf(186,plain,
    ! [SV17: b] :
      ( ( ( f @ ( sK8_SV20 @ SV17 ) )
        = $true )
      | ( ( g @ SV17 )
        = $false )
      | ( ( f @ SV17 )
        = $true )
      | ( sK2_REN = $true ) ),
    inference(sim,[status(thm)],[160]) ).

thf(187,plain,
    ! [SV17: b] :
      ( ( ( f @ ( sK8_SV20 @ SV17 ) )
        = $false )
      | ( ( g @ SV17 )
        = $false )
      | ( ( f @ SV17 )
        = $true )
      | ( sK2_REN = $true ) ),
    inference(sim,[status(thm)],[170]) ).

thf(188,plain,
    ! [SV17: b] :
      ( ( ( f @ ( sK9_SV21 @ SV17 ) )
        = $true )
      | ( ( g @ SV17 )
        = $true )
      | ( ( f @ SV17 )
        = $false )
      | ( sK2_REN = $true ) ),
    inference(sim,[status(thm)],[162]) ).

thf(189,plain,
    ! [SV17: b] :
      ( ( ( f @ ( sK9_SV21 @ SV17 ) )
        = $false )
      | ( ( g @ SV17 )
        = $true )
      | ( ( f @ SV17 )
        = $false )
      | ( sK2_REN = $true ) ),
    inference(sim,[status(thm)],[171]) ).

thf(190,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[15,189,188,187,186,185,184,183,182,181,180,179,178,177,176,127,111,110,57,56,48,46,44,38,37,36]) ).

thf(191,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[190]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem  : SYO359^5 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.14  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.16/0.36  % Computer : n027.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit : 300
% 0.16/0.36  % WCLimit  : 600
% 0.16/0.36  % DateTime : Sat Jul  9 04:04:46 EDT 2022
% 0.16/0.36  % CPUTime  : 
% 0.16/0.36  
% 0.16/0.36   No.of.Axioms: 0
% 0.16/0.36  
% 0.16/0.36   Length.of.Defs: 0
% 0.16/0.36  
% 0.16/0.36   Contains.Choice.Funs: false
% 0.16/0.37  (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)...
% 0.22/0.46  
% 0.22/0.46  ********************************
% 0.22/0.46  *   All subproblems solved!    *
% 0.22/0.46  ********************************
% 0.22/0.46  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:2,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:190,loop_count:0,foatp_calls:2,translation:fof_full)
% 0.22/0.47  
% 0.22/0.47  %**** Beginning of derivation protocol ****
% 0.22/0.47  % SZS output start CNFRefutation
% See solution above
% 0.22/0.47  
% 0.22/0.47  %**** End of derivation protocol ****
% 0.22/0.47  %**** no. of clauses in derivation: 127 ****
% 0.22/0.47  %**** clause counter: 190 ****
% 0.22/0.47  
% 0.22/0.47  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:2,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:190,loop_count:0,foatp_calls:2,translation:fof_full)
%------------------------------------------------------------------------------