TSTP Solution File: SEV386^5 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SEV386^5 : 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 : n009.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 : Tue Jul 19 17:36:28 EDT 2022

% Result   : Theorem 0.12s 0.41s
% Output   : CNFRefutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   22
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   84 (  48 unt;   6 typ;   0 def)
%            Number of atoms       :  455 ( 225 equ;   0 cnn)
%            Maximal formula atoms :    4 (   5 avg)
%            Number of connectives :  394 ( 135   ~;  80   |;  15   &; 150   @)
%                                         (   3 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   2 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :    3 (   3   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :  114 (  25   ^  75   !;  14   ?; 114   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_a,type,
    a: $tType ).

thf(tp_p,type,
    p: a > $o ).

thf(tp_sK1_Xz,type,
    sK1_Xz: a > a ).

thf(tp_sK2_SY0,type,
    sK2_SY0: a ).

thf(tp_sK3_Xy,type,
    sK3_Xy: a ).

thf(tp_sK4_SV5,type,
    sK4_SV5: a > a ).

thf(1,conjecture,
    ( ? [Xy: a] :
        ( p
        = ( ^ [Xx: a,Xy: a] : ( Xx = Xy )
          @ Xy ) )
  <=> ? [Xy: a] :
        ( ( p @ Xy )
        & ! [Xz: a] :
            ( ( p @ Xz )
           => ( Xy = Xz ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTTTP5306A_pme) ).

thf(2,negated_conjecture,
    ( ( ? [Xy: a] :
          ( p
          = ( ^ [Xx: a,Xy: a] : ( Xx = Xy )
            @ Xy ) )
    <=> ? [Xy: a] :
          ( ( p @ Xy )
          & ! [Xz: a] :
              ( ( p @ Xz )
             => ( Xy = Xz ) ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ( ( ? [SY0: a] :
          ( p
          = ( ^ [SY1: a] : ( SY0 = SY1 ) ) )
    <=> ? [Xy: a] :
          ( ( p @ Xy )
          & ! [Xz: a] :
              ( ( p @ Xz )
             => ( Xy = Xz ) ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(4,plain,
    ( ( ? [SY0: a] :
          ( p
          = ( ^ [SY1: a] : ( SY0 = SY1 ) ) )
     => ? [Xy: a] :
          ( ( p @ Xy )
          & ! [Xz: a] :
              ( ( p @ Xz )
             => ( Xy = Xz ) ) ) )
    = $false ),
    inference(split_conjecture,[split_conjecture(split,[])],[3]) ).

thf(5,plain,
    ( ( ? [Xy: a] :
          ( ( p @ Xy )
          & ! [Xz: a] :
              ( ( p @ Xz )
             => ( Xy = Xz ) ) )
     => ? [SY0: a] :
          ( p
          = ( ^ [SY1: a] : ( SY0 = SY1 ) ) ) )
    = $false ),
    inference(split_conjecture,[split_conjecture(split,[])],[3]) ).

thf(6,plain,
    ( ( ~ ( ? [SY0: a] :
              ( p
              = ( ^ [SY1: a] : ( SY0 = SY1 ) ) )
         => ? [Xy: a] :
              ( ( p @ Xy )
              & ! [Xz: a] :
                  ( ( p @ Xz )
                 => ( Xy = Xz ) ) ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[4]) ).

thf(7,plain,
    ( ( ~ ( ? [Xy: a] :
              ( ( p @ Xy )
              & ! [Xz: a] :
                  ( ( p @ Xz )
                 => ( Xy = Xz ) ) )
         => ? [SY0: a] :
              ( p
              = ( ^ [SY1: a] : ( SY0 = SY1 ) ) ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[5]) ).

thf(8,plain,
    ( ( ( p
        = ( ^ [SY8: a] : ( sK2_SY0 = SY8 ) ) )
      & ! [Xy: a] :
          ( ( ( p @ ( sK1_Xz @ Xy ) )
            & ( Xy
             != ( sK1_Xz @ Xy ) ) )
          | ~ ( p @ Xy ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[6]) ).

thf(9,plain,
    ( ( ! [SY9: a] :
          ( ~ ( p @ SY9 )
          | ( sK3_Xy = SY9 ) )
      & ( p @ sK3_Xy )
      & ! [SY0: a] :
          ( p
         != ( ^ [SY1: a] : ( SY0 = SY1 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[7]) ).

thf(10,plain,
    ( ( ( p
        = ( ^ [SY8: a] : ( sK2_SY0 = SY8 ) ) )
      & ! [Xy: a] :
          ( ( ( p @ ( sK1_Xz @ Xy ) )
            & ( Xy
             != ( sK1_Xz @ Xy ) ) )
          | ~ ( p @ Xy ) ) )
    = $true ),
    inference(copy,[status(thm)],[8]) ).

thf(11,plain,
    ( ( ~ ( ( p
           != ( ^ [SX0: a] : ( sK2_SY0 = SX0 ) ) )
          | ~ ! [SX0: a] :
                ( ~ ( ~ ( p @ ( sK1_Xz @ SX0 ) )
                    | ~ ( ( SX0
                         != ( sK1_Xz @ SX0 ) ) ) )
                | ~ ( p @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10]) ).

thf(12,plain,
    ( ( ( p
       != ( ^ [SX0: a] : ( sK2_SY0 = SX0 ) ) )
      | ~ ! [SX0: a] :
            ( ~ ( ~ ( p @ ( sK1_Xz @ SX0 ) )
                | ~ ( ( SX0
                     != ( sK1_Xz @ SX0 ) ) ) )
            | ~ ( p @ SX0 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[11]) ).

thf(13,plain,
    ( ( ( p
       != ( ^ [SX0: a] : ( sK2_SY0 = SX0 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[12]) ).

thf(14,plain,
    ( ( ~ ! [SX0: a] :
            ( ~ ( ~ ( p @ ( sK1_Xz @ SX0 ) )
                | ~ ( ( SX0
                     != ( sK1_Xz @ SX0 ) ) ) )
            | ~ ( p @ SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[12]) ).

thf(15,plain,
    ( ( p
      = ( ^ [SX0: a] : ( sK2_SY0 = SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[13]) ).

thf(16,plain,
    ( ( ! [SX0: a] :
          ( ~ ( ~ ( p @ ( sK1_Xz @ SX0 ) )
              | ~ ( ( SX0
                   != ( sK1_Xz @ SX0 ) ) ) )
          | ~ ( p @ SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[14]) ).

thf(17,plain,
    ( ( ! [SV1: a] :
          ( ( p @ SV1 )
          = ( sK2_SY0 = SV1 ) ) )
    = $true ),
    inference(extcnf_equal_pos,[status(thm)],[15]) ).

thf(18,plain,
    ( ( p
      = ( ^ [SX0: a] : ( sK2_SY0 = SX0 ) ) )
    = $true ),
    inference(extcnf_equal_pos,[status(thm)],[15]) ).

thf(19,plain,
    ! [SV2: a] :
      ( ( ~ ( ~ ( p @ ( sK1_Xz @ SV2 ) )
            | ~ ( ( SV2
                 != ( sK1_Xz @ SV2 ) ) ) )
        | ~ ( p @ SV2 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[16]) ).

thf(20,plain,
    ! [SV3: a] :
      ( ( ( p @ SV3 )
        = ( sK2_SY0 = SV3 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[17]) ).

thf(21,plain,
    ! [SV2: a] :
      ( ( ( ~ ( ~ ( p @ ( sK1_Xz @ SV2 ) )
              | ~ ( ( SV2
                   != ( sK1_Xz @ SV2 ) ) ) ) )
        = $true )
      | ( ( ~ ( p @ SV2 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[19]) ).

thf(22,plain,
    ! [SV3: a] :
      ( ( ~ ( ( p @ SV3 )
            | ( sK2_SY0 = SV3 ) )
        | ~ ( ~ ( p @ SV3 )
            | ( sK2_SY0 != SV3 ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[20]) ).

thf(23,plain,
    ! [SV3: a] :
      ( ( ( p @ SV3 )
        = ( sK2_SY0 = SV3 ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[20]) ).

thf(24,plain,
    ! [SV2: a] :
      ( ( ( ~ ( p @ ( sK1_Xz @ SV2 ) )
          | ~ ( ( SV2
               != ( sK1_Xz @ SV2 ) ) ) )
        = $false )
      | ( ( ~ ( p @ SV2 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[21]) ).

thf(25,plain,
    ! [SV3: a] :
      ( ( ( ~ ( ( p @ SV3 )
              | ( sK2_SY0 = SV3 ) ) )
        = $true )
      | ( ( ~ ( ~ ( p @ SV3 )
              | ( sK2_SY0 != SV3 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[22]) ).

thf(26,plain,
    ! [SV2: a] :
      ( ( ( ~ ( p @ ( sK1_Xz @ SV2 ) ) )
        = $false )
      | ( ( ~ ( p @ SV2 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[24]) ).

thf(27,plain,
    ! [SV2: a] :
      ( ( ( ~ ( ( SV2
               != ( sK1_Xz @ SV2 ) ) ) )
        = $false )
      | ( ( ~ ( p @ SV2 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[24]) ).

thf(28,plain,
    ! [SV3: a] :
      ( ( ( ( p @ SV3 )
          | ( sK2_SY0 = SV3 ) )
        = $false )
      | ( ( ~ ( ~ ( p @ SV3 )
              | ( sK2_SY0 != SV3 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[25]) ).

thf(29,plain,
    ! [SV2: a] :
      ( ( ( p @ ( sK1_Xz @ SV2 ) )
        = $true )
      | ( ( ~ ( p @ SV2 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[26]) ).

thf(30,plain,
    ! [SV2: a] :
      ( ( ( ( SV2
           != ( sK1_Xz @ SV2 ) ) )
        = $true )
      | ( ( ~ ( p @ SV2 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[27]) ).

thf(31,plain,
    ! [SV3: a] :
      ( ( ( p @ SV3 )
        = $false )
      | ( ( ~ ( ~ ( p @ SV3 )
              | ( sK2_SY0 != SV3 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[28]) ).

thf(32,plain,
    ! [SV3: a] :
      ( ( ( sK2_SY0 = SV3 )
        = $false )
      | ( ( ~ ( ~ ( p @ SV3 )
              | ( sK2_SY0 != SV3 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[28]) ).

thf(33,plain,
    ! [SV2: a] :
      ( ( ( p @ SV2 )
        = $false )
      | ( ( p @ ( sK1_Xz @ SV2 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[29]) ).

thf(34,plain,
    ! [SV2: a] :
      ( ( ( SV2
          = ( sK1_Xz @ SV2 ) )
        = $false )
      | ( ( ~ ( p @ SV2 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[30]) ).

thf(35,plain,
    ! [SV3: a] :
      ( ( ( ~ ( p @ SV3 )
          | ( sK2_SY0 != SV3 ) )
        = $false )
      | ( ( p @ SV3 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[31]) ).

thf(36,plain,
    ! [SV3: a] :
      ( ( ( ~ ( p @ SV3 )
          | ( sK2_SY0 != SV3 ) )
        = $false )
      | ( ( sK2_SY0 = SV3 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[32]) ).

thf(37,plain,
    ! [SV2: a] :
      ( ( ( p @ SV2 )
        = $false )
      | ( ( SV2
          = ( sK1_Xz @ SV2 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[34]) ).

thf(38,plain,
    ! [SV3: a] :
      ( ( ( ~ ( p @ SV3 ) )
        = $false )
      | ( ( p @ SV3 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[35]) ).

thf(39,plain,
    ! [SV3: a] :
      ( ( ( ( sK2_SY0 != SV3 ) )
        = $false )
      | ( ( p @ SV3 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[35]) ).

thf(40,plain,
    ! [SV3: a] :
      ( ( ( ~ ( p @ SV3 ) )
        = $false )
      | ( ( sK2_SY0 = SV3 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[36]) ).

thf(41,plain,
    ! [SV3: a] :
      ( ( ( ( sK2_SY0 != SV3 ) )
        = $false )
      | ( ( sK2_SY0 = SV3 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[36]) ).

thf(42,plain,
    ! [SV3: a] :
      ( ( ( p @ SV3 )
        = $true )
      | ( ( p @ SV3 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[38]) ).

thf(43,plain,
    ! [SV3: a] :
      ( ( ( sK2_SY0 = SV3 )
        = $true )
      | ( ( p @ SV3 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[39]) ).

thf(44,plain,
    ! [SV3: a] :
      ( ( ( p @ SV3 )
        = $true )
      | ( ( sK2_SY0 = SV3 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[40]) ).

thf(45,plain,
    ! [SV3: a] :
      ( ( ( sK2_SY0 = SV3 )
        = $true )
      | ( ( sK2_SY0 = SV3 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[41]) ).

thf(46,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[18,45,44,43,42,37,33,23]) ).

thf(47,plain,
    ( ( ! [SY9: a] :
          ( ~ ( p @ SY9 )
          | ( sK3_Xy = SY9 ) )
      & ( p @ sK3_Xy )
      & ! [SY0: a] :
          ( p
         != ( ^ [SY1: a] : ( SY0 = SY1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[9]) ).

thf(48,plain,
    ( ( ~ ( ~ ~ ( ~ ! [SX0: a] :
                      ( ~ ( p @ SX0 )
                      | ( sK3_Xy = SX0 ) )
                | ~ ( p @ sK3_Xy ) )
          | ~ ! [SX0: a] :
                ( p
               != ( ^ [SX1: a] : ( SX0 = SX1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[47]) ).

thf(49,plain,
    ( ( ~ ~ ( ~ ! [SX0: a] :
                  ( ~ ( p @ SX0 )
                  | ( sK3_Xy = SX0 ) )
            | ~ ( p @ sK3_Xy ) )
      | ~ ! [SX0: a] :
            ( p
           != ( ^ [SX1: a] : ( SX0 = SX1 ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[48]) ).

thf(50,plain,
    ( ( ~ ~ ( ~ ! [SX0: a] :
                  ( ~ ( p @ SX0 )
                  | ( sK3_Xy = SX0 ) )
            | ~ ( p @ sK3_Xy ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[49]) ).

thf(51,plain,
    ( ( ~ ! [SX0: a] :
            ( p
           != ( ^ [SX1: a] : ( SX0 = SX1 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[49]) ).

thf(52,plain,
    ( ( ~ ( ~ ! [SX0: a] :
                ( ~ ( p @ SX0 )
                | ( sK3_Xy = SX0 ) )
          | ~ ( p @ sK3_Xy ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[50]) ).

thf(53,plain,
    ( ( ! [SX0: a] :
          ( p
         != ( ^ [SX1: a] : ( SX0 = SX1 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[51]) ).

thf(54,plain,
    ( ( ~ ! [SX0: a] :
            ( ~ ( p @ SX0 )
            | ( sK3_Xy = SX0 ) )
      | ~ ( p @ sK3_Xy ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[52]) ).

thf(55,plain,
    ! [SV4: a] :
      ( ( ( p
         != ( ^ [SY10: a] : ( SV4 = SY10 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[53]) ).

thf(56,plain,
    ( ( ~ ! [SX0: a] :
            ( ~ ( p @ SX0 )
            | ( sK3_Xy = SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[54]) ).

thf(57,plain,
    ( ( ~ ( p @ sK3_Xy ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[54]) ).

thf(58,plain,
    ! [SV4: a] :
      ( ( p
        = ( ^ [SY10: a] : ( SV4 = SY10 ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[55]) ).

thf(59,plain,
    ( ( ! [SX0: a] :
          ( ~ ( p @ SX0 )
          | ( sK3_Xy = SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[56]) ).

thf(60,plain,
    ( ( p @ sK3_Xy )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[57]) ).

thf(61,plain,
    ! [SV4: a] :
      ( ( ! [SV5: a] :
            ( ( p @ SV5 )
            = ( SV4 = SV5 ) ) )
      = $false ),
    inference(extcnf_equal_neg,[status(thm)],[58]) ).

thf(62,plain,
    ! [SV4: a] :
      ( ( p
        = ( ^ [SY10: a] : ( SV4 = SY10 ) ) )
      = $false ),
    inference(extcnf_equal_neg,[status(thm)],[58]) ).

thf(63,plain,
    ! [SV6: a] :
      ( ( ~ ( p @ SV6 )
        | ( sK3_Xy = SV6 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[59]) ).

thf(64,plain,
    ! [SV4: a] :
      ( ( ( p @ ( sK4_SV5 @ SV4 ) )
        = ( SV4
          = ( sK4_SV5 @ SV4 ) ) )
      = $false ),
    inference(extcnf_forall_neg,[status(esa)],[61]) ).

thf(65,plain,
    ! [SV6: a] :
      ( ( ( ~ ( p @ SV6 ) )
        = $true )
      | ( ( sK3_Xy = SV6 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[63]) ).

thf(66,plain,
    ! [SV4: a] :
      ( ( ~ ( ( p @ ( sK4_SV5 @ SV4 ) )
            | ( SV4
              = ( sK4_SV5 @ SV4 ) ) )
        | ~ ( ~ ( p @ ( sK4_SV5 @ SV4 ) )
            | ( SV4
             != ( sK4_SV5 @ SV4 ) ) ) )
      = $false ),
    inference(extcnf_equal_neg,[status(thm)],[64]) ).

thf(67,plain,
    ! [SV4: a] :
      ( ( ( p @ ( sK4_SV5 @ SV4 ) )
        = ( SV4
          = ( sK4_SV5 @ SV4 ) ) )
      = $false ),
    inference(extcnf_equal_neg,[status(thm)],[64]) ).

thf(68,plain,
    ! [SV6: a] :
      ( ( ( p @ SV6 )
        = $false )
      | ( ( sK3_Xy = SV6 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[65]) ).

thf(69,plain,
    ! [SV4: a] :
      ( ( ~ ( ( p @ ( sK4_SV5 @ SV4 ) )
            | ( SV4
              = ( sK4_SV5 @ SV4 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[66]) ).

thf(70,plain,
    ! [SV4: a] :
      ( ( ~ ( ~ ( p @ ( sK4_SV5 @ SV4 ) )
            | ( SV4
             != ( sK4_SV5 @ SV4 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[66]) ).

thf(71,plain,
    ! [SV4: a] :
      ( ( ( p @ ( sK4_SV5 @ SV4 ) )
        | ( SV4
          = ( sK4_SV5 @ SV4 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[69]) ).

thf(72,plain,
    ! [SV4: a] :
      ( ( ~ ( p @ ( sK4_SV5 @ SV4 ) )
        | ( SV4
         != ( sK4_SV5 @ SV4 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[70]) ).

thf(73,plain,
    ! [SV4: a] :
      ( ( ( p @ ( sK4_SV5 @ SV4 ) )
        = $true )
      | ( ( SV4
          = ( sK4_SV5 @ SV4 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[71]) ).

thf(74,plain,
    ! [SV4: a] :
      ( ( ( ~ ( p @ ( sK4_SV5 @ SV4 ) ) )
        = $true )
      | ( ( ( SV4
           != ( sK4_SV5 @ SV4 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[72]) ).

thf(75,plain,
    ! [SV4: a] :
      ( ( ( p @ ( sK4_SV5 @ SV4 ) )
        = $false )
      | ( ( ( SV4
           != ( sK4_SV5 @ SV4 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[74]) ).

thf(76,plain,
    ! [SV4: a] :
      ( ( ( SV4
          = ( sK4_SV5 @ SV4 ) )
        = $false )
      | ( ( p @ ( sK4_SV5 @ SV4 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[75]) ).

thf(77,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[60,76,73,68,67,62]) ).

thf(78,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[77,46]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : SEV386^5 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.34  % Computer : n009.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Mon Jun 27 18:04:22 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.35  
% 0.12/0.35   No.of.Axioms: 0
% 0.12/0.35  
% 0.12/0.35   Length.of.Defs: 0
% 0.12/0.35  
% 0.12/0.35   Contains.Choice.Funs: false
% 0.12/0.35  (rf:0,axioms: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)..
% 0.12/0.41  
% 0.12/0.41  ********************************
% 0.12/0.41  *   All subproblems solved!    *
% 0.12/0.41  ********************************
% 0.12/0.41  % 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:77,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.12/0.41  
% 0.12/0.41  %**** Beginning of derivation protocol ****
% 0.12/0.41  % SZS output start CNFRefutation
% See solution above
% 0.12/0.41  
% 0.12/0.41  %**** End of derivation protocol ****
% 0.12/0.41  %**** no. of clauses in derivation: 78 ****
% 0.12/0.41  %**** clause counter: 77 ****
% 0.12/0.41  
% 0.12/0.41  % 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:77,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------