TSTP Solution File: SEU280+1 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SEU280+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n029.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 12:09:29 EDT 2022

% Result   : Theorem 0.20s 0.52s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   23
%            Number of leaves      :   19
% Syntax   : Number of formulae    :  151 (  63 unt;  13 typ;   0 def)
%            Number of atoms       : 1007 ( 332 equ;   0 cnn)
%            Maximal formula atoms :    9 (   7 avg)
%            Number of connectives : 1615 ( 470   ~; 329   |;  49   &; 748   @)
%                                         (   7 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    9 (   9   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   16 (  13 usr;   8 con; 0-2 aty)
%            Number of variables   :  193 (   0   ^ 182   !;  11   ?; 193   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_epsilon_connected,type,
    epsilon_connected: $i > $o ).

thf(tp_epsilon_transitive,type,
    epsilon_transitive: $i > $o ).

thf(tp_in,type,
    in: $i > $i > $o ).

thf(tp_ordinal,type,
    ordinal: $i > $o ).

thf(tp_sK1_A,type,
    sK1_A: $i ).

thf(tp_sK2_SY16,type,
    sK2_SY16: $i > $i ).

thf(tp_sK3_B,type,
    sK3_B: $i > $i ).

thf(tp_sK4_D,type,
    sK4_D: $i > $i > $i ).

thf(tp_sK5_B,type,
    sK5_B: $i ).

thf(tp_sK6_SY21,type,
    sK6_SY21: $i ).

thf(tp_sK7_SY23,type,
    sK7_SY23: $i ).

thf(tp_sK8_REN,type,
    sK8_REN: $o ).

thf(tp_sK9_A,type,
    sK9_A: $i ).

thf(1,axiom,
    ! [A: $i] :
      ( ! [B: $i,C: $i,D: $i] :
          ( ( ( B = C )
            & ( ordinal @ C )
            & ( B = D )
            & ( ordinal @ D ) )
         => ( C = D ) )
     => ? [B: $i] :
        ! [C: $i] :
          ( ( in @ C @ B )
        <=> ? [D: $i] :
              ( ( in @ D @ A )
              & ( D = C )
              & ( ordinal @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_tarski__e6_22__wellord2__1) ).

thf(2,axiom,
    ! [A: $i] :
      ( ( ordinal @ A )
     => ( ( epsilon_transitive @ A )
        & ( epsilon_connected @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_ordinal1) ).

thf(3,axiom,
    ! [A: $i,B: $i] :
      ( ( in @ A @ B )
     => ~ ( in @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).

thf(4,axiom,
    ? [A: $i] :
      ( ( epsilon_transitive @ A )
      & ( epsilon_connected @ A )
      & ( ordinal @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_ordinal1) ).

thf(5,axiom,
    ! [A: $i] :
      ( ( ( epsilon_transitive @ A )
        & ( epsilon_connected @ A ) )
     => ( ordinal @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_ordinal1) ).

thf(6,conjecture,
    ! [A: $i] :
    ? [B: $i] :
    ! [C: $i] :
      ( ( in @ C @ B )
    <=> ( ( in @ C @ A )
        & ( ordinal @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0__e6_22__wellord2) ).

thf(7,negated_conjecture,
    ( ( ! [A: $i] :
        ? [B: $i] :
        ! [C: $i] :
          ( ( in @ C @ B )
        <=> ( ( in @ C @ A )
            & ( ordinal @ C ) ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[6]) ).

thf(8,plain,
    ( ( ! [A: $i] :
        ? [B: $i] :
        ! [C: $i] :
          ( ( in @ C @ B )
        <=> ( ( in @ C @ A )
            & ( ordinal @ C ) ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[7]) ).

thf(9,plain,
    ( ( ! [A: $i] :
          ( ! [B: $i,C: $i,D: $i] :
              ( ( ( B = C )
                & ( ordinal @ C )
                & ( B = D )
                & ( ordinal @ D ) )
             => ( C = D ) )
         => ? [B: $i] :
            ! [C: $i] :
              ( ( in @ C @ B )
            <=> ? [D: $i] :
                  ( ( in @ D @ A )
                  & ( D = C )
                  & ( ordinal @ C ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(10,plain,
    ( ( ! [A: $i] :
          ( ( ordinal @ A )
         => ( ( epsilon_transitive @ A )
            & ( epsilon_connected @ A ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(11,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( in @ A @ B )
         => ~ ( in @ B @ A ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3]) ).

thf(12,plain,
    ( ( ? [A: $i] :
          ( ( epsilon_transitive @ A )
          & ( epsilon_connected @ A )
          & ( ordinal @ A ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4]) ).

thf(13,plain,
    ( ( ! [A: $i] :
          ( ( ( epsilon_transitive @ A )
            & ( epsilon_connected @ A ) )
         => ( ordinal @ A ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5]) ).

thf(14,plain,
    ( ( ? [SY15: $i] :
        ! [SY16: $i] :
          ( ( in @ SY16 @ SY15 )
        <=> ( ( in @ SY16 @ sK1_A )
            & ( ordinal @ SY16 ) ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[8]) ).

thf(15,plain,
    ( ( ~ ? [SY15: $i] :
          ! [SY16: $i] :
            ( ( in @ SY16 @ SY15 )
          <=> ( ( in @ SY16 @ sK1_A )
              & ( ordinal @ SY16 ) ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[14]) ).

thf(16,plain,
    ( ( ! [SY15: $i] :
          ( ( ~ ( in @ ( sK2_SY16 @ SY15 ) @ sK1_A )
            | ~ ( ordinal @ ( sK2_SY16 @ SY15 ) )
            | ~ ( in @ ( sK2_SY16 @ SY15 ) @ SY15 ) )
          & ( ( in @ ( sK2_SY16 @ SY15 ) @ sK1_A )
            | ( in @ ( sK2_SY16 @ SY15 ) @ SY15 ) )
          & ( ( ordinal @ ( sK2_SY16 @ SY15 ) )
            | ( in @ ( sK2_SY16 @ SY15 ) @ SY15 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[15]) ).

thf(17,plain,
    ( ( ( sK8_REN
        | ! [A: $i] :
            ( ! [SY17: $i] :
                ( ! [D: $i] :
                    ( ( D != SY17 )
                    | ~ ( in @ D @ A ) )
                | ~ ( ordinal @ SY17 )
                | ( in @ SY17 @ ( sK3_B @ A ) ) )
            & ! [SY19: $i] :
                ( ~ ( in @ SY19 @ ( sK3_B @ A ) )
                | ( ( ( sK4_D @ SY19 @ A )
                    = SY19 )
                  & ( in @ ( sK4_D @ SY19 @ A ) @ A )
                  & ( ordinal @ SY19 ) ) ) ) )
      & ( sK8_REN
       => ( ( sK5_B = sK6_SY21 )
          & ( ordinal @ sK6_SY21 )
          & ( sK5_B = sK7_SY23 )
          & ( ordinal @ sK7_SY23 )
          & ( sK6_SY21 != sK7_SY23 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[9]) ).

thf(18,plain,
    ( ( ! [A: $i] :
          ( ~ ( ordinal @ A )
          | ( epsilon_connected @ A ) )
      & ! [A: $i] :
          ( ~ ( ordinal @ A )
          | ( epsilon_transitive @ A ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[10]) ).

thf(19,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ( in @ A @ B )
          | ~ ( in @ B @ A ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[11]) ).

thf(20,plain,
    ( ( ( epsilon_connected @ sK9_A )
      & ( epsilon_transitive @ sK9_A )
      & ( ordinal @ sK9_A ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[12]) ).

thf(21,plain,
    ( ( ! [A: $i] :
          ( ~ ( epsilon_connected @ A )
          | ~ ( epsilon_transitive @ A )
          | ( ordinal @ A ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[13]) ).

thf(22,plain,
    ( ( ! [A: $i] :
          ( ~ ( epsilon_connected @ A )
          | ~ ( epsilon_transitive @ A )
          | ( ordinal @ A ) ) )
    = $true ),
    inference(copy,[status(thm)],[21]) ).

thf(23,plain,
    ( ( ( epsilon_connected @ sK9_A )
      & ( epsilon_transitive @ sK9_A )
      & ( ordinal @ sK9_A ) )
    = $true ),
    inference(copy,[status(thm)],[20]) ).

thf(24,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ( in @ A @ B )
          | ~ ( in @ B @ A ) ) )
    = $true ),
    inference(copy,[status(thm)],[19]) ).

thf(25,plain,
    ( ( ! [A: $i] :
          ( ~ ( ordinal @ A )
          | ( epsilon_connected @ A ) )
      & ! [A: $i] :
          ( ~ ( ordinal @ A )
          | ( epsilon_transitive @ A ) ) )
    = $true ),
    inference(copy,[status(thm)],[18]) ).

thf(26,plain,
    ( ( ( sK8_REN
        | ! [A: $i] :
            ( ! [SY17: $i] :
                ( ! [D: $i] :
                    ( ( D != SY17 )
                    | ~ ( in @ D @ A ) )
                | ~ ( ordinal @ SY17 )
                | ( in @ SY17 @ ( sK3_B @ A ) ) )
            & ! [SY19: $i] :
                ( ~ ( in @ SY19 @ ( sK3_B @ A ) )
                | ( ( ( sK4_D @ SY19 @ A )
                    = SY19 )
                  & ( in @ ( sK4_D @ SY19 @ A ) @ A )
                  & ( ordinal @ SY19 ) ) ) ) )
      & ( sK8_REN
       => ( ( sK5_B = sK6_SY21 )
          & ( ordinal @ sK6_SY21 )
          & ( sK5_B = sK7_SY23 )
          & ( ordinal @ sK7_SY23 )
          & ( sK6_SY21 != sK7_SY23 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[17]) ).

thf(27,plain,
    ( ( ! [SY15: $i] :
          ( ( ~ ( in @ ( sK2_SY16 @ SY15 ) @ sK1_A )
            | ~ ( ordinal @ ( sK2_SY16 @ SY15 ) )
            | ~ ( in @ ( sK2_SY16 @ SY15 ) @ SY15 ) )
          & ( ( in @ ( sK2_SY16 @ SY15 ) @ sK1_A )
            | ( in @ ( sK2_SY16 @ SY15 ) @ SY15 ) )
          & ( ( ordinal @ ( sK2_SY16 @ SY15 ) )
            | ( in @ ( sK2_SY16 @ SY15 ) @ SY15 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[16]) ).

thf(28,plain,
    ( ( ~ ( ~ ( sK8_REN
              | ! [SX0: $i] :
                  ~ ( ~ ! [SX1: $i] :
                          ( ! [SX2: $i] :
                              ( ( SX2 != SX1 )
                              | ~ ( in @ SX2 @ SX0 ) )
                          | ~ ( ordinal @ SX1 )
                          | ( in @ SX1 @ ( sK3_B @ SX0 ) ) )
                    | ~ ! [SX1: $i] :
                          ( ~ ( in @ SX1 @ ( sK3_B @ SX0 ) )
                          | ~ ( ~ ~ ( ( ( sK4_D @ SX1 @ SX0 )
                                     != SX1 )
                                    | ~ ( in @ ( sK4_D @ SX1 @ SX0 ) @ SX0 ) )
                              | ~ ( ordinal @ SX1 ) ) ) ) )
          | ~ ( ~ sK8_REN
              | ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( sK5_B != sK6_SY21 )
                                    | ~ ( ordinal @ sK6_SY21 ) )
                              | ( sK5_B != sK7_SY23 ) )
                        | ~ ( ordinal @ sK7_SY23 ) )
                  | ~ ( ( sK6_SY21 != sK7_SY23 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[26]) ).

thf(29,plain,
    ( ( ! [SX0: $i] :
          ~ ( ~ ( ~ ( in @ ( sK2_SY16 @ SX0 ) @ sK1_A )
                | ~ ( ordinal @ ( sK2_SY16 @ SX0 ) )
                | ~ ( in @ ( sK2_SY16 @ SX0 ) @ SX0 ) )
            | ~ ~ ( ~ ( ( in @ ( sK2_SY16 @ SX0 ) @ sK1_A )
                      | ( in @ ( sK2_SY16 @ SX0 ) @ SX0 ) )
                  | ~ ( ( ordinal @ ( sK2_SY16 @ SX0 ) )
                      | ( in @ ( sK2_SY16 @ SX0 ) @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[27]) ).

thf(30,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( ordinal @ SX0 )
                | ( epsilon_connected @ SX0 ) )
          | ~ ! [SX0: $i] :
                ( ~ ( ordinal @ SX0 )
                | ( epsilon_transitive @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[25]) ).

thf(31,plain,
    ( ( ~ ( ~ ~ ( ~ ( epsilon_connected @ sK9_A )
                | ~ ( epsilon_transitive @ sK9_A ) )
          | ~ ( ordinal @ sK9_A ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[23]) ).

thf(32,plain,
    ! [SV1: $i] :
      ( ( ~ ( epsilon_connected @ SV1 )
        | ~ ( epsilon_transitive @ SV1 )
        | ( ordinal @ SV1 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[22]) ).

thf(33,plain,
    ! [SV2: $i] :
      ( ( ! [SY24: $i] :
            ( ~ ( in @ SV2 @ SY24 )
            | ~ ( in @ SY24 @ SV2 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[24]) ).

thf(34,plain,
    ( ( ~ ( sK8_REN
          | ! [SX0: $i] :
              ~ ( ~ ! [SX1: $i] :
                      ( ! [SX2: $i] :
                          ( ( SX2 != SX1 )
                          | ~ ( in @ SX2 @ SX0 ) )
                      | ~ ( ordinal @ SX1 )
                      | ( in @ SX1 @ ( sK3_B @ SX0 ) ) )
                | ~ ! [SX1: $i] :
                      ( ~ ( in @ SX1 @ ( sK3_B @ SX0 ) )
                      | ~ ( ~ ~ ( ( ( sK4_D @ SX1 @ SX0 )
                                 != SX1 )
                                | ~ ( in @ ( sK4_D @ SX1 @ SX0 ) @ SX0 ) )
                          | ~ ( ordinal @ SX1 ) ) ) ) )
      | ~ ( ~ sK8_REN
          | ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( sK5_B != sK6_SY21 )
                                | ~ ( ordinal @ sK6_SY21 ) )
                          | ( sK5_B != sK7_SY23 ) )
                    | ~ ( ordinal @ sK7_SY23 ) )
              | ~ ( ( sK6_SY21 != sK7_SY23 ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[28]) ).

thf(35,plain,
    ! [SV3: $i] :
      ( ( ~ ( ~ ( ~ ( in @ ( sK2_SY16 @ SV3 ) @ sK1_A )
                | ~ ( ordinal @ ( sK2_SY16 @ SV3 ) )
                | ~ ( in @ ( sK2_SY16 @ SV3 ) @ SV3 ) )
            | ~ ~ ( ~ ( ( in @ ( sK2_SY16 @ SV3 ) @ sK1_A )
                      | ( in @ ( sK2_SY16 @ SV3 ) @ SV3 ) )
                  | ~ ( ( ordinal @ ( sK2_SY16 @ SV3 ) )
                      | ( in @ ( sK2_SY16 @ SV3 ) @ SV3 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[29]) ).

thf(36,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( ordinal @ SX0 )
            | ( epsilon_connected @ SX0 ) )
      | ~ ! [SX0: $i] :
            ( ~ ( ordinal @ SX0 )
            | ( epsilon_transitive @ SX0 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[30]) ).

thf(37,plain,
    ( ( ~ ~ ( ~ ( epsilon_connected @ sK9_A )
            | ~ ( epsilon_transitive @ sK9_A ) )
      | ~ ( ordinal @ sK9_A ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[31]) ).

thf(38,plain,
    ! [SV1: $i] :
      ( ( ( ~ ( epsilon_connected @ SV1 )
          | ~ ( epsilon_transitive @ SV1 ) )
        = $true )
      | ( ( ordinal @ SV1 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[32]) ).

thf(39,plain,
    ! [SV4: $i,SV2: $i] :
      ( ( ~ ( in @ SV2 @ SV4 )
        | ~ ( in @ SV4 @ SV2 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[33]) ).

thf(40,plain,
    ( ( ~ ( sK8_REN
          | ! [SX0: $i] :
              ~ ( ~ ! [SX1: $i] :
                      ( ! [SX2: $i] :
                          ( ( SX2 != SX1 )
                          | ~ ( in @ SX2 @ SX0 ) )
                      | ~ ( ordinal @ SX1 )
                      | ( in @ SX1 @ ( sK3_B @ SX0 ) ) )
                | ~ ! [SX1: $i] :
                      ( ~ ( in @ SX1 @ ( sK3_B @ SX0 ) )
                      | ~ ( ~ ~ ( ( ( sK4_D @ SX1 @ SX0 )
                                 != SX1 )
                                | ~ ( in @ ( sK4_D @ SX1 @ SX0 ) @ SX0 ) )
                          | ~ ( ordinal @ SX1 ) ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[34]) ).

thf(41,plain,
    ( ( ~ ( ~ sK8_REN
          | ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( sK5_B != sK6_SY21 )
                                | ~ ( ordinal @ sK6_SY21 ) )
                          | ( sK5_B != sK7_SY23 ) )
                    | ~ ( ordinal @ sK7_SY23 ) )
              | ~ ( ( sK6_SY21 != sK7_SY23 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[34]) ).

thf(42,plain,
    ! [SV3: $i] :
      ( ( ~ ( ~ ( in @ ( sK2_SY16 @ SV3 ) @ sK1_A )
            | ~ ( ordinal @ ( sK2_SY16 @ SV3 ) )
            | ~ ( in @ ( sK2_SY16 @ SV3 ) @ SV3 ) )
        | ~ ~ ( ~ ( ( in @ ( sK2_SY16 @ SV3 ) @ sK1_A )
                  | ( in @ ( sK2_SY16 @ SV3 ) @ SV3 ) )
              | ~ ( ( ordinal @ ( sK2_SY16 @ SV3 ) )
                  | ( in @ ( sK2_SY16 @ SV3 ) @ SV3 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[35]) ).

thf(43,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( ordinal @ SX0 )
            | ( epsilon_connected @ SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[36]) ).

thf(44,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( ordinal @ SX0 )
            | ( epsilon_transitive @ SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[36]) ).

thf(45,plain,
    ( ( ~ ~ ( ~ ( epsilon_connected @ sK9_A )
            | ~ ( epsilon_transitive @ sK9_A ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[37]) ).

thf(46,plain,
    ( ( ~ ( ordinal @ sK9_A ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[37]) ).

thf(47,plain,
    ! [SV1: $i] :
      ( ( ( ~ ( epsilon_connected @ SV1 ) )
        = $true )
      | ( ( ~ ( epsilon_transitive @ SV1 ) )
        = $true )
      | ( ( ordinal @ SV1 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[38]) ).

thf(48,plain,
    ! [SV4: $i,SV2: $i] :
      ( ( ( ~ ( in @ SV2 @ SV4 ) )
        = $true )
      | ( ( ~ ( in @ SV4 @ SV2 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[39]) ).

thf(49,plain,
    ( ( sK8_REN
      | ! [SX0: $i] :
          ~ ( ~ ! [SX1: $i] :
                  ( ! [SX2: $i] :
                      ( ( SX2 != SX1 )
                      | ~ ( in @ SX2 @ SX0 ) )
                  | ~ ( ordinal @ SX1 )
                  | ( in @ SX1 @ ( sK3_B @ SX0 ) ) )
            | ~ ! [SX1: $i] :
                  ( ~ ( in @ SX1 @ ( sK3_B @ SX0 ) )
                  | ~ ( ~ ~ ( ( ( sK4_D @ SX1 @ SX0 )
                             != SX1 )
                            | ~ ( in @ ( sK4_D @ SX1 @ SX0 ) @ SX0 ) )
                      | ~ ( ordinal @ SX1 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[40]) ).

thf(50,plain,
    ( ( ~ sK8_REN
      | ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( sK5_B != sK6_SY21 )
                            | ~ ( ordinal @ sK6_SY21 ) )
                      | ( sK5_B != sK7_SY23 ) )
                | ~ ( ordinal @ sK7_SY23 ) )
          | ~ ( ( sK6_SY21 != sK7_SY23 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[41]) ).

thf(51,plain,
    ! [SV3: $i] :
      ( ( ~ ( ~ ( in @ ( sK2_SY16 @ SV3 ) @ sK1_A )
            | ~ ( ordinal @ ( sK2_SY16 @ SV3 ) )
            | ~ ( in @ ( sK2_SY16 @ SV3 ) @ SV3 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[42]) ).

thf(52,plain,
    ! [SV3: $i] :
      ( ( ~ ~ ( ~ ( ( in @ ( sK2_SY16 @ SV3 ) @ sK1_A )
                  | ( in @ ( sK2_SY16 @ SV3 ) @ SV3 ) )
              | ~ ( ( ordinal @ ( sK2_SY16 @ SV3 ) )
                  | ( in @ ( sK2_SY16 @ SV3 ) @ SV3 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[42]) ).

thf(53,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( ordinal @ SX0 )
          | ( epsilon_connected @ SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[43]) ).

thf(54,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( ordinal @ SX0 )
          | ( epsilon_transitive @ SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[44]) ).

thf(55,plain,
    ( ( ~ ( ~ ( epsilon_connected @ sK9_A )
          | ~ ( epsilon_transitive @ sK9_A ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[45]) ).

thf(56,plain,
    ( ( ordinal @ sK9_A )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[46]) ).

thf(57,plain,
    ! [SV1: $i] :
      ( ( ( epsilon_connected @ SV1 )
        = $false )
      | ( ( ~ ( epsilon_transitive @ SV1 ) )
        = $true )
      | ( ( ordinal @ SV1 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[47]) ).

thf(58,plain,
    ! [SV4: $i,SV2: $i] :
      ( ( ( in @ SV2 @ SV4 )
        = $false )
      | ( ( ~ ( in @ SV4 @ SV2 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[48]) ).

thf(59,plain,
    ( ( sK8_REN = $true )
    | ( ( ! [SX0: $i] :
            ~ ( ~ ! [SX1: $i] :
                    ( ! [SX2: $i] :
                        ( ( SX2 != SX1 )
                        | ~ ( in @ SX2 @ SX0 ) )
                    | ~ ( ordinal @ SX1 )
                    | ( in @ SX1 @ ( sK3_B @ SX0 ) ) )
              | ~ ! [SX1: $i] :
                    ( ~ ( in @ SX1 @ ( sK3_B @ SX0 ) )
                    | ~ ( ~ ~ ( ( ( sK4_D @ SX1 @ SX0 )
                               != SX1 )
                              | ~ ( in @ ( sK4_D @ SX1 @ SX0 ) @ SX0 ) )
                        | ~ ( ordinal @ SX1 ) ) ) ) )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[49]) ).

thf(60,plain,
    ( ( ( ~ sK8_REN )
      = $true )
    | ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( sK5_B != sK6_SY21 )
                              | ~ ( ordinal @ sK6_SY21 ) )
                        | ( sK5_B != sK7_SY23 ) )
                  | ~ ( ordinal @ sK7_SY23 ) )
            | ~ ( ( sK6_SY21 != sK7_SY23 ) ) ) )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[50]) ).

thf(61,plain,
    ! [SV3: $i] :
      ( ( ~ ( in @ ( sK2_SY16 @ SV3 ) @ sK1_A )
        | ~ ( ordinal @ ( sK2_SY16 @ SV3 ) )
        | ~ ( in @ ( sK2_SY16 @ SV3 ) @ SV3 ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[51]) ).

thf(62,plain,
    ! [SV3: $i] :
      ( ( ~ ( ~ ( ( in @ ( sK2_SY16 @ SV3 ) @ sK1_A )
                | ( in @ ( sK2_SY16 @ SV3 ) @ SV3 ) )
            | ~ ( ( ordinal @ ( sK2_SY16 @ SV3 ) )
                | ( in @ ( sK2_SY16 @ SV3 ) @ SV3 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[52]) ).

thf(63,plain,
    ! [SV5: $i] :
      ( ( ~ ( ordinal @ SV5 )
        | ( epsilon_connected @ SV5 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[53]) ).

thf(64,plain,
    ! [SV6: $i] :
      ( ( ~ ( ordinal @ SV6 )
        | ( epsilon_transitive @ SV6 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[54]) ).

thf(65,plain,
    ( ( ~ ( epsilon_connected @ sK9_A )
      | ~ ( epsilon_transitive @ sK9_A ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[55]) ).

thf(66,plain,
    ! [SV1: $i] :
      ( ( ( epsilon_transitive @ SV1 )
        = $false )
      | ( ( epsilon_connected @ SV1 )
        = $false )
      | ( ( ordinal @ SV1 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[57]) ).

thf(67,plain,
    ! [SV2: $i,SV4: $i] :
      ( ( ( in @ SV4 @ SV2 )
        = $false )
      | ( ( in @ SV2 @ SV4 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[58]) ).

thf(68,plain,
    ! [SV7: $i] :
      ( ( ( ~ ( ~ ! [SY25: $i] :
                    ( ! [SY26: $i] :
                        ( ( SY26 != SY25 )
                        | ~ ( in @ SY26 @ SV7 ) )
                    | ~ ( ordinal @ SY25 )
                    | ( in @ SY25 @ ( sK3_B @ SV7 ) ) )
              | ~ ! [SY27: $i] :
                    ( ~ ( in @ SY27 @ ( sK3_B @ SV7 ) )
                    | ~ ( ~ ~ ( ( ( sK4_D @ SY27 @ SV7 )
                               != SY27 )
                              | ~ ( in @ ( sK4_D @ SY27 @ SV7 ) @ SV7 ) )
                        | ~ ( ordinal @ SY27 ) ) ) ) )
        = $true )
      | ( sK8_REN = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[59]) ).

thf(69,plain,
    ( ( sK8_REN = $false )
    | ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( sK5_B != sK6_SY21 )
                              | ~ ( ordinal @ sK6_SY21 ) )
                        | ( sK5_B != sK7_SY23 ) )
                  | ~ ( ordinal @ sK7_SY23 ) )
            | ~ ( ( sK6_SY21 != sK7_SY23 ) ) ) )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[60]) ).

thf(70,plain,
    ! [SV3: $i] :
      ( ( ( ~ ( in @ ( sK2_SY16 @ SV3 ) @ sK1_A )
          | ~ ( ordinal @ ( sK2_SY16 @ SV3 ) ) )
        = $true )
      | ( ( ~ ( in @ ( sK2_SY16 @ SV3 ) @ SV3 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[61]) ).

thf(71,plain,
    ! [SV3: $i] :
      ( ( ~ ( ( in @ ( sK2_SY16 @ SV3 ) @ sK1_A )
            | ( in @ ( sK2_SY16 @ SV3 ) @ SV3 ) )
        | ~ ( ( ordinal @ ( sK2_SY16 @ SV3 ) )
            | ( in @ ( sK2_SY16 @ SV3 ) @ SV3 ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[62]) ).

thf(72,plain,
    ! [SV5: $i] :
      ( ( ( ~ ( ordinal @ SV5 ) )
        = $true )
      | ( ( epsilon_connected @ SV5 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[63]) ).

thf(73,plain,
    ! [SV6: $i] :
      ( ( ( ~ ( ordinal @ SV6 ) )
        = $true )
      | ( ( epsilon_transitive @ SV6 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[64]) ).

thf(74,plain,
    ( ( ~ ( epsilon_connected @ sK9_A ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[65]) ).

thf(75,plain,
    ( ( ~ ( epsilon_transitive @ sK9_A ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[65]) ).

thf(76,plain,
    ! [SV7: $i] :
      ( ( ( ~ ! [SY25: $i] :
                ( ! [SY26: $i] :
                    ( ( SY26 != SY25 )
                    | ~ ( in @ SY26 @ SV7 ) )
                | ~ ( ordinal @ SY25 )
                | ( in @ SY25 @ ( sK3_B @ SV7 ) ) )
          | ~ ! [SY27: $i] :
                ( ~ ( in @ SY27 @ ( sK3_B @ SV7 ) )
                | ~ ( ~ ~ ( ( ( sK4_D @ SY27 @ SV7 )
                           != SY27 )
                          | ~ ( in @ ( sK4_D @ SY27 @ SV7 ) @ SV7 ) )
                    | ~ ( ordinal @ SY27 ) ) ) )
        = $false )
      | ( sK8_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[68]) ).

thf(77,plain,
    ( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ( sK5_B != sK6_SY21 )
                          | ~ ( ordinal @ sK6_SY21 ) )
                    | ( sK5_B != sK7_SY23 ) )
              | ~ ( ordinal @ sK7_SY23 ) )
        | ~ ( ( sK6_SY21 != sK7_SY23 ) ) )
      = $false )
    | ( sK8_REN = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[69]) ).

thf(78,plain,
    ! [SV3: $i] :
      ( ( ( ~ ( in @ ( sK2_SY16 @ SV3 ) @ sK1_A ) )
        = $true )
      | ( ( ~ ( ordinal @ ( sK2_SY16 @ SV3 ) ) )
        = $true )
      | ( ( ~ ( in @ ( sK2_SY16 @ SV3 ) @ SV3 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[70]) ).

thf(79,plain,
    ! [SV3: $i] :
      ( ( ~ ( ( in @ ( sK2_SY16 @ SV3 ) @ sK1_A )
            | ( in @ ( sK2_SY16 @ SV3 ) @ SV3 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[71]) ).

thf(80,plain,
    ! [SV3: $i] :
      ( ( ~ ( ( ordinal @ ( sK2_SY16 @ SV3 ) )
            | ( in @ ( sK2_SY16 @ SV3 ) @ SV3 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[71]) ).

thf(81,plain,
    ! [SV5: $i] :
      ( ( ( ordinal @ SV5 )
        = $false )
      | ( ( epsilon_connected @ SV5 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[72]) ).

thf(82,plain,
    ! [SV6: $i] :
      ( ( ( ordinal @ SV6 )
        = $false )
      | ( ( epsilon_transitive @ SV6 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[73]) ).

thf(83,plain,
    ( ( epsilon_connected @ sK9_A )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[74]) ).

thf(84,plain,
    ( ( epsilon_transitive @ sK9_A )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[75]) ).

thf(85,plain,
    ! [SV7: $i] :
      ( ( ( ~ ! [SY25: $i] :
                ( ! [SY26: $i] :
                    ( ( SY26 != SY25 )
                    | ~ ( in @ SY26 @ SV7 ) )
                | ~ ( ordinal @ SY25 )
                | ( in @ SY25 @ ( sK3_B @ SV7 ) ) ) )
        = $false )
      | ( sK8_REN = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[76]) ).

thf(86,plain,
    ! [SV7: $i] :
      ( ( ( ~ ! [SY27: $i] :
                ( ~ ( in @ SY27 @ ( sK3_B @ SV7 ) )
                | ~ ( ~ ~ ( ( ( sK4_D @ SY27 @ SV7 )
                           != SY27 )
                          | ~ ( in @ ( sK4_D @ SY27 @ SV7 ) @ SV7 ) )
                    | ~ ( ordinal @ SY27 ) ) ) )
        = $false )
      | ( sK8_REN = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[76]) ).

thf(87,plain,
    ( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ( sK5_B != sK6_SY21 )
                          | ~ ( ordinal @ sK6_SY21 ) )
                    | ( sK5_B != sK7_SY23 ) )
              | ~ ( ordinal @ sK7_SY23 ) ) )
      = $false )
    | ( sK8_REN = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[77]) ).

thf(88,plain,
    ( ( ( ~ ( ( sK6_SY21 != sK7_SY23 ) ) )
      = $false )
    | ( sK8_REN = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[77]) ).

thf(89,plain,
    ! [SV3: $i] :
      ( ( ( in @ ( sK2_SY16 @ SV3 ) @ sK1_A )
        = $false )
      | ( ( ~ ( ordinal @ ( sK2_SY16 @ SV3 ) ) )
        = $true )
      | ( ( ~ ( in @ ( sK2_SY16 @ SV3 ) @ SV3 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[78]) ).

thf(90,plain,
    ! [SV3: $i] :
      ( ( ( in @ ( sK2_SY16 @ SV3 ) @ sK1_A )
        | ( in @ ( sK2_SY16 @ SV3 ) @ SV3 ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[79]) ).

thf(91,plain,
    ! [SV3: $i] :
      ( ( ( ordinal @ ( sK2_SY16 @ SV3 ) )
        | ( in @ ( sK2_SY16 @ SV3 ) @ SV3 ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[80]) ).

thf(92,plain,
    ! [SV7: $i] :
      ( ( ( ! [SY25: $i] :
              ( ! [SY26: $i] :
                  ( ( SY26 != SY25 )
                  | ~ ( in @ SY26 @ SV7 ) )
              | ~ ( ordinal @ SY25 )
              | ( in @ SY25 @ ( sK3_B @ SV7 ) ) ) )
        = $true )
      | ( sK8_REN = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[85]) ).

thf(93,plain,
    ! [SV7: $i] :
      ( ( ( ! [SY27: $i] :
              ( ~ ( in @ SY27 @ ( sK3_B @ SV7 ) )
              | ~ ( ~ ~ ( ( ( sK4_D @ SY27 @ SV7 )
                         != SY27 )
                        | ~ ( in @ ( sK4_D @ SY27 @ SV7 ) @ SV7 ) )
                  | ~ ( ordinal @ SY27 ) ) ) )
        = $true )
      | ( sK8_REN = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[86]) ).

thf(94,plain,
    ( ( ( ~ ( ~ ~ ( ~ ~ ( ( sK5_B != sK6_SY21 )
                        | ~ ( ordinal @ sK6_SY21 ) )
                  | ( sK5_B != sK7_SY23 ) )
            | ~ ( ordinal @ sK7_SY23 ) ) )
      = $true )
    | ( sK8_REN = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[87]) ).

thf(95,plain,
    ( ( ( ( sK6_SY21 != sK7_SY23 ) )
      = $true )
    | ( sK8_REN = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[88]) ).

thf(96,plain,
    ! [SV3: $i] :
      ( ( ( ordinal @ ( sK2_SY16 @ SV3 ) )
        = $false )
      | ( ( in @ ( sK2_SY16 @ SV3 ) @ sK1_A )
        = $false )
      | ( ( ~ ( in @ ( sK2_SY16 @ SV3 ) @ SV3 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[89]) ).

thf(97,plain,
    ! [SV3: $i] :
      ( ( ( in @ ( sK2_SY16 @ SV3 ) @ sK1_A )
        = $true )
      | ( ( in @ ( sK2_SY16 @ SV3 ) @ SV3 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[90]) ).

thf(98,plain,
    ! [SV3: $i] :
      ( ( ( ordinal @ ( sK2_SY16 @ SV3 ) )
        = $true )
      | ( ( in @ ( sK2_SY16 @ SV3 ) @ SV3 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[91]) ).

thf(99,plain,
    ! [SV7: $i,SV8: $i] :
      ( ( ( ! [SY28: $i] :
              ( ( SY28 != SV8 )
              | ~ ( in @ SY28 @ SV7 ) )
          | ~ ( ordinal @ SV8 )
          | ( in @ SV8 @ ( sK3_B @ SV7 ) ) )
        = $true )
      | ( sK8_REN = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[92]) ).

thf(100,plain,
    ! [SV7: $i,SV9: $i] :
      ( ( ( ~ ( in @ SV9 @ ( sK3_B @ SV7 ) )
          | ~ ( ~ ~ ( ( ( sK4_D @ SV9 @ SV7 )
                     != SV9 )
                    | ~ ( in @ ( sK4_D @ SV9 @ SV7 ) @ SV7 ) )
              | ~ ( ordinal @ SV9 ) ) )
        = $true )
      | ( sK8_REN = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[93]) ).

thf(101,plain,
    ( ( ( ~ ~ ( ~ ~ ( ( sK5_B != sK6_SY21 )
                    | ~ ( ordinal @ sK6_SY21 ) )
              | ( sK5_B != sK7_SY23 ) )
        | ~ ( ordinal @ sK7_SY23 ) )
      = $false )
    | ( sK8_REN = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[94]) ).

thf(102,plain,
    ( ( ( sK6_SY21 = sK7_SY23 )
      = $false )
    | ( sK8_REN = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[95]) ).

thf(103,plain,
    ! [SV3: $i] :
      ( ( ( in @ ( sK2_SY16 @ SV3 ) @ SV3 )
        = $false )
      | ( ( in @ ( sK2_SY16 @ SV3 ) @ sK1_A )
        = $false )
      | ( ( ordinal @ ( sK2_SY16 @ SV3 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[96]) ).

thf(104,plain,
    ! [SV7: $i,SV8: $i] :
      ( ( ( ! [SY28: $i] :
              ( ( SY28 != SV8 )
              | ~ ( in @ SY28 @ SV7 ) )
          | ~ ( ordinal @ SV8 ) )
        = $true )
      | ( ( in @ SV8 @ ( sK3_B @ SV7 ) )
        = $true )
      | ( sK8_REN = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[99]) ).

thf(105,plain,
    ! [SV7: $i,SV9: $i] :
      ( ( ( ~ ( in @ SV9 @ ( sK3_B @ SV7 ) ) )
        = $true )
      | ( ( ~ ( ~ ~ ( ( ( sK4_D @ SV9 @ SV7 )
                     != SV9 )
                    | ~ ( in @ ( sK4_D @ SV9 @ SV7 ) @ SV7 ) )
              | ~ ( ordinal @ SV9 ) ) )
        = $true )
      | ( sK8_REN = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[100]) ).

thf(106,plain,
    ( ( ( ~ ~ ( ~ ~ ( ( sK5_B != sK6_SY21 )
                    | ~ ( ordinal @ sK6_SY21 ) )
              | ( sK5_B != sK7_SY23 ) ) )
      = $false )
    | ( sK8_REN = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[101]) ).

thf(107,plain,
    ( ( ( ~ ( ordinal @ sK7_SY23 ) )
      = $false )
    | ( sK8_REN = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[101]) ).

thf(108,plain,
    ! [SV7: $i,SV8: $i] :
      ( ( ( ! [SY28: $i] :
              ( ( SY28 != SV8 )
              | ~ ( in @ SY28 @ SV7 ) ) )
        = $true )
      | ( ( ~ ( ordinal @ SV8 ) )
        = $true )
      | ( ( in @ SV8 @ ( sK3_B @ SV7 ) )
        = $true )
      | ( sK8_REN = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[104]) ).

thf(109,plain,
    ! [SV7: $i,SV9: $i] :
      ( ( ( in @ SV9 @ ( sK3_B @ SV7 ) )
        = $false )
      | ( ( ~ ( ~ ~ ( ( ( sK4_D @ SV9 @ SV7 )
                     != SV9 )
                    | ~ ( in @ ( sK4_D @ SV9 @ SV7 ) @ SV7 ) )
              | ~ ( ordinal @ SV9 ) ) )
        = $true )
      | ( sK8_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[105]) ).

thf(110,plain,
    ( ( ( ~ ( ~ ~ ( ( sK5_B != sK6_SY21 )
                  | ~ ( ordinal @ sK6_SY21 ) )
            | ( sK5_B != sK7_SY23 ) ) )
      = $true )
    | ( sK8_REN = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[106]) ).

thf(111,plain,
    ( ( ( ordinal @ sK7_SY23 )
      = $true )
    | ( sK8_REN = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[107]) ).

thf(112,plain,
    ! [SV7: $i,SV8: $i,SV10: $i] :
      ( ( ( ( SV10 != SV8 )
          | ~ ( in @ SV10 @ SV7 ) )
        = $true )
      | ( ( ~ ( ordinal @ SV8 ) )
        = $true )
      | ( ( in @ SV8 @ ( sK3_B @ SV7 ) )
        = $true )
      | ( sK8_REN = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[108]) ).

thf(113,plain,
    ! [SV7: $i,SV9: $i] :
      ( ( ( ~ ~ ( ( ( sK4_D @ SV9 @ SV7 )
                 != SV9 )
                | ~ ( in @ ( sK4_D @ SV9 @ SV7 ) @ SV7 ) )
          | ~ ( ordinal @ SV9 ) )
        = $false )
      | ( ( in @ SV9 @ ( sK3_B @ SV7 ) )
        = $false )
      | ( sK8_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[109]) ).

thf(114,plain,
    ( ( ( ~ ~ ( ( sK5_B != sK6_SY21 )
              | ~ ( ordinal @ sK6_SY21 ) )
        | ( sK5_B != sK7_SY23 ) )
      = $false )
    | ( sK8_REN = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[110]) ).

thf(115,plain,
    ! [SV7: $i,SV8: $i,SV10: $i] :
      ( ( ( ( SV10 != SV8 ) )
        = $true )
      | ( ( ~ ( in @ SV10 @ SV7 ) )
        = $true )
      | ( ( ~ ( ordinal @ SV8 ) )
        = $true )
      | ( ( in @ SV8 @ ( sK3_B @ SV7 ) )
        = $true )
      | ( sK8_REN = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[112]) ).

thf(116,plain,
    ! [SV7: $i,SV9: $i] :
      ( ( ( ~ ~ ( ( ( sK4_D @ SV9 @ SV7 )
                 != SV9 )
                | ~ ( in @ ( sK4_D @ SV9 @ SV7 ) @ SV7 ) ) )
        = $false )
      | ( ( in @ SV9 @ ( sK3_B @ SV7 ) )
        = $false )
      | ( sK8_REN = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[113]) ).

thf(117,plain,
    ! [SV7: $i,SV9: $i] :
      ( ( ( ~ ( ordinal @ SV9 ) )
        = $false )
      | ( ( in @ SV9 @ ( sK3_B @ SV7 ) )
        = $false )
      | ( sK8_REN = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[113]) ).

thf(118,plain,
    ( ( ( ~ ~ ( ( sK5_B != sK6_SY21 )
              | ~ ( ordinal @ sK6_SY21 ) ) )
      = $false )
    | ( sK8_REN = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[114]) ).

thf(119,plain,
    ( ( ( ( sK5_B != sK7_SY23 ) )
      = $false )
    | ( sK8_REN = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[114]) ).

thf(120,plain,
    ! [SV7: $i,SV8: $i,SV10: $i] :
      ( ( ( SV10 = SV8 )
        = $false )
      | ( ( ~ ( in @ SV10 @ SV7 ) )
        = $true )
      | ( ( ~ ( ordinal @ SV8 ) )
        = $true )
      | ( ( in @ SV8 @ ( sK3_B @ SV7 ) )
        = $true )
      | ( sK8_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[115]) ).

thf(121,plain,
    ! [SV7: $i,SV9: $i] :
      ( ( ( ~ ( ( ( sK4_D @ SV9 @ SV7 )
               != SV9 )
              | ~ ( in @ ( sK4_D @ SV9 @ SV7 ) @ SV7 ) ) )
        = $true )
      | ( ( in @ SV9 @ ( sK3_B @ SV7 ) )
        = $false )
      | ( sK8_REN = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[116]) ).

thf(122,plain,
    ! [SV7: $i,SV9: $i] :
      ( ( ( ordinal @ SV9 )
        = $true )
      | ( ( in @ SV9 @ ( sK3_B @ SV7 ) )
        = $false )
      | ( sK8_REN = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[117]) ).

thf(123,plain,
    ( ( ( ~ ( ( sK5_B != sK6_SY21 )
            | ~ ( ordinal @ sK6_SY21 ) ) )
      = $true )
    | ( sK8_REN = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[118]) ).

thf(124,plain,
    ( ( ( sK5_B = sK7_SY23 )
      = $true )
    | ( sK8_REN = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[119]) ).

thf(125,plain,
    ! [SV8: $i,SV7: $i,SV10: $i] :
      ( ( ( in @ SV10 @ SV7 )
        = $false )
      | ( ( SV10 = SV8 )
        = $false )
      | ( ( ~ ( ordinal @ SV8 ) )
        = $true )
      | ( ( in @ SV8 @ ( sK3_B @ SV7 ) )
        = $true )
      | ( sK8_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[120]) ).

thf(126,plain,
    ! [SV7: $i,SV9: $i] :
      ( ( ( ( ( sK4_D @ SV9 @ SV7 )
           != SV9 )
          | ~ ( in @ ( sK4_D @ SV9 @ SV7 ) @ SV7 ) )
        = $false )
      | ( ( in @ SV9 @ ( sK3_B @ SV7 ) )
        = $false )
      | ( sK8_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[121]) ).

thf(127,plain,
    ( ( ( ( sK5_B != sK6_SY21 )
        | ~ ( ordinal @ sK6_SY21 ) )
      = $false )
    | ( sK8_REN = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[123]) ).

thf(128,plain,
    ! [SV7: $i,SV10: $i,SV8: $i] :
      ( ( ( ordinal @ SV8 )
        = $false )
      | ( ( SV10 = SV8 )
        = $false )
      | ( ( in @ SV10 @ SV7 )
        = $false )
      | ( ( in @ SV8 @ ( sK3_B @ SV7 ) )
        = $true )
      | ( sK8_REN = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[125]) ).

thf(129,plain,
    ! [SV7: $i,SV9: $i] :
      ( ( ( ( ( sK4_D @ SV9 @ SV7 )
           != SV9 ) )
        = $false )
      | ( ( in @ SV9 @ ( sK3_B @ SV7 ) )
        = $false )
      | ( sK8_REN = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[126]) ).

thf(130,plain,
    ! [SV7: $i,SV9: $i] :
      ( ( ( ~ ( in @ ( sK4_D @ SV9 @ SV7 ) @ SV7 ) )
        = $false )
      | ( ( in @ SV9 @ ( sK3_B @ SV7 ) )
        = $false )
      | ( sK8_REN = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[126]) ).

thf(131,plain,
    ( ( ( ( sK5_B != sK6_SY21 ) )
      = $false )
    | ( sK8_REN = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[127]) ).

thf(132,plain,
    ( ( ( ~ ( ordinal @ sK6_SY21 ) )
      = $false )
    | ( sK8_REN = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[127]) ).

thf(133,plain,
    ! [SV7: $i,SV9: $i] :
      ( ( ( ( sK4_D @ SV9 @ SV7 )
          = SV9 )
        = $true )
      | ( ( in @ SV9 @ ( sK3_B @ SV7 ) )
        = $false )
      | ( sK8_REN = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[129]) ).

thf(134,plain,
    ! [SV7: $i,SV9: $i] :
      ( ( ( in @ ( sK4_D @ SV9 @ SV7 ) @ SV7 )
        = $true )
      | ( ( in @ SV9 @ ( sK3_B @ SV7 ) )
        = $false )
      | ( sK8_REN = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[130]) ).

thf(135,plain,
    ( ( ( sK5_B = sK6_SY21 )
      = $true )
    | ( sK8_REN = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[131]) ).

thf(136,plain,
    ( ( ( ordinal @ sK6_SY21 )
      = $true )
    | ( sK8_REN = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[132]) ).

thf(137,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[56,136,135,134,133,128,124,122,111,103,102,98,97,84,83,82,81,67,66]) ).

thf(138,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[137]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : SEU280+1 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34  % Computer : n029.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 Jun 20 01:35:00 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  
% 0.13/0.35   No.of.Axioms: 5
% 0.13/0.35  
% 0.13/0.35   Length.of.Defs: 0
% 0.13/0.35  
% 0.13/0.35   Contains.Choice.Funs: false
% 0.13/0.36  (rf:0,axioms:5,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:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:7,loop_count:0,foatp_calls:0,translation:fof_full)......
% 0.20/0.52  
% 0.20/0.52  ********************************
% 0.20/0.52  *   All subproblems solved!    *
% 0.20/0.52  ********************************
% 0.20/0.52  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:5,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:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:137,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.20/0.53  
% 0.20/0.53  %**** Beginning of derivation protocol ****
% 0.20/0.53  % SZS output start CNFRefutation
% See solution above
% 0.20/0.53  
% 0.20/0.53  %**** End of derivation protocol ****
% 0.20/0.53  %**** no. of clauses in derivation: 138 ****
% 0.20/0.53  %**** clause counter: 137 ****
% 0.20/0.53  
% 0.20/0.53  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:5,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:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:137,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------