TSTP Solution File: SEU797^2 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SEU797^2 : TPTP v8.1.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n003.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 12:14:49 EDT 2022

% Result   : Theorem 201.88s 202.15s
% Output   : CNFRefutation 201.93s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   25
%            Number of leaves      :   25
% Syntax   : Number of formulae    :  128 (  38 unt;  23 typ;   1 def)
%            Number of atoms       :  749 ( 302 equ;   0 cnn)
%            Maximal formula atoms :    4 (   7 avg)
%            Number of connectives : 1456 ( 106   ~; 155   |;  16   &;1168   @)
%                                         (   3 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  159 ( 159   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   26 (  23 usr;  11 con; 0-5 aty)
%            Number of variables   :  480 ( 133   ^ 339   !;   8   ?; 480   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_image1,type,
    image1: $i > ( $i > $i ) > $i ).

thf(tp_image1Equiv,type,
    image1Equiv: $o ).

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

thf(tp_sK10_E,type,
    sK10_E: $i ).

thf(tp_sK11_E,type,
    sK11_E: $i > $i > ( $i > $i ) > ( $i > $i ) > $i ).

thf(tp_sK12_E,type,
    sK12_E: $i > $i > ( $i > $i ) > ( $i > $i ) > $i ).

thf(tp_sK13_E,type,
    sK13_E: $i ).

thf(tp_sK14_E,type,
    sK14_E: $i > ( $i > $i ) > $i ).

thf(tp_sK15_E,type,
    sK15_E: $i > ( $i > $i ) > $i ).

thf(tp_sK16_E,type,
    sK16_E: $i ).

thf(tp_sK17_E,type,
    sK17_E: $i ).

thf(tp_sK18_E,type,
    sK18_E: $i ).

thf(tp_sK19_E,type,
    sK19_E: $i > $i > ( $i > $i ) > $i ).

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

thf(tp_sK20_E,type,
    sK20_E: $i > $i > ( $i > $i ) > $i ).

thf(tp_sK2_SY430,type,
    sK2_SY430: $i > $i ).

thf(tp_sK3_SY434,type,
    sK3_SY434: $i ).

thf(tp_sK4_SY437,type,
    sK4_SY437: $i ).

thf(tp_sK5_Xy,type,
    sK5_Xy: $i > ( $i > $i ) > $i > $i ).

thf(tp_sK6_E,type,
    sK6_E: $i > ( $i > $i ) > $i ).

thf(tp_sK7_E,type,
    sK7_E: $i > $i > $i > ( $i > $i ) > ( $i > $i ) > $i ).

thf(tp_sK8_E,type,
    sK8_E: $i > $i > $i > ( $i > $i ) > ( $i > $i ) > $i ).

thf(tp_sK9_E,type,
    sK9_E: $i > $i ).

thf(image1Equiv,definition,
    ( image1Equiv
    = ( ! [A: $i,Xf: $i > $i,Xx: $i] :
          ( ( in @ Xx
            @ ( image1 @ A
              @ ^ [Xy: $i] : ( Xf @ Xy ) ) )
        <=> ? [Xy: $i] :
              ( ( in @ Xy @ A )
              & ( Xx
                = ( Xf @ Xy ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',image1Equiv) ).

thf(1,conjecture,
    ( image1Equiv
   => ! [A: $i,Xf: $i > $i,Xx: $i] :
        ( ? [Xy: $i] :
            ( ( in @ Xy @ A )
            & ( Xx
              = ( Xf @ Xy ) ) )
       => ( in @ Xx
          @ ( image1 @ A
            @ ^ [Xy: $i] : ( Xf @ Xy ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',image1I) ).

thf(2,negated_conjecture,
    ( ( image1Equiv
     => ! [A: $i,Xf: $i > $i,Xx: $i] :
          ( ? [Xy: $i] :
              ( ( in @ Xy @ A )
              & ( Xx
                = ( Xf @ Xy ) ) )
         => ( in @ Xx
            @ ( image1 @ A
              @ ^ [Xy: $i] : ( Xf @ Xy ) ) ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ( ( ! [A: $i,Xf: $i > $i,Xx: $i] :
          ( ( in @ Xx
            @ ( image1 @ A
              @ ^ [Xy: $i] : ( Xf @ Xy ) ) )
        <=> ? [Xy: $i] :
              ( ( in @ Xy @ A )
              & ( Xx
                = ( Xf @ Xy ) ) ) )
     => ! [A: $i,Xf: $i > $i,Xx: $i] :
          ( ? [Xy: $i] :
              ( ( in @ Xy @ A )
              & ( Xx
                = ( Xf @ Xy ) ) )
         => ( in @ Xx
            @ ( image1 @ A
              @ ^ [Xy: $i] : ( Xf @ Xy ) ) ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[2,image1Equiv]) ).

thf(4,plain,
    ( ( ! [A: $i,Xf: $i > $i,Xx: $i] :
          ( ( in @ Xx
            @ ( image1 @ A
              @ ^ [Xy: $i] : ( Xf @ Xy ) ) )
        <=> ? [Xy: $i] :
              ( ( in @ Xy @ A )
              & ( Xx
                = ( Xf @ Xy ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(5,plain,
    ( ( ! [A: $i,Xf: $i > $i,Xx: $i] :
          ( ? [Xy: $i] :
              ( ( in @ Xy @ A )
              & ( Xx
                = ( Xf @ Xy ) ) )
         => ( in @ Xx
            @ ( image1 @ A
              @ ^ [Xy: $i] : ( Xf @ Xy ) ) ) ) )
    = $false ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(6,plain,
    ( ( ~ ! [A: $i,Xf: $i > $i,Xx: $i] :
            ( ? [Xy: $i] :
                ( ( in @ Xy @ A )
                & ( Xx
                  = ( Xf @ Xy ) ) )
           => ( in @ Xx
              @ ( image1 @ A
                @ ^ [Xy: $i] : ( Xf @ Xy ) ) ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[5]) ).

thf(7,plain,
    ( ( ( sK3_SY434
        = ( sK2_SY430 @ sK4_SY437 ) )
      & ( in @ sK4_SY437 @ sK1_A )
      & ~ ( in @ sK3_SY434
          @ ( image1 @ sK1_A
            @ ^ [SY436: $i] : ( sK2_SY430 @ SY436 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[6]) ).

thf(8,plain,
    ( ( ! [A: $i] :
          ( ! [Xf: $i > $i,Xx: $i] :
              ( ! [Xy: $i] :
                  ( ( Xx
                   != ( Xf @ Xy ) )
                  | ~ ( in @ Xy @ A ) )
              | ( in @ Xx
                @ ( image1 @ A
                  @ ^ [Xy: $i] : ( Xf @ Xy ) ) ) )
          & ! [Xf: $i > $i,Xx: $i] :
              ( ~ ( in @ Xx
                  @ ( image1 @ A
                    @ ^ [Xy: $i] : ( Xf @ Xy ) ) )
              | ( ( Xx
                  = ( Xf @ ( sK5_Xy @ Xx @ Xf @ A ) ) )
                & ( in @ ( sK5_Xy @ Xx @ Xf @ A ) @ A ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[4]) ).

thf(9,plain,
    ( ( ! [A: $i] :
          ( ! [Xf: $i > $i,Xx: $i] :
              ( ! [Xy: $i] :
                  ( ( Xx
                   != ( Xf @ Xy ) )
                  | ~ ( in @ Xy @ A ) )
              | ( in @ Xx
                @ ( image1 @ A
                  @ ^ [Xy: $i] : ( Xf @ Xy ) ) ) )
          & ! [Xf: $i > $i,Xx: $i] :
              ( ~ ( in @ Xx
                  @ ( image1 @ A
                    @ ^ [Xy: $i] : ( Xf @ Xy ) ) )
              | ( ( Xx
                  = ( Xf @ ( sK5_Xy @ Xx @ Xf @ A ) ) )
                & ( in @ ( sK5_Xy @ Xx @ Xf @ A ) @ A ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[8]) ).

thf(10,plain,
    ( ( ( sK3_SY434
        = ( sK2_SY430 @ sK4_SY437 ) )
      & ( in @ sK4_SY437 @ sK1_A )
      & ~ ( in @ sK3_SY434
          @ ( image1 @ sK1_A
            @ ^ [SY436: $i] : ( sK2_SY430 @ SY436 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[7]) ).

thf(11,plain,
    ( ( ! [SX0: $i] :
          ~ ( ~ ! [SX1: $i > $i,SX2: $i] :
                  ( ! [SX3: $i] :
                      ( ( SX2
                       != ( SX1 @ SX3 ) )
                      | ~ ( in @ SX3 @ SX0 ) )
                  | ( in @ SX2
                    @ ( image1 @ SX0
                      @ ^ [SX3: $i] : ( SX1 @ SX3 ) ) ) )
            | ~ ! [SX1: $i > $i,SX2: $i] :
                  ( ~ ( in @ SX2
                      @ ( image1 @ SX0
                        @ ^ [SX3: $i] : ( SX1 @ SX3 ) ) )
                  | ~ ( ( SX2
                       != ( SX1 @ ( sK5_Xy @ SX2 @ SX1 @ SX0 ) ) )
                      | ~ ( in @ ( sK5_Xy @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9,image1Equiv]) ).

thf(12,plain,
    ( ( ~ ( ~ ~ ( ( sK3_SY434
                 != ( sK2_SY430 @ sK4_SY437 ) )
                | ~ ( in @ sK4_SY437 @ sK1_A ) )
          | ~ ~ ( in @ sK3_SY434
                @ ( image1 @ sK1_A
                  @ ^ [SX0: $i] : ( sK2_SY430 @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10,image1Equiv]) ).

thf(13,plain,
    ! [SV1: $i] :
      ( ( ~ ( ~ ! [SY439: $i > $i,SY440: $i] :
                  ( ! [SY441: $i] :
                      ( ( SY440
                       != ( SY439 @ SY441 ) )
                      | ~ ( in @ SY441 @ SV1 ) )
                  | ( in @ SY440
                    @ ( image1 @ SV1
                      @ ^ [SX3: $i] : ( SY439 @ SX3 ) ) ) )
            | ~ ! [SY443: $i > $i,SY444: $i] :
                  ( ~ ( in @ SY444
                      @ ( image1 @ SV1
                        @ ^ [SX3: $i] : ( SY443 @ SX3 ) ) )
                  | ~ ( ( SY444
                       != ( SY443 @ ( sK5_Xy @ SY444 @ SY443 @ SV1 ) ) )
                      | ~ ( in @ ( sK5_Xy @ SY444 @ SY443 @ SV1 ) @ SV1 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11]) ).

thf(14,plain,
    ( ( ~ ~ ( ( sK3_SY434
             != ( sK2_SY430 @ sK4_SY437 ) )
            | ~ ( in @ sK4_SY437 @ sK1_A ) )
      | ~ ~ ( in @ sK3_SY434
            @ ( image1 @ sK1_A
              @ ^ [SX0: $i] : ( sK2_SY430 @ SX0 ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[12]) ).

thf(15,plain,
    ! [SV1: $i] :
      ( ( ~ ! [SY439: $i > $i,SY440: $i] :
              ( ! [SY441: $i] :
                  ( ( SY440
                   != ( SY439 @ SY441 ) )
                  | ~ ( in @ SY441 @ SV1 ) )
              | ( in @ SY440
                @ ( image1 @ SV1
                  @ ^ [SX3: $i] : ( SY439 @ SX3 ) ) ) )
        | ~ ! [SY443: $i > $i,SY444: $i] :
              ( ~ ( in @ SY444
                  @ ( image1 @ SV1
                    @ ^ [SX3: $i] : ( SY443 @ SX3 ) ) )
              | ~ ( ( SY444
                   != ( SY443 @ ( sK5_Xy @ SY444 @ SY443 @ SV1 ) ) )
                  | ~ ( in @ ( sK5_Xy @ SY444 @ SY443 @ SV1 ) @ SV1 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[13]) ).

thf(16,plain,
    ( ( ~ ~ ( ( sK3_SY434
             != ( sK2_SY430 @ sK4_SY437 ) )
            | ~ ( in @ sK4_SY437 @ sK1_A ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[14]) ).

thf(17,plain,
    ( ( ~ ~ ( in @ sK3_SY434
            @ ( image1 @ sK1_A
              @ ^ [SX0: $i] : ( sK2_SY430 @ SX0 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[14]) ).

thf(18,plain,
    ! [SV1: $i] :
      ( ( ~ ! [SY439: $i > $i,SY440: $i] :
              ( ! [SY441: $i] :
                  ( ( SY440
                   != ( SY439 @ SY441 ) )
                  | ~ ( in @ SY441 @ SV1 ) )
              | ( in @ SY440
                @ ( image1 @ SV1
                  @ ^ [SX3: $i] : ( SY439 @ SX3 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[15]) ).

thf(19,plain,
    ! [SV1: $i] :
      ( ( ~ ! [SY443: $i > $i,SY444: $i] :
              ( ~ ( in @ SY444
                  @ ( image1 @ SV1
                    @ ^ [SX3: $i] : ( SY443 @ SX3 ) ) )
              | ~ ( ( SY444
                   != ( SY443 @ ( sK5_Xy @ SY444 @ SY443 @ SV1 ) ) )
                  | ~ ( in @ ( sK5_Xy @ SY444 @ SY443 @ SV1 ) @ SV1 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[15]) ).

thf(20,plain,
    ( ( ~ ( ( sK3_SY434
           != ( sK2_SY430 @ sK4_SY437 ) )
          | ~ ( in @ sK4_SY437 @ sK1_A ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[16]) ).

thf(21,plain,
    ( ( ~ ( in @ sK3_SY434
          @ ( image1 @ sK1_A
            @ ^ [SX0: $i] : ( sK2_SY430 @ SX0 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[17]) ).

thf(22,plain,
    ! [SV1: $i] :
      ( ( ! [SY439: $i > $i,SY440: $i] :
            ( ! [SY441: $i] :
                ( ( SY440
                 != ( SY439 @ SY441 ) )
                | ~ ( in @ SY441 @ SV1 ) )
            | ( in @ SY440
              @ ( image1 @ SV1
                @ ^ [SX3: $i] : ( SY439 @ SX3 ) ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[18]) ).

thf(23,plain,
    ! [SV1: $i] :
      ( ( ! [SY443: $i > $i,SY444: $i] :
            ( ~ ( in @ SY444
                @ ( image1 @ SV1
                  @ ^ [SX3: $i] : ( SY443 @ SX3 ) ) )
            | ~ ( ( SY444
                 != ( SY443 @ ( sK5_Xy @ SY444 @ SY443 @ SV1 ) ) )
                | ~ ( in @ ( sK5_Xy @ SY444 @ SY443 @ SV1 ) @ SV1 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[19]) ).

thf(24,plain,
    ( ( ( sK3_SY434
       != ( sK2_SY430 @ sK4_SY437 ) )
      | ~ ( in @ sK4_SY437 @ sK1_A ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[20]) ).

thf(25,plain,
    ( ( in @ sK3_SY434
      @ ( image1 @ sK1_A
        @ ^ [SX0: $i] : ( sK2_SY430 @ SX0 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[21]) ).

thf(26,plain,
    ! [SV1: $i,SV2: $i > $i] :
      ( ( ! [SY446: $i] :
            ( ! [SY447: $i] :
                ( ( SY446
                 != ( SV2 @ SY447 ) )
                | ~ ( in @ SY447 @ SV1 ) )
            | ( in @ SY446
              @ ( image1 @ SV1
                @ ^ [SY448: $i] : ( SV2 @ SY448 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[22]) ).

thf(27,plain,
    ! [SV3: $i > $i,SV1: $i] :
      ( ( ! [SY449: $i] :
            ( ~ ( in @ SY449
                @ ( image1 @ SV1
                  @ ^ [SY450: $i] : ( SV3 @ SY450 ) ) )
            | ~ ( ( SY449
                 != ( SV3 @ ( sK5_Xy @ SY449 @ SV3 @ SV1 ) ) )
                | ~ ( in @ ( sK5_Xy @ SY449 @ SV3 @ SV1 ) @ SV1 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[23]) ).

thf(28,plain,
    ( ( ( sK3_SY434
       != ( sK2_SY430 @ sK4_SY437 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[24]) ).

thf(29,plain,
    ( ( ~ ( in @ sK4_SY437 @ sK1_A ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[24]) ).

thf(30,plain,
    ! [SV1: $i,SV2: $i > $i,SV4: $i] :
      ( ( ! [SY451: $i] :
            ( ( SV4
             != ( SV2 @ SY451 ) )
            | ~ ( in @ SY451 @ SV1 ) )
        | ( in @ SV4
          @ ( image1 @ SV1
            @ ^ [SY448: $i] : ( SV2 @ SY448 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[26]) ).

thf(31,plain,
    ! [SV3: $i > $i,SV1: $i,SV5: $i] :
      ( ( ~ ( in @ SV5
            @ ( image1 @ SV1
              @ ^ [SY450: $i] : ( SV3 @ SY450 ) ) )
        | ~ ( ( SV5
             != ( SV3 @ ( sK5_Xy @ SV5 @ SV3 @ SV1 ) ) )
            | ~ ( in @ ( sK5_Xy @ SV5 @ SV3 @ SV1 ) @ SV1 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[27]) ).

thf(32,plain,
    ( ( sK3_SY434
      = ( sK2_SY430 @ sK4_SY437 ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[28]) ).

thf(33,plain,
    ( ( in @ sK4_SY437 @ sK1_A )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[29]) ).

thf(34,plain,
    ! [SV1: $i,SV2: $i > $i,SV4: $i] :
      ( ( ( ! [SY451: $i] :
              ( ( SV4
               != ( SV2 @ SY451 ) )
              | ~ ( in @ SY451 @ SV1 ) ) )
        = $true )
      | ( ( in @ SV4
          @ ( image1 @ SV1
            @ ^ [SY448: $i] : ( SV2 @ SY448 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[30]) ).

thf(35,plain,
    ! [SV3: $i > $i,SV1: $i,SV5: $i] :
      ( ( ( ~ ( in @ SV5
              @ ( image1 @ SV1
                @ ^ [SY450: $i] : ( SV3 @ SY450 ) ) ) )
        = $true )
      | ( ( ~ ( ( SV5
               != ( SV3 @ ( sK5_Xy @ SV5 @ SV3 @ SV1 ) ) )
              | ~ ( in @ ( sK5_Xy @ SV5 @ SV3 @ SV1 ) @ SV1 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[31]) ).

thf(36,plain,
    ! [SV1: $i,SV6: $i,SV2: $i > $i,SV4: $i] :
      ( ( ( ( SV4
           != ( SV2 @ SV6 ) )
          | ~ ( in @ SV6 @ SV1 ) )
        = $true )
      | ( ( in @ SV4
          @ ( image1 @ SV1
            @ ^ [SY448: $i] : ( SV2 @ SY448 ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[34]) ).

thf(37,plain,
    ! [SV3: $i > $i,SV1: $i,SV5: $i] :
      ( ( ( in @ SV5
          @ ( image1 @ SV1
            @ ^ [SY450: $i] : ( SV3 @ SY450 ) ) )
        = $false )
      | ( ( ~ ( ( SV5
               != ( SV3 @ ( sK5_Xy @ SV5 @ SV3 @ SV1 ) ) )
              | ~ ( in @ ( sK5_Xy @ SV5 @ SV3 @ SV1 ) @ SV1 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[35]) ).

thf(38,plain,
    ! [SV1: $i,SV6: $i,SV2: $i > $i,SV4: $i] :
      ( ( ( ( SV4
           != ( SV2 @ SV6 ) ) )
        = $true )
      | ( ( ~ ( in @ SV6 @ SV1 ) )
        = $true )
      | ( ( in @ SV4
          @ ( image1 @ SV1
            @ ^ [SY448: $i] : ( SV2 @ SY448 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[36]) ).

thf(39,plain,
    ! [SV1: $i,SV3: $i > $i,SV5: $i] :
      ( ( ( ( SV5
           != ( SV3 @ ( sK5_Xy @ SV5 @ SV3 @ SV1 ) ) )
          | ~ ( in @ ( sK5_Xy @ SV5 @ SV3 @ SV1 ) @ SV1 ) )
        = $false )
      | ( ( in @ SV5
          @ ( image1 @ SV1
            @ ^ [SY450: $i] : ( SV3 @ SY450 ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[37]) ).

thf(40,plain,
    ! [SV1: $i,SV6: $i,SV2: $i > $i,SV4: $i] :
      ( ( ( SV4
          = ( SV2 @ SV6 ) )
        = $false )
      | ( ( ~ ( in @ SV6 @ SV1 ) )
        = $true )
      | ( ( in @ SV4
          @ ( image1 @ SV1
            @ ^ [SY448: $i] : ( SV2 @ SY448 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[38]) ).

thf(41,plain,
    ! [SV1: $i,SV3: $i > $i,SV5: $i] :
      ( ( ( ( SV5
           != ( SV3 @ ( sK5_Xy @ SV5 @ SV3 @ SV1 ) ) ) )
        = $false )
      | ( ( in @ SV5
          @ ( image1 @ SV1
            @ ^ [SY450: $i] : ( SV3 @ SY450 ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[39]) ).

thf(42,plain,
    ! [SV1: $i,SV3: $i > $i,SV5: $i] :
      ( ( ( ~ ( in @ ( sK5_Xy @ SV5 @ SV3 @ SV1 ) @ SV1 ) )
        = $false )
      | ( ( in @ SV5
          @ ( image1 @ SV1
            @ ^ [SY450: $i] : ( SV3 @ SY450 ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[39]) ).

thf(43,plain,
    ! [SV2: $i > $i,SV4: $i,SV1: $i,SV6: $i] :
      ( ( ( in @ SV6 @ SV1 )
        = $false )
      | ( ( SV4
          = ( SV2 @ SV6 ) )
        = $false )
      | ( ( in @ SV4
          @ ( image1 @ SV1
            @ ^ [SY448: $i] : ( SV2 @ SY448 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[40]) ).

thf(44,plain,
    ! [SV1: $i,SV3: $i > $i,SV5: $i] :
      ( ( ( SV5
          = ( SV3 @ ( sK5_Xy @ SV5 @ SV3 @ SV1 ) ) )
        = $true )
      | ( ( in @ SV5
          @ ( image1 @ SV1
            @ ^ [SY450: $i] : ( SV3 @ SY450 ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[41]) ).

thf(45,plain,
    ! [SV1: $i,SV3: $i > $i,SV5: $i] :
      ( ( ( in @ ( sK5_Xy @ SV5 @ SV3 @ SV1 ) @ SV1 )
        = $true )
      | ( ( in @ SV5
          @ ( image1 @ SV1
            @ ^ [SY450: $i] : ( SV3 @ SY450 ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[42]) ).

thf(46,plain,
    ! [SV1: $i,SV6: $i,SV2: $i > $i] :
      ( ( ( in @ ( SV2 @ SV6 )
          @ ( image1 @ SV1
            @ ^ [SX0: $i] : ( SV2 @ SX0 ) ) )
        = $true )
      | ( ( in @ SV6 @ SV1 )
        = $false ) ),
    inference(extuni,[status(esa)],[43:[bind(SV4,$thf( SV2 @ SV6 ))]]) ).

thf(49,plain,
    ! [SV7: $i > $i,SV8: $i,SV9: $i,SV10: $i] :
      ( ( ( in @ SV10 @ SV9 )
        = $false )
      | ( ( SV8
          = ( SV7 @ SV10 ) )
        = $false )
      | ( ( in @ SV8
          @ ( image1 @ SV9
            @ ^ [SX0: $i] : ( SV7 @ SX0 ) ) )
        = $true ) ),
    inference(rename,[status(thm)],[43]) ).

thf(55,plain,
    ! [SV7: $i > $i,SV8: $i,SV9: $i,SV10: $i] :
      ( ( ( ( in @ SV10 @ SV9 )
          = ( in @ sK4_SY437 @ sK1_A ) )
        = $false )
      | ( ( SV8
          = ( SV7 @ SV10 ) )
        = $false )
      | ( ( in @ SV8
          @ ( image1 @ SV9
            @ ^ [SX0: $i] : ( SV7 @ SX0 ) ) )
        = $true ) ),
    inference(res,[status(thm)],[49,33]) ).

thf(56,plain,
    ! [SV7: $i > $i,SV8: $i,SV9: $i,SV10: $i] :
      ( ( ( ( SV8
            = ( SV7 @ SV10 ) )
          = ( sK3_SY434
            = ( sK2_SY430 @ sK4_SY437 ) ) )
        = $false )
      | ( ( in @ SV10 @ SV9 )
        = $false )
      | ( ( in @ SV8
          @ ( image1 @ SV9
            @ ^ [SX0: $i] : ( SV7 @ SX0 ) ) )
        = $true ) ),
    inference(res,[status(thm)],[49,32]) ).

thf(59,plain,
    ! [SV9: $i] :
      ( ( ( in @ ( sK2_SY430 @ sK4_SY437 )
          @ ( image1 @ SV9
            @ ^ [SX0: $i] : SX0 ) )
        = $true )
      | ( ( in @ sK3_SY434 @ SV9 )
        = $false ) ),
    inference(extuni,[status(esa)],[56:[bind(SV8,$thf( sK2_SY430 @ sK4_SY437 )),bind(SV10,$thf( sK3_SY434 )),bind(SV7,$thf( ^ [SX0: $i] : SX0 ))]]) ).

thf(60,plain,
    ! [SV10: $i,SV9: $i] :
      ( ( ( in @ ( sK2_SY430 @ sK4_SY437 )
          @ ( image1 @ SV9
            @ ^ [SX0: $i] : sK3_SY434 ) )
        = $true )
      | ( ( in @ SV10 @ SV9 )
        = $false ) ),
    inference(extuni,[status(esa)],[56:[bind(SV8,$thf( sK2_SY430 @ sK4_SY437 )),bind(SV7,$thf( ^ [SX0: $i] : sK3_SY434 ))]]) ).

thf(61,plain,
    ! [SV9: $i] :
      ( ( ( in @ sK3_SY434
          @ ( image1 @ SV9
            @ ^ [SX0: $i] : ( sK2_SY430 @ SX0 ) ) )
        = $true )
      | ( ( in @ sK4_SY437 @ SV9 )
        = $false ) ),
    inference(extuni,[status(esa)],[56:[bind(SV10,$thf( sK4_SY437 )),bind(SV7,$thf( ^ [SX0: $i] : ( sK2_SY430 @ SX0 ) )),bind(SV8,$thf( sK3_SY434 ))]]) ).

thf(62,plain,
    ! [SV10: $i,SV9: $i] :
      ( ( ( in @ sK3_SY434
          @ ( image1 @ SV9
            @ ^ [SX0: $i] : ( sK2_SY430 @ sK4_SY437 ) ) )
        = $true )
      | ( ( in @ SV10 @ SV9 )
        = $false ) ),
    inference(extuni,[status(esa)],[56:[bind(SV7,$thf( ^ [SX0: $i] : ( sK2_SY430 @ sK4_SY437 ) )),bind(SV8,$thf( sK3_SY434 ))]]) ).

thf(63,plain,
    ! [SV9: $i] :
      ( ( ( in @ sK3_SY434
          @ ( image1 @ SV9
            @ ^ [SX0: $i] : SX0 ) )
        = $true )
      | ( ( in @ ( sK2_SY430 @ sK4_SY437 ) @ SV9 )
        = $false ) ),
    inference(extuni,[status(esa)],[56:[bind(SV10,$thf( sK2_SY430 @ sK4_SY437 )),bind(SV7,$thf( ^ [SX0: $i] : SX0 )),bind(SV8,$thf( sK3_SY434 ))]]) ).

thf(64,plain,
    ! [SV7: $i > $i] :
      ( ( in @ ( SV7 @ sK4_SY437 )
        @ ( image1 @ sK1_A
          @ ^ [SX0: $i] : ( SV7 @ SX0 ) ) )
      = $true ),
    inference(extuni,[status(esa)],[55:[bind(SV8,$thf( SV7 @ sK4_SY437 )),bind(SV9,$thf( sK1_A )),bind(SV10,$thf( sK4_SY437 ))]]) ).

thf(65,plain,
    ! [SV9: $i,SV10: $i,SV7: $i > $i] :
      ( ( ( in @ ( SV7 @ SV10 )
          @ ( image1 @ SV9
            @ ^ [SX0: $i] : ( SV7 @ SX0 ) ) )
        = $true )
      | ( ( in @ SV10 @ SV9 )
        = $false ) ),
    inference(extuni,[status(esa)],[49:[bind(SV8,$thf( SV7 @ SV10 ))]]) ).

thf(66,plain,
    ! [SV25: $i,SV26: $i > $i,SV27: $i] :
      ( ( ( SV27
          = ( SV26 @ ( sK5_Xy @ SV27 @ SV26 @ SV25 ) ) )
        = $true )
      | ( ( in @ SV27
          @ ( image1 @ SV25
            @ ^ [SX0: $i] : ( SV26 @ SX0 ) ) )
        = $false ) ),
    inference(rename,[status(thm)],[44]) ).

thf(69,plain,
    ! [SV25: $i,SV26: $i > $i,SV27: $i,SV7: $i > $i,SV8: $i,SV9: $i,SV10: $i] :
      ( ( ( ( in @ SV27
            @ ( image1 @ SV25
              @ ^ [SX0: $i] : ( SV26 @ SX0 ) ) )
          = ( in @ SV8
            @ ( image1 @ SV9
              @ ^ [SX0: $i] : ( SV7 @ SX0 ) ) ) )
        = $false )
      | ( ( SV27
          = ( SV26 @ ( sK5_Xy @ SV27 @ SV26 @ SV25 ) ) )
        = $true )
      | ( ( in @ SV10 @ SV9 )
        = $false )
      | ( ( SV8
          = ( SV7 @ SV10 ) )
        = $false ) ),
    inference(res,[status(thm)],[66,49]) ).

thf(70,plain,
    ! [SV25: $i,SV26: $i > $i,SV27: $i,SV7: $i > $i,SV8: $i,SV9: $i,SV10: $i] :
      ( ( ( ( SV27
            = ( SV26 @ ( sK5_Xy @ SV27 @ SV26 @ SV25 ) ) )
          = ( SV8
            = ( SV7 @ SV10 ) ) )
        = $false )
      | ( ( in @ SV27
          @ ( image1 @ SV25
            @ ^ [SX0: $i] : ( SV26 @ SX0 ) ) )
        = $false )
      | ( ( in @ SV10 @ SV9 )
        = $false )
      | ( ( in @ SV8
          @ ( image1 @ SV9
            @ ^ [SX0: $i] : ( SV7 @ SX0 ) ) )
        = $true ) ),
    inference(res,[status(thm)],[66,49]) ).

thf(75,plain,
    ! [SV9: $i,SV25: $i,SV10: $i,SV7: $i > $i,SV26: $i > $i] :
      ( ( ( in @ ( SV26 @ ( sK5_Xy @ ( SV7 @ SV10 ) @ SV26 @ SV25 ) )
          @ ( image1 @ SV9
            @ ^ [SX0: $i] : ( SV7 @ SX0 ) ) )
        = $true )
      | ( ( in @ SV10 @ SV9 )
        = $false )
      | ( ( in @ ( SV7 @ SV10 )
          @ ( image1 @ SV25
            @ ^ [SX0: $i] : ( SV26 @ SX0 ) ) )
        = $false ) ),
    inference(extuni,[status(esa)],[70:[bind(SV27,$thf( SV7 @ SV10 )),bind(SV8,$thf( SV26 @ ( sK5_Xy @ ( SV7 @ SV10 ) @ SV26 @ SV25 ) ))]]) ).

thf(76,plain,
    ! [SV9: $i,SV10: $i,SV7: $i > $i,SV25: $i,SV8: $i,SV26: $i > $i] :
      ( ( ( in @ SV8
          @ ( image1 @ SV9
            @ ^ [SX0: $i] : ( SV7 @ SX0 ) ) )
        = $true )
      | ( ( in @ SV10 @ SV9 )
        = $false )
      | ( ( in @ SV8
          @ ( image1 @ SV25
            @ ^ [SX0: $i] : ( SV26 @ SX0 ) ) )
        = $false )
      | ( ( ( SV26 @ ( sK5_Xy @ SV8 @ SV26 @ SV25 ) )
          = ( SV7 @ SV10 ) )
        = $false ) ),
    inference(extuni,[status(esa)],[70:[bind(SV27,$thf( SV8 ))]]) ).

thf(77,plain,
    ! [SV7: $i > $i,SV9: $i,SV10: $i,SV26: $i > $i] :
      ( ( ( in @ SV10 @ SV9 )
        = $false )
      | ( ( ( SV7 @ SV10 )
          = ( SV26 @ ( sK5_Xy @ ( SV7 @ SV10 ) @ SV26 @ SV9 ) ) )
        = $true )
      | ( ( ( SV26 @ ( sK7_E @ SV10 @ SV9 @ ( SV7 @ SV10 ) @ SV7 @ SV26 ) )
          = ( SV7 @ ( sK7_E @ SV10 @ SV9 @ ( SV7 @ SV10 ) @ SV7 @ SV26 ) ) )
        = $false ) ),
    inference(extuni,[status(esa)],[69:[bind(SV8,$thf( SV7 @ SV10 )),bind(SV25,$thf( SV9 )),bind(SV27,$thf( SV7 @ SV10 ))]]) ).

thf(78,plain,
    ! [SV28: $i,SV29: $i > $i,SV30: $i] :
      ( ( ( in @ ( sK5_Xy @ SV30 @ SV29 @ SV28 ) @ SV28 )
        = $true )
      | ( ( in @ SV30
          @ ( image1 @ SV28
            @ ^ [SX0: $i] : ( SV29 @ SX0 ) ) )
        = $false ) ),
    inference(rename,[status(thm)],[45]) ).

thf(81,plain,
    ! [SV28: $i,SV29: $i > $i,SV30: $i,SV25: $i,SV26: $i > $i,SV27: $i] :
      ( ( ( ( in @ ( sK5_Xy @ SV30 @ SV29 @ SV28 ) @ SV28 )
          = ( in @ SV27
            @ ( image1 @ SV25
              @ ^ [SX0: $i] : ( SV26 @ SX0 ) ) ) )
        = $false )
      | ( ( in @ SV30
          @ ( image1 @ SV28
            @ ^ [SX0: $i] : ( SV29 @ SX0 ) ) )
        = $false )
      | ( ( SV27
          = ( SV26 @ ( sK5_Xy @ SV27 @ SV26 @ SV25 ) ) )
        = $true ) ),
    inference(res,[status(thm)],[78,66]) ).

thf(83,plain,
    ! [SV28: $i,SV29: $i > $i,SV30: $i,SV7: $i > $i,SV8: $i,SV9: $i,SV10: $i] :
      ( ( ( ( in @ SV30
            @ ( image1 @ SV28
              @ ^ [SX0: $i] : ( SV29 @ SX0 ) ) )
          = ( in @ SV8
            @ ( image1 @ SV9
              @ ^ [SX0: $i] : ( SV7 @ SX0 ) ) ) )
        = $false )
      | ( ( in @ ( sK5_Xy @ SV30 @ SV29 @ SV28 ) @ SV28 )
        = $true )
      | ( ( in @ SV10 @ SV9 )
        = $false )
      | ( ( SV8
          = ( SV7 @ SV10 ) )
        = $false ) ),
    inference(res,[status(thm)],[78,49]) ).

thf(85,plain,
    ! [SV28: $i,SV29: $i > $i,SV30: $i,SV7: $i > $i,SV8: $i,SV9: $i,SV10: $i] :
      ( ( ( ( in @ ( sK5_Xy @ SV30 @ SV29 @ SV28 ) @ SV28 )
          = ( in @ SV10 @ SV9 ) )
        = $false )
      | ( ( in @ SV30
          @ ( image1 @ SV28
            @ ^ [SX0: $i] : ( SV29 @ SX0 ) ) )
        = $false )
      | ( ( SV8
          = ( SV7 @ SV10 ) )
        = $false )
      | ( ( in @ SV8
          @ ( image1 @ SV9
            @ ^ [SX0: $i] : ( SV7 @ SX0 ) ) )
        = $true ) ),
    inference(res,[status(thm)],[78,49]) ).

thf(89,plain,
    ! [SV9: $i,SV29: $i > $i,SV30: $i,SV7: $i > $i] :
      ( ( ( in @ ( SV7 @ ( sK5_Xy @ SV30 @ SV29 @ SV9 ) )
          @ ( image1 @ SV9
            @ ^ [SX0: $i] : ( SV7 @ SX0 ) ) )
        = $true )
      | ( ( in @ SV30
          @ ( image1 @ SV9
            @ ^ [SX0: $i] : ( SV29 @ SX0 ) ) )
        = $false ) ),
    inference(extuni,[status(esa)],[85:[bind(SV8,$thf( SV7 @ ( sK5_Xy @ SV30 @ SV29 @ SV9 ) )),bind(SV28,$thf( SV9 )),bind(SV10,$thf( sK5_Xy @ SV30 @ SV29 @ SV9 ))]]) ).

thf(90,plain,
    ! [SV7: $i > $i,SV9: $i,SV10: $i,SV29: $i > $i] :
      ( ( ( in @ SV10 @ SV9 )
        = $false )
      | ( ( in @ ( sK5_Xy @ ( SV7 @ SV10 ) @ SV29 @ SV9 ) @ SV9 )
        = $true )
      | ( ( ( SV29 @ ( sK8_E @ SV10 @ SV9 @ ( SV7 @ SV10 ) @ SV7 @ SV29 ) )
          = ( SV7 @ ( sK8_E @ SV10 @ SV9 @ ( SV7 @ SV10 ) @ SV7 @ SV29 ) ) )
        = $false ) ),
    inference(extuni,[status(esa)],[83:[bind(SV8,$thf( SV7 @ SV10 )),bind(SV28,$thf( SV9 )),bind(SV30,$thf( SV7 @ SV10 ))]]) ).

thf(91,plain,
    ! [SV26: $i > $i,SV25: $i,SV29: $i > $i,SV30: $i] :
      ( ( ( ( sK5_Xy @ SV30 @ SV29
            @ ( image1 @ SV25
              @ ^ [SX0: $i] : ( SV26 @ SX0 ) ) )
          = ( SV26
            @ ( sK5_Xy
              @ ( sK5_Xy @ SV30 @ SV29
                @ ( image1 @ SV25
                  @ ^ [SX0: $i] : ( SV26 @ SX0 ) ) )
              @ SV26
              @ SV25 ) ) )
        = $true )
      | ( ( in @ SV30
          @ ( image1
            @ ( image1 @ SV25
              @ ^ [SX0: $i] : ( SV26 @ SX0 ) )
            @ ^ [SX0: $i] : ( SV29 @ SX0 ) ) )
        = $false ) ),
    inference(extuni,[status(esa)],[81:[bind(SV28,$thf( image1 @ SV25 @ ^ [SX0: $i] : ( SV26 @ SX0 ) )),bind(SV27,$thf( sK5_Xy @ SV30 @ SV29 @ ( image1 @ SV25 @ ^ [SX0: $i] : ( SV26 @ SX0 ) ) ))]]) ).

thf(92,plain,
    ! [SV31: $i,SV32: $i,SV33: $i > $i] :
      ( ( ( in @ ( SV33 @ SV32 )
          @ ( image1 @ SV31
            @ ^ [SX0: $i] : ( SV33 @ SX0 ) ) )
        = $true )
      | ( ( in @ SV32 @ SV31 )
        = $false ) ),
    inference(rename,[status(thm)],[46]) ).

thf(95,plain,
    ! [SV31: $i,SV32: $i,SV33: $i > $i,SV28: $i,SV29: $i > $i,SV30: $i] :
      ( ( ( ( in @ ( SV33 @ SV32 )
            @ ( image1 @ SV31
              @ ^ [SX0: $i] : ( SV33 @ SX0 ) ) )
          = ( in @ SV30
            @ ( image1 @ SV28
              @ ^ [SX0: $i] : ( SV29 @ SX0 ) ) ) )
        = $false )
      | ( ( in @ SV32 @ SV31 )
        = $false )
      | ( ( in @ ( sK5_Xy @ SV30 @ SV29 @ SV28 ) @ SV28 )
        = $true ) ),
    inference(res,[status(thm)],[92,78]) ).

thf(96,plain,
    ! [SV31: $i,SV32: $i,SV33: $i > $i,SV28: $i,SV29: $i > $i,SV30: $i] :
      ( ( ( ( in @ SV32 @ SV31 )
          = ( in @ ( sK5_Xy @ SV30 @ SV29 @ SV28 ) @ SV28 ) )
        = $false )
      | ( ( in @ ( SV33 @ SV32 )
          @ ( image1 @ SV31
            @ ^ [SX0: $i] : ( SV33 @ SX0 ) ) )
        = $true )
      | ( ( in @ SV30
          @ ( image1 @ SV28
            @ ^ [SX0: $i] : ( SV29 @ SX0 ) ) )
        = $false ) ),
    inference(res,[status(thm)],[92,78]) ).

thf(97,plain,
    ! [SV31: $i,SV32: $i,SV33: $i > $i,SV25: $i,SV26: $i > $i,SV27: $i] :
      ( ( ( ( in @ ( SV33 @ SV32 )
            @ ( image1 @ SV31
              @ ^ [SX0: $i] : ( SV33 @ SX0 ) ) )
          = ( in @ SV27
            @ ( image1 @ SV25
              @ ^ [SX0: $i] : ( SV26 @ SX0 ) ) ) )
        = $false )
      | ( ( in @ SV32 @ SV31 )
        = $false )
      | ( ( SV27
          = ( SV26 @ ( sK5_Xy @ SV27 @ SV26 @ SV25 ) ) )
        = $true ) ),
    inference(res,[status(thm)],[92,66]) ).

thf(99,plain,
    ! [SV31: $i,SV32: $i,SV33: $i > $i,SV7: $i > $i,SV8: $i,SV9: $i,SV10: $i] :
      ( ( ( ( in @ SV32 @ SV31 )
          = ( in @ SV8
            @ ( image1 @ SV9
              @ ^ [SX0: $i] : ( SV7 @ SX0 ) ) ) )
        = $false )
      | ( ( in @ ( SV33 @ SV32 )
          @ ( image1 @ SV31
            @ ^ [SX0: $i] : ( SV33 @ SX0 ) ) )
        = $true )
      | ( ( in @ SV10 @ SV9 )
        = $false )
      | ( ( SV8
          = ( SV7 @ SV10 ) )
        = $false ) ),
    inference(res,[status(thm)],[92,49]) ).

thf(101,plain,
    ! [SV31: $i,SV32: $i,SV33: $i > $i,SV7: $i > $i,SV8: $i,SV9: $i,SV10: $i] :
      ( ( ( ( in @ ( SV33 @ SV32 )
            @ ( image1 @ SV31
              @ ^ [SX0: $i] : ( SV33 @ SX0 ) ) )
          = ( in @ SV10 @ SV9 ) )
        = $false )
      | ( ( in @ SV32 @ SV31 )
        = $false )
      | ( ( SV8
          = ( SV7 @ SV10 ) )
        = $false )
      | ( ( in @ SV8
          @ ( image1 @ SV9
            @ ^ [SX0: $i] : ( SV7 @ SX0 ) ) )
        = $true ) ),
    inference(res,[status(thm)],[92,49]) ).

thf(102,plain,
    ! [SV31: $i,SV32: $i,SV33: $i > $i] :
      ( ( ( ( in @ SV32 @ SV31 )
          = ( in @ sK4_SY437 @ sK1_A ) )
        = $false )
      | ( ( in @ ( SV33 @ SV32 )
          @ ( image1 @ SV31
            @ ^ [SX0: $i] : ( SV33 @ SX0 ) ) )
        = $true ) ),
    inference(res,[status(thm)],[92,33]) ).

thf(105,plain,
    ! [SV33: $i > $i] :
      ( ( in @ ( SV33 @ sK4_SY437 )
        @ ( image1 @ sK1_A
          @ ^ [SX0: $i] : ( SV33 @ SX0 ) ) )
      = $true ),
    inference(extuni,[status(esa)],[102:[bind(SV31,$thf( sK1_A )),bind(SV32,$thf( sK4_SY437 ))]]) ).

thf(106,plain,
    ! [SV31: $i,SV32: $i,SV33: $i > $i,SV7: $i > $i] :
      ( ( ( in @ ( SV7 @ ( SV33 @ SV32 ) )
          @ ( image1
            @ ( image1 @ SV31
              @ ^ [SX0: $i] : ( SV33 @ SX0 ) )
            @ ^ [SX0: $i] : ( SV7 @ SX0 ) ) )
        = $true )
      | ( ( in @ SV32 @ SV31 )
        = $false ) ),
    inference(extuni,[status(esa)],[101:[bind(SV8,$thf( SV7 @ ( SV33 @ SV32 ) )),bind(SV9,$thf( image1 @ SV31 @ ^ [SX0: $i] : ( SV33 @ SX0 ) )),bind(SV10,$thf( SV33 @ SV32 ))]]) ).

thf(107,plain,
    ! [SV7: $i > $i,SV33: $i > $i,SV9: $i,SV10: $i] :
      ( ( ( in @ SV10 @ SV9 )
        = $false )
      | ( ( in @ ( SV33 @ ( SV7 @ SV10 ) )
          @ ( image1
            @ ( image1 @ SV9
              @ ^ [SX0: $i] : ( SV7 @ SX0 ) )
            @ ^ [SX0: $i] : ( SV33 @ SX0 ) ) )
        = $true ) ),
    inference(extuni,[status(esa)],[99:[bind(SV8,$thf( SV7 @ SV10 )),bind(SV31,$thf( image1 @ SV9 @ ^ [SX0: $i] : ( SV7 @ SX0 ) )),bind(SV32,$thf( SV7 @ SV10 ))]]) ).

thf(108,plain,
    ! [SV26: $i > $i,SV32: $i,SV25: $i,SV33: $i > $i] :
      ( ( ( ( SV33 @ SV32 )
          = ( SV26 @ ( sK5_Xy @ ( SV33 @ SV32 ) @ SV26 @ SV25 ) ) )
        = $true )
      | ( ( in @ SV32 @ SV25 )
        = $false )
      | ( ( ( SV33 @ ( sK11_E @ SV25 @ SV32 @ SV26 @ SV33 ) )
          = ( SV26 @ ( sK11_E @ SV25 @ SV32 @ SV26 @ SV33 ) ) )
        = $false ) ),
    inference(extuni,[status(esa)],[97:[bind(SV31,$thf( SV25 )),bind(SV27,$thf( SV33 @ SV32 ))]]) ).

thf(109,plain,
    ! [SV33: $i > $i,SV29: $i > $i,SV28: $i,SV30: $i] :
      ( ( ( in @ SV30
          @ ( image1 @ SV28
            @ ^ [SX0: $i] : ( SV29 @ SX0 ) ) )
        = $false )
      | ( ( in @ ( SV33 @ ( sK5_Xy @ SV30 @ SV29 @ SV28 ) )
          @ ( image1 @ SV28
            @ ^ [SX0: $i] : ( SV33 @ SX0 ) ) )
        = $true ) ),
    inference(extuni,[status(esa)],[96:[bind(SV31,$thf( SV28 )),bind(SV32,$thf( sK5_Xy @ SV30 @ SV29 @ SV28 ))]]) ).

thf(110,plain,
    ! [SV29: $i > $i,SV32: $i,SV28: $i,SV33: $i > $i] :
      ( ( ( in @ ( sK5_Xy @ ( SV33 @ SV32 ) @ SV29 @ SV28 ) @ SV28 )
        = $true )
      | ( ( in @ SV32 @ SV28 )
        = $false )
      | ( ( ( SV33 @ ( sK12_E @ SV28 @ SV32 @ SV29 @ SV33 ) )
          = ( SV29 @ ( sK12_E @ SV28 @ SV32 @ SV29 @ SV33 ) ) )
        = $false ) ),
    inference(extuni,[status(esa)],[95:[bind(SV31,$thf( SV28 )),bind(SV30,$thf( SV33 @ SV32 ))]]) ).

thf(111,plain,
    ! [SV36: $i] :
      ( ( ( in @ ( sK2_SY430 @ sK4_SY437 )
          @ ( image1 @ SV36
            @ ^ [SX0: $i] : SX0 ) )
        = $true )
      | ( ( in @ sK3_SY434 @ SV36 )
        = $false ) ),
    inference(rename,[status(thm)],[59]) ).

thf(114,plain,
    ! [SV36: $i,SV31: $i,SV32: $i,SV33: $i > $i] :
      ( ( ( ( in @ ( sK2_SY430 @ sK4_SY437 )
            @ ( image1 @ SV36
              @ ^ [SX0: $i] : SX0 ) )
          = ( in @ SV32 @ SV31 ) )
        = $false )
      | ( ( in @ sK3_SY434 @ SV36 )
        = $false )
      | ( ( in @ ( SV33 @ SV32 )
          @ ( image1 @ SV31
            @ ^ [SX0: $i] : ( SV33 @ SX0 ) ) )
        = $true ) ),
    inference(res,[status(thm)],[111,92]) ).

thf(122,plain,
    ! [SV36: $i,SV7: $i > $i,SV8: $i,SV9: $i,SV10: $i] :
      ( ( ( ( in @ ( sK2_SY430 @ sK4_SY437 )
            @ ( image1 @ SV36
              @ ^ [SX0: $i] : SX0 ) )
          = ( in @ SV10 @ SV9 ) )
        = $false )
      | ( ( in @ sK3_SY434 @ SV36 )
        = $false )
      | ( ( SV8
          = ( SV7 @ SV10 ) )
        = $false )
      | ( ( in @ SV8
          @ ( image1 @ SV9
            @ ^ [SX0: $i] : ( SV7 @ SX0 ) ) )
        = $true ) ),
    inference(res,[status(thm)],[111,49]) ).

thf(126,plain,
    ! [SV36: $i,SV7: $i > $i] :
      ( ( ( in @ ( SV7 @ ( sK2_SY430 @ sK4_SY437 ) )
          @ ( image1
            @ ( image1 @ SV36
              @ ^ [SX0: $i] : SX0 )
            @ ^ [SX0: $i] : ( SV7 @ SX0 ) ) )
        = $true )
      | ( ( in @ sK3_SY434 @ SV36 )
        = $false ) ),
    inference(extuni,[status(esa)],[122:[bind(SV8,$thf( SV7 @ ( sK2_SY430 @ sK4_SY437 ) )),bind(SV9,$thf( image1 @ SV36 @ ^ [SX0: $i] : SX0 )),bind(SV10,$thf( sK2_SY430 @ sK4_SY437 ))]]) ).

thf(127,plain,
    ! [SV36: $i,SV33: $i > $i] :
      ( ( ( in @ ( SV33 @ ( sK2_SY430 @ sK4_SY437 ) )
          @ ( image1
            @ ( image1 @ SV36
              @ ^ [SX0: $i] : SX0 )
            @ ^ [SX0: $i] : ( SV33 @ SX0 ) ) )
        = $true )
      | ( ( in @ sK3_SY434 @ SV36 )
        = $false ) ),
    inference(extuni,[status(esa)],[114:[bind(SV31,$thf( image1 @ SV36 @ ^ [SX0: $i] : SX0 )),bind(SV32,$thf( sK2_SY430 @ sK4_SY437 ))]]) ).

thf(128,plain,
    ! [SV37: $i,SV38: $i] :
      ( ( ( in @ ( sK2_SY430 @ sK4_SY437 )
          @ ( image1 @ SV38
            @ ^ [SX0: $i] : sK3_SY434 ) )
        = $true )
      | ( ( in @ SV37 @ SV38 )
        = $false ) ),
    inference(rename,[status(thm)],[60]) ).

thf(132,plain,
    ! [SV37: $i,SV38: $i,SV36: $i] :
      ( ( ( ( in @ SV37 @ SV38 )
          = ( in @ ( sK2_SY430 @ sK4_SY437 )
            @ ( image1 @ SV36
              @ ^ [SX0: $i] : SX0 ) ) )
        = $false )
      | ( ( in @ ( sK2_SY430 @ sK4_SY437 )
          @ ( image1 @ SV38
            @ ^ [SX0: $i] : sK3_SY434 ) )
        = $true )
      | ( ( in @ sK3_SY434 @ SV36 )
        = $false ) ),
    inference(res,[status(thm)],[128,111]) ).

thf(133,plain,
    ! [SV37: $i,SV38: $i,SV31: $i,SV32: $i,SV33: $i > $i] :
      ( ( ( ( in @ ( sK2_SY430 @ sK4_SY437 )
            @ ( image1 @ SV38
              @ ^ [SX0: $i] : sK3_SY434 ) )
          = ( in @ SV32 @ SV31 ) )
        = $false )
      | ( ( in @ SV37 @ SV38 )
        = $false )
      | ( ( in @ ( SV33 @ SV32 )
          @ ( image1 @ SV31
            @ ^ [SX0: $i] : ( SV33 @ SX0 ) ) )
        = $true ) ),
    inference(res,[status(thm)],[128,92]) ).

thf(134,plain,
    ! [SV37: $i,SV38: $i,SV31: $i,SV32: $i,SV33: $i > $i] :
      ( ( ( ( in @ SV37 @ SV38 )
          = ( in @ ( SV33 @ SV32 )
            @ ( image1 @ SV31
              @ ^ [SX0: $i] : ( SV33 @ SX0 ) ) ) )
        = $false )
      | ( ( in @ ( sK2_SY430 @ sK4_SY437 )
          @ ( image1 @ SV38
            @ ^ [SX0: $i] : sK3_SY434 ) )
        = $true )
      | ( ( in @ SV32 @ SV31 )
        = $false ) ),
    inference(res,[status(thm)],[128,92]) ).

thf(136,plain,
    ! [SV37: $i,SV38: $i,SV28: $i,SV29: $i > $i,SV30: $i] :
      ( ( ( ( in @ SV37 @ SV38 )
          = ( in @ ( sK5_Xy @ SV30 @ SV29 @ SV28 ) @ SV28 ) )
        = $false )
      | ( ( in @ ( sK2_SY430 @ sK4_SY437 )
          @ ( image1 @ SV38
            @ ^ [SX0: $i] : sK3_SY434 ) )
        = $true )
      | ( ( in @ SV30
          @ ( image1 @ SV28
            @ ^ [SX0: $i] : ( SV29 @ SX0 ) ) )
        = $false ) ),
    inference(res,[status(thm)],[128,78]) ).

thf(139,plain,
    ! [SV37: $i,SV38: $i,SV7: $i > $i,SV8: $i,SV9: $i,SV10: $i] :
      ( ( ( ( in @ SV37 @ SV38 )
          = ( in @ SV8
            @ ( image1 @ SV9
              @ ^ [SX0: $i] : ( SV7 @ SX0 ) ) ) )
        = $false )
      | ( ( in @ ( sK2_SY430 @ sK4_SY437 )
          @ ( image1 @ SV38
            @ ^ [SX0: $i] : sK3_SY434 ) )
        = $true )
      | ( ( in @ SV10 @ SV9 )
        = $false )
      | ( ( SV8
          = ( SV7 @ SV10 ) )
        = $false ) ),
    inference(res,[status(thm)],[128,49]) ).

thf(141,plain,
    ! [SV37: $i,SV38: $i,SV7: $i > $i,SV8: $i,SV9: $i,SV10: $i] :
      ( ( ( ( in @ ( sK2_SY430 @ sK4_SY437 )
            @ ( image1 @ SV38
              @ ^ [SX0: $i] : sK3_SY434 ) )
          = ( in @ SV10 @ SV9 ) )
        = $false )
      | ( ( in @ SV37 @ SV38 )
        = $false )
      | ( ( SV8
          = ( SV7 @ SV10 ) )
        = $false )
      | ( ( in @ SV8
          @ ( image1 @ SV9
            @ ^ [SX0: $i] : ( SV7 @ SX0 ) ) )
        = $true ) ),
    inference(res,[status(thm)],[128,49]) ).

thf(142,plain,
    ! [SV37: $i,SV38: $i] :
      ( ( ( ( in @ SV37 @ SV38 )
          = ( in @ sK4_SY437 @ sK1_A ) )
        = $false )
      | ( ( in @ ( sK2_SY430 @ sK4_SY437 )
          @ ( image1 @ SV38
            @ ^ [SX0: $i] : sK3_SY434 ) )
        = $true ) ),
    inference(res,[status(thm)],[128,33]) ).

thf(145,plain,
    ( ( in @ ( sK2_SY430 @ sK4_SY437 )
      @ ( image1 @ sK1_A
        @ ^ [SX0: $i] : sK3_SY434 ) )
    = $true ),
    inference(extuni,[status(esa)],[142:[bind(SV38,$thf( sK1_A )),bind(SV37,$thf( sK4_SY437 ))]]) ).

thf(146,plain,
    ! [SV37: $i,SV38: $i,SV7: $i > $i] :
      ( ( ( in @ ( SV7 @ ( sK2_SY430 @ sK4_SY437 ) )
          @ ( image1
            @ ( image1 @ SV38
              @ ^ [SX0: $i] : sK3_SY434 )
            @ ^ [SX0: $i] : ( SV7 @ SX0 ) ) )
        = $true )
      | ( ( in @ SV37 @ SV38 )
        = $false ) ),
    inference(extuni,[status(esa)],[141:[bind(SV8,$thf( SV7 @ ( sK2_SY430 @ sK4_SY437 ) )),bind(SV9,$thf( image1 @ SV38 @ ^ [SX0: $i] : sK3_SY434 )),bind(SV10,$thf( sK2_SY430 @ sK4_SY437 ))]]) ).

thf(147,plain,
    ! [SV7: $i > $i,SV9: $i,SV10: $i] :
      ( ( ( in @ SV10 @ SV9 )
        = $false )
      | ( ( in @ ( sK2_SY430 @ sK4_SY437 )
          @ ( image1
            @ ( image1 @ SV9
              @ ^ [SX0: $i] : ( SV7 @ SX0 ) )
            @ ^ [SX0: $i] : sK3_SY434 ) )
        = $true ) ),
    inference(extuni,[status(esa)],[139:[bind(SV8,$thf( SV7 @ SV10 )),bind(SV38,$thf( image1 @ SV9 @ ^ [SX0: $i] : ( SV7 @ SX0 ) )),bind(SV37,$thf( SV7 @ SV10 ))]]) ).

thf(148,plain,
    ! [SV29: $i > $i,SV28: $i,SV30: $i] :
      ( ( ( in @ SV30
          @ ( image1 @ SV28
            @ ^ [SX0: $i] : ( SV29 @ SX0 ) ) )
        = $false )
      | ( ( in @ ( sK2_SY430 @ sK4_SY437 )
          @ ( image1 @ SV28
            @ ^ [SX0: $i] : sK3_SY434 ) )
        = $true ) ),
    inference(extuni,[status(esa)],[136:[bind(SV38,$thf( SV28 )),bind(SV37,$thf( sK5_Xy @ SV30 @ SV29 @ SV28 ))]]) ).

thf(149,plain,
    ! [SV33: $i > $i,SV31: $i,SV32: $i] :
      ( ( ( in @ SV32 @ SV31 )
        = $false )
      | ( ( in @ ( sK2_SY430 @ sK4_SY437 )
          @ ( image1
            @ ( image1 @ SV31
              @ ^ [SX0: $i] : ( SV33 @ SX0 ) )
            @ ^ [SX0: $i] : sK3_SY434 ) )
        = $true ) ),
    inference(extuni,[status(esa)],[134:[bind(SV38,$thf( image1 @ SV31 @ ^ [SX0: $i] : ( SV33 @ SX0 ) )),bind(SV37,$thf( SV33 @ SV32 ))]]) ).

thf(150,plain,
    ! [SV37: $i,SV38: $i,SV33: $i > $i] :
      ( ( ( in @ ( SV33 @ ( sK2_SY430 @ sK4_SY437 ) )
          @ ( image1
            @ ( image1 @ SV38
              @ ^ [SX0: $i] : sK3_SY434 )
            @ ^ [SX0: $i] : ( SV33 @ SX0 ) ) )
        = $true )
      | ( ( in @ SV37 @ SV38 )
        = $false ) ),
    inference(extuni,[status(esa)],[133:[bind(SV31,$thf( image1 @ SV38 @ ^ [SX0: $i] : sK3_SY434 )),bind(SV32,$thf( sK2_SY430 @ sK4_SY437 ))]]) ).

thf(151,plain,
    ! [SV36: $i] :
      ( ( ( in @ sK3_SY434 @ SV36 )
        = $false )
      | ( ( in @ ( sK2_SY430 @ sK4_SY437 )
          @ ( image1
            @ ( image1 @ SV36
              @ ^ [SX0: $i] : SX0 )
            @ ^ [SX0: $i] : sK3_SY434 ) )
        = $true ) ),
    inference(extuni,[status(esa)],[132:[bind(SV38,$thf( image1 @ SV36 @ ^ [SX0: $i] : SX0 )),bind(SV37,$thf( sK2_SY430 @ sK4_SY437 ))]]) ).

thf(152,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[25,151,150,149,148,147,146,145,128,127,126,111,110,109,108,107,106,105,92,91,90,89,78,77,76,75,66,65,64,63,62,61,49,33,32]) ).

thf(153,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[152]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11  % Problem  : SEU797^2 : TPTP v8.1.0. Released v3.7.0.
% 0.07/0.12  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.33  % Computer : n003.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Mon Jun 20 07:39:29 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  
% 0.13/0.34   No.of.Axioms: 0
% 0.13/0.34  
% 0.13/0.34   Length.of.Defs: 236
% 0.13/0.34  
% 0.13/0.34   Contains.Choice.Funs: false
% 0.13/0.34  (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)...eprover: CPU time limit exceeded, terminating
% 50.16/50.41  eprover: CPU time limit exceeded, terminating
% 50.48/50.69  .........
% 75.07/75.29  (rf:0,axioms:0,ps:2,u:1,ude:false,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)..eprover: CPU time limit exceeded, terminating
% 125.11/125.32  eprover: CPU time limit exceeded, terminating
% 125.14/125.34  ...eprover: CPU time limit exceeded, terminating
% 149.55/149.78  .
% 150.17/150.39  (rf:0,axioms:0,ps:3,u:8,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:false,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)...eprover: CPU time limit exceeded, terminating
% 200.13/200.45  eprover: CPU time limit exceeded, terminating
% 200.25/200.47  ....
% 201.88/202.15  
% 201.88/202.15  ********************************
% 201.88/202.15  *   All subproblems solved!    *
% 201.88/202.15  ********************************
% 201.88/202.15  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:1,ps:3,u:8,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:false,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:23,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:152,loop_count:10,foatp_calls:3,translation:fof_full)
% 201.93/202.16  
% 201.93/202.16  %**** Beginning of derivation protocol ****
% 201.93/202.16  % SZS output start CNFRefutation
% See solution above
% 201.93/202.16  
% 201.93/202.16  %**** End of derivation protocol ****
% 201.93/202.16  %**** no. of clauses in derivation: 104 ****
% 201.93/202.16  %**** clause counter: 152 ****
% 201.93/202.16  
% 201.93/202.16  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:1,ps:3,u:8,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:false,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:23,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:152,loop_count:10,foatp_calls:3,translation:fof_full)
%------------------------------------------------------------------------------