TSTP Solution File: SEU777^2 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SEU777^2 : 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 : n021.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 12:14:38 EDT 2022

% Result   : Theorem 76.59s 76.84s
% Output   : CNFRefutation 76.59s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   23
%            Number of leaves      :   38
% Syntax   : Number of formulae    :  154 (  49 unt;  33 typ;   4 def)
%            Number of atoms       :  750 ( 321 equ;   0 cnn)
%            Maximal formula atoms :    6 (   6 avg)
%            Number of connectives : 1669 ( 155   ~; 144   |;   8   &;1343   @)
%                                         (   0 <=>;  19  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  156 ( 156   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   36 (  33 usr;  17 con; 0-3 aty)
%            Number of variables   :  513 ( 187   ^ 326   !;   0   ?; 513   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_breln,type,
    breln: $i > $i > $i > $o ).

thf(tp_breln1,type,
    breln1: $i > $i > $o ).

thf(tp_breln1invset,type,
    breln1invset: $i > $i > $i ).

thf(tp_cartprod,type,
    cartprod: $i > $i > $i ).

thf(tp_dpsetconstr,type,
    dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).

thf(tp_dpsetconstrER,type,
    dpsetconstrER: $o ).

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

thf(tp_kpair,type,
    kpair: $i > $i > $i ).

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

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

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

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

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

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

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

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

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

thf(tp_sK21_E,type,
    sK21_E: ( $i > $i > $o ) > $i ).

thf(tp_sK22_E,type,
    sK22_E: ( $i > $i > $o ) > $i ).

thf(tp_sK23_E,type,
    sK23_E: $i > $i > ( $i > $i > $o ) > $i ).

thf(tp_sK24_E,type,
    sK24_E: $i > $i > ( $i > $i > $o ) > $i ).

thf(tp_sK2_SY402,type,
    sK2_SY402: $i ).

thf(tp_sK3_SY405,type,
    sK3_SY405: $i ).

thf(tp_sK4_SY407,type,
    sK4_SY407: $i ).

thf(tp_sK5_E,type,
    sK5_E: ( $i > $i > $o ) > $i ).

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

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

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

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

thf(tp_subset,type,
    subset: $i > $i > $o ).

thf(breln,definition,
    ( breln
    = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln) ).

thf(breln1,definition,
    ( breln1
    = ( ^ [A: $i,R: $i] : ( breln @ A @ A @ R ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1) ).

thf(breln1invset,definition,
    ( breln1invset
    = ( ^ [A: $i,R: $i] :
          ( dpsetconstr @ A @ A
          @ ^ [Xx: $i,Xy: $i] : ( in @ ( kpair @ Xy @ Xx ) @ R ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1invset) ).

thf(dpsetconstrER,definition,
    ( dpsetconstrER
    = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
          ( ( in @ ( kpair @ Xx @ Xy )
            @ ( dpsetconstr @ A @ B
              @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
         => ( Xphi @ Xx @ Xy ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrER) ).

thf(1,conjecture,
    ( dpsetconstrER
   => ! [A: $i,R: $i] :
        ( ( breln1 @ A @ R )
       => ! [Xx: $i] :
            ( ( in @ Xx @ A )
           => ! [Xy: $i] :
                ( ( in @ Xy @ A )
               => ( ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) )
                 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1invE) ).

thf(2,negated_conjecture,
    ( ( dpsetconstrER
     => ! [A: $i,R: $i] :
          ( ( breln1 @ A @ R )
         => ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ! [Xy: $i] :
                  ( ( in @ Xy @ A )
                 => ( ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) )
                   => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    dpsetconstrER = $true,
    inference(standard_cnf,[status(thm)],[2]) ).

thf(4,plain,
    ( ( ! [A: $i,R: $i] :
          ( ( breln1 @ A @ R )
         => ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ! [Xy: $i] :
                  ( ( in @ Xy @ A )
                 => ( ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) )
                   => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) )
    = $false ),
    inference(standard_cnf,[status(thm)],[2]) ).

thf(5,plain,
    ( ( ~ ! [A: $i,R: $i] :
            ( ( breln1 @ A @ R )
           => ! [Xx: $i] :
                ( ( in @ Xx @ A )
               => ! [Xy: $i] :
                    ( ( in @ Xy @ A )
                   => ( ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) )
                     => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[4]) ).

thf(6,plain,
    ( ( ( breln1 @ sK1_A @ sK2_SY402 )
      & ( in @ sK3_SY405 @ sK1_A )
      & ( in @ sK4_SY407 @ sK1_A )
      & ( in @ ( kpair @ sK4_SY407 @ sK3_SY405 ) @ ( breln1invset @ sK1_A @ sK2_SY402 ) )
      & ~ ( in @ ( kpair @ sK3_SY405 @ sK4_SY407 ) @ sK2_SY402 ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5]) ).

thf(7,plain,
    dpsetconstrER = $true,
    inference(copy,[status(thm)],[3]) ).

thf(8,plain,
    ( ( ( breln1 @ sK1_A @ sK2_SY402 )
      & ( in @ sK3_SY405 @ sK1_A )
      & ( in @ sK4_SY407 @ sK1_A )
      & ( in @ ( kpair @ sK4_SY407 @ sK3_SY405 ) @ ( breln1invset @ sK1_A @ sK2_SY402 ) )
      & ~ ( in @ ( kpair @ sK3_SY405 @ sK4_SY407 ) @ sK2_SY402 ) )
    = $true ),
    inference(copy,[status(thm)],[6]) ).

thf(9,plain,
    ( ( ~ ( ~ ( subset @ sK2_SY402 @ ( cartprod @ sK1_A @ sK1_A ) )
          | ~ ~ ( ~ ( in @ sK3_SY405 @ sK1_A )
                | ~ ~ ( ~ ( in @ sK4_SY407 @ sK1_A )
                      | ~ ~ ( ~ ( in @ ( kpair @ sK4_SY407 @ sK3_SY405 )
                                @ ( dpsetconstr @ sK1_A @ sK1_A
                                  @ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY402 ) ) )
                            | ~ ~ ( in @ ( kpair @ sK3_SY405 @ sK4_SY407 ) @ sK2_SY402 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8,breln,breln1,breln1invset,dpsetconstrER]) ).

thf(10,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i > $i > $o,SX3: $i,SX4: $i] :
          ( ~ ( in @ ( kpair @ SX3 @ SX4 )
              @ ( dpsetconstr @ SX0 @ SX1
                @ ^ [SX5: $i,SX6: $i] : ( SX2 @ SX5 @ SX6 ) ) )
          | ( SX2 @ SX3 @ SX4 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7,breln,breln1,breln1invset,dpsetconstrER]) ).

thf(11,plain,
    ( ( ~ ( subset @ sK2_SY402 @ ( cartprod @ sK1_A @ sK1_A ) )
      | ~ ~ ( ~ ( in @ sK3_SY405 @ sK1_A )
            | ~ ~ ( ~ ( in @ sK4_SY407 @ sK1_A )
                  | ~ ~ ( ~ ( in @ ( kpair @ sK4_SY407 @ sK3_SY405 )
                            @ ( dpsetconstr @ sK1_A @ sK1_A
                              @ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY402 ) ) )
                        | ~ ~ ( in @ ( kpair @ sK3_SY405 @ sK4_SY407 ) @ sK2_SY402 ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[9]) ).

thf(12,plain,
    ! [SV1: $i] :
      ( ( ! [SY408: $i,SY409: $i > $i > $o,SY410: $i,SY411: $i] :
            ( ~ ( in @ ( kpair @ SY410 @ SY411 )
                @ ( dpsetconstr @ SV1 @ SY408
                  @ ^ [SX5: $i,SX6: $i] : ( SY409 @ SX5 @ SX6 ) ) )
            | ( SY409 @ SY410 @ SY411 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10]) ).

thf(13,plain,
    ( ( ~ ( subset @ sK2_SY402 @ ( cartprod @ sK1_A @ sK1_A ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[11]) ).

thf(14,plain,
    ( ( ~ ~ ( ~ ( in @ sK3_SY405 @ sK1_A )
            | ~ ~ ( ~ ( in @ sK4_SY407 @ sK1_A )
                  | ~ ~ ( ~ ( in @ ( kpair @ sK4_SY407 @ sK3_SY405 )
                            @ ( dpsetconstr @ sK1_A @ sK1_A
                              @ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY402 ) ) )
                        | ~ ~ ( in @ ( kpair @ sK3_SY405 @ sK4_SY407 ) @ sK2_SY402 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[11]) ).

thf(15,plain,
    ! [SV2: $i,SV1: $i] :
      ( ( ! [SY414: $i > $i > $o,SY415: $i,SY416: $i] :
            ( ~ ( in @ ( kpair @ SY415 @ SY416 )
                @ ( dpsetconstr @ SV1 @ SV2
                  @ ^ [SX5: $i,SX6: $i] : ( SY414 @ SX5 @ SX6 ) ) )
            | ( SY414 @ SY415 @ SY416 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[12]) ).

thf(16,plain,
    ( ( subset @ sK2_SY402 @ ( cartprod @ sK1_A @ sK1_A ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[13]) ).

thf(17,plain,
    ( ( ~ ( ~ ( in @ sK3_SY405 @ sK1_A )
          | ~ ~ ( ~ ( in @ sK4_SY407 @ sK1_A )
                | ~ ~ ( ~ ( in @ ( kpair @ sK4_SY407 @ sK3_SY405 )
                          @ ( dpsetconstr @ sK1_A @ sK1_A
                            @ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY402 ) ) )
                      | ~ ~ ( in @ ( kpair @ sK3_SY405 @ sK4_SY407 ) @ sK2_SY402 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[14]) ).

thf(18,plain,
    ! [SV3: $i > $i > $o,SV2: $i,SV1: $i] :
      ( ( ! [SY419: $i,SY420: $i] :
            ( ~ ( in @ ( kpair @ SY419 @ SY420 )
                @ ( dpsetconstr @ SV1 @ SV2
                  @ ^ [SY421: $i,SY422: $i] : ( SV3 @ SY421 @ SY422 ) ) )
            | ( SV3 @ SY419 @ SY420 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[15]) ).

thf(19,plain,
    ( ( ~ ( in @ sK3_SY405 @ sK1_A )
      | ~ ~ ( ~ ( in @ sK4_SY407 @ sK1_A )
            | ~ ~ ( ~ ( in @ ( kpair @ sK4_SY407 @ sK3_SY405 )
                      @ ( dpsetconstr @ sK1_A @ sK1_A
                        @ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY402 ) ) )
                  | ~ ~ ( in @ ( kpair @ sK3_SY405 @ sK4_SY407 ) @ sK2_SY402 ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[17]) ).

thf(20,plain,
    ! [SV3: $i > $i > $o,SV2: $i,SV1: $i,SV4: $i] :
      ( ( ! [SY423: $i] :
            ( ~ ( in @ ( kpair @ SV4 @ SY423 )
                @ ( dpsetconstr @ SV1 @ SV2
                  @ ^ [SY421: $i,SY422: $i] : ( SV3 @ SY421 @ SY422 ) ) )
            | ( SV3 @ SV4 @ SY423 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[18]) ).

thf(21,plain,
    ( ( ~ ( in @ sK3_SY405 @ sK1_A ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[19]) ).

thf(22,plain,
    ( ( ~ ~ ( ~ ( in @ sK4_SY407 @ sK1_A )
            | ~ ~ ( ~ ( in @ ( kpair @ sK4_SY407 @ sK3_SY405 )
                      @ ( dpsetconstr @ sK1_A @ sK1_A
                        @ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY402 ) ) )
                  | ~ ~ ( in @ ( kpair @ sK3_SY405 @ sK4_SY407 ) @ sK2_SY402 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[19]) ).

thf(23,plain,
    ! [SV3: $i > $i > $o,SV2: $i,SV1: $i,SV5: $i,SV4: $i] :
      ( ( ~ ( in @ ( kpair @ SV4 @ SV5 )
            @ ( dpsetconstr @ SV1 @ SV2
              @ ^ [SY421: $i,SY422: $i] : ( SV3 @ SY421 @ SY422 ) ) )
        | ( SV3 @ SV4 @ SV5 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[20]) ).

thf(24,plain,
    ( ( in @ sK3_SY405 @ sK1_A )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[21]) ).

thf(25,plain,
    ( ( ~ ( ~ ( in @ sK4_SY407 @ sK1_A )
          | ~ ~ ( ~ ( in @ ( kpair @ sK4_SY407 @ sK3_SY405 )
                    @ ( dpsetconstr @ sK1_A @ sK1_A
                      @ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY402 ) ) )
                | ~ ~ ( in @ ( kpair @ sK3_SY405 @ sK4_SY407 ) @ sK2_SY402 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[22]) ).

thf(26,plain,
    ! [SV3: $i > $i > $o,SV2: $i,SV1: $i,SV5: $i,SV4: $i] :
      ( ( ( ~ ( in @ ( kpair @ SV4 @ SV5 )
              @ ( dpsetconstr @ SV1 @ SV2
                @ ^ [SY421: $i,SY422: $i] : ( SV3 @ SY421 @ SY422 ) ) ) )
        = $true )
      | ( ( SV3 @ SV4 @ SV5 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[23]) ).

thf(27,plain,
    ( ( ~ ( in @ sK4_SY407 @ sK1_A )
      | ~ ~ ( ~ ( in @ ( kpair @ sK4_SY407 @ sK3_SY405 )
                @ ( dpsetconstr @ sK1_A @ sK1_A
                  @ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY402 ) ) )
            | ~ ~ ( in @ ( kpair @ sK3_SY405 @ sK4_SY407 ) @ sK2_SY402 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[25]) ).

thf(28,plain,
    ! [SV3: $i > $i > $o,SV2: $i,SV1: $i,SV5: $i,SV4: $i] :
      ( ( ( in @ ( kpair @ SV4 @ SV5 )
          @ ( dpsetconstr @ SV1 @ SV2
            @ ^ [SY421: $i,SY422: $i] : ( SV3 @ SY421 @ SY422 ) ) )
        = $false )
      | ( ( SV3 @ SV4 @ SV5 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[26]) ).

thf(29,plain,
    ( ( ~ ( in @ sK4_SY407 @ sK1_A ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[27]) ).

thf(30,plain,
    ( ( ~ ~ ( ~ ( in @ ( kpair @ sK4_SY407 @ sK3_SY405 )
                @ ( dpsetconstr @ sK1_A @ sK1_A
                  @ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY402 ) ) )
            | ~ ~ ( in @ ( kpair @ sK3_SY405 @ sK4_SY407 ) @ sK2_SY402 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[27]) ).

thf(31,plain,
    ( ( in @ sK4_SY407 @ sK1_A )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[29]) ).

thf(32,plain,
    ( ( ~ ( ~ ( in @ ( kpair @ sK4_SY407 @ sK3_SY405 )
              @ ( dpsetconstr @ sK1_A @ sK1_A
                @ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY402 ) ) )
          | ~ ~ ( in @ ( kpair @ sK3_SY405 @ sK4_SY407 ) @ sK2_SY402 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[30]) ).

thf(33,plain,
    ( ( ~ ( in @ ( kpair @ sK4_SY407 @ sK3_SY405 )
          @ ( dpsetconstr @ sK1_A @ sK1_A
            @ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY402 ) ) )
      | ~ ~ ( in @ ( kpair @ sK3_SY405 @ sK4_SY407 ) @ sK2_SY402 ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[32]) ).

thf(34,plain,
    ( ( ~ ( in @ ( kpair @ sK4_SY407 @ sK3_SY405 )
          @ ( dpsetconstr @ sK1_A @ sK1_A
            @ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY402 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[33]) ).

thf(35,plain,
    ( ( ~ ~ ( in @ ( kpair @ sK3_SY405 @ sK4_SY407 ) @ sK2_SY402 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[33]) ).

thf(36,plain,
    ( ( in @ ( kpair @ sK4_SY407 @ sK3_SY405 )
      @ ( dpsetconstr @ sK1_A @ sK1_A
        @ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY402 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[34]) ).

thf(37,plain,
    ( ( ~ ( in @ ( kpair @ sK3_SY405 @ sK4_SY407 ) @ sK2_SY402 ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[35]) ).

thf(38,plain,
    ( ( in @ ( kpair @ sK3_SY405 @ sK4_SY407 ) @ sK2_SY402 )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[37]) ).

thf(40,plain,
    ! [SV2: $i,SV1: $i,SV5: $i,SV4: $i] :
      ( ( ( in @ ( kpair @ SV4 @ SV5 )
          @ ( dpsetconstr @ SV1 @ SV2
            @ ^ [SX0: $i,SX1: $i] : $false ) )
        = $false )
      | ( $false = $true ) ),
    inference(prim_subst,[status(thm)],[28:[bind(SV3,$thf( ^ [SV9: $i] : ^ [SV10: $i] : $false ))]]) ).

thf(41,plain,
    ! [SV8: $i > $i > $o,SV2: $i,SV1: $i,SV5: $i,SV4: $i] :
      ( ( ( in @ ( kpair @ SV4 @ SV5 )
          @ ( dpsetconstr @ SV1 @ SV2
            @ ^ [SX0: $i,SX1: $i] :
                ~ ( SV8 @ SX0 @ SX1 ) ) )
        = $false )
      | ( ( ~ ( SV8 @ SV4 @ SV5 ) )
        = $true ) ),
    inference(prim_subst,[status(thm)],[28:[bind(SV3,$thf( ^ [SV6: $i] : ^ [SV7: $i] : ~ ( SV8 @ SV6 @ SV7 ) ))]]) ).

thf(42,plain,
    ! [SV2: $i,SV1: $i,SV5: $i,SV4: $i] :
      ( ( ( in @ ( kpair @ SV4 @ SV5 )
          @ ( dpsetconstr @ SV1 @ SV2
            @ ^ [SX0: $i,SX1: $i] : ( SX0 != SX1 ) ) )
        = $false )
      | ( ( ( SV4 != SV5 ) )
        = $true ) ),
    inference(prim_subst,[status(thm)],[28:[bind(SV3,$thf( ^ [SY434: $i] : ^ [SY435: $i] : ( SY434 != SY435 ) ))]]) ).

thf(43,plain,
    ! [SV2: $i,SV1: $i,SV5: $i,SV4: $i] :
      ( ( ( in @ ( kpair @ SV4 @ SV5 )
          @ ( dpsetconstr @ SV1 @ SV2
            @ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) ) )
        = $false )
      | ( ( SV4 = SV5 )
        = $true ) ),
    inference(prim_subst,[status(thm)],[28:[bind(SV3,$thf( ^ [SV14: $i] : ^ [SV13: $i] : ( SV14 = SV13 ) ))]]) ).

thf(44,plain,
    ! [SV3: $i > $i > $o,SV2: $i,SV1: $i,SV5: $i,SV4: $i] :
      ( ( ( SV3 @ SV4 @ SV5 )
        = $true )
      | ( ( ( SV3 @ SV4 @ SV5 )
          = ( ~ ( in @ ( kpair @ SV4 @ SV5 )
                @ ( dpsetconstr @ SV1 @ SV2
                  @ ^ [SY421: $i,SY422: $i] : ( SV3 @ SY421 @ SY422 ) ) ) ) )
        = $false ) ),
    inference(fac_restr,[status(thm)],[28]) ).

thf(45,plain,
    ! [SV2: $i,SV1: $i,SV5: $i,SV4: $i,SV3: $i > $i > $o] :
      ( ( ( ~ ( ( SV3 @ SV4 @ SV5 )
              | ~ ( in @ ( kpair @ SV4 @ SV5 )
                  @ ( dpsetconstr @ SV1 @ SV2
                    @ ^ [SY421: $i,SY422: $i] : ( SV3 @ SY421 @ SY422 ) ) ) )
          | ~ ( ~ ( SV3 @ SV4 @ SV5 )
              | ~ ~ ( in @ ( kpair @ SV4 @ SV5 )
                    @ ( dpsetconstr @ SV1 @ SV2
                      @ ^ [SY421: $i,SY422: $i] : ( SV3 @ SY421 @ SY422 ) ) ) ) )
        = $false )
      | ( ( SV3 @ SV4 @ SV5 )
        = $true ) ),
    inference(extcnf_equal_neg,[status(thm)],[44]) ).

thf(47,plain,
    ! [SV2: $i,SV1: $i,SV5: $i,SV4: $i,SV3: $i > $i > $o] :
      ( ( ( ~ ( ( SV3 @ SV4 @ SV5 )
              | ~ ( in @ ( kpair @ SV4 @ SV5 )
                  @ ( dpsetconstr @ SV1 @ SV2
                    @ ^ [SY421: $i,SY422: $i] : ( SV3 @ SY421 @ SY422 ) ) ) ) )
        = $false )
      | ( ( SV3 @ SV4 @ SV5 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[45]) ).

thf(49,plain,
    ! [SV2: $i,SV1: $i,SV5: $i,SV4: $i,SV3: $i > $i > $o] :
      ( ( ( ( SV3 @ SV4 @ SV5 )
          | ~ ( in @ ( kpair @ SV4 @ SV5 )
              @ ( dpsetconstr @ SV1 @ SV2
                @ ^ [SY421: $i,SY422: $i] : ( SV3 @ SY421 @ SY422 ) ) ) )
        = $true )
      | ( ( SV3 @ SV4 @ SV5 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[47]) ).

thf(51,plain,
    ! [SV2: $i,SV1: $i,SV5: $i,SV4: $i,SV3: $i > $i > $o] :
      ( ( ( SV3 @ SV4 @ SV5 )
        = $true )
      | ( ( ~ ( in @ ( kpair @ SV4 @ SV5 )
              @ ( dpsetconstr @ SV1 @ SV2
                @ ^ [SY421: $i,SY422: $i] : ( SV3 @ SY421 @ SY422 ) ) ) )
        = $true )
      | ( ( SV3 @ SV4 @ SV5 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[49]) ).

thf(53,plain,
    ! [SV3: $i > $i > $o,SV2: $i,SV1: $i,SV5: $i,SV4: $i] :
      ( ( ( in @ ( kpair @ SV4 @ SV5 )
          @ ( dpsetconstr @ SV1 @ SV2
            @ ^ [SY421: $i,SY422: $i] : ( SV3 @ SY421 @ SY422 ) ) )
        = $false )
      | ( ( SV3 @ SV4 @ SV5 )
        = $true )
      | ( ( SV3 @ SV4 @ SV5 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[51]) ).

thf(57,plain,
    ! [SV2: $i,SV1: $i,SV5: $i,SV4: $i,SV8: $i > $i > $o] :
      ( ( ( SV8 @ SV4 @ SV5 )
        = $false )
      | ( ( in @ ( kpair @ SV4 @ SV5 )
          @ ( dpsetconstr @ SV1 @ SV2
            @ ^ [SX0: $i,SX1: $i] :
                ~ ( SV8 @ SX0 @ SX1 ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[41]) ).

thf(58,plain,
    ! [SV2: $i,SV1: $i,SV5: $i,SV4: $i] :
      ( ( ( SV4 = SV5 )
        = $false )
      | ( ( in @ ( kpair @ SV4 @ SV5 )
          @ ( dpsetconstr @ SV1 @ SV2
            @ ^ [SX0: $i,SX1: $i] : ( SX0 != SX1 ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[42]) ).

thf(59,plain,
    ! [SV2: $i,SV1: $i,SV5: $i] :
      ( ( in @ ( kpair @ SV5 @ SV5 )
        @ ( dpsetconstr @ SV1 @ SV2
          @ ^ [SX0: $i,SX1: $i] : ( SX0 != SX1 ) ) )
      = $false ),
    inference(extuni,[status(esa)],[58:[bind(SV4,$thf( SV5 ))]]) ).

thf(60,plain,
    ! [SV3: $i > $i > $o,SV2: $i,SV1: $i,SV5: $i,SV4: $i] :
      ( ( ( in @ ( kpair @ SV4 @ SV5 )
          @ ( dpsetconstr @ SV1 @ SV2
            @ ^ [SY421: $i,SY422: $i] : ( SV3 @ SY421 @ SY422 ) ) )
        = $false )
      | ( ( SV3 @ SV4 @ SV5 )
        = $true ) ),
    inference(sim,[status(thm)],[53]) ).

thf(61,plain,
    ! [SV2: $i,SV1: $i,SV5: $i,SV4: $i] :
      ( ( in @ ( kpair @ SV4 @ SV5 )
        @ ( dpsetconstr @ SV1 @ SV2
          @ ^ [SX0: $i,SX1: $i] : $false ) )
      = $false ),
    inference(sim,[status(thm)],[40]) ).

thf(62,plain,
    ! [SV20: $i > $i > $o,SV21: $i,SV22: $i,SV23: $i,SV24: $i] :
      ( ( ( in @ ( kpair @ SV24 @ SV23 )
          @ ( dpsetconstr @ SV22 @ SV21
            @ ^ [SX0: $i,SX1: $i] : ( SV20 @ SX0 @ SX1 ) ) )
        = $false )
      | ( ( SV20 @ SV24 @ SV23 )
        = $true ) ),
    inference(rename,[status(thm)],[28]) ).

thf(65,plain,
    ! [SV20: $i > $i > $o,SV21: $i,SV22: $i,SV23: $i,SV24: $i] :
      ( ( ( ( in @ ( kpair @ SV24 @ SV23 )
            @ ( dpsetconstr @ SV22 @ SV21
              @ ^ [SX0: $i,SX1: $i] : ( SV20 @ SX0 @ SX1 ) ) )
          = ( in @ sK3_SY405 @ sK1_A ) )
        = $false )
      | ( ( SV20 @ SV24 @ SV23 )
        = $true ) ),
    inference(res,[status(thm)],[62,24]) ).

thf(68,plain,
    ! [SV21: $i,SV22: $i,SV23: $i,SV24: $i] :
      ( ( ( in @ ( kpair @ SV24 @ SV23 )
          @ ( dpsetconstr @ SV22 @ SV21
            @ ^ [SX0: $i,SX1: $i] : $false ) )
        = $false )
      | ( $false = $true ) ),
    inference(prim_subst,[status(thm)],[62:[bind(SV20,$thf( ^ [SV28: $i] : ^ [SV29: $i] : $false ))]]) ).

thf(69,plain,
    ! [SV21: $i,SV22: $i,SV23: $i,SV24: $i] :
      ( ( in @ ( kpair @ SV24 @ SV23 )
        @ ( dpsetconstr @ SV22 @ SV21
          @ ^ [SX0: $i,SX1: $i] : $false ) )
      = $false ),
    inference(sim,[status(thm)],[68]) ).

thf(70,plain,
    ! [SV27: $i > $i > $o,SV21: $i,SV22: $i,SV23: $i,SV24: $i] :
      ( ( ( in @ ( kpair @ SV24 @ SV23 )
          @ ( dpsetconstr @ SV22 @ SV21
            @ ^ [SX0: $i,SX1: $i] :
                ~ ( SV27 @ SX0 @ SX1 ) ) )
        = $false )
      | ( ( ~ ( SV27 @ SV24 @ SV23 ) )
        = $true ) ),
    inference(prim_subst,[status(thm)],[62:[bind(SV20,$thf( ^ [SV25: $i] : ^ [SV26: $i] : ~ ( SV27 @ SV25 @ SV26 ) ))]]) ).

thf(71,plain,
    ! [SV21: $i,SV22: $i,SV23: $i,SV24: $i] :
      ( ( ( in @ ( kpair @ SV24 @ SV23 )
          @ ( dpsetconstr @ SV22 @ SV21
            @ ^ [SX0: $i,SX1: $i] : ( SX0 != SX1 ) ) )
        = $false )
      | ( ( ( SV24 != SV23 ) )
        = $true ) ),
    inference(prim_subst,[status(thm)],[62:[bind(SV20,$thf( ^ [SY447: $i] : ^ [SY448: $i] : ( SY447 != SY448 ) ))]]) ).

thf(72,plain,
    ! [SV21: $i,SV22: $i,SV23: $i,SV24: $i] :
      ( ( ( in @ ( kpair @ SV24 @ SV23 )
          @ ( dpsetconstr @ SV22 @ SV21
            @ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) ) )
        = $false )
      | ( ( SV24 = SV23 )
        = $true ) ),
    inference(prim_subst,[status(thm)],[62:[bind(SV20,$thf( ^ [SV33: $i] : ^ [SV32: $i] : ( SV33 = SV32 ) ))]]) ).

thf(74,plain,
    ! [SV21: $i,SV22: $i,SV23: $i,SV24: $i,SV20: $i > $i > $o] :
      ( ( ( SV20 @ SV24 @ SV23 )
        = $true )
      | ( ( ( dpsetconstr @ SV22 @ SV21
            @ ^ [SX0: $i,SX1: $i] : ( SV20 @ SX0 @ SX1 ) )
          = sK1_A )
        = $false )
      | ( ( ( kpair @ SV24 @ SV23 )
          = sK3_SY405 )
        = $false ) ),
    inference(extuni,[status(esa)],[65]) ).

thf(75,plain,
    ! [SV21: $i,SV22: $i,SV23: $i,SV24: $i,SV27: $i > $i > $o] :
      ( ( ( SV27 @ SV24 @ SV23 )
        = $false )
      | ( ( in @ ( kpair @ SV24 @ SV23 )
          @ ( dpsetconstr @ SV22 @ SV21
            @ ^ [SX0: $i,SX1: $i] :
                ~ ( SV27 @ SX0 @ SX1 ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[70]) ).

thf(76,plain,
    ! [SV21: $i,SV22: $i,SV23: $i,SV24: $i] :
      ( ( ( SV24 = SV23 )
        = $false )
      | ( ( in @ ( kpair @ SV24 @ SV23 )
          @ ( dpsetconstr @ SV22 @ SV21
            @ ^ [SX0: $i,SX1: $i] : ( SX0 != SX1 ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[71]) ).

thf(77,plain,
    ! [SV20: $i > $i > $o,SV21: $i,SV22: $i,SV23: $i,SV24: $i] :
      ( ( ( ( in @ sK4_SY407 @ sK1_A )
          = ( in @ ( kpair @ SV24 @ SV23 )
            @ ( dpsetconstr @ SV22 @ SV21
              @ ^ [SX0: $i,SX1: $i] : ( SV20 @ SX0 @ SX1 ) ) ) )
        = $false )
      | ( ( SV20 @ SV24 @ SV23 )
        = $true ) ),
    inference(res,[status(thm)],[31,62]) ).

thf(78,plain,
    ! [SV21: $i,SV22: $i,SV23: $i,SV24: $i,SV20: $i > $i > $o] :
      ( ( ( SV20 @ SV24 @ SV23 )
        = $true )
      | ( ( sK1_A
          = ( dpsetconstr @ SV22 @ SV21
            @ ^ [SX0: $i,SX1: $i] : ( SV20 @ SX0 @ SX1 ) ) )
        = $false )
      | ( ( sK4_SY407
          = ( kpair @ SV24 @ SV23 ) )
        = $false ) ),
    inference(extuni,[status(esa)],[77]) ).

thf(79,plain,
    ! [SV20: $i > $i > $o,SV21: $i,SV22: $i,SV23: $i,SV24: $i] :
      ( ( ( ( in @ ( kpair @ sK4_SY407 @ sK3_SY405 )
            @ ( dpsetconstr @ sK1_A @ sK1_A
              @ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY402 ) ) )
          = ( in @ ( kpair @ SV24 @ SV23 )
            @ ( dpsetconstr @ SV22 @ SV21
              @ ^ [SX0: $i,SX1: $i] : ( SV20 @ SX0 @ SX1 ) ) ) )
        = $false )
      | ( ( SV20 @ SV24 @ SV23 )
        = $true ) ),
    inference(res,[status(thm)],[36,62]) ).

thf(80,plain,
    ! [SV20: $i > $i > $o] :
      ( ( ( SV20 @ sK4_SY407 @ sK3_SY405 )
        = $true )
      | ( ( in @ ( kpair @ ( sK6_E @ SV20 ) @ ( sK5_E @ SV20 ) ) @ sK2_SY402 )
        = $true )
      | ( ( SV20 @ ( sK5_E @ SV20 ) @ ( sK6_E @ SV20 ) )
        = $true ) ),
    inference(extuni,[status(esa)],[79:[bind(SV21,$thf( sK1_A )),bind(SV22,$thf( sK1_A )),bind(SV23,$thf( sK3_SY405 )),bind(SV24,$thf( sK4_SY407 ))]]) ).

thf(81,plain,
    ! [SV20: $i > $i > $o] :
      ( ( ( SV20 @ sK4_SY407 @ sK3_SY405 )
        = $true )
      | ( ( in @ ( kpair @ ( sK6_E @ SV20 ) @ ( sK5_E @ SV20 ) ) @ sK2_SY402 )
        = $false )
      | ( ( SV20 @ ( sK5_E @ SV20 ) @ ( sK6_E @ SV20 ) )
        = $false ) ),
    inference(extuni,[status(esa)],[79:[bind(SV21,$thf( sK1_A )),bind(SV22,$thf( sK1_A )),bind(SV23,$thf( sK3_SY405 )),bind(SV24,$thf( sK4_SY407 ))]]) ).

thf(82,plain,
    ! [SV21: $i,SV22: $i,SV20: $i > $i > $o] :
      ( ( ( SV20 @ sK4_SY407 @ sK3_SY405 )
        = $true )
      | ( ( ( dpsetconstr @ sK1_A @ sK1_A
            @ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY402 ) )
          = ( dpsetconstr @ SV22 @ SV21
            @ ^ [SX0: $i,SX1: $i] : ( SV20 @ SX0 @ SX1 ) ) )
        = $false ) ),
    inference(extuni,[status(esa)],[79:[bind(SV23,$thf( sK3_SY405 )),bind(SV24,$thf( sK4_SY407 ))]]) ).

thf(83,plain,
    ! [SV23: $i,SV24: $i,SV20: $i > $i > $o] :
      ( ( ( SV20 @ SV24 @ SV23 )
        = $true )
      | ( ( in @ ( kpair @ ( sK8_E @ SV20 @ SV24 @ SV23 ) @ ( sK7_E @ SV23 @ SV24 @ SV20 ) ) @ sK2_SY402 )
        = $true )
      | ( ( SV20 @ ( sK7_E @ SV23 @ SV24 @ SV20 ) @ ( sK8_E @ SV20 @ SV24 @ SV23 ) )
        = $true )
      | ( ( ( kpair @ sK4_SY407 @ sK3_SY405 )
          = ( kpair @ SV24 @ SV23 ) )
        = $false ) ),
    inference(extuni,[status(esa)],[79:[bind(SV21,$thf( sK1_A )),bind(SV22,$thf( sK1_A ))]]) ).

thf(84,plain,
    ! [SV23: $i,SV24: $i,SV20: $i > $i > $o] :
      ( ( ( SV20 @ SV24 @ SV23 )
        = $true )
      | ( ( in @ ( kpair @ ( sK8_E @ SV20 @ SV24 @ SV23 ) @ ( sK7_E @ SV23 @ SV24 @ SV20 ) ) @ sK2_SY402 )
        = $false )
      | ( ( SV20 @ ( sK7_E @ SV23 @ SV24 @ SV20 ) @ ( sK8_E @ SV20 @ SV24 @ SV23 ) )
        = $false )
      | ( ( ( kpair @ sK4_SY407 @ sK3_SY405 )
          = ( kpair @ SV24 @ SV23 ) )
        = $false ) ),
    inference(extuni,[status(esa)],[79:[bind(SV21,$thf( sK1_A )),bind(SV22,$thf( sK1_A ))]]) ).

thf(85,plain,
    ! [SV21: $i,SV22: $i,SV23: $i,SV24: $i,SV20: $i > $i > $o] :
      ( ( ( SV20 @ SV24 @ SV23 )
        = $true )
      | ( ( ( dpsetconstr @ sK1_A @ sK1_A
            @ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY402 ) )
          = ( dpsetconstr @ SV22 @ SV21
            @ ^ [SX0: $i,SX1: $i] : ( SV20 @ SX0 @ SX1 ) ) )
        = $false )
      | ( ( ( kpair @ sK4_SY407 @ sK3_SY405 )
          = ( kpair @ SV24 @ SV23 ) )
        = $false ) ),
    inference(extuni,[status(esa)],[79]) ).

thf(87,plain,
    ( ( ( in @ ( kpair @ sK3_SY405 @ sK4_SY407 ) @ sK2_SY402 )
      = ( in @ ( kpair @ sK4_SY407 @ sK3_SY405 )
        @ ( dpsetconstr @ sK1_A @ sK1_A
          @ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY402 ) ) ) )
    = $false ),
    inference(res,[status(thm)],[38,36]) ).

thf(88,plain,
    ( ( ( in @ ( kpair @ sK3_SY405 @ sK4_SY407 ) @ sK2_SY402 )
      = ( in @ sK4_SY407 @ sK1_A ) )
    = $false ),
    inference(res,[status(thm)],[38,31]) ).

thf(89,plain,
    ( ( ( in @ ( kpair @ sK3_SY405 @ sK4_SY407 ) @ sK2_SY402 )
      = ( in @ sK3_SY405 @ sK1_A ) )
    = $false ),
    inference(res,[status(thm)],[38,24]) ).

thf(91,plain,
    ( ( ( sK2_SY402 = sK1_A )
      = $false )
    | ( ( ( kpair @ sK3_SY405 @ sK4_SY407 )
        = sK3_SY405 )
      = $false ) ),
    inference(extuni,[status(esa)],[89]) ).

thf(92,plain,
    ( ( ( sK2_SY402 = sK1_A )
      = $false )
    | ( ( ( kpair @ sK3_SY405 @ sK4_SY407 )
        = sK4_SY407 )
      = $false ) ),
    inference(extuni,[status(esa)],[88]) ).

thf(93,plain,
    ( ( ( sK2_SY402
        = ( dpsetconstr @ sK1_A @ sK1_A
          @ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY402 ) ) )
      = $false )
    | ( ( sK4_SY407 = sK3_SY405 )
      = $false )
    | ( ( sK3_SY405 = sK4_SY407 )
      = $false ) ),
    inference(extuni,[status(esa)],[87]) ).

thf(94,plain,
    ( ( ( sK2_SY402
        = ( dpsetconstr @ sK1_A @ sK1_A
          @ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY402 ) ) )
      = $false )
    | ( ( ( kpair @ sK3_SY405 @ sK4_SY407 )
        = ( kpair @ sK4_SY407 @ sK3_SY405 ) )
      = $false ) ),
    inference(extuni,[status(esa)],[87]) ).

thf(95,plain,
    ! [SV81: $i,SV82: $i,SV83: $i,SV84: $i] :
      ( ( ( in @ ( kpair @ SV84 @ SV83 )
          @ ( dpsetconstr @ SV82 @ SV81
            @ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) ) )
        = $false )
      | ( ( SV84 = SV83 )
        = $true ) ),
    inference(rename,[status(thm)],[43]) ).

thf(101,plain,
    ! [SV81: $i,SV82: $i,SV83: $i,SV84: $i] :
      ( ( ( ( in @ ( kpair @ SV84 @ SV83 )
            @ ( dpsetconstr @ SV82 @ SV81
              @ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) ) )
          = ( in @ ( kpair @ sK4_SY407 @ sK3_SY405 )
            @ ( dpsetconstr @ sK1_A @ sK1_A
              @ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY402 ) ) ) )
        = $false )
      | ( ( SV84 = SV83 )
        = $true ) ),
    inference(res,[status(thm)],[95,36]) ).

thf(102,plain,
    ! [SV81: $i,SV82: $i,SV83: $i,SV84: $i] :
      ( ( ( ( in @ ( kpair @ SV84 @ SV83 )
            @ ( dpsetconstr @ SV82 @ SV81
              @ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) ) )
          = ( in @ sK4_SY407 @ sK1_A ) )
        = $false )
      | ( ( SV84 = SV83 )
        = $true ) ),
    inference(res,[status(thm)],[95,31]) ).

thf(103,plain,
    ! [SV81: $i,SV82: $i,SV83: $i,SV84: $i] :
      ( ( ( ( in @ ( kpair @ SV84 @ SV83 )
            @ ( dpsetconstr @ SV82 @ SV81
              @ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) ) )
          = ( in @ sK3_SY405 @ sK1_A ) )
        = $false )
      | ( ( SV84 = SV83 )
        = $true ) ),
    inference(res,[status(thm)],[95,24]) ).

thf(105,plain,
    ! [SV81: $i,SV82: $i,SV83: $i,SV84: $i] :
      ( ( ( SV84 = SV83 )
        = $true )
      | ( ( ( dpsetconstr @ SV82 @ SV81
            @ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) )
          = sK1_A )
        = $false )
      | ( ( ( kpair @ SV84 @ SV83 )
          = sK3_SY405 )
        = $false ) ),
    inference(extuni,[status(esa)],[103]) ).

thf(106,plain,
    ! [SV81: $i,SV82: $i,SV83: $i,SV84: $i] :
      ( ( ( SV84 = SV83 )
        = $true )
      | ( ( ( dpsetconstr @ SV82 @ SV81
            @ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) )
          = sK1_A )
        = $false )
      | ( ( ( kpair @ SV84 @ SV83 )
          = sK4_SY407 )
        = $false ) ),
    inference(extuni,[status(esa)],[102]) ).

thf(107,plain,
    ( ( ( sK4_SY407 = sK3_SY405 )
      = $true )
    | ( ( sK13_E = sK14_E )
      = $true )
    | ( ( in @ ( kpair @ sK14_E @ sK13_E ) @ sK2_SY402 )
      = $true ) ),
    inference(extuni,[status(esa)],[101:[bind(SV81,$thf( sK1_A )),bind(SV82,$thf( sK1_A )),bind(SV83,$thf( sK3_SY405 )),bind(SV84,$thf( sK4_SY407 ))]]) ).

thf(108,plain,
    ( ( ( sK4_SY407 = sK3_SY405 )
      = $true )
    | ( ( sK13_E = sK14_E )
      = $false )
    | ( ( in @ ( kpair @ sK14_E @ sK13_E ) @ sK2_SY402 )
      = $false ) ),
    inference(extuni,[status(esa)],[101:[bind(SV81,$thf( sK1_A )),bind(SV82,$thf( sK1_A )),bind(SV83,$thf( sK3_SY405 )),bind(SV84,$thf( sK4_SY407 ))]]) ).

thf(109,plain,
    ! [SV81: $i,SV82: $i] :
      ( ( ( sK4_SY407 = sK3_SY405 )
        = $true )
      | ( ( ( dpsetconstr @ SV82 @ SV81
            @ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) )
          = ( dpsetconstr @ sK1_A @ sK1_A
            @ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY402 ) ) )
        = $false ) ),
    inference(extuni,[status(esa)],[101:[bind(SV83,$thf( sK3_SY405 )),bind(SV84,$thf( sK4_SY407 ))]]) ).

thf(110,plain,
    ! [SV83: $i,SV84: $i] :
      ( ( ( SV84 = SV83 )
        = $true )
      | ( ( ( sK15_E @ SV83 @ SV84 )
          = ( sK16_E @ SV84 @ SV83 ) )
        = $true )
      | ( ( in @ ( kpair @ ( sK16_E @ SV84 @ SV83 ) @ ( sK15_E @ SV83 @ SV84 ) ) @ sK2_SY402 )
        = $true )
      | ( ( ( kpair @ SV84 @ SV83 )
          = ( kpair @ sK4_SY407 @ sK3_SY405 ) )
        = $false ) ),
    inference(extuni,[status(esa)],[101:[bind(SV81,$thf( sK1_A )),bind(SV82,$thf( sK1_A ))]]) ).

thf(111,plain,
    ! [SV83: $i,SV84: $i] :
      ( ( ( SV84 = SV83 )
        = $true )
      | ( ( ( sK15_E @ SV83 @ SV84 )
          = ( sK16_E @ SV84 @ SV83 ) )
        = $false )
      | ( ( in @ ( kpair @ ( sK16_E @ SV84 @ SV83 ) @ ( sK15_E @ SV83 @ SV84 ) ) @ sK2_SY402 )
        = $false )
      | ( ( ( kpair @ SV84 @ SV83 )
          = ( kpair @ sK4_SY407 @ sK3_SY405 ) )
        = $false ) ),
    inference(extuni,[status(esa)],[101:[bind(SV81,$thf( sK1_A )),bind(SV82,$thf( sK1_A ))]]) ).

thf(112,plain,
    ! [SV81: $i,SV82: $i,SV83: $i,SV84: $i] :
      ( ( ( SV84 = SV83 )
        = $true )
      | ( ( ( dpsetconstr @ SV82 @ SV81
            @ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) )
          = ( dpsetconstr @ sK1_A @ sK1_A
            @ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY402 ) ) )
        = $false )
      | ( ( ( kpair @ SV84 @ SV83 )
          = ( kpair @ sK4_SY407 @ sK3_SY405 ) )
        = $false ) ),
    inference(extuni,[status(esa)],[101]) ).

thf(113,plain,
    ! [SV85: $i,SV86: $i,SV87: $i,SV88: $i,SV89: $i > $i > $o] :
      ( ( ( SV89 @ SV88 @ SV87 )
        = $false )
      | ( ( in @ ( kpair @ SV88 @ SV87 )
          @ ( dpsetconstr @ SV86 @ SV85
            @ ^ [SX0: $i,SX1: $i] :
                ~ ( SV89 @ SX0 @ SX1 ) ) )
        = $false ) ),
    inference(rename,[status(thm)],[57]) ).

thf(118,plain,
    ! [SV85: $i,SV86: $i,SV87: $i,SV88: $i,SV89: $i > $i > $o] :
      ( ( ( ( in @ ( kpair @ SV88 @ SV87 )
            @ ( dpsetconstr @ SV86 @ SV85
              @ ^ [SX0: $i,SX1: $i] :
                  ~ ( SV89 @ SX0 @ SX1 ) ) )
          = ( in @ ( kpair @ sK4_SY407 @ sK3_SY405 )
            @ ( dpsetconstr @ sK1_A @ sK1_A
              @ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY402 ) ) ) )
        = $false )
      | ( ( SV89 @ SV88 @ SV87 )
        = $false ) ),
    inference(res,[status(thm)],[113,36]) ).

thf(120,plain,
    ! [SV85: $i,SV86: $i,SV87: $i,SV88: $i,SV89: $i > $i > $o] :
      ( ( ( ( in @ ( kpair @ SV88 @ SV87 )
            @ ( dpsetconstr @ SV86 @ SV85
              @ ^ [SX0: $i,SX1: $i] :
                  ~ ( SV89 @ SX0 @ SX1 ) ) )
          = ( in @ sK4_SY407 @ sK1_A ) )
        = $false )
      | ( ( SV89 @ SV88 @ SV87 )
        = $false ) ),
    inference(res,[status(thm)],[113,31]) ).

thf(122,plain,
    ! [SV85: $i,SV86: $i,SV87: $i,SV88: $i,SV89: $i > $i > $o] :
      ( ( ( ( in @ ( kpair @ SV88 @ SV87 )
            @ ( dpsetconstr @ SV86 @ SV85
              @ ^ [SX0: $i,SX1: $i] :
                  ~ ( SV89 @ SX0 @ SX1 ) ) )
          = ( in @ sK3_SY405 @ sK1_A ) )
        = $false )
      | ( ( SV89 @ SV88 @ SV87 )
        = $false ) ),
    inference(res,[status(thm)],[113,24]) ).

thf(126,plain,
    ! [SV85: $i,SV86: $i,SV87: $i,SV88: $i] :
      ( ( $true = $false )
      | ( ( in @ ( kpair @ SV88 @ SV87 )
          @ ( dpsetconstr @ SV86 @ SV85
            @ ^ [SX0: $i,SX1: $i] : ~ $true ) )
        = $false ) ),
    inference(prim_subst,[status(thm)],[113:[bind(SV89,$thf( ^ [SV95: $i] : ^ [SV96: $i] : $true ))]]) ).

thf(127,plain,
    ! [SV85: $i,SV86: $i,SV87: $i,SV88: $i] :
      ( ( in @ ( kpair @ SV88 @ SV87 )
        @ ( dpsetconstr @ SV86 @ SV85
          @ ^ [SX0: $i,SX1: $i] : ~ $true ) )
      = $false ),
    inference(sim,[status(thm)],[126]) ).

thf(129,plain,
    ! [SV85: $i,SV86: $i,SV87: $i,SV88: $i,SV92: $i > $i > $o] :
      ( ( ( ~ ( SV92 @ SV88 @ SV87 ) )
        = $false )
      | ( ( in @ ( kpair @ SV88 @ SV87 )
          @ ( dpsetconstr @ SV86 @ SV85
            @ ^ [SX0: $i,SX1: $i] :
                ~ ~ ( SV92 @ SX0 @ SX1 ) ) )
        = $false ) ),
    inference(prim_subst,[status(thm)],[113:[bind(SV89,$thf( ^ [SV90: $i] : ^ [SV91: $i] : ~ ( SV92 @ SV90 @ SV91 ) ))]]) ).

thf(130,plain,
    ! [SV85: $i,SV86: $i,SV87: $i,SV88: $i] :
      ( ( ( ( SV88 != SV87 ) )
        = $false )
      | ( ( in @ ( kpair @ SV88 @ SV87 )
          @ ( dpsetconstr @ SV86 @ SV85
            @ ^ [SX0: $i,SX1: $i] :
                ~ ( ( SX0 != SX1 ) ) ) )
        = $false ) ),
    inference(prim_subst,[status(thm)],[113:[bind(SV89,$thf( ^ [SY499: $i] : ^ [SY500: $i] : ( SY499 != SY500 ) ))]]) ).

thf(131,plain,
    ! [SV85: $i,SV86: $i,SV87: $i,SV88: $i] :
      ( ( ( SV88 = SV87 )
        = $false )
      | ( ( in @ ( kpair @ SV88 @ SV87 )
          @ ( dpsetconstr @ SV86 @ SV85
            @ ^ [SX0: $i,SX1: $i] : ( SX0 != SX1 ) ) )
        = $false ) ),
    inference(prim_subst,[status(thm)],[113:[bind(SV89,$thf( ^ [SV98: $i] : ^ [SV97: $i] : ( SV98 = SV97 ) ))]]) ).

thf(133,plain,
    ! [SV85: $i,SV86: $i,SV87: $i,SV88: $i,SV89: $i > $i > $o] :
      ( ( ( SV89 @ SV88 @ SV87 )
        = $false )
      | ( ( ( dpsetconstr @ SV86 @ SV85
            @ ^ [SX0: $i,SX1: $i] :
                ~ ( SV89 @ SX0 @ SX1 ) )
          = sK1_A )
        = $false )
      | ( ( ( kpair @ SV88 @ SV87 )
          = sK3_SY405 )
        = $false ) ),
    inference(extuni,[status(esa)],[122]) ).

thf(134,plain,
    ! [SV85: $i,SV86: $i,SV87: $i,SV88: $i,SV89: $i > $i > $o] :
      ( ( ( SV89 @ SV88 @ SV87 )
        = $false )
      | ( ( ( dpsetconstr @ SV86 @ SV85
            @ ^ [SX0: $i,SX1: $i] :
                ~ ( SV89 @ SX0 @ SX1 ) )
          = sK1_A )
        = $false )
      | ( ( ( kpair @ SV88 @ SV87 )
          = sK4_SY407 )
        = $false ) ),
    inference(extuni,[status(esa)],[120]) ).

thf(135,plain,
    ! [SV89: $i > $i > $o] :
      ( ( ( SV89 @ sK4_SY407 @ sK3_SY405 )
        = $false )
      | ( ( ~ ( SV89 @ ( sK21_E @ SV89 ) @ ( sK22_E @ SV89 ) ) )
        = $true )
      | ( ( in @ ( kpair @ ( sK22_E @ SV89 ) @ ( sK21_E @ SV89 ) ) @ sK2_SY402 )
        = $true ) ),
    inference(extuni,[status(esa)],[118:[bind(SV85,$thf( sK1_A )),bind(SV86,$thf( sK1_A )),bind(SV87,$thf( sK3_SY405 )),bind(SV88,$thf( sK4_SY407 ))]]) ).

thf(136,plain,
    ! [SV89: $i > $i > $o] :
      ( ( ( SV89 @ sK4_SY407 @ sK3_SY405 )
        = $false )
      | ( ( ~ ( SV89 @ ( sK21_E @ SV89 ) @ ( sK22_E @ SV89 ) ) )
        = $false )
      | ( ( in @ ( kpair @ ( sK22_E @ SV89 ) @ ( sK21_E @ SV89 ) ) @ sK2_SY402 )
        = $false ) ),
    inference(extuni,[status(esa)],[118:[bind(SV85,$thf( sK1_A )),bind(SV86,$thf( sK1_A )),bind(SV87,$thf( sK3_SY405 )),bind(SV88,$thf( sK4_SY407 ))]]) ).

thf(137,plain,
    ! [SV85: $i,SV86: $i,SV89: $i > $i > $o] :
      ( ( ( SV89 @ sK4_SY407 @ sK3_SY405 )
        = $false )
      | ( ( ( dpsetconstr @ SV86 @ SV85
            @ ^ [SX0: $i,SX1: $i] :
                ~ ( SV89 @ SX0 @ SX1 ) )
          = ( dpsetconstr @ sK1_A @ sK1_A
            @ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY402 ) ) )
        = $false ) ),
    inference(extuni,[status(esa)],[118:[bind(SV87,$thf( sK3_SY405 )),bind(SV88,$thf( sK4_SY407 ))]]) ).

thf(138,plain,
    ! [SV87: $i,SV88: $i,SV89: $i > $i > $o] :
      ( ( ( SV89 @ SV88 @ SV87 )
        = $false )
      | ( ( ~ ( SV89 @ ( sK23_E @ SV87 @ SV88 @ SV89 ) @ ( sK24_E @ SV88 @ SV87 @ SV89 ) ) )
        = $true )
      | ( ( in @ ( kpair @ ( sK24_E @ SV88 @ SV87 @ SV89 ) @ ( sK23_E @ SV87 @ SV88 @ SV89 ) ) @ sK2_SY402 )
        = $true )
      | ( ( ( kpair @ SV88 @ SV87 )
          = ( kpair @ sK4_SY407 @ sK3_SY405 ) )
        = $false ) ),
    inference(extuni,[status(esa)],[118:[bind(SV85,$thf( sK1_A )),bind(SV86,$thf( sK1_A ))]]) ).

thf(139,plain,
    ! [SV87: $i,SV88: $i,SV89: $i > $i > $o] :
      ( ( ( SV89 @ SV88 @ SV87 )
        = $false )
      | ( ( ~ ( SV89 @ ( sK23_E @ SV87 @ SV88 @ SV89 ) @ ( sK24_E @ SV88 @ SV87 @ SV89 ) ) )
        = $false )
      | ( ( in @ ( kpair @ ( sK24_E @ SV88 @ SV87 @ SV89 ) @ ( sK23_E @ SV87 @ SV88 @ SV89 ) ) @ sK2_SY402 )
        = $false )
      | ( ( ( kpair @ SV88 @ SV87 )
          = ( kpair @ sK4_SY407 @ sK3_SY405 ) )
        = $false ) ),
    inference(extuni,[status(esa)],[118:[bind(SV85,$thf( sK1_A )),bind(SV86,$thf( sK1_A ))]]) ).

thf(140,plain,
    ! [SV85: $i,SV86: $i,SV87: $i,SV88: $i,SV89: $i > $i > $o] :
      ( ( ( SV89 @ SV88 @ SV87 )
        = $false )
      | ( ( ( dpsetconstr @ SV86 @ SV85
            @ ^ [SX0: $i,SX1: $i] :
                ~ ( SV89 @ SX0 @ SX1 ) )
          = ( dpsetconstr @ sK1_A @ sK1_A
            @ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY402 ) ) )
        = $false )
      | ( ( ( kpair @ SV88 @ SV87 )
          = ( kpair @ sK4_SY407 @ sK3_SY405 ) )
        = $false ) ),
    inference(extuni,[status(esa)],[118]) ).

thf(141,plain,
    ! [SV85: $i,SV86: $i,SV87: $i] :
      ( ( in @ ( kpair @ SV87 @ SV87 )
        @ ( dpsetconstr @ SV86 @ SV85
          @ ^ [SX0: $i,SX1: $i] : ( SX0 != SX1 ) ) )
      = $false ),
    inference(extuni,[status(esa)],[131:[bind(SV88,$thf( SV87 ))]]) ).

thf(142,plain,
    ! [SV88: $i,SV87: $i,SV89: $i > $i > $o] :
      ( ( ( SV89 @ ( sK23_E @ SV87 @ SV88 @ SV89 ) @ ( sK24_E @ SV88 @ SV87 @ SV89 ) )
        = $true )
      | ( ( SV89 @ SV88 @ SV87 )
        = $false )
      | ( ( in @ ( kpair @ ( sK24_E @ SV88 @ SV87 @ SV89 ) @ ( sK23_E @ SV87 @ SV88 @ SV89 ) ) @ sK2_SY402 )
        = $false )
      | ( ( ( kpair @ SV88 @ SV87 )
          = ( kpair @ sK4_SY407 @ sK3_SY405 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[139]) ).

thf(143,plain,
    ! [SV88: $i,SV87: $i,SV89: $i > $i > $o] :
      ( ( ( SV89 @ ( sK23_E @ SV87 @ SV88 @ SV89 ) @ ( sK24_E @ SV88 @ SV87 @ SV89 ) )
        = $false )
      | ( ( SV89 @ SV88 @ SV87 )
        = $false )
      | ( ( in @ ( kpair @ ( sK24_E @ SV88 @ SV87 @ SV89 ) @ ( sK23_E @ SV87 @ SV88 @ SV89 ) ) @ sK2_SY402 )
        = $true )
      | ( ( ( kpair @ SV88 @ SV87 )
          = ( kpair @ sK4_SY407 @ sK3_SY405 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[138]) ).

thf(144,plain,
    ! [SV89: $i > $i > $o] :
      ( ( ( SV89 @ ( sK21_E @ SV89 ) @ ( sK22_E @ SV89 ) )
        = $true )
      | ( ( SV89 @ sK4_SY407 @ sK3_SY405 )
        = $false )
      | ( ( in @ ( kpair @ ( sK22_E @ SV89 ) @ ( sK21_E @ SV89 ) ) @ sK2_SY402 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[136]) ).

thf(145,plain,
    ! [SV89: $i > $i > $o] :
      ( ( ( SV89 @ ( sK21_E @ SV89 ) @ ( sK22_E @ SV89 ) )
        = $false )
      | ( ( SV89 @ sK4_SY407 @ sK3_SY405 )
        = $false )
      | ( ( in @ ( kpair @ ( sK22_E @ SV89 ) @ ( sK21_E @ SV89 ) ) @ sK2_SY402 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[135]) ).

thf(146,plain,
    ! [SV85: $i,SV86: $i,SV87: $i,SV88: $i,SV92: $i > $i > $o] :
      ( ( ( SV92 @ SV88 @ SV87 )
        = $true )
      | ( ( in @ ( kpair @ SV88 @ SV87 )
          @ ( dpsetconstr @ SV86 @ SV85
            @ ^ [SX0: $i,SX1: $i] :
                ~ ~ ( SV92 @ SX0 @ SX1 ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[129]) ).

thf(147,plain,
    ! [SV85: $i,SV86: $i,SV87: $i,SV88: $i] :
      ( ( ( SV88 = SV87 )
        = $true )
      | ( ( in @ ( kpair @ SV88 @ SV87 )
          @ ( dpsetconstr @ SV86 @ SV85
            @ ^ [SX0: $i,SX1: $i] :
                ~ ( ( SX0 != SX1 ) ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[130]) ).

thf(148,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[16,147,146,145,144,143,142,141,140,137,134,133,127,113,112,111,110,109,108,107,106,105,95,94,93,92,91,85,84,83,82,81,80,78,76,75,74,72,69,62,61,60,59,38,36,31,24]) ).

thf(149,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[148]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : SEU777^2 : TPTP v8.1.0. Released v3.7.0.
% 0.06/0.12  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.33  % Computer : n021.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 : Sun Jun 19 19:17:33 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.13/0.34  
% 0.13/0.34   No.of.Axioms: 0
% 0.13/0.34  
% 0.13/0.34   Length.of.Defs: 750
% 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)...
% 1.07/1.25  
% 1.07/1.25   Prim_subst applied to clause 
% 1.07/1.25   
% 1.07/1.25  91:[ 0:<(in@((kpair@SV62)@SV61))@(((dpsetconstr@SV60)@SV59)@(^[SX0:$i,SX1:$i]: ((SV58@SX0)@SX1))) = $false>-w(1)-i() 1:<(SV58@SV62)@SV61 = $true>-w(1)-i() ]-mln(2)-w(2)-i(rename 28)-o(AXIOM)-fv([ SV58 SV59 SV60 SV61 SV62 ])
% 1.12/1.34  .........
% 75.46/75.66  (rf:0,axioms:0,ps:2,u:1,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2,loop_count:0,foatp_calls:0,translation:fof_full)..
% 75.58/75.76  
% 75.58/75.76   Prim_subst applied to clause 
% 75.58/75.76   
% 75.58/75.76  62:[ 0:<(in@((kpair@SV24)@SV23))@(((dpsetconstr@SV22)@SV21)@(^[SX0:$i,SX1:$i]: ((SV20@SX0)@SX1))) = $false>-w(1)-i() 1:<(SV20@SV24)@SV23 = $true>-w(1)-i() ]-mln(2)-w(2)-i(rename 28)-o(AXIOM)-fv([ SV20 SV21 SV22 SV23 SV24 ])
% 75.60/75.78  ...
% 76.21/76.40  
% 76.21/76.40   Prim_subst applied to clause 
% 76.21/76.40   
% 76.21/76.40  113:[ 0:<(SV89@SV88)@SV87 = $false>-w(1)-i() 1:<(in@((kpair@SV88)@SV87))@(((dpsetconstr@SV86)@SV85)@(^[SX0:$i,SX1:$i]: (~ ((SV89@SX0)@SX1)))) = $false>-w(1)-i() ]-mln(2)-w(2)-i(rename 57)-o(AXIOM)-fv([ SV85 SV86 SV87 SV88 SV89 ])
% 76.59/76.84  
% 76.59/76.84  ********************************
% 76.59/76.84  *   All subproblems solved!    *
% 76.59/76.84  ********************************
% 76.59/76.84  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:1,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:148,loop_count:8,foatp_calls:3,translation:fof_full)
% 76.59/76.86  
% 76.59/76.86  %**** Beginning of derivation protocol ****
% 76.59/76.86  % SZS output start CNFRefutation
% See solution above
% 76.59/76.86  
% 76.59/76.86  %**** End of derivation protocol ****
% 76.59/76.86  %**** no. of clauses in derivation: 117 ****
% 76.59/76.86  %**** clause counter: 148 ****
% 76.59/76.86  
% 76.59/76.86  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:1,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:148,loop_count:8,foatp_calls:3,translation:fof_full)
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