TSTP Solution File: SEV195^5 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SEV195^5 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n018.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 600s
% DateTime : Tue Jul 19 17:35:37 EDT 2022

% Result   : Theorem 77.11s 77.36s
% Output   : CNFRefutation 77.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   32
%            Number of leaves      :    7
% Syntax   : Number of formulae    :  267 (  87 unt;   6 typ;   0 def)
%            Number of atoms       : 1682 (1174 equ;   0 cnn)
%            Maximal formula atoms :    6 (   6 avg)
%            Number of connectives : 1725 ( 334   ~; 342   |;  21   &;1017   @)
%                                         (   0 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   4 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   68 (  68   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :  782 ( 240   ^ 534   !;   8   ?; 782   :)

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

thf(tp_cP,type,
    cP: a > a > a ).

thf(tp_cZ,type,
    cZ: a ).

thf(tp_sK1_Xx,type,
    sK1_Xx: a ).

thf(tp_sK2_Xx,type,
    sK2_Xx: ( a > $o ) > a ).

thf(tp_sK3_SY281,type,
    sK3_SY281: ( a > $o ) > a ).

thf(1,conjecture,
    ( ( ! [Xx: a,Xy: a] :
          ( ( cP @ Xx @ Xy )
         != cZ )
      & ! [Xx: a,Xy: a,Xu: a,Xv: a] :
          ( ( ( cP @ Xx @ Xu )
            = ( cP @ Xy @ Xv ) )
         => ( ( Xx = Xy )
            & ( Xu = Xv ) ) )
      & ! [X: a > $o] :
          ( ( ( X @ cZ )
            & ! [Xx: a,Xy: a] :
                ( ( ( X @ Xx )
                  & ( X @ Xy ) )
               => ( X @ ( cP @ Xx @ Xy ) ) ) )
         => ! [Xx: a] : ( X @ Xx ) ) )
   => ! [Xx: a] :
        ( ( Xx = cZ )
        | ? [Xy: a,Xz: a] :
            ( Xx
            = ( cP @ Xy @ Xz ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cS_LEM1D_pme) ).

thf(2,negated_conjecture,
    ( ( ( ! [Xx: a,Xy: a] :
            ( ( cP @ Xx @ Xy )
           != cZ )
        & ! [Xx: a,Xy: a,Xu: a,Xv: a] :
            ( ( ( cP @ Xx @ Xu )
              = ( cP @ Xy @ Xv ) )
           => ( ( Xx = Xy )
              & ( Xu = Xv ) ) )
        & ! [X: a > $o] :
            ( ( ( X @ cZ )
              & ! [Xx: a,Xy: a] :
                  ( ( ( X @ Xx )
                    & ( X @ Xy ) )
                 => ( X @ ( cP @ Xx @ Xy ) ) ) )
           => ! [Xx: a] : ( X @ Xx ) ) )
     => ! [Xx: a] :
          ( ( Xx = cZ )
          | ? [Xy: a,Xz: a] :
              ( Xx
              = ( cP @ Xy @ Xz ) ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ( ( ! [Xx: a,Xy: a] :
          ( ( cP @ Xx @ Xy )
         != cZ ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[2]) ).

thf(4,plain,
    ( ( ! [Xx: a,Xy: a,Xu: a,Xv: a] :
          ( ( ( cP @ Xx @ Xu )
            = ( cP @ Xy @ Xv ) )
         => ( ( Xx = Xy )
            & ( Xu = Xv ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[2]) ).

thf(5,plain,
    ( ( ! [X: a > $o] :
          ( ( ( X @ cZ )
            & ! [Xx: a,Xy: a] :
                ( ( ( X @ Xx )
                  & ( X @ Xy ) )
               => ( X @ ( cP @ Xx @ Xy ) ) ) )
         => ! [Xx: a] : ( X @ Xx ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[2]) ).

thf(6,plain,
    ( ( ! [Xx: a] :
          ( ( Xx = cZ )
          | ? [Xy: a,Xz: a] :
              ( Xx
              = ( cP @ Xy @ Xz ) ) ) )
    = $false ),
    inference(standard_cnf,[status(thm)],[2]) ).

thf(7,plain,
    ( ( ~ ! [Xx: a] :
            ( ( Xx = cZ )
            | ? [Xy: a,Xz: a] :
                ( Xx
                = ( cP @ Xy @ Xz ) ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[6]) ).

thf(8,plain,
    ( ( ( sK1_Xx != cZ )
      & ! [SY279: a,SY280: a] :
          ( sK1_Xx
         != ( cP @ SY279 @ SY280 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[7]) ).

thf(9,plain,
    ( ( ! [Xx: a,Xy: a] :
          ( ( cP @ Xx @ Xy )
         != cZ ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[3]) ).

thf(10,plain,
    ( ( ! [Xx: a,Xy: a] :
          ( ( ! [Xu: a,Xv: a] :
                ( ( cP @ Xx @ Xu )
               != ( cP @ Xy @ Xv ) )
            | ( Xx = Xy ) )
          & ! [Xu: a,Xv: a] :
              ( ( ( cP @ Xx @ Xu )
               != ( cP @ Xy @ Xv ) )
              | ( Xu = Xv ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[4]) ).

thf(11,plain,
    ( ( ! [X: a > $o] :
          ( ( ( X @ ( sK2_Xx @ X ) )
            & ( X @ ( sK3_SY281 @ X ) )
            & ~ ( X @ ( cP @ ( sK2_Xx @ X ) @ ( sK3_SY281 @ X ) ) ) )
          | ~ ( X @ cZ )
          | ! [Xx: a] : ( X @ Xx ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5]) ).

thf(12,plain,
    ( ( ! [X: a > $o] :
          ( ( ( X @ ( sK2_Xx @ X ) )
            & ( X @ ( sK3_SY281 @ X ) )
            & ~ ( X @ ( cP @ ( sK2_Xx @ X ) @ ( sK3_SY281 @ X ) ) ) )
          | ~ ( X @ cZ )
          | ! [Xx: a] : ( X @ Xx ) ) )
    = $true ),
    inference(copy,[status(thm)],[11]) ).

thf(13,plain,
    ( ( ! [Xx: a,Xy: a] :
          ( ( ! [Xu: a,Xv: a] :
                ( ( cP @ Xx @ Xu )
               != ( cP @ Xy @ Xv ) )
            | ( Xx = Xy ) )
          & ! [Xu: a,Xv: a] :
              ( ( ( cP @ Xx @ Xu )
               != ( cP @ Xy @ Xv ) )
              | ( Xu = Xv ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10]) ).

thf(14,plain,
    ( ( ! [Xx: a,Xy: a] :
          ( ( cP @ Xx @ Xy )
         != cZ ) )
    = $true ),
    inference(copy,[status(thm)],[9]) ).

thf(15,plain,
    ( ( ( sK1_Xx != cZ )
      & ! [SY279: a,SY280: a] :
          ( sK1_Xx
         != ( cP @ SY279 @ SY280 ) ) )
    = $true ),
    inference(copy,[status(thm)],[8]) ).

thf(16,plain,
    ( ( ! [SX0: a,SX1: a] :
          ~ ( ~ ( ! [SX2: a,SX3: a] :
                    ( ( cP @ SX0 @ SX2 )
                   != ( cP @ SX1 @ SX3 ) )
                | ( SX0 = SX1 ) )
            | ~ ! [SX2: a,SX3: a] :
                  ( ( ( cP @ SX0 @ SX2 )
                   != ( cP @ SX1 @ SX3 ) )
                  | ( SX2 = SX3 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[13]) ).

thf(17,plain,
    ( ( ! [SX0: a > $o] :
          ( ~ ( ~ ~ ( ~ ( SX0 @ ( sK2_Xx @ SX0 ) )
                    | ~ ( SX0 @ ( sK3_SY281 @ SX0 ) ) )
              | ~ ~ ( SX0 @ ( cP @ ( sK2_Xx @ SX0 ) @ ( sK3_SY281 @ SX0 ) ) ) )
          | ~ ( SX0 @ cZ )
          | ! [SX1: a] : ( SX0 @ SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[12]) ).

thf(18,plain,
    ( ( ~ ( ~ ( ( sK1_Xx != cZ ) )
          | ~ ! [SX0: a,SX1: a] :
                ( sK1_Xx
               != ( cP @ SX0 @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[15]) ).

thf(19,plain,
    ! [SV1: a] :
      ( ( ! [SY282: a] :
            ( ( cP @ SV1 @ SY282 )
           != cZ ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[14]) ).

thf(20,plain,
    ! [SV2: a] :
      ( ( ! [SY283: a] :
            ~ ( ~ ( ! [SY284: a,SY285: a] :
                      ( ( cP @ SV2 @ SY284 )
                     != ( cP @ SY283 @ SY285 ) )
                  | ( SV2 = SY283 ) )
              | ~ ! [SY286: a,SY287: a] :
                    ( ( ( cP @ SV2 @ SY286 )
                     != ( cP @ SY283 @ SY287 ) )
                    | ( SY286 = SY287 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[16]) ).

thf(21,plain,
    ! [SV3: a > $o] :
      ( ( ~ ( ~ ~ ( ~ ( SV3 @ ( sK2_Xx @ SV3 ) )
                  | ~ ( SV3 @ ( sK3_SY281 @ SV3 ) ) )
            | ~ ~ ( SV3 @ ( cP @ ( sK2_Xx @ SV3 ) @ ( sK3_SY281 @ SV3 ) ) ) )
        | ~ ( SV3 @ cZ )
        | ! [SY288: a] : ( SV3 @ SY288 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[17]) ).

thf(22,plain,
    ( ( ~ ( ( sK1_Xx != cZ ) )
      | ~ ! [SX0: a,SX1: a] :
            ( sK1_Xx
           != ( cP @ SX0 @ SX1 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[18]) ).

thf(23,plain,
    ! [SV4: a,SV1: a] :
      ( ( ( ( cP @ SV1 @ SV4 )
         != cZ ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[19]) ).

thf(24,plain,
    ! [SV5: a,SV2: a] :
      ( ( ~ ( ~ ( ! [SY289: a,SY290: a] :
                    ( ( cP @ SV2 @ SY289 )
                   != ( cP @ SV5 @ SY290 ) )
                | ( SV2 = SV5 ) )
            | ~ ! [SY291: a,SY292: a] :
                  ( ( ( cP @ SV2 @ SY291 )
                   != ( cP @ SV5 @ SY292 ) )
                  | ( SY291 = SY292 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[20]) ).

thf(25,plain,
    ! [SV3: a > $o] :
      ( ( ( ~ ( ~ ~ ( ~ ( SV3 @ ( sK2_Xx @ SV3 ) )
                    | ~ ( SV3 @ ( sK3_SY281 @ SV3 ) ) )
              | ~ ~ ( SV3 @ ( cP @ ( sK2_Xx @ SV3 ) @ ( sK3_SY281 @ SV3 ) ) ) )
          | ~ ( SV3 @ cZ ) )
        = $true )
      | ( ( ! [SY288: a] : ( SV3 @ SY288 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[21]) ).

thf(26,plain,
    ( ( ~ ( ( sK1_Xx != cZ ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[22]) ).

thf(27,plain,
    ( ( ~ ! [SX0: a,SX1: a] :
            ( sK1_Xx
           != ( cP @ SX0 @ SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[22]) ).

thf(28,plain,
    ! [SV4: a,SV1: a] :
      ( ( ( cP @ SV1 @ SV4 )
        = cZ )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[23]) ).

thf(29,plain,
    ! [SV5: a,SV2: a] :
      ( ( ~ ( ! [SY289: a,SY290: a] :
                ( ( cP @ SV2 @ SY289 )
               != ( cP @ SV5 @ SY290 ) )
            | ( SV2 = SV5 ) )
        | ~ ! [SY291: a,SY292: a] :
              ( ( ( cP @ SV2 @ SY291 )
               != ( cP @ SV5 @ SY292 ) )
              | ( SY291 = SY292 ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[24]) ).

thf(30,plain,
    ! [SV3: a > $o] :
      ( ( ( ~ ( ~ ~ ( ~ ( SV3 @ ( sK2_Xx @ SV3 ) )
                    | ~ ( SV3 @ ( sK3_SY281 @ SV3 ) ) )
              | ~ ~ ( SV3 @ ( cP @ ( sK2_Xx @ SV3 ) @ ( sK3_SY281 @ SV3 ) ) ) ) )
        = $true )
      | ( ( ~ ( SV3 @ cZ ) )
        = $true )
      | ( ( ! [SY288: a] : ( SV3 @ SY288 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[25]) ).

thf(31,plain,
    ( ( ( sK1_Xx != cZ ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[26]) ).

thf(32,plain,
    ( ( ! [SX0: a,SX1: a] :
          ( sK1_Xx
         != ( cP @ SX0 @ SX1 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[27]) ).

thf(33,plain,
    ! [SV5: a,SV2: a] :
      ( ( ~ ( ! [SY289: a,SY290: a] :
                ( ( cP @ SV2 @ SY289 )
               != ( cP @ SV5 @ SY290 ) )
            | ( SV2 = SV5 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[29]) ).

thf(34,plain,
    ! [SV5: a,SV2: a] :
      ( ( ~ ! [SY291: a,SY292: a] :
              ( ( ( cP @ SV2 @ SY291 )
               != ( cP @ SV5 @ SY292 ) )
              | ( SY291 = SY292 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[29]) ).

thf(35,plain,
    ! [SV3: a > $o] :
      ( ( ( ~ ~ ( ~ ( SV3 @ ( sK2_Xx @ SV3 ) )
                | ~ ( SV3 @ ( sK3_SY281 @ SV3 ) ) )
          | ~ ~ ( SV3 @ ( cP @ ( sK2_Xx @ SV3 ) @ ( sK3_SY281 @ SV3 ) ) ) )
        = $false )
      | ( ( ~ ( SV3 @ cZ ) )
        = $true )
      | ( ( ! [SY288: a] : ( SV3 @ SY288 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[30]) ).

thf(36,plain,
    ( ( sK1_Xx = cZ )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[31]) ).

thf(37,plain,
    ! [SV6: a] :
      ( ( ! [SY293: a] :
            ( sK1_Xx
           != ( cP @ SV6 @ SY293 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[32]) ).

thf(38,plain,
    ! [SV5: a,SV2: a] :
      ( ( ! [SY289: a,SY290: a] :
            ( ( cP @ SV2 @ SY289 )
           != ( cP @ SV5 @ SY290 ) )
        | ( SV2 = SV5 ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[33]) ).

thf(39,plain,
    ! [SV5: a,SV2: a] :
      ( ( ! [SY291: a,SY292: a] :
            ( ( ( cP @ SV2 @ SY291 )
             != ( cP @ SV5 @ SY292 ) )
            | ( SY291 = SY292 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[34]) ).

thf(40,plain,
    ! [SV3: a > $o] :
      ( ( ( ~ ~ ( ~ ( SV3 @ ( sK2_Xx @ SV3 ) )
                | ~ ( SV3 @ ( sK3_SY281 @ SV3 ) ) ) )
        = $false )
      | ( ( ~ ( SV3 @ cZ ) )
        = $true )
      | ( ( ! [SY288: a] : ( SV3 @ SY288 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[35]) ).

thf(41,plain,
    ! [SV3: a > $o] :
      ( ( ( ~ ~ ( SV3 @ ( cP @ ( sK2_Xx @ SV3 ) @ ( sK3_SY281 @ SV3 ) ) ) )
        = $false )
      | ( ( ~ ( SV3 @ cZ ) )
        = $true )
      | ( ( ! [SY288: a] : ( SV3 @ SY288 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[35]) ).

thf(42,plain,
    ! [SV7: a,SV6: a] :
      ( ( ( sK1_Xx
         != ( cP @ SV6 @ SV7 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[37]) ).

thf(43,plain,
    ! [SV5: a,SV2: a] :
      ( ( ( ! [SY289: a,SY290: a] :
              ( ( cP @ SV2 @ SY289 )
             != ( cP @ SV5 @ SY290 ) ) )
        = $true )
      | ( ( SV2 = SV5 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[38]) ).

thf(44,plain,
    ! [SV5: a,SV8: a,SV2: a] :
      ( ( ! [SY294: a] :
            ( ( ( cP @ SV2 @ SV8 )
             != ( cP @ SV5 @ SY294 ) )
            | ( SV8 = SY294 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[39]) ).

thf(45,plain,
    ! [SV3: a > $o] :
      ( ( ( ~ ( ~ ( SV3 @ ( sK2_Xx @ SV3 ) )
              | ~ ( SV3 @ ( sK3_SY281 @ SV3 ) ) ) )
        = $true )
      | ( ( ~ ( SV3 @ cZ ) )
        = $true )
      | ( ( ! [SY288: a] : ( SV3 @ SY288 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[40]) ).

thf(46,plain,
    ! [SV3: a > $o] :
      ( ( ( ~ ( SV3 @ ( cP @ ( sK2_Xx @ SV3 ) @ ( sK3_SY281 @ SV3 ) ) ) )
        = $true )
      | ( ( ~ ( SV3 @ cZ ) )
        = $true )
      | ( ( ! [SY288: a] : ( SV3 @ SY288 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[41]) ).

thf(47,plain,
    ! [SV7: a,SV6: a] :
      ( ( sK1_Xx
        = ( cP @ SV6 @ SV7 ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[42]) ).

thf(48,plain,
    ! [SV5: a,SV9: a,SV2: a] :
      ( ( ( ! [SY295: a] :
              ( ( cP @ SV2 @ SV9 )
             != ( cP @ SV5 @ SY295 ) ) )
        = $true )
      | ( ( SV2 = SV5 )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[43]) ).

thf(49,plain,
    ! [SV10: a,SV5: a,SV8: a,SV2: a] :
      ( ( ( ( cP @ SV2 @ SV8 )
         != ( cP @ SV5 @ SV10 ) )
        | ( SV8 = SV10 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[44]) ).

thf(50,plain,
    ! [SV3: a > $o] :
      ( ( ( ~ ( SV3 @ ( sK2_Xx @ SV3 ) )
          | ~ ( SV3 @ ( sK3_SY281 @ SV3 ) ) )
        = $false )
      | ( ( ~ ( SV3 @ cZ ) )
        = $true )
      | ( ( ! [SY288: a] : ( SV3 @ SY288 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[45]) ).

thf(51,plain,
    ! [SV3: a > $o] :
      ( ( ( SV3 @ ( cP @ ( sK2_Xx @ SV3 ) @ ( sK3_SY281 @ SV3 ) ) )
        = $false )
      | ( ( ~ ( SV3 @ cZ ) )
        = $true )
      | ( ( ! [SY288: a] : ( SV3 @ SY288 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[46]) ).

thf(52,plain,
    ! [SV11: a,SV5: a,SV9: a,SV2: a] :
      ( ( ( ( ( cP @ SV2 @ SV9 )
           != ( cP @ SV5 @ SV11 ) ) )
        = $true )
      | ( ( SV2 = SV5 )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[48]) ).

thf(53,plain,
    ! [SV10: a,SV5: a,SV8: a,SV2: a] :
      ( ( ( ( ( cP @ SV2 @ SV8 )
           != ( cP @ SV5 @ SV10 ) ) )
        = $true )
      | ( ( SV8 = SV10 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[49]) ).

thf(54,plain,
    ! [SV3: a > $o] :
      ( ( ( ~ ( SV3 @ ( sK2_Xx @ SV3 ) ) )
        = $false )
      | ( ( ~ ( SV3 @ cZ ) )
        = $true )
      | ( ( ! [SY288: a] : ( SV3 @ SY288 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[50]) ).

thf(55,plain,
    ! [SV3: a > $o] :
      ( ( ( ~ ( SV3 @ ( sK3_SY281 @ SV3 ) ) )
        = $false )
      | ( ( ~ ( SV3 @ cZ ) )
        = $true )
      | ( ( ! [SY288: a] : ( SV3 @ SY288 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[50]) ).

thf(56,plain,
    ! [SV3: a > $o] :
      ( ( ( SV3 @ cZ )
        = $false )
      | ( ( SV3 @ ( cP @ ( sK2_Xx @ SV3 ) @ ( sK3_SY281 @ SV3 ) ) )
        = $false )
      | ( ( ! [SY288: a] : ( SV3 @ SY288 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[51]) ).

thf(57,plain,
    ! [SV11: a,SV5: a,SV9: a,SV2: a] :
      ( ( ( ( cP @ SV2 @ SV9 )
          = ( cP @ SV5 @ SV11 ) )
        = $false )
      | ( ( SV2 = SV5 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[52]) ).

thf(58,plain,
    ! [SV10: a,SV5: a,SV8: a,SV2: a] :
      ( ( ( ( cP @ SV2 @ SV8 )
          = ( cP @ SV5 @ SV10 ) )
        = $false )
      | ( ( SV8 = SV10 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[53]) ).

thf(59,plain,
    ! [SV3: a > $o] :
      ( ( ( SV3 @ ( sK2_Xx @ SV3 ) )
        = $true )
      | ( ( ~ ( SV3 @ cZ ) )
        = $true )
      | ( ( ! [SY288: a] : ( SV3 @ SY288 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[54]) ).

thf(60,plain,
    ! [SV3: a > $o] :
      ( ( ( SV3 @ ( sK3_SY281 @ SV3 ) )
        = $true )
      | ( ( ~ ( SV3 @ cZ ) )
        = $true )
      | ( ( ! [SY288: a] : ( SV3 @ SY288 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[55]) ).

thf(61,plain,
    ! [SV12: a,SV3: a > $o] :
      ( ( ( SV3 @ SV12 )
        = $true )
      | ( ( SV3 @ ( cP @ ( sK2_Xx @ SV3 ) @ ( sK3_SY281 @ SV3 ) ) )
        = $false )
      | ( ( SV3 @ cZ )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[56]) ).

thf(62,plain,
    ! [SV3: a > $o] :
      ( ( ( SV3 @ cZ )
        = $false )
      | ( ( SV3 @ ( sK2_Xx @ SV3 ) )
        = $true )
      | ( ( ! [SY288: a] : ( SV3 @ SY288 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[59]) ).

thf(63,plain,
    ! [SV3: a > $o] :
      ( ( ( SV3 @ cZ )
        = $false )
      | ( ( SV3 @ ( sK3_SY281 @ SV3 ) )
        = $true )
      | ( ( ! [SY288: a] : ( SV3 @ SY288 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[60]) ).

thf(64,plain,
    ! [SV13: a,SV3: a > $o] :
      ( ( ( SV3 @ SV13 )
        = $true )
      | ( ( SV3 @ ( sK2_Xx @ SV3 ) )
        = $true )
      | ( ( SV3 @ cZ )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[62]) ).

thf(65,plain,
    ! [SV14: a,SV3: a > $o] :
      ( ( ( SV3 @ SV14 )
        = $true )
      | ( ( SV3 @ ( sK3_SY281 @ SV3 ) )
        = $true )
      | ( ( SV3 @ cZ )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[63]) ).

thf(66,plain,
    ! [SV12: a] :
      ( ( ( SV12 = cZ )
        = $true )
      | ( ( ( cP
            @ ( sK2_Xx
              @ ^ [SX0: a] : ( SX0 = cZ ) )
            @ ( sK3_SY281
              @ ^ [SX0: a] : ( SX0 = cZ ) ) )
          = cZ )
        = $false )
      | ( ( cZ = cZ )
        = $false ) ),
    inference(replace_leibnizEQ,[status(thm)],[61:[bind(SV3,$thf( ^ [SV15: a] : ( SV15 = cZ ) ))]]) ).

thf(67,plain,
    ! [SV12: a] :
      ( ( ( SV12 = cZ )
        = $true )
      | ( ( ( cP
            @ ( sK2_Xx
              @ ^ [SX0: a] : ( SX0 = cZ ) )
            @ ( sK3_SY281
              @ ^ [SX0: a] : ( SX0 = cZ ) ) )
          = cZ )
        = $false ) ),
    inference(sim,[status(thm)],[66]) ).

thf(68,plain,
    ! [SV13: a] :
      ( ( ( SV13 = cZ )
        = $true )
      | ( ( ( sK2_Xx
            @ ^ [SX0: a] : ( SX0 = cZ ) )
          = cZ )
        = $true )
      | ( ( cZ = cZ )
        = $false ) ),
    inference(replace_leibnizEQ,[status(thm)],[64:[bind(SV3,$thf( ^ [SV16: a] : ( SV16 = cZ ) ))]]) ).

thf(69,plain,
    ! [SV13: a] :
      ( ( ( SV13 = cZ )
        = $true )
      | ( ( ( sK2_Xx
            @ ^ [SX0: a] : ( SX0 = cZ ) )
          = cZ )
        = $true ) ),
    inference(sim,[status(thm)],[68]) ).

thf(70,plain,
    ! [SV14: a] :
      ( ( ( SV14 = cZ )
        = $true )
      | ( ( ( sK3_SY281
            @ ^ [SX0: a] : ( SX0 = cZ ) )
          = cZ )
        = $true )
      | ( ( cZ = cZ )
        = $false ) ),
    inference(replace_leibnizEQ,[status(thm)],[65:[bind(SV3,$thf( ^ [SV17: a] : ( SV17 = cZ ) ))]]) ).

thf(71,plain,
    ! [SV14: a] :
      ( ( ( SV14 = cZ )
        = $true )
      | ( ( ( sK3_SY281
            @ ^ [SX0: a] : ( SX0 = cZ ) )
          = cZ )
        = $true ) ),
    inference(sim,[status(thm)],[70]) ).

thf(74,plain,
    ! [SV12: a,SV19: a > $o] :
      ( ( ( ~ ( SV19 @ SV12 ) )
        = $true )
      | ( ( ~ ( SV19
              @ ( cP
                @ ( sK2_Xx
                  @ ^ [SX0: a] :
                      ~ ( SV19 @ SX0 ) )
                @ ( sK3_SY281
                  @ ^ [SX0: a] :
                      ~ ( SV19 @ SX0 ) ) ) ) )
        = $false )
      | ( ( ~ ( SV19 @ cZ ) )
        = $false ) ),
    inference(prim_subst,[status(thm)],[61:[bind(SV3,$thf( ^ [SV18: a] : ~ ( SV19 @ SV18 ) ))]]) ).

thf(77,plain,
    ! [SV13: a,SV19: a > $o] :
      ( ( ( ~ ( SV19 @ SV13 ) )
        = $true )
      | ( ( ~ ( SV19
              @ ( sK2_Xx
                @ ^ [SX0: a] :
                    ~ ( SV19 @ SX0 ) ) ) )
        = $true )
      | ( ( ~ ( SV19 @ cZ ) )
        = $false ) ),
    inference(prim_subst,[status(thm)],[64:[bind(SV3,$thf( ^ [SV18: a] : ~ ( SV19 @ SV18 ) ))]]) ).

thf(80,plain,
    ! [SV14: a,SV19: a > $o] :
      ( ( ( ~ ( SV19 @ SV14 ) )
        = $true )
      | ( ( ~ ( SV19
              @ ( sK3_SY281
                @ ^ [SX0: a] :
                    ~ ( SV19 @ SX0 ) ) ) )
        = $true )
      | ( ( ~ ( SV19 @ cZ ) )
        = $false ) ),
    inference(prim_subst,[status(thm)],[65:[bind(SV3,$thf( ^ [SV18: a] : ~ ( SV19 @ SV18 ) ))]]) ).

thf(81,plain,
    ! [SV13: a] :
      ( ( ( ( sK2_Xx
            @ ^ [SX0: a] : ( SX0 = cZ ) )
          = cZ )
        = $true )
      | ( ( ( SV13 = cZ )
          = ( ( sK2_Xx
              @ ^ [SX0: a] : ( SX0 = cZ ) )
            = cZ ) )
        = $false ) ),
    inference(fac_restr,[status(thm)],[69]) ).

thf(82,plain,
    ! [SV14: a] :
      ( ( ( ( sK3_SY281
            @ ^ [SX0: a] : ( SX0 = cZ ) )
          = cZ )
        = $true )
      | ( ( ( SV14 = cZ )
          = ( ( sK3_SY281
              @ ^ [SX0: a] : ( SX0 = cZ ) )
            = cZ ) )
        = $false ) ),
    inference(fac_restr,[status(thm)],[71]) ).

thf(83,plain,
    ! [SV13: a] :
      ( ( ( ~ ( ( SV13 = cZ )
              | ( ( sK2_Xx
                  @ ^ [SX0: a] : ( SX0 = cZ ) )
                = cZ ) )
          | ~ ( ( SV13 != cZ )
              | ( ( sK2_Xx
                  @ ^ [SX0: a] : ( SX0 = cZ ) )
               != cZ ) ) )
        = $false )
      | ( ( ( sK2_Xx
            @ ^ [SX0: a] : ( SX0 = cZ ) )
          = cZ )
        = $true ) ),
    inference(extcnf_equal_neg,[status(thm)],[81]) ).

thf(84,plain,
    ! [SV13: a] :
      ( ( ( ( SV13 = cZ )
          = ( ( sK2_Xx
              @ ^ [SX0: a] : ( SX0 = cZ ) )
            = cZ ) )
        = $false )
      | ( ( ( sK2_Xx
            @ ^ [SX0: a] : ( SX0 = cZ ) )
          = cZ )
        = $true ) ),
    inference(extcnf_equal_neg,[status(thm)],[81]) ).

thf(85,plain,
    ! [SV14: a] :
      ( ( ( ~ ( ( SV14 = cZ )
              | ( ( sK3_SY281
                  @ ^ [SX0: a] : ( SX0 = cZ ) )
                = cZ ) )
          | ~ ( ( SV14 != cZ )
              | ( ( sK3_SY281
                  @ ^ [SX0: a] : ( SX0 = cZ ) )
               != cZ ) ) )
        = $false )
      | ( ( ( sK3_SY281
            @ ^ [SX0: a] : ( SX0 = cZ ) )
          = cZ )
        = $true ) ),
    inference(extcnf_equal_neg,[status(thm)],[82]) ).

thf(86,plain,
    ! [SV14: a] :
      ( ( ( ( SV14 = cZ )
          = ( ( sK3_SY281
              @ ^ [SX0: a] : ( SX0 = cZ ) )
            = cZ ) )
        = $false )
      | ( ( ( sK3_SY281
            @ ^ [SX0: a] : ( SX0 = cZ ) )
          = cZ )
        = $true ) ),
    inference(extcnf_equal_neg,[status(thm)],[82]) ).

thf(87,plain,
    ! [SV13: a] :
      ( ( ( ~ ( ( SV13 = cZ )
              | ( ( sK2_Xx
                  @ ^ [SX0: a] : ( SX0 = cZ ) )
                = cZ ) ) )
        = $false )
      | ( ( ( sK2_Xx
            @ ^ [SX0: a] : ( SX0 = cZ ) )
          = cZ )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[83]) ).

thf(89,plain,
    ! [SV14: a] :
      ( ( ( ~ ( ( SV14 = cZ )
              | ( ( sK3_SY281
                  @ ^ [SX0: a] : ( SX0 = cZ ) )
                = cZ ) ) )
        = $false )
      | ( ( ( sK3_SY281
            @ ^ [SX0: a] : ( SX0 = cZ ) )
          = cZ )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[85]) ).

thf(91,plain,
    ! [SV13: a] :
      ( ( ( ( SV13 = cZ )
          | ( ( sK2_Xx
              @ ^ [SX0: a] : ( SX0 = cZ ) )
            = cZ ) )
        = $true )
      | ( ( ( sK2_Xx
            @ ^ [SX0: a] : ( SX0 = cZ ) )
          = cZ )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[87]) ).

thf(93,plain,
    ! [SV14: a] :
      ( ( ( ( SV14 = cZ )
          | ( ( sK3_SY281
              @ ^ [SX0: a] : ( SX0 = cZ ) )
            = cZ ) )
        = $true )
      | ( ( ( sK3_SY281
            @ ^ [SX0: a] : ( SX0 = cZ ) )
          = cZ )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[89]) ).

thf(95,plain,
    ! [SV13: a] :
      ( ( ( SV13 = cZ )
        = $true )
      | ( ( ( sK2_Xx
            @ ^ [SX0: a] : ( SX0 = cZ ) )
          = cZ )
        = $true )
      | ( ( ( sK2_Xx
            @ ^ [SX0: a] : ( SX0 = cZ ) )
          = cZ )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[91]) ).

thf(97,plain,
    ! [SV14: a] :
      ( ( ( SV14 = cZ )
        = $true )
      | ( ( ( sK3_SY281
            @ ^ [SX0: a] : ( SX0 = cZ ) )
          = cZ )
        = $true )
      | ( ( ( sK3_SY281
            @ ^ [SX0: a] : ( SX0 = cZ ) )
          = cZ )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[93]) ).

thf(103,plain,
    ( ( ( ( sK2_Xx
          @ ^ [SX0: a] : ( SX0 = cZ ) )
        = cZ )
      = $true )
    | ( ( cZ
        = ( sK2_Xx
          @ ^ [SX0: a] : ( SX0 = cZ ) ) )
      = $false ) ),
    inference(extuni,[status(esa)],[84:[bind(SV13,$thf( cZ ))]]) ).

thf(104,plain,
    ( ( ( sK2_Xx
        @ ^ [SX0: a] : ( SX0 = cZ ) )
      = cZ )
    = $true ),
    inference(extuni,[status(esa)],[84:[bind(SV13,$thf( sK2_Xx @ ^ [SX0: a] : ( SX0 = cZ ) ))]]) ).

thf(105,plain,
    ( ( ( ( sK3_SY281
          @ ^ [SX0: a] : ( SX0 = cZ ) )
        = cZ )
      = $true )
    | ( ( cZ
        = ( sK3_SY281
          @ ^ [SX0: a] : ( SX0 = cZ ) ) )
      = $false ) ),
    inference(extuni,[status(esa)],[86:[bind(SV14,$thf( cZ ))]]) ).

thf(106,plain,
    ( ( ( sK3_SY281
        @ ^ [SX0: a] : ( SX0 = cZ ) )
      = cZ )
    = $true ),
    inference(extuni,[status(esa)],[86:[bind(SV14,$thf( sK3_SY281 @ ^ [SX0: a] : ( SX0 = cZ ) ))]]) ).

thf(109,plain,
    ! [SV12: a,SV19: a > $o] :
      ( ( ( SV19 @ SV12 )
        = $false )
      | ( ( ~ ( SV19
              @ ( cP
                @ ( sK2_Xx
                  @ ^ [SX0: a] :
                      ~ ( SV19 @ SX0 ) )
                @ ( sK3_SY281
                  @ ^ [SX0: a] :
                      ~ ( SV19 @ SX0 ) ) ) ) )
        = $false )
      | ( ( ~ ( SV19 @ cZ ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[74]) ).

thf(110,plain,
    ! [SV13: a,SV19: a > $o] :
      ( ( ( SV19 @ SV13 )
        = $false )
      | ( ( ~ ( SV19
              @ ( sK2_Xx
                @ ^ [SX0: a] :
                    ~ ( SV19 @ SX0 ) ) ) )
        = $true )
      | ( ( ~ ( SV19 @ cZ ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[77]) ).

thf(111,plain,
    ! [SV14: a,SV19: a > $o] :
      ( ( ( SV19 @ SV14 )
        = $false )
      | ( ( ~ ( SV19
              @ ( sK3_SY281
                @ ^ [SX0: a] :
                    ~ ( SV19 @ SX0 ) ) ) )
        = $true )
      | ( ( ~ ( SV19 @ cZ ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[80]) ).

thf(112,plain,
    ! [SV12: a,SV19: a > $o] :
      ( ( ( SV19
          @ ( cP
            @ ( sK2_Xx
              @ ^ [SX0: a] :
                  ~ ( SV19 @ SX0 ) )
            @ ( sK3_SY281
              @ ^ [SX0: a] :
                  ~ ( SV19 @ SX0 ) ) ) )
        = $true )
      | ( ( SV19 @ SV12 )
        = $false )
      | ( ( ~ ( SV19 @ cZ ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[109]) ).

thf(113,plain,
    ! [SV13: a,SV19: a > $o] :
      ( ( ( SV19
          @ ( sK2_Xx
            @ ^ [SX0: a] :
                ~ ( SV19 @ SX0 ) ) )
        = $false )
      | ( ( SV19 @ SV13 )
        = $false )
      | ( ( ~ ( SV19 @ cZ ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[110]) ).

thf(114,plain,
    ! [SV14: a,SV19: a > $o] :
      ( ( ( SV19
          @ ( sK3_SY281
            @ ^ [SX0: a] :
                ~ ( SV19 @ SX0 ) ) )
        = $false )
      | ( ( SV19 @ SV14 )
        = $false )
      | ( ( ~ ( SV19 @ cZ ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[111]) ).

thf(115,plain,
    ! [SV12: a,SV19: a > $o] :
      ( ( ( SV19 @ cZ )
        = $true )
      | ( ( SV19 @ SV12 )
        = $false )
      | ( ( SV19
          @ ( cP
            @ ( sK2_Xx
              @ ^ [SX0: a] :
                  ~ ( SV19 @ SX0 ) )
            @ ( sK3_SY281
              @ ^ [SX0: a] :
                  ~ ( SV19 @ SX0 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[112]) ).

thf(116,plain,
    ! [SV13: a,SV19: a > $o] :
      ( ( ( SV19 @ cZ )
        = $true )
      | ( ( SV19 @ SV13 )
        = $false )
      | ( ( SV19
          @ ( sK2_Xx
            @ ^ [SX0: a] :
                ~ ( SV19 @ SX0 ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[113]) ).

thf(117,plain,
    ! [SV14: a,SV19: a > $o] :
      ( ( ( SV19 @ cZ )
        = $true )
      | ( ( SV19 @ SV14 )
        = $false )
      | ( ( SV19
          @ ( sK3_SY281
            @ ^ [SX0: a] :
                ~ ( SV19 @ SX0 ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[114]) ).

thf(118,plain,
    ! [SV13: a] :
      ( ( ( SV13 = cZ )
        = $true )
      | ( ( ( sK2_Xx
            @ ^ [SX0: a] : ( SX0 = cZ ) )
          = cZ )
        = $true ) ),
    inference(sim,[status(thm)],[95]) ).

thf(119,plain,
    ! [SV14: a] :
      ( ( ( SV14 = cZ )
        = $true )
      | ( ( ( sK3_SY281
            @ ^ [SX0: a] : ( SX0 = cZ ) )
          = cZ )
        = $true ) ),
    inference(sim,[status(thm)],[97]) ).

thf(120,plain,
    ! [SV24: a,SV25: a] :
      ( ( ( cP @ SV25 @ SV24 )
        = cZ )
      = $false ),
    inference(rename,[status(thm)],[28]) ).

thf(121,plain,
    ! [SV26: a,SV27: a] :
      ( ( sK1_Xx
        = ( cP @ SV27 @ SV26 ) )
      = $false ),
    inference(rename,[status(thm)],[47]) ).

thf(122,plain,
    ! [SV28: a,SV29: a,SV30: a,SV31: a] :
      ( ( ( ( cP @ SV31 @ SV30 )
          = ( cP @ SV29 @ SV28 ) )
        = $false )
      | ( ( SV31 = SV29 )
        = $true ) ),
    inference(rename,[status(thm)],[57]) ).

thf(125,plain,
    ! [SV28: a,SV29: a,SV30: a,SV31: a,SV26: a,SV27: a] :
      ( ( ( ( SV31 = SV29 )
          = ( sK1_Xx
            = ( cP @ SV27 @ SV26 ) ) )
        = $false )
      | ( ( ( cP @ SV31 @ SV30 )
          = ( cP @ SV29 @ SV28 ) )
        = $false ) ),
    inference(res,[status(thm)],[122,121]) ).

thf(126,plain,
    ! [SV28: a,SV29: a,SV30: a,SV31: a,SV24: a,SV25: a] :
      ( ( ( ( SV31 = SV29 )
          = ( ( cP @ SV25 @ SV24 )
            = cZ ) )
        = $false )
      | ( ( ( cP @ SV31 @ SV30 )
          = ( cP @ SV29 @ SV28 ) )
        = $false ) ),
    inference(res,[status(thm)],[122,120]) ).

thf(127,plain,
    ! [SV28: a,SV29: a,SV30: a,SV31: a] :
      ( ( ( ( SV31 = SV29 )
          = ( sK1_Xx = cZ ) )
        = $false )
      | ( ( ( cP @ SV31 @ SV30 )
          = ( cP @ SV29 @ SV28 ) )
        = $false ) ),
    inference(res,[status(thm)],[122,36]) ).

thf(128,plain,
    ( ( cZ = sK1_Xx )
    = $false ),
    inference(extuni,[status(esa)],[127:[bind(SV30,$thf( SV28 )),bind(SV31,$thf( cZ )),bind(SV29,$thf( sK1_Xx ))]]) ).

thf(129,plain,
    ! [SV28: a,SV30: a] :
      ( ( ( cP @ cZ @ SV30 )
        = ( cP @ sK1_Xx @ SV28 ) )
      = $false ),
    inference(extuni,[status(esa)],[127:[bind(SV31,$thf( cZ )),bind(SV29,$thf( sK1_Xx ))]]) ).

thf(130,plain,
    ( ( sK1_Xx = cZ )
    = $false ),
    inference(extuni,[status(esa)],[127:[bind(SV30,$thf( SV28 )),bind(SV29,$thf( cZ )),bind(SV31,$thf( sK1_Xx ))]]) ).

thf(131,plain,
    ! [SV28: a,SV30: a] :
      ( ( ( cP @ sK1_Xx @ SV30 )
        = ( cP @ cZ @ SV28 ) )
      = $false ),
    inference(extuni,[status(esa)],[127:[bind(SV29,$thf( cZ )),bind(SV31,$thf( sK1_Xx ))]]) ).

thf(132,plain,
    ! [SV24: a,SV25: a] :
      ( ( cZ
        = ( cP @ SV25 @ SV24 ) )
      = $false ),
    inference(extuni,[status(esa)],[126:[bind(SV30,$thf( SV28 )),bind(SV31,$thf( cZ )),bind(SV29,$thf( cP @ SV25 @ SV24 ))]]) ).

thf(133,plain,
    ! [SV28: a,SV24: a,SV25: a,SV30: a] :
      ( ( ( cP @ cZ @ SV30 )
        = ( cP @ ( cP @ SV25 @ SV24 ) @ SV28 ) )
      = $false ),
    inference(extuni,[status(esa)],[126:[bind(SV31,$thf( cZ )),bind(SV29,$thf( cP @ SV25 @ SV24 ))]]) ).

thf(134,plain,
    ! [SV24: a,SV25: a] :
      ( ( ( cP @ SV25 @ SV24 )
        = cZ )
      = $false ),
    inference(extuni,[status(esa)],[126:[bind(SV30,$thf( SV28 )),bind(SV29,$thf( cZ )),bind(SV31,$thf( cP @ SV25 @ SV24 ))]]) ).

thf(135,plain,
    ! [SV28: a,SV30: a,SV24: a,SV25: a] :
      ( ( ( cP @ ( cP @ SV25 @ SV24 ) @ SV30 )
        = ( cP @ cZ @ SV28 ) )
      = $false ),
    inference(extuni,[status(esa)],[126:[bind(SV29,$thf( cZ )),bind(SV31,$thf( cP @ SV25 @ SV24 ))]]) ).

thf(136,plain,
    ! [SV26: a,SV27: a] :
      ( ( ( cP @ SV27 @ SV26 )
        = sK1_Xx )
      = $false ),
    inference(extuni,[status(esa)],[125:[bind(SV30,$thf( SV28 )),bind(SV31,$thf( cP @ SV27 @ SV26 )),bind(SV29,$thf( sK1_Xx ))]]) ).

thf(137,plain,
    ! [SV28: a,SV30: a,SV26: a,SV27: a] :
      ( ( ( cP @ ( cP @ SV27 @ SV26 ) @ SV30 )
        = ( cP @ sK1_Xx @ SV28 ) )
      = $false ),
    inference(extuni,[status(esa)],[125:[bind(SV31,$thf( cP @ SV27 @ SV26 )),bind(SV29,$thf( sK1_Xx ))]]) ).

thf(138,plain,
    ! [SV26: a,SV27: a] :
      ( ( sK1_Xx
        = ( cP @ SV27 @ SV26 ) )
      = $false ),
    inference(extuni,[status(esa)],[125:[bind(SV30,$thf( SV28 )),bind(SV29,$thf( cP @ SV27 @ SV26 )),bind(SV31,$thf( sK1_Xx ))]]) ).

thf(139,plain,
    ! [SV28: a,SV26: a,SV27: a,SV30: a] :
      ( ( ( cP @ sK1_Xx @ SV30 )
        = ( cP @ ( cP @ SV27 @ SV26 ) @ SV28 ) )
      = $false ),
    inference(extuni,[status(esa)],[125:[bind(SV29,$thf( cP @ SV27 @ SV26 )),bind(SV31,$thf( sK1_Xx ))]]) ).

thf(141,plain,
    ! [SV32: a,SV33: a,SV34: a,SV35: a] :
      ( ( ( ( cP @ SV35 @ SV34 )
          = ( cP @ SV33 @ SV32 ) )
        = $false )
      | ( ( SV34 = SV32 )
        = $true ) ),
    inference(rename,[status(thm)],[58]) ).

thf(144,plain,
    ! [SV32: a,SV33: a,SV34: a,SV35: a,SV28: a,SV29: a,SV30: a,SV31: a] :
      ( ( ( ( ( cP @ SV35 @ SV34 )
            = ( cP @ SV33 @ SV32 ) )
          = ( SV31 = SV29 ) )
        = $false )
      | ( ( SV34 = SV32 )
        = $true )
      | ( ( ( cP @ SV31 @ SV30 )
          = ( cP @ SV29 @ SV28 ) )
        = $false ) ),
    inference(res,[status(thm)],[141,122]) ).

thf(145,plain,
    ! [SV32: a,SV33: a,SV34: a,SV35: a,SV28: a,SV29: a,SV30: a,SV31: a] :
      ( ( ( ( SV34 = SV32 )
          = ( ( cP @ SV31 @ SV30 )
            = ( cP @ SV29 @ SV28 ) ) )
        = $false )
      | ( ( ( cP @ SV35 @ SV34 )
          = ( cP @ SV33 @ SV32 ) )
        = $false )
      | ( ( SV31 = SV29 )
        = $true ) ),
    inference(res,[status(thm)],[141,122]) ).

thf(146,plain,
    ! [SV32: a,SV33: a,SV34: a,SV35: a,SV26: a,SV27: a] :
      ( ( ( ( SV34 = SV32 )
          = ( sK1_Xx
            = ( cP @ SV27 @ SV26 ) ) )
        = $false )
      | ( ( ( cP @ SV35 @ SV34 )
          = ( cP @ SV33 @ SV32 ) )
        = $false ) ),
    inference(res,[status(thm)],[141,121]) ).

thf(147,plain,
    ! [SV32: a,SV33: a,SV34: a,SV35: a,SV24: a,SV25: a] :
      ( ( ( ( SV34 = SV32 )
          = ( ( cP @ SV25 @ SV24 )
            = cZ ) )
        = $false )
      | ( ( ( cP @ SV35 @ SV34 )
          = ( cP @ SV33 @ SV32 ) )
        = $false ) ),
    inference(res,[status(thm)],[141,120]) ).

thf(148,plain,
    ! [SV32: a,SV33: a,SV34: a,SV35: a] :
      ( ( ( ( SV34 = SV32 )
          = ( sK1_Xx = cZ ) )
        = $false )
      | ( ( ( cP @ SV35 @ SV34 )
          = ( cP @ SV33 @ SV32 ) )
        = $false ) ),
    inference(res,[status(thm)],[141,36]) ).

thf(149,plain,
    ( ( cZ = sK1_Xx )
    = $false ),
    inference(extuni,[status(esa)],[148:[bind(SV35,$thf( SV33 )),bind(SV34,$thf( cZ )),bind(SV32,$thf( sK1_Xx ))]]) ).

thf(150,plain,
    ! [SV33: a,SV35: a] :
      ( ( ( cP @ SV35 @ cZ )
        = ( cP @ SV33 @ sK1_Xx ) )
      = $false ),
    inference(extuni,[status(esa)],[148:[bind(SV34,$thf( cZ )),bind(SV32,$thf( sK1_Xx ))]]) ).

thf(151,plain,
    ( ( sK1_Xx = cZ )
    = $false ),
    inference(extuni,[status(esa)],[148:[bind(SV35,$thf( SV33 )),bind(SV32,$thf( cZ )),bind(SV34,$thf( sK1_Xx ))]]) ).

thf(152,plain,
    ! [SV33: a,SV35: a] :
      ( ( ( cP @ SV35 @ sK1_Xx )
        = ( cP @ SV33 @ cZ ) )
      = $false ),
    inference(extuni,[status(esa)],[148:[bind(SV32,$thf( cZ )),bind(SV34,$thf( sK1_Xx ))]]) ).

thf(153,plain,
    ! [SV24: a,SV25: a] :
      ( ( cZ
        = ( cP @ SV25 @ SV24 ) )
      = $false ),
    inference(extuni,[status(esa)],[147:[bind(SV35,$thf( SV33 )),bind(SV34,$thf( cZ )),bind(SV32,$thf( cP @ SV25 @ SV24 ))]]) ).

thf(154,plain,
    ! [SV24: a,SV25: a,SV33: a,SV35: a] :
      ( ( ( cP @ SV35 @ cZ )
        = ( cP @ SV33 @ ( cP @ SV25 @ SV24 ) ) )
      = $false ),
    inference(extuni,[status(esa)],[147:[bind(SV34,$thf( cZ )),bind(SV32,$thf( cP @ SV25 @ SV24 ))]]) ).

thf(155,plain,
    ! [SV24: a,SV25: a] :
      ( ( ( cP @ SV25 @ SV24 )
        = cZ )
      = $false ),
    inference(extuni,[status(esa)],[147:[bind(SV35,$thf( SV33 )),bind(SV32,$thf( cZ )),bind(SV34,$thf( cP @ SV25 @ SV24 ))]]) ).

thf(156,plain,
    ! [SV33: a,SV24: a,SV25: a,SV35: a] :
      ( ( ( cP @ SV35 @ ( cP @ SV25 @ SV24 ) )
        = ( cP @ SV33 @ cZ ) )
      = $false ),
    inference(extuni,[status(esa)],[147:[bind(SV32,$thf( cZ )),bind(SV34,$thf( cP @ SV25 @ SV24 ))]]) ).

thf(157,plain,
    ! [SV26: a,SV27: a] :
      ( ( ( cP @ SV27 @ SV26 )
        = sK1_Xx )
      = $false ),
    inference(extuni,[status(esa)],[146:[bind(SV35,$thf( SV33 )),bind(SV34,$thf( cP @ SV27 @ SV26 )),bind(SV32,$thf( sK1_Xx ))]]) ).

thf(158,plain,
    ! [SV33: a,SV26: a,SV27: a,SV35: a] :
      ( ( ( cP @ SV35 @ ( cP @ SV27 @ SV26 ) )
        = ( cP @ SV33 @ sK1_Xx ) )
      = $false ),
    inference(extuni,[status(esa)],[146:[bind(SV34,$thf( cP @ SV27 @ SV26 )),bind(SV32,$thf( sK1_Xx ))]]) ).

thf(159,plain,
    ! [SV26: a,SV27: a] :
      ( ( sK1_Xx
        = ( cP @ SV27 @ SV26 ) )
      = $false ),
    inference(extuni,[status(esa)],[146:[bind(SV35,$thf( SV33 )),bind(SV32,$thf( cP @ SV27 @ SV26 )),bind(SV34,$thf( sK1_Xx ))]]) ).

thf(160,plain,
    ! [SV26: a,SV27: a,SV33: a,SV35: a] :
      ( ( ( cP @ SV35 @ sK1_Xx )
        = ( cP @ SV33 @ ( cP @ SV27 @ SV26 ) ) )
      = $false ),
    inference(extuni,[status(esa)],[146:[bind(SV32,$thf( cP @ SV27 @ SV26 )),bind(SV34,$thf( sK1_Xx ))]]) ).

thf(162,plain,
    ! [SV30: a,SV28: a,SV29: a,SV31: a] :
      ( ( ( SV31 = SV29 )
        = $true )
      | ( ( ( cP @ SV29 @ SV28 )
          = ( cP @ SV31 @ SV30 ) )
        = $false ) ),
    inference(extuni,[status(esa)],[145:[bind(SV35,$thf( SV33 )),bind(SV34,$thf( cP @ SV29 @ SV28 )),bind(SV32,$thf( cP @ SV31 @ SV30 ))]]) ).

thf(163,plain,
    ! [SV30: a,SV33: a,SV28: a,SV35: a,SV29: a,SV31: a] :
      ( ( ( SV31 = SV29 )
        = $true )
      | ( ( ( cP @ SV35 @ ( cP @ SV29 @ SV28 ) )
          = ( cP @ SV33 @ ( cP @ SV31 @ SV30 ) ) )
        = $false ) ),
    inference(extuni,[status(esa)],[145:[bind(SV34,$thf( cP @ SV29 @ SV28 )),bind(SV32,$thf( cP @ SV31 @ SV30 ))]]) ).

thf(165,plain,
    ! [SV28: a,SV30: a,SV29: a,SV31: a] :
      ( ( ( SV31 = SV29 )
        = $true )
      | ( ( ( cP @ SV31 @ SV30 )
          = ( cP @ SV29 @ SV28 ) )
        = $false ) ),
    inference(extuni,[status(esa)],[145:[bind(SV35,$thf( SV33 )),bind(SV32,$thf( cP @ SV29 @ SV28 )),bind(SV34,$thf( cP @ SV31 @ SV30 ))]]) ).

thf(166,plain,
    ! [SV28: a,SV33: a,SV30: a,SV35: a,SV29: a,SV31: a] :
      ( ( ( SV31 = SV29 )
        = $true )
      | ( ( ( cP @ SV35 @ ( cP @ SV31 @ SV30 ) )
          = ( cP @ SV33 @ ( cP @ SV29 @ SV28 ) ) )
        = $false ) ),
    inference(extuni,[status(esa)],[145:[bind(SV32,$thf( cP @ SV29 @ SV28 )),bind(SV34,$thf( cP @ SV31 @ SV30 ))]]) ).

thf(168,plain,
    ! [SV34: a,SV35: a,SV32: a,SV33: a] :
      ( ( ( ( cP @ SV33 @ SV32 )
          = ( cP @ SV35 @ SV34 ) )
        = $false )
      | ( ( SV34 = SV32 )
        = $true ) ),
    inference(extuni,[status(esa)],[144:[bind(SV30,$thf( SV28 )),bind(SV29,$thf( cP @ SV35 @ SV34 )),bind(SV31,$thf( cP @ SV33 @ SV32 ))]]) ).

thf(169,plain,
    ! [SV28: a,SV34: a,SV35: a,SV30: a,SV32: a,SV33: a] :
      ( ( ( ( cP @ ( cP @ SV33 @ SV32 ) @ SV30 )
          = ( cP @ ( cP @ SV35 @ SV34 ) @ SV28 ) )
        = $false )
      | ( ( SV34 = SV32 )
        = $true ) ),
    inference(extuni,[status(esa)],[144:[bind(SV29,$thf( cP @ SV35 @ SV34 )),bind(SV31,$thf( cP @ SV33 @ SV32 ))]]) ).

thf(171,plain,
    ! [SV32: a,SV33: a,SV34: a,SV35: a] :
      ( ( ( ( cP @ SV35 @ SV34 )
          = ( cP @ SV33 @ SV32 ) )
        = $false )
      | ( ( SV34 = SV32 )
        = $true ) ),
    inference(extuni,[status(esa)],[144:[bind(SV30,$thf( SV28 )),bind(SV29,$thf( cP @ SV33 @ SV32 )),bind(SV31,$thf( cP @ SV35 @ SV34 ))]]) ).

thf(172,plain,
    ! [SV28: a,SV32: a,SV33: a,SV30: a,SV34: a,SV35: a] :
      ( ( ( ( cP @ ( cP @ SV35 @ SV34 ) @ SV30 )
          = ( cP @ ( cP @ SV33 @ SV32 ) @ SV28 ) )
        = $false )
      | ( ( SV34 = SV32 )
        = $true ) ),
    inference(extuni,[status(esa)],[144:[bind(SV29,$thf( cP @ SV33 @ SV32 )),bind(SV31,$thf( cP @ SV35 @ SV34 ))]]) ).

thf(174,plain,
    ! [SV12: a] :
      ( ( ( SV12 = cZ )
        = $true )
      | ( ( ( cP
            @ ( sK2_Xx
              @ ^ [SX0: a] : ( SX0 = cZ ) )
            @ ( sK3_SY281
              @ ^ [SX0: a] : ( SX0 = cZ ) ) )
          = cZ )
        = $false )
      | ( ( cZ = cZ )
        = $false ) ),
    inference(replace_leibnizEQ,[status(thm)],[61:[bind(SV3,$thf( ^ [SV36: a] : ( SV36 = cZ ) ))]]) ).

thf(175,plain,
    ! [SV12: a] :
      ( ( ( SV12 = cZ )
        = $true )
      | ( ( ( cP
            @ ( sK2_Xx
              @ ^ [SX0: a] : ( SX0 = cZ ) )
            @ ( sK3_SY281
              @ ^ [SX0: a] : ( SX0 = cZ ) ) )
          = cZ )
        = $false ) ),
    inference(sim,[status(thm)],[174]) ).

thf(176,plain,
    ! [SV13: a] :
      ( ( ( SV13 = cZ )
        = $true )
      | ( ( ( sK2_Xx
            @ ^ [SX0: a] : ( SX0 = cZ ) )
          = cZ )
        = $true )
      | ( ( cZ = cZ )
        = $false ) ),
    inference(replace_leibnizEQ,[status(thm)],[64:[bind(SV3,$thf( ^ [SV37: a] : ( SV37 = cZ ) ))]]) ).

thf(177,plain,
    ! [SV13: a] :
      ( ( ( SV13 = cZ )
        = $true )
      | ( ( ( sK2_Xx
            @ ^ [SX0: a] : ( SX0 = cZ ) )
          = cZ )
        = $true ) ),
    inference(sim,[status(thm)],[176]) ).

thf(178,plain,
    ! [SV14: a] :
      ( ( ( SV14 = cZ )
        = $true )
      | ( ( ( sK3_SY281
            @ ^ [SX0: a] : ( SX0 = cZ ) )
          = cZ )
        = $true )
      | ( ( cZ = cZ )
        = $false ) ),
    inference(replace_leibnizEQ,[status(thm)],[65:[bind(SV3,$thf( ^ [SV38: a] : ( SV38 = cZ ) ))]]) ).

thf(179,plain,
    ! [SV14: a] :
      ( ( ( SV14 = cZ )
        = $true )
      | ( ( ( sK3_SY281
            @ ^ [SX0: a] : ( SX0 = cZ ) )
          = cZ )
        = $true ) ),
    inference(sim,[status(thm)],[178]) ).

thf(180,plain,
    ! [SV12: a] :
      ( ( ( cZ = SV12 )
        = $true )
      | ( ( SV12 = SV12 )
        = $false )
      | ( ( ( cP
            @ ( sK2_Xx
              @ ^ [SX0: a] : ( SX0 != SV12 ) )
            @ ( sK3_SY281
              @ ^ [SX0: a] : ( SX0 != SV12 ) ) )
          = SV12 )
        = $true ) ),
    inference(replace_leibnizEQ,[status(thm)],[115:[bind(SV19,$thf( ^ [SV39: a] : ( SV39 = SV12 ) ))]]) ).

thf(181,plain,
    ! [SV12: a] :
      ( ( ( cZ = SV12 )
        = $true )
      | ( ( ( cP
            @ ( sK2_Xx
              @ ^ [SX0: a] : ( SX0 != SV12 ) )
            @ ( sK3_SY281
              @ ^ [SX0: a] : ( SX0 != SV12 ) ) )
          = SV12 )
        = $true ) ),
    inference(sim,[status(thm)],[180]) ).

thf(182,plain,
    ! [SV13: a] :
      ( ( ( cZ = SV13 )
        = $true )
      | ( ( SV13 = SV13 )
        = $false )
      | ( ( ( sK2_Xx
            @ ^ [SX0: a] : ( SX0 != SV13 ) )
          = SV13 )
        = $false ) ),
    inference(replace_leibnizEQ,[status(thm)],[116:[bind(SV19,$thf( ^ [SV40: a] : ( SV40 = SV13 ) ))]]) ).

thf(183,plain,
    ! [SV13: a] :
      ( ( ( cZ = SV13 )
        = $true )
      | ( ( ( sK2_Xx
            @ ^ [SX0: a] : ( SX0 != SV13 ) )
          = SV13 )
        = $false ) ),
    inference(sim,[status(thm)],[182]) ).

thf(184,plain,
    ! [SV14: a] :
      ( ( ( cZ = SV14 )
        = $true )
      | ( ( SV14 = SV14 )
        = $false )
      | ( ( ( sK3_SY281
            @ ^ [SX0: a] : ( SX0 != SV14 ) )
          = SV14 )
        = $false ) ),
    inference(replace_leibnizEQ,[status(thm)],[117:[bind(SV19,$thf( ^ [SV41: a] : ( SV41 = SV14 ) ))]]) ).

thf(185,plain,
    ! [SV14: a] :
      ( ( ( cZ = SV14 )
        = $true )
      | ( ( ( sK3_SY281
            @ ^ [SX0: a] : ( SX0 != SV14 ) )
          = SV14 )
        = $false ) ),
    inference(sim,[status(thm)],[184]) ).

thf(188,plain,
    ! [SV12: a,SV49: a > $o] :
      ( ( ( ~ ( SV49 @ SV12 ) )
        = $true )
      | ( ( ~ ( SV49
              @ ( cP
                @ ( sK2_Xx
                  @ ^ [SX0: a] :
                      ~ ( SV49 @ SX0 ) )
                @ ( sK3_SY281
                  @ ^ [SX0: a] :
                      ~ ( SV49 @ SX0 ) ) ) ) )
        = $false )
      | ( ( ~ ( SV49 @ cZ ) )
        = $false ) ),
    inference(prim_subst,[status(thm)],[61:[bind(SV3,$thf( ^ [SV48: a] : ~ ( SV49 @ SV48 ) ))]]) ).

thf(191,plain,
    ! [SV13: a,SV49: a > $o] :
      ( ( ( ~ ( SV49 @ SV13 ) )
        = $true )
      | ( ( ~ ( SV49
              @ ( sK2_Xx
                @ ^ [SX0: a] :
                    ~ ( SV49 @ SX0 ) ) ) )
        = $true )
      | ( ( ~ ( SV49 @ cZ ) )
        = $false ) ),
    inference(prim_subst,[status(thm)],[64:[bind(SV3,$thf( ^ [SV48: a] : ~ ( SV49 @ SV48 ) ))]]) ).

thf(194,plain,
    ! [SV14: a,SV49: a > $o] :
      ( ( ( ~ ( SV49 @ SV14 ) )
        = $true )
      | ( ( ~ ( SV49
              @ ( sK3_SY281
                @ ^ [SX0: a] :
                    ~ ( SV49 @ SX0 ) ) ) )
        = $true )
      | ( ( ~ ( SV49 @ cZ ) )
        = $false ) ),
    inference(prim_subst,[status(thm)],[65:[bind(SV3,$thf( ^ [SV48: a] : ~ ( SV49 @ SV48 ) ))]]) ).

thf(197,plain,
    ! [SV12: a,SV43: a > $o] :
      ( ( ( ~ ( SV43 @ cZ ) )
        = $true )
      | ( ( ~ ( SV43 @ SV12 ) )
        = $false )
      | ( ( ~ ( SV43
              @ ( cP
                @ ( sK2_Xx
                  @ ^ [SX0: a] :
                      ~ ~ ( SV43 @ SX0 ) )
                @ ( sK3_SY281
                  @ ^ [SX0: a] :
                      ~ ~ ( SV43 @ SX0 ) ) ) ) )
        = $true ) ),
    inference(prim_subst,[status(thm)],[115:[bind(SV19,$thf( ^ [SV42: a] : ~ ( SV43 @ SV42 ) ))]]) ).

thf(200,plain,
    ! [SV13: a,SV43: a > $o] :
      ( ( ( ~ ( SV43 @ cZ ) )
        = $true )
      | ( ( ~ ( SV43 @ SV13 ) )
        = $false )
      | ( ( ~ ( SV43
              @ ( sK2_Xx
                @ ^ [SX0: a] :
                    ~ ~ ( SV43 @ SX0 ) ) ) )
        = $false ) ),
    inference(prim_subst,[status(thm)],[116:[bind(SV19,$thf( ^ [SV42: a] : ~ ( SV43 @ SV42 ) ))]]) ).

thf(203,plain,
    ! [SV14: a,SV43: a > $o] :
      ( ( ( ~ ( SV43 @ cZ ) )
        = $true )
      | ( ( ~ ( SV43 @ SV14 ) )
        = $false )
      | ( ( ~ ( SV43
              @ ( sK3_SY281
                @ ^ [SX0: a] :
                    ~ ~ ( SV43 @ SX0 ) ) ) )
        = $false ) ),
    inference(prim_subst,[status(thm)],[117:[bind(SV19,$thf( ^ [SV42: a] : ~ ( SV43 @ SV42 ) ))]]) ).

thf(204,plain,
    ! [SV13: a] :
      ( ( ( ( sK2_Xx
            @ ^ [SX0: a] : ( SX0 = cZ ) )
          = cZ )
        = $true )
      | ( ( ( SV13 = cZ )
          = ( ( sK2_Xx
              @ ^ [SX0: a] : ( SX0 = cZ ) )
            = cZ ) )
        = $false ) ),
    inference(fac_restr,[status(thm)],[177]) ).

thf(205,plain,
    ! [SV14: a] :
      ( ( ( ( sK3_SY281
            @ ^ [SX0: a] : ( SX0 = cZ ) )
          = cZ )
        = $true )
      | ( ( ( SV14 = cZ )
          = ( ( sK3_SY281
              @ ^ [SX0: a] : ( SX0 = cZ ) )
            = cZ ) )
        = $false ) ),
    inference(fac_restr,[status(thm)],[179]) ).

thf(206,plain,
    ! [SV13: a] :
      ( ( ( ( sK2_Xx
            @ ^ [SX0: a] : ( SX0 = cZ ) )
          = cZ )
        = $true )
      | ( ( ( SV13 = cZ )
          = ( ( sK2_Xx
              @ ^ [SX0: a] : ( SX0 = cZ ) )
            = cZ ) )
        = $false ) ),
    inference(fac_restr,[status(thm)],[69]) ).

thf(207,plain,
    ! [SV14: a] :
      ( ( ( ( sK3_SY281
            @ ^ [SX0: a] : ( SX0 = cZ ) )
          = cZ )
        = $true )
      | ( ( ( SV14 = cZ )
          = ( ( sK3_SY281
              @ ^ [SX0: a] : ( SX0 = cZ ) )
            = cZ ) )
        = $false ) ),
    inference(fac_restr,[status(thm)],[71]) ).

thf(208,plain,
    ! [SV12: a] :
      ( ( ( ( cP
            @ ( sK2_Xx
              @ ^ [SX0: a] : ( SX0 != SV12 ) )
            @ ( sK3_SY281
              @ ^ [SX0: a] : ( SX0 != SV12 ) ) )
          = SV12 )
        = $true )
      | ( ( ( cZ = SV12 )
          = ( ( cP
              @ ( sK2_Xx
                @ ^ [SX0: a] : ( SX0 != SV12 ) )
              @ ( sK3_SY281
                @ ^ [SX0: a] : ( SX0 != SV12 ) ) )
            = SV12 ) )
        = $false ) ),
    inference(fac_restr,[status(thm)],[181]) ).

thf(209,plain,
    ! [SV13: a] :
      ( ( ( ( sK2_Xx
            @ ^ [SX0: a] : ( SX0 = cZ ) )
          = cZ )
        = $true )
      | ( ( ( SV13 = cZ )
          = ( ( sK2_Xx
              @ ^ [SX0: a] : ( SX0 = cZ ) )
            = cZ ) )
        = $false ) ),
    inference(fac_restr,[status(thm)],[118]) ).

thf(210,plain,
    ! [SV14: a] :
      ( ( ( ( sK3_SY281
            @ ^ [SX0: a] : ( SX0 = cZ ) )
          = cZ )
        = $true )
      | ( ( ( SV14 = cZ )
          = ( ( sK3_SY281
              @ ^ [SX0: a] : ( SX0 = cZ ) )
            = cZ ) )
        = $false ) ),
    inference(fac_restr,[status(thm)],[119]) ).

thf(211,plain,
    ! [SV13: a] :
      ( ( ( ~ ( ( SV13 = cZ )
              | ( ( sK2_Xx
                  @ ^ [SX0: a] : ( SX0 = cZ ) )
                = cZ ) )
          | ~ ( ( SV13 != cZ )
              | ( ( sK2_Xx
                  @ ^ [SX0: a] : ( SX0 = cZ ) )
               != cZ ) ) )
        = $false )
      | ( ( ( sK2_Xx
            @ ^ [SX0: a] : ( SX0 = cZ ) )
          = cZ )
        = $true ) ),
    inference(extcnf_equal_neg,[status(thm)],[204]) ).

thf(212,plain,
    ! [SV13: a] :
      ( ( ( ( SV13 = cZ )
          = ( ( sK2_Xx
              @ ^ [SX0: a] : ( SX0 = cZ ) )
            = cZ ) )
        = $false )
      | ( ( ( sK2_Xx
            @ ^ [SX0: a] : ( SX0 = cZ ) )
          = cZ )
        = $true ) ),
    inference(extcnf_equal_neg,[status(thm)],[204]) ).

thf(213,plain,
    ! [SV14: a] :
      ( ( ( ~ ( ( SV14 = cZ )
              | ( ( sK3_SY281
                  @ ^ [SX0: a] : ( SX0 = cZ ) )
                = cZ ) )
          | ~ ( ( SV14 != cZ )
              | ( ( sK3_SY281
                  @ ^ [SX0: a] : ( SX0 = cZ ) )
               != cZ ) ) )
        = $false )
      | ( ( ( sK3_SY281
            @ ^ [SX0: a] : ( SX0 = cZ ) )
          = cZ )
        = $true ) ),
    inference(extcnf_equal_neg,[status(thm)],[205]) ).

thf(214,plain,
    ! [SV14: a] :
      ( ( ( ( SV14 = cZ )
          = ( ( sK3_SY281
              @ ^ [SX0: a] : ( SX0 = cZ ) )
            = cZ ) )
        = $false )
      | ( ( ( sK3_SY281
            @ ^ [SX0: a] : ( SX0 = cZ ) )
          = cZ )
        = $true ) ),
    inference(extcnf_equal_neg,[status(thm)],[205]) ).

thf(215,plain,
    ! [SV13: a] :
      ( ( ( ~ ( ( SV13 = cZ )
              | ( ( sK2_Xx
                  @ ^ [SX0: a] : ( SX0 = cZ ) )
                = cZ ) )
          | ~ ( ( SV13 != cZ )
              | ( ( sK2_Xx
                  @ ^ [SX0: a] : ( SX0 = cZ ) )
               != cZ ) ) )
        = $false )
      | ( ( ( sK2_Xx
            @ ^ [SX0: a] : ( SX0 = cZ ) )
          = cZ )
        = $true ) ),
    inference(extcnf_equal_neg,[status(thm)],[206]) ).

thf(216,plain,
    ! [SV13: a] :
      ( ( ( ( SV13 = cZ )
          = ( ( sK2_Xx
              @ ^ [SX0: a] : ( SX0 = cZ ) )
            = cZ ) )
        = $false )
      | ( ( ( sK2_Xx
            @ ^ [SX0: a] : ( SX0 = cZ ) )
          = cZ )
        = $true ) ),
    inference(extcnf_equal_neg,[status(thm)],[206]) ).

thf(217,plain,
    ! [SV14: a] :
      ( ( ( ~ ( ( SV14 = cZ )
              | ( ( sK3_SY281
                  @ ^ [SX0: a] : ( SX0 = cZ ) )
                = cZ ) )
          | ~ ( ( SV14 != cZ )
              | ( ( sK3_SY281
                  @ ^ [SX0: a] : ( SX0 = cZ ) )
               != cZ ) ) )
        = $false )
      | ( ( ( sK3_SY281
            @ ^ [SX0: a] : ( SX0 = cZ ) )
          = cZ )
        = $true ) ),
    inference(extcnf_equal_neg,[status(thm)],[207]) ).

thf(218,plain,
    ! [SV14: a] :
      ( ( ( ( SV14 = cZ )
          = ( ( sK3_SY281
              @ ^ [SX0: a] : ( SX0 = cZ ) )
            = cZ ) )
        = $false )
      | ( ( ( sK3_SY281
            @ ^ [SX0: a] : ( SX0 = cZ ) )
          = cZ )
        = $true ) ),
    inference(extcnf_equal_neg,[status(thm)],[207]) ).

thf(219,plain,
    ! [SV12: a] :
      ( ( ( ~ ( ( cZ = SV12 )
              | ( ( cP
                  @ ( sK2_Xx
                    @ ^ [SX0: a] : ( SX0 != SV12 ) )
                  @ ( sK3_SY281
                    @ ^ [SX0: a] : ( SX0 != SV12 ) ) )
                = SV12 ) )
          | ~ ( ( cZ != SV12 )
              | ( ( cP
                  @ ( sK2_Xx
                    @ ^ [SX0: a] : ( SX0 != SV12 ) )
                  @ ( sK3_SY281
                    @ ^ [SX0: a] : ( SX0 != SV12 ) ) )
               != SV12 ) ) )
        = $false )
      | ( ( ( cP
            @ ( sK2_Xx
              @ ^ [SX0: a] : ( SX0 != SV12 ) )
            @ ( sK3_SY281
              @ ^ [SX0: a] : ( SX0 != SV12 ) ) )
          = SV12 )
        = $true ) ),
    inference(extcnf_equal_neg,[status(thm)],[208]) ).

thf(220,plain,
    ! [SV12: a] :
      ( ( ( ( cZ = SV12 )
          = ( ( cP
              @ ( sK2_Xx
                @ ^ [SX0: a] : ( SX0 != SV12 ) )
              @ ( sK3_SY281
                @ ^ [SX0: a] : ( SX0 != SV12 ) ) )
            = SV12 ) )
        = $false )
      | ( ( ( cP
            @ ( sK2_Xx
              @ ^ [SX0: a] : ( SX0 != SV12 ) )
            @ ( sK3_SY281
              @ ^ [SX0: a] : ( SX0 != SV12 ) ) )
          = SV12 )
        = $true ) ),
    inference(extcnf_equal_neg,[status(thm)],[208]) ).

thf(221,plain,
    ! [SV13: a] :
      ( ( ( ~ ( ( SV13 = cZ )
              | ( ( sK2_Xx
                  @ ^ [SX0: a] : ( SX0 = cZ ) )
                = cZ ) )
          | ~ ( ( SV13 != cZ )
              | ( ( sK2_Xx
                  @ ^ [SX0: a] : ( SX0 = cZ ) )
               != cZ ) ) )
        = $false )
      | ( ( ( sK2_Xx
            @ ^ [SX0: a] : ( SX0 = cZ ) )
          = cZ )
        = $true ) ),
    inference(extcnf_equal_neg,[status(thm)],[209]) ).

thf(222,plain,
    ! [SV13: a] :
      ( ( ( ( SV13 = cZ )
          = ( ( sK2_Xx
              @ ^ [SX0: a] : ( SX0 = cZ ) )
            = cZ ) )
        = $false )
      | ( ( ( sK2_Xx
            @ ^ [SX0: a] : ( SX0 = cZ ) )
          = cZ )
        = $true ) ),
    inference(extcnf_equal_neg,[status(thm)],[209]) ).

thf(223,plain,
    ! [SV14: a] :
      ( ( ( ~ ( ( SV14 = cZ )
              | ( ( sK3_SY281
                  @ ^ [SX0: a] : ( SX0 = cZ ) )
                = cZ ) )
          | ~ ( ( SV14 != cZ )
              | ( ( sK3_SY281
                  @ ^ [SX0: a] : ( SX0 = cZ ) )
               != cZ ) ) )
        = $false )
      | ( ( ( sK3_SY281
            @ ^ [SX0: a] : ( SX0 = cZ ) )
          = cZ )
        = $true ) ),
    inference(extcnf_equal_neg,[status(thm)],[210]) ).

thf(224,plain,
    ! [SV14: a] :
      ( ( ( ( SV14 = cZ )
          = ( ( sK3_SY281
              @ ^ [SX0: a] : ( SX0 = cZ ) )
            = cZ ) )
        = $false )
      | ( ( ( sK3_SY281
            @ ^ [SX0: a] : ( SX0 = cZ ) )
          = cZ )
        = $true ) ),
    inference(extcnf_equal_neg,[status(thm)],[210]) ).

thf(225,plain,
    ! [SV13: a] :
      ( ( ( ~ ( ( SV13 = cZ )
              | ( ( sK2_Xx
                  @ ^ [SX0: a] : ( SX0 = cZ ) )
                = cZ ) ) )
        = $false )
      | ( ( ( sK2_Xx
            @ ^ [SX0: a] : ( SX0 = cZ ) )
          = cZ )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[211]) ).

thf(227,plain,
    ! [SV14: a] :
      ( ( ( ~ ( ( SV14 = cZ )
              | ( ( sK3_SY281
                  @ ^ [SX0: a] : ( SX0 = cZ ) )
                = cZ ) ) )
        = $false )
      | ( ( ( sK3_SY281
            @ ^ [SX0: a] : ( SX0 = cZ ) )
          = cZ )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[213]) ).

thf(229,plain,
    ! [SV13: a] :
      ( ( ( ~ ( ( SV13 = cZ )
              | ( ( sK2_Xx
                  @ ^ [SX0: a] : ( SX0 = cZ ) )
                = cZ ) ) )
        = $false )
      | ( ( ( sK2_Xx
            @ ^ [SX0: a] : ( SX0 = cZ ) )
          = cZ )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[215]) ).

thf(231,plain,
    ! [SV14: a] :
      ( ( ( ~ ( ( SV14 = cZ )
              | ( ( sK3_SY281
                  @ ^ [SX0: a] : ( SX0 = cZ ) )
                = cZ ) ) )
        = $false )
      | ( ( ( sK3_SY281
            @ ^ [SX0: a] : ( SX0 = cZ ) )
          = cZ )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[217]) ).

thf(233,plain,
    ! [SV12: a] :
      ( ( ( ~ ( ( cZ = SV12 )
              | ( ( cP
                  @ ( sK2_Xx
                    @ ^ [SX0: a] : ( SX0 != SV12 ) )
                  @ ( sK3_SY281
                    @ ^ [SX0: a] : ( SX0 != SV12 ) ) )
                = SV12 ) ) )
        = $false )
      | ( ( ( cP
            @ ( sK2_Xx
              @ ^ [SX0: a] : ( SX0 != SV12 ) )
            @ ( sK3_SY281
              @ ^ [SX0: a] : ( SX0 != SV12 ) ) )
          = SV12 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[219]) ).

thf(235,plain,
    ! [SV13: a] :
      ( ( ( ~ ( ( SV13 = cZ )
              | ( ( sK2_Xx
                  @ ^ [SX0: a] : ( SX0 = cZ ) )
                = cZ ) ) )
        = $false )
      | ( ( ( sK2_Xx
            @ ^ [SX0: a] : ( SX0 = cZ ) )
          = cZ )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[221]) ).

thf(237,plain,
    ! [SV14: a] :
      ( ( ( ~ ( ( SV14 = cZ )
              | ( ( sK3_SY281
                  @ ^ [SX0: a] : ( SX0 = cZ ) )
                = cZ ) ) )
        = $false )
      | ( ( ( sK3_SY281
            @ ^ [SX0: a] : ( SX0 = cZ ) )
          = cZ )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[223]) ).

thf(239,plain,
    ! [SV13: a] :
      ( ( ( ( SV13 = cZ )
          | ( ( sK2_Xx
              @ ^ [SX0: a] : ( SX0 = cZ ) )
            = cZ ) )
        = $true )
      | ( ( ( sK2_Xx
            @ ^ [SX0: a] : ( SX0 = cZ ) )
          = cZ )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[225]) ).

thf(241,plain,
    ! [SV14: a] :
      ( ( ( ( SV14 = cZ )
          | ( ( sK3_SY281
              @ ^ [SX0: a] : ( SX0 = cZ ) )
            = cZ ) )
        = $true )
      | ( ( ( sK3_SY281
            @ ^ [SX0: a] : ( SX0 = cZ ) )
          = cZ )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[227]) ).

thf(243,plain,
    ! [SV13: a] :
      ( ( ( ( SV13 = cZ )
          | ( ( sK2_Xx
              @ ^ [SX0: a] : ( SX0 = cZ ) )
            = cZ ) )
        = $true )
      | ( ( ( sK2_Xx
            @ ^ [SX0: a] : ( SX0 = cZ ) )
          = cZ )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[229]) ).

thf(245,plain,
    ! [SV14: a] :
      ( ( ( ( SV14 = cZ )
          | ( ( sK3_SY281
              @ ^ [SX0: a] : ( SX0 = cZ ) )
            = cZ ) )
        = $true )
      | ( ( ( sK3_SY281
            @ ^ [SX0: a] : ( SX0 = cZ ) )
          = cZ )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[231]) ).

thf(247,plain,
    ! [SV12: a] :
      ( ( ( ( cZ = SV12 )
          | ( ( cP
              @ ( sK2_Xx
                @ ^ [SX0: a] : ( SX0 != SV12 ) )
              @ ( sK3_SY281
                @ ^ [SX0: a] : ( SX0 != SV12 ) ) )
            = SV12 ) )
        = $true )
      | ( ( ( cP
            @ ( sK2_Xx
              @ ^ [SX0: a] : ( SX0 != SV12 ) )
            @ ( sK3_SY281
              @ ^ [SX0: a] : ( SX0 != SV12 ) ) )
          = SV12 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[233]) ).

thf(249,plain,
    ! [SV13: a] :
      ( ( ( ( SV13 = cZ )
          | ( ( sK2_Xx
              @ ^ [SX0: a] : ( SX0 = cZ ) )
            = cZ ) )
        = $true )
      | ( ( ( sK2_Xx
            @ ^ [SX0: a] : ( SX0 = cZ ) )
          = cZ )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[235]) ).

thf(251,plain,
    ! [SV14: a] :
      ( ( ( ( SV14 = cZ )
          | ( ( sK3_SY281
              @ ^ [SX0: a] : ( SX0 = cZ ) )
            = cZ ) )
        = $true )
      | ( ( ( sK3_SY281
            @ ^ [SX0: a] : ( SX0 = cZ ) )
          = cZ )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[237]) ).

thf(253,plain,
    ! [SV13: a] :
      ( ( ( SV13 = cZ )
        = $true )
      | ( ( ( sK2_Xx
            @ ^ [SX0: a] : ( SX0 = cZ ) )
          = cZ )
        = $true )
      | ( ( ( sK2_Xx
            @ ^ [SX0: a] : ( SX0 = cZ ) )
          = cZ )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[239]) ).

thf(255,plain,
    ! [SV14: a] :
      ( ( ( SV14 = cZ )
        = $true )
      | ( ( ( sK3_SY281
            @ ^ [SX0: a] : ( SX0 = cZ ) )
          = cZ )
        = $true )
      | ( ( ( sK3_SY281
            @ ^ [SX0: a] : ( SX0 = cZ ) )
          = cZ )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[241]) ).

thf(257,plain,
    ! [SV13: a] :
      ( ( ( SV13 = cZ )
        = $true )
      | ( ( ( sK2_Xx
            @ ^ [SX0: a] : ( SX0 = cZ ) )
          = cZ )
        = $true )
      | ( ( ( sK2_Xx
            @ ^ [SX0: a] : ( SX0 = cZ ) )
          = cZ )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[243]) ).

thf(259,plain,
    ! [SV14: a] :
      ( ( ( SV14 = cZ )
        = $true )
      | ( ( ( sK3_SY281
            @ ^ [SX0: a] : ( SX0 = cZ ) )
          = cZ )
        = $true )
      | ( ( ( sK3_SY281
            @ ^ [SX0: a] : ( SX0 = cZ ) )
          = cZ )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[245]) ).

thf(261,plain,
    ! [SV12: a] :
      ( ( ( cZ = SV12 )
        = $true )
      | ( ( ( cP
            @ ( sK2_Xx
              @ ^ [SX0: a] : ( SX0 != SV12 ) )
            @ ( sK3_SY281
              @ ^ [SX0: a] : ( SX0 != SV12 ) ) )
          = SV12 )
        = $true )
      | ( ( ( cP
            @ ( sK2_Xx
              @ ^ [SX0: a] : ( SX0 != SV12 ) )
            @ ( sK3_SY281
              @ ^ [SX0: a] : ( SX0 != SV12 ) ) )
          = SV12 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[247]) ).

thf(263,plain,
    ! [SV13: a] :
      ( ( ( SV13 = cZ )
        = $true )
      | ( ( ( sK2_Xx
            @ ^ [SX0: a] : ( SX0 = cZ ) )
          = cZ )
        = $true )
      | ( ( ( sK2_Xx
            @ ^ [SX0: a] : ( SX0 = cZ ) )
          = cZ )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[249]) ).

thf(265,plain,
    ! [SV14: a] :
      ( ( ( SV14 = cZ )
        = $true )
      | ( ( ( sK3_SY281
            @ ^ [SX0: a] : ( SX0 = cZ ) )
          = cZ )
        = $true )
      | ( ( ( sK3_SY281
            @ ^ [SX0: a] : ( SX0 = cZ ) )
          = cZ )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[251]) ).

thf(281,plain,
    ( ( ( ( sK2_Xx
          @ ^ [SX0: a] : ( SX0 = cZ ) )
        = cZ )
      = $true )
    | ( ( cZ
        = ( sK2_Xx
          @ ^ [SX0: a] : ( SX0 = cZ ) ) )
      = $false ) ),
    inference(extuni,[status(esa)],[212:[bind(SV13,$thf( cZ ))]]) ).

thf(282,plain,
    ( ( ( sK2_Xx
        @ ^ [SX0: a] : ( SX0 = cZ ) )
      = cZ )
    = $true ),
    inference(extuni,[status(esa)],[212:[bind(SV13,$thf( sK2_Xx @ ^ [SX0: a] : ( SX0 = cZ ) ))]]) ).

thf(283,plain,
    ( ( ( ( sK3_SY281
          @ ^ [SX0: a] : ( SX0 = cZ ) )
        = cZ )
      = $true )
    | ( ( cZ
        = ( sK3_SY281
          @ ^ [SX0: a] : ( SX0 = cZ ) ) )
      = $false ) ),
    inference(extuni,[status(esa)],[214:[bind(SV14,$thf( cZ ))]]) ).

thf(284,plain,
    ( ( ( sK3_SY281
        @ ^ [SX0: a] : ( SX0 = cZ ) )
      = cZ )
    = $true ),
    inference(extuni,[status(esa)],[214:[bind(SV14,$thf( sK3_SY281 @ ^ [SX0: a] : ( SX0 = cZ ) ))]]) ).

thf(285,plain,
    ( ( ( ( sK2_Xx
          @ ^ [SX0: a] : ( SX0 = cZ ) )
        = cZ )
      = $true )
    | ( ( cZ
        = ( sK2_Xx
          @ ^ [SX0: a] : ( SX0 = cZ ) ) )
      = $false ) ),
    inference(extuni,[status(esa)],[216:[bind(SV13,$thf( cZ ))]]) ).

thf(286,plain,
    ( ( ( sK2_Xx
        @ ^ [SX0: a] : ( SX0 = cZ ) )
      = cZ )
    = $true ),
    inference(extuni,[status(esa)],[216:[bind(SV13,$thf( sK2_Xx @ ^ [SX0: a] : ( SX0 = cZ ) ))]]) ).

thf(287,plain,
    ( ( ( ( sK3_SY281
          @ ^ [SX0: a] : ( SX0 = cZ ) )
        = cZ )
      = $true )
    | ( ( cZ
        = ( sK3_SY281
          @ ^ [SX0: a] : ( SX0 = cZ ) ) )
      = $false ) ),
    inference(extuni,[status(esa)],[218:[bind(SV14,$thf( cZ ))]]) ).

thf(288,plain,
    ( ( ( sK3_SY281
        @ ^ [SX0: a] : ( SX0 = cZ ) )
      = cZ )
    = $true ),
    inference(extuni,[status(esa)],[218:[bind(SV14,$thf( sK3_SY281 @ ^ [SX0: a] : ( SX0 = cZ ) ))]]) ).

thf(289,plain,
    ! [SV12: a] :
      ( ( ( ( cP
            @ ( sK2_Xx
              @ ^ [SX0: a] : ( SX0 != SV12 ) )
            @ ( sK3_SY281
              @ ^ [SX0: a] : ( SX0 != SV12 ) ) )
          = SV12 )
        = $true )
      | ( ( cZ
          = ( cP
            @ ( sK2_Xx
              @ ^ [SX0: a] : ( SX0 != SV12 ) )
            @ ( sK3_SY281
              @ ^ [SX0: a] : ( SX0 != SV12 ) ) ) )
        = $false ) ),
    inference(extuni,[status(esa)],[220]) ).

thf(290,plain,
    ( ( ( ( sK2_Xx
          @ ^ [SX0: a] : ( SX0 = cZ ) )
        = cZ )
      = $true )
    | ( ( cZ
        = ( sK2_Xx
          @ ^ [SX0: a] : ( SX0 = cZ ) ) )
      = $false ) ),
    inference(extuni,[status(esa)],[222:[bind(SV13,$thf( cZ ))]]) ).

thf(291,plain,
    ( ( ( sK2_Xx
        @ ^ [SX0: a] : ( SX0 = cZ ) )
      = cZ )
    = $true ),
    inference(extuni,[status(esa)],[222:[bind(SV13,$thf( sK2_Xx @ ^ [SX0: a] : ( SX0 = cZ ) ))]]) ).

thf(292,plain,
    ( ( ( ( sK3_SY281
          @ ^ [SX0: a] : ( SX0 = cZ ) )
        = cZ )
      = $true )
    | ( ( cZ
        = ( sK3_SY281
          @ ^ [SX0: a] : ( SX0 = cZ ) ) )
      = $false ) ),
    inference(extuni,[status(esa)],[224:[bind(SV14,$thf( cZ ))]]) ).

thf(293,plain,
    ( ( ( sK3_SY281
        @ ^ [SX0: a] : ( SX0 = cZ ) )
      = cZ )
    = $true ),
    inference(extuni,[status(esa)],[224:[bind(SV14,$thf( sK3_SY281 @ ^ [SX0: a] : ( SX0 = cZ ) ))]]) ).

thf(295,plain,
    ( ( cZ = sK1_Xx )
    = $false ),
    inference(extuni,[status(esa)],[129:[bind(SV30,$thf( SV28 ))]]) ).

thf(296,plain,
    ( ( sK1_Xx = cZ )
    = $false ),
    inference(extuni,[status(esa)],[131:[bind(SV30,$thf( SV28 ))]]) ).

thf(297,plain,
    ! [SV24: a,SV25: a] :
      ( ( cZ
        = ( cP @ SV25 @ SV24 ) )
      = $false ),
    inference(extuni,[status(esa)],[133:[bind(SV30,$thf( SV28 ))]]) ).

thf(298,plain,
    ! [SV24: a,SV25: a] :
      ( ( ( cP @ SV25 @ SV24 )
        = cZ )
      = $false ),
    inference(extuni,[status(esa)],[135:[bind(SV30,$thf( SV28 ))]]) ).

thf(299,plain,
    ! [SV26: a,SV27: a] :
      ( ( ( cP @ SV27 @ SV26 )
        = sK1_Xx )
      = $false ),
    inference(extuni,[status(esa)],[137:[bind(SV30,$thf( SV28 ))]]) ).

thf(300,plain,
    ! [SV26: a,SV27: a] :
      ( ( sK1_Xx
        = ( cP @ SV27 @ SV26 ) )
      = $false ),
    inference(extuni,[status(esa)],[139:[bind(SV30,$thf( SV28 ))]]) ).

thf(302,plain,
    ( ( cZ = sK1_Xx )
    = $false ),
    inference(extuni,[status(esa)],[150:[bind(SV35,$thf( SV33 ))]]) ).

thf(303,plain,
    ( ( sK1_Xx = cZ )
    = $false ),
    inference(extuni,[status(esa)],[152:[bind(SV35,$thf( SV33 ))]]) ).

thf(304,plain,
    ! [SV24: a,SV25: a] :
      ( ( cZ
        = ( cP @ SV25 @ SV24 ) )
      = $false ),
    inference(extuni,[status(esa)],[154:[bind(SV35,$thf( SV33 ))]]) ).

thf(305,plain,
    ! [SV24: a,SV25: a] :
      ( ( ( cP @ SV25 @ SV24 )
        = cZ )
      = $false ),
    inference(extuni,[status(esa)],[156:[bind(SV35,$thf( SV33 ))]]) ).

thf(306,plain,
    ! [SV26: a,SV27: a] :
      ( ( ( cP @ SV27 @ SV26 )
        = sK1_Xx )
      = $false ),
    inference(extuni,[status(esa)],[158:[bind(SV35,$thf( SV33 ))]]) ).

thf(307,plain,
    ! [SV26: a,SV27: a] :
      ( ( sK1_Xx
        = ( cP @ SV27 @ SV26 ) )
      = $false ),
    inference(extuni,[status(esa)],[160:[bind(SV35,$thf( SV33 ))]]) ).

thf(310,plain,
    ! [SV30: a,SV31: a,SV28: a,SV29: a] :
      ( ( ( ( cP @ SV29 @ SV28 )
          = ( cP @ SV31 @ SV30 ) )
        = $false )
      | ( ( SV31 = SV29 )
        = $true ) ),
    inference(extuni,[status(esa)],[163:[bind(SV35,$thf( SV33 ))]]) ).

thf(313,plain,
    ! [SV28: a,SV29: a,SV30: a,SV31: a] :
      ( ( ( ( cP @ SV31 @ SV30 )
          = ( cP @ SV29 @ SV28 ) )
        = $false )
      | ( ( SV31 = SV29 )
        = $true ) ),
    inference(extuni,[status(esa)],[166:[bind(SV35,$thf( SV33 ))]]) ).

thf(316,plain,
    ! [SV35: a,SV33: a,SV32: a,SV34: a] :
      ( ( ( SV34 = SV32 )
        = $true )
      | ( ( ( cP @ SV33 @ SV32 )
          = ( cP @ SV35 @ SV34 ) )
        = $false ) ),
    inference(extuni,[status(esa)],[169:[bind(SV30,$thf( SV28 ))]]) ).

thf(319,plain,
    ! [SV33: a,SV35: a,SV32: a,SV34: a] :
      ( ( ( SV34 = SV32 )
        = $true )
      | ( ( ( cP @ SV35 @ SV34 )
          = ( cP @ SV33 @ SV32 ) )
        = $false ) ),
    inference(extuni,[status(esa)],[172:[bind(SV30,$thf( SV28 ))]]) ).

thf(320,plain,
    ! [SV12: a,SV49: a > $o] :
      ( ( ( SV49 @ SV12 )
        = $false )
      | ( ( ~ ( SV49
              @ ( cP
                @ ( sK2_Xx
                  @ ^ [SX0: a] :
                      ~ ( SV49 @ SX0 ) )
                @ ( sK3_SY281
                  @ ^ [SX0: a] :
                      ~ ( SV49 @ SX0 ) ) ) ) )
        = $false )
      | ( ( ~ ( SV49 @ cZ ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[188]) ).

thf(321,plain,
    ! [SV13: a,SV49: a > $o] :
      ( ( ( SV49 @ SV13 )
        = $false )
      | ( ( ~ ( SV49
              @ ( sK2_Xx
                @ ^ [SX0: a] :
                    ~ ( SV49 @ SX0 ) ) ) )
        = $true )
      | ( ( ~ ( SV49 @ cZ ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[191]) ).

thf(322,plain,
    ! [SV14: a,SV49: a > $o] :
      ( ( ( SV49 @ SV14 )
        = $false )
      | ( ( ~ ( SV49
              @ ( sK3_SY281
                @ ^ [SX0: a] :
                    ~ ( SV49 @ SX0 ) ) ) )
        = $true )
      | ( ( ~ ( SV49 @ cZ ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[194]) ).

thf(323,plain,
    ! [SV12: a,SV43: a > $o] :
      ( ( ( SV43 @ cZ )
        = $false )
      | ( ( ~ ( SV43 @ SV12 ) )
        = $false )
      | ( ( ~ ( SV43
              @ ( cP
                @ ( sK2_Xx
                  @ ^ [SX0: a] :
                      ~ ~ ( SV43 @ SX0 ) )
                @ ( sK3_SY281
                  @ ^ [SX0: a] :
                      ~ ~ ( SV43 @ SX0 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[197]) ).

thf(324,plain,
    ! [SV13: a,SV43: a > $o] :
      ( ( ( SV43 @ cZ )
        = $false )
      | ( ( ~ ( SV43 @ SV13 ) )
        = $false )
      | ( ( ~ ( SV43
              @ ( sK2_Xx
                @ ^ [SX0: a] :
                    ~ ~ ( SV43 @ SX0 ) ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[200]) ).

thf(325,plain,
    ! [SV14: a,SV43: a > $o] :
      ( ( ( SV43 @ cZ )
        = $false )
      | ( ( ~ ( SV43 @ SV14 ) )
        = $false )
      | ( ( ~ ( SV43
              @ ( sK3_SY281
                @ ^ [SX0: a] :
                    ~ ~ ( SV43 @ SX0 ) ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[203]) ).

thf(326,plain,
    ! [SV12: a,SV49: a > $o] :
      ( ( ( SV49
          @ ( cP
            @ ( sK2_Xx
              @ ^ [SX0: a] :
                  ~ ( SV49 @ SX0 ) )
            @ ( sK3_SY281
              @ ^ [SX0: a] :
                  ~ ( SV49 @ SX0 ) ) ) )
        = $true )
      | ( ( SV49 @ SV12 )
        = $false )
      | ( ( ~ ( SV49 @ cZ ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[320]) ).

thf(327,plain,
    ! [SV13: a,SV49: a > $o] :
      ( ( ( SV49
          @ ( sK2_Xx
            @ ^ [SX0: a] :
                ~ ( SV49 @ SX0 ) ) )
        = $false )
      | ( ( SV49 @ SV13 )
        = $false )
      | ( ( ~ ( SV49 @ cZ ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[321]) ).

thf(328,plain,
    ! [SV14: a,SV49: a > $o] :
      ( ( ( SV49
          @ ( sK3_SY281
            @ ^ [SX0: a] :
                ~ ( SV49 @ SX0 ) ) )
        = $false )
      | ( ( SV49 @ SV14 )
        = $false )
      | ( ( ~ ( SV49 @ cZ ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[322]) ).

thf(329,plain,
    ! [SV12: a,SV43: a > $o] :
      ( ( ( SV43 @ SV12 )
        = $true )
      | ( ( SV43 @ cZ )
        = $false )
      | ( ( ~ ( SV43
              @ ( cP
                @ ( sK2_Xx
                  @ ^ [SX0: a] :
                      ~ ~ ( SV43 @ SX0 ) )
                @ ( sK3_SY281
                  @ ^ [SX0: a] :
                      ~ ~ ( SV43 @ SX0 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[323]) ).

thf(330,plain,
    ! [SV13: a,SV43: a > $o] :
      ( ( ( SV43 @ SV13 )
        = $true )
      | ( ( SV43 @ cZ )
        = $false )
      | ( ( ~ ( SV43
              @ ( sK2_Xx
                @ ^ [SX0: a] :
                    ~ ~ ( SV43 @ SX0 ) ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[324]) ).

thf(331,plain,
    ! [SV14: a,SV43: a > $o] :
      ( ( ( SV43 @ SV14 )
        = $true )
      | ( ( SV43 @ cZ )
        = $false )
      | ( ( ~ ( SV43
              @ ( sK3_SY281
                @ ^ [SX0: a] :
                    ~ ~ ( SV43 @ SX0 ) ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[325]) ).

thf(332,plain,
    ! [SV12: a,SV49: a > $o] :
      ( ( ( SV49 @ cZ )
        = $true )
      | ( ( SV49 @ SV12 )
        = $false )
      | ( ( SV49
          @ ( cP
            @ ( sK2_Xx
              @ ^ [SX0: a] :
                  ~ ( SV49 @ SX0 ) )
            @ ( sK3_SY281
              @ ^ [SX0: a] :
                  ~ ( SV49 @ SX0 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[326]) ).

thf(333,plain,
    ! [SV13: a,SV49: a > $o] :
      ( ( ( SV49 @ cZ )
        = $true )
      | ( ( SV49 @ SV13 )
        = $false )
      | ( ( SV49
          @ ( sK2_Xx
            @ ^ [SX0: a] :
                ~ ( SV49 @ SX0 ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[327]) ).

thf(334,plain,
    ! [SV14: a,SV49: a > $o] :
      ( ( ( SV49 @ cZ )
        = $true )
      | ( ( SV49 @ SV14 )
        = $false )
      | ( ( SV49
          @ ( sK3_SY281
            @ ^ [SX0: a] :
                ~ ( SV49 @ SX0 ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[328]) ).

thf(335,plain,
    ! [SV12: a,SV43: a > $o] :
      ( ( ( SV43
          @ ( cP
            @ ( sK2_Xx
              @ ^ [SX0: a] :
                  ~ ~ ( SV43 @ SX0 ) )
            @ ( sK3_SY281
              @ ^ [SX0: a] :
                  ~ ~ ( SV43 @ SX0 ) ) ) )
        = $false )
      | ( ( SV43 @ cZ )
        = $false )
      | ( ( SV43 @ SV12 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[329]) ).

thf(336,plain,
    ! [SV13: a,SV43: a > $o] :
      ( ( ( SV43
          @ ( sK2_Xx
            @ ^ [SX0: a] :
                ~ ~ ( SV43 @ SX0 ) ) )
        = $true )
      | ( ( SV43 @ cZ )
        = $false )
      | ( ( SV43 @ SV13 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[330]) ).

thf(337,plain,
    ! [SV14: a,SV43: a > $o] :
      ( ( ( SV43
          @ ( sK3_SY281
            @ ^ [SX0: a] :
                ~ ~ ( SV43 @ SX0 ) ) )
        = $true )
      | ( ( SV43 @ cZ )
        = $false )
      | ( ( SV43 @ SV14 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[331]) ).

thf(338,plain,
    ! [SV13: a] :
      ( ( ( SV13 = cZ )
        = $true )
      | ( ( ( sK2_Xx
            @ ^ [SX0: a] : ( SX0 = cZ ) )
          = cZ )
        = $true ) ),
    inference(sim,[status(thm)],[253]) ).

thf(339,plain,
    ! [SV14: a] :
      ( ( ( SV14 = cZ )
        = $true )
      | ( ( ( sK3_SY281
            @ ^ [SX0: a] : ( SX0 = cZ ) )
          = cZ )
        = $true ) ),
    inference(sim,[status(thm)],[255]) ).

thf(340,plain,
    ! [SV13: a] :
      ( ( ( SV13 = cZ )
        = $true )
      | ( ( ( sK2_Xx
            @ ^ [SX0: a] : ( SX0 = cZ ) )
          = cZ )
        = $true ) ),
    inference(sim,[status(thm)],[257]) ).

thf(341,plain,
    ! [SV14: a] :
      ( ( ( SV14 = cZ )
        = $true )
      | ( ( ( sK3_SY281
            @ ^ [SX0: a] : ( SX0 = cZ ) )
          = cZ )
        = $true ) ),
    inference(sim,[status(thm)],[259]) ).

thf(342,plain,
    ! [SV12: a] :
      ( ( ( cZ = SV12 )
        = $true )
      | ( ( ( cP
            @ ( sK2_Xx
              @ ^ [SX0: a] : ( SX0 != SV12 ) )
            @ ( sK3_SY281
              @ ^ [SX0: a] : ( SX0 != SV12 ) ) )
          = SV12 )
        = $true ) ),
    inference(sim,[status(thm)],[261]) ).

thf(343,plain,
    ! [SV13: a] :
      ( ( ( SV13 = cZ )
        = $true )
      | ( ( ( sK2_Xx
            @ ^ [SX0: a] : ( SX0 = cZ ) )
          = cZ )
        = $true ) ),
    inference(sim,[status(thm)],[263]) ).

thf(344,plain,
    ! [SV14: a] :
      ( ( ( SV14 = cZ )
        = $true )
      | ( ( ( sK3_SY281
            @ ^ [SX0: a] : ( SX0 = cZ ) )
          = cZ )
        = $true ) ),
    inference(sim,[status(thm)],[265]) ).

thf(345,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[36,344,343,342,341,340,339,338,337,336,335,334,333,332,319,316,313,310,307,306,305,304,303,302,300,299,298,297,296,295,293,292,291,290,289,288,287,286,285,284,283,282,281,185,183,181,179,177,175,172,171,169,168,166,165,163,162,160,159,158,157,156,155,154,153,152,151,150,149,141,139,138,137,136,135,134,133,132,131,130,129,128,122,121,120,119,118,117,116,115,106,105,104,103,71,69,67,65,64,61]) ).

thf(346,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[345]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SEV195^5 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.34  % Computer : n018.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Mon Jun 27 21:48:58 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.35  
% 0.12/0.35   No.of.Axioms: 0
% 0.12/0.35  
% 0.12/0.35   Length.of.Defs: 0
% 0.12/0.35  
% 0.12/0.35   Contains.Choice.Funs: false
% 0.12/0.35  (rf:0,axioms:0,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2,loop_count:0,foatp_calls:0,translation:fof_full).......
% 1.46/1.63  
% 1.46/1.63   Prim_subst applied to clause 
% 1.46/1.63   
% 1.46/1.63  183:[ 0:<SV37@SV36 = $true>-w(1)-i() 1:<SV37@((cP@(sK2_Xx@SV37))@(sK3_SY15@SV37)) = $false>-w(1)-i() 2:<SV37@cZ = $false>-w(1)-i() ]-mln(3)-w(3)-i(rename 62)-o(AXIOM)-fv([ SV36 SV37 ])
% 1.46/1.68  
% 1.46/1.68   Prim_subst applied to clause 
% 1.46/1.68   
% 1.46/1.68  183:[ 0:<SV37@SV36 = $true>-w(1)-i() 1:<SV37@((cP@(sK2_Xx@SV37))@(sK3_SY15@SV37)) = $false>-w(1)-i() 2:<SV37@cZ = $false>-w(1)-i() ]-mln(3)-w(3)-i(rename 62)-o(AXIOM)-fv([ SV36 SV37 ])
% 1.52/1.73  
% 1.52/1.73   Prim_subst applied to clause 
% 1.52/1.73   
% 1.52/1.73  183:[ 0:<SV37@SV36 = $true>-w(1)-i() 1:<SV37@((cP@(sK2_Xx@SV37))@(sK3_SY15@SV37)) = $false>-w(1)-i() 2:<SV37@cZ = $false>-w(1)-i() ]-mln(3)-w(3)-i(rename 62)-o(AXIOM)-fv([ SV36 SV37 ])
% 1.96/2.19  .......
% 75.24/75.50  (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)...........
% 77.11/77.36  
% 77.11/77.36  ********************************
% 77.11/77.36  *   All subproblems solved!    *
% 77.11/77.36  ********************************
% 77.11/77.36  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:3,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:345,loop_count:5,foatp_calls:4,translation:fof_full)
% 77.20/77.41  
% 77.20/77.41  %**** Beginning of derivation protocol ****
% 77.20/77.41  % SZS output start CNFRefutation
% See solution above
% 77.20/77.41  
% 77.20/77.41  %**** End of derivation protocol ****
% 77.20/77.41  %**** no. of clauses in derivation: 261 ****
% 77.20/77.41  %**** clause counter: 345 ****
% 77.20/77.41  
% 77.20/77.41  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:3,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:345,loop_count:5,foatp_calls:4,translation:fof_full)
%------------------------------------------------------------------------------