TSTP Solution File: SEU997^5 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SEU997^5 : 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 : n025.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 12:16:01 EDT 2022

% Result   : Theorem 0.40s 0.81s
% Output   : CNFRefutation 0.40s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   25
%            Number of leaves      :   10
% Syntax   : Number of formulae    :  108 (  98 unt;   9 typ;   0 def)
%            Number of atoms       :  481 ( 382 equ;   0 cnn)
%            Maximal formula atoms :   21 (   4 avg)
%            Number of connectives : 1263 (  99   ~;  29   |; 143   &; 976   @)
%                                         (   0 <=>;  16  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   23 (   2 avg)
%            Number of types       :    1 (   1 usr)
%            Number of type conns  :   19 (  19   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   11 (   8 usr;   7 con; 0-2 aty)
%            Number of variables   :  362 (   0   ^ 354   !;   8   ?; 362   :)

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

thf(tp_sK1_JOIN,type,
    sK1_JOIN: a > a > a ).

thf(tp_sK2_SY35,type,
    sK2_SY35: a > a > a ).

thf(tp_sK3_SY69,type,
    sK3_SY69: a ).

thf(tp_sK4_SY102,type,
    sK4_SY102: a ).

thf(tp_sK5_SY162,type,
    sK5_SY162: a ).

thf(tp_sK6_SY165,type,
    sK6_SY165: a ).

thf(tp_sK7_SY167,type,
    sK7_SY167: a ).

thf(tp_sK8_SY161,type,
    sK8_SY161: a > a ).

thf(1,conjecture,
    ! [JOIN: a > a > a,MEET: a > a > a,TOP: a,BOTTOM: a] :
      ( ( ! [Xx: a] :
            ( ( JOIN @ Xx @ Xx )
            = Xx )
        & ! [Xx: a] :
            ( ( MEET @ Xx @ Xx )
            = Xx )
        & ! [Xx: a,Xy: a,Xz: a] :
            ( ( JOIN @ ( JOIN @ Xx @ Xy ) @ Xz )
            = ( JOIN @ Xx @ ( JOIN @ Xy @ Xz ) ) )
        & ! [Xx: a,Xy: a,Xz: a] :
            ( ( MEET @ ( MEET @ Xx @ Xy ) @ Xz )
            = ( MEET @ Xx @ ( MEET @ Xy @ Xz ) ) )
        & ! [Xx: a,Xy: a] :
            ( ( JOIN @ Xx @ Xy )
            = ( JOIN @ Xy @ Xx ) )
        & ! [Xx: a,Xy: a] :
            ( ( MEET @ Xx @ Xy )
            = ( MEET @ Xy @ Xx ) )
        & ! [Xx: a,Xy: a] :
            ( ( JOIN @ ( MEET @ Xx @ Xy ) @ Xy )
            = Xy )
        & ! [Xx: a,Xy: a] :
            ( ( MEET @ ( JOIN @ Xx @ Xy ) @ Xy )
            = Xy )
        & ! [Xx: a,Xy: a,Xz: a] :
            ( ( MEET @ Xx @ ( JOIN @ Xy @ Xz ) )
            = ( JOIN @ ( MEET @ Xx @ Xy ) @ ( MEET @ Xx @ Xz ) ) )
        & ! [Xx: a,Xy: a,Xz: a] :
            ( ( JOIN @ Xx @ ( MEET @ Xy @ Xz ) )
            = ( MEET @ ( JOIN @ Xx @ Xy ) @ ( JOIN @ Xx @ Xz ) ) )
        & ! [Xx: a] :
            ( ( MEET @ TOP @ Xx )
            = Xx )
        & ! [Xx: a] :
            ( ( JOIN @ TOP @ Xx )
            = TOP )
        & ! [Xx: a] :
            ( ( MEET @ BOTTOM @ Xx )
            = BOTTOM )
        & ! [Xx: a] :
            ( ( JOIN @ BOTTOM @ Xx )
            = Xx )
        & ! [Xx: a] :
          ? [Xy: a] :
            ( ( ( JOIN @ Xx @ Xy )
              = TOP )
            & ( ( MEET @ Xx @ Xy )
              = BOTTOM ) ) )
     => ! [Xx: a,Xy: a,Xz: a] :
          ( ( ( ( JOIN @ Xx @ Xy )
              = TOP )
            & ( ( MEET @ Xx @ Xy )
              = BOTTOM )
            & ( ( JOIN @ Xx @ Xz )
              = TOP )
            & ( ( MEET @ Xx @ Xz )
              = BOTTOM ) )
         => ( Xy = Xz ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cCD_LATTICE_THM_pme) ).

thf(2,negated_conjecture,
    ( ( ! [JOIN: a > a > a,MEET: a > a > a,TOP: a,BOTTOM: a] :
          ( ( ! [Xx: a] :
                ( ( JOIN @ Xx @ Xx )
                = Xx )
            & ! [Xx: a] :
                ( ( MEET @ Xx @ Xx )
                = Xx )
            & ! [Xx: a,Xy: a,Xz: a] :
                ( ( JOIN @ ( JOIN @ Xx @ Xy ) @ Xz )
                = ( JOIN @ Xx @ ( JOIN @ Xy @ Xz ) ) )
            & ! [Xx: a,Xy: a,Xz: a] :
                ( ( MEET @ ( MEET @ Xx @ Xy ) @ Xz )
                = ( MEET @ Xx @ ( MEET @ Xy @ Xz ) ) )
            & ! [Xx: a,Xy: a] :
                ( ( JOIN @ Xx @ Xy )
                = ( JOIN @ Xy @ Xx ) )
            & ! [Xx: a,Xy: a] :
                ( ( MEET @ Xx @ Xy )
                = ( MEET @ Xy @ Xx ) )
            & ! [Xx: a,Xy: a] :
                ( ( JOIN @ ( MEET @ Xx @ Xy ) @ Xy )
                = Xy )
            & ! [Xx: a,Xy: a] :
                ( ( MEET @ ( JOIN @ Xx @ Xy ) @ Xy )
                = Xy )
            & ! [Xx: a,Xy: a,Xz: a] :
                ( ( MEET @ Xx @ ( JOIN @ Xy @ Xz ) )
                = ( JOIN @ ( MEET @ Xx @ Xy ) @ ( MEET @ Xx @ Xz ) ) )
            & ! [Xx: a,Xy: a,Xz: a] :
                ( ( JOIN @ Xx @ ( MEET @ Xy @ Xz ) )
                = ( MEET @ ( JOIN @ Xx @ Xy ) @ ( JOIN @ Xx @ Xz ) ) )
            & ! [Xx: a] :
                ( ( MEET @ TOP @ Xx )
                = Xx )
            & ! [Xx: a] :
                ( ( JOIN @ TOP @ Xx )
                = TOP )
            & ! [Xx: a] :
                ( ( MEET @ BOTTOM @ Xx )
                = BOTTOM )
            & ! [Xx: a] :
                ( ( JOIN @ BOTTOM @ Xx )
                = Xx )
            & ! [Xx: a] :
              ? [Xy: a] :
                ( ( ( JOIN @ Xx @ Xy )
                  = TOP )
                & ( ( MEET @ Xx @ Xy )
                  = BOTTOM ) ) )
         => ! [Xx: a,Xy: a,Xz: a] :
              ( ( ( ( JOIN @ Xx @ Xy )
                  = TOP )
                & ( ( MEET @ Xx @ Xy )
                  = BOTTOM )
                & ( ( JOIN @ Xx @ Xz )
                  = TOP )
                & ( ( MEET @ Xx @ Xz )
                  = BOTTOM ) )
             => ( Xy = Xz ) ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ( ( ! [JOIN: a > a > a,MEET: a > a > a,TOP: a,BOTTOM: a] :
          ( ( ! [Xx: a] :
                ( ( JOIN @ Xx @ Xx )
                = Xx )
            & ! [Xx: a] :
                ( ( MEET @ Xx @ Xx )
                = Xx )
            & ! [Xx: a,Xy: a,Xz: a] :
                ( ( JOIN @ ( JOIN @ Xx @ Xy ) @ Xz )
                = ( JOIN @ Xx @ ( JOIN @ Xy @ Xz ) ) )
            & ! [Xx: a,Xy: a,Xz: a] :
                ( ( MEET @ ( MEET @ Xx @ Xy ) @ Xz )
                = ( MEET @ Xx @ ( MEET @ Xy @ Xz ) ) )
            & ! [Xx: a,Xy: a] :
                ( ( JOIN @ Xx @ Xy )
                = ( JOIN @ Xy @ Xx ) )
            & ! [Xx: a,Xy: a] :
                ( ( MEET @ Xx @ Xy )
                = ( MEET @ Xy @ Xx ) )
            & ! [Xx: a,Xy: a] :
                ( ( JOIN @ ( MEET @ Xx @ Xy ) @ Xy )
                = Xy )
            & ! [Xx: a,Xy: a] :
                ( ( MEET @ ( JOIN @ Xx @ Xy ) @ Xy )
                = Xy )
            & ! [Xx: a,Xy: a,Xz: a] :
                ( ( MEET @ Xx @ ( JOIN @ Xy @ Xz ) )
                = ( JOIN @ ( MEET @ Xx @ Xy ) @ ( MEET @ Xx @ Xz ) ) )
            & ! [Xx: a,Xy: a,Xz: a] :
                ( ( JOIN @ Xx @ ( MEET @ Xy @ Xz ) )
                = ( MEET @ ( JOIN @ Xx @ Xy ) @ ( JOIN @ Xx @ Xz ) ) )
            & ! [Xx: a] :
                ( ( MEET @ TOP @ Xx )
                = Xx )
            & ! [Xx: a] :
                ( ( JOIN @ TOP @ Xx )
                = TOP )
            & ! [Xx: a] :
                ( ( MEET @ BOTTOM @ Xx )
                = BOTTOM )
            & ! [Xx: a] :
                ( ( JOIN @ BOTTOM @ Xx )
                = Xx )
            & ! [Xx: a] :
              ? [Xy: a] :
                ( ( ( JOIN @ Xx @ Xy )
                  = TOP )
                & ( ( MEET @ Xx @ Xy )
                  = BOTTOM ) ) )
         => ! [Xx: a,Xy: a,Xz: a] :
              ( ( ( ( JOIN @ Xx @ Xy )
                  = TOP )
                & ( ( MEET @ Xx @ Xy )
                  = BOTTOM )
                & ( ( JOIN @ Xx @ Xz )
                  = TOP )
                & ( ( MEET @ Xx @ Xz )
                  = BOTTOM ) )
             => ( Xy = Xz ) ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(4,plain,
    ( ( ! [SY35: a > a > a,SY36: a,SY37: a] :
          ( ( ! [SY38: a] :
                ( ( sK1_JOIN @ SY38 @ SY38 )
                = SY38 )
            & ! [Xx: a] :
                ( ( SY35 @ Xx @ Xx )
                = Xx )
            & ! [SY40: a,SY41: a,SY42: a] :
                ( ( sK1_JOIN @ ( sK1_JOIN @ SY40 @ SY41 ) @ SY42 )
                = ( sK1_JOIN @ SY40 @ ( sK1_JOIN @ SY41 @ SY42 ) ) )
            & ! [Xx: a,Xy: a,Xz: a] :
                ( ( SY35 @ ( SY35 @ Xx @ Xy ) @ Xz )
                = ( SY35 @ Xx @ ( SY35 @ Xy @ Xz ) ) )
            & ! [SY46: a,SY47: a] :
                ( ( sK1_JOIN @ SY46 @ SY47 )
                = ( sK1_JOIN @ SY47 @ SY46 ) )
            & ! [Xx: a,Xy: a] :
                ( ( SY35 @ Xx @ Xy )
                = ( SY35 @ Xy @ Xx ) )
            & ! [SY50: a,SY51: a] :
                ( ( sK1_JOIN @ ( SY35 @ SY50 @ SY51 ) @ SY51 )
                = SY51 )
            & ! [SY52: a,SY53: a] :
                ( ( SY35 @ ( sK1_JOIN @ SY52 @ SY53 ) @ SY53 )
                = SY53 )
            & ! [SY54: a,SY55: a,SY56: a] :
                ( ( SY35 @ SY54 @ ( sK1_JOIN @ SY55 @ SY56 ) )
                = ( sK1_JOIN @ ( SY35 @ SY54 @ SY55 ) @ ( SY35 @ SY54 @ SY56 ) ) )
            & ! [SY57: a,SY58: a,SY59: a] :
                ( ( sK1_JOIN @ SY57 @ ( SY35 @ SY58 @ SY59 ) )
                = ( SY35 @ ( sK1_JOIN @ SY57 @ SY58 ) @ ( sK1_JOIN @ SY57 @ SY59 ) ) )
            & ! [Xx: a] :
                ( ( SY35 @ SY36 @ Xx )
                = Xx )
            & ! [SY61: a] :
                ( ( sK1_JOIN @ SY36 @ SY61 )
                = SY36 )
            & ! [Xx: a] :
                ( ( SY35 @ SY37 @ Xx )
                = SY37 )
            & ! [SY63: a] :
                ( ( sK1_JOIN @ SY37 @ SY63 )
                = SY63 )
            & ! [SY64: a] :
              ? [SY65: a] :
                ( ( ( sK1_JOIN @ SY64 @ SY65 )
                  = SY36 )
                & ( ( SY35 @ SY64 @ SY65 )
                  = SY37 ) ) )
         => ! [SY66: a,SY67: a,SY68: a] :
              ( ( ( ( sK1_JOIN @ SY66 @ SY67 )
                  = SY36 )
                & ( ( SY35 @ SY66 @ SY67 )
                  = SY37 )
                & ( ( sK1_JOIN @ SY66 @ SY68 )
                  = SY36 )
                & ( ( SY35 @ SY66 @ SY68 )
                  = SY37 ) )
             => ( SY67 = SY68 ) ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[3]) ).

thf(5,plain,
    ( ( ! [SY69: a,SY70: a] :
          ( ( ! [SY38: a] :
                ( ( sK1_JOIN @ SY38 @ SY38 )
                = SY38 )
            & ! [SY72: a] :
                ( ( sK2_SY35 @ SY72 @ SY72 )
                = SY72 )
            & ! [SY40: a,SY41: a,SY42: a] :
                ( ( sK1_JOIN @ ( sK1_JOIN @ SY40 @ SY41 ) @ SY42 )
                = ( sK1_JOIN @ SY40 @ ( sK1_JOIN @ SY41 @ SY42 ) ) )
            & ! [SY76: a,SY77: a,SY78: a] :
                ( ( sK2_SY35 @ ( sK2_SY35 @ SY76 @ SY77 ) @ SY78 )
                = ( sK2_SY35 @ SY76 @ ( sK2_SY35 @ SY77 @ SY78 ) ) )
            & ! [SY46: a,SY47: a] :
                ( ( sK1_JOIN @ SY46 @ SY47 )
                = ( sK1_JOIN @ SY47 @ SY46 ) )
            & ! [SY81: a,SY82: a] :
                ( ( sK2_SY35 @ SY81 @ SY82 )
                = ( sK2_SY35 @ SY82 @ SY81 ) )
            & ! [SY83: a,SY84: a] :
                ( ( sK1_JOIN @ ( sK2_SY35 @ SY83 @ SY84 ) @ SY84 )
                = SY84 )
            & ! [SY85: a,SY86: a] :
                ( ( sK2_SY35 @ ( sK1_JOIN @ SY85 @ SY86 ) @ SY86 )
                = SY86 )
            & ! [SY87: a,SY88: a,SY89: a] :
                ( ( sK2_SY35 @ SY87 @ ( sK1_JOIN @ SY88 @ SY89 ) )
                = ( sK1_JOIN @ ( sK2_SY35 @ SY87 @ SY88 ) @ ( sK2_SY35 @ SY87 @ SY89 ) ) )
            & ! [SY90: a,SY91: a,SY92: a] :
                ( ( sK1_JOIN @ SY90 @ ( sK2_SY35 @ SY91 @ SY92 ) )
                = ( sK2_SY35 @ ( sK1_JOIN @ SY90 @ SY91 ) @ ( sK1_JOIN @ SY90 @ SY92 ) ) )
            & ! [SY93: a] :
                ( ( sK2_SY35 @ SY69 @ SY93 )
                = SY93 )
            & ! [SY61: a] :
                ( ( sK1_JOIN @ SY69 @ SY61 )
                = SY69 )
            & ! [SY95: a] :
                ( ( sK2_SY35 @ SY70 @ SY95 )
                = SY70 )
            & ! [SY63: a] :
                ( ( sK1_JOIN @ SY70 @ SY63 )
                = SY63 )
            & ! [SY97: a] :
              ? [SY98: a] :
                ( ( ( sK1_JOIN @ SY97 @ SY98 )
                  = SY69 )
                & ( ( sK2_SY35 @ SY97 @ SY98 )
                  = SY70 ) ) )
         => ! [SY99: a,SY100: a,SY101: a] :
              ( ( ( ( sK1_JOIN @ SY99 @ SY100 )
                  = SY69 )
                & ( ( sK2_SY35 @ SY99 @ SY100 )
                  = SY70 )
                & ( ( sK1_JOIN @ SY99 @ SY101 )
                  = SY69 )
                & ( ( sK2_SY35 @ SY99 @ SY101 )
                  = SY70 ) )
             => ( SY100 = SY101 ) ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[4]) ).

thf(6,plain,
    ( ( ! [SY102: a] :
          ( ( ! [SY38: a] :
                ( ( sK1_JOIN @ SY38 @ SY38 )
                = SY38 )
            & ! [SY72: a] :
                ( ( sK2_SY35 @ SY72 @ SY72 )
                = SY72 )
            & ! [SY40: a,SY41: a,SY42: a] :
                ( ( sK1_JOIN @ ( sK1_JOIN @ SY40 @ SY41 ) @ SY42 )
                = ( sK1_JOIN @ SY40 @ ( sK1_JOIN @ SY41 @ SY42 ) ) )
            & ! [SY76: a,SY77: a,SY78: a] :
                ( ( sK2_SY35 @ ( sK2_SY35 @ SY76 @ SY77 ) @ SY78 )
                = ( sK2_SY35 @ SY76 @ ( sK2_SY35 @ SY77 @ SY78 ) ) )
            & ! [SY46: a,SY47: a] :
                ( ( sK1_JOIN @ SY46 @ SY47 )
                = ( sK1_JOIN @ SY47 @ SY46 ) )
            & ! [SY81: a,SY82: a] :
                ( ( sK2_SY35 @ SY81 @ SY82 )
                = ( sK2_SY35 @ SY82 @ SY81 ) )
            & ! [SY83: a,SY84: a] :
                ( ( sK1_JOIN @ ( sK2_SY35 @ SY83 @ SY84 ) @ SY84 )
                = SY84 )
            & ! [SY85: a,SY86: a] :
                ( ( sK2_SY35 @ ( sK1_JOIN @ SY85 @ SY86 ) @ SY86 )
                = SY86 )
            & ! [SY87: a,SY88: a,SY89: a] :
                ( ( sK2_SY35 @ SY87 @ ( sK1_JOIN @ SY88 @ SY89 ) )
                = ( sK1_JOIN @ ( sK2_SY35 @ SY87 @ SY88 ) @ ( sK2_SY35 @ SY87 @ SY89 ) ) )
            & ! [SY90: a,SY91: a,SY92: a] :
                ( ( sK1_JOIN @ SY90 @ ( sK2_SY35 @ SY91 @ SY92 ) )
                = ( sK2_SY35 @ ( sK1_JOIN @ SY90 @ SY91 ) @ ( sK1_JOIN @ SY90 @ SY92 ) ) )
            & ! [SY125: a] :
                ( ( sK2_SY35 @ sK3_SY69 @ SY125 )
                = SY125 )
            & ! [SY126: a] :
                ( ( sK1_JOIN @ sK3_SY69 @ SY126 )
                = sK3_SY69 )
            & ! [SY95: a] :
                ( ( sK2_SY35 @ SY102 @ SY95 )
                = SY102 )
            & ! [SY63: a] :
                ( ( sK1_JOIN @ SY102 @ SY63 )
                = SY63 )
            & ! [SY129: a] :
              ? [SY130: a] :
                ( ( ( sK1_JOIN @ SY129 @ SY130 )
                  = sK3_SY69 )
                & ( ( sK2_SY35 @ SY129 @ SY130 )
                  = SY102 ) ) )
         => ! [SY131: a,SY132: a,SY133: a] :
              ( ( ( ( sK1_JOIN @ SY131 @ SY132 )
                  = sK3_SY69 )
                & ( ( sK2_SY35 @ SY131 @ SY132 )
                  = SY102 )
                & ( ( sK1_JOIN @ SY131 @ SY133 )
                  = sK3_SY69 )
                & ( ( sK2_SY35 @ SY131 @ SY133 )
                  = SY102 ) )
             => ( SY132 = SY133 ) ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[5]) ).

thf(7,plain,
    ( ( ( ! [SY38: a] :
            ( ( sK1_JOIN @ SY38 @ SY38 )
            = SY38 )
        & ! [SY72: a] :
            ( ( sK2_SY35 @ SY72 @ SY72 )
            = SY72 )
        & ! [SY40: a,SY41: a,SY42: a] :
            ( ( sK1_JOIN @ ( sK1_JOIN @ SY40 @ SY41 ) @ SY42 )
            = ( sK1_JOIN @ SY40 @ ( sK1_JOIN @ SY41 @ SY42 ) ) )
        & ! [SY76: a,SY77: a,SY78: a] :
            ( ( sK2_SY35 @ ( sK2_SY35 @ SY76 @ SY77 ) @ SY78 )
            = ( sK2_SY35 @ SY76 @ ( sK2_SY35 @ SY77 @ SY78 ) ) )
        & ! [SY46: a,SY47: a] :
            ( ( sK1_JOIN @ SY46 @ SY47 )
            = ( sK1_JOIN @ SY47 @ SY46 ) )
        & ! [SY81: a,SY82: a] :
            ( ( sK2_SY35 @ SY81 @ SY82 )
            = ( sK2_SY35 @ SY82 @ SY81 ) )
        & ! [SY83: a,SY84: a] :
            ( ( sK1_JOIN @ ( sK2_SY35 @ SY83 @ SY84 ) @ SY84 )
            = SY84 )
        & ! [SY85: a,SY86: a] :
            ( ( sK2_SY35 @ ( sK1_JOIN @ SY85 @ SY86 ) @ SY86 )
            = SY86 )
        & ! [SY87: a,SY88: a,SY89: a] :
            ( ( sK2_SY35 @ SY87 @ ( sK1_JOIN @ SY88 @ SY89 ) )
            = ( sK1_JOIN @ ( sK2_SY35 @ SY87 @ SY88 ) @ ( sK2_SY35 @ SY87 @ SY89 ) ) )
        & ! [SY90: a,SY91: a,SY92: a] :
            ( ( sK1_JOIN @ SY90 @ ( sK2_SY35 @ SY91 @ SY92 ) )
            = ( sK2_SY35 @ ( sK1_JOIN @ SY90 @ SY91 ) @ ( sK1_JOIN @ SY90 @ SY92 ) ) )
        & ! [SY125: a] :
            ( ( sK2_SY35 @ sK3_SY69 @ SY125 )
            = SY125 )
        & ! [SY126: a] :
            ( ( sK1_JOIN @ sK3_SY69 @ SY126 )
            = sK3_SY69 )
        & ! [SY158: a] :
            ( ( sK2_SY35 @ sK4_SY102 @ SY158 )
            = sK4_SY102 )
        & ! [SY159: a] :
            ( ( sK1_JOIN @ sK4_SY102 @ SY159 )
            = SY159 )
        & ! [SY160: a] :
          ? [SY161: a] :
            ( ( ( sK1_JOIN @ SY160 @ SY161 )
              = sK3_SY69 )
            & ( ( sK2_SY35 @ SY160 @ SY161 )
              = sK4_SY102 ) ) )
     => ! [SY162: a,SY163: a,SY164: a] :
          ( ( ( ( sK1_JOIN @ SY162 @ SY163 )
              = sK3_SY69 )
            & ( ( sK2_SY35 @ SY162 @ SY163 )
              = sK4_SY102 )
            & ( ( sK1_JOIN @ SY162 @ SY164 )
              = sK3_SY69 )
            & ( ( sK2_SY35 @ SY162 @ SY164 )
              = sK4_SY102 ) )
         => ( SY163 = SY164 ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[6]) ).

thf(8,plain,
    ( ( ! [SY38: a] :
          ( ( sK1_JOIN @ SY38 @ SY38 )
          = SY38 ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[7]) ).

thf(9,plain,
    ( ( ! [SY72: a] :
          ( ( sK2_SY35 @ SY72 @ SY72 )
          = SY72 ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[7]) ).

thf(10,plain,
    ( ( ! [SY40: a,SY41: a,SY42: a] :
          ( ( sK1_JOIN @ ( sK1_JOIN @ SY40 @ SY41 ) @ SY42 )
          = ( sK1_JOIN @ SY40 @ ( sK1_JOIN @ SY41 @ SY42 ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[7]) ).

thf(11,plain,
    ( ( ! [SY76: a,SY77: a,SY78: a] :
          ( ( sK2_SY35 @ ( sK2_SY35 @ SY76 @ SY77 ) @ SY78 )
          = ( sK2_SY35 @ SY76 @ ( sK2_SY35 @ SY77 @ SY78 ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[7]) ).

thf(12,plain,
    ( ( ! [SY46: a,SY47: a] :
          ( ( sK1_JOIN @ SY46 @ SY47 )
          = ( sK1_JOIN @ SY47 @ SY46 ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[7]) ).

thf(13,plain,
    ( ( ! [SY81: a,SY82: a] :
          ( ( sK2_SY35 @ SY81 @ SY82 )
          = ( sK2_SY35 @ SY82 @ SY81 ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[7]) ).

thf(14,plain,
    ( ( ! [SY83: a,SY84: a] :
          ( ( sK1_JOIN @ ( sK2_SY35 @ SY83 @ SY84 ) @ SY84 )
          = SY84 ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[7]) ).

thf(15,plain,
    ( ( ! [SY85: a,SY86: a] :
          ( ( sK2_SY35 @ ( sK1_JOIN @ SY85 @ SY86 ) @ SY86 )
          = SY86 ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[7]) ).

thf(16,plain,
    ( ( ! [SY87: a,SY88: a,SY89: a] :
          ( ( sK2_SY35 @ SY87 @ ( sK1_JOIN @ SY88 @ SY89 ) )
          = ( sK1_JOIN @ ( sK2_SY35 @ SY87 @ SY88 ) @ ( sK2_SY35 @ SY87 @ SY89 ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[7]) ).

thf(17,plain,
    ( ( ! [SY90: a,SY91: a,SY92: a] :
          ( ( sK1_JOIN @ SY90 @ ( sK2_SY35 @ SY91 @ SY92 ) )
          = ( sK2_SY35 @ ( sK1_JOIN @ SY90 @ SY91 ) @ ( sK1_JOIN @ SY90 @ SY92 ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[7]) ).

thf(18,plain,
    ( ( ! [SY125: a] :
          ( ( sK2_SY35 @ sK3_SY69 @ SY125 )
          = SY125 ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[7]) ).

thf(19,plain,
    ( ( ! [SY126: a] :
          ( ( sK1_JOIN @ sK3_SY69 @ SY126 )
          = sK3_SY69 ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[7]) ).

thf(20,plain,
    ( ( ! [SY158: a] :
          ( ( sK2_SY35 @ sK4_SY102 @ SY158 )
          = sK4_SY102 ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[7]) ).

thf(21,plain,
    ( ( ! [SY159: a] :
          ( ( sK1_JOIN @ sK4_SY102 @ SY159 )
          = SY159 ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[7]) ).

thf(22,plain,
    ( ( ! [SY160: a] :
        ? [SY161: a] :
          ( ( ( sK1_JOIN @ SY160 @ SY161 )
            = sK3_SY69 )
          & ( ( sK2_SY35 @ SY160 @ SY161 )
            = sK4_SY102 ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[7]) ).

thf(23,plain,
    ( ( ! [SY162: a,SY163: a,SY164: a] :
          ( ( ( ( sK1_JOIN @ SY162 @ SY163 )
              = sK3_SY69 )
            & ( ( sK2_SY35 @ SY162 @ SY163 )
              = sK4_SY102 )
            & ( ( sK1_JOIN @ SY162 @ SY164 )
              = sK3_SY69 )
            & ( ( sK2_SY35 @ SY162 @ SY164 )
              = sK4_SY102 ) )
         => ( SY163 = SY164 ) ) )
    = $false ),
    inference(standard_cnf,[status(thm)],[7]) ).

thf(24,plain,
    ( ( ~ ! [SY162: a,SY163: a,SY164: a] :
            ( ( ( ( sK1_JOIN @ SY162 @ SY163 )
                = sK3_SY69 )
              & ( ( sK2_SY35 @ SY162 @ SY163 )
                = sK4_SY102 )
              & ( ( sK1_JOIN @ SY162 @ SY164 )
                = sK3_SY69 )
              & ( ( sK2_SY35 @ SY162 @ SY164 )
                = sK4_SY102 ) )
           => ( SY163 = SY164 ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[23]) ).

thf(25,plain,
    ( ( ( ( sK1_JOIN @ sK5_SY162 @ sK6_SY165 )
        = sK3_SY69 )
      & ( ( sK2_SY35 @ sK5_SY162 @ sK6_SY165 )
        = sK4_SY102 )
      & ( ( sK1_JOIN @ sK5_SY162 @ sK7_SY167 )
        = sK3_SY69 )
      & ( ( sK2_SY35 @ sK5_SY162 @ sK7_SY167 )
        = sK4_SY102 )
      & ( sK6_SY165 != sK7_SY167 ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[24]) ).

thf(26,plain,
    ( ( ! [SY160: a] :
          ( ( ( sK1_JOIN @ SY160 @ ( sK8_SY161 @ SY160 ) )
            = sK3_SY69 )
          & ( ( sK2_SY35 @ SY160 @ ( sK8_SY161 @ SY160 ) )
            = sK4_SY102 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[22]) ).

thf(27,plain,
    ( ( ! [SY160: a] :
          ( ( ( sK1_JOIN @ SY160 @ ( sK8_SY161 @ SY160 ) )
            = sK3_SY69 )
          & ( ( sK2_SY35 @ SY160 @ ( sK8_SY161 @ SY160 ) )
            = sK4_SY102 ) ) )
    = $true ),
    inference(copy,[status(thm)],[26]) ).

thf(28,plain,
    ( ( ! [SY159: a] :
          ( ( sK1_JOIN @ sK4_SY102 @ SY159 )
          = SY159 ) )
    = $true ),
    inference(copy,[status(thm)],[21]) ).

thf(29,plain,
    ( ( ! [SY158: a] :
          ( ( sK2_SY35 @ sK4_SY102 @ SY158 )
          = sK4_SY102 ) )
    = $true ),
    inference(copy,[status(thm)],[20]) ).

thf(30,plain,
    ( ( ! [SY126: a] :
          ( ( sK1_JOIN @ sK3_SY69 @ SY126 )
          = sK3_SY69 ) )
    = $true ),
    inference(copy,[status(thm)],[19]) ).

thf(31,plain,
    ( ( ! [SY125: a] :
          ( ( sK2_SY35 @ sK3_SY69 @ SY125 )
          = SY125 ) )
    = $true ),
    inference(copy,[status(thm)],[18]) ).

thf(32,plain,
    ( ( ! [SY90: a,SY91: a,SY92: a] :
          ( ( sK1_JOIN @ SY90 @ ( sK2_SY35 @ SY91 @ SY92 ) )
          = ( sK2_SY35 @ ( sK1_JOIN @ SY90 @ SY91 ) @ ( sK1_JOIN @ SY90 @ SY92 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[17]) ).

thf(33,plain,
    ( ( ! [SY87: a,SY88: a,SY89: a] :
          ( ( sK2_SY35 @ SY87 @ ( sK1_JOIN @ SY88 @ SY89 ) )
          = ( sK1_JOIN @ ( sK2_SY35 @ SY87 @ SY88 ) @ ( sK2_SY35 @ SY87 @ SY89 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[16]) ).

thf(34,plain,
    ( ( ! [SY85: a,SY86: a] :
          ( ( sK2_SY35 @ ( sK1_JOIN @ SY85 @ SY86 ) @ SY86 )
          = SY86 ) )
    = $true ),
    inference(copy,[status(thm)],[15]) ).

thf(35,plain,
    ( ( ! [SY83: a,SY84: a] :
          ( ( sK1_JOIN @ ( sK2_SY35 @ SY83 @ SY84 ) @ SY84 )
          = SY84 ) )
    = $true ),
    inference(copy,[status(thm)],[14]) ).

thf(36,plain,
    ( ( ! [SY81: a,SY82: a] :
          ( ( sK2_SY35 @ SY81 @ SY82 )
          = ( sK2_SY35 @ SY82 @ SY81 ) ) )
    = $true ),
    inference(copy,[status(thm)],[13]) ).

thf(37,plain,
    ( ( ! [SY46: a,SY47: a] :
          ( ( sK1_JOIN @ SY46 @ SY47 )
          = ( sK1_JOIN @ SY47 @ SY46 ) ) )
    = $true ),
    inference(copy,[status(thm)],[12]) ).

thf(38,plain,
    ( ( ! [SY76: a,SY77: a,SY78: a] :
          ( ( sK2_SY35 @ ( sK2_SY35 @ SY76 @ SY77 ) @ SY78 )
          = ( sK2_SY35 @ SY76 @ ( sK2_SY35 @ SY77 @ SY78 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[11]) ).

thf(39,plain,
    ( ( ! [SY40: a,SY41: a,SY42: a] :
          ( ( sK1_JOIN @ ( sK1_JOIN @ SY40 @ SY41 ) @ SY42 )
          = ( sK1_JOIN @ SY40 @ ( sK1_JOIN @ SY41 @ SY42 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10]) ).

thf(40,plain,
    ( ( ! [SY72: a] :
          ( ( sK2_SY35 @ SY72 @ SY72 )
          = SY72 ) )
    = $true ),
    inference(copy,[status(thm)],[9]) ).

thf(41,plain,
    ( ( ! [SY38: a] :
          ( ( sK1_JOIN @ SY38 @ SY38 )
          = SY38 ) )
    = $true ),
    inference(copy,[status(thm)],[8]) ).

thf(42,plain,
    ( ( ( ( sK1_JOIN @ sK5_SY162 @ sK6_SY165 )
        = sK3_SY69 )
      & ( ( sK2_SY35 @ sK5_SY162 @ sK6_SY165 )
        = sK4_SY102 )
      & ( ( sK1_JOIN @ sK5_SY162 @ sK7_SY167 )
        = sK3_SY69 )
      & ( ( sK2_SY35 @ sK5_SY162 @ sK7_SY167 )
        = sK4_SY102 )
      & ( sK6_SY165 != sK7_SY167 ) )
    = $true ),
    inference(copy,[status(thm)],[25]) ).

thf(43,plain,
    ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sK1_JOIN @ sK5_SY162 @ sK6_SY165 )
                             != sK3_SY69 )
                            | ( ( sK2_SY35 @ sK5_SY162 @ sK6_SY165 )
                             != sK4_SY102 ) )
                      | ( ( sK1_JOIN @ sK5_SY162 @ sK7_SY167 )
                       != sK3_SY69 ) )
                | ( ( sK2_SY35 @ sK5_SY162 @ sK7_SY167 )
                 != sK4_SY102 ) )
          | ~ ( ( sK6_SY165 != sK7_SY167 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[42]) ).

thf(44,plain,
    ( ( ! [SX0: a] :
          ~ ( ( ( sK1_JOIN @ SX0 @ ( sK8_SY161 @ SX0 ) )
             != sK3_SY69 )
            | ( ( sK2_SY35 @ SX0 @ ( sK8_SY161 @ SX0 ) )
             != sK4_SY102 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[27]) ).

thf(45,plain,
    ! [SV1: a] :
      ( ( ( sK1_JOIN @ sK4_SY102 @ SV1 )
        = SV1 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[28]) ).

thf(46,plain,
    ! [SV2: a] :
      ( ( ( sK2_SY35 @ sK4_SY102 @ SV2 )
        = sK4_SY102 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[29]) ).

thf(47,plain,
    ! [SV3: a] :
      ( ( ( sK1_JOIN @ sK3_SY69 @ SV3 )
        = sK3_SY69 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[30]) ).

thf(48,plain,
    ! [SV4: a] :
      ( ( ( sK2_SY35 @ sK3_SY69 @ SV4 )
        = SV4 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[31]) ).

thf(49,plain,
    ! [SV5: a] :
      ( ( ! [SY168: a,SY169: a] :
            ( ( sK1_JOIN @ SV5 @ ( sK2_SY35 @ SY168 @ SY169 ) )
            = ( sK2_SY35 @ ( sK1_JOIN @ SV5 @ SY168 ) @ ( sK1_JOIN @ SV5 @ SY169 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[32]) ).

thf(50,plain,
    ! [SV6: a] :
      ( ( ! [SY170: a,SY171: a] :
            ( ( sK2_SY35 @ SV6 @ ( sK1_JOIN @ SY170 @ SY171 ) )
            = ( sK1_JOIN @ ( sK2_SY35 @ SV6 @ SY170 ) @ ( sK2_SY35 @ SV6 @ SY171 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[33]) ).

thf(51,plain,
    ! [SV7: a] :
      ( ( ! [SY172: a] :
            ( ( sK2_SY35 @ ( sK1_JOIN @ SV7 @ SY172 ) @ SY172 )
            = SY172 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[34]) ).

thf(52,plain,
    ! [SV8: a] :
      ( ( ! [SY173: a] :
            ( ( sK1_JOIN @ ( sK2_SY35 @ SV8 @ SY173 ) @ SY173 )
            = SY173 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[35]) ).

thf(53,plain,
    ! [SV9: a] :
      ( ( ! [SY174: a] :
            ( ( sK2_SY35 @ SV9 @ SY174 )
            = ( sK2_SY35 @ SY174 @ SV9 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[36]) ).

thf(54,plain,
    ! [SV10: a] :
      ( ( ! [SY175: a] :
            ( ( sK1_JOIN @ SV10 @ SY175 )
            = ( sK1_JOIN @ SY175 @ SV10 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[37]) ).

thf(55,plain,
    ! [SV11: a] :
      ( ( ! [SY176: a,SY177: a] :
            ( ( sK2_SY35 @ ( sK2_SY35 @ SV11 @ SY176 ) @ SY177 )
            = ( sK2_SY35 @ SV11 @ ( sK2_SY35 @ SY176 @ SY177 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[38]) ).

thf(56,plain,
    ! [SV12: a] :
      ( ( ! [SY178: a,SY179: a] :
            ( ( sK1_JOIN @ ( sK1_JOIN @ SV12 @ SY178 ) @ SY179 )
            = ( sK1_JOIN @ SV12 @ ( sK1_JOIN @ SY178 @ SY179 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[39]) ).

thf(57,plain,
    ! [SV13: a] :
      ( ( ( sK2_SY35 @ SV13 @ SV13 )
        = SV13 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[40]) ).

thf(58,plain,
    ! [SV14: a] :
      ( ( ( sK1_JOIN @ SV14 @ SV14 )
        = SV14 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[41]) ).

thf(59,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sK1_JOIN @ sK5_SY162 @ sK6_SY165 )
                         != sK3_SY69 )
                        | ( ( sK2_SY35 @ sK5_SY162 @ sK6_SY165 )
                         != sK4_SY102 ) )
                  | ( ( sK1_JOIN @ sK5_SY162 @ sK7_SY167 )
                   != sK3_SY69 ) )
            | ( ( sK2_SY35 @ sK5_SY162 @ sK7_SY167 )
             != sK4_SY102 ) )
      | ~ ( ( sK6_SY165 != sK7_SY167 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[43]) ).

thf(60,plain,
    ! [SV15: a] :
      ( ( ~ ( ( ( sK1_JOIN @ SV15 @ ( sK8_SY161 @ SV15 ) )
             != sK3_SY69 )
            | ( ( sK2_SY35 @ SV15 @ ( sK8_SY161 @ SV15 ) )
             != sK4_SY102 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[44]) ).

thf(61,plain,
    ! [SV16: a,SV5: a] :
      ( ( ! [SY180: a] :
            ( ( sK1_JOIN @ SV5 @ ( sK2_SY35 @ SV16 @ SY180 ) )
            = ( sK2_SY35 @ ( sK1_JOIN @ SV5 @ SV16 ) @ ( sK1_JOIN @ SV5 @ SY180 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[49]) ).

thf(62,plain,
    ! [SV17: a,SV6: a] :
      ( ( ! [SY181: a] :
            ( ( sK2_SY35 @ SV6 @ ( sK1_JOIN @ SV17 @ SY181 ) )
            = ( sK1_JOIN @ ( sK2_SY35 @ SV6 @ SV17 ) @ ( sK2_SY35 @ SV6 @ SY181 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[50]) ).

thf(63,plain,
    ! [SV18: a,SV7: a] :
      ( ( ( sK2_SY35 @ ( sK1_JOIN @ SV7 @ SV18 ) @ SV18 )
        = SV18 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[51]) ).

thf(64,plain,
    ! [SV19: a,SV8: a] :
      ( ( ( sK1_JOIN @ ( sK2_SY35 @ SV8 @ SV19 ) @ SV19 )
        = SV19 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[52]) ).

thf(65,plain,
    ! [SV20: a,SV9: a] :
      ( ( ( sK2_SY35 @ SV9 @ SV20 )
        = ( sK2_SY35 @ SV20 @ SV9 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[53]) ).

thf(66,plain,
    ! [SV21: a,SV10: a] :
      ( ( ( sK1_JOIN @ SV10 @ SV21 )
        = ( sK1_JOIN @ SV21 @ SV10 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[54]) ).

thf(67,plain,
    ! [SV22: a,SV11: a] :
      ( ( ! [SY182: a] :
            ( ( sK2_SY35 @ ( sK2_SY35 @ SV11 @ SV22 ) @ SY182 )
            = ( sK2_SY35 @ SV11 @ ( sK2_SY35 @ SV22 @ SY182 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[55]) ).

thf(68,plain,
    ! [SV23: a,SV12: a] :
      ( ( ! [SY183: a] :
            ( ( sK1_JOIN @ ( sK1_JOIN @ SV12 @ SV23 ) @ SY183 )
            = ( sK1_JOIN @ SV12 @ ( sK1_JOIN @ SV23 @ SY183 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[56]) ).

thf(69,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sK1_JOIN @ sK5_SY162 @ sK6_SY165 )
                         != sK3_SY69 )
                        | ( ( sK2_SY35 @ sK5_SY162 @ sK6_SY165 )
                         != sK4_SY102 ) )
                  | ( ( sK1_JOIN @ sK5_SY162 @ sK7_SY167 )
                   != sK3_SY69 ) )
            | ( ( sK2_SY35 @ sK5_SY162 @ sK7_SY167 )
             != sK4_SY102 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[59]) ).

thf(70,plain,
    ( ( ~ ( ( sK6_SY165 != sK7_SY167 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[59]) ).

thf(71,plain,
    ! [SV15: a] :
      ( ( ( ( sK1_JOIN @ SV15 @ ( sK8_SY161 @ SV15 ) )
         != sK3_SY69 )
        | ( ( sK2_SY35 @ SV15 @ ( sK8_SY161 @ SV15 ) )
         != sK4_SY102 ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[60]) ).

thf(72,plain,
    ! [SV24: a,SV16: a,SV5: a] :
      ( ( ( sK1_JOIN @ SV5 @ ( sK2_SY35 @ SV16 @ SV24 ) )
        = ( sK2_SY35 @ ( sK1_JOIN @ SV5 @ SV16 ) @ ( sK1_JOIN @ SV5 @ SV24 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[61]) ).

thf(73,plain,
    ! [SV25: a,SV17: a,SV6: a] :
      ( ( ( sK2_SY35 @ SV6 @ ( sK1_JOIN @ SV17 @ SV25 ) )
        = ( sK1_JOIN @ ( sK2_SY35 @ SV6 @ SV17 ) @ ( sK2_SY35 @ SV6 @ SV25 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[62]) ).

thf(74,plain,
    ! [SV26: a,SV22: a,SV11: a] :
      ( ( ( sK2_SY35 @ ( sK2_SY35 @ SV11 @ SV22 ) @ SV26 )
        = ( sK2_SY35 @ SV11 @ ( sK2_SY35 @ SV22 @ SV26 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[67]) ).

thf(75,plain,
    ! [SV27: a,SV23: a,SV12: a] :
      ( ( ( sK1_JOIN @ ( sK1_JOIN @ SV12 @ SV23 ) @ SV27 )
        = ( sK1_JOIN @ SV12 @ ( sK1_JOIN @ SV23 @ SV27 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[68]) ).

thf(76,plain,
    ( ( ~ ( ~ ~ ( ~ ~ ( ( ( sK1_JOIN @ sK5_SY162 @ sK6_SY165 )
                       != sK3_SY69 )
                      | ( ( sK2_SY35 @ sK5_SY162 @ sK6_SY165 )
                       != sK4_SY102 ) )
                | ( ( sK1_JOIN @ sK5_SY162 @ sK7_SY167 )
                 != sK3_SY69 ) )
          | ( ( sK2_SY35 @ sK5_SY162 @ sK7_SY167 )
           != sK4_SY102 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[69]) ).

thf(77,plain,
    ( ( ( sK6_SY165 != sK7_SY167 ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[70]) ).

thf(78,plain,
    ! [SV15: a] :
      ( ( ( ( sK1_JOIN @ SV15 @ ( sK8_SY161 @ SV15 ) )
         != sK3_SY69 ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[71]) ).

thf(79,plain,
    ! [SV15: a] :
      ( ( ( ( sK2_SY35 @ SV15 @ ( sK8_SY161 @ SV15 ) )
         != sK4_SY102 ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[71]) ).

thf(80,plain,
    ( ( ~ ~ ( ~ ~ ( ( ( sK1_JOIN @ sK5_SY162 @ sK6_SY165 )
                   != sK3_SY69 )
                  | ( ( sK2_SY35 @ sK5_SY162 @ sK6_SY165 )
                   != sK4_SY102 ) )
            | ( ( sK1_JOIN @ sK5_SY162 @ sK7_SY167 )
             != sK3_SY69 ) )
      | ( ( sK2_SY35 @ sK5_SY162 @ sK7_SY167 )
       != sK4_SY102 ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[76]) ).

thf(81,plain,
    ( ( sK6_SY165 = sK7_SY167 )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[77]) ).

thf(82,plain,
    ! [SV15: a] :
      ( ( ( sK1_JOIN @ SV15 @ ( sK8_SY161 @ SV15 ) )
        = sK3_SY69 )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[78]) ).

thf(83,plain,
    ! [SV15: a] :
      ( ( ( sK2_SY35 @ SV15 @ ( sK8_SY161 @ SV15 ) )
        = sK4_SY102 )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[79]) ).

thf(84,plain,
    ( ( ~ ~ ( ~ ~ ( ( ( sK1_JOIN @ sK5_SY162 @ sK6_SY165 )
                   != sK3_SY69 )
                  | ( ( sK2_SY35 @ sK5_SY162 @ sK6_SY165 )
                   != sK4_SY102 ) )
            | ( ( sK1_JOIN @ sK5_SY162 @ sK7_SY167 )
             != sK3_SY69 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[80]) ).

thf(85,plain,
    ( ( ( ( sK2_SY35 @ sK5_SY162 @ sK7_SY167 )
       != sK4_SY102 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[80]) ).

thf(86,plain,
    ( ( ~ ( ~ ~ ( ( ( sK1_JOIN @ sK5_SY162 @ sK6_SY165 )
                 != sK3_SY69 )
                | ( ( sK2_SY35 @ sK5_SY162 @ sK6_SY165 )
                 != sK4_SY102 ) )
          | ( ( sK1_JOIN @ sK5_SY162 @ sK7_SY167 )
           != sK3_SY69 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[84]) ).

thf(87,plain,
    ( ( ( sK2_SY35 @ sK5_SY162 @ sK7_SY167 )
      = sK4_SY102 )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[85]) ).

thf(88,plain,
    ( ( ~ ~ ( ( ( sK1_JOIN @ sK5_SY162 @ sK6_SY165 )
             != sK3_SY69 )
            | ( ( sK2_SY35 @ sK5_SY162 @ sK6_SY165 )
             != sK4_SY102 ) )
      | ( ( sK1_JOIN @ sK5_SY162 @ sK7_SY167 )
       != sK3_SY69 ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[86]) ).

thf(89,plain,
    ( ( ~ ~ ( ( ( sK1_JOIN @ sK5_SY162 @ sK6_SY165 )
             != sK3_SY69 )
            | ( ( sK2_SY35 @ sK5_SY162 @ sK6_SY165 )
             != sK4_SY102 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[88]) ).

thf(90,plain,
    ( ( ( ( sK1_JOIN @ sK5_SY162 @ sK7_SY167 )
       != sK3_SY69 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[88]) ).

thf(91,plain,
    ( ( ~ ( ( ( sK1_JOIN @ sK5_SY162 @ sK6_SY165 )
           != sK3_SY69 )
          | ( ( sK2_SY35 @ sK5_SY162 @ sK6_SY165 )
           != sK4_SY102 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[89]) ).

thf(92,plain,
    ( ( ( sK1_JOIN @ sK5_SY162 @ sK7_SY167 )
      = sK3_SY69 )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[90]) ).

thf(93,plain,
    ( ( ( ( sK1_JOIN @ sK5_SY162 @ sK6_SY165 )
       != sK3_SY69 )
      | ( ( sK2_SY35 @ sK5_SY162 @ sK6_SY165 )
       != sK4_SY102 ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[91]) ).

thf(94,plain,
    ( ( ( ( sK1_JOIN @ sK5_SY162 @ sK6_SY165 )
       != sK3_SY69 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[93]) ).

thf(95,plain,
    ( ( ( ( sK2_SY35 @ sK5_SY162 @ sK6_SY165 )
       != sK4_SY102 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[93]) ).

thf(96,plain,
    ( ( ( sK1_JOIN @ sK5_SY162 @ sK6_SY165 )
      = sK3_SY69 )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[94]) ).

thf(97,plain,
    ( ( ( sK2_SY35 @ sK5_SY162 @ sK6_SY165 )
      = sK4_SY102 )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[95]) ).

thf(98,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[45,97,96,92,87,83,82,81,75,74,73,72,66,65,64,63,58,57,48,47,46]) ).

thf(99,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[98]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEU997^5 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.34  % Computer : n025.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 600
% 0.14/0.34  % DateTime : Mon Jun 20 12:25:15 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 0.20/0.40  
% 0.20/0.40   No.of.Axioms: 0
% 0.20/0.40  
% 0.20/0.40   Length.of.Defs: 0
% 0.20/0.40  
% 0.20/0.40   Contains.Choice.Funs: false
% 0.20/0.45  (rf:0,axioms:0,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2,loop_count:0,foatp_calls:0,translation:fof_full)........
% 0.40/0.81  
% 0.40/0.81  ********************************
% 0.40/0.81  *   All subproblems solved!    *
% 0.40/0.81  ********************************
% 0.40/0.81  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:15,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:98,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.40/0.82  
% 0.40/0.82  %**** Beginning of derivation protocol ****
% 0.40/0.82  % SZS output start CNFRefutation
% See solution above
% 0.40/0.82  
% 0.40/0.82  %**** End of derivation protocol ****
% 0.40/0.82  %**** no. of clauses in derivation: 99 ****
% 0.40/0.82  %**** clause counter: 98 ****
% 0.40/0.82  
% 0.40/0.82  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:15,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:98,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------