TSTP Solution File: SEV034^5 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SEV034^5 : 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 : n028.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 17:34:27 EDT 2022

% Result   : Theorem 0.18s 0.48s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   30
%            Number of leaves      :    9
% Syntax   : Number of formulae    :  120 (  60 unt;   8 typ;   0 def)
%            Number of atoms       :  819 ( 220 equ;   0 cnn)
%            Maximal formula atoms :    4 (   7 avg)
%            Number of connectives : 1718 ( 177   ~; 195   |;  52   &;1201   @)
%                                         (   0 <=>;  93  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   22 (   4 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :   36 (  36   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   6 usr;   4 con; 0-3 aty)
%            Number of variables   :  483 (   0   ^ 483   !;   0   ?; 483   :)

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

thf(tp_b,type,
    b: $tType ).

thf(tp_sK1_Xp,type,
    sK1_Xp: a > a > $o ).

thf(tp_sK2_SY21,type,
    sK2_SY21: a > b > b > $o ).

thf(tp_sK3_SY41,type,
    sK3_SY41: a > b ).

thf(tp_sK4_SY60,type,
    sK4_SY60: a > b ).

thf(tp_sK5_SY93,type,
    sK5_SY93: a ).

thf(tp_sK6_SY95,type,
    sK6_SY95: a ).

thf(1,conjecture,
    ! [Xp: a > a > $o,Xq: a > b > b > $o,Xf: a > b,Xg: a > b] :
      ( ! [Xx: a] :
          ( ( Xp @ Xx @ Xx )
         => ( Xq @ Xx @ ( Xf @ Xx ) @ ( Xg @ Xx ) ) )
     => ( ! [Xx: a,Xy: a] :
            ( ( Xp @ Xx @ Xy )
           => ( Xq @ Xx @ ( Xf @ Xx ) @ ( Xf @ Xy ) ) )
       => ( ( ! [Xx: a,Xy: a] :
                ( ( Xp @ Xx @ Xy )
               => ( Xp @ Xy @ Xx ) )
            & ! [Xx: a,Xy: a,Xz: a] :
                ( ( ( Xp @ Xx @ Xy )
                  & ( Xp @ Xy @ Xz ) )
               => ( Xp @ Xx @ Xz ) )
            & ( Xp = Xp ) )
         => ( ! [Xx: a,Xy: a] :
                ( ( Xp @ Xx @ Xy )
               => ( ! [Xx0: b,Xy0: b] :
                      ( ( Xq @ Xx @ Xx0 @ Xy0 )
                     => ( Xq @ Xx @ Xy0 @ Xx0 ) )
                  & ! [Xx0: b,Xy0: b,Xz: b] :
                      ( ( ( Xq @ Xx @ Xx0 @ Xy0 )
                        & ( Xq @ Xx @ Xy0 @ Xz ) )
                     => ( Xq @ Xx @ Xx0 @ Xz ) )
                  & ( ( Xq @ Xx )
                    = ( Xq @ Xy ) ) ) )
           => ! [Xx: a,Xy: a] :
                ( ( Xp @ Xx @ Xy )
               => ( Xq @ Xx @ ( Xf @ Xx ) @ ( Xg @ Xy ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM518_pme) ).

thf(2,negated_conjecture,
    ( ( ! [Xp: a > a > $o,Xq: a > b > b > $o,Xf: a > b,Xg: a > b] :
          ( ! [Xx: a] :
              ( ( Xp @ Xx @ Xx )
             => ( Xq @ Xx @ ( Xf @ Xx ) @ ( Xg @ Xx ) ) )
         => ( ! [Xx: a,Xy: a] :
                ( ( Xp @ Xx @ Xy )
               => ( Xq @ Xx @ ( Xf @ Xx ) @ ( Xf @ Xy ) ) )
           => ( ( ! [Xx: a,Xy: a] :
                    ( ( Xp @ Xx @ Xy )
                   => ( Xp @ Xy @ Xx ) )
                & ! [Xx: a,Xy: a,Xz: a] :
                    ( ( ( Xp @ Xx @ Xy )
                      & ( Xp @ Xy @ Xz ) )
                   => ( Xp @ Xx @ Xz ) )
                & ( Xp = Xp ) )
             => ( ! [Xx: a,Xy: a] :
                    ( ( Xp @ Xx @ Xy )
                   => ( ! [Xx0: b,Xy0: b] :
                          ( ( Xq @ Xx @ Xx0 @ Xy0 )
                         => ( Xq @ Xx @ Xy0 @ Xx0 ) )
                      & ! [Xx0: b,Xy0: b,Xz: b] :
                          ( ( ( Xq @ Xx @ Xx0 @ Xy0 )
                            & ( Xq @ Xx @ Xy0 @ Xz ) )
                         => ( Xq @ Xx @ Xx0 @ Xz ) )
                      & ( ( Xq @ Xx )
                        = ( Xq @ Xy ) ) ) )
               => ! [Xx: a,Xy: a] :
                    ( ( Xp @ Xx @ Xy )
                   => ( Xq @ Xx @ ( Xf @ Xx ) @ ( Xg @ Xy ) ) ) ) ) ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ( ( ! [Xp: a > a > $o,Xq: a > b > b > $o,Xf: a > b,Xg: a > b] :
          ( ! [Xx: a] :
              ( ( Xp @ Xx @ Xx )
             => ( Xq @ Xx @ ( Xf @ Xx ) @ ( Xg @ Xx ) ) )
         => ( ! [Xx: a,Xy: a] :
                ( ( Xp @ Xx @ Xy )
               => ( Xq @ Xx @ ( Xf @ Xx ) @ ( Xf @ Xy ) ) )
           => ( ( ! [Xx: a,Xy: a] :
                    ( ( Xp @ Xx @ Xy )
                   => ( Xp @ Xy @ Xx ) )
                & ! [Xx: a,Xy: a,Xz: a] :
                    ( ( ( Xp @ Xx @ Xy )
                      & ( Xp @ Xy @ Xz ) )
                   => ( Xp @ Xx @ Xz ) )
                & ( Xp = Xp ) )
             => ( ! [Xx: a,Xy: a] :
                    ( ( Xp @ Xx @ Xy )
                   => ( ! [Xx0: b,Xy0: b] :
                          ( ( Xq @ Xx @ Xx0 @ Xy0 )
                         => ( Xq @ Xx @ Xy0 @ Xx0 ) )
                      & ! [Xx0: b,Xy0: b,Xz: b] :
                          ( ( ( Xq @ Xx @ Xx0 @ Xy0 )
                            & ( Xq @ Xx @ Xy0 @ Xz ) )
                         => ( Xq @ Xx @ Xx0 @ Xz ) )
                      & ( ( Xq @ Xx )
                        = ( Xq @ Xy ) ) ) )
               => ! [Xx: a,Xy: a] :
                    ( ( Xp @ Xx @ Xy )
                   => ( Xq @ Xx @ ( Xf @ Xx ) @ ( Xg @ Xy ) ) ) ) ) ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(4,plain,
    ( ( ! [SY21: a > b > b > $o,SY22: a > b,SY23: a > b] :
          ( ! [SY24: a] :
              ( ( sK1_Xp @ SY24 @ SY24 )
             => ( SY21 @ SY24 @ ( SY22 @ SY24 ) @ ( SY23 @ SY24 ) ) )
         => ( ! [SY25: a,SY26: a] :
                ( ( sK1_Xp @ SY25 @ SY26 )
               => ( SY21 @ SY25 @ ( SY22 @ SY25 ) @ ( SY22 @ SY26 ) ) )
           => ( ( ! [SY27: a,SY28: a] :
                    ( ( sK1_Xp @ SY27 @ SY28 )
                   => ( sK1_Xp @ SY28 @ SY27 ) )
                & ! [SY29: a,SY30: a,SY31: a] :
                    ( ( ( sK1_Xp @ SY29 @ SY30 )
                      & ( sK1_Xp @ SY30 @ SY31 ) )
                   => ( sK1_Xp @ SY29 @ SY31 ) )
                & ( sK1_Xp = sK1_Xp ) )
             => ( ! [SY32: a,SY33: a] :
                    ( ( sK1_Xp @ SY32 @ SY33 )
                   => ( ! [Xx0: b,Xy0: b] :
                          ( ( SY21 @ SY32 @ Xx0 @ Xy0 )
                         => ( SY21 @ SY32 @ Xy0 @ Xx0 ) )
                      & ! [Xx0: b,Xy0: b,Xz: b] :
                          ( ( ( SY21 @ SY32 @ Xx0 @ Xy0 )
                            & ( SY21 @ SY32 @ Xy0 @ Xz ) )
                         => ( SY21 @ SY32 @ Xx0 @ Xz ) )
                      & ( ( SY21 @ SY32 )
                        = ( SY21 @ SY33 ) ) ) )
               => ! [SY39: a,SY40: a] :
                    ( ( sK1_Xp @ SY39 @ SY40 )
                   => ( SY21 @ SY39 @ ( SY22 @ SY39 ) @ ( SY23 @ SY40 ) ) ) ) ) ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[3]) ).

thf(5,plain,
    ( ( ! [SY41: a > b,SY42: a > b] :
          ( ! [SY43: a] :
              ( ( sK1_Xp @ SY43 @ SY43 )
             => ( sK2_SY21 @ SY43 @ ( SY41 @ SY43 ) @ ( SY42 @ SY43 ) ) )
         => ( ! [SY44: a,SY45: a] :
                ( ( sK1_Xp @ SY44 @ SY45 )
               => ( sK2_SY21 @ SY44 @ ( SY41 @ SY44 ) @ ( SY41 @ SY45 ) ) )
           => ( ( ! [SY27: a,SY28: a] :
                    ( ( sK1_Xp @ SY27 @ SY28 )
                   => ( sK1_Xp @ SY28 @ SY27 ) )
                & ! [SY29: a,SY30: a,SY31: a] :
                    ( ( ( sK1_Xp @ SY29 @ SY30 )
                      & ( sK1_Xp @ SY30 @ SY31 ) )
                   => ( sK1_Xp @ SY29 @ SY31 ) )
                & ( sK1_Xp = sK1_Xp ) )
             => ( ! [SY51: a,SY52: a] :
                    ( ( sK1_Xp @ SY51 @ SY52 )
                   => ( ! [SY53: b,SY54: b] :
                          ( ( sK2_SY21 @ SY51 @ SY53 @ SY54 )
                         => ( sK2_SY21 @ SY51 @ SY54 @ SY53 ) )
                      & ! [SY55: b,SY56: b,SY57: b] :
                          ( ( ( sK2_SY21 @ SY51 @ SY55 @ SY56 )
                            & ( sK2_SY21 @ SY51 @ SY56 @ SY57 ) )
                         => ( sK2_SY21 @ SY51 @ SY55 @ SY57 ) )
                      & ( ( sK2_SY21 @ SY51 )
                        = ( sK2_SY21 @ SY52 ) ) ) )
               => ! [SY58: a,SY59: a] :
                    ( ( sK1_Xp @ SY58 @ SY59 )
                   => ( sK2_SY21 @ SY58 @ ( SY41 @ SY58 ) @ ( SY42 @ SY59 ) ) ) ) ) ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[4]) ).

thf(6,plain,
    ( ( ! [SY60: a > b] :
          ( ! [SY61: a] :
              ( ( sK1_Xp @ SY61 @ SY61 )
             => ( sK2_SY21 @ SY61 @ ( sK3_SY41 @ SY61 ) @ ( SY60 @ SY61 ) ) )
         => ( ! [SY62: a,SY63: a] :
                ( ( sK1_Xp @ SY62 @ SY63 )
               => ( sK2_SY21 @ SY62 @ ( sK3_SY41 @ SY62 ) @ ( sK3_SY41 @ SY63 ) ) )
           => ( ( ! [SY27: a,SY28: a] :
                    ( ( sK1_Xp @ SY27 @ SY28 )
                   => ( sK1_Xp @ SY28 @ SY27 ) )
                & ! [SY29: a,SY30: a,SY31: a] :
                    ( ( ( sK1_Xp @ SY29 @ SY30 )
                      & ( sK1_Xp @ SY30 @ SY31 ) )
                   => ( sK1_Xp @ SY29 @ SY31 ) )
                & ( sK1_Xp = sK1_Xp ) )
             => ( ! [SY51: a,SY52: a] :
                    ( ( sK1_Xp @ SY51 @ SY52 )
                   => ( ! [SY53: b,SY54: b] :
                          ( ( sK2_SY21 @ SY51 @ SY53 @ SY54 )
                         => ( sK2_SY21 @ SY51 @ SY54 @ SY53 ) )
                      & ! [SY55: b,SY56: b,SY57: b] :
                          ( ( ( sK2_SY21 @ SY51 @ SY55 @ SY56 )
                            & ( sK2_SY21 @ SY51 @ SY56 @ SY57 ) )
                         => ( sK2_SY21 @ SY51 @ SY55 @ SY57 ) )
                      & ( ( sK2_SY21 @ SY51 )
                        = ( sK2_SY21 @ SY52 ) ) ) )
               => ! [SY76: a,SY77: a] :
                    ( ( sK1_Xp @ SY76 @ SY77 )
                   => ( sK2_SY21 @ SY76 @ ( sK3_SY41 @ SY76 ) @ ( SY60 @ SY77 ) ) ) ) ) ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[5]) ).

thf(7,plain,
    ( ( ! [SY78: a] :
          ( ( sK1_Xp @ SY78 @ SY78 )
         => ( sK2_SY21 @ SY78 @ ( sK3_SY41 @ SY78 ) @ ( sK4_SY60 @ SY78 ) ) )
     => ( ! [SY62: a,SY63: a] :
            ( ( sK1_Xp @ SY62 @ SY63 )
           => ( sK2_SY21 @ SY62 @ ( sK3_SY41 @ SY62 ) @ ( sK3_SY41 @ SY63 ) ) )
       => ( ( ! [SY27: a,SY28: a] :
                ( ( sK1_Xp @ SY27 @ SY28 )
               => ( sK1_Xp @ SY28 @ SY27 ) )
            & ! [SY29: a,SY30: a,SY31: a] :
                ( ( ( sK1_Xp @ SY29 @ SY30 )
                  & ( sK1_Xp @ SY30 @ SY31 ) )
               => ( sK1_Xp @ SY29 @ SY31 ) )
            & ( sK1_Xp = sK1_Xp ) )
         => ( ! [SY51: a,SY52: a] :
                ( ( sK1_Xp @ SY51 @ SY52 )
               => ( ! [SY53: b,SY54: b] :
                      ( ( sK2_SY21 @ SY51 @ SY53 @ SY54 )
                     => ( sK2_SY21 @ SY51 @ SY54 @ SY53 ) )
                  & ! [SY55: b,SY56: b,SY57: b] :
                      ( ( ( sK2_SY21 @ SY51 @ SY55 @ SY56 )
                        & ( sK2_SY21 @ SY51 @ SY56 @ SY57 ) )
                     => ( sK2_SY21 @ SY51 @ SY55 @ SY57 ) )
                  & ( ( sK2_SY21 @ SY51 )
                    = ( sK2_SY21 @ SY52 ) ) ) )
           => ! [SY93: a,SY94: a] :
                ( ( sK1_Xp @ SY93 @ SY94 )
               => ( sK2_SY21 @ SY93 @ ( sK3_SY41 @ SY93 ) @ ( sK4_SY60 @ SY94 ) ) ) ) ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[6]) ).

thf(8,plain,
    ( ( ! [SY78: a] :
          ( ( sK1_Xp @ SY78 @ SY78 )
         => ( sK2_SY21 @ SY78 @ ( sK3_SY41 @ SY78 ) @ ( sK4_SY60 @ SY78 ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[7]) ).

thf(9,plain,
    ( ( ! [SY62: a,SY63: a] :
          ( ( sK1_Xp @ SY62 @ SY63 )
         => ( sK2_SY21 @ SY62 @ ( sK3_SY41 @ SY62 ) @ ( sK3_SY41 @ SY63 ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[7]) ).

thf(10,plain,
    ( ( ! [SY27: a,SY28: a] :
          ( ( sK1_Xp @ SY27 @ SY28 )
         => ( sK1_Xp @ SY28 @ SY27 ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[7]) ).

thf(11,plain,
    ( ( ! [SY29: a,SY30: a,SY31: a] :
          ( ( ( sK1_Xp @ SY29 @ SY30 )
            & ( sK1_Xp @ SY30 @ SY31 ) )
         => ( sK1_Xp @ SY29 @ SY31 ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[7]) ).

thf(12,plain,
    ( ( sK1_Xp = sK1_Xp )
    = $true ),
    inference(standard_cnf,[status(thm)],[7]) ).

thf(13,plain,
    ( ( ! [SY51: a,SY52: a] :
          ( ( sK1_Xp @ SY51 @ SY52 )
         => ( ! [SY53: b,SY54: b] :
                ( ( sK2_SY21 @ SY51 @ SY53 @ SY54 )
               => ( sK2_SY21 @ SY51 @ SY54 @ SY53 ) )
            & ! [SY55: b,SY56: b,SY57: b] :
                ( ( ( sK2_SY21 @ SY51 @ SY55 @ SY56 )
                  & ( sK2_SY21 @ SY51 @ SY56 @ SY57 ) )
               => ( sK2_SY21 @ SY51 @ SY55 @ SY57 ) )
            & ( ( sK2_SY21 @ SY51 )
              = ( sK2_SY21 @ SY52 ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[7]) ).

thf(14,plain,
    ( ( ! [SY93: a,SY94: a] :
          ( ( sK1_Xp @ SY93 @ SY94 )
         => ( sK2_SY21 @ SY93 @ ( sK3_SY41 @ SY93 ) @ ( sK4_SY60 @ SY94 ) ) ) )
    = $false ),
    inference(standard_cnf,[status(thm)],[7]) ).

thf(15,plain,
    ( ( ~ ! [SY93: a,SY94: a] :
            ( ( sK1_Xp @ SY93 @ SY94 )
           => ( sK2_SY21 @ SY93 @ ( sK3_SY41 @ SY93 ) @ ( sK4_SY60 @ SY94 ) ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[14]) ).

thf(16,plain,
    ( ( ( sK1_Xp @ sK5_SY93 @ sK6_SY95 )
      & ~ ( sK2_SY21 @ sK5_SY93 @ ( sK3_SY41 @ sK5_SY93 ) @ ( sK4_SY60 @ sK6_SY95 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[15]) ).

thf(17,plain,
    ( ( ! [SY78: a] :
          ( ~ ( sK1_Xp @ SY78 @ SY78 )
          | ( sK2_SY21 @ SY78 @ ( sK3_SY41 @ SY78 ) @ ( sK4_SY60 @ SY78 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[8]) ).

thf(18,plain,
    ( ( ! [SY62: a,SY63: a] :
          ( ~ ( sK1_Xp @ SY62 @ SY63 )
          | ( sK2_SY21 @ SY62 @ ( sK3_SY41 @ SY62 ) @ ( sK3_SY41 @ SY63 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[9]) ).

thf(19,plain,
    ( ( ! [SY27: a,SY28: a] :
          ( ~ ( sK1_Xp @ SY27 @ SY28 )
          | ( sK1_Xp @ SY28 @ SY27 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[10]) ).

thf(20,plain,
    ( ( ! [SY29: a,SY30: a,SY31: a] :
          ( ~ ( sK1_Xp @ SY29 @ SY30 )
          | ~ ( sK1_Xp @ SY30 @ SY31 )
          | ( sK1_Xp @ SY29 @ SY31 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[11]) ).

thf(21,plain,
    $true = $true,
    inference(extcnf_combined,[status(esa)],[12]) ).

thf(22,plain,
    ( ( ! [SY51: a] :
          ( ! [SY52: a] :
              ~ ( sK1_Xp @ SY51 @ SY52 )
          | ! [SY53: b,SY54: b] :
              ( ~ ( sK2_SY21 @ SY51 @ SY53 @ SY54 )
              | ( sK2_SY21 @ SY51 @ SY54 @ SY53 ) ) )
      & ! [SY51: a] :
          ( ! [SY52: a] :
              ~ ( sK1_Xp @ SY51 @ SY52 )
          | ! [SY55: b,SY56: b,SY57: b] :
              ( ~ ( sK2_SY21 @ SY51 @ SY55 @ SY56 )
              | ~ ( sK2_SY21 @ SY51 @ SY56 @ SY57 )
              | ( sK2_SY21 @ SY51 @ SY55 @ SY57 ) ) )
      & ! [SY51: a,SY52: a] :
          ( ~ ( sK1_Xp @ SY51 @ SY52 )
          | ( ( sK2_SY21 @ SY51 )
            = ( sK2_SY21 @ SY52 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[13]) ).

thf(23,plain,
    ( ( ! [SY51: a] :
          ( ! [SY52: a] :
              ~ ( sK1_Xp @ SY51 @ SY52 )
          | ! [SY53: b,SY54: b] :
              ( ~ ( sK2_SY21 @ SY51 @ SY53 @ SY54 )
              | ( sK2_SY21 @ SY51 @ SY54 @ SY53 ) ) )
      & ! [SY51: a] :
          ( ! [SY52: a] :
              ~ ( sK1_Xp @ SY51 @ SY52 )
          | ! [SY55: b,SY56: b,SY57: b] :
              ( ~ ( sK2_SY21 @ SY51 @ SY55 @ SY56 )
              | ~ ( sK2_SY21 @ SY51 @ SY56 @ SY57 )
              | ( sK2_SY21 @ SY51 @ SY55 @ SY57 ) ) )
      & ! [SY51: a,SY52: a] :
          ( ~ ( sK1_Xp @ SY51 @ SY52 )
          | ( ( sK2_SY21 @ SY51 )
            = ( sK2_SY21 @ SY52 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[22]) ).

thf(24,plain,
    $true = $true,
    inference(copy,[status(thm)],[21]) ).

thf(25,plain,
    ( ( ! [SY29: a,SY30: a,SY31: a] :
          ( ~ ( sK1_Xp @ SY29 @ SY30 )
          | ~ ( sK1_Xp @ SY30 @ SY31 )
          | ( sK1_Xp @ SY29 @ SY31 ) ) )
    = $true ),
    inference(copy,[status(thm)],[20]) ).

thf(26,plain,
    ( ( ! [SY27: a,SY28: a] :
          ( ~ ( sK1_Xp @ SY27 @ SY28 )
          | ( sK1_Xp @ SY28 @ SY27 ) ) )
    = $true ),
    inference(copy,[status(thm)],[19]) ).

thf(27,plain,
    ( ( ! [SY62: a,SY63: a] :
          ( ~ ( sK1_Xp @ SY62 @ SY63 )
          | ( sK2_SY21 @ SY62 @ ( sK3_SY41 @ SY62 ) @ ( sK3_SY41 @ SY63 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[18]) ).

thf(28,plain,
    ( ( ! [SY78: a] :
          ( ~ ( sK1_Xp @ SY78 @ SY78 )
          | ( sK2_SY21 @ SY78 @ ( sK3_SY41 @ SY78 ) @ ( sK4_SY60 @ SY78 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[17]) ).

thf(29,plain,
    ( ( ( sK1_Xp @ sK5_SY93 @ sK6_SY95 )
      & ~ ( sK2_SY21 @ sK5_SY93 @ ( sK3_SY41 @ sK5_SY93 ) @ ( sK4_SY60 @ sK6_SY95 ) ) )
    = $true ),
    inference(copy,[status(thm)],[16]) ).

thf(30,plain,
    ( ( ~ ( ~ ( sK1_Xp @ sK5_SY93 @ sK6_SY95 )
          | ~ ~ ( sK2_SY21 @ sK5_SY93 @ ( sK3_SY41 @ sK5_SY93 ) @ ( sK4_SY60 @ sK6_SY95 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[29]) ).

thf(31,plain,
    ( ( ~ ( ~ ~ ( ~ ! [SX0: a] :
                      ( ! [SX1: a] :
                          ~ ( sK1_Xp @ SX0 @ SX1 )
                      | ! [SX1: b,SX2: b] :
                          ( ~ ( sK2_SY21 @ SX0 @ SX1 @ SX2 )
                          | ( sK2_SY21 @ SX0 @ SX2 @ SX1 ) ) )
                | ~ ! [SX0: a] :
                      ( ! [SX1: a] :
                          ~ ( sK1_Xp @ SX0 @ SX1 )
                      | ! [SX1: b,SX2: b,SX3: b] :
                          ( ~ ( sK2_SY21 @ SX0 @ SX1 @ SX2 )
                          | ~ ( sK2_SY21 @ SX0 @ SX2 @ SX3 )
                          | ( sK2_SY21 @ SX0 @ SX1 @ SX3 ) ) ) )
          | ~ ! [SX0: a,SX1: a] :
                ( ~ ( sK1_Xp @ SX0 @ SX1 )
                | ( ( sK2_SY21 @ SX0 )
                  = ( sK2_SY21 @ SX1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[23]) ).

thf(32,plain,
    ! [SV1: a] :
      ( ( ! [SY96: a,SY97: a] :
            ( ~ ( sK1_Xp @ SV1 @ SY96 )
            | ~ ( sK1_Xp @ SY96 @ SY97 )
            | ( sK1_Xp @ SV1 @ SY97 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[25]) ).

thf(33,plain,
    ! [SV2: a] :
      ( ( ! [SY98: a] :
            ( ~ ( sK1_Xp @ SV2 @ SY98 )
            | ( sK1_Xp @ SY98 @ SV2 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[26]) ).

thf(34,plain,
    ! [SV3: a] :
      ( ( ! [SY99: a] :
            ( ~ ( sK1_Xp @ SV3 @ SY99 )
            | ( sK2_SY21 @ SV3 @ ( sK3_SY41 @ SV3 ) @ ( sK3_SY41 @ SY99 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[27]) ).

thf(35,plain,
    ! [SV4: a] :
      ( ( ~ ( sK1_Xp @ SV4 @ SV4 )
        | ( sK2_SY21 @ SV4 @ ( sK3_SY41 @ SV4 ) @ ( sK4_SY60 @ SV4 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[28]) ).

thf(36,plain,
    ( ( ~ ( sK1_Xp @ sK5_SY93 @ sK6_SY95 )
      | ~ ~ ( sK2_SY21 @ sK5_SY93 @ ( sK3_SY41 @ sK5_SY93 ) @ ( sK4_SY60 @ sK6_SY95 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[30]) ).

thf(37,plain,
    ( ( ~ ~ ( ~ ! [SX0: a] :
                  ( ! [SX1: a] :
                      ~ ( sK1_Xp @ SX0 @ SX1 )
                  | ! [SX1: b,SX2: b] :
                      ( ~ ( sK2_SY21 @ SX0 @ SX1 @ SX2 )
                      | ( sK2_SY21 @ SX0 @ SX2 @ SX1 ) ) )
            | ~ ! [SX0: a] :
                  ( ! [SX1: a] :
                      ~ ( sK1_Xp @ SX0 @ SX1 )
                  | ! [SX1: b,SX2: b,SX3: b] :
                      ( ~ ( sK2_SY21 @ SX0 @ SX1 @ SX2 )
                      | ~ ( sK2_SY21 @ SX0 @ SX2 @ SX3 )
                      | ( sK2_SY21 @ SX0 @ SX1 @ SX3 ) ) ) )
      | ~ ! [SX0: a,SX1: a] :
            ( ~ ( sK1_Xp @ SX0 @ SX1 )
            | ( ( sK2_SY21 @ SX0 )
              = ( sK2_SY21 @ SX1 ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[31]) ).

thf(38,plain,
    ! [SV5: a,SV1: a] :
      ( ( ! [SY100: a] :
            ( ~ ( sK1_Xp @ SV1 @ SV5 )
            | ~ ( sK1_Xp @ SV5 @ SY100 )
            | ( sK1_Xp @ SV1 @ SY100 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[32]) ).

thf(39,plain,
    ! [SV6: a,SV2: a] :
      ( ( ~ ( sK1_Xp @ SV2 @ SV6 )
        | ( sK1_Xp @ SV6 @ SV2 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[33]) ).

thf(40,plain,
    ! [SV7: a,SV3: a] :
      ( ( ~ ( sK1_Xp @ SV3 @ SV7 )
        | ( sK2_SY21 @ SV3 @ ( sK3_SY41 @ SV3 ) @ ( sK3_SY41 @ SV7 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[34]) ).

thf(41,plain,
    ! [SV4: a] :
      ( ( ( ~ ( sK1_Xp @ SV4 @ SV4 ) )
        = $true )
      | ( ( sK2_SY21 @ SV4 @ ( sK3_SY41 @ SV4 ) @ ( sK4_SY60 @ SV4 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[35]) ).

thf(42,plain,
    ( ( ~ ( sK1_Xp @ sK5_SY93 @ sK6_SY95 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[36]) ).

thf(43,plain,
    ( ( ~ ~ ( sK2_SY21 @ sK5_SY93 @ ( sK3_SY41 @ sK5_SY93 ) @ ( sK4_SY60 @ sK6_SY95 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[36]) ).

thf(44,plain,
    ( ( ~ ~ ( ~ ! [SX0: a] :
                  ( ! [SX1: a] :
                      ~ ( sK1_Xp @ SX0 @ SX1 )
                  | ! [SX1: b,SX2: b] :
                      ( ~ ( sK2_SY21 @ SX0 @ SX1 @ SX2 )
                      | ( sK2_SY21 @ SX0 @ SX2 @ SX1 ) ) )
            | ~ ! [SX0: a] :
                  ( ! [SX1: a] :
                      ~ ( sK1_Xp @ SX0 @ SX1 )
                  | ! [SX1: b,SX2: b,SX3: b] :
                      ( ~ ( sK2_SY21 @ SX0 @ SX1 @ SX2 )
                      | ~ ( sK2_SY21 @ SX0 @ SX2 @ SX3 )
                      | ( sK2_SY21 @ SX0 @ SX1 @ SX3 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[37]) ).

thf(45,plain,
    ( ( ~ ! [SX0: a,SX1: a] :
            ( ~ ( sK1_Xp @ SX0 @ SX1 )
            | ( ( sK2_SY21 @ SX0 )
              = ( sK2_SY21 @ SX1 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[37]) ).

thf(46,plain,
    ! [SV8: a,SV5: a,SV1: a] :
      ( ( ~ ( sK1_Xp @ SV1 @ SV5 )
        | ~ ( sK1_Xp @ SV5 @ SV8 )
        | ( sK1_Xp @ SV1 @ SV8 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[38]) ).

thf(47,plain,
    ! [SV6: a,SV2: a] :
      ( ( ( ~ ( sK1_Xp @ SV2 @ SV6 ) )
        = $true )
      | ( ( sK1_Xp @ SV6 @ SV2 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[39]) ).

thf(48,plain,
    ! [SV7: a,SV3: a] :
      ( ( ( ~ ( sK1_Xp @ SV3 @ SV7 ) )
        = $true )
      | ( ( sK2_SY21 @ SV3 @ ( sK3_SY41 @ SV3 ) @ ( sK3_SY41 @ SV7 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[40]) ).

thf(49,plain,
    ! [SV4: a] :
      ( ( ( sK1_Xp @ SV4 @ SV4 )
        = $false )
      | ( ( sK2_SY21 @ SV4 @ ( sK3_SY41 @ SV4 ) @ ( sK4_SY60 @ SV4 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[41]) ).

thf(50,plain,
    ( ( sK1_Xp @ sK5_SY93 @ sK6_SY95 )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[42]) ).

thf(51,plain,
    ( ( ~ ( sK2_SY21 @ sK5_SY93 @ ( sK3_SY41 @ sK5_SY93 ) @ ( sK4_SY60 @ sK6_SY95 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[43]) ).

thf(52,plain,
    ( ( ~ ( ~ ! [SX0: a] :
                ( ! [SX1: a] :
                    ~ ( sK1_Xp @ SX0 @ SX1 )
                | ! [SX1: b,SX2: b] :
                    ( ~ ( sK2_SY21 @ SX0 @ SX1 @ SX2 )
                    | ( sK2_SY21 @ SX0 @ SX2 @ SX1 ) ) )
          | ~ ! [SX0: a] :
                ( ! [SX1: a] :
                    ~ ( sK1_Xp @ SX0 @ SX1 )
                | ! [SX1: b,SX2: b,SX3: b] :
                    ( ~ ( sK2_SY21 @ SX0 @ SX1 @ SX2 )
                    | ~ ( sK2_SY21 @ SX0 @ SX2 @ SX3 )
                    | ( sK2_SY21 @ SX0 @ SX1 @ SX3 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[44]) ).

thf(53,plain,
    ( ( ! [SX0: a,SX1: a] :
          ( ~ ( sK1_Xp @ SX0 @ SX1 )
          | ( ( sK2_SY21 @ SX0 )
            = ( sK2_SY21 @ SX1 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[45]) ).

thf(54,plain,
    ! [SV8: a,SV5: a,SV1: a] :
      ( ( ( ~ ( sK1_Xp @ SV1 @ SV5 )
          | ~ ( sK1_Xp @ SV5 @ SV8 ) )
        = $true )
      | ( ( sK1_Xp @ SV1 @ SV8 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[46]) ).

thf(55,plain,
    ! [SV6: a,SV2: a] :
      ( ( ( sK1_Xp @ SV2 @ SV6 )
        = $false )
      | ( ( sK1_Xp @ SV6 @ SV2 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[47]) ).

thf(56,plain,
    ! [SV7: a,SV3: a] :
      ( ( ( sK1_Xp @ SV3 @ SV7 )
        = $false )
      | ( ( sK2_SY21 @ SV3 @ ( sK3_SY41 @ SV3 ) @ ( sK3_SY41 @ SV7 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[48]) ).

thf(57,plain,
    ( ( sK2_SY21 @ sK5_SY93 @ ( sK3_SY41 @ sK5_SY93 ) @ ( sK4_SY60 @ sK6_SY95 ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[51]) ).

thf(58,plain,
    ( ( ~ ! [SX0: a] :
            ( ! [SX1: a] :
                ~ ( sK1_Xp @ SX0 @ SX1 )
            | ! [SX1: b,SX2: b] :
                ( ~ ( sK2_SY21 @ SX0 @ SX1 @ SX2 )
                | ( sK2_SY21 @ SX0 @ SX2 @ SX1 ) ) )
      | ~ ! [SX0: a] :
            ( ! [SX1: a] :
                ~ ( sK1_Xp @ SX0 @ SX1 )
            | ! [SX1: b,SX2: b,SX3: b] :
                ( ~ ( sK2_SY21 @ SX0 @ SX1 @ SX2 )
                | ~ ( sK2_SY21 @ SX0 @ SX2 @ SX3 )
                | ( sK2_SY21 @ SX0 @ SX1 @ SX3 ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[52]) ).

thf(59,plain,
    ! [SV9: a] :
      ( ( ! [SY101: a] :
            ( ~ ( sK1_Xp @ SV9 @ SY101 )
            | ( ( sK2_SY21 @ SV9 )
              = ( sK2_SY21 @ SY101 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[53]) ).

thf(60,plain,
    ! [SV8: a,SV5: a,SV1: a] :
      ( ( ( ~ ( sK1_Xp @ SV1 @ SV5 ) )
        = $true )
      | ( ( ~ ( sK1_Xp @ SV5 @ SV8 ) )
        = $true )
      | ( ( sK1_Xp @ SV1 @ SV8 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[54]) ).

thf(61,plain,
    ( ( ~ ! [SX0: a] :
            ( ! [SX1: a] :
                ~ ( sK1_Xp @ SX0 @ SX1 )
            | ! [SX1: b,SX2: b] :
                ( ~ ( sK2_SY21 @ SX0 @ SX1 @ SX2 )
                | ( sK2_SY21 @ SX0 @ SX2 @ SX1 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[58]) ).

thf(62,plain,
    ( ( ~ ! [SX0: a] :
            ( ! [SX1: a] :
                ~ ( sK1_Xp @ SX0 @ SX1 )
            | ! [SX1: b,SX2: b,SX3: b] :
                ( ~ ( sK2_SY21 @ SX0 @ SX1 @ SX2 )
                | ~ ( sK2_SY21 @ SX0 @ SX2 @ SX3 )
                | ( sK2_SY21 @ SX0 @ SX1 @ SX3 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[58]) ).

thf(63,plain,
    ! [SV10: a,SV9: a] :
      ( ( ~ ( sK1_Xp @ SV9 @ SV10 )
        | ( ( sK2_SY21 @ SV9 )
          = ( sK2_SY21 @ SV10 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[59]) ).

thf(64,plain,
    ! [SV8: a,SV5: a,SV1: a] :
      ( ( ( sK1_Xp @ SV1 @ SV5 )
        = $false )
      | ( ( ~ ( sK1_Xp @ SV5 @ SV8 ) )
        = $true )
      | ( ( sK1_Xp @ SV1 @ SV8 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[60]) ).

thf(65,plain,
    ( ( ! [SX0: a] :
          ( ! [SX1: a] :
              ~ ( sK1_Xp @ SX0 @ SX1 )
          | ! [SX1: b,SX2: b] :
              ( ~ ( sK2_SY21 @ SX0 @ SX1 @ SX2 )
              | ( sK2_SY21 @ SX0 @ SX2 @ SX1 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[61]) ).

thf(66,plain,
    ( ( ! [SX0: a] :
          ( ! [SX1: a] :
              ~ ( sK1_Xp @ SX0 @ SX1 )
          | ! [SX1: b,SX2: b,SX3: b] :
              ( ~ ( sK2_SY21 @ SX0 @ SX1 @ SX2 )
              | ~ ( sK2_SY21 @ SX0 @ SX2 @ SX3 )
              | ( sK2_SY21 @ SX0 @ SX1 @ SX3 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[62]) ).

thf(67,plain,
    ! [SV10: a,SV9: a] :
      ( ( ( ~ ( sK1_Xp @ SV9 @ SV10 ) )
        = $true )
      | ( ( ( sK2_SY21 @ SV9 )
          = ( sK2_SY21 @ SV10 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[63]) ).

thf(68,plain,
    ! [SV1: a,SV8: a,SV5: a] :
      ( ( ( sK1_Xp @ SV5 @ SV8 )
        = $false )
      | ( ( sK1_Xp @ SV1 @ SV5 )
        = $false )
      | ( ( sK1_Xp @ SV1 @ SV8 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[64]) ).

thf(69,plain,
    ! [SV11: a] :
      ( ( ! [SY102: a] :
            ~ ( sK1_Xp @ SV11 @ SY102 )
        | ! [SY103: b,SY104: b] :
            ( ~ ( sK2_SY21 @ SV11 @ SY103 @ SY104 )
            | ( sK2_SY21 @ SV11 @ SY104 @ SY103 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[65]) ).

thf(70,plain,
    ! [SV12: a] :
      ( ( ! [SY105: a] :
            ~ ( sK1_Xp @ SV12 @ SY105 )
        | ! [SY106: b,SY107: b,SY108: b] :
            ( ~ ( sK2_SY21 @ SV12 @ SY106 @ SY107 )
            | ~ ( sK2_SY21 @ SV12 @ SY107 @ SY108 )
            | ( sK2_SY21 @ SV12 @ SY106 @ SY108 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[66]) ).

thf(71,plain,
    ! [SV10: a,SV9: a] :
      ( ( ( sK1_Xp @ SV9 @ SV10 )
        = $false )
      | ( ( ( sK2_SY21 @ SV9 )
          = ( sK2_SY21 @ SV10 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[67]) ).

thf(72,plain,
    ! [SV11: a] :
      ( ( ( ! [SY102: a] :
              ~ ( sK1_Xp @ SV11 @ SY102 ) )
        = $true )
      | ( ( ! [SY103: b,SY104: b] :
              ( ~ ( sK2_SY21 @ SV11 @ SY103 @ SY104 )
              | ( sK2_SY21 @ SV11 @ SY104 @ SY103 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[69]) ).

thf(73,plain,
    ! [SV12: a] :
      ( ( ( ! [SY105: a] :
              ~ ( sK1_Xp @ SV12 @ SY105 ) )
        = $true )
      | ( ( ! [SY106: b,SY107: b,SY108: b] :
              ( ~ ( sK2_SY21 @ SV12 @ SY106 @ SY107 )
              | ~ ( sK2_SY21 @ SV12 @ SY107 @ SY108 )
              | ( sK2_SY21 @ SV12 @ SY106 @ SY108 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[70]) ).

thf(74,plain,
    ! [SV10: a,SV9: a] :
      ( ( ( ! [SV13: b] :
              ( ( sK2_SY21 @ SV9 @ SV13 )
              = ( sK2_SY21 @ SV10 @ SV13 ) ) )
        = $true )
      | ( ( sK1_Xp @ SV9 @ SV10 )
        = $false ) ),
    inference(extcnf_equal_pos,[status(thm)],[71]) ).

thf(75,plain,
    ! [SV10: a,SV9: a] :
      ( ( ( ( sK2_SY21 @ SV9 )
          = ( sK2_SY21 @ SV10 ) )
        = $true )
      | ( ( sK1_Xp @ SV9 @ SV10 )
        = $false ) ),
    inference(extcnf_equal_pos,[status(thm)],[71]) ).

thf(76,plain,
    ! [SV14: a,SV11: a] :
      ( ( ( ~ ( sK1_Xp @ SV11 @ SV14 ) )
        = $true )
      | ( ( ! [SY103: b,SY104: b] :
              ( ~ ( sK2_SY21 @ SV11 @ SY103 @ SY104 )
              | ( sK2_SY21 @ SV11 @ SY104 @ SY103 ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[72]) ).

thf(77,plain,
    ! [SV15: a,SV12: a] :
      ( ( ( ~ ( sK1_Xp @ SV12 @ SV15 ) )
        = $true )
      | ( ( ! [SY106: b,SY107: b,SY108: b] :
              ( ~ ( sK2_SY21 @ SV12 @ SY106 @ SY107 )
              | ~ ( sK2_SY21 @ SV12 @ SY107 @ SY108 )
              | ( sK2_SY21 @ SV12 @ SY106 @ SY108 ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[73]) ).

thf(78,plain,
    ! [SV10: a,SV16: b,SV9: a] :
      ( ( ( ( sK2_SY21 @ SV9 @ SV16 )
          = ( sK2_SY21 @ SV10 @ SV16 ) )
        = $true )
      | ( ( sK1_Xp @ SV9 @ SV10 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[74]) ).

thf(79,plain,
    ! [SV14: a,SV11: a] :
      ( ( ( sK1_Xp @ SV11 @ SV14 )
        = $false )
      | ( ( ! [SY103: b,SY104: b] :
              ( ~ ( sK2_SY21 @ SV11 @ SY103 @ SY104 )
              | ( sK2_SY21 @ SV11 @ SY104 @ SY103 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[76]) ).

thf(80,plain,
    ! [SV15: a,SV12: a] :
      ( ( ( sK1_Xp @ SV12 @ SV15 )
        = $false )
      | ( ( ! [SY106: b,SY107: b,SY108: b] :
              ( ~ ( sK2_SY21 @ SV12 @ SY106 @ SY107 )
              | ~ ( sK2_SY21 @ SV12 @ SY107 @ SY108 )
              | ( sK2_SY21 @ SV12 @ SY106 @ SY108 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[77]) ).

thf(81,plain,
    ! [SV10: a,SV16: b,SV9: a] :
      ( ( ( ! [SV17: b] :
              ( ( sK2_SY21 @ SV9 @ SV16 @ SV17 )
              = ( sK2_SY21 @ SV10 @ SV16 @ SV17 ) ) )
        = $true )
      | ( ( sK1_Xp @ SV9 @ SV10 )
        = $false ) ),
    inference(extcnf_equal_pos,[status(thm)],[78]) ).

thf(82,plain,
    ! [SV10: a,SV16: b,SV9: a] :
      ( ( ( ( sK2_SY21 @ SV9 @ SV16 )
          = ( sK2_SY21 @ SV10 @ SV16 ) )
        = $true )
      | ( ( sK1_Xp @ SV9 @ SV10 )
        = $false ) ),
    inference(extcnf_equal_pos,[status(thm)],[78]) ).

thf(83,plain,
    ! [SV14: a,SV18: b,SV11: a] :
      ( ( ( ! [SY109: b] :
              ( ~ ( sK2_SY21 @ SV11 @ SV18 @ SY109 )
              | ( sK2_SY21 @ SV11 @ SY109 @ SV18 ) ) )
        = $true )
      | ( ( sK1_Xp @ SV11 @ SV14 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[79]) ).

thf(84,plain,
    ! [SV15: a,SV19: b,SV12: a] :
      ( ( ( ! [SY110: b,SY111: b] :
              ( ~ ( sK2_SY21 @ SV12 @ SV19 @ SY110 )
              | ~ ( sK2_SY21 @ SV12 @ SY110 @ SY111 )
              | ( sK2_SY21 @ SV12 @ SV19 @ SY111 ) ) )
        = $true )
      | ( ( sK1_Xp @ SV12 @ SV15 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[80]) ).

thf(85,plain,
    ! [SV10: a,SV20: b,SV16: b,SV9: a] :
      ( ( ( ( sK2_SY21 @ SV9 @ SV16 @ SV20 )
          = ( sK2_SY21 @ SV10 @ SV16 @ SV20 ) )
        = $true )
      | ( ( sK1_Xp @ SV9 @ SV10 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[81]) ).

thf(86,plain,
    ! [SV14: a,SV21: b,SV18: b,SV11: a] :
      ( ( ( ~ ( sK2_SY21 @ SV11 @ SV18 @ SV21 )
          | ( sK2_SY21 @ SV11 @ SV21 @ SV18 ) )
        = $true )
      | ( ( sK1_Xp @ SV11 @ SV14 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[83]) ).

thf(87,plain,
    ! [SV15: a,SV22: b,SV19: b,SV12: a] :
      ( ( ( ! [SY112: b] :
              ( ~ ( sK2_SY21 @ SV12 @ SV19 @ SV22 )
              | ~ ( sK2_SY21 @ SV12 @ SV22 @ SY112 )
              | ( sK2_SY21 @ SV12 @ SV19 @ SY112 ) ) )
        = $true )
      | ( ( sK1_Xp @ SV12 @ SV15 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[84]) ).

thf(88,plain,
    ! [SV10: a,SV20: b,SV16: b,SV9: a] :
      ( ( ( ~ ( ( sK2_SY21 @ SV9 @ SV16 @ SV20 )
              | ( sK2_SY21 @ SV10 @ SV16 @ SV20 ) )
          | ~ ( ~ ( sK2_SY21 @ SV9 @ SV16 @ SV20 )
              | ~ ( sK2_SY21 @ SV10 @ SV16 @ SV20 ) ) )
        = $true )
      | ( ( sK1_Xp @ SV9 @ SV10 )
        = $false ) ),
    inference(extcnf_equal_pos,[status(thm)],[85]) ).

thf(89,plain,
    ! [SV10: a,SV20: b,SV16: b,SV9: a] :
      ( ( ( ( sK2_SY21 @ SV9 @ SV16 @ SV20 )
          = ( sK2_SY21 @ SV10 @ SV16 @ SV20 ) )
        = $true )
      | ( ( sK1_Xp @ SV9 @ SV10 )
        = $false ) ),
    inference(extcnf_equal_pos,[status(thm)],[85]) ).

thf(90,plain,
    ! [SV14: a,SV21: b,SV18: b,SV11: a] :
      ( ( ( ~ ( sK2_SY21 @ SV11 @ SV18 @ SV21 ) )
        = $true )
      | ( ( sK2_SY21 @ SV11 @ SV21 @ SV18 )
        = $true )
      | ( ( sK1_Xp @ SV11 @ SV14 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[86]) ).

thf(91,plain,
    ! [SV15: a,SV23: b,SV22: b,SV19: b,SV12: a] :
      ( ( ( ~ ( sK2_SY21 @ SV12 @ SV19 @ SV22 )
          | ~ ( sK2_SY21 @ SV12 @ SV22 @ SV23 )
          | ( sK2_SY21 @ SV12 @ SV19 @ SV23 ) )
        = $true )
      | ( ( sK1_Xp @ SV12 @ SV15 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[87]) ).

thf(92,plain,
    ! [SV10: a,SV20: b,SV16: b,SV9: a] :
      ( ( ( ~ ( ( sK2_SY21 @ SV9 @ SV16 @ SV20 )
              | ( sK2_SY21 @ SV10 @ SV16 @ SV20 ) ) )
        = $true )
      | ( ( ~ ( ~ ( sK2_SY21 @ SV9 @ SV16 @ SV20 )
              | ~ ( sK2_SY21 @ SV10 @ SV16 @ SV20 ) ) )
        = $true )
      | ( ( sK1_Xp @ SV9 @ SV10 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[88]) ).

thf(93,plain,
    ! [SV14: a,SV21: b,SV18: b,SV11: a] :
      ( ( ( sK2_SY21 @ SV11 @ SV18 @ SV21 )
        = $false )
      | ( ( sK2_SY21 @ SV11 @ SV21 @ SV18 )
        = $true )
      | ( ( sK1_Xp @ SV11 @ SV14 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[90]) ).

thf(94,plain,
    ! [SV15: a,SV23: b,SV22: b,SV19: b,SV12: a] :
      ( ( ( ~ ( sK2_SY21 @ SV12 @ SV19 @ SV22 )
          | ~ ( sK2_SY21 @ SV12 @ SV22 @ SV23 ) )
        = $true )
      | ( ( sK2_SY21 @ SV12 @ SV19 @ SV23 )
        = $true )
      | ( ( sK1_Xp @ SV12 @ SV15 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[91]) ).

thf(95,plain,
    ! [SV10: a,SV20: b,SV16: b,SV9: a] :
      ( ( ( ( sK2_SY21 @ SV9 @ SV16 @ SV20 )
          | ( sK2_SY21 @ SV10 @ SV16 @ SV20 ) )
        = $false )
      | ( ( ~ ( ~ ( sK2_SY21 @ SV9 @ SV16 @ SV20 )
              | ~ ( sK2_SY21 @ SV10 @ SV16 @ SV20 ) ) )
        = $true )
      | ( ( sK1_Xp @ SV9 @ SV10 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[92]) ).

thf(96,plain,
    ! [SV15: a,SV23: b,SV22: b,SV19: b,SV12: a] :
      ( ( ( ~ ( sK2_SY21 @ SV12 @ SV19 @ SV22 ) )
        = $true )
      | ( ( ~ ( sK2_SY21 @ SV12 @ SV22 @ SV23 ) )
        = $true )
      | ( ( sK2_SY21 @ SV12 @ SV19 @ SV23 )
        = $true )
      | ( ( sK1_Xp @ SV12 @ SV15 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[94]) ).

thf(97,plain,
    ! [SV10: a,SV20: b,SV16: b,SV9: a] :
      ( ( ( sK2_SY21 @ SV9 @ SV16 @ SV20 )
        = $false )
      | ( ( ~ ( ~ ( sK2_SY21 @ SV9 @ SV16 @ SV20 )
              | ~ ( sK2_SY21 @ SV10 @ SV16 @ SV20 ) ) )
        = $true )
      | ( ( sK1_Xp @ SV9 @ SV10 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[95]) ).

thf(98,plain,
    ! [SV9: a,SV20: b,SV16: b,SV10: a] :
      ( ( ( sK2_SY21 @ SV10 @ SV16 @ SV20 )
        = $false )
      | ( ( ~ ( ~ ( sK2_SY21 @ SV9 @ SV16 @ SV20 )
              | ~ ( sK2_SY21 @ SV10 @ SV16 @ SV20 ) ) )
        = $true )
      | ( ( sK1_Xp @ SV9 @ SV10 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[95]) ).

thf(99,plain,
    ! [SV15: a,SV23: b,SV22: b,SV19: b,SV12: a] :
      ( ( ( sK2_SY21 @ SV12 @ SV19 @ SV22 )
        = $false )
      | ( ( ~ ( sK2_SY21 @ SV12 @ SV22 @ SV23 ) )
        = $true )
      | ( ( sK2_SY21 @ SV12 @ SV19 @ SV23 )
        = $true )
      | ( ( sK1_Xp @ SV12 @ SV15 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[96]) ).

thf(100,plain,
    ! [SV10: a,SV20: b,SV16: b,SV9: a] :
      ( ( ( ~ ( sK2_SY21 @ SV9 @ SV16 @ SV20 )
          | ~ ( sK2_SY21 @ SV10 @ SV16 @ SV20 ) )
        = $false )
      | ( ( sK2_SY21 @ SV9 @ SV16 @ SV20 )
        = $false )
      | ( ( sK1_Xp @ SV9 @ SV10 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[97]) ).

thf(101,plain,
    ! [SV10: a,SV20: b,SV16: b,SV9: a] :
      ( ( ( ~ ( sK2_SY21 @ SV9 @ SV16 @ SV20 )
          | ~ ( sK2_SY21 @ SV10 @ SV16 @ SV20 ) )
        = $false )
      | ( ( sK2_SY21 @ SV10 @ SV16 @ SV20 )
        = $false )
      | ( ( sK1_Xp @ SV9 @ SV10 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[98]) ).

thf(102,plain,
    ! [SV15: a,SV19: b,SV23: b,SV22: b,SV12: a] :
      ( ( ( sK2_SY21 @ SV12 @ SV22 @ SV23 )
        = $false )
      | ( ( sK2_SY21 @ SV12 @ SV19 @ SV22 )
        = $false )
      | ( ( sK2_SY21 @ SV12 @ SV19 @ SV23 )
        = $true )
      | ( ( sK1_Xp @ SV12 @ SV15 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[99]) ).

thf(103,plain,
    ! [SV10: a,SV20: b,SV16: b,SV9: a] :
      ( ( ( ~ ( sK2_SY21 @ SV9 @ SV16 @ SV20 ) )
        = $false )
      | ( ( sK2_SY21 @ SV9 @ SV16 @ SV20 )
        = $false )
      | ( ( sK1_Xp @ SV9 @ SV10 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[100]) ).

thf(104,plain,
    ! [SV9: a,SV20: b,SV16: b,SV10: a] :
      ( ( ( ~ ( sK2_SY21 @ SV10 @ SV16 @ SV20 ) )
        = $false )
      | ( ( sK2_SY21 @ SV9 @ SV16 @ SV20 )
        = $false )
      | ( ( sK1_Xp @ SV9 @ SV10 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[100]) ).

thf(105,plain,
    ! [SV10: a,SV20: b,SV16: b,SV9: a] :
      ( ( ( ~ ( sK2_SY21 @ SV9 @ SV16 @ SV20 ) )
        = $false )
      | ( ( sK2_SY21 @ SV10 @ SV16 @ SV20 )
        = $false )
      | ( ( sK1_Xp @ SV9 @ SV10 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[101]) ).

thf(106,plain,
    ! [SV9: a,SV20: b,SV16: b,SV10: a] :
      ( ( ( ~ ( sK2_SY21 @ SV10 @ SV16 @ SV20 ) )
        = $false )
      | ( ( sK2_SY21 @ SV10 @ SV16 @ SV20 )
        = $false )
      | ( ( sK1_Xp @ SV9 @ SV10 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[101]) ).

thf(107,plain,
    ! [SV10: a,SV20: b,SV16: b,SV9: a] :
      ( ( ( sK2_SY21 @ SV9 @ SV16 @ SV20 )
        = $true )
      | ( ( sK2_SY21 @ SV9 @ SV16 @ SV20 )
        = $false )
      | ( ( sK1_Xp @ SV9 @ SV10 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[103]) ).

thf(108,plain,
    ! [SV9: a,SV20: b,SV16: b,SV10: a] :
      ( ( ( sK2_SY21 @ SV10 @ SV16 @ SV20 )
        = $true )
      | ( ( sK2_SY21 @ SV9 @ SV16 @ SV20 )
        = $false )
      | ( ( sK1_Xp @ SV9 @ SV10 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[104]) ).

thf(109,plain,
    ! [SV10: a,SV20: b,SV16: b,SV9: a] :
      ( ( ( sK2_SY21 @ SV9 @ SV16 @ SV20 )
        = $true )
      | ( ( sK2_SY21 @ SV10 @ SV16 @ SV20 )
        = $false )
      | ( ( sK1_Xp @ SV9 @ SV10 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[105]) ).

thf(110,plain,
    ! [SV9: a,SV20: b,SV16: b,SV10: a] :
      ( ( ( sK2_SY21 @ SV10 @ SV16 @ SV20 )
        = $true )
      | ( ( sK2_SY21 @ SV10 @ SV16 @ SV20 )
        = $false )
      | ( ( sK1_Xp @ SV9 @ SV10 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[106]) ).

thf(111,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[24,110,109,108,107,102,93,89,82,75,68,57,56,55,50,49]) ).

thf(112,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[111]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : SEV034^5 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.12  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.33  % Computer : n028.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Tue Jun 28 01:28:26 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.13/0.35  
% 0.13/0.35   No.of.Axioms: 0
% 0.13/0.35  
% 0.13/0.35   Length.of.Defs: 0
% 0.13/0.35  
% 0.13/0.35   Contains.Choice.Funs: false
% 0.13/0.37  (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)........
% 0.18/0.48  
% 0.18/0.48  ********************************
% 0.18/0.48  *   All subproblems solved!    *
% 0.18/0.48  ********************************
% 0.18/0.48  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:6,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:111,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.18/0.49  
% 0.18/0.49  %**** Beginning of derivation protocol ****
% 0.18/0.49  % SZS output start CNFRefutation
% See solution above
% 0.18/0.49  
% 0.18/0.49  %**** End of derivation protocol ****
% 0.18/0.49  %**** no. of clauses in derivation: 112 ****
% 0.18/0.49  %**** clause counter: 111 ****
% 0.18/0.49  
% 0.18/0.49  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:6,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:111,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------