TSTP Solution File: SYO544^1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SYO544^1 : TPTP v8.2.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n015.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  : 300s
% DateTime : Tue May 21 08:48:01 EDT 2024

% Result   : Theorem 0.19s 0.52s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   46
% Syntax   : Number of formulae    :  140 (  15 unt;  27 typ;   0 def)
%            Number of atoms       : 2675 ( 669 equ;   0 cnn)
%            Maximal formula atoms :  453 (  23 avg)
%            Number of connectives : 4491 (1066   ~;1831   |; 378   &;1158   @)
%                                         (  56 <=>;   1  =>;   0  <=;   1 <~>)
%            Maximal formula depth :   82 (   8 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   33 (  33   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   31 (  27 usr;   8 con; 0-5 aty)
%            Number of variables   :  155 (  26   ^ 128   !;   1   ?; 155   :)

% Comments : 
%------------------------------------------------------------------------------
thf(decl_22,type,
    eps: ( $i > $o ) > $i ).

thf(decl_23,type,
    case: ( $o > $o ) > $i > $i > $i > $i > $i ).

thf(decl_24,type,
    f0: $o > $o ).

thf(decl_25,type,
    f1: $o > $o ).

thf(decl_26,type,
    f2: $o > $o ).

thf(decl_27,type,
    f3: $o > $o ).

thf(decl_28,type,
    esk1_0: $i ).

thf(decl_29,type,
    esk2_0: $i ).

thf(decl_30,type,
    esk3_0: $i ).

thf(decl_31,type,
    esk4_0: $i ).

thf(decl_32,type,
    epred1_0: $i > $o ).

thf(decl_33,type,
    epred2_0: $i > $o ).

thf(decl_34,type,
    epred3_0: $i > $o ).

thf(decl_35,type,
    epred4_0: $i > $o ).

thf(decl_36,type,
    epred5_1: $i > $o ).

thf(decl_37,type,
    epred6_1: $i > $o ).

thf(decl_38,type,
    epred7_1: $i > $o ).

thf(decl_39,type,
    epred8_1: $i > $o ).

thf(decl_40,type,
    epred9_1: $i > $o ).

thf(decl_41,type,
    epred10_1: $i > $o ).

thf(decl_42,type,
    epred11_1: $i > $o ).

thf(decl_43,type,
    epred12_1: $i > $o ).

thf(decl_44,type,
    epred13_1: $i > $o ).

thf(decl_45,type,
    epred14_1: $i > $o ).

thf(decl_46,type,
    epred15_1: $i > $o ).

thf(decl_47,type,
    epred16_1: $i > $o ).

thf(decl_49,type,
    esk6_0: $o ).

thf(f0f,axiom,
    ( ( f0 @ ~ $true )
  <=> ~ $true ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f0f) ).

thf(f3f,axiom,
    ( ( f3 @ ~ $true )
  <=> $true ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f3f) ).

thf(f0t,axiom,
    ( ( f0 @ $true )
  <=> ~ $true ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f0t) ).

thf(f3t,axiom,
    ( ( f3 @ $true )
  <=> $true ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f3t) ).

thf(f1f,axiom,
    ( ( f1 @ ~ $true )
  <=> $true ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f1f) ).

thf(f1t,axiom,
    ( ( f1 @ $true )
  <=> ~ $true ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f1t) ).

thf(f2f,axiom,
    ( ( f2 @ ~ $true )
  <=> ~ $true ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f2f) ).

thf(f2t,axiom,
    ( ( f2 @ $true )
  <=> $true ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f2t) ).

thf(caseood,axiom,
    ( case
    = ( ^ [X3: $o > $o,X2: $i,X4: $i,X5: $i,X6: $i] :
          ( eps
          @ ^ [X7: $i] :
              ( ( ( X3
                  = ( ^ [X8: $o] : ~ $true ) )
                & ( X7 = X2 ) )
              | ( ( X3 = $not )
                & ( X7 = X4 ) )
              | ( ( X3
                  = ( ^ [X8: $o] : X8 ) )
                & ( X7 = X5 ) )
              | ( ( X3
                  = ( ^ [X8: $o] : $true ) )
                & ( X7 = X6 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',caseood) ).

thf(choiceax,axiom,
    ! [X1: $i > $o] :
      ( ? [X2: $i] : ( X1 @ X2 )
     => ( X1 @ ( eps @ X1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',choiceax) ).

thf(conj,conjecture,
    ! [X2: $i,X4: $i,X5: $i,X6: $i] :
      ( ( ( case @ f0 @ X2 @ X4 @ X5 @ X6 )
        = X2 )
      & ( ( case @ f1 @ X2 @ X4 @ X5 @ X6 )
        = X4 )
      & ( ( case @ f2 @ X2 @ X4 @ X5 @ X6 )
        = X5 )
      & ( ( case @ f3 @ X2 @ X4 @ X5 @ X6 )
        = X6 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).

thf(c_0_11,axiom,
    ( ( ( ~ ~ $true
        | ( f0 @ $true ) )
      & ( ~ $true
        | ( f0 @ $false ) ) )
  <=> ~ $true ),
    inference(fool_unroll,[status(thm)],[f0f]) ).

thf(c_0_12,axiom,
    ( ( ( ~ ~ $true
        | ( f3 @ $true ) )
      & ( ~ $true
        | ( f3 @ $false ) ) )
  <=> $true ),
    inference(fool_unroll,[status(thm)],[f3f]) ).

thf(c_0_13,plain,
    ( ( ~ ( f0 @ $true )
      | ~ $true )
    & ( $true
      | ( f0 @ $true ) ) ),
    inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[f0t])]) ).

thf(c_0_14,plain,
    ! [X49: $i,X50: $o,X51: $o,X52: $o] :
      ( ( ~ ( f0 @ X52 )
        | $true
        | ~ ( f0 @ X51 )
        | X51
        | ( f0 = $not )
        | ~ ( f0 @ X50 )
        | ~ $true
        | ~ ( epred1_0 @ X49 ) )
      & ( ~ $true
        | ( f0 @ X52 )
        | ~ ( f0 @ X51 )
        | X51
        | ( f0 = $not )
        | ~ ( f0 @ X50 )
        | ~ $true
        | ~ ( epred1_0 @ X49 ) )
      & ( ( X49 = esk4_0 )
        | ~ ( f0 @ X51 )
        | X51
        | ( f0 = $not )
        | ~ ( f0 @ X50 )
        | ~ $true
        | ~ ( epred1_0 @ X49 ) )
      & ( ~ ( f0 @ X52 )
        | $true
        | ~ X51
        | ( f0 @ X51 )
        | ( f0 = $not )
        | ~ ( f0 @ X50 )
        | ~ $true
        | ~ ( epred1_0 @ X49 ) )
      & ( ~ $true
        | ( f0 @ X52 )
        | ~ X51
        | ( f0 @ X51 )
        | ( f0 = $not )
        | ~ ( f0 @ X50 )
        | ~ $true
        | ~ ( epred1_0 @ X49 ) )
      & ( ( X49 = esk4_0 )
        | ~ X51
        | ( f0 @ X51 )
        | ( f0 = $not )
        | ~ ( f0 @ X50 )
        | ~ $true
        | ~ ( epred1_0 @ X49 ) )
      & ( ~ ( f0 @ X52 )
        | $true
        | ( X49 = esk3_0 )
        | ( f0 = $not )
        | ~ ( f0 @ X50 )
        | ~ $true
        | ~ ( epred1_0 @ X49 ) )
      & ( ~ $true
        | ( f0 @ X52 )
        | ( X49 = esk3_0 )
        | ( f0 = $not )
        | ~ ( f0 @ X50 )
        | ~ $true
        | ~ ( epred1_0 @ X49 ) )
      & ( ( X49 = esk4_0 )
        | ( X49 = esk3_0 )
        | ( f0 = $not )
        | ~ ( f0 @ X50 )
        | ~ $true
        | ~ ( epred1_0 @ X49 ) )
      & ( ~ ( f0 @ X52 )
        | $true
        | ~ ( f0 @ X51 )
        | X51
        | ( X49 = esk2_0 )
        | ~ ( f0 @ X50 )
        | ~ $true
        | ~ ( epred1_0 @ X49 ) )
      & ( ~ $true
        | ( f0 @ X52 )
        | ~ ( f0 @ X51 )
        | X51
        | ( X49 = esk2_0 )
        | ~ ( f0 @ X50 )
        | ~ $true
        | ~ ( epred1_0 @ X49 ) )
      & ( ( X49 = esk4_0 )
        | ~ ( f0 @ X51 )
        | X51
        | ( X49 = esk2_0 )
        | ~ ( f0 @ X50 )
        | ~ $true
        | ~ ( epred1_0 @ X49 ) )
      & ( ~ ( f0 @ X52 )
        | $true
        | ~ X51
        | ( f0 @ X51 )
        | ( X49 = esk2_0 )
        | ~ ( f0 @ X50 )
        | ~ $true
        | ~ ( epred1_0 @ X49 ) )
      & ( ~ $true
        | ( f0 @ X52 )
        | ~ X51
        | ( f0 @ X51 )
        | ( X49 = esk2_0 )
        | ~ ( f0 @ X50 )
        | ~ $true
        | ~ ( epred1_0 @ X49 ) )
      & ( ( X49 = esk4_0 )
        | ~ X51
        | ( f0 @ X51 )
        | ( X49 = esk2_0 )
        | ~ ( f0 @ X50 )
        | ~ $true
        | ~ ( epred1_0 @ X49 ) )
      & ( ~ ( f0 @ X52 )
        | $true
        | ( X49 = esk3_0 )
        | ( X49 = esk2_0 )
        | ~ ( f0 @ X50 )
        | ~ $true
        | ~ ( epred1_0 @ X49 ) )
      & ( ~ $true
        | ( f0 @ X52 )
        | ( X49 = esk3_0 )
        | ( X49 = esk2_0 )
        | ~ ( f0 @ X50 )
        | ~ $true
        | ~ ( epred1_0 @ X49 ) )
      & ( ( X49 = esk4_0 )
        | ( X49 = esk3_0 )
        | ( X49 = esk2_0 )
        | ~ ( f0 @ X50 )
        | ~ $true
        | ~ ( epred1_0 @ X49 ) )
      & ( ~ ( f0 @ X52 )
        | $true
        | ~ ( f0 @ X51 )
        | X51
        | ( f0 = $not )
        | $true
        | ( f0 @ X50 )
        | ~ ( epred1_0 @ X49 ) )
      & ( ~ $true
        | ( f0 @ X52 )
        | ~ ( f0 @ X51 )
        | X51
        | ( f0 = $not )
        | $true
        | ( f0 @ X50 )
        | ~ ( epred1_0 @ X49 ) )
      & ( ( X49 = esk4_0 )
        | ~ ( f0 @ X51 )
        | X51
        | ( f0 = $not )
        | $true
        | ( f0 @ X50 )
        | ~ ( epred1_0 @ X49 ) )
      & ( ~ ( f0 @ X52 )
        | $true
        | ~ X51
        | ( f0 @ X51 )
        | ( f0 = $not )
        | $true
        | ( f0 @ X50 )
        | ~ ( epred1_0 @ X49 ) )
      & ( ~ $true
        | ( f0 @ X52 )
        | ~ X51
        | ( f0 @ X51 )
        | ( f0 = $not )
        | $true
        | ( f0 @ X50 )
        | ~ ( epred1_0 @ X49 ) )
      & ( ( X49 = esk4_0 )
        | ~ X51
        | ( f0 @ X51 )
        | ( f0 = $not )
        | $true
        | ( f0 @ X50 )
        | ~ ( epred1_0 @ X49 ) )
      & ( ~ ( f0 @ X52 )
        | $true
        | ( X49 = esk3_0 )
        | ( f0 = $not )
        | $true
        | ( f0 @ X50 )
        | ~ ( epred1_0 @ X49 ) )
      & ( ~ $true
        | ( f0 @ X52 )
        | ( X49 = esk3_0 )
        | ( f0 = $not )
        | $true
        | ( f0 @ X50 )
        | ~ ( epred1_0 @ X49 ) )
      & ( ( X49 = esk4_0 )
        | ( X49 = esk3_0 )
        | ( f0 = $not )
        | $true
        | ( f0 @ X50 )
        | ~ ( epred1_0 @ X49 ) )
      & ( ~ ( f0 @ X52 )
        | $true
        | ~ ( f0 @ X51 )
        | X51
        | ( X49 = esk2_0 )
        | $true
        | ( f0 @ X50 )
        | ~ ( epred1_0 @ X49 ) )
      & ( ~ $true
        | ( f0 @ X52 )
        | ~ ( f0 @ X51 )
        | X51
        | ( X49 = esk2_0 )
        | $true
        | ( f0 @ X50 )
        | ~ ( epred1_0 @ X49 ) )
      & ( ( X49 = esk4_0 )
        | ~ ( f0 @ X51 )
        | X51
        | ( X49 = esk2_0 )
        | $true
        | ( f0 @ X50 )
        | ~ ( epred1_0 @ X49 ) )
      & ( ~ ( f0 @ X52 )
        | $true
        | ~ X51
        | ( f0 @ X51 )
        | ( X49 = esk2_0 )
        | $true
        | ( f0 @ X50 )
        | ~ ( epred1_0 @ X49 ) )
      & ( ~ $true
        | ( f0 @ X52 )
        | ~ X51
        | ( f0 @ X51 )
        | ( X49 = esk2_0 )
        | $true
        | ( f0 @ X50 )
        | ~ ( epred1_0 @ X49 ) )
      & ( ( X49 = esk4_0 )
        | ~ X51
        | ( f0 @ X51 )
        | ( X49 = esk2_0 )
        | $true
        | ( f0 @ X50 )
        | ~ ( epred1_0 @ X49 ) )
      & ( ~ ( f0 @ X52 )
        | $true
        | ( X49 = esk3_0 )
        | ( X49 = esk2_0 )
        | $true
        | ( f0 @ X50 )
        | ~ ( epred1_0 @ X49 ) )
      & ( ~ $true
        | ( f0 @ X52 )
        | ( X49 = esk3_0 )
        | ( X49 = esk2_0 )
        | $true
        | ( f0 @ X50 )
        | ~ ( epred1_0 @ X49 ) )
      & ( ( X49 = esk4_0 )
        | ( X49 = esk3_0 )
        | ( X49 = esk2_0 )
        | $true
        | ( f0 @ X50 )
        | ~ ( epred1_0 @ X49 ) )
      & ( ~ ( f0 @ X52 )
        | $true
        | ~ ( f0 @ X51 )
        | X51
        | ( f0 = $not )
        | ( X49 = esk1_0 )
        | ~ ( epred1_0 @ X49 ) )
      & ( ~ $true
        | ( f0 @ X52 )
        | ~ ( f0 @ X51 )
        | X51
        | ( f0 = $not )
        | ( X49 = esk1_0 )
        | ~ ( epred1_0 @ X49 ) )
      & ( ( X49 = esk4_0 )
        | ~ ( f0 @ X51 )
        | X51
        | ( f0 = $not )
        | ( X49 = esk1_0 )
        | ~ ( epred1_0 @ X49 ) )
      & ( ~ ( f0 @ X52 )
        | $true
        | ~ X51
        | ( f0 @ X51 )
        | ( f0 = $not )
        | ( X49 = esk1_0 )
        | ~ ( epred1_0 @ X49 ) )
      & ( ~ $true
        | ( f0 @ X52 )
        | ~ X51
        | ( f0 @ X51 )
        | ( f0 = $not )
        | ( X49 = esk1_0 )
        | ~ ( epred1_0 @ X49 ) )
      & ( ( X49 = esk4_0 )
        | ~ X51
        | ( f0 @ X51 )
        | ( f0 = $not )
        | ( X49 = esk1_0 )
        | ~ ( epred1_0 @ X49 ) )
      & ( ~ ( f0 @ X52 )
        | $true
        | ( X49 = esk3_0 )
        | ( f0 = $not )
        | ( X49 = esk1_0 )
        | ~ ( epred1_0 @ X49 ) )
      & ( ~ $true
        | ( f0 @ X52 )
        | ( X49 = esk3_0 )
        | ( f0 = $not )
        | ( X49 = esk1_0 )
        | ~ ( epred1_0 @ X49 ) )
      & ( ( X49 = esk4_0 )
        | ( X49 = esk3_0 )
        | ( f0 = $not )
        | ( X49 = esk1_0 )
        | ~ ( epred1_0 @ X49 ) )
      & ( ~ ( f0 @ X52 )
        | $true
        | ~ ( f0 @ X51 )
        | X51
        | ( X49 = esk2_0 )
        | ( X49 = esk1_0 )
        | ~ ( epred1_0 @ X49 ) )
      & ( ~ $true
        | ( f0 @ X52 )
        | ~ ( f0 @ X51 )
        | X51
        | ( X49 = esk2_0 )
        | ( X49 = esk1_0 )
        | ~ ( epred1_0 @ X49 ) )
      & ( ( X49 = esk4_0 )
        | ~ ( f0 @ X51 )
        | X51
        | ( X49 = esk2_0 )
        | ( X49 = esk1_0 )
        | ~ ( epred1_0 @ X49 ) )
      & ( ~ ( f0 @ X52 )
        | $true
        | ~ X51
        | ( f0 @ X51 )
        | ( X49 = esk2_0 )
        | ( X49 = esk1_0 )
        | ~ ( epred1_0 @ X49 ) )
      & ( ~ $true
        | ( f0 @ X52 )
        | ~ X51
        | ( f0 @ X51 )
        | ( X49 = esk2_0 )
        | ( X49 = esk1_0 )
        | ~ ( epred1_0 @ X49 ) )
      & ( ( X49 = esk4_0 )
        | ~ X51
        | ( f0 @ X51 )
        | ( X49 = esk2_0 )
        | ( X49 = esk1_0 )
        | ~ ( epred1_0 @ X49 ) )
      & ( ~ ( f0 @ X52 )
        | $true
        | ( X49 = esk3_0 )
        | ( X49 = esk2_0 )
        | ( X49 = esk1_0 )
        | ~ ( epred1_0 @ X49 ) )
      & ( ~ $true
        | ( f0 @ X52 )
        | ( X49 = esk3_0 )
        | ( X49 = esk2_0 )
        | ( X49 = esk1_0 )
        | ~ ( epred1_0 @ X49 ) )
      & ( ( X49 = esk4_0 )
        | ( X49 = esk3_0 )
        | ( X49 = esk2_0 )
        | ( X49 = esk1_0 )
        | ~ ( epred1_0 @ X49 ) )
      & ( ~ ( epred5_1 @ X49 )
        | ( epred5_1 @ X49 )
        | $true
        | ( X49 != esk1_0 )
        | ( epred1_0 @ X49 ) )
      & ( ~ ( f0 @ $false )
        | ( epred5_1 @ X49 )
        | $true
        | ( X49 != esk1_0 )
        | ( epred1_0 @ X49 ) )
      & ( ~ ( epred5_1 @ X49 )
        | ~ ( f0 @ $true )
        | $true
        | ( X49 != esk1_0 )
        | ( epred1_0 @ X49 ) )
      & ( ~ ( f0 @ $false )
        | ~ ( f0 @ $true )
        | $true
        | ( X49 != esk1_0 )
        | ( epred1_0 @ X49 ) )
      & ( ~ ( epred5_1 @ X49 )
        | ( f0 @ $true )
        | ~ $true
        | ( X49 != esk1_0 )
        | ( epred1_0 @ X49 ) )
      & ( ( epred5_1 @ X49 )
        | ( f0 @ $false )
        | ~ $true
        | ( X49 != esk1_0 )
        | ( epred1_0 @ X49 ) )
      & ( ( f0 != $not )
        | ( X49 != esk2_0 )
        | ( epred1_0 @ X49 ) )
      & ( ~ ( epred6_1 @ X49 )
        | ( epred6_1 @ X49 )
        | ~ ( epred6_1 @ X49 )
        | ( X49 != esk3_0 )
        | ( epred1_0 @ X49 ) )
      & ( ~ ( f0 @ $false )
        | ( epred6_1 @ X49 )
        | ~ ( epred6_1 @ X49 )
        | ( X49 != esk3_0 )
        | ( epred1_0 @ X49 ) )
      & ( ~ ( epred6_1 @ X49 )
        | ~ ( f0 @ $true )
        | ~ ( epred6_1 @ X49 )
        | ( X49 != esk3_0 )
        | ( epred1_0 @ X49 ) )
      & ( ~ ( f0 @ $false )
        | ~ ( f0 @ $true )
        | ~ ( epred6_1 @ X49 )
        | ( X49 != esk3_0 )
        | ( epred1_0 @ X49 ) )
      & ( ~ ( epred6_1 @ X49 )
        | ( f0 @ $true )
        | ( epred6_1 @ X49 )
        | ( X49 != esk3_0 )
        | ( epred1_0 @ X49 ) )
      & ( ( epred6_1 @ X49 )
        | ( f0 @ $false )
        | ( epred6_1 @ X49 )
        | ( X49 != esk3_0 )
        | ( epred1_0 @ X49 ) )
      & ( ~ ( epred7_1 @ X49 )
        | ( epred7_1 @ X49 )
        | ~ $true
        | ( X49 != esk4_0 )
        | ( epred1_0 @ X49 ) )
      & ( ~ ( f0 @ $false )
        | ( epred7_1 @ X49 )
        | ~ $true
        | ( X49 != esk4_0 )
        | ( epred1_0 @ X49 ) )
      & ( ~ ( epred7_1 @ X49 )
        | ~ ( f0 @ $true )
        | ~ $true
        | ( X49 != esk4_0 )
        | ( epred1_0 @ X49 ) )
      & ( ~ ( f0 @ $false )
        | ~ ( f0 @ $true )
        | ~ $true
        | ( X49 != esk4_0 )
        | ( epred1_0 @ X49 ) )
      & ( ~ ( epred7_1 @ X49 )
        | ( f0 @ $true )
        | $true
        | ( X49 != esk4_0 )
        | ( epred1_0 @ X49 ) )
      & ( ( epred7_1 @ X49 )
        | ( f0 @ $false )
        | $true
        | ( X49 != esk4_0 )
        | ( epred1_0 @ X49 ) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[])])])])])])]) ).

thf(c_0_15,plain,
    ( ( $true
      | ~ $true
      | ~ $true )
    & ( ~ ( f0 @ $false )
      | ~ $true
      | ~ $true )
    & ( $true
      | ~ ( f0 @ $true )
      | ~ $true )
    & ( ~ ( f0 @ $false )
      | ~ ( f0 @ $true )
      | ~ $true )
    & ( $true
      | ( f0 @ $true )
      | $true )
    & ( ~ $true
      | ( f0 @ $false )
      | $true ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])]) ).

thf(c_0_16,plain,
    ( ( $true
      | ~ $true
      | $true )
    & ( ~ ( f3 @ $false )
      | ~ $true
      | $true )
    & ( $true
      | ~ ( f3 @ $true )
      | $true )
    & ( ~ ( f3 @ $false )
      | ~ ( f3 @ $true )
      | $true )
    & ( $true
      | ( f3 @ $true )
      | ~ $true )
    & ( ~ $true
      | ( f3 @ $false )
      | ~ $true ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])]) ).

thf(c_0_17,plain,
    ( ~ ( f0 @ $true )
    | ~ $true ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

thf(c_0_18,plain,
    ! [X2: $i] :
      ( ( epred5_1 @ X2 )
      | ( f0 @ ~ $true )
      | ( epred1_0 @ X2 )
      | ~ $true
      | ( X2 != esk1_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

thf(c_0_19,plain,
    ( ~ ( f0 @ ~ $true )
    | ~ $true
    | ~ $true ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

thf(c_0_20,plain,
    ! [X70: $i,X71: $o,X72: $o,X73: $o] :
      ( ( ~ ( f3 @ X73 )
        | $true
        | ~ ( f3 @ X72 )
        | X72
        | ( f3 = $not )
        | ~ ( f3 @ X71 )
        | ~ $true
        | ~ ( epred4_0 @ X70 ) )
      & ( ~ $true
        | ( f3 @ X73 )
        | ~ ( f3 @ X72 )
        | X72
        | ( f3 = $not )
        | ~ ( f3 @ X71 )
        | ~ $true
        | ~ ( epred4_0 @ X70 ) )
      & ( ( X70 = esk4_0 )
        | ~ ( f3 @ X72 )
        | X72
        | ( f3 = $not )
        | ~ ( f3 @ X71 )
        | ~ $true
        | ~ ( epred4_0 @ X70 ) )
      & ( ~ ( f3 @ X73 )
        | $true
        | ~ X72
        | ( f3 @ X72 )
        | ( f3 = $not )
        | ~ ( f3 @ X71 )
        | ~ $true
        | ~ ( epred4_0 @ X70 ) )
      & ( ~ $true
        | ( f3 @ X73 )
        | ~ X72
        | ( f3 @ X72 )
        | ( f3 = $not )
        | ~ ( f3 @ X71 )
        | ~ $true
        | ~ ( epred4_0 @ X70 ) )
      & ( ( X70 = esk4_0 )
        | ~ X72
        | ( f3 @ X72 )
        | ( f3 = $not )
        | ~ ( f3 @ X71 )
        | ~ $true
        | ~ ( epred4_0 @ X70 ) )
      & ( ~ ( f3 @ X73 )
        | $true
        | ( X70 = esk3_0 )
        | ( f3 = $not )
        | ~ ( f3 @ X71 )
        | ~ $true
        | ~ ( epred4_0 @ X70 ) )
      & ( ~ $true
        | ( f3 @ X73 )
        | ( X70 = esk3_0 )
        | ( f3 = $not )
        | ~ ( f3 @ X71 )
        | ~ $true
        | ~ ( epred4_0 @ X70 ) )
      & ( ( X70 = esk4_0 )
        | ( X70 = esk3_0 )
        | ( f3 = $not )
        | ~ ( f3 @ X71 )
        | ~ $true
        | ~ ( epred4_0 @ X70 ) )
      & ( ~ ( f3 @ X73 )
        | $true
        | ~ ( f3 @ X72 )
        | X72
        | ( X70 = esk2_0 )
        | ~ ( f3 @ X71 )
        | ~ $true
        | ~ ( epred4_0 @ X70 ) )
      & ( ~ $true
        | ( f3 @ X73 )
        | ~ ( f3 @ X72 )
        | X72
        | ( X70 = esk2_0 )
        | ~ ( f3 @ X71 )
        | ~ $true
        | ~ ( epred4_0 @ X70 ) )
      & ( ( X70 = esk4_0 )
        | ~ ( f3 @ X72 )
        | X72
        | ( X70 = esk2_0 )
        | ~ ( f3 @ X71 )
        | ~ $true
        | ~ ( epred4_0 @ X70 ) )
      & ( ~ ( f3 @ X73 )
        | $true
        | ~ X72
        | ( f3 @ X72 )
        | ( X70 = esk2_0 )
        | ~ ( f3 @ X71 )
        | ~ $true
        | ~ ( epred4_0 @ X70 ) )
      & ( ~ $true
        | ( f3 @ X73 )
        | ~ X72
        | ( f3 @ X72 )
        | ( X70 = esk2_0 )
        | ~ ( f3 @ X71 )
        | ~ $true
        | ~ ( epred4_0 @ X70 ) )
      & ( ( X70 = esk4_0 )
        | ~ X72
        | ( f3 @ X72 )
        | ( X70 = esk2_0 )
        | ~ ( f3 @ X71 )
        | ~ $true
        | ~ ( epred4_0 @ X70 ) )
      & ( ~ ( f3 @ X73 )
        | $true
        | ( X70 = esk3_0 )
        | ( X70 = esk2_0 )
        | ~ ( f3 @ X71 )
        | ~ $true
        | ~ ( epred4_0 @ X70 ) )
      & ( ~ $true
        | ( f3 @ X73 )
        | ( X70 = esk3_0 )
        | ( X70 = esk2_0 )
        | ~ ( f3 @ X71 )
        | ~ $true
        | ~ ( epred4_0 @ X70 ) )
      & ( ( X70 = esk4_0 )
        | ( X70 = esk3_0 )
        | ( X70 = esk2_0 )
        | ~ ( f3 @ X71 )
        | ~ $true
        | ~ ( epred4_0 @ X70 ) )
      & ( ~ ( f3 @ X73 )
        | $true
        | ~ ( f3 @ X72 )
        | X72
        | ( f3 = $not )
        | $true
        | ( f3 @ X71 )
        | ~ ( epred4_0 @ X70 ) )
      & ( ~ $true
        | ( f3 @ X73 )
        | ~ ( f3 @ X72 )
        | X72
        | ( f3 = $not )
        | $true
        | ( f3 @ X71 )
        | ~ ( epred4_0 @ X70 ) )
      & ( ( X70 = esk4_0 )
        | ~ ( f3 @ X72 )
        | X72
        | ( f3 = $not )
        | $true
        | ( f3 @ X71 )
        | ~ ( epred4_0 @ X70 ) )
      & ( ~ ( f3 @ X73 )
        | $true
        | ~ X72
        | ( f3 @ X72 )
        | ( f3 = $not )
        | $true
        | ( f3 @ X71 )
        | ~ ( epred4_0 @ X70 ) )
      & ( ~ $true
        | ( f3 @ X73 )
        | ~ X72
        | ( f3 @ X72 )
        | ( f3 = $not )
        | $true
        | ( f3 @ X71 )
        | ~ ( epred4_0 @ X70 ) )
      & ( ( X70 = esk4_0 )
        | ~ X72
        | ( f3 @ X72 )
        | ( f3 = $not )
        | $true
        | ( f3 @ X71 )
        | ~ ( epred4_0 @ X70 ) )
      & ( ~ ( f3 @ X73 )
        | $true
        | ( X70 = esk3_0 )
        | ( f3 = $not )
        | $true
        | ( f3 @ X71 )
        | ~ ( epred4_0 @ X70 ) )
      & ( ~ $true
        | ( f3 @ X73 )
        | ( X70 = esk3_0 )
        | ( f3 = $not )
        | $true
        | ( f3 @ X71 )
        | ~ ( epred4_0 @ X70 ) )
      & ( ( X70 = esk4_0 )
        | ( X70 = esk3_0 )
        | ( f3 = $not )
        | $true
        | ( f3 @ X71 )
        | ~ ( epred4_0 @ X70 ) )
      & ( ~ ( f3 @ X73 )
        | $true
        | ~ ( f3 @ X72 )
        | X72
        | ( X70 = esk2_0 )
        | $true
        | ( f3 @ X71 )
        | ~ ( epred4_0 @ X70 ) )
      & ( ~ $true
        | ( f3 @ X73 )
        | ~ ( f3 @ X72 )
        | X72
        | ( X70 = esk2_0 )
        | $true
        | ( f3 @ X71 )
        | ~ ( epred4_0 @ X70 ) )
      & ( ( X70 = esk4_0 )
        | ~ ( f3 @ X72 )
        | X72
        | ( X70 = esk2_0 )
        | $true
        | ( f3 @ X71 )
        | ~ ( epred4_0 @ X70 ) )
      & ( ~ ( f3 @ X73 )
        | $true
        | ~ X72
        | ( f3 @ X72 )
        | ( X70 = esk2_0 )
        | $true
        | ( f3 @ X71 )
        | ~ ( epred4_0 @ X70 ) )
      & ( ~ $true
        | ( f3 @ X73 )
        | ~ X72
        | ( f3 @ X72 )
        | ( X70 = esk2_0 )
        | $true
        | ( f3 @ X71 )
        | ~ ( epred4_0 @ X70 ) )
      & ( ( X70 = esk4_0 )
        | ~ X72
        | ( f3 @ X72 )
        | ( X70 = esk2_0 )
        | $true
        | ( f3 @ X71 )
        | ~ ( epred4_0 @ X70 ) )
      & ( ~ ( f3 @ X73 )
        | $true
        | ( X70 = esk3_0 )
        | ( X70 = esk2_0 )
        | $true
        | ( f3 @ X71 )
        | ~ ( epred4_0 @ X70 ) )
      & ( ~ $true
        | ( f3 @ X73 )
        | ( X70 = esk3_0 )
        | ( X70 = esk2_0 )
        | $true
        | ( f3 @ X71 )
        | ~ ( epred4_0 @ X70 ) )
      & ( ( X70 = esk4_0 )
        | ( X70 = esk3_0 )
        | ( X70 = esk2_0 )
        | $true
        | ( f3 @ X71 )
        | ~ ( epred4_0 @ X70 ) )
      & ( ~ ( f3 @ X73 )
        | $true
        | ~ ( f3 @ X72 )
        | X72
        | ( f3 = $not )
        | ( X70 = esk1_0 )
        | ~ ( epred4_0 @ X70 ) )
      & ( ~ $true
        | ( f3 @ X73 )
        | ~ ( f3 @ X72 )
        | X72
        | ( f3 = $not )
        | ( X70 = esk1_0 )
        | ~ ( epred4_0 @ X70 ) )
      & ( ( X70 = esk4_0 )
        | ~ ( f3 @ X72 )
        | X72
        | ( f3 = $not )
        | ( X70 = esk1_0 )
        | ~ ( epred4_0 @ X70 ) )
      & ( ~ ( f3 @ X73 )
        | $true
        | ~ X72
        | ( f3 @ X72 )
        | ( f3 = $not )
        | ( X70 = esk1_0 )
        | ~ ( epred4_0 @ X70 ) )
      & ( ~ $true
        | ( f3 @ X73 )
        | ~ X72
        | ( f3 @ X72 )
        | ( f3 = $not )
        | ( X70 = esk1_0 )
        | ~ ( epred4_0 @ X70 ) )
      & ( ( X70 = esk4_0 )
        | ~ X72
        | ( f3 @ X72 )
        | ( f3 = $not )
        | ( X70 = esk1_0 )
        | ~ ( epred4_0 @ X70 ) )
      & ( ~ ( f3 @ X73 )
        | $true
        | ( X70 = esk3_0 )
        | ( f3 = $not )
        | ( X70 = esk1_0 )
        | ~ ( epred4_0 @ X70 ) )
      & ( ~ $true
        | ( f3 @ X73 )
        | ( X70 = esk3_0 )
        | ( f3 = $not )
        | ( X70 = esk1_0 )
        | ~ ( epred4_0 @ X70 ) )
      & ( ( X70 = esk4_0 )
        | ( X70 = esk3_0 )
        | ( f3 = $not )
        | ( X70 = esk1_0 )
        | ~ ( epred4_0 @ X70 ) )
      & ( ~ ( f3 @ X73 )
        | $true
        | ~ ( f3 @ X72 )
        | X72
        | ( X70 = esk2_0 )
        | ( X70 = esk1_0 )
        | ~ ( epred4_0 @ X70 ) )
      & ( ~ $true
        | ( f3 @ X73 )
        | ~ ( f3 @ X72 )
        | X72
        | ( X70 = esk2_0 )
        | ( X70 = esk1_0 )
        | ~ ( epred4_0 @ X70 ) )
      & ( ( X70 = esk4_0 )
        | ~ ( f3 @ X72 )
        | X72
        | ( X70 = esk2_0 )
        | ( X70 = esk1_0 )
        | ~ ( epred4_0 @ X70 ) )
      & ( ~ ( f3 @ X73 )
        | $true
        | ~ X72
        | ( f3 @ X72 )
        | ( X70 = esk2_0 )
        | ( X70 = esk1_0 )
        | ~ ( epred4_0 @ X70 ) )
      & ( ~ $true
        | ( f3 @ X73 )
        | ~ X72
        | ( f3 @ X72 )
        | ( X70 = esk2_0 )
        | ( X70 = esk1_0 )
        | ~ ( epred4_0 @ X70 ) )
      & ( ( X70 = esk4_0 )
        | ~ X72
        | ( f3 @ X72 )
        | ( X70 = esk2_0 )
        | ( X70 = esk1_0 )
        | ~ ( epred4_0 @ X70 ) )
      & ( ~ ( f3 @ X73 )
        | $true
        | ( X70 = esk3_0 )
        | ( X70 = esk2_0 )
        | ( X70 = esk1_0 )
        | ~ ( epred4_0 @ X70 ) )
      & ( ~ $true
        | ( f3 @ X73 )
        | ( X70 = esk3_0 )
        | ( X70 = esk2_0 )
        | ( X70 = esk1_0 )
        | ~ ( epred4_0 @ X70 ) )
      & ( ( X70 = esk4_0 )
        | ( X70 = esk3_0 )
        | ( X70 = esk2_0 )
        | ( X70 = esk1_0 )
        | ~ ( epred4_0 @ X70 ) )
      & ( ~ ( epred14_1 @ X70 )
        | ( epred14_1 @ X70 )
        | $true
        | ( X70 != esk1_0 )
        | ( epred4_0 @ X70 ) )
      & ( ~ ( f3 @ $false )
        | ( epred14_1 @ X70 )
        | $true
        | ( X70 != esk1_0 )
        | ( epred4_0 @ X70 ) )
      & ( ~ ( epred14_1 @ X70 )
        | ~ ( f3 @ $true )
        | $true
        | ( X70 != esk1_0 )
        | ( epred4_0 @ X70 ) )
      & ( ~ ( f3 @ $false )
        | ~ ( f3 @ $true )
        | $true
        | ( X70 != esk1_0 )
        | ( epred4_0 @ X70 ) )
      & ( ~ ( epred14_1 @ X70 )
        | ( f3 @ $true )
        | ~ $true
        | ( X70 != esk1_0 )
        | ( epred4_0 @ X70 ) )
      & ( ( epred14_1 @ X70 )
        | ( f3 @ $false )
        | ~ $true
        | ( X70 != esk1_0 )
        | ( epred4_0 @ X70 ) )
      & ( ( f3 != $not )
        | ( X70 != esk2_0 )
        | ( epred4_0 @ X70 ) )
      & ( ~ ( epred15_1 @ X70 )
        | ( epred15_1 @ X70 )
        | ~ ( epred15_1 @ X70 )
        | ( X70 != esk3_0 )
        | ( epred4_0 @ X70 ) )
      & ( ~ ( f3 @ $false )
        | ( epred15_1 @ X70 )
        | ~ ( epred15_1 @ X70 )
        | ( X70 != esk3_0 )
        | ( epred4_0 @ X70 ) )
      & ( ~ ( epred15_1 @ X70 )
        | ~ ( f3 @ $true )
        | ~ ( epred15_1 @ X70 )
        | ( X70 != esk3_0 )
        | ( epred4_0 @ X70 ) )
      & ( ~ ( f3 @ $false )
        | ~ ( f3 @ $true )
        | ~ ( epred15_1 @ X70 )
        | ( X70 != esk3_0 )
        | ( epred4_0 @ X70 ) )
      & ( ~ ( epred15_1 @ X70 )
        | ( f3 @ $true )
        | ( epred15_1 @ X70 )
        | ( X70 != esk3_0 )
        | ( epred4_0 @ X70 ) )
      & ( ( epred15_1 @ X70 )
        | ( f3 @ $false )
        | ( epred15_1 @ X70 )
        | ( X70 != esk3_0 )
        | ( epred4_0 @ X70 ) )
      & ( ~ ( epred16_1 @ X70 )
        | ( epred16_1 @ X70 )
        | ~ $true
        | ( X70 != esk4_0 )
        | ( epred4_0 @ X70 ) )
      & ( ~ ( f3 @ $false )
        | ( epred16_1 @ X70 )
        | ~ $true
        | ( X70 != esk4_0 )
        | ( epred4_0 @ X70 ) )
      & ( ~ ( epred16_1 @ X70 )
        | ~ ( f3 @ $true )
        | ~ $true
        | ( X70 != esk4_0 )
        | ( epred4_0 @ X70 ) )
      & ( ~ ( f3 @ $false )
        | ~ ( f3 @ $true )
        | ~ $true
        | ( X70 != esk4_0 )
        | ( epred4_0 @ X70 ) )
      & ( ~ ( epred16_1 @ X70 )
        | ( f3 @ $true )
        | $true
        | ( X70 != esk4_0 )
        | ( epred4_0 @ X70 ) )
      & ( ( epred16_1 @ X70 )
        | ( f3 @ $false )
        | $true
        | ( X70 != esk4_0 )
        | ( epred4_0 @ X70 ) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[])])])])])])]) ).

thf(c_0_21,plain,
    ( ( f3 @ ~ $true )
    | ~ $true
    | ~ $true ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

thf(c_0_22,plain,
    ! [X56: $i,X57: $o,X58: $o,X59: $o] :
      ( ( ~ ( f1 @ X59 )
        | $true
        | ~ ( f1 @ X58 )
        | X58
        | ( f1 = $not )
        | ~ ( f1 @ X57 )
        | ~ $true
        | ~ ( epred2_0 @ X56 ) )
      & ( ~ $true
        | ( f1 @ X59 )
        | ~ ( f1 @ X58 )
        | X58
        | ( f1 = $not )
        | ~ ( f1 @ X57 )
        | ~ $true
        | ~ ( epred2_0 @ X56 ) )
      & ( ( X56 = esk4_0 )
        | ~ ( f1 @ X58 )
        | X58
        | ( f1 = $not )
        | ~ ( f1 @ X57 )
        | ~ $true
        | ~ ( epred2_0 @ X56 ) )
      & ( ~ ( f1 @ X59 )
        | $true
        | ~ X58
        | ( f1 @ X58 )
        | ( f1 = $not )
        | ~ ( f1 @ X57 )
        | ~ $true
        | ~ ( epred2_0 @ X56 ) )
      & ( ~ $true
        | ( f1 @ X59 )
        | ~ X58
        | ( f1 @ X58 )
        | ( f1 = $not )
        | ~ ( f1 @ X57 )
        | ~ $true
        | ~ ( epred2_0 @ X56 ) )
      & ( ( X56 = esk4_0 )
        | ~ X58
        | ( f1 @ X58 )
        | ( f1 = $not )
        | ~ ( f1 @ X57 )
        | ~ $true
        | ~ ( epred2_0 @ X56 ) )
      & ( ~ ( f1 @ X59 )
        | $true
        | ( X56 = esk3_0 )
        | ( f1 = $not )
        | ~ ( f1 @ X57 )
        | ~ $true
        | ~ ( epred2_0 @ X56 ) )
      & ( ~ $true
        | ( f1 @ X59 )
        | ( X56 = esk3_0 )
        | ( f1 = $not )
        | ~ ( f1 @ X57 )
        | ~ $true
        | ~ ( epred2_0 @ X56 ) )
      & ( ( X56 = esk4_0 )
        | ( X56 = esk3_0 )
        | ( f1 = $not )
        | ~ ( f1 @ X57 )
        | ~ $true
        | ~ ( epred2_0 @ X56 ) )
      & ( ~ ( f1 @ X59 )
        | $true
        | ~ ( f1 @ X58 )
        | X58
        | ( X56 = esk2_0 )
        | ~ ( f1 @ X57 )
        | ~ $true
        | ~ ( epred2_0 @ X56 ) )
      & ( ~ $true
        | ( f1 @ X59 )
        | ~ ( f1 @ X58 )
        | X58
        | ( X56 = esk2_0 )
        | ~ ( f1 @ X57 )
        | ~ $true
        | ~ ( epred2_0 @ X56 ) )
      & ( ( X56 = esk4_0 )
        | ~ ( f1 @ X58 )
        | X58
        | ( X56 = esk2_0 )
        | ~ ( f1 @ X57 )
        | ~ $true
        | ~ ( epred2_0 @ X56 ) )
      & ( ~ ( f1 @ X59 )
        | $true
        | ~ X58
        | ( f1 @ X58 )
        | ( X56 = esk2_0 )
        | ~ ( f1 @ X57 )
        | ~ $true
        | ~ ( epred2_0 @ X56 ) )
      & ( ~ $true
        | ( f1 @ X59 )
        | ~ X58
        | ( f1 @ X58 )
        | ( X56 = esk2_0 )
        | ~ ( f1 @ X57 )
        | ~ $true
        | ~ ( epred2_0 @ X56 ) )
      & ( ( X56 = esk4_0 )
        | ~ X58
        | ( f1 @ X58 )
        | ( X56 = esk2_0 )
        | ~ ( f1 @ X57 )
        | ~ $true
        | ~ ( epred2_0 @ X56 ) )
      & ( ~ ( f1 @ X59 )
        | $true
        | ( X56 = esk3_0 )
        | ( X56 = esk2_0 )
        | ~ ( f1 @ X57 )
        | ~ $true
        | ~ ( epred2_0 @ X56 ) )
      & ( ~ $true
        | ( f1 @ X59 )
        | ( X56 = esk3_0 )
        | ( X56 = esk2_0 )
        | ~ ( f1 @ X57 )
        | ~ $true
        | ~ ( epred2_0 @ X56 ) )
      & ( ( X56 = esk4_0 )
        | ( X56 = esk3_0 )
        | ( X56 = esk2_0 )
        | ~ ( f1 @ X57 )
        | ~ $true
        | ~ ( epred2_0 @ X56 ) )
      & ( ~ ( f1 @ X59 )
        | $true
        | ~ ( f1 @ X58 )
        | X58
        | ( f1 = $not )
        | $true
        | ( f1 @ X57 )
        | ~ ( epred2_0 @ X56 ) )
      & ( ~ $true
        | ( f1 @ X59 )
        | ~ ( f1 @ X58 )
        | X58
        | ( f1 = $not )
        | $true
        | ( f1 @ X57 )
        | ~ ( epred2_0 @ X56 ) )
      & ( ( X56 = esk4_0 )
        | ~ ( f1 @ X58 )
        | X58
        | ( f1 = $not )
        | $true
        | ( f1 @ X57 )
        | ~ ( epred2_0 @ X56 ) )
      & ( ~ ( f1 @ X59 )
        | $true
        | ~ X58
        | ( f1 @ X58 )
        | ( f1 = $not )
        | $true
        | ( f1 @ X57 )
        | ~ ( epred2_0 @ X56 ) )
      & ( ~ $true
        | ( f1 @ X59 )
        | ~ X58
        | ( f1 @ X58 )
        | ( f1 = $not )
        | $true
        | ( f1 @ X57 )
        | ~ ( epred2_0 @ X56 ) )
      & ( ( X56 = esk4_0 )
        | ~ X58
        | ( f1 @ X58 )
        | ( f1 = $not )
        | $true
        | ( f1 @ X57 )
        | ~ ( epred2_0 @ X56 ) )
      & ( ~ ( f1 @ X59 )
        | $true
        | ( X56 = esk3_0 )
        | ( f1 = $not )
        | $true
        | ( f1 @ X57 )
        | ~ ( epred2_0 @ X56 ) )
      & ( ~ $true
        | ( f1 @ X59 )
        | ( X56 = esk3_0 )
        | ( f1 = $not )
        | $true
        | ( f1 @ X57 )
        | ~ ( epred2_0 @ X56 ) )
      & ( ( X56 = esk4_0 )
        | ( X56 = esk3_0 )
        | ( f1 = $not )
        | $true
        | ( f1 @ X57 )
        | ~ ( epred2_0 @ X56 ) )
      & ( ~ ( f1 @ X59 )
        | $true
        | ~ ( f1 @ X58 )
        | X58
        | ( X56 = esk2_0 )
        | $true
        | ( f1 @ X57 )
        | ~ ( epred2_0 @ X56 ) )
      & ( ~ $true
        | ( f1 @ X59 )
        | ~ ( f1 @ X58 )
        | X58
        | ( X56 = esk2_0 )
        | $true
        | ( f1 @ X57 )
        | ~ ( epred2_0 @ X56 ) )
      & ( ( X56 = esk4_0 )
        | ~ ( f1 @ X58 )
        | X58
        | ( X56 = esk2_0 )
        | $true
        | ( f1 @ X57 )
        | ~ ( epred2_0 @ X56 ) )
      & ( ~ ( f1 @ X59 )
        | $true
        | ~ X58
        | ( f1 @ X58 )
        | ( X56 = esk2_0 )
        | $true
        | ( f1 @ X57 )
        | ~ ( epred2_0 @ X56 ) )
      & ( ~ $true
        | ( f1 @ X59 )
        | ~ X58
        | ( f1 @ X58 )
        | ( X56 = esk2_0 )
        | $true
        | ( f1 @ X57 )
        | ~ ( epred2_0 @ X56 ) )
      & ( ( X56 = esk4_0 )
        | ~ X58
        | ( f1 @ X58 )
        | ( X56 = esk2_0 )
        | $true
        | ( f1 @ X57 )
        | ~ ( epred2_0 @ X56 ) )
      & ( ~ ( f1 @ X59 )
        | $true
        | ( X56 = esk3_0 )
        | ( X56 = esk2_0 )
        | $true
        | ( f1 @ X57 )
        | ~ ( epred2_0 @ X56 ) )
      & ( ~ $true
        | ( f1 @ X59 )
        | ( X56 = esk3_0 )
        | ( X56 = esk2_0 )
        | $true
        | ( f1 @ X57 )
        | ~ ( epred2_0 @ X56 ) )
      & ( ( X56 = esk4_0 )
        | ( X56 = esk3_0 )
        | ( X56 = esk2_0 )
        | $true
        | ( f1 @ X57 )
        | ~ ( epred2_0 @ X56 ) )
      & ( ~ ( f1 @ X59 )
        | $true
        | ~ ( f1 @ X58 )
        | X58
        | ( f1 = $not )
        | ( X56 = esk1_0 )
        | ~ ( epred2_0 @ X56 ) )
      & ( ~ $true
        | ( f1 @ X59 )
        | ~ ( f1 @ X58 )
        | X58
        | ( f1 = $not )
        | ( X56 = esk1_0 )
        | ~ ( epred2_0 @ X56 ) )
      & ( ( X56 = esk4_0 )
        | ~ ( f1 @ X58 )
        | X58
        | ( f1 = $not )
        | ( X56 = esk1_0 )
        | ~ ( epred2_0 @ X56 ) )
      & ( ~ ( f1 @ X59 )
        | $true
        | ~ X58
        | ( f1 @ X58 )
        | ( f1 = $not )
        | ( X56 = esk1_0 )
        | ~ ( epred2_0 @ X56 ) )
      & ( ~ $true
        | ( f1 @ X59 )
        | ~ X58
        | ( f1 @ X58 )
        | ( f1 = $not )
        | ( X56 = esk1_0 )
        | ~ ( epred2_0 @ X56 ) )
      & ( ( X56 = esk4_0 )
        | ~ X58
        | ( f1 @ X58 )
        | ( f1 = $not )
        | ( X56 = esk1_0 )
        | ~ ( epred2_0 @ X56 ) )
      & ( ~ ( f1 @ X59 )
        | $true
        | ( X56 = esk3_0 )
        | ( f1 = $not )
        | ( X56 = esk1_0 )
        | ~ ( epred2_0 @ X56 ) )
      & ( ~ $true
        | ( f1 @ X59 )
        | ( X56 = esk3_0 )
        | ( f1 = $not )
        | ( X56 = esk1_0 )
        | ~ ( epred2_0 @ X56 ) )
      & ( ( X56 = esk4_0 )
        | ( X56 = esk3_0 )
        | ( f1 = $not )
        | ( X56 = esk1_0 )
        | ~ ( epred2_0 @ X56 ) )
      & ( ~ ( f1 @ X59 )
        | $true
        | ~ ( f1 @ X58 )
        | X58
        | ( X56 = esk2_0 )
        | ( X56 = esk1_0 )
        | ~ ( epred2_0 @ X56 ) )
      & ( ~ $true
        | ( f1 @ X59 )
        | ~ ( f1 @ X58 )
        | X58
        | ( X56 = esk2_0 )
        | ( X56 = esk1_0 )
        | ~ ( epred2_0 @ X56 ) )
      & ( ( X56 = esk4_0 )
        | ~ ( f1 @ X58 )
        | X58
        | ( X56 = esk2_0 )
        | ( X56 = esk1_0 )
        | ~ ( epred2_0 @ X56 ) )
      & ( ~ ( f1 @ X59 )
        | $true
        | ~ X58
        | ( f1 @ X58 )
        | ( X56 = esk2_0 )
        | ( X56 = esk1_0 )
        | ~ ( epred2_0 @ X56 ) )
      & ( ~ $true
        | ( f1 @ X59 )
        | ~ X58
        | ( f1 @ X58 )
        | ( X56 = esk2_0 )
        | ( X56 = esk1_0 )
        | ~ ( epred2_0 @ X56 ) )
      & ( ( X56 = esk4_0 )
        | ~ X58
        | ( f1 @ X58 )
        | ( X56 = esk2_0 )
        | ( X56 = esk1_0 )
        | ~ ( epred2_0 @ X56 ) )
      & ( ~ ( f1 @ X59 )
        | $true
        | ( X56 = esk3_0 )
        | ( X56 = esk2_0 )
        | ( X56 = esk1_0 )
        | ~ ( epred2_0 @ X56 ) )
      & ( ~ $true
        | ( f1 @ X59 )
        | ( X56 = esk3_0 )
        | ( X56 = esk2_0 )
        | ( X56 = esk1_0 )
        | ~ ( epred2_0 @ X56 ) )
      & ( ( X56 = esk4_0 )
        | ( X56 = esk3_0 )
        | ( X56 = esk2_0 )
        | ( X56 = esk1_0 )
        | ~ ( epred2_0 @ X56 ) )
      & ( ~ ( epred8_1 @ X56 )
        | ( epred8_1 @ X56 )
        | $true
        | ( X56 != esk1_0 )
        | ( epred2_0 @ X56 ) )
      & ( ~ ( f1 @ $false )
        | ( epred8_1 @ X56 )
        | $true
        | ( X56 != esk1_0 )
        | ( epred2_0 @ X56 ) )
      & ( ~ ( epred8_1 @ X56 )
        | ~ ( f1 @ $true )
        | $true
        | ( X56 != esk1_0 )
        | ( epred2_0 @ X56 ) )
      & ( ~ ( f1 @ $false )
        | ~ ( f1 @ $true )
        | $true
        | ( X56 != esk1_0 )
        | ( epred2_0 @ X56 ) )
      & ( ~ ( epred8_1 @ X56 )
        | ( f1 @ $true )
        | ~ $true
        | ( X56 != esk1_0 )
        | ( epred2_0 @ X56 ) )
      & ( ( epred8_1 @ X56 )
        | ( f1 @ $false )
        | ~ $true
        | ( X56 != esk1_0 )
        | ( epred2_0 @ X56 ) )
      & ( ( f1 != $not )
        | ( X56 != esk2_0 )
        | ( epred2_0 @ X56 ) )
      & ( ~ ( epred9_1 @ X56 )
        | ( epred9_1 @ X56 )
        | ~ ( epred9_1 @ X56 )
        | ( X56 != esk3_0 )
        | ( epred2_0 @ X56 ) )
      & ( ~ ( f1 @ $false )
        | ( epred9_1 @ X56 )
        | ~ ( epred9_1 @ X56 )
        | ( X56 != esk3_0 )
        | ( epred2_0 @ X56 ) )
      & ( ~ ( epred9_1 @ X56 )
        | ~ ( f1 @ $true )
        | ~ ( epred9_1 @ X56 )
        | ( X56 != esk3_0 )
        | ( epred2_0 @ X56 ) )
      & ( ~ ( f1 @ $false )
        | ~ ( f1 @ $true )
        | ~ ( epred9_1 @ X56 )
        | ( X56 != esk3_0 )
        | ( epred2_0 @ X56 ) )
      & ( ~ ( epred9_1 @ X56 )
        | ( f1 @ $true )
        | ( epred9_1 @ X56 )
        | ( X56 != esk3_0 )
        | ( epred2_0 @ X56 ) )
      & ( ( epred9_1 @ X56 )
        | ( f1 @ $false )
        | ( epred9_1 @ X56 )
        | ( X56 != esk3_0 )
        | ( epred2_0 @ X56 ) )
      & ( ~ ( epred10_1 @ X56 )
        | ( epred10_1 @ X56 )
        | ~ $true
        | ( X56 != esk4_0 )
        | ( epred2_0 @ X56 ) )
      & ( ~ ( f1 @ $false )
        | ( epred10_1 @ X56 )
        | ~ $true
        | ( X56 != esk4_0 )
        | ( epred2_0 @ X56 ) )
      & ( ~ ( epred10_1 @ X56 )
        | ~ ( f1 @ $true )
        | ~ $true
        | ( X56 != esk4_0 )
        | ( epred2_0 @ X56 ) )
      & ( ~ ( f1 @ $false )
        | ~ ( f1 @ $true )
        | ~ $true
        | ( X56 != esk4_0 )
        | ( epred2_0 @ X56 ) )
      & ( ~ ( epred10_1 @ X56 )
        | ( f1 @ $true )
        | $true
        | ( X56 != esk4_0 )
        | ( epred2_0 @ X56 ) )
      & ( ( epred10_1 @ X56 )
        | ( f1 @ $false )
        | $true
        | ( X56 != esk4_0 )
        | ( epred2_0 @ X56 ) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[])])])])])])]) ).

thf(c_0_23,plain,
    ! [X8: $o,X2: $i] :
      ( ( f0 @ X8 )
      | ( f0 @ $true )
      | ( f0 = $not )
      | ( X2 = esk1_0 )
      | ~ ( epred1_0 @ X2 ) ),
    inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_14])])]) ).

thf(c_0_24,plain,
    ~ ( f0 @ $true ),
    inference(cn,[status(thm)],[c_0_17]) ).

thf(c_0_25,plain,
    ! [X2: $i] :
      ( ( f0 @ $true )
      | ( epred1_0 @ X2 )
      | ~ ( epred5_1 @ X2 )
      | ~ $true
      | ( X2 != esk1_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

thf(c_0_26,plain,
    ! [X2: $i] :
      ( ( epred1_0 @ X2 )
      | ( epred5_1 @ X2 )
      | ( f0 @ ~ $true )
      | ( X2 != esk1_0 ) ),
    inference(cn,[status(thm)],[c_0_18]) ).

thf(c_0_27,plain,
    ~ ( f0 @ ~ $true ),
    inference(cn,[status(thm)],[c_0_19]) ).

thf(c_0_28,plain,
    ! [X15: $o,X2: $i] :
      ( ( X2 = esk4_0 )
      | ( f3 = $not )
      | ~ ( f3 @ ~ $true )
      | ~ ( f3 @ X15 )
      | ~ ( epred4_0 @ X2 ) ),
    inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_20])])]) ).

thf(c_0_29,plain,
    f3 @ ~ $true,
    inference(cn,[status(thm)],[c_0_21]) ).

thf(c_0_30,plain,
    ( ( ~ ( f3 @ $true )
      | $true )
    & ( ~ $true
      | ( f3 @ $true ) ) ),
    inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[f3t])]) ).

thf(c_0_31,axiom,
    ( ( ( ~ ~ $true
        | ( f1 @ $true ) )
      & ( ~ $true
        | ( f1 @ $false ) ) )
  <=> $true ),
    inference(fool_unroll,[status(thm)],[f1f]) ).

thf(c_0_32,plain,
    ! [X2: $i] :
      ( ( epred2_0 @ X2 )
      | ( f1 != $not )
      | ( X2 != esk2_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

thf(c_0_33,plain,
    ( ( ~ ( f1 @ $true )
      | ~ $true )
    & ( $true
      | ( f1 @ $true ) ) ),
    inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[f1t])]) ).

thf(c_0_34,plain,
    ! [X63: $i,X64: $o,X65: $o,X66: $o] :
      ( ( ~ ( f2 @ X66 )
        | $true
        | ~ ( f2 @ X65 )
        | X65
        | ( f2 = $not )
        | ~ ( f2 @ X64 )
        | ~ $true
        | ~ ( epred3_0 @ X63 ) )
      & ( ~ $true
        | ( f2 @ X66 )
        | ~ ( f2 @ X65 )
        | X65
        | ( f2 = $not )
        | ~ ( f2 @ X64 )
        | ~ $true
        | ~ ( epred3_0 @ X63 ) )
      & ( ( X63 = esk4_0 )
        | ~ ( f2 @ X65 )
        | X65
        | ( f2 = $not )
        | ~ ( f2 @ X64 )
        | ~ $true
        | ~ ( epred3_0 @ X63 ) )
      & ( ~ ( f2 @ X66 )
        | $true
        | ~ X65
        | ( f2 @ X65 )
        | ( f2 = $not )
        | ~ ( f2 @ X64 )
        | ~ $true
        | ~ ( epred3_0 @ X63 ) )
      & ( ~ $true
        | ( f2 @ X66 )
        | ~ X65
        | ( f2 @ X65 )
        | ( f2 = $not )
        | ~ ( f2 @ X64 )
        | ~ $true
        | ~ ( epred3_0 @ X63 ) )
      & ( ( X63 = esk4_0 )
        | ~ X65
        | ( f2 @ X65 )
        | ( f2 = $not )
        | ~ ( f2 @ X64 )
        | ~ $true
        | ~ ( epred3_0 @ X63 ) )
      & ( ~ ( f2 @ X66 )
        | $true
        | ( X63 = esk3_0 )
        | ( f2 = $not )
        | ~ ( f2 @ X64 )
        | ~ $true
        | ~ ( epred3_0 @ X63 ) )
      & ( ~ $true
        | ( f2 @ X66 )
        | ( X63 = esk3_0 )
        | ( f2 = $not )
        | ~ ( f2 @ X64 )
        | ~ $true
        | ~ ( epred3_0 @ X63 ) )
      & ( ( X63 = esk4_0 )
        | ( X63 = esk3_0 )
        | ( f2 = $not )
        | ~ ( f2 @ X64 )
        | ~ $true
        | ~ ( epred3_0 @ X63 ) )
      & ( ~ ( f2 @ X66 )
        | $true
        | ~ ( f2 @ X65 )
        | X65
        | ( X63 = esk2_0 )
        | ~ ( f2 @ X64 )
        | ~ $true
        | ~ ( epred3_0 @ X63 ) )
      & ( ~ $true
        | ( f2 @ X66 )
        | ~ ( f2 @ X65 )
        | X65
        | ( X63 = esk2_0 )
        | ~ ( f2 @ X64 )
        | ~ $true
        | ~ ( epred3_0 @ X63 ) )
      & ( ( X63 = esk4_0 )
        | ~ ( f2 @ X65 )
        | X65
        | ( X63 = esk2_0 )
        | ~ ( f2 @ X64 )
        | ~ $true
        | ~ ( epred3_0 @ X63 ) )
      & ( ~ ( f2 @ X66 )
        | $true
        | ~ X65
        | ( f2 @ X65 )
        | ( X63 = esk2_0 )
        | ~ ( f2 @ X64 )
        | ~ $true
        | ~ ( epred3_0 @ X63 ) )
      & ( ~ $true
        | ( f2 @ X66 )
        | ~ X65
        | ( f2 @ X65 )
        | ( X63 = esk2_0 )
        | ~ ( f2 @ X64 )
        | ~ $true
        | ~ ( epred3_0 @ X63 ) )
      & ( ( X63 = esk4_0 )
        | ~ X65
        | ( f2 @ X65 )
        | ( X63 = esk2_0 )
        | ~ ( f2 @ X64 )
        | ~ $true
        | ~ ( epred3_0 @ X63 ) )
      & ( ~ ( f2 @ X66 )
        | $true
        | ( X63 = esk3_0 )
        | ( X63 = esk2_0 )
        | ~ ( f2 @ X64 )
        | ~ $true
        | ~ ( epred3_0 @ X63 ) )
      & ( ~ $true
        | ( f2 @ X66 )
        | ( X63 = esk3_0 )
        | ( X63 = esk2_0 )
        | ~ ( f2 @ X64 )
        | ~ $true
        | ~ ( epred3_0 @ X63 ) )
      & ( ( X63 = esk4_0 )
        | ( X63 = esk3_0 )
        | ( X63 = esk2_0 )
        | ~ ( f2 @ X64 )
        | ~ $true
        | ~ ( epred3_0 @ X63 ) )
      & ( ~ ( f2 @ X66 )
        | $true
        | ~ ( f2 @ X65 )
        | X65
        | ( f2 = $not )
        | $true
        | ( f2 @ X64 )
        | ~ ( epred3_0 @ X63 ) )
      & ( ~ $true
        | ( f2 @ X66 )
        | ~ ( f2 @ X65 )
        | X65
        | ( f2 = $not )
        | $true
        | ( f2 @ X64 )
        | ~ ( epred3_0 @ X63 ) )
      & ( ( X63 = esk4_0 )
        | ~ ( f2 @ X65 )
        | X65
        | ( f2 = $not )
        | $true
        | ( f2 @ X64 )
        | ~ ( epred3_0 @ X63 ) )
      & ( ~ ( f2 @ X66 )
        | $true
        | ~ X65
        | ( f2 @ X65 )
        | ( f2 = $not )
        | $true
        | ( f2 @ X64 )
        | ~ ( epred3_0 @ X63 ) )
      & ( ~ $true
        | ( f2 @ X66 )
        | ~ X65
        | ( f2 @ X65 )
        | ( f2 = $not )
        | $true
        | ( f2 @ X64 )
        | ~ ( epred3_0 @ X63 ) )
      & ( ( X63 = esk4_0 )
        | ~ X65
        | ( f2 @ X65 )
        | ( f2 = $not )
        | $true
        | ( f2 @ X64 )
        | ~ ( epred3_0 @ X63 ) )
      & ( ~ ( f2 @ X66 )
        | $true
        | ( X63 = esk3_0 )
        | ( f2 = $not )
        | $true
        | ( f2 @ X64 )
        | ~ ( epred3_0 @ X63 ) )
      & ( ~ $true
        | ( f2 @ X66 )
        | ( X63 = esk3_0 )
        | ( f2 = $not )
        | $true
        | ( f2 @ X64 )
        | ~ ( epred3_0 @ X63 ) )
      & ( ( X63 = esk4_0 )
        | ( X63 = esk3_0 )
        | ( f2 = $not )
        | $true
        | ( f2 @ X64 )
        | ~ ( epred3_0 @ X63 ) )
      & ( ~ ( f2 @ X66 )
        | $true
        | ~ ( f2 @ X65 )
        | X65
        | ( X63 = esk2_0 )
        | $true
        | ( f2 @ X64 )
        | ~ ( epred3_0 @ X63 ) )
      & ( ~ $true
        | ( f2 @ X66 )
        | ~ ( f2 @ X65 )
        | X65
        | ( X63 = esk2_0 )
        | $true
        | ( f2 @ X64 )
        | ~ ( epred3_0 @ X63 ) )
      & ( ( X63 = esk4_0 )
        | ~ ( f2 @ X65 )
        | X65
        | ( X63 = esk2_0 )
        | $true
        | ( f2 @ X64 )
        | ~ ( epred3_0 @ X63 ) )
      & ( ~ ( f2 @ X66 )
        | $true
        | ~ X65
        | ( f2 @ X65 )
        | ( X63 = esk2_0 )
        | $true
        | ( f2 @ X64 )
        | ~ ( epred3_0 @ X63 ) )
      & ( ~ $true
        | ( f2 @ X66 )
        | ~ X65
        | ( f2 @ X65 )
        | ( X63 = esk2_0 )
        | $true
        | ( f2 @ X64 )
        | ~ ( epred3_0 @ X63 ) )
      & ( ( X63 = esk4_0 )
        | ~ X65
        | ( f2 @ X65 )
        | ( X63 = esk2_0 )
        | $true
        | ( f2 @ X64 )
        | ~ ( epred3_0 @ X63 ) )
      & ( ~ ( f2 @ X66 )
        | $true
        | ( X63 = esk3_0 )
        | ( X63 = esk2_0 )
        | $true
        | ( f2 @ X64 )
        | ~ ( epred3_0 @ X63 ) )
      & ( ~ $true
        | ( f2 @ X66 )
        | ( X63 = esk3_0 )
        | ( X63 = esk2_0 )
        | $true
        | ( f2 @ X64 )
        | ~ ( epred3_0 @ X63 ) )
      & ( ( X63 = esk4_0 )
        | ( X63 = esk3_0 )
        | ( X63 = esk2_0 )
        | $true
        | ( f2 @ X64 )
        | ~ ( epred3_0 @ X63 ) )
      & ( ~ ( f2 @ X66 )
        | $true
        | ~ ( f2 @ X65 )
        | X65
        | ( f2 = $not )
        | ( X63 = esk1_0 )
        | ~ ( epred3_0 @ X63 ) )
      & ( ~ $true
        | ( f2 @ X66 )
        | ~ ( f2 @ X65 )
        | X65
        | ( f2 = $not )
        | ( X63 = esk1_0 )
        | ~ ( epred3_0 @ X63 ) )
      & ( ( X63 = esk4_0 )
        | ~ ( f2 @ X65 )
        | X65
        | ( f2 = $not )
        | ( X63 = esk1_0 )
        | ~ ( epred3_0 @ X63 ) )
      & ( ~ ( f2 @ X66 )
        | $true
        | ~ X65
        | ( f2 @ X65 )
        | ( f2 = $not )
        | ( X63 = esk1_0 )
        | ~ ( epred3_0 @ X63 ) )
      & ( ~ $true
        | ( f2 @ X66 )
        | ~ X65
        | ( f2 @ X65 )
        | ( f2 = $not )
        | ( X63 = esk1_0 )
        | ~ ( epred3_0 @ X63 ) )
      & ( ( X63 = esk4_0 )
        | ~ X65
        | ( f2 @ X65 )
        | ( f2 = $not )
        | ( X63 = esk1_0 )
        | ~ ( epred3_0 @ X63 ) )
      & ( ~ ( f2 @ X66 )
        | $true
        | ( X63 = esk3_0 )
        | ( f2 = $not )
        | ( X63 = esk1_0 )
        | ~ ( epred3_0 @ X63 ) )
      & ( ~ $true
        | ( f2 @ X66 )
        | ( X63 = esk3_0 )
        | ( f2 = $not )
        | ( X63 = esk1_0 )
        | ~ ( epred3_0 @ X63 ) )
      & ( ( X63 = esk4_0 )
        | ( X63 = esk3_0 )
        | ( f2 = $not )
        | ( X63 = esk1_0 )
        | ~ ( epred3_0 @ X63 ) )
      & ( ~ ( f2 @ X66 )
        | $true
        | ~ ( f2 @ X65 )
        | X65
        | ( X63 = esk2_0 )
        | ( X63 = esk1_0 )
        | ~ ( epred3_0 @ X63 ) )
      & ( ~ $true
        | ( f2 @ X66 )
        | ~ ( f2 @ X65 )
        | X65
        | ( X63 = esk2_0 )
        | ( X63 = esk1_0 )
        | ~ ( epred3_0 @ X63 ) )
      & ( ( X63 = esk4_0 )
        | ~ ( f2 @ X65 )
        | X65
        | ( X63 = esk2_0 )
        | ( X63 = esk1_0 )
        | ~ ( epred3_0 @ X63 ) )
      & ( ~ ( f2 @ X66 )
        | $true
        | ~ X65
        | ( f2 @ X65 )
        | ( X63 = esk2_0 )
        | ( X63 = esk1_0 )
        | ~ ( epred3_0 @ X63 ) )
      & ( ~ $true
        | ( f2 @ X66 )
        | ~ X65
        | ( f2 @ X65 )
        | ( X63 = esk2_0 )
        | ( X63 = esk1_0 )
        | ~ ( epred3_0 @ X63 ) )
      & ( ( X63 = esk4_0 )
        | ~ X65
        | ( f2 @ X65 )
        | ( X63 = esk2_0 )
        | ( X63 = esk1_0 )
        | ~ ( epred3_0 @ X63 ) )
      & ( ~ ( f2 @ X66 )
        | $true
        | ( X63 = esk3_0 )
        | ( X63 = esk2_0 )
        | ( X63 = esk1_0 )
        | ~ ( epred3_0 @ X63 ) )
      & ( ~ $true
        | ( f2 @ X66 )
        | ( X63 = esk3_0 )
        | ( X63 = esk2_0 )
        | ( X63 = esk1_0 )
        | ~ ( epred3_0 @ X63 ) )
      & ( ( X63 = esk4_0 )
        | ( X63 = esk3_0 )
        | ( X63 = esk2_0 )
        | ( X63 = esk1_0 )
        | ~ ( epred3_0 @ X63 ) )
      & ( ~ ( epred11_1 @ X63 )
        | ( epred11_1 @ X63 )
        | $true
        | ( X63 != esk1_0 )
        | ( epred3_0 @ X63 ) )
      & ( ~ ( f2 @ $false )
        | ( epred11_1 @ X63 )
        | $true
        | ( X63 != esk1_0 )
        | ( epred3_0 @ X63 ) )
      & ( ~ ( epred11_1 @ X63 )
        | ~ ( f2 @ $true )
        | $true
        | ( X63 != esk1_0 )
        | ( epred3_0 @ X63 ) )
      & ( ~ ( f2 @ $false )
        | ~ ( f2 @ $true )
        | $true
        | ( X63 != esk1_0 )
        | ( epred3_0 @ X63 ) )
      & ( ~ ( epred11_1 @ X63 )
        | ( f2 @ $true )
        | ~ $true
        | ( X63 != esk1_0 )
        | ( epred3_0 @ X63 ) )
      & ( ( epred11_1 @ X63 )
        | ( f2 @ $false )
        | ~ $true
        | ( X63 != esk1_0 )
        | ( epred3_0 @ X63 ) )
      & ( ( f2 != $not )
        | ( X63 != esk2_0 )
        | ( epred3_0 @ X63 ) )
      & ( ~ ( epred12_1 @ X63 )
        | ( epred12_1 @ X63 )
        | ~ ( epred12_1 @ X63 )
        | ( X63 != esk3_0 )
        | ( epred3_0 @ X63 ) )
      & ( ~ ( f2 @ $false )
        | ( epred12_1 @ X63 )
        | ~ ( epred12_1 @ X63 )
        | ( X63 != esk3_0 )
        | ( epred3_0 @ X63 ) )
      & ( ~ ( epred12_1 @ X63 )
        | ~ ( f2 @ $true )
        | ~ ( epred12_1 @ X63 )
        | ( X63 != esk3_0 )
        | ( epred3_0 @ X63 ) )
      & ( ~ ( f2 @ $false )
        | ~ ( f2 @ $true )
        | ~ ( epred12_1 @ X63 )
        | ( X63 != esk3_0 )
        | ( epred3_0 @ X63 ) )
      & ( ~ ( epred12_1 @ X63 )
        | ( f2 @ $true )
        | ( epred12_1 @ X63 )
        | ( X63 != esk3_0 )
        | ( epred3_0 @ X63 ) )
      & ( ( epred12_1 @ X63 )
        | ( f2 @ $false )
        | ( epred12_1 @ X63 )
        | ( X63 != esk3_0 )
        | ( epred3_0 @ X63 ) )
      & ( ~ ( epred13_1 @ X63 )
        | ( epred13_1 @ X63 )
        | ~ $true
        | ( X63 != esk4_0 )
        | ( epred3_0 @ X63 ) )
      & ( ~ ( f2 @ $false )
        | ( epred13_1 @ X63 )
        | ~ $true
        | ( X63 != esk4_0 )
        | ( epred3_0 @ X63 ) )
      & ( ~ ( epred13_1 @ X63 )
        | ~ ( f2 @ $true )
        | ~ $true
        | ( X63 != esk4_0 )
        | ( epred3_0 @ X63 ) )
      & ( ~ ( f2 @ $false )
        | ~ ( f2 @ $true )
        | ~ $true
        | ( X63 != esk4_0 )
        | ( epred3_0 @ X63 ) )
      & ( ~ ( epred13_1 @ X63 )
        | ( f2 @ $true )
        | $true
        | ( X63 != esk4_0 )
        | ( epred3_0 @ X63 ) )
      & ( ( epred13_1 @ X63 )
        | ( f2 @ $false )
        | $true
        | ( X63 != esk4_0 )
        | ( epred3_0 @ X63 ) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[])])])])])])]) ).

thf(c_0_35,axiom,
    ( ( ( ~ ~ $true
        | ( f2 @ $true ) )
      & ( ~ $true
        | ( f2 @ $false ) ) )
  <=> ~ $true ),
    inference(fool_unroll,[status(thm)],[f2f]) ).

thf(c_0_36,plain,
    ( ( ~ ( f2 @ $true )
      | $true )
    & ( ~ $true
      | ( f2 @ $true ) ) ),
    inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[f2t])]) ).

thf(c_0_37,plain,
    ( case
    = ( ^ [Z0: $o > $o,Z1: $i,Z2: $i,Z3: $i,Z4: $i] :
          ( eps
          @ ^ [Z5: $i] :
              ( ( ( Z0
                  = ( ^ [Z6: $o] : ~ $true ) )
                & ( Z5 = Z1 ) )
              | ( ( Z0 = $not )
                & ( Z5 = Z2 ) )
              | ( ( Z0
                  = ( ^ [Z6: $o] : Z6 ) )
                & ( Z5 = Z3 ) )
              | ( ( Z0
                  = ( ^ [Z6: $o] : $true ) )
                & Z5 ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[caseood]) ).

thf(c_0_38,plain,
    ! [X2: $i] :
      ( ( $not = f0 )
      | ( X2 = esk1_0 )
      | ~ ( epred1_0 @ X2 ) ),
    inference(sr,[status(thm)],[inference(condense,[status(thm)],[c_0_23]),c_0_24]) ).

thf(c_0_39,plain,
    ! [X31: $i > $o,X32: $i] :
      ( ~ ( X31 @ X32 )
      | ( X31 @ ( eps @ X31 ) ) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[choiceax])])])]) ).

thf(c_0_40,plain,
    ! [X2: $i] :
      ( ( epred1_0 @ X2 )
      | ( f0 @ $true )
      | ( X2 != esk1_0 )
      | ~ ( epred5_1 @ X2 ) ),
    inference(cn,[status(thm)],[c_0_25]) ).

thf(c_0_41,plain,
    ( ( epred1_0 @ esk1_0 )
    | ( epred5_1 @ esk1_0 ) ),
    inference(er,[status(thm)],[inference(sr,[status(thm)],[c_0_26,c_0_27])]) ).

thf(c_0_42,plain,
    ! [X8: $o,X2: $i] :
      ( ( $not = f3 )
      | ( X2 = esk4_0 )
      | ~ ( f3 @ X8 )
      | ~ ( epred4_0 @ X2 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_29])]) ).

thf(c_0_43,plain,
    ( ( f3 @ $true )
    | ~ $true ),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

thf(c_0_44,plain,
    ! [X2: $i] :
      ( ( epred4_0 @ X2 )
      | ~ ( f3 @ ~ $true )
      | ~ ( f3 @ $true )
      | ~ $true
      | ( X2 != esk4_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

thf(c_0_45,plain,
    ( ( $true
      | ~ $true
      | $true )
    & ( ~ ( f1 @ $false )
      | ~ $true
      | $true )
    & ( $true
      | ~ ( f1 @ $true )
      | $true )
    & ( ~ ( f1 @ $false )
      | ~ ( f1 @ $true )
      | $true )
    & ( $true
      | ( f1 @ $true )
      | ~ $true )
    & ( ~ $true
      | ( f1 @ $false )
      | ~ $true ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_31])])]) ).

thf(c_0_46,plain,
    ( ( epred2_0 @ esk2_0 )
    | ( $not != f1 ) ),
    inference(er,[status(thm)],[c_0_32]) ).

thf(c_0_47,plain,
    ( ~ ( f1 @ $true )
    | ~ $true ),
    inference(split_conjunct,[status(thm)],[c_0_33]) ).

thf(c_0_48,plain,
    ! [X8: $o,X2: $i] :
      ( ( X2 = esk4_0 )
      | ( X2 = esk3_0 )
      | ( f2 = $not )
      | ~ ( f2 @ X8 )
      | ~ $true
      | ~ ( epred3_0 @ X2 ) ),
    inference(split_conjunct,[status(thm)],[c_0_34]) ).

thf(c_0_49,plain,
    ( ( $true
      | ~ $true
      | ~ $true )
    & ( ~ ( f2 @ $false )
      | ~ $true
      | ~ $true )
    & ( $true
      | ~ ( f2 @ $true )
      | ~ $true )
    & ( ~ ( f2 @ $false )
      | ~ ( f2 @ $true )
      | ~ $true )
    & ( $true
      | ( f2 @ $true )
      | $true )
    & ( ~ $true
      | ( f2 @ $false )
      | $true ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_35])])]) ).

thf(c_0_50,plain,
    ! [X2: $i] :
      ( ( epred3_0 @ X2 )
      | ~ ( epred12_1 @ X2 )
      | ~ ( f2 @ $true )
      | ~ ( epred12_1 @ X2 )
      | ( X2 != esk3_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_34]) ).

thf(c_0_51,plain,
    ( ( f2 @ $true )
    | ~ $true ),
    inference(split_conjunct,[status(thm)],[c_0_36]) ).

thf(c_0_52,negated_conjecture,
    ~ ! [X2: $i,X4: $i,X5: $i,X6: $i] :
        ( ( ( eps
            @ ^ [Z0: $i] :
                ( ( ! [X15: $o] :
                      ( ( f0 @ X15 )
                    <=> ~ $true )
                  & ( Z0 = X2 ) )
                | ( ( f0 = $not )
                  & ( Z0 = X4 ) )
                | ( ! [X16: $o] :
                      ( ( f0 @ X16 )
                    <=> X16 )
                  & ( Z0 = X5 ) )
                | ( ! [X17: $o] :
                      ( ( f0 @ X17 )
                    <=> $true )
                  & ( Z0 = X6 ) ) ) )
          = X2 )
        & ( ( eps
            @ ^ [Z0: $i] :
                ( ( ! [X18: $o] :
                      ( ( f1 @ X18 )
                    <=> ~ $true )
                  & ( Z0 = X2 ) )
                | ( ( f1 = $not )
                  & ( Z0 = X4 ) )
                | ( ! [X19: $o] :
                      ( ( f1 @ X19 )
                    <=> X19 )
                  & ( Z0 = X5 ) )
                | ( ! [X20: $o] :
                      ( ( f1 @ X20 )
                    <=> $true )
                  & ( Z0 = X6 ) ) ) )
          = X4 )
        & ( ( eps
            @ ^ [Z0: $i] :
                ( ( ! [X21: $o] :
                      ( ( f2 @ X21 )
                    <=> ~ $true )
                  & ( Z0 = X2 ) )
                | ( ( f2 = $not )
                  & ( Z0 = X4 ) )
                | ( ! [X22: $o] :
                      ( ( f2 @ X22 )
                    <=> X22 )
                  & ( Z0 = X5 ) )
                | ( ! [X23: $o] :
                      ( ( f2 @ X23 )
                    <=> $true )
                  & ( Z0 = X6 ) ) ) )
          = X5 )
        & ( ( eps
            @ ^ [Z0: $i] :
                ( ( ! [X24: $o] :
                      ( ( f3 @ X24 )
                    <=> ~ $true )
                  & ( Z0 = X2 ) )
                | ( ( f3 = $not )
                  & ( Z0 = X4 ) )
                | ( ! [X25: $o] :
                      ( ( f3 @ X25 )
                    <=> X25 )
                  & ( Z0 = X5 ) )
                | ( ! [X26: $o] :
                      ( ( f3 @ X26 )
                    <=> $true )
                  & ( Z0 = X6 ) ) ) )
          = X6 ) ),
    inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[conj]),c_0_37])]) ).

thf(c_0_53,plain,
    ! [X77: $o,X2: $i] :
      ( ( ~ X77
      <=> ( f0 @ X77 ) )
      | ( X2 = esk1_0 )
      | ~ ( epred1_0 @ X2 ) ),
    inference(arg_cong,[status(thm)],[c_0_38]) ).

thf(c_0_54,plain,
    ! [X1: $i > $o,X2: $i] :
      ( ( X1 @ ( eps @ X1 ) )
      | ~ ( X1 @ X2 ) ),
    inference(split_conjunct,[status(thm)],[c_0_39]) ).

thf(c_0_55,plain,
    epred1_0 @ esk1_0,
    inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(sr,[status(thm)],[c_0_40,c_0_24])]),c_0_41]) ).

thf(c_0_56,plain,
    ! [X94: $o,X8: $o,X2: $i] :
      ( ( ~ X94
      <=> ( f3 @ X94 ) )
      | ( X2 = esk4_0 )
      | ~ ( f3 @ X8 )
      | ~ ( epred4_0 @ X2 ) ),
    inference(arg_cong,[status(thm)],[c_0_42]) ).

thf(c_0_57,plain,
    f3 @ $true,
    inference(cn,[status(thm)],[c_0_43]) ).

thf(c_0_58,plain,
    ! [X2: $i] :
      ( ( epred4_0 @ X2 )
      | ( X2 != esk4_0 )
      | ~ ( f3 @ $true )
      | ~ ( f3 @ ~ $true ) ),
    inference(cn,[status(thm)],[c_0_44]) ).

thf(c_0_59,plain,
    ( ( f1 @ ~ $true )
    | ~ $true
    | ~ $true ),
    inference(split_conjunct,[status(thm)],[c_0_45]) ).

thf(c_0_60,plain,
    ( ( epred2_0 @ esk2_0 )
    | ( ~ esk6_0
    <~> ( f1 @ esk6_0 ) ) ),
    inference(neg_ext,[status(thm)],[c_0_46]) ).

thf(c_0_61,plain,
    ~ ( f1 @ $true ),
    inference(cn,[status(thm)],[c_0_47]) ).

thf(c_0_62,plain,
    ! [X8: $o,X2: $i] :
      ( ( X2 = esk3_0 )
      | ( X2 = esk4_0 )
      | ( f2 = $not )
      | ~ ( f2 @ X8 )
      | ~ ( epred3_0 @ X2 ) ),
    inference(cn,[status(thm)],[c_0_48]) ).

thf(c_0_63,plain,
    ! [X2: $i] :
      ( ( epred12_1 @ X2 )
      | ( f2 @ ~ $true )
      | ( epred12_1 @ X2 )
      | ( epred3_0 @ X2 )
      | ( X2 != esk3_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_34]) ).

thf(c_0_64,plain,
    ( ~ ( f2 @ ~ $true )
    | ~ $true
    | ~ $true ),
    inference(split_conjunct,[status(thm)],[c_0_49]) ).

thf(c_0_65,plain,
    ! [X2: $i] :
      ( ( epred3_0 @ X2 )
      | ( X2 != esk3_0 )
      | ~ ( epred12_1 @ X2 )
      | ~ ( f2 @ $true ) ),
    inference(cn,[status(thm)],[c_0_50]) ).

thf(c_0_66,plain,
    f2 @ $true,
    inference(cn,[status(thm)],[c_0_51]) ).

thf(c_0_67,negated_conjecture,
    ( ( ( eps
        @ ^ [Z0: $i] :
            ( ( ! [X15: $o] :
                  ( ( f0 @ X15 )
                <=> ~ $true )
              & ( Z0 = esk1_0 ) )
            | ( ( f0 = $not )
              & ( Z0 = esk2_0 ) )
            | ( ! [X16: $o] :
                  ( ( f0 @ X16 )
                <=> X16 )
              & ( Z0 = esk3_0 ) )
            | ( ! [X17: $o] :
                  ( ( f0 @ X17 )
                <=> $true )
              & ( Z0 = esk4_0 ) ) ) )
     != esk1_0 )
    | ( ( eps
        @ ^ [Z0: $i] :
            ( ( ! [X18: $o] :
                  ( ( f1 @ X18 )
                <=> ~ $true )
              & ( Z0 = esk1_0 ) )
            | ( ( f1 = $not )
              & ( Z0 = esk2_0 ) )
            | ( ! [X19: $o] :
                  ( ( f1 @ X19 )
                <=> X19 )
              & ( Z0 = esk3_0 ) )
            | ( ! [X20: $o] :
                  ( ( f1 @ X20 )
                <=> $true )
              & ( Z0 = esk4_0 ) ) ) )
     != esk2_0 )
    | ( ( eps
        @ ^ [Z0: $i] :
            ( ( ! [X21: $o] :
                  ( ( f2 @ X21 )
                <=> ~ $true )
              & ( Z0 = esk1_0 ) )
            | ( ( f2 = $not )
              & ( Z0 = esk2_0 ) )
            | ( ! [X22: $o] :
                  ( ( f2 @ X22 )
                <=> X22 )
              & ( Z0 = esk3_0 ) )
            | ( ! [X23: $o] :
                  ( ( f2 @ X23 )
                <=> $true )
              & ( Z0 = esk4_0 ) ) ) )
     != esk3_0 )
    | ( ( eps
        @ ^ [Z0: $i] :
            ( ( ! [X24: $o] :
                  ( ( f3 @ X24 )
                <=> ~ $true )
              & ( Z0 = esk1_0 ) )
            | ( ( f3 = $not )
              & ( Z0 = esk2_0 ) )
            | ( ! [X25: $o] :
                  ( ( f3 @ X25 )
                <=> X25 )
              & ( Z0 = esk3_0 ) )
            | ( ! [X26: $o] :
                  ( ( f3 @ X26 )
                <=> $true )
              & ( Z0 = esk4_0 ) ) ) )
     != esk4_0 ) ),
    inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_52])])])]) ).

thf(c_0_68,plain,
    ! [X48: $i] :
      ( ( epred4_0 @ X48 )
    <=> ( ( ! [X45: $o] :
              ( ( f3 @ X45 )
            <=> ~ $true )
          & ( X48 = esk1_0 ) )
        | ( ( f3 = $not )
          & ( X48 = esk2_0 ) )
        | ( ! [X46: $o] :
              ( ( f3 @ X46 )
            <=> X46 )
          & ( X48 = esk3_0 ) )
        | ( ! [X47: $o] :
              ( ( f3 @ X47 )
            <=> $true )
          & ( X48 = esk4_0 ) ) ) ),
    introduced(definition) ).

thf(c_0_69,plain,
    ! [X44: $i] :
      ( ( epred3_0 @ X44 )
    <=> ( ( ! [X41: $o] :
              ( ( f2 @ X41 )
            <=> ~ $true )
          & ( X44 = esk1_0 ) )
        | ( ( f2 = $not )
          & ( X44 = esk2_0 ) )
        | ( ! [X42: $o] :
              ( ( f2 @ X42 )
            <=> X42 )
          & ( X44 = esk3_0 ) )
        | ( ! [X43: $o] :
              ( ( f2 @ X43 )
            <=> $true )
          & ( X44 = esk4_0 ) ) ) ),
    introduced(definition) ).

thf(c_0_70,plain,
    ! [X40: $i] :
      ( ( epred2_0 @ X40 )
    <=> ( ( ! [X37: $o] :
              ( ( f1 @ X37 )
            <=> ~ $true )
          & ( X40 = esk1_0 ) )
        | ( ( f1 = $not )
          & ( X40 = esk2_0 ) )
        | ( ! [X38: $o] :
              ( ( f1 @ X38 )
            <=> X38 )
          & ( X40 = esk3_0 ) )
        | ( ! [X39: $o] :
              ( ( f1 @ X39 )
            <=> $true )
          & ( X40 = esk4_0 ) ) ) ),
    introduced(definition) ).

thf(c_0_71,plain,
    ! [X36: $i] :
      ( ( epred1_0 @ X36 )
    <=> ( ( ! [X33: $o] :
              ( ( f0 @ X33 )
            <=> ~ $true )
          & ( X36 = esk1_0 ) )
        | ( ( f0 = $not )
          & ( X36 = esk2_0 ) )
        | ( ! [X34: $o] :
              ( ( f0 @ X34 )
            <=> X34 )
          & ( X36 = esk3_0 ) )
        | ( ! [X35: $o] :
              ( ( f0 @ X35 )
            <=> $true )
          & ( X36 = esk4_0 ) ) ) ),
    introduced(definition) ).

thf(c_0_72,plain,
    ! [X2: $i] :
      ( ( X2 = esk1_0 )
      | ~ ( epred1_0 @ X2 ) ),
    inference(sr,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_53]),c_0_27]) ).

thf(c_0_73,plain,
    epred1_0 @ ( eps @ epred1_0 ),
    inference(spm,[status(thm)],[c_0_54,c_0_55]) ).

thf(c_0_74,plain,
    ! [X8: $o,X2: $i] :
      ( ( X2 = esk4_0 )
      | ~ ( f3 @ X8 )
      | ~ ( epred4_0 @ X2 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_56]),c_0_57])]) ).

thf(c_0_75,plain,
    epred4_0 @ esk4_0,
    inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_57]),c_0_29])])]) ).

thf(c_0_76,plain,
    ! [X16: $o,X8: $o,X2: $i] :
      ( ( f1 @ X8 )
      | ( f1 @ $true )
      | ( X2 = esk2_0 )
      | ~ ( f1 @ X16 )
      | ~ ( epred2_0 @ X2 ) ),
    inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_22])])]) ).

thf(c_0_77,plain,
    f1 @ ~ $true,
    inference(cn,[status(thm)],[c_0_59]) ).

thf(c_0_78,plain,
    ( ( epred2_0 @ esk2_0 )
    | ~ esk6_0 ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_60])]),c_0_61]) ).

thf(c_0_79,plain,
    ! [X100: $o,X8: $o,X2: $i] :
      ( ( ~ X100
      <=> ( f2 @ X100 ) )
      | ( X2 = esk4_0 )
      | ( X2 = esk3_0 )
      | ~ ( f2 @ X8 )
      | ~ ( epred3_0 @ X2 ) ),
    inference(arg_cong,[status(thm)],[c_0_62]) ).

thf(c_0_80,plain,
    ! [X2: $i] :
      ( ( epred3_0 @ X2 )
      | ( epred12_1 @ X2 )
      | ( f2 @ ~ $true )
      | ( X2 != esk3_0 ) ),
    inference(cn,[status(thm)],[c_0_63]) ).

thf(c_0_81,plain,
    ~ ( f2 @ ~ $true ),
    inference(cn,[status(thm)],[c_0_64]) ).

thf(c_0_82,plain,
    ( ( epred3_0 @ esk3_0 )
    | ~ ( epred12_1 @ esk3_0 ) ),
    inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_66])])]) ).

thf(c_0_83,negated_conjecture,
    ( ( ( eps @ epred1_0 )
     != esk1_0 )
    | ( ( eps @ epred2_0 )
     != esk2_0 )
    | ( ( eps @ epred3_0 )
     != esk3_0 )
    | ( ( eps @ epred4_0 )
     != esk4_0 ) ),
    inference(lift_lambdas,[status(thm)],[inference(lift_lambdas,[status(thm)],[inference(lift_lambdas,[status(thm)],[inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_67]),c_0_68]),c_0_69]),c_0_70]),c_0_71]) ).

thf(c_0_84,plain,
    ( ( eps @ epred1_0 )
    = esk1_0 ),
    inference(spm,[status(thm)],[c_0_72,c_0_73]) ).

thf(c_0_85,plain,
    ! [X2: $i] :
      ( ( X2 = esk4_0 )
      | ~ ( epred4_0 @ X2 ) ),
    inference(spm,[status(thm)],[c_0_74,c_0_29]) ).

thf(c_0_86,plain,
    epred4_0 @ ( eps @ epred4_0 ),
    inference(spm,[status(thm)],[c_0_54,c_0_75]) ).

thf(c_0_87,plain,
    ! [X8: $o,X2: $i] :
      ( ( X2 = esk2_0 )
      | ~ ( f1 @ X8 )
      | ~ ( epred2_0 @ X2 ) ),
    inference(sr,[status(thm)],[inference(condense,[status(thm)],[c_0_76]),c_0_61]) ).

thf(c_0_88,plain,
    epred2_0 @ esk2_0,
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_60]),c_0_77])]),c_0_78]) ).

thf(c_0_89,plain,
    ! [X8: $o,X2: $i] :
      ( ( X2 = esk3_0 )
      | ( X2 = esk4_0 )
      | ~ ( f2 @ X8 )
      | ~ ( epred3_0 @ X2 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_79]),c_0_66])]) ).

thf(c_0_90,plain,
    epred3_0 @ esk3_0,
    inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(sr,[status(thm)],[c_0_80,c_0_81])]),c_0_82]) ).

thf(c_0_91,negated_conjecture,
    ( ( ( eps @ epred2_0 )
     != esk2_0 )
    | ( ( eps @ epred3_0 )
     != esk3_0 )
    | ( ( eps @ epred4_0 )
     != esk4_0 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_83,c_0_84])]) ).

thf(c_0_92,plain,
    ( ( eps @ epred4_0 )
    = esk4_0 ),
    inference(spm,[status(thm)],[c_0_85,c_0_86]) ).

thf(c_0_93,plain,
    ! [X2: $i] :
      ( ( X2 = esk2_0 )
      | ~ ( epred2_0 @ X2 ) ),
    inference(spm,[status(thm)],[c_0_87,c_0_77]) ).

thf(c_0_94,plain,
    epred2_0 @ ( eps @ epred2_0 ),
    inference(spm,[status(thm)],[c_0_54,c_0_88]) ).

thf(c_0_95,plain,
    ! [X2: $i] :
      ( ( X2 = esk4_0 )
      | ( X2 = esk3_0 )
      | ~ ( epred3_0 @ X2 ) ),
    inference(spm,[status(thm)],[c_0_89,c_0_66]) ).

thf(c_0_96,plain,
    epred3_0 @ ( eps @ epred3_0 ),
    inference(spm,[status(thm)],[c_0_54,c_0_90]) ).

thf(c_0_97,plain,
    ! [X15: $o,X8: $o,X2: $i] :
      ( ( f2 @ X8 )
      | ( X2 = esk3_0 )
      | ( f2 = $not )
      | ~ $true
      | ~ ( f2 @ X15 )
      | ~ $true
      | ~ ( epred3_0 @ X2 ) ),
    inference(split_conjunct,[status(thm)],[c_0_34]) ).

thf(c_0_98,negated_conjecture,
    ( ( ( eps @ epred2_0 )
     != esk2_0 )
    | ( ( eps @ epred3_0 )
     != esk3_0 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_91,c_0_92])]) ).

thf(c_0_99,plain,
    ( ( eps @ epred2_0 )
    = esk2_0 ),
    inference(spm,[status(thm)],[c_0_93,c_0_94]) ).

thf(c_0_100,plain,
    ( ( ( eps @ epred3_0 )
      = esk3_0 )
    | ( ( eps @ epred3_0 )
      = esk4_0 ) ),
    inference(spm,[status(thm)],[c_0_95,c_0_96]) ).

thf(c_0_101,plain,
    ! [X15: $o,X8: $o,X2: $i] :
      ( ( X2 = esk3_0 )
      | ( f2 = $not )
      | ( f2 @ X8 )
      | ~ ( f2 @ X15 )
      | ~ ( epred3_0 @ X2 ) ),
    inference(cn,[status(thm)],[c_0_97]) ).

thf(c_0_102,negated_conjecture,
    ( ( eps @ epred3_0 )
   != esk3_0 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_98,c_0_99])]) ).

thf(c_0_103,plain,
    ( ( ( eps @ epred3_0 )
      = esk4_0 )
    | ( esk3_0 != esk4_0 ) ),
    inference(ef,[status(thm)],[c_0_100]) ).

thf(c_0_104,plain,
    ! [X121: $o,X15: $o,X8: $o,X2: $i] :
      ( ( ~ X121
      <=> ( f2 @ X121 ) )
      | ( X2 = esk3_0 )
      | ( f2 @ X8 )
      | ~ ( f2 @ X15 )
      | ~ ( epred3_0 @ X2 ) ),
    inference(arg_cong,[status(thm)],[c_0_101]) ).

thf(c_0_105,plain,
    ( ( eps @ epred3_0 )
    = esk4_0 ),
    inference(sr,[status(thm)],[c_0_100,c_0_102]) ).

thf(c_0_106,negated_conjecture,
    ( ( ( eps @ epred2_0 )
     != esk2_0 )
    | ( esk3_0 != esk4_0 ) ),
    inference(spm,[status(thm)],[c_0_98,c_0_103]) ).

thf(c_0_107,plain,
    ! [X15: $o,X8: $o,X2: $i] :
      ( ( X2 = esk3_0 )
      | ( f2 @ X8 )
      | ~ ( f2 @ X15 )
      | ~ ( epred3_0 @ X2 ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_104]),c_0_66])]) ).

thf(c_0_108,plain,
    epred3_0 @ esk4_0,
    inference(rw,[status(thm)],[c_0_96,c_0_105]) ).

thf(c_0_109,negated_conjecture,
    esk3_0 != esk4_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_106,c_0_99])]) ).

thf(c_0_110,plain,
    ! [X8: $o,X15: $o] :
      ( ( f2 @ X8 )
      | ~ ( f2 @ X15 ) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_109]) ).

thf(c_0_111,plain,
    ! [X8: $o] : ( f2 @ X8 ),
    inference(spm,[status(thm)],[c_0_110,c_0_66]) ).

thf(c_0_112,plain,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_81,c_0_111])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem    : SYO544^1 : TPTP v8.2.0. Released v5.2.0.
% 0.04/0.13  % Command    : run_E %s %d THM
% 0.13/0.34  % Computer : n015.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Mon May 20 10:31:08 EDT 2024
% 0.13/0.34  % CPUTime    : 
% 0.19/0.47  Running higher-order theorem proving
% 0.19/0.47  Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.52  # Version: 3.1.0-ho
% 0.19/0.52  # partial match(1): HSLSSMSSSSMCHSA
% 0.19/0.52  # Preprocessing class: HSMSSMSSSSMCHSA.
% 0.19/0.52  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.52  # Starting post_as_ho6 with 1500s (5) cores
% 0.19/0.52  # Starting post_as_ho7 with 300s (1) cores
% 0.19/0.52  # Starting post_as_ho8 with 300s (1) cores
% 0.19/0.52  # Starting lpo8_s with 300s (1) cores
% 0.19/0.52  # lpo8_s with pid 8406 completed with status 0
% 0.19/0.52  # Result found by lpo8_s
% 0.19/0.52  # partial match(1): HSLSSMSSSSMCHSA
% 0.19/0.52  # Preprocessing class: HSMSSMSSSSMCHSA.
% 0.19/0.52  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.52  # Starting post_as_ho6 with 1500s (5) cores
% 0.19/0.52  # Starting post_as_ho7 with 300s (1) cores
% 0.19/0.52  # Starting post_as_ho8 with 300s (1) cores
% 0.19/0.52  # Starting lpo8_s with 300s (1) cores
% 0.19/0.52  # SinE strategy is GSinE(CountFormulas,hypos,4.0,,6,20000,1.0)
% 0.19/0.52  # Search class: HGHSF-FSLS11-SHSFFFBC
% 0.19/0.52  # partial match(4): HGHSM-FSLM32-SHSFFFBC
% 0.19/0.52  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.19/0.52  # Starting new_ho_10 with 163s (1) cores
% 0.19/0.52  # new_ho_10 with pid 8414 completed with status 0
% 0.19/0.52  # Result found by new_ho_10
% 0.19/0.52  # partial match(1): HSLSSMSSSSMCHSA
% 0.19/0.52  # Preprocessing class: HSMSSMSSSSMCHSA.
% 0.19/0.52  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.52  # Starting post_as_ho6 with 1500s (5) cores
% 0.19/0.52  # Starting post_as_ho7 with 300s (1) cores
% 0.19/0.52  # Starting post_as_ho8 with 300s (1) cores
% 0.19/0.52  # Starting lpo8_s with 300s (1) cores
% 0.19/0.52  # SinE strategy is GSinE(CountFormulas,hypos,4.0,,6,20000,1.0)
% 0.19/0.52  # Search class: HGHSF-FSLS11-SHSFFFBC
% 0.19/0.52  # partial match(4): HGHSM-FSLM32-SHSFFFBC
% 0.19/0.52  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.19/0.52  # Starting new_ho_10 with 163s (1) cores
% 0.19/0.52  # Preprocessing time       : 0.003 s
% 0.19/0.52  # Presaturation interreduction done
% 0.19/0.52  
% 0.19/0.52  # Proof found!
% 0.19/0.52  # SZS status Theorem
% 0.19/0.52  # SZS output start CNFRefutation
% See solution above
% 0.19/0.52  # Parsed axioms                        : 17
% 0.19/0.52  # Removed by relevancy pruning/SinE    : 6
% 0.19/0.52  # Initial clauses                      : 326
% 0.19/0.52  # Removed in clause preprocessing      : 182
% 0.19/0.52  # Initial clauses in saturation        : 144
% 0.19/0.52  # Processed clauses                    : 348
% 0.19/0.52  # ...of these trivial                  : 25
% 0.19/0.52  # ...subsumed                          : 80
% 0.19/0.52  # ...remaining for further processing  : 243
% 0.19/0.52  # Other redundant clauses eliminated   : 18
% 0.19/0.52  # Clauses deleted for lack of memory   : 0
% 0.19/0.52  # Backward-subsumed                    : 78
% 0.19/0.52  # Backward-rewritten                   : 28
% 0.19/0.52  # Generated clauses                    : 362
% 0.19/0.52  # ...of the previous two non-redundant : 264
% 0.19/0.52  # ...aggressively subsumed             : 0
% 0.19/0.52  # Contextual simplify-reflections      : 3
% 0.19/0.52  # Paramodulations                      : 202
% 0.19/0.52  # Factorizations                       : 9
% 0.19/0.52  # NegExts                              : 14
% 0.19/0.52  # Equation resolutions                 : 18
% 0.19/0.52  # Disequality decompositions           : 0
% 0.19/0.52  # Total rewrite steps                  : 193
% 0.19/0.52  # ...of those cached                   : 163
% 0.19/0.52  # Propositional unsat checks           : 0
% 0.19/0.52  #    Propositional check models        : 0
% 0.19/0.52  #    Propositional check unsatisfiable : 0
% 0.19/0.52  #    Propositional clauses             : 0
% 0.19/0.52  #    Propositional clauses after purity: 0
% 0.19/0.52  #    Propositional unsat core size     : 0
% 0.19/0.52  #    Propositional preprocessing time  : 0.000
% 0.19/0.52  #    Propositional encoding time       : 0.000
% 0.19/0.52  #    Propositional solver time         : 0.000
% 0.19/0.52  #    Success case prop preproc time    : 0.000
% 0.19/0.52  #    Success case prop encoding time   : 0.000
% 0.19/0.52  #    Success case prop solver time     : 0.000
% 0.19/0.52  # Current number of processed clauses  : 53
% 0.19/0.52  #    Positive orientable unit clauses  : 13
% 0.19/0.52  #    Positive unorientable unit clauses: 0
% 0.19/0.52  #    Negative unit clauses             : 4
% 0.19/0.52  #    Non-unit-clauses                  : 36
% 0.19/0.52  # Current number of unprocessed clauses: 85
% 0.19/0.52  # ...number of literals in the above   : 253
% 0.19/0.52  # Current number of archived formulas  : 0
% 0.19/0.52  # Current number of archived clauses   : 172
% 0.19/0.52  # Clause-clause subsumption calls (NU) : 1254
% 0.19/0.52  # Rec. Clause-clause subsumption calls : 565
% 0.19/0.52  # Non-unit clause-clause subsumptions  : 120
% 0.19/0.52  # Unit Clause-clause subsumption calls : 207
% 0.19/0.52  # Rewrite failures with RHS unbound    : 0
% 0.19/0.52  # BW rewrite match attempts            : 18
% 0.19/0.52  # BW rewrite match successes           : 17
% 0.19/0.52  # Condensation attempts                : 348
% 0.19/0.52  # Condensation successes               : 18
% 0.19/0.52  # Termbank termtop insertions          : 23643
% 0.19/0.52  # Search garbage collected termcells   : 3768
% 0.19/0.52  
% 0.19/0.52  # -------------------------------------------------
% 0.19/0.52  # User time                : 0.031 s
% 0.19/0.52  # System time              : 0.007 s
% 0.19/0.52  # Total time               : 0.038 s
% 0.19/0.52  # Maximum resident set size: 3288 pages
% 0.19/0.52  
% 0.19/0.52  # -------------------------------------------------
% 0.19/0.52  # User time                : 0.033 s
% 0.19/0.52  # System time              : 0.009 s
% 0.19/0.52  # Total time               : 0.041 s
% 0.19/0.52  # Maximum resident set size: 1772 pages
% 0.19/0.52  % E---3.1 exiting
% 0.19/0.52  % E exiting
%------------------------------------------------------------------------------