TSTP Solution File: SYO889^16 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SYO889^16 : TPTP v8.1.0. Released v8.1.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n020.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 : Thu Jul 21 17:38:12 EDT 2022

% Result   : Theorem 0.12s 0.41s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   33
%            Number of leaves      :   35
% Syntax   : Number of formulae    :  131 (  64 unt;  20 typ;  10 def)
%            Number of atoms       :  815 ( 189 equ;   0 cnn)
%            Maximal formula atoms :   17 (   7 avg)
%            Number of connectives : 1709 ( 580   ~; 265   |;   5   &; 853   @)
%                                         (   1 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   3 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   66 (  66   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   22 (  19 usr;   5 con; 0-3 aty)
%            Number of variables   :  291 (  35   ^ 253   !;   3   ?; 291   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_mworld,type,
    mworld: $tType ).

thf(tp_a,type,
    a: $i > mworld > $o ).

thf(tp_b,type,
    b: $i > mworld > $o ).

thf(tp_eiw_di,type,
    eiw_di: $i > mworld > $o ).

thf(tp_mactual,type,
    mactual: mworld ).

thf(tp_mand,type,
    mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).

thf(tp_mbox,type,
    mbox: ( mworld > $o ) > mworld > $o ).

thf(tp_mdia,type,
    mdia: ( mworld > $o ) > mworld > $o ).

thf(tp_mequiv,type,
    mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).

thf(tp_mexists_di,type,
    mexists_di: ( $i > mworld > $o ) > mworld > $o ).

thf(tp_mforall_di,type,
    mforall_di: ( $i > mworld > $o ) > mworld > $o ).

thf(tp_mimplies,type,
    mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).

thf(tp_mlocal,type,
    mlocal: ( mworld > $o ) > $o ).

thf(tp_mnot,type,
    mnot: ( mworld > $o ) > mworld > $o ).

thf(tp_mor,type,
    mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).

thf(tp_mrel,type,
    mrel: mworld > mworld > $o ).

thf(tp_sK1_X,type,
    sK1_X: mworld > $i ).

thf(tp_sK2_SX0,type,
    sK2_SX0: mworld ).

thf(tp_sK3_SY10,type,
    sK3_SY10: $i ).

thf(tp_sK4_SY12,type,
    sK4_SY12: $i > mworld > mworld ).

thf(mand,definition,
    ( mand
    = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
          ( ( A @ W )
          & ( B @ W ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mand) ).

thf(mbox,definition,
    ( mbox
    = ( ^ [Phi: mworld > $o,W: mworld] :
        ! [V: mworld] :
          ( ( mrel @ W @ V )
         => ( Phi @ V ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox) ).

thf(mdia,definition,
    ( mdia
    = ( ^ [Phi: mworld > $o,W: mworld] :
        ? [V: mworld] :
          ( ( mrel @ W @ V )
          & ( Phi @ V ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mdia) ).

thf(mequiv,definition,
    ( mequiv
    = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
          ( ( A @ W )
        <=> ( B @ W ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mequiv) ).

thf(mexists_di,definition,
    ( mexists_di
    = ( ^ [A: $i > mworld > $o,W: mworld] :
        ? [X: $i] :
          ( ( eiw_di @ X @ W )
          & ( A @ X @ W ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mexists_di) ).

thf(mforall_di,definition,
    ( mforall_di
    = ( ^ [A: $i > mworld > $o,W: mworld] :
        ! [X: $i] :
          ( ( eiw_di @ X @ W )
         => ( A @ X @ W ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mforall_di) ).

thf(mimplies,definition,
    ( mimplies
    = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
          ( ( A @ W )
         => ( B @ W ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies) ).

thf(mlocal,definition,
    ( mlocal
    = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mlocal) ).

thf(mnot,definition,
    ( mnot
    = ( ^ [A: mworld > $o,W: mworld] :
          ~ ( A @ W ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot) ).

thf(mor,definition,
    ( mor
    = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
          ( ( A @ W )
          | ( B @ W ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor) ).

thf(1,axiom,
    ! [W: mworld,V: mworld,X: $i] :
      ( ( ( eiw_di @ X @ W )
        & ( mrel @ W @ V ) )
     => ( eiw_di @ X @ V ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eiw_di_cumul) ).

thf(2,axiom,
    ! [W: mworld] :
    ? [X: $i] : ( eiw_di @ X @ W ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eiw_di_nonempty) ).

thf(3,axiom,
    ! [W: mworld,V: mworld,U: mworld] :
      ( ( ( mrel @ W @ V )
        & ( mrel @ V @ U ) )
     => ( mrel @ W @ U ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_transitive) ).

thf(4,axiom,
    ! [W: mworld] : ( mrel @ W @ W ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_reflexive) ).

thf(5,conjecture,
    ( mlocal
    @ ( mimplies
      @ ( mand
        @ ( mdia
          @ ( mexists_di
            @ ^ [X: $i] : ( mbox @ ( a @ X ) ) ) )
        @ ( mbox
          @ ( mforall_di
            @ ^ [X: $i] : ( mdia @ ( b @ X ) ) ) ) )
      @ ( mdia
        @ ( mexists_di
          @ ^ [X: $i] : ( mdia @ ( mand @ ( a @ X ) @ ( b @ X ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).

thf(6,negated_conjecture,
    ( ( mlocal
      @ ( mimplies
        @ ( mand
          @ ( mdia
            @ ( mexists_di
              @ ^ [X: $i] : ( mbox @ ( a @ X ) ) ) )
          @ ( mbox
            @ ( mforall_di
              @ ^ [X: $i] : ( mdia @ ( b @ X ) ) ) ) )
        @ ( mdia
          @ ( mexists_di
            @ ^ [X: $i] : ( mdia @ ( mand @ ( a @ X ) @ ( b @ X ) ) ) ) ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[5]) ).

thf(7,plain,
    ( ( ~ ( mlocal
          @ ( mimplies
            @ ( mand
              @ ( mdia
                @ ( mexists_di
                  @ ^ [X: $i] : ( mbox @ ( a @ X ) ) ) )
              @ ( mbox
                @ ( mforall_di
                  @ ^ [X: $i] : ( mdia @ ( b @ X ) ) ) ) )
            @ ( mdia
              @ ( mexists_di
                @ ^ [X: $i] : ( mdia @ ( mand @ ( a @ X ) @ ( b @ X ) ) ) ) ) ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[6]) ).

thf(8,plain,
    ( ( ! [W: mworld,V: mworld,X: $i] :
          ( ~ ( eiw_di @ X @ W )
          | ~ ( mrel @ W @ V )
          | ( eiw_di @ X @ V ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[1]) ).

thf(9,plain,
    ( ( ! [W: mworld] : ( eiw_di @ ( sK1_X @ W ) @ W ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2]) ).

thf(10,plain,
    ( ( ! [W: mworld,V: mworld,U: mworld] :
          ( ~ ( mrel @ W @ V )
          | ~ ( mrel @ V @ U )
          | ( mrel @ W @ U ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[3]) ).

thf(11,plain,
    ( ( ! [W: mworld] : ( mrel @ W @ W ) )
    = $true ),
    inference(copy,[status(thm)],[4]) ).

thf(12,plain,
    ( ( ! [W: mworld,V: mworld,U: mworld] :
          ( ~ ( mrel @ W @ V )
          | ~ ( mrel @ V @ U )
          | ( mrel @ W @ U ) ) )
    = $true ),
    inference(copy,[status(thm)],[10]) ).

thf(13,plain,
    ( ( ! [W: mworld] : ( eiw_di @ ( sK1_X @ W ) @ W ) )
    = $true ),
    inference(copy,[status(thm)],[9]) ).

thf(14,plain,
    ( ( ! [W: mworld,V: mworld,X: $i] :
          ( ~ ( eiw_di @ X @ W )
          | ~ ( mrel @ W @ V )
          | ( eiw_di @ X @ V ) ) )
    = $true ),
    inference(copy,[status(thm)],[8]) ).

thf(15,plain,
    ( ( ~ ( mlocal
          @ ( mimplies
            @ ( mand
              @ ( mdia
                @ ( mexists_di
                  @ ^ [X: $i] : ( mbox @ ( a @ X ) ) ) )
              @ ( mbox
                @ ( mforall_di
                  @ ^ [X: $i] : ( mdia @ ( b @ X ) ) ) ) )
            @ ( mdia
              @ ( mexists_di
                @ ^ [X: $i] : ( mdia @ ( mand @ ( a @ X ) @ ( b @ X ) ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[7]) ).

thf(16,plain,
    ( ( ~ ( ~ ~ ( ~ ~ ! [SX0: mworld] :
                        ~ ~ ( ~ ( mrel @ mactual @ SX0 )
                            | ~ ~ ! [SX1: $i] :
                                    ~ ~ ( ~ ( eiw_di @ SX1 @ SX0 )
                                        | ~ ! [SX2: mworld] :
                                              ( ~ ( mrel @ SX0 @ SX2 )
                                              | ( a @ SX1 @ SX2 ) ) ) )
                | ~ ! [SX0: mworld] :
                      ( ~ ( mrel @ mactual @ SX0 )
                      | ! [SX1: $i] :
                          ( ~ ( eiw_di @ SX1 @ SX0 )
                          | ~ ! [SX2: mworld] :
                                ~ ~ ( ~ ( mrel @ SX0 @ SX2 )
                                    | ~ ( b @ SX1 @ SX2 ) ) ) ) )
          | ~ ! [SX0: mworld] :
                ~ ~ ( ~ ( mrel @ mactual @ SX0 )
                    | ~ ~ ! [SX1: $i] :
                            ~ ~ ( ~ ( eiw_di @ SX1 @ SX0 )
                                | ~ ~ ! [SX2: mworld] :
                                        ~ ~ ( ~ ( mrel @ SX0 @ SX2 )
                                            | ~ ~ ( ~ ( a @ SX1 @ SX2 )
                                                  | ~ ( b @ SX1 @ SX2 ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[15,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).

thf(17,plain,
    ! [SV1: mworld] :
      ( ( mrel @ SV1 @ SV1 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11]) ).

thf(18,plain,
    ! [SV2: mworld] :
      ( ( ! [SY0: mworld,SY1: mworld] :
            ( ~ ( mrel @ SV2 @ SY0 )
            | ~ ( mrel @ SY0 @ SY1 )
            | ( mrel @ SV2 @ SY1 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[12]) ).

thf(19,plain,
    ! [SV3: mworld] :
      ( ( eiw_di @ ( sK1_X @ SV3 ) @ SV3 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[13]) ).

thf(20,plain,
    ! [SV4: mworld] :
      ( ( ! [SY2: mworld,SY3: $i] :
            ( ~ ( eiw_di @ SY3 @ SV4 )
            | ~ ( mrel @ SV4 @ SY2 )
            | ( eiw_di @ SY3 @ SY2 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[14]) ).

thf(21,plain,
    ( ( ~ ~ ( ~ ~ ! [SX0: mworld] :
                    ~ ~ ( ~ ( mrel @ mactual @ SX0 )
                        | ~ ~ ! [SX1: $i] :
                                ~ ~ ( ~ ( eiw_di @ SX1 @ SX0 )
                                    | ~ ! [SX2: mworld] :
                                          ( ~ ( mrel @ SX0 @ SX2 )
                                          | ( a @ SX1 @ SX2 ) ) ) )
            | ~ ! [SX0: mworld] :
                  ( ~ ( mrel @ mactual @ SX0 )
                  | ! [SX1: $i] :
                      ( ~ ( eiw_di @ SX1 @ SX0 )
                      | ~ ! [SX2: mworld] :
                            ~ ~ ( ~ ( mrel @ SX0 @ SX2 )
                                | ~ ( b @ SX1 @ SX2 ) ) ) ) )
      | ~ ! [SX0: mworld] :
            ~ ~ ( ~ ( mrel @ mactual @ SX0 )
                | ~ ~ ! [SX1: $i] :
                        ~ ~ ( ~ ( eiw_di @ SX1 @ SX0 )
                            | ~ ~ ! [SX2: mworld] :
                                    ~ ~ ( ~ ( mrel @ SX0 @ SX2 )
                                        | ~ ~ ( ~ ( a @ SX1 @ SX2 )
                                              | ~ ( b @ SX1 @ SX2 ) ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[16]) ).

thf(22,plain,
    ! [SV5: mworld,SV2: mworld] :
      ( ( ! [SY4: mworld] :
            ( ~ ( mrel @ SV2 @ SV5 )
            | ~ ( mrel @ SV5 @ SY4 )
            | ( mrel @ SV2 @ SY4 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[18]) ).

thf(23,plain,
    ! [SV6: mworld,SV4: mworld] :
      ( ( ! [SY5: $i] :
            ( ~ ( eiw_di @ SY5 @ SV4 )
            | ~ ( mrel @ SV4 @ SV6 )
            | ( eiw_di @ SY5 @ SV6 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[20]) ).

thf(24,plain,
    ( ( ~ ~ ( ~ ~ ! [SX0: mworld] :
                    ~ ~ ( ~ ( mrel @ mactual @ SX0 )
                        | ~ ~ ! [SX1: $i] :
                                ~ ~ ( ~ ( eiw_di @ SX1 @ SX0 )
                                    | ~ ! [SX2: mworld] :
                                          ( ~ ( mrel @ SX0 @ SX2 )
                                          | ( a @ SX1 @ SX2 ) ) ) )
            | ~ ! [SX0: mworld] :
                  ( ~ ( mrel @ mactual @ SX0 )
                  | ! [SX1: $i] :
                      ( ~ ( eiw_di @ SX1 @ SX0 )
                      | ~ ! [SX2: mworld] :
                            ~ ~ ( ~ ( mrel @ SX0 @ SX2 )
                                | ~ ( b @ SX1 @ SX2 ) ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[21]) ).

thf(25,plain,
    ( ( ~ ! [SX0: mworld] :
            ~ ~ ( ~ ( mrel @ mactual @ SX0 )
                | ~ ~ ! [SX1: $i] :
                        ~ ~ ( ~ ( eiw_di @ SX1 @ SX0 )
                            | ~ ~ ! [SX2: mworld] :
                                    ~ ~ ( ~ ( mrel @ SX0 @ SX2 )
                                        | ~ ~ ( ~ ( a @ SX1 @ SX2 )
                                              | ~ ( b @ SX1 @ SX2 ) ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[21]) ).

thf(26,plain,
    ! [SV7: mworld,SV5: mworld,SV2: mworld] :
      ( ( ~ ( mrel @ SV2 @ SV5 )
        | ~ ( mrel @ SV5 @ SV7 )
        | ( mrel @ SV2 @ SV7 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[22]) ).

thf(27,plain,
    ! [SV6: mworld,SV4: mworld,SV8: $i] :
      ( ( ~ ( eiw_di @ SV8 @ SV4 )
        | ~ ( mrel @ SV4 @ SV6 )
        | ( eiw_di @ SV8 @ SV6 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[23]) ).

thf(28,plain,
    ( ( ~ ( ~ ~ ! [SX0: mworld] :
                  ~ ~ ( ~ ( mrel @ mactual @ SX0 )
                      | ~ ~ ! [SX1: $i] :
                              ~ ~ ( ~ ( eiw_di @ SX1 @ SX0 )
                                  | ~ ! [SX2: mworld] :
                                        ( ~ ( mrel @ SX0 @ SX2 )
                                        | ( a @ SX1 @ SX2 ) ) ) )
          | ~ ! [SX0: mworld] :
                ( ~ ( mrel @ mactual @ SX0 )
                | ! [SX1: $i] :
                    ( ~ ( eiw_di @ SX1 @ SX0 )
                    | ~ ! [SX2: mworld] :
                          ~ ~ ( ~ ( mrel @ SX0 @ SX2 )
                              | ~ ( b @ SX1 @ SX2 ) ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[24]) ).

thf(29,plain,
    ( ( ! [SX0: mworld] :
          ~ ~ ( ~ ( mrel @ mactual @ SX0 )
              | ~ ~ ! [SX1: $i] :
                      ~ ~ ( ~ ( eiw_di @ SX1 @ SX0 )
                          | ~ ~ ! [SX2: mworld] :
                                  ~ ~ ( ~ ( mrel @ SX0 @ SX2 )
                                      | ~ ~ ( ~ ( a @ SX1 @ SX2 )
                                            | ~ ( b @ SX1 @ SX2 ) ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[25]) ).

thf(30,plain,
    ! [SV7: mworld,SV5: mworld,SV2: mworld] :
      ( ( ( ~ ( mrel @ SV2 @ SV5 )
          | ~ ( mrel @ SV5 @ SV7 ) )
        = $true )
      | ( ( mrel @ SV2 @ SV7 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[26]) ).

thf(31,plain,
    ! [SV6: mworld,SV4: mworld,SV8: $i] :
      ( ( ( ~ ( eiw_di @ SV8 @ SV4 )
          | ~ ( mrel @ SV4 @ SV6 ) )
        = $true )
      | ( ( eiw_di @ SV8 @ SV6 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[27]) ).

thf(32,plain,
    ( ( ~ ~ ! [SX0: mworld] :
              ~ ~ ( ~ ( mrel @ mactual @ SX0 )
                  | ~ ~ ! [SX1: $i] :
                          ~ ~ ( ~ ( eiw_di @ SX1 @ SX0 )
                              | ~ ! [SX2: mworld] :
                                    ( ~ ( mrel @ SX0 @ SX2 )
                                    | ( a @ SX1 @ SX2 ) ) ) )
      | ~ ! [SX0: mworld] :
            ( ~ ( mrel @ mactual @ SX0 )
            | ! [SX1: $i] :
                ( ~ ( eiw_di @ SX1 @ SX0 )
                | ~ ! [SX2: mworld] :
                      ~ ~ ( ~ ( mrel @ SX0 @ SX2 )
                          | ~ ( b @ SX1 @ SX2 ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[28]) ).

thf(33,plain,
    ! [SV9: mworld] :
      ( ( ~ ~ ( ~ ( mrel @ mactual @ SV9 )
              | ~ ~ ! [SY6: $i] :
                      ~ ~ ( ~ ( eiw_di @ SY6 @ SV9 )
                          | ~ ~ ! [SY7: mworld] :
                                  ~ ~ ( ~ ( mrel @ SV9 @ SY7 )
                                      | ~ ~ ( ~ ( a @ SY6 @ SY7 )
                                            | ~ ( b @ SY6 @ SY7 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[29]) ).

thf(34,plain,
    ! [SV7: mworld,SV5: mworld,SV2: mworld] :
      ( ( ( ~ ( mrel @ SV2 @ SV5 ) )
        = $true )
      | ( ( ~ ( mrel @ SV5 @ SV7 ) )
        = $true )
      | ( ( mrel @ SV2 @ SV7 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[30]) ).

thf(35,plain,
    ! [SV6: mworld,SV4: mworld,SV8: $i] :
      ( ( ( ~ ( eiw_di @ SV8 @ SV4 ) )
        = $true )
      | ( ( ~ ( mrel @ SV4 @ SV6 ) )
        = $true )
      | ( ( eiw_di @ SV8 @ SV6 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[31]) ).

thf(36,plain,
    ( ( ~ ~ ! [SX0: mworld] :
              ~ ~ ( ~ ( mrel @ mactual @ SX0 )
                  | ~ ~ ! [SX1: $i] :
                          ~ ~ ( ~ ( eiw_di @ SX1 @ SX0 )
                              | ~ ! [SX2: mworld] :
                                    ( ~ ( mrel @ SX0 @ SX2 )
                                    | ( a @ SX1 @ SX2 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[32]) ).

thf(37,plain,
    ( ( ~ ! [SX0: mworld] :
            ( ~ ( mrel @ mactual @ SX0 )
            | ! [SX1: $i] :
                ( ~ ( eiw_di @ SX1 @ SX0 )
                | ~ ! [SX2: mworld] :
                      ~ ~ ( ~ ( mrel @ SX0 @ SX2 )
                          | ~ ( b @ SX1 @ SX2 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[32]) ).

thf(38,plain,
    ! [SV9: mworld] :
      ( ( ~ ( ~ ( mrel @ mactual @ SV9 )
            | ~ ~ ! [SY6: $i] :
                    ~ ~ ( ~ ( eiw_di @ SY6 @ SV9 )
                        | ~ ~ ! [SY7: mworld] :
                                ~ ~ ( ~ ( mrel @ SV9 @ SY7 )
                                    | ~ ~ ( ~ ( a @ SY6 @ SY7 )
                                          | ~ ( b @ SY6 @ SY7 ) ) ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[33]) ).

thf(39,plain,
    ! [SV7: mworld,SV5: mworld,SV2: mworld] :
      ( ( ( mrel @ SV2 @ SV5 )
        = $false )
      | ( ( ~ ( mrel @ SV5 @ SV7 ) )
        = $true )
      | ( ( mrel @ SV2 @ SV7 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[34]) ).

thf(40,plain,
    ! [SV6: mworld,SV4: mworld,SV8: $i] :
      ( ( ( eiw_di @ SV8 @ SV4 )
        = $false )
      | ( ( ~ ( mrel @ SV4 @ SV6 ) )
        = $true )
      | ( ( eiw_di @ SV8 @ SV6 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[35]) ).

thf(41,plain,
    ( ( ~ ! [SX0: mworld] :
            ~ ~ ( ~ ( mrel @ mactual @ SX0 )
                | ~ ~ ! [SX1: $i] :
                        ~ ~ ( ~ ( eiw_di @ SX1 @ SX0 )
                            | ~ ! [SX2: mworld] :
                                  ( ~ ( mrel @ SX0 @ SX2 )
                                  | ( a @ SX1 @ SX2 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[36]) ).

thf(42,plain,
    ( ( ! [SX0: mworld] :
          ( ~ ( mrel @ mactual @ SX0 )
          | ! [SX1: $i] :
              ( ~ ( eiw_di @ SX1 @ SX0 )
              | ~ ! [SX2: mworld] :
                    ~ ~ ( ~ ( mrel @ SX0 @ SX2 )
                        | ~ ( b @ SX1 @ SX2 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[37]) ).

thf(43,plain,
    ! [SV9: mworld] :
      ( ( ~ ( mrel @ mactual @ SV9 )
        | ~ ~ ! [SY6: $i] :
                ~ ~ ( ~ ( eiw_di @ SY6 @ SV9 )
                    | ~ ~ ! [SY7: mworld] :
                            ~ ~ ( ~ ( mrel @ SV9 @ SY7 )
                                | ~ ~ ( ~ ( a @ SY6 @ SY7 )
                                      | ~ ( b @ SY6 @ SY7 ) ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[38]) ).

thf(44,plain,
    ! [SV2: mworld,SV7: mworld,SV5: mworld] :
      ( ( ( mrel @ SV5 @ SV7 )
        = $false )
      | ( ( mrel @ SV2 @ SV5 )
        = $false )
      | ( ( mrel @ SV2 @ SV7 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[39]) ).

thf(45,plain,
    ! [SV8: $i,SV6: mworld,SV4: mworld] :
      ( ( ( mrel @ SV4 @ SV6 )
        = $false )
      | ( ( eiw_di @ SV8 @ SV4 )
        = $false )
      | ( ( eiw_di @ SV8 @ SV6 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[40]) ).

thf(46,plain,
    ( ( ! [SX0: mworld] :
          ~ ~ ( ~ ( mrel @ mactual @ SX0 )
              | ~ ~ ! [SX1: $i] :
                      ~ ~ ( ~ ( eiw_di @ SX1 @ SX0 )
                          | ~ ! [SX2: mworld] :
                                ( ~ ( mrel @ SX0 @ SX2 )
                                | ( a @ SX1 @ SX2 ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[41]) ).

thf(47,plain,
    ! [SV10: mworld] :
      ( ( ~ ( mrel @ mactual @ SV10 )
        | ! [SY8: $i] :
            ( ~ ( eiw_di @ SY8 @ SV10 )
            | ~ ! [SY9: mworld] :
                  ~ ~ ( ~ ( mrel @ SV10 @ SY9 )
                      | ~ ( b @ SY8 @ SY9 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[42]) ).

thf(48,plain,
    ! [SV9: mworld] :
      ( ( ( ~ ( mrel @ mactual @ SV9 ) )
        = $true )
      | ( ( ~ ~ ! [SY6: $i] :
                  ~ ~ ( ~ ( eiw_di @ SY6 @ SV9 )
                      | ~ ~ ! [SY7: mworld] :
                              ~ ~ ( ~ ( mrel @ SV9 @ SY7 )
                                  | ~ ~ ( ~ ( a @ SY6 @ SY7 )
                                        | ~ ( b @ SY6 @ SY7 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[43]) ).

thf(49,plain,
    ( ( ~ ~ ( ~ ( mrel @ mactual @ sK2_SX0 )
            | ~ ~ ! [SY10: $i] :
                    ~ ~ ( ~ ( eiw_di @ SY10 @ sK2_SX0 )
                        | ~ ! [SY11: mworld] :
                              ( ~ ( mrel @ sK2_SX0 @ SY11 )
                              | ( a @ SY10 @ SY11 ) ) ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[46]) ).

thf(50,plain,
    ! [SV10: mworld] :
      ( ( ( ~ ( mrel @ mactual @ SV10 ) )
        = $true )
      | ( ( ! [SY8: $i] :
              ( ~ ( eiw_di @ SY8 @ SV10 )
              | ~ ! [SY9: mworld] :
                    ~ ~ ( ~ ( mrel @ SV10 @ SY9 )
                        | ~ ( b @ SY8 @ SY9 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[47]) ).

thf(51,plain,
    ! [SV9: mworld] :
      ( ( ( mrel @ mactual @ SV9 )
        = $false )
      | ( ( ~ ~ ! [SY6: $i] :
                  ~ ~ ( ~ ( eiw_di @ SY6 @ SV9 )
                      | ~ ~ ! [SY7: mworld] :
                              ~ ~ ( ~ ( mrel @ SV9 @ SY7 )
                                  | ~ ~ ( ~ ( a @ SY6 @ SY7 )
                                        | ~ ( b @ SY6 @ SY7 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[48]) ).

thf(52,plain,
    ( ( ~ ( ~ ( mrel @ mactual @ sK2_SX0 )
          | ~ ~ ! [SY10: $i] :
                  ~ ~ ( ~ ( eiw_di @ SY10 @ sK2_SX0 )
                      | ~ ! [SY11: mworld] :
                            ( ~ ( mrel @ sK2_SX0 @ SY11 )
                            | ( a @ SY10 @ SY11 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[49]) ).

thf(53,plain,
    ! [SV10: mworld] :
      ( ( ( mrel @ mactual @ SV10 )
        = $false )
      | ( ( ! [SY8: $i] :
              ( ~ ( eiw_di @ SY8 @ SV10 )
              | ~ ! [SY9: mworld] :
                    ~ ~ ( ~ ( mrel @ SV10 @ SY9 )
                        | ~ ( b @ SY8 @ SY9 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[50]) ).

thf(54,plain,
    ! [SV9: mworld] :
      ( ( ( ~ ! [SY6: $i] :
                ~ ~ ( ~ ( eiw_di @ SY6 @ SV9 )
                    | ~ ~ ! [SY7: mworld] :
                            ~ ~ ( ~ ( mrel @ SV9 @ SY7 )
                                | ~ ~ ( ~ ( a @ SY6 @ SY7 )
                                      | ~ ( b @ SY6 @ SY7 ) ) ) ) )
        = $false )
      | ( ( mrel @ mactual @ SV9 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[51]) ).

thf(55,plain,
    ( ( ~ ( mrel @ mactual @ sK2_SX0 )
      | ~ ~ ! [SY10: $i] :
              ~ ~ ( ~ ( eiw_di @ SY10 @ sK2_SX0 )
                  | ~ ! [SY11: mworld] :
                        ( ~ ( mrel @ sK2_SX0 @ SY11 )
                        | ( a @ SY10 @ SY11 ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[52]) ).

thf(56,plain,
    ! [SV10: mworld,SV11: $i] :
      ( ( ( ~ ( eiw_di @ SV11 @ SV10 )
          | ~ ! [SY12: mworld] :
                ~ ~ ( ~ ( mrel @ SV10 @ SY12 )
                    | ~ ( b @ SV11 @ SY12 ) ) )
        = $true )
      | ( ( mrel @ mactual @ SV10 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[53]) ).

thf(57,plain,
    ! [SV9: mworld] :
      ( ( ( ! [SY6: $i] :
              ~ ~ ( ~ ( eiw_di @ SY6 @ SV9 )
                  | ~ ~ ! [SY7: mworld] :
                          ~ ~ ( ~ ( mrel @ SV9 @ SY7 )
                              | ~ ~ ( ~ ( a @ SY6 @ SY7 )
                                    | ~ ( b @ SY6 @ SY7 ) ) ) ) )
        = $true )
      | ( ( mrel @ mactual @ SV9 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[54]) ).

thf(58,plain,
    ( ( ~ ( mrel @ mactual @ sK2_SX0 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[55]) ).

thf(59,plain,
    ( ( ~ ~ ! [SY10: $i] :
              ~ ~ ( ~ ( eiw_di @ SY10 @ sK2_SX0 )
                  | ~ ! [SY11: mworld] :
                        ( ~ ( mrel @ sK2_SX0 @ SY11 )
                        | ( a @ SY10 @ SY11 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[55]) ).

thf(60,plain,
    ! [SV10: mworld,SV11: $i] :
      ( ( ( ~ ( eiw_di @ SV11 @ SV10 ) )
        = $true )
      | ( ( ~ ! [SY12: mworld] :
                ~ ~ ( ~ ( mrel @ SV10 @ SY12 )
                    | ~ ( b @ SV11 @ SY12 ) ) )
        = $true )
      | ( ( mrel @ mactual @ SV10 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[56]) ).

thf(61,plain,
    ! [SV9: mworld,SV12: $i] :
      ( ( ( ~ ~ ( ~ ( eiw_di @ SV12 @ SV9 )
                | ~ ~ ! [SY13: mworld] :
                        ~ ~ ( ~ ( mrel @ SV9 @ SY13 )
                            | ~ ~ ( ~ ( a @ SV12 @ SY13 )
                                  | ~ ( b @ SV12 @ SY13 ) ) ) ) )
        = $true )
      | ( ( mrel @ mactual @ SV9 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[57]) ).

thf(62,plain,
    ( ( mrel @ mactual @ sK2_SX0 )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[58]) ).

thf(63,plain,
    ( ( ~ ! [SY10: $i] :
            ~ ~ ( ~ ( eiw_di @ SY10 @ sK2_SX0 )
                | ~ ! [SY11: mworld] :
                      ( ~ ( mrel @ sK2_SX0 @ SY11 )
                      | ( a @ SY10 @ SY11 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[59]) ).

thf(64,plain,
    ! [SV10: mworld,SV11: $i] :
      ( ( ( eiw_di @ SV11 @ SV10 )
        = $false )
      | ( ( ~ ! [SY12: mworld] :
                ~ ~ ( ~ ( mrel @ SV10 @ SY12 )
                    | ~ ( b @ SV11 @ SY12 ) ) )
        = $true )
      | ( ( mrel @ mactual @ SV10 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[60]) ).

thf(65,plain,
    ! [SV9: mworld,SV12: $i] :
      ( ( ( ~ ( ~ ( eiw_di @ SV12 @ SV9 )
              | ~ ~ ! [SY13: mworld] :
                      ~ ~ ( ~ ( mrel @ SV9 @ SY13 )
                          | ~ ~ ( ~ ( a @ SV12 @ SY13 )
                                | ~ ( b @ SV12 @ SY13 ) ) ) ) )
        = $false )
      | ( ( mrel @ mactual @ SV9 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[61]) ).

thf(66,plain,
    ( ( ! [SY10: $i] :
          ~ ~ ( ~ ( eiw_di @ SY10 @ sK2_SX0 )
              | ~ ! [SY11: mworld] :
                    ( ~ ( mrel @ sK2_SX0 @ SY11 )
                    | ( a @ SY10 @ SY11 ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[63]) ).

thf(67,plain,
    ! [SV11: $i,SV10: mworld] :
      ( ( ( ! [SY12: mworld] :
              ~ ~ ( ~ ( mrel @ SV10 @ SY12 )
                  | ~ ( b @ SV11 @ SY12 ) ) )
        = $false )
      | ( ( eiw_di @ SV11 @ SV10 )
        = $false )
      | ( ( mrel @ mactual @ SV10 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[64]) ).

thf(68,plain,
    ! [SV9: mworld,SV12: $i] :
      ( ( ( ~ ( eiw_di @ SV12 @ SV9 )
          | ~ ~ ! [SY13: mworld] :
                  ~ ~ ( ~ ( mrel @ SV9 @ SY13 )
                      | ~ ~ ( ~ ( a @ SV12 @ SY13 )
                            | ~ ( b @ SV12 @ SY13 ) ) ) )
        = $true )
      | ( ( mrel @ mactual @ SV9 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[65]) ).

thf(69,plain,
    ( ( ~ ~ ( ~ ( eiw_di @ sK3_SY10 @ sK2_SX0 )
            | ~ ! [SY14: mworld] :
                  ( ~ ( mrel @ sK2_SX0 @ SY14 )
                  | ( a @ sK3_SY10 @ SY14 ) ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[66]) ).

thf(70,plain,
    ! [SV11: $i,SV10: mworld] :
      ( ( ( ~ ~ ( ~ ( mrel @ SV10 @ ( sK4_SY12 @ SV11 @ SV10 ) )
                | ~ ( b @ SV11 @ ( sK4_SY12 @ SV11 @ SV10 ) ) ) )
        = $false )
      | ( ( eiw_di @ SV11 @ SV10 )
        = $false )
      | ( ( mrel @ mactual @ SV10 )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[67]) ).

thf(71,plain,
    ! [SV9: mworld,SV12: $i] :
      ( ( ( ~ ( eiw_di @ SV12 @ SV9 ) )
        = $true )
      | ( ( ~ ~ ! [SY13: mworld] :
                  ~ ~ ( ~ ( mrel @ SV9 @ SY13 )
                      | ~ ~ ( ~ ( a @ SV12 @ SY13 )
                            | ~ ( b @ SV12 @ SY13 ) ) ) )
        = $true )
      | ( ( mrel @ mactual @ SV9 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[68]) ).

thf(72,plain,
    ( ( ~ ( ~ ( eiw_di @ sK3_SY10 @ sK2_SX0 )
          | ~ ! [SY14: mworld] :
                ( ~ ( mrel @ sK2_SX0 @ SY14 )
                | ( a @ sK3_SY10 @ SY14 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[69]) ).

thf(73,plain,
    ! [SV11: $i,SV10: mworld] :
      ( ( ( ~ ( ~ ( mrel @ SV10 @ ( sK4_SY12 @ SV11 @ SV10 ) )
              | ~ ( b @ SV11 @ ( sK4_SY12 @ SV11 @ SV10 ) ) ) )
        = $true )
      | ( ( eiw_di @ SV11 @ SV10 )
        = $false )
      | ( ( mrel @ mactual @ SV10 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[70]) ).

thf(74,plain,
    ! [SV9: mworld,SV12: $i] :
      ( ( ( eiw_di @ SV12 @ SV9 )
        = $false )
      | ( ( ~ ~ ! [SY13: mworld] :
                  ~ ~ ( ~ ( mrel @ SV9 @ SY13 )
                      | ~ ~ ( ~ ( a @ SV12 @ SY13 )
                            | ~ ( b @ SV12 @ SY13 ) ) ) )
        = $true )
      | ( ( mrel @ mactual @ SV9 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[71]) ).

thf(75,plain,
    ( ( ~ ( eiw_di @ sK3_SY10 @ sK2_SX0 )
      | ~ ! [SY14: mworld] :
            ( ~ ( mrel @ sK2_SX0 @ SY14 )
            | ( a @ sK3_SY10 @ SY14 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[72]) ).

thf(76,plain,
    ! [SV11: $i,SV10: mworld] :
      ( ( ( ~ ( mrel @ SV10 @ ( sK4_SY12 @ SV11 @ SV10 ) )
          | ~ ( b @ SV11 @ ( sK4_SY12 @ SV11 @ SV10 ) ) )
        = $false )
      | ( ( eiw_di @ SV11 @ SV10 )
        = $false )
      | ( ( mrel @ mactual @ SV10 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[73]) ).

thf(77,plain,
    ! [SV12: $i,SV9: mworld] :
      ( ( ( ~ ! [SY13: mworld] :
                ~ ~ ( ~ ( mrel @ SV9 @ SY13 )
                    | ~ ~ ( ~ ( a @ SV12 @ SY13 )
                          | ~ ( b @ SV12 @ SY13 ) ) ) )
        = $false )
      | ( ( eiw_di @ SV12 @ SV9 )
        = $false )
      | ( ( mrel @ mactual @ SV9 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[74]) ).

thf(78,plain,
    ( ( ~ ( eiw_di @ sK3_SY10 @ sK2_SX0 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[75]) ).

thf(79,plain,
    ( ( ~ ! [SY14: mworld] :
            ( ~ ( mrel @ sK2_SX0 @ SY14 )
            | ( a @ sK3_SY10 @ SY14 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[75]) ).

thf(80,plain,
    ! [SV11: $i,SV10: mworld] :
      ( ( ( ~ ( mrel @ SV10 @ ( sK4_SY12 @ SV11 @ SV10 ) ) )
        = $false )
      | ( ( eiw_di @ SV11 @ SV10 )
        = $false )
      | ( ( mrel @ mactual @ SV10 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[76]) ).

thf(81,plain,
    ! [SV10: mworld,SV11: $i] :
      ( ( ( ~ ( b @ SV11 @ ( sK4_SY12 @ SV11 @ SV10 ) ) )
        = $false )
      | ( ( eiw_di @ SV11 @ SV10 )
        = $false )
      | ( ( mrel @ mactual @ SV10 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[76]) ).

thf(82,plain,
    ! [SV12: $i,SV9: mworld] :
      ( ( ( ! [SY13: mworld] :
              ~ ~ ( ~ ( mrel @ SV9 @ SY13 )
                  | ~ ~ ( ~ ( a @ SV12 @ SY13 )
                        | ~ ( b @ SV12 @ SY13 ) ) ) )
        = $true )
      | ( ( eiw_di @ SV12 @ SV9 )
        = $false )
      | ( ( mrel @ mactual @ SV9 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[77]) ).

thf(83,plain,
    ( ( eiw_di @ sK3_SY10 @ sK2_SX0 )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[78]) ).

thf(84,plain,
    ( ( ! [SY14: mworld] :
          ( ~ ( mrel @ sK2_SX0 @ SY14 )
          | ( a @ sK3_SY10 @ SY14 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[79]) ).

thf(85,plain,
    ! [SV11: $i,SV10: mworld] :
      ( ( ( mrel @ SV10 @ ( sK4_SY12 @ SV11 @ SV10 ) )
        = $true )
      | ( ( eiw_di @ SV11 @ SV10 )
        = $false )
      | ( ( mrel @ mactual @ SV10 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[80]) ).

thf(86,plain,
    ! [SV10: mworld,SV11: $i] :
      ( ( ( b @ SV11 @ ( sK4_SY12 @ SV11 @ SV10 ) )
        = $true )
      | ( ( eiw_di @ SV11 @ SV10 )
        = $false )
      | ( ( mrel @ mactual @ SV10 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[81]) ).

thf(87,plain,
    ! [SV12: $i,SV13: mworld,SV9: mworld] :
      ( ( ( ~ ~ ( ~ ( mrel @ SV9 @ SV13 )
                | ~ ~ ( ~ ( a @ SV12 @ SV13 )
                      | ~ ( b @ SV12 @ SV13 ) ) ) )
        = $true )
      | ( ( eiw_di @ SV12 @ SV9 )
        = $false )
      | ( ( mrel @ mactual @ SV9 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[82]) ).

thf(88,plain,
    ! [SV14: mworld] :
      ( ( ~ ( mrel @ sK2_SX0 @ SV14 )
        | ( a @ sK3_SY10 @ SV14 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[84]) ).

thf(89,plain,
    ! [SV12: $i,SV13: mworld,SV9: mworld] :
      ( ( ( ~ ( ~ ( mrel @ SV9 @ SV13 )
              | ~ ~ ( ~ ( a @ SV12 @ SV13 )
                    | ~ ( b @ SV12 @ SV13 ) ) ) )
        = $false )
      | ( ( eiw_di @ SV12 @ SV9 )
        = $false )
      | ( ( mrel @ mactual @ SV9 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[87]) ).

thf(90,plain,
    ! [SV14: mworld] :
      ( ( ( ~ ( mrel @ sK2_SX0 @ SV14 ) )
        = $true )
      | ( ( a @ sK3_SY10 @ SV14 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[88]) ).

thf(91,plain,
    ! [SV12: $i,SV13: mworld,SV9: mworld] :
      ( ( ( ~ ( mrel @ SV9 @ SV13 )
          | ~ ~ ( ~ ( a @ SV12 @ SV13 )
                | ~ ( b @ SV12 @ SV13 ) ) )
        = $true )
      | ( ( eiw_di @ SV12 @ SV9 )
        = $false )
      | ( ( mrel @ mactual @ SV9 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[89]) ).

thf(92,plain,
    ! [SV14: mworld] :
      ( ( ( mrel @ sK2_SX0 @ SV14 )
        = $false )
      | ( ( a @ sK3_SY10 @ SV14 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[90]) ).

thf(93,plain,
    ! [SV12: $i,SV13: mworld,SV9: mworld] :
      ( ( ( ~ ( mrel @ SV9 @ SV13 ) )
        = $true )
      | ( ( ~ ~ ( ~ ( a @ SV12 @ SV13 )
                | ~ ( b @ SV12 @ SV13 ) ) )
        = $true )
      | ( ( eiw_di @ SV12 @ SV9 )
        = $false )
      | ( ( mrel @ mactual @ SV9 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[91]) ).

thf(94,plain,
    ! [SV12: $i,SV13: mworld,SV9: mworld] :
      ( ( ( mrel @ SV9 @ SV13 )
        = $false )
      | ( ( ~ ~ ( ~ ( a @ SV12 @ SV13 )
                | ~ ( b @ SV12 @ SV13 ) ) )
        = $true )
      | ( ( eiw_di @ SV12 @ SV9 )
        = $false )
      | ( ( mrel @ mactual @ SV9 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[93]) ).

thf(95,plain,
    ! [SV9: mworld,SV13: mworld,SV12: $i] :
      ( ( ( ~ ( ~ ( a @ SV12 @ SV13 )
              | ~ ( b @ SV12 @ SV13 ) ) )
        = $false )
      | ( ( mrel @ SV9 @ SV13 )
        = $false )
      | ( ( eiw_di @ SV12 @ SV9 )
        = $false )
      | ( ( mrel @ mactual @ SV9 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[94]) ).

thf(96,plain,
    ! [SV9: mworld,SV13: mworld,SV12: $i] :
      ( ( ( ~ ( a @ SV12 @ SV13 )
          | ~ ( b @ SV12 @ SV13 ) )
        = $true )
      | ( ( mrel @ SV9 @ SV13 )
        = $false )
      | ( ( eiw_di @ SV12 @ SV9 )
        = $false )
      | ( ( mrel @ mactual @ SV9 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[95]) ).

thf(97,plain,
    ! [SV9: mworld,SV13: mworld,SV12: $i] :
      ( ( ( ~ ( a @ SV12 @ SV13 ) )
        = $true )
      | ( ( ~ ( b @ SV12 @ SV13 ) )
        = $true )
      | ( ( mrel @ SV9 @ SV13 )
        = $false )
      | ( ( eiw_di @ SV12 @ SV9 )
        = $false )
      | ( ( mrel @ mactual @ SV9 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[96]) ).

thf(98,plain,
    ! [SV9: mworld,SV13: mworld,SV12: $i] :
      ( ( ( a @ SV12 @ SV13 )
        = $false )
      | ( ( ~ ( b @ SV12 @ SV13 ) )
        = $true )
      | ( ( mrel @ SV9 @ SV13 )
        = $false )
      | ( ( eiw_di @ SV12 @ SV9 )
        = $false )
      | ( ( mrel @ mactual @ SV9 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[97]) ).

thf(99,plain,
    ! [SV9: mworld,SV13: mworld,SV12: $i] :
      ( ( ( b @ SV12 @ SV13 )
        = $false )
      | ( ( a @ SV12 @ SV13 )
        = $false )
      | ( ( mrel @ SV9 @ SV13 )
        = $false )
      | ( ( eiw_di @ SV12 @ SV9 )
        = $false )
      | ( ( mrel @ mactual @ SV9 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[98]) ).

thf(100,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[17,99,92,86,85,83,62,45,44,19]) ).

thf(101,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[100]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : SYO889^16 : TPTP v8.1.0. Released v8.1.0.
% 0.11/0.12  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33  % Computer : n020.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Fri Jul  8 17:26:58 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.34  
% 0.12/0.34   No.of.Axioms: 4
% 0.12/0.34  
% 0.12/0.34   Length.of.Defs: 1623
% 0.12/0.34  
% 0.12/0.34   Contains.Choice.Funs: false
% 0.12/0.34  (rf:0,axioms:4,ps:3,u:6,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:6,loop_count:0,foatp_calls:0,translation:fof_full)......
% 0.12/0.41  
% 0.12/0.41  ********************************
% 0.12/0.41  *   All subproblems solved!    *
% 0.12/0.41  ********************************
% 0.12/0.41  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:4,ps:3,u:6,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:100,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.18/0.41  
% 0.18/0.41  %**** Beginning of derivation protocol ****
% 0.18/0.41  % SZS output start CNFRefutation
% See solution above
% 0.18/0.41  
% 0.18/0.41  %**** End of derivation protocol ****
% 0.18/0.41  %**** no. of clauses in derivation: 101 ****
% 0.18/0.41  %**** clause counter: 100 ****
% 0.18/0.41  
% 0.18/0.41  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:4,ps:3,u:6,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:100,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------