TSTP Solution File: NLP266^4 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : NLP266^4 : 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 : n029.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 : Mon Jul 18 03:05:32 EDT 2022

% Result   : Theorem 0.45s 0.62s
% Output   : CNFRefutation 0.46s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   40
%            Number of leaves      :   46
% Syntax   : Number of formulae    :  165 (  54 unt;  30 typ;  10 def)
%            Number of atoms       : 1210 ( 276 equ;   0 cnn)
%            Maximal formula atoms :   18 (   8 avg)
%            Number of connectives : 3108 ( 612   ~; 412   |;   3   &;2077   @)
%                                         (   1 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (   5 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :  100 ( 100   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   32 (  29 usr;   7 con; 0-4 aty)
%            Number of variables   :  576 (  57   ^ 517   !;   2   ?; 576   :)

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

thf(tp_do,type,
    do: $i > $i > $i > mworld > $o ).

thf(tp_entry_box,type,
    entry_box: $i > mworld > $o ).

thf(tp_in,type,
    in: $i > $i > $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_number,type,
    number: $i > $i > mworld > $o ).

thf(tp_one,type,
    one: $i ).

thf(tp_sK1_SX0,type,
    sK1_SX0: $i ).

thf(tp_sK2_SX0,type,
    sK2_SX0: mworld ).

thf(tp_sK3_SY8,type,
    sK3_SY8: mworld > $i ).

thf(tp_sK4_SY35,type,
    sK4_SY35: $i > $i > $i > mworld > $i ).

thf(tp_sK5_SY40,type,
    sK5_SY40: $i > $i > $i > $i > mworld ).

thf(tp_sK6_SY50,type,
    sK6_SY50: $i > $i > $i > $i > mworld ).

thf(tp_sK7_SY53,type,
    sK7_SY53: $i > $i > $i > $i > $i ).

thf(tp_sK8_SY50,type,
    sK8_SY50: $i > $i > $i > $i > mworld ).

thf(tp_sK9_SY54,type,
    sK9_SY54: $i > $i > $i > $i > $i ).

thf(tp_string,type,
    string: $i > mworld > $o ).

thf(tp_u,type,
    u: $i ).

thf(tp_userid,type,
    userid: $i > $i > mworld > $o ).

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

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

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

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

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

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

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

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

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

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

thf(1,axiom,
    ( mlocal
    @ ( mbox
      @ ( mforall_di
        @ ^ [S: $i] :
            ( mforall_di
            @ ^ [I: $i] :
                ( mforall_di
                @ ^ [B: $i] :
                    ( mimplies @ ( mand @ ( string @ I ) @ ( entry_box @ B ) )
                    @ ( mexists_di
                      @ ^ [A: $i] :
                          ( mbox
                          @ ( mforall_di
                            @ ^ [S2: $i] : ( mimplies @ ( do @ S @ A @ S2 ) @ ( in @ I @ B @ S2 ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).

thf(2,axiom,
    ( mlocal
    @ ( mexists_di
      @ ^ [B: $i] : ( mbox @ ( mand @ ( entry_box @ B ) @ ( number @ B @ one ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).

thf(3,axiom,
    ( mlocal
    @ ( mbox
      @ ( mexists_di
        @ ^ [I: $i] : ( mbox @ ( mand @ ( userid @ u @ I ) @ ( string @ I ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).

thf(4,axiom,
    ! [W: mworld,V: mworld,U: mworld] :
      ( ( ( mrel @ W @ V )
        & ( mrel @ V @ U ) )
     => ( mrel @ W @ U ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_transitive) ).

thf(5,axiom,
    ! [W: mworld] : ( mrel @ W @ W ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_reflexive) ).

thf(6,conjecture,
    ( mlocal
    @ ( mbox
      @ ( mexists_di
        @ ^ [I: $i] :
            ( mexists_di
            @ ^ [B: $i] :
                ( mexists_di
                @ ^ [A: $i] :
                    ( mexists_di
                    @ ^ [S: $i] :
                        ( mand @ ( mbox @ ( mand @ ( userid @ u @ I ) @ ( mand @ ( entry_box @ B ) @ ( number @ B @ one ) ) ) )
                        @ ( mbox
                          @ ( mforall_di
                            @ ^ [S2: $i] : ( mimplies @ ( do @ S @ A @ S2 ) @ ( in @ I @ B @ S2 ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).

thf(7,negated_conjecture,
    ( ( mlocal
      @ ( mbox
        @ ( mexists_di
          @ ^ [I: $i] :
              ( mexists_di
              @ ^ [B: $i] :
                  ( mexists_di
                  @ ^ [A: $i] :
                      ( mexists_di
                      @ ^ [S: $i] :
                          ( mand @ ( mbox @ ( mand @ ( userid @ u @ I ) @ ( mand @ ( entry_box @ B ) @ ( number @ B @ one ) ) ) )
                          @ ( mbox
                            @ ( mforall_di
                              @ ^ [S2: $i] : ( mimplies @ ( do @ S @ A @ S2 ) @ ( in @ I @ B @ S2 ) ) ) ) ) ) ) ) ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[6]) ).

thf(8,plain,
    ( ( ~ ( mlocal
          @ ( mbox
            @ ( mexists_di
              @ ^ [I: $i] :
                  ( mexists_di
                  @ ^ [B: $i] :
                      ( mexists_di
                      @ ^ [A: $i] :
                          ( mexists_di
                          @ ^ [S: $i] :
                              ( mand @ ( mbox @ ( mand @ ( userid @ u @ I ) @ ( mand @ ( entry_box @ B ) @ ( number @ B @ one ) ) ) )
                              @ ( mbox
                                @ ( mforall_di
                                  @ ^ [S2: $i] : ( mimplies @ ( do @ S @ A @ S2 ) @ ( in @ I @ B @ S2 ) ) ) ) ) ) ) ) ) ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[7]) ).

thf(9,plain,
    ( ( ! [W: mworld,V: mworld,U: mworld] :
          ( ~ ( mrel @ W @ V )
          | ~ ( mrel @ V @ U )
          | ( mrel @ W @ U ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[4]) ).

thf(10,plain,
    ( ( ! [W: mworld] : ( mrel @ W @ W ) )
    = $true ),
    inference(copy,[status(thm)],[5]) ).

thf(11,plain,
    ( ( ! [W: mworld,V: mworld,U: mworld] :
          ( ~ ( mrel @ W @ V )
          | ~ ( mrel @ V @ U )
          | ( mrel @ W @ U ) ) )
    = $true ),
    inference(copy,[status(thm)],[9]) ).

thf(12,plain,
    ( ( mlocal
      @ ( mbox
        @ ( mexists_di
          @ ^ [I: $i] : ( mbox @ ( mand @ ( userid @ u @ I ) @ ( string @ I ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[3]) ).

thf(13,plain,
    ( ( mlocal
      @ ( mexists_di
        @ ^ [B: $i] : ( mbox @ ( mand @ ( entry_box @ B ) @ ( number @ B @ one ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2]) ).

thf(14,plain,
    ( ( mlocal
      @ ( mbox
        @ ( mforall_di
          @ ^ [S: $i] :
              ( mforall_di
              @ ^ [I: $i] :
                  ( mforall_di
                  @ ^ [B: $i] :
                      ( mimplies @ ( mand @ ( string @ I ) @ ( entry_box @ B ) )
                      @ ( mexists_di
                        @ ^ [A: $i] :
                            ( mbox
                            @ ( mforall_di
                              @ ^ [S2: $i] : ( mimplies @ ( do @ S @ A @ S2 ) @ ( in @ I @ B @ S2 ) ) ) ) ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1]) ).

thf(15,plain,
    ( ( ~ ( mlocal
          @ ( mbox
            @ ( mexists_di
              @ ^ [I: $i] :
                  ( mexists_di
                  @ ^ [B: $i] :
                      ( mexists_di
                      @ ^ [A: $i] :
                          ( mexists_di
                          @ ^ [S: $i] :
                              ( mand @ ( mbox @ ( mand @ ( userid @ u @ I ) @ ( mand @ ( entry_box @ B ) @ ( number @ B @ one ) ) ) )
                              @ ( mbox
                                @ ( mforall_di
                                  @ ^ [S2: $i] : ( mimplies @ ( do @ S @ A @ S2 ) @ ( in @ I @ B @ S2 ) ) ) ) ) ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[8]) ).

thf(16,plain,
    ( ( ! [SX0: mworld] :
          ( ~ ( mrel @ mactual @ SX0 )
          | ! [SX1: $i,SX2: $i,SX3: $i] :
              ( ~ ~ ( ~ ( string @ SX2 @ SX0 )
                    | ~ ( entry_box @ SX3 @ SX0 ) )
              | ~ ! [SX4: $i] :
                    ~ ! [SX5: mworld] :
                        ( ~ ( mrel @ SX0 @ SX5 )
                        | ! [SX6: $i] :
                            ( ~ ( do @ SX1 @ SX4 @ SX6 @ SX5 )
                            | ( in @ SX2 @ SX3 @ SX6 @ SX5 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[14,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).

thf(17,plain,
    ( ( ~ ! [SX0: $i] :
            ~ ! [SX1: mworld] :
                ( ~ ( mrel @ mactual @ SX1 )
                | ~ ( ~ ( entry_box @ SX0 @ SX1 )
                    | ~ ( number @ SX0 @ one @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[13,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).

thf(18,plain,
    ( ( ! [SX0: mworld] :
          ( ~ ( mrel @ mactual @ SX0 )
          | ~ ! [SX1: $i] :
                ~ ! [SX2: mworld] :
                    ( ~ ( mrel @ SX0 @ SX2 )
                    | ~ ( ~ ( userid @ u @ SX1 @ SX2 )
                        | ~ ( string @ SX1 @ SX2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[12,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).

thf(19,plain,
    ( ( ~ ! [SX0: mworld] :
            ( ~ ( mrel @ mactual @ SX0 )
            | ~ ! [SX1: $i] :
                  ~ ~ ! [SX2: $i] :
                        ~ ~ ! [SX3: $i] :
                              ~ ~ ! [SX4: $i] :
                                    ~ ~ ( ~ ! [SX5: mworld] :
                                              ( ~ ( mrel @ SX0 @ SX5 )
                                              | ~ ( ~ ( userid @ u @ SX1 @ SX5 )
                                                  | ~ ~ ( ~ ( entry_box @ SX2 @ SX5 )
                                                        | ~ ( number @ SX2 @ one @ SX5 ) ) ) )
                                        | ~ ! [SX5: mworld] :
                                              ( ~ ( mrel @ SX0 @ SX5 )
                                              | ! [SX6: $i] :
                                                  ( ~ ( do @ SX4 @ SX3 @ SX6 @ SX5 )
                                                  | ( in @ SX1 @ SX2 @ SX6 @ SX5 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[15,mand,mbox,mdia,mequiv,mexists_di,mforall_di,mimplies,mlocal,mnot,mor]) ).

thf(20,plain,
    ! [SV1: mworld] :
      ( ( mrel @ SV1 @ SV1 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10]) ).

thf(21,plain,
    ! [SV2: mworld] :
      ( ( ! [SY0: mworld,SY1: mworld] :
            ( ~ ( mrel @ SV2 @ SY0 )
            | ~ ( mrel @ SY0 @ SY1 )
            | ( mrel @ SV2 @ SY1 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11]) ).

thf(22,plain,
    ! [SV3: mworld] :
      ( ( ~ ( mrel @ mactual @ SV3 )
        | ! [SY2: $i,SY3: $i,SY4: $i] :
            ( ~ ~ ( ~ ( string @ SY3 @ SV3 )
                  | ~ ( entry_box @ SY4 @ SV3 ) )
            | ~ ! [SY5: $i] :
                  ~ ! [SY6: mworld] :
                      ( ~ ( mrel @ SV3 @ SY6 )
                      | ! [SX6: $i] :
                          ( ~ ( do @ SY2 @ SY5 @ SX6 @ SY6 )
                          | ( in @ SY3 @ SY4 @ SX6 @ SY6 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[16]) ).

thf(23,plain,
    ( ( ! [SX0: $i] :
          ~ ! [SX1: mworld] :
              ( ~ ( mrel @ mactual @ SX1 )
              | ~ ( ~ ( entry_box @ SX0 @ SX1 )
                  | ~ ( number @ SX0 @ one @ SX1 ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[17]) ).

thf(24,plain,
    ! [SV4: mworld] :
      ( ( ~ ( mrel @ mactual @ SV4 )
        | ~ ! [SY8: $i] :
              ~ ! [SY9: mworld] :
                  ( ~ ( mrel @ SV4 @ SY9 )
                  | ~ ( ~ ( userid @ u @ SY8 @ SY9 )
                      | ~ ( string @ SY8 @ SY9 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[18]) ).

thf(25,plain,
    ( ( ! [SX0: mworld] :
          ( ~ ( mrel @ mactual @ SX0 )
          | ~ ! [SX1: $i] :
                ~ ~ ! [SX2: $i] :
                      ~ ~ ! [SX3: $i] :
                            ~ ~ ! [SX4: $i] :
                                  ~ ~ ( ~ ! [SX5: mworld] :
                                            ( ~ ( mrel @ SX0 @ SX5 )
                                            | ~ ( ~ ( userid @ u @ SX1 @ SX5 )
                                                | ~ ~ ( ~ ( entry_box @ SX2 @ SX5 )
                                                      | ~ ( number @ SX2 @ one @ SX5 ) ) ) )
                                      | ~ ! [SX5: mworld] :
                                            ( ~ ( mrel @ SX0 @ SX5 )
                                            | ! [SX6: $i] :
                                                ( ~ ( do @ SX4 @ SX3 @ SX6 @ SX5 )
                                                | ( in @ SX1 @ SX2 @ SX6 @ SX5 ) ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[19]) ).

thf(26,plain,
    ! [SV5: mworld,SV2: mworld] :
      ( ( ! [SY10: mworld] :
            ( ~ ( mrel @ SV2 @ SV5 )
            | ~ ( mrel @ SV5 @ SY10 )
            | ( mrel @ SV2 @ SY10 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[21]) ).

thf(27,plain,
    ! [SV3: mworld] :
      ( ( ( ~ ( mrel @ mactual @ SV3 ) )
        = $true )
      | ( ( ! [SY2: $i,SY3: $i,SY4: $i] :
              ( ~ ~ ( ~ ( string @ SY3 @ SV3 )
                    | ~ ( entry_box @ SY4 @ SV3 ) )
              | ~ ! [SY5: $i] :
                    ~ ! [SY6: mworld] :
                        ( ~ ( mrel @ SV3 @ SY6 )
                        | ! [SX6: $i] :
                            ( ~ ( do @ SY2 @ SY5 @ SX6 @ SY6 )
                            | ( in @ SY3 @ SY4 @ SX6 @ SY6 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[22]) ).

thf(28,plain,
    ( ( ~ ! [SY11: mworld] :
            ( ~ ( mrel @ mactual @ SY11 )
            | ~ ( ~ ( entry_box @ sK1_SX0 @ SY11 )
                | ~ ( number @ sK1_SX0 @ one @ SY11 ) ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[23]) ).

thf(29,plain,
    ! [SV4: mworld] :
      ( ( ( ~ ( mrel @ mactual @ SV4 ) )
        = $true )
      | ( ( ~ ! [SY8: $i] :
                ~ ! [SY9: mworld] :
                    ( ~ ( mrel @ SV4 @ SY9 )
                    | ~ ( ~ ( userid @ u @ SY8 @ SY9 )
                        | ~ ( string @ SY8 @ SY9 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[24]) ).

thf(30,plain,
    ( ( ~ ( mrel @ mactual @ sK2_SX0 )
      | ~ ! [SY12: $i] :
            ~ ~ ! [SY13: $i] :
                  ~ ~ ! [SY14: $i] :
                        ~ ~ ! [SY15: $i] :
                              ~ ~ ( ~ ! [SY16: mworld] :
                                        ( ~ ( mrel @ sK2_SX0 @ SY16 )
                                        | ~ ( ~ ( userid @ u @ SY12 @ SY16 )
                                            | ~ ~ ( ~ ( entry_box @ SY13 @ SY16 )
                                                  | ~ ( number @ SY13 @ one @ SY16 ) ) ) )
                                  | ~ ! [SY17: mworld] :
                                        ( ~ ( mrel @ sK2_SX0 @ SY17 )
                                        | ! [SX6: $i] :
                                            ( ~ ( do @ SY15 @ SY14 @ SX6 @ SY17 )
                                            | ( in @ SY12 @ SY13 @ SX6 @ SY17 ) ) ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[25]) ).

thf(31,plain,
    ! [SV6: mworld,SV5: mworld,SV2: mworld] :
      ( ( ~ ( mrel @ SV2 @ SV5 )
        | ~ ( mrel @ SV5 @ SV6 )
        | ( mrel @ SV2 @ SV6 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[26]) ).

thf(32,plain,
    ! [SV3: mworld] :
      ( ( ( mrel @ mactual @ SV3 )
        = $false )
      | ( ( ! [SY2: $i,SY3: $i,SY4: $i] :
              ( ~ ~ ( ~ ( string @ SY3 @ SV3 )
                    | ~ ( entry_box @ SY4 @ SV3 ) )
              | ~ ! [SY5: $i] :
                    ~ ! [SY6: mworld] :
                        ( ~ ( mrel @ SV3 @ SY6 )
                        | ! [SX6: $i] :
                            ( ~ ( do @ SY2 @ SY5 @ SX6 @ SY6 )
                            | ( in @ SY3 @ SY4 @ SX6 @ SY6 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[27]) ).

thf(33,plain,
    ( ( ! [SY11: mworld] :
          ( ~ ( mrel @ mactual @ SY11 )
          | ~ ( ~ ( entry_box @ sK1_SX0 @ SY11 )
              | ~ ( number @ sK1_SX0 @ one @ SY11 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[28]) ).

thf(34,plain,
    ! [SV4: mworld] :
      ( ( ( mrel @ mactual @ SV4 )
        = $false )
      | ( ( ~ ! [SY8: $i] :
                ~ ! [SY9: mworld] :
                    ( ~ ( mrel @ SV4 @ SY9 )
                    | ~ ( ~ ( userid @ u @ SY8 @ SY9 )
                        | ~ ( string @ SY8 @ SY9 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[29]) ).

thf(35,plain,
    ( ( ~ ( mrel @ mactual @ sK2_SX0 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[30]) ).

thf(36,plain,
    ( ( ~ ! [SY12: $i] :
            ~ ~ ! [SY13: $i] :
                  ~ ~ ! [SY14: $i] :
                        ~ ~ ! [SY15: $i] :
                              ~ ~ ( ~ ! [SY16: mworld] :
                                        ( ~ ( mrel @ sK2_SX0 @ SY16 )
                                        | ~ ( ~ ( userid @ u @ SY12 @ SY16 )
                                            | ~ ~ ( ~ ( entry_box @ SY13 @ SY16 )
                                                  | ~ ( number @ SY13 @ one @ SY16 ) ) ) )
                                  | ~ ! [SY17: mworld] :
                                        ( ~ ( mrel @ sK2_SX0 @ SY17 )
                                        | ! [SX6: $i] :
                                            ( ~ ( do @ SY15 @ SY14 @ SX6 @ SY17 )
                                            | ( in @ SY12 @ SY13 @ SX6 @ SY17 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[30]) ).

thf(37,plain,
    ! [SV6: mworld,SV5: mworld,SV2: mworld] :
      ( ( ( ~ ( mrel @ SV2 @ SV5 )
          | ~ ( mrel @ SV5 @ SV6 ) )
        = $true )
      | ( ( mrel @ SV2 @ SV6 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[31]) ).

thf(38,plain,
    ! [SV7: $i,SV3: mworld] :
      ( ( ( ! [SY19: $i,SY20: $i] :
              ( ~ ~ ( ~ ( string @ SY19 @ SV3 )
                    | ~ ( entry_box @ SY20 @ SV3 ) )
              | ~ ! [SY21: $i] :
                    ~ ! [SY22: mworld] :
                        ( ~ ( mrel @ SV3 @ SY22 )
                        | ! [SY23: $i] :
                            ( ~ ( do @ SV7 @ SY21 @ SY23 @ SY22 )
                            | ( in @ SY19 @ SY20 @ SY23 @ SY22 ) ) ) ) )
        = $true )
      | ( ( mrel @ mactual @ SV3 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[32]) ).

thf(39,plain,
    ! [SV8: mworld] :
      ( ( ~ ( mrel @ mactual @ SV8 )
        | ~ ( ~ ( entry_box @ sK1_SX0 @ SV8 )
            | ~ ( number @ sK1_SX0 @ one @ SV8 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[33]) ).

thf(40,plain,
    ! [SV4: mworld] :
      ( ( ( ! [SY8: $i] :
              ~ ! [SY9: mworld] :
                  ( ~ ( mrel @ SV4 @ SY9 )
                  | ~ ( ~ ( userid @ u @ SY8 @ SY9 )
                      | ~ ( string @ SY8 @ SY9 ) ) ) )
        = $false )
      | ( ( mrel @ mactual @ SV4 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[34]) ).

thf(41,plain,
    ( ( mrel @ mactual @ sK2_SX0 )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[35]) ).

thf(42,plain,
    ( ( ! [SY12: $i] :
          ~ ~ ! [SY13: $i] :
                ~ ~ ! [SY14: $i] :
                      ~ ~ ! [SY15: $i] :
                            ~ ~ ( ~ ! [SY16: mworld] :
                                      ( ~ ( mrel @ sK2_SX0 @ SY16 )
                                      | ~ ( ~ ( userid @ u @ SY12 @ SY16 )
                                          | ~ ~ ( ~ ( entry_box @ SY13 @ SY16 )
                                                | ~ ( number @ SY13 @ one @ SY16 ) ) ) )
                                | ~ ! [SY17: mworld] :
                                      ( ~ ( mrel @ sK2_SX0 @ SY17 )
                                      | ! [SX6: $i] :
                                          ( ~ ( do @ SY15 @ SY14 @ SX6 @ SY17 )
                                          | ( in @ SY12 @ SY13 @ SX6 @ SY17 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[36]) ).

thf(43,plain,
    ! [SV6: mworld,SV5: mworld,SV2: mworld] :
      ( ( ( ~ ( mrel @ SV2 @ SV5 ) )
        = $true )
      | ( ( ~ ( mrel @ SV5 @ SV6 ) )
        = $true )
      | ( ( mrel @ SV2 @ SV6 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[37]) ).

thf(44,plain,
    ! [SV7: $i,SV3: mworld,SV9: $i] :
      ( ( ( ! [SY24: $i] :
              ( ~ ~ ( ~ ( string @ SV9 @ SV3 )
                    | ~ ( entry_box @ SY24 @ SV3 ) )
              | ~ ! [SY25: $i] :
                    ~ ! [SY26: mworld] :
                        ( ~ ( mrel @ SV3 @ SY26 )
                        | ! [SY27: $i] :
                            ( ~ ( do @ SV7 @ SY25 @ SY27 @ SY26 )
                            | ( in @ SV9 @ SY24 @ SY27 @ SY26 ) ) ) ) )
        = $true )
      | ( ( mrel @ mactual @ SV3 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[38]) ).

thf(45,plain,
    ! [SV8: mworld] :
      ( ( ( ~ ( mrel @ mactual @ SV8 ) )
        = $true )
      | ( ( ~ ( ~ ( entry_box @ sK1_SX0 @ SV8 )
              | ~ ( number @ sK1_SX0 @ one @ SV8 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[39]) ).

thf(46,plain,
    ! [SV4: mworld] :
      ( ( ( ~ ! [SY28: mworld] :
                ( ~ ( mrel @ SV4 @ SY28 )
                | ~ ( ~ ( userid @ u @ ( sK3_SY8 @ SV4 ) @ SY28 )
                    | ~ ( string @ ( sK3_SY8 @ SV4 ) @ SY28 ) ) ) )
        = $false )
      | ( ( mrel @ mactual @ SV4 )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[40]) ).

thf(47,plain,
    ! [SV10: $i] :
      ( ( ~ ~ ! [SY29: $i] :
                ~ ~ ! [SY30: $i] :
                      ~ ~ ! [SY31: $i] :
                            ~ ~ ( ~ ! [SY32: mworld] :
                                      ( ~ ( mrel @ sK2_SX0 @ SY32 )
                                      | ~ ( ~ ( userid @ u @ SV10 @ SY32 )
                                          | ~ ~ ( ~ ( entry_box @ SY29 @ SY32 )
                                                | ~ ( number @ SY29 @ one @ SY32 ) ) ) )
                                | ~ ! [SY33: mworld] :
                                      ( ~ ( mrel @ sK2_SX0 @ SY33 )
                                      | ! [SY34: $i] :
                                          ( ~ ( do @ SY31 @ SY30 @ SY34 @ SY33 )
                                          | ( in @ SV10 @ SY29 @ SY34 @ SY33 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[42]) ).

thf(48,plain,
    ! [SV6: mworld,SV5: mworld,SV2: mworld] :
      ( ( ( mrel @ SV2 @ SV5 )
        = $false )
      | ( ( ~ ( mrel @ SV5 @ SV6 ) )
        = $true )
      | ( ( mrel @ SV2 @ SV6 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[43]) ).

thf(49,plain,
    ! [SV7: $i,SV11: $i,SV3: mworld,SV9: $i] :
      ( ( ( ~ ~ ( ~ ( string @ SV9 @ SV3 )
                | ~ ( entry_box @ SV11 @ SV3 ) )
          | ~ ! [SY35: $i] :
                ~ ! [SY36: mworld] :
                    ( ~ ( mrel @ SV3 @ SY36 )
                    | ! [SY37: $i] :
                        ( ~ ( do @ SV7 @ SY35 @ SY37 @ SY36 )
                        | ( in @ SV9 @ SV11 @ SY37 @ SY36 ) ) ) )
        = $true )
      | ( ( mrel @ mactual @ SV3 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[44]) ).

thf(50,plain,
    ! [SV8: mworld] :
      ( ( ( mrel @ mactual @ SV8 )
        = $false )
      | ( ( ~ ( ~ ( entry_box @ sK1_SX0 @ SV8 )
              | ~ ( number @ sK1_SX0 @ one @ SV8 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[45]) ).

thf(51,plain,
    ! [SV4: mworld] :
      ( ( ( ! [SY28: mworld] :
              ( ~ ( mrel @ SV4 @ SY28 )
              | ~ ( ~ ( userid @ u @ ( sK3_SY8 @ SV4 ) @ SY28 )
                  | ~ ( string @ ( sK3_SY8 @ SV4 ) @ SY28 ) ) ) )
        = $true )
      | ( ( mrel @ mactual @ SV4 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[46]) ).

thf(52,plain,
    ! [SV10: $i] :
      ( ( ~ ! [SY29: $i] :
              ~ ~ ! [SY30: $i] :
                    ~ ~ ! [SY31: $i] :
                          ~ ~ ( ~ ! [SY32: mworld] :
                                    ( ~ ( mrel @ sK2_SX0 @ SY32 )
                                    | ~ ( ~ ( userid @ u @ SV10 @ SY32 )
                                        | ~ ~ ( ~ ( entry_box @ SY29 @ SY32 )
                                              | ~ ( number @ SY29 @ one @ SY32 ) ) ) )
                              | ~ ! [SY33: mworld] :
                                    ( ~ ( mrel @ sK2_SX0 @ SY33 )
                                    | ! [SY34: $i] :
                                        ( ~ ( do @ SY31 @ SY30 @ SY34 @ SY33 )
                                        | ( in @ SV10 @ SY29 @ SY34 @ SY33 ) ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[47]) ).

thf(53,plain,
    ! [SV2: mworld,SV6: mworld,SV5: mworld] :
      ( ( ( mrel @ SV5 @ SV6 )
        = $false )
      | ( ( mrel @ SV2 @ SV5 )
        = $false )
      | ( ( mrel @ SV2 @ SV6 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[48]) ).

thf(54,plain,
    ! [SV7: $i,SV11: $i,SV3: mworld,SV9: $i] :
      ( ( ( ~ ~ ( ~ ( string @ SV9 @ SV3 )
                | ~ ( entry_box @ SV11 @ SV3 ) ) )
        = $true )
      | ( ( ~ ! [SY35: $i] :
                ~ ! [SY36: mworld] :
                    ( ~ ( mrel @ SV3 @ SY36 )
                    | ! [SY37: $i] :
                        ( ~ ( do @ SV7 @ SY35 @ SY37 @ SY36 )
                        | ( in @ SV9 @ SV11 @ SY37 @ SY36 ) ) ) )
        = $true )
      | ( ( mrel @ mactual @ SV3 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[49]) ).

thf(55,plain,
    ! [SV8: mworld] :
      ( ( ( ~ ( entry_box @ sK1_SX0 @ SV8 )
          | ~ ( number @ sK1_SX0 @ one @ SV8 ) )
        = $false )
      | ( ( mrel @ mactual @ SV8 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[50]) ).

thf(56,plain,
    ! [SV12: mworld,SV4: mworld] :
      ( ( ( ~ ( mrel @ SV4 @ SV12 )
          | ~ ( ~ ( userid @ u @ ( sK3_SY8 @ SV4 ) @ SV12 )
              | ~ ( string @ ( sK3_SY8 @ SV4 ) @ SV12 ) ) )
        = $true )
      | ( ( mrel @ mactual @ SV4 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[51]) ).

thf(57,plain,
    ! [SV10: $i] :
      ( ( ! [SY29: $i] :
            ~ ~ ! [SY30: $i] :
                  ~ ~ ! [SY31: $i] :
                        ~ ~ ( ~ ! [SY32: mworld] :
                                  ( ~ ( mrel @ sK2_SX0 @ SY32 )
                                  | ~ ( ~ ( userid @ u @ SV10 @ SY32 )
                                      | ~ ~ ( ~ ( entry_box @ SY29 @ SY32 )
                                            | ~ ( number @ SY29 @ one @ SY32 ) ) ) )
                            | ~ ! [SY33: mworld] :
                                  ( ~ ( mrel @ sK2_SX0 @ SY33 )
                                  | ! [SY34: $i] :
                                      ( ~ ( do @ SY31 @ SY30 @ SY34 @ SY33 )
                                      | ( in @ SV10 @ SY29 @ SY34 @ SY33 ) ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[52]) ).

thf(58,plain,
    ! [SV7: $i,SV11: $i,SV3: mworld,SV9: $i] :
      ( ( ( ~ ( ~ ( string @ SV9 @ SV3 )
              | ~ ( entry_box @ SV11 @ SV3 ) ) )
        = $false )
      | ( ( ~ ! [SY35: $i] :
                ~ ! [SY36: mworld] :
                    ( ~ ( mrel @ SV3 @ SY36 )
                    | ! [SY37: $i] :
                        ( ~ ( do @ SV7 @ SY35 @ SY37 @ SY36 )
                        | ( in @ SV9 @ SV11 @ SY37 @ SY36 ) ) ) )
        = $true )
      | ( ( mrel @ mactual @ SV3 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[54]) ).

thf(59,plain,
    ! [SV8: mworld] :
      ( ( ( ~ ( entry_box @ sK1_SX0 @ SV8 ) )
        = $false )
      | ( ( mrel @ mactual @ SV8 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[55]) ).

thf(60,plain,
    ! [SV8: mworld] :
      ( ( ( ~ ( number @ sK1_SX0 @ one @ SV8 ) )
        = $false )
      | ( ( mrel @ mactual @ SV8 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[55]) ).

thf(61,plain,
    ! [SV12: mworld,SV4: mworld] :
      ( ( ( ~ ( mrel @ SV4 @ SV12 ) )
        = $true )
      | ( ( ~ ( ~ ( userid @ u @ ( sK3_SY8 @ SV4 ) @ SV12 )
              | ~ ( string @ ( sK3_SY8 @ SV4 ) @ SV12 ) ) )
        = $true )
      | ( ( mrel @ mactual @ SV4 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[56]) ).

thf(62,plain,
    ! [SV13: $i,SV10: $i] :
      ( ( ~ ~ ! [SY38: $i] :
                ~ ~ ! [SY39: $i] :
                      ~ ~ ( ~ ! [SY40: mworld] :
                                ( ~ ( mrel @ sK2_SX0 @ SY40 )
                                | ~ ( ~ ( userid @ u @ SV10 @ SY40 )
                                    | ~ ~ ( ~ ( entry_box @ SV13 @ SY40 )
                                          | ~ ( number @ SV13 @ one @ SY40 ) ) ) )
                          | ~ ! [SY41: mworld] :
                                ( ~ ( mrel @ sK2_SX0 @ SY41 )
                                | ! [SY42: $i] :
                                    ( ~ ( do @ SY39 @ SY38 @ SY42 @ SY41 )
                                    | ( in @ SV10 @ SV13 @ SY42 @ SY41 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[57]) ).

thf(63,plain,
    ! [SV7: $i,SV11: $i,SV3: mworld,SV9: $i] :
      ( ( ( ~ ( string @ SV9 @ SV3 )
          | ~ ( entry_box @ SV11 @ SV3 ) )
        = $true )
      | ( ( ~ ! [SY35: $i] :
                ~ ! [SY36: mworld] :
                    ( ~ ( mrel @ SV3 @ SY36 )
                    | ! [SY37: $i] :
                        ( ~ ( do @ SV7 @ SY35 @ SY37 @ SY36 )
                        | ( in @ SV9 @ SV11 @ SY37 @ SY36 ) ) ) )
        = $true )
      | ( ( mrel @ mactual @ SV3 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[58]) ).

thf(64,plain,
    ! [SV8: mworld] :
      ( ( ( entry_box @ sK1_SX0 @ SV8 )
        = $true )
      | ( ( mrel @ mactual @ SV8 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[59]) ).

thf(65,plain,
    ! [SV8: mworld] :
      ( ( ( number @ sK1_SX0 @ one @ SV8 )
        = $true )
      | ( ( mrel @ mactual @ SV8 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[60]) ).

thf(66,plain,
    ! [SV12: mworld,SV4: mworld] :
      ( ( ( mrel @ SV4 @ SV12 )
        = $false )
      | ( ( ~ ( ~ ( userid @ u @ ( sK3_SY8 @ SV4 ) @ SV12 )
              | ~ ( string @ ( sK3_SY8 @ SV4 ) @ SV12 ) ) )
        = $true )
      | ( ( mrel @ mactual @ SV4 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[61]) ).

thf(67,plain,
    ! [SV13: $i,SV10: $i] :
      ( ( ~ ! [SY38: $i] :
              ~ ~ ! [SY39: $i] :
                    ~ ~ ( ~ ! [SY40: mworld] :
                              ( ~ ( mrel @ sK2_SX0 @ SY40 )
                              | ~ ( ~ ( userid @ u @ SV10 @ SY40 )
                                  | ~ ~ ( ~ ( entry_box @ SV13 @ SY40 )
                                        | ~ ( number @ SV13 @ one @ SY40 ) ) ) )
                        | ~ ! [SY41: mworld] :
                              ( ~ ( mrel @ sK2_SX0 @ SY41 )
                              | ! [SY42: $i] :
                                  ( ~ ( do @ SY39 @ SY38 @ SY42 @ SY41 )
                                  | ( in @ SV10 @ SV13 @ SY42 @ SY41 ) ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[62]) ).

thf(68,plain,
    ! [SV7: $i,SV11: $i,SV3: mworld,SV9: $i] :
      ( ( ( ~ ( string @ SV9 @ SV3 ) )
        = $true )
      | ( ( ~ ( entry_box @ SV11 @ SV3 ) )
        = $true )
      | ( ( ~ ! [SY35: $i] :
                ~ ! [SY36: mworld] :
                    ( ~ ( mrel @ SV3 @ SY36 )
                    | ! [SY37: $i] :
                        ( ~ ( do @ SV7 @ SY35 @ SY37 @ SY36 )
                        | ( in @ SV9 @ SV11 @ SY37 @ SY36 ) ) ) )
        = $true )
      | ( ( mrel @ mactual @ SV3 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[63]) ).

thf(69,plain,
    ! [SV12: mworld,SV4: mworld] :
      ( ( ( ~ ( userid @ u @ ( sK3_SY8 @ SV4 ) @ SV12 )
          | ~ ( string @ ( sK3_SY8 @ SV4 ) @ SV12 ) )
        = $false )
      | ( ( mrel @ SV4 @ SV12 )
        = $false )
      | ( ( mrel @ mactual @ SV4 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[66]) ).

thf(70,plain,
    ! [SV13: $i,SV10: $i] :
      ( ( ! [SY38: $i] :
            ~ ~ ! [SY39: $i] :
                  ~ ~ ( ~ ! [SY40: mworld] :
                            ( ~ ( mrel @ sK2_SX0 @ SY40 )
                            | ~ ( ~ ( userid @ u @ SV10 @ SY40 )
                                | ~ ~ ( ~ ( entry_box @ SV13 @ SY40 )
                                      | ~ ( number @ SV13 @ one @ SY40 ) ) ) )
                      | ~ ! [SY41: mworld] :
                            ( ~ ( mrel @ sK2_SX0 @ SY41 )
                            | ! [SY42: $i] :
                                ( ~ ( do @ SY39 @ SY38 @ SY42 @ SY41 )
                                | ( in @ SV10 @ SV13 @ SY42 @ SY41 ) ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[67]) ).

thf(71,plain,
    ! [SV7: $i,SV11: $i,SV3: mworld,SV9: $i] :
      ( ( ( string @ SV9 @ SV3 )
        = $false )
      | ( ( ~ ( entry_box @ SV11 @ SV3 ) )
        = $true )
      | ( ( ~ ! [SY35: $i] :
                ~ ! [SY36: mworld] :
                    ( ~ ( mrel @ SV3 @ SY36 )
                    | ! [SY37: $i] :
                        ( ~ ( do @ SV7 @ SY35 @ SY37 @ SY36 )
                        | ( in @ SV9 @ SV11 @ SY37 @ SY36 ) ) ) )
        = $true )
      | ( ( mrel @ mactual @ SV3 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[68]) ).

thf(72,plain,
    ! [SV12: mworld,SV4: mworld] :
      ( ( ( ~ ( userid @ u @ ( sK3_SY8 @ SV4 ) @ SV12 ) )
        = $false )
      | ( ( mrel @ SV4 @ SV12 )
        = $false )
      | ( ( mrel @ mactual @ SV4 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[69]) ).

thf(73,plain,
    ! [SV12: mworld,SV4: mworld] :
      ( ( ( ~ ( string @ ( sK3_SY8 @ SV4 ) @ SV12 ) )
        = $false )
      | ( ( mrel @ SV4 @ SV12 )
        = $false )
      | ( ( mrel @ mactual @ SV4 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[69]) ).

thf(74,plain,
    ! [SV14: $i,SV13: $i,SV10: $i] :
      ( ( ~ ~ ! [SY43: $i] :
                ~ ~ ( ~ ! [SY40: mworld] :
                          ( ~ ( mrel @ sK2_SX0 @ SY40 )
                          | ~ ( ~ ( userid @ u @ SV10 @ SY40 )
                              | ~ ~ ( ~ ( entry_box @ SV13 @ SY40 )
                                    | ~ ( number @ SV13 @ one @ SY40 ) ) ) )
                    | ~ ! [SY45: mworld] :
                          ( ~ ( mrel @ sK2_SX0 @ SY45 )
                          | ! [SY46: $i] :
                              ( ~ ( do @ SY43 @ SV14 @ SY46 @ SY45 )
                              | ( in @ SV10 @ SV13 @ SY46 @ SY45 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[70]) ).

thf(75,plain,
    ! [SV7: $i,SV9: $i,SV3: mworld,SV11: $i] :
      ( ( ( entry_box @ SV11 @ SV3 )
        = $false )
      | ( ( string @ SV9 @ SV3 )
        = $false )
      | ( ( ~ ! [SY35: $i] :
                ~ ! [SY36: mworld] :
                    ( ~ ( mrel @ SV3 @ SY36 )
                    | ! [SY37: $i] :
                        ( ~ ( do @ SV7 @ SY35 @ SY37 @ SY36 )
                        | ( in @ SV9 @ SV11 @ SY37 @ SY36 ) ) ) )
        = $true )
      | ( ( mrel @ mactual @ SV3 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[71]) ).

thf(76,plain,
    ! [SV12: mworld,SV4: mworld] :
      ( ( ( userid @ u @ ( sK3_SY8 @ SV4 ) @ SV12 )
        = $true )
      | ( ( mrel @ SV4 @ SV12 )
        = $false )
      | ( ( mrel @ mactual @ SV4 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[72]) ).

thf(77,plain,
    ! [SV12: mworld,SV4: mworld] :
      ( ( ( string @ ( sK3_SY8 @ SV4 ) @ SV12 )
        = $true )
      | ( ( mrel @ SV4 @ SV12 )
        = $false )
      | ( ( mrel @ mactual @ SV4 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[73]) ).

thf(78,plain,
    ! [SV14: $i,SV13: $i,SV10: $i] :
      ( ( ~ ! [SY43: $i] :
              ~ ~ ( ~ ! [SY40: mworld] :
                        ( ~ ( mrel @ sK2_SX0 @ SY40 )
                        | ~ ( ~ ( userid @ u @ SV10 @ SY40 )
                            | ~ ~ ( ~ ( entry_box @ SV13 @ SY40 )
                                  | ~ ( number @ SV13 @ one @ SY40 ) ) ) )
                  | ~ ! [SY45: mworld] :
                        ( ~ ( mrel @ sK2_SX0 @ SY45 )
                        | ! [SY46: $i] :
                            ( ~ ( do @ SY43 @ SV14 @ SY46 @ SY45 )
                            | ( in @ SV10 @ SV13 @ SY46 @ SY45 ) ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[74]) ).

thf(79,plain,
    ! [SV11: $i,SV9: $i,SV7: $i,SV3: mworld] :
      ( ( ( ! [SY35: $i] :
              ~ ! [SY36: mworld] :
                  ( ~ ( mrel @ SV3 @ SY36 )
                  | ! [SY37: $i] :
                      ( ~ ( do @ SV7 @ SY35 @ SY37 @ SY36 )
                      | ( in @ SV9 @ SV11 @ SY37 @ SY36 ) ) ) )
        = $false )
      | ( ( string @ SV9 @ SV3 )
        = $false )
      | ( ( entry_box @ SV11 @ SV3 )
        = $false )
      | ( ( mrel @ mactual @ SV3 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[75]) ).

thf(80,plain,
    ! [SV14: $i,SV13: $i,SV10: $i] :
      ( ( ! [SY43: $i] :
            ~ ~ ( ~ ! [SY40: mworld] :
                      ( ~ ( mrel @ sK2_SX0 @ SY40 )
                      | ~ ( ~ ( userid @ u @ SV10 @ SY40 )
                          | ~ ~ ( ~ ( entry_box @ SV13 @ SY40 )
                                | ~ ( number @ SV13 @ one @ SY40 ) ) ) )
                | ~ ! [SY45: mworld] :
                      ( ~ ( mrel @ sK2_SX0 @ SY45 )
                      | ! [SY46: $i] :
                          ( ~ ( do @ SY43 @ SV14 @ SY46 @ SY45 )
                          | ( in @ SV10 @ SV13 @ SY46 @ SY45 ) ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[78]) ).

thf(81,plain,
    ! [SV9: $i,SV11: $i,SV7: $i,SV3: mworld] :
      ( ( ( ~ ! [SY47: mworld] :
                ( ~ ( mrel @ SV3 @ SY47 )
                | ! [SY48: $i] :
                    ( ~ ( do @ SV7 @ ( sK4_SY35 @ SV11 @ SV9 @ SV7 @ SV3 ) @ SY48 @ SY47 )
                    | ( in @ SV9 @ SV11 @ SY48 @ SY47 ) ) ) )
        = $false )
      | ( ( string @ SV9 @ SV3 )
        = $false )
      | ( ( entry_box @ SV11 @ SV3 )
        = $false )
      | ( ( mrel @ mactual @ SV3 )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[79]) ).

thf(82,plain,
    ! [SV14: $i,SV15: $i,SV13: $i,SV10: $i] :
      ( ( ~ ~ ( ~ ! [SY40: mworld] :
                    ( ~ ( mrel @ sK2_SX0 @ SY40 )
                    | ~ ( ~ ( userid @ u @ SV10 @ SY40 )
                        | ~ ~ ( ~ ( entry_box @ SV13 @ SY40 )
                              | ~ ( number @ SV13 @ one @ SY40 ) ) ) )
              | ~ ! [SY50: mworld] :
                    ( ~ ( mrel @ sK2_SX0 @ SY50 )
                    | ! [SY51: $i] :
                        ( ~ ( do @ SV15 @ SV14 @ SY51 @ SY50 )
                        | ( in @ SV10 @ SV13 @ SY51 @ SY50 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[80]) ).

thf(83,plain,
    ! [SV9: $i,SV11: $i,SV7: $i,SV3: mworld] :
      ( ( ( ! [SY47: mworld] :
              ( ~ ( mrel @ SV3 @ SY47 )
              | ! [SY48: $i] :
                  ( ~ ( do @ SV7 @ ( sK4_SY35 @ SV11 @ SV9 @ SV7 @ SV3 ) @ SY48 @ SY47 )
                  | ( in @ SV9 @ SV11 @ SY48 @ SY47 ) ) ) )
        = $true )
      | ( ( string @ SV9 @ SV3 )
        = $false )
      | ( ( entry_box @ SV11 @ SV3 )
        = $false )
      | ( ( mrel @ mactual @ SV3 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[81]) ).

thf(84,plain,
    ! [SV14: $i,SV15: $i,SV13: $i,SV10: $i] :
      ( ( ~ ( ~ ! [SY40: mworld] :
                  ( ~ ( mrel @ sK2_SX0 @ SY40 )
                  | ~ ( ~ ( userid @ u @ SV10 @ SY40 )
                      | ~ ~ ( ~ ( entry_box @ SV13 @ SY40 )
                            | ~ ( number @ SV13 @ one @ SY40 ) ) ) )
            | ~ ! [SY50: mworld] :
                  ( ~ ( mrel @ sK2_SX0 @ SY50 )
                  | ! [SY51: $i] :
                      ( ~ ( do @ SV15 @ SV14 @ SY51 @ SY50 )
                      | ( in @ SV10 @ SV13 @ SY51 @ SY50 ) ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[82]) ).

thf(85,plain,
    ! [SV9: $i,SV11: $i,SV7: $i,SV16: mworld,SV3: mworld] :
      ( ( ( ~ ( mrel @ SV3 @ SV16 )
          | ! [SY52: $i] :
              ( ~ ( do @ SV7 @ ( sK4_SY35 @ SV11 @ SV9 @ SV7 @ SV3 ) @ SY52 @ SV16 )
              | ( in @ SV9 @ SV11 @ SY52 @ SV16 ) ) )
        = $true )
      | ( ( string @ SV9 @ SV3 )
        = $false )
      | ( ( entry_box @ SV11 @ SV3 )
        = $false )
      | ( ( mrel @ mactual @ SV3 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[83]) ).

thf(86,plain,
    ! [SV14: $i,SV15: $i,SV13: $i,SV10: $i] :
      ( ( ~ ! [SY40: mworld] :
              ( ~ ( mrel @ sK2_SX0 @ SY40 )
              | ~ ( ~ ( userid @ u @ SV10 @ SY40 )
                  | ~ ~ ( ~ ( entry_box @ SV13 @ SY40 )
                        | ~ ( number @ SV13 @ one @ SY40 ) ) ) )
        | ~ ! [SY50: mworld] :
              ( ~ ( mrel @ sK2_SX0 @ SY50 )
              | ! [SY51: $i] :
                  ( ~ ( do @ SV15 @ SV14 @ SY51 @ SY50 )
                  | ( in @ SV10 @ SV13 @ SY51 @ SY50 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[84]) ).

thf(87,plain,
    ! [SV9: $i,SV11: $i,SV7: $i,SV16: mworld,SV3: mworld] :
      ( ( ( ~ ( mrel @ SV3 @ SV16 ) )
        = $true )
      | ( ( ! [SY52: $i] :
              ( ~ ( do @ SV7 @ ( sK4_SY35 @ SV11 @ SV9 @ SV7 @ SV3 ) @ SY52 @ SV16 )
              | ( in @ SV9 @ SV11 @ SY52 @ SV16 ) ) )
        = $true )
      | ( ( string @ SV9 @ SV3 )
        = $false )
      | ( ( entry_box @ SV11 @ SV3 )
        = $false )
      | ( ( mrel @ mactual @ SV3 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[85]) ).

thf(88,plain,
    ! [SV14: $i,SV15: $i,SV13: $i,SV10: $i] :
      ( ( ( ~ ! [SY40: mworld] :
                ( ~ ( mrel @ sK2_SX0 @ SY40 )
                | ~ ( ~ ( userid @ u @ SV10 @ SY40 )
                    | ~ ~ ( ~ ( entry_box @ SV13 @ SY40 )
                          | ~ ( number @ SV13 @ one @ SY40 ) ) ) ) )
        = $true )
      | ( ( ~ ! [SY50: mworld] :
                ( ~ ( mrel @ sK2_SX0 @ SY50 )
                | ! [SY51: $i] :
                    ( ~ ( do @ SV15 @ SV14 @ SY51 @ SY50 )
                    | ( in @ SV10 @ SV13 @ SY51 @ SY50 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[86]) ).

thf(89,plain,
    ! [SV9: $i,SV11: $i,SV7: $i,SV16: mworld,SV3: mworld] :
      ( ( ( mrel @ SV3 @ SV16 )
        = $false )
      | ( ( ! [SY52: $i] :
              ( ~ ( do @ SV7 @ ( sK4_SY35 @ SV11 @ SV9 @ SV7 @ SV3 ) @ SY52 @ SV16 )
              | ( in @ SV9 @ SV11 @ SY52 @ SV16 ) ) )
        = $true )
      | ( ( string @ SV9 @ SV3 )
        = $false )
      | ( ( entry_box @ SV11 @ SV3 )
        = $false )
      | ( ( mrel @ mactual @ SV3 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[87]) ).

thf(90,plain,
    ! [SV14: $i,SV15: $i,SV13: $i,SV10: $i] :
      ( ( ( ! [SY40: mworld] :
              ( ~ ( mrel @ sK2_SX0 @ SY40 )
              | ~ ( ~ ( userid @ u @ SV10 @ SY40 )
                  | ~ ~ ( ~ ( entry_box @ SV13 @ SY40 )
                        | ~ ( number @ SV13 @ one @ SY40 ) ) ) ) )
        = $false )
      | ( ( ~ ! [SY50: mworld] :
                ( ~ ( mrel @ sK2_SX0 @ SY50 )
                | ! [SY51: $i] :
                    ( ~ ( do @ SV15 @ SV14 @ SY51 @ SY50 )
                    | ( in @ SV10 @ SV13 @ SY51 @ SY50 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[88]) ).

thf(91,plain,
    ! [SV16: mworld,SV17: $i,SV3: mworld,SV9: $i,SV11: $i,SV7: $i] :
      ( ( ( ~ ( do @ SV7 @ ( sK4_SY35 @ SV11 @ SV9 @ SV7 @ SV3 ) @ SV17 @ SV16 )
          | ( in @ SV9 @ SV11 @ SV17 @ SV16 ) )
        = $true )
      | ( ( mrel @ SV3 @ SV16 )
        = $false )
      | ( ( string @ SV9 @ SV3 )
        = $false )
      | ( ( entry_box @ SV11 @ SV3 )
        = $false )
      | ( ( mrel @ mactual @ SV3 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[89]) ).

thf(92,plain,
    ! [SV10: $i,SV13: $i,SV15: $i,SV14: $i] :
      ( ( ( ~ ( mrel @ sK2_SX0 @ ( sK5_SY40 @ SV14 @ SV15 @ SV13 @ SV10 ) )
          | ~ ( ~ ( userid @ u @ SV10 @ ( sK5_SY40 @ SV14 @ SV15 @ SV13 @ SV10 ) )
              | ~ ~ ( ~ ( entry_box @ SV13 @ ( sK5_SY40 @ SV14 @ SV15 @ SV13 @ SV10 ) )
                    | ~ ( number @ SV13 @ one @ ( sK5_SY40 @ SV14 @ SV15 @ SV13 @ SV10 ) ) ) ) )
        = $false )
      | ( ( ~ ! [SY50: mworld] :
                ( ~ ( mrel @ sK2_SX0 @ SY50 )
                | ! [SY51: $i] :
                    ( ~ ( do @ SV15 @ SV14 @ SY51 @ SY50 )
                    | ( in @ SV10 @ SV13 @ SY51 @ SY50 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[90]) ).

thf(93,plain,
    ! [SV16: mworld,SV17: $i,SV3: mworld,SV9: $i,SV11: $i,SV7: $i] :
      ( ( ( ~ ( do @ SV7 @ ( sK4_SY35 @ SV11 @ SV9 @ SV7 @ SV3 ) @ SV17 @ SV16 ) )
        = $true )
      | ( ( in @ SV9 @ SV11 @ SV17 @ SV16 )
        = $true )
      | ( ( mrel @ SV3 @ SV16 )
        = $false )
      | ( ( string @ SV9 @ SV3 )
        = $false )
      | ( ( entry_box @ SV11 @ SV3 )
        = $false )
      | ( ( mrel @ mactual @ SV3 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[91]) ).

thf(94,plain,
    ! [SV10: $i,SV13: $i,SV15: $i,SV14: $i] :
      ( ( ( ~ ( mrel @ sK2_SX0 @ ( sK5_SY40 @ SV14 @ SV15 @ SV13 @ SV10 ) ) )
        = $false )
      | ( ( ~ ! [SY50: mworld] :
                ( ~ ( mrel @ sK2_SX0 @ SY50 )
                | ! [SY51: $i] :
                    ( ~ ( do @ SV15 @ SV14 @ SY51 @ SY50 )
                    | ( in @ SV10 @ SV13 @ SY51 @ SY50 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[92]) ).

thf(95,plain,
    ! [SV13: $i,SV15: $i,SV14: $i,SV10: $i] :
      ( ( ( ~ ( ~ ( userid @ u @ SV10 @ ( sK5_SY40 @ SV14 @ SV15 @ SV13 @ SV10 ) )
              | ~ ~ ( ~ ( entry_box @ SV13 @ ( sK5_SY40 @ SV14 @ SV15 @ SV13 @ SV10 ) )
                    | ~ ( number @ SV13 @ one @ ( sK5_SY40 @ SV14 @ SV15 @ SV13 @ SV10 ) ) ) ) )
        = $false )
      | ( ( ~ ! [SY50: mworld] :
                ( ~ ( mrel @ sK2_SX0 @ SY50 )
                | ! [SY51: $i] :
                    ( ~ ( do @ SV15 @ SV14 @ SY51 @ SY50 )
                    | ( in @ SV10 @ SV13 @ SY51 @ SY50 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[92]) ).

thf(96,plain,
    ! [SV16: mworld,SV17: $i,SV3: mworld,SV9: $i,SV11: $i,SV7: $i] :
      ( ( ( do @ SV7 @ ( sK4_SY35 @ SV11 @ SV9 @ SV7 @ SV3 ) @ SV17 @ SV16 )
        = $false )
      | ( ( in @ SV9 @ SV11 @ SV17 @ SV16 )
        = $true )
      | ( ( mrel @ SV3 @ SV16 )
        = $false )
      | ( ( string @ SV9 @ SV3 )
        = $false )
      | ( ( entry_box @ SV11 @ SV3 )
        = $false )
      | ( ( mrel @ mactual @ SV3 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[93]) ).

thf(97,plain,
    ! [SV10: $i,SV13: $i,SV15: $i,SV14: $i] :
      ( ( ( mrel @ sK2_SX0 @ ( sK5_SY40 @ SV14 @ SV15 @ SV13 @ SV10 ) )
        = $true )
      | ( ( ~ ! [SY50: mworld] :
                ( ~ ( mrel @ sK2_SX0 @ SY50 )
                | ! [SY51: $i] :
                    ( ~ ( do @ SV15 @ SV14 @ SY51 @ SY50 )
                    | ( in @ SV10 @ SV13 @ SY51 @ SY50 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[94]) ).

thf(98,plain,
    ! [SV13: $i,SV15: $i,SV14: $i,SV10: $i] :
      ( ( ( ~ ( userid @ u @ SV10 @ ( sK5_SY40 @ SV14 @ SV15 @ SV13 @ SV10 ) )
          | ~ ~ ( ~ ( entry_box @ SV13 @ ( sK5_SY40 @ SV14 @ SV15 @ SV13 @ SV10 ) )
                | ~ ( number @ SV13 @ one @ ( sK5_SY40 @ SV14 @ SV15 @ SV13 @ SV10 ) ) ) )
        = $true )
      | ( ( ~ ! [SY50: mworld] :
                ( ~ ( mrel @ sK2_SX0 @ SY50 )
                | ! [SY51: $i] :
                    ( ~ ( do @ SV15 @ SV14 @ SY51 @ SY50 )
                    | ( in @ SV10 @ SV13 @ SY51 @ SY50 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[95]) ).

thf(99,plain,
    ! [SV13: $i,SV10: $i,SV14: $i,SV15: $i] :
      ( ( ( ! [SY50: mworld] :
              ( ~ ( mrel @ sK2_SX0 @ SY50 )
              | ! [SY51: $i] :
                  ( ~ ( do @ SV15 @ SV14 @ SY51 @ SY50 )
                  | ( in @ SV10 @ SV13 @ SY51 @ SY50 ) ) ) )
        = $false )
      | ( ( mrel @ sK2_SX0 @ ( sK5_SY40 @ SV14 @ SV15 @ SV13 @ SV10 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[97]) ).

thf(100,plain,
    ! [SV13: $i,SV15: $i,SV14: $i,SV10: $i] :
      ( ( ( ~ ( userid @ u @ SV10 @ ( sK5_SY40 @ SV14 @ SV15 @ SV13 @ SV10 ) ) )
        = $true )
      | ( ( ~ ~ ( ~ ( entry_box @ SV13 @ ( sK5_SY40 @ SV14 @ SV15 @ SV13 @ SV10 ) )
                | ~ ( number @ SV13 @ one @ ( sK5_SY40 @ SV14 @ SV15 @ SV13 @ SV10 ) ) ) )
        = $true )
      | ( ( ~ ! [SY50: mworld] :
                ( ~ ( mrel @ sK2_SX0 @ SY50 )
                | ! [SY51: $i] :
                    ( ~ ( do @ SV15 @ SV14 @ SY51 @ SY50 )
                    | ( in @ SV10 @ SV13 @ SY51 @ SY50 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[98]) ).

thf(101,plain,
    ! [SV15: $i,SV14: $i,SV10: $i,SV13: $i] :
      ( ( ( ~ ( mrel @ sK2_SX0 @ ( sK6_SY50 @ SV13 @ SV10 @ SV14 @ SV15 ) )
          | ! [SY53: $i] :
              ( ~ ( do @ SV15 @ SV14 @ SY53 @ ( sK6_SY50 @ SV13 @ SV10 @ SV14 @ SV15 ) )
              | ( in @ SV10 @ SV13 @ SY53 @ ( sK6_SY50 @ SV13 @ SV10 @ SV14 @ SV15 ) ) ) )
        = $false )
      | ( ( mrel @ sK2_SX0 @ ( sK5_SY40 @ SV14 @ SV15 @ SV13 @ SV10 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[99]) ).

thf(102,plain,
    ! [SV13: $i,SV15: $i,SV14: $i,SV10: $i] :
      ( ( ( userid @ u @ SV10 @ ( sK5_SY40 @ SV14 @ SV15 @ SV13 @ SV10 ) )
        = $false )
      | ( ( ~ ~ ( ~ ( entry_box @ SV13 @ ( sK5_SY40 @ SV14 @ SV15 @ SV13 @ SV10 ) )
                | ~ ( number @ SV13 @ one @ ( sK5_SY40 @ SV14 @ SV15 @ SV13 @ SV10 ) ) ) )
        = $true )
      | ( ( ~ ! [SY50: mworld] :
                ( ~ ( mrel @ sK2_SX0 @ SY50 )
                | ! [SY51: $i] :
                    ( ~ ( do @ SV15 @ SV14 @ SY51 @ SY50 )
                    | ( in @ SV10 @ SV13 @ SY51 @ SY50 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[100]) ).

thf(103,plain,
    ! [SV15: $i,SV14: $i,SV10: $i,SV13: $i] :
      ( ( ( ~ ( mrel @ sK2_SX0 @ ( sK6_SY50 @ SV13 @ SV10 @ SV14 @ SV15 ) ) )
        = $false )
      | ( ( mrel @ sK2_SX0 @ ( sK5_SY40 @ SV14 @ SV15 @ SV13 @ SV10 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[101]) ).

thf(104,plain,
    ! [SV10: $i,SV13: $i,SV14: $i,SV15: $i] :
      ( ( ( ! [SY53: $i] :
              ( ~ ( do @ SV15 @ SV14 @ SY53 @ ( sK6_SY50 @ SV13 @ SV10 @ SV14 @ SV15 ) )
              | ( in @ SV10 @ SV13 @ SY53 @ ( sK6_SY50 @ SV13 @ SV10 @ SV14 @ SV15 ) ) ) )
        = $false )
      | ( ( mrel @ sK2_SX0 @ ( sK5_SY40 @ SV14 @ SV15 @ SV13 @ SV10 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[101]) ).

thf(105,plain,
    ! [SV10: $i,SV15: $i,SV14: $i,SV13: $i] :
      ( ( ( ~ ( ~ ( entry_box @ SV13 @ ( sK5_SY40 @ SV14 @ SV15 @ SV13 @ SV10 ) )
              | ~ ( number @ SV13 @ one @ ( sK5_SY40 @ SV14 @ SV15 @ SV13 @ SV10 ) ) ) )
        = $false )
      | ( ( userid @ u @ SV10 @ ( sK5_SY40 @ SV14 @ SV15 @ SV13 @ SV10 ) )
        = $false )
      | ( ( ~ ! [SY50: mworld] :
                ( ~ ( mrel @ sK2_SX0 @ SY50 )
                | ! [SY51: $i] :
                    ( ~ ( do @ SV15 @ SV14 @ SY51 @ SY50 )
                    | ( in @ SV10 @ SV13 @ SY51 @ SY50 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[102]) ).

thf(106,plain,
    ! [SV15: $i,SV14: $i,SV10: $i,SV13: $i] :
      ( ( ( mrel @ sK2_SX0 @ ( sK6_SY50 @ SV13 @ SV10 @ SV14 @ SV15 ) )
        = $true )
      | ( ( mrel @ sK2_SX0 @ ( sK5_SY40 @ SV14 @ SV15 @ SV13 @ SV10 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[103]) ).

thf(107,plain,
    ! [SV13: $i,SV10: $i,SV14: $i,SV15: $i] :
      ( ( ( ~ ( do @ SV15 @ SV14 @ ( sK7_SY53 @ SV10 @ SV13 @ SV14 @ SV15 ) @ ( sK6_SY50 @ SV13 @ SV10 @ SV14 @ SV15 ) )
          | ( in @ SV10 @ SV13 @ ( sK7_SY53 @ SV10 @ SV13 @ SV14 @ SV15 ) @ ( sK6_SY50 @ SV13 @ SV10 @ SV14 @ SV15 ) ) )
        = $false )
      | ( ( mrel @ sK2_SX0 @ ( sK5_SY40 @ SV14 @ SV15 @ SV13 @ SV10 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[104]) ).

thf(108,plain,
    ! [SV10: $i,SV15: $i,SV14: $i,SV13: $i] :
      ( ( ( ~ ( entry_box @ SV13 @ ( sK5_SY40 @ SV14 @ SV15 @ SV13 @ SV10 ) )
          | ~ ( number @ SV13 @ one @ ( sK5_SY40 @ SV14 @ SV15 @ SV13 @ SV10 ) ) )
        = $true )
      | ( ( userid @ u @ SV10 @ ( sK5_SY40 @ SV14 @ SV15 @ SV13 @ SV10 ) )
        = $false )
      | ( ( ~ ! [SY50: mworld] :
                ( ~ ( mrel @ sK2_SX0 @ SY50 )
                | ! [SY51: $i] :
                    ( ~ ( do @ SV15 @ SV14 @ SY51 @ SY50 )
                    | ( in @ SV10 @ SV13 @ SY51 @ SY50 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[105]) ).

thf(109,plain,
    ! [SV13: $i,SV10: $i,SV14: $i,SV15: $i] :
      ( ( ( ~ ( do @ SV15 @ SV14 @ ( sK7_SY53 @ SV10 @ SV13 @ SV14 @ SV15 ) @ ( sK6_SY50 @ SV13 @ SV10 @ SV14 @ SV15 ) ) )
        = $false )
      | ( ( mrel @ sK2_SX0 @ ( sK5_SY40 @ SV14 @ SV15 @ SV13 @ SV10 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[107]) ).

thf(110,plain,
    ! [SV15: $i,SV14: $i,SV13: $i,SV10: $i] :
      ( ( ( in @ SV10 @ SV13 @ ( sK7_SY53 @ SV10 @ SV13 @ SV14 @ SV15 ) @ ( sK6_SY50 @ SV13 @ SV10 @ SV14 @ SV15 ) )
        = $false )
      | ( ( mrel @ sK2_SX0 @ ( sK5_SY40 @ SV14 @ SV15 @ SV13 @ SV10 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[107]) ).

thf(111,plain,
    ! [SV10: $i,SV15: $i,SV14: $i,SV13: $i] :
      ( ( ( ~ ( entry_box @ SV13 @ ( sK5_SY40 @ SV14 @ SV15 @ SV13 @ SV10 ) ) )
        = $true )
      | ( ( ~ ( number @ SV13 @ one @ ( sK5_SY40 @ SV14 @ SV15 @ SV13 @ SV10 ) ) )
        = $true )
      | ( ( userid @ u @ SV10 @ ( sK5_SY40 @ SV14 @ SV15 @ SV13 @ SV10 ) )
        = $false )
      | ( ( ~ ! [SY50: mworld] :
                ( ~ ( mrel @ sK2_SX0 @ SY50 )
                | ! [SY51: $i] :
                    ( ~ ( do @ SV15 @ SV14 @ SY51 @ SY50 )
                    | ( in @ SV10 @ SV13 @ SY51 @ SY50 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[108]) ).

thf(112,plain,
    ! [SV13: $i,SV10: $i,SV14: $i,SV15: $i] :
      ( ( ( do @ SV15 @ SV14 @ ( sK7_SY53 @ SV10 @ SV13 @ SV14 @ SV15 ) @ ( sK6_SY50 @ SV13 @ SV10 @ SV14 @ SV15 ) )
        = $true )
      | ( ( mrel @ sK2_SX0 @ ( sK5_SY40 @ SV14 @ SV15 @ SV13 @ SV10 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[109]) ).

thf(113,plain,
    ! [SV10: $i,SV15: $i,SV14: $i,SV13: $i] :
      ( ( ( entry_box @ SV13 @ ( sK5_SY40 @ SV14 @ SV15 @ SV13 @ SV10 ) )
        = $false )
      | ( ( ~ ( number @ SV13 @ one @ ( sK5_SY40 @ SV14 @ SV15 @ SV13 @ SV10 ) ) )
        = $true )
      | ( ( userid @ u @ SV10 @ ( sK5_SY40 @ SV14 @ SV15 @ SV13 @ SV10 ) )
        = $false )
      | ( ( ~ ! [SY50: mworld] :
                ( ~ ( mrel @ sK2_SX0 @ SY50 )
                | ! [SY51: $i] :
                    ( ~ ( do @ SV15 @ SV14 @ SY51 @ SY50 )
                    | ( in @ SV10 @ SV13 @ SY51 @ SY50 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[111]) ).

thf(114,plain,
    ! [SV10: $i,SV15: $i,SV14: $i,SV13: $i] :
      ( ( ( number @ SV13 @ one @ ( sK5_SY40 @ SV14 @ SV15 @ SV13 @ SV10 ) )
        = $false )
      | ( ( entry_box @ SV13 @ ( sK5_SY40 @ SV14 @ SV15 @ SV13 @ SV10 ) )
        = $false )
      | ( ( userid @ u @ SV10 @ ( sK5_SY40 @ SV14 @ SV15 @ SV13 @ SV10 ) )
        = $false )
      | ( ( ~ ! [SY50: mworld] :
                ( ~ ( mrel @ sK2_SX0 @ SY50 )
                | ! [SY51: $i] :
                    ( ~ ( do @ SV15 @ SV14 @ SY51 @ SY50 )
                    | ( in @ SV10 @ SV13 @ SY51 @ SY50 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[113]) ).

thf(115,plain,
    ! [SV13: $i,SV10: $i,SV14: $i,SV15: $i] :
      ( ( ( ! [SY50: mworld] :
              ( ~ ( mrel @ sK2_SX0 @ SY50 )
              | ! [SY51: $i] :
                  ( ~ ( do @ SV15 @ SV14 @ SY51 @ SY50 )
                  | ( in @ SV10 @ SV13 @ SY51 @ SY50 ) ) ) )
        = $false )
      | ( ( userid @ u @ SV10 @ ( sK5_SY40 @ SV14 @ SV15 @ SV13 @ SV10 ) )
        = $false )
      | ( ( entry_box @ SV13 @ ( sK5_SY40 @ SV14 @ SV15 @ SV13 @ SV10 ) )
        = $false )
      | ( ( number @ SV13 @ one @ ( sK5_SY40 @ SV14 @ SV15 @ SV13 @ SV10 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[114]) ).

thf(116,plain,
    ! [SV15: $i,SV14: $i,SV10: $i,SV13: $i] :
      ( ( ( ~ ( mrel @ sK2_SX0 @ ( sK8_SY50 @ SV13 @ SV10 @ SV14 @ SV15 ) )
          | ! [SY54: $i] :
              ( ~ ( do @ SV15 @ SV14 @ SY54 @ ( sK8_SY50 @ SV13 @ SV10 @ SV14 @ SV15 ) )
              | ( in @ SV10 @ SV13 @ SY54 @ ( sK8_SY50 @ SV13 @ SV10 @ SV14 @ SV15 ) ) ) )
        = $false )
      | ( ( userid @ u @ SV10 @ ( sK5_SY40 @ SV14 @ SV15 @ SV13 @ SV10 ) )
        = $false )
      | ( ( entry_box @ SV13 @ ( sK5_SY40 @ SV14 @ SV15 @ SV13 @ SV10 ) )
        = $false )
      | ( ( number @ SV13 @ one @ ( sK5_SY40 @ SV14 @ SV15 @ SV13 @ SV10 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[115]) ).

thf(117,plain,
    ! [SV15: $i,SV14: $i,SV10: $i,SV13: $i] :
      ( ( ( ~ ( mrel @ sK2_SX0 @ ( sK8_SY50 @ SV13 @ SV10 @ SV14 @ SV15 ) ) )
        = $false )
      | ( ( userid @ u @ SV10 @ ( sK5_SY40 @ SV14 @ SV15 @ SV13 @ SV10 ) )
        = $false )
      | ( ( entry_box @ SV13 @ ( sK5_SY40 @ SV14 @ SV15 @ SV13 @ SV10 ) )
        = $false )
      | ( ( number @ SV13 @ one @ ( sK5_SY40 @ SV14 @ SV15 @ SV13 @ SV10 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[116]) ).

thf(118,plain,
    ! [SV10: $i,SV13: $i,SV14: $i,SV15: $i] :
      ( ( ( ! [SY54: $i] :
              ( ~ ( do @ SV15 @ SV14 @ SY54 @ ( sK8_SY50 @ SV13 @ SV10 @ SV14 @ SV15 ) )
              | ( in @ SV10 @ SV13 @ SY54 @ ( sK8_SY50 @ SV13 @ SV10 @ SV14 @ SV15 ) ) ) )
        = $false )
      | ( ( userid @ u @ SV10 @ ( sK5_SY40 @ SV14 @ SV15 @ SV13 @ SV10 ) )
        = $false )
      | ( ( entry_box @ SV13 @ ( sK5_SY40 @ SV14 @ SV15 @ SV13 @ SV10 ) )
        = $false )
      | ( ( number @ SV13 @ one @ ( sK5_SY40 @ SV14 @ SV15 @ SV13 @ SV10 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[116]) ).

thf(119,plain,
    ! [SV15: $i,SV14: $i,SV10: $i,SV13: $i] :
      ( ( ( mrel @ sK2_SX0 @ ( sK8_SY50 @ SV13 @ SV10 @ SV14 @ SV15 ) )
        = $true )
      | ( ( userid @ u @ SV10 @ ( sK5_SY40 @ SV14 @ SV15 @ SV13 @ SV10 ) )
        = $false )
      | ( ( entry_box @ SV13 @ ( sK5_SY40 @ SV14 @ SV15 @ SV13 @ SV10 ) )
        = $false )
      | ( ( number @ SV13 @ one @ ( sK5_SY40 @ SV14 @ SV15 @ SV13 @ SV10 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[117]) ).

thf(120,plain,
    ! [SV13: $i,SV10: $i,SV14: $i,SV15: $i] :
      ( ( ( ~ ( do @ SV15 @ SV14 @ ( sK9_SY54 @ SV10 @ SV13 @ SV14 @ SV15 ) @ ( sK8_SY50 @ SV13 @ SV10 @ SV14 @ SV15 ) )
          | ( in @ SV10 @ SV13 @ ( sK9_SY54 @ SV10 @ SV13 @ SV14 @ SV15 ) @ ( sK8_SY50 @ SV13 @ SV10 @ SV14 @ SV15 ) ) )
        = $false )
      | ( ( userid @ u @ SV10 @ ( sK5_SY40 @ SV14 @ SV15 @ SV13 @ SV10 ) )
        = $false )
      | ( ( entry_box @ SV13 @ ( sK5_SY40 @ SV14 @ SV15 @ SV13 @ SV10 ) )
        = $false )
      | ( ( number @ SV13 @ one @ ( sK5_SY40 @ SV14 @ SV15 @ SV13 @ SV10 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[118]) ).

thf(121,plain,
    ! [SV13: $i,SV10: $i,SV14: $i,SV15: $i] :
      ( ( ( ~ ( do @ SV15 @ SV14 @ ( sK9_SY54 @ SV10 @ SV13 @ SV14 @ SV15 ) @ ( sK8_SY50 @ SV13 @ SV10 @ SV14 @ SV15 ) ) )
        = $false )
      | ( ( userid @ u @ SV10 @ ( sK5_SY40 @ SV14 @ SV15 @ SV13 @ SV10 ) )
        = $false )
      | ( ( entry_box @ SV13 @ ( sK5_SY40 @ SV14 @ SV15 @ SV13 @ SV10 ) )
        = $false )
      | ( ( number @ SV13 @ one @ ( sK5_SY40 @ SV14 @ SV15 @ SV13 @ SV10 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[120]) ).

thf(122,plain,
    ! [SV15: $i,SV14: $i,SV13: $i,SV10: $i] :
      ( ( ( in @ SV10 @ SV13 @ ( sK9_SY54 @ SV10 @ SV13 @ SV14 @ SV15 ) @ ( sK8_SY50 @ SV13 @ SV10 @ SV14 @ SV15 ) )
        = $false )
      | ( ( userid @ u @ SV10 @ ( sK5_SY40 @ SV14 @ SV15 @ SV13 @ SV10 ) )
        = $false )
      | ( ( entry_box @ SV13 @ ( sK5_SY40 @ SV14 @ SV15 @ SV13 @ SV10 ) )
        = $false )
      | ( ( number @ SV13 @ one @ ( sK5_SY40 @ SV14 @ SV15 @ SV13 @ SV10 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[120]) ).

thf(123,plain,
    ! [SV13: $i,SV10: $i,SV14: $i,SV15: $i] :
      ( ( ( do @ SV15 @ SV14 @ ( sK9_SY54 @ SV10 @ SV13 @ SV14 @ SV15 ) @ ( sK8_SY50 @ SV13 @ SV10 @ SV14 @ SV15 ) )
        = $true )
      | ( ( userid @ u @ SV10 @ ( sK5_SY40 @ SV14 @ SV15 @ SV13 @ SV10 ) )
        = $false )
      | ( ( entry_box @ SV13 @ ( sK5_SY40 @ SV14 @ SV15 @ SV13 @ SV10 ) )
        = $false )
      | ( ( number @ SV13 @ one @ ( sK5_SY40 @ SV14 @ SV15 @ SV13 @ SV10 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[121]) ).

thf(124,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[20,123,122,119,112,110,106,96,77,76,65,64,53,41]) ).

thf(125,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[124]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : NLP266^4 : TPTP v8.1.0. Released v8.1.0.
% 0.07/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.34  % Computer : n029.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 600
% 0.14/0.34  % DateTime : Fri Jul  1 12:53:54 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 0.14/0.39  
% 0.14/0.39   No.of.Axioms: 5
% 0.14/0.39  
% 0.14/0.39   Length.of.Defs: 1574
% 0.14/0.39  
% 0.14/0.39   Contains.Choice.Funs: false
% 0.21/0.42  (rf:0,axioms:5,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:7,loop_count:0,foatp_calls:0,translation:fof_full)..........
% 0.45/0.62  
% 0.45/0.62  ********************************
% 0.45/0.62  *   All subproblems solved!    *
% 0.45/0.62  ********************************
% 0.45/0.62  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:5,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:124,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.46/0.63  
% 0.46/0.63  %**** Beginning of derivation protocol ****
% 0.46/0.63  % SZS output start CNFRefutation
% See solution above
% 0.46/0.63  
% 0.46/0.63  %**** End of derivation protocol ****
% 0.46/0.63  %**** no. of clauses in derivation: 125 ****
% 0.46/0.63  %**** clause counter: 124 ****
% 0.46/0.63  
% 0.46/0.63  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:5,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:124,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------