TSTP Solution File: GRP001+6 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : GRP001+6 : TPTP v8.1.0. Released v3.1.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n015.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 600s
% DateTime : Sat Jul 16 10:15:18 EDT 2022

% Result   : Theorem 0.20s 0.56s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   74 (  54 unt;   7 typ;   0 def)
%            Number of atoms       :  413 (  95 equ;   0 cnn)
%            Maximal formula atoms :   16 (   6 avg)
%            Number of connectives :  927 (  86   ~;  86   |;  46   &; 685   @)
%                                         (   0 <=>;  24  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   7 usr;   6 con; 0-3 aty)
%            Number of variables   :  307 (   0   ^ 302   !;   5   ?; 307   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_inverse,type,
    inverse: $i > $i ).

thf(tp_product,type,
    product: $i > $i > $i > $o ).

thf(tp_sK1_E,type,
    sK1_E: $i ).

thf(tp_sK2_U,type,
    sK2_U: $i ).

thf(tp_sK3_SY47,type,
    sK3_SY47: $i ).

thf(tp_sK4_SY49,type,
    sK4_SY49: $i ).

thf(tp_sK5_Z,type,
    sK5_Z: $i > $i > $i ).

thf(1,conjecture,
    ! [E: $i] :
      ( ( ! [X: $i,Y: $i] :
          ? [Z: $i] : ( product @ X @ Y @ Z )
        & ! [X: $i,Y: $i,Z: $i,U: $i,V: $i,W: $i] :
            ( ( ( product @ X @ Y @ U )
              & ( product @ Y @ Z @ V )
              & ( product @ U @ Z @ W ) )
           => ( product @ X @ V @ W ) )
        & ! [X: $i,Y: $i,Z: $i,U: $i,V: $i,W: $i] :
            ( ( ( product @ X @ Y @ U )
              & ( product @ Y @ Z @ V )
              & ( product @ X @ V @ W ) )
           => ( product @ U @ Z @ W ) )
        & ! [X: $i] : ( product @ X @ E @ X )
        & ! [X: $i] : ( product @ E @ X @ X )
        & ! [X: $i] : ( product @ X @ ( inverse @ X ) @ E )
        & ! [X: $i] : ( product @ ( inverse @ X ) @ X @ E ) )
     => ( ! [X: $i] : ( product @ X @ X @ E )
       => ! [U: $i,V: $i,W: $i] :
            ( ( product @ U @ V @ W )
           => ( product @ V @ U @ W ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity) ).

thf(2,negated_conjecture,
    ( ( ! [E: $i] :
          ( ( ! [X: $i,Y: $i] :
              ? [Z: $i] : ( product @ X @ Y @ Z )
            & ! [X: $i,Y: $i,Z: $i,U: $i,V: $i,W: $i] :
                ( ( ( product @ X @ Y @ U )
                  & ( product @ Y @ Z @ V )
                  & ( product @ U @ Z @ W ) )
               => ( product @ X @ V @ W ) )
            & ! [X: $i,Y: $i,Z: $i,U: $i,V: $i,W: $i] :
                ( ( ( product @ X @ Y @ U )
                  & ( product @ Y @ Z @ V )
                  & ( product @ X @ V @ W ) )
               => ( product @ U @ Z @ W ) )
            & ! [X: $i] : ( product @ X @ E @ X )
            & ! [X: $i] : ( product @ E @ X @ X )
            & ! [X: $i] : ( product @ X @ ( inverse @ X ) @ E )
            & ! [X: $i] : ( product @ ( inverse @ X ) @ X @ E ) )
         => ( ! [X: $i] : ( product @ X @ X @ E )
           => ! [U: $i,V: $i,W: $i] :
                ( ( product @ U @ V @ W )
               => ( product @ V @ U @ W ) ) ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ( ( ! [E: $i] :
          ( ( ! [X: $i,Y: $i] :
              ? [Z: $i] : ( product @ X @ Y @ Z )
            & ! [X: $i,Y: $i,Z: $i,U: $i,V: $i,W: $i] :
                ( ( ( product @ X @ Y @ U )
                  & ( product @ Y @ Z @ V )
                  & ( product @ U @ Z @ W ) )
               => ( product @ X @ V @ W ) )
            & ! [X: $i,Y: $i,Z: $i,U: $i,V: $i,W: $i] :
                ( ( ( product @ X @ Y @ U )
                  & ( product @ Y @ Z @ V )
                  & ( product @ X @ V @ W ) )
               => ( product @ U @ Z @ W ) )
            & ! [X: $i] : ( product @ X @ E @ X )
            & ! [X: $i] : ( product @ E @ X @ X )
            & ! [X: $i] : ( product @ X @ ( inverse @ X ) @ E )
            & ! [X: $i] : ( product @ ( inverse @ X ) @ X @ E ) )
         => ( ! [X: $i] : ( product @ X @ X @ E )
           => ! [U: $i,V: $i,W: $i] :
                ( ( product @ U @ V @ W )
               => ( product @ V @ U @ W ) ) ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(4,plain,
    ( ( ( ! [X: $i,Y: $i] :
          ? [Z: $i] : ( product @ X @ Y @ Z )
        & ! [X: $i,Y: $i,Z: $i,U: $i,V: $i,W: $i] :
            ( ( ( product @ X @ Y @ U )
              & ( product @ Y @ Z @ V )
              & ( product @ U @ Z @ W ) )
           => ( product @ X @ V @ W ) )
        & ! [X: $i,Y: $i,Z: $i,U: $i,V: $i,W: $i] :
            ( ( ( product @ X @ Y @ U )
              & ( product @ Y @ Z @ V )
              & ( product @ X @ V @ W ) )
           => ( product @ U @ Z @ W ) )
        & ! [SY39: $i] : ( product @ SY39 @ sK1_E @ SY39 )
        & ! [SY40: $i] : ( product @ sK1_E @ SY40 @ SY40 )
        & ! [SY41: $i] : ( product @ SY41 @ ( inverse @ SY41 ) @ sK1_E )
        & ! [SY42: $i] : ( product @ ( inverse @ SY42 ) @ SY42 @ sK1_E ) )
     => ( ! [SY43: $i] : ( product @ SY43 @ SY43 @ sK1_E )
       => ! [U: $i,V: $i,W: $i] :
            ( ( product @ U @ V @ W )
           => ( product @ V @ U @ W ) ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[3]) ).

thf(5,plain,
    ( ( ! [X: $i,Y: $i] :
        ? [Z: $i] : ( product @ X @ Y @ Z ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[4]) ).

thf(6,plain,
    ( ( ! [X: $i,Y: $i,Z: $i,U: $i,V: $i,W: $i] :
          ( ( ( product @ X @ Y @ U )
            & ( product @ Y @ Z @ V )
            & ( product @ U @ Z @ W ) )
         => ( product @ X @ V @ W ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[4]) ).

thf(7,plain,
    ( ( ! [X: $i,Y: $i,Z: $i,U: $i,V: $i,W: $i] :
          ( ( ( product @ X @ Y @ U )
            & ( product @ Y @ Z @ V )
            & ( product @ X @ V @ W ) )
         => ( product @ U @ Z @ W ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[4]) ).

thf(8,plain,
    ( ( ! [SY39: $i] : ( product @ SY39 @ sK1_E @ SY39 ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[4]) ).

thf(9,plain,
    ( ( ! [SY40: $i] : ( product @ sK1_E @ SY40 @ SY40 ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[4]) ).

thf(10,plain,
    ( ( ! [SY41: $i] : ( product @ SY41 @ ( inverse @ SY41 ) @ sK1_E ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[4]) ).

thf(11,plain,
    ( ( ! [SY42: $i] : ( product @ ( inverse @ SY42 ) @ SY42 @ sK1_E ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[4]) ).

thf(12,plain,
    ( ( ! [SY43: $i] : ( product @ SY43 @ SY43 @ sK1_E ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[4]) ).

thf(13,plain,
    ( ( ! [U: $i,V: $i,W: $i] :
          ( ( product @ U @ V @ W )
         => ( product @ V @ U @ W ) ) )
    = $false ),
    inference(standard_cnf,[status(thm)],[4]) ).

thf(14,plain,
    ( ( ~ ! [U: $i,V: $i,W: $i] :
            ( ( product @ U @ V @ W )
           => ( product @ V @ U @ W ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[13]) ).

thf(15,plain,
    ( ( ( product @ sK2_U @ sK3_SY47 @ sK4_SY49 )
      & ~ ( product @ sK3_SY47 @ sK2_U @ sK4_SY49 ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[14]) ).

thf(16,plain,
    ( ( ! [X: $i,Y: $i] : ( product @ X @ Y @ ( sK5_Z @ Y @ X ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5]) ).

thf(17,plain,
    ( ( ! [X: $i,Y: $i,Z: $i,U: $i,V: $i,W: $i] :
          ( ~ ( product @ X @ Y @ U )
          | ~ ( product @ Y @ Z @ V )
          | ~ ( product @ U @ Z @ W )
          | ( product @ X @ V @ W ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[6]) ).

thf(18,plain,
    ( ( ! [X: $i,Y: $i,Z: $i,U: $i,V: $i,W: $i] :
          ( ~ ( product @ X @ Y @ U )
          | ~ ( product @ Y @ Z @ V )
          | ~ ( product @ X @ V @ W )
          | ( product @ U @ Z @ W ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[7]) ).

thf(19,plain,
    ( ( ! [SY43: $i] : ( product @ SY43 @ SY43 @ sK1_E ) )
    = $true ),
    inference(copy,[status(thm)],[12]) ).

thf(20,plain,
    ( ( ! [SY42: $i] : ( product @ ( inverse @ SY42 ) @ SY42 @ sK1_E ) )
    = $true ),
    inference(copy,[status(thm)],[11]) ).

thf(21,plain,
    ( ( ! [SY41: $i] : ( product @ SY41 @ ( inverse @ SY41 ) @ sK1_E ) )
    = $true ),
    inference(copy,[status(thm)],[10]) ).

thf(22,plain,
    ( ( ! [SY40: $i] : ( product @ sK1_E @ SY40 @ SY40 ) )
    = $true ),
    inference(copy,[status(thm)],[9]) ).

thf(23,plain,
    ( ( ! [SY39: $i] : ( product @ SY39 @ sK1_E @ SY39 ) )
    = $true ),
    inference(copy,[status(thm)],[8]) ).

thf(24,plain,
    ( ( ! [X: $i,Y: $i,Z: $i,U: $i,V: $i,W: $i] :
          ( ~ ( product @ X @ Y @ U )
          | ~ ( product @ Y @ Z @ V )
          | ~ ( product @ X @ V @ W )
          | ( product @ U @ Z @ W ) ) )
    = $true ),
    inference(copy,[status(thm)],[18]) ).

thf(25,plain,
    ( ( ! [X: $i,Y: $i,Z: $i,U: $i,V: $i,W: $i] :
          ( ~ ( product @ X @ Y @ U )
          | ~ ( product @ Y @ Z @ V )
          | ~ ( product @ U @ Z @ W )
          | ( product @ X @ V @ W ) ) )
    = $true ),
    inference(copy,[status(thm)],[17]) ).

thf(26,plain,
    ( ( ! [X: $i,Y: $i] : ( product @ X @ Y @ ( sK5_Z @ Y @ X ) ) )
    = $true ),
    inference(copy,[status(thm)],[16]) ).

thf(27,plain,
    ( ( ( product @ sK2_U @ sK3_SY47 @ sK4_SY49 )
      & ~ ( product @ sK3_SY47 @ sK2_U @ sK4_SY49 ) )
    = $true ),
    inference(copy,[status(thm)],[15]) ).

thf(28,plain,
    ( ( ~ ( ~ ( product @ sK2_U @ sK3_SY47 @ sK4_SY49 )
          | ~ ~ ( product @ sK3_SY47 @ sK2_U @ sK4_SY49 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[27]) ).

thf(29,plain,
    ! [SV1: $i] :
      ( ( product @ SV1 @ SV1 @ sK1_E )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[19]) ).

thf(30,plain,
    ! [SV2: $i] :
      ( ( product @ ( inverse @ SV2 ) @ SV2 @ sK1_E )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[20]) ).

thf(31,plain,
    ! [SV3: $i] :
      ( ( product @ SV3 @ ( inverse @ SV3 ) @ sK1_E )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[21]) ).

thf(32,plain,
    ! [SV4: $i] :
      ( ( product @ sK1_E @ SV4 @ SV4 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[22]) ).

thf(33,plain,
    ! [SV5: $i] :
      ( ( product @ SV5 @ sK1_E @ SV5 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[23]) ).

thf(34,plain,
    ! [SV6: $i] :
      ( ( ! [SY50: $i,SY51: $i,SY52: $i,SY53: $i,SY54: $i] :
            ( ~ ( product @ SV6 @ SY50 @ SY52 )
            | ~ ( product @ SY50 @ SY51 @ SY53 )
            | ~ ( product @ SV6 @ SY53 @ SY54 )
            | ( product @ SY52 @ SY51 @ SY54 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[24]) ).

thf(35,plain,
    ! [SV7: $i] :
      ( ( ! [SY55: $i,SY56: $i,SY57: $i,SY58: $i,SY59: $i] :
            ( ~ ( product @ SV7 @ SY55 @ SY57 )
            | ~ ( product @ SY55 @ SY56 @ SY58 )
            | ~ ( product @ SY57 @ SY56 @ SY59 )
            | ( product @ SV7 @ SY58 @ SY59 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[25]) ).

thf(36,plain,
    ! [SV8: $i] :
      ( ( ! [SY60: $i] : ( product @ SV8 @ SY60 @ ( sK5_Z @ SY60 @ SV8 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[26]) ).

thf(37,plain,
    ( ( ~ ( product @ sK2_U @ sK3_SY47 @ sK4_SY49 )
      | ~ ~ ( product @ sK3_SY47 @ sK2_U @ sK4_SY49 ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[28]) ).

thf(38,plain,
    ! [SV9: $i,SV6: $i] :
      ( ( ! [SY61: $i,SY62: $i,SY63: $i,SY64: $i] :
            ( ~ ( product @ SV6 @ SV9 @ SY62 )
            | ~ ( product @ SV9 @ SY61 @ SY63 )
            | ~ ( product @ SV6 @ SY63 @ SY64 )
            | ( product @ SY62 @ SY61 @ SY64 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[34]) ).

thf(39,plain,
    ! [SV10: $i,SV7: $i] :
      ( ( ! [SY65: $i,SY66: $i,SY67: $i,SY68: $i] :
            ( ~ ( product @ SV7 @ SV10 @ SY66 )
            | ~ ( product @ SV10 @ SY65 @ SY67 )
            | ~ ( product @ SY66 @ SY65 @ SY68 )
            | ( product @ SV7 @ SY67 @ SY68 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[35]) ).

thf(40,plain,
    ! [SV11: $i,SV8: $i] :
      ( ( product @ SV8 @ SV11 @ ( sK5_Z @ SV11 @ SV8 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[36]) ).

thf(41,plain,
    ( ( ~ ( product @ sK2_U @ sK3_SY47 @ sK4_SY49 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[37]) ).

thf(42,plain,
    ( ( ~ ~ ( product @ sK3_SY47 @ sK2_U @ sK4_SY49 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[37]) ).

thf(43,plain,
    ! [SV12: $i,SV9: $i,SV6: $i] :
      ( ( ! [SY69: $i,SY70: $i,SY71: $i] :
            ( ~ ( product @ SV6 @ SV9 @ SY69 )
            | ~ ( product @ SV9 @ SV12 @ SY70 )
            | ~ ( product @ SV6 @ SY70 @ SY71 )
            | ( product @ SY69 @ SV12 @ SY71 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[38]) ).

thf(44,plain,
    ! [SV13: $i,SV10: $i,SV7: $i] :
      ( ( ! [SY72: $i,SY73: $i,SY74: $i] :
            ( ~ ( product @ SV7 @ SV10 @ SY72 )
            | ~ ( product @ SV10 @ SV13 @ SY73 )
            | ~ ( product @ SY72 @ SV13 @ SY74 )
            | ( product @ SV7 @ SY73 @ SY74 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[39]) ).

thf(45,plain,
    ( ( product @ sK2_U @ sK3_SY47 @ sK4_SY49 )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[41]) ).

thf(46,plain,
    ( ( ~ ( product @ sK3_SY47 @ sK2_U @ sK4_SY49 ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[42]) ).

thf(47,plain,
    ! [SV12: $i,SV14: $i,SV9: $i,SV6: $i] :
      ( ( ! [SY75: $i,SY76: $i] :
            ( ~ ( product @ SV6 @ SV9 @ SV14 )
            | ~ ( product @ SV9 @ SV12 @ SY75 )
            | ~ ( product @ SV6 @ SY75 @ SY76 )
            | ( product @ SV14 @ SV12 @ SY76 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[43]) ).

thf(48,plain,
    ! [SV13: $i,SV15: $i,SV10: $i,SV7: $i] :
      ( ( ! [SY77: $i,SY78: $i] :
            ( ~ ( product @ SV7 @ SV10 @ SV15 )
            | ~ ( product @ SV10 @ SV13 @ SY77 )
            | ~ ( product @ SV15 @ SV13 @ SY78 )
            | ( product @ SV7 @ SY77 @ SY78 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[44]) ).

thf(49,plain,
    ( ( product @ sK3_SY47 @ sK2_U @ sK4_SY49 )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[46]) ).

thf(50,plain,
    ! [SV16: $i,SV12: $i,SV14: $i,SV9: $i,SV6: $i] :
      ( ( ! [SY79: $i] :
            ( ~ ( product @ SV6 @ SV9 @ SV14 )
            | ~ ( product @ SV9 @ SV12 @ SV16 )
            | ~ ( product @ SV6 @ SV16 @ SY79 )
            | ( product @ SV14 @ SV12 @ SY79 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[47]) ).

thf(51,plain,
    ! [SV17: $i,SV13: $i,SV15: $i,SV10: $i,SV7: $i] :
      ( ( ! [SY80: $i] :
            ( ~ ( product @ SV7 @ SV10 @ SV15 )
            | ~ ( product @ SV10 @ SV13 @ SV17 )
            | ~ ( product @ SV15 @ SV13 @ SY80 )
            | ( product @ SV7 @ SV17 @ SY80 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[48]) ).

thf(52,plain,
    ! [SV18: $i,SV16: $i,SV12: $i,SV14: $i,SV9: $i,SV6: $i] :
      ( ( ~ ( product @ SV6 @ SV9 @ SV14 )
        | ~ ( product @ SV9 @ SV12 @ SV16 )
        | ~ ( product @ SV6 @ SV16 @ SV18 )
        | ( product @ SV14 @ SV12 @ SV18 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[50]) ).

thf(53,plain,
    ! [SV19: $i,SV17: $i,SV13: $i,SV15: $i,SV10: $i,SV7: $i] :
      ( ( ~ ( product @ SV7 @ SV10 @ SV15 )
        | ~ ( product @ SV10 @ SV13 @ SV17 )
        | ~ ( product @ SV15 @ SV13 @ SV19 )
        | ( product @ SV7 @ SV17 @ SV19 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[51]) ).

thf(54,plain,
    ! [SV18: $i,SV16: $i,SV12: $i,SV14: $i,SV9: $i,SV6: $i] :
      ( ( ( ~ ( product @ SV6 @ SV9 @ SV14 )
          | ~ ( product @ SV9 @ SV12 @ SV16 )
          | ~ ( product @ SV6 @ SV16 @ SV18 ) )
        = $true )
      | ( ( product @ SV14 @ SV12 @ SV18 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[52]) ).

thf(55,plain,
    ! [SV19: $i,SV17: $i,SV13: $i,SV15: $i,SV10: $i,SV7: $i] :
      ( ( ( ~ ( product @ SV7 @ SV10 @ SV15 )
          | ~ ( product @ SV10 @ SV13 @ SV17 )
          | ~ ( product @ SV15 @ SV13 @ SV19 ) )
        = $true )
      | ( ( product @ SV7 @ SV17 @ SV19 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[53]) ).

thf(56,plain,
    ! [SV18: $i,SV16: $i,SV12: $i,SV14: $i,SV9: $i,SV6: $i] :
      ( ( ( ~ ( product @ SV6 @ SV9 @ SV14 )
          | ~ ( product @ SV9 @ SV12 @ SV16 ) )
        = $true )
      | ( ( ~ ( product @ SV6 @ SV16 @ SV18 ) )
        = $true )
      | ( ( product @ SV14 @ SV12 @ SV18 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[54]) ).

thf(57,plain,
    ! [SV19: $i,SV17: $i,SV13: $i,SV15: $i,SV10: $i,SV7: $i] :
      ( ( ( ~ ( product @ SV7 @ SV10 @ SV15 )
          | ~ ( product @ SV10 @ SV13 @ SV17 ) )
        = $true )
      | ( ( ~ ( product @ SV15 @ SV13 @ SV19 ) )
        = $true )
      | ( ( product @ SV7 @ SV17 @ SV19 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[55]) ).

thf(58,plain,
    ! [SV18: $i,SV16: $i,SV12: $i,SV14: $i,SV9: $i,SV6: $i] :
      ( ( ( ~ ( product @ SV6 @ SV9 @ SV14 ) )
        = $true )
      | ( ( ~ ( product @ SV9 @ SV12 @ SV16 ) )
        = $true )
      | ( ( ~ ( product @ SV6 @ SV16 @ SV18 ) )
        = $true )
      | ( ( product @ SV14 @ SV12 @ SV18 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[56]) ).

thf(59,plain,
    ! [SV19: $i,SV17: $i,SV13: $i,SV15: $i,SV10: $i,SV7: $i] :
      ( ( ( ~ ( product @ SV7 @ SV10 @ SV15 ) )
        = $true )
      | ( ( ~ ( product @ SV10 @ SV13 @ SV17 ) )
        = $true )
      | ( ( ~ ( product @ SV15 @ SV13 @ SV19 ) )
        = $true )
      | ( ( product @ SV7 @ SV17 @ SV19 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[57]) ).

thf(60,plain,
    ! [SV18: $i,SV16: $i,SV12: $i,SV14: $i,SV9: $i,SV6: $i] :
      ( ( ( product @ SV6 @ SV9 @ SV14 )
        = $false )
      | ( ( ~ ( product @ SV9 @ SV12 @ SV16 ) )
        = $true )
      | ( ( ~ ( product @ SV6 @ SV16 @ SV18 ) )
        = $true )
      | ( ( product @ SV14 @ SV12 @ SV18 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[58]) ).

thf(61,plain,
    ! [SV19: $i,SV17: $i,SV13: $i,SV15: $i,SV10: $i,SV7: $i] :
      ( ( ( product @ SV7 @ SV10 @ SV15 )
        = $false )
      | ( ( ~ ( product @ SV10 @ SV13 @ SV17 ) )
        = $true )
      | ( ( ~ ( product @ SV15 @ SV13 @ SV19 ) )
        = $true )
      | ( ( product @ SV7 @ SV17 @ SV19 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[59]) ).

thf(62,plain,
    ! [SV18: $i,SV14: $i,SV6: $i,SV16: $i,SV12: $i,SV9: $i] :
      ( ( ( product @ SV9 @ SV12 @ SV16 )
        = $false )
      | ( ( product @ SV6 @ SV9 @ SV14 )
        = $false )
      | ( ( ~ ( product @ SV6 @ SV16 @ SV18 ) )
        = $true )
      | ( ( product @ SV14 @ SV12 @ SV18 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[60]) ).

thf(63,plain,
    ! [SV19: $i,SV15: $i,SV7: $i,SV17: $i,SV13: $i,SV10: $i] :
      ( ( ( product @ SV10 @ SV13 @ SV17 )
        = $false )
      | ( ( product @ SV7 @ SV10 @ SV15 )
        = $false )
      | ( ( ~ ( product @ SV15 @ SV13 @ SV19 ) )
        = $true )
      | ( ( product @ SV7 @ SV17 @ SV19 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[61]) ).

thf(64,plain,
    ! [SV12: $i,SV14: $i,SV9: $i,SV18: $i,SV16: $i,SV6: $i] :
      ( ( ( product @ SV6 @ SV16 @ SV18 )
        = $false )
      | ( ( product @ SV6 @ SV9 @ SV14 )
        = $false )
      | ( ( product @ SV9 @ SV12 @ SV16 )
        = $false )
      | ( ( product @ SV14 @ SV12 @ SV18 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[62]) ).

thf(65,plain,
    ! [SV17: $i,SV10: $i,SV7: $i,SV19: $i,SV13: $i,SV15: $i] :
      ( ( ( product @ SV15 @ SV13 @ SV19 )
        = $false )
      | ( ( product @ SV7 @ SV10 @ SV15 )
        = $false )
      | ( ( product @ SV10 @ SV13 @ SV17 )
        = $false )
      | ( ( product @ SV7 @ SV17 @ SV19 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[63]) ).

thf(66,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[29,65,64,49,45,40,33,32,31,30]) ).

thf(67,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[66]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem  : GRP001+6 : TPTP v8.1.0. Released v3.1.0.
% 0.11/0.12  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33  % Computer : n015.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 : Mon Jun 13 14:53:08 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.35  
% 0.12/0.35   No.of.Axioms: 0
% 0.12/0.35  
% 0.12/0.35   Length.of.Defs: 0
% 0.12/0.35  
% 0.12/0.35   Contains.Choice.Funs: false
% 0.12/0.36  (rf:0,axioms:0,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2,loop_count:0,foatp_calls:0,translation:fof_full)....
% 0.20/0.56  
% 0.20/0.56  ********************************
% 0.20/0.56  *   All subproblems solved!    *
% 0.20/0.56  ********************************
% 0.20/0.56  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:8,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:66,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.20/0.56  
% 0.20/0.56  %**** Beginning of derivation protocol ****
% 0.20/0.56  % SZS output start CNFRefutation
% See solution above
% 0.20/0.56  
% 0.20/0.56  %**** End of derivation protocol ****
% 0.20/0.56  %**** no. of clauses in derivation: 67 ****
% 0.20/0.56  %**** clause counter: 66 ****
% 0.20/0.56  
% 0.20/0.56  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:8,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:66,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------