TSTP Solution File: GRP012+5 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : GRP012+5 : 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 : n023.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 10:15:24 EDT 2022

% Result   : Theorem 0.70s 0.92s
% Output   : CNFRefutation 0.70s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   77 (  56 unt;   8 typ;   0 def)
%            Number of atoms       :  428 (  97 equ;   0 cnn)
%            Maximal formula atoms :   16 (   6 avg)
%            Number of connectives : 1041 ( 102   ~;  91   |;  54   &; 774   @)
%                                         (   0 <=>;  20  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   11 (   8 usr;   7 con; 0-3 aty)
%            Number of variables   :  306 (   0   ^ 301   !;   5   ?; 306   :)

% 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_SY43,type,
    sK2_SY43: $i ).

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

thf(tp_sK4_SY50,type,
    sK4_SY50: $i ).

thf(tp_sK5_SY52,type,
    sK5_SY52: $i ).

thf(tp_sK6_Z,type,
    sK6_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 ) )
     => ! [U: $i,V: $i,W: $i,X: $i] :
          ( ( ( product @ ( inverse @ U ) @ ( inverse @ V ) @ W )
            & ( product @ V @ U @ X ) )
         => ( product @ ( inverse @ W ) @ ( inverse @ X ) @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_distribution) ).

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 ) )
         => ! [U: $i,V: $i,W: $i,X: $i] :
              ( ( ( product @ ( inverse @ U ) @ ( inverse @ V ) @ W )
                & ( product @ V @ U @ X ) )
             => ( product @ ( inverse @ W ) @ ( inverse @ X ) @ E ) ) ) )
    = $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 ) )
         => ! [U: $i,V: $i,W: $i,X: $i] :
              ( ( ( product @ ( inverse @ U ) @ ( inverse @ V ) @ W )
                & ( product @ V @ U @ X ) )
             => ( product @ ( inverse @ W ) @ ( inverse @ X ) @ E ) ) ) )
    = $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,SY44: $i,SY45: $i,SY46: $i] :
          ( ( ( product @ ( inverse @ SY43 ) @ ( inverse @ SY44 ) @ SY45 )
            & ( product @ SY44 @ SY43 @ SY46 ) )
         => ( product @ ( inverse @ SY45 ) @ ( inverse @ SY46 ) @ sK1_E ) ) )
    = $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,SY44: $i,SY45: $i,SY46: $i] :
          ( ( ( product @ ( inverse @ SY43 ) @ ( inverse @ SY44 ) @ SY45 )
            & ( product @ SY44 @ SY43 @ SY46 ) )
         => ( product @ ( inverse @ SY45 ) @ ( inverse @ SY46 ) @ sK1_E ) ) )
    = $false ),
    inference(standard_cnf,[status(thm)],[4]) ).

thf(13,plain,
    ( ( ~ ! [SY43: $i,SY44: $i,SY45: $i,SY46: $i] :
            ( ( ( product @ ( inverse @ SY43 ) @ ( inverse @ SY44 ) @ SY45 )
              & ( product @ SY44 @ SY43 @ SY46 ) )
           => ( product @ ( inverse @ SY45 ) @ ( inverse @ SY46 ) @ sK1_E ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[12]) ).

thf(14,plain,
    ( ( ( product @ ( inverse @ sK2_SY43 ) @ ( inverse @ sK3_SY47 ) @ sK4_SY50 )
      & ( product @ sK3_SY47 @ sK2_SY43 @ sK5_SY52 )
      & ~ ( product @ ( inverse @ sK4_SY50 ) @ ( inverse @ sK5_SY52 ) @ sK1_E ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[13]) ).

thf(15,plain,
    ( ( ! [X: $i,Y: $i] : ( product @ X @ Y @ ( sK6_Z @ Y @ X ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5]) ).

thf(16,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(17,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(18,plain,
    ( ( ! [SY42: $i] : ( product @ ( inverse @ SY42 ) @ SY42 @ sK1_E ) )
    = $true ),
    inference(copy,[status(thm)],[11]) ).

thf(19,plain,
    ( ( ! [SY41: $i] : ( product @ SY41 @ ( inverse @ SY41 ) @ sK1_E ) )
    = $true ),
    inference(copy,[status(thm)],[10]) ).

thf(20,plain,
    ( ( ! [SY40: $i] : ( product @ sK1_E @ SY40 @ SY40 ) )
    = $true ),
    inference(copy,[status(thm)],[9]) ).

thf(21,plain,
    ( ( ! [SY39: $i] : ( product @ SY39 @ sK1_E @ SY39 ) )
    = $true ),
    inference(copy,[status(thm)],[8]) ).

thf(22,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)],[17]) ).

thf(23,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)],[16]) ).

thf(24,plain,
    ( ( ! [X: $i,Y: $i] : ( product @ X @ Y @ ( sK6_Z @ Y @ X ) ) )
    = $true ),
    inference(copy,[status(thm)],[15]) ).

thf(25,plain,
    ( ( ( product @ ( inverse @ sK2_SY43 ) @ ( inverse @ sK3_SY47 ) @ sK4_SY50 )
      & ( product @ sK3_SY47 @ sK2_SY43 @ sK5_SY52 )
      & ~ ( product @ ( inverse @ sK4_SY50 ) @ ( inverse @ sK5_SY52 ) @ sK1_E ) )
    = $true ),
    inference(copy,[status(thm)],[14]) ).

thf(26,plain,
    ( ( ~ ( ~ ~ ( ~ ( product @ ( inverse @ sK2_SY43 ) @ ( inverse @ sK3_SY47 ) @ sK4_SY50 )
                | ~ ( product @ sK3_SY47 @ sK2_SY43 @ sK5_SY52 ) )
          | ~ ~ ( product @ ( inverse @ sK4_SY50 ) @ ( inverse @ sK5_SY52 ) @ sK1_E ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[25]) ).

thf(27,plain,
    ! [SV1: $i] :
      ( ( product @ ( inverse @ SV1 ) @ SV1 @ sK1_E )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[18]) ).

thf(28,plain,
    ! [SV2: $i] :
      ( ( product @ SV2 @ ( inverse @ SV2 ) @ sK1_E )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[19]) ).

thf(29,plain,
    ! [SV3: $i] :
      ( ( product @ sK1_E @ SV3 @ SV3 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[20]) ).

thf(30,plain,
    ! [SV4: $i] :
      ( ( product @ SV4 @ sK1_E @ SV4 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[21]) ).

thf(31,plain,
    ! [SV5: $i] :
      ( ( ! [SY53: $i,SY54: $i,SY55: $i,SY56: $i,SY57: $i] :
            ( ~ ( product @ SV5 @ SY53 @ SY55 )
            | ~ ( product @ SY53 @ SY54 @ SY56 )
            | ~ ( product @ SV5 @ SY56 @ SY57 )
            | ( product @ SY55 @ SY54 @ SY57 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[22]) ).

thf(32,plain,
    ! [SV6: $i] :
      ( ( ! [SY58: $i,SY59: $i,SY60: $i,SY61: $i,SY62: $i] :
            ( ~ ( product @ SV6 @ SY58 @ SY60 )
            | ~ ( product @ SY58 @ SY59 @ SY61 )
            | ~ ( product @ SY60 @ SY59 @ SY62 )
            | ( product @ SV6 @ SY61 @ SY62 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[23]) ).

thf(33,plain,
    ! [SV7: $i] :
      ( ( ! [SY63: $i] : ( product @ SV7 @ SY63 @ ( sK6_Z @ SY63 @ SV7 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[24]) ).

thf(34,plain,
    ( ( ~ ~ ( ~ ( product @ ( inverse @ sK2_SY43 ) @ ( inverse @ sK3_SY47 ) @ sK4_SY50 )
            | ~ ( product @ sK3_SY47 @ sK2_SY43 @ sK5_SY52 ) )
      | ~ ~ ( product @ ( inverse @ sK4_SY50 ) @ ( inverse @ sK5_SY52 ) @ sK1_E ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[26]) ).

thf(35,plain,
    ! [SV8: $i,SV5: $i] :
      ( ( ! [SY64: $i,SY65: $i,SY66: $i,SY67: $i] :
            ( ~ ( product @ SV5 @ SV8 @ SY65 )
            | ~ ( product @ SV8 @ SY64 @ SY66 )
            | ~ ( product @ SV5 @ SY66 @ SY67 )
            | ( product @ SY65 @ SY64 @ SY67 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[31]) ).

thf(36,plain,
    ! [SV9: $i,SV6: $i] :
      ( ( ! [SY68: $i,SY69: $i,SY70: $i,SY71: $i] :
            ( ~ ( product @ SV6 @ SV9 @ SY69 )
            | ~ ( product @ SV9 @ SY68 @ SY70 )
            | ~ ( product @ SY69 @ SY68 @ SY71 )
            | ( product @ SV6 @ SY70 @ SY71 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[32]) ).

thf(37,plain,
    ! [SV10: $i,SV7: $i] :
      ( ( product @ SV7 @ SV10 @ ( sK6_Z @ SV10 @ SV7 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[33]) ).

thf(38,plain,
    ( ( ~ ~ ( ~ ( product @ ( inverse @ sK2_SY43 ) @ ( inverse @ sK3_SY47 ) @ sK4_SY50 )
            | ~ ( product @ sK3_SY47 @ sK2_SY43 @ sK5_SY52 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[34]) ).

thf(39,plain,
    ( ( ~ ~ ( product @ ( inverse @ sK4_SY50 ) @ ( inverse @ sK5_SY52 ) @ sK1_E ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[34]) ).

thf(40,plain,
    ! [SV11: $i,SV8: $i,SV5: $i] :
      ( ( ! [SY72: $i,SY73: $i,SY74: $i] :
            ( ~ ( product @ SV5 @ SV8 @ SY72 )
            | ~ ( product @ SV8 @ SV11 @ SY73 )
            | ~ ( product @ SV5 @ SY73 @ SY74 )
            | ( product @ SY72 @ SV11 @ SY74 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[35]) ).

thf(41,plain,
    ! [SV12: $i,SV9: $i,SV6: $i] :
      ( ( ! [SY75: $i,SY76: $i,SY77: $i] :
            ( ~ ( product @ SV6 @ SV9 @ SY75 )
            | ~ ( product @ SV9 @ SV12 @ SY76 )
            | ~ ( product @ SY75 @ SV12 @ SY77 )
            | ( product @ SV6 @ SY76 @ SY77 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[36]) ).

thf(42,plain,
    ( ( ~ ( ~ ( product @ ( inverse @ sK2_SY43 ) @ ( inverse @ sK3_SY47 ) @ sK4_SY50 )
          | ~ ( product @ sK3_SY47 @ sK2_SY43 @ sK5_SY52 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[38]) ).

thf(43,plain,
    ( ( ~ ( product @ ( inverse @ sK4_SY50 ) @ ( inverse @ sK5_SY52 ) @ sK1_E ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[39]) ).

thf(44,plain,
    ! [SV11: $i,SV13: $i,SV8: $i,SV5: $i] :
      ( ( ! [SY78: $i,SY79: $i] :
            ( ~ ( product @ SV5 @ SV8 @ SV13 )
            | ~ ( product @ SV8 @ SV11 @ SY78 )
            | ~ ( product @ SV5 @ SY78 @ SY79 )
            | ( product @ SV13 @ SV11 @ SY79 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[40]) ).

thf(45,plain,
    ! [SV12: $i,SV14: $i,SV9: $i,SV6: $i] :
      ( ( ! [SY80: $i,SY81: $i] :
            ( ~ ( product @ SV6 @ SV9 @ SV14 )
            | ~ ( product @ SV9 @ SV12 @ SY80 )
            | ~ ( product @ SV14 @ SV12 @ SY81 )
            | ( product @ SV6 @ SY80 @ SY81 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[41]) ).

thf(46,plain,
    ( ( ~ ( product @ ( inverse @ sK2_SY43 ) @ ( inverse @ sK3_SY47 ) @ sK4_SY50 )
      | ~ ( product @ sK3_SY47 @ sK2_SY43 @ sK5_SY52 ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[42]) ).

thf(47,plain,
    ( ( product @ ( inverse @ sK4_SY50 ) @ ( inverse @ sK5_SY52 ) @ sK1_E )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[43]) ).

thf(48,plain,
    ! [SV15: $i,SV11: $i,SV13: $i,SV8: $i,SV5: $i] :
      ( ( ! [SY82: $i] :
            ( ~ ( product @ SV5 @ SV8 @ SV13 )
            | ~ ( product @ SV8 @ SV11 @ SV15 )
            | ~ ( product @ SV5 @ SV15 @ SY82 )
            | ( product @ SV13 @ SV11 @ SY82 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[44]) ).

thf(49,plain,
    ! [SV16: $i,SV12: $i,SV14: $i,SV9: $i,SV6: $i] :
      ( ( ! [SY83: $i] :
            ( ~ ( product @ SV6 @ SV9 @ SV14 )
            | ~ ( product @ SV9 @ SV12 @ SV16 )
            | ~ ( product @ SV14 @ SV12 @ SY83 )
            | ( product @ SV6 @ SV16 @ SY83 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[45]) ).

thf(50,plain,
    ( ( ~ ( product @ ( inverse @ sK2_SY43 ) @ ( inverse @ sK3_SY47 ) @ sK4_SY50 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[46]) ).

thf(51,plain,
    ( ( ~ ( product @ sK3_SY47 @ sK2_SY43 @ sK5_SY52 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[46]) ).

thf(52,plain,
    ! [SV17: $i,SV15: $i,SV11: $i,SV13: $i,SV8: $i,SV5: $i] :
      ( ( ~ ( product @ SV5 @ SV8 @ SV13 )
        | ~ ( product @ SV8 @ SV11 @ SV15 )
        | ~ ( product @ SV5 @ SV15 @ SV17 )
        | ( product @ SV13 @ SV11 @ SV17 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[48]) ).

thf(53,plain,
    ! [SV18: $i,SV16: $i,SV12: $i,SV14: $i,SV9: $i,SV6: $i] :
      ( ( ~ ( product @ SV6 @ SV9 @ SV14 )
        | ~ ( product @ SV9 @ SV12 @ SV16 )
        | ~ ( product @ SV14 @ SV12 @ SV18 )
        | ( product @ SV6 @ SV16 @ SV18 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[49]) ).

thf(54,plain,
    ( ( product @ ( inverse @ sK2_SY43 ) @ ( inverse @ sK3_SY47 ) @ sK4_SY50 )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[50]) ).

thf(55,plain,
    ( ( product @ sK3_SY47 @ sK2_SY43 @ sK5_SY52 )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[51]) ).

thf(56,plain,
    ! [SV17: $i,SV15: $i,SV11: $i,SV13: $i,SV8: $i,SV5: $i] :
      ( ( ( ~ ( product @ SV5 @ SV8 @ SV13 )
          | ~ ( product @ SV8 @ SV11 @ SV15 )
          | ~ ( product @ SV5 @ SV15 @ SV17 ) )
        = $true )
      | ( ( product @ SV13 @ SV11 @ SV17 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[52]) ).

thf(57,plain,
    ! [SV18: $i,SV16: $i,SV12: $i,SV14: $i,SV9: $i,SV6: $i] :
      ( ( ( ~ ( product @ SV6 @ SV9 @ SV14 )
          | ~ ( product @ SV9 @ SV12 @ SV16 )
          | ~ ( product @ SV14 @ SV12 @ SV18 ) )
        = $true )
      | ( ( product @ SV6 @ SV16 @ SV18 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[53]) ).

thf(58,plain,
    ! [SV17: $i,SV15: $i,SV11: $i,SV13: $i,SV8: $i,SV5: $i] :
      ( ( ( ~ ( product @ SV5 @ SV8 @ SV13 )
          | ~ ( product @ SV8 @ SV11 @ SV15 ) )
        = $true )
      | ( ( ~ ( product @ SV5 @ SV15 @ SV17 ) )
        = $true )
      | ( ( product @ SV13 @ SV11 @ SV17 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[56]) ).

thf(59,plain,
    ! [SV18: $i,SV16: $i,SV12: $i,SV14: $i,SV9: $i,SV6: $i] :
      ( ( ( ~ ( product @ SV6 @ SV9 @ SV14 )
          | ~ ( product @ SV9 @ SV12 @ SV16 ) )
        = $true )
      | ( ( ~ ( product @ SV14 @ SV12 @ SV18 ) )
        = $true )
      | ( ( product @ SV6 @ SV16 @ SV18 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[57]) ).

thf(60,plain,
    ! [SV17: $i,SV15: $i,SV11: $i,SV13: $i,SV8: $i,SV5: $i] :
      ( ( ( ~ ( product @ SV5 @ SV8 @ SV13 ) )
        = $true )
      | ( ( ~ ( product @ SV8 @ SV11 @ SV15 ) )
        = $true )
      | ( ( ~ ( product @ SV5 @ SV15 @ SV17 ) )
        = $true )
      | ( ( product @ SV13 @ SV11 @ SV17 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[58]) ).

thf(61,plain,
    ! [SV18: $i,SV16: $i,SV12: $i,SV14: $i,SV9: $i,SV6: $i] :
      ( ( ( ~ ( product @ SV6 @ SV9 @ SV14 ) )
        = $true )
      | ( ( ~ ( product @ SV9 @ SV12 @ SV16 ) )
        = $true )
      | ( ( ~ ( product @ SV14 @ SV12 @ SV18 ) )
        = $true )
      | ( ( product @ SV6 @ SV16 @ SV18 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[59]) ).

thf(62,plain,
    ! [SV17: $i,SV15: $i,SV11: $i,SV13: $i,SV8: $i,SV5: $i] :
      ( ( ( product @ SV5 @ SV8 @ SV13 )
        = $false )
      | ( ( ~ ( product @ SV8 @ SV11 @ SV15 ) )
        = $true )
      | ( ( ~ ( product @ SV5 @ SV15 @ SV17 ) )
        = $true )
      | ( ( product @ SV13 @ SV11 @ SV17 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[60]) ).

thf(63,plain,
    ! [SV18: $i,SV16: $i,SV12: $i,SV14: $i,SV9: $i,SV6: $i] :
      ( ( ( product @ SV6 @ SV9 @ SV14 )
        = $false )
      | ( ( ~ ( product @ SV9 @ SV12 @ SV16 ) )
        = $true )
      | ( ( ~ ( product @ SV14 @ SV12 @ SV18 ) )
        = $true )
      | ( ( product @ SV6 @ SV16 @ SV18 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[61]) ).

thf(64,plain,
    ! [SV17: $i,SV13: $i,SV5: $i,SV15: $i,SV11: $i,SV8: $i] :
      ( ( ( product @ SV8 @ SV11 @ SV15 )
        = $false )
      | ( ( product @ SV5 @ SV8 @ SV13 )
        = $false )
      | ( ( ~ ( product @ SV5 @ SV15 @ SV17 ) )
        = $true )
      | ( ( product @ SV13 @ SV11 @ SV17 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[62]) ).

thf(65,plain,
    ! [SV18: $i,SV14: $i,SV6: $i,SV16: $i,SV12: $i,SV9: $i] :
      ( ( ( product @ SV9 @ SV12 @ SV16 )
        = $false )
      | ( ( product @ SV6 @ SV9 @ SV14 )
        = $false )
      | ( ( ~ ( product @ SV14 @ SV12 @ SV18 ) )
        = $true )
      | ( ( product @ SV6 @ SV16 @ SV18 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[63]) ).

thf(66,plain,
    ! [SV11: $i,SV13: $i,SV8: $i,SV17: $i,SV15: $i,SV5: $i] :
      ( ( ( product @ SV5 @ SV15 @ SV17 )
        = $false )
      | ( ( product @ SV5 @ SV8 @ SV13 )
        = $false )
      | ( ( product @ SV8 @ SV11 @ SV15 )
        = $false )
      | ( ( product @ SV13 @ SV11 @ SV17 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[64]) ).

thf(67,plain,
    ! [SV16: $i,SV9: $i,SV6: $i,SV18: $i,SV12: $i,SV14: $i] :
      ( ( ( product @ SV14 @ SV12 @ SV18 )
        = $false )
      | ( ( product @ SV6 @ SV9 @ SV14 )
        = $false )
      | ( ( product @ SV9 @ SV12 @ SV16 )
        = $false )
      | ( ( product @ SV6 @ SV16 @ SV18 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[65]) ).

thf(68,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[27,67,66,55,54,47,37,30,29,28]) ).

thf(69,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[68]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem  : GRP012+5 : TPTP v8.1.0. Released v3.1.0.
% 0.04/0.14  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.36  % Computer : n023.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 600
% 0.14/0.36  % DateTime : Tue Jun 14 14:07:35 EDT 2022
% 0.14/0.36  % CPUTime  : 
% 0.21/0.38  
% 0.21/0.38   No.of.Axioms: 0
% 0.21/0.38  
% 0.21/0.38   Length.of.Defs: 0
% 0.21/0.38  
% 0.21/0.38   Contains.Choice.Funs: false
% 0.21/0.39  (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)....
% 0.70/0.92  
% 0.70/0.92  ********************************
% 0.70/0.92  *   All subproblems solved!    *
% 0.70/0.92  ********************************
% 0.70/0.92  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:7,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:68,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.70/0.92  
% 0.70/0.92  %**** Beginning of derivation protocol ****
% 0.70/0.92  % SZS output start CNFRefutation
% See solution above
% 0.70/0.92  
% 0.70/0.92  %**** End of derivation protocol ****
% 0.70/0.92  %**** no. of clauses in derivation: 69 ****
% 0.70/0.92  %**** clause counter: 68 ****
% 0.70/0.92  
% 0.70/0.92  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:7,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:68,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------