TSTP Solution File: GRP775+1 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : GRP775+1 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n014.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 10:19:57 EDT 2022

% Result   : Theorem 236.33s 236.72s
% Output   : CNFRefutation 236.33s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :   13
% Syntax   : Number of formulae    :  238 ( 153 unt;   7 typ;   0 def)
%            Number of atoms       : 1328 ( 613 equ;   0 cnn)
%            Maximal formula atoms :    4 (   5 avg)
%            Number of connectives : 2487 ( 448   ~; 369   |;  39   &;1616   @)
%                                         (  11 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   10 (  10   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :  533 (   0   ^ 531   !;   2   ?; 533   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_d,type,
    d: $i > $i > $o ).

thf(tp_l,type,
    l: $i > $i > $o ).

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

thf(tp_r,type,
    r: $i > $i > $o ).

thf(tp_sK1_X7,type,
    sK1_X7: $i ).

thf(tp_sK2_SY81,type,
    sK2_SY81: $i ).

thf(tp_sK3_X6,type,
    sK3_X6: $i > $i > $i ).

thf(1,axiom,
    ! [X4: $i,X5: $i] :
      ( ( d @ X4 @ X5 )
    <=> ? [X6: $i] :
          ( ( r @ X4 @ X6 )
          & ( l @ X6 @ X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos05) ).

thf(2,axiom,
    ! [X2: $i,X3: $i] :
      ( ( r @ X2 @ X3 )
    <=> ( ( ( product @ X2 @ X3 )
          = X3 )
        & ( ( product @ X3 @ X2 )
          = X2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos04) ).

thf(3,axiom,
    ! [X0: $i,X1: $i] :
      ( ( l @ X0 @ X1 )
    <=> ( ( ( product @ X0 @ X1 )
          = X0 )
        & ( ( product @ X1 @ X0 )
          = X1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos03) ).

thf(4,axiom,
    ! [A: $i] :
      ( ( product @ A @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos02) ).

thf(5,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( product @ ( product @ A @ B ) @ C )
      = ( product @ A @ ( product @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos01) ).

thf(6,conjecture,
    ! [X7: $i,X8: $i] :
      ( ( d @ X7 @ X8 )
    <=> ( ( ( product @ X7 @ ( product @ X8 @ X7 ) )
          = X7 )
        & ( ( product @ X8 @ ( product @ X7 @ X8 ) )
          = X8 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).

thf(7,negated_conjecture,
    ( ( ! [X7: $i,X8: $i] :
          ( ( d @ X7 @ X8 )
        <=> ( ( ( product @ X7 @ ( product @ X8 @ X7 ) )
              = X7 )
            & ( ( product @ X8 @ ( product @ X7 @ X8 ) )
              = X8 ) ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[6]) ).

thf(8,plain,
    ( ( ! [X7: $i,X8: $i] :
          ( ( d @ X7 @ X8 )
        <=> ( ( ( product @ X7 @ ( product @ X8 @ X7 ) )
              = X7 )
            & ( ( product @ X8 @ ( product @ X7 @ X8 ) )
              = X8 ) ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[7]) ).

thf(9,plain,
    ( ( ! [X4: $i,X5: $i] :
          ( ( d @ X4 @ X5 )
        <=> ? [X6: $i] :
              ( ( r @ X4 @ X6 )
              & ( l @ X6 @ X5 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(10,plain,
    ( ( ! [X2: $i,X3: $i] :
          ( ( r @ X2 @ X3 )
        <=> ( ( ( product @ X2 @ X3 )
              = X3 )
            & ( ( product @ X3 @ X2 )
              = X2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(11,plain,
    ( ( ! [X0: $i,X1: $i] :
          ( ( l @ X0 @ X1 )
        <=> ( ( ( product @ X0 @ X1 )
              = X0 )
            & ( ( product @ X1 @ X0 )
              = X1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3]) ).

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

thf(13,plain,
    ( ( ! [C: $i,B: $i,A: $i] :
          ( ( product @ ( product @ A @ B ) @ C )
          = ( product @ A @ ( product @ B @ C ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5]) ).

thf(14,plain,
    ( ( ! [SY81: $i] :
          ( ( d @ sK1_X7 @ SY81 )
        <=> ( ( ( product @ sK1_X7 @ ( product @ SY81 @ sK1_X7 ) )
              = sK1_X7 )
            & ( ( product @ SY81 @ ( product @ sK1_X7 @ SY81 ) )
              = SY81 ) ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[8]) ).

thf(15,plain,
    ( ( ( d @ sK1_X7 @ sK2_SY81 )
    <=> ( ( ( product @ sK1_X7 @ ( product @ sK2_SY81 @ sK1_X7 ) )
          = sK1_X7 )
        & ( ( product @ sK2_SY81 @ ( product @ sK1_X7 @ sK2_SY81 ) )
          = sK2_SY81 ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[14]) ).

thf(16,plain,
    ( ( ( d @ sK1_X7 @ sK2_SY81 )
     => ( ( ( product @ sK1_X7 @ ( product @ sK2_SY81 @ sK1_X7 ) )
          = sK1_X7 )
        & ( ( product @ sK2_SY81 @ ( product @ sK1_X7 @ sK2_SY81 ) )
          = sK2_SY81 ) ) )
    = $false ),
    inference(split_conjecture,[split_conjecture(split,[])],[15]) ).

thf(17,plain,
    ( ( ( ( ( product @ sK1_X7 @ ( product @ sK2_SY81 @ sK1_X7 ) )
          = sK1_X7 )
        & ( ( product @ sK2_SY81 @ ( product @ sK1_X7 @ sK2_SY81 ) )
          = sK2_SY81 ) )
     => ( d @ sK1_X7 @ sK2_SY81 ) )
    = $false ),
    inference(split_conjecture,[split_conjecture(split,[])],[15]) ).

thf(18,plain,
    ( ( ~ ( ( d @ sK1_X7 @ sK2_SY81 )
         => ( ( ( product @ sK1_X7 @ ( product @ sK2_SY81 @ sK1_X7 ) )
              = sK1_X7 )
            & ( ( product @ sK2_SY81 @ ( product @ sK1_X7 @ sK2_SY81 ) )
              = sK2_SY81 ) ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[16]) ).

thf(19,plain,
    ( ( ~ ( ( ( ( product @ sK1_X7 @ ( product @ sK2_SY81 @ sK1_X7 ) )
              = sK1_X7 )
            & ( ( product @ sK2_SY81 @ ( product @ sK1_X7 @ sK2_SY81 ) )
              = sK2_SY81 ) )
         => ( d @ sK1_X7 @ sK2_SY81 ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[17]) ).

thf(20,plain,
    ( ( ( d @ sK1_X7 @ sK2_SY81 )
      & ( ( ( product @ sK1_X7 @ ( product @ sK2_SY81 @ sK1_X7 ) )
         != sK1_X7 )
        | ( ( product @ sK2_SY81 @ ( product @ sK1_X7 @ sK2_SY81 ) )
         != sK2_SY81 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[18]) ).

thf(21,plain,
    ( ( ( ( product @ sK1_X7 @ ( product @ sK2_SY81 @ sK1_X7 ) )
        = sK1_X7 )
      & ( ( product @ sK2_SY81 @ ( product @ sK1_X7 @ sK2_SY81 ) )
        = sK2_SY81 )
      & ~ ( d @ sK1_X7 @ sK2_SY81 ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[19]) ).

thf(22,plain,
    ( ( ! [X4: $i,X5: $i] :
          ( ! [X6: $i] :
              ( ~ ( l @ X6 @ X5 )
              | ~ ( r @ X4 @ X6 ) )
          | ( d @ X4 @ X5 ) )
      & ! [X4: $i,X5: $i] :
          ( ~ ( d @ X4 @ X5 )
          | ( ( l @ ( sK3_X6 @ X5 @ X4 ) @ X5 )
            & ( r @ X4 @ ( sK3_X6 @ X5 @ X4 ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[9]) ).

thf(23,plain,
    ( ( ! [X2: $i,X3: $i] :
          ( ( ( product @ X2 @ X3 )
           != X3 )
          | ( ( product @ X3 @ X2 )
           != X2 )
          | ( r @ X2 @ X3 ) )
      & ! [X2: $i,X3: $i] :
          ( ~ ( r @ X2 @ X3 )
          | ( ( product @ X2 @ X3 )
            = X3 ) )
      & ! [X2: $i,X3: $i] :
          ( ~ ( r @ X2 @ X3 )
          | ( ( product @ X3 @ X2 )
            = X2 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[10]) ).

thf(24,plain,
    ( ( ! [X0: $i,X1: $i] :
          ( ( ( product @ X0 @ X1 )
           != X0 )
          | ( ( product @ X1 @ X0 )
           != X1 )
          | ( l @ X0 @ X1 ) )
      & ! [X0: $i,X1: $i] :
          ( ~ ( l @ X0 @ X1 )
          | ( ( product @ X0 @ X1 )
            = X0 ) )
      & ! [X0: $i,X1: $i] :
          ( ~ ( l @ X0 @ X1 )
          | ( ( product @ X1 @ X0 )
            = X1 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[11]) ).

thf(25,plain,
    ( ( ! [C: $i,B: $i,A: $i] :
          ( ( product @ ( product @ A @ B ) @ C )
          = ( product @ A @ ( product @ B @ C ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[13]) ).

thf(26,plain,
    ( ( ! [A: $i] :
          ( ( product @ A @ A )
          = A ) )
    = $true ),
    inference(copy,[status(thm)],[12]) ).

thf(27,plain,
    ( ( ! [X0: $i,X1: $i] :
          ( ( ( product @ X0 @ X1 )
           != X0 )
          | ( ( product @ X1 @ X0 )
           != X1 )
          | ( l @ X0 @ X1 ) )
      & ! [X0: $i,X1: $i] :
          ( ~ ( l @ X0 @ X1 )
          | ( ( product @ X0 @ X1 )
            = X0 ) )
      & ! [X0: $i,X1: $i] :
          ( ~ ( l @ X0 @ X1 )
          | ( ( product @ X1 @ X0 )
            = X1 ) ) )
    = $true ),
    inference(copy,[status(thm)],[24]) ).

thf(28,plain,
    ( ( ! [X2: $i,X3: $i] :
          ( ( ( product @ X2 @ X3 )
           != X3 )
          | ( ( product @ X3 @ X2 )
           != X2 )
          | ( r @ X2 @ X3 ) )
      & ! [X2: $i,X3: $i] :
          ( ~ ( r @ X2 @ X3 )
          | ( ( product @ X2 @ X3 )
            = X3 ) )
      & ! [X2: $i,X3: $i] :
          ( ~ ( r @ X2 @ X3 )
          | ( ( product @ X3 @ X2 )
            = X2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[23]) ).

thf(29,plain,
    ( ( ! [X4: $i,X5: $i] :
          ( ! [X6: $i] :
              ( ~ ( l @ X6 @ X5 )
              | ~ ( r @ X4 @ X6 ) )
          | ( d @ X4 @ X5 ) )
      & ! [X4: $i,X5: $i] :
          ( ~ ( d @ X4 @ X5 )
          | ( ( l @ ( sK3_X6 @ X5 @ X4 ) @ X5 )
            & ( r @ X4 @ ( sK3_X6 @ X5 @ X4 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[22]) ).

thf(30,plain,
    ( ( ( d @ sK1_X7 @ sK2_SY81 )
      & ( ( ( product @ sK1_X7 @ ( product @ sK2_SY81 @ sK1_X7 ) )
         != sK1_X7 )
        | ( ( product @ sK2_SY81 @ ( product @ sK1_X7 @ sK2_SY81 ) )
         != sK2_SY81 ) ) )
    = $true ),
    inference(copy,[status(thm)],[20]) ).

thf(31,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ! [SX2: $i] :
                    ( ~ ( l @ SX2 @ SX1 )
                    | ~ ( r @ SX0 @ SX2 ) )
                | ( d @ SX0 @ SX1 ) )
          | ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( d @ SX0 @ SX1 )
                | ~ ( ~ ( l @ ( sK3_X6 @ SX1 @ SX0 ) @ SX1 )
                    | ~ ( r @ SX0 @ ( sK3_X6 @ SX1 @ SX0 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[29]) ).

thf(32,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ( ( product @ SX0 @ SX1 )
                 != SX0 )
                | ( ( product @ SX1 @ SX0 )
                 != SX1 )
                | ( l @ SX0 @ SX1 ) )
          | ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
                      ( ~ ( l @ SX0 @ SX1 )
                      | ( ( product @ SX0 @ SX1 )
                        = SX0 ) )
                | ~ ! [SX0: $i,SX1: $i] :
                      ( ~ ( l @ SX0 @ SX1 )
                      | ( ( product @ SX1 @ SX0 )
                        = SX1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[27]) ).

thf(33,plain,
    ( ( ~ ( ~ ( d @ sK1_X7 @ sK2_SY81 )
          | ~ ( ( ( product @ sK1_X7 @ ( product @ sK2_SY81 @ sK1_X7 ) )
               != sK1_X7 )
              | ( ( product @ sK2_SY81 @ ( product @ sK1_X7 @ sK2_SY81 ) )
               != sK2_SY81 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[30]) ).

thf(34,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ( ( product @ SX0 @ SX1 )
                 != SX1 )
                | ( ( product @ SX1 @ SX0 )
                 != SX0 )
                | ( r @ SX0 @ SX1 ) )
          | ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
                      ( ~ ( r @ SX0 @ SX1 )
                      | ( ( product @ SX0 @ SX1 )
                        = SX1 ) )
                | ~ ! [SX0: $i,SX1: $i] :
                      ( ~ ( r @ SX0 @ SX1 )
                      | ( ( product @ SX1 @ SX0 )
                        = SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[28]) ).

thf(35,plain,
    ! [SV1: $i] :
      ( ( ! [SY82: $i,SY83: $i] :
            ( ( product @ ( product @ SY83 @ SY82 ) @ SV1 )
            = ( product @ SY83 @ ( product @ SY82 @ SV1 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[25]) ).

thf(36,plain,
    ! [SV2: $i] :
      ( ( ( product @ SV2 @ SV2 )
        = SV2 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[26]) ).

thf(37,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ! [SX2: $i] :
                ( ~ ( l @ SX2 @ SX1 )
                | ~ ( r @ SX0 @ SX2 ) )
            | ( d @ SX0 @ SX1 ) )
      | ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( d @ SX0 @ SX1 )
            | ~ ( ~ ( l @ ( sK3_X6 @ SX1 @ SX0 ) @ SX1 )
                | ~ ( r @ SX0 @ ( sK3_X6 @ SX1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[31]) ).

thf(38,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ( ( product @ SX0 @ SX1 )
             != SX0 )
            | ( ( product @ SX1 @ SX0 )
             != SX1 )
            | ( l @ SX0 @ SX1 ) )
      | ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
                  ( ~ ( l @ SX0 @ SX1 )
                  | ( ( product @ SX0 @ SX1 )
                    = SX0 ) )
            | ~ ! [SX0: $i,SX1: $i] :
                  ( ~ ( l @ SX0 @ SX1 )
                  | ( ( product @ SX1 @ SX0 )
                    = SX1 ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[32]) ).

thf(39,plain,
    ( ( ~ ( d @ sK1_X7 @ sK2_SY81 )
      | ~ ( ( ( product @ sK1_X7 @ ( product @ sK2_SY81 @ sK1_X7 ) )
           != sK1_X7 )
          | ( ( product @ sK2_SY81 @ ( product @ sK1_X7 @ sK2_SY81 ) )
           != sK2_SY81 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[33]) ).

thf(40,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ( ( product @ SX0 @ SX1 )
             != SX1 )
            | ( ( product @ SX1 @ SX0 )
             != SX0 )
            | ( r @ SX0 @ SX1 ) )
      | ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
                  ( ~ ( r @ SX0 @ SX1 )
                  | ( ( product @ SX0 @ SX1 )
                    = SX1 ) )
            | ~ ! [SX0: $i,SX1: $i] :
                  ( ~ ( r @ SX0 @ SX1 )
                  | ( ( product @ SX1 @ SX0 )
                    = SX0 ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[34]) ).

thf(41,plain,
    ! [SV1: $i,SV3: $i] :
      ( ( ! [SY84: $i] :
            ( ( product @ ( product @ SY84 @ SV3 ) @ SV1 )
            = ( product @ SY84 @ ( product @ SV3 @ SV1 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[35]) ).

thf(42,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ! [SX2: $i] :
                ( ~ ( l @ SX2 @ SX1 )
                | ~ ( r @ SX0 @ SX2 ) )
            | ( d @ SX0 @ SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[37]) ).

thf(43,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( d @ SX0 @ SX1 )
            | ~ ( ~ ( l @ ( sK3_X6 @ SX1 @ SX0 ) @ SX1 )
                | ~ ( r @ SX0 @ ( sK3_X6 @ SX1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[37]) ).

thf(44,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ( ( product @ SX0 @ SX1 )
             != SX0 )
            | ( ( product @ SX1 @ SX0 )
             != SX1 )
            | ( l @ SX0 @ SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[38]) ).

thf(45,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
                  ( ~ ( l @ SX0 @ SX1 )
                  | ( ( product @ SX0 @ SX1 )
                    = SX0 ) )
            | ~ ! [SX0: $i,SX1: $i] :
                  ( ~ ( l @ SX0 @ SX1 )
                  | ( ( product @ SX1 @ SX0 )
                    = SX1 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[38]) ).

thf(46,plain,
    ( ( ~ ( d @ sK1_X7 @ sK2_SY81 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[39]) ).

thf(47,plain,
    ( ( ~ ( ( ( product @ sK1_X7 @ ( product @ sK2_SY81 @ sK1_X7 ) )
           != sK1_X7 )
          | ( ( product @ sK2_SY81 @ ( product @ sK1_X7 @ sK2_SY81 ) )
           != sK2_SY81 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[39]) ).

thf(48,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ( ( product @ SX0 @ SX1 )
             != SX1 )
            | ( ( product @ SX1 @ SX0 )
             != SX0 )
            | ( r @ SX0 @ SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[40]) ).

thf(49,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
                  ( ~ ( r @ SX0 @ SX1 )
                  | ( ( product @ SX0 @ SX1 )
                    = SX1 ) )
            | ~ ! [SX0: $i,SX1: $i] :
                  ( ~ ( r @ SX0 @ SX1 )
                  | ( ( product @ SX1 @ SX0 )
                    = SX0 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[40]) ).

thf(50,plain,
    ! [SV1: $i,SV3: $i,SV4: $i] :
      ( ( ( product @ ( product @ SV4 @ SV3 ) @ SV1 )
        = ( product @ SV4 @ ( product @ SV3 @ SV1 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[41]) ).

thf(51,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ! [SX2: $i] :
              ( ~ ( l @ SX2 @ SX1 )
              | ~ ( r @ SX0 @ SX2 ) )
          | ( d @ SX0 @ SX1 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[42]) ).

thf(52,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( d @ SX0 @ SX1 )
          | ~ ( ~ ( l @ ( sK3_X6 @ SX1 @ SX0 ) @ SX1 )
              | ~ ( r @ SX0 @ ( sK3_X6 @ SX1 @ SX0 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[43]) ).

thf(53,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( ( product @ SX0 @ SX1 )
           != SX0 )
          | ( ( product @ SX1 @ SX0 )
           != SX1 )
          | ( l @ SX0 @ SX1 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[44]) ).

thf(54,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( l @ SX0 @ SX1 )
                | ( ( product @ SX0 @ SX1 )
                  = SX0 ) )
          | ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( l @ SX0 @ SX1 )
                | ( ( product @ SX1 @ SX0 )
                  = SX1 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[45]) ).

thf(55,plain,
    ( ( d @ sK1_X7 @ sK2_SY81 )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[46]) ).

thf(56,plain,
    ( ( ( ( product @ sK1_X7 @ ( product @ sK2_SY81 @ sK1_X7 ) )
       != sK1_X7 )
      | ( ( product @ sK2_SY81 @ ( product @ sK1_X7 @ sK2_SY81 ) )
       != sK2_SY81 ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[47]) ).

thf(57,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( ( product @ SX0 @ SX1 )
           != SX1 )
          | ( ( product @ SX1 @ SX0 )
           != SX0 )
          | ( r @ SX0 @ SX1 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[48]) ).

thf(58,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( r @ SX0 @ SX1 )
                | ( ( product @ SX0 @ SX1 )
                  = SX1 ) )
          | ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( r @ SX0 @ SX1 )
                | ( ( product @ SX1 @ SX0 )
                  = SX0 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[49]) ).

thf(59,plain,
    ! [SV5: $i] :
      ( ( ! [SY85: $i] :
            ( ! [SY86: $i] :
                ( ~ ( l @ SY86 @ SY85 )
                | ~ ( r @ SV5 @ SY86 ) )
            | ( d @ SV5 @ SY85 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[51]) ).

thf(60,plain,
    ! [SV6: $i] :
      ( ( ! [SY87: $i] :
            ( ~ ( d @ SV6 @ SY87 )
            | ~ ( ~ ( l @ ( sK3_X6 @ SY87 @ SV6 ) @ SY87 )
                | ~ ( r @ SV6 @ ( sK3_X6 @ SY87 @ SV6 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[52]) ).

thf(61,plain,
    ! [SV7: $i] :
      ( ( ! [SY88: $i] :
            ( ( ( product @ SV7 @ SY88 )
             != SV7 )
            | ( ( product @ SY88 @ SV7 )
             != SY88 )
            | ( l @ SV7 @ SY88 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[53]) ).

thf(62,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( l @ SX0 @ SX1 )
            | ( ( product @ SX0 @ SX1 )
              = SX0 ) )
      | ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( l @ SX0 @ SX1 )
            | ( ( product @ SX1 @ SX0 )
              = SX1 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[54]) ).

thf(63,plain,
    ( ( ( ( ( product @ sK1_X7 @ ( product @ sK2_SY81 @ sK1_X7 ) )
         != sK1_X7 ) )
      = $true )
    | ( ( ( ( product @ sK2_SY81 @ ( product @ sK1_X7 @ sK2_SY81 ) )
         != sK2_SY81 ) )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[56]) ).

thf(64,plain,
    ! [SV8: $i] :
      ( ( ! [SY89: $i] :
            ( ( ( product @ SV8 @ SY89 )
             != SY89 )
            | ( ( product @ SY89 @ SV8 )
             != SV8 )
            | ( r @ SV8 @ SY89 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[57]) ).

thf(65,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( r @ SX0 @ SX1 )
            | ( ( product @ SX0 @ SX1 )
              = SX1 ) )
      | ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( r @ SX0 @ SX1 )
            | ( ( product @ SX1 @ SX0 )
              = SX0 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[58]) ).

thf(66,plain,
    ! [SV5: $i,SV9: $i] :
      ( ( ! [SY90: $i] :
            ( ~ ( l @ SY90 @ SV9 )
            | ~ ( r @ SV5 @ SY90 ) )
        | ( d @ SV5 @ SV9 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[59]) ).

thf(67,plain,
    ! [SV10: $i,SV6: $i] :
      ( ( ~ ( d @ SV6 @ SV10 )
        | ~ ( ~ ( l @ ( sK3_X6 @ SV10 @ SV6 ) @ SV10 )
            | ~ ( r @ SV6 @ ( sK3_X6 @ SV10 @ SV6 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[60]) ).

thf(68,plain,
    ! [SV11: $i,SV7: $i] :
      ( ( ( ( product @ SV7 @ SV11 )
         != SV7 )
        | ( ( product @ SV11 @ SV7 )
         != SV11 )
        | ( l @ SV7 @ SV11 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[61]) ).

thf(69,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( l @ SX0 @ SX1 )
            | ( ( product @ SX0 @ SX1 )
              = SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[62]) ).

thf(70,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( l @ SX0 @ SX1 )
            | ( ( product @ SX1 @ SX0 )
              = SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[62]) ).

thf(71,plain,
    ( ( ( ( product @ sK1_X7 @ ( product @ sK2_SY81 @ sK1_X7 ) )
        = sK1_X7 )
      = $false )
    | ( ( ( ( product @ sK2_SY81 @ ( product @ sK1_X7 @ sK2_SY81 ) )
         != sK2_SY81 ) )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[63]) ).

thf(72,plain,
    ! [SV12: $i,SV8: $i] :
      ( ( ( ( product @ SV8 @ SV12 )
         != SV12 )
        | ( ( product @ SV12 @ SV8 )
         != SV8 )
        | ( r @ SV8 @ SV12 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[64]) ).

thf(73,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( r @ SX0 @ SX1 )
            | ( ( product @ SX0 @ SX1 )
              = SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[65]) ).

thf(74,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( r @ SX0 @ SX1 )
            | ( ( product @ SX1 @ SX0 )
              = SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[65]) ).

thf(75,plain,
    ! [SV5: $i,SV9: $i] :
      ( ( ( ! [SY90: $i] :
              ( ~ ( l @ SY90 @ SV9 )
              | ~ ( r @ SV5 @ SY90 ) ) )
        = $true )
      | ( ( d @ SV5 @ SV9 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[66]) ).

thf(76,plain,
    ! [SV10: $i,SV6: $i] :
      ( ( ( ~ ( d @ SV6 @ SV10 ) )
        = $true )
      | ( ( ~ ( ~ ( l @ ( sK3_X6 @ SV10 @ SV6 ) @ SV10 )
              | ~ ( r @ SV6 @ ( sK3_X6 @ SV10 @ SV6 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[67]) ).

thf(77,plain,
    ! [SV11: $i,SV7: $i] :
      ( ( ( ( ( product @ SV7 @ SV11 )
           != SV7 )
          | ( ( product @ SV11 @ SV7 )
           != SV11 ) )
        = $true )
      | ( ( l @ SV7 @ SV11 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[68]) ).

thf(78,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( l @ SX0 @ SX1 )
          | ( ( product @ SX0 @ SX1 )
            = SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[69]) ).

thf(79,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( l @ SX0 @ SX1 )
          | ( ( product @ SX1 @ SX0 )
            = SX1 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[70]) ).

thf(80,plain,
    ( ( ( ( product @ sK2_SY81 @ ( product @ sK1_X7 @ sK2_SY81 ) )
        = sK2_SY81 )
      = $false )
    | ( ( ( product @ sK1_X7 @ ( product @ sK2_SY81 @ sK1_X7 ) )
        = sK1_X7 )
      = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[71]) ).

thf(81,plain,
    ! [SV12: $i,SV8: $i] :
      ( ( ( ( ( product @ SV8 @ SV12 )
           != SV12 )
          | ( ( product @ SV12 @ SV8 )
           != SV8 ) )
        = $true )
      | ( ( r @ SV8 @ SV12 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[72]) ).

thf(82,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( r @ SX0 @ SX1 )
          | ( ( product @ SX0 @ SX1 )
            = SX1 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[73]) ).

thf(83,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( r @ SX0 @ SX1 )
          | ( ( product @ SX1 @ SX0 )
            = SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[74]) ).

thf(84,plain,
    ! [SV5: $i,SV9: $i,SV13: $i] :
      ( ( ( ~ ( l @ SV13 @ SV9 )
          | ~ ( r @ SV5 @ SV13 ) )
        = $true )
      | ( ( d @ SV5 @ SV9 )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[75]) ).

thf(85,plain,
    ! [SV10: $i,SV6: $i] :
      ( ( ( d @ SV6 @ SV10 )
        = $false )
      | ( ( ~ ( ~ ( l @ ( sK3_X6 @ SV10 @ SV6 ) @ SV10 )
              | ~ ( r @ SV6 @ ( sK3_X6 @ SV10 @ SV6 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[76]) ).

thf(86,plain,
    ! [SV11: $i,SV7: $i] :
      ( ( ( ( ( product @ SV7 @ SV11 )
           != SV7 ) )
        = $true )
      | ( ( ( ( product @ SV11 @ SV7 )
           != SV11 ) )
        = $true )
      | ( ( l @ SV7 @ SV11 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[77]) ).

thf(87,plain,
    ! [SV14: $i] :
      ( ( ! [SY91: $i] :
            ( ~ ( l @ SV14 @ SY91 )
            | ( ( product @ SV14 @ SY91 )
              = SV14 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[78]) ).

thf(88,plain,
    ! [SV15: $i] :
      ( ( ! [SY92: $i] :
            ( ~ ( l @ SV15 @ SY92 )
            | ( ( product @ SY92 @ SV15 )
              = SY92 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[79]) ).

thf(89,plain,
    ! [SV12: $i,SV8: $i] :
      ( ( ( ( ( product @ SV8 @ SV12 )
           != SV12 ) )
        = $true )
      | ( ( ( ( product @ SV12 @ SV8 )
           != SV8 ) )
        = $true )
      | ( ( r @ SV8 @ SV12 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[81]) ).

thf(90,plain,
    ! [SV16: $i] :
      ( ( ! [SY93: $i] :
            ( ~ ( r @ SV16 @ SY93 )
            | ( ( product @ SV16 @ SY93 )
              = SY93 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[82]) ).

thf(91,plain,
    ! [SV17: $i] :
      ( ( ! [SY94: $i] :
            ( ~ ( r @ SV17 @ SY94 )
            | ( ( product @ SY94 @ SV17 )
              = SV17 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[83]) ).

thf(92,plain,
    ! [SV5: $i,SV9: $i,SV13: $i] :
      ( ( ( ~ ( l @ SV13 @ SV9 ) )
        = $true )
      | ( ( ~ ( r @ SV5 @ SV13 ) )
        = $true )
      | ( ( d @ SV5 @ SV9 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[84]) ).

thf(93,plain,
    ! [SV6: $i,SV10: $i] :
      ( ( ( ~ ( l @ ( sK3_X6 @ SV10 @ SV6 ) @ SV10 )
          | ~ ( r @ SV6 @ ( sK3_X6 @ SV10 @ SV6 ) ) )
        = $false )
      | ( ( d @ SV6 @ SV10 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[85]) ).

thf(94,plain,
    ! [SV11: $i,SV7: $i] :
      ( ( ( ( product @ SV7 @ SV11 )
          = SV7 )
        = $false )
      | ( ( ( ( product @ SV11 @ SV7 )
           != SV11 ) )
        = $true )
      | ( ( l @ SV7 @ SV11 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[86]) ).

thf(95,plain,
    ! [SV18: $i,SV14: $i] :
      ( ( ~ ( l @ SV14 @ SV18 )
        | ( ( product @ SV14 @ SV18 )
          = SV14 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[87]) ).

thf(96,plain,
    ! [SV19: $i,SV15: $i] :
      ( ( ~ ( l @ SV15 @ SV19 )
        | ( ( product @ SV19 @ SV15 )
          = SV19 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[88]) ).

thf(97,plain,
    ! [SV12: $i,SV8: $i] :
      ( ( ( ( product @ SV8 @ SV12 )
          = SV12 )
        = $false )
      | ( ( ( ( product @ SV12 @ SV8 )
           != SV8 ) )
        = $true )
      | ( ( r @ SV8 @ SV12 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[89]) ).

thf(98,plain,
    ! [SV20: $i,SV16: $i] :
      ( ( ~ ( r @ SV16 @ SV20 )
        | ( ( product @ SV16 @ SV20 )
          = SV20 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[90]) ).

thf(99,plain,
    ! [SV21: $i,SV17: $i] :
      ( ( ~ ( r @ SV17 @ SV21 )
        | ( ( product @ SV21 @ SV17 )
          = SV17 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[91]) ).

thf(100,plain,
    ! [SV5: $i,SV9: $i,SV13: $i] :
      ( ( ( l @ SV13 @ SV9 )
        = $false )
      | ( ( ~ ( r @ SV5 @ SV13 ) )
        = $true )
      | ( ( d @ SV5 @ SV9 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[92]) ).

thf(101,plain,
    ! [SV6: $i,SV10: $i] :
      ( ( ( ~ ( l @ ( sK3_X6 @ SV10 @ SV6 ) @ SV10 ) )
        = $false )
      | ( ( d @ SV6 @ SV10 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[93]) ).

thf(102,plain,
    ! [SV10: $i,SV6: $i] :
      ( ( ( ~ ( r @ SV6 @ ( sK3_X6 @ SV10 @ SV6 ) ) )
        = $false )
      | ( ( d @ SV6 @ SV10 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[93]) ).

thf(103,plain,
    ! [SV7: $i,SV11: $i] :
      ( ( ( ( product @ SV11 @ SV7 )
          = SV11 )
        = $false )
      | ( ( ( product @ SV7 @ SV11 )
          = SV7 )
        = $false )
      | ( ( l @ SV7 @ SV11 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[94]) ).

thf(104,plain,
    ! [SV18: $i,SV14: $i] :
      ( ( ( ~ ( l @ SV14 @ SV18 ) )
        = $true )
      | ( ( ( product @ SV14 @ SV18 )
          = SV14 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[95]) ).

thf(105,plain,
    ! [SV19: $i,SV15: $i] :
      ( ( ( ~ ( l @ SV15 @ SV19 ) )
        = $true )
      | ( ( ( product @ SV19 @ SV15 )
          = SV19 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[96]) ).

thf(106,plain,
    ! [SV8: $i,SV12: $i] :
      ( ( ( ( product @ SV12 @ SV8 )
          = SV8 )
        = $false )
      | ( ( ( product @ SV8 @ SV12 )
          = SV12 )
        = $false )
      | ( ( r @ SV8 @ SV12 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[97]) ).

thf(107,plain,
    ! [SV20: $i,SV16: $i] :
      ( ( ( ~ ( r @ SV16 @ SV20 ) )
        = $true )
      | ( ( ( product @ SV16 @ SV20 )
          = SV20 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[98]) ).

thf(108,plain,
    ! [SV21: $i,SV17: $i] :
      ( ( ( ~ ( r @ SV17 @ SV21 ) )
        = $true )
      | ( ( ( product @ SV21 @ SV17 )
          = SV17 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[99]) ).

thf(109,plain,
    ! [SV9: $i,SV13: $i,SV5: $i] :
      ( ( ( r @ SV5 @ SV13 )
        = $false )
      | ( ( l @ SV13 @ SV9 )
        = $false )
      | ( ( d @ SV5 @ SV9 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[100]) ).

thf(110,plain,
    ! [SV6: $i,SV10: $i] :
      ( ( ( l @ ( sK3_X6 @ SV10 @ SV6 ) @ SV10 )
        = $true )
      | ( ( d @ SV6 @ SV10 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[101]) ).

thf(111,plain,
    ! [SV10: $i,SV6: $i] :
      ( ( ( r @ SV6 @ ( sK3_X6 @ SV10 @ SV6 ) )
        = $true )
      | ( ( d @ SV6 @ SV10 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[102]) ).

thf(112,plain,
    ! [SV18: $i,SV14: $i] :
      ( ( ( l @ SV14 @ SV18 )
        = $false )
      | ( ( ( product @ SV14 @ SV18 )
          = SV14 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[104]) ).

thf(113,plain,
    ! [SV19: $i,SV15: $i] :
      ( ( ( l @ SV15 @ SV19 )
        = $false )
      | ( ( ( product @ SV19 @ SV15 )
          = SV19 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[105]) ).

thf(114,plain,
    ! [SV20: $i,SV16: $i] :
      ( ( ( r @ SV16 @ SV20 )
        = $false )
      | ( ( ( product @ SV16 @ SV20 )
          = SV20 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[107]) ).

thf(115,plain,
    ! [SV21: $i,SV17: $i] :
      ( ( ( r @ SV17 @ SV21 )
        = $false )
      | ( ( ( product @ SV21 @ SV17 )
          = SV17 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[108]) ).

thf(127,plain,
    ! [SV22: $i] :
      ( ( ( product @ SV22 @ SV22 )
        = SV22 )
      = $true ),
    inference(rename,[status(thm)],[36]) ).

thf(128,plain,
    ! [SV23: $i,SV24: $i,SV25: $i] :
      ( ( ( product @ ( product @ SV25 @ SV24 ) @ SV23 )
        = ( product @ SV25 @ ( product @ SV24 @ SV23 ) ) )
      = $true ),
    inference(rename,[status(thm)],[50]) ).

thf(136,plain,
    ! [SV26: $i,SV27: $i] :
      ( ( ( ( product @ SV27 @ SV26 )
          = SV27 )
        = $false )
      | ( ( ( product @ SV26 @ SV27 )
          = SV26 )
        = $false )
      | ( ( l @ SV26 @ SV27 )
        = $true ) ),
    inference(rename,[status(thm)],[103]) ).

thf(149,plain,
    ! [SV28: $i,SV29: $i] :
      ( ( ( ( product @ SV29 @ SV28 )
          = SV28 )
        = $false )
      | ( ( ( product @ SV28 @ SV29 )
          = SV29 )
        = $false )
      | ( ( r @ SV28 @ SV29 )
        = $true ) ),
    inference(rename,[status(thm)],[106]) ).

thf(166,plain,
    ! [SV30: $i,SV31: $i,SV32: $i] :
      ( ( ( r @ SV32 @ SV31 )
        = $false )
      | ( ( l @ SV31 @ SV30 )
        = $false )
      | ( ( d @ SV32 @ SV30 )
        = $true ) ),
    inference(rename,[status(thm)],[109]) ).

thf(187,plain,
    ! [SV33: $i,SV34: $i] :
      ( ( ( l @ ( sK3_X6 @ SV34 @ SV33 ) @ SV34 )
        = $true )
      | ( ( d @ SV33 @ SV34 )
        = $false ) ),
    inference(rename,[status(thm)],[110]) ).

thf(190,plain,
    ! [SV33: $i,SV34: $i,SV30: $i,SV31: $i,SV32: $i] :
      ( ( ( ( d @ SV33 @ SV34 )
          = ( d @ SV32 @ SV30 ) )
        = $false )
      | ( ( l @ ( sK3_X6 @ SV34 @ SV33 ) @ SV34 )
        = $true )
      | ( ( r @ SV32 @ SV31 )
        = $false )
      | ( ( l @ SV31 @ SV30 )
        = $false ) ),
    inference(res,[status(thm)],[187,166]) ).

thf(191,plain,
    ! [SV33: $i,SV34: $i,SV30: $i,SV31: $i,SV32: $i] :
      ( ( ( ( l @ ( sK3_X6 @ SV34 @ SV33 ) @ SV34 )
          = ( l @ SV31 @ SV30 ) )
        = $false )
      | ( ( d @ SV33 @ SV34 )
        = $false )
      | ( ( r @ SV32 @ SV31 )
        = $false )
      | ( ( d @ SV32 @ SV30 )
        = $true ) ),
    inference(res,[status(thm)],[187,166]) ).

thf(203,plain,
    ! [SV33: $i,SV34: $i] :
      ( ( ( ( d @ SV33 @ SV34 )
          = ( d @ sK1_X7 @ sK2_SY81 ) )
        = $false )
      | ( ( l @ ( sK3_X6 @ SV34 @ SV33 ) @ SV34 )
        = $true ) ),
    inference(res,[status(thm)],[187,55]) ).

thf(204,plain,
    ( ( l @ ( sK3_X6 @ sK2_SY81 @ sK1_X7 ) @ sK2_SY81 )
    = $true ),
    inference(extuni,[status(esa)],[203:[bind(SV34,$thf( sK2_SY81 )),bind(SV33,$thf( sK1_X7 ))]]) ).

thf(205,plain,
    ! [SV33: $i,SV30: $i,SV32: $i] :
      ( ( ( d @ SV32 @ SV30 )
        = $true )
      | ( ( r @ SV32 @ ( sK3_X6 @ SV30 @ SV33 ) )
        = $false )
      | ( ( d @ SV33 @ SV30 )
        = $false ) ),
    inference(extuni,[status(esa)],[191:[bind(SV34,$thf( SV30 )),bind(SV31,$thf( sK3_X6 @ SV30 @ SV33 ))]]) ).

thf(206,plain,
    ! [SV32: $i,SV30: $i,SV31: $i] :
      ( ( ( l @ SV31 @ SV30 )
        = $false )
      | ( ( r @ SV32 @ SV31 )
        = $false )
      | ( ( l @ ( sK3_X6 @ SV30 @ SV32 ) @ SV30 )
        = $true ) ),
    inference(extuni,[status(esa)],[190:[bind(SV34,$thf( SV30 )),bind(SV33,$thf( SV32 ))]]) ).

thf(207,plain,
    ! [SV35: $i,SV36: $i] :
      ( ( ( r @ SV36 @ ( sK3_X6 @ SV35 @ SV36 ) )
        = $true )
      | ( ( d @ SV36 @ SV35 )
        = $false ) ),
    inference(rename,[status(thm)],[111]) ).

thf(212,plain,
    ! [SV35: $i,SV36: $i,SV30: $i,SV31: $i,SV32: $i] :
      ( ( ( ( d @ SV36 @ SV35 )
          = ( d @ SV32 @ SV30 ) )
        = $false )
      | ( ( r @ SV36 @ ( sK3_X6 @ SV35 @ SV36 ) )
        = $true )
      | ( ( r @ SV32 @ SV31 )
        = $false )
      | ( ( l @ SV31 @ SV30 )
        = $false ) ),
    inference(res,[status(thm)],[207,166]) ).

thf(214,plain,
    ! [SV35: $i,SV36: $i,SV30: $i,SV31: $i,SV32: $i] :
      ( ( ( ( r @ SV36 @ ( sK3_X6 @ SV35 @ SV36 ) )
          = ( r @ SV32 @ SV31 ) )
        = $false )
      | ( ( d @ SV36 @ SV35 )
        = $false )
      | ( ( l @ SV31 @ SV30 )
        = $false )
      | ( ( d @ SV32 @ SV30 )
        = $true ) ),
    inference(res,[status(thm)],[207,166]) ).

thf(225,plain,
    ! [SV35: $i,SV36: $i] :
      ( ( ( ( d @ SV36 @ SV35 )
          = ( d @ sK1_X7 @ sK2_SY81 ) )
        = $false )
      | ( ( r @ SV36 @ ( sK3_X6 @ SV35 @ SV36 ) )
        = $true ) ),
    inference(res,[status(thm)],[207,55]) ).

thf(226,plain,
    ( ( r @ sK1_X7 @ ( sK3_X6 @ sK2_SY81 @ sK1_X7 ) )
    = $true ),
    inference(extuni,[status(esa)],[225:[bind(SV35,$thf( sK2_SY81 )),bind(SV36,$thf( sK1_X7 ))]]) ).

thf(227,plain,
    ! [SV35: $i,SV30: $i,SV32: $i] :
      ( ( ( d @ SV32 @ SV30 )
        = $true )
      | ( ( l @ ( sK3_X6 @ SV35 @ SV32 ) @ SV30 )
        = $false )
      | ( ( d @ SV32 @ SV35 )
        = $false ) ),
    inference(extuni,[status(esa)],[214:[bind(SV31,$thf( sK3_X6 @ SV35 @ SV32 )),bind(SV36,$thf( SV32 ))]]) ).

thf(228,plain,
    ! [SV32: $i,SV30: $i,SV31: $i] :
      ( ( ( l @ SV31 @ SV30 )
        = $false )
      | ( ( r @ SV32 @ SV31 )
        = $false )
      | ( ( r @ SV32 @ ( sK3_X6 @ SV30 @ SV32 ) )
        = $true ) ),
    inference(extuni,[status(esa)],[212:[bind(SV35,$thf( SV30 )),bind(SV36,$thf( SV32 ))]]) ).

thf(229,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[55,228,227,226,207,206,205,204,187,166,149,136,128,127,115,114,113,112,80]) ).

thf(230,plain,
    ( ( ! [C: $i,B: $i,A: $i] :
          ( ( product @ ( product @ A @ B ) @ C )
          = ( product @ A @ ( product @ B @ C ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[13]) ).

thf(231,plain,
    ( ( ! [A: $i] :
          ( ( product @ A @ A )
          = A ) )
    = $true ),
    inference(copy,[status(thm)],[12]) ).

thf(232,plain,
    ( ( ! [X0: $i,X1: $i] :
          ( ( ( product @ X0 @ X1 )
           != X0 )
          | ( ( product @ X1 @ X0 )
           != X1 )
          | ( l @ X0 @ X1 ) )
      & ! [X0: $i,X1: $i] :
          ( ~ ( l @ X0 @ X1 )
          | ( ( product @ X0 @ X1 )
            = X0 ) )
      & ! [X0: $i,X1: $i] :
          ( ~ ( l @ X0 @ X1 )
          | ( ( product @ X1 @ X0 )
            = X1 ) ) )
    = $true ),
    inference(copy,[status(thm)],[24]) ).

thf(233,plain,
    ( ( ! [X2: $i,X3: $i] :
          ( ( ( product @ X2 @ X3 )
           != X3 )
          | ( ( product @ X3 @ X2 )
           != X2 )
          | ( r @ X2 @ X3 ) )
      & ! [X2: $i,X3: $i] :
          ( ~ ( r @ X2 @ X3 )
          | ( ( product @ X2 @ X3 )
            = X3 ) )
      & ! [X2: $i,X3: $i] :
          ( ~ ( r @ X2 @ X3 )
          | ( ( product @ X3 @ X2 )
            = X2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[23]) ).

thf(234,plain,
    ( ( ! [X4: $i,X5: $i] :
          ( ! [X6: $i] :
              ( ~ ( l @ X6 @ X5 )
              | ~ ( r @ X4 @ X6 ) )
          | ( d @ X4 @ X5 ) )
      & ! [X4: $i,X5: $i] :
          ( ~ ( d @ X4 @ X5 )
          | ( ( l @ ( sK3_X6 @ X5 @ X4 ) @ X5 )
            & ( r @ X4 @ ( sK3_X6 @ X5 @ X4 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[22]) ).

thf(235,plain,
    ( ( ( ( product @ sK1_X7 @ ( product @ sK2_SY81 @ sK1_X7 ) )
        = sK1_X7 )
      & ( ( product @ sK2_SY81 @ ( product @ sK1_X7 @ sK2_SY81 ) )
        = sK2_SY81 )
      & ~ ( d @ sK1_X7 @ sK2_SY81 ) )
    = $true ),
    inference(copy,[status(thm)],[21]) ).

thf(236,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ( ( product @ SX0 @ SX1 )
                 != SX0 )
                | ( ( product @ SX1 @ SX0 )
                 != SX1 )
                | ( l @ SX0 @ SX1 ) )
          | ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
                      ( ~ ( l @ SX0 @ SX1 )
                      | ( ( product @ SX0 @ SX1 )
                        = SX0 ) )
                | ~ ! [SX0: $i,SX1: $i] :
                      ( ~ ( l @ SX0 @ SX1 )
                      | ( ( product @ SX1 @ SX0 )
                        = SX1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[232]) ).

thf(237,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ! [SX2: $i] :
                    ( ~ ( l @ SX2 @ SX1 )
                    | ~ ( r @ SX0 @ SX2 ) )
                | ( d @ SX0 @ SX1 ) )
          | ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( d @ SX0 @ SX1 )
                | ~ ( ~ ( l @ ( sK3_X6 @ SX1 @ SX0 ) @ SX1 )
                    | ~ ( r @ SX0 @ ( sK3_X6 @ SX1 @ SX0 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[234]) ).

thf(238,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ( ( product @ SX0 @ SX1 )
                 != SX1 )
                | ( ( product @ SX1 @ SX0 )
                 != SX0 )
                | ( r @ SX0 @ SX1 ) )
          | ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
                      ( ~ ( r @ SX0 @ SX1 )
                      | ( ( product @ SX0 @ SX1 )
                        = SX1 ) )
                | ~ ! [SX0: $i,SX1: $i] :
                      ( ~ ( r @ SX0 @ SX1 )
                      | ( ( product @ SX1 @ SX0 )
                        = SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[233]) ).

thf(239,plain,
    ( ( ~ ( ~ ~ ( ( ( product @ sK1_X7 @ ( product @ sK2_SY81 @ sK1_X7 ) )
                 != sK1_X7 )
                | ( ( product @ sK2_SY81 @ ( product @ sK1_X7 @ sK2_SY81 ) )
                 != sK2_SY81 ) )
          | ~ ~ ( d @ sK1_X7 @ sK2_SY81 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[235]) ).

thf(240,plain,
    ! [SV37: $i] :
      ( ( ! [SY95: $i,SY96: $i] :
            ( ( product @ ( product @ SY96 @ SY95 ) @ SV37 )
            = ( product @ SY96 @ ( product @ SY95 @ SV37 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[230]) ).

thf(241,plain,
    ! [SV38: $i] :
      ( ( ( product @ SV38 @ SV38 )
        = SV38 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[231]) ).

thf(242,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ( ( product @ SX0 @ SX1 )
             != SX0 )
            | ( ( product @ SX1 @ SX0 )
             != SX1 )
            | ( l @ SX0 @ SX1 ) )
      | ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
                  ( ~ ( l @ SX0 @ SX1 )
                  | ( ( product @ SX0 @ SX1 )
                    = SX0 ) )
            | ~ ! [SX0: $i,SX1: $i] :
                  ( ~ ( l @ SX0 @ SX1 )
                  | ( ( product @ SX1 @ SX0 )
                    = SX1 ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[236]) ).

thf(243,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ! [SX2: $i] :
                ( ~ ( l @ SX2 @ SX1 )
                | ~ ( r @ SX0 @ SX2 ) )
            | ( d @ SX0 @ SX1 ) )
      | ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( d @ SX0 @ SX1 )
            | ~ ( ~ ( l @ ( sK3_X6 @ SX1 @ SX0 ) @ SX1 )
                | ~ ( r @ SX0 @ ( sK3_X6 @ SX1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[237]) ).

thf(244,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ( ( product @ SX0 @ SX1 )
             != SX1 )
            | ( ( product @ SX1 @ SX0 )
             != SX0 )
            | ( r @ SX0 @ SX1 ) )
      | ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
                  ( ~ ( r @ SX0 @ SX1 )
                  | ( ( product @ SX0 @ SX1 )
                    = SX1 ) )
            | ~ ! [SX0: $i,SX1: $i] :
                  ( ~ ( r @ SX0 @ SX1 )
                  | ( ( product @ SX1 @ SX0 )
                    = SX0 ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[238]) ).

thf(245,plain,
    ( ( ~ ~ ( ( ( product @ sK1_X7 @ ( product @ sK2_SY81 @ sK1_X7 ) )
             != sK1_X7 )
            | ( ( product @ sK2_SY81 @ ( product @ sK1_X7 @ sK2_SY81 ) )
             != sK2_SY81 ) )
      | ~ ~ ( d @ sK1_X7 @ sK2_SY81 ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[239]) ).

thf(246,plain,
    ! [SV37: $i,SV39: $i] :
      ( ( ! [SY97: $i] :
            ( ( product @ ( product @ SY97 @ SV39 ) @ SV37 )
            = ( product @ SY97 @ ( product @ SV39 @ SV37 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[240]) ).

thf(247,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ( ( product @ SX0 @ SX1 )
             != SX0 )
            | ( ( product @ SX1 @ SX0 )
             != SX1 )
            | ( l @ SX0 @ SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[242]) ).

thf(248,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
                  ( ~ ( l @ SX0 @ SX1 )
                  | ( ( product @ SX0 @ SX1 )
                    = SX0 ) )
            | ~ ! [SX0: $i,SX1: $i] :
                  ( ~ ( l @ SX0 @ SX1 )
                  | ( ( product @ SX1 @ SX0 )
                    = SX1 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[242]) ).

thf(249,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ! [SX2: $i] :
                ( ~ ( l @ SX2 @ SX1 )
                | ~ ( r @ SX0 @ SX2 ) )
            | ( d @ SX0 @ SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[243]) ).

thf(250,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( d @ SX0 @ SX1 )
            | ~ ( ~ ( l @ ( sK3_X6 @ SX1 @ SX0 ) @ SX1 )
                | ~ ( r @ SX0 @ ( sK3_X6 @ SX1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[243]) ).

thf(251,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ( ( product @ SX0 @ SX1 )
             != SX1 )
            | ( ( product @ SX1 @ SX0 )
             != SX0 )
            | ( r @ SX0 @ SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[244]) ).

thf(252,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
                  ( ~ ( r @ SX0 @ SX1 )
                  | ( ( product @ SX0 @ SX1 )
                    = SX1 ) )
            | ~ ! [SX0: $i,SX1: $i] :
                  ( ~ ( r @ SX0 @ SX1 )
                  | ( ( product @ SX1 @ SX0 )
                    = SX0 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[244]) ).

thf(253,plain,
    ( ( ~ ~ ( ( ( product @ sK1_X7 @ ( product @ sK2_SY81 @ sK1_X7 ) )
             != sK1_X7 )
            | ( ( product @ sK2_SY81 @ ( product @ sK1_X7 @ sK2_SY81 ) )
             != sK2_SY81 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[245]) ).

thf(254,plain,
    ( ( ~ ~ ( d @ sK1_X7 @ sK2_SY81 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[245]) ).

thf(255,plain,
    ! [SV37: $i,SV39: $i,SV40: $i] :
      ( ( ( product @ ( product @ SV40 @ SV39 ) @ SV37 )
        = ( product @ SV40 @ ( product @ SV39 @ SV37 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[246]) ).

thf(256,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( ( product @ SX0 @ SX1 )
           != SX0 )
          | ( ( product @ SX1 @ SX0 )
           != SX1 )
          | ( l @ SX0 @ SX1 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[247]) ).

thf(257,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( l @ SX0 @ SX1 )
                | ( ( product @ SX0 @ SX1 )
                  = SX0 ) )
          | ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( l @ SX0 @ SX1 )
                | ( ( product @ SX1 @ SX0 )
                  = SX1 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[248]) ).

thf(258,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ! [SX2: $i] :
              ( ~ ( l @ SX2 @ SX1 )
              | ~ ( r @ SX0 @ SX2 ) )
          | ( d @ SX0 @ SX1 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[249]) ).

thf(259,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( d @ SX0 @ SX1 )
          | ~ ( ~ ( l @ ( sK3_X6 @ SX1 @ SX0 ) @ SX1 )
              | ~ ( r @ SX0 @ ( sK3_X6 @ SX1 @ SX0 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[250]) ).

thf(260,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( ( product @ SX0 @ SX1 )
           != SX1 )
          | ( ( product @ SX1 @ SX0 )
           != SX0 )
          | ( r @ SX0 @ SX1 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[251]) ).

thf(261,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( r @ SX0 @ SX1 )
                | ( ( product @ SX0 @ SX1 )
                  = SX1 ) )
          | ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( r @ SX0 @ SX1 )
                | ( ( product @ SX1 @ SX0 )
                  = SX0 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[252]) ).

thf(262,plain,
    ( ( ~ ( ( ( product @ sK1_X7 @ ( product @ sK2_SY81 @ sK1_X7 ) )
           != sK1_X7 )
          | ( ( product @ sK2_SY81 @ ( product @ sK1_X7 @ sK2_SY81 ) )
           != sK2_SY81 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[253]) ).

thf(263,plain,
    ( ( ~ ( d @ sK1_X7 @ sK2_SY81 ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[254]) ).

thf(264,plain,
    ! [SV41: $i] :
      ( ( ! [SY98: $i] :
            ( ( ( product @ SV41 @ SY98 )
             != SV41 )
            | ( ( product @ SY98 @ SV41 )
             != SY98 )
            | ( l @ SV41 @ SY98 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[256]) ).

thf(265,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( l @ SX0 @ SX1 )
            | ( ( product @ SX0 @ SX1 )
              = SX0 ) )
      | ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( l @ SX0 @ SX1 )
            | ( ( product @ SX1 @ SX0 )
              = SX1 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[257]) ).

thf(266,plain,
    ! [SV42: $i] :
      ( ( ! [SY99: $i] :
            ( ! [SY100: $i] :
                ( ~ ( l @ SY100 @ SY99 )
                | ~ ( r @ SV42 @ SY100 ) )
            | ( d @ SV42 @ SY99 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[258]) ).

thf(267,plain,
    ! [SV43: $i] :
      ( ( ! [SY101: $i] :
            ( ~ ( d @ SV43 @ SY101 )
            | ~ ( ~ ( l @ ( sK3_X6 @ SY101 @ SV43 ) @ SY101 )
                | ~ ( r @ SV43 @ ( sK3_X6 @ SY101 @ SV43 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[259]) ).

thf(268,plain,
    ! [SV44: $i] :
      ( ( ! [SY102: $i] :
            ( ( ( product @ SV44 @ SY102 )
             != SY102 )
            | ( ( product @ SY102 @ SV44 )
             != SV44 )
            | ( r @ SV44 @ SY102 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[260]) ).

thf(269,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( r @ SX0 @ SX1 )
            | ( ( product @ SX0 @ SX1 )
              = SX1 ) )
      | ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( r @ SX0 @ SX1 )
            | ( ( product @ SX1 @ SX0 )
              = SX0 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[261]) ).

thf(270,plain,
    ( ( ( ( product @ sK1_X7 @ ( product @ sK2_SY81 @ sK1_X7 ) )
       != sK1_X7 )
      | ( ( product @ sK2_SY81 @ ( product @ sK1_X7 @ sK2_SY81 ) )
       != sK2_SY81 ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[262]) ).

thf(271,plain,
    ( ( d @ sK1_X7 @ sK2_SY81 )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[263]) ).

thf(272,plain,
    ! [SV45: $i,SV41: $i] :
      ( ( ( ( product @ SV41 @ SV45 )
         != SV41 )
        | ( ( product @ SV45 @ SV41 )
         != SV45 )
        | ( l @ SV41 @ SV45 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[264]) ).

thf(273,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( l @ SX0 @ SX1 )
            | ( ( product @ SX0 @ SX1 )
              = SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[265]) ).

thf(274,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( l @ SX0 @ SX1 )
            | ( ( product @ SX1 @ SX0 )
              = SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[265]) ).

thf(275,plain,
    ! [SV42: $i,SV46: $i] :
      ( ( ! [SY103: $i] :
            ( ~ ( l @ SY103 @ SV46 )
            | ~ ( r @ SV42 @ SY103 ) )
        | ( d @ SV42 @ SV46 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[266]) ).

thf(276,plain,
    ! [SV47: $i,SV43: $i] :
      ( ( ~ ( d @ SV43 @ SV47 )
        | ~ ( ~ ( l @ ( sK3_X6 @ SV47 @ SV43 ) @ SV47 )
            | ~ ( r @ SV43 @ ( sK3_X6 @ SV47 @ SV43 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[267]) ).

thf(277,plain,
    ! [SV48: $i,SV44: $i] :
      ( ( ( ( product @ SV44 @ SV48 )
         != SV48 )
        | ( ( product @ SV48 @ SV44 )
         != SV44 )
        | ( r @ SV44 @ SV48 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[268]) ).

thf(278,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( r @ SX0 @ SX1 )
            | ( ( product @ SX0 @ SX1 )
              = SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[269]) ).

thf(279,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( r @ SX0 @ SX1 )
            | ( ( product @ SX1 @ SX0 )
              = SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[269]) ).

thf(280,plain,
    ( ( ( ( product @ sK1_X7 @ ( product @ sK2_SY81 @ sK1_X7 ) )
       != sK1_X7 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[270]) ).

thf(281,plain,
    ( ( ( ( product @ sK2_SY81 @ ( product @ sK1_X7 @ sK2_SY81 ) )
       != sK2_SY81 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[270]) ).

thf(282,plain,
    ! [SV45: $i,SV41: $i] :
      ( ( ( ( ( product @ SV41 @ SV45 )
           != SV41 )
          | ( ( product @ SV45 @ SV41 )
           != SV45 ) )
        = $true )
      | ( ( l @ SV41 @ SV45 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[272]) ).

thf(283,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( l @ SX0 @ SX1 )
          | ( ( product @ SX0 @ SX1 )
            = SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[273]) ).

thf(284,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( l @ SX0 @ SX1 )
          | ( ( product @ SX1 @ SX0 )
            = SX1 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[274]) ).

thf(285,plain,
    ! [SV42: $i,SV46: $i] :
      ( ( ( ! [SY103: $i] :
              ( ~ ( l @ SY103 @ SV46 )
              | ~ ( r @ SV42 @ SY103 ) ) )
        = $true )
      | ( ( d @ SV42 @ SV46 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[275]) ).

thf(286,plain,
    ! [SV47: $i,SV43: $i] :
      ( ( ( ~ ( d @ SV43 @ SV47 ) )
        = $true )
      | ( ( ~ ( ~ ( l @ ( sK3_X6 @ SV47 @ SV43 ) @ SV47 )
              | ~ ( r @ SV43 @ ( sK3_X6 @ SV47 @ SV43 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[276]) ).

thf(287,plain,
    ! [SV48: $i,SV44: $i] :
      ( ( ( ( ( product @ SV44 @ SV48 )
           != SV48 )
          | ( ( product @ SV48 @ SV44 )
           != SV44 ) )
        = $true )
      | ( ( r @ SV44 @ SV48 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[277]) ).

thf(288,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( r @ SX0 @ SX1 )
          | ( ( product @ SX0 @ SX1 )
            = SX1 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[278]) ).

thf(289,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( r @ SX0 @ SX1 )
          | ( ( product @ SX1 @ SX0 )
            = SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[279]) ).

thf(290,plain,
    ( ( ( product @ sK1_X7 @ ( product @ sK2_SY81 @ sK1_X7 ) )
      = sK1_X7 )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[280]) ).

thf(291,plain,
    ( ( ( product @ sK2_SY81 @ ( product @ sK1_X7 @ sK2_SY81 ) )
      = sK2_SY81 )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[281]) ).

thf(292,plain,
    ! [SV45: $i,SV41: $i] :
      ( ( ( ( ( product @ SV41 @ SV45 )
           != SV41 ) )
        = $true )
      | ( ( ( ( product @ SV45 @ SV41 )
           != SV45 ) )
        = $true )
      | ( ( l @ SV41 @ SV45 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[282]) ).

thf(293,plain,
    ! [SV49: $i] :
      ( ( ! [SY104: $i] :
            ( ~ ( l @ SV49 @ SY104 )
            | ( ( product @ SV49 @ SY104 )
              = SV49 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[283]) ).

thf(294,plain,
    ! [SV50: $i] :
      ( ( ! [SY105: $i] :
            ( ~ ( l @ SV50 @ SY105 )
            | ( ( product @ SY105 @ SV50 )
              = SY105 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[284]) ).

thf(295,plain,
    ! [SV42: $i,SV46: $i,SV51: $i] :
      ( ( ( ~ ( l @ SV51 @ SV46 )
          | ~ ( r @ SV42 @ SV51 ) )
        = $true )
      | ( ( d @ SV42 @ SV46 )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[285]) ).

thf(296,plain,
    ! [SV47: $i,SV43: $i] :
      ( ( ( d @ SV43 @ SV47 )
        = $false )
      | ( ( ~ ( ~ ( l @ ( sK3_X6 @ SV47 @ SV43 ) @ SV47 )
              | ~ ( r @ SV43 @ ( sK3_X6 @ SV47 @ SV43 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[286]) ).

thf(297,plain,
    ! [SV48: $i,SV44: $i] :
      ( ( ( ( ( product @ SV44 @ SV48 )
           != SV48 ) )
        = $true )
      | ( ( ( ( product @ SV48 @ SV44 )
           != SV44 ) )
        = $true )
      | ( ( r @ SV44 @ SV48 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[287]) ).

thf(298,plain,
    ! [SV52: $i] :
      ( ( ! [SY106: $i] :
            ( ~ ( r @ SV52 @ SY106 )
            | ( ( product @ SV52 @ SY106 )
              = SY106 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[288]) ).

thf(299,plain,
    ! [SV53: $i] :
      ( ( ! [SY107: $i] :
            ( ~ ( r @ SV53 @ SY107 )
            | ( ( product @ SY107 @ SV53 )
              = SV53 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[289]) ).

thf(300,plain,
    ! [SV45: $i,SV41: $i] :
      ( ( ( ( product @ SV41 @ SV45 )
          = SV41 )
        = $false )
      | ( ( ( ( product @ SV45 @ SV41 )
           != SV45 ) )
        = $true )
      | ( ( l @ SV41 @ SV45 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[292]) ).

thf(301,plain,
    ! [SV54: $i,SV49: $i] :
      ( ( ~ ( l @ SV49 @ SV54 )
        | ( ( product @ SV49 @ SV54 )
          = SV49 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[293]) ).

thf(302,plain,
    ! [SV55: $i,SV50: $i] :
      ( ( ~ ( l @ SV50 @ SV55 )
        | ( ( product @ SV55 @ SV50 )
          = SV55 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[294]) ).

thf(303,plain,
    ! [SV42: $i,SV46: $i,SV51: $i] :
      ( ( ( ~ ( l @ SV51 @ SV46 ) )
        = $true )
      | ( ( ~ ( r @ SV42 @ SV51 ) )
        = $true )
      | ( ( d @ SV42 @ SV46 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[295]) ).

thf(304,plain,
    ! [SV43: $i,SV47: $i] :
      ( ( ( ~ ( l @ ( sK3_X6 @ SV47 @ SV43 ) @ SV47 )
          | ~ ( r @ SV43 @ ( sK3_X6 @ SV47 @ SV43 ) ) )
        = $false )
      | ( ( d @ SV43 @ SV47 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[296]) ).

thf(305,plain,
    ! [SV48: $i,SV44: $i] :
      ( ( ( ( product @ SV44 @ SV48 )
          = SV48 )
        = $false )
      | ( ( ( ( product @ SV48 @ SV44 )
           != SV44 ) )
        = $true )
      | ( ( r @ SV44 @ SV48 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[297]) ).

thf(306,plain,
    ! [SV56: $i,SV52: $i] :
      ( ( ~ ( r @ SV52 @ SV56 )
        | ( ( product @ SV52 @ SV56 )
          = SV56 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[298]) ).

thf(307,plain,
    ! [SV57: $i,SV53: $i] :
      ( ( ~ ( r @ SV53 @ SV57 )
        | ( ( product @ SV57 @ SV53 )
          = SV53 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[299]) ).

thf(308,plain,
    ! [SV41: $i,SV45: $i] :
      ( ( ( ( product @ SV45 @ SV41 )
          = SV45 )
        = $false )
      | ( ( ( product @ SV41 @ SV45 )
          = SV41 )
        = $false )
      | ( ( l @ SV41 @ SV45 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[300]) ).

thf(309,plain,
    ! [SV54: $i,SV49: $i] :
      ( ( ( ~ ( l @ SV49 @ SV54 ) )
        = $true )
      | ( ( ( product @ SV49 @ SV54 )
          = SV49 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[301]) ).

thf(310,plain,
    ! [SV55: $i,SV50: $i] :
      ( ( ( ~ ( l @ SV50 @ SV55 ) )
        = $true )
      | ( ( ( product @ SV55 @ SV50 )
          = SV55 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[302]) ).

thf(311,plain,
    ! [SV42: $i,SV46: $i,SV51: $i] :
      ( ( ( l @ SV51 @ SV46 )
        = $false )
      | ( ( ~ ( r @ SV42 @ SV51 ) )
        = $true )
      | ( ( d @ SV42 @ SV46 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[303]) ).

thf(312,plain,
    ! [SV43: $i,SV47: $i] :
      ( ( ( ~ ( l @ ( sK3_X6 @ SV47 @ SV43 ) @ SV47 ) )
        = $false )
      | ( ( d @ SV43 @ SV47 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[304]) ).

thf(313,plain,
    ! [SV47: $i,SV43: $i] :
      ( ( ( ~ ( r @ SV43 @ ( sK3_X6 @ SV47 @ SV43 ) ) )
        = $false )
      | ( ( d @ SV43 @ SV47 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[304]) ).

thf(314,plain,
    ! [SV44: $i,SV48: $i] :
      ( ( ( ( product @ SV48 @ SV44 )
          = SV44 )
        = $false )
      | ( ( ( product @ SV44 @ SV48 )
          = SV48 )
        = $false )
      | ( ( r @ SV44 @ SV48 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[305]) ).

thf(315,plain,
    ! [SV56: $i,SV52: $i] :
      ( ( ( ~ ( r @ SV52 @ SV56 ) )
        = $true )
      | ( ( ( product @ SV52 @ SV56 )
          = SV56 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[306]) ).

thf(316,plain,
    ! [SV57: $i,SV53: $i] :
      ( ( ( ~ ( r @ SV53 @ SV57 ) )
        = $true )
      | ( ( ( product @ SV57 @ SV53 )
          = SV53 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[307]) ).

thf(317,plain,
    ! [SV54: $i,SV49: $i] :
      ( ( ( l @ SV49 @ SV54 )
        = $false )
      | ( ( ( product @ SV49 @ SV54 )
          = SV49 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[309]) ).

thf(318,plain,
    ! [SV55: $i,SV50: $i] :
      ( ( ( l @ SV50 @ SV55 )
        = $false )
      | ( ( ( product @ SV55 @ SV50 )
          = SV55 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[310]) ).

thf(319,plain,
    ! [SV46: $i,SV51: $i,SV42: $i] :
      ( ( ( r @ SV42 @ SV51 )
        = $false )
      | ( ( l @ SV51 @ SV46 )
        = $false )
      | ( ( d @ SV42 @ SV46 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[311]) ).

thf(320,plain,
    ! [SV43: $i,SV47: $i] :
      ( ( ( l @ ( sK3_X6 @ SV47 @ SV43 ) @ SV47 )
        = $true )
      | ( ( d @ SV43 @ SV47 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[312]) ).

thf(321,plain,
    ! [SV47: $i,SV43: $i] :
      ( ( ( r @ SV43 @ ( sK3_X6 @ SV47 @ SV43 ) )
        = $true )
      | ( ( d @ SV43 @ SV47 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[313]) ).

thf(322,plain,
    ! [SV56: $i,SV52: $i] :
      ( ( ( r @ SV52 @ SV56 )
        = $false )
      | ( ( ( product @ SV52 @ SV56 )
          = SV56 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[315]) ).

thf(323,plain,
    ! [SV57: $i,SV53: $i] :
      ( ( ( r @ SV53 @ SV57 )
        = $false )
      | ( ( ( product @ SV57 @ SV53 )
          = SV53 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[316]) ).

thf(324,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[241,323,322,321,320,319,318,317,314,308,291,290,271,255]) ).

thf(325,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[324,229]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : GRP775+1 : TPTP v8.1.0. Released v4.1.0.
% 0.12/0.12  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33  % Computer : n014.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
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Tue Jun 14 13:28:06 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.19/0.34  
% 0.19/0.34   No.of.Axioms: 5
% 0.19/0.34  
% 0.19/0.34   Length.of.Defs: 0
% 0.19/0.34  
% 0.19/0.34   Contains.Choice.Funs: false
% 0.19/0.35  (rf:0,axioms:5,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:7,loop_count:0,foatp_calls:0,translation:fof_full).......eprover: CPU time limit exceeded, terminating
% 74.25/74.55  ..
% 74.99/75.25  (rf:0,axioms:5,ps:2,u:1,ude:false,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:7,loop_count:0,foatp_calls:0,translation:fof_full)......eprover: CPU time limit exceeded, terminating
% 150.05/150.35  .
% 150.05/150.35  (rf:0,axioms:5,ps:3,u:8,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:false,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:7,loop_count:0,foatp_calls:0,translation:fof_full).......eprover: CPU time limit exceeded, terminating
% 224.26/224.51  ...
% 224.95/225.21  (rf:2,axioms:5,ps:1,u:3,ude:true,rLeibEQ:false,rAndEQ:false,use_choice:false,use_extuni:false,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:7,loop_count:0,foatp_calls:0,translation:fof_full).............
% 236.33/236.72  
% 236.33/236.72  ********************************
% 236.33/236.72  *   All subproblems solved!    *
% 236.33/236.72  ********************************
% 236.33/236.72  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:2,axioms:5,ps:1,u:3,ude:true,rLeibEQ:false,rAndEQ:false,use_choice:false,use_extuni:false,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:63,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:324,loop_count:0,foatp_calls:1,translation:fof_full)
% 236.33/236.74  
% 236.33/236.74  %**** Beginning of derivation protocol ****
% 236.33/236.74  % SZS output start CNFRefutation
% See solution above
% 236.33/236.74  
% 236.33/236.74  %**** End of derivation protocol ****
% 236.33/236.74  %**** no. of clauses in derivation: 231 ****
% 236.33/236.74  %**** clause counter: 324 ****
% 236.33/236.74  
% 236.33/236.74  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:2,axioms:5,ps:1,u:3,ude:true,rLeibEQ:false,rAndEQ:false,use_choice:false,use_extuni:false,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:63,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:324,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------