TSTP Solution File: LAT030-1 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : LAT030-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n010.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 : Sun Jul 17 05:44:05 EDT 2022

% Result   : Unsatisfiable 14.88s 15.07s
% Output   : CNFRefutation 14.88s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   37 (  20 unt;   5 typ;   0 def)
%            Number of atoms       :  233 ( 162 equ;   0 cnn)
%            Maximal formula atoms :    6 (   7 avg)
%            Number of connectives : 1204 (  61   ~;  75   |;   0   &;1068   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   5 usr;   5 con; 0-2 aty)
%            Number of variables   :   54 (   0   ^  54   !;   0   ?;  54   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_a,type,
    a: $i ).

thf(tp_b,type,
    b: $i ).

thf(tp_c,type,
    c: $i ).

thf(tp_join,type,
    join: $i > $i > $i ).

thf(tp_meet,type,
    meet: $i > $i > $i ).

thf(1,axiom,
    ! [X: $i,Y: $i,Z: $i,X1: $i,X2: $i,U: $i] :
      ( ( join @ ( meet @ ( join @ ( meet @ X @ Y ) @ ( meet @ Y @ ( join @ X @ Y ) ) ) @ Z ) @ ( meet @ ( join @ ( meet @ X @ ( join @ ( join @ ( meet @ Y @ X1 ) @ ( meet @ X2 @ Y ) ) @ Y ) ) @ ( meet @ ( join @ ( meet @ Y @ ( meet @ ( meet @ ( join @ Y @ X1 ) @ ( join @ X2 @ Y ) ) @ Y ) ) @ ( meet @ U @ ( join @ Y @ ( meet @ ( meet @ ( join @ Y @ X1 ) @ ( join @ X2 @ Y ) ) @ Y ) ) ) ) @ ( join @ X @ ( join @ ( join @ ( meet @ Y @ X1 ) @ ( meet @ X2 @ Y ) ) @ Y ) ) ) ) @ ( join @ ( join @ ( meet @ X @ Y ) @ ( meet @ Y @ ( join @ X @ Y ) ) ) @ Z ) ) )
      = Y ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).

thf(2,conjecture,
    $false,
    file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).

thf(3,negated_conjecture,
    $false = $false,
    inference(negate_conjecture,[status(cth)],[2]) ).

thf(4,negated_conjecture,
    ( ( ( meet @ a @ a )
     != a )
    | ( ( meet @ b @ a )
     != ( meet @ a @ b ) )
    | ( ( join @ a @ a )
     != a )
    | ( ( join @ b @ a )
     != ( join @ a @ b ) )
    | ( ( meet @ ( meet @ ( join @ a @ b ) @ ( join @ c @ b ) ) @ b )
     != b )
    | ( ( join @ ( join @ ( meet @ a @ b ) @ ( meet @ c @ b ) ) @ b )
     != b ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_wal_axioms) ).

thf(5,plain,
    $false = $false,
    inference(unfold_def,[status(thm)],[3]) ).

thf(6,plain,
    ( ( ! [X: $i,Y: $i,Z: $i,X1: $i,X2: $i,U: $i] :
          ( ( join @ ( meet @ ( join @ ( meet @ X @ Y ) @ ( meet @ Y @ ( join @ X @ Y ) ) ) @ Z ) @ ( meet @ ( join @ ( meet @ X @ ( join @ ( join @ ( meet @ Y @ X1 ) @ ( meet @ X2 @ Y ) ) @ Y ) ) @ ( meet @ ( join @ ( meet @ Y @ ( meet @ ( meet @ ( join @ Y @ X1 ) @ ( join @ X2 @ Y ) ) @ Y ) ) @ ( meet @ U @ ( join @ Y @ ( meet @ ( meet @ ( join @ Y @ X1 ) @ ( join @ X2 @ Y ) ) @ Y ) ) ) ) @ ( join @ X @ ( join @ ( join @ ( meet @ Y @ X1 ) @ ( meet @ X2 @ Y ) ) @ Y ) ) ) ) @ ( join @ ( join @ ( meet @ X @ Y ) @ ( meet @ Y @ ( join @ X @ Y ) ) ) @ Z ) ) )
          = Y ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(7,plain,
    ( ( ( ( meet @ a @ a )
       != a )
      | ( ( meet @ b @ a )
       != ( meet @ a @ b ) )
      | ( ( join @ a @ a )
       != a )
      | ( ( join @ b @ a )
       != ( join @ a @ b ) )
      | ( ( meet @ ( meet @ ( join @ a @ b ) @ ( join @ c @ b ) ) @ b )
       != b )
      | ( ( join @ ( join @ ( meet @ a @ b ) @ ( meet @ c @ b ) ) @ b )
       != b ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4]) ).

thf(8,plain,
    ( ( ~ $false )
    = $true ),
    inference(polarity_switch,[status(thm)],[5]) ).

thf(9,plain,
    ( ( ( ( meet @ a @ a )
       != a )
      | ( ( meet @ b @ a )
       != ( meet @ a @ b ) )
      | ( ( join @ a @ a )
       != a )
      | ( ( join @ b @ a )
       != ( join @ a @ b ) )
      | ( ( meet @ ( meet @ ( join @ a @ b ) @ ( join @ c @ b ) ) @ b )
       != b )
      | ( ( join @ ( join @ ( meet @ a @ b ) @ ( meet @ c @ b ) ) @ b )
       != b ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[7]) ).

thf(10,plain,
    ( ( ( ( meet @ a @ a )
       != a )
      | ( ( meet @ b @ a )
       != ( meet @ a @ b ) )
      | ( ( join @ a @ a )
       != a )
      | ( ( join @ b @ a )
       != ( join @ a @ b ) )
      | ( ( meet @ ( meet @ ( join @ a @ b ) @ ( join @ c @ b ) ) @ b )
       != b )
      | ( ( join @ ( join @ ( meet @ a @ b ) @ ( meet @ c @ b ) ) @ b )
       != b ) )
    = $true ),
    inference(copy,[status(thm)],[9]) ).

thf(11,plain,
    ( ( ! [X: $i,Y: $i,Z: $i,X1: $i,X2: $i,U: $i] :
          ( ( join @ ( meet @ ( join @ ( meet @ X @ Y ) @ ( meet @ Y @ ( join @ X @ Y ) ) ) @ Z ) @ ( meet @ ( join @ ( meet @ X @ ( join @ ( join @ ( meet @ Y @ X1 ) @ ( meet @ X2 @ Y ) ) @ Y ) ) @ ( meet @ ( join @ ( meet @ Y @ ( meet @ ( meet @ ( join @ Y @ X1 ) @ ( join @ X2 @ Y ) ) @ Y ) ) @ ( meet @ U @ ( join @ Y @ ( meet @ ( meet @ ( join @ Y @ X1 ) @ ( join @ X2 @ Y ) ) @ Y ) ) ) ) @ ( join @ X @ ( join @ ( join @ ( meet @ Y @ X1 ) @ ( meet @ X2 @ Y ) ) @ Y ) ) ) ) @ ( join @ ( join @ ( meet @ X @ Y ) @ ( meet @ Y @ ( join @ X @ Y ) ) ) @ Z ) ) )
          = Y ) )
    = $true ),
    inference(copy,[status(thm)],[6]) ).

thf(12,plain,
    ( ( ~ $false )
    = $true ),
    inference(copy,[status(thm)],[8]) ).

thf(13,plain,
    ( ( ( ( ( meet @ a @ a )
         != a ) )
      = $true )
    | ( ( ( ( meet @ b @ a )
         != ( meet @ a @ b ) )
        | ( ( join @ a @ a )
         != a )
        | ( ( join @ b @ a )
         != ( join @ a @ b ) )
        | ( ( meet @ ( meet @ ( join @ a @ b ) @ ( join @ c @ b ) ) @ b )
         != b )
        | ( ( join @ ( join @ ( meet @ a @ b ) @ ( meet @ c @ b ) ) @ b )
         != b ) )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[10]) ).

thf(14,plain,
    ! [SV1: $i] :
      ( ( ! [SY6: $i,SY7: $i,SY8: $i,SY9: $i,SY10: $i] :
            ( ( join @ ( meet @ ( join @ ( meet @ SV1 @ SY6 ) @ ( meet @ SY6 @ ( join @ SV1 @ SY6 ) ) ) @ SY7 ) @ ( meet @ ( join @ ( meet @ SV1 @ ( join @ ( join @ ( meet @ SY6 @ SY8 ) @ ( meet @ SY9 @ SY6 ) ) @ SY6 ) ) @ ( meet @ ( join @ ( meet @ SY6 @ ( meet @ ( meet @ ( join @ SY6 @ SY8 ) @ ( join @ SY9 @ SY6 ) ) @ SY6 ) ) @ ( meet @ SY10 @ ( join @ SY6 @ ( meet @ ( meet @ ( join @ SY6 @ SY8 ) @ ( join @ SY9 @ SY6 ) ) @ SY6 ) ) ) ) @ ( join @ SV1 @ ( join @ ( join @ ( meet @ SY6 @ SY8 ) @ ( meet @ SY9 @ SY6 ) ) @ SY6 ) ) ) ) @ ( join @ ( join @ ( meet @ SV1 @ SY6 ) @ ( meet @ SY6 @ ( join @ SV1 @ SY6 ) ) ) @ SY7 ) ) )
            = SY6 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11]) ).

thf(15,plain,
    $false = $false,
    inference(extcnf_not_pos,[status(thm)],[12]) ).

thf(16,plain,
    ( ( ( ( meet @ a @ a )
        = a )
      = $false )
    | ( ( ( ( meet @ b @ a )
         != ( meet @ a @ b ) )
        | ( ( join @ a @ a )
         != a )
        | ( ( join @ b @ a )
         != ( join @ a @ b ) )
        | ( ( meet @ ( meet @ ( join @ a @ b ) @ ( join @ c @ b ) ) @ b )
         != b )
        | ( ( join @ ( join @ ( meet @ a @ b ) @ ( meet @ c @ b ) ) @ b )
         != b ) )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13]) ).

thf(17,plain,
    ! [SV2: $i,SV1: $i] :
      ( ( ! [SY11: $i,SY12: $i,SY13: $i,SY14: $i] :
            ( ( join @ ( meet @ ( join @ ( meet @ SV1 @ SV2 ) @ ( meet @ SV2 @ ( join @ SV1 @ SV2 ) ) ) @ SY11 ) @ ( meet @ ( join @ ( meet @ SV1 @ ( join @ ( join @ ( meet @ SV2 @ SY12 ) @ ( meet @ SY13 @ SV2 ) ) @ SV2 ) ) @ ( meet @ ( join @ ( meet @ SV2 @ ( meet @ ( meet @ ( join @ SV2 @ SY12 ) @ ( join @ SY13 @ SV2 ) ) @ SV2 ) ) @ ( meet @ SY14 @ ( join @ SV2 @ ( meet @ ( meet @ ( join @ SV2 @ SY12 ) @ ( join @ SY13 @ SV2 ) ) @ SV2 ) ) ) ) @ ( join @ SV1 @ ( join @ ( join @ ( meet @ SV2 @ SY12 ) @ ( meet @ SY13 @ SV2 ) ) @ SV2 ) ) ) ) @ ( join @ ( join @ ( meet @ SV1 @ SV2 ) @ ( meet @ SV2 @ ( join @ SV1 @ SV2 ) ) ) @ SY11 ) ) )
            = SV2 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[14]) ).

thf(18,plain,
    ( ( ( ( ( meet @ b @ a )
         != ( meet @ a @ b ) ) )
      = $true )
    | ( ( ( ( join @ a @ a )
         != a )
        | ( ( join @ b @ a )
         != ( join @ a @ b ) )
        | ( ( meet @ ( meet @ ( join @ a @ b ) @ ( join @ c @ b ) ) @ b )
         != b )
        | ( ( join @ ( join @ ( meet @ a @ b ) @ ( meet @ c @ b ) ) @ b )
         != b ) )
      = $true )
    | ( ( ( meet @ a @ a )
        = a )
      = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[16]) ).

thf(19,plain,
    ! [SV3: $i,SV2: $i,SV1: $i] :
      ( ( ! [SY15: $i,SY16: $i,SY17: $i] :
            ( ( join @ ( meet @ ( join @ ( meet @ SV1 @ SV2 ) @ ( meet @ SV2 @ ( join @ SV1 @ SV2 ) ) ) @ SV3 ) @ ( meet @ ( join @ ( meet @ SV1 @ ( join @ ( join @ ( meet @ SV2 @ SY15 ) @ ( meet @ SY16 @ SV2 ) ) @ SV2 ) ) @ ( meet @ ( join @ ( meet @ SV2 @ ( meet @ ( meet @ ( join @ SV2 @ SY15 ) @ ( join @ SY16 @ SV2 ) ) @ SV2 ) ) @ ( meet @ SY17 @ ( join @ SV2 @ ( meet @ ( meet @ ( join @ SV2 @ SY15 ) @ ( join @ SY16 @ SV2 ) ) @ SV2 ) ) ) ) @ ( join @ SV1 @ ( join @ ( join @ ( meet @ SV2 @ SY15 ) @ ( meet @ SY16 @ SV2 ) ) @ SV2 ) ) ) ) @ ( join @ ( join @ ( meet @ SV1 @ SV2 ) @ ( meet @ SV2 @ ( join @ SV1 @ SV2 ) ) ) @ SV3 ) ) )
            = SV2 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[17]) ).

thf(20,plain,
    ( ( ( ( meet @ b @ a )
        = ( meet @ a @ b ) )
      = $false )
    | ( ( ( ( join @ a @ a )
         != a )
        | ( ( join @ b @ a )
         != ( join @ a @ b ) )
        | ( ( meet @ ( meet @ ( join @ a @ b ) @ ( join @ c @ b ) ) @ b )
         != b )
        | ( ( join @ ( join @ ( meet @ a @ b ) @ ( meet @ c @ b ) ) @ b )
         != b ) )
      = $true )
    | ( ( ( meet @ a @ a )
        = a )
      = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[18]) ).

thf(21,plain,
    ! [SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
      ( ( ! [SY18: $i,SY19: $i] :
            ( ( join @ ( meet @ ( join @ ( meet @ SV1 @ SV2 ) @ ( meet @ SV2 @ ( join @ SV1 @ SV2 ) ) ) @ SV3 ) @ ( meet @ ( join @ ( meet @ SV1 @ ( join @ ( join @ ( meet @ SV2 @ SV4 ) @ ( meet @ SY18 @ SV2 ) ) @ SV2 ) ) @ ( meet @ ( join @ ( meet @ SV2 @ ( meet @ ( meet @ ( join @ SV2 @ SV4 ) @ ( join @ SY18 @ SV2 ) ) @ SV2 ) ) @ ( meet @ SY19 @ ( join @ SV2 @ ( meet @ ( meet @ ( join @ SV2 @ SV4 ) @ ( join @ SY18 @ SV2 ) ) @ SV2 ) ) ) ) @ ( join @ SV1 @ ( join @ ( join @ ( meet @ SV2 @ SV4 ) @ ( meet @ SY18 @ SV2 ) ) @ SV2 ) ) ) ) @ ( join @ ( join @ ( meet @ SV1 @ SV2 ) @ ( meet @ SV2 @ ( join @ SV1 @ SV2 ) ) ) @ SV3 ) ) )
            = SV2 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[19]) ).

thf(22,plain,
    ( ( ( ( ( join @ a @ a )
         != a ) )
      = $true )
    | ( ( ( ( join @ b @ a )
         != ( join @ a @ b ) )
        | ( ( meet @ ( meet @ ( join @ a @ b ) @ ( join @ c @ b ) ) @ b )
         != b )
        | ( ( join @ ( join @ ( meet @ a @ b ) @ ( meet @ c @ b ) ) @ b )
         != b ) )
      = $true )
    | ( ( ( meet @ b @ a )
        = ( meet @ a @ b ) )
      = $false )
    | ( ( ( meet @ a @ a )
        = a )
      = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[20]) ).

thf(23,plain,
    ! [SV5: $i,SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
      ( ( ! [SY20: $i] :
            ( ( join @ ( meet @ ( join @ ( meet @ SV1 @ SV2 ) @ ( meet @ SV2 @ ( join @ SV1 @ SV2 ) ) ) @ SV3 ) @ ( meet @ ( join @ ( meet @ SV1 @ ( join @ ( join @ ( meet @ SV2 @ SV4 ) @ ( meet @ SV5 @ SV2 ) ) @ SV2 ) ) @ ( meet @ ( join @ ( meet @ SV2 @ ( meet @ ( meet @ ( join @ SV2 @ SV4 ) @ ( join @ SV5 @ SV2 ) ) @ SV2 ) ) @ ( meet @ SY20 @ ( join @ SV2 @ ( meet @ ( meet @ ( join @ SV2 @ SV4 ) @ ( join @ SV5 @ SV2 ) ) @ SV2 ) ) ) ) @ ( join @ SV1 @ ( join @ ( join @ ( meet @ SV2 @ SV4 ) @ ( meet @ SV5 @ SV2 ) ) @ SV2 ) ) ) ) @ ( join @ ( join @ ( meet @ SV1 @ SV2 ) @ ( meet @ SV2 @ ( join @ SV1 @ SV2 ) ) ) @ SV3 ) ) )
            = SV2 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[21]) ).

thf(24,plain,
    ( ( ( ( join @ a @ a )
        = a )
      = $false )
    | ( ( ( ( join @ b @ a )
         != ( join @ a @ b ) )
        | ( ( meet @ ( meet @ ( join @ a @ b ) @ ( join @ c @ b ) ) @ b )
         != b )
        | ( ( join @ ( join @ ( meet @ a @ b ) @ ( meet @ c @ b ) ) @ b )
         != b ) )
      = $true )
    | ( ( ( meet @ b @ a )
        = ( meet @ a @ b ) )
      = $false )
    | ( ( ( meet @ a @ a )
        = a )
      = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[22]) ).

thf(25,plain,
    ! [SV6: $i,SV5: $i,SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
      ( ( ( join @ ( meet @ ( join @ ( meet @ SV1 @ SV2 ) @ ( meet @ SV2 @ ( join @ SV1 @ SV2 ) ) ) @ SV3 ) @ ( meet @ ( join @ ( meet @ SV1 @ ( join @ ( join @ ( meet @ SV2 @ SV4 ) @ ( meet @ SV5 @ SV2 ) ) @ SV2 ) ) @ ( meet @ ( join @ ( meet @ SV2 @ ( meet @ ( meet @ ( join @ SV2 @ SV4 ) @ ( join @ SV5 @ SV2 ) ) @ SV2 ) ) @ ( meet @ SV6 @ ( join @ SV2 @ ( meet @ ( meet @ ( join @ SV2 @ SV4 ) @ ( join @ SV5 @ SV2 ) ) @ SV2 ) ) ) ) @ ( join @ SV1 @ ( join @ ( join @ ( meet @ SV2 @ SV4 ) @ ( meet @ SV5 @ SV2 ) ) @ SV2 ) ) ) ) @ ( join @ ( join @ ( meet @ SV1 @ SV2 ) @ ( meet @ SV2 @ ( join @ SV1 @ SV2 ) ) ) @ SV3 ) ) )
        = SV2 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[23]) ).

thf(26,plain,
    ( ( ( ( ( join @ b @ a )
         != ( join @ a @ b ) ) )
      = $true )
    | ( ( ( ( meet @ ( meet @ ( join @ a @ b ) @ ( join @ c @ b ) ) @ b )
         != b )
        | ( ( join @ ( join @ ( meet @ a @ b ) @ ( meet @ c @ b ) ) @ b )
         != b ) )
      = $true )
    | ( ( ( join @ a @ a )
        = a )
      = $false )
    | ( ( ( meet @ b @ a )
        = ( meet @ a @ b ) )
      = $false )
    | ( ( ( meet @ a @ a )
        = a )
      = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[24]) ).

thf(27,plain,
    ( ( ( ( join @ b @ a )
        = ( join @ a @ b ) )
      = $false )
    | ( ( ( ( meet @ ( meet @ ( join @ a @ b ) @ ( join @ c @ b ) ) @ b )
         != b )
        | ( ( join @ ( join @ ( meet @ a @ b ) @ ( meet @ c @ b ) ) @ b )
         != b ) )
      = $true )
    | ( ( ( join @ a @ a )
        = a )
      = $false )
    | ( ( ( meet @ b @ a )
        = ( meet @ a @ b ) )
      = $false )
    | ( ( ( meet @ a @ a )
        = a )
      = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[26]) ).

thf(28,plain,
    ( ( ( ( ( meet @ ( meet @ ( join @ a @ b ) @ ( join @ c @ b ) ) @ b )
         != b ) )
      = $true )
    | ( ( ( ( join @ ( join @ ( meet @ a @ b ) @ ( meet @ c @ b ) ) @ b )
         != b ) )
      = $true )
    | ( ( ( join @ b @ a )
        = ( join @ a @ b ) )
      = $false )
    | ( ( ( join @ a @ a )
        = a )
      = $false )
    | ( ( ( meet @ b @ a )
        = ( meet @ a @ b ) )
      = $false )
    | ( ( ( meet @ a @ a )
        = a )
      = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[27]) ).

thf(29,plain,
    ( ( ( ( meet @ ( meet @ ( join @ a @ b ) @ ( join @ c @ b ) ) @ b )
        = b )
      = $false )
    | ( ( ( ( join @ ( join @ ( meet @ a @ b ) @ ( meet @ c @ b ) ) @ b )
         != b ) )
      = $true )
    | ( ( ( join @ b @ a )
        = ( join @ a @ b ) )
      = $false )
    | ( ( ( join @ a @ a )
        = a )
      = $false )
    | ( ( ( meet @ b @ a )
        = ( meet @ a @ b ) )
      = $false )
    | ( ( ( meet @ a @ a )
        = a )
      = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[28]) ).

thf(30,plain,
    ( ( ( ( join @ ( join @ ( meet @ a @ b ) @ ( meet @ c @ b ) ) @ b )
        = b )
      = $false )
    | ( ( ( meet @ ( meet @ ( join @ a @ b ) @ ( join @ c @ b ) ) @ b )
        = b )
      = $false )
    | ( ( ( join @ b @ a )
        = ( join @ a @ b ) )
      = $false )
    | ( ( ( join @ a @ a )
        = a )
      = $false )
    | ( ( ( meet @ b @ a )
        = ( meet @ a @ b ) )
      = $false )
    | ( ( ( meet @ a @ a )
        = a )
      = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[29]) ).

thf(31,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[15,30,25]) ).

thf(32,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[31]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07  % Problem  : LAT030-1 : TPTP v8.1.0. Released v2.2.0.
% 0.00/0.07  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.06/0.25  % Computer : n010.cluster.edu
% 0.06/0.25  % Model    : x86_64 x86_64
% 0.06/0.25  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.25  % Memory   : 8042.1875MB
% 0.06/0.25  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.06/0.25  % CPULimit : 300
% 0.06/0.25  % WCLimit  : 600
% 0.06/0.25  % DateTime : Wed Jun 29 06:06:04 EDT 2022
% 0.06/0.25  % CPUTime  : 
% 0.06/0.26  
% 0.06/0.26   No.of.Axioms: 2
% 0.06/0.26  
% 0.06/0.26   Length.of.Defs: 0
% 0.06/0.26  
% 0.06/0.26   Contains.Choice.Funs: false
% 0.06/0.27  (rf:0,axioms:2,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:4,loop_count:0,foatp_calls:0,translation:fof_full)..
% 14.88/15.07  
% 14.88/15.07  ********************************
% 14.88/15.07  *   All subproblems solved!    *
% 14.88/15.07  ********************************
% 14.88/15.07  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:2,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:31,loop_count:0,foatp_calls:1,translation:fof_full)
% 14.88/15.07  
% 14.88/15.07  %**** Beginning of derivation protocol ****
% 14.88/15.07  % SZS output start CNFRefutation
% See solution above
% 14.88/15.07  
% 14.88/15.07  %**** End of derivation protocol ****
% 14.88/15.07  %**** no. of clauses in derivation: 32 ****
% 14.88/15.07  %**** clause counter: 31 ****
% 14.88/15.07  
% 14.88/15.07  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:2,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:31,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------