TSTP Solution File: LAT038-1 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : LAT038-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n007.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 05:44:08 EDT 2022

% Result   : Unsatisfiable 39.73s 40.04s
% Output   : CNFRefutation 39.73s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   26
% Syntax   : Number of formulae    :   99 (  91 unt;   8 typ;   0 def)
%            Number of atoms       :  235 ( 155 equ;   0 cnn)
%            Maximal formula atoms :    1 (   2 avg)
%            Number of connectives :  534 (   6   ~;   0   |;   0   &; 528   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   11 (   8 usr;   7 con; 0-2 aty)
%            Number of variables   :  164 (   0   ^ 164   !;   0   ?; 164   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_aa,type,
    aa: $i ).

thf(tp_bb,type,
    bb: $i ).

thf(tp_cc,type,
    cc: $i ).

thf(tp_dd,type,
    dd: $i ).

thf(tp_f,type,
    f: $i > $i > $i ).

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

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

thf(tp_n0,type,
    n0: $i ).

thf(1,axiom,
    ! [W: $i] :
      ( ( f @ W @ n0 )
      = n0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f_on_right_bottom) ).

thf(2,axiom,
    ! [W: $i,U: $i,V: $i] :
      ( ( f @ W @ ( join @ U @ V ) )
      = ( join @ ( f @ W @ U ) @ ( f @ W @ V ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f_on_right_join) ).

thf(3,axiom,
    ! [W: $i] :
      ( ( f @ n0 @ W )
      = n0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f_on_left_bottom) ).

thf(4,axiom,
    ! [U: $i,V: $i,W: $i] :
      ( ( f @ ( join @ U @ V ) @ W )
      = ( join @ ( f @ U @ W ) @ ( f @ V @ W ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f_on_left_join) ).

thf(5,axiom,
    ! [X: $i,Y: $i,Z: $i] :
      ( ( join @ ( join @ X @ Y ) @ Z )
      = ( join @ X @ ( join @ Y @ Z ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_join) ).

thf(6,axiom,
    ! [X: $i,Y: $i,Z: $i] :
      ( ( meet @ ( meet @ X @ Y ) @ Z )
      = ( meet @ X @ ( meet @ Y @ Z ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_meet) ).

thf(7,axiom,
    ! [X: $i,Y: $i] :
      ( ( join @ X @ Y )
      = ( join @ Y @ X ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_join) ).

thf(8,axiom,
    ! [X: $i,Y: $i] :
      ( ( meet @ X @ Y )
      = ( meet @ Y @ X ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_meet) ).

thf(9,axiom,
    ! [X: $i,Y: $i] :
      ( ( join @ X @ ( meet @ X @ Y ) )
      = X ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',absorption2) ).

thf(10,axiom,
    ! [X: $i,Y: $i] :
      ( ( meet @ X @ ( join @ X @ Y ) )
      = X ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',absorption1) ).

thf(11,axiom,
    ! [X: $i] :
      ( ( join @ X @ X )
      = X ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_of_join) ).

thf(12,axiom,
    ! [X: $i] :
      ( ( meet @ X @ X )
      = X ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_of_meet) ).

thf(13,axiom,
    ( ( meet @ ( f @ aa @ dd ) @ ( f @ bb @ dd ) )
    = ( meet @ ( f @ cc @ dd ) @ ( f @ bb @ dd ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lhs2) ).

thf(14,axiom,
    ( ( f @ ( join @ aa @ bb ) @ dd )
    = ( f @ ( join @ cc @ bb ) @ dd ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lhs1) ).

thf(15,axiom,
    ! [X: $i,Y: $i,Z: $i] :
      ( ( meet @ X @ ( join @ Y @ Z ) )
      = ( join @ ( meet @ X @ Y ) @ ( meet @ X @ Z ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dist_meet) ).

thf(16,axiom,
    ! [X: $i,Y: $i,Z: $i] :
      ( ( join @ X @ ( meet @ Y @ Z ) )
      = ( meet @ ( join @ X @ Y ) @ ( join @ X @ Z ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dist_join) ).

thf(17,conjecture,
    $false,
    file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).

thf(18,negated_conjecture,
    $false = $false,
    inference(negate_conjecture,[status(cth)],[17]) ).

thf(19,negated_conjecture,
    ( f @ aa @ dd )
 != ( f @ cc @ dd ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rhs) ).

thf(20,plain,
    $false = $false,
    inference(unfold_def,[status(thm)],[18]) ).

thf(21,plain,
    ( ( ! [W: $i] :
          ( ( f @ W @ n0 )
          = n0 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(22,plain,
    ( ( ! [W: $i,U: $i,V: $i] :
          ( ( f @ W @ ( join @ U @ V ) )
          = ( join @ ( f @ W @ U ) @ ( f @ W @ V ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(23,plain,
    ( ( ! [W: $i] :
          ( ( f @ n0 @ W )
          = n0 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3]) ).

thf(24,plain,
    ( ( ! [U: $i,V: $i,W: $i] :
          ( ( f @ ( join @ U @ V ) @ W )
          = ( join @ ( f @ U @ W ) @ ( f @ V @ W ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4]) ).

thf(25,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ( join @ ( join @ X @ Y ) @ Z )
          = ( join @ X @ ( join @ Y @ Z ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5]) ).

thf(26,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ( meet @ ( meet @ X @ Y ) @ Z )
          = ( meet @ X @ ( meet @ Y @ Z ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6]) ).

thf(27,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( join @ X @ Y )
          = ( join @ Y @ X ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7]) ).

thf(28,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( meet @ X @ Y )
          = ( meet @ Y @ X ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8]) ).

thf(29,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( join @ X @ ( meet @ X @ Y ) )
          = X ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9]) ).

thf(30,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( meet @ X @ ( join @ X @ Y ) )
          = X ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10]) ).

thf(31,plain,
    ( ( ! [X: $i] :
          ( ( join @ X @ X )
          = X ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11]) ).

thf(32,plain,
    ( ( ! [X: $i] :
          ( ( meet @ X @ X )
          = X ) )
    = $true ),
    inference(unfold_def,[status(thm)],[12]) ).

thf(33,plain,
    ( ( ( meet @ ( f @ aa @ dd ) @ ( f @ bb @ dd ) )
      = ( meet @ ( f @ cc @ dd ) @ ( f @ bb @ dd ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[13]) ).

thf(34,plain,
    ( ( ( f @ ( join @ aa @ bb ) @ dd )
      = ( f @ ( join @ cc @ bb ) @ dd ) )
    = $true ),
    inference(unfold_def,[status(thm)],[14]) ).

thf(35,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ( meet @ X @ ( join @ Y @ Z ) )
          = ( join @ ( meet @ X @ Y ) @ ( meet @ X @ Z ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[15]) ).

thf(36,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ( join @ X @ ( meet @ Y @ Z ) )
          = ( meet @ ( join @ X @ Y ) @ ( join @ X @ Z ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[16]) ).

thf(37,plain,
    ( ( ( ( f @ aa @ dd )
       != ( f @ cc @ dd ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[19]) ).

thf(38,plain,
    ( ( ~ $false )
    = $true ),
    inference(polarity_switch,[status(thm)],[20]) ).

thf(39,plain,
    ( ( ( ( f @ aa @ dd )
       != ( f @ cc @ dd ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[37]) ).

thf(40,plain,
    ( ( ( ( f @ aa @ dd )
       != ( f @ cc @ dd ) ) )
    = $true ),
    inference(copy,[status(thm)],[39]) ).

thf(41,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ( join @ X @ ( meet @ Y @ Z ) )
          = ( meet @ ( join @ X @ Y ) @ ( join @ X @ Z ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[36]) ).

thf(42,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ( meet @ X @ ( join @ Y @ Z ) )
          = ( join @ ( meet @ X @ Y ) @ ( meet @ X @ Z ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[35]) ).

thf(43,plain,
    ( ( ( f @ ( join @ aa @ bb ) @ dd )
      = ( f @ ( join @ cc @ bb ) @ dd ) )
    = $true ),
    inference(copy,[status(thm)],[34]) ).

thf(44,plain,
    ( ( ( meet @ ( f @ aa @ dd ) @ ( f @ bb @ dd ) )
      = ( meet @ ( f @ cc @ dd ) @ ( f @ bb @ dd ) ) )
    = $true ),
    inference(copy,[status(thm)],[33]) ).

thf(45,plain,
    ( ( ! [X: $i] :
          ( ( meet @ X @ X )
          = X ) )
    = $true ),
    inference(copy,[status(thm)],[32]) ).

thf(46,plain,
    ( ( ! [X: $i] :
          ( ( join @ X @ X )
          = X ) )
    = $true ),
    inference(copy,[status(thm)],[31]) ).

thf(47,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( meet @ X @ ( join @ X @ Y ) )
          = X ) )
    = $true ),
    inference(copy,[status(thm)],[30]) ).

thf(48,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( join @ X @ ( meet @ X @ Y ) )
          = X ) )
    = $true ),
    inference(copy,[status(thm)],[29]) ).

thf(49,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( meet @ X @ Y )
          = ( meet @ Y @ X ) ) )
    = $true ),
    inference(copy,[status(thm)],[28]) ).

thf(50,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( join @ X @ Y )
          = ( join @ Y @ X ) ) )
    = $true ),
    inference(copy,[status(thm)],[27]) ).

thf(51,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ( meet @ ( meet @ X @ Y ) @ Z )
          = ( meet @ X @ ( meet @ Y @ Z ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[26]) ).

thf(52,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ( join @ ( join @ X @ Y ) @ Z )
          = ( join @ X @ ( join @ Y @ Z ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[25]) ).

thf(53,plain,
    ( ( ! [U: $i,V: $i,W: $i] :
          ( ( f @ ( join @ U @ V ) @ W )
          = ( join @ ( f @ U @ W ) @ ( f @ V @ W ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[24]) ).

thf(54,plain,
    ( ( ! [W: $i] :
          ( ( f @ n0 @ W )
          = n0 ) )
    = $true ),
    inference(copy,[status(thm)],[23]) ).

thf(55,plain,
    ( ( ! [W: $i,U: $i,V: $i] :
          ( ( f @ W @ ( join @ U @ V ) )
          = ( join @ ( f @ W @ U ) @ ( f @ W @ V ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[22]) ).

thf(56,plain,
    ( ( ! [W: $i] :
          ( ( f @ W @ n0 )
          = n0 ) )
    = $true ),
    inference(copy,[status(thm)],[21]) ).

thf(57,plain,
    ( ( ~ $false )
    = $true ),
    inference(copy,[status(thm)],[38]) ).

thf(58,plain,
    ( ( ( f @ aa @ dd )
      = ( f @ cc @ dd ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[40]) ).

thf(59,plain,
    ! [SV1: $i] :
      ( ( ! [SY30: $i,SY31: $i] :
            ( ( join @ SV1 @ ( meet @ SY30 @ SY31 ) )
            = ( meet @ ( join @ SV1 @ SY30 ) @ ( join @ SV1 @ SY31 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[41]) ).

thf(60,plain,
    ! [SV2: $i] :
      ( ( ! [SY32: $i,SY33: $i] :
            ( ( meet @ SV2 @ ( join @ SY32 @ SY33 ) )
            = ( join @ ( meet @ SV2 @ SY32 ) @ ( meet @ SV2 @ SY33 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[42]) ).

thf(61,plain,
    ! [SV3: $i] :
      ( ( ( meet @ SV3 @ SV3 )
        = SV3 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[45]) ).

thf(62,plain,
    ! [SV4: $i] :
      ( ( ( join @ SV4 @ SV4 )
        = SV4 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[46]) ).

thf(63,plain,
    ! [SV5: $i] :
      ( ( ! [SY34: $i] :
            ( ( meet @ SV5 @ ( join @ SV5 @ SY34 ) )
            = SV5 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[47]) ).

thf(64,plain,
    ! [SV6: $i] :
      ( ( ! [SY35: $i] :
            ( ( join @ SV6 @ ( meet @ SV6 @ SY35 ) )
            = SV6 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[48]) ).

thf(65,plain,
    ! [SV7: $i] :
      ( ( ! [SY36: $i] :
            ( ( meet @ SV7 @ SY36 )
            = ( meet @ SY36 @ SV7 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[49]) ).

thf(66,plain,
    ! [SV8: $i] :
      ( ( ! [SY37: $i] :
            ( ( join @ SV8 @ SY37 )
            = ( join @ SY37 @ SV8 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[50]) ).

thf(67,plain,
    ! [SV9: $i] :
      ( ( ! [SY38: $i,SY39: $i] :
            ( ( meet @ ( meet @ SV9 @ SY38 ) @ SY39 )
            = ( meet @ SV9 @ ( meet @ SY38 @ SY39 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[51]) ).

thf(68,plain,
    ! [SV10: $i] :
      ( ( ! [SY40: $i,SY41: $i] :
            ( ( join @ ( join @ SV10 @ SY40 ) @ SY41 )
            = ( join @ SV10 @ ( join @ SY40 @ SY41 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[52]) ).

thf(69,plain,
    ! [SV11: $i] :
      ( ( ! [SY42: $i,SY43: $i] :
            ( ( f @ ( join @ SV11 @ SY42 ) @ SY43 )
            = ( join @ ( f @ SV11 @ SY43 ) @ ( f @ SY42 @ SY43 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[53]) ).

thf(70,plain,
    ! [SV12: $i] :
      ( ( ( f @ n0 @ SV12 )
        = n0 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[54]) ).

thf(71,plain,
    ! [SV13: $i] :
      ( ( ! [SY44: $i,SY45: $i] :
            ( ( f @ SV13 @ ( join @ SY44 @ SY45 ) )
            = ( join @ ( f @ SV13 @ SY44 ) @ ( f @ SV13 @ SY45 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[55]) ).

thf(72,plain,
    ! [SV14: $i] :
      ( ( ( f @ SV14 @ n0 )
        = n0 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[56]) ).

thf(73,plain,
    $false = $false,
    inference(extcnf_not_pos,[status(thm)],[57]) ).

thf(74,plain,
    ! [SV15: $i,SV1: $i] :
      ( ( ! [SY46: $i] :
            ( ( join @ SV1 @ ( meet @ SV15 @ SY46 ) )
            = ( meet @ ( join @ SV1 @ SV15 ) @ ( join @ SV1 @ SY46 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[59]) ).

thf(75,plain,
    ! [SV16: $i,SV2: $i] :
      ( ( ! [SY47: $i] :
            ( ( meet @ SV2 @ ( join @ SV16 @ SY47 ) )
            = ( join @ ( meet @ SV2 @ SV16 ) @ ( meet @ SV2 @ SY47 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[60]) ).

thf(76,plain,
    ! [SV17: $i,SV5: $i] :
      ( ( ( meet @ SV5 @ ( join @ SV5 @ SV17 ) )
        = SV5 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[63]) ).

thf(77,plain,
    ! [SV18: $i,SV6: $i] :
      ( ( ( join @ SV6 @ ( meet @ SV6 @ SV18 ) )
        = SV6 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[64]) ).

thf(78,plain,
    ! [SV19: $i,SV7: $i] :
      ( ( ( meet @ SV7 @ SV19 )
        = ( meet @ SV19 @ SV7 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[65]) ).

thf(79,plain,
    ! [SV20: $i,SV8: $i] :
      ( ( ( join @ SV8 @ SV20 )
        = ( join @ SV20 @ SV8 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[66]) ).

thf(80,plain,
    ! [SV21: $i,SV9: $i] :
      ( ( ! [SY48: $i] :
            ( ( meet @ ( meet @ SV9 @ SV21 ) @ SY48 )
            = ( meet @ SV9 @ ( meet @ SV21 @ SY48 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[67]) ).

thf(81,plain,
    ! [SV22: $i,SV10: $i] :
      ( ( ! [SY49: $i] :
            ( ( join @ ( join @ SV10 @ SV22 ) @ SY49 )
            = ( join @ SV10 @ ( join @ SV22 @ SY49 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[68]) ).

thf(82,plain,
    ! [SV23: $i,SV11: $i] :
      ( ( ! [SY50: $i] :
            ( ( f @ ( join @ SV11 @ SV23 ) @ SY50 )
            = ( join @ ( f @ SV11 @ SY50 ) @ ( f @ SV23 @ SY50 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[69]) ).

thf(83,plain,
    ! [SV24: $i,SV13: $i] :
      ( ( ! [SY51: $i] :
            ( ( f @ SV13 @ ( join @ SV24 @ SY51 ) )
            = ( join @ ( f @ SV13 @ SV24 ) @ ( f @ SV13 @ SY51 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[71]) ).

thf(84,plain,
    ! [SV25: $i,SV15: $i,SV1: $i] :
      ( ( ( join @ SV1 @ ( meet @ SV15 @ SV25 ) )
        = ( meet @ ( join @ SV1 @ SV15 ) @ ( join @ SV1 @ SV25 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[74]) ).

thf(85,plain,
    ! [SV26: $i,SV16: $i,SV2: $i] :
      ( ( ( meet @ SV2 @ ( join @ SV16 @ SV26 ) )
        = ( join @ ( meet @ SV2 @ SV16 ) @ ( meet @ SV2 @ SV26 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[75]) ).

thf(86,plain,
    ! [SV27: $i,SV21: $i,SV9: $i] :
      ( ( ( meet @ ( meet @ SV9 @ SV21 ) @ SV27 )
        = ( meet @ SV9 @ ( meet @ SV21 @ SV27 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[80]) ).

thf(87,plain,
    ! [SV28: $i,SV22: $i,SV10: $i] :
      ( ( ( join @ ( join @ SV10 @ SV22 ) @ SV28 )
        = ( join @ SV10 @ ( join @ SV22 @ SV28 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[81]) ).

thf(88,plain,
    ! [SV29: $i,SV23: $i,SV11: $i] :
      ( ( ( f @ ( join @ SV11 @ SV23 ) @ SV29 )
        = ( join @ ( f @ SV11 @ SV29 ) @ ( f @ SV23 @ SV29 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[82]) ).

thf(89,plain,
    ! [SV30: $i,SV24: $i,SV13: $i] :
      ( ( ( f @ SV13 @ ( join @ SV24 @ SV30 ) )
        = ( join @ ( f @ SV13 @ SV24 ) @ ( f @ SV13 @ SV30 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[83]) ).

thf(90,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[43,89,88,87,86,85,84,79,78,77,76,73,72,70,62,61,58,44]) ).

thf(91,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[90]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : LAT038-1 : TPTP v8.1.0. Released v2.4.0.
% 0.10/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34  % Computer : n007.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Wed Jun 29 15:09:52 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.13/0.36  
% 0.13/0.36   No.of.Axioms: 17
% 0.13/0.36  
% 0.13/0.36   Length.of.Defs: 0
% 0.13/0.36  
% 0.13/0.36   Contains.Choice.Funs: false
% 0.13/0.36  (rf:0,axioms:17,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:19,loop_count:0,foatp_calls:0,translation:fof_full).....
% 39.73/40.04  
% 39.73/40.04  ********************************
% 39.73/40.04  *   All subproblems solved!    *
% 39.73/40.04  ********************************
% 39.73/40.04  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:17,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:90,loop_count:0,foatp_calls:1,translation:fof_full)
% 39.73/40.04  
% 39.73/40.04  %**** Beginning of derivation protocol ****
% 39.73/40.04  % SZS output start CNFRefutation
% See solution above
% 39.73/40.05  
% 39.73/40.05  %**** End of derivation protocol ****
% 39.73/40.05  %**** no. of clauses in derivation: 91 ****
% 39.73/40.05  %**** clause counter: 90 ****
% 39.73/40.05  
% 39.73/40.05  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:17,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:90,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------