TSTP Solution File: REL005+4 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : REL005+4 : TPTP v8.1.0. Released v4.0.0.
% 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 : Mon Jul 18 19:38:22 EDT 2022

% Result   : Theorem 5.91s 6.17s
% Output   : CNFRefutation 5.91s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   27
% Syntax   : Number of formulae    :  158 ( 147 unt;  10 typ;   0 def)
%            Number of atoms       :  413 ( 280 equ;   0 cnn)
%            Maximal formula atoms :    2 (   2 avg)
%            Number of connectives : 1702 (   4   ~;   0   |;   5   &;1693   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    8 (   8   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   13 (  10 usr;   7 con; 0-2 aty)
%            Number of variables   :  307 (   0   ^ 307   !;   0   ?; 307   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_complement,type,
    complement: $i > $i ).

thf(tp_composition,type,
    composition: $i > $i > $i ).

thf(tp_converse,type,
    converse: $i > $i ).

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

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

thf(tp_one,type,
    one: $i ).

thf(tp_sK1_X0,type,
    sK1_X0: $i ).

thf(tp_sK2_SY36,type,
    sK2_SY36: $i ).

thf(tp_top,type,
    top: $i ).

thf(tp_zero,type,
    zero: $i ).

thf(1,axiom,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( join @ ( meet @ ( composition @ X0 @ X1 ) @ X2 ) @ ( meet @ ( composition @ ( meet @ X0 @ ( composition @ X2 @ ( converse @ X1 ) ) ) @ X1 ) @ X2 ) )
      = ( meet @ ( composition @ ( meet @ X0 @ ( composition @ X2 @ ( converse @ X1 ) ) ) @ X1 ) @ X2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',modular_law_2) ).

thf(2,axiom,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( join @ ( meet @ ( composition @ X0 @ X1 ) @ X2 ) @ ( meet @ ( composition @ X0 @ ( meet @ X1 @ ( composition @ ( converse @ X0 ) @ X2 ) ) ) @ X2 ) )
      = ( meet @ ( composition @ X0 @ ( meet @ X1 @ ( composition @ ( converse @ X0 ) @ X2 ) ) ) @ X2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',modular_law_1) ).

thf(3,axiom,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( join @ ( meet @ ( composition @ X0 @ X1 ) @ X2 ) @ ( composition @ ( meet @ X0 @ ( composition @ X2 @ ( converse @ X1 ) ) ) @ ( meet @ X1 @ ( composition @ ( converse @ X0 ) @ X2 ) ) ) )
      = ( composition @ ( meet @ X0 @ ( composition @ X2 @ ( converse @ X1 ) ) ) @ ( meet @ X1 @ ( composition @ ( converse @ X0 ) @ X2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dedekind_law) ).

thf(4,axiom,
    ! [X0: $i] :
      ( zero
      = ( meet @ X0 @ ( complement @ X0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_zero) ).

thf(5,axiom,
    ! [X0: $i] :
      ( top
      = ( join @ X0 @ ( complement @ X0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_top) ).

thf(6,axiom,
    ! [X0: $i,X1: $i] :
      ( ( join @ ( composition @ ( converse @ X0 ) @ ( complement @ ( composition @ X0 @ X1 ) ) ) @ ( complement @ X1 ) )
      = ( complement @ X1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_cancellativity) ).

thf(7,axiom,
    ! [X0: $i,X1: $i] :
      ( ( converse @ ( composition @ X0 @ X1 ) )
      = ( composition @ ( converse @ X1 ) @ ( converse @ X0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_multiplicativity) ).

thf(8,axiom,
    ! [X0: $i,X1: $i] :
      ( ( converse @ ( join @ X0 @ X1 ) )
      = ( join @ ( converse @ X0 ) @ ( converse @ X1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_additivity) ).

thf(9,axiom,
    ! [X0: $i] :
      ( ( converse @ ( converse @ X0 ) )
      = X0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_idempotence) ).

thf(10,axiom,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( composition @ ( join @ X0 @ X1 ) @ X2 )
      = ( join @ ( composition @ X0 @ X2 ) @ ( composition @ X1 @ X2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_distributivity) ).

thf(11,axiom,
    ! [X0: $i] :
      ( ( composition @ X0 @ one )
      = X0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_identity) ).

thf(12,axiom,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( composition @ X0 @ ( composition @ X1 @ X2 ) )
      = ( composition @ ( composition @ X0 @ X1 ) @ X2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_associativity) ).

thf(13,axiom,
    ! [X0: $i,X1: $i] :
      ( ( meet @ X0 @ X1 )
      = ( complement @ ( join @ ( complement @ X0 ) @ ( complement @ X1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux4_definiton_of_meet) ).

thf(14,axiom,
    ! [X0: $i,X1: $i] :
      ( X0
      = ( join @ ( complement @ ( join @ ( complement @ X0 ) @ ( complement @ X1 ) ) ) @ ( complement @ ( join @ ( complement @ X0 ) @ X1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux3_a_kind_of_de_Morgan) ).

thf(15,axiom,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( join @ X0 @ ( join @ X1 @ X2 ) )
      = ( join @ ( join @ X0 @ X1 ) @ X2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux2_join_associativity) ).

thf(16,axiom,
    ! [X0: $i,X1: $i] :
      ( ( join @ X0 @ X1 )
      = ( join @ X1 @ X0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux1_join_commutativity) ).

thf(17,conjecture,
    ! [X0: $i,X1: $i] :
      ( ( ( join @ ( converse @ ( meet @ X0 @ X1 ) ) @ ( meet @ ( converse @ X0 ) @ ( converse @ X1 ) ) )
        = ( meet @ ( converse @ X0 ) @ ( converse @ X1 ) ) )
      & ( ( join @ ( meet @ ( converse @ X0 ) @ ( converse @ X1 ) ) @ ( converse @ ( meet @ X0 @ X1 ) ) )
        = ( converse @ ( meet @ X0 @ X1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).

thf(18,negated_conjecture,
    ( ( ! [X0: $i,X1: $i] :
          ( ( ( join @ ( converse @ ( meet @ X0 @ X1 ) ) @ ( meet @ ( converse @ X0 ) @ ( converse @ X1 ) ) )
            = ( meet @ ( converse @ X0 ) @ ( converse @ X1 ) ) )
          & ( ( join @ ( meet @ ( converse @ X0 ) @ ( converse @ X1 ) ) @ ( converse @ ( meet @ X0 @ X1 ) ) )
            = ( converse @ ( meet @ X0 @ X1 ) ) ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[17]) ).

thf(19,plain,
    ( ( ! [X0: $i,X1: $i] :
          ( ( ( join @ ( converse @ ( meet @ X0 @ X1 ) ) @ ( meet @ ( converse @ X0 ) @ ( converse @ X1 ) ) )
            = ( meet @ ( converse @ X0 ) @ ( converse @ X1 ) ) )
          & ( ( join @ ( meet @ ( converse @ X0 ) @ ( converse @ X1 ) ) @ ( converse @ ( meet @ X0 @ X1 ) ) )
            = ( converse @ ( meet @ X0 @ X1 ) ) ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[18]) ).

thf(20,plain,
    ( ( ! [X0: $i,X1: $i,X2: $i] :
          ( ( join @ ( meet @ ( composition @ X0 @ X1 ) @ X2 ) @ ( meet @ ( composition @ ( meet @ X0 @ ( composition @ X2 @ ( converse @ X1 ) ) ) @ X1 ) @ X2 ) )
          = ( meet @ ( composition @ ( meet @ X0 @ ( composition @ X2 @ ( converse @ X1 ) ) ) @ X1 ) @ X2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(21,plain,
    ( ( ! [X0: $i,X1: $i,X2: $i] :
          ( ( join @ ( meet @ ( composition @ X0 @ X1 ) @ X2 ) @ ( meet @ ( composition @ X0 @ ( meet @ X1 @ ( composition @ ( converse @ X0 ) @ X2 ) ) ) @ X2 ) )
          = ( meet @ ( composition @ X0 @ ( meet @ X1 @ ( composition @ ( converse @ X0 ) @ X2 ) ) ) @ X2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(22,plain,
    ( ( ! [X0: $i,X1: $i,X2: $i] :
          ( ( join @ ( meet @ ( composition @ X0 @ X1 ) @ X2 ) @ ( composition @ ( meet @ X0 @ ( composition @ X2 @ ( converse @ X1 ) ) ) @ ( meet @ X1 @ ( composition @ ( converse @ X0 ) @ X2 ) ) ) )
          = ( composition @ ( meet @ X0 @ ( composition @ X2 @ ( converse @ X1 ) ) ) @ ( meet @ X1 @ ( composition @ ( converse @ X0 ) @ X2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3]) ).

thf(23,plain,
    ( ( ! [X0: $i] :
          ( zero
          = ( meet @ X0 @ ( complement @ X0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4]) ).

thf(24,plain,
    ( ( ! [X0: $i] :
          ( top
          = ( join @ X0 @ ( complement @ X0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5]) ).

thf(25,plain,
    ( ( ! [X0: $i,X1: $i] :
          ( ( join @ ( composition @ ( converse @ X0 ) @ ( complement @ ( composition @ X0 @ X1 ) ) ) @ ( complement @ X1 ) )
          = ( complement @ X1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6]) ).

thf(26,plain,
    ( ( ! [X0: $i,X1: $i] :
          ( ( converse @ ( composition @ X0 @ X1 ) )
          = ( composition @ ( converse @ X1 ) @ ( converse @ X0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7]) ).

thf(27,plain,
    ( ( ! [X0: $i,X1: $i] :
          ( ( converse @ ( join @ X0 @ X1 ) )
          = ( join @ ( converse @ X0 ) @ ( converse @ X1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8]) ).

thf(28,plain,
    ( ( ! [X0: $i] :
          ( ( converse @ ( converse @ X0 ) )
          = X0 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9]) ).

thf(29,plain,
    ( ( ! [X0: $i,X1: $i,X2: $i] :
          ( ( composition @ ( join @ X0 @ X1 ) @ X2 )
          = ( join @ ( composition @ X0 @ X2 ) @ ( composition @ X1 @ X2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10]) ).

thf(30,plain,
    ( ( ! [X0: $i] :
          ( ( composition @ X0 @ one )
          = X0 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11]) ).

thf(31,plain,
    ( ( ! [X0: $i,X1: $i,X2: $i] :
          ( ( composition @ X0 @ ( composition @ X1 @ X2 ) )
          = ( composition @ ( composition @ X0 @ X1 ) @ X2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[12]) ).

thf(32,plain,
    ( ( ! [X0: $i,X1: $i] :
          ( ( meet @ X0 @ X1 )
          = ( complement @ ( join @ ( complement @ X0 ) @ ( complement @ X1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[13]) ).

thf(33,plain,
    ( ( ! [X0: $i,X1: $i] :
          ( X0
          = ( join @ ( complement @ ( join @ ( complement @ X0 ) @ ( complement @ X1 ) ) ) @ ( complement @ ( join @ ( complement @ X0 ) @ X1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[14]) ).

thf(34,plain,
    ( ( ! [X0: $i,X1: $i,X2: $i] :
          ( ( join @ X0 @ ( join @ X1 @ X2 ) )
          = ( join @ ( join @ X0 @ X1 ) @ X2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[15]) ).

thf(35,plain,
    ( ( ! [X0: $i,X1: $i] :
          ( ( join @ X0 @ X1 )
          = ( join @ X1 @ X0 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[16]) ).

thf(36,plain,
    ( ( ! [SY36: $i] :
          ( ( ( join @ ( converse @ ( meet @ sK1_X0 @ SY36 ) ) @ ( meet @ ( converse @ sK1_X0 ) @ ( converse @ SY36 ) ) )
            = ( meet @ ( converse @ sK1_X0 ) @ ( converse @ SY36 ) ) )
          & ( ( join @ ( meet @ ( converse @ sK1_X0 ) @ ( converse @ SY36 ) ) @ ( converse @ ( meet @ sK1_X0 @ SY36 ) ) )
            = ( converse @ ( meet @ sK1_X0 @ SY36 ) ) ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[19]) ).

thf(37,plain,
    ( ( ( ( join @ ( converse @ ( meet @ sK1_X0 @ sK2_SY36 ) ) @ ( meet @ ( converse @ sK1_X0 ) @ ( converse @ sK2_SY36 ) ) )
        = ( meet @ ( converse @ sK1_X0 ) @ ( converse @ sK2_SY36 ) ) )
      & ( ( join @ ( meet @ ( converse @ sK1_X0 ) @ ( converse @ sK2_SY36 ) ) @ ( converse @ ( meet @ sK1_X0 @ sK2_SY36 ) ) )
        = ( converse @ ( meet @ sK1_X0 @ sK2_SY36 ) ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[36]) ).

thf(38,plain,
    ( ( ( join @ ( converse @ ( meet @ sK1_X0 @ sK2_SY36 ) ) @ ( meet @ ( converse @ sK1_X0 ) @ ( converse @ sK2_SY36 ) ) )
      = ( meet @ ( converse @ sK1_X0 ) @ ( converse @ sK2_SY36 ) ) )
    = $false ),
    inference(split_conjecture,[split_conjecture(split,[])],[37]) ).

thf(39,plain,
    ( ( ( join @ ( meet @ ( converse @ sK1_X0 ) @ ( converse @ sK2_SY36 ) ) @ ( converse @ ( meet @ sK1_X0 @ sK2_SY36 ) ) )
      = ( converse @ ( meet @ sK1_X0 @ sK2_SY36 ) ) )
    = $false ),
    inference(split_conjecture,[split_conjecture(split,[])],[37]) ).

thf(40,plain,
    ( ( ( ( join @ ( converse @ ( meet @ sK1_X0 @ sK2_SY36 ) ) @ ( meet @ ( converse @ sK1_X0 ) @ ( converse @ sK2_SY36 ) ) )
       != ( meet @ ( converse @ sK1_X0 ) @ ( converse @ sK2_SY36 ) ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[38]) ).

thf(41,plain,
    ( ( ( ( join @ ( meet @ ( converse @ sK1_X0 ) @ ( converse @ sK2_SY36 ) ) @ ( converse @ ( meet @ sK1_X0 @ sK2_SY36 ) ) )
       != ( converse @ ( meet @ sK1_X0 @ sK2_SY36 ) ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[39]) ).

thf(42,plain,
    ( ( ! [X0: $i,X1: $i] :
          ( ( join @ X0 @ X1 )
          = ( join @ X1 @ X0 ) ) )
    = $true ),
    inference(copy,[status(thm)],[35]) ).

thf(43,plain,
    ( ( ! [X0: $i,X1: $i,X2: $i] :
          ( ( join @ X0 @ ( join @ X1 @ X2 ) )
          = ( join @ ( join @ X0 @ X1 ) @ X2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[34]) ).

thf(44,plain,
    ( ( ! [X0: $i,X1: $i] :
          ( X0
          = ( join @ ( complement @ ( join @ ( complement @ X0 ) @ ( complement @ X1 ) ) ) @ ( complement @ ( join @ ( complement @ X0 ) @ X1 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[33]) ).

thf(45,plain,
    ( ( ! [X0: $i,X1: $i] :
          ( ( meet @ X0 @ X1 )
          = ( complement @ ( join @ ( complement @ X0 ) @ ( complement @ X1 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[32]) ).

thf(46,plain,
    ( ( ! [X0: $i,X1: $i,X2: $i] :
          ( ( composition @ X0 @ ( composition @ X1 @ X2 ) )
          = ( composition @ ( composition @ X0 @ X1 ) @ X2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[31]) ).

thf(47,plain,
    ( ( ! [X0: $i] :
          ( ( composition @ X0 @ one )
          = X0 ) )
    = $true ),
    inference(copy,[status(thm)],[30]) ).

thf(48,plain,
    ( ( ! [X0: $i,X1: $i,X2: $i] :
          ( ( composition @ ( join @ X0 @ X1 ) @ X2 )
          = ( join @ ( composition @ X0 @ X2 ) @ ( composition @ X1 @ X2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[29]) ).

thf(49,plain,
    ( ( ! [X0: $i] :
          ( ( converse @ ( converse @ X0 ) )
          = X0 ) )
    = $true ),
    inference(copy,[status(thm)],[28]) ).

thf(50,plain,
    ( ( ! [X0: $i,X1: $i] :
          ( ( converse @ ( join @ X0 @ X1 ) )
          = ( join @ ( converse @ X0 ) @ ( converse @ X1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[27]) ).

thf(51,plain,
    ( ( ! [X0: $i,X1: $i] :
          ( ( converse @ ( composition @ X0 @ X1 ) )
          = ( composition @ ( converse @ X1 ) @ ( converse @ X0 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[26]) ).

thf(52,plain,
    ( ( ! [X0: $i,X1: $i] :
          ( ( join @ ( composition @ ( converse @ X0 ) @ ( complement @ ( composition @ X0 @ X1 ) ) ) @ ( complement @ X1 ) )
          = ( complement @ X1 ) ) )
    = $true ),
    inference(copy,[status(thm)],[25]) ).

thf(53,plain,
    ( ( ! [X0: $i] :
          ( top
          = ( join @ X0 @ ( complement @ X0 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[24]) ).

thf(54,plain,
    ( ( ! [X0: $i] :
          ( zero
          = ( meet @ X0 @ ( complement @ X0 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[23]) ).

thf(55,plain,
    ( ( ! [X0: $i,X1: $i,X2: $i] :
          ( ( join @ ( meet @ ( composition @ X0 @ X1 ) @ X2 ) @ ( composition @ ( meet @ X0 @ ( composition @ X2 @ ( converse @ X1 ) ) ) @ ( meet @ X1 @ ( composition @ ( converse @ X0 ) @ X2 ) ) ) )
          = ( composition @ ( meet @ X0 @ ( composition @ X2 @ ( converse @ X1 ) ) ) @ ( meet @ X1 @ ( composition @ ( converse @ X0 ) @ X2 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[22]) ).

thf(56,plain,
    ( ( ! [X0: $i,X1: $i,X2: $i] :
          ( ( join @ ( meet @ ( composition @ X0 @ X1 ) @ X2 ) @ ( meet @ ( composition @ X0 @ ( meet @ X1 @ ( composition @ ( converse @ X0 ) @ X2 ) ) ) @ X2 ) )
          = ( meet @ ( composition @ X0 @ ( meet @ X1 @ ( composition @ ( converse @ X0 ) @ X2 ) ) ) @ X2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[21]) ).

thf(57,plain,
    ( ( ! [X0: $i,X1: $i,X2: $i] :
          ( ( join @ ( meet @ ( composition @ X0 @ X1 ) @ X2 ) @ ( meet @ ( composition @ ( meet @ X0 @ ( composition @ X2 @ ( converse @ X1 ) ) ) @ X1 ) @ X2 ) )
          = ( meet @ ( composition @ ( meet @ X0 @ ( composition @ X2 @ ( converse @ X1 ) ) ) @ X1 ) @ X2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[20]) ).

thf(58,plain,
    ( ( ( ( join @ ( converse @ ( meet @ sK1_X0 @ sK2_SY36 ) ) @ ( meet @ ( converse @ sK1_X0 ) @ ( converse @ sK2_SY36 ) ) )
       != ( meet @ ( converse @ sK1_X0 ) @ ( converse @ sK2_SY36 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[40]) ).

thf(59,plain,
    ! [SV1: $i] :
      ( ( ! [SY37: $i] :
            ( ( join @ SV1 @ SY37 )
            = ( join @ SY37 @ SV1 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[42]) ).

thf(60,plain,
    ! [SV2: $i] :
      ( ( ! [SY38: $i,SY39: $i] :
            ( ( join @ SV2 @ ( join @ SY38 @ SY39 ) )
            = ( join @ ( join @ SV2 @ SY38 ) @ SY39 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[43]) ).

thf(61,plain,
    ! [SV3: $i] :
      ( ( ! [SY40: $i] :
            ( SV3
            = ( join @ ( complement @ ( join @ ( complement @ SV3 ) @ ( complement @ SY40 ) ) ) @ ( complement @ ( join @ ( complement @ SV3 ) @ SY40 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[44]) ).

thf(62,plain,
    ! [SV4: $i] :
      ( ( ! [SY41: $i] :
            ( ( meet @ SV4 @ SY41 )
            = ( complement @ ( join @ ( complement @ SV4 ) @ ( complement @ SY41 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[45]) ).

thf(63,plain,
    ! [SV5: $i] :
      ( ( ! [SY42: $i,SY43: $i] :
            ( ( composition @ SV5 @ ( composition @ SY42 @ SY43 ) )
            = ( composition @ ( composition @ SV5 @ SY42 ) @ SY43 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[46]) ).

thf(64,plain,
    ! [SV6: $i] :
      ( ( ( composition @ SV6 @ one )
        = SV6 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[47]) ).

thf(65,plain,
    ! [SV7: $i] :
      ( ( ! [SY44: $i,SY45: $i] :
            ( ( composition @ ( join @ SV7 @ SY44 ) @ SY45 )
            = ( join @ ( composition @ SV7 @ SY45 ) @ ( composition @ SY44 @ SY45 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[48]) ).

thf(66,plain,
    ! [SV8: $i] :
      ( ( ( converse @ ( converse @ SV8 ) )
        = SV8 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[49]) ).

thf(67,plain,
    ! [SV9: $i] :
      ( ( ! [SY46: $i] :
            ( ( converse @ ( join @ SV9 @ SY46 ) )
            = ( join @ ( converse @ SV9 ) @ ( converse @ SY46 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[50]) ).

thf(68,plain,
    ! [SV10: $i] :
      ( ( ! [SY47: $i] :
            ( ( converse @ ( composition @ SV10 @ SY47 ) )
            = ( composition @ ( converse @ SY47 ) @ ( converse @ SV10 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[51]) ).

thf(69,plain,
    ! [SV11: $i] :
      ( ( ! [SY48: $i] :
            ( ( join @ ( composition @ ( converse @ SV11 ) @ ( complement @ ( composition @ SV11 @ SY48 ) ) ) @ ( complement @ SY48 ) )
            = ( complement @ SY48 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[52]) ).

thf(70,plain,
    ! [SV12: $i] :
      ( ( top
        = ( join @ SV12 @ ( complement @ SV12 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[53]) ).

thf(71,plain,
    ! [SV13: $i] :
      ( ( zero
        = ( meet @ SV13 @ ( complement @ SV13 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[54]) ).

thf(72,plain,
    ! [SV14: $i] :
      ( ( ! [SY49: $i,SY50: $i] :
            ( ( join @ ( meet @ ( composition @ SV14 @ SY49 ) @ SY50 ) @ ( composition @ ( meet @ SV14 @ ( composition @ SY50 @ ( converse @ SY49 ) ) ) @ ( meet @ SY49 @ ( composition @ ( converse @ SV14 ) @ SY50 ) ) ) )
            = ( composition @ ( meet @ SV14 @ ( composition @ SY50 @ ( converse @ SY49 ) ) ) @ ( meet @ SY49 @ ( composition @ ( converse @ SV14 ) @ SY50 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[55]) ).

thf(73,plain,
    ! [SV15: $i] :
      ( ( ! [SY51: $i,SY52: $i] :
            ( ( join @ ( meet @ ( composition @ SV15 @ SY51 ) @ SY52 ) @ ( meet @ ( composition @ SV15 @ ( meet @ SY51 @ ( composition @ ( converse @ SV15 ) @ SY52 ) ) ) @ SY52 ) )
            = ( meet @ ( composition @ SV15 @ ( meet @ SY51 @ ( composition @ ( converse @ SV15 ) @ SY52 ) ) ) @ SY52 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[56]) ).

thf(74,plain,
    ! [SV16: $i] :
      ( ( ! [SY53: $i,SY54: $i] :
            ( ( join @ ( meet @ ( composition @ SV16 @ SY53 ) @ SY54 ) @ ( meet @ ( composition @ ( meet @ SV16 @ ( composition @ SY54 @ ( converse @ SY53 ) ) ) @ SY53 ) @ SY54 ) )
            = ( meet @ ( composition @ ( meet @ SV16 @ ( composition @ SY54 @ ( converse @ SY53 ) ) ) @ SY53 ) @ SY54 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[57]) ).

thf(75,plain,
    ( ( ( join @ ( converse @ ( meet @ sK1_X0 @ sK2_SY36 ) ) @ ( meet @ ( converse @ sK1_X0 ) @ ( converse @ sK2_SY36 ) ) )
      = ( meet @ ( converse @ sK1_X0 ) @ ( converse @ sK2_SY36 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[58]) ).

thf(76,plain,
    ! [SV17: $i,SV1: $i] :
      ( ( ( join @ SV1 @ SV17 )
        = ( join @ SV17 @ SV1 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[59]) ).

thf(77,plain,
    ! [SV18: $i,SV2: $i] :
      ( ( ! [SY55: $i] :
            ( ( join @ SV2 @ ( join @ SV18 @ SY55 ) )
            = ( join @ ( join @ SV2 @ SV18 ) @ SY55 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[60]) ).

thf(78,plain,
    ! [SV19: $i,SV3: $i] :
      ( ( SV3
        = ( join @ ( complement @ ( join @ ( complement @ SV3 ) @ ( complement @ SV19 ) ) ) @ ( complement @ ( join @ ( complement @ SV3 ) @ SV19 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[61]) ).

thf(79,plain,
    ! [SV20: $i,SV4: $i] :
      ( ( ( meet @ SV4 @ SV20 )
        = ( complement @ ( join @ ( complement @ SV4 ) @ ( complement @ SV20 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[62]) ).

thf(80,plain,
    ! [SV21: $i,SV5: $i] :
      ( ( ! [SY56: $i] :
            ( ( composition @ SV5 @ ( composition @ SV21 @ SY56 ) )
            = ( composition @ ( composition @ SV5 @ SV21 ) @ SY56 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[63]) ).

thf(81,plain,
    ! [SV22: $i,SV7: $i] :
      ( ( ! [SY57: $i] :
            ( ( composition @ ( join @ SV7 @ SV22 ) @ SY57 )
            = ( join @ ( composition @ SV7 @ SY57 ) @ ( composition @ SV22 @ SY57 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[65]) ).

thf(82,plain,
    ! [SV23: $i,SV9: $i] :
      ( ( ( converse @ ( join @ SV9 @ SV23 ) )
        = ( join @ ( converse @ SV9 ) @ ( converse @ SV23 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[67]) ).

thf(83,plain,
    ! [SV24: $i,SV10: $i] :
      ( ( ( converse @ ( composition @ SV10 @ SV24 ) )
        = ( composition @ ( converse @ SV24 ) @ ( converse @ SV10 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[68]) ).

thf(84,plain,
    ! [SV25: $i,SV11: $i] :
      ( ( ( join @ ( composition @ ( converse @ SV11 ) @ ( complement @ ( composition @ SV11 @ SV25 ) ) ) @ ( complement @ SV25 ) )
        = ( complement @ SV25 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[69]) ).

thf(85,plain,
    ! [SV26: $i,SV14: $i] :
      ( ( ! [SY58: $i] :
            ( ( join @ ( meet @ ( composition @ SV14 @ SV26 ) @ SY58 ) @ ( composition @ ( meet @ SV14 @ ( composition @ SY58 @ ( converse @ SV26 ) ) ) @ ( meet @ SV26 @ ( composition @ ( converse @ SV14 ) @ SY58 ) ) ) )
            = ( composition @ ( meet @ SV14 @ ( composition @ SY58 @ ( converse @ SV26 ) ) ) @ ( meet @ SV26 @ ( composition @ ( converse @ SV14 ) @ SY58 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[72]) ).

thf(86,plain,
    ! [SV27: $i,SV15: $i] :
      ( ( ! [SY59: $i] :
            ( ( join @ ( meet @ ( composition @ SV15 @ SV27 ) @ SY59 ) @ ( meet @ ( composition @ SV15 @ ( meet @ SV27 @ ( composition @ ( converse @ SV15 ) @ SY59 ) ) ) @ SY59 ) )
            = ( meet @ ( composition @ SV15 @ ( meet @ SV27 @ ( composition @ ( converse @ SV15 ) @ SY59 ) ) ) @ SY59 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[73]) ).

thf(87,plain,
    ! [SV28: $i,SV16: $i] :
      ( ( ! [SY60: $i] :
            ( ( join @ ( meet @ ( composition @ SV16 @ SV28 ) @ SY60 ) @ ( meet @ ( composition @ ( meet @ SV16 @ ( composition @ SY60 @ ( converse @ SV28 ) ) ) @ SV28 ) @ SY60 ) )
            = ( meet @ ( composition @ ( meet @ SV16 @ ( composition @ SY60 @ ( converse @ SV28 ) ) ) @ SV28 ) @ SY60 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[74]) ).

thf(88,plain,
    ! [SV29: $i,SV18: $i,SV2: $i] :
      ( ( ( join @ SV2 @ ( join @ SV18 @ SV29 ) )
        = ( join @ ( join @ SV2 @ SV18 ) @ SV29 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[77]) ).

thf(89,plain,
    ! [SV30: $i,SV21: $i,SV5: $i] :
      ( ( ( composition @ SV5 @ ( composition @ SV21 @ SV30 ) )
        = ( composition @ ( composition @ SV5 @ SV21 ) @ SV30 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[80]) ).

thf(90,plain,
    ! [SV31: $i,SV22: $i,SV7: $i] :
      ( ( ( composition @ ( join @ SV7 @ SV22 ) @ SV31 )
        = ( join @ ( composition @ SV7 @ SV31 ) @ ( composition @ SV22 @ SV31 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[81]) ).

thf(91,plain,
    ! [SV32: $i,SV26: $i,SV14: $i] :
      ( ( ( join @ ( meet @ ( composition @ SV14 @ SV26 ) @ SV32 ) @ ( composition @ ( meet @ SV14 @ ( composition @ SV32 @ ( converse @ SV26 ) ) ) @ ( meet @ SV26 @ ( composition @ ( converse @ SV14 ) @ SV32 ) ) ) )
        = ( composition @ ( meet @ SV14 @ ( composition @ SV32 @ ( converse @ SV26 ) ) ) @ ( meet @ SV26 @ ( composition @ ( converse @ SV14 ) @ SV32 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[85]) ).

thf(92,plain,
    ! [SV33: $i,SV27: $i,SV15: $i] :
      ( ( ( join @ ( meet @ ( composition @ SV15 @ SV27 ) @ SV33 ) @ ( meet @ ( composition @ SV15 @ ( meet @ SV27 @ ( composition @ ( converse @ SV15 ) @ SV33 ) ) ) @ SV33 ) )
        = ( meet @ ( composition @ SV15 @ ( meet @ SV27 @ ( composition @ ( converse @ SV15 ) @ SV33 ) ) ) @ SV33 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[86]) ).

thf(93,plain,
    ! [SV34: $i,SV28: $i,SV16: $i] :
      ( ( ( join @ ( meet @ ( composition @ SV16 @ SV28 ) @ SV34 ) @ ( meet @ ( composition @ ( meet @ SV16 @ ( composition @ SV34 @ ( converse @ SV28 ) ) ) @ SV28 ) @ SV34 ) )
        = ( meet @ ( composition @ ( meet @ SV16 @ ( composition @ SV34 @ ( converse @ SV28 ) ) ) @ SV28 ) @ SV34 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[87]) ).

thf(94,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[64,93,92,91,90,89,88,84,83,82,79,78,76,75,71,70,66]) ).

thf(95,plain,
    ( ( ! [X0: $i,X1: $i] :
          ( ( join @ X0 @ X1 )
          = ( join @ X1 @ X0 ) ) )
    = $true ),
    inference(copy,[status(thm)],[35]) ).

thf(96,plain,
    ( ( ! [X0: $i,X1: $i,X2: $i] :
          ( ( join @ X0 @ ( join @ X1 @ X2 ) )
          = ( join @ ( join @ X0 @ X1 ) @ X2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[34]) ).

thf(97,plain,
    ( ( ! [X0: $i,X1: $i] :
          ( X0
          = ( join @ ( complement @ ( join @ ( complement @ X0 ) @ ( complement @ X1 ) ) ) @ ( complement @ ( join @ ( complement @ X0 ) @ X1 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[33]) ).

thf(98,plain,
    ( ( ! [X0: $i,X1: $i] :
          ( ( meet @ X0 @ X1 )
          = ( complement @ ( join @ ( complement @ X0 ) @ ( complement @ X1 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[32]) ).

thf(99,plain,
    ( ( ! [X0: $i,X1: $i,X2: $i] :
          ( ( composition @ X0 @ ( composition @ X1 @ X2 ) )
          = ( composition @ ( composition @ X0 @ X1 ) @ X2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[31]) ).

thf(100,plain,
    ( ( ! [X0: $i] :
          ( ( composition @ X0 @ one )
          = X0 ) )
    = $true ),
    inference(copy,[status(thm)],[30]) ).

thf(101,plain,
    ( ( ! [X0: $i,X1: $i,X2: $i] :
          ( ( composition @ ( join @ X0 @ X1 ) @ X2 )
          = ( join @ ( composition @ X0 @ X2 ) @ ( composition @ X1 @ X2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[29]) ).

thf(102,plain,
    ( ( ! [X0: $i] :
          ( ( converse @ ( converse @ X0 ) )
          = X0 ) )
    = $true ),
    inference(copy,[status(thm)],[28]) ).

thf(103,plain,
    ( ( ! [X0: $i,X1: $i] :
          ( ( converse @ ( join @ X0 @ X1 ) )
          = ( join @ ( converse @ X0 ) @ ( converse @ X1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[27]) ).

thf(104,plain,
    ( ( ! [X0: $i,X1: $i] :
          ( ( converse @ ( composition @ X0 @ X1 ) )
          = ( composition @ ( converse @ X1 ) @ ( converse @ X0 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[26]) ).

thf(105,plain,
    ( ( ! [X0: $i,X1: $i] :
          ( ( join @ ( composition @ ( converse @ X0 ) @ ( complement @ ( composition @ X0 @ X1 ) ) ) @ ( complement @ X1 ) )
          = ( complement @ X1 ) ) )
    = $true ),
    inference(copy,[status(thm)],[25]) ).

thf(106,plain,
    ( ( ! [X0: $i] :
          ( top
          = ( join @ X0 @ ( complement @ X0 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[24]) ).

thf(107,plain,
    ( ( ! [X0: $i] :
          ( zero
          = ( meet @ X0 @ ( complement @ X0 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[23]) ).

thf(108,plain,
    ( ( ! [X0: $i,X1: $i,X2: $i] :
          ( ( join @ ( meet @ ( composition @ X0 @ X1 ) @ X2 ) @ ( composition @ ( meet @ X0 @ ( composition @ X2 @ ( converse @ X1 ) ) ) @ ( meet @ X1 @ ( composition @ ( converse @ X0 ) @ X2 ) ) ) )
          = ( composition @ ( meet @ X0 @ ( composition @ X2 @ ( converse @ X1 ) ) ) @ ( meet @ X1 @ ( composition @ ( converse @ X0 ) @ X2 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[22]) ).

thf(109,plain,
    ( ( ! [X0: $i,X1: $i,X2: $i] :
          ( ( join @ ( meet @ ( composition @ X0 @ X1 ) @ X2 ) @ ( meet @ ( composition @ X0 @ ( meet @ X1 @ ( composition @ ( converse @ X0 ) @ X2 ) ) ) @ X2 ) )
          = ( meet @ ( composition @ X0 @ ( meet @ X1 @ ( composition @ ( converse @ X0 ) @ X2 ) ) ) @ X2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[21]) ).

thf(110,plain,
    ( ( ! [X0: $i,X1: $i,X2: $i] :
          ( ( join @ ( meet @ ( composition @ X0 @ X1 ) @ X2 ) @ ( meet @ ( composition @ ( meet @ X0 @ ( composition @ X2 @ ( converse @ X1 ) ) ) @ X1 ) @ X2 ) )
          = ( meet @ ( composition @ ( meet @ X0 @ ( composition @ X2 @ ( converse @ X1 ) ) ) @ X1 ) @ X2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[20]) ).

thf(111,plain,
    ( ( ( ( join @ ( meet @ ( converse @ sK1_X0 ) @ ( converse @ sK2_SY36 ) ) @ ( converse @ ( meet @ sK1_X0 @ sK2_SY36 ) ) )
       != ( converse @ ( meet @ sK1_X0 @ sK2_SY36 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[41]) ).

thf(112,plain,
    ! [SV35: $i] :
      ( ( ! [SY61: $i] :
            ( ( join @ SV35 @ SY61 )
            = ( join @ SY61 @ SV35 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[95]) ).

thf(113,plain,
    ! [SV36: $i] :
      ( ( ! [SY62: $i,SY63: $i] :
            ( ( join @ SV36 @ ( join @ SY62 @ SY63 ) )
            = ( join @ ( join @ SV36 @ SY62 ) @ SY63 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[96]) ).

thf(114,plain,
    ! [SV37: $i] :
      ( ( ! [SY64: $i] :
            ( SV37
            = ( join @ ( complement @ ( join @ ( complement @ SV37 ) @ ( complement @ SY64 ) ) ) @ ( complement @ ( join @ ( complement @ SV37 ) @ SY64 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[97]) ).

thf(115,plain,
    ! [SV38: $i] :
      ( ( ! [SY65: $i] :
            ( ( meet @ SV38 @ SY65 )
            = ( complement @ ( join @ ( complement @ SV38 ) @ ( complement @ SY65 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[98]) ).

thf(116,plain,
    ! [SV39: $i] :
      ( ( ! [SY66: $i,SY67: $i] :
            ( ( composition @ SV39 @ ( composition @ SY66 @ SY67 ) )
            = ( composition @ ( composition @ SV39 @ SY66 ) @ SY67 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[99]) ).

thf(117,plain,
    ! [SV40: $i] :
      ( ( ( composition @ SV40 @ one )
        = SV40 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[100]) ).

thf(118,plain,
    ! [SV41: $i] :
      ( ( ! [SY68: $i,SY69: $i] :
            ( ( composition @ ( join @ SV41 @ SY68 ) @ SY69 )
            = ( join @ ( composition @ SV41 @ SY69 ) @ ( composition @ SY68 @ SY69 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[101]) ).

thf(119,plain,
    ! [SV42: $i] :
      ( ( ( converse @ ( converse @ SV42 ) )
        = SV42 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[102]) ).

thf(120,plain,
    ! [SV43: $i] :
      ( ( ! [SY70: $i] :
            ( ( converse @ ( join @ SV43 @ SY70 ) )
            = ( join @ ( converse @ SV43 ) @ ( converse @ SY70 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[103]) ).

thf(121,plain,
    ! [SV44: $i] :
      ( ( ! [SY71: $i] :
            ( ( converse @ ( composition @ SV44 @ SY71 ) )
            = ( composition @ ( converse @ SY71 ) @ ( converse @ SV44 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[104]) ).

thf(122,plain,
    ! [SV45: $i] :
      ( ( ! [SY72: $i] :
            ( ( join @ ( composition @ ( converse @ SV45 ) @ ( complement @ ( composition @ SV45 @ SY72 ) ) ) @ ( complement @ SY72 ) )
            = ( complement @ SY72 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[105]) ).

thf(123,plain,
    ! [SV46: $i] :
      ( ( top
        = ( join @ SV46 @ ( complement @ SV46 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[106]) ).

thf(124,plain,
    ! [SV47: $i] :
      ( ( zero
        = ( meet @ SV47 @ ( complement @ SV47 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[107]) ).

thf(125,plain,
    ! [SV48: $i] :
      ( ( ! [SY73: $i,SY74: $i] :
            ( ( join @ ( meet @ ( composition @ SV48 @ SY73 ) @ SY74 ) @ ( composition @ ( meet @ SV48 @ ( composition @ SY74 @ ( converse @ SY73 ) ) ) @ ( meet @ SY73 @ ( composition @ ( converse @ SV48 ) @ SY74 ) ) ) )
            = ( composition @ ( meet @ SV48 @ ( composition @ SY74 @ ( converse @ SY73 ) ) ) @ ( meet @ SY73 @ ( composition @ ( converse @ SV48 ) @ SY74 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[108]) ).

thf(126,plain,
    ! [SV49: $i] :
      ( ( ! [SY75: $i,SY76: $i] :
            ( ( join @ ( meet @ ( composition @ SV49 @ SY75 ) @ SY76 ) @ ( meet @ ( composition @ SV49 @ ( meet @ SY75 @ ( composition @ ( converse @ SV49 ) @ SY76 ) ) ) @ SY76 ) )
            = ( meet @ ( composition @ SV49 @ ( meet @ SY75 @ ( composition @ ( converse @ SV49 ) @ SY76 ) ) ) @ SY76 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[109]) ).

thf(127,plain,
    ! [SV50: $i] :
      ( ( ! [SY77: $i,SY78: $i] :
            ( ( join @ ( meet @ ( composition @ SV50 @ SY77 ) @ SY78 ) @ ( meet @ ( composition @ ( meet @ SV50 @ ( composition @ SY78 @ ( converse @ SY77 ) ) ) @ SY77 ) @ SY78 ) )
            = ( meet @ ( composition @ ( meet @ SV50 @ ( composition @ SY78 @ ( converse @ SY77 ) ) ) @ SY77 ) @ SY78 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[110]) ).

thf(128,plain,
    ( ( ( join @ ( meet @ ( converse @ sK1_X0 ) @ ( converse @ sK2_SY36 ) ) @ ( converse @ ( meet @ sK1_X0 @ sK2_SY36 ) ) )
      = ( converse @ ( meet @ sK1_X0 @ sK2_SY36 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[111]) ).

thf(129,plain,
    ! [SV51: $i,SV35: $i] :
      ( ( ( join @ SV35 @ SV51 )
        = ( join @ SV51 @ SV35 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[112]) ).

thf(130,plain,
    ! [SV52: $i,SV36: $i] :
      ( ( ! [SY79: $i] :
            ( ( join @ SV36 @ ( join @ SV52 @ SY79 ) )
            = ( join @ ( join @ SV36 @ SV52 ) @ SY79 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[113]) ).

thf(131,plain,
    ! [SV53: $i,SV37: $i] :
      ( ( SV37
        = ( join @ ( complement @ ( join @ ( complement @ SV37 ) @ ( complement @ SV53 ) ) ) @ ( complement @ ( join @ ( complement @ SV37 ) @ SV53 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[114]) ).

thf(132,plain,
    ! [SV54: $i,SV38: $i] :
      ( ( ( meet @ SV38 @ SV54 )
        = ( complement @ ( join @ ( complement @ SV38 ) @ ( complement @ SV54 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[115]) ).

thf(133,plain,
    ! [SV55: $i,SV39: $i] :
      ( ( ! [SY80: $i] :
            ( ( composition @ SV39 @ ( composition @ SV55 @ SY80 ) )
            = ( composition @ ( composition @ SV39 @ SV55 ) @ SY80 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[116]) ).

thf(134,plain,
    ! [SV56: $i,SV41: $i] :
      ( ( ! [SY81: $i] :
            ( ( composition @ ( join @ SV41 @ SV56 ) @ SY81 )
            = ( join @ ( composition @ SV41 @ SY81 ) @ ( composition @ SV56 @ SY81 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[118]) ).

thf(135,plain,
    ! [SV57: $i,SV43: $i] :
      ( ( ( converse @ ( join @ SV43 @ SV57 ) )
        = ( join @ ( converse @ SV43 ) @ ( converse @ SV57 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[120]) ).

thf(136,plain,
    ! [SV58: $i,SV44: $i] :
      ( ( ( converse @ ( composition @ SV44 @ SV58 ) )
        = ( composition @ ( converse @ SV58 ) @ ( converse @ SV44 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[121]) ).

thf(137,plain,
    ! [SV59: $i,SV45: $i] :
      ( ( ( join @ ( composition @ ( converse @ SV45 ) @ ( complement @ ( composition @ SV45 @ SV59 ) ) ) @ ( complement @ SV59 ) )
        = ( complement @ SV59 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[122]) ).

thf(138,plain,
    ! [SV60: $i,SV48: $i] :
      ( ( ! [SY82: $i] :
            ( ( join @ ( meet @ ( composition @ SV48 @ SV60 ) @ SY82 ) @ ( composition @ ( meet @ SV48 @ ( composition @ SY82 @ ( converse @ SV60 ) ) ) @ ( meet @ SV60 @ ( composition @ ( converse @ SV48 ) @ SY82 ) ) ) )
            = ( composition @ ( meet @ SV48 @ ( composition @ SY82 @ ( converse @ SV60 ) ) ) @ ( meet @ SV60 @ ( composition @ ( converse @ SV48 ) @ SY82 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[125]) ).

thf(139,plain,
    ! [SV61: $i,SV49: $i] :
      ( ( ! [SY83: $i] :
            ( ( join @ ( meet @ ( composition @ SV49 @ SV61 ) @ SY83 ) @ ( meet @ ( composition @ SV49 @ ( meet @ SV61 @ ( composition @ ( converse @ SV49 ) @ SY83 ) ) ) @ SY83 ) )
            = ( meet @ ( composition @ SV49 @ ( meet @ SV61 @ ( composition @ ( converse @ SV49 ) @ SY83 ) ) ) @ SY83 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[126]) ).

thf(140,plain,
    ! [SV62: $i,SV50: $i] :
      ( ( ! [SY84: $i] :
            ( ( join @ ( meet @ ( composition @ SV50 @ SV62 ) @ SY84 ) @ ( meet @ ( composition @ ( meet @ SV50 @ ( composition @ SY84 @ ( converse @ SV62 ) ) ) @ SV62 ) @ SY84 ) )
            = ( meet @ ( composition @ ( meet @ SV50 @ ( composition @ SY84 @ ( converse @ SV62 ) ) ) @ SV62 ) @ SY84 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[127]) ).

thf(141,plain,
    ! [SV63: $i,SV52: $i,SV36: $i] :
      ( ( ( join @ SV36 @ ( join @ SV52 @ SV63 ) )
        = ( join @ ( join @ SV36 @ SV52 ) @ SV63 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[130]) ).

thf(142,plain,
    ! [SV64: $i,SV55: $i,SV39: $i] :
      ( ( ( composition @ SV39 @ ( composition @ SV55 @ SV64 ) )
        = ( composition @ ( composition @ SV39 @ SV55 ) @ SV64 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[133]) ).

thf(143,plain,
    ! [SV65: $i,SV56: $i,SV41: $i] :
      ( ( ( composition @ ( join @ SV41 @ SV56 ) @ SV65 )
        = ( join @ ( composition @ SV41 @ SV65 ) @ ( composition @ SV56 @ SV65 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[134]) ).

thf(144,plain,
    ! [SV66: $i,SV60: $i,SV48: $i] :
      ( ( ( join @ ( meet @ ( composition @ SV48 @ SV60 ) @ SV66 ) @ ( composition @ ( meet @ SV48 @ ( composition @ SV66 @ ( converse @ SV60 ) ) ) @ ( meet @ SV60 @ ( composition @ ( converse @ SV48 ) @ SV66 ) ) ) )
        = ( composition @ ( meet @ SV48 @ ( composition @ SV66 @ ( converse @ SV60 ) ) ) @ ( meet @ SV60 @ ( composition @ ( converse @ SV48 ) @ SV66 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[138]) ).

thf(145,plain,
    ! [SV67: $i,SV61: $i,SV49: $i] :
      ( ( ( join @ ( meet @ ( composition @ SV49 @ SV61 ) @ SV67 ) @ ( meet @ ( composition @ SV49 @ ( meet @ SV61 @ ( composition @ ( converse @ SV49 ) @ SV67 ) ) ) @ SV67 ) )
        = ( meet @ ( composition @ SV49 @ ( meet @ SV61 @ ( composition @ ( converse @ SV49 ) @ SV67 ) ) ) @ SV67 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[139]) ).

thf(146,plain,
    ! [SV68: $i,SV62: $i,SV50: $i] :
      ( ( ( join @ ( meet @ ( composition @ SV50 @ SV62 ) @ SV68 ) @ ( meet @ ( composition @ ( meet @ SV50 @ ( composition @ SV68 @ ( converse @ SV62 ) ) ) @ SV62 ) @ SV68 ) )
        = ( meet @ ( composition @ ( meet @ SV50 @ ( composition @ SV68 @ ( converse @ SV62 ) ) ) @ SV62 ) @ SV68 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[140]) ).

thf(147,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[117,146,145,144,143,142,141,137,136,135,132,131,129,128,124,123,119]) ).

thf(148,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[147,94]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : REL005+4 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34  % Computer : n010.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 : Fri Jul  8 14:19:31 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.36  
% 0.13/0.36   No.of.Axioms: 16
% 0.13/0.36  
% 0.13/0.36   Length.of.Defs: 0
% 0.13/0.36  
% 0.13/0.36   Contains.Choice.Funs: false
% 0.13/0.37  (rf:0,axioms:16,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:18,loop_count:0,foatp_calls:0,translation:fof_full)........
% 5.91/6.17  
% 5.91/6.17  ********************************
% 5.91/6.17  *   All subproblems solved!    *
% 5.91/6.17  ********************************
% 5.91/6.17  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:16,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:72,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:147,loop_count:0,foatp_calls:1,translation:fof_full)
% 5.91/6.18  
% 5.91/6.18  %**** Beginning of derivation protocol ****
% 5.91/6.18  % SZS output start CNFRefutation
% See solution above
% 5.91/6.18  
% 5.91/6.18  %**** End of derivation protocol ****
% 5.91/6.18  %**** no. of clauses in derivation: 148 ****
% 5.91/6.18  %**** clause counter: 147 ****
% 5.91/6.18  
% 5.91/6.18  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:16,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:72,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:147,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------