TSTP Solution File: LAT276-2 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : LAT276-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n026.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 05:45:27 EDT 2022

% Result   : Unsatisfiable 0.19s 0.46s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   29
% Syntax   : Number of formulae    :  107 (  47 unt;  16 typ;   0 def)
%            Number of atoms       :  509 ( 137 equ;   0 cnn)
%            Maximal formula atoms :    4 (   5 avg)
%            Number of connectives : 1904 ( 108   ~; 156   |;   0   &;1640   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   25 (  25   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   19 (  16 usr;   9 con; 0-4 aty)
%            Number of variables   :  127 (   0   ^ 127   !;   0   ?; 127   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_c_Pair,type,
    c_Pair: $i > $i > $i > $i > $i ).

thf(tp_c_Tarski_Olub,type,
    c_Tarski_Olub: $i > $i > $i > $i ).

thf(tp_c_Tarski_Opotype_Oorder,type,
    c_Tarski_Opotype_Oorder: $i > $i > $i > $i ).

thf(tp_c_Tarski_Opotype_Opset,type,
    c_Tarski_Opotype_Opset: $i > $i > $i > $i ).

thf(tp_c_in,type,
    c_in: $i > $i > $i > $o ).

thf(tp_c_lessequals,type,
    c_lessequals: $i > $i > $i > $o ).

thf(tp_t_a,type,
    t_a: $i ).

thf(tp_tc_Product__Type_Ounit,type,
    tc_Product__Type_Ounit: $i ).

thf(tp_tc_prod,type,
    tc_prod: $i > $i > $i ).

thf(tp_tc_set,type,
    tc_set: $i > $i ).

thf(tp_v_A,type,
    v_A: $i ).

thf(tp_v_S,type,
    v_S: $i ).

thf(tp_v_cl,type,
    v_cl: $i ).

thf(tp_v_r,type,
    v_r: $i ).

thf(tp_v_sko__4mP,type,
    v_sko__4mP: $i > $i > $i > $i ).

thf(tp_v_xa,type,
    v_xa: $i ).

thf(1,axiom,
    ( v_r
    = ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_Or_A_61_61_Aorder_Acl_0) ).

thf(2,axiom,
    ! [V_x: $i,V_S: $i] :
      ( ~ ( c_in @ V_x @ V_S @ t_a )
      | ~ ( c_lessequals @ V_S @ v_A @ ( tc_set @ t_a ) )
      | ( c_in @ ( c_Pair @ V_x @ ( c_Tarski_Olub @ V_S @ v_cl @ t_a ) @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_O_91_124_AS1_A_60_61_AA_59_Ax1_A_58_AS1_A_124_93_A_61_61_62_A_Ix1_M_Alub_AS1_Acl_J_A_58_Ar_A_61_61_ATrue_0) ).

thf(3,axiom,
    ! [V_L: $i,V_S: $i] :
      ( ~ ( c_in @ V_L @ v_A @ t_a )
      | ~ ( c_in @ ( c_Pair @ ( v_sko__4mP @ V_L @ V_S @ v_r ) @ V_L @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
      | ~ ( c_lessequals @ V_S @ v_A @ ( tc_set @ t_a ) )
      | ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ V_S @ v_cl @ t_a ) @ V_L @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AL1_A_58_AA_59_AALL_Ax_58S1_O_A_Ix_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ilub_AS1_Acl_M_AL1_J_A_58_Ar_A_61_61_ATrue_1) ).

thf(4,axiom,
    ! [V_L: $i,V_S: $i] :
      ( ~ ( c_in @ V_L @ v_A @ t_a )
      | ~ ( c_lessequals @ V_S @ v_A @ ( tc_set @ t_a ) )
      | ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ V_S @ v_cl @ t_a ) @ V_L @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
      | ( c_in @ ( v_sko__4mP @ V_L @ V_S @ v_r ) @ V_S @ t_a ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AL1_A_58_AA_59_AALL_Ax_58S1_O_A_Ix_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ilub_AS1_Acl_M_AL1_J_A_58_Ar_A_61_61_ATrue_0) ).

thf(5,axiom,
    ( v_A
    = ( c_Tarski_Opotype_Opset @ v_cl @ t_a @ tc_Product__Type_Ounit ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_OA_A_61_61_Apset_Acl_0) ).

thf(6,axiom,
    ! [V_c: $i,V_A: $i,T_a: $i,V_B: $i] :
      ( ~ ( c_in @ V_c @ V_A @ T_a )
      | ~ ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) )
      | ( c_in @ V_c @ V_B @ T_a ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).

thf(7,conjecture,
    $false,
    file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).

thf(8,negated_conjecture,
    $false = $false,
    inference(negate_conjecture,[status(cth)],[7]) ).

thf(9,negated_conjecture,
    ! [V_U: $i] :
      ( ( c_in @ ( c_Pair @ V_U @ v_xa @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) )
      | ~ ( c_in @ V_U @ v_S @ t_a )
      | ( c_in @ v_xa @ v_S @ t_a ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_9) ).

thf(10,negated_conjecture,
    ( ~ ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ v_S @ v_cl @ t_a ) @ v_xa @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) )
    | ~ ( c_in @ ( c_Pair @ v_xa @ ( c_Tarski_Olub @ v_S @ v_cl @ t_a ) @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_6) ).

thf(11,negated_conjecture,
    ( ~ ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ v_S @ v_cl @ t_a ) @ v_xa @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) )
    | ( c_in @ v_xa @ v_S @ t_a ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).

thf(12,negated_conjecture,
    ( ( c_in @ v_xa @ ( c_Tarski_Opotype_Opset @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ t_a )
    | ( c_in @ v_xa @ v_S @ t_a ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).

thf(13,negated_conjecture,
    ! [V_V: $i] :
      ( ( c_in @ ( c_Pair @ V_V @ v_xa @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) )
      | ~ ( c_in @ V_V @ v_S @ t_a )
      | ~ ( c_in @ ( c_Pair @ v_xa @ ( c_Tarski_Olub @ v_S @ v_cl @ t_a ) @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_10) ).

thf(14,negated_conjecture,
    c_lessequals @ v_S @ v_A @ ( tc_set @ t_a ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(15,plain,
    $false = $false,
    inference(unfold_def,[status(thm)],[8]) ).

thf(16,plain,
    ( ( v_r
      = ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(17,plain,
    ( ( ! [V_x: $i,V_S: $i] :
          ( ~ ( c_in @ V_x @ V_S @ t_a )
          | ~ ( c_lessequals @ V_S @ v_A @ ( tc_set @ t_a ) )
          | ( c_in @ ( c_Pair @ V_x @ ( c_Tarski_Olub @ V_S @ v_cl @ t_a ) @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(18,plain,
    ( ( ! [V_L: $i,V_S: $i] :
          ( ~ ( c_in @ V_L @ v_A @ t_a )
          | ~ ( c_in @ ( c_Pair @ ( v_sko__4mP @ V_L @ V_S @ v_r ) @ V_L @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
          | ~ ( c_lessequals @ V_S @ v_A @ ( tc_set @ t_a ) )
          | ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ V_S @ v_cl @ t_a ) @ V_L @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3]) ).

thf(19,plain,
    ( ( ! [V_L: $i,V_S: $i] :
          ( ~ ( c_in @ V_L @ v_A @ t_a )
          | ~ ( c_lessequals @ V_S @ v_A @ ( tc_set @ t_a ) )
          | ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ V_S @ v_cl @ t_a ) @ V_L @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
          | ( c_in @ ( v_sko__4mP @ V_L @ V_S @ v_r ) @ V_S @ t_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4]) ).

thf(20,plain,
    ( ( v_A
      = ( c_Tarski_Opotype_Opset @ v_cl @ t_a @ tc_Product__Type_Ounit ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5]) ).

thf(21,plain,
    ( ( ! [V_c: $i,V_A: $i,T_a: $i,V_B: $i] :
          ( ~ ( c_in @ V_c @ V_A @ T_a )
          | ~ ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) )
          | ( c_in @ V_c @ V_B @ T_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6]) ).

thf(22,plain,
    ( ( ! [V_U: $i] :
          ( ( c_in @ ( c_Pair @ V_U @ v_xa @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) )
          | ~ ( c_in @ V_U @ v_S @ t_a )
          | ( c_in @ v_xa @ v_S @ t_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9]) ).

thf(23,plain,
    ( ( ~ ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ v_S @ v_cl @ t_a ) @ v_xa @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) )
      | ~ ( c_in @ ( c_Pair @ v_xa @ ( c_Tarski_Olub @ v_S @ v_cl @ t_a ) @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10]) ).

thf(24,plain,
    ( ( ~ ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ v_S @ v_cl @ t_a ) @ v_xa @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) )
      | ( c_in @ v_xa @ v_S @ t_a ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11]) ).

thf(25,plain,
    ( ( ( c_in @ v_xa @ ( c_Tarski_Opotype_Opset @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ t_a )
      | ( c_in @ v_xa @ v_S @ t_a ) )
    = $true ),
    inference(unfold_def,[status(thm)],[12]) ).

thf(26,plain,
    ( ( ! [V_V: $i] :
          ( ( c_in @ ( c_Pair @ V_V @ v_xa @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) )
          | ~ ( c_in @ V_V @ v_S @ t_a )
          | ~ ( c_in @ ( c_Pair @ v_xa @ ( c_Tarski_Olub @ v_S @ v_cl @ t_a ) @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[13]) ).

thf(27,plain,
    ( ( c_lessequals @ v_S @ v_A @ ( tc_set @ t_a ) )
    = $true ),
    inference(unfold_def,[status(thm)],[14]) ).

thf(28,plain,
    ( ( ~ $false )
    = $true ),
    inference(polarity_switch,[status(thm)],[15]) ).

thf(29,plain,
    ( ( ! [V_L: $i] :
          ( ~ ( c_in @ V_L @ v_A @ t_a )
          | ! [V_S: $i] :
              ( ~ ( c_in @ ( c_Pair @ ( v_sko__4mP @ V_L @ V_S @ v_r ) @ V_L @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
              | ~ ( c_lessequals @ V_S @ v_A @ ( tc_set @ t_a ) )
              | ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ V_S @ v_cl @ t_a ) @ V_L @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[18]) ).

thf(30,plain,
    ( ( ! [V_L: $i] :
          ( ~ ( c_in @ V_L @ v_A @ t_a )
          | ! [V_S: $i] :
              ( ~ ( c_lessequals @ V_S @ v_A @ ( tc_set @ t_a ) )
              | ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ V_S @ v_cl @ t_a ) @ V_L @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
              | ( c_in @ ( v_sko__4mP @ V_L @ V_S @ v_r ) @ V_S @ t_a ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[19]) ).

thf(31,plain,
    ( ( ! [V_c: $i,V_A: $i,T_a: $i] :
          ( ~ ( c_in @ V_c @ V_A @ T_a )
          | ! [V_B: $i] :
              ( ~ ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) )
              | ( c_in @ V_c @ V_B @ T_a ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[21]) ).

thf(32,plain,
    ( ( c_lessequals @ v_S @ v_A @ ( tc_set @ t_a ) )
    = $true ),
    inference(copy,[status(thm)],[27]) ).

thf(33,plain,
    ( ( ! [V_V: $i] :
          ( ( c_in @ ( c_Pair @ V_V @ v_xa @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) )
          | ~ ( c_in @ V_V @ v_S @ t_a )
          | ~ ( c_in @ ( c_Pair @ v_xa @ ( c_Tarski_Olub @ v_S @ v_cl @ t_a ) @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[26]) ).

thf(34,plain,
    ( ( ( c_in @ v_xa @ ( c_Tarski_Opotype_Opset @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ t_a )
      | ( c_in @ v_xa @ v_S @ t_a ) )
    = $true ),
    inference(copy,[status(thm)],[25]) ).

thf(35,plain,
    ( ( ~ ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ v_S @ v_cl @ t_a ) @ v_xa @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) )
      | ( c_in @ v_xa @ v_S @ t_a ) )
    = $true ),
    inference(copy,[status(thm)],[24]) ).

thf(36,plain,
    ( ( ~ ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ v_S @ v_cl @ t_a ) @ v_xa @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) )
      | ~ ( c_in @ ( c_Pair @ v_xa @ ( c_Tarski_Olub @ v_S @ v_cl @ t_a ) @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) ) )
    = $true ),
    inference(copy,[status(thm)],[23]) ).

thf(37,plain,
    ( ( ! [V_U: $i] :
          ( ( c_in @ ( c_Pair @ V_U @ v_xa @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) )
          | ~ ( c_in @ V_U @ v_S @ t_a )
          | ( c_in @ v_xa @ v_S @ t_a ) ) )
    = $true ),
    inference(copy,[status(thm)],[22]) ).

thf(38,plain,
    ( ( ! [V_c: $i,V_A: $i,T_a: $i] :
          ( ~ ( c_in @ V_c @ V_A @ T_a )
          | ! [V_B: $i] :
              ( ~ ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) )
              | ( c_in @ V_c @ V_B @ T_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[31]) ).

thf(39,plain,
    ( ( v_A
      = ( c_Tarski_Opotype_Opset @ v_cl @ t_a @ tc_Product__Type_Ounit ) )
    = $true ),
    inference(copy,[status(thm)],[20]) ).

thf(40,plain,
    ( ( ! [V_L: $i] :
          ( ~ ( c_in @ V_L @ v_A @ t_a )
          | ! [V_S: $i] :
              ( ~ ( c_lessequals @ V_S @ v_A @ ( tc_set @ t_a ) )
              | ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ V_S @ v_cl @ t_a ) @ V_L @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
              | ( c_in @ ( v_sko__4mP @ V_L @ V_S @ v_r ) @ V_S @ t_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[30]) ).

thf(41,plain,
    ( ( ! [V_L: $i] :
          ( ~ ( c_in @ V_L @ v_A @ t_a )
          | ! [V_S: $i] :
              ( ~ ( c_in @ ( c_Pair @ ( v_sko__4mP @ V_L @ V_S @ v_r ) @ V_L @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
              | ~ ( c_lessequals @ V_S @ v_A @ ( tc_set @ t_a ) )
              | ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ V_S @ v_cl @ t_a ) @ V_L @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[29]) ).

thf(42,plain,
    ( ( ! [V_x: $i,V_S: $i] :
          ( ~ ( c_in @ V_x @ V_S @ t_a )
          | ~ ( c_lessequals @ V_S @ v_A @ ( tc_set @ t_a ) )
          | ( c_in @ ( c_Pair @ V_x @ ( c_Tarski_Olub @ V_S @ v_cl @ t_a ) @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[17]) ).

thf(43,plain,
    ( ( v_r
      = ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) )
    = $true ),
    inference(copy,[status(thm)],[16]) ).

thf(44,plain,
    ( ( ~ $false )
    = $true ),
    inference(copy,[status(thm)],[28]) ).

thf(45,plain,
    ! [SV1: $i] :
      ( ( ( c_in @ ( c_Pair @ SV1 @ v_xa @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) )
        | ~ ( c_in @ SV1 @ v_S @ t_a )
        | ~ ( c_in @ ( c_Pair @ v_xa @ ( c_Tarski_Olub @ v_S @ v_cl @ t_a ) @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[33]) ).

thf(46,plain,
    ( ( ( c_in @ v_xa @ ( c_Tarski_Opotype_Opset @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ t_a )
      = $true )
    | ( ( c_in @ v_xa @ v_S @ t_a )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[34]) ).

thf(47,plain,
    ( ( ( ~ ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ v_S @ v_cl @ t_a ) @ v_xa @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) ) )
      = $true )
    | ( ( c_in @ v_xa @ v_S @ t_a )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[35]) ).

thf(48,plain,
    ( ( ( ~ ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ v_S @ v_cl @ t_a ) @ v_xa @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) ) )
      = $true )
    | ( ( ~ ( c_in @ ( c_Pair @ v_xa @ ( c_Tarski_Olub @ v_S @ v_cl @ t_a ) @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) ) )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[36]) ).

thf(49,plain,
    ! [SV2: $i] :
      ( ( ( c_in @ ( c_Pair @ SV2 @ v_xa @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) )
        | ~ ( c_in @ SV2 @ v_S @ t_a )
        | ( c_in @ v_xa @ v_S @ t_a ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[37]) ).

thf(50,plain,
    ! [SV3: $i] :
      ( ( ! [SY12: $i,SY13: $i] :
            ( ~ ( c_in @ SV3 @ SY12 @ SY13 )
            | ! [SY14: $i] :
                ( ~ ( c_lessequals @ SY12 @ SY14 @ ( tc_set @ SY13 ) )
                | ( c_in @ SV3 @ SY14 @ SY13 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[38]) ).

thf(51,plain,
    ! [SV4: $i] :
      ( ( ~ ( c_in @ SV4 @ v_A @ t_a )
        | ! [SY15: $i] :
            ( ~ ( c_lessequals @ SY15 @ v_A @ ( tc_set @ t_a ) )
            | ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ SY15 @ v_cl @ t_a ) @ SV4 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
            | ( c_in @ ( v_sko__4mP @ SV4 @ SY15 @ v_r ) @ SY15 @ t_a ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[40]) ).

thf(52,plain,
    ! [SV5: $i] :
      ( ( ~ ( c_in @ SV5 @ v_A @ t_a )
        | ! [SY16: $i] :
            ( ~ ( c_in @ ( c_Pair @ ( v_sko__4mP @ SV5 @ SY16 @ v_r ) @ SV5 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
            | ~ ( c_lessequals @ SY16 @ v_A @ ( tc_set @ t_a ) )
            | ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ SY16 @ v_cl @ t_a ) @ SV5 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[41]) ).

thf(53,plain,
    ! [SV6: $i] :
      ( ( ! [SY17: $i] :
            ( ~ ( c_in @ SV6 @ SY17 @ t_a )
            | ~ ( c_lessequals @ SY17 @ v_A @ ( tc_set @ t_a ) )
            | ( c_in @ ( c_Pair @ SV6 @ ( c_Tarski_Olub @ SY17 @ v_cl @ t_a ) @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[42]) ).

thf(54,plain,
    $false = $false,
    inference(extcnf_not_pos,[status(thm)],[44]) ).

thf(55,plain,
    ! [SV1: $i] :
      ( ( ( c_in @ ( c_Pair @ SV1 @ v_xa @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) )
        = $true )
      | ( ( ~ ( c_in @ SV1 @ v_S @ t_a )
          | ~ ( c_in @ ( c_Pair @ v_xa @ ( c_Tarski_Olub @ v_S @ v_cl @ t_a ) @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[45]) ).

thf(56,plain,
    ( ( ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ v_S @ v_cl @ t_a ) @ v_xa @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) )
      = $false )
    | ( ( c_in @ v_xa @ v_S @ t_a )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[47]) ).

thf(57,plain,
    ( ( ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ v_S @ v_cl @ t_a ) @ v_xa @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) )
      = $false )
    | ( ( ~ ( c_in @ ( c_Pair @ v_xa @ ( c_Tarski_Olub @ v_S @ v_cl @ t_a ) @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) ) )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[48]) ).

thf(58,plain,
    ! [SV2: $i] :
      ( ( ( c_in @ ( c_Pair @ SV2 @ v_xa @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) )
        = $true )
      | ( ( ~ ( c_in @ SV2 @ v_S @ t_a )
          | ( c_in @ v_xa @ v_S @ t_a ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[49]) ).

thf(59,plain,
    ! [SV7: $i,SV3: $i] :
      ( ( ! [SY18: $i] :
            ( ~ ( c_in @ SV3 @ SV7 @ SY18 )
            | ! [SY19: $i] :
                ( ~ ( c_lessequals @ SV7 @ SY19 @ ( tc_set @ SY18 ) )
                | ( c_in @ SV3 @ SY19 @ SY18 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[50]) ).

thf(60,plain,
    ! [SV4: $i] :
      ( ( ( ~ ( c_in @ SV4 @ v_A @ t_a ) )
        = $true )
      | ( ( ! [SY15: $i] :
              ( ~ ( c_lessequals @ SY15 @ v_A @ ( tc_set @ t_a ) )
              | ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ SY15 @ v_cl @ t_a ) @ SV4 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
              | ( c_in @ ( v_sko__4mP @ SV4 @ SY15 @ v_r ) @ SY15 @ t_a ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[51]) ).

thf(61,plain,
    ! [SV5: $i] :
      ( ( ( ~ ( c_in @ SV5 @ v_A @ t_a ) )
        = $true )
      | ( ( ! [SY16: $i] :
              ( ~ ( c_in @ ( c_Pair @ ( v_sko__4mP @ SV5 @ SY16 @ v_r ) @ SV5 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
              | ~ ( c_lessequals @ SY16 @ v_A @ ( tc_set @ t_a ) )
              | ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ SY16 @ v_cl @ t_a ) @ SV5 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[52]) ).

thf(62,plain,
    ! [SV8: $i,SV6: $i] :
      ( ( ~ ( c_in @ SV6 @ SV8 @ t_a )
        | ~ ( c_lessequals @ SV8 @ v_A @ ( tc_set @ t_a ) )
        | ( c_in @ ( c_Pair @ SV6 @ ( c_Tarski_Olub @ SV8 @ v_cl @ t_a ) @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[53]) ).

thf(63,plain,
    ! [SV1: $i] :
      ( ( ( ~ ( c_in @ SV1 @ v_S @ t_a ) )
        = $true )
      | ( ( ~ ( c_in @ ( c_Pair @ v_xa @ ( c_Tarski_Olub @ v_S @ v_cl @ t_a ) @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) ) )
        = $true )
      | ( ( c_in @ ( c_Pair @ SV1 @ v_xa @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[55]) ).

thf(64,plain,
    ( ( ( c_in @ ( c_Pair @ v_xa @ ( c_Tarski_Olub @ v_S @ v_cl @ t_a ) @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) )
      = $false )
    | ( ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ v_S @ v_cl @ t_a ) @ v_xa @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) )
      = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[57]) ).

thf(65,plain,
    ! [SV2: $i] :
      ( ( ( ~ ( c_in @ SV2 @ v_S @ t_a ) )
        = $true )
      | ( ( c_in @ v_xa @ v_S @ t_a )
        = $true )
      | ( ( c_in @ ( c_Pair @ SV2 @ v_xa @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[58]) ).

thf(66,plain,
    ! [SV9: $i,SV7: $i,SV3: $i] :
      ( ( ~ ( c_in @ SV3 @ SV7 @ SV9 )
        | ! [SY20: $i] :
            ( ~ ( c_lessequals @ SV7 @ SY20 @ ( tc_set @ SV9 ) )
            | ( c_in @ SV3 @ SY20 @ SV9 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[59]) ).

thf(67,plain,
    ! [SV4: $i] :
      ( ( ( c_in @ SV4 @ v_A @ t_a )
        = $false )
      | ( ( ! [SY15: $i] :
              ( ~ ( c_lessequals @ SY15 @ v_A @ ( tc_set @ t_a ) )
              | ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ SY15 @ v_cl @ t_a ) @ SV4 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
              | ( c_in @ ( v_sko__4mP @ SV4 @ SY15 @ v_r ) @ SY15 @ t_a ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[60]) ).

thf(68,plain,
    ! [SV5: $i] :
      ( ( ( c_in @ SV5 @ v_A @ t_a )
        = $false )
      | ( ( ! [SY16: $i] :
              ( ~ ( c_in @ ( c_Pair @ ( v_sko__4mP @ SV5 @ SY16 @ v_r ) @ SV5 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
              | ~ ( c_lessequals @ SY16 @ v_A @ ( tc_set @ t_a ) )
              | ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ SY16 @ v_cl @ t_a ) @ SV5 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[61]) ).

thf(69,plain,
    ! [SV8: $i,SV6: $i] :
      ( ( ( ~ ( c_in @ SV6 @ SV8 @ t_a ) )
        = $true )
      | ( ( ~ ( c_lessequals @ SV8 @ v_A @ ( tc_set @ t_a ) )
          | ( c_in @ ( c_Pair @ SV6 @ ( c_Tarski_Olub @ SV8 @ v_cl @ t_a ) @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[62]) ).

thf(70,plain,
    ! [SV1: $i] :
      ( ( ( c_in @ SV1 @ v_S @ t_a )
        = $false )
      | ( ( ~ ( c_in @ ( c_Pair @ v_xa @ ( c_Tarski_Olub @ v_S @ v_cl @ t_a ) @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) ) )
        = $true )
      | ( ( c_in @ ( c_Pair @ SV1 @ v_xa @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[63]) ).

thf(71,plain,
    ! [SV2: $i] :
      ( ( ( c_in @ SV2 @ v_S @ t_a )
        = $false )
      | ( ( c_in @ v_xa @ v_S @ t_a )
        = $true )
      | ( ( c_in @ ( c_Pair @ SV2 @ v_xa @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[65]) ).

thf(72,plain,
    ! [SV9: $i,SV7: $i,SV3: $i] :
      ( ( ( ~ ( c_in @ SV3 @ SV7 @ SV9 ) )
        = $true )
      | ( ( ! [SY20: $i] :
              ( ~ ( c_lessequals @ SV7 @ SY20 @ ( tc_set @ SV9 ) )
              | ( c_in @ SV3 @ SY20 @ SV9 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[66]) ).

thf(73,plain,
    ! [SV4: $i,SV10: $i] :
      ( ( ( ~ ( c_lessequals @ SV10 @ v_A @ ( tc_set @ t_a ) )
          | ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ SV10 @ v_cl @ t_a ) @ SV4 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
          | ( c_in @ ( v_sko__4mP @ SV4 @ SV10 @ v_r ) @ SV10 @ t_a ) )
        = $true )
      | ( ( c_in @ SV4 @ v_A @ t_a )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[67]) ).

thf(74,plain,
    ! [SV11: $i,SV5: $i] :
      ( ( ( ~ ( c_in @ ( c_Pair @ ( v_sko__4mP @ SV5 @ SV11 @ v_r ) @ SV5 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
          | ~ ( c_lessequals @ SV11 @ v_A @ ( tc_set @ t_a ) )
          | ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ SV11 @ v_cl @ t_a ) @ SV5 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) )
        = $true )
      | ( ( c_in @ SV5 @ v_A @ t_a )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[68]) ).

thf(75,plain,
    ! [SV8: $i,SV6: $i] :
      ( ( ( c_in @ SV6 @ SV8 @ t_a )
        = $false )
      | ( ( ~ ( c_lessequals @ SV8 @ v_A @ ( tc_set @ t_a ) )
          | ( c_in @ ( c_Pair @ SV6 @ ( c_Tarski_Olub @ SV8 @ v_cl @ t_a ) @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[69]) ).

thf(76,plain,
    ! [SV1: $i] :
      ( ( ( c_in @ ( c_Pair @ v_xa @ ( c_Tarski_Olub @ v_S @ v_cl @ t_a ) @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) )
        = $false )
      | ( ( c_in @ SV1 @ v_S @ t_a )
        = $false )
      | ( ( c_in @ ( c_Pair @ SV1 @ v_xa @ t_a @ t_a ) @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ ( tc_prod @ t_a @ t_a ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[70]) ).

thf(77,plain,
    ! [SV9: $i,SV7: $i,SV3: $i] :
      ( ( ( c_in @ SV3 @ SV7 @ SV9 )
        = $false )
      | ( ( ! [SY20: $i] :
              ( ~ ( c_lessequals @ SV7 @ SY20 @ ( tc_set @ SV9 ) )
              | ( c_in @ SV3 @ SY20 @ SV9 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[72]) ).

thf(78,plain,
    ! [SV4: $i,SV10: $i] :
      ( ( ( ~ ( c_lessequals @ SV10 @ v_A @ ( tc_set @ t_a ) ) )
        = $true )
      | ( ( ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ SV10 @ v_cl @ t_a ) @ SV4 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
          | ( c_in @ ( v_sko__4mP @ SV4 @ SV10 @ v_r ) @ SV10 @ t_a ) )
        = $true )
      | ( ( c_in @ SV4 @ v_A @ t_a )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[73]) ).

thf(79,plain,
    ! [SV11: $i,SV5: $i] :
      ( ( ( ~ ( c_in @ ( c_Pair @ ( v_sko__4mP @ SV5 @ SV11 @ v_r ) @ SV5 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) )
        = $true )
      | ( ( ~ ( c_lessequals @ SV11 @ v_A @ ( tc_set @ t_a ) )
          | ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ SV11 @ v_cl @ t_a ) @ SV5 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) )
        = $true )
      | ( ( c_in @ SV5 @ v_A @ t_a )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[74]) ).

thf(80,plain,
    ! [SV6: $i,SV8: $i] :
      ( ( ( ~ ( c_lessequals @ SV8 @ v_A @ ( tc_set @ t_a ) ) )
        = $true )
      | ( ( c_in @ ( c_Pair @ SV6 @ ( c_Tarski_Olub @ SV8 @ v_cl @ t_a ) @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
        = $true )
      | ( ( c_in @ SV6 @ SV8 @ t_a )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[75]) ).

thf(81,plain,
    ! [SV3: $i,SV9: $i,SV12: $i,SV7: $i] :
      ( ( ( ~ ( c_lessequals @ SV7 @ SV12 @ ( tc_set @ SV9 ) )
          | ( c_in @ SV3 @ SV12 @ SV9 ) )
        = $true )
      | ( ( c_in @ SV3 @ SV7 @ SV9 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[77]) ).

thf(82,plain,
    ! [SV4: $i,SV10: $i] :
      ( ( ( c_lessequals @ SV10 @ v_A @ ( tc_set @ t_a ) )
        = $false )
      | ( ( ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ SV10 @ v_cl @ t_a ) @ SV4 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
          | ( c_in @ ( v_sko__4mP @ SV4 @ SV10 @ v_r ) @ SV10 @ t_a ) )
        = $true )
      | ( ( c_in @ SV4 @ v_A @ t_a )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[78]) ).

thf(83,plain,
    ! [SV11: $i,SV5: $i] :
      ( ( ( c_in @ ( c_Pair @ ( v_sko__4mP @ SV5 @ SV11 @ v_r ) @ SV5 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
        = $false )
      | ( ( ~ ( c_lessequals @ SV11 @ v_A @ ( tc_set @ t_a ) )
          | ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ SV11 @ v_cl @ t_a ) @ SV5 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) )
        = $true )
      | ( ( c_in @ SV5 @ v_A @ t_a )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[79]) ).

thf(84,plain,
    ! [SV6: $i,SV8: $i] :
      ( ( ( c_lessequals @ SV8 @ v_A @ ( tc_set @ t_a ) )
        = $false )
      | ( ( c_in @ ( c_Pair @ SV6 @ ( c_Tarski_Olub @ SV8 @ v_cl @ t_a ) @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
        = $true )
      | ( ( c_in @ SV6 @ SV8 @ t_a )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[80]) ).

thf(85,plain,
    ! [SV3: $i,SV9: $i,SV12: $i,SV7: $i] :
      ( ( ( ~ ( c_lessequals @ SV7 @ SV12 @ ( tc_set @ SV9 ) ) )
        = $true )
      | ( ( c_in @ SV3 @ SV12 @ SV9 )
        = $true )
      | ( ( c_in @ SV3 @ SV7 @ SV9 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[81]) ).

thf(86,plain,
    ! [SV4: $i,SV10: $i] :
      ( ( ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ SV10 @ v_cl @ t_a ) @ SV4 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
        = $true )
      | ( ( c_in @ ( v_sko__4mP @ SV4 @ SV10 @ v_r ) @ SV10 @ t_a )
        = $true )
      | ( ( c_lessequals @ SV10 @ v_A @ ( tc_set @ t_a ) )
        = $false )
      | ( ( c_in @ SV4 @ v_A @ t_a )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[82]) ).

thf(87,plain,
    ! [SV5: $i,SV11: $i] :
      ( ( ( ~ ( c_lessequals @ SV11 @ v_A @ ( tc_set @ t_a ) ) )
        = $true )
      | ( ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ SV11 @ v_cl @ t_a ) @ SV5 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
        = $true )
      | ( ( c_in @ ( c_Pair @ ( v_sko__4mP @ SV5 @ SV11 @ v_r ) @ SV5 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
        = $false )
      | ( ( c_in @ SV5 @ v_A @ t_a )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[83]) ).

thf(88,plain,
    ! [SV3: $i,SV9: $i,SV12: $i,SV7: $i] :
      ( ( ( c_lessequals @ SV7 @ SV12 @ ( tc_set @ SV9 ) )
        = $false )
      | ( ( c_in @ SV3 @ SV12 @ SV9 )
        = $true )
      | ( ( c_in @ SV3 @ SV7 @ SV9 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[85]) ).

thf(89,plain,
    ! [SV5: $i,SV11: $i] :
      ( ( ( c_lessequals @ SV11 @ v_A @ ( tc_set @ t_a ) )
        = $false )
      | ( ( c_in @ ( c_Pair @ ( c_Tarski_Olub @ SV11 @ v_cl @ t_a ) @ SV5 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
        = $true )
      | ( ( c_in @ ( c_Pair @ ( v_sko__4mP @ SV5 @ SV11 @ v_r ) @ SV5 @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
        = $false )
      | ( ( c_in @ SV5 @ v_A @ t_a )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[87]) ).

thf(90,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[32,89,88,86,84,76,71,64,56,54,46,43,39]) ).

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : LAT276-2 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34  % Computer : n026.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 15:30:48 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.36  
% 0.13/0.36   No.of.Axioms: 12
% 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:12,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:14,loop_count:0,foatp_calls:0,translation:fof_full)....
% 0.19/0.46  
% 0.19/0.46  ********************************
% 0.19/0.46  *   All subproblems solved!    *
% 0.19/0.46  ********************************
% 0.19/0.46  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:12,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)
% 0.19/0.46  
% 0.19/0.46  %**** Beginning of derivation protocol ****
% 0.19/0.46  % SZS output start CNFRefutation
% See solution above
% 0.19/0.46  
% 0.19/0.46  %**** End of derivation protocol ****
% 0.19/0.46  %**** no. of clauses in derivation: 91 ****
% 0.19/0.46  %**** clause counter: 90 ****
% 0.19/0.46  
% 0.19/0.46  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:12,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)
%------------------------------------------------------------------------------