TSTP Solution File: LAT269-2 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : LAT269-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n017.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  : 300s
% DateTime : Sat Sep 17 18:32:33 EDT 2022

% Result   : Unsatisfiable 0.21s 0.40s
% Output   : Proof 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   36
% Syntax   : Number of formulae    :   56 (  12 unt;  17 typ;   0 def)
%            Number of atoms       :  232 (  56 equ)
%            Maximal formula atoms :   16 (   5 avg)
%            Number of connectives :  323 ( 145   ~; 155   |;   0   &)
%                                         (  23 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of FOOLs       :   15 (  15 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   22 (   7   >;  15   *;   0   +;   0  <<)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-3 aty)
%            Number of functors    :   16 (  16 usr;  10 con; 0-5 aty)
%            Number of variables   :   55 (  50   !;   0   ?;  55   :)

% Comments : 
%------------------------------------------------------------------------------
tff(c_emptyset_type,type,
    c_emptyset: $i ).

tff(c_Tarski_Ointerval_type,type,
    c_Tarski_Ointerval: ( $i * $i * $i * $i ) > $i ).

tff(t_a_type,type,
    t_a: $i ).

tff(c_Tarski_OTop_type,type,
    c_Tarski_OTop: ( $i * $i ) > $i ).

tff(v_cl_type,type,
    v_cl: $i ).

tff(c_Tarski_Olub_type,type,
    c_Tarski_Olub: ( $i * $i * $i ) > $i ).

tff(v_Y_type,type,
    v_Y: $i ).

tff(v_r_type,type,
    v_r: $i ).

tff(c_in_type,type,
    c_in: ( $i * $i * $i ) > $o ).

tff(v_A_type,type,
    v_A: $i ).

tff(tc_Tarski_Opotype_Opotype__ext__type_type,type,
    tc_Tarski_Opotype_Opotype__ext__type: ( $i * $i ) > $i ).

tff(tc_Product__Type_Ounit_type,type,
    tc_Product__Type_Ounit: $i ).

tff(c_Tarski_OCompleteLattice_type,type,
    c_Tarski_OCompleteLattice: $i ).

tff(c_Tarski_Opotype_Opotype__ext_type,type,
    c_Tarski_Opotype_Opotype__ext: ( $i * $i * $i * $i * $i ) > $i ).

tff(c_Product__Type_OUnity_type,type,
    c_Product__Type_OUnity: $i ).

tff(c_Tarski_Oinduced_type,type,
    c_Tarski_Oinduced: ( $i * $i * $i ) > $i ).

tff(v_intY1_type,type,
    v_intY1: $i ).

tff(1,plain,
    ( c_in(c_Tarski_Olub(v_Y,v_cl,t_a),v_A,t_a)
  <=> c_in(c_Tarski_Olub(v_Y,v_cl,t_a),v_A,t_a) ),
    inference(rewrite,[status(thm)],]) ).

tff(2,axiom,
    c_in(c_Tarski_Olub(v_Y,v_cl,t_a),v_A,t_a),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_Olub_AY_Acl_A_58_AA_A_61_61_ATrue_0) ).

tff(3,plain,
    c_in(c_Tarski_Olub(v_Y,v_cl,t_a),v_A,t_a),
    inference(modus_ponens,[status(thm)],[2,1]) ).

tff(4,plain,
    ^ [V_b: $i,V_a: $i] :
      refl(
        ( ( ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_emptyset )
          | c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
          | ~ c_in(V_a,v_A,t_a)
          | ~ c_in(V_b,v_A,t_a) )
      <=> ( ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_emptyset )
          | c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
          | ~ c_in(V_a,v_A,t_a)
          | ~ c_in(V_b,v_A,t_a) ) )),
    inference(bind,[status(th)],]) ).

tff(5,plain,
    ( ! [V_b: $i,V_a: $i] :
        ( ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_emptyset )
        | c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
        | ~ c_in(V_a,v_A,t_a)
        | ~ c_in(V_b,v_A,t_a) )
  <=> ! [V_b: $i,V_a: $i] :
        ( ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_emptyset )
        | c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
        | ~ c_in(V_a,v_A,t_a)
        | ~ c_in(V_b,v_A,t_a) ) ),
    inference(quant_intro,[status(thm)],[4]) ).

tff(6,plain,
    ( ! [V_b: $i,V_a: $i] :
        ( ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_emptyset )
        | c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
        | ~ c_in(V_a,v_A,t_a)
        | ~ c_in(V_b,v_A,t_a) )
  <=> ! [V_b: $i,V_a: $i] :
        ( ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_emptyset )
        | c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
        | ~ c_in(V_a,v_A,t_a)
        | ~ c_in(V_b,v_A,t_a) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(7,plain,
    ^ [V_b: $i,V_a: $i] :
      trans(
        monotonicity(
          trans(
            monotonicity(
              rewrite(
                ( ( ~ c_in(V_b,v_A,t_a)
                  | ~ c_in(V_a,v_A,t_a) )
              <=> ( ~ c_in(V_a,v_A,t_a)
                  | ~ c_in(V_b,v_A,t_a) ) )),
              ( ( ~ c_in(V_b,v_A,t_a)
                | ~ c_in(V_a,v_A,t_a)
                | c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) )
            <=> ( ~ c_in(V_a,v_A,t_a)
                | ~ c_in(V_b,v_A,t_a)
                | c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) ) )),
            rewrite(
              ( ( ~ c_in(V_a,v_A,t_a)
                | ~ c_in(V_b,v_A,t_a)
                | c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) )
            <=> ( c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
                | ~ c_in(V_a,v_A,t_a)
                | ~ c_in(V_b,v_A,t_a) ) )),
            ( ( ~ c_in(V_b,v_A,t_a)
              | ~ c_in(V_a,v_A,t_a)
              | c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) )
          <=> ( c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
              | ~ c_in(V_a,v_A,t_a)
              | ~ c_in(V_b,v_A,t_a) ) )),
          ( ( ~ c_in(V_b,v_A,t_a)
            | ~ c_in(V_a,v_A,t_a)
            | c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
            | ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_emptyset ) )
        <=> ( c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
            | ~ c_in(V_a,v_A,t_a)
            | ~ c_in(V_b,v_A,t_a)
            | ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_emptyset ) ) )),
        rewrite(
          ( ( c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
            | ~ c_in(V_a,v_A,t_a)
            | ~ c_in(V_b,v_A,t_a)
            | ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_emptyset ) )
        <=> ( ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_emptyset )
            | c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
            | ~ c_in(V_a,v_A,t_a)
            | ~ c_in(V_b,v_A,t_a) ) )),
        ( ( ~ c_in(V_b,v_A,t_a)
          | ~ c_in(V_a,v_A,t_a)
          | c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
          | ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_emptyset ) )
      <=> ( ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_emptyset )
          | c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
          | ~ c_in(V_a,v_A,t_a)
          | ~ c_in(V_b,v_A,t_a) ) )),
    inference(bind,[status(th)],]) ).

tff(8,plain,
    ( ! [V_b: $i,V_a: $i] :
        ( ~ c_in(V_b,v_A,t_a)
        | ~ c_in(V_a,v_A,t_a)
        | c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
        | ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_emptyset ) )
  <=> ! [V_b: $i,V_a: $i] :
        ( ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_emptyset )
        | c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
        | ~ c_in(V_a,v_A,t_a)
        | ~ c_in(V_b,v_A,t_a) ) ),
    inference(quant_intro,[status(thm)],[7]) ).

tff(9,axiom,
    ! [V_b: $i,V_a: $i] :
      ( ~ c_in(V_b,v_A,t_a)
      | ~ c_in(V_a,v_A,t_a)
      | c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
      | ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_emptyset ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_O_91_124_Aa2_A_58_AA_59_Ab2_A_58_AA_59_Ainterval_Ar_Aa2_Ab2_A_126_61_A_123_125_A_124_93_A_61_61_62_A_I_124_Apset_A_61_Ainterval_Ar_Aa2_Ab2_M_Aorder_A_61_Ainduced_A_Iinterval_Ar_Aa2_Ab2_J_Ar_A_124_J_A_58_ACompleteLattice_A_61_61_ATrue_0) ).

tff(10,plain,
    ! [V_b: $i,V_a: $i] :
      ( ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_emptyset )
      | c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
      | ~ c_in(V_a,v_A,t_a)
      | ~ c_in(V_b,v_A,t_a) ),
    inference(modus_ponens,[status(thm)],[9,8]) ).

tff(11,plain,
    ! [V_b: $i,V_a: $i] :
      ( ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_emptyset )
      | c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
      | ~ c_in(V_a,v_A,t_a)
      | ~ c_in(V_b,v_A,t_a) ),
    inference(modus_ponens,[status(thm)],[10,6]) ).

tff(12,plain,
    ! [V_b: $i,V_a: $i] :
      ( ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_emptyset )
      | c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
      | ~ c_in(V_a,v_A,t_a)
      | ~ c_in(V_b,v_A,t_a) ),
    inference(skolemize,[status(sab)],[11]) ).

tff(13,plain,
    ! [V_b: $i,V_a: $i] :
      ( ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_emptyset )
      | c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
      | ~ c_in(V_a,v_A,t_a)
      | ~ c_in(V_b,v_A,t_a) ),
    inference(modus_ponens,[status(thm)],[12,5]) ).

tff(14,plain,
    ( c_in(c_Tarski_OTop(v_cl,t_a),v_A,t_a)
  <=> c_in(c_Tarski_OTop(v_cl,t_a),v_A,t_a) ),
    inference(rewrite,[status(thm)],]) ).

tff(15,axiom,
    c_in(c_Tarski_OTop(v_cl,t_a),v_A,t_a),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_OTop_Acl_A_58_AA_A_61_61_ATrue_0) ).

tff(16,plain,
    c_in(c_Tarski_OTop(v_cl,t_a),v_A,t_a),
    inference(modus_ponens,[status(thm)],[15,14]) ).

tff(17,plain,
    ( ~ c_in(c_Tarski_Opotype_Opotype__ext(v_intY1,c_Tarski_Oinduced(v_intY1,v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
  <=> ~ c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) ),
    inference(rewrite,[status(thm)],]) ).

tff(18,plain,
    ( ~ c_in(c_Tarski_Opotype_Opotype__ext(v_intY1,c_Tarski_Oinduced(v_intY1,v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
  <=> ~ c_in(c_Tarski_Opotype_Opotype__ext(v_intY1,c_Tarski_Oinduced(v_intY1,v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) ),
    inference(rewrite,[status(thm)],]) ).

tff(19,axiom,
    ~ c_in(c_Tarski_Opotype_Opotype__ext(v_intY1,c_Tarski_Oinduced(v_intY1,v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

tff(20,plain,
    ~ c_in(c_Tarski_Opotype_Opotype__ext(v_intY1,c_Tarski_Oinduced(v_intY1,v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),
    inference(modus_ponens,[status(thm)],[19,18]) ).

tff(21,plain,
    ~ c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),
    inference(modus_ponens,[status(thm)],[20,17]) ).

tff(22,plain,
    ( ( ~ ! [V_b: $i,V_a: $i] :
            ( ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_emptyset )
            | c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
            | ~ c_in(V_a,v_A,t_a)
            | ~ c_in(V_b,v_A,t_a) )
      | c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
      | ( c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a) = c_emptyset )
      | ~ c_in(c_Tarski_Olub(v_Y,v_cl,t_a),v_A,t_a)
      | ~ c_in(c_Tarski_OTop(v_cl,t_a),v_A,t_a) )
  <=> ( ~ ! [V_b: $i,V_a: $i] :
            ( ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_emptyset )
            | c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
            | ~ c_in(V_a,v_A,t_a)
            | ~ c_in(V_b,v_A,t_a) )
      | c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
      | ( c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a) = c_emptyset )
      | ~ c_in(c_Tarski_Olub(v_Y,v_cl,t_a),v_A,t_a)
      | ~ c_in(c_Tarski_OTop(v_cl,t_a),v_A,t_a) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(23,plain,
    ( ( ( c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a) = c_emptyset )
      | c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
      | ~ c_in(c_Tarski_Olub(v_Y,v_cl,t_a),v_A,t_a)
      | ~ c_in(c_Tarski_OTop(v_cl,t_a),v_A,t_a) )
  <=> ( c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
      | ( c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a) = c_emptyset )
      | ~ c_in(c_Tarski_Olub(v_Y,v_cl,t_a),v_A,t_a)
      | ~ c_in(c_Tarski_OTop(v_cl,t_a),v_A,t_a) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(24,plain,
    ( ( ~ ! [V_b: $i,V_a: $i] :
            ( ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_emptyset )
            | c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
            | ~ c_in(V_a,v_A,t_a)
            | ~ c_in(V_b,v_A,t_a) )
      | ( c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a) = c_emptyset )
      | c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
      | ~ c_in(c_Tarski_Olub(v_Y,v_cl,t_a),v_A,t_a)
      | ~ c_in(c_Tarski_OTop(v_cl,t_a),v_A,t_a) )
  <=> ( ~ ! [V_b: $i,V_a: $i] :
            ( ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_emptyset )
            | c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
            | ~ c_in(V_a,v_A,t_a)
            | ~ c_in(V_b,v_A,t_a) )
      | c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
      | ( c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a) = c_emptyset )
      | ~ c_in(c_Tarski_Olub(v_Y,v_cl,t_a),v_A,t_a)
      | ~ c_in(c_Tarski_OTop(v_cl,t_a),v_A,t_a) ) ),
    inference(monotonicity,[status(thm)],[23]) ).

tff(25,plain,
    ( ( ~ ! [V_b: $i,V_a: $i] :
            ( ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_emptyset )
            | c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
            | ~ c_in(V_a,v_A,t_a)
            | ~ c_in(V_b,v_A,t_a) )
      | ( c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a) = c_emptyset )
      | c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
      | ~ c_in(c_Tarski_Olub(v_Y,v_cl,t_a),v_A,t_a)
      | ~ c_in(c_Tarski_OTop(v_cl,t_a),v_A,t_a) )
  <=> ( ~ ! [V_b: $i,V_a: $i] :
            ( ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_emptyset )
            | c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
            | ~ c_in(V_a,v_A,t_a)
            | ~ c_in(V_b,v_A,t_a) )
      | c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
      | ( c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a) = c_emptyset )
      | ~ c_in(c_Tarski_Olub(v_Y,v_cl,t_a),v_A,t_a)
      | ~ c_in(c_Tarski_OTop(v_cl,t_a),v_A,t_a) ) ),
    inference(transitivity,[status(thm)],[24,22]) ).

tff(26,plain,
    ( ~ ! [V_b: $i,V_a: $i] :
          ( ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_emptyset )
          | c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
          | ~ c_in(V_a,v_A,t_a)
          | ~ c_in(V_b,v_A,t_a) )
    | ( c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a) = c_emptyset )
    | c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
    | ~ c_in(c_Tarski_Olub(v_Y,v_cl,t_a),v_A,t_a)
    | ~ c_in(c_Tarski_OTop(v_cl,t_a),v_A,t_a) ),
    inference(quant_inst,[status(thm)],]) ).

tff(27,plain,
    ( ~ ! [V_b: $i,V_a: $i] :
          ( ( c_Tarski_Ointerval(v_r,V_a,V_b,t_a) = c_emptyset )
          | c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,V_a,V_b,t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
          | ~ c_in(V_a,v_A,t_a)
          | ~ c_in(V_b,v_A,t_a) )
    | c_in(c_Tarski_Opotype_Opotype__ext(c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),c_Tarski_Oinduced(c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a),v_r,t_a),c_Product__Type_OUnity,t_a,tc_Product__Type_Ounit),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
    | ( c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a) = c_emptyset )
    | ~ c_in(c_Tarski_Olub(v_Y,v_cl,t_a),v_A,t_a)
    | ~ c_in(c_Tarski_OTop(v_cl,t_a),v_A,t_a) ),
    inference(modus_ponens,[status(thm)],[26,25]) ).

tff(28,plain,
    c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a) = c_emptyset,
    inference(unit_resolution,[status(thm)],[27,21,16,13,3]) ).

tff(29,plain,
    ^ [V_x: $i] :
      refl(
        ( ( ~ c_in(V_x,v_A,t_a)
          | ( c_Tarski_Ointerval(v_r,V_x,c_Tarski_OTop(v_cl,t_a),t_a) != c_emptyset ) )
      <=> ( ~ c_in(V_x,v_A,t_a)
          | ( c_Tarski_Ointerval(v_r,V_x,c_Tarski_OTop(v_cl,t_a),t_a) != c_emptyset ) ) )),
    inference(bind,[status(th)],]) ).

tff(30,plain,
    ( ! [V_x: $i] :
        ( ~ c_in(V_x,v_A,t_a)
        | ( c_Tarski_Ointerval(v_r,V_x,c_Tarski_OTop(v_cl,t_a),t_a) != c_emptyset ) )
  <=> ! [V_x: $i] :
        ( ~ c_in(V_x,v_A,t_a)
        | ( c_Tarski_Ointerval(v_r,V_x,c_Tarski_OTop(v_cl,t_a),t_a) != c_emptyset ) ) ),
    inference(quant_intro,[status(thm)],[29]) ).

tff(31,plain,
    ( ! [V_x: $i] :
        ( ~ c_in(V_x,v_A,t_a)
        | ( c_Tarski_Ointerval(v_r,V_x,c_Tarski_OTop(v_cl,t_a),t_a) != c_emptyset ) )
  <=> ! [V_x: $i] :
        ( ~ c_in(V_x,v_A,t_a)
        | ( c_Tarski_Ointerval(v_r,V_x,c_Tarski_OTop(v_cl,t_a),t_a) != c_emptyset ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(32,axiom,
    ! [V_x: $i] :
      ( ~ c_in(V_x,v_A,t_a)
      | ( c_Tarski_Ointerval(v_r,V_x,c_Tarski_OTop(v_cl,t_a),t_a) != c_emptyset ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_Ox1_A_58_AA_A_61_61_62_Ainterval_Ar_Ax1_A_ITop_Acl_J_A_61_A_123_125_A_61_61_AFalse_0) ).

tff(33,plain,
    ! [V_x: $i] :
      ( ~ c_in(V_x,v_A,t_a)
      | ( c_Tarski_Ointerval(v_r,V_x,c_Tarski_OTop(v_cl,t_a),t_a) != c_emptyset ) ),
    inference(modus_ponens,[status(thm)],[32,31]) ).

tff(34,plain,
    ! [V_x: $i] :
      ( ~ c_in(V_x,v_A,t_a)
      | ( c_Tarski_Ointerval(v_r,V_x,c_Tarski_OTop(v_cl,t_a),t_a) != c_emptyset ) ),
    inference(skolemize,[status(sab)],[33]) ).

tff(35,plain,
    ! [V_x: $i] :
      ( ~ c_in(V_x,v_A,t_a)
      | ( c_Tarski_Ointerval(v_r,V_x,c_Tarski_OTop(v_cl,t_a),t_a) != c_emptyset ) ),
    inference(modus_ponens,[status(thm)],[34,30]) ).

tff(36,plain,
    ( ( ~ ! [V_x: $i] :
            ( ~ c_in(V_x,v_A,t_a)
            | ( c_Tarski_Ointerval(v_r,V_x,c_Tarski_OTop(v_cl,t_a),t_a) != c_emptyset ) )
      | ~ c_in(c_Tarski_Olub(v_Y,v_cl,t_a),v_A,t_a)
      | ( c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a) != c_emptyset ) )
  <=> ( ~ ! [V_x: $i] :
            ( ~ c_in(V_x,v_A,t_a)
            | ( c_Tarski_Ointerval(v_r,V_x,c_Tarski_OTop(v_cl,t_a),t_a) != c_emptyset ) )
      | ~ c_in(c_Tarski_Olub(v_Y,v_cl,t_a),v_A,t_a)
      | ( c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a) != c_emptyset ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(37,plain,
    ( ~ ! [V_x: $i] :
          ( ~ c_in(V_x,v_A,t_a)
          | ( c_Tarski_Ointerval(v_r,V_x,c_Tarski_OTop(v_cl,t_a),t_a) != c_emptyset ) )
    | ~ c_in(c_Tarski_Olub(v_Y,v_cl,t_a),v_A,t_a)
    | ( c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a) != c_emptyset ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(38,plain,
    ( ~ ! [V_x: $i] :
          ( ~ c_in(V_x,v_A,t_a)
          | ( c_Tarski_Ointerval(v_r,V_x,c_Tarski_OTop(v_cl,t_a),t_a) != c_emptyset ) )
    | ~ c_in(c_Tarski_Olub(v_Y,v_cl,t_a),v_A,t_a)
    | ( c_Tarski_Ointerval(v_r,c_Tarski_Olub(v_Y,v_cl,t_a),c_Tarski_OTop(v_cl,t_a),t_a) != c_emptyset ) ),
    inference(modus_ponens,[status(thm)],[37,36]) ).

tff(39,plain,
    $false,
    inference(unit_resolution,[status(thm)],[38,3,35,28]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : LAT269-2 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.14  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35  % Computer : n017.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Thu Sep  1 12:19:52 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 0.14/0.36  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.36  Usage: tptp [options] [-file:]file
% 0.14/0.36    -h, -?       prints this message.
% 0.14/0.36    -smt2        print SMT-LIB2 benchmark.
% 0.14/0.36    -m, -model   generate model.
% 0.14/0.36    -p, -proof   generate proof.
% 0.14/0.36    -c, -core    generate unsat core of named formulas.
% 0.14/0.36    -st, -statistics display statistics.
% 0.14/0.36    -t:timeout   set timeout (in second).
% 0.14/0.36    -smt2status  display status in smt2 format instead of SZS.
% 0.14/0.36    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.36    -<param>:<value> configuration parameter and value.
% 0.14/0.36    -o:<output-file> file to place output in.
% 0.21/0.40  % SZS status Unsatisfiable
% 0.21/0.40  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------