TSTP Solution File: LAT259-2 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : LAT259-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n009.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 18:32:28 EDT 2022

% Result   : Unsatisfiable 0.18s 0.37s
% Output   : Proof 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   34
% Syntax   : Number of formulae    :   54 (  15 unt;  13 typ;   0 def)
%            Number of atoms       :  180 (  31 equ)
%            Maximal formula atoms :   16 (   4 avg)
%            Number of connectives :  248 ( 118   ~; 111   |;   0   &)
%                                         (  19 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of FOOLs       :    9 (   9 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   16 (   6   >;  10   *;   0   +;   0  <<)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-3 aty)
%            Number of functors    :   11 (  11 usr;   7 con; 0-4 aty)
%            Number of variables   :   94 (  84   !;   0   ?;  94   :)

% Comments : 
%------------------------------------------------------------------------------
tff(c_Relation_Oantisym_type,type,
    c_Relation_Oantisym: ( $i * $i ) > $o ).

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

tff(c_Tarski_Opotype_Oorder_type,type,
    c_Tarski_Opotype_Oorder: ( $i * $i * $i ) > $i ).

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

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

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

tff(tc_prod_type,type,
    tc_prod: ( $i * $i ) > $i ).

tff(c_Pair_type,type,
    c_Pair: ( $i * $i * $i * $i ) > $i ).

tff(v_b_type,type,
    v_b: $i ).

tff(v_a_type,type,
    v_a: $i ).

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

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

tff(c_Tarski_OPartialOrder_type,type,
    c_Tarski_OPartialOrder: $i ).

tff(1,plain,
    ^ [V_V: $i,V_U: $i,V_r: $i,T_a: $i] :
      refl(
        ( ( ( V_U = V_V )
          | ~ c_in(c_Pair(V_U,V_V,T_a,T_a),V_r,tc_prod(T_a,T_a))
          | ~ c_in(c_Pair(V_V,V_U,T_a,T_a),V_r,tc_prod(T_a,T_a))
          | ~ c_Relation_Oantisym(V_r,T_a) )
      <=> ( ( V_U = V_V )
          | ~ c_in(c_Pair(V_U,V_V,T_a,T_a),V_r,tc_prod(T_a,T_a))
          | ~ c_in(c_Pair(V_V,V_U,T_a,T_a),V_r,tc_prod(T_a,T_a))
          | ~ c_Relation_Oantisym(V_r,T_a) ) )),
    inference(bind,[status(th)],]) ).

tff(2,plain,
    ( ! [V_V: $i,V_U: $i,V_r: $i,T_a: $i] :
        ( ( V_U = V_V )
        | ~ c_in(c_Pair(V_U,V_V,T_a,T_a),V_r,tc_prod(T_a,T_a))
        | ~ c_in(c_Pair(V_V,V_U,T_a,T_a),V_r,tc_prod(T_a,T_a))
        | ~ c_Relation_Oantisym(V_r,T_a) )
  <=> ! [V_V: $i,V_U: $i,V_r: $i,T_a: $i] :
        ( ( V_U = V_V )
        | ~ c_in(c_Pair(V_U,V_V,T_a,T_a),V_r,tc_prod(T_a,T_a))
        | ~ c_in(c_Pair(V_V,V_U,T_a,T_a),V_r,tc_prod(T_a,T_a))
        | ~ c_Relation_Oantisym(V_r,T_a) ) ),
    inference(quant_intro,[status(thm)],[1]) ).

tff(3,plain,
    ( ! [V_V: $i,V_U: $i,V_r: $i,T_a: $i] :
        ( ( V_U = V_V )
        | ~ c_in(c_Pair(V_U,V_V,T_a,T_a),V_r,tc_prod(T_a,T_a))
        | ~ c_in(c_Pair(V_V,V_U,T_a,T_a),V_r,tc_prod(T_a,T_a))
        | ~ c_Relation_Oantisym(V_r,T_a) )
  <=> ! [V_V: $i,V_U: $i,V_r: $i,T_a: $i] :
        ( ( V_U = V_V )
        | ~ c_in(c_Pair(V_U,V_V,T_a,T_a),V_r,tc_prod(T_a,T_a))
        | ~ c_in(c_Pair(V_V,V_U,T_a,T_a),V_r,tc_prod(T_a,T_a))
        | ~ c_Relation_Oantisym(V_r,T_a) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(4,plain,
    ^ [V_V: $i,V_U: $i,V_r: $i,T_a: $i] :
      trans(
        monotonicity(
          rewrite(
            ( ( ~ c_Relation_Oantisym(V_r,T_a)
              | ~ c_in(c_Pair(V_V,V_U,T_a,T_a),V_r,tc_prod(T_a,T_a))
              | ~ c_in(c_Pair(V_U,V_V,T_a,T_a),V_r,tc_prod(T_a,T_a)) )
          <=> ( ~ c_in(c_Pair(V_U,V_V,T_a,T_a),V_r,tc_prod(T_a,T_a))
              | ~ c_in(c_Pair(V_V,V_U,T_a,T_a),V_r,tc_prod(T_a,T_a))
              | ~ c_Relation_Oantisym(V_r,T_a) ) )),
          ( ( ~ c_Relation_Oantisym(V_r,T_a)
            | ~ c_in(c_Pair(V_V,V_U,T_a,T_a),V_r,tc_prod(T_a,T_a))
            | ~ c_in(c_Pair(V_U,V_V,T_a,T_a),V_r,tc_prod(T_a,T_a))
            | ( V_U = V_V ) )
        <=> ( ~ c_in(c_Pair(V_U,V_V,T_a,T_a),V_r,tc_prod(T_a,T_a))
            | ~ c_in(c_Pair(V_V,V_U,T_a,T_a),V_r,tc_prod(T_a,T_a))
            | ~ c_Relation_Oantisym(V_r,T_a)
            | ( V_U = V_V ) ) )),
        rewrite(
          ( ( ~ c_in(c_Pair(V_U,V_V,T_a,T_a),V_r,tc_prod(T_a,T_a))
            | ~ c_in(c_Pair(V_V,V_U,T_a,T_a),V_r,tc_prod(T_a,T_a))
            | ~ c_Relation_Oantisym(V_r,T_a)
            | ( V_U = V_V ) )
        <=> ( ( V_U = V_V )
            | ~ c_in(c_Pair(V_U,V_V,T_a,T_a),V_r,tc_prod(T_a,T_a))
            | ~ c_in(c_Pair(V_V,V_U,T_a,T_a),V_r,tc_prod(T_a,T_a))
            | ~ c_Relation_Oantisym(V_r,T_a) ) )),
        ( ( ~ c_Relation_Oantisym(V_r,T_a)
          | ~ c_in(c_Pair(V_V,V_U,T_a,T_a),V_r,tc_prod(T_a,T_a))
          | ~ c_in(c_Pair(V_U,V_V,T_a,T_a),V_r,tc_prod(T_a,T_a))
          | ( V_U = V_V ) )
      <=> ( ( V_U = V_V )
          | ~ c_in(c_Pair(V_U,V_V,T_a,T_a),V_r,tc_prod(T_a,T_a))
          | ~ c_in(c_Pair(V_V,V_U,T_a,T_a),V_r,tc_prod(T_a,T_a))
          | ~ c_Relation_Oantisym(V_r,T_a) ) )),
    inference(bind,[status(th)],]) ).

tff(5,plain,
    ( ! [V_V: $i,V_U: $i,V_r: $i,T_a: $i] :
        ( ~ c_Relation_Oantisym(V_r,T_a)
        | ~ c_in(c_Pair(V_V,V_U,T_a,T_a),V_r,tc_prod(T_a,T_a))
        | ~ c_in(c_Pair(V_U,V_V,T_a,T_a),V_r,tc_prod(T_a,T_a))
        | ( V_U = V_V ) )
  <=> ! [V_V: $i,V_U: $i,V_r: $i,T_a: $i] :
        ( ( V_U = V_V )
        | ~ c_in(c_Pair(V_U,V_V,T_a,T_a),V_r,tc_prod(T_a,T_a))
        | ~ c_in(c_Pair(V_V,V_U,T_a,T_a),V_r,tc_prod(T_a,T_a))
        | ~ c_Relation_Oantisym(V_r,T_a) ) ),
    inference(quant_intro,[status(thm)],[4]) ).

tff(6,axiom,
    ! [V_V: $i,V_U: $i,V_r: $i,T_a: $i] :
      ( ~ c_Relation_Oantisym(V_r,T_a)
      | ~ c_in(c_Pair(V_V,V_U,T_a,T_a),V_r,tc_prod(T_a,T_a))
      | ~ c_in(c_Pair(V_U,V_V,T_a,T_a),V_r,tc_prod(T_a,T_a))
      | ( V_U = V_V ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Oantisym__def_0) ).

tff(7,plain,
    ! [V_V: $i,V_U: $i,V_r: $i,T_a: $i] :
      ( ( V_U = V_V )
      | ~ c_in(c_Pair(V_U,V_V,T_a,T_a),V_r,tc_prod(T_a,T_a))
      | ~ c_in(c_Pair(V_V,V_U,T_a,T_a),V_r,tc_prod(T_a,T_a))
      | ~ c_Relation_Oantisym(V_r,T_a) ),
    inference(modus_ponens,[status(thm)],[6,5]) ).

tff(8,plain,
    ! [V_V: $i,V_U: $i,V_r: $i,T_a: $i] :
      ( ( V_U = V_V )
      | ~ c_in(c_Pair(V_U,V_V,T_a,T_a),V_r,tc_prod(T_a,T_a))
      | ~ c_in(c_Pair(V_V,V_U,T_a,T_a),V_r,tc_prod(T_a,T_a))
      | ~ c_Relation_Oantisym(V_r,T_a) ),
    inference(modus_ponens,[status(thm)],[7,3]) ).

tff(9,plain,
    ! [V_V: $i,V_U: $i,V_r: $i,T_a: $i] :
      ( ( V_U = V_V )
      | ~ c_in(c_Pair(V_U,V_V,T_a,T_a),V_r,tc_prod(T_a,T_a))
      | ~ c_in(c_Pair(V_V,V_U,T_a,T_a),V_r,tc_prod(T_a,T_a))
      | ~ c_Relation_Oantisym(V_r,T_a) ),
    inference(skolemize,[status(sab)],[8]) ).

tff(10,plain,
    ! [V_V: $i,V_U: $i,V_r: $i,T_a: $i] :
      ( ( V_U = V_V )
      | ~ c_in(c_Pair(V_U,V_V,T_a,T_a),V_r,tc_prod(T_a,T_a))
      | ~ c_in(c_Pair(V_V,V_U,T_a,T_a),V_r,tc_prod(T_a,T_a))
      | ~ c_Relation_Oantisym(V_r,T_a) ),
    inference(modus_ponens,[status(thm)],[9,2]) ).

tff(11,plain,
    ( ( v_a != v_b )
  <=> ( v_a != v_b ) ),
    inference(rewrite,[status(thm)],]) ).

tff(12,axiom,
    v_a != v_b,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).

tff(13,plain,
    v_a != v_b,
    inference(modus_ponens,[status(thm)],[12,11]) ).

tff(14,plain,
    ( c_in(c_Pair(v_b,v_a,t_a,t_a),v_r,tc_prod(t_a,t_a))
  <=> c_in(c_Pair(v_b,v_a,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ),
    inference(rewrite,[status(thm)],]) ).

tff(15,plain,
    ( c_in(c_Pair(v_b,v_a,t_a,t_a),v_r,tc_prod(t_a,t_a))
  <=> c_in(c_Pair(v_b,v_a,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
    inference(rewrite,[status(thm)],]) ).

tff(16,axiom,
    c_in(c_Pair(v_b,v_a,t_a,t_a),v_r,tc_prod(t_a,t_a)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).

tff(17,plain,
    c_in(c_Pair(v_b,v_a,t_a,t_a),v_r,tc_prod(t_a,t_a)),
    inference(modus_ponens,[status(thm)],[16,15]) ).

tff(18,plain,
    c_in(c_Pair(v_b,v_a,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),
    inference(modus_ponens,[status(thm)],[17,14]) ).

tff(19,plain,
    ( c_in(c_Pair(v_a,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
  <=> c_in(c_Pair(v_a,v_b,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ),
    inference(rewrite,[status(thm)],]) ).

tff(20,plain,
    ( c_in(c_Pair(v_a,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
  <=> c_in(c_Pair(v_a,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
    inference(rewrite,[status(thm)],]) ).

tff(21,axiom,
    c_in(c_Pair(v_a,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

tff(22,plain,
    c_in(c_Pair(v_a,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a)),
    inference(modus_ponens,[status(thm)],[21,20]) ).

tff(23,plain,
    c_in(c_Pair(v_a,v_b,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),
    inference(modus_ponens,[status(thm)],[22,19]) ).

tff(24,plain,
    ( ( ~ ! [V_V: $i,V_U: $i,V_r: $i,T_a: $i] :
            ( ( V_U = V_V )
            | ~ c_in(c_Pair(V_U,V_V,T_a,T_a),V_r,tc_prod(T_a,T_a))
            | ~ c_in(c_Pair(V_V,V_U,T_a,T_a),V_r,tc_prod(T_a,T_a))
            | ~ c_Relation_Oantisym(V_r,T_a) )
      | ( v_a = v_b )
      | ~ c_in(c_Pair(v_a,v_b,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_b,v_a,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))
      | ~ c_Relation_Oantisym(c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),t_a) )
  <=> ( ~ ! [V_V: $i,V_U: $i,V_r: $i,T_a: $i] :
            ( ( V_U = V_V )
            | ~ c_in(c_Pair(V_U,V_V,T_a,T_a),V_r,tc_prod(T_a,T_a))
            | ~ c_in(c_Pair(V_V,V_U,T_a,T_a),V_r,tc_prod(T_a,T_a))
            | ~ c_Relation_Oantisym(V_r,T_a) )
      | ( v_a = v_b )
      | ~ c_in(c_Pair(v_a,v_b,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_b,v_a,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))
      | ~ c_Relation_Oantisym(c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),t_a) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(25,plain,
    ( ~ ! [V_V: $i,V_U: $i,V_r: $i,T_a: $i] :
          ( ( V_U = V_V )
          | ~ c_in(c_Pair(V_U,V_V,T_a,T_a),V_r,tc_prod(T_a,T_a))
          | ~ c_in(c_Pair(V_V,V_U,T_a,T_a),V_r,tc_prod(T_a,T_a))
          | ~ c_Relation_Oantisym(V_r,T_a) )
    | ( v_a = v_b )
    | ~ c_in(c_Pair(v_a,v_b,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_b,v_a,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))
    | ~ c_Relation_Oantisym(c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),t_a) ),
    inference(quant_inst,[status(thm)],]) ).

tff(26,plain,
    ( ~ ! [V_V: $i,V_U: $i,V_r: $i,T_a: $i] :
          ( ( V_U = V_V )
          | ~ c_in(c_Pair(V_U,V_V,T_a,T_a),V_r,tc_prod(T_a,T_a))
          | ~ c_in(c_Pair(V_V,V_U,T_a,T_a),V_r,tc_prod(T_a,T_a))
          | ~ c_Relation_Oantisym(V_r,T_a) )
    | ( v_a = v_b )
    | ~ c_in(c_Pair(v_a,v_b,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_b,v_a,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))
    | ~ c_Relation_Oantisym(c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),t_a) ),
    inference(modus_ponens,[status(thm)],[25,24]) ).

tff(27,plain,
    ~ c_Relation_Oantisym(c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),t_a),
    inference(unit_resolution,[status(thm)],[26,23,18,13,10]) ).

tff(28,plain,
    ( c_in(v_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
  <=> c_in(v_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) ),
    inference(rewrite,[status(thm)],]) ).

tff(29,axiom,
    c_in(v_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_Ocl_A_58_APartialOrder_0) ).

tff(30,plain,
    c_in(v_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),
    inference(modus_ponens,[status(thm)],[29,28]) ).

tff(31,plain,
    ^ [T_a: $i,V_P: $i] :
      refl(
        ( ( ~ c_in(V_P,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
          | c_Relation_Oantisym(c_Tarski_Opotype_Oorder(V_P,T_a,tc_Product__Type_Ounit),T_a) )
      <=> ( ~ c_in(V_P,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
          | c_Relation_Oantisym(c_Tarski_Opotype_Oorder(V_P,T_a,tc_Product__Type_Ounit),T_a) ) )),
    inference(bind,[status(th)],]) ).

tff(32,plain,
    ( ! [T_a: $i,V_P: $i] :
        ( ~ c_in(V_P,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
        | c_Relation_Oantisym(c_Tarski_Opotype_Oorder(V_P,T_a,tc_Product__Type_Ounit),T_a) )
  <=> ! [T_a: $i,V_P: $i] :
        ( ~ c_in(V_P,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
        | c_Relation_Oantisym(c_Tarski_Opotype_Oorder(V_P,T_a,tc_Product__Type_Ounit),T_a) ) ),
    inference(quant_intro,[status(thm)],[31]) ).

tff(33,plain,
    ( ! [T_a: $i,V_P: $i] :
        ( ~ c_in(V_P,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
        | c_Relation_Oantisym(c_Tarski_Opotype_Oorder(V_P,T_a,tc_Product__Type_Ounit),T_a) )
  <=> ! [T_a: $i,V_P: $i] :
        ( ~ c_in(V_P,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
        | c_Relation_Oantisym(c_Tarski_Opotype_Oorder(V_P,T_a,tc_Product__Type_Ounit),T_a) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(34,axiom,
    ! [T_a: $i,V_P: $i] :
      ( ~ c_in(V_P,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
      | c_Relation_Oantisym(c_Tarski_Opotype_Oorder(V_P,T_a,tc_Product__Type_Ounit),T_a) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_OPartialOrder__iff_1) ).

tff(35,plain,
    ! [T_a: $i,V_P: $i] :
      ( ~ c_in(V_P,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
      | c_Relation_Oantisym(c_Tarski_Opotype_Oorder(V_P,T_a,tc_Product__Type_Ounit),T_a) ),
    inference(modus_ponens,[status(thm)],[34,33]) ).

tff(36,plain,
    ! [T_a: $i,V_P: $i] :
      ( ~ c_in(V_P,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
      | c_Relation_Oantisym(c_Tarski_Opotype_Oorder(V_P,T_a,tc_Product__Type_Ounit),T_a) ),
    inference(skolemize,[status(sab)],[35]) ).

tff(37,plain,
    ! [T_a: $i,V_P: $i] :
      ( ~ c_in(V_P,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
      | c_Relation_Oantisym(c_Tarski_Opotype_Oorder(V_P,T_a,tc_Product__Type_Ounit),T_a) ),
    inference(modus_ponens,[status(thm)],[36,32]) ).

tff(38,plain,
    ( ( ~ ! [T_a: $i,V_P: $i] :
            ( ~ c_in(V_P,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
            | c_Relation_Oantisym(c_Tarski_Opotype_Oorder(V_P,T_a,tc_Product__Type_Ounit),T_a) )
      | ~ c_in(v_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
      | c_Relation_Oantisym(c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),t_a) )
  <=> ( ~ ! [T_a: $i,V_P: $i] :
            ( ~ c_in(V_P,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
            | c_Relation_Oantisym(c_Tarski_Opotype_Oorder(V_P,T_a,tc_Product__Type_Ounit),T_a) )
      | ~ c_in(v_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
      | c_Relation_Oantisym(c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),t_a) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(39,plain,
    ( ~ ! [T_a: $i,V_P: $i] :
          ( ~ c_in(V_P,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
          | c_Relation_Oantisym(c_Tarski_Opotype_Oorder(V_P,T_a,tc_Product__Type_Ounit),T_a) )
    | ~ c_in(v_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
    | c_Relation_Oantisym(c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),t_a) ),
    inference(quant_inst,[status(thm)],]) ).

tff(40,plain,
    ( ~ ! [T_a: $i,V_P: $i] :
          ( ~ c_in(V_P,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
          | c_Relation_Oantisym(c_Tarski_Opotype_Oorder(V_P,T_a,tc_Product__Type_Ounit),T_a) )
    | ~ c_in(v_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
    | c_Relation_Oantisym(c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),t_a) ),
    inference(modus_ponens,[status(thm)],[39,38]) ).

tff(41,plain,
    $false,
    inference(unit_resolution,[status(thm)],[40,37,30,27]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : LAT259-2 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.12  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.32  % Computer : n009.cluster.edu
% 0.13/0.32  % Model    : x86_64 x86_64
% 0.13/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32  % Memory   : 8042.1875MB
% 0.13/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32  % CPULimit : 300
% 0.13/0.32  % WCLimit  : 300
% 0.13/0.32  % DateTime : Thu Sep  1 12:50:05 EDT 2022
% 0.13/0.32  % CPUTime  : 
% 0.13/0.32  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.32  Usage: tptp [options] [-file:]file
% 0.13/0.32    -h, -?       prints this message.
% 0.13/0.32    -smt2        print SMT-LIB2 benchmark.
% 0.13/0.32    -m, -model   generate model.
% 0.13/0.32    -p, -proof   generate proof.
% 0.13/0.32    -c, -core    generate unsat core of named formulas.
% 0.13/0.32    -st, -statistics display statistics.
% 0.13/0.32    -t:timeout   set timeout (in second).
% 0.13/0.32    -smt2status  display status in smt2 format instead of SZS.
% 0.13/0.32    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.32    -<param>:<value> configuration parameter and value.
% 0.13/0.32    -o:<output-file> file to place output in.
% 0.18/0.37  % SZS status Unsatisfiable
% 0.18/0.37  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------