SET007 Axioms: SET007+59.ax


%------------------------------------------------------------------------------
% File     : SET007+59 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Partially Ordered Sets
% Version  : [Urb08] axioms.
% English  :

% Refs     : [Mat90] Matuszewski (1990), Formalized Mathematics
%          : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
%          : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source   : [Urb08]
% Names    : orders_1 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  215 ( 108 unit)
%            Number of atoms       :  635 (  40 equality)
%            Maximal formula depth :   18 (   4 average)
%            Number of connectives :  495 (  75 ~  ;   4  |; 202  &)
%                                         (  22 <=>; 192 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   39 (   1 propositional; 0-3 arity)
%            Number of functors    :   21 (   3 constant; 0-3 arity)
%            Number of variables   :  260 (   0 singleton; 254 !;   6 ?)
%            Maximal term depth    :    3 (   1 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(fc1_orders_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ~ v1_xboole_0(k1_orders_1(A)) ) )).

fof(d1_orders_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ( ~ r2_hidden(k1_xboole_0,A)
       => ! [B] :
            ( ( v1_funct_1(B)
              & v1_funct_2(B,A,k3_tarski(A))
              & m2_relset_1(B,A,k3_tarski(A)) )
           => ( m1_orders_1(B,A)
            <=> ! [C] :
                  ( r2_hidden(C,A)
                 => r2_hidden(k1_funct_1(B,C),C) ) ) ) ) ) )).

fof(d2_orders_1,axiom,(
    ! [A] : k1_orders_1(A) = k4_xboole_0(k1_zfmisc_1(A),k1_tarski(k1_xboole_0)) )).

fof(t1_orders_1,axiom,(
    $true )).

fof(t2_orders_1,axiom,(
    $true )).

fof(t3_orders_1,axiom,(
    $true )).

fof(t4_orders_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ~ r2_hidden(k1_xboole_0,k1_orders_1(A)) ) )).

fof(t5_orders_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ( r1_tarski(A,B)
          <=> r2_hidden(A,k1_orders_1(B)) ) ) ) )).

fof(t6_orders_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ( m1_subset_1(A,k1_zfmisc_1(B))
          <=> r2_hidden(A,k1_orders_1(B)) ) ) ) )).

fof(t7_orders_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => r2_hidden(A,k1_orders_1(A)) ) )).

fof(t8_orders_1,axiom,(
    $true )).

fof(t9_orders_1,axiom,(
    $true )).

fof(t10_orders_1,axiom,(
    $true )).

fof(t11_orders_1,axiom,(
    $true )).

fof(t12_orders_1,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_2(C)
        & v4_relat_2(C)
        & v8_relat_2(C)
        & v1_partfun1(C,A,A)
        & m2_relset_1(C,A,A) )
     => ( r2_hidden(B,A)
       => r2_hidden(k4_tarski(B,B),C) ) ) )).

fof(t13_orders_1,axiom,(
    ! [A,B,C,D] :
      ( ( v1_relat_2(D)
        & v4_relat_2(D)
        & v8_relat_2(D)
        & v1_partfun1(D,A,A)
        & m2_relset_1(D,A,A) )
     => ( ( r2_hidden(B,A)
          & r2_hidden(C,A)
          & r2_hidden(k4_tarski(B,C),D)
          & r2_hidden(k4_tarski(C,B),D) )
       => B = C ) ) )).

fof(t14_orders_1,axiom,(
    ! [A,B,C,D,E] :
      ( ( v1_relat_2(E)
        & v4_relat_2(E)
        & v8_relat_2(E)
        & v1_partfun1(E,A,A)
        & m2_relset_1(E,A,A) )
     => ( ( r2_hidden(B,A)
          & r2_hidden(C,A)
          & r2_hidden(D,A)
          & r2_hidden(k4_tarski(B,C),E)
          & r2_hidden(k4_tarski(C,D),E) )
       => r2_hidden(k4_tarski(B,D),E) ) ) )).

fof(t15_orders_1,axiom,(
    $true )).

fof(t16_orders_1,axiom,(
    $true )).

fof(t17_orders_1,axiom,(
    $true )).

fof(t18_orders_1,axiom,(
    $true )).

fof(t19_orders_1,axiom,(
    $true )).

fof(t20_orders_1,axiom,(
    $true )).

fof(t21_orders_1,axiom,(
    $true )).

fof(t22_orders_1,axiom,(
    $true )).

fof(t23_orders_1,axiom,(
    $true )).

fof(t24_orders_1,axiom,(
    $true )).

fof(t25_orders_1,axiom,(
    $true )).

fof(t26_orders_1,axiom,(
    $true )).

fof(t27_orders_1,axiom,(
    $true )).

fof(t28_orders_1,axiom,(
    $true )).

fof(t29_orders_1,axiom,(
    $true )).

fof(t30_orders_1,axiom,(
    $true )).

fof(t31_orders_1,axiom,(
    $true )).

fof(t32_orders_1,axiom,(
    $true )).

fof(t33_orders_1,axiom,(
    $true )).

fof(t34_orders_1,axiom,(
    $true )).

fof(t35_orders_1,axiom,(
    $true )).

fof(t36_orders_1,axiom,(
    $true )).

fof(t37_orders_1,axiom,(
    $true )).

fof(t38_orders_1,axiom,(
    $true )).

fof(t39_orders_1,axiom,(
    $true )).

fof(t40_orders_1,axiom,(
    $true )).

fof(t41_orders_1,axiom,(
    $true )).

fof(t42_orders_1,axiom,(
    $true )).

fof(t43_orders_1,axiom,(
    $true )).

fof(t44_orders_1,axiom,(
    $true )).

fof(t45_orders_1,axiom,(
    $true )).

fof(t46_orders_1,axiom,(
    $true )).

fof(t47_orders_1,axiom,(
    $true )).

fof(t48_orders_1,axiom,(
    $true )).

fof(t49_orders_1,axiom,(
    $true )).

fof(t50_orders_1,axiom,(
    $true )).

fof(t51_orders_1,axiom,(
    $true )).

fof(t52_orders_1,axiom,(
    $true )).

fof(t53_orders_1,axiom,(
    $true )).

fof(t54_orders_1,axiom,(
    $true )).

fof(t55_orders_1,axiom,(
    $true )).

fof(t56_orders_1,axiom,(
    $true )).

fof(t57_orders_1,axiom,(
    $true )).

fof(t58_orders_1,axiom,(
    $true )).

fof(t59_orders_1,axiom,(
    $true )).

fof(t60_orders_1,axiom,(
    $true )).

fof(t61_orders_1,axiom,(
    $true )).

fof(t62_orders_1,axiom,(
    $true )).

fof(t63_orders_1,axiom,(
    $true )).

fof(t64_orders_1,axiom,(
    $true )).

fof(t65_orders_1,axiom,(
    $true )).

fof(t66_orders_1,axiom,(
    $true )).

fof(t67_orders_1,axiom,(
    $true )).

fof(t68_orders_1,axiom,(
    $true )).

fof(t69_orders_1,axiom,(
    $true )).

fof(t70_orders_1,axiom,(
    $true )).

fof(t71_orders_1,axiom,(
    $true )).

fof(t72_orders_1,axiom,(
    $true )).

fof(t73_orders_1,axiom,(
    $true )).

fof(t74_orders_1,axiom,(
    $true )).

fof(t75_orders_1,axiom,(
    $true )).

fof(t76_orders_1,axiom,(
    $true )).

fof(t77_orders_1,axiom,(
    $true )).

fof(t78_orders_1,axiom,(
    $true )).

fof(t79_orders_1,axiom,(
    $true )).

fof(t80_orders_1,axiom,(
    $true )).

fof(t81_orders_1,axiom,(
    $true )).

fof(t82_orders_1,axiom,(
    $true )).

fof(t83_orders_1,axiom,(
    $true )).

fof(t84_orders_1,axiom,(
    $true )).

fof(t85_orders_1,axiom,(
    $true )).

fof(t86_orders_1,axiom,(
    $true )).

fof(t87_orders_1,axiom,(
    $true )).

fof(t88_orders_1,axiom,(
    $true )).

fof(t89_orders_1,axiom,(
    $true )).

fof(t90_orders_1,axiom,(
    $true )).

fof(t91_orders_1,axiom,(
    ! [A] :
      ( ~ ( ? [B] :
              ( B != k1_xboole_0
              & r2_hidden(B,A) )
          & k3_tarski(A) = k1_xboole_0 )
      & ~ ( k3_tarski(A) != k1_xboole_0
          & ! [B] :
              ~ ( B != k1_xboole_0
                & r2_hidden(B,A) ) ) ) )).

fof(t92_orders_1,axiom,(
    ! [A,B] :
      ( v1_relat_1(B)
     => ( r7_relat_2(B,A)
      <=> ( r1_relat_2(B,A)
          & r6_relat_2(B,A) ) ) ) )).

fof(t93_orders_1,axiom,(
    ! [A,B,C] :
      ( v1_relat_1(C)
     => ( ( r1_relat_2(C,A)
          & r1_tarski(B,A) )
       => r1_relat_2(C,B) ) ) )).

fof(t94_orders_1,axiom,(
    ! [A,B,C] :
      ( v1_relat_1(C)
     => ( ( r4_relat_2(C,A)
          & r1_tarski(B,A) )
       => r4_relat_2(C,B) ) ) )).

fof(t95_orders_1,axiom,(
    ! [A,B,C] :
      ( v1_relat_1(C)
     => ( ( r8_relat_2(C,A)
          & r1_tarski(B,A) )
       => r8_relat_2(C,B) ) ) )).

fof(t96_orders_1,axiom,(
    ! [A,B,C] :
      ( v1_relat_1(C)
     => ( ( r7_relat_2(C,A)
          & r1_tarski(B,A) )
       => r7_relat_2(C,B) ) ) )).

fof(t97_orders_1,axiom,(
    ! [A,B] :
      ( ( v1_partfun1(B,A,A)
        & m2_relset_1(B,A,A) )
     => k3_relat_1(B) = A ) )).

fof(t98_orders_1,axiom,(
    ! [A,B] :
      ( m2_relset_1(B,A,A)
     => ( r1_relat_2(B,A)
       => ( k4_relset_1(A,A,B) = A
          & k3_relat_1(B) = A ) ) ) )).

fof(t99_orders_1,axiom,(
    ! [A,B] :
      ( ( v1_relat_2(B)
        & v4_relat_2(B)
        & v8_relat_2(B)
        & v1_partfun1(B,A,A)
        & m2_relset_1(B,A,A) )
     => ( k4_relset_1(A,A,B) = A
        & k5_relset_1(A,A,B) = A ) ) )).

fof(t100_orders_1,axiom,(
    ! [A,B] :
      ( ( v1_relat_2(B)
        & v4_relat_2(B)
        & v8_relat_2(B)
        & v1_partfun1(B,A,A)
        & m2_relset_1(B,A,A) )
     => k3_relat_1(B) = A ) )).

fof(d3_orders_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ( v1_orders_1(A)
      <=> ( v1_relat_2(A)
          & v8_relat_2(A) ) ) ) )).

fof(d4_orders_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ( v2_orders_1(A)
      <=> ( v1_relat_2(A)
          & v8_relat_2(A)
          & v4_relat_2(A) ) ) ) )).

fof(d5_orders_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ( v3_orders_1(A)
      <=> ( v1_relat_2(A)
          & v8_relat_2(A)
          & v4_relat_2(A)
          & v6_relat_2(A) ) ) ) )).

fof(t101_orders_1,axiom,(
    $true )).

fof(t102_orders_1,axiom,(
    $true )).

fof(t103_orders_1,axiom,(
    $true )).

fof(t104_orders_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ( v1_orders_1(A)
       => v1_orders_1(k4_relat_1(A)) ) ) )).

fof(t105_orders_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ( v2_orders_1(A)
       => v2_orders_1(k4_relat_1(A)) ) ) )).

fof(t106_orders_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ( v3_orders_1(A)
       => v3_orders_1(k4_relat_1(A)) ) ) )).

fof(t107_orders_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ( v2_wellord1(A)
       => ( v1_orders_1(A)
          & v2_orders_1(A)
          & v3_orders_1(A) ) ) ) )).

fof(t108_orders_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ( v3_orders_1(A)
       => ( v1_orders_1(A)
          & v2_orders_1(A) ) ) ) )).

fof(t109_orders_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ( v2_orders_1(A)
       => v1_orders_1(A) ) ) )).

fof(t110_orders_1,axiom,(
    ! [A,B] :
      ( ( v1_relat_2(B)
        & v4_relat_2(B)
        & v8_relat_2(B)
        & v1_partfun1(B,A,A)
        & m2_relset_1(B,A,A) )
     => v2_orders_1(B) ) )).

fof(t111_orders_1,axiom,(
    ! [A,B] :
      ( ( v1_relat_2(B)
        & v4_relat_2(B)
        & v8_relat_2(B)
        & v1_partfun1(B,A,A)
        & m2_relset_1(B,A,A) )
     => v1_orders_1(B) ) )).

fof(t112_orders_1,axiom,(
    ! [A,B] :
      ( ( v1_relat_2(B)
        & v4_relat_2(B)
        & v8_relat_2(B)
        & v1_partfun1(B,A,A)
        & m2_relset_1(B,A,A) )
     => ( v6_relat_2(B)
       => v3_orders_1(B) ) ) )).

fof(t113_orders_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( v1_orders_1(A)
         => v1_orders_1(k2_wellord1(A,B)) ) ) )).

fof(t114_orders_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( v2_orders_1(A)
         => v2_orders_1(k2_wellord1(A,B)) ) ) )).

fof(t115_orders_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( v3_orders_1(A)
         => v3_orders_1(k2_wellord1(A,B)) ) ) )).

fof(t116_orders_1,axiom,(
    $true )).

fof(t117_orders_1,axiom,(
    $true )).

fof(t118_orders_1,axiom,(
    $true )).

fof(t119_orders_1,axiom,
    ( v1_orders_1(k1_xboole_0)
    & v2_orders_1(k1_xboole_0)
    & v3_orders_1(k1_xboole_0)
    & v2_wellord1(k1_xboole_0) )).

fof(t120_orders_1,axiom,(
    ! [A] :
      ( v1_orders_1(k6_partfun1(A))
      & v2_orders_1(k6_partfun1(A)) ) )).

fof(d6_orders_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( r1_orders_1(A,B)
        <=> ( r1_relat_2(A,B)
            & r8_relat_2(A,B) ) ) ) )).

fof(d7_orders_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( r2_orders_1(A,B)
        <=> ( r1_relat_2(A,B)
            & r8_relat_2(A,B)
            & r4_relat_2(A,B) ) ) ) )).

fof(d8_orders_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( r3_orders_1(A,B)
        <=> ( r1_relat_2(A,B)
            & r8_relat_2(A,B)
            & r4_relat_2(A,B)
            & r6_relat_2(A,B) ) ) ) )).

fof(t121_orders_1,axiom,(
    $true )).

fof(t122_orders_1,axiom,(
    $true )).

fof(t123_orders_1,axiom,(
    $true )).

fof(t124_orders_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( r2_wellord1(A,B)
         => ( r1_orders_1(A,B)
            & r2_orders_1(A,B)
            & r3_orders_1(A,B) ) ) ) )).

fof(t125_orders_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( r3_orders_1(A,B)
         => ( r1_orders_1(A,B)
            & r2_orders_1(A,B) ) ) ) )).

fof(t126_orders_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( r2_orders_1(A,B)
         => r1_orders_1(A,B) ) ) )).

fof(t127_orders_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ( v1_orders_1(A)
       => r1_orders_1(A,k3_relat_1(A)) ) ) )).

fof(t128_orders_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B,C] :
          ( ( r1_orders_1(A,B)
            & r1_tarski(C,B) )
         => r1_orders_1(A,C) ) ) )).

fof(t129_orders_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( r1_orders_1(A,B)
         => v1_orders_1(k2_wellord1(A,B)) ) ) )).

fof(t130_orders_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ( v2_orders_1(A)
       => r2_orders_1(A,k3_relat_1(A)) ) ) )).

fof(t131_orders_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B,C] :
          ( ( r2_orders_1(A,B)
            & r1_tarski(C,B) )
         => r2_orders_1(A,C) ) ) )).

fof(t132_orders_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( r2_orders_1(A,B)
         => v2_orders_1(k2_wellord1(A,B)) ) ) )).

fof(t133_orders_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ( v3_orders_1(A)
       => r3_orders_1(A,k3_relat_1(A)) ) ) )).

fof(t134_orders_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B,C] :
          ( ( r3_orders_1(A,B)
            & r1_tarski(C,B) )
         => r3_orders_1(A,C) ) ) )).

fof(t135_orders_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( r3_orders_1(A,B)
         => v3_orders_1(k2_wellord1(A,B)) ) ) )).

fof(t136_orders_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( r1_orders_1(A,B)
         => r1_orders_1(k4_relat_1(A),B) ) ) )).

fof(t137_orders_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( r2_orders_1(A,B)
         => r2_orders_1(k4_relat_1(A),B) ) ) )).

fof(t138_orders_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( r3_orders_1(A,B)
         => r3_orders_1(k4_relat_1(A),B) ) ) )).

fof(t139_orders_1,axiom,(
    ! [A,B] :
      ( ( v1_relat_2(B)
        & v4_relat_2(B)
        & v8_relat_2(B)
        & v1_partfun1(B,A,A)
        & m2_relset_1(B,A,A) )
     => r1_orders_1(B,A) ) )).

fof(t140_orders_1,axiom,(
    ! [A,B] :
      ( ( v1_relat_2(B)
        & v4_relat_2(B)
        & v8_relat_2(B)
        & v1_partfun1(B,A,A)
        & m2_relset_1(B,A,A) )
     => r2_orders_1(B,A) ) )).

fof(t141_orders_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( r2_orders_1(A,B)
         => ( v1_relat_2(k2_wellord1(A,B))
            & v4_relat_2(k2_wellord1(A,B))
            & v8_relat_2(k2_wellord1(A,B))
            & v1_partfun1(k2_wellord1(A,B),B,B)
            & m2_relset_1(k2_wellord1(A,B),B,B) ) ) ) )).

fof(t142_orders_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( r3_orders_1(A,B)
         => ( v1_relat_2(k2_wellord1(A,B))
            & v4_relat_2(k2_wellord1(A,B))
            & v8_relat_2(k2_wellord1(A,B))
            & v1_partfun1(k2_wellord1(A,B),B,B)
            & m2_relset_1(k2_wellord1(A,B),B,B) ) ) ) )).

fof(t143_orders_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( r2_wellord1(A,B)
         => ( v1_relat_2(k2_wellord1(A,B))
            & v4_relat_2(k2_wellord1(A,B))
            & v8_relat_2(k2_wellord1(A,B))
            & v1_partfun1(k2_wellord1(A,B),B,B)
            & m2_relset_1(k2_wellord1(A,B),B,B) ) ) ) )).

fof(t144_orders_1,axiom,(
    $true )).

fof(t145_orders_1,axiom,(
    $true )).

fof(t146_orders_1,axiom,(
    ! [A] :
      ( r1_orders_1(k6_partfun1(A),A)
      & r2_orders_1(k6_partfun1(A),A) ) )).

fof(d9_orders_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( r4_orders_1(A,B)
        <=> ! [C] :
              ~ ( r1_tarski(C,B)
                & v3_orders_1(k2_wellord1(A,C))
                & ! [D] :
                    ~ ( r2_hidden(D,B)
                      & ! [E] :
                          ( r2_hidden(E,C)
                         => r2_hidden(k4_tarski(E,D),A) ) ) ) ) ) )).

fof(d10_orders_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( r5_orders_1(A,B)
        <=> ! [C] :
              ~ ( r1_tarski(C,B)
                & v3_orders_1(k2_wellord1(A,C))
                & ! [D] :
                    ~ ( r2_hidden(D,B)
                      & ! [E] :
                          ( r2_hidden(E,C)
                         => r2_hidden(k4_tarski(D,E),A) ) ) ) ) ) )).

fof(t147_orders_1,axiom,(
    $true )).

fof(t148_orders_1,axiom,(
    $true )).

fof(t149_orders_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ~ ( r4_orders_1(A,B)
            & B = k1_xboole_0 ) ) )).

fof(t150_orders_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ~ ( r5_orders_1(A,B)
            & B = k1_xboole_0 ) ) )).

fof(t151_orders_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( r4_orders_1(A,B)
        <=> r5_orders_1(k4_relat_1(A),B) ) ) )).

fof(t152_orders_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( r4_orders_1(k4_relat_1(A),B)
        <=> r5_orders_1(A,B) ) ) )).

fof(d11_orders_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( r6_orders_1(A,B)
        <=> ( r2_hidden(B,k3_relat_1(A))
            & ! [C] :
                ~ ( r2_hidden(C,k3_relat_1(A))
                  & C != B
                  & r2_hidden(k4_tarski(B,C),A) ) ) ) ) )).

fof(d12_orders_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( r7_orders_1(A,B)
        <=> ( r2_hidden(B,k3_relat_1(A))
            & ! [C] :
                ~ ( r2_hidden(C,k3_relat_1(A))
                  & C != B
                  & r2_hidden(k4_tarski(C,B),A) ) ) ) ) )).

fof(d13_orders_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( r8_orders_1(A,B)
        <=> ( r2_hidden(B,k3_relat_1(A))
            & ! [C] :
                ( r2_hidden(C,k3_relat_1(A))
               => ( C = B
                  | r2_hidden(k4_tarski(C,B),A) ) ) ) ) ) )).

fof(d14_orders_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( r9_orders_1(A,B)
        <=> ( r2_hidden(B,k3_relat_1(A))
            & ! [C] :
                ( r2_hidden(C,k3_relat_1(A))
               => ( C = B
                  | r2_hidden(k4_tarski(B,C),A) ) ) ) ) ) )).

fof(t153_orders_1,axiom,(
    $true )).

fof(t154_orders_1,axiom,(
    $true )).

fof(t155_orders_1,axiom,(
    $true )).

fof(t156_orders_1,axiom,(
    $true )).

fof(t157_orders_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( ( r9_orders_1(A,B)
            & v4_relat_2(A) )
         => r7_orders_1(A,B) ) ) )).

fof(t158_orders_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( ( r8_orders_1(A,B)
            & v4_relat_2(A) )
         => r6_orders_1(A,B) ) ) )).

fof(t159_orders_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( ( r7_orders_1(A,B)
            & v6_relat_2(A) )
         => r9_orders_1(A,B) ) ) )).

fof(t160_orders_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( ( r6_orders_1(A,B)
            & v6_relat_2(A) )
         => r8_orders_1(A,B) ) ) )).

fof(t161_orders_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B,C] :
          ( ( r2_hidden(B,C)
            & r8_orders_1(A,B)
            & r1_tarski(C,k3_relat_1(A))
            & v1_relat_2(A) )
         => r4_orders_1(A,C) ) ) )).

fof(t162_orders_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B,C] :
          ( ( r2_hidden(B,C)
            & r9_orders_1(A,B)
            & r1_tarski(C,k3_relat_1(A))
            & v1_relat_2(A) )
         => r5_orders_1(A,C) ) ) )).

fof(t163_orders_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( r7_orders_1(A,B)
        <=> r6_orders_1(k4_relat_1(A),B) ) ) )).

fof(t164_orders_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( r7_orders_1(k4_relat_1(A),B)
        <=> r6_orders_1(A,B) ) ) )).

fof(t165_orders_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( r9_orders_1(A,B)
        <=> r8_orders_1(k4_relat_1(A),B) ) ) )).

fof(t166_orders_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( r9_orders_1(k4_relat_1(A),B)
        <=> r8_orders_1(A,B) ) ) )).

fof(t167_orders_1,axiom,(
    $true )).

fof(t168_orders_1,axiom,(
    $true )).

fof(t169_orders_1,axiom,(
    $true )).

fof(t170_orders_1,axiom,(
    $true )).

fof(t171_orders_1,axiom,(
    $true )).

fof(t172_orders_1,axiom,(
    $true )).

fof(t173_orders_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ~ ( r2_orders_1(A,B)
            & k3_relat_1(A) = B
            & r4_orders_1(A,B)
            & ! [C] : ~ r6_orders_1(A,C) ) ) )).

fof(t174_orders_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ~ ( r2_orders_1(A,B)
            & k3_relat_1(A) = B
            & r5_orders_1(A,B)
            & ! [C] : ~ r7_orders_1(A,C) ) ) )).

fof(t175_orders_1,axiom,(
    ! [A] :
      ~ ( A != k1_xboole_0
        & ! [B] :
            ~ ( r1_tarski(B,A)
              & v6_ordinal1(B)
              & ! [C] :
                  ~ ( r2_hidden(C,A)
                    & ! [D] :
                        ( r2_hidden(D,B)
                       => r1_tarski(D,C) ) ) )
        & ! [B] :
            ~ ( r2_hidden(B,A)
              & ! [C] :
                  ~ ( r2_hidden(C,A)
                    & C != B
                    & r1_tarski(B,C) ) ) ) )).

fof(t176_orders_1,axiom,(
    ! [A] :
      ~ ( A != k1_xboole_0
        & ! [B] :
            ~ ( r1_tarski(B,A)
              & v6_ordinal1(B)
              & ! [C] :
                  ~ ( r2_hidden(C,A)
                    & ! [D] :
                        ( r2_hidden(D,B)
                       => r1_tarski(C,D) ) ) )
        & ! [B] :
            ~ ( r2_hidden(B,A)
              & ! [C] :
                  ~ ( r2_hidden(C,A)
                    & C != B
                    & r1_tarski(C,B) ) ) ) )).

fof(t177_orders_1,axiom,(
    ! [A] :
      ~ ( A != k1_xboole_0
        & ! [B] :
            ( ( r1_tarski(B,A)
              & v6_ordinal1(B) )
           => ( B = k1_xboole_0
              | r2_hidden(k3_tarski(B),A) ) )
        & ! [B] :
            ~ ( r2_hidden(B,A)
              & ! [C] :
                  ~ ( r2_hidden(C,A)
                    & C != B
                    & r1_tarski(B,C) ) ) ) )).

fof(t178_orders_1,axiom,(
    ! [A] :
      ~ ( A != k1_xboole_0
        & ! [B] :
            ( ( r1_tarski(B,A)
              & v6_ordinal1(B) )
           => ( B = k1_xboole_0
              | r2_hidden(k1_setfam_1(B),A) ) )
        & ! [B] :
            ~ ( r2_hidden(B,A)
              & ! [C] :
                  ~ ( r2_hidden(C,A)
                    & C != B
                    & r1_tarski(C,B) ) ) ) )).

fof(t179_orders_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ~ ( r2_orders_1(A,B)
            & k3_relat_1(A) = B
            & ! [C] :
                ( v1_relat_1(C)
               => ~ ( r1_tarski(A,C)
                    & r3_orders_1(C,B)
                    & k3_relat_1(C) = B ) ) ) ) )).

fof(t180_orders_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => r1_tarski(A,k2_zfmisc_1(k3_relat_1(A),k3_relat_1(A))) ) )).

fof(t181_orders_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( ( v1_relat_2(A)
            & r1_tarski(B,k3_relat_1(A)) )
         => k3_relat_1(k2_wellord1(A,B)) = B ) ) )).

fof(t182_orders_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( r1_relat_2(A,B)
         => v1_relat_2(k2_wellord1(A,B)) ) ) )).

fof(t183_orders_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( r8_relat_2(A,B)
         => v8_relat_2(k2_wellord1(A,B)) ) ) )).

fof(t184_orders_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( r4_relat_2(A,B)
         => v4_relat_2(k2_wellord1(A,B)) ) ) )).

fof(t185_orders_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( r6_relat_2(A,B)
         => v6_relat_2(k2_wellord1(A,B)) ) ) )).

fof(t186_orders_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B,C] :
          ( ( r6_relat_2(A,B)
            & r1_tarski(C,B) )
         => r6_relat_2(A,C) ) ) )).

fof(t187_orders_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B,C] :
          ( ( r2_wellord1(A,B)
            & r1_tarski(C,B) )
         => r2_wellord1(A,C) ) ) )).

fof(t188_orders_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ( v6_relat_2(A)
       => v6_relat_2(k4_relat_1(A)) ) ) )).

fof(t189_orders_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( r1_relat_2(A,B)
         => r1_relat_2(k4_relat_1(A),B) ) ) )).

fof(t190_orders_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( r8_relat_2(A,B)
         => r8_relat_2(k4_relat_1(A),B) ) ) )).

fof(t191_orders_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( r4_relat_2(A,B)
         => r4_relat_2(k4_relat_1(A),B) ) ) )).

fof(t192_orders_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( r6_relat_2(A,B)
         => r6_relat_2(k4_relat_1(A),B) ) ) )).

fof(t193_orders_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] : k4_relat_1(k2_wellord1(A,B)) = k2_wellord1(k4_relat_1(A),B) ) )).

fof(t194_orders_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => k2_wellord1(A,k1_xboole_0) = k1_xboole_0 ) )).

fof(t195_orders_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ~ ( v1_finset_1(B)
            & r1_tarski(B,k2_relat_1(A))
            & ! [C] :
                ~ ( r1_tarski(C,k1_relat_1(A))
                  & v1_finset_1(C)
                  & k9_relat_1(A,C) = B ) ) ) )).

fof(s1_orders_1,axiom,
    ( ( ! [A] :
          ( m1_subset_1(A,f1_s1_orders_1)
         => p1_s1_orders_1(A,A) )
      & ! [A] :
          ( m1_subset_1(A,f1_s1_orders_1)
         => ! [B] :
              ( m1_subset_1(B,f1_s1_orders_1)
             => ( ( p1_s1_orders_1(A,B)
                  & p1_s1_orders_1(B,A) )
               => A = B ) ) )
      & ! [A] :
          ( m1_subset_1(A,f1_s1_orders_1)
         => ! [B] :
              ( m1_subset_1(B,f1_s1_orders_1)
             => ! [C] :
                  ( m1_subset_1(C,f1_s1_orders_1)
                 => ( ( p1_s1_orders_1(A,B)
                      & p1_s1_orders_1(B,C) )
                   => p1_s1_orders_1(A,C) ) ) ) )
      & ! [A] :
          ~ ( r1_tarski(A,f1_s1_orders_1)
            & ! [B] :
                ( m1_subset_1(B,f1_s1_orders_1)
               => ! [C] :
                    ( m1_subset_1(C,f1_s1_orders_1)
                   => ~ ( r2_hidden(B,A)
                        & r2_hidden(C,A)
                        & ~ p1_s1_orders_1(B,C)
                        & ~ p1_s1_orders_1(C,B) ) ) )
            & ! [B] :
                ( m1_subset_1(B,f1_s1_orders_1)
               => ? [C] :
                    ( m1_subset_1(C,f1_s1_orders_1)
                    & r2_hidden(C,A)
                    & ~ p1_s1_orders_1(C,B) ) ) ) )
   => ? [A] :
        ( m1_subset_1(A,f1_s1_orders_1)
        & ! [B] :
            ( m1_subset_1(B,f1_s1_orders_1)
           => ~ ( A != B
                & p1_s1_orders_1(A,B) ) ) ) )).

fof(s2_orders_1,axiom,
    ( ( ! [A] :
          ( m1_subset_1(A,f1_s2_orders_1)
         => p1_s2_orders_1(A,A) )
      & ! [A] :
          ( m1_subset_1(A,f1_s2_orders_1)
         => ! [B] :
              ( m1_subset_1(B,f1_s2_orders_1)
             => ( ( p1_s2_orders_1(A,B)
                  & p1_s2_orders_1(B,A) )
               => A = B ) ) )
      & ! [A] :
          ( m1_subset_1(A,f1_s2_orders_1)
         => ! [B] :
              ( m1_subset_1(B,f1_s2_orders_1)
             => ! [C] :
                  ( m1_subset_1(C,f1_s2_orders_1)
                 => ( ( p1_s2_orders_1(A,B)
                      & p1_s2_orders_1(B,C) )
                   => p1_s2_orders_1(A,C) ) ) ) )
      & ! [A] :
          ~ ( r1_tarski(A,f1_s2_orders_1)
            & ! [B] :
                ( m1_subset_1(B,f1_s2_orders_1)
               => ! [C] :
                    ( m1_subset_1(C,f1_s2_orders_1)
                   => ~ ( r2_hidden(B,A)
                        & r2_hidden(C,A)
                        & ~ p1_s2_orders_1(B,C)
                        & ~ p1_s2_orders_1(C,B) ) ) )
            & ! [B] :
                ( m1_subset_1(B,f1_s2_orders_1)
               => ? [C] :
                    ( m1_subset_1(C,f1_s2_orders_1)
                    & r2_hidden(C,A)
                    & ~ p1_s2_orders_1(B,C) ) ) ) )
   => ? [A] :
        ( m1_subset_1(A,f1_s2_orders_1)
        & ! [B] :
            ( m1_subset_1(B,f1_s2_orders_1)
           => ~ ( A != B
                & p1_s2_orders_1(B,A) ) ) ) )).

fof(dt_m1_orders_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_orders_1(B,A)
         => ( v1_funct_1(B)
            & v1_funct_2(B,A,k3_tarski(A))
            & m2_relset_1(B,A,k3_tarski(A)) ) ) ) )).

fof(existence_m1_orders_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ? [B] : m1_orders_1(B,A) ) )).

fof(dt_k1_orders_1,axiom,(
    $true )).
%------------------------------------------------------------------------------