SET007 Axioms: SET007+87.ax


%------------------------------------------------------------------------------
% File     : SET007+87 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Equalities and Inequalities in Real Numbers
% 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    : real_2 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  204 ( 141 unit)
%            Number of atoms       :  670 (   5 equality)
%            Maximal formula depth :   16 (   4 average)
%            Number of connectives :  683 ( 217 ~  ;  35  |; 203  &)
%                                         (   0 <=>; 228 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :    6 (   1 propositional; 0-2 arity)
%            Number of functors    :   11 (   4 constant; 0-2 arity)
%            Number of variables   :  164 (   0 singleton; 163 !;   1 ?)
%            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(t1_real_2,axiom,(
    $true )).

fof(t2_real_2,axiom,(
    $true )).

fof(t3_real_2,axiom,(
    $true )).

fof(t4_real_2,axiom,(
    $true )).

fof(t5_real_2,axiom,(
    $true )).

fof(t6_real_2,axiom,(
    $true )).

fof(t7_real_2,axiom,(
    $true )).

fof(t8_real_2,axiom,(
    $true )).

fof(t9_real_2,axiom,(
    $true )).

fof(t10_real_2,axiom,(
    $true )).

fof(t11_real_2,axiom,(
    $true )).

fof(t12_real_2,axiom,(
    $true )).

fof(t13_real_2,axiom,(
    $true )).

fof(t14_real_2,axiom,(
    $true )).

fof(t15_real_2,axiom,(
    $true )).

fof(t16_real_2,axiom,(
    $true )).

fof(t17_real_2,axiom,(
    $true )).

fof(t18_real_2,axiom,(
    $true )).

fof(t19_real_2,axiom,(
    $true )).

fof(t20_real_2,axiom,(
    $true )).

fof(t21_real_2,axiom,(
    $true )).

fof(t22_real_2,axiom,(
    $true )).

fof(t23_real_2,axiom,(
    $true )).

fof(t24_real_2,axiom,(
    $true )).

fof(t25_real_2,axiom,(
    $true )).

fof(t26_real_2,axiom,(
    $true )).

fof(t27_real_2,axiom,(
    $true )).

fof(t28_real_2,axiom,(
    $true )).

fof(t29_real_2,axiom,(
    $true )).

fof(t30_real_2,axiom,(
    $true )).

fof(t31_real_2,axiom,(
    $true )).

fof(t32_real_2,axiom,(
    $true )).

fof(t33_real_2,axiom,(
    $true )).

fof(t34_real_2,axiom,(
    $true )).

fof(t35_real_2,axiom,(
    $true )).

fof(t36_real_2,axiom,(
    $true )).

fof(t37_real_2,axiom,(
    $true )).

fof(t38_real_2,axiom,(
    $true )).

fof(t39_real_2,axiom,(
    $true )).

fof(t40_real_2,axiom,(
    $true )).

fof(t41_real_2,axiom,(
    $true )).

fof(t42_real_2,axiom,(
    $true )).

fof(t43_real_2,axiom,(
    $true )).

fof(t44_real_2,axiom,(
    $true )).

fof(t45_real_2,axiom,(
    $true )).

fof(t46_real_2,axiom,(
    $true )).

fof(t47_real_2,axiom,(
    $true )).

fof(t48_real_2,axiom,(
    $true )).

fof(t49_real_2,axiom,(
    $true )).

fof(t50_real_2,axiom,(
    $true )).

fof(t51_real_2,axiom,(
    $true )).

fof(t52_real_2,axiom,(
    $true )).

fof(t53_real_2,axiom,(
    $true )).

fof(t54_real_2,axiom,(
    $true )).

fof(t55_real_2,axiom,(
    $true )).

fof(t56_real_2,axiom,(
    $true )).

fof(t57_real_2,axiom,(
    $true )).

fof(t58_real_2,axiom,(
    $true )).

fof(t59_real_2,axiom,(
    $true )).

fof(t60_real_2,axiom,(
    $true )).

fof(t61_real_2,axiom,(
    $true )).

fof(t62_real_2,axiom,(
    $true )).

fof(t63_real_2,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ? [C] :
              ( v1_xreal_0(C)
              & A = k6_xcmplx_0(B,C) ) ) ) )).

fof(t64_real_2,axiom,(
    $true )).

fof(t65_real_2,axiom,(
    $true )).

fof(t66_real_2,axiom,(
    $true )).

fof(t67_real_2,axiom,(
    $true )).

fof(t68_real_2,axiom,(
    $true )).

fof(t69_real_2,axiom,(
    $true )).

fof(t70_real_2,axiom,(
    $true )).

fof(t71_real_2,axiom,(
    $true )).

fof(t72_real_2,axiom,(
    $true )).

fof(t73_real_2,axiom,(
    $true )).

fof(t74_real_2,axiom,(
    $true )).

fof(t75_real_2,axiom,(
    $true )).

fof(t76_real_2,axiom,(
    $true )).

fof(t77_real_2,axiom,(
    $true )).

fof(t78_real_2,axiom,(
    $true )).

fof(t79_real_2,axiom,(
    $true )).

fof(t80_real_2,axiom,(
    $true )).

fof(t81_real_2,axiom,(
    $true )).

fof(t82_real_2,axiom,(
    $true )).

fof(t83_real_2,axiom,(
    $true )).

fof(t84_real_2,axiom,(
    $true )).

fof(t85_real_2,axiom,(
    $true )).

fof(t86_real_2,axiom,(
    $true )).

fof(t87_real_2,axiom,(
    $true )).

fof(t88_real_2,axiom,(
    $true )).

fof(t89_real_2,axiom,(
    $true )).

fof(t90_real_2,axiom,(
    $true )).

fof(t91_real_2,axiom,(
    $true )).

fof(t92_real_2,axiom,(
    $true )).

fof(t93_real_2,axiom,(
    $true )).

fof(t94_real_2,axiom,(
    $true )).

fof(t95_real_2,axiom,(
    $true )).

fof(t96_real_2,axiom,(
    $true )).

fof(t97_real_2,axiom,(
    $true )).

fof(t98_real_2,axiom,(
    $true )).

fof(t99_real_2,axiom,(
    $true )).

fof(t100_real_2,axiom,(
    $true )).

fof(t101_real_2,axiom,(
    $true )).

fof(t102_real_2,axiom,(
    $true )).

fof(t103_real_2,axiom,(
    $true )).

fof(t104_real_2,axiom,(
    $true )).

fof(t105_real_2,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ( ~ ( ~ r1_xreal_0(k2_xcmplx_0(A,k4_xcmplx_0(B)),np__0)
                    & ~ r1_xreal_0(np__0,k6_xcmplx_0(B,A))
                    & ~ r1_xreal_0(np__0,k2_xcmplx_0(B,k4_xcmplx_0(A)))
                    & ~ r1_xreal_0(k6_xcmplx_0(A,C),k2_xcmplx_0(B,k4_xcmplx_0(C)))
                    & ~ r1_xreal_0(k2_xcmplx_0(A,k4_xcmplx_0(C)),k6_xcmplx_0(B,C))
                    & ~ r1_xreal_0(k6_xcmplx_0(C,B),k6_xcmplx_0(C,A)) )
               => r1_xreal_0(A,B) ) ) ) ) )).

fof(t106_real_2,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ~ ( ~ ( r1_xreal_0(np__0,k2_xcmplx_0(A,k4_xcmplx_0(B)))
                      & r1_xreal_0(k6_xcmplx_0(B,A),np__0)
                      & r1_xreal_0(k2_xcmplx_0(k4_xcmplx_0(A),B),np__0)
                      & r1_xreal_0(k2_xcmplx_0(B,k4_xcmplx_0(C)),k6_xcmplx_0(A,C))
                      & r1_xreal_0(k6_xcmplx_0(B,C),k2_xcmplx_0(A,k4_xcmplx_0(C)))
                      & r1_xreal_0(k6_xcmplx_0(C,A),k6_xcmplx_0(C,B)) )
                  & r1_xreal_0(B,A) ) ) ) ) )).

fof(t107_real_2,axiom,(
    $true )).

fof(t108_real_2,axiom,(
    $true )).

fof(t109_real_2,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ( r1_xreal_0(A,k4_xcmplx_0(B))
           => ( r1_xreal_0(k2_xcmplx_0(A,B),np__0)
              & r1_xreal_0(B,k4_xcmplx_0(A)) ) ) ) ) )).

fof(t110_real_2,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ( ~ r1_xreal_0(k4_xcmplx_0(B),A)
           => ( ~ r1_xreal_0(np__0,k2_xcmplx_0(A,B))
              & ~ r1_xreal_0(k4_xcmplx_0(A),B) ) ) ) ) )).

fof(t111_real_2,axiom,(
    $true )).

fof(t112_real_2,axiom,(
    $true )).

fof(t113_real_2,axiom,(
    $true )).

fof(t114_real_2,axiom,(
    $true )).

fof(t115_real_2,axiom,(
    $true )).

fof(t116_real_2,axiom,(
    $true )).

fof(t117_real_2,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ( ~ r1_xreal_0(A,np__0)
           => ( ~ ( ~ r1_xreal_0(k7_xcmplx_0(B,A),np__1)
                  & r1_xreal_0(B,A) )
              & ~ ( ~ r1_xreal_0(np__1,k7_xcmplx_0(B,A))
                  & r1_xreal_0(A,B) )
              & ( ~ r1_xreal_0(k7_xcmplx_0(B,A),k4_xcmplx_0(np__1))
               => ( ~ r1_xreal_0(B,k4_xcmplx_0(A))
                  & ~ r1_xreal_0(A,k4_xcmplx_0(B)) ) )
              & ( ~ r1_xreal_0(k4_xcmplx_0(np__1),k7_xcmplx_0(B,A))
               => ( ~ r1_xreal_0(k4_xcmplx_0(A),B)
                  & ~ r1_xreal_0(k4_xcmplx_0(B),A) ) ) ) ) ) ) )).

fof(t118_real_2,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ( ~ r1_xreal_0(A,np__0)
           => ( ( r1_xreal_0(np__1,k7_xcmplx_0(B,A))
               => r1_xreal_0(A,B) )
              & ( r1_xreal_0(k7_xcmplx_0(B,A),np__1)
               => r1_xreal_0(B,A) )
              & ( r1_xreal_0(k4_xcmplx_0(np__1),k7_xcmplx_0(B,A))
               => ( r1_xreal_0(k4_xcmplx_0(A),B)
                  & r1_xreal_0(k4_xcmplx_0(B),A) ) )
              & ( r1_xreal_0(k7_xcmplx_0(B,A),k4_xcmplx_0(np__1))
               => ( r1_xreal_0(B,k4_xcmplx_0(A))
                  & r1_xreal_0(A,k4_xcmplx_0(B)) ) ) ) ) ) ) )).

fof(t119_real_2,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ( ~ r1_xreal_0(np__0,A)
           => ( ~ ( ~ r1_xreal_0(k7_xcmplx_0(B,A),np__1)
                  & r1_xreal_0(A,B) )
              & ~ ( ~ r1_xreal_0(np__1,k7_xcmplx_0(B,A))
                  & r1_xreal_0(B,A) )
              & ( ~ r1_xreal_0(k7_xcmplx_0(B,A),k4_xcmplx_0(np__1))
               => ( ~ r1_xreal_0(k4_xcmplx_0(A),B)
                  & ~ r1_xreal_0(k4_xcmplx_0(B),A) ) )
              & ( ~ r1_xreal_0(k4_xcmplx_0(np__1),k7_xcmplx_0(B,A))
               => ( ~ r1_xreal_0(B,k4_xcmplx_0(A))
                  & ~ r1_xreal_0(A,k4_xcmplx_0(B)) ) ) ) ) ) ) )).

fof(t120_real_2,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ( ~ r1_xreal_0(np__0,A)
           => ( ( r1_xreal_0(np__1,k7_xcmplx_0(B,A))
               => r1_xreal_0(B,A) )
              & ( r1_xreal_0(k7_xcmplx_0(B,A),np__1)
               => r1_xreal_0(A,B) )
              & ( r1_xreal_0(k4_xcmplx_0(np__1),k7_xcmplx_0(B,A))
               => ( r1_xreal_0(B,k4_xcmplx_0(A))
                  & r1_xreal_0(A,k4_xcmplx_0(B)) ) )
              & ( r1_xreal_0(k7_xcmplx_0(B,A),k4_xcmplx_0(np__1))
               => ( r1_xreal_0(k4_xcmplx_0(A),B)
                  & r1_xreal_0(k4_xcmplx_0(B),A) ) ) ) ) ) ) )).

fof(t121_real_2,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ( ( ( r1_xreal_0(np__0,A)
                & r1_xreal_0(np__0,B) )
              | ( r1_xreal_0(A,np__0)
                & r1_xreal_0(B,np__0) ) )
           => r1_xreal_0(np__0,k3_xcmplx_0(A,B)) ) ) ) )).

fof(t122_real_2,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ~ ( ( ( ~ r1_xreal_0(np__0,A)
                  & ~ r1_xreal_0(np__0,B) )
                | ( ~ r1_xreal_0(A,np__0)
                  & ~ r1_xreal_0(B,np__0) ) )
              & r1_xreal_0(k3_xcmplx_0(A,B),np__0) ) ) ) )).

fof(t123_real_2,axiom,(
    $true )).

fof(t124_real_2,axiom,(
    $true )).

fof(t125_real_2,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ( ( ( r1_xreal_0(A,np__0)
                & r1_xreal_0(B,np__0) )
              | ( r1_xreal_0(np__0,A)
                & r1_xreal_0(np__0,B) ) )
           => r1_xreal_0(np__0,k7_xcmplx_0(A,B)) ) ) ) )).

fof(t126_real_2,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ( ( ( r1_xreal_0(np__0,A)
                & ~ r1_xreal_0(np__0,B) )
              | ( r1_xreal_0(A,np__0)
                & ~ r1_xreal_0(B,np__0) ) )
           => r1_xreal_0(k7_xcmplx_0(A,B),np__0) ) ) ) )).

fof(t127_real_2,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ~ ( ( ( ~ r1_xreal_0(A,np__0)
                  & ~ r1_xreal_0(B,np__0) )
                | ( ~ r1_xreal_0(np__0,A)
                  & ~ r1_xreal_0(np__0,B) ) )
              & r1_xreal_0(k7_xcmplx_0(A,B),np__0) ) ) ) )).

fof(t128_real_2,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ~ ( ~ r1_xreal_0(np__0,A)
              & ~ r1_xreal_0(B,np__0)
              & ~ ( ~ r1_xreal_0(np__0,k7_xcmplx_0(A,B))
                  & ~ r1_xreal_0(np__0,k7_xcmplx_0(B,A)) ) ) ) ) )).

fof(t129_real_2,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ~ ( r1_xreal_0(k3_xcmplx_0(A,B),np__0)
              & ~ ( r1_xreal_0(np__0,A)
                  & r1_xreal_0(B,np__0) )
              & ~ ( r1_xreal_0(A,np__0)
                  & r1_xreal_0(np__0,B) ) ) ) ) )).

fof(t130_real_2,axiom,(
    $true )).

fof(t131_real_2,axiom,(
    $true )).

fof(t132_real_2,axiom,(
    $true )).

fof(t133_real_2,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ~ ( A != np__0
              & r1_xreal_0(k7_xcmplx_0(B,A),np__0)
              & ~ ( ~ r1_xreal_0(A,np__0)
                  & r1_xreal_0(B,np__0) )
              & ~ ( ~ r1_xreal_0(np__0,A)
                  & r1_xreal_0(np__0,B) ) ) ) ) )).

fof(t134_real_2,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ~ ( A != np__0
              & r1_xreal_0(np__0,k7_xcmplx_0(B,A))
              & ~ ( ~ r1_xreal_0(A,np__0)
                  & r1_xreal_0(np__0,B) )
              & ~ ( ~ r1_xreal_0(np__0,A)
                  & r1_xreal_0(B,np__0) ) ) ) ) )).

fof(t135_real_2,axiom,(
    $true )).

fof(t136_real_2,axiom,(
    $true )).

fof(t137_real_2,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ~ ( ( ( ~ r1_xreal_0(A,np__1)
                  & ~ ( r1_xreal_0(B,np__1)
                      & ~ r1_xreal_0(np__1,B) ) )
                | ( ~ r1_xreal_0(k4_xcmplx_0(np__1),A)
                  & ~ ( r1_xreal_0(k4_xcmplx_0(np__1),B)
                      & ~ r1_xreal_0(B,k4_xcmplx_0(np__1)) ) ) )
              & r1_xreal_0(k3_xcmplx_0(A,B),np__1) ) ) ) )).

fof(t138_real_2,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ( ( ( r1_xreal_0(np__1,A)
                & r1_xreal_0(np__1,B) )
              | ( r1_xreal_0(A,k4_xcmplx_0(np__1))
                & r1_xreal_0(B,k4_xcmplx_0(np__1)) ) )
           => r1_xreal_0(np__1,k3_xcmplx_0(A,B)) ) ) ) )).

fof(t139_real_2,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ~ ( ( ( r1_xreal_0(np__0,A)
                  & ~ r1_xreal_0(np__1,A)
                  & r1_xreal_0(np__0,B)
                  & r1_xreal_0(B,np__1) )
                | ( r1_xreal_0(A,np__0)
                  & ~ r1_xreal_0(A,k4_xcmplx_0(np__1))
                  & r1_xreal_0(B,np__0)
                  & r1_xreal_0(k4_xcmplx_0(np__1),B) ) )
              & r1_xreal_0(np__1,k3_xcmplx_0(A,B)) ) ) ) )).

fof(t140_real_2,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ( ( ( r1_xreal_0(np__0,A)
                & r1_xreal_0(A,np__1)
                & r1_xreal_0(np__0,B)
                & r1_xreal_0(B,np__1) )
              | ( r1_xreal_0(A,np__0)
                & r1_xreal_0(k4_xcmplx_0(np__1),A)
                & r1_xreal_0(B,np__0)
                & r1_xreal_0(k4_xcmplx_0(np__1),B) ) )
           => r1_xreal_0(k3_xcmplx_0(A,B),np__1) ) ) ) )).

fof(t141_real_2,axiom,(
    $true )).

fof(t142_real_2,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ( ( ( ~ r1_xreal_0(A,np__0)
                & ~ r1_xreal_0(B,A) )
              | ( ~ r1_xreal_0(A,B)
                & ~ r1_xreal_0(np__0,A) ) )
           => ( ~ r1_xreal_0(np__1,k7_xcmplx_0(A,B))
              & ~ r1_xreal_0(k7_xcmplx_0(B,A),np__1) ) ) ) ) )).

fof(t143_real_2,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ( ( ( ~ r1_xreal_0(A,np__0)
                & r1_xreal_0(A,B) )
              | ( r1_xreal_0(B,A)
                & ~ r1_xreal_0(np__0,A) ) )
           => ( r1_xreal_0(k7_xcmplx_0(A,B),np__1)
              & r1_xreal_0(np__1,k7_xcmplx_0(B,A)) ) ) ) ) )).

fof(t144_real_2,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ~ ( ( ( ~ r1_xreal_0(A,np__0)
                  & ~ r1_xreal_0(B,np__1) )
                | ( ~ r1_xreal_0(np__0,A)
                  & ~ r1_xreal_0(np__1,B) ) )
              & r1_xreal_0(k3_xcmplx_0(A,B),A) ) ) ) )).

fof(t145_real_2,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ~ ( ( ( ~ r1_xreal_0(A,np__0)
                  & ~ r1_xreal_0(np__1,B) )
                | ( ~ r1_xreal_0(np__0,A)
                  & ~ r1_xreal_0(B,np__1) ) )
              & r1_xreal_0(A,k3_xcmplx_0(A,B)) ) ) ) )).

fof(t146_real_2,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ( ( ( r1_xreal_0(np__0,A)
                & r1_xreal_0(np__1,B) )
              | ( r1_xreal_0(A,np__0)
                & r1_xreal_0(B,np__1) ) )
           => r1_xreal_0(A,k3_xcmplx_0(A,B)) ) ) ) )).

fof(t147_real_2,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ( ( ( r1_xreal_0(np__0,A)
                & r1_xreal_0(B,np__1) )
              | ( r1_xreal_0(A,np__0)
                & r1_xreal_0(np__1,B) ) )
           => r1_xreal_0(k3_xcmplx_0(A,B),A) ) ) ) )).

fof(t148_real_2,axiom,(
    $true )).

fof(t149_real_2,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ( ~ r1_xreal_0(np__0,A)
       => ( ~ r1_xreal_0(np__0,k7_xcmplx_0(np__1,A))
          & ~ r1_xreal_0(np__0,k5_xcmplx_0(A)) ) ) ) )).

fof(t150_real_2,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ( ~ ( ~ r1_xreal_0(np__0,k7_xcmplx_0(np__1,A))
            & r1_xreal_0(np__0,A) )
        & ~ ( ~ r1_xreal_0(k7_xcmplx_0(np__1,A),np__0)
            & r1_xreal_0(A,np__0) ) ) ) )).

fof(t151_real_2,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ~ ( ~ ( r1_xreal_0(A,np__0)
                  & r1_xreal_0(np__0,B) )
              & ~ r1_xreal_0(B,A)
              & r1_xreal_0(k7_xcmplx_0(np__1,A),k7_xcmplx_0(np__1,B)) ) ) ) )).

fof(t152_real_2,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ( r1_xreal_0(A,B)
           => ( ( r1_xreal_0(A,np__0)
                & r1_xreal_0(np__0,B) )
              | r1_xreal_0(k7_xcmplx_0(np__1,B),k7_xcmplx_0(np__1,A)) ) ) ) ) )).

fof(t153_real_2,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ~ ( ~ r1_xreal_0(np__0,A)
              & ~ r1_xreal_0(B,np__0)
              & r1_xreal_0(k7_xcmplx_0(np__1,B),k7_xcmplx_0(np__1,A)) ) ) ) )).

fof(t154_real_2,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ~ ( ~ ( r1_xreal_0(k7_xcmplx_0(np__1,A),np__0)
                  & r1_xreal_0(np__0,k7_xcmplx_0(np__1,B)) )
              & ~ r1_xreal_0(k7_xcmplx_0(np__1,B),k7_xcmplx_0(np__1,A))
              & r1_xreal_0(A,B) ) ) ) )).

fof(t155_real_2,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ( r1_xreal_0(k7_xcmplx_0(np__1,A),k7_xcmplx_0(np__1,B))
           => ( ( r1_xreal_0(k7_xcmplx_0(np__1,A),np__0)
                & r1_xreal_0(np__0,k7_xcmplx_0(np__1,B)) )
              | r1_xreal_0(B,A) ) ) ) ) )).

fof(t156_real_2,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ~ ( ~ r1_xreal_0(np__0,k7_xcmplx_0(np__1,A))
              & ~ r1_xreal_0(k7_xcmplx_0(np__1,B),np__0)
              & r1_xreal_0(B,A) ) ) ) )).

fof(t157_real_2,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ~ ( ~ r1_xreal_0(k4_xcmplx_0(np__1),A)
          & r1_xreal_0(k7_xcmplx_0(np__1,A),k4_xcmplx_0(np__1)) ) ) )).

fof(t158_real_2,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ( r1_xreal_0(A,k4_xcmplx_0(np__1))
       => r1_xreal_0(k4_xcmplx_0(np__1),k7_xcmplx_0(np__1,A)) ) ) )).

fof(t159_real_2,axiom,(
    $true )).

fof(t160_real_2,axiom,(
    $true )).

fof(t161_real_2,axiom,(
    $true )).

fof(t162_real_2,axiom,(
    $true )).

fof(t163_real_2,axiom,(
    $true )).

fof(t164_real_2,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ( r1_xreal_0(np__1,A)
       => r1_xreal_0(k7_xcmplx_0(np__1,A),np__1) ) ) )).

fof(t165_real_2,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ( ( r1_xreal_0(A,k6_xcmplx_0(B,C))
                 => r1_xreal_0(C,k6_xcmplx_0(B,A)) )
                & ( r1_xreal_0(k6_xcmplx_0(B,C),A)
                 => r1_xreal_0(k6_xcmplx_0(B,A),C) ) ) ) ) ) )).

fof(t166_real_2,axiom,(
    $true )).

fof(t167_real_2,axiom,(
    $true )).

fof(t168_real_2,axiom,(
    $true )).

fof(t169_real_2,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( r1_xreal_0(k6_xcmplx_0(A,B),k6_xcmplx_0(C,D))
                   => ( r1_xreal_0(k2_xcmplx_0(A,D),k2_xcmplx_0(C,B))
                      & r1_xreal_0(k6_xcmplx_0(A,C),k6_xcmplx_0(B,D))
                      & r1_xreal_0(k6_xcmplx_0(D,B),k6_xcmplx_0(C,A))
                      & r1_xreal_0(k6_xcmplx_0(D,C),k6_xcmplx_0(B,A)) ) ) ) ) ) ) )).

fof(t170_real_2,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( ~ r1_xreal_0(k6_xcmplx_0(C,D),k6_xcmplx_0(A,B))
                   => ( ~ r1_xreal_0(k2_xcmplx_0(C,B),k2_xcmplx_0(A,D))
                      & ~ r1_xreal_0(k6_xcmplx_0(B,D),k6_xcmplx_0(A,C))
                      & ~ r1_xreal_0(k6_xcmplx_0(C,A),k6_xcmplx_0(D,B))
                      & ~ r1_xreal_0(k6_xcmplx_0(B,A),k6_xcmplx_0(D,C)) ) ) ) ) ) ) )).

fof(t171_real_2,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( ( r1_xreal_0(k2_xcmplx_0(A,B),k6_xcmplx_0(C,D))
                     => r1_xreal_0(k2_xcmplx_0(A,D),k6_xcmplx_0(C,B)) )
                    & ( r1_xreal_0(k6_xcmplx_0(C,D),k2_xcmplx_0(A,B))
                     => r1_xreal_0(k6_xcmplx_0(C,B),k2_xcmplx_0(A,D)) ) ) ) ) ) ) )).

fof(t172_real_2,axiom,(
    $true )).

fof(t173_real_2,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ( ( ~ r1_xreal_0(np__0,A)
             => ( ~ r1_xreal_0(B,k2_xcmplx_0(A,B))
                & ~ r1_xreal_0(k6_xcmplx_0(B,A),B) ) )
            & ~ ( ~ ( r1_xreal_0(B,k2_xcmplx_0(A,B))
                    & r1_xreal_0(k6_xcmplx_0(B,A),B) )
                & r1_xreal_0(np__0,A) ) ) ) ) )).

fof(t174_real_2,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ( ( r1_xreal_0(A,np__0)
             => ( r1_xreal_0(k2_xcmplx_0(A,B),B)
                & r1_xreal_0(B,k6_xcmplx_0(B,A)) ) )
            & ( ( r1_xreal_0(k2_xcmplx_0(A,B),B)
                | r1_xreal_0(B,k6_xcmplx_0(B,A)) )
             => r1_xreal_0(A,np__0) ) ) ) ) )).

fof(t175_real_2,axiom,(
    $true )).

fof(t176_real_2,axiom,(
    $true )).

fof(t177_real_2,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ( ( r1_xreal_0(k3_xcmplx_0(B,A),C)
                 => ( r1_xreal_0(A,np__0)
                    | r1_xreal_0(B,k7_xcmplx_0(C,A)) ) )
                & ( r1_xreal_0(k3_xcmplx_0(B,A),C)
                 => ( r1_xreal_0(np__0,A)
                    | r1_xreal_0(k7_xcmplx_0(C,A),B) ) )
                & ( r1_xreal_0(C,k3_xcmplx_0(B,A))
                 => ( r1_xreal_0(A,np__0)
                    | r1_xreal_0(k7_xcmplx_0(C,A),B) ) )
                & ( r1_xreal_0(C,k3_xcmplx_0(B,A))
                 => ( r1_xreal_0(np__0,A)
                    | r1_xreal_0(B,k7_xcmplx_0(C,A)) ) ) ) ) ) ) )).

fof(t178_real_2,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ( ~ ( ~ r1_xreal_0(A,np__0)
                    & ~ r1_xreal_0(C,k3_xcmplx_0(B,A))
                    & r1_xreal_0(k7_xcmplx_0(C,A),B) )
                & ~ ( ~ r1_xreal_0(np__0,A)
                    & ~ r1_xreal_0(C,k3_xcmplx_0(B,A))
                    & r1_xreal_0(B,k7_xcmplx_0(C,A)) )
                & ~ ( ~ r1_xreal_0(A,np__0)
                    & ~ r1_xreal_0(k3_xcmplx_0(B,A),C)
                    & r1_xreal_0(B,k7_xcmplx_0(C,A)) )
                & ~ ( ~ r1_xreal_0(np__0,A)
                    & ~ r1_xreal_0(k3_xcmplx_0(B,A),C)
                    & r1_xreal_0(k7_xcmplx_0(C,A),B) ) ) ) ) ) )).

fof(t179_real_2,axiom,(
    $true )).

fof(t180_real_2,axiom,(
    $true )).

fof(t181_real_2,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ( ( ! [C] :
                  ( v1_xreal_0(C)
                 => ( ~ r1_xreal_0(C,np__0)
                   => r1_xreal_0(B,k2_xcmplx_0(A,C)) ) )
              | ! [C] :
                  ( v1_xreal_0(C)
                 => ( ~ r1_xreal_0(np__0,C)
                   => r1_xreal_0(B,k6_xcmplx_0(A,C)) ) ) )
           => r1_xreal_0(B,A) ) ) ) )).

fof(t182_real_2,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ( ( ! [C] :
                  ( v1_xreal_0(C)
                 => ( ~ r1_xreal_0(C,np__0)
                   => r1_xreal_0(k6_xcmplx_0(A,C),B) ) )
              | ! [C] :
                  ( v1_xreal_0(C)
                 => ( ~ r1_xreal_0(np__0,C)
                   => r1_xreal_0(k2_xcmplx_0(A,C),B) ) ) )
           => r1_xreal_0(A,B) ) ) ) )).

fof(t183_real_2,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ( ( ! [C] :
                  ( v1_xreal_0(C)
                 => ( ~ r1_xreal_0(C,np__1)
                   => r1_xreal_0(B,k3_xcmplx_0(A,C)) ) )
              | ! [C] :
                  ( v1_xreal_0(C)
                 => ~ ( ~ r1_xreal_0(C,np__0)
                      & ~ r1_xreal_0(np__1,C)
                      & ~ r1_xreal_0(B,k7_xcmplx_0(A,C)) ) ) )
           => r1_xreal_0(B,A) ) ) ) )).

fof(t184_real_2,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ( ( ! [C] :
                  ( v1_xreal_0(C)
                 => ~ ( ~ r1_xreal_0(C,np__0)
                      & ~ r1_xreal_0(np__1,C)
                      & ~ r1_xreal_0(k3_xcmplx_0(A,C),B) ) )
              | ! [C] :
                  ( v1_xreal_0(C)
                 => ( ~ r1_xreal_0(C,np__1)
                   => r1_xreal_0(k7_xcmplx_0(A,C),B) ) ) )
           => r1_xreal_0(A,B) ) ) ) )).

fof(t185_real_2,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ~ ( ( ( ~ r1_xreal_0(A,np__0)
                          & ~ r1_xreal_0(B,np__0) )
                        | ( ~ r1_xreal_0(np__0,A)
                          & ~ r1_xreal_0(np__0,B) ) )
                      & ~ r1_xreal_0(k3_xcmplx_0(D,A),k3_xcmplx_0(C,B))
                      & r1_xreal_0(k7_xcmplx_0(D,B),k7_xcmplx_0(C,A)) ) ) ) ) ) )).

fof(t186_real_2,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ~ ( ( ( ~ r1_xreal_0(A,np__0)
                          & ~ r1_xreal_0(np__0,B) )
                        | ( ~ r1_xreal_0(np__0,A)
                          & ~ r1_xreal_0(B,np__0) ) )
                      & ~ r1_xreal_0(k3_xcmplx_0(D,A),k3_xcmplx_0(C,B))
                      & r1_xreal_0(k7_xcmplx_0(C,A),k7_xcmplx_0(D,B)) ) ) ) ) ) )).

fof(t187_real_2,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( r1_xreal_0(k3_xcmplx_0(C,B),k3_xcmplx_0(D,A))
                   => ( ( ~ ( ~ r1_xreal_0(A,np__0)
                            & ~ r1_xreal_0(B,np__0) )
                        & ~ ( ~ r1_xreal_0(np__0,A)
                            & ~ r1_xreal_0(np__0,B) ) )
                      | r1_xreal_0(k7_xcmplx_0(C,A),k7_xcmplx_0(D,B)) ) ) ) ) ) ) )).

fof(t188_real_2,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( r1_xreal_0(k3_xcmplx_0(C,B),k3_xcmplx_0(D,A))
                   => ( ( ~ ( ~ r1_xreal_0(A,np__0)
                            & ~ r1_xreal_0(np__0,B) )
                        & ~ ( ~ r1_xreal_0(np__0,A)
                            & ~ r1_xreal_0(B,np__0) ) )
                      | r1_xreal_0(k7_xcmplx_0(D,B),k7_xcmplx_0(C,A)) ) ) ) ) ) ) )).

fof(t189_real_2,axiom,(
    $true )).

fof(t190_real_2,axiom,(
    $true )).

fof(t191_real_2,axiom,(
    $true )).

fof(t192_real_2,axiom,(
    $true )).

fof(t193_real_2,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( ( ( ~ r1_xreal_0(np__0,A)
                        & ~ r1_xreal_0(np__0,B) )
                      | ( ~ r1_xreal_0(A,np__0)
                        & ~ r1_xreal_0(B,np__0) ) )
                   => ( ~ ( ~ r1_xreal_0(k7_xcmplx_0(D,B),k3_xcmplx_0(C,A))
                          & r1_xreal_0(k7_xcmplx_0(D,A),k3_xcmplx_0(C,B)) )
                      & ~ ( ~ r1_xreal_0(k3_xcmplx_0(C,A),k7_xcmplx_0(D,B))
                          & r1_xreal_0(k3_xcmplx_0(C,B),k7_xcmplx_0(D,A)) ) ) ) ) ) ) ) )).

fof(t194_real_2,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ( ( ( ~ r1_xreal_0(np__0,A)
                        & ~ r1_xreal_0(B,np__0) )
                      | ( ~ r1_xreal_0(A,np__0)
                        & ~ r1_xreal_0(np__0,B) ) )
                   => ( ~ ( ~ r1_xreal_0(k7_xcmplx_0(D,B),k3_xcmplx_0(C,A))
                          & r1_xreal_0(k3_xcmplx_0(C,B),k7_xcmplx_0(D,A)) )
                      & ~ ( ~ r1_xreal_0(k3_xcmplx_0(C,A),k7_xcmplx_0(D,B))
                          & r1_xreal_0(k7_xcmplx_0(D,A),k3_xcmplx_0(C,B)) ) ) ) ) ) ) ) )).

fof(t195_real_2,axiom,(
    $true )).

fof(t196_real_2,axiom,(
    $true )).

fof(t197_real_2,axiom,(
    $true )).

fof(t198_real_2,axiom,(
    $true )).

fof(t199_real_2,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ~ ( ( ( ~ r1_xreal_0(A,np__0)
                          & r1_xreal_0(A,B)
                          & ~ r1_xreal_0(C,np__0)
                          & ~ r1_xreal_0(D,C) )
                        | ( ~ r1_xreal_0(np__0,A)
                          & r1_xreal_0(B,A)
                          & ~ r1_xreal_0(np__0,C)
                          & ~ r1_xreal_0(C,D) ) )
                      & r1_xreal_0(k3_xcmplx_0(B,D),k3_xcmplx_0(A,C)) ) ) ) ) ) )).

fof(t200_real_2,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ( ~ ( ~ r1_xreal_0(A,np__0)
                    & ~ r1_xreal_0(B,np__0)
                    & ~ r1_xreal_0(C,B)
                    & r1_xreal_0(k7_xcmplx_0(A,B),k7_xcmplx_0(A,C)) )
                & ~ ( ~ r1_xreal_0(A,np__0)
                    & ~ r1_xreal_0(np__0,C)
                    & ~ r1_xreal_0(C,B)
                    & r1_xreal_0(k7_xcmplx_0(A,B),k7_xcmplx_0(A,C)) ) ) ) ) ) )).

fof(t201_real_2,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ( ( r1_xreal_0(np__0,A)
                  & r1_xreal_0(B,C) )
               => ( ( r1_xreal_0(B,np__0)
                    & r1_xreal_0(np__0,C) )
                  | r1_xreal_0(k7_xcmplx_0(A,C),k7_xcmplx_0(A,B)) ) ) ) ) ) )).

fof(t202_real_2,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ~ ( ~ r1_xreal_0(np__0,A)
                  & ~ ( r1_xreal_0(B,np__0)
                      & r1_xreal_0(np__0,C) )
                  & ~ r1_xreal_0(C,B)
                  & r1_xreal_0(k7_xcmplx_0(A,C),k7_xcmplx_0(A,B)) ) ) ) ) )).

fof(t203_real_2,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ( ( r1_xreal_0(A,np__0)
                  & r1_xreal_0(B,C) )
               => ( ( r1_xreal_0(B,np__0)
                    & r1_xreal_0(np__0,C) )
                  | r1_xreal_0(k7_xcmplx_0(A,B),k7_xcmplx_0(A,C)) ) ) ) ) ) )).

fof(t204_real_2,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_numbers))
         => ~ ( A != k1_xboole_0
              & B != k1_xboole_0
              & ! [C] :
                  ( v1_xreal_0(C)
                 => ! [D] :
                      ( v1_xreal_0(D)
                     => ( ( r2_hidden(C,A)
                          & r2_hidden(D,B) )
                       => r1_xreal_0(C,D) ) ) )
              & ! [C] :
                  ( v1_xreal_0(C)
                 => ~ ( ! [D] :
                          ( v1_xreal_0(D)
                         => ( r2_hidden(D,A)
                           => r1_xreal_0(D,C) ) )
                      & ! [D] :
                          ( v1_xreal_0(D)
                         => ( r2_hidden(D,B)
                           => r1_xreal_0(C,D) ) ) ) ) ) ) ) )).
%------------------------------------------------------------------------------