SET007 Axioms: SET007+43.ax
%------------------------------------------------------------------------------
% File : SET007+43 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Real Numbers - Basic Theorems
% 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 : xreal_1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 227 ( 0 unt; 0 def)
% Number of atoms : 1289 ( 23 equ)
% Maximal formula atoms : 14 ( 5 avg)
% Number of connectives : 1428 ( 366 ~; 29 |; 346 &)
% ( 7 <=>; 680 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 9 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 0 prp; 1-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 573 ( 571 !; 2 ?)
% 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_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( ( r1_xreal_0(A,B)
& r1_xreal_0(B,A) )
=> A = B ) ) ) ).
fof(t2_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ( ( r1_xreal_0(A,B)
& r1_xreal_0(B,C) )
=> r1_xreal_0(A,C) ) ) ) ) ).
fof(t3_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ~ ! [B] :
( v1_xreal_0(B)
=> r1_xreal_0(B,A) ) ) ).
fof(t4_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ~ ! [B] :
( v1_xreal_0(B)
=> r1_xreal_0(A,B) ) ) ).
fof(t5_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ? [C] :
( v1_xreal_0(C)
& ~ r1_xreal_0(C,A)
& ~ r1_xreal_0(C,B) ) ) ) ).
fof(t6_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ? [C] :
( v1_xreal_0(C)
& ~ r1_xreal_0(A,C)
& ~ r1_xreal_0(B,C) ) ) ) ).
fof(t7_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ~ ( ~ r1_xreal_0(B,A)
& ! [C] :
( v1_xreal_0(C)
=> ~ ( ~ r1_xreal_0(C,A)
& ~ r1_xreal_0(B,C) ) ) ) ) ) ).
fof(t8_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ( r1_xreal_0(A,B)
<=> r1_xreal_0(k2_xcmplx_0(A,C),k2_xcmplx_0(B,C)) ) ) ) ) ).
fof(t9_xreal_1,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,B)
& r1_xreal_0(C,D) )
=> r1_xreal_0(k2_xcmplx_0(A,C),k2_xcmplx_0(B,D)) ) ) ) ) ) ).
fof(t10_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ~ ( ~ r1_xreal_0(B,A)
& r1_xreal_0(C,D)
& r1_xreal_0(k2_xcmplx_0(B,D),k2_xcmplx_0(A,C)) ) ) ) ) ) ).
fof(t11_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ( r1_xreal_0(A,B)
<=> r1_xreal_0(k6_xcmplx_0(A,C),k6_xcmplx_0(B,C)) ) ) ) ) ).
fof(t12_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ( r1_xreal_0(A,B)
<=> r1_xreal_0(k6_xcmplx_0(C,B),k6_xcmplx_0(C,A)) ) ) ) ) ).
fof(t13_xreal_1,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)) ) ) ) ) ).
fof(t14_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ( r1_xreal_0(k6_xcmplx_0(A,B),C)
=> r1_xreal_0(k6_xcmplx_0(A,C),B) ) ) ) ) ).
fof(t15_xreal_1,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,B)
& r1_xreal_0(C,D) )
=> r1_xreal_0(k6_xcmplx_0(A,D),k6_xcmplx_0(B,C)) ) ) ) ) ) ).
fof(t16_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ~ ( ~ r1_xreal_0(B,A)
& r1_xreal_0(C,D)
& r1_xreal_0(k6_xcmplx_0(B,C),k6_xcmplx_0(A,D)) ) ) ) ) ) ).
fof(t17_xreal_1,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,B)
& ~ r1_xreal_0(D,C)
& r1_xreal_0(k6_xcmplx_0(B,C),k6_xcmplx_0(A,D)) ) ) ) ) ) ).
fof(t18_xreal_1,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(k6_xcmplx_0(A,C),k6_xcmplx_0(B,D)) ) ) ) ) ) ).
fof(t19_xreal_1,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(k6_xcmplx_0(D,B),k6_xcmplx_0(C,A)) ) ) ) ) ) ).
fof(t20_xreal_1,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(k6_xcmplx_0(D,C),k6_xcmplx_0(B,A)) ) ) ) ) ) ).
fof(t21_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ( r1_xreal_0(k2_xcmplx_0(A,B),C)
<=> r1_xreal_0(A,k6_xcmplx_0(C,B)) ) ) ) ) ).
fof(t22_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ( r1_xreal_0(A,k2_xcmplx_0(B,C))
<=> r1_xreal_0(k6_xcmplx_0(A,B),C) ) ) ) ) ).
fof(t23_xreal_1,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),k2_xcmplx_0(C,D))
<=> r1_xreal_0(k6_xcmplx_0(A,C),k6_xcmplx_0(D,B)) ) ) ) ) ) ).
fof(t24_xreal_1,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)) ) ) ) ) ) ).
fof(t25_xreal_1,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),k2_xcmplx_0(C,D))
=> r1_xreal_0(k6_xcmplx_0(A,D),k2_xcmplx_0(C,B)) ) ) ) ) ) ).
fof(t26_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( r1_xreal_0(A,B)
<=> r1_xreal_0(k4_xcmplx_0(B),k4_xcmplx_0(A)) ) ) ) ).
fof(t27_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( r1_xreal_0(A,k4_xcmplx_0(B))
=> r1_xreal_0(B,k4_xcmplx_0(A)) ) ) ) ).
fof(t28_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( r1_xreal_0(k4_xcmplx_0(A),B)
=> r1_xreal_0(k4_xcmplx_0(B),A) ) ) ) ).
fof(t29_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( ( r1_xreal_0(np__0,A)
& r1_xreal_0(np__0,B)
& k2_xcmplx_0(A,B) = np__0 )
=> A = np__0 ) ) ) ).
fof(t30_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( ( r1_xreal_0(A,np__0)
& r1_xreal_0(B,np__0)
& k2_xcmplx_0(A,B) = np__0 )
=> A = np__0 ) ) ) ).
fof(t31_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ~ ( ~ r1_xreal_0(A,np__0)
& r1_xreal_0(k2_xcmplx_0(B,A),B) ) ) ) ).
fof(t32_xreal_1,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)) ) ) ) ).
fof(t33_xreal_1,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)) ) ) ) ).
fof(t34_xreal_1,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) ) ) ) ).
fof(t35_xreal_1,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(np__0,k2_xcmplx_0(A,B)) ) ) ) ).
fof(t36_xreal_1,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(k2_xcmplx_0(A,B),np__0) ) ) ) ).
fof(t37_xreal_1,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(k2_xcmplx_0(B,A),C) ) ) ) ) ).
fof(t38_xreal_1,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,B)
& r1_xreal_0(C,k2_xcmplx_0(B,A)) ) ) ) ) ).
fof(t39_xreal_1,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(C,k2_xcmplx_0(B,A)) ) ) ) ) ).
fof(t40_xreal_1,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,k2_xcmplx_0(A,C)) ) ) ) ) ).
fof(t41_xreal_1,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(k2_xcmplx_0(A,C),B) ) ) ) ) ).
fof(t42_xreal_1,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(C,B)
& r1_xreal_0(k2_xcmplx_0(A,C),B) ) ) ) ) ).
fof(t43_xreal_1,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(A,k2_xcmplx_0(B,C)) ) )
=> r1_xreal_0(A,B) ) ) ) ).
fof(t44_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(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(t45_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( r1_xreal_0(np__0,A)
=> r1_xreal_0(k6_xcmplx_0(B,A),B) ) ) ) ).
fof(t46_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ~ ( ~ r1_xreal_0(A,np__0)
& r1_xreal_0(B,k6_xcmplx_0(B,A)) ) ) ) ).
fof(t47_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( r1_xreal_0(A,np__0)
=> r1_xreal_0(B,k6_xcmplx_0(B,A)) ) ) ) ).
fof(t48_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ~ ( ~ r1_xreal_0(np__0,A)
& r1_xreal_0(k6_xcmplx_0(B,A),B) ) ) ) ).
fof(t49_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( r1_xreal_0(A,B)
=> r1_xreal_0(k6_xcmplx_0(A,B),np__0) ) ) ) ).
fof(t50_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( r1_xreal_0(A,B)
=> r1_xreal_0(np__0,k6_xcmplx_0(B,A)) ) ) ) ).
fof(t51_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ~ ( ~ r1_xreal_0(B,A)
& r1_xreal_0(np__0,k6_xcmplx_0(A,B)) ) ) ) ).
fof(t52_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ~ ( ~ r1_xreal_0(B,A)
& r1_xreal_0(k6_xcmplx_0(B,A),np__0) ) ) ) ).
fof(t53_xreal_1,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(C,B)
& r1_xreal_0(C,k6_xcmplx_0(B,A)) ) ) ) ) ).
fof(t54_xreal_1,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,k6_xcmplx_0(C,A)) ) ) ) ) ).
fof(t55_xreal_1,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,B)
& r1_xreal_0(k6_xcmplx_0(C,A),B) ) ) ) ) ).
fof(t56_xreal_1,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(k6_xcmplx_0(C,A),B) ) ) ) ) ).
fof(t57_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ~ ( A != B
& r1_xreal_0(k6_xcmplx_0(A,B),np__0)
& r1_xreal_0(k6_xcmplx_0(B,A),np__0) ) ) ) ).
fof(t58_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( ! [C] :
( v1_xreal_0(C)
=> ( ~ r1_xreal_0(np__0,C)
=> r1_xreal_0(A,k6_xcmplx_0(B,C)) ) )
=> r1_xreal_0(A,B) ) ) ) ).
fof(t59_xreal_1,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) ) )
=> r1_xreal_0(A,B) ) ) ) ).
fof(t60_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ( ~ ( ~ r1_xreal_0(np__0,A)
& r1_xreal_0(k4_xcmplx_0(A),np__0) )
& ~ ( ~ r1_xreal_0(k4_xcmplx_0(A),np__0)
& r1_xreal_0(np__0,A) ) ) ) ).
fof(t61_xreal_1,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) ) ) ) ).
fof(t62_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( r1_xreal_0(k4_xcmplx_0(A),B)
=> r1_xreal_0(np__0,k2_xcmplx_0(A,B)) ) ) ) ).
fof(t63_xreal_1,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)) ) ) ) ).
fof(t64_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ~ ( ~ r1_xreal_0(B,k4_xcmplx_0(A))
& r1_xreal_0(k2_xcmplx_0(B,A),np__0) ) ) ) ).
fof(t65_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> r1_xreal_0(np__0,k3_xcmplx_0(A,A)) ) ).
fof(t66_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ( ( r1_xreal_0(A,B)
& r1_xreal_0(np__0,C) )
=> r1_xreal_0(k3_xcmplx_0(A,C),k3_xcmplx_0(B,C)) ) ) ) ) ).
fof(t67_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ( ( r1_xreal_0(A,B)
& r1_xreal_0(C,np__0) )
=> r1_xreal_0(k3_xcmplx_0(B,C),k3_xcmplx_0(A,C)) ) ) ) ) ).
fof(t68_xreal_1,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(A,B)
& r1_xreal_0(np__0,C)
& r1_xreal_0(C,D) )
=> r1_xreal_0(k3_xcmplx_0(A,C),k3_xcmplx_0(B,D)) ) ) ) ) ) ).
fof(t69_xreal_1,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,A)
& r1_xreal_0(C,np__0)
& r1_xreal_0(D,C) )
=> r1_xreal_0(k3_xcmplx_0(A,C),k3_xcmplx_0(B,D)) ) ) ) ) ) ).
fof(t70_xreal_1,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,B)
& r1_xreal_0(k3_xcmplx_0(C,A),k3_xcmplx_0(B,A)) ) ) ) ) ).
fof(t71_xreal_1,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(C,B)
& r1_xreal_0(k3_xcmplx_0(B,A),k3_xcmplx_0(C,A)) ) ) ) ) ).
fof(t72_xreal_1,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,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(t73_xreal_1,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(np__0,C)
& r1_xreal_0(np__0,D)
& k2_xcmplx_0(k3_xcmplx_0(A,C),k3_xcmplx_0(B,D)) = np__0
& A != np__0
& C != np__0 ) ) ) ) ) ).
fof(t74_xreal_1,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(k7_xcmplx_0(B,A),k7_xcmplx_0(C,A)) ) ) ) ) ).
fof(t75_xreal_1,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(k7_xcmplx_0(C,A),k7_xcmplx_0(B,A)) ) ) ) ) ).
fof(t76_xreal_1,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,B)
& r1_xreal_0(k7_xcmplx_0(C,A),k7_xcmplx_0(B,A)) ) ) ) ) ).
fof(t77_xreal_1,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(C,B)
& r1_xreal_0(k7_xcmplx_0(B,A),k7_xcmplx_0(C,A)) ) ) ) ) ).
fof(t78_xreal_1,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)) ) ) ) ) ).
fof(t79_xreal_1,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)) ) ) ) ) ) ).
fof(t80_xreal_1,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(np__0,A)
| r1_xreal_0(k7_xcmplx_0(C,A),B) ) ) ) ) ) ).
fof(t81_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ( r1_xreal_0(B,k3_xcmplx_0(C,A))
=> ( r1_xreal_0(A,np__0)
| r1_xreal_0(k7_xcmplx_0(B,A),C) ) ) ) ) ) ).
fof(t82_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ( r1_xreal_0(B,k3_xcmplx_0(C,A))
=> ( r1_xreal_0(np__0,A)
| r1_xreal_0(C,k7_xcmplx_0(B,A)) ) ) ) ) ) ).
fof(t83_xreal_1,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) ) ) ) ) ).
fof(t84_xreal_1,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(C,k3_xcmplx_0(B,A))
& r1_xreal_0(B,k7_xcmplx_0(C,A)) ) ) ) ) ).
fof(t85_xreal_1,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(k3_xcmplx_0(C,A),B)
& r1_xreal_0(C,k7_xcmplx_0(B,A)) ) ) ) ) ).
fof(t86_xreal_1,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(k3_xcmplx_0(C,A),B)
& r1_xreal_0(k7_xcmplx_0(B,A),C) ) ) ) ) ).
fof(t87_xreal_1,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(k5_xcmplx_0(B),k5_xcmplx_0(A)) ) ) ) ) ).
fof(t88_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( r1_xreal_0(B,A)
=> ( r1_xreal_0(np__0,A)
| r1_xreal_0(k5_xcmplx_0(A),k5_xcmplx_0(B)) ) ) ) ) ).
fof(t89_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ~ ( ~ r1_xreal_0(np__0,A)
& ~ r1_xreal_0(A,B)
& r1_xreal_0(k5_xcmplx_0(B),k5_xcmplx_0(A)) ) ) ) ).
fof(t90_xreal_1,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(k5_xcmplx_0(A),k5_xcmplx_0(B)) ) ) ) ).
fof(t91_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( r1_xreal_0(k5_xcmplx_0(A),k5_xcmplx_0(B))
=> ( r1_xreal_0(k5_xcmplx_0(A),np__0)
| r1_xreal_0(B,A) ) ) ) ) ).
fof(t92_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( r1_xreal_0(k5_xcmplx_0(B),k5_xcmplx_0(A))
=> ( r1_xreal_0(np__0,k5_xcmplx_0(A))
| r1_xreal_0(A,B) ) ) ) ) ).
fof(t93_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ~ ( ~ r1_xreal_0(k5_xcmplx_0(A),np__0)
& ~ r1_xreal_0(k5_xcmplx_0(B),k5_xcmplx_0(A))
& r1_xreal_0(A,B) ) ) ) ).
fof(t94_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ~ ( ~ r1_xreal_0(np__0,k5_xcmplx_0(A))
& ~ r1_xreal_0(k5_xcmplx_0(A),k5_xcmplx_0(B))
& r1_xreal_0(B,A) ) ) ) ).
fof(t95_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( ( r1_xreal_0(np__0,A)
& r1_xreal_0(k3_xcmplx_0(k6_xcmplx_0(B,A),k2_xcmplx_0(B,A)),np__0) )
=> ( r1_xreal_0(k4_xcmplx_0(A),B)
& r1_xreal_0(B,A) ) ) ) ) ).
fof(t96_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( r1_xreal_0(np__0,A)
=> ( r1_xreal_0(np__0,k3_xcmplx_0(k6_xcmplx_0(B,A),k2_xcmplx_0(B,A)))
| ( ~ r1_xreal_0(B,k4_xcmplx_0(A))
& ~ r1_xreal_0(A,B) ) ) ) ) ) ).
fof(t97_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ~ ( r1_xreal_0(np__0,A)
& r1_xreal_0(np__0,k3_xcmplx_0(k6_xcmplx_0(B,A),k2_xcmplx_0(B,A)))
& ~ r1_xreal_0(B,k4_xcmplx_0(A))
& ~ r1_xreal_0(A,B) ) ) ) ).
fof(t98_xreal_1,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(C,A)
& ~ r1_xreal_0(D,B)
& r1_xreal_0(k3_xcmplx_0(C,D),k3_xcmplx_0(A,B)) ) ) ) ) ) ).
fof(t99_xreal_1,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(C,A)
& r1_xreal_0(B,D)
& r1_xreal_0(k3_xcmplx_0(C,D),k3_xcmplx_0(A,B)) ) ) ) ) ) ).
fof(t100_xreal_1,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(A,C)
& ~ r1_xreal_0(D,B)
& r1_xreal_0(k3_xcmplx_0(C,D),k3_xcmplx_0(A,B)) ) ) ) ) ) ).
fof(t101_xreal_1,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(np__0,B)
& ~ r1_xreal_0(B,C)
& r1_xreal_0(k7_xcmplx_0(A,C),k7_xcmplx_0(A,B)) ) ) ) ) ).
fof(t102_xreal_1,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(C,B)
& r1_xreal_0(k7_xcmplx_0(A,C),k7_xcmplx_0(A,B)) ) ) ) ) ).
fof(t103_xreal_1,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(np__0,B)
& ~ r1_xreal_0(B,C)
& r1_xreal_0(k7_xcmplx_0(A,B),k7_xcmplx_0(A,C)) ) ) ) ) ).
fof(t104_xreal_1,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(k7_xcmplx_0(C,A),k7_xcmplx_0(D,B)) ) ) ) ) ) ) ).
fof(t105_xreal_1,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(np__0,A)
| r1_xreal_0(np__0,B)
| r1_xreal_0(k7_xcmplx_0(C,A),k7_xcmplx_0(D,B)) ) ) ) ) ) ) ).
fof(t106_xreal_1,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(k7_xcmplx_0(D,B),k7_xcmplx_0(C,A)) ) ) ) ) ) ) ).
fof(t107_xreal_1,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(np__0,A)
| r1_xreal_0(B,np__0)
| r1_xreal_0(k7_xcmplx_0(D,B),k7_xcmplx_0(C,A)) ) ) ) ) ) ) ).
fof(t108_xreal_1,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(k3_xcmplx_0(D,A),k3_xcmplx_0(C,B))
& r1_xreal_0(k7_xcmplx_0(D,B),k7_xcmplx_0(C,A)) ) ) ) ) ) ).
fof(t109_xreal_1,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(k3_xcmplx_0(D,A),k3_xcmplx_0(C,B))
& r1_xreal_0(k7_xcmplx_0(D,B),k7_xcmplx_0(C,A)) ) ) ) ) ) ).
fof(t110_xreal_1,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(k3_xcmplx_0(D,A),k3_xcmplx_0(C,B))
& r1_xreal_0(k7_xcmplx_0(C,A),k7_xcmplx_0(D,B)) ) ) ) ) ) ).
fof(t111_xreal_1,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(k3_xcmplx_0(D,A),k3_xcmplx_0(C,B))
& r1_xreal_0(k7_xcmplx_0(C,A),k7_xcmplx_0(D,B)) ) ) ) ) ) ).
fof(t112_xreal_1,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(k7_xcmplx_0(D,B),k3_xcmplx_0(C,A))
& r1_xreal_0(k7_xcmplx_0(D,A),k3_xcmplx_0(C,B)) ) ) ) ) ) ).
fof(t113_xreal_1,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(k7_xcmplx_0(D,B),k3_xcmplx_0(C,A))
& r1_xreal_0(k7_xcmplx_0(D,A),k3_xcmplx_0(C,B)) ) ) ) ) ) ).
fof(t114_xreal_1,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(k3_xcmplx_0(D,A),k7_xcmplx_0(C,B))
& r1_xreal_0(k3_xcmplx_0(D,B),k7_xcmplx_0(C,A)) ) ) ) ) ) ).
fof(t115_xreal_1,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(k3_xcmplx_0(D,A),k7_xcmplx_0(C,B))
& r1_xreal_0(k3_xcmplx_0(D,B),k7_xcmplx_0(C,A)) ) ) ) ) ) ).
fof(t116_xreal_1,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(k7_xcmplx_0(D,B),k3_xcmplx_0(C,A))
& r1_xreal_0(k3_xcmplx_0(C,B),k7_xcmplx_0(D,A)) ) ) ) ) ) ).
fof(t117_xreal_1,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(k7_xcmplx_0(D,B),k3_xcmplx_0(C,A))
& r1_xreal_0(k3_xcmplx_0(C,B),k7_xcmplx_0(D,A)) ) ) ) ) ) ).
fof(t118_xreal_1,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(k3_xcmplx_0(D,A),k7_xcmplx_0(C,B))
& r1_xreal_0(k7_xcmplx_0(C,A),k3_xcmplx_0(D,B)) ) ) ) ) ) ).
fof(t119_xreal_1,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(k3_xcmplx_0(D,A),k7_xcmplx_0(C,B))
& r1_xreal_0(k7_xcmplx_0(C,A),k3_xcmplx_0(D,B)) ) ) ) ) ) ).
fof(t120_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ( ( r1_xreal_0(np__0,B)
& r1_xreal_0(A,C) )
=> ( r1_xreal_0(A,np__0)
| r1_xreal_0(k7_xcmplx_0(B,C),k7_xcmplx_0(B,A)) ) ) ) ) ) ).
fof(t121_xreal_1,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(C,B) )
=> ( r1_xreal_0(np__0,B)
| r1_xreal_0(k7_xcmplx_0(A,B),k7_xcmplx_0(A,C)) ) ) ) ) ) ).
fof(t122_xreal_1,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(k7_xcmplx_0(A,B),k7_xcmplx_0(A,C)) ) ) ) ) ) ).
fof(t123_xreal_1,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,B) )
=> ( r1_xreal_0(np__0,B)
| r1_xreal_0(k7_xcmplx_0(A,C),k7_xcmplx_0(A,B)) ) ) ) ) ) ).
fof(t124_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ( ~ ( ~ r1_xreal_0(A,np__0)
& r1_xreal_0(k5_xcmplx_0(A),np__0) )
& ~ ( ~ r1_xreal_0(k5_xcmplx_0(A),np__0)
& r1_xreal_0(A,np__0) ) ) ) ).
fof(t125_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ( ~ ( ~ r1_xreal_0(np__0,A)
& r1_xreal_0(np__0,k5_xcmplx_0(A)) )
& ~ ( ~ r1_xreal_0(np__0,k5_xcmplx_0(A))
& r1_xreal_0(np__0,A) ) ) ) ).
fof(t126_xreal_1,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(k5_xcmplx_0(B),k5_xcmplx_0(A)) ) ) ) ).
fof(t127_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ~ ( ~ r1_xreal_0(np__0,k5_xcmplx_0(A))
& ~ r1_xreal_0(k5_xcmplx_0(B),np__0)
& r1_xreal_0(B,A) ) ) ) ).
fof(t128_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( ( r1_xreal_0(A,np__0)
& r1_xreal_0(np__0,A) )
=> np__0 = k3_xcmplx_0(A,B) ) ) ) ).
fof(t129_xreal_1,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(np__0,k3_xcmplx_0(A,B)) ) ) ) ).
fof(t130_xreal_1,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,k3_xcmplx_0(A,B)) ) ) ) ).
fof(t131_xreal_1,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(k3_xcmplx_0(A,B),np__0) ) ) ) ).
fof(t132_xreal_1,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(k3_xcmplx_0(A,B),np__0) ) ) ) ).
fof(t133_xreal_1,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(k3_xcmplx_0(A,B),np__0) ) ) ) ).
fof(t134_xreal_1,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(np__0,k3_xcmplx_0(A,B)) ) ) ) ).
fof(t135_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ~ ( ~ r1_xreal_0(np__0,k3_xcmplx_0(A,B))
& ~ ( ~ 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(t136_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ~ ( ~ r1_xreal_0(k3_xcmplx_0(A,B),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(t137_xreal_1,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,k7_xcmplx_0(A,B)) ) ) ) ).
fof(t138_xreal_1,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(np__0,k7_xcmplx_0(A,B)) ) ) ) ).
fof(t139_xreal_1,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(A,B),np__0) ) ) ) ).
fof(t140_xreal_1,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(k7_xcmplx_0(A,B),np__0) ) ) ) ).
fof(t141_xreal_1,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(k7_xcmplx_0(A,B),np__0) ) ) ) ).
fof(t142_xreal_1,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(k7_xcmplx_0(A,B),np__0) ) ) ) ).
fof(t143_xreal_1,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)) ) ) ) ).
fof(t144_xreal_1,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(B,A)) ) ) ) ).
fof(t145_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ~ ( ~ r1_xreal_0(np__0,k7_xcmplx_0(A,B))
& ~ ( ~ r1_xreal_0(np__0,B)
& ~ r1_xreal_0(A,np__0) )
& ~ ( ~ r1_xreal_0(B,np__0)
& ~ r1_xreal_0(np__0,A) ) ) ) ) ).
fof(t146_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ~ ( ~ r1_xreal_0(k7_xcmplx_0(A,B),np__0)
& ~ ( ~ r1_xreal_0(B,np__0)
& ~ r1_xreal_0(A,np__0) )
& ~ ( ~ r1_xreal_0(np__0,B)
& ~ r1_xreal_0(np__0,A) ) ) ) ) ).
fof(t147_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ~ ( r1_xreal_0(A,B)
& r1_xreal_0(k2_xcmplx_0(B,np__1),A) ) ) ) ).
fof(t148_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ~ r1_xreal_0(A,k6_xcmplx_0(A,np__1)) ) ).
fof(t149_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ~ ( r1_xreal_0(A,B)
& r1_xreal_0(B,k6_xcmplx_0(A,np__1)) ) ) ) ).
fof(t150_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ~ ( ~ r1_xreal_0(A,k4_xcmplx_0(np__1))
& r1_xreal_0(k2_xcmplx_0(np__1,A),np__0) ) ) ).
fof(t151_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ~ ( ~ r1_xreal_0(np__1,A)
& r1_xreal_0(k6_xcmplx_0(np__1,A),np__0) ) ) ).
fof(t152_xreal_1,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)
& k3_xcmplx_0(A,B) = np__1 )
=> A = np__1 ) ) ) ).
fof(t153_xreal_1,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,k3_xcmplx_0(A,B)) ) ) ) ).
fof(t154_xreal_1,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(A,k3_xcmplx_0(A,B)) ) ) ) ).
fof(t155_xreal_1,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(k3_xcmplx_0(A,B),A) ) ) ) ).
fof(t156_xreal_1,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(k3_xcmplx_0(A,B),A) ) ) ) ).
fof(t157_xreal_1,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(k3_xcmplx_0(A,B),A) ) ) ) ).
fof(t158_xreal_1,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(k3_xcmplx_0(A,B),A) ) ) ) ).
fof(t159_xreal_1,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(A,k3_xcmplx_0(A,B)) ) ) ) ).
fof(t160_xreal_1,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,k3_xcmplx_0(A,B)) ) ) ) ).
fof(t161_xreal_1,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(np__1,k3_xcmplx_0(A,B)) ) ) ) ).
fof(t162_xreal_1,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(k3_xcmplx_0(A,B),np__1) ) ) ) ).
fof(t163_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ~ ( ~ r1_xreal_0(A,np__1)
& r1_xreal_0(np__1,B)
& r1_xreal_0(k3_xcmplx_0(A,B),np__1) ) ) ) ).
fof(t164_xreal_1,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(np__1,k3_xcmplx_0(A,B)) ) ) ) ).
fof(t165_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(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(t166_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ~ ( ~ r1_xreal_0(k4_xcmplx_0(np__1),A)
& r1_xreal_0(B,k4_xcmplx_0(np__1))
& r1_xreal_0(k3_xcmplx_0(A,B),np__1) ) ) ) ).
fof(t167_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( ( 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(t168_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ~ ( 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(t169_xreal_1,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(A,k3_xcmplx_0(B,C)) ) )
=> r1_xreal_0(A,B) ) ) ) ).
fof(t170_xreal_1,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) ) )
=> r1_xreal_0(A,B) ) ) ) ).
fof(t171_xreal_1,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(A,k3_xcmplx_0(C,B)) ) )
=> r1_xreal_0(A,np__0) ) ) ) ).
fof(t172_xreal_1,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(A,np__1)
& r1_xreal_0(np__0,B)
& r1_xreal_0(np__0,C)
& k2_xcmplx_0(k3_xcmplx_0(A,B),k3_xcmplx_0(k6_xcmplx_0(np__1,A),C)) = np__0
& ~ ( A = np__0
& C = np__0 )
& ~ ( A = np__1
& B = np__0 )
& ~ ( B = np__0
& C = np__0 ) ) ) ) ) ).
fof(t173_xreal_1,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(A,np__1)
& r1_xreal_0(B,C) )
=> r1_xreal_0(B,k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(np__1,A),B),k3_xcmplx_0(A,C))) ) ) ) ) ).
fof(t174_xreal_1,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(A,np__1)
& r1_xreal_0(B,C) )
=> r1_xreal_0(k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(np__1,A),B),k3_xcmplx_0(A,C)),C) ) ) ) ) ).
fof(t175_xreal_1,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(A,np__1)
& r1_xreal_0(B,C)
& r1_xreal_0(B,D) )
=> r1_xreal_0(B,k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(np__1,A),C),k3_xcmplx_0(A,D))) ) ) ) ) ) ).
fof(t176_xreal_1,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(A,np__1)
& r1_xreal_0(B,C)
& r1_xreal_0(D,C) )
=> r1_xreal_0(k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(np__1,A),B),k3_xcmplx_0(A,D)),C) ) ) ) ) ) ).
fof(t177_xreal_1,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(A,np__1)
& ~ r1_xreal_0(C,B)
& ~ r1_xreal_0(D,B)
& r1_xreal_0(k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(np__1,A),C),k3_xcmplx_0(A,D)),B) ) ) ) ) ) ).
fof(t178_xreal_1,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(A,np__1)
& ~ r1_xreal_0(C,B)
& ~ r1_xreal_0(C,D)
& r1_xreal_0(C,k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(np__1,A),B),k3_xcmplx_0(A,D))) ) ) ) ) ) ).
fof(t179_xreal_1,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__1,A)
& r1_xreal_0(B,C)
& ~ r1_xreal_0(D,B)
& r1_xreal_0(k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(np__1,A),C),k3_xcmplx_0(A,D)),B) ) ) ) ) ) ).
fof(t180_xreal_1,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__1,A)
& ~ r1_xreal_0(C,B)
& r1_xreal_0(D,C)
& r1_xreal_0(C,k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(np__1,A),B),k3_xcmplx_0(A,D))) ) ) ) ) ) ).
fof(t181_xreal_1,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(A,np__1)
& r1_xreal_0(B,k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(np__1,A),B),k3_xcmplx_0(A,C))) )
=> ( r1_xreal_0(k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(np__1,A),B),k3_xcmplx_0(A,C)),C)
| A = np__0 ) ) ) ) ) ).
fof(t182_xreal_1,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(A,np__1)
& r1_xreal_0(k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(np__1,A),B),k3_xcmplx_0(A,C)),B) )
=> ( r1_xreal_0(C,k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(np__1,A),B),k3_xcmplx_0(A,C)))
| A = np__0 ) ) ) ) ) ).
fof(t183_xreal_1,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__1,k7_xcmplx_0(B,A)) ) ) ) ) ).
fof(t184_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( r1_xreal_0(B,A)
=> ( r1_xreal_0(np__0,A)
| r1_xreal_0(np__1,k7_xcmplx_0(B,A)) ) ) ) ) ).
fof(t185_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( ( r1_xreal_0(np__0,A)
& r1_xreal_0(A,B) )
=> r1_xreal_0(k7_xcmplx_0(A,B),np__1) ) ) ) ).
fof(t186_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( ( r1_xreal_0(A,B)
& r1_xreal_0(B,np__0) )
=> r1_xreal_0(k7_xcmplx_0(B,A),np__1) ) ) ) ).
fof(t187_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( ( r1_xreal_0(np__0,A)
& r1_xreal_0(B,A) )
=> r1_xreal_0(k7_xcmplx_0(B,A),np__1) ) ) ) ).
fof(t188_xreal_1,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(k7_xcmplx_0(B,A),np__1) ) ) ) ).
fof(t189_xreal_1,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(k7_xcmplx_0(B,A),np__1) ) ) ) ).
fof(t190_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ~ ( ~ r1_xreal_0(np__0,A)
& ~ r1_xreal_0(A,B)
& r1_xreal_0(k7_xcmplx_0(B,A),np__1) ) ) ) ).
fof(t191_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ~ ( r1_xreal_0(np__0,A)
& ~ r1_xreal_0(B,A)
& r1_xreal_0(np__1,k7_xcmplx_0(A,B)) ) ) ) ).
fof(t192_xreal_1,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(np__1,k7_xcmplx_0(A,B)) ) ) ) ).
fof(t193_xreal_1,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(np__1,k7_xcmplx_0(B,A)) ) ) ) ).
fof(t194_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ~ ( ~ r1_xreal_0(np__0,A)
& ~ r1_xreal_0(B,A)
& r1_xreal_0(np__1,k7_xcmplx_0(B,A)) ) ) ) ).
fof(t195_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( ( r1_xreal_0(np__0,A)
& r1_xreal_0(k4_xcmplx_0(A),B) )
=> r1_xreal_0(k4_xcmplx_0(np__1),k7_xcmplx_0(B,A)) ) ) ) ).
fof(t196_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( ( r1_xreal_0(np__0,A)
& r1_xreal_0(k4_xcmplx_0(B),A) )
=> r1_xreal_0(k4_xcmplx_0(np__1),k7_xcmplx_0(B,A)) ) ) ) ).
fof(t197_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( ( r1_xreal_0(A,np__0)
& r1_xreal_0(B,k4_xcmplx_0(A)) )
=> r1_xreal_0(k4_xcmplx_0(np__1),k7_xcmplx_0(B,A)) ) ) ) ).
fof(t198_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( ( r1_xreal_0(A,np__0)
& r1_xreal_0(A,k4_xcmplx_0(B)) )
=> r1_xreal_0(k4_xcmplx_0(np__1),k7_xcmplx_0(B,A)) ) ) ) ).
fof(t199_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ~ ( ~ r1_xreal_0(A,np__0)
& ~ r1_xreal_0(B,k4_xcmplx_0(A))
& r1_xreal_0(k7_xcmplx_0(B,A),k4_xcmplx_0(np__1)) ) ) ) ).
fof(t200_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ~ ( ~ r1_xreal_0(A,np__0)
& ~ r1_xreal_0(A,k4_xcmplx_0(B))
& r1_xreal_0(k7_xcmplx_0(B,A),k4_xcmplx_0(np__1)) ) ) ) ).
fof(t201_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ~ ( ~ r1_xreal_0(np__0,A)
& ~ r1_xreal_0(k4_xcmplx_0(A),B)
& r1_xreal_0(k7_xcmplx_0(B,A),k4_xcmplx_0(np__1)) ) ) ) ).
fof(t202_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ~ ( ~ r1_xreal_0(np__0,A)
& ~ r1_xreal_0(k4_xcmplx_0(B),A)
& r1_xreal_0(k7_xcmplx_0(B,A),k4_xcmplx_0(np__1)) ) ) ) ).
fof(t203_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( r1_xreal_0(B,k4_xcmplx_0(A))
=> ( r1_xreal_0(A,np__0)
| r1_xreal_0(k7_xcmplx_0(B,A),k4_xcmplx_0(np__1)) ) ) ) ) ).
fof(t204_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( r1_xreal_0(A,k4_xcmplx_0(B))
=> ( r1_xreal_0(A,np__0)
| r1_xreal_0(k7_xcmplx_0(B,A),k4_xcmplx_0(np__1)) ) ) ) ) ).
fof(t205_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( r1_xreal_0(k4_xcmplx_0(A),B)
=> ( r1_xreal_0(np__0,A)
| r1_xreal_0(k7_xcmplx_0(B,A),k4_xcmplx_0(np__1)) ) ) ) ) ).
fof(t206_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( r1_xreal_0(k4_xcmplx_0(B),A)
=> ( r1_xreal_0(np__0,A)
| r1_xreal_0(k7_xcmplx_0(B,A),k4_xcmplx_0(np__1)) ) ) ) ) ).
fof(t207_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ~ ( ~ r1_xreal_0(A,np__0)
& ~ r1_xreal_0(k4_xcmplx_0(A),B)
& r1_xreal_0(k4_xcmplx_0(np__1),k7_xcmplx_0(B,A)) ) ) ) ).
fof(t208_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ~ ( ~ r1_xreal_0(A,np__0)
& ~ r1_xreal_0(k4_xcmplx_0(B),A)
& r1_xreal_0(k4_xcmplx_0(np__1),k7_xcmplx_0(B,A)) ) ) ) ).
fof(t209_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ~ ( ~ r1_xreal_0(np__0,A)
& ~ r1_xreal_0(B,k4_xcmplx_0(A))
& r1_xreal_0(k4_xcmplx_0(np__1),k7_xcmplx_0(B,A)) ) ) ) ).
fof(t210_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ~ ( ~ r1_xreal_0(np__0,A)
& ~ r1_xreal_0(A,k4_xcmplx_0(B))
& r1_xreal_0(k4_xcmplx_0(np__1),k7_xcmplx_0(B,A)) ) ) ) ).
fof(t211_xreal_1,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(A,k7_xcmplx_0(B,C)) ) )
=> r1_xreal_0(A,B) ) ) ) ).
fof(t212_xreal_1,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(k7_xcmplx_0(A,C),B) ) )
=> r1_xreal_0(A,B) ) ) ) ).
fof(t213_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ( r1_xreal_0(np__1,A)
=> r1_xreal_0(k5_xcmplx_0(A),np__1) ) ) ).
fof(t214_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ~ ( ~ r1_xreal_0(A,np__1)
& r1_xreal_0(np__1,k5_xcmplx_0(A)) ) ) ).
fof(t215_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ( r1_xreal_0(A,k4_xcmplx_0(np__1))
=> r1_xreal_0(k4_xcmplx_0(np__1),k5_xcmplx_0(A)) ) ) ).
fof(t216_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ~ ( ~ r1_xreal_0(k4_xcmplx_0(np__1),A)
& r1_xreal_0(k5_xcmplx_0(A),k4_xcmplx_0(np__1)) ) ) ).
fof(t217_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ~ ( ~ r1_xreal_0(A,np__0)
& r1_xreal_0(k7_xcmplx_0(A,np__2),np__0) ) ) ).
fof(t218_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ~ ( ~ r1_xreal_0(A,np__0)
& r1_xreal_0(A,k7_xcmplx_0(A,np__2)) ) ) ).
fof(t219_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ( r1_xreal_0(A,k7_xcmplx_0(np__1,np__2))
=> r1_xreal_0(k6_xcmplx_0(k3_xcmplx_0(np__2,A),np__1),np__0) ) ) ).
fof(t220_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ( r1_xreal_0(A,k7_xcmplx_0(np__1,np__2))
=> r1_xreal_0(np__0,k6_xcmplx_0(np__1,k3_xcmplx_0(np__2,A))) ) ) ).
fof(t221_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ( r1_xreal_0(k7_xcmplx_0(np__1,np__2),A)
=> r1_xreal_0(np__0,k6_xcmplx_0(k3_xcmplx_0(np__2,A),np__1)) ) ) ).
fof(t222_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ( r1_xreal_0(k7_xcmplx_0(np__1,np__2),A)
=> r1_xreal_0(k6_xcmplx_0(np__1,k3_xcmplx_0(np__2,A)),np__0) ) ) ).
fof(t223_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ~ ( ~ r1_xreal_0(A,np__0)
& r1_xreal_0(A,k7_xcmplx_0(A,np__3)) ) ) ).
fof(t224_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ~ ( ~ r1_xreal_0(A,np__0)
& r1_xreal_0(k7_xcmplx_0(A,np__3),np__0) ) ) ).
fof(t225_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ~ ( ~ r1_xreal_0(A,np__0)
& r1_xreal_0(A,k7_xcmplx_0(A,np__4)) ) ) ).
fof(t226_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ~ ( ~ r1_xreal_0(A,np__0)
& r1_xreal_0(k7_xcmplx_0(A,np__4),np__0) ) ) ).
fof(t227_xreal_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ~ ( B != np__0
& ! [C] :
( v1_xreal_0(C)
=> A != k7_xcmplx_0(B,C) ) ) ) ) ).
%------------------------------------------------------------------------------