SET007 Axioms: SET007+87.ax
%------------------------------------------------------------------------------
% File : SET007+87 : TPTP v9.0.0. 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 unt; 0 def)
% Number of atoms : 670 ( 5 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 683 ( 217 ~; 35 |; 203 &)
% ( 0 <=>; 228 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-2 aty)
% Number of variables : 164 ( 163 !; 1 ?)
% 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) ) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------