SET007 Axioms: SET007+42.ax
%------------------------------------------------------------------------------
% File : SET007+42 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Complex 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 : xcmplx_1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 237 ( 2 unt; 0 def)
% Number of atoms : 934 ( 352 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 779 ( 82 ~; 18 |; 30 &)
% ( 0 <=>; 649 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 581 ( 581 !; 0 ?)
% 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_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> k2_xcmplx_0(A,k2_xcmplx_0(B,C)) = k2_xcmplx_0(k2_xcmplx_0(A,B),C) ) ) ) ).
fof(t2_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> ( k2_xcmplx_0(A,B) = k2_xcmplx_0(C,B)
=> A = C ) ) ) ) ).
fof(t3_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ( A = k2_xcmplx_0(A,B)
=> B = np__0 ) ) ) ).
fof(t4_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> k3_xcmplx_0(A,k3_xcmplx_0(B,C)) = k3_xcmplx_0(k3_xcmplx_0(A,B),C) ) ) ) ).
fof(t5_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> ( k3_xcmplx_0(B,A) = k3_xcmplx_0(C,A)
=> ( A = np__0
| B = C ) ) ) ) ) ).
fof(t6_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ~ ( k3_xcmplx_0(A,B) = np__0
& A != np__0
& B != np__0 ) ) ) ).
fof(t7_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ( k3_xcmplx_0(B,A) = A
=> ( A = np__0
| B = np__1 ) ) ) ) ).
fof(t8_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> k3_xcmplx_0(A,k2_xcmplx_0(B,C)) = k2_xcmplx_0(k3_xcmplx_0(A,B),k3_xcmplx_0(A,C)) ) ) ) ).
fof(t9_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> ! [D] :
( v1_xcmplx_0(D)
=> k3_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(A,B),C),D) = k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,D),k3_xcmplx_0(B,D)),k3_xcmplx_0(C,D)) ) ) ) ) ).
fof(t10_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> ! [D] :
( v1_xcmplx_0(D)
=> k3_xcmplx_0(k2_xcmplx_0(A,B),k2_xcmplx_0(C,D)) = k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,C),k3_xcmplx_0(A,D)),k3_xcmplx_0(B,C)),k3_xcmplx_0(B,D)) ) ) ) ) ).
fof(t11_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> k3_xcmplx_0(np__2,A) = k2_xcmplx_0(A,A) ) ).
fof(t12_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> k3_xcmplx_0(np__3,A) = k2_xcmplx_0(k2_xcmplx_0(A,A),A) ) ).
fof(t13_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> k3_xcmplx_0(np__4,A) = k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(A,A),A),A) ) ).
fof(t14_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> k6_xcmplx_0(A,A) = np__0 ) ).
fof(t15_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ( k6_xcmplx_0(A,B) = np__0
=> A = B ) ) ) ).
fof(t16_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ( k6_xcmplx_0(A,B) = A
=> B = np__0 ) ) ) ).
fof(t17_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> A = k6_xcmplx_0(A,k6_xcmplx_0(B,B)) ) ) ).
fof(t18_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> k6_xcmplx_0(A,k6_xcmplx_0(A,B)) = B ) ) ).
fof(t19_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> ( k6_xcmplx_0(A,B) = k6_xcmplx_0(C,B)
=> A = C ) ) ) ) ).
fof(t20_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> ( k6_xcmplx_0(A,B) = k6_xcmplx_0(A,C)
=> B = C ) ) ) ) ).
fof(t21_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> k6_xcmplx_0(k6_xcmplx_0(A,B),C) = k6_xcmplx_0(k6_xcmplx_0(A,C),B) ) ) ) ).
fof(t22_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> k6_xcmplx_0(A,B) = k6_xcmplx_0(k6_xcmplx_0(A,C),k6_xcmplx_0(B,C)) ) ) ) ).
fof(t23_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> k6_xcmplx_0(k6_xcmplx_0(A,B),k6_xcmplx_0(A,C)) = k6_xcmplx_0(C,B) ) ) ) ).
fof(t24_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> ! [D] :
( v1_xcmplx_0(D)
=> ( k6_xcmplx_0(A,B) = k6_xcmplx_0(C,D)
=> k6_xcmplx_0(A,C) = k6_xcmplx_0(B,D) ) ) ) ) ) ).
fof(t25_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> A = k2_xcmplx_0(A,k6_xcmplx_0(B,B)) ) ) ).
fof(t26_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> A = k6_xcmplx_0(k2_xcmplx_0(A,B),B) ) ) ).
fof(t27_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> A = k2_xcmplx_0(k6_xcmplx_0(A,B),B) ) ) ).
fof(t28_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> k2_xcmplx_0(A,B) = k2_xcmplx_0(k2_xcmplx_0(A,C),k6_xcmplx_0(B,C)) ) ) ) ).
fof(t29_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> k6_xcmplx_0(k2_xcmplx_0(A,B),C) = k2_xcmplx_0(k6_xcmplx_0(A,C),B) ) ) ) ).
fof(t30_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> k2_xcmplx_0(k6_xcmplx_0(A,B),C) = k2_xcmplx_0(k6_xcmplx_0(C,B),A) ) ) ) ).
fof(t31_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> k2_xcmplx_0(A,B) = k6_xcmplx_0(k2_xcmplx_0(A,C),k6_xcmplx_0(C,B)) ) ) ) ).
fof(t32_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> k6_xcmplx_0(A,B) = k6_xcmplx_0(k2_xcmplx_0(A,C),k2_xcmplx_0(B,C)) ) ) ) ).
fof(t33_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> ! [D] :
( v1_xcmplx_0(D)
=> ( k2_xcmplx_0(A,B) = k2_xcmplx_0(C,D)
=> k6_xcmplx_0(A,C) = k6_xcmplx_0(D,B) ) ) ) ) ) ).
fof(t34_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> ! [D] :
( v1_xcmplx_0(D)
=> ( k6_xcmplx_0(A,B) = k6_xcmplx_0(C,D)
=> k2_xcmplx_0(A,D) = k2_xcmplx_0(B,C) ) ) ) ) ) ).
fof(t35_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> ! [D] :
( v1_xcmplx_0(D)
=> ( k2_xcmplx_0(A,B) = k6_xcmplx_0(C,D)
=> k2_xcmplx_0(A,D) = k6_xcmplx_0(C,B) ) ) ) ) ) ).
fof(t36_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> k6_xcmplx_0(A,k2_xcmplx_0(B,C)) = k6_xcmplx_0(k6_xcmplx_0(A,B),C) ) ) ) ).
fof(t37_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> k6_xcmplx_0(A,k6_xcmplx_0(B,C)) = k2_xcmplx_0(k6_xcmplx_0(A,B),C) ) ) ) ).
fof(t38_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> k6_xcmplx_0(A,k6_xcmplx_0(B,C)) = k2_xcmplx_0(A,k6_xcmplx_0(C,B)) ) ) ) ).
fof(t39_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> k6_xcmplx_0(A,B) = k2_xcmplx_0(k6_xcmplx_0(A,C),k6_xcmplx_0(C,B)) ) ) ) ).
fof(t40_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> k3_xcmplx_0(A,k6_xcmplx_0(B,C)) = k6_xcmplx_0(k3_xcmplx_0(A,B),k3_xcmplx_0(A,C)) ) ) ) ).
fof(t41_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> ! [D] :
( v1_xcmplx_0(D)
=> k3_xcmplx_0(k6_xcmplx_0(A,B),k6_xcmplx_0(C,D)) = k3_xcmplx_0(k6_xcmplx_0(B,A),k6_xcmplx_0(D,C)) ) ) ) ) ).
fof(t42_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> ! [D] :
( v1_xcmplx_0(D)
=> k3_xcmplx_0(k6_xcmplx_0(k6_xcmplx_0(A,B),C),D) = k6_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(A,D),k3_xcmplx_0(B,D)),k3_xcmplx_0(C,D)) ) ) ) ) ).
fof(t43_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> ! [D] :
( v1_xcmplx_0(D)
=> k3_xcmplx_0(k6_xcmplx_0(k2_xcmplx_0(A,B),C),D) = k6_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,D),k3_xcmplx_0(B,D)),k3_xcmplx_0(C,D)) ) ) ) ) ).
fof(t44_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> ! [D] :
( v1_xcmplx_0(D)
=> k3_xcmplx_0(k2_xcmplx_0(k6_xcmplx_0(A,B),C),D) = k2_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(A,D),k3_xcmplx_0(B,D)),k3_xcmplx_0(C,D)) ) ) ) ) ).
fof(t45_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> ! [D] :
( v1_xcmplx_0(D)
=> k3_xcmplx_0(k2_xcmplx_0(A,B),k6_xcmplx_0(C,D)) = k6_xcmplx_0(k2_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(A,C),k3_xcmplx_0(A,D)),k3_xcmplx_0(B,C)),k3_xcmplx_0(B,D)) ) ) ) ) ).
fof(t46_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> ! [D] :
( v1_xcmplx_0(D)
=> k3_xcmplx_0(k6_xcmplx_0(A,B),k2_xcmplx_0(C,D)) = k6_xcmplx_0(k6_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,C),k3_xcmplx_0(A,D)),k3_xcmplx_0(B,C)),k3_xcmplx_0(B,D)) ) ) ) ) ).
fof(t47_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> ! [D] :
( v1_xcmplx_0(D)
=> k3_xcmplx_0(k6_xcmplx_0(A,B),k6_xcmplx_0(C,D)) = k2_xcmplx_0(k6_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(A,C),k3_xcmplx_0(A,D)),k3_xcmplx_0(B,C)),k3_xcmplx_0(B,D)) ) ) ) ) ).
fof(t48_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> k7_xcmplx_0(k7_xcmplx_0(A,B),C) = k7_xcmplx_0(k7_xcmplx_0(A,C),B) ) ) ) ).
fof(t49_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> k7_xcmplx_0(A,np__0) = np__0 ) ).
fof(t50_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ~ ( A != np__0
& B != np__0
& k7_xcmplx_0(A,B) = np__0 ) ) ) ).
fof(t51_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ( A != np__0
=> B = k7_xcmplx_0(B,k7_xcmplx_0(A,A)) ) ) ) ).
fof(t52_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ( A != np__0
=> k7_xcmplx_0(A,k7_xcmplx_0(A,B)) = B ) ) ) ).
fof(t53_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> ( k7_xcmplx_0(B,A) = k7_xcmplx_0(C,A)
=> ( A = np__0
| B = C ) ) ) ) ) ).
fof(t54_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ( k7_xcmplx_0(A,B) != np__0
=> B = k7_xcmplx_0(A,k7_xcmplx_0(A,B)) ) ) ) ).
fof(t55_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> ( A != np__0
=> k7_xcmplx_0(B,C) = k7_xcmplx_0(k7_xcmplx_0(B,A),k7_xcmplx_0(C,A)) ) ) ) ) ).
fof(t56_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> k7_xcmplx_0(np__1,k7_xcmplx_0(np__1,A)) = A ) ).
fof(t57_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> k7_xcmplx_0(np__1,k7_xcmplx_0(A,B)) = k7_xcmplx_0(B,A) ) ) ).
fof(t58_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ( k7_xcmplx_0(A,B) = np__1
=> A = B ) ) ) ).
fof(t59_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ( k7_xcmplx_0(np__1,A) = k7_xcmplx_0(np__1,B)
=> A = B ) ) ) ).
fof(t60_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ( A != np__0
=> k7_xcmplx_0(A,A) = np__1 ) ) ).
fof(t61_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ( k7_xcmplx_0(A,B) = A
=> ( A = np__0
| B = np__1 ) ) ) ) ).
fof(t62_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> k7_xcmplx_0(A,np__0) = np__0 ) ).
fof(t63_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> k2_xcmplx_0(k7_xcmplx_0(A,B),k7_xcmplx_0(C,B)) = k7_xcmplx_0(k2_xcmplx_0(A,C),B) ) ) ) ).
fof(t64_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> ! [D] :
( v1_xcmplx_0(D)
=> k7_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(A,B),C),D) = k2_xcmplx_0(k2_xcmplx_0(k7_xcmplx_0(A,D),k7_xcmplx_0(B,D)),k7_xcmplx_0(C,D)) ) ) ) ) ).
fof(t65_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> k7_xcmplx_0(k2_xcmplx_0(A,A),np__2) = A ) ).
fof(t66_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> k2_xcmplx_0(k7_xcmplx_0(A,np__2),k7_xcmplx_0(A,np__2)) = A ) ).
fof(t67_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ( A = k7_xcmplx_0(k2_xcmplx_0(A,B),np__2)
=> A = B ) ) ) ).
fof(t68_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> k7_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(A,A),A),np__3) = A ) ).
fof(t69_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> k2_xcmplx_0(k2_xcmplx_0(k7_xcmplx_0(A,np__3),k7_xcmplx_0(A,np__3)),k7_xcmplx_0(A,np__3)) = A ) ).
fof(t70_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> k7_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(A,A),A),A),np__4) = A ) ).
fof(t71_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k7_xcmplx_0(A,np__4),k7_xcmplx_0(A,np__4)),k7_xcmplx_0(A,np__4)),k7_xcmplx_0(A,np__4)) = A ) ).
fof(t72_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> k2_xcmplx_0(k7_xcmplx_0(A,np__4),k7_xcmplx_0(A,np__4)) = k7_xcmplx_0(A,np__2) ) ).
fof(t73_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> k7_xcmplx_0(k2_xcmplx_0(A,A),np__4) = k7_xcmplx_0(A,np__2) ) ).
fof(t74_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ( k3_xcmplx_0(A,B) = np__1
=> A = k7_xcmplx_0(np__1,B) ) ) ) ).
fof(t75_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> k3_xcmplx_0(A,k7_xcmplx_0(B,C)) = k7_xcmplx_0(k3_xcmplx_0(A,B),C) ) ) ) ).
fof(t76_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> k3_xcmplx_0(k7_xcmplx_0(A,B),C) = k3_xcmplx_0(k7_xcmplx_0(C,B),A) ) ) ) ).
fof(t77_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> ! [D] :
( v1_xcmplx_0(D)
=> k3_xcmplx_0(k7_xcmplx_0(A,B),k7_xcmplx_0(C,D)) = k7_xcmplx_0(k3_xcmplx_0(A,C),k3_xcmplx_0(B,D)) ) ) ) ) ).
fof(t78_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> k7_xcmplx_0(A,k7_xcmplx_0(B,C)) = k7_xcmplx_0(k3_xcmplx_0(A,C),B) ) ) ) ).
fof(t79_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> k7_xcmplx_0(A,k3_xcmplx_0(B,C)) = k7_xcmplx_0(k7_xcmplx_0(A,B),C) ) ) ) ).
fof(t80_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> k7_xcmplx_0(A,k7_xcmplx_0(B,C)) = k3_xcmplx_0(A,k7_xcmplx_0(C,B)) ) ) ) ).
fof(t81_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> k7_xcmplx_0(A,k7_xcmplx_0(B,C)) = k3_xcmplx_0(k7_xcmplx_0(C,B),A) ) ) ) ).
fof(t82_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> k7_xcmplx_0(A,k7_xcmplx_0(B,C)) = k3_xcmplx_0(C,k7_xcmplx_0(A,B)) ) ) ) ).
fof(t83_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> k7_xcmplx_0(A,k7_xcmplx_0(B,C)) = k3_xcmplx_0(k7_xcmplx_0(A,B),C) ) ) ) ).
fof(t84_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> ! [D] :
( v1_xcmplx_0(D)
=> k7_xcmplx_0(k3_xcmplx_0(A,B),k3_xcmplx_0(C,D)) = k7_xcmplx_0(k3_xcmplx_0(k7_xcmplx_0(A,C),B),D) ) ) ) ) ).
fof(t85_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> ! [D] :
( v1_xcmplx_0(D)
=> k7_xcmplx_0(k7_xcmplx_0(A,B),k7_xcmplx_0(C,D)) = k7_xcmplx_0(k3_xcmplx_0(A,D),k3_xcmplx_0(B,C)) ) ) ) ) ).
fof(t86_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> ! [D] :
( v1_xcmplx_0(D)
=> k3_xcmplx_0(k7_xcmplx_0(A,B),k7_xcmplx_0(C,D)) = k3_xcmplx_0(k7_xcmplx_0(A,D),k7_xcmplx_0(C,B)) ) ) ) ) ).
fof(t87_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> ! [D] :
( v1_xcmplx_0(D)
=> ! [E] :
( v1_xcmplx_0(E)
=> k7_xcmplx_0(A,k3_xcmplx_0(k3_xcmplx_0(B,C),k7_xcmplx_0(D,E))) = k3_xcmplx_0(k7_xcmplx_0(E,C),k7_xcmplx_0(A,k3_xcmplx_0(B,D))) ) ) ) ) ) ).
fof(t88_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ( A != np__0
=> k3_xcmplx_0(k7_xcmplx_0(B,A),A) = B ) ) ) ).
fof(t89_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ( A != np__0
=> B = k3_xcmplx_0(B,k7_xcmplx_0(A,A)) ) ) ) ).
fof(t90_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ( A != np__0
=> B = k7_xcmplx_0(k3_xcmplx_0(B,A),A) ) ) ) ).
fof(t91_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> ( A != np__0
=> k3_xcmplx_0(B,C) = k3_xcmplx_0(k3_xcmplx_0(B,A),k7_xcmplx_0(C,A)) ) ) ) ) ).
fof(t92_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> ( A != np__0
=> k7_xcmplx_0(B,C) = k7_xcmplx_0(k3_xcmplx_0(B,A),k3_xcmplx_0(C,A)) ) ) ) ) ).
fof(t93_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> ( A != np__0
=> k7_xcmplx_0(B,C) = k3_xcmplx_0(k7_xcmplx_0(B,k3_xcmplx_0(C,A)),A) ) ) ) ) ).
fof(t94_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> ( A != np__0
=> k3_xcmplx_0(B,C) = k7_xcmplx_0(k3_xcmplx_0(B,A),k7_xcmplx_0(A,C)) ) ) ) ) ).
fof(t95_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> ! [D] :
( v1_xcmplx_0(D)
=> ( k3_xcmplx_0(C,A) = k3_xcmplx_0(D,B)
=> ( A = np__0
| B = np__0
| k7_xcmplx_0(C,B) = k7_xcmplx_0(D,A) ) ) ) ) ) ) ).
fof(t96_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> ! [D] :
( v1_xcmplx_0(D)
=> ( k7_xcmplx_0(C,B) = k7_xcmplx_0(D,A)
=> ( A = np__0
| B = np__0
| k3_xcmplx_0(C,A) = k3_xcmplx_0(D,B) ) ) ) ) ) ) ).
fof(t97_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> ! [D] :
( v1_xcmplx_0(D)
=> ( k3_xcmplx_0(C,A) = k7_xcmplx_0(D,B)
=> ( A = np__0
| B = np__0
| k3_xcmplx_0(C,B) = k7_xcmplx_0(D,A) ) ) ) ) ) ) ).
fof(t98_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> ( A != np__0
=> k7_xcmplx_0(B,C) = k3_xcmplx_0(A,k7_xcmplx_0(k7_xcmplx_0(B,A),C)) ) ) ) ) ).
fof(t99_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> ( A != np__0
=> k7_xcmplx_0(B,C) = k3_xcmplx_0(k7_xcmplx_0(B,A),k7_xcmplx_0(A,C)) ) ) ) ) ).
fof(t100_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> k3_xcmplx_0(A,k7_xcmplx_0(np__1,B)) = k7_xcmplx_0(A,B) ) ) ).
fof(t101_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> k7_xcmplx_0(A,k7_xcmplx_0(np__1,B)) = k3_xcmplx_0(A,B) ) ) ).
fof(t102_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> k3_xcmplx_0(k7_xcmplx_0(A,B),C) = k3_xcmplx_0(k3_xcmplx_0(k7_xcmplx_0(np__1,B),C),A) ) ) ) ).
fof(t103_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> k3_xcmplx_0(k7_xcmplx_0(np__1,A),k7_xcmplx_0(np__1,B)) = k7_xcmplx_0(np__1,k3_xcmplx_0(A,B)) ) ) ).
fof(t104_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> k3_xcmplx_0(k7_xcmplx_0(np__1,A),k7_xcmplx_0(B,C)) = k7_xcmplx_0(B,k3_xcmplx_0(C,A)) ) ) ) ).
fof(t105_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> k7_xcmplx_0(k7_xcmplx_0(A,B),C) = k3_xcmplx_0(k7_xcmplx_0(np__1,B),k7_xcmplx_0(A,C)) ) ) ) ).
fof(t106_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> k7_xcmplx_0(k7_xcmplx_0(A,B),C) = k3_xcmplx_0(k7_xcmplx_0(np__1,C),k7_xcmplx_0(A,B)) ) ) ) ).
fof(t107_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ( A != np__0
=> k3_xcmplx_0(A,k7_xcmplx_0(np__1,A)) = np__1 ) ) ).
fof(t108_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ( A != np__0
=> B = k3_xcmplx_0(k3_xcmplx_0(B,A),k7_xcmplx_0(np__1,A)) ) ) ) ).
fof(t109_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ( A != np__0
=> B = k3_xcmplx_0(B,k3_xcmplx_0(k7_xcmplx_0(np__1,A),A)) ) ) ) ).
fof(t110_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ( A != np__0
=> B = k3_xcmplx_0(k3_xcmplx_0(B,k7_xcmplx_0(np__1,A)),A) ) ) ) ).
fof(t111_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ( A != np__0
=> B = k7_xcmplx_0(B,k3_xcmplx_0(A,k7_xcmplx_0(np__1,A))) ) ) ) ).
fof(t112_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ~ ( A != np__0
& B != np__0
& k7_xcmplx_0(np__1,k3_xcmplx_0(A,B)) = np__0 ) ) ) ).
fof(t113_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ~ ( A != np__0
& B != np__0
& k3_xcmplx_0(k7_xcmplx_0(A,B),k7_xcmplx_0(B,A)) != np__1 ) ) ) ).
fof(t114_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> ( A != np__0
=> k2_xcmplx_0(k7_xcmplx_0(B,A),C) = k7_xcmplx_0(k2_xcmplx_0(B,k3_xcmplx_0(A,C)),A) ) ) ) ) ).
fof(t115_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> ( A != np__0
=> k2_xcmplx_0(B,C) = k3_xcmplx_0(A,k2_xcmplx_0(k7_xcmplx_0(B,A),k7_xcmplx_0(C,A))) ) ) ) ) ).
fof(t116_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> ( A != np__0
=> k2_xcmplx_0(B,C) = k7_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(B,A),k3_xcmplx_0(C,A)),A) ) ) ) ) ).
fof(t117_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> ! [D] :
( v1_xcmplx_0(D)
=> ~ ( A != np__0
& B != np__0
& k2_xcmplx_0(k7_xcmplx_0(C,A),k7_xcmplx_0(D,B)) != k7_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(C,B),k3_xcmplx_0(D,A)),k3_xcmplx_0(A,B)) ) ) ) ) ) ).
fof(t118_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ( A != np__0
=> k2_xcmplx_0(A,B) = k3_xcmplx_0(A,k2_xcmplx_0(np__1,k7_xcmplx_0(B,A))) ) ) ) ).
fof(t119_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> k2_xcmplx_0(k7_xcmplx_0(A,k3_xcmplx_0(np__2,B)),k7_xcmplx_0(A,k3_xcmplx_0(np__2,B))) = k7_xcmplx_0(A,B) ) ) ).
fof(t120_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> k2_xcmplx_0(k2_xcmplx_0(k7_xcmplx_0(A,k3_xcmplx_0(np__3,B)),k7_xcmplx_0(A,k3_xcmplx_0(np__3,B))),k7_xcmplx_0(A,k3_xcmplx_0(np__3,B))) = k7_xcmplx_0(A,B) ) ) ).
fof(t121_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> k6_xcmplx_0(k7_xcmplx_0(A,B),k7_xcmplx_0(C,B)) = k7_xcmplx_0(k6_xcmplx_0(A,C),B) ) ) ) ).
fof(t122_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> k6_xcmplx_0(A,k7_xcmplx_0(A,np__2)) = k7_xcmplx_0(A,np__2) ) ).
fof(t123_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> ! [D] :
( v1_xcmplx_0(D)
=> k7_xcmplx_0(k6_xcmplx_0(k6_xcmplx_0(A,B),C),D) = k6_xcmplx_0(k6_xcmplx_0(k7_xcmplx_0(A,D),k7_xcmplx_0(B,D)),k7_xcmplx_0(C,D)) ) ) ) ) ).
fof(t124_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> ! [D] :
( v1_xcmplx_0(D)
=> ( k7_xcmplx_0(C,A) = k7_xcmplx_0(D,B)
=> ( A = np__0
| B = np__0
| A = B
| k7_xcmplx_0(C,A) = k7_xcmplx_0(k6_xcmplx_0(C,D),k6_xcmplx_0(A,B)) ) ) ) ) ) ) ).
fof(t125_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> ! [D] :
( v1_xcmplx_0(D)
=> k7_xcmplx_0(k6_xcmplx_0(k2_xcmplx_0(A,B),C),D) = k6_xcmplx_0(k2_xcmplx_0(k7_xcmplx_0(A,D),k7_xcmplx_0(B,D)),k7_xcmplx_0(C,D)) ) ) ) ) ).
fof(t126_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> ! [D] :
( v1_xcmplx_0(D)
=> k7_xcmplx_0(k2_xcmplx_0(k6_xcmplx_0(A,B),C),D) = k2_xcmplx_0(k6_xcmplx_0(k7_xcmplx_0(A,D),k7_xcmplx_0(B,D)),k7_xcmplx_0(C,D)) ) ) ) ) ).
fof(t127_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> ( A != np__0
=> k6_xcmplx_0(k7_xcmplx_0(B,A),C) = k7_xcmplx_0(k6_xcmplx_0(B,k3_xcmplx_0(C,A)),A) ) ) ) ) ).
fof(t128_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> ( A != np__0
=> k6_xcmplx_0(B,k7_xcmplx_0(C,A)) = k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(B,A),C),A) ) ) ) ) ).
fof(t129_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> ( A != np__0
=> k6_xcmplx_0(B,C) = k3_xcmplx_0(A,k6_xcmplx_0(k7_xcmplx_0(B,A),k7_xcmplx_0(C,A))) ) ) ) ) ).
fof(t130_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> ( A != np__0
=> k6_xcmplx_0(B,C) = k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(B,A),k3_xcmplx_0(C,A)),A) ) ) ) ) ).
fof(t131_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> ! [D] :
( v1_xcmplx_0(D)
=> ~ ( A != np__0
& B != np__0
& k6_xcmplx_0(k7_xcmplx_0(C,A),k7_xcmplx_0(D,B)) != k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(C,B),k3_xcmplx_0(D,A)),k3_xcmplx_0(A,B)) ) ) ) ) ) ).
fof(t132_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ( A != np__0
=> k6_xcmplx_0(A,B) = k3_xcmplx_0(A,k6_xcmplx_0(np__1,k7_xcmplx_0(B,A))) ) ) ) ).
fof(t133_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> ( A != np__0
=> B = k7_xcmplx_0(k6_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,B),C),C),A) ) ) ) ) ).
fof(t134_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ( k4_xcmplx_0(A) = k4_xcmplx_0(B)
=> A = B ) ) ) ).
fof(t135_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ( k4_xcmplx_0(A) = np__0
=> A = np__0 ) ) ).
fof(t136_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ( k2_xcmplx_0(A,k4_xcmplx_0(B)) = np__0
=> A = B ) ) ) ).
fof(t137_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> A = k2_xcmplx_0(k2_xcmplx_0(A,B),k4_xcmplx_0(B)) ) ) ).
fof(t138_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> A = k2_xcmplx_0(A,k2_xcmplx_0(B,k4_xcmplx_0(B))) ) ) ).
fof(t139_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> A = k2_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(B),A),B) ) ) ).
fof(t140_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> k4_xcmplx_0(k2_xcmplx_0(A,B)) = k2_xcmplx_0(k4_xcmplx_0(A),k4_xcmplx_0(B)) ) ) ).
fof(t141_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> k4_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(A),B)) = k2_xcmplx_0(A,k4_xcmplx_0(B)) ) ) ).
fof(t142_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> k2_xcmplx_0(A,B) = k4_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(A),k4_xcmplx_0(B))) ) ) ).
fof(t143_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> k4_xcmplx_0(k6_xcmplx_0(A,B)) = k6_xcmplx_0(B,A) ) ) ).
fof(t144_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> k6_xcmplx_0(k4_xcmplx_0(A),B) = k6_xcmplx_0(k4_xcmplx_0(B),A) ) ) ).
fof(t145_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> A = k6_xcmplx_0(k4_xcmplx_0(B),k6_xcmplx_0(k4_xcmplx_0(A),B)) ) ) ).
fof(t146_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> k6_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(A),B),C) = k6_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(A),C),B) ) ) ) ).
fof(t147_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> k6_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(A),B),C) = k6_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(B),C),A) ) ) ) ).
fof(t148_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> k6_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(A),B),C) = k6_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(C),B),A) ) ) ) ).
fof(t149_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> k6_xcmplx_0(k6_xcmplx_0(A,B),k6_xcmplx_0(A,C)) = k4_xcmplx_0(k6_xcmplx_0(B,C)) ) ) ) ).
fof(t150_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> k6_xcmplx_0(np__0,A) = k4_xcmplx_0(A) ) ).
fof(t151_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> k2_xcmplx_0(A,B) = k6_xcmplx_0(A,k4_xcmplx_0(B)) ) ) ).
fof(t152_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> A = k6_xcmplx_0(A,k2_xcmplx_0(B,k4_xcmplx_0(B))) ) ) ).
fof(t153_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> ( k6_xcmplx_0(A,B) = k2_xcmplx_0(C,k4_xcmplx_0(B))
=> A = C ) ) ) ) ).
fof(t154_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> ( k6_xcmplx_0(A,B) = k2_xcmplx_0(A,k4_xcmplx_0(C))
=> B = C ) ) ) ) ).
fof(t155_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> k6_xcmplx_0(k2_xcmplx_0(A,B),C) = k2_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(C),A),B) ) ) ) ).
fof(t156_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> k2_xcmplx_0(k6_xcmplx_0(A,B),C) = k2_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(B),C),A) ) ) ) ).
fof(t157_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> k6_xcmplx_0(A,k6_xcmplx_0(k4_xcmplx_0(B),C)) = k2_xcmplx_0(k2_xcmplx_0(A,B),C) ) ) ) ).
fof(t158_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> k6_xcmplx_0(k6_xcmplx_0(A,B),C) = k2_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(B),C),A) ) ) ) ).
fof(t159_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> k6_xcmplx_0(k6_xcmplx_0(A,B),C) = k6_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(C),A),B) ) ) ) ).
fof(t160_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> k6_xcmplx_0(k6_xcmplx_0(A,B),C) = k2_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(C),B),A) ) ) ) ).
fof(t161_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> k4_xcmplx_0(k2_xcmplx_0(A,B)) = k6_xcmplx_0(k4_xcmplx_0(B),A) ) ) ).
fof(t162_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> k4_xcmplx_0(k6_xcmplx_0(A,B)) = k2_xcmplx_0(k4_xcmplx_0(A),B) ) ) ).
fof(t163_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> k4_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(A),B)) = k6_xcmplx_0(A,B) ) ) ).
fof(t164_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> k2_xcmplx_0(A,B) = k4_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(A),B)) ) ) ).
fof(t165_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> k6_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(A),B),C) = k6_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(C),B),A) ) ) ) ).
fof(t166_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> k6_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(A),B),C) = k2_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(C),A),B) ) ) ) ).
fof(t167_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> k4_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(A,B),C)) = k6_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(A),B),C) ) ) ) ).
fof(t168_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> k4_xcmplx_0(k6_xcmplx_0(k2_xcmplx_0(A,B),C)) = k2_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(A),B),C) ) ) ) ).
fof(t169_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> k4_xcmplx_0(k2_xcmplx_0(k6_xcmplx_0(A,B),C)) = k6_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(A),B),C) ) ) ) ).
fof(t170_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> k4_xcmplx_0(k6_xcmplx_0(k6_xcmplx_0(A,B),C)) = k2_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(A),B),C) ) ) ) ).
fof(t171_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> k4_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(A),B),C)) = k6_xcmplx_0(k6_xcmplx_0(A,B),C) ) ) ) ).
fof(t172_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> k4_xcmplx_0(k6_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(A),B),C)) = k2_xcmplx_0(k6_xcmplx_0(A,B),C) ) ) ) ).
fof(t173_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> k4_xcmplx_0(k2_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(A),B),C)) = k6_xcmplx_0(k2_xcmplx_0(A,B),C) ) ) ) ).
fof(t174_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> k4_xcmplx_0(k6_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(A),B),C)) = k2_xcmplx_0(k2_xcmplx_0(A,B),C) ) ) ) ).
fof(t175_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> k3_xcmplx_0(k4_xcmplx_0(A),B) = k4_xcmplx_0(k3_xcmplx_0(A,B)) ) ) ).
fof(t176_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> k3_xcmplx_0(k4_xcmplx_0(A),B) = k3_xcmplx_0(A,k4_xcmplx_0(B)) ) ) ).
fof(t177_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> k3_xcmplx_0(k4_xcmplx_0(A),k4_xcmplx_0(B)) = k3_xcmplx_0(A,B) ) ) ).
fof(t178_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> k4_xcmplx_0(k3_xcmplx_0(A,k4_xcmplx_0(B))) = k3_xcmplx_0(A,B) ) ) ).
fof(t179_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> k4_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(A),B)) = k3_xcmplx_0(A,B) ) ) ).
fof(t180_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> k3_xcmplx_0(k4_xcmplx_0(np__1),A) = k4_xcmplx_0(A) ) ).
fof(t181_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> k3_xcmplx_0(k4_xcmplx_0(A),k4_xcmplx_0(np__1)) = A ) ).
fof(t182_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ( k3_xcmplx_0(B,A) = k4_xcmplx_0(A)
=> ( A = np__0
| B = k4_xcmplx_0(np__1) ) ) ) ) ).
fof(t183_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ~ ( k3_xcmplx_0(A,A) = np__1
& A != np__1
& A != k4_xcmplx_0(np__1) ) ) ).
fof(t184_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> k2_xcmplx_0(k4_xcmplx_0(A),k3_xcmplx_0(np__2,A)) = A ) ).
fof(t185_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> k3_xcmplx_0(k6_xcmplx_0(A,B),C) = k3_xcmplx_0(k6_xcmplx_0(B,A),k4_xcmplx_0(C)) ) ) ) ).
fof(t186_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> k3_xcmplx_0(k6_xcmplx_0(A,B),C) = k4_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(B,A),C)) ) ) ) ).
fof(t187_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> k6_xcmplx_0(A,k3_xcmplx_0(np__2,A)) = k4_xcmplx_0(A) ) ).
fof(t188_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> k4_xcmplx_0(k7_xcmplx_0(A,B)) = k7_xcmplx_0(k4_xcmplx_0(A),B) ) ) ).
fof(t189_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> k7_xcmplx_0(A,k4_xcmplx_0(B)) = k4_xcmplx_0(k7_xcmplx_0(A,B)) ) ) ).
fof(t190_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> k4_xcmplx_0(k7_xcmplx_0(A,k4_xcmplx_0(B))) = k7_xcmplx_0(A,B) ) ) ).
fof(t191_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> k4_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(A),B)) = k7_xcmplx_0(A,B) ) ) ).
fof(t192_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> k7_xcmplx_0(k4_xcmplx_0(A),k4_xcmplx_0(B)) = k7_xcmplx_0(A,B) ) ) ).
fof(t193_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> k7_xcmplx_0(k4_xcmplx_0(A),B) = k7_xcmplx_0(A,k4_xcmplx_0(B)) ) ) ).
fof(t194_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> k4_xcmplx_0(A) = k7_xcmplx_0(A,k4_xcmplx_0(np__1)) ) ).
fof(t195_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> A = k7_xcmplx_0(k4_xcmplx_0(A),k4_xcmplx_0(np__1)) ) ).
fof(t196_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ( k7_xcmplx_0(A,B) = k4_xcmplx_0(np__1)
=> ( A = k4_xcmplx_0(B)
& B = k4_xcmplx_0(A) ) ) ) ) ).
fof(t197_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ( k7_xcmplx_0(A,B) = k4_xcmplx_0(A)
=> ( A = np__0
| B = k4_xcmplx_0(np__1) ) ) ) ) ).
fof(t198_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ( A != np__0
=> k7_xcmplx_0(k4_xcmplx_0(A),A) = k4_xcmplx_0(np__1) ) ) ).
fof(t199_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ( A != np__0
=> k7_xcmplx_0(A,k4_xcmplx_0(A)) = k4_xcmplx_0(np__1) ) ) ).
fof(t200_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ~ ( A != np__0
& A = k7_xcmplx_0(np__1,A)
& A != np__1
& A != k4_xcmplx_0(np__1) ) ) ).
fof(t201_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> ! [D] :
( v1_xcmplx_0(D)
=> ( k7_xcmplx_0(C,A) = k7_xcmplx_0(D,B)
=> ( A = np__0
| B = np__0
| A = k4_xcmplx_0(B)
| k7_xcmplx_0(C,A) = k7_xcmplx_0(k2_xcmplx_0(C,D),k2_xcmplx_0(A,B)) ) ) ) ) ) ) ).
fof(t202_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ( k5_xcmplx_0(A) = k5_xcmplx_0(B)
=> A = B ) ) ) ).
fof(t203_xcmplx_1,axiom,
k5_xcmplx_0(np__0) = np__0 ).
fof(t204_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ( A != np__0
=> B = k3_xcmplx_0(k3_xcmplx_0(B,A),k5_xcmplx_0(A)) ) ) ) ).
fof(t205_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> k3_xcmplx_0(k5_xcmplx_0(A),k5_xcmplx_0(B)) = k5_xcmplx_0(k3_xcmplx_0(A,B)) ) ) ).
fof(t206_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> k5_xcmplx_0(k3_xcmplx_0(A,k5_xcmplx_0(B))) = k3_xcmplx_0(k5_xcmplx_0(A),B) ) ) ).
fof(t207_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> k5_xcmplx_0(k3_xcmplx_0(k5_xcmplx_0(A),k5_xcmplx_0(B))) = k3_xcmplx_0(A,B) ) ) ).
fof(t208_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ~ ( A != np__0
& B != np__0
& k3_xcmplx_0(A,k5_xcmplx_0(B)) = np__0 ) ) ) ).
fof(t209_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ~ ( A != np__0
& B != np__0
& k3_xcmplx_0(k5_xcmplx_0(A),k5_xcmplx_0(B)) = np__0 ) ) ) ).
fof(t210_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ( k3_xcmplx_0(A,k5_xcmplx_0(B)) = np__1
=> A = B ) ) ) ).
fof(t211_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ( k3_xcmplx_0(A,B) = np__1
=> A = k5_xcmplx_0(B) ) ) ) ).
fof(t212_xcmplx_1,axiom,
$true ).
fof(t213_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ~ ( A != np__0
& B != np__0
& k2_xcmplx_0(k5_xcmplx_0(A),k5_xcmplx_0(B)) != k3_xcmplx_0(k2_xcmplx_0(A,B),k5_xcmplx_0(k3_xcmplx_0(A,B))) ) ) ) ).
fof(t214_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ~ ( A != np__0
& B != np__0
& k6_xcmplx_0(k5_xcmplx_0(A),k5_xcmplx_0(B)) != k3_xcmplx_0(k6_xcmplx_0(B,A),k5_xcmplx_0(k3_xcmplx_0(A,B))) ) ) ) ).
fof(t215_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> k5_xcmplx_0(k7_xcmplx_0(A,B)) = k7_xcmplx_0(B,A) ) ) ).
fof(t216_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> k7_xcmplx_0(k5_xcmplx_0(A),k5_xcmplx_0(B)) = k7_xcmplx_0(B,A) ) ) ).
fof(t217_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> k7_xcmplx_0(np__1,A) = k5_xcmplx_0(A) ) ).
fof(t218_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> k7_xcmplx_0(np__1,k5_xcmplx_0(A)) = A ) ).
fof(t219_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> k5_xcmplx_0(k7_xcmplx_0(np__1,A)) = A ) ).
fof(t220_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ( k7_xcmplx_0(np__1,A) = k5_xcmplx_0(B)
=> A = B ) ) ) ).
fof(t221_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> k7_xcmplx_0(A,k5_xcmplx_0(B)) = k3_xcmplx_0(A,B) ) ) ).
fof(t222_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> k3_xcmplx_0(k5_xcmplx_0(A),k7_xcmplx_0(B,C)) = k7_xcmplx_0(B,k3_xcmplx_0(A,C)) ) ) ) ).
fof(t223_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> k7_xcmplx_0(k5_xcmplx_0(A),B) = k5_xcmplx_0(k3_xcmplx_0(A,B)) ) ) ).
fof(t224_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> k5_xcmplx_0(k4_xcmplx_0(A)) = k4_xcmplx_0(k5_xcmplx_0(A)) ) ).
fof(t225_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ~ ( A != np__0
& A = k5_xcmplx_0(A)
& A != np__1
& A != k4_xcmplx_0(np__1) ) ) ).
fof(t226_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> k6_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(A,B),C),B) = k2_xcmplx_0(A,C) ) ) ) ).
fof(t227_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> k2_xcmplx_0(k2_xcmplx_0(k6_xcmplx_0(A,B),C),B) = k2_xcmplx_0(A,C) ) ) ) ).
fof(t228_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> k6_xcmplx_0(k6_xcmplx_0(k2_xcmplx_0(A,B),C),B) = k6_xcmplx_0(A,C) ) ) ) ).
fof(t229_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> k2_xcmplx_0(k6_xcmplx_0(k6_xcmplx_0(A,B),C),B) = k6_xcmplx_0(A,C) ) ) ) ).
fof(t230_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> k6_xcmplx_0(k6_xcmplx_0(A,A),B) = k4_xcmplx_0(B) ) ) ).
fof(t231_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> k6_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(A),A),B) = k4_xcmplx_0(B) ) ) ).
fof(t232_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> k6_xcmplx_0(k6_xcmplx_0(A,B),A) = k4_xcmplx_0(B) ) ) ).
fof(t233_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> k2_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(A),B),A) = k4_xcmplx_0(B) ) ) ).
fof(t234_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ~ ( B != np__0
& ! [C] :
( v1_xcmplx_0(C)
=> A != k7_xcmplx_0(B,C) ) ) ) ) ).
fof(t235_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> ! [D] :
( v1_xcmplx_0(D)
=> ! [E] :
( v1_xcmplx_0(E)
=> k7_xcmplx_0(A,k3_xcmplx_0(k3_xcmplx_0(B,C),k7_xcmplx_0(D,E))) = k3_xcmplx_0(k7_xcmplx_0(E,C),k7_xcmplx_0(A,k3_xcmplx_0(B,D))) ) ) ) ) ) ).
fof(t236_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> ! [D] :
( v1_xcmplx_0(D)
=> k2_xcmplx_0(k3_xcmplx_0(k7_xcmplx_0(k6_xcmplx_0(A,B),C),D),B) = k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(np__1,k7_xcmplx_0(D,C)),B),k3_xcmplx_0(k7_xcmplx_0(D,C),A)) ) ) ) ) ).
fof(t237_xcmplx_1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( v1_xcmplx_0(C)
=> ( A != np__0
=> k2_xcmplx_0(k3_xcmplx_0(A,B),C) = k3_xcmplx_0(A,k2_xcmplx_0(B,k7_xcmplx_0(C,A))) ) ) ) ) ).
%------------------------------------------------------------------------------