SET007 Axioms: SET007+849.ax
%------------------------------------------------------------------------------
% File : SET007+849 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Short Sheffer Stroke-Based Single Axiom for Boolean Algebras
% 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 : sheffer2 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 171 ( 0 unt; 0 def)
% Number of atoms : 1394 ( 158 equ)
% Maximal formula atoms : 27 ( 8 avg)
% Number of connectives : 1401 ( 178 ~; 0 |; 602 &)
% ( 1 <=>; 620 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 9 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 31 ( 30 usr; 0 prp; 1-2 aty)
% Number of functors : 2 ( 2 usr; 0 con; 1-3 aty)
% Number of variables : 612 ( 610 !; 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(cc1_sheffer2,axiom,
! [A] :
( l1_sheffer1(A)
=> ( ( ~ v3_struct_0(A)
& v3_realset2(A) )
=> ( ~ v3_struct_0(A)
& v1_sheffer2(A) ) ) ) ).
fof(rc1_sheffer2,axiom,
? [A] :
( l1_sheffer1(A)
& ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& v1_sheffer2(A) ) ).
fof(rc2_sheffer2,axiom,
? [A] :
( l3_sheffer1(A)
& ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v6_lattices(A)
& v7_lattices(A)
& v8_lattices(A)
& v9_lattices(A)
& v10_lattices(A)
& v11_lattices(A)
& v12_lattices(A)
& v13_lattices(A)
& v14_lattices(A)
& v15_lattices(A)
& v16_lattices(A)
& v17_lattices(A)
& v7_robbins1(A)
& v9_robbins1(A)
& v1_sheffer1(A)
& v2_sheffer1(A)
& v3_sheffer1(A)
& v4_sheffer1(A)
& v9_sheffer1(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& v1_sheffer2(A) ) ).
fof(cc2_sheffer2,axiom,
! [A] :
( l3_sheffer1(A)
=> ( ( ~ v3_struct_0(A)
& v9_sheffer1(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A) )
=> ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v6_lattices(A)
& v7_lattices(A)
& v8_lattices(A)
& v9_lattices(A)
& v10_lattices(A)
& v11_lattices(A)
& v12_lattices(A)
& v13_lattices(A)
& v14_lattices(A)
& v15_lattices(A)
& v16_lattices(A)
& v17_lattices(A)
& v1_sheffer1(A)
& v2_sheffer1(A)
& v3_sheffer1(A)
& v4_sheffer1(A) ) ) ) ).
fof(cc3_sheffer2,axiom,
! [A] :
( l3_sheffer1(A)
=> ( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v17_lattices(A)
& v7_robbins1(A)
& v9_sheffer1(A) )
=> ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A) ) ) ) ).
fof(cc4_sheffer2,axiom,
! [A] :
( l1_sheffer1(A)
=> ( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A) )
=> ( ~ v3_struct_0(A)
& v1_sheffer2(A) ) ) ) ).
fof(cc5_sheffer2,axiom,
! [A] :
( l1_sheffer1(A)
=> ( ( ~ v3_struct_0(A)
& v1_sheffer2(A) )
=> ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A) ) ) ) ).
fof(cc6_sheffer2,axiom,
! [A] :
( l3_sheffer1(A)
=> ( ( ~ v3_struct_0(A)
& v9_sheffer1(A)
& v1_sheffer2(A) )
=> ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v6_lattices(A)
& v7_lattices(A)
& v8_lattices(A)
& v9_lattices(A)
& v10_lattices(A)
& v11_lattices(A)
& v12_lattices(A)
& v13_lattices(A)
& v14_lattices(A)
& v15_lattices(A)
& v16_lattices(A)
& v17_lattices(A)
& v1_sheffer1(A)
& v2_sheffer1(A)
& v3_sheffer1(A)
& v4_sheffer1(A) ) ) ) ).
fof(cc7_sheffer2,axiom,
! [A] :
( l3_sheffer1(A)
=> ( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v17_lattices(A)
& v7_robbins1(A)
& v9_sheffer1(A) )
=> ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& v1_sheffer2(A) ) ) ) ).
fof(d1_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_sheffer1(A) )
=> ( v1_sheffer2(A)
<=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,B,k5_sheffer1(A,k5_sheffer1(A,C,B),B)),k5_sheffer1(A,C,k5_sheffer1(A,D,B))) = C ) ) ) ) ) ).
fof(t1_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_sheffer2(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,B,k5_sheffer1(A,C,D)),k5_sheffer1(A,B,k5_sheffer1(A,B,k5_sheffer1(A,C,D)))),k5_sheffer1(A,k5_sheffer1(A,D,k5_sheffer1(A,k5_sheffer1(A,B,D),D)),k5_sheffer1(A,E,k5_sheffer1(A,B,k5_sheffer1(A,C,D))))) = k5_sheffer1(A,D,k5_sheffer1(A,k5_sheffer1(A,B,D),D)) ) ) ) ) ) ).
fof(t2_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_sheffer2(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,B,C),k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,C,k5_sheffer1(A,k5_sheffer1(A,D,C),C)),k5_sheffer1(A,B,C)),k5_sheffer1(A,B,C))),D) = k5_sheffer1(A,C,k5_sheffer1(A,k5_sheffer1(A,D,C),C)) ) ) ) ) ).
fof(t3_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_sheffer2(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,B,k5_sheffer1(A,k5_sheffer1(A,C,B),B)),k5_sheffer1(A,C,k5_sheffer1(A,D,k5_sheffer1(A,k5_sheffer1(A,B,D),D)))) = C ) ) ) ) ).
fof(t4_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_sheffer2(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k5_sheffer1(A,B,k5_sheffer1(A,k5_sheffer1(A,B,k5_sheffer1(A,k5_sheffer1(A,B,B),B)),k5_sheffer1(A,C,k5_sheffer1(A,B,k5_sheffer1(A,k5_sheffer1(A,B,B),B))))) = k5_sheffer1(A,B,k5_sheffer1(A,k5_sheffer1(A,B,B),B)) ) ) ) ).
fof(t5_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_sheffer2(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k5_sheffer1(A,B,k5_sheffer1(A,k5_sheffer1(A,B,B),B)) = k5_sheffer1(A,B,B) ) ) ).
fof(t6_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_sheffer2(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,B,k5_sheffer1(A,k5_sheffer1(A,B,B),B)),k5_sheffer1(A,B,B)) = B ) ) ).
fof(t7_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_sheffer2(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,B,B),k5_sheffer1(A,B,k5_sheffer1(A,C,B))) = B ) ) ) ).
fof(t8_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_sheffer2(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,B,k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,C,C),B),B)),C) = k5_sheffer1(A,C,C) ) ) ) ).
fof(t9_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_sheffer2(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,B,C),k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,B,C),k5_sheffer1(A,B,C)),k5_sheffer1(A,B,C))),k5_sheffer1(A,k5_sheffer1(A,B,C),k5_sheffer1(A,B,C))) = k5_sheffer1(A,C,k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,B,C),k5_sheffer1(A,B,C)),C),C)) ) ) ) ).
fof(t10_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_sheffer2(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k5_sheffer1(A,B,k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,C,B),k5_sheffer1(A,C,B)),B),B)) = k5_sheffer1(A,C,B) ) ) ) ).
fof(t11_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_sheffer2(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,B,B),k5_sheffer1(A,C,B)) = B ) ) ) ).
fof(t12_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_sheffer2(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k5_sheffer1(A,B,k5_sheffer1(A,C,k5_sheffer1(A,B,B))) = k5_sheffer1(A,B,B) ) ) ) ).
fof(t13_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_sheffer2(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,B,C),k5_sheffer1(A,B,C)),C) = k5_sheffer1(A,B,C) ) ) ) ).
fof(t14_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_sheffer2(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k5_sheffer1(A,B,k5_sheffer1(A,k5_sheffer1(A,C,B),B)) = k5_sheffer1(A,C,B) ) ) ) ).
fof(t15_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_sheffer2(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,B,C),k5_sheffer1(A,B,k5_sheffer1(A,D,C))) = B ) ) ) ) ).
fof(t16_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_sheffer2(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,B,k5_sheffer1(A,C,D)),k5_sheffer1(A,B,D)) = B ) ) ) ) ).
fof(t17_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_sheffer2(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k5_sheffer1(A,B,k5_sheffer1(A,k5_sheffer1(A,B,C),k5_sheffer1(A,D,C))) = k5_sheffer1(A,B,C) ) ) ) ) ).
fof(t18_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_sheffer2(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,B,k5_sheffer1(A,C,D)),D),B) = k5_sheffer1(A,B,k5_sheffer1(A,C,D)) ) ) ) ) ).
fof(t19_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_sheffer2(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k5_sheffer1(A,B,k5_sheffer1(A,k5_sheffer1(A,C,B),B)) = k5_sheffer1(A,B,C) ) ) ) ).
fof(t20_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_sheffer2(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k5_sheffer1(A,B,C) = k5_sheffer1(A,C,B) ) ) ) ).
fof(t21_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_sheffer2(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,B,C),k5_sheffer1(A,B,B)) = B ) ) ) ).
fof(t22_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_sheffer2(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,B,C),k5_sheffer1(A,C,k5_sheffer1(A,D,B))) = C ) ) ) ) ).
fof(t23_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_sheffer2(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,B,k5_sheffer1(A,C,D)),k5_sheffer1(A,D,B)) = B ) ) ) ) ).
fof(t24_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_sheffer2(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,B,C),k5_sheffer1(A,C,k5_sheffer1(A,B,D))) = C ) ) ) ) ).
fof(t25_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_sheffer2(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,B,k5_sheffer1(A,C,D)),k5_sheffer1(A,C,B)) = B ) ) ) ) ).
fof(t26_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_sheffer2(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,B,C),k5_sheffer1(A,B,D)),D) = k5_sheffer1(A,B,D) ) ) ) ) ).
fof(t27_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_sheffer2(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k5_sheffer1(A,B,k5_sheffer1(A,C,k5_sheffer1(A,B,k5_sheffer1(A,C,D)))) = k5_sheffer1(A,B,k5_sheffer1(A,C,D)) ) ) ) ) ).
fof(t28_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_sheffer2(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,B,k5_sheffer1(A,C,k5_sheffer1(A,B,D))),C) = k5_sheffer1(A,C,k5_sheffer1(A,B,D)) ) ) ) ) ).
fof(t29_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_sheffer2(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,B,k5_sheffer1(A,C,D)),k5_sheffer1(A,B,k5_sheffer1(A,E,k5_sheffer1(A,C,B)))) = k5_sheffer1(A,k5_sheffer1(A,B,k5_sheffer1(A,C,D)),k5_sheffer1(A,C,B)) ) ) ) ) ) ).
fof(t30_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_sheffer2(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,B,k5_sheffer1(A,C,k5_sheffer1(A,B,D))),C) = k5_sheffer1(A,C,k5_sheffer1(A,D,B)) ) ) ) ) ).
fof(t31_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_sheffer2(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,B,k5_sheffer1(A,C,D)),k5_sheffer1(A,B,k5_sheffer1(A,E,k5_sheffer1(A,C,B)))) = B ) ) ) ) ) ).
fof(t32_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_sheffer2(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k5_sheffer1(A,B,k5_sheffer1(A,C,k5_sheffer1(A,B,C))) = k5_sheffer1(A,B,B) ) ) ) ).
fof(t33_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_sheffer2(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k5_sheffer1(A,B,k5_sheffer1(A,C,D)) = k5_sheffer1(A,B,k5_sheffer1(A,D,C)) ) ) ) ) ).
fof(t34_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_sheffer2(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k5_sheffer1(A,B,k5_sheffer1(A,C,k5_sheffer1(A,B,k5_sheffer1(A,D,k5_sheffer1(A,C,B))))) = k5_sheffer1(A,B,B) ) ) ) ) ).
fof(t35_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_sheffer2(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,B,k5_sheffer1(A,C,D)),k5_sheffer1(A,k5_sheffer1(A,C,B),B)) = k5_sheffer1(A,k5_sheffer1(A,B,k5_sheffer1(A,C,D)),k5_sheffer1(A,B,k5_sheffer1(A,C,D))) ) ) ) ) ).
fof(t36_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_sheffer2(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,B,k5_sheffer1(A,C,B)),C) = k5_sheffer1(A,C,C) ) ) ) ).
fof(t37_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_sheffer2(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,B,C),D) = k5_sheffer1(A,D,k5_sheffer1(A,C,B)) ) ) ) ) ).
fof(t38_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_sheffer2(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k5_sheffer1(A,B,k5_sheffer1(A,C,k5_sheffer1(A,D,k5_sheffer1(A,B,C)))) = k5_sheffer1(A,B,k5_sheffer1(A,C,C)) ) ) ) ) ).
fof(t39_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_sheffer2(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,B,C),C),k5_sheffer1(A,C,k5_sheffer1(A,D,B))) = k5_sheffer1(A,k5_sheffer1(A,C,k5_sheffer1(A,D,B)),k5_sheffer1(A,C,k5_sheffer1(A,D,B))) ) ) ) ) ).
fof(t40_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_sheffer2(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,B,C),k5_sheffer1(A,D,E)) = k5_sheffer1(A,k5_sheffer1(A,E,D),k5_sheffer1(A,C,B)) ) ) ) ) ) ).
fof(t41_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_sheffer2(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k5_sheffer1(A,B,k5_sheffer1(A,C,k5_sheffer1(A,k5_sheffer1(A,C,B),D))) = k5_sheffer1(A,B,k5_sheffer1(A,C,C)) ) ) ) ) ).
fof(t42_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_sheffer2(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k5_sheffer1(A,B,k5_sheffer1(A,C,B)) = k5_sheffer1(A,B,k5_sheffer1(A,C,C)) ) ) ) ).
fof(t43_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_sheffer2(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,B,C),C) = k5_sheffer1(A,C,k5_sheffer1(A,B,B)) ) ) ) ).
fof(t44_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_sheffer2(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k5_sheffer1(A,B,k5_sheffer1(A,C,C)) = k5_sheffer1(A,B,k5_sheffer1(A,B,C)) ) ) ) ).
fof(t45_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_sheffer2(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,B,k5_sheffer1(A,C,C)),k5_sheffer1(A,B,k5_sheffer1(A,D,C))) = k5_sheffer1(A,k5_sheffer1(A,B,k5_sheffer1(A,D,C)),k5_sheffer1(A,B,k5_sheffer1(A,D,C))) ) ) ) ) ).
fof(t46_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_sheffer2(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,B,k5_sheffer1(A,C,D)),k5_sheffer1(A,B,k5_sheffer1(A,C,C))) = k5_sheffer1(A,k5_sheffer1(A,B,k5_sheffer1(A,C,D)),k5_sheffer1(A,B,k5_sheffer1(A,C,D))) ) ) ) ) ).
fof(t47_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_sheffer2(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k5_sheffer1(A,B,k5_sheffer1(A,k5_sheffer1(A,C,C),k5_sheffer1(A,D,k5_sheffer1(A,B,k5_sheffer1(A,B,C))))) = k5_sheffer1(A,B,k5_sheffer1(A,k5_sheffer1(A,C,C),k5_sheffer1(A,C,C))) ) ) ) ) ).
fof(t48_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_sheffer2(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,B,k5_sheffer1(A,C,D)),k5_sheffer1(A,B,k5_sheffer1(A,C,D))),k5_sheffer1(A,C,C)) = k5_sheffer1(A,B,k5_sheffer1(A,C,C)) ) ) ) ) ).
fof(t49_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_sheffer2(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k5_sheffer1(A,B,k5_sheffer1(A,k5_sheffer1(A,C,C),k5_sheffer1(A,D,k5_sheffer1(A,B,k5_sheffer1(A,B,C))))) = k5_sheffer1(A,B,C) ) ) ) ) ).
fof(t50_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_sheffer2(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,B,C),k5_sheffer1(A,B,C)),k5_sheffer1(A,k5_sheffer1(A,D,k5_sheffer1(A,k5_sheffer1(A,B,C),D)),k5_sheffer1(A,B,C))),k5_sheffer1(A,B,B)) = k5_sheffer1(A,k5_sheffer1(A,D,k5_sheffer1(A,k5_sheffer1(A,B,C),D)),k5_sheffer1(A,B,B)) ) ) ) ) ).
fof(t51_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_sheffer2(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,B,k5_sheffer1(A,k5_sheffer1(A,C,D),B)),k5_sheffer1(A,C,C)) = k5_sheffer1(A,k5_sheffer1(A,C,D),k5_sheffer1(A,C,C)) ) ) ) ) ).
fof(t52_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_sheffer2(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,B,k5_sheffer1(A,k5_sheffer1(A,C,D),B)),k5_sheffer1(A,C,C)) = C ) ) ) ) ).
fof(t53_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_sheffer2(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k5_sheffer1(A,B,k5_sheffer1(A,k5_sheffer1(A,C,k5_sheffer1(A,k5_sheffer1(A,B,D),C)),B)) = k5_sheffer1(A,C,k5_sheffer1(A,k5_sheffer1(A,B,D),C)) ) ) ) ) ).
fof(t54_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_sheffer2(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k5_sheffer1(A,B,k5_sheffer1(A,k5_sheffer1(A,C,k5_sheffer1(A,C,k5_sheffer1(A,D,B))),B)) = k5_sheffer1(A,C,k5_sheffer1(A,k5_sheffer1(A,B,k5_sheffer1(A,C,k5_sheffer1(A,B,D))),C)) ) ) ) ) ).
fof(t55_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_sheffer2(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k5_sheffer1(A,B,k5_sheffer1(A,k5_sheffer1(A,C,k5_sheffer1(A,C,k5_sheffer1(A,D,B))),B)) = k5_sheffer1(A,C,k5_sheffer1(A,C,k5_sheffer1(A,D,B))) ) ) ) ) ).
fof(t56_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_sheffer2(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> k5_sheffer1(A,B,k5_sheffer1(A,C,k5_sheffer1(A,D,k5_sheffer1(A,D,k5_sheffer1(A,E,k5_sheffer1(A,C,B)))))) = k5_sheffer1(A,B,k5_sheffer1(A,C,C)) ) ) ) ) ) ).
fof(t57_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_sheffer2(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k5_sheffer1(A,B,k5_sheffer1(A,C,k5_sheffer1(A,C,k5_sheffer1(A,D,k5_sheffer1(A,B,C))))) = k5_sheffer1(A,B,k5_sheffer1(A,C,k5_sheffer1(A,B,B))) ) ) ) ) ).
fof(t58_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_sheffer2(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k5_sheffer1(A,B,k5_sheffer1(A,C,k5_sheffer1(A,C,k5_sheffer1(A,D,k5_sheffer1(A,B,C))))) = k5_sheffer1(A,B,B) ) ) ) ) ).
fof(t59_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_sheffer2(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k5_sheffer1(A,B,k5_sheffer1(A,C,k5_sheffer1(A,C,C))) = k5_sheffer1(A,B,B) ) ) ) ).
fof(t60_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_sheffer2(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k5_sheffer1(A,B,k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,C,k5_sheffer1(A,D,B)),k5_sheffer1(A,C,k5_sheffer1(A,D,B))),k5_sheffer1(A,D,D))) = k5_sheffer1(A,B,k5_sheffer1(A,C,k5_sheffer1(A,D,B))) ) ) ) ) ).
fof(t61_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_sheffer2(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k5_sheffer1(A,B,k5_sheffer1(A,C,k5_sheffer1(A,D,D))) = k5_sheffer1(A,B,k5_sheffer1(A,C,k5_sheffer1(A,D,B))) ) ) ) ) ).
fof(t62_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_sheffer2(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k5_sheffer1(A,B,k5_sheffer1(A,C,k5_sheffer1(A,k5_sheffer1(A,D,D),B))) = k5_sheffer1(A,B,k5_sheffer1(A,C,D)) ) ) ) ) ).
fof(t63_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_sheffer2(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,B,k5_sheffer1(A,C,C)),k5_sheffer1(A,B,k5_sheffer1(A,D,k5_sheffer1(A,k5_sheffer1(A,C,C),B)))) = k5_sheffer1(A,k5_sheffer1(A,B,k5_sheffer1(A,D,C)),k5_sheffer1(A,B,k5_sheffer1(A,D,C))) ) ) ) ) ).
fof(t64_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_sheffer2(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,B,k5_sheffer1(A,C,C)),k5_sheffer1(A,B,k5_sheffer1(A,D,k5_sheffer1(A,B,k5_sheffer1(A,C,C))))) = k5_sheffer1(A,k5_sheffer1(A,B,k5_sheffer1(A,D,C)),k5_sheffer1(A,B,k5_sheffer1(A,D,C))) ) ) ) ) ).
fof(t65_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_sheffer2(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,B,k5_sheffer1(A,C,C)),k5_sheffer1(A,B,k5_sheffer1(A,D,D))) = k5_sheffer1(A,k5_sheffer1(A,B,k5_sheffer1(A,D,C)),k5_sheffer1(A,B,k5_sheffer1(A,D,C))) ) ) ) ) ).
fof(t66_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_sheffer2(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,B,B),C),k5_sheffer1(A,k5_sheffer1(A,D,D),C)) = k5_sheffer1(A,k5_sheffer1(A,C,k5_sheffer1(A,B,D)),k5_sheffer1(A,C,k5_sheffer1(A,B,D))) ) ) ) ) ).
fof(t67_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_sheffer1(A) )
=> ( v1_sheffer2(A)
=> v10_sheffer1(A) ) ) ).
fof(t68_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_sheffer1(A) )
=> ( v1_sheffer2(A)
=> v11_sheffer1(A) ) ) ).
fof(t69_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_sheffer1(A) )
=> ( v1_sheffer2(A)
=> v12_sheffer1(A) ) ) ).
fof(t70_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k5_sheffer1(A,C,k5_sheffer1(A,k5_sheffer1(A,B,B),B)) = k5_sheffer1(A,C,C) ) ) ) ).
fof(t71_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> C = k5_sheffer1(A,k5_sheffer1(A,C,C),k5_sheffer1(A,B,k5_sheffer1(A,B,B))) ) ) ) ).
fof(t72_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,C,C),k5_sheffer1(A,C,k5_sheffer1(A,B,k5_sheffer1(A,B,B)))) = C ) ) ) ).
fof(t73_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,E,k5_sheffer1(A,D,k5_sheffer1(A,D,D))),C),k5_sheffer1(A,k5_sheffer1(A,B,B),C)) = k5_sheffer1(A,k5_sheffer1(A,C,k5_sheffer1(A,E,B)),k5_sheffer1(A,C,k5_sheffer1(A,E,B))) ) ) ) ) ) ).
fof(t74_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,D,C),k5_sheffer1(A,k5_sheffer1(A,B,B),C)) = k5_sheffer1(A,k5_sheffer1(A,C,k5_sheffer1(A,k5_sheffer1(A,D,D),B)),k5_sheffer1(A,C,k5_sheffer1(A,k5_sheffer1(A,D,D),B))) ) ) ) ) ).
fof(t75_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,B,B),C),k5_sheffer1(A,k5_sheffer1(A,E,k5_sheffer1(A,D,k5_sheffer1(A,D,D))),C)) = k5_sheffer1(A,k5_sheffer1(A,C,k5_sheffer1(A,B,E)),k5_sheffer1(A,C,k5_sheffer1(A,B,E))) ) ) ) ) ) ).
fof(t76_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> C = k5_sheffer1(A,k5_sheffer1(A,C,C),k5_sheffer1(A,k5_sheffer1(A,B,B),B)) ) ) ) ).
fof(t77_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,C,C),k5_sheffer1(A,C,k5_sheffer1(A,k5_sheffer1(A,B,B),B))) = C ) ) ) ).
fof(t78_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,C,k5_sheffer1(A,k5_sheffer1(A,B,B),B)),k5_sheffer1(A,C,C)) = C ) ) ) ).
fof(t79_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,D,k5_sheffer1(A,k5_sheffer1(A,C,C),C)),k5_sheffer1(A,B,k5_sheffer1(A,B,B))) = D ) ) ) ) ).
fof(t80_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,D,k5_sheffer1(A,C,C)),k5_sheffer1(A,D,k5_sheffer1(A,C,C))),k5_sheffer1(A,B,k5_sheffer1(A,B,B))) = k5_sheffer1(A,k5_sheffer1(A,C,C),D) ) ) ) ) ).
fof(t81_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k5_sheffer1(A,C,k5_sheffer1(A,B,B)) = k5_sheffer1(A,k5_sheffer1(A,B,B),C) ) ) ) ).
fof(t82_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k5_sheffer1(A,C,B) = k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,B,B),k5_sheffer1(A,B,B)),C) ) ) ) ).
fof(t83_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k5_sheffer1(A,C,B) = k5_sheffer1(A,B,C) ) ) ) ).
fof(t84_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,C,B),k5_sheffer1(A,C,k5_sheffer1(A,k5_sheffer1(A,B,B),k5_sheffer1(A,B,B)))) = k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,B,B),k5_sheffer1(A,B,B)),C),k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,B,B),k5_sheffer1(A,B,B)),C)) ) ) ) ).
fof(t85_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,C,B),k5_sheffer1(A,C,B)) = k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,B,B),k5_sheffer1(A,B,B)),C),k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,B,B),k5_sheffer1(A,B,B)),C)) ) ) ) ).
fof(t86_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,C,B),k5_sheffer1(A,C,B)) = k5_sheffer1(A,k5_sheffer1(A,B,C),k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,B,B),k5_sheffer1(A,B,B)),C)) ) ) ) ).
fof(t87_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,C,B),k5_sheffer1(A,C,B)) = k5_sheffer1(A,k5_sheffer1(A,B,C),k5_sheffer1(A,B,C)) ) ) ) ).
fof(t88_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,D,C),k5_sheffer1(A,k5_sheffer1(A,B,B),B)),k5_sheffer1(A,k5_sheffer1(A,D,C),k5_sheffer1(A,D,C))) = k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,D,D),k5_sheffer1(A,D,C)),k5_sheffer1(A,k5_sheffer1(A,C,C),k5_sheffer1(A,D,C))) ) ) ) ) ).
fof(t89_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k5_sheffer1(A,C,B) = k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,C,C),k5_sheffer1(A,C,B)),k5_sheffer1(A,k5_sheffer1(A,B,B),k5_sheffer1(A,C,B))) ) ) ) ).
fof(t90_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,C,C),k5_sheffer1(A,C,k5_sheffer1(A,k5_sheffer1(A,B,B),B))) = k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,B,B),k5_sheffer1(A,B,B)),C),k5_sheffer1(A,k5_sheffer1(A,B,B),C)) ) ) ) ).
fof(t91_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> B = k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,C,C),k5_sheffer1(A,C,C)),B),k5_sheffer1(A,k5_sheffer1(A,C,C),B)) ) ) ) ).
fof(t92_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> B = k5_sheffer1(A,k5_sheffer1(A,C,B),k5_sheffer1(A,k5_sheffer1(A,C,C),B)) ) ) ) ).
fof(t93_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,D,D),C),k5_sheffer1(A,k5_sheffer1(A,B,B),C)),k5_sheffer1(A,k5_sheffer1(A,C,k5_sheffer1(A,D,B)),k5_sheffer1(A,C,k5_sheffer1(A,D,B)))) = k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,C,C),k5_sheffer1(A,C,k5_sheffer1(A,D,B))),k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,D,B),k5_sheffer1(A,D,B)),k5_sheffer1(A,C,k5_sheffer1(A,D,B)))) ) ) ) ) ).
fof(t94_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,D,D),C),k5_sheffer1(A,k5_sheffer1(A,B,B),C)),k5_sheffer1(A,k5_sheffer1(A,C,k5_sheffer1(A,D,B)),k5_sheffer1(A,C,k5_sheffer1(A,D,B)))) = k5_sheffer1(A,C,k5_sheffer1(A,D,B)) ) ) ) ) ).
fof(t95_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,C,C),k5_sheffer1(A,C,k5_sheffer1(A,B,k5_sheffer1(A,B,B)))) = k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,B,B),C),k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,B,B),k5_sheffer1(A,B,B)),C)) ) ) ) ).
fof(t96_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> B = k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,C,C),B),k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,C,C),k5_sheffer1(A,C,C)),B)) ) ) ) ).
fof(t97_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> B = k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,C,C),B),k5_sheffer1(A,C,B)) ) ) ) ).
fof(t98_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,D,D),C),k5_sheffer1(A,k5_sheffer1(A,B,B),C)),k5_sheffer1(A,k5_sheffer1(A,C,k5_sheffer1(A,D,B)),k5_sheffer1(A,C,k5_sheffer1(A,D,B)))) = k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,B,B),k5_sheffer1(A,B,B)),k5_sheffer1(A,k5_sheffer1(A,D,D),C)),k5_sheffer1(A,k5_sheffer1(A,C,C),k5_sheffer1(A,k5_sheffer1(A,D,D),C))) ) ) ) ) ).
fof(t99_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k5_sheffer1(A,B,k5_sheffer1(A,D,C)) = k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,C,C),k5_sheffer1(A,C,C)),k5_sheffer1(A,k5_sheffer1(A,D,D),B)),k5_sheffer1(A,k5_sheffer1(A,B,B),k5_sheffer1(A,k5_sheffer1(A,D,D),B))) ) ) ) ) ).
fof(t100_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k5_sheffer1(A,B,k5_sheffer1(A,D,C)) = k5_sheffer1(A,k5_sheffer1(A,C,k5_sheffer1(A,k5_sheffer1(A,D,D),B)),k5_sheffer1(A,k5_sheffer1(A,B,B),k5_sheffer1(A,k5_sheffer1(A,D,D),B))) ) ) ) ) ).
fof(t101_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k5_sheffer1(A,B,B) = k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,C,C),C),B) ) ) ) ).
fof(t102_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,C,B),k5_sheffer1(A,k5_sheffer1(A,B,B),C)) = C ) ) ) ).
fof(t103_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,C,C),k5_sheffer1(A,k5_sheffer1(A,C,C),k5_sheffer1(A,k5_sheffer1(A,B,B),B))) = k5_sheffer1(A,k5_sheffer1(A,B,B),B) ) ) ) ).
fof(t104_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,C,C),C) = k5_sheffer1(A,k5_sheffer1(A,B,B),B) ) ) ) ).
fof(t105_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,C,B),k5_sheffer1(A,B,k5_sheffer1(A,C,C))) = B ) ) ) ).
fof(t106_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,C,k5_sheffer1(A,B,B)),k5_sheffer1(A,B,C)) = C ) ) ) ).
fof(t107_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,C,B),k5_sheffer1(A,C,k5_sheffer1(A,B,B))) = C ) ) ) ).
fof(t108_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k5_sheffer1(A,C,k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,C,k5_sheffer1(A,B,B)),k5_sheffer1(A,C,k5_sheffer1(A,B,B))),k5_sheffer1(A,B,C))) = k5_sheffer1(A,B,C) ) ) ) ).
fof(t109_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,C,k5_sheffer1(A,B,B)),k5_sheffer1(A,C,B)) = C ) ) ) ).
fof(t110_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,E,E),E),D),k5_sheffer1(A,k5_sheffer1(A,C,C),D)) = k5_sheffer1(A,k5_sheffer1(A,D,k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,B,k5_sheffer1(A,B,B)),k5_sheffer1(A,B,k5_sheffer1(A,B,B))),C)),k5_sheffer1(A,D,k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,B,k5_sheffer1(A,B,B)),k5_sheffer1(A,B,k5_sheffer1(A,B,B))),C))) ) ) ) ) ) ).
fof(t111_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,B,B),k5_sheffer1(A,k5_sheffer1(A,C,C),B)) = k5_sheffer1(A,k5_sheffer1(A,B,k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,D,k5_sheffer1(A,D,D)),k5_sheffer1(A,D,k5_sheffer1(A,D,D))),C)),k5_sheffer1(A,B,k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,D,k5_sheffer1(A,D,D)),k5_sheffer1(A,D,k5_sheffer1(A,D,D))),C))) ) ) ) ) ).
fof(t112_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,B,D),k5_sheffer1(A,B,k5_sheffer1(A,D,k5_sheffer1(A,C,k5_sheffer1(A,C,C))))) = B ) ) ) ) ).
fof(t113_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,B,k5_sheffer1(A,D,k5_sheffer1(A,C,k5_sheffer1(A,C,C)))),k5_sheffer1(A,B,D)) = B ) ) ) ) ).
fof(t114_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,D,D),D),C),k5_sheffer1(A,k5_sheffer1(A,B,B),C)) = k5_sheffer1(A,k5_sheffer1(A,C,k5_sheffer1(A,k5_sheffer1(A,C,C),B)),k5_sheffer1(A,C,k5_sheffer1(A,k5_sheffer1(A,C,C),B))) ) ) ) ) ).
fof(t115_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,B,k5_sheffer1(A,k5_sheffer1(A,D,D),C)),k5_sheffer1(A,B,k5_sheffer1(A,k5_sheffer1(A,D,D),C))),k5_sheffer1(A,k5_sheffer1(A,D,B),k5_sheffer1(A,k5_sheffer1(A,C,C),B))) = k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,C,C),k5_sheffer1(A,C,C)),k5_sheffer1(A,D,B)),k5_sheffer1(A,k5_sheffer1(A,B,B),k5_sheffer1(A,D,B))) ) ) ) ) ).
fof(t116_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,B,k5_sheffer1(A,k5_sheffer1(A,D,D),C)),k5_sheffer1(A,B,k5_sheffer1(A,k5_sheffer1(A,D,D),C))),k5_sheffer1(A,k5_sheffer1(A,D,B),k5_sheffer1(A,k5_sheffer1(A,C,C),B))) = k5_sheffer1(A,k5_sheffer1(A,C,k5_sheffer1(A,D,B)),k5_sheffer1(A,k5_sheffer1(A,B,B),k5_sheffer1(A,D,B))) ) ) ) ) ).
fof(t117_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,B,B),k5_sheffer1(A,k5_sheffer1(A,D,D),C)),k5_sheffer1(A,k5_sheffer1(A,C,k5_sheffer1(A,k5_sheffer1(A,C,C),D)),k5_sheffer1(A,C,k5_sheffer1(A,k5_sheffer1(A,C,C),D)))) = k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,D,D),C),k5_sheffer1(A,B,C)),k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,D,D),C),k5_sheffer1(A,B,C))) ) ) ) ) ).
fof(t118_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,C,k5_sheffer1(A,D,C)),k5_sheffer1(A,C,k5_sheffer1(A,D,C))),k5_sheffer1(A,B,k5_sheffer1(A,B,B))) = k5_sheffer1(A,k5_sheffer1(A,D,D),C) ) ) ) ) ).
fof(t119_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k5_sheffer1(A,B,k5_sheffer1(A,C,B)) = k5_sheffer1(A,k5_sheffer1(A,C,C),B) ) ) ) ).
fof(t120_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,C,B),k5_sheffer1(A,k5_sheffer1(A,C,C),B)) = k5_sheffer1(A,k5_sheffer1(A,B,B),k5_sheffer1(A,C,B)) ) ) ) ).
fof(t121_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> B = k5_sheffer1(A,k5_sheffer1(A,B,B),k5_sheffer1(A,C,B)) ) ) ) ).
fof(t122_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,C,B),B) = k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,B,k5_sheffer1(A,C,C)),k5_sheffer1(A,B,k5_sheffer1(A,C,C))),k5_sheffer1(A,C,B)) ) ) ) ).
fof(t123_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,B,k5_sheffer1(A,k5_sheffer1(A,D,D),C)),k5_sheffer1(A,B,k5_sheffer1(A,k5_sheffer1(A,D,D),C))),k5_sheffer1(A,k5_sheffer1(A,D,B),k5_sheffer1(A,k5_sheffer1(A,C,C),B))) = k5_sheffer1(A,k5_sheffer1(A,C,k5_sheffer1(A,D,B)),B) ) ) ) ) ).
fof(t124_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,B,k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,D,k5_sheffer1(A,D,D)),k5_sheffer1(A,D,k5_sheffer1(A,D,D))),C)),k5_sheffer1(A,B,k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,D,k5_sheffer1(A,D,D)),k5_sheffer1(A,D,k5_sheffer1(A,D,D))),C))) = B ) ) ) ) ).
fof(t125_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,B,k5_sheffer1(A,k5_sheffer1(A,D,D),C)),C) = k5_sheffer1(A,C,k5_sheffer1(A,D,B)) ) ) ) ) ).
fof(t126_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k5_sheffer1(A,B,k5_sheffer1(A,k5_sheffer1(A,C,B),B)) = k5_sheffer1(A,C,B) ) ) ) ).
fof(t127_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> C = k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,D,D),D),C),k5_sheffer1(A,k5_sheffer1(A,B,B),C)) ) ) ) ) ).
fof(t128_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,C,k5_sheffer1(A,k5_sheffer1(A,C,C),B)),k5_sheffer1(A,C,k5_sheffer1(A,k5_sheffer1(A,C,C),B))) = C ) ) ) ).
fof(t129_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,D,D),C),k5_sheffer1(A,B,C)),k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,D,D),C),k5_sheffer1(A,B,C))) = k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,B,B),k5_sheffer1(A,k5_sheffer1(A,D,D),C)),C) ) ) ) ) ).
fof(t130_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,D,D),C),k5_sheffer1(A,B,C)),k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,D,D),C),k5_sheffer1(A,B,C))) = k5_sheffer1(A,C,k5_sheffer1(A,D,k5_sheffer1(A,B,B))) ) ) ) ) ).
fof(t131_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,C,B),k5_sheffer1(A,C,B)),C) = k5_sheffer1(A,C,B) ) ) ) ).
fof(t132_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,C,C),k5_sheffer1(A,C,B)) = C ) ) ) ).
fof(t133_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,C,B),k5_sheffer1(A,B,B)) = B ) ) ) ).
fof(t134_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,D,k5_sheffer1(A,C,k5_sheffer1(A,C,C))),k5_sheffer1(A,D,B)) = D ) ) ) ) ).
fof(t135_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,C,B),k5_sheffer1(A,C,C)) = C ) ) ) ).
fof(t136_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,D,C),k5_sheffer1(A,D,k5_sheffer1(A,B,k5_sheffer1(A,B,B)))) = D ) ) ) ) ).
fof(t137_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,F,k5_sheffer1(A,E,k5_sheffer1(A,E,E))),D),k5_sheffer1(A,k5_sheffer1(A,C,C),D)),k5_sheffer1(A,k5_sheffer1(A,D,k5_sheffer1(A,F,C)),k5_sheffer1(A,D,k5_sheffer1(A,F,C)))) = k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,D,k5_sheffer1(A,B,k5_sheffer1(A,B,B))),k5_sheffer1(A,D,k5_sheffer1(A,F,C))),k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,F,C),k5_sheffer1(A,F,C)),k5_sheffer1(A,D,k5_sheffer1(A,F,C)))) ) ) ) ) ) ) ).
fof(t138_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,E,k5_sheffer1(A,D,k5_sheffer1(A,D,D))),C),k5_sheffer1(A,k5_sheffer1(A,B,B),C)),k5_sheffer1(A,k5_sheffer1(A,C,k5_sheffer1(A,E,B)),k5_sheffer1(A,C,k5_sheffer1(A,E,B)))) = k5_sheffer1(A,C,k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,E,B),k5_sheffer1(A,E,B)),k5_sheffer1(A,C,k5_sheffer1(A,E,B)))) ) ) ) ) ) ).
fof(t139_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,E,k5_sheffer1(A,D,k5_sheffer1(A,D,D))),C),k5_sheffer1(A,k5_sheffer1(A,B,B),C)),k5_sheffer1(A,k5_sheffer1(A,C,k5_sheffer1(A,E,B)),k5_sheffer1(A,C,k5_sheffer1(A,E,B)))) = k5_sheffer1(A,C,k5_sheffer1(A,E,B)) ) ) ) ) ) ).
fof(t140_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,F,k5_sheffer1(A,E,k5_sheffer1(A,E,E))),D),k5_sheffer1(A,k5_sheffer1(A,B,B),D)),k5_sheffer1(A,k5_sheffer1(A,D,k5_sheffer1(A,F,B)),k5_sheffer1(A,D,k5_sheffer1(A,F,B)))) = k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,B,B),k5_sheffer1(A,C,k5_sheffer1(A,C,C))),k5_sheffer1(A,k5_sheffer1(A,F,k5_sheffer1(A,E,k5_sheffer1(A,E,E))),D)),k5_sheffer1(A,k5_sheffer1(A,D,D),k5_sheffer1(A,k5_sheffer1(A,F,k5_sheffer1(A,E,k5_sheffer1(A,E,E))),D))) ) ) ) ) ) ) ).
fof(t141_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> k5_sheffer1(A,D,k5_sheffer1(A,F,B)) = k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,B,B),k5_sheffer1(A,C,k5_sheffer1(A,C,C))),k5_sheffer1(A,k5_sheffer1(A,F,k5_sheffer1(A,E,k5_sheffer1(A,E,E))),D)),k5_sheffer1(A,k5_sheffer1(A,D,D),k5_sheffer1(A,k5_sheffer1(A,F,k5_sheffer1(A,E,k5_sheffer1(A,E,E))),D))) ) ) ) ) ) ) ).
fof(t142_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> k5_sheffer1(A,C,k5_sheffer1(A,E,B)) = k5_sheffer1(A,k5_sheffer1(A,B,k5_sheffer1(A,k5_sheffer1(A,E,k5_sheffer1(A,D,k5_sheffer1(A,D,D))),C)),k5_sheffer1(A,k5_sheffer1(A,C,C),k5_sheffer1(A,k5_sheffer1(A,E,k5_sheffer1(A,D,k5_sheffer1(A,D,D))),C))) ) ) ) ) ) ).
fof(t143_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> k5_sheffer1(A,C,k5_sheffer1(A,E,B)) = k5_sheffer1(A,k5_sheffer1(A,B,k5_sheffer1(A,k5_sheffer1(A,E,k5_sheffer1(A,D,k5_sheffer1(A,D,D))),C)),C) ) ) ) ) ) ).
fof(t144_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,C,k5_sheffer1(A,D,k5_sheffer1(A,F,E))),k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,F,k5_sheffer1(A,B,k5_sheffer1(A,B,B))),D),k5_sheffer1(A,k5_sheffer1(A,E,E),D))) = k5_sheffer1(A,D,k5_sheffer1(A,F,E)) ) ) ) ) ) ) ).
fof(t145_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,B,k5_sheffer1(A,k5_sheffer1(A,D,D),C)),k5_sheffer1(A,B,k5_sheffer1(A,k5_sheffer1(A,D,D),C))),k5_sheffer1(A,k5_sheffer1(A,D,B),k5_sheffer1(A,k5_sheffer1(A,C,C),B))) = k5_sheffer1(A,B,k5_sheffer1(A,k5_sheffer1(A,D,D),C)) ) ) ) ) ).
fof(t146_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,B,k5_sheffer1(A,D,C)),C) = k5_sheffer1(A,C,k5_sheffer1(A,k5_sheffer1(A,D,D),B)) ) ) ) ) ).
fof(t147_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,B,B),C),k5_sheffer1(A,k5_sheffer1(A,E,k5_sheffer1(A,D,k5_sheffer1(A,D,D))),C)),C) = k5_sheffer1(A,C,k5_sheffer1(A,B,E)) ) ) ) ) ) ).
fof(t148_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k5_sheffer1(A,C,k5_sheffer1(A,B,k5_sheffer1(A,k5_sheffer1(A,D,D),C))) = k5_sheffer1(A,C,k5_sheffer1(A,D,B)) ) ) ) ) ).
fof(t149_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,C,k5_sheffer1(A,E,B)),k5_sheffer1(A,C,k5_sheffer1(A,E,B))),k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,E,k5_sheffer1(A,D,k5_sheffer1(A,D,D))),C),k5_sheffer1(A,k5_sheffer1(A,B,B),C))) = k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,B,B),C),k5_sheffer1(A,k5_sheffer1(A,E,k5_sheffer1(A,D,k5_sheffer1(A,D,D))),C)),k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,B,B),C),k5_sheffer1(A,k5_sheffer1(A,E,k5_sheffer1(A,D,k5_sheffer1(A,D,D))),C))) ) ) ) ) ) ).
fof(t150_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> k5_sheffer1(A,C,k5_sheffer1(A,E,B)) = k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,B,B),C),k5_sheffer1(A,k5_sheffer1(A,E,k5_sheffer1(A,D,k5_sheffer1(A,D,D))),C)),k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,B,B),C),k5_sheffer1(A,k5_sheffer1(A,E,k5_sheffer1(A,D,k5_sheffer1(A,D,D))),C))) ) ) ) ) ) ).
fof(t151_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> k5_sheffer1(A,B,k5_sheffer1(A,E,C)) = k5_sheffer1(A,B,k5_sheffer1(A,C,k5_sheffer1(A,k5_sheffer1(A,E,k5_sheffer1(A,D,k5_sheffer1(A,D,D))),k5_sheffer1(A,E,k5_sheffer1(A,D,k5_sheffer1(A,D,D)))))) ) ) ) ) ) ).
fof(t152_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k5_sheffer1(A,B,k5_sheffer1(A,D,C)) = k5_sheffer1(A,B,k5_sheffer1(A,C,D)) ) ) ) ) ).
fof(t153_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,D,C),B) = k5_sheffer1(A,B,k5_sheffer1(A,C,D)) ) ) ) ) ).
fof(t154_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,D,C),B),D) = k5_sheffer1(A,D,k5_sheffer1(A,k5_sheffer1(A,C,C),B)) ) ) ) ) ).
fof(t155_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> k5_sheffer1(A,C,E) = k5_sheffer1(A,C,k5_sheffer1(A,k5_sheffer1(A,E,B),k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,E,k5_sheffer1(A,D,k5_sheffer1(A,D,D))),k5_sheffer1(A,E,k5_sheffer1(A,D,k5_sheffer1(A,D,D)))),C))) ) ) ) ) ) ).
fof(t156_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k5_sheffer1(A,B,D) = k5_sheffer1(A,B,k5_sheffer1(A,k5_sheffer1(A,D,C),k5_sheffer1(A,D,B))) ) ) ) ) ).
fof(t157_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,C,E),k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,C,k5_sheffer1(A,E,k5_sheffer1(A,D,k5_sheffer1(A,D,D)))),B),C)) = k5_sheffer1(A,k5_sheffer1(A,C,E),k5_sheffer1(A,C,k5_sheffer1(A,E,k5_sheffer1(A,D,k5_sheffer1(A,D,D))))) ) ) ) ) ) ).
fof(t158_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,B,E),k5_sheffer1(A,B,k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,E,k5_sheffer1(A,D,k5_sheffer1(A,D,D))),k5_sheffer1(A,E,k5_sheffer1(A,D,k5_sheffer1(A,D,D)))),C))) = k5_sheffer1(A,k5_sheffer1(A,B,E),k5_sheffer1(A,B,k5_sheffer1(A,E,k5_sheffer1(A,D,k5_sheffer1(A,D,D))))) ) ) ) ) ) ).
fof(t159_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,C,E),k5_sheffer1(A,C,k5_sheffer1(A,E,D))) = k5_sheffer1(A,k5_sheffer1(A,C,E),k5_sheffer1(A,C,k5_sheffer1(A,E,k5_sheffer1(A,B,k5_sheffer1(A,B,B))))) ) ) ) ) ) ).
fof(t160_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k5_sheffer1(A,k5_sheffer1(A,B,D),k5_sheffer1(A,B,k5_sheffer1(A,D,C))) = B ) ) ) ) ).
fof(t161_sheffer2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_sheffer1(A)
& v11_sheffer1(A)
& v12_sheffer1(A)
& l1_sheffer1(A) )
=> v1_sheffer2(A) ) ).
%------------------------------------------------------------------------------