% Mizar problem: t19_yellow20,yellow20,711,5 
fof(t19_yellow20, conjecture,  (! [A] :  (l2_altcat_1(A) =>  (! [B] :  (l2_altcat_1(B) =>  (r1_yellow20(A, B) => k2_yellow20(A, B)=k2_yellow20(B, A)) ) ) ) ) ).
fof(abstractness_v6_altcat_1, axiom,  (! [A] :  (l2_altcat_1(A) =>  (v6_altcat_1(A) => A=g2_altcat_1(u1_struct_0(A), u1_altcat_1(A), u2_altcat_1(A))) ) ) ).
fof(cc1_xtuple_0, axiom,  (! [A] :  (v2_xtuple_0(A) => v1_xtuple_0(A)) ) ).
fof(cc2_funcop_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v2_funcop_1(A)) ) ) ) ).
fof(cc3_pboole, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v1_funct_1(C) & v1_partfun1(C, A)) ) ) )  =>  (! [D] :  (m2_pboole(D, A, B, C) => v1_funcop_1(D)) ) ) ) ).
fof(commutativity_k1_yellow20, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v1_funct_1(A))  &  (v1_relat_1(B) & v1_funct_1(B)) )  => k1_yellow20(A, B)=k1_yellow20(B, A)) ) ).
fof(commutativity_k3_xboole_0, axiom,  (! [A, B] : k3_xboole_0(A, B)=k3_xboole_0(B, A)) ).
fof(d1_yellow20, axiom,  (! [A] :  (l2_altcat_1(A) =>  (! [B] :  (l2_altcat_1(B) =>  (r1_yellow20(A, B) <=>  (! [C] :  (! [D] :  (! [E] : r1_partfun1(k1_funct_1(u2_altcat_1(A), k3_xtuple_0(C, D, E)), k1_funct_1(u2_altcat_1(B), k3_xtuple_0(C, D, E)))) ) ) ) ) ) ) ) ).
fof(d3_yellow20, axiom,  (! [A] :  (l2_altcat_1(A) =>  (! [B] :  (l2_altcat_1(B) =>  (r1_yellow20(A, B) =>  (! [C] :  ( (v6_altcat_1(C) & l2_altcat_1(C))  =>  (C=k2_yellow20(A, B) <=>  (u1_struct_0(C)=k3_xboole_0(u1_struct_0(A), u1_struct_0(B)) &  (u1_altcat_1(C)=k1_yellow20(u1_altcat_1(A), u1_altcat_1(B)) & u2_altcat_1(C)=k1_yellow20(u2_altcat_1(A), u2_altcat_1(B))) ) ) ) ) ) ) ) ) ) ).
fof(dt_g2_altcat_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) &  (v4_relat_1(B, k2_zfmisc_1(A, A)) &  (v1_funct_1(B) & v1_partfun1(B, k2_zfmisc_1(A, A))) ) )  & m2_pboole(C, k3_zfmisc_1(A, A, A), k3_altcat_1(A, B, B), k2_altcat_1(A, B)))  =>  (v6_altcat_1(g2_altcat_1(A, B, C)) & l2_altcat_1(g2_altcat_1(A, B, C))) ) ) ).
fof(dt_k1_funct_1, axiom, $true).
fof(dt_k1_yellow20, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v1_funct_1(A))  &  (v1_relat_1(B) & v1_funct_1(B)) )  =>  (v1_relat_1(k1_yellow20(A, B)) & v1_funct_1(k1_yellow20(A, B))) ) ) ).
fof(dt_k2_altcat_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, k2_zfmisc_1(A, A)) &  (v1_funct_1(B) & v1_partfun1(B, k2_zfmisc_1(A, A))) ) )  =>  (v1_relat_1(k2_altcat_1(A, B)) &  (v4_relat_1(k2_altcat_1(A, B), k3_zfmisc_1(A, A, A)) &  (v1_funct_1(k2_altcat_1(A, B)) & v1_partfun1(k2_altcat_1(A, B), k3_zfmisc_1(A, A, A))) ) ) ) ) ).
fof(dt_k2_yellow20, axiom,  (! [A, B] :  ( (l2_altcat_1(A) & l2_altcat_1(B))  =>  (v6_altcat_1(k2_yellow20(A, B)) & l2_altcat_1(k2_yellow20(A, B))) ) ) ).
fof(dt_k2_zfmisc_1, axiom, $true).
fof(dt_k3_altcat_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) &  (v4_relat_1(B, k2_zfmisc_1(A, A)) &  (v1_funct_1(B) & v1_partfun1(B, k2_zfmisc_1(A, A))) ) )  &  (v1_relat_1(C) &  (v4_relat_1(C, k2_zfmisc_1(A, A)) &  (v1_funct_1(C) & v1_partfun1(C, k2_zfmisc_1(A, A))) ) ) )  =>  (v1_relat_1(k3_altcat_1(A, B, C)) &  (v4_relat_1(k3_altcat_1(A, B, C), k3_zfmisc_1(A, A, A)) &  (v1_funct_1(k3_altcat_1(A, B, C)) & v1_partfun1(k3_altcat_1(A, B, C), k3_zfmisc_1(A, A, A))) ) ) ) ) ).
fof(dt_k3_xboole_0, axiom, $true).
fof(dt_k3_xtuple_0, axiom, $true).
fof(dt_k3_zfmisc_1, axiom, $true).
fof(dt_l1_altcat_1, axiom,  (! [A] :  (l1_altcat_1(A) => l1_struct_0(A)) ) ).
fof(dt_l1_struct_0, axiom, $true).
fof(dt_l2_altcat_1, axiom,  (! [A] :  (l2_altcat_1(A) => l1_altcat_1(A)) ) ).
fof(dt_m2_pboole, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v1_funct_1(C) & v1_partfun1(C, A)) ) ) )  =>  (! [D] :  (m2_pboole(D, A, B, C) =>  (v1_relat_1(D) &  (v4_relat_1(D, A) &  (v1_funct_1(D) & v1_partfun1(D, A)) ) ) ) ) ) ) ).
fof(dt_u1_altcat_1, axiom,  (! [A] :  (l1_altcat_1(A) =>  (v1_relat_1(u1_altcat_1(A)) &  (v4_relat_1(u1_altcat_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A))) &  (v1_funct_1(u1_altcat_1(A)) & v1_partfun1(u1_altcat_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)))) ) ) ) ) ).
fof(dt_u1_struct_0, axiom, $true).
fof(dt_u2_altcat_1, axiom,  (! [A] :  (l2_altcat_1(A) => m2_pboole(u2_altcat_1(A), k3_zfmisc_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A)), k3_altcat_1(u1_struct_0(A), u1_altcat_1(A), u1_altcat_1(A)), k2_altcat_1(u1_struct_0(A), u1_altcat_1(A)))) ) ).
fof(existence_l1_altcat_1, axiom,  (? [A] : l1_altcat_1(A)) ).
fof(existence_l1_struct_0, axiom,  (? [A] : l1_struct_0(A)) ).
fof(existence_l2_altcat_1, axiom,  (? [A] : l2_altcat_1(A)) ).
fof(existence_m2_pboole, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v1_funct_1(C) & v1_partfun1(C, A)) ) ) )  =>  (? [D] : m2_pboole(D, A, B, C)) ) ) ).
fof(fc1_relat_1, axiom,  (! [A, B] :  (v1_relat_1(A) => v1_relat_1(k3_xboole_0(A, B))) ) ).
fof(fc2_relset_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) & v4_relat_1(B, A))  & v1_relat_1(C))  => v4_relat_1(k3_xboole_0(B, C), A)) ) ).
fof(fc2_xtuple_0, axiom,  (! [A, B, C] : v2_xtuple_0(k3_xtuple_0(A, B, C))) ).
fof(fc6_relat_1, axiom,  (! [A, B] : v1_relat_1(k2_zfmisc_1(A, B))) ).
fof(fc9_funcop_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) )  =>  (v1_relat_1(k1_funct_1(A, B)) & v1_funct_1(k1_funct_1(A, B))) ) ) ).
fof(free_g2_altcat_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) &  (v4_relat_1(B, k2_zfmisc_1(A, A)) &  (v1_funct_1(B) & v1_partfun1(B, k2_zfmisc_1(A, A))) ) )  & m2_pboole(C, k3_zfmisc_1(A, A, A), k3_altcat_1(A, B, B), k2_altcat_1(A, B)))  =>  (! [D, E, F] :  (g2_altcat_1(A, B, C)=g2_altcat_1(D, E, F) =>  (A=D &  (B=E & C=F) ) ) ) ) ) ).
fof(idempotence_k3_xboole_0, axiom,  (! [A, B] : k3_xboole_0(A, A)=A) ).
fof(rc1_funcop_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) ) ) ).
fof(rc1_funct_1, axiom,  (? [A] :  (v1_relat_1(A) & v1_funct_1(A)) ) ).
fof(rc1_pboole, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) ) ) ) ).
fof(rc1_xtuple_0, axiom,  (? [A] : v1_xtuple_0(A)) ).
fof(rc2_xtuple_0, axiom,  (? [A] : v2_xtuple_0(A)) ).
fof(rc4_pboole, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) &  (v1_partfun1(B, A) & v1_funcop_1(B)) ) ) ) ) ) ).
fof(reflexivity_r1_partfun1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v1_funct_1(A))  &  (v1_relat_1(B) & v1_funct_1(B)) )  => r1_partfun1(A, A)) ) ).
fof(symmetry_r1_partfun1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v1_funct_1(A))  &  (v1_relat_1(B) & v1_funct_1(B)) )  =>  (r1_partfun1(A, B) => r1_partfun1(B, A)) ) ) ).
fof(symmetry_r1_yellow20, axiom,  (! [A, B] :  ( (l2_altcat_1(A) & l2_altcat_1(B))  =>  (r1_yellow20(A, B) => r1_yellow20(B, A)) ) ) ).
