% Mizar problem: t47_ordinal3,ordinal3,1061,5 
fof(t47_ordinal3, conjecture,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  (v3_ordinal1(B) =>  ~ ( ( ~ (A=k1_xboole_0)  &  (! [C] :  (v3_ordinal1(C) =>  (! [D] :  (v3_ordinal1(D) =>  ~ ( (B=k10_ordinal2(k11_ordinal2(C, A), D) & r2_tarski(D, A)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(antisymmetry_r2_hidden, axiom,  (! [A, B] :  (r2_hidden(A, B) =>  ~ (r2_hidden(B, A)) ) ) ).
fof(asymmetry_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) =>  ~ (r2_tarski(B, A)) ) ) ).
fof(asymmetry_r2_xboole_0, axiom,  (! [A, B] :  (r2_xboole_0(A, B) =>  ~ (r2_xboole_0(B, A)) ) ) ).
fof(cc10_ordinal1, axiom,  (! [A] :  (v6_ordinal1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v6_ordinal1(B)) ) ) ) ).
fof(cc11_ordinal1, axiom,  (! [A] :  (v8_ordinal1(A) => v7_ordinal1(A)) ) ).
fof(cc12_ordinal1, axiom,  (! [A] :  (v8_ordinal1(A) => v1_zfmisc_1(A)) ) ).
fof(cc13_ordinal1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  ~ (v8_ordinal1(A)) ) ) ).
fof(cc14_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) =>  ~ (v10_ordinal1(A)) ) ) ).
fof(cc16_ordinal1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v10_ordinal1(A)) )  =>  (! [B] :  (m1_subset_1(B, A) =>  ~ (v8_ordinal1(B)) ) ) ) ) ).
fof(cc17_ordinal1, axiom,  (! [A] :  ( ~ (v10_ordinal1(A))  => v1_setfam_1(A)) ) ).
fof(cc18_ordinal1, axiom,  (! [A] :  (v10_ordinal1(A) =>  ~ (v1_setfam_1(A)) ) ) ).
fof(cc19_ordinal1, axiom,  (! [A] :  (v1_setfam_1(A) =>  ~ (v10_ordinal1(A)) ) ) ).
fof(cc1_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) =>  (v1_ordinal1(A) & v2_ordinal1(A)) ) ) ).
fof(cc20_ordinal1, axiom,  (! [A] :  ( ~ (v1_setfam_1(A))  => v10_ordinal1(A)) ) ).
fof(cc2_ordinal1, axiom,  (! [A] :  ( (v1_ordinal1(A) & v2_ordinal1(A))  => v3_ordinal1(A)) ) ).
fof(cc2_ordinal2, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  (m1_subset_1(B, A) => v3_ordinal1(B)) ) ) ) ).
fof(cc3_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v3_ordinal1(A)) ) ).
fof(cc4_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v5_ordinal1(A)) ) ).
fof(cc5_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  (m1_subset_1(B, A) => v3_ordinal1(B)) ) ) ) ).
fof(cc6_ordinal1, axiom,  (! [A] :  (v7_ordinal1(A) => v3_ordinal1(A)) ) ).
fof(cc7_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v7_ordinal1(A)) ) ).
fof(cc8_ordinal1, axiom,  (! [A] :  (m1_subset_1(A, k4_ordinal1) => v7_ordinal1(A)) ) ).
fof(cc9_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v6_ordinal1(A)) ) ).
fof(commutativity_k2_xboole_0, axiom,  (! [A, B] : k2_xboole_0(A, B)=k2_xboole_0(B, A)) ).
fof(connectedness_r1_ordinal1, axiom,  (! [A, B] :  ( (v3_ordinal1(A) & v3_ordinal1(B))  =>  (r1_ordinal1(A, B) | r1_ordinal1(B, A)) ) ) ).
fof(d13_ordinal1, axiom, k5_ordinal1=k1_xboole_0).
fof(d1_ordinal1, axiom,  (! [A] : k1_ordinal1(A)=k2_xboole_0(A, k1_tarski(A))) ).
fof(d3_tarski, axiom,  (! [A] :  (! [B] :  (r1_tarski(A, B) <=>  (! [C] :  (r2_hidden(C, A) => r2_hidden(C, B)) ) ) ) ) ).
fof(d5_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  (v3_ordinal1(B) =>  (r1_ordinal1(A, B) <=>  (! [C] :  (v3_ordinal1(C) =>  (r2_tarski(C, A) => r2_tarski(C, B)) ) ) ) ) ) ) ) ).
fof(d8_xboole_0, axiom,  (! [A] :  (! [B] :  (r2_xboole_0(A, B) <=>  (r1_tarski(A, B) &  ~ (A=B) ) ) ) ) ).
fof(dt_k10_ordinal2, axiom,  (! [A, B] :  ( (v3_ordinal1(A) & v3_ordinal1(B))  => v3_ordinal1(k10_ordinal2(A, B))) ) ).
fof(dt_k11_ordinal2, axiom,  (! [A, B] :  ( (v3_ordinal1(A) & v3_ordinal1(B))  => v3_ordinal1(k11_ordinal2(A, B))) ) ).
fof(dt_k1_ordinal1, axiom, $true).
fof(dt_k1_tarski, axiom, $true).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k2_xboole_0, axiom, $true).
fof(dt_k4_ordinal1, axiom, $true).
fof(dt_k5_ordinal1, axiom, $true).
fof(dt_m1_subset_1, axiom, $true).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(fc1_ordinal1, axiom,  (! [A] :  ~ (v1_xboole_0(k1_ordinal1(A))) ) ).
fof(fc1_ordinal3, axiom,  (! [A, B] :  ( (v3_ordinal1(A) & v3_ordinal1(B))  => v3_ordinal1(k2_xboole_0(A, B))) ) ).
fof(fc1_xboole_0, axiom, v1_xboole_0(k1_xboole_0)).
fof(fc2_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) =>  ( ~ (v1_xboole_0(k1_ordinal1(A)))  & v3_ordinal1(k1_ordinal1(A))) ) ) ).
fof(fc2_xboole_0, axiom,  (! [A] :  ~ (v1_xboole_0(k1_tarski(A))) ) ).
fof(fc4_xboole_0, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(A))  =>  ~ (v1_xboole_0(k2_xboole_0(A, B))) ) ) ).
fof(fc5_ordinal2, axiom,  (! [A, B] :  ( (v7_ordinal1(A) & v7_ordinal1(B))  =>  (v3_ordinal1(k10_ordinal2(A, B)) & v7_ordinal1(k10_ordinal2(A, B))) ) ) ).
fof(fc5_xboole_0, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(A))  =>  ~ (v1_xboole_0(k2_xboole_0(B, A))) ) ) ).
fof(fc6_ordinal1, axiom,  ( ~ (v1_xboole_0(k4_ordinal1))  & v3_ordinal1(k4_ordinal1)) ).
fof(fc7_ordinal1, axiom,  (! [A] :  ( (v3_ordinal1(A) & v7_ordinal1(A))  => v7_ordinal1(k1_ordinal1(A))) ) ).
fof(fc8_ordinal1, axiom, v7_ordinal1(k5_ordinal1)).
fof(fc9_ordinal1, axiom, v8_ordinal1(k5_ordinal1)).
fof(idempotence_k2_xboole_0, axiom,  (! [A, B] : k2_xboole_0(A, A)=A) ).
fof(irreflexivity_r2_xboole_0, axiom,  (! [A, B] :  ~ (r2_xboole_0(A, A)) ) ).
fof(rc10_ordinal1, axiom,  (? [A] :  ~ (v8_ordinal1(A)) ) ).
fof(rc11_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  ~ (v10_ordinal1(A)) ) ) ).
fof(rc1_ordinal1, axiom,  (? [A] :  (v1_ordinal1(A) & v2_ordinal1(A)) ) ).
fof(rc1_ordinal2, axiom,  (? [A] :  (v1_ordinal1(A) &  (v2_ordinal1(A) &  (v3_ordinal1(A) & v4_ordinal1(A)) ) ) ) ).
fof(rc1_xboole_0, axiom,  (? [A] : v1_xboole_0(A)) ).
fof(rc2_ordinal1, axiom,  (? [A] : v3_ordinal1(A)) ).
fof(rc2_xboole_0, axiom,  (? [A] :  ~ (v1_xboole_0(A)) ) ).
fof(rc3_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_ordinal1(A) &  (v2_ordinal1(A) & v3_ordinal1(A)) ) ) ) ).
fof(rc5_ordinal1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc6_ordinal1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc7_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v7_ordinal1(A)) ) ).
fof(rc8_ordinal1, axiom,  (? [A] : v8_ordinal1(A)) ).
fof(rc9_ordinal1, axiom,  (? [A] : v8_ordinal1(A)) ).
fof(redefinition_r1_ordinal1, axiom,  (! [A, B] :  ( (v3_ordinal1(A) & v3_ordinal1(B))  =>  (r1_ordinal1(A, B) <=> r1_tarski(A, B)) ) ) ).
fof(redefinition_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) <=> r2_hidden(A, B)) ) ).
fof(reflexivity_r1_ordinal1, axiom,  (! [A, B] :  ( (v3_ordinal1(A) & v3_ordinal1(B))  => r1_ordinal1(A, A)) ) ).
fof(reflexivity_r1_tarski, axiom,  (! [A, B] : r1_tarski(A, A)) ).
fof(rqSucc__k1_ordinal1__r0_r1, axiom, k1_ordinal1(0)=1).
fof(s1_ordinal1__e5_46_1_1__ordinal3, axiom,  (! [A, B] :  ( (v3_ordinal1(A) & v3_ordinal1(B))  =>  ( (? [C] :  (v3_ordinal1(C) &  (r2_tarski(C, B) & r2_tarski(B, k11_ordinal2(C, A))) ) )  =>  (? [C] :  (v3_ordinal1(C) &  ( (r2_tarski(C, B) & r2_tarski(B, k11_ordinal2(C, A)))  &  (! [D] :  (v3_ordinal1(D) =>  ( (r2_tarski(D, B) & r2_tarski(B, k11_ordinal2(D, A)))  => r1_ordinal1(C, D)) ) ) ) ) ) ) ) ) ).
fof(s1_ordinal2__e5_46__ordinal3, axiom,  (! [A] :  (v3_ordinal1(A) =>  ( ( (? [B] :  (v3_ordinal1(B) &  (? [C] :  (v3_ordinal1(C) &  (k5_ordinal1=k10_ordinal2(k11_ordinal2(B, A), C) & r2_tarski(C, A)) ) ) ) )  &  ( (! [D] :  (v3_ordinal1(D) =>  ( (? [E] :  (v3_ordinal1(E) &  (? [F] :  (v3_ordinal1(F) &  (D=k10_ordinal2(k11_ordinal2(E, A), F) & r2_tarski(F, A)) ) ) ) )  =>  (? [G] :  (v3_ordinal1(G) &  (? [H] :  (v3_ordinal1(H) &  (k1_ordinal1(D)=k10_ordinal2(k11_ordinal2(G, A), H) & r2_tarski(H, A)) ) ) ) ) ) ) )  &  (! [D] :  (v3_ordinal1(D) =>  ( (v4_ordinal1(D) &  (! [I] :  (v3_ordinal1(I) =>  (r2_tarski(I, D) =>  (? [J] :  (v3_ordinal1(J) &  (? [K] :  (v3_ordinal1(K) &  (I=k10_ordinal2(k11_ordinal2(J, A), K) & r2_tarski(K, A)) ) ) ) ) ) ) ) )  =>  (D=k5_ordinal1 |  (? [L] :  (v3_ordinal1(L) &  (? [M] :  (v3_ordinal1(M) &  (D=k10_ordinal2(k11_ordinal2(L, A), M) & r2_tarski(M, A)) ) ) ) ) ) ) ) ) ) )  =>  (! [D] :  (v3_ordinal1(D) =>  (? [N] :  (v3_ordinal1(N) &  (? [O] :  (v3_ordinal1(O) &  (D=k10_ordinal2(k11_ordinal2(N, A), O) & r2_tarski(O, A)) ) ) ) ) ) ) ) ) ) ).
fof(spc0_boole, axiom, v1_xboole_0(0)).
fof(spc0_numerals, axiom, m1_subset_1(0, k4_ordinal1)).
fof(spc1_boole, axiom,  ~ (v1_xboole_0(1)) ).
fof(spc1_numerals, axiom,  (v2_xxreal_0(1) & m1_subset_1(1, k4_ordinal1)) ).
fof(t10_ordinal1, axiom,  (! [A] :  (! [B] :  (! [C] :  (v1_ordinal1(C) =>  ( (r2_tarski(A, B) & r2_tarski(B, C))  => r2_tarski(A, C)) ) ) ) ) ).
fof(t11_ordinal1, axiom,  (! [A] :  (v1_ordinal1(A) =>  (! [B] :  (v3_ordinal1(B) =>  (r2_xboole_0(A, B) => r2_tarski(A, B)) ) ) ) ) ).
fof(t16_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  (v3_ordinal1(B) =>  (r1_ordinal1(A, B) | r2_tarski(B, A)) ) ) ) ) ).
fof(t1_boole, axiom,  (! [A] : k2_xboole_0(A, k1_xboole_0)=A) ).
fof(t1_numerals, axiom, m1_subset_1(k1_xboole_0, k4_ordinal1)).
fof(t1_subset, axiom,  (! [A] :  (! [B] :  (r2_tarski(A, B) => m1_subset_1(A, B)) ) ) ).
fof(t21_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  (v3_ordinal1(B) =>  (r2_tarski(A, B) <=> r1_ordinal1(k1_ordinal1(A), B)) ) ) ) ) ).
fof(t22_ordinal3, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  (v3_ordinal1(B) =>  (! [C] :  (v3_ordinal1(C) =>  (r2_tarski(k10_ordinal2(A, B), k10_ordinal2(A, C)) => r2_tarski(B, C)) ) ) ) ) ) ) ).
fof(t27_ordinal2, axiom,  (! [A] :  (v3_ordinal1(A) => k10_ordinal2(A, k5_ordinal1)=A) ) ).
fof(t27_ordinal3, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  (v3_ordinal1(B) =>  ~ ( (r1_ordinal1(A, B) &  (! [C] :  (v3_ordinal1(C) =>  ~ (B=k10_ordinal2(A, C)) ) ) ) ) ) ) ) ) ).
fof(t28_ordinal2, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  (v3_ordinal1(B) => k10_ordinal2(A, k1_ordinal1(B))=k1_ordinal1(k10_ordinal2(A, B))) ) ) ) ).
fof(t29_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) =>  ( ~ ( ( ~ (v4_ordinal1(A))  &  (! [B] :  (v3_ordinal1(B) =>  ~ (A=k1_ordinal1(B)) ) ) ) )  &  ~ ( ( (? [B] :  (v3_ordinal1(B) & A=k1_ordinal1(B)) )  & v4_ordinal1(A)) ) ) ) ) ).
fof(t2_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, B) =>  (v1_xboole_0(B) | r2_tarski(A, B)) ) ) ) ).
fof(t35_ordinal2, axiom,  (! [A] :  (v3_ordinal1(A) => k11_ordinal2(k5_ordinal1, A)=k5_ordinal1) ) ).
fof(t36_ordinal2, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  (v3_ordinal1(B) => k11_ordinal2(k1_ordinal1(B), A)=k10_ordinal2(k11_ordinal2(B, A), A)) ) ) ) ).
fof(t39_ordinal2, axiom,  (! [A] :  (v3_ordinal1(A) =>  (k11_ordinal2(1, A)=A & k11_ordinal2(A, 1)=A) ) ) ).
fof(t3_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) ) ) ).
fof(t41_ordinal3, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  (v3_ordinal1(B) =>  (! [C] :  (v3_ordinal1(C) =>  ~ ( (r2_tarski(A, k11_ordinal2(B, C)) &  (v4_ordinal1(B) &  (! [D] :  (v3_ordinal1(D) =>  ~ ( (r2_tarski(D, B) & r2_tarski(A, k11_ordinal2(D, C))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t42_ordinal2, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  (v3_ordinal1(B) =>  (! [C] :  (v3_ordinal1(C) =>  (r1_ordinal1(A, B) => r1_ordinal1(k11_ordinal2(C, A), k11_ordinal2(C, B))) ) ) ) ) ) ) ).
fof(t4_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ( (r2_tarski(A, B) & m1_subset_1(B, k1_zfmisc_1(C)))  => m1_subset_1(A, C)) ) ) ) ).
fof(t5_ordinal1, axiom,  (! [A] :  (! [B] :  ~ ( (r2_tarski(B, A) & r1_tarski(A, B)) ) ) ) ).
fof(t5_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ~ ( (r2_tarski(A, B) &  (m1_subset_1(B, k1_zfmisc_1(C)) & v1_xboole_0(C)) ) ) ) ) ) ).
fof(t6_boole, axiom,  (! [A] :  (v1_xboole_0(A) => A=k1_xboole_0) ) ).
fof(t6_ordinal1, axiom,  (! [A] : r2_tarski(A, k1_ordinal1(A))) ).
fof(t7_boole, axiom,  (! [A] :  (! [B] :  ~ ( (r2_tarski(A, B) & v1_xboole_0(B)) ) ) ) ).
fof(t8_boole, axiom,  (! [A] :  (! [B] :  ~ ( (v1_xboole_0(A) &  ( ~ (A=B)  & v1_xboole_0(B)) ) ) ) ) ).
fof(t8_ordinal3, axiom,  (! [A] :  (v3_ordinal1(A) =>  ( ~ (A=k1_xboole_0)  => r2_tarski(k1_xboole_0, A)) ) ) ).
