% Mizar problem: t142_gtarski3,gtarski3,3801,53 
fof(t142_gtarski3, conjecture,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v3_gtarski3(A) &  (v4_gtarski3(A) &  (v5_gtarski3(A) &  (v7_gtarski3(A) &  (v8_gtarski3(A) &  (v9_gtarski3(A) &  (v10_gtarski3(A) &  (v11_gtarski3(A) &  (v12_gtarski3(A) &  (v13_gtarski3(A) & l1_gtarski1(A)) ) ) ) ) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(A))  &  (v2_gtarski3(A) &  (v3_gtarski3(A) &  (v4_gtarski3(A) &  (v5_gtarski3(A) &  (v6_gtarski3(A) &  (v7_gtarski3(A) &  (v8_gtarski3(A) &  (v9_gtarski3(A) &  (v10_gtarski3(A) &  (v11_gtarski3(A) &  (v12_gtarski3(A) & l1_gtarski1(A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(antisymmetry_r2_hidden, axiom,  (! [A, B] :  (r2_hidden(A, B) =>  ~ (r2_hidden(B, A)) ) ) ).
fof(cc19_ordinal1, axiom,  (! [A] :  (v1_setfam_1(A) =>  ~ (v10_ordinal1(A)) ) ) ).
fof(cc20_ordinal1, axiom,  (! [A] :  ( ~ (v1_setfam_1(A))  => v10_ordinal1(A)) ) ).
fof(asymmetry_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) =>  ~ (r2_tarski(B, A)) ) ) ).
fof(redefinition_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) <=> r2_hidden(A, B)) ) ).
fof(dt_k1_xboole_0, axiom, $true).
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(cc2_ordinal1, axiom,  (! [A] :  ( (v1_ordinal1(A) & v2_ordinal1(A))  => v3_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(rc3_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_ordinal1(A) &  (v2_ordinal1(A) & v3_ordinal1(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(t8_boole, axiom,  (! [A] :  (! [B] :  ~ ( (v1_xboole_0(A) &  ( ~ (A=B)  & v1_xboole_0(B)) ) ) ) ) ).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(dt_k4_ordinal1, axiom, $true).
fof(dt_m1_subset_1, axiom, $true).
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(cc1_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) =>  (v1_ordinal1(A) & v2_ordinal1(A)) ) ) ).
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(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(fc6_ordinal1, axiom,  ( ~ (v1_xboole_0(k4_ordinal1))  & v3_ordinal1(k4_ordinal1)) ).
fof(rc2_ordinal1, axiom,  (? [A] : v3_ordinal1(A)) ).
fof(rc7_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v7_ordinal1(A)) ) ).
fof(t2_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, B) =>  (v1_xboole_0(B) | r2_tarski(A, B)) ) ) ) ).
fof(t6_boole, axiom,  (! [A] :  (v1_xboole_0(A) => A=k1_xboole_0) ) ).
fof(t7_boole, axiom,  (! [A] :  (! [B] :  ~ ( (r2_tarski(A, B) & v1_xboole_0(B)) ) ) ) ).
fof(cc11_ordinal1, axiom,  (! [A] :  (v8_ordinal1(A) => v7_ordinal1(A)) ) ).
fof(cc11_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v13_struct_0(A, 1) =>  ( ~ (v2_struct_0(A))  & v7_struct_0(A)) ) ) ) ).
fof(cc12_ordinal1, axiom,  (! [A] :  (v8_ordinal1(A) => v1_zfmisc_1(A)) ) ).
fof(cc6_ordinal1, axiom,  (! [A] :  (v7_ordinal1(A) => v3_ordinal1(A)) ) ).
fof(rc10_ordinal1, axiom,  (? [A] :  ~ (v8_ordinal1(A)) ) ).
fof(rc5_ordinal1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc6_ordinal1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc8_ordinal1, axiom,  (? [A] : v8_ordinal1(A)) ).
fof(rc9_ordinal1, axiom,  (? [A] : v8_ordinal1(A)) ).
fof(spc1_boole, axiom,  ~ (v1_xboole_0(1)) ).
fof(spc1_numerals, axiom,  (v2_xxreal_0(1) & m1_subset_1(1, k4_ordinal1)) ).
fof(dt_k5_ordinal1, axiom, $true).
fof(cc10_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ( ~ (v2_struct_0(A))  & v7_struct_0(A))  => v13_struct_0(A, 1)) ) ) ).
fof(cc17_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v7_struct_0(A))  =>  ~ (v2_struct_0(A)) ) ) ) ).
fof(cc1_gtarski3, axiom,  (! [A] :  (l1_gtarski1(A) =>  ( (v2_gtarski1(A) &  (v3_gtarski1(A) & v1_gtarski3(A)) )  =>  (v2_gtarski1(A) &  (v3_gtarski1(A) & v6_gtarski1(A)) ) ) ) ) ).
fof(cc2_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v7_struct_0(A))  =>  ~ (v2_struct_0(A)) ) ) ) ).
fof(cc5_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v8_struct_0(A))  =>  ( ~ (v2_struct_0(A))  &  ~ (v8_struct_0(A)) ) ) ) ) ).
fof(cc6_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v7_struct_0(A) => v8_struct_0(A)) ) ) ).
fof(cc7_gtarski1, axiom,  (! [A] :  (l1_gtarski1(A) =>  (v9_gtarski1(A) =>  (v2_gtarski1(A) &  (v3_gtarski1(A) &  (v4_gtarski1(A) &  (v5_gtarski1(A) &  (v6_gtarski1(A) &  (v7_gtarski1(A) & v8_gtarski1(A)) ) ) ) ) ) ) ) ) ).
fof(cc7_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v8_struct_0(A))  =>  ~ (v7_struct_0(A)) ) ) ) ).
fof(cc9_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v13_struct_0(A, k5_ordinal1) => v2_struct_0(A)) ) ) ).
fof(fc8_ordinal1, axiom, v7_ordinal1(k5_ordinal1)).
fof(fc9_ordinal1, axiom, v8_ordinal1(k5_ordinal1)).
fof(rc10_gtarski3, axiom,  (? [A] :  (l1_gtarski1(A) &  ( ~ (v2_struct_0(A))  &  (v7_struct_0(A) &  (v4_gtarski1(A) & v4_gtarski3(A)) ) ) ) ) ).
fof(rc11_gtarski3, axiom,  (? [A] :  (l1_gtarski1(A) &  ( ~ (v2_struct_0(A))  &  (v7_struct_0(A) &  (v4_gtarski1(A) &  (v5_gtarski1(A) &  (v4_gtarski3(A) & v5_gtarski3(A)) ) ) ) ) ) ) ).
fof(rc1_gtarski3, axiom,  (? [A] :  (l1_gtarski1(A) &  (v2_gtarski1(A) &  (v3_gtarski1(A) &  (v4_gtarski1(A) &  (v5_gtarski1(A) &  (v6_gtarski1(A) &  (v7_gtarski1(A) &  (v8_gtarski1(A) &  (v9_gtarski1(A) &  (v1_gtarski2(A) & v1_gtarski3(A)) ) ) ) ) ) ) ) ) ) ) ).
fof(rc2_gtarski3, axiom,  (? [A] :  (l1_gtarski1(A) &  ( ~ (v2_struct_0(A))  &  (v2_gtarski1(A) &  (v3_gtarski1(A) &  (v4_gtarski1(A) &  (v5_gtarski1(A) &  (v6_gtarski1(A) &  (v7_gtarski1(A) &  (v8_gtarski1(A) &  (v9_gtarski1(A) &  (v1_gtarski2(A) & v1_gtarski3(A)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc5_gtarski1, axiom,  (? [A] :  (l1_gtarski1(A) &  ( ~ (v2_struct_0(A))  & v9_gtarski1(A)) ) ) ).
fof(rc7_gtarski3, axiom,  (? [A] :  (l1_gtarski1(A) &  (v2_gtarski1(A) &  (v3_gtarski1(A) &  (v6_gtarski1(A) &  (v1_gtarski3(A) &  (v2_gtarski3(A) &  (v3_gtarski3(A) &  (v5_gtarski3(A) &  (v6_gtarski3(A) & v13_gtarski3(A)) ) ) ) ) ) ) ) ) ) ).
fof(existence_l1_struct_0, axiom,  (? [A] : l1_struct_0(A)) ).
fof(dt_l1_struct_0, axiom, $true).
fof(cc13_gtarski3, axiom,  (! [A] :  (l1_gtarski1(A) =>  (v2_gtarski1(A) => v2_gtarski3(A)) ) ) ).
fof(cc14_gtarski3, axiom,  (! [A] :  (l1_gtarski1(A) =>  (v3_gtarski1(A) => v3_gtarski3(A)) ) ) ).
fof(cc15_gtarski3, axiom,  (! [A] :  (l1_gtarski1(A) =>  (v4_gtarski1(A) => v4_gtarski3(A)) ) ) ).
fof(cc16_gtarski3, axiom,  (! [A] :  (l1_gtarski1(A) =>  (v5_gtarski1(A) => v5_gtarski3(A)) ) ) ).
fof(cc17_gtarski3, axiom,  (! [A] :  (l1_gtarski1(A) =>  (v7_gtarski1(A) => v7_gtarski3(A)) ) ) ).
fof(cc18_gtarski3, axiom,  (! [A] :  (l1_gtarski1(A) =>  (v8_gtarski1(A) => v8_gtarski3(A)) ) ) ).
fof(cc19_gtarski3, axiom,  (! [A] :  (l1_gtarski1(A) =>  (v1_gtarski2(A) => v9_gtarski3(A)) ) ) ).
fof(cc1_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) => v7_struct_0(A)) ) ) ).
fof(cc20_gtarski3, axiom,  (! [A] :  (l1_gtarski1(A) =>  (v2_gtarski2(A) => v10_gtarski3(A)) ) ) ).
fof(cc21_gtarski3, axiom,  (! [A] :  (l1_gtarski1(A) =>  (v3_gtarski2(A) => v11_gtarski3(A)) ) ) ).
fof(cc22_gtarski3, axiom,  (! [A] :  (l1_gtarski1(A) =>  ( ( ~ (v2_struct_0(A))  & v4_gtarski2(A))  =>  ( ~ (v2_struct_0(A))  & v12_gtarski3(A)) ) ) ) ).
fof(cc2_gtarski3, axiom,  (! [A] :  (l1_gtarski1(A) =>  ( (v2_gtarski1(A) &  (v3_gtarski1(A) & v6_gtarski1(A)) )  =>  (v2_gtarski1(A) &  (v3_gtarski1(A) & v1_gtarski3(A)) ) ) ) ) ).
fof(cc4_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) =>  (v2_struct_0(A) & v8_struct_0(A)) ) ) ) ).
fof(cc6_gtarski1, axiom,  (! [A] :  (l1_gtarski1(A) =>  ( (v2_gtarski1(A) &  (v3_gtarski1(A) &  (v4_gtarski1(A) &  (v5_gtarski1(A) &  (v6_gtarski1(A) &  (v7_gtarski1(A) & v8_gtarski1(A)) ) ) ) ) )  => v9_gtarski1(A)) ) ) ).
fof(cc8_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) => v13_struct_0(A, k5_ordinal1)) ) ) ).
fof(rc12_gtarski3, axiom,  (? [A] :  (l1_gtarski1(A) &  ( ~ (v2_struct_0(A))  &  (v3_gtarski1(A) &  (v4_gtarski1(A) &  (v5_gtarski1(A) &  (v3_gtarski3(A) &  (v4_gtarski3(A) &  (v5_gtarski3(A) & v14_gtarski3(A)) ) ) ) ) ) ) ) ) ).
fof(rc13_gtarski3, axiom,  (? [A] :  (l1_gtarski1(A) &  ( ~ (v2_struct_0(A))  &  (v3_gtarski1(A) &  (v4_gtarski1(A) &  (v5_gtarski1(A) &  (v3_gtarski3(A) &  (v4_gtarski3(A) &  (v5_gtarski3(A) & v13_gtarski3(A)) ) ) ) ) ) ) ) ) ).
fof(rc4_gtarski3, axiom,  (? [A] :  (l1_gtarski1(A) &  (v2_gtarski1(A) &  (v3_gtarski1(A) &  (v2_gtarski3(A) &  (v3_gtarski3(A) & v6_gtarski3(A)) ) ) ) ) ) ).
fof(rc6_gtarski3, axiom,  (? [A] :  (l1_gtarski1(A) &  (v2_gtarski1(A) &  (v3_gtarski1(A) &  (v2_gtarski3(A) &  (v3_gtarski3(A) & v13_gtarski3(A)) ) ) ) ) ) ).
fof(rc8_gtarski3, axiom,  (? [A] :  (l1_gtarski1(A) &  (v4_gtarski1(A) &  (v4_gtarski3(A) & v14_gtarski3(A)) ) ) ) ).
fof(rc9_gtarski3, axiom,  (? [A] :  (l1_gtarski1(A) &  (v4_gtarski1(A) &  (v4_gtarski3(A) &  (v5_gtarski3(A) & v14_gtarski3(A)) ) ) ) ) ).
fof(existence_l1_gtarski1, axiom,  (? [A] : l1_gtarski1(A)) ).
fof(dt_l1_gtarski1, axiom,  (! [A] :  (l1_gtarski1(A) => l1_struct_0(A)) ) ).
fof(cc10_gtarski3, axiom,  (! [A] :  (l1_gtarski1(A) =>  (v10_gtarski3(A) => v2_gtarski2(A)) ) ) ).
fof(cc11_gtarski3, axiom,  (! [A] :  (l1_gtarski1(A) =>  (v11_gtarski3(A) => v3_gtarski2(A)) ) ) ).
fof(cc12_gtarski3, axiom,  (! [A] :  (l1_gtarski1(A) =>  (v12_gtarski3(A) => v4_gtarski2(A)) ) ) ).
fof(cc23_gtarski3, axiom,  (! [A] :  (l1_gtarski1(A) =>  ( (v2_gtarski3(A) &  (v3_gtarski3(A) & v6_gtarski3(A)) )  =>  (v6_gtarski1(A) &  (v2_gtarski3(A) & v3_gtarski3(A)) ) ) ) ) ).
fof(cc24_gtarski3, axiom,  (! [A] :  (l1_gtarski1(A) =>  ( (v2_gtarski3(A) &  (v3_gtarski3(A) & v13_gtarski3(A)) )  =>  (v2_gtarski3(A) &  (v3_gtarski3(A) & v6_gtarski3(A)) ) ) ) ) ).
fof(cc25_gtarski3, axiom,  (! [A] :  (l1_gtarski1(A) =>  ( (v3_gtarski3(A) &  (v5_gtarski3(A) & v13_gtarski3(A)) )  => v14_gtarski3(A)) ) ) ).
fof(cc26_gtarski3, axiom,  (! [A] :  (l1_gtarski1(A) =>  ( (v2_gtarski3(A) &  (v3_gtarski3(A) & v6_gtarski3(A)) )  => v13_gtarski3(A)) ) ) ).
fof(cc27_gtarski3, axiom,  (! [A] :  (l1_gtarski1(A) =>  ( ( ~ (v2_struct_0(A))  &  (v3_gtarski3(A) &  (v4_gtarski3(A) &  (v5_gtarski3(A) & v13_gtarski3(A)) ) ) )  =>  ( ~ (v2_struct_0(A))  & v6_gtarski3(A)) ) ) ) ).
fof(cc28_gtarski3, axiom,  (! [A] :  (l1_gtarski1(A) =>  ( ( ~ (v2_struct_0(A))  &  (v3_gtarski3(A) &  (v4_gtarski3(A) &  (v5_gtarski3(A) & v13_gtarski3(A)) ) ) )  =>  ( ~ (v2_struct_0(A))  & v2_gtarski3(A)) ) ) ) ).
fof(cc29_gtarski3, axiom,  (! [A] :  (l1_gtarski1(A) =>  ( ( ~ (v2_struct_0(A))  &  (v3_gtarski3(A) &  (v4_gtarski3(A) &  (v5_gtarski3(A) & v13_gtarski3(A)) ) ) )  =>  ( ~ (v2_struct_0(A))  & v6_gtarski1(A)) ) ) ) ).
fof(cc3_gtarski3, axiom,  (! [A] :  (l1_gtarski1(A) =>  (v2_gtarski3(A) => v2_gtarski1(A)) ) ) ).
fof(cc4_gtarski3, axiom,  (! [A] :  (l1_gtarski1(A) =>  (v3_gtarski3(A) => v3_gtarski1(A)) ) ) ).
fof(cc5_gtarski3, axiom,  (! [A] :  (l1_gtarski1(A) =>  (v4_gtarski3(A) => v4_gtarski1(A)) ) ) ).
fof(cc6_gtarski3, axiom,  (! [A] :  (l1_gtarski1(A) =>  (v5_gtarski3(A) => v5_gtarski1(A)) ) ) ).
fof(cc7_gtarski3, axiom,  (! [A] :  (l1_gtarski1(A) =>  (v7_gtarski3(A) => v7_gtarski1(A)) ) ) ).
fof(cc8_gtarski3, axiom,  (! [A] :  (l1_gtarski1(A) =>  (v8_gtarski3(A) => v8_gtarski1(A)) ) ) ).
fof(cc9_gtarski3, axiom,  (! [A] :  (l1_gtarski1(A) =>  (v9_gtarski3(A) => v1_gtarski2(A)) ) ) ).
fof(rc14_gtarski3, axiom,  (? [A] :  (l1_gtarski1(A) &  ( ~ (v2_struct_0(A))  &  (v2_gtarski3(A) &  (v3_gtarski3(A) &  (v4_gtarski3(A) &  (v5_gtarski3(A) &  (v6_gtarski3(A) &  (v7_gtarski3(A) &  (v8_gtarski3(A) &  (v9_gtarski3(A) &  (v10_gtarski3(A) &  (v11_gtarski3(A) & v12_gtarski3(A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc3_gtarski3, axiom,  (? [A] :  (l1_gtarski1(A) &  (v2_gtarski3(A) & v3_gtarski3(A)) ) ) ).
fof(rc5_gtarski3, axiom,  (? [A] :  (l1_gtarski1(A) &  (v3_gtarski3(A) & v5_gtarski3(A)) ) ) ).
