% Mizar problem: t7_ordinal7,ordinal7,174,5 
fof(t7_ordinal7, conjecture,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v5_ordinal1(A)) )  =>  (! [B] :  ( (v1_relat_1(B) &  (v1_funct_1(B) & v5_ordinal1(B)) )  =>  (v1_ordinal2(k1_ordinal4(A, B)) =>  (v1_ordinal2(A) & v1_ordinal2(B)) ) ) ) ) ) ).
fof(cc1_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) =>  (v1_ordinal1(A) & v2_ordinal1(A)) ) ) ).
fof(cc1_ordinal6, axiom,  (! [A] :  (v3_ordinal1(A) => v1_ordinal6(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(cc2_ordinal6, axiom,  (! [A] :  (v1_ordinal6(A) =>  (! [B] :  (m1_subset_1(B, A) => v3_ordinal1(B)) ) ) ) ).
fof(cc2_relat_1, axiom,  (! [A] :  (v1_relat_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_relat_1(B)) ) ) ) ).
fof(cc3_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_funct_1(B)) ) ) ) ).
fof(cc5_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  (m1_subset_1(B, A) => v3_ordinal1(B)) ) ) ) ).
fof(d4_ordinal2, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (v1_ordinal2(A) <=>  (? [B] :  (v3_ordinal1(B) & r1_tarski(k10_xtuple_0(A), B)) ) ) ) ) ).
fof(dt_k10_xtuple_0, axiom, $true).
fof(dt_k1_ordinal4, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v5_ordinal1(A) & v1_funct_1(A)) )  &  (v1_relat_1(B) &  (v5_ordinal1(B) & v1_funct_1(B)) ) )  =>  (v1_relat_1(k1_ordinal4(A, B)) &  (v5_ordinal1(k1_ordinal4(A, B)) & v1_funct_1(k1_ordinal4(A, B))) ) ) ) ).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_m1_subset_1, axiom, $true).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(fc2_ordinal4, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v5_ordinal1(A) &  (v1_funct_1(A) & v1_ordinal2(A)) ) )  &  (v1_relat_1(B) &  (v5_ordinal1(B) &  (v1_funct_1(B) & v1_ordinal2(B)) ) ) )  =>  (v1_relat_1(k1_ordinal4(A, B)) &  (v5_ordinal1(k1_ordinal4(A, B)) &  (v1_funct_1(k1_ordinal4(A, B)) & v1_ordinal2(k1_ordinal4(A, B))) ) ) ) ) ).
fof(fc4_ordinal6, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_ordinal2(A)) )  => v1_ordinal6(k10_xtuple_0(A))) ) ).
fof(rc1_funct_1, axiom,  (? [A] :  (v1_relat_1(A) & v1_funct_1(A)) ) ).
fof(rc1_ordinal1, axiom,  (? [A] :  (v1_ordinal1(A) & v2_ordinal1(A)) ) ).
fof(rc1_ordinal6, axiom,  (? [A] : v1_ordinal6(A)) ).
fof(rc2_ordinal1, axiom,  (? [A] : v3_ordinal1(A)) ).
fof(rc2_ordinal2, axiom,  (? [A] :  (v1_relat_1(A) &  (v5_ordinal1(A) &  (v1_funct_1(A) & v1_ordinal2(A)) ) ) ) ).
fof(reflexivity_r1_tarski, axiom,  (! [A, B] : r1_tarski(A, A)) ).
fof(t1_xboole_1, axiom,  (! [A] :  (! [B] :  (! [C] :  ( (r1_tarski(A, B) & r1_tarski(B, C))  => r1_tarski(A, C)) ) ) ) ).
fof(t39_ordinal4, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v5_ordinal1(A) & v1_funct_1(A)) )  =>  (! [B] :  ( (v1_relat_1(B) &  (v5_ordinal1(B) & v1_funct_1(B)) )  => r1_tarski(k10_xtuple_0(A), k10_xtuple_0(k1_ordinal4(A, B)))) ) ) ) ).
fof(t3_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) ) ) ).
fof(t40_ordinal4, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v5_ordinal1(A) & v1_funct_1(A)) )  =>  (! [B] :  ( (v1_relat_1(B) &  (v5_ordinal1(B) & v1_funct_1(B)) )  => r1_tarski(k10_xtuple_0(B), k10_xtuple_0(k1_ordinal4(A, B)))) ) ) ) ).
