% Mizar problem: e22_3_1_4,recdef_1,436,53 
include('Axioms/SET010^0.ax').
thf(c1_3_1_4_type,type,( c1_3_1_4__recdef_1: $i )).
thf(k1_xtuple_0_type,type,( k1_xtuple_0: $i > $i )).
thf(k2_xtuple_0_type,type,( k2_xtuple_0: $i > $i )).
thf(k4_classes1_type,type,( k4_classes1: $i > $i )).
thf(p1_s1_recdef_1_type,type,( p1_s1_recdef_1: $i > $i > $i > $o )).
thf(r1_ordinal1_type,type,( r1_ordinal1: $i > $i > $o )).
thf(r1_tarski_type,type,( r1_tarski: $i > $i > $o )).
thf(v1_ordinal1_type,type,( v1_ordinal1: $i > $o )).
thf(v2_ordinal1_type,type,( v2_ordinal1: $i > $o )).
thf(v3_ordinal1_type,type,( v3_ordinal1: $i > $o )).
thf(cc2_ordinal1,axiom,( ! [A: $i] : ( ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc2_ordinal1)).
thf(reflexivity_r1_ordinal1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v3_ordinal1 @ A ) & ( v3_ordinal1 @ B ) ) => ( r1_ordinal1 @ A @ A ) ) ),file(ordinal1,r1_ordinal1)).
thf(connectedness_r1_ordinal1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v3_ordinal1 @ A ) & ( v3_ordinal1 @ B ) ) => ( ( r1_ordinal1 @ A @ B ) | ( r1_ordinal1 @ B @ A ) ) ) ),file(ordinal1,r1_ordinal1)).
thf(reflexivity_r1_tarski,axiom,( ! [A: $i] : ! [B: $i] : ( r1_tarski @ A @ A ) ),file(tarski,r1_tarski)).
thf(redefinition_r1_ordinal1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v3_ordinal1 @ A ) & ( v3_ordinal1 @ B ) ) => ( ( r1_ordinal1 @ A @ B ) <=> ( r1_tarski @ A @ B ) ) ) ),file(ordinal1,r1_ordinal1)).
thf(dt_k1_xtuple_0,axiom,( $true ),file(xtuple_0,k1_xtuple_0)).
thf(dt_k2_xtuple_0,axiom,( $true ),file(xtuple_0,k2_xtuple_0)).
thf(dt_k4_classes1,axiom,( $true ),file(classes1,k4_classes1)).
thf(dt_c1_3_1_4__recdef_1,axiom,( $true ),file(recdef_1,c1_3_1_4__recdef_1)).
thf(cc1_ordinal1,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) ) ),file(ordinal1,cc1_ordinal1)).
thf(rc1_ordinal1,axiom,( ? [A: $i] : ( v3_ordinal1 @ A ) ),file(ordinal1,rc1_ordinal1)).
thf(e21_3_1_4__recdef_1,axiom,( ? [A: $i] : ( ( v3_ordinal1 @ A ) & ? [B: $i] : ( ( r1_tarski @ B @ ( k4_classes1 @ A ) ) & ( p1_s1_recdef_1 @ ( k2_xtuple_0 @ c1_3_1_4__recdef_1 ) @ ( k1_xtuple_0 @ c1_3_1_4__recdef_1 ) @ B ) ) ) ),file(recdef_1,e21_3_1_4__recdef_1)).
thf(s1_ordinal1,axiom,( ! [A: $i > $o] : ( ? [B: $i] : ( ( v3_ordinal1 @ B ) & ( A @ B ) ) => ? [B: $i] : ( ( v3_ordinal1 @ B ) & ( A @ B ) & ! [C: $i] : ( ( v3_ordinal1 @ C ) => ( ( A @ C ) => ( r1_ordinal1 @ B @ C ) ) ) ) ) ),file(ordinal1,s1_ordinal1)).
thf(e22_3_1_4__recdef_1,conjecture,( ? [A: $i] : ( ( v3_ordinal1 @ A ) & ? [B: $i] : ( ( r1_tarski @ B @ ( k4_classes1 @ A ) ) & ( p1_s1_recdef_1 @ ( k2_xtuple_0 @ c1_3_1_4__recdef_1 ) @ ( k1_xtuple_0 @ c1_3_1_4__recdef_1 ) @ B ) ) & ! [B: $i] : ( ( v3_ordinal1 @ B ) => ( ? [C: $i] : ( ( r1_tarski @ C @ ( k4_classes1 @ B ) ) & ( p1_s1_recdef_1 @ ( k2_xtuple_0 @ c1_3_1_4__recdef_1 ) @ ( k1_xtuple_0 @ c1_3_1_4__recdef_1 ) @ C ) ) => ( r1_ordinal1 @ A @ B ) ) ) ) ),file(recdef_1,e22_3_1_4__recdef_1)).
