% Mizar problem: e5_33,classes2,1043,35 
include('Axioms/SET010^0.ax').
thf(c1_33_type,type,( c1_33__classes2: $i )).
thf(c2_33_type,type,( c2_33__classes2: $i )).
thf(k6_classes1_type,type,( k6_classes1: $i > $i )).
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(reflexivity_r1_tarski,axiom,( ! [A: $i] : ! [B: $i] : ( r1_tarski @ A @ A ) ),file(tarski,r1_tarski)).
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(antisymmetry_r2_hidden,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ~ ( r2_hidden @ B @ A ) ) ),file(hidden,r2_hidden)).
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_k6_classes1,axiom,( ! [A: $i] : ( v3_ordinal1 @ ( k6_classes1 @ A ) ) ),file(classes1,k6_classes1)).
thf(dt_c1_33__classes2,axiom,( v3_ordinal1 @ c1_33__classes2 ),file(classes2,c1_33__classes2)).
thf(dt_c2_33__classes2,axiom,( $true ),file(classes2,c2_33__classes2)).
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(e4_33__classes2,axiom,( ? [A: $i] : ( ( v3_ordinal1 @ A ) & ? [B: $i] : ( ( r2_hidden @ c1_33__classes2 @ A ) & ( r2_hidden @ B @ c2_33__classes2 ) & ( = @ ( k6_classes1 @ B ) @ A ) ) ) ),file(classes2,e4_33__classes2)).
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(e5_33__classes2,conjecture,( ? [A: $i] : ( ( v3_ordinal1 @ A ) & ? [B: $i] : ( ( r2_hidden @ c1_33__classes2 @ A ) & ( r2_hidden @ B @ c2_33__classes2 ) & ( = @ ( k6_classes1 @ B ) @ A ) ) & ! [B: $i] : ( ( v3_ordinal1 @ B ) => ( ? [C: $i] : ( ( r2_hidden @ c1_33__classes2 @ B ) & ( r2_hidden @ C @ c2_33__classes2 ) & ( = @ ( k6_classes1 @ C ) @ B ) ) => ( r1_ordinal1 @ A @ B ) ) ) ) ),file(classes2,e5_33__classes2)).
