% Mizar problem: e2_9_1_1,card_1,142,42 
include('Axioms/SET010^0.ax').
thf(c1_9_type,type,( c1_9__card_1: $i )).
thf(r1_ordinal1_type,type,( r1_ordinal1: $i > $i > $o )).
thf(r1_tarski_type,type,( r1_tarski: $i > $i > $o )).
thf(r2_tarski_type,type,( r2_tarski: $i > $i > $o )).
thf(r2_wellord2_type,type,( r2_wellord2: $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(symmetry_r2_wellord2,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_wellord2 @ A @ B ) => ( r2_wellord2 @ B @ A ) ) ),file(wellord2,r2_wellord2)).
thf(reflexivity_r2_wellord2,axiom,( ! [A: $i] : ! [B: $i] : ( r2_wellord2 @ A @ A ) ),file(wellord2,r2_wellord2)).
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(redefinition_r2_wellord2,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_wellord2 @ A @ B ) <=> ( r2_tarski @ A @ B ) ) ),file(wellord2,r2_wellord2)).
thf(dt_c1_9__card_1,axiom,( $true ),file(card_1,c1_9__card_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(e1_9_1_1__card_1,axiom,( ? [A: $i] : ( ( v3_ordinal1 @ A ) & ( r2_wellord2 @ A @ c1_9__card_1 ) ) ),file(card_1,e1_9_1_1__card_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(e2_9_1_1__card_1,conjecture,( ? [A: $i] : ( ( v3_ordinal1 @ A ) & ( r2_wellord2 @ A @ c1_9__card_1 ) & ! [B: $i] : ( ( v3_ordinal1 @ B ) => ( ( r2_wellord2 @ B @ c1_9__card_1 ) => ( r1_ordinal1 @ A @ B ) ) ) ) ),file(card_1,e2_9_1_1__card_1)).
