% Mizar problem: e2_10,card_5,518,35 
include('Axioms/SET010^0.ax').
thf(c1_10_type,type,( c1_10__card_5: $i )).
thf(k1_card_1_type,type,( k1_card_1: $i > $i )).
thf(r1_ordinal1_type,type,( r1_ordinal1: $i > $i > $o )).
thf(r1_tarski_type,type,( r1_tarski: $i > $i > $o )).
thf(r2_ordinal2_type,type,( r2_ordinal2: $i > $i > $o )).
thf(v1_card_1_type,type,( v1_card_1: $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(cc1_card_1,axiom,( ! [A: $i] : ( ( v1_card_1 @ A ) => ( v3_ordinal1 @ A ) ) ),file(card_1,cc1_card_1)).
thf(cc2_ordinal1,axiom,( ! [A: $i] : ( ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc2_ordinal1)).
thf(rc1_card_1,axiom,( ? [A: $i] : ( v1_card_1 @ A ) ),file(card_1,rc1_card_1)).
thf(projectivity_k1_card_1,axiom,( ! [A: $i] : ( = @ ( k1_card_1 @ ( k1_card_1 @ A ) ) @ ( k1_card_1 @ A ) ) ),file(card_1,k1_card_1)).
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_r2_ordinal2,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v3_ordinal1 @ A ) & ( v3_ordinal1 @ B ) ) => ( r2_ordinal2 @ A @ A ) ) ),file(ordinal2,r2_ordinal2)).
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_card_1,axiom,( ! [A: $i] : ( v1_card_1 @ ( k1_card_1 @ A ) ) ),file(card_1,k1_card_1)).
thf(dt_c1_10__card_5,axiom,( v3_ordinal1 @ c1_10__card_5 ),file(card_5,c1_10__card_5)).
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_10__card_5,axiom,( ? [A: $i] : ( ( v3_ordinal1 @ A ) & ( r1_ordinal1 @ A @ ( k1_card_1 @ c1_10__card_5 ) ) & ( r2_ordinal2 @ c1_10__card_5 @ A ) ) ),file(card_5,e1_10__card_5)).
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_10__card_5,conjecture,( ? [A: $i] : ( ( v3_ordinal1 @ A ) & ( r1_ordinal1 @ A @ ( k1_card_1 @ c1_10__card_5 ) ) & ( r2_ordinal2 @ c1_10__card_5 @ A ) & ! [B: $i] : ( ( v3_ordinal1 @ B ) => ( ( ( r1_ordinal1 @ B @ ( k1_card_1 @ c1_10__card_5 ) ) & ( r2_ordinal2 @ c1_10__card_5 @ B ) ) => ( r1_ordinal1 @ A @ B ) ) ) ) ),file(card_5,e2_10__card_5)).
