% Mizar problem: e10_9_3_1_1_2,card_5,473,46 
include('Axioms/SET010^0.ax').
thf(c4_9_3_type,type,( c4_9_3__card_5: $i )).
thf(c5_9_type,type,( c5_9__card_5: $i )).
thf(k1_funct_1_type,type,( k1_funct_1: $i > $i > $i )).
thf(r1_ordinal1_type,type,( r1_ordinal1: $i > $i > $o )).
thf(r1_tarski_type,type,( r1_tarski: $i > $i > $o )).
thf(v1_funct_1_type,type,( v1_funct_1: $i > $o )).
thf(v1_ordinal1_type,type,( v1_ordinal1: $i > $o )).
thf(v1_ordinal2_type,type,( v1_ordinal2: $i > $o )).
thf(v1_relat_1_type,type,( v1_relat_1: $i > $o )).
thf(v2_ordinal1_type,type,( v2_ordinal1: $i > $o )).
thf(v3_ordinal1_type,type,( v3_ordinal1: $i > $o )).
thf(v5_ordinal1_type,type,( v5_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_k1_funct_1,axiom,( $true ),file(funct_1,k1_funct_1)).
thf(dt_c4_9_3__card_5,axiom,( v3_ordinal1 @ c4_9_3__card_5 ),file(card_5,c4_9_3__card_5)).
thf(dt_c5_9__card_5,axiom,( ( v1_relat_1 @ c5_9__card_5 ) & ( v1_funct_1 @ c5_9__card_5 ) & ( v5_ordinal1 @ c5_9__card_5 ) & ( v1_ordinal2 @ c5_9__card_5 ) ),file(card_5,c5_9__card_5)).
thf(cc1_ordinal1,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) ) ),file(ordinal1,cc1_ordinal1)).
thf(fc2_ordinal2,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v5_ordinal1 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_ordinal2 @ A ) & ( v3_ordinal1 @ B ) ) => ( v3_ordinal1 @ ( k1_funct_1 @ A @ B ) ) ) ),file(ordinal2,fc2_ordinal2)).
thf(rc1_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ),file(funct_1,rc1_funct_1)).
thf(rc1_ordinal1,axiom,( ? [A: $i] : ( v3_ordinal1 @ A ) ),file(ordinal1,rc1_ordinal1)).
thf(rc2_ordinal2,axiom,( ? [A: $i] : ( ( v5_ordinal1 @ A ) & ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_ordinal2 @ A ) ) ),file(ordinal2,rc2_ordinal2)).
thf(e9_9_3_1_1_2__card_5,axiom,( ? [A: $i] : ( ( v3_ordinal1 @ A ) & ( r2_hidden @ A @ c4_9_3__card_5 ) & ( r2_hidden @ ( k1_funct_1 @ c5_9__card_5 @ c4_9_3__card_5 ) @ ( k1_funct_1 @ c5_9__card_5 @ A ) ) ) ),file(card_5,e9_9_3_1_1_2__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(e10_9_3_1_1_2__card_5,conjecture,( ? [A: $i] : ( ( v3_ordinal1 @ A ) & ( r2_hidden @ A @ c4_9_3__card_5 ) & ( r2_hidden @ ( k1_funct_1 @ c5_9__card_5 @ c4_9_3__card_5 ) @ ( k1_funct_1 @ c5_9__card_5 @ A ) ) & ! [B: $i] : ( ( v3_ordinal1 @ B ) => ( ( ( r2_hidden @ B @ c4_9_3__card_5 ) & ( r2_hidden @ ( k1_funct_1 @ c5_9__card_5 @ c4_9_3__card_5 ) @ ( k1_funct_1 @ c5_9__card_5 @ B ) ) ) => ( r1_ordinal1 @ A @ B ) ) ) ) ),file(card_5,e10_9_3_1_1_2__card_5)).
