% Mizar problem: e5_11,card_5,594,16 
include('Axioms/SET010^0.ax').
thf(c1_11_type,type,( c1_11__card_5: $i )).
thf(c2_11_type,type,( c2_11__card_5: $i )).
thf(k1_funct_1_type,type,( k1_funct_1: $i > $i > $i )).
thf(k9_xtuple_0_type,type,( k9_xtuple_0: $i > $i )).
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(cc2_ordinal1,axiom,( ! [A: $i] : ( ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc2_ordinal1)).
thf(antisymmetry_r2_hidden,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ~ ( r2_hidden @ B @ A ) ) ),file(hidden,r2_hidden)).
thf(dt_k1_funct_1,axiom,( $true ),file(funct_1,k1_funct_1)).
thf(dt_k9_xtuple_0,axiom,( $true ),file(xtuple_0,k9_xtuple_0)).
thf(dt_c1_11__card_5,axiom,( ( v1_relat_1 @ c1_11__card_5 ) & ( v1_funct_1 @ c1_11__card_5 ) & ( v5_ordinal1 @ c1_11__card_5 ) & ( v1_ordinal2 @ c1_11__card_5 ) ),file(card_5,c1_11__card_5)).
thf(dt_c2_11__card_5,axiom,( ( v1_relat_1 @ c2_11__card_5 ) & ( v1_funct_1 @ c2_11__card_5 ) & ( v5_ordinal1 @ c2_11__card_5 ) & ( v1_ordinal2 @ c2_11__card_5 ) ),file(card_5,c2_11__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(fc4_ordinal1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v5_ordinal1 @ A ) ) => ( v3_ordinal1 @ ( k9_xtuple_0 @ A ) ) ) ),file(ordinal1,fc4_ordinal1)).
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(e4_11__card_5,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ( ! [B: $i] : ( ( v3_ordinal1 @ B ) => ( ( r2_hidden @ B @ A ) => ( ( r2_hidden @ B @ ( k9_xtuple_0 @ c1_11__card_5 ) ) => ( ( r2_hidden @ B @ ( k9_xtuple_0 @ c2_11__card_5 ) ) & ( = @ ( k1_funct_1 @ c1_11__card_5 @ B ) @ ( k1_funct_1 @ c2_11__card_5 @ B ) ) ) ) ) ) => ( ( r2_hidden @ A @ ( k9_xtuple_0 @ c1_11__card_5 ) ) => ( ( r2_hidden @ A @ ( k9_xtuple_0 @ c2_11__card_5 ) ) & ( = @ ( k1_funct_1 @ c1_11__card_5 @ A ) @ ( k1_funct_1 @ c2_11__card_5 @ A ) ) ) ) ) ) ),file(card_5,e4_11__card_5)).
thf(s2_ordinal1,axiom,( ! [A: $i > $o] : ( ! [B: $i] : ( ( v3_ordinal1 @ B ) => ( ! [C: $i] : ( ( v3_ordinal1 @ C ) => ( ( r2_hidden @ C @ B ) => ( A @ C ) ) ) => ( A @ B ) ) ) => ! [B: $i] : ( ( v3_ordinal1 @ B ) => ( A @ B ) ) ) ),file(ordinal1,s2_ordinal1)).
thf(e5_11__card_5,conjecture,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ( ( r2_hidden @ A @ ( k9_xtuple_0 @ c1_11__card_5 ) ) => ( ( r2_hidden @ A @ ( k9_xtuple_0 @ c2_11__card_5 ) ) & ( = @ ( k1_funct_1 @ c1_11__card_5 @ A ) @ ( k1_funct_1 @ c2_11__card_5 @ A ) ) ) ) ) ),file(card_5,e5_11__card_5)).
