% Mizar problem: e1_9_4_1,card_3,199,58 
include('Axioms/SET010^0.ax').
thf(c1_9_type,type,( c1_9__card_3: $i )).
thf(k10_xtuple_0_type,type,( k10_xtuple_0: $i > $i )).
thf(k1_funct_1_type,type,( k1_funct_1: $i > $i > $i )).
thf(k1_funct_2_type,type,( k1_funct_2: $i > $i > $i )).
thf(k3_tarski_type,type,( k3_tarski: $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_relat_1_type,type,( v1_relat_1: $i > $o )).
thf(antisymmetry_r2_hidden,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ~ ( r2_hidden @ B @ A ) ) ),file(hidden,r2_hidden)).
thf(dt_k10_xtuple_0,axiom,( $true ),file(xtuple_0,k10_xtuple_0)).
thf(dt_k1_funct_1,axiom,( $true ),file(funct_1,k1_funct_1)).
thf(dt_k1_funct_2,axiom,( $true ),file(funct_2,k1_funct_2)).
thf(dt_k3_tarski,axiom,( $true ),file(tarski,k3_tarski)).
thf(dt_k9_xtuple_0,axiom,( $true ),file(xtuple_0,k9_xtuple_0)).
thf(dt_c1_9__card_3,axiom,( ( v1_relat_1 @ c1_9__card_3 ) & ( v1_funct_1 @ c1_9__card_3 ) ),file(card_3,c1_9__card_3)).
thf(rc1_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ),file(funct_1,rc1_funct_1)).
thf(s1_xboole_0,axiom,( ! [A: $i > $o] : ! [B: $i] : ? [C: $i] : ! [D: $i] : ( ( r2_hidden @ D @ C ) <=> ( ( r2_hidden @ D @ B ) & ( A @ D ) ) ) ),file(xboole_0,s1_xboole_0)).
thf(e1_9_4_1__card_3,conjecture,( ? [A: $i] : ! [B: $i] : ( ( r2_hidden @ B @ A ) <=> ( ( r2_hidden @ B @ ( k1_funct_2 @ ( k9_xtuple_0 @ c1_9__card_3 ) @ ( k3_tarski @ ( k10_xtuple_0 @ c1_9__card_3 ) ) ) ) & ? [C: $i] : ( ( v1_relat_1 @ C ) & ( v1_funct_1 @ C ) & ( = @ B @ C ) & ( = @ ( k9_xtuple_0 @ C ) @ ( k9_xtuple_0 @ c1_9__card_3 ) ) & ! [D: $i] : ( ( r2_hidden @ D @ ( k9_xtuple_0 @ c1_9__card_3 ) ) => ( r2_hidden @ ( k1_funct_1 @ C @ D ) @ ( k1_funct_1 @ c1_9__card_3 @ D ) ) ) ) ) ) ),file(card_3,e1_9_4_1__card_3)).
