% Mizar problem: e13_41,card_1,862,46 
include('Axioms/SET010^0.ax').
thf(c1_41_type,type,( c1_41__card_1: $i )).
thf(c2_41_type,type,( c2_41__card_1: $i )).
thf(c5_41_type,type,( c5_41__card_1: $i )).
thf(c6_41_type,type,( c6_41__card_1: $i )).
thf(k1_funct_1_type,type,( k1_funct_1: $i > $i > $i )).
thf(k2_xboole_0_type,type,( k2_xboole_0: $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_relat_1_type,type,( v1_relat_1: $i > $o )).
thf(commutativity_k2_xboole_0,axiom,( ! [A: $i] : ! [B: $i] : ( = @ ( k2_xboole_0 @ A @ B ) @ ( k2_xboole_0 @ B @ A ) ) ),file(xboole_0,k2_xboole_0)).
thf(idempotence_k2_xboole_0,axiom,( ! [A: $i] : ! [B: $i] : ( = @ ( k2_xboole_0 @ A @ A ) @ A ) ),file(xboole_0,k2_xboole_0)).
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_k2_xboole_0,axiom,( $true ),file(xboole_0,k2_xboole_0)).
thf(dt_k9_xtuple_0,axiom,( $true ),file(xtuple_0,k9_xtuple_0)).
thf(dt_c1_41__card_1,axiom,( $true ),file(card_1,c1_41__card_1)).
thf(dt_c2_41__card_1,axiom,( $true ),file(card_1,c2_41__card_1)).
thf(dt_c5_41__card_1,axiom,( ( v1_relat_1 @ c5_41__card_1 ) & ( v1_funct_1 @ c5_41__card_1 ) ),file(card_1,c5_41__card_1)).
thf(dt_c6_41__card_1,axiom,( ( v1_relat_1 @ c6_41__card_1 ) & ( v1_funct_1 @ c6_41__card_1 ) ),file(card_1,c6_41__card_1)).
thf(rc1_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ),file(funct_1,rc1_funct_1)).
thf(e12_41__card_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( r2_hidden @ A @ ( k2_xboole_0 @ c1_41__card_1 @ c2_41__card_1 ) ) & ( ( ( r2_hidden @ A @ c1_41__card_1 ) & ( = @ B @ ( k1_funct_1 @ c5_41__card_1 @ A ) ) ) | ( ( r2_hidden @ A @ c2_41__card_1 ) & ( = @ B @ ( k1_funct_1 @ c6_41__card_1 @ A ) ) ) ) & ( ( ( r2_hidden @ A @ c1_41__card_1 ) & ( = @ C @ ( k1_funct_1 @ c5_41__card_1 @ A ) ) ) | ( ( r2_hidden @ A @ c2_41__card_1 ) & ( = @ C @ ( k1_funct_1 @ c6_41__card_1 @ A ) ) ) ) ) => ( = @ B @ C ) ) ),file(card_1,e12_41__card_1)).
thf(e11_41__card_1,axiom,( ! [A: $i] : ~ ( ( r2_hidden @ A @ ( k2_xboole_0 @ c1_41__card_1 @ c2_41__card_1 ) ) & ! [B: $i] : ~ ( ( ( r2_hidden @ A @ c1_41__card_1 ) & ( = @ B @ ( k1_funct_1 @ c5_41__card_1 @ A ) ) ) | ( ( r2_hidden @ A @ c2_41__card_1 ) & ( = @ B @ ( k1_funct_1 @ c6_41__card_1 @ A ) ) ) ) ) ),file(card_1,e11_41__card_1)).
thf(s2_funct_1,axiom,( ! [A: $i > $i > $o] : ! [B: $i] : ( ( ! [C: $i] : ! [D: $i] : ! [E: $i] : ( ( ( r2_hidden @ C @ B ) & ( A @ C @ D ) & ( A @ C @ E ) ) => ( = @ D @ E ) ) & ! [C: $i] : ~ ( ( r2_hidden @ C @ B ) & ! [D: $i] : ~ ( A @ C @ D ) ) ) => ? [C: $i] : ( ( v1_relat_1 @ C ) & ( v1_funct_1 @ C ) & ( = @ ( k9_xtuple_0 @ C ) @ B ) & ! [D: $i] : ( ( r2_hidden @ D @ B ) => ( A @ D @ ( k1_funct_1 @ C @ D ) ) ) ) ) ),file(funct_1,s2_funct_1)).
thf(e13_41__card_1,conjecture,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( = @ ( k9_xtuple_0 @ A ) @ ( k2_xboole_0 @ c1_41__card_1 @ c2_41__card_1 ) ) & ! [B: $i] : ( ( r2_hidden @ B @ ( k2_xboole_0 @ c1_41__card_1 @ c2_41__card_1 ) ) => ( ( ( r2_hidden @ B @ c1_41__card_1 ) & ( = @ ( k1_funct_1 @ A @ B ) @ ( k1_funct_1 @ c5_41__card_1 @ B ) ) ) | ( ( r2_hidden @ B @ c2_41__card_1 ) & ( = @ ( k1_funct_1 @ A @ B ) @ ( k1_funct_1 @ c6_41__card_1 @ B ) ) ) ) ) ) ),file(card_1,e13_41__card_1)).
