% Mizar problem: e1_14_1_1,yellow20,439,52 
include('Axioms/SET010^0.ax').
thf(c1_14_type,type,( c1_14__yellow20: $i )).
thf(c2_14_type,type,( c2_14__yellow20: $i )).
thf(k1_funct_1_type,type,( k1_funct_1: $i > $i > $i )).
thf(k3_xboole_0_type,type,( k3_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_k3_xboole_0,axiom,( ! [A: $i] : ! [B: $i] : ( = @ ( k3_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ B @ A ) ) ),file(xboole_0,k3_xboole_0)).
thf(idempotence_k3_xboole_0,axiom,( ! [A: $i] : ! [B: $i] : ( = @ ( k3_xboole_0 @ A @ A ) @ A ) ),file(xboole_0,k3_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_k3_xboole_0,axiom,( $true ),file(xboole_0,k3_xboole_0)).
thf(dt_k9_xtuple_0,axiom,( $true ),file(xtuple_0,k9_xtuple_0)).
thf(dt_c1_14__yellow20,axiom,( ( v1_relat_1 @ c1_14__yellow20 ) & ( v1_funct_1 @ c1_14__yellow20 ) ),file(yellow20,c1_14__yellow20)).
thf(dt_c2_14__yellow20,axiom,( ( v1_relat_1 @ c2_14__yellow20 ) & ( v1_funct_1 @ c2_14__yellow20 ) ),file(yellow20,c2_14__yellow20)).
thf(fc1_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_relat_1 @ A ) => ( v1_relat_1 @ ( k3_xboole_0 @ A @ B ) ) ) ),file(relat_1,fc1_relat_1)).
thf(rc1_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ),file(funct_1,rc1_funct_1)).
thf(s3_funct_1,axiom,( ! [A: $i > $i] : ! [B: $i] : ? [C: $i] : ( ( v1_relat_1 @ C ) & ( v1_funct_1 @ C ) & ( = @ ( k9_xtuple_0 @ C ) @ B ) & ! [D: $i] : ( ( r2_hidden @ D @ B ) => ( = @ ( k1_funct_1 @ C @ D ) @ ( A @ D ) ) ) ) ),file(funct_1,s3_funct_1)).
thf(e1_14_1_1__yellow20,conjecture,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( = @ ( k9_xtuple_0 @ A ) @ ( k3_xboole_0 @ ( k9_xtuple_0 @ c1_14__yellow20 ) @ ( k9_xtuple_0 @ c2_14__yellow20 ) ) ) & ! [B: $i] : ( ( r2_hidden @ B @ ( k3_xboole_0 @ ( k9_xtuple_0 @ c1_14__yellow20 ) @ ( k9_xtuple_0 @ c2_14__yellow20 ) ) ) => ( = @ ( k1_funct_1 @ A @ B ) @ ( k3_xboole_0 @ ( k1_funct_1 @ c1_14__yellow20 @ B ) @ ( k1_funct_1 @ c2_14__yellow20 @ B ) ) ) ) ) ),file(yellow20,e1_14_1_1__yellow20)).
