% Mizar problem: e1_61,funct_5,1530,15 
include('Axioms/SET010^0.ax').
thf(c1_61_type,type,( c1_61__funct_5: $i )).
thf(c2_61_type,type,( c2_61__funct_5: $i )).
thf(c3_61_type,type,( c3_61__funct_5: $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(k2_xboole_0_type,type,( k2_xboole_0: $i > $i > $i )).
thf(k4_tarski_type,type,( k4_tarski: $i > $i > $i )).
thf(k5_relat_1_type,type,( k5_relat_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_relat_1_type,type,( v1_relat_1: $i > $o )).
thf(v1_xtuple_0_type,type,( v1_xtuple_0: $i > $o )).
thf(rc1_xtuple_0,axiom,( ? [A: $i] : ( v1_xtuple_0 @ A ) ),file(xtuple_0,rc1_xtuple_0)).
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_k1_funct_2,axiom,( $true ),file(funct_2,k1_funct_2)).
thf(dt_k2_xboole_0,axiom,( $true ),file(xboole_0,k2_xboole_0)).
thf(dt_k4_tarski,axiom,( $true ),file(tarski,k4_tarski)).
thf(dt_k5_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_relat_1 @ A ) => ( v1_relat_1 @ ( k5_relat_1 @ A @ B ) ) ) ),file(relat_1,k5_relat_1)).
thf(dt_k9_xtuple_0,axiom,( $true ),file(xtuple_0,k9_xtuple_0)).
thf(dt_c1_61__funct_5,axiom,( $true ),file(funct_5,c1_61__funct_5)).
thf(dt_c2_61__funct_5,axiom,( $true ),file(funct_5,c2_61__funct_5)).
thf(dt_c3_61__funct_5,axiom,( $true ),file(funct_5,c3_61__funct_5)).
thf(fc1_xtuple_0,axiom,( ! [A: $i] : ! [B: $i] : ( v1_xtuple_0 @ ( k4_tarski @ A @ B ) ) ),file(xtuple_0,fc1_xtuple_0)).
thf(fc3_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_relat_1 @ B ) ) => ( v1_relat_1 @ ( k2_xboole_0 @ A @ B ) ) ) ),file(relat_1,fc3_relat_1)).
thf(fc8_funct_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) => ( ( v1_relat_1 @ ( k5_relat_1 @ A @ B ) ) & ( v1_funct_1 @ ( k5_relat_1 @ A @ B ) ) ) ) ),file(funct_1,fc8_funct_1)).
thf(rc1_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ),file(funct_1,rc1_funct_1)).
thf(rd4_relat_1,axiom,( ! [A: $i] : ( ( v1_relat_1 @ A ) => ( = @ ( k5_relat_1 @ A @ ( k9_xtuple_0 @ A ) ) @ A ) ) ),file(relat_1,rd4_relat_1)).
thf(rd5_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_relat_1 @ A ) => ( = @ ( k5_relat_1 @ ( k5_relat_1 @ A @ B ) @ B ) @ ( k5_relat_1 @ A @ B ) ) ) ),file(relat_1,rd5_relat_1)).
thf(s1_funct_5,axiom,( ! [A: $i > $i] : ! [B: $i] : ? [C: $i] : ( ( v1_relat_1 @ C ) & ( v1_funct_1 @ C ) & ( = @ ( k9_xtuple_0 @ C ) @ B ) & ! [D: $i] : ( ( ( v1_relat_1 @ D ) & ( v1_funct_1 @ D ) ) => ( ( r2_hidden @ D @ B ) => ( = @ ( k1_funct_1 @ C @ D ) @ ( A @ D ) ) ) ) ) ),file(funct_5,s1_funct_5)).
thf(e1_61__funct_5,conjecture,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( = @ ( k9_xtuple_0 @ A ) @ ( k1_funct_2 @ ( k2_xboole_0 @ c1_61__funct_5 @ c2_61__funct_5 ) @ c3_61__funct_5 ) ) & ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) ) => ( ( r2_hidden @ B @ ( k1_funct_2 @ ( k2_xboole_0 @ c1_61__funct_5 @ c2_61__funct_5 ) @ c3_61__funct_5 ) ) => ( = @ ( k1_funct_1 @ A @ B ) @ ( k4_tarski @ ( k5_relat_1 @ B @ c1_61__funct_5 ) @ ( k5_relat_1 @ B @ c2_61__funct_5 ) ) ) ) ) ) ),file(funct_5,e1_61__funct_5)).
