% Mizar problem: e1_11_1_1,funct_4,234,10 
include('Axioms/SET010^0.ax').
thf(c1_11_type,type,( c1_11__funct_4: $i )).
thf(c2_11_type,type,( c2_11__funct_4: $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_11__funct_4,axiom,( ( v1_relat_1 @ c1_11__funct_4 ) & ( v1_funct_1 @ c1_11__funct_4 ) ),file(funct_4,c1_11__funct_4)).
thf(dt_c2_11__funct_4,axiom,( ( v1_relat_1 @ c2_11__funct_4 ) & ( v1_funct_1 @ c2_11__funct_4 ) ),file(funct_4,c2_11__funct_4)).
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(rc1_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ),file(funct_1,rc1_funct_1)).
thf(s1_partfun1,axiom,( ! [A: $i > $i] : ! [B: $i > $i] : ! [C: $i > $o] : ! [D: $i] : ? [E: $i] : ( ( v1_relat_1 @ E ) & ( v1_funct_1 @ E ) & ( = @ ( k9_xtuple_0 @ E ) @ D ) & ! [F: $i] : ( ( r2_hidden @ F @ D ) => ( ( ( C @ F ) => ( = @ ( k1_funct_1 @ E @ F ) @ ( B @ F ) ) ) & ( ~ ( C @ F ) => ( = @ ( k1_funct_1 @ E @ F ) @ ( A @ F ) ) ) ) ) ) ),file(partfun1,s1_partfun1)).
thf(e1_11_1_1__funct_4,conjecture,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( = @ ( k9_xtuple_0 @ A ) @ ( k2_xboole_0 @ ( k9_xtuple_0 @ c1_11__funct_4 ) @ ( k9_xtuple_0 @ c2_11__funct_4 ) ) ) & ! [B: $i] : ( ( r2_hidden @ B @ ( k2_xboole_0 @ ( k9_xtuple_0 @ c1_11__funct_4 ) @ ( k9_xtuple_0 @ c2_11__funct_4 ) ) ) => ( ( ( r2_hidden @ B @ ( k9_xtuple_0 @ c2_11__funct_4 ) ) => ( = @ ( k1_funct_1 @ A @ B ) @ ( k1_funct_1 @ c2_11__funct_4 @ B ) ) ) & ( ~ ( r2_hidden @ B @ ( k9_xtuple_0 @ c2_11__funct_4 ) ) => ( = @ ( k1_funct_1 @ A @ B ) @ ( k1_funct_1 @ c1_11__funct_4 @ B ) ) ) ) ) ) ),file(funct_4,e1_11_1_1__funct_4)).
