% Mizar problem: e2_8_1_1,lexbfs,220,14 
include('Axioms/SET010^0.ax').
thf(c1_8_type,type,( c1_8__lexbfs: $i )).
thf(c2_8_type,type,( c2_8__lexbfs: $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_8__lexbfs,axiom,( ( v1_relat_1 @ c1_8__lexbfs ) & ( v1_funct_1 @ c1_8__lexbfs ) ),file(lexbfs,c1_8__lexbfs)).
thf(dt_c2_8__lexbfs,axiom,( ( v1_relat_1 @ c2_8__lexbfs ) & ( v1_funct_1 @ c2_8__lexbfs ) ),file(lexbfs,c2_8__lexbfs)).
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(e1_8_1_1__lexbfs,axiom,( ! [A: $i] : ~ ( ( r2_hidden @ A @ ( k2_xboole_0 @ ( k9_xtuple_0 @ c1_8__lexbfs ) @ ( k9_xtuple_0 @ c2_8__lexbfs ) ) ) & ! [B: $i] : ~ ( = @ ( k2_xboole_0 @ ( k1_funct_1 @ c1_8__lexbfs @ A ) @ ( k1_funct_1 @ c2_8__lexbfs @ A ) ) @ B ) ) ),file(lexbfs,e1_8_1_1__lexbfs)).
thf(s1_classes1,axiom,( ! [A: $i > $i > $o] : ! [B: $i] : ( ! [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(classes1,s1_classes1)).
thf(e2_8_1_1__lexbfs,conjecture,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( = @ ( k9_xtuple_0 @ A ) @ ( k2_xboole_0 @ ( k9_xtuple_0 @ c1_8__lexbfs ) @ ( k9_xtuple_0 @ c2_8__lexbfs ) ) ) & ! [B: $i] : ( ( r2_hidden @ B @ ( k2_xboole_0 @ ( k9_xtuple_0 @ c1_8__lexbfs ) @ ( k9_xtuple_0 @ c2_8__lexbfs ) ) ) => ( = @ ( k2_xboole_0 @ ( k1_funct_1 @ c1_8__lexbfs @ B ) @ ( k1_funct_1 @ c2_8__lexbfs @ B ) ) @ ( k1_funct_1 @ A @ B ) ) ) ) ),file(lexbfs,e2_8_1_1__lexbfs)).
