% Mizar problem: e2_158_1_1,pboole,2241,17 
include('Axioms/SET010^0.ax').
thf(c1_158_type,type,( c1_158__pboole: $i )).
thf(c2_158_type,type,( c2_158__pboole: $i )).
thf(k1_funct_1_type,type,( k1_funct_1: $i > $i > $i )).
thf(k3_relat_1_type,type,( k3_relat_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_funcop_1_type,type,( v1_funcop_1: $i > $o )).
thf(v1_funct_1_type,type,( v1_funct_1: $i > $o )).
thf(v1_relat_1_type,type,( v1_relat_1: $i > $o )).
thf(v2_funcop_1_type,type,( v2_funcop_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_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ( v1_relat_1 @ ( k3_relat_1 @ A @ B ) ) ),file(relat_1,k3_relat_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_158__pboole,axiom,( ( v1_relat_1 @ c1_158__pboole ) & ( v1_funct_1 @ c1_158__pboole ) & ( v1_funcop_1 @ c1_158__pboole ) ),file(pboole,c1_158__pboole)).
thf(dt_c2_158__pboole,axiom,( ( v1_relat_1 @ c2_158__pboole ) & ( v1_funct_1 @ c2_158__pboole ) & ( v1_funcop_1 @ c2_158__pboole ) ),file(pboole,c2_158__pboole)).
thf(cc2_funcop_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_funcop_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_funcop_1 @ A ) ) ) ),file(funcop_1,cc2_funcop_1)).
thf(fc2_funct_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) ) => ( ( v1_relat_1 @ ( k3_relat_1 @ A @ B ) ) & ( v1_funct_1 @ ( k3_relat_1 @ A @ B ) ) ) ) ),file(funct_1,fc2_funct_1)).
thf(fc8_funcop_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_funcop_1 @ A ) ) => ( ( v1_relat_1 @ ( k1_funct_1 @ A @ B ) ) & ( v1_funct_1 @ ( k1_funct_1 @ A @ B ) ) ) ) ),file(funcop_1,fc8_funcop_1)).
thf(fc9_funcop_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_funcop_1 @ A ) & ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) ) => ( ( v1_relat_1 @ ( k3_relat_1 @ B @ A ) ) & ( v1_funcop_1 @ ( k3_relat_1 @ B @ A ) ) ) ) ),file(funcop_1,fc9_funcop_1)).
thf(rc1_funcop_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_funcop_1 @ A ) ) ),file(funcop_1,rc1_funcop_1)).
thf(rc1_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ),file(funct_1,rc1_funct_1)).
thf(e1_158_1_1__pboole,axiom,( ! [A: $i] : ~ ( ( r2_hidden @ A @ ( k3_xboole_0 @ ( k9_xtuple_0 @ c1_158__pboole ) @ ( k9_xtuple_0 @ c2_158__pboole ) ) ) & ! [B: $i] : ~ ( = @ B @ ( k3_relat_1 @ ( k1_funct_1 @ c1_158__pboole @ A ) @ ( k1_funct_1 @ c2_158__pboole @ A ) ) ) ) ),file(pboole,e1_158_1_1__pboole)).
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_158_1_1__pboole,conjecture,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( = @ ( k9_xtuple_0 @ A ) @ ( k3_xboole_0 @ ( k9_xtuple_0 @ c1_158__pboole ) @ ( k9_xtuple_0 @ c2_158__pboole ) ) ) & ! [B: $i] : ( ( r2_hidden @ B @ ( k3_xboole_0 @ ( k9_xtuple_0 @ c1_158__pboole ) @ ( k9_xtuple_0 @ c2_158__pboole ) ) ) => ( = @ ( k1_funct_1 @ A @ B ) @ ( k3_relat_1 @ ( k1_funct_1 @ c1_158__pboole @ B ) @ ( k1_funct_1 @ c2_158__pboole @ B ) ) ) ) ) ),file(pboole,e2_158_1_1__pboole)).
