% Mizar problem: e1_1_1_1,mboolean,44,12 
include('Axioms/SET010^0.ax').
thf(c1_1_type,type,( c1_1__mboolean: $i )).
thf(c2_1_type,type,( c2_1__mboolean: $i )).
thf(k1_funct_1_type,type,( k1_funct_1: $i > $i > $i )).
thf(k1_zfmisc_1_type,type,( k1_zfmisc_1: $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_partfun1_type,type,( v1_partfun1: $i > $i > $o )).
thf(v1_relat_1_type,type,( v1_relat_1: $i > $o )).
thf(v1_xboole_0_type,type,( v1_xboole_0: $i > $o )).
thf(v2_funcop_1_type,type,( v2_funcop_1: $i > $o )).
thf(v4_relat_1_type,type,( v4_relat_1: $i > $i > $o )).
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(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(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(cc3_funcop_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_xboole_0 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_funcop_1 @ A ) ) ) ),file(funcop_1,cc3_funcop_1)).
thf(rc1_xboole_0,axiom,( ? [A: $i] : ( v1_xboole_0 @ A ) ),file(xboole_0,rc1_xboole_0)).
thf(rc2_xboole_0,axiom,( ? [A: $i] : ~ ( v1_xboole_0 @ A ) ),file(xboole_0,rc2_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_zfmisc_1,axiom,( $true ),file(zfmisc_1,k1_zfmisc_1)).
thf(dt_c1_1__mboolean,axiom,( $true ),file(mboolean,c1_1__mboolean)).
thf(dt_c2_1__mboolean,axiom,( ( v1_relat_1 @ c2_1__mboolean ) & ( v4_relat_1 @ c2_1__mboolean @ c1_1__mboolean ) & ( v1_funct_1 @ c2_1__mboolean ) & ( v1_partfun1 @ c2_1__mboolean @ c1_1__mboolean ) ),file(mboolean,c2_1__mboolean)).
thf(fc1_subset_1,axiom,( ! [A: $i] : ~ ( v1_xboole_0 @ ( k1_zfmisc_1 @ A ) ) ),file(subset_1,fc1_subset_1)).
thf(s4_pboole,axiom,( ! [A: $i > $i] : ! [B: $i] : ? [C: $i] : ( ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ B ) & ( v1_funct_1 @ C ) & ( v1_partfun1 @ C @ B ) & ! [D: $i] : ( ( r2_hidden @ D @ B ) => ( = @ ( k1_funct_1 @ C @ D ) @ ( A @ D ) ) ) ) ),file(pboole,s4_pboole)).
thf(e1_1_1_1__mboolean,conjecture,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v4_relat_1 @ A @ c1_1__mboolean ) & ( v1_funct_1 @ A ) & ( v1_partfun1 @ A @ c1_1__mboolean ) & ! [B: $i] : ( ( r2_hidden @ B @ c1_1__mboolean ) => ( = @ ( k1_funct_1 @ A @ B ) @ ( k1_zfmisc_1 @ ( k1_funct_1 @ c2_1__mboolean @ B ) ) ) ) ) ),file(mboolean,e1_1_1_1__mboolean)).
