% Mizar problem: e3_31_1,mboolean,627,46 
include('Axioms/SET010^0.ax').
thf(c1_31_type,type,( c1_31__mboolean: $i )).
thf(c2_31_type,type,( c2_31__mboolean: $i )).
thf(c3_31_type,type,( c3_31__mboolean: $i )).
thf(k1_funct_1_type,type,( k1_funct_1: $i > $i > $i )).
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(v4_relat_1_type,type,( v4_relat_1: $i > $i > $o )).
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_c1_31__mboolean,axiom,( $true ),file(mboolean,c1_31__mboolean)).
thf(dt_c2_31__mboolean,axiom,( ( v1_relat_1 @ c2_31__mboolean ) & ( v4_relat_1 @ c2_31__mboolean @ c1_31__mboolean ) & ( v1_funct_1 @ c2_31__mboolean ) & ( v1_partfun1 @ c2_31__mboolean @ c1_31__mboolean ) ),file(mboolean,c2_31__mboolean)).
thf(dt_c3_31__mboolean,axiom,( ( v1_relat_1 @ c3_31__mboolean ) & ( v4_relat_1 @ c3_31__mboolean @ c1_31__mboolean ) & ( v1_funct_1 @ c3_31__mboolean ) & ( v1_partfun1 @ c3_31__mboolean @ c1_31__mboolean ) ),file(mboolean,c3_31__mboolean)).
thf(e2_31_1__mboolean,axiom,( ! [A: $i] : ~ ( ( r2_hidden @ A @ c1_31__mboolean ) & ! [B: $i] : ~ ( ( r2_hidden @ ( k1_funct_1 @ c2_31__mboolean @ A ) @ B ) & ( r2_hidden @ B @ ( k1_funct_1 @ c3_31__mboolean @ A ) ) ) ) ),file(mboolean,e2_31_1__mboolean)).
thf(s3_pboole,axiom,( ! [A: $i > $i > $o] : ! [B: $i] : ( ! [C: $i] : ~ ( ( r2_hidden @ C @ B ) & ! [D: $i] : ~ ( A @ C @ D ) ) => ? [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 ) => ( A @ D @ ( k1_funct_1 @ C @ D ) ) ) ) ) ),file(pboole,s3_pboole)).
thf(e3_31_1__mboolean,conjecture,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v4_relat_1 @ A @ c1_31__mboolean ) & ( v1_funct_1 @ A ) & ( v1_partfun1 @ A @ c1_31__mboolean ) & ! [B: $i] : ( ( r2_hidden @ B @ c1_31__mboolean ) => ( ( r2_hidden @ ( k1_funct_1 @ c2_31__mboolean @ B ) @ ( k1_funct_1 @ A @ B ) ) & ( r2_hidden @ ( k1_funct_1 @ A @ B ) @ ( k1_funct_1 @ c3_31__mboolean @ B ) ) ) ) ) ),file(mboolean,e3_31_1__mboolean)).
