% Mizar problem: e2_4_1,pre_circ,113,41 
include('Axioms/SET010^0.ax').
thf(f1_s2_pre_circ_type,type,( f1_s2_pre_circ: $i )).
thf(f2_s2_pre_circ_type,type,( f2_s2_pre_circ: $i > $i )).
thf(f3_s2_pre_circ_type,type,( f3_s2_pre_circ: $i > $i )).
thf(k1_funct_1_type,type,( k1_funct_1: $i > $i > $i )).
thf(p1_s2_pre_circ_type,type,( p1_s2_pre_circ: $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(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_f1_s2_pre_circ,axiom,( $true ),file(pre_circ,f1_s2_pre_circ)).
thf(dt_f2_s2_pre_circ,axiom,( $true ),file(pre_circ,f2_s2_pre_circ)).
thf(dt_f3_s2_pre_circ,axiom,( $true ),file(pre_circ,f3_s2_pre_circ)).
thf(rc1_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ),file(funct_1,rc1_funct_1)).
thf(rc1_pboole,axiom,( ! [A: $i] : ? [B: $i] : ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) ),file(pboole,rc1_pboole)).
thf(e1_4_1__pre_circ,axiom,( ! [A: $i] : ~ ( ( r2_hidden @ A @ f1_s2_pre_circ ) & ! [B: $i] : ~ ( ( ( p1_s2_pre_circ @ A ) => ( = @ B @ ( f2_s2_pre_circ @ A ) ) ) & ( ~ ( p1_s2_pre_circ @ A ) => ( = @ B @ ( f3_s2_pre_circ @ A ) ) ) ) ) ),file(pre_circ,e1_4_1__pre_circ)).
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(e2_4_1__pre_circ,conjecture,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v4_relat_1 @ A @ f1_s2_pre_circ ) & ( v1_funct_1 @ A ) & ( v1_partfun1 @ A @ f1_s2_pre_circ ) & ! [B: $i] : ( ( r2_hidden @ B @ f1_s2_pre_circ ) => ( ( ( p1_s2_pre_circ @ B ) => ( = @ ( k1_funct_1 @ A @ B ) @ ( f2_s2_pre_circ @ B ) ) ) & ( ~ ( p1_s2_pre_circ @ B ) => ( = @ ( k1_funct_1 @ A @ B ) @ ( f3_s2_pre_circ @ B ) ) ) ) ) ) ),file(pre_circ,e2_4_1__pre_circ)).
