% Mizar problem: e2_65_1_1,closure1,1213,39 
include('Axioms/SET010^0.ax').
thf(c1_65_type,type,( c1_65__closure1: $i )).
thf(c2_65_type,type,( c2_65__closure1: $i )).
thf(c3_65_type,type,( c3_65__closure1: $i )).
thf(k1_funct_1_type,type,( k1_funct_1: $i > $i > $i )).
thf(k9_xtuple_0_type,type,( k9_xtuple_0: $i > $i )).
thf(m2_pboole_type,type,( m2_pboole: $i > $i > $i > $i > $o )).
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(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(rc4_pboole,axiom,( ! [A: $i] : ? [B: $i] : ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ( v1_funcop_1 @ B ) ) ),file(pboole,rc4_pboole)).
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_k9_xtuple_0,axiom,( $true ),file(xtuple_0,k9_xtuple_0)).
thf(dt_m2_pboole,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v1_funct_1 @ C ) & ( v1_partfun1 @ C @ A ) ) => ! [D: $i] : ( ( m2_pboole @ D @ A @ B @ C ) => ( ( v1_relat_1 @ D ) & ( v4_relat_1 @ D @ A ) & ( v1_funct_1 @ D ) & ( v1_partfun1 @ D @ A ) ) ) ) ),file(pboole,m2_pboole)).
thf(dt_c1_65__closure1,axiom,( $true ),file(closure1,c1_65__closure1)).
thf(dt_c2_65__closure1,axiom,( ( v1_relat_1 @ c2_65__closure1 ) & ( v4_relat_1 @ c2_65__closure1 @ c1_65__closure1 ) & ( v1_funct_1 @ c2_65__closure1 ) & ( v1_partfun1 @ c2_65__closure1 @ c1_65__closure1 ) ),file(closure1,c2_65__closure1)).
thf(dt_c3_65__closure1,axiom,( m2_pboole @ c3_65__closure1 @ c1_65__closure1 @ c2_65__closure1 @ c2_65__closure1 ),file(closure1,c3_65__closure1)).
thf(cc3_pboole,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v1_funct_1 @ C ) & ( v1_partfun1 @ C @ A ) ) => ! [D: $i] : ( ( m2_pboole @ D @ A @ B @ C ) => ( v1_funcop_1 @ D ) ) ) ),file(pboole,cc3_pboole)).
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_65_1_1__closure1,axiom,( ! [A: $i] : ~ ( ( r2_hidden @ A @ c1_65__closure1 ) & ! [B: $i] : ~ ( ! [C: $i] : ( ( r2_hidden @ C @ B ) <=> ( ( r2_hidden @ C @ ( k1_funct_1 @ c2_65__closure1 @ A ) ) & ? [D: $i] : ( ( v1_relat_1 @ D ) & ( v1_funct_1 @ D ) & ( = @ D @ ( k1_funct_1 @ c3_65__closure1 @ A ) ) & ( r2_hidden @ C @ ( k9_xtuple_0 @ D ) ) & ( = @ ( k1_funct_1 @ D @ C ) @ C ) ) ) ) ) ) ),file(closure1,e1_65_1_1__closure1)).
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_65_1_1__closure1,conjecture,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v4_relat_1 @ A @ c1_65__closure1 ) & ( v1_funct_1 @ A ) & ( v1_partfun1 @ A @ c1_65__closure1 ) & ! [B: $i] : ( ( r2_hidden @ B @ c1_65__closure1 ) => ! [C: $i] : ( ( r2_hidden @ C @ ( k1_funct_1 @ A @ B ) ) <=> ( ( r2_hidden @ C @ ( k1_funct_1 @ c2_65__closure1 @ B ) ) & ? [D: $i] : ( ( v1_relat_1 @ D ) & ( v1_funct_1 @ D ) & ( = @ D @ ( k1_funct_1 @ c3_65__closure1 @ B ) ) & ( r2_hidden @ C @ ( k9_xtuple_0 @ D ) ) & ( = @ ( k1_funct_1 @ D @ C ) @ C ) ) ) ) ) ) ),file(closure1,e2_65_1_1__closure1)).
