% Mizar problem: e3_14_2,extens_1,574,49 
include('Axioms/SET010^0.ax').
thf(c1_14_type,type,( c1_14__extens_1: $i )).
thf(c1_14_2_type,type,( c1_14_2__extens_1: $i )).
thf(c2_14_type,type,( c2_14__extens_1: $i )).
thf(c5_14_type,type,( c5_14__extens_1: $i )).
thf(c6_14_type,type,( c6_14__extens_1: $i )).
thf(c7_14_type,type,( c7_14__extens_1: $i )).
thf(k14_funcop_1_type,type,( k14_funcop_1: $i > $i > $i > $i > $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(k2_msualg_3_type,type,( k2_msualg_3: $i > $i > $i )).
thf(k2_zfmisc_1_type,type,( k2_zfmisc_1: $i > $i > $i )).
thf(m1_subset_1_type,type,( m1_subset_1: $i > $i > $o )).
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_funct_2_type,type,( v1_funct_2: $i > $i > $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(v5_relat_1_type,type,( v5_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(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_c2_14__extens_1,axiom,( ( v1_relat_1 @ c2_14__extens_1 ) & ( v4_relat_1 @ c2_14__extens_1 @ c1_14__extens_1 ) & ( v1_funct_1 @ c2_14__extens_1 ) & ( v1_partfun1 @ c2_14__extens_1 @ c1_14__extens_1 ) ),file(extens_1,c2_14__extens_1)).
thf(dt_c6_14__extens_1,axiom,( $true ),file(extens_1,c6_14__extens_1)).
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(rc6_funct_1,axiom,( ! [A: $i] : ! [B: $i] : ? [C: $i] : ( ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v5_relat_1 @ C @ B ) & ( v1_funct_1 @ C ) ) ),file(funct_1,rc6_funct_1)).
thf(antisymmetry_r2_hidden,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ~ ( r2_hidden @ B @ A ) ) ),file(hidden,r2_hidden)).
thf(dt_k14_funcop_1,axiom,( $true ),file(funcop_1,k14_funcop_1)).
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_k2_msualg_3,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) => ( m2_pboole @ ( k2_msualg_3 @ A @ B ) @ A @ B @ B ) ) ),file(msualg_3,k2_msualg_3)).
thf(dt_k2_zfmisc_1,axiom,( $true ),file(zfmisc_1,k2_zfmisc_1)).
thf(dt_m1_subset_1,axiom,( $true ),file(subset_1,m1_subset_1)).
thf(dt_c1_14__extens_1,axiom,( $true ),file(extens_1,c1_14__extens_1)).
thf(dt_c1_14_2__extens_1,axiom,( ( v1_relat_1 @ c1_14_2__extens_1 ) & ( v4_relat_1 @ c1_14_2__extens_1 @ c1_14__extens_1 ) & ( v1_funct_1 @ c1_14_2__extens_1 ) & ( v1_partfun1 @ c1_14_2__extens_1 @ c1_14__extens_1 ) ),file(extens_1,c1_14_2__extens_1)).
thf(dt_c5_14__extens_1,axiom,( $true ),file(extens_1,c5_14__extens_1)).
thf(dt_c7_14__extens_1,axiom,( ( v1_funct_1 @ c7_14__extens_1 ) & ( v1_funct_2 @ c7_14__extens_1 @ c6_14__extens_1 @ ( k1_funct_1 @ c2_14__extens_1 @ c5_14__extens_1 ) ) & ( m1_subset_1 @ c7_14__extens_1 @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ c6_14__extens_1 @ ( k1_funct_1 @ c2_14__extens_1 @ c5_14__extens_1 ) ) ) ) ),file(extens_1,c7_14__extens_1)).
thf(cc1_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( v1_relat_1 @ C ) ) ),file(relset_1,cc1_relset_1)).
thf(cc2_relset_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( ( v4_relat_1 @ C @ A ) & ( v5_relat_1 @ C @ B ) ) ) ),file(relset_1,cc2_relset_1)).
thf(cc3_funct_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v1_funct_1 @ B ) ) ) ),file(funct_1,cc3_funct_1)).
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(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(e3_14_2__extens_1,conjecture,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v4_relat_1 @ A @ c1_14__extens_1 ) & ( v1_funct_1 @ A ) & ( v1_partfun1 @ A @ c1_14__extens_1 ) & ! [B: $i] : ( ( r2_hidden @ B @ c1_14__extens_1 ) => ( = @ ( k1_funct_1 @ A @ B ) @ ( k14_funcop_1 @ B @ c5_14__extens_1 @ c7_14__extens_1 @ ( k1_funct_1 @ ( k2_msualg_3 @ c1_14__extens_1 @ c1_14_2__extens_1 ) @ B ) ) ) ) ) ),file(extens_1,e3_14_2__extens_1)).
