% Mizar problem: e1_4_1_1,prvect_2,154,68 
include('Axioms/SET010^0.ax').
thf(c1_4_type,type,( c1_4__prvect_2: $i )).
thf(c2_4_type,type,( c2_4__prvect_2: $i )).
thf(k10_funct_3_type,type,( k10_funct_3: $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_zfmisc_1_type,type,( k2_zfmisc_1: $i > $i > $i )).
thf(k8_funct_3_type,type,( k8_funct_3: $i > $i > $i )).
thf(k9_xtuple_0_type,type,( k9_xtuple_0: $i > $i )).
thf(m1_subset_1_type,type,( m1_subset_1: $i > $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(cc1_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( m1_subset_1 @ C @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) ) ) => ( ( v1_partfun1 @ C @ A ) => ( v1_funct_2 @ C @ A @ B ) ) ) ),file(funct_2,cc1_funct_2)).
thf(dt_k1_zfmisc_1,axiom,( $true ),file(zfmisc_1,k1_zfmisc_1)).
thf(dt_k2_zfmisc_1,axiom,( $true ),file(zfmisc_1,k2_zfmisc_1)).
thf(dt_k8_funct_3,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_relat_1 @ ( k8_funct_3 @ A @ B ) ) & ( v1_funct_1 @ ( k8_funct_3 @ A @ B ) ) ) ),file(funct_3,k8_funct_3)).
thf(dt_m1_subset_1,axiom,( $true ),file(subset_1,m1_subset_1)).
thf(cc2_relat_1,axiom,( ! [A: $i] : ( ( v1_relat_1 @ A ) => ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ A ) ) => ( v1_relat_1 @ B ) ) ) ),file(relat_1,cc2_relat_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(cc4_funct_2,axiom,( ! [A: $i] : ! [B: $i] : ( ( m1_subset_1 @ B @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ A @ A ) ) ) => ( ( v1_funct_2 @ B @ A @ A ) => ( v1_partfun1 @ B @ A ) ) ) ),file(funct_2,cc4_funct_2)).
thf(fc6_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ( v1_relat_1 @ ( k2_zfmisc_1 @ A @ B ) ) ),file(relat_1,fc6_relat_1)).
thf(antisymmetry_r2_hidden,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ~ ( r2_hidden @ B @ A ) ) ),file(hidden,r2_hidden)).
thf(redefinition_k10_funct_3,axiom,( ! [A: $i] : ! [B: $i] : ( = @ ( k10_funct_3 @ A @ B ) @ ( k8_funct_3 @ A @ B ) ) ),file(funct_3,k10_funct_3)).
thf(dt_k10_funct_3,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_funct_1 @ ( k10_funct_3 @ A @ B ) ) & ( v1_funct_2 @ ( k10_funct_3 @ A @ B ) @ ( k2_zfmisc_1 @ A @ B ) @ B ) & ( m1_subset_1 @ ( k10_funct_3 @ A @ B ) @ ( k1_zfmisc_1 @ ( k2_zfmisc_1 @ ( k2_zfmisc_1 @ A @ B ) @ B ) ) ) ) ),file(funct_3,k10_funct_3)).
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_c1_4__prvect_2,axiom,( ( v1_relat_1 @ c1_4__prvect_2 ) & ( v1_funct_1 @ c1_4__prvect_2 ) ),file(prvect_2,c1_4__prvect_2)).
thf(dt_c2_4__prvect_2,axiom,( $true ),file(prvect_2,c2_4__prvect_2)).
thf(rc1_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ),file(funct_1,rc1_funct_1)).
thf(s3_funct_1,axiom,( ! [A: $i > $i] : ! [B: $i] : ? [C: $i] : ( ( v1_relat_1 @ C ) & ( v1_funct_1 @ C ) & ( = @ ( k9_xtuple_0 @ C ) @ B ) & ! [D: $i] : ( ( r2_hidden @ D @ B ) => ( = @ ( k1_funct_1 @ C @ D ) @ ( A @ D ) ) ) ) ),file(funct_1,s3_funct_1)).
thf(e1_4_1_1__prvect_2,conjecture,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( = @ ( k9_xtuple_0 @ A ) @ ( k9_xtuple_0 @ c1_4__prvect_2 ) ) & ! [B: $i] : ( ( r2_hidden @ B @ ( k9_xtuple_0 @ c1_4__prvect_2 ) ) => ( = @ ( k1_funct_1 @ A @ B ) @ ( k10_funct_3 @ c2_4__prvect_2 @ ( k1_funct_1 @ c1_4__prvect_2 @ B ) ) ) ) ) ),file(prvect_2,e1_4_1_1__prvect_2)).
