% Mizar problem: e1_51_1_1,funct_3,1070,31 
include('Axioms/SET010^0.ax').
thf(c1_51_type,type,( c1_51__funct_3: $i )).
thf(c2_51_type,type,( c2_51__funct_3: $i )).
thf(k1_binop_1_type,type,( k1_binop_1: $i > $i > $i > $i )).
thf(k2_zfmisc_1_type,type,( k2_zfmisc_1: $i > $i > $i )).
thf(k9_xtuple_0_type,type,( k9_xtuple_0: $i > $i )).
thf(v1_funct_1_type,type,( v1_funct_1: $i > $o )).
thf(v1_relat_1_type,type,( v1_relat_1: $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_binop_1,axiom,( $true ),file(binop_1,k1_binop_1)).
thf(dt_k2_zfmisc_1,axiom,( $true ),file(zfmisc_1,k2_zfmisc_1)).
thf(dt_k9_xtuple_0,axiom,( $true ),file(xtuple_0,k9_xtuple_0)).
thf(dt_c1_51__funct_3,axiom,( $true ),file(funct_3,c1_51__funct_3)).
thf(dt_c2_51__funct_3,axiom,( $true ),file(funct_3,c2_51__funct_3)).
thf(fc6_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ( v1_relat_1 @ ( k2_zfmisc_1 @ A @ B ) ) ),file(relat_1,fc6_relat_1)).
thf(rc1_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ),file(funct_1,rc1_funct_1)).
thf(s2_funct_3,axiom,( ! [A: $i > $i > $i] : ! [B: $i] : ! [C: $i] : ? [D: $i] : ( ( v1_relat_1 @ D ) & ( v1_funct_1 @ D ) & ( = @ ( k9_xtuple_0 @ D ) @ ( k2_zfmisc_1 @ C @ B ) ) & ! [E: $i] : ! [F: $i] : ( ( ( r2_hidden @ E @ C ) & ( r2_hidden @ F @ B ) ) => ( = @ ( k1_binop_1 @ D @ E @ F ) @ ( A @ E @ F ) ) ) ) ),file(funct_3,s2_funct_3)).
thf(e1_51_1_1__funct_3,conjecture,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( = @ ( k9_xtuple_0 @ A ) @ ( k2_zfmisc_1 @ c1_51__funct_3 @ c2_51__funct_3 ) ) & ! [B: $i] : ! [C: $i] : ( ( ( r2_hidden @ B @ c1_51__funct_3 ) & ( r2_hidden @ C @ c2_51__funct_3 ) ) => ( = @ ( k1_binop_1 @ A @ B @ C ) @ B ) ) ) ),file(funct_3,e1_51_1_1__funct_3)).
