% Mizar problem: e1_128_1_1,valued_2,2237,25 
include('Axioms/SET010^0.ax').
thf(c1_128_type,type,( c1_128__valued_2: $i )).
thf(k1_funct_1_type,type,( k1_funct_1: $i > $i > $i )).
thf(k30_valued_1_type,type,( k30_valued_1: $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(v1_valued_0_type,type,( v1_valued_0: $i > $o )).
thf(v1_xcmplx_0_type,type,( v1_xcmplx_0: $i > $o )).
thf(v7_valued_2_type,type,( v7_valued_2: $i > $o )).
thf(rc1_xcmplx_0,axiom,( ? [A: $i] : ( v1_xcmplx_0 @ A ) ),file(xcmplx_0,rc1_xcmplx_0)).
thf(fc55_valued_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_valued_0 @ A ) ) => ( ( v1_relat_1 @ ( k30_valued_1 @ A ) ) & ( v1_funct_1 @ ( k30_valued_1 @ A ) ) & ( v1_valued_0 @ ( k30_valued_1 @ A ) ) ) ) ),file(valued_1,fc55_valued_1)).
thf(fc61_valued_0,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_valued_0 @ A ) ) => ( v1_xcmplx_0 @ ( k1_funct_1 @ A @ B ) ) ) ),file(valued_0,fc61_valued_0)).
thf(involutiveness_k30_valued_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_valued_0 @ A ) ) => ( = @ ( k30_valued_1 @ ( k30_valued_1 @ A ) ) @ A ) ) ),file(valued_1,k30_valued_1)).
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_k30_valued_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_valued_0 @ A ) ) => ( ( v1_relat_1 @ ( k30_valued_1 @ A ) ) & ( v1_funct_1 @ ( k30_valued_1 @ A ) ) & ( v1_valued_0 @ ( k30_valued_1 @ A ) ) ) ) ),file(valued_1,k30_valued_1)).
thf(dt_k9_xtuple_0,axiom,( $true ),file(xtuple_0,k9_xtuple_0)).
thf(dt_c1_128__valued_2,axiom,( ( v1_relat_1 @ c1_128__valued_2 ) & ( v1_funct_1 @ c1_128__valued_2 ) & ( v7_valued_2 @ c1_128__valued_2 ) ),file(valued_2,c1_128__valued_2)).
thf(fc40_valued_2,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v7_valued_2 @ A ) ) => ( ( v1_relat_1 @ ( k1_funct_1 @ A @ B ) ) & ( v1_funct_1 @ ( k1_funct_1 @ A @ B ) ) ) ) ),file(valued_2,fc40_valued_2)).
thf(fc42_valued_2,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v7_valued_2 @ A ) ) => ( v1_valued_0 @ ( k1_funct_1 @ A @ B ) ) ) ),file(valued_2,fc42_valued_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_128_1_1__valued_2,conjecture,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( = @ ( k9_xtuple_0 @ A ) @ ( k9_xtuple_0 @ c1_128__valued_2 ) ) & ! [B: $i] : ( ( r2_hidden @ B @ ( k9_xtuple_0 @ c1_128__valued_2 ) ) => ( = @ ( k1_funct_1 @ A @ B ) @ ( k30_valued_1 @ ( k1_funct_1 @ c1_128__valued_2 @ B ) ) ) ) ) ),file(valued_2,e1_128_1_1__valued_2)).
