% Mizar problem: e1_7_2_1,bvfunc_1,285,25 
include('Axioms/SET010^0.ax').
thf(c1_7_type,type,( c1_7__bvfunc_1: $i )).
thf(c2_7_type,type,( c2_7__bvfunc_1: $i )).
thf(k1_funct_1_type,type,( k1_funct_1: $i > $i > $i )).
thf(k3_xboole_0_type,type,( k3_xboole_0: $i > $i > $i )).
thf(k7_xboolean_type,type,( k7_xboolean: $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_margrel1_type,type,( v1_margrel1: $i > $o )).
thf(v1_relat_1_type,type,( v1_relat_1: $i > $o )).
thf(v1_xboolean_type,type,( v1_xboolean: $i > $o )).
thf(v1_xcmplx_0_type,type,( v1_xcmplx_0: $i > $o )).
thf(v1_xreal_0_type,type,( v1_xreal_0: $i > $o )).
thf(v1_xxreal_0_type,type,( v1_xxreal_0: $i > $o )).
thf(v7_ordinal1_type,type,( v7_ordinal1: $i > $o )).
thf(cc3_xreal_0,axiom,( ! [A: $i] : ( ( v1_xreal_0 @ A ) => ( v1_xcmplx_0 @ A ) ) ),file(xreal_0,cc3_xreal_0)).
thf(cc4_xreal_0,axiom,( ! [A: $i] : ( ( v1_xreal_0 @ A ) => ( v1_xxreal_0 @ A ) ) ),file(xreal_0,cc4_xreal_0)).
thf(rc1_xreal_0,axiom,( ? [A: $i] : ( v1_xreal_0 @ A ) ),file(xreal_0,rc1_xreal_0)).
thf(cc2_xreal_0,axiom,( ! [A: $i] : ( ( v7_ordinal1 @ A ) => ( v1_xreal_0 @ A ) ) ),file(xreal_0,cc2_xreal_0)).
thf(cc1_xboolean,axiom,( ! [A: $i] : ( ( v1_xboolean @ A ) => ( v7_ordinal1 @ A ) ) ),file(xboolean,cc1_xboolean)).
thf(fc6_xboolean,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_xboolean @ A ) & ( v1_xboolean @ B ) ) => ( v1_xboolean @ ( k7_xboolean @ A @ B ) ) ) ),file(xboolean,fc6_xboolean)).
thf(rc1_xboolean,axiom,( ? [A: $i] : ( v1_xboolean @ A ) ),file(xboolean,rc1_xboolean)).
thf(commutativity_k3_xboole_0,axiom,( ! [A: $i] : ! [B: $i] : ( = @ ( k3_xboole_0 @ A @ B ) @ ( k3_xboole_0 @ B @ A ) ) ),file(xboole_0,k3_xboole_0)).
thf(idempotence_k3_xboole_0,axiom,( ! [A: $i] : ! [B: $i] : ( = @ ( k3_xboole_0 @ A @ A ) @ A ) ),file(xboole_0,k3_xboole_0)).
thf(commutativity_k7_xboolean,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_xboolean @ A ) & ( v1_xboolean @ B ) ) => ( = @ ( k7_xboolean @ A @ B ) @ ( k7_xboolean @ B @ A ) ) ) ),file(xboolean,k7_xboolean)).
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_k3_xboole_0,axiom,( $true ),file(xboole_0,k3_xboole_0)).
thf(dt_k7_xboolean,axiom,( $true ),file(xboolean,k7_xboolean)).
thf(dt_k9_xtuple_0,axiom,( $true ),file(xtuple_0,k9_xtuple_0)).
thf(dt_c1_7__bvfunc_1,axiom,( ( v1_relat_1 @ c1_7__bvfunc_1 ) & ( v1_funct_1 @ c1_7__bvfunc_1 ) & ( v1_margrel1 @ c1_7__bvfunc_1 ) ),file(bvfunc_1,c1_7__bvfunc_1)).
thf(dt_c2_7__bvfunc_1,axiom,( ( v1_relat_1 @ c2_7__bvfunc_1 ) & ( v1_funct_1 @ c2_7__bvfunc_1 ) & ( v1_margrel1 @ c2_7__bvfunc_1 ) ),file(bvfunc_1,c2_7__bvfunc_1)).
thf(fc4_margrel1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_margrel1 @ A ) ) => ( v1_xboolean @ ( k1_funct_1 @ A @ B ) ) ) ),file(margrel1,fc4_margrel1)).
thf(rc1_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ),file(funct_1,rc1_funct_1)).
thf(rc2_margrel1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_margrel1 @ A ) ) ),file(margrel1,rc2_margrel1)).
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_7_2_1__bvfunc_1,conjecture,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( = @ ( k9_xtuple_0 @ A ) @ ( k3_xboole_0 @ ( k9_xtuple_0 @ c1_7__bvfunc_1 ) @ ( k9_xtuple_0 @ c2_7__bvfunc_1 ) ) ) & ! [B: $i] : ( ( r2_hidden @ B @ ( k3_xboole_0 @ ( k9_xtuple_0 @ c1_7__bvfunc_1 ) @ ( k9_xtuple_0 @ c2_7__bvfunc_1 ) ) ) => ( = @ ( k1_funct_1 @ A @ B ) @ ( k7_xboolean @ ( k1_funct_1 @ c1_7__bvfunc_1 @ B ) @ ( k1_funct_1 @ c2_7__bvfunc_1 @ B ) ) ) ) ) ),file(bvfunc_1,e1_7_2_1__bvfunc_1)).
