% Mizar problem: e1_25_1_2,catalg_1,746,63 
include('Axioms/SET010^0.ax').
thf(c1_25_type,type,( c1_25__catalg_1: $i )).
thf(k10_xtuple_0_type,type,( k10_xtuple_0: $i > $i )).
thf(k2_xboole_0_type,type,( k2_xboole_0: $i > $i > $i )).
thf(k4_tarski_type,type,( k4_tarski: $i > $i > $i )).
thf(u1_struct_0_type,type,( u1_struct_0: $i > $i )).
thf(u4_struct_0_type,type,( u4_struct_0: $i > $i )).
thf(l1_msualg_1_type,type,( l1_msualg_1: $i > $o )).
thf(l1_struct_0_type,type,( l1_struct_0: $i > $o )).
thf(l5_struct_0_type,type,( l5_struct_0: $i > $o )).
thf(v1_funct_1_type,type,( v1_funct_1: $i > $o )).
thf(v1_relat_1_type,type,( v1_relat_1: $i > $o )).
thf(v1_xtuple_0_type,type,( v1_xtuple_0: $i > $o )).
thf(dt_l1_struct_0,axiom,( $true ),file(struct_0,l1_struct_0)).
thf(dt_l5_struct_0,axiom,( ! [A: $i] : ( ( l5_struct_0 @ A ) => ( l1_struct_0 @ A ) ) ),file(struct_0,l5_struct_0)).
thf(rc1_xtuple_0,axiom,( ? [A: $i] : ( v1_xtuple_0 @ A ) ),file(xtuple_0,rc1_xtuple_0)).
thf(commutativity_k2_xboole_0,axiom,( ! [A: $i] : ! [B: $i] : ( = @ ( k2_xboole_0 @ A @ B ) @ ( k2_xboole_0 @ B @ A ) ) ),file(xboole_0,k2_xboole_0)).
thf(idempotence_k2_xboole_0,axiom,( ! [A: $i] : ! [B: $i] : ( = @ ( k2_xboole_0 @ A @ A ) @ A ) ),file(xboole_0,k2_xboole_0)).
thf(antisymmetry_r2_hidden,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ~ ( r2_hidden @ B @ A ) ) ),file(hidden,r2_hidden)).
thf(dt_k10_xtuple_0,axiom,( $true ),file(xtuple_0,k10_xtuple_0)).
thf(dt_k2_xboole_0,axiom,( $true ),file(xboole_0,k2_xboole_0)).
thf(dt_k4_tarski,axiom,( $true ),file(tarski,k4_tarski)).
thf(dt_l1_msualg_1,axiom,( ! [A: $i] : ( ( l1_msualg_1 @ A ) => ( l5_struct_0 @ A ) ) ),file(msualg_1,l1_msualg_1)).
thf(dt_u1_struct_0,axiom,( $true ),file(struct_0,u1_struct_0)).
thf(dt_u4_struct_0,axiom,( $true ),file(struct_0,u4_struct_0)).
thf(dt_c1_25__catalg_1,axiom,( l1_msualg_1 @ c1_25__catalg_1 ),file(catalg_1,c1_25__catalg_1)).
thf(fc1_xtuple_0,axiom,( ! [A: $i] : ! [B: $i] : ( v1_xtuple_0 @ ( k4_tarski @ A @ B ) ) ),file(xtuple_0,fc1_xtuple_0)).
thf(fc3_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_relat_1 @ B ) ) => ( v1_relat_1 @ ( k2_xboole_0 @ A @ B ) ) ) ),file(relat_1,fc3_relat_1)).
thf(rc1_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ),file(funct_1,rc1_funct_1)).
thf(s3_xboole_0,axiom,( ! [A: $i > $o] : ! [B: $i] : ! [C: $i] : ( ( ! [D: $i] : ( ( r2_hidden @ D @ B ) <=> ( A @ D ) ) & ! [D: $i] : ( ( r2_hidden @ D @ C ) <=> ( A @ D ) ) ) => ( = @ B @ C ) ) ),file(xboole_0,s3_xboole_0)).
thf(e1_25_1_2__catalg_1,conjecture,( ! [A: $i] : ! [B: $i] : ( ( ! [C: $i] : ( ( r2_hidden @ C @ A ) <=> ? [D: $i] : ? [E: $i] : ( ( v1_relat_1 @ E ) & ( v1_funct_1 @ E ) & ( r2_hidden @ ( k4_tarski @ D @ E ) @ ( k2_xboole_0 @ ( u1_struct_0 @ c1_25__catalg_1 ) @ ( u4_struct_0 @ c1_25__catalg_1 ) ) ) & ( r2_hidden @ C @ ( k10_xtuple_0 @ E ) ) ) ) & ! [C: $i] : ( ( r2_hidden @ C @ B ) <=> ? [D: $i] : ? [E: $i] : ( ( v1_relat_1 @ E ) & ( v1_funct_1 @ E ) & ( r2_hidden @ ( k4_tarski @ D @ E ) @ ( k2_xboole_0 @ ( u1_struct_0 @ c1_25__catalg_1 ) @ ( u4_struct_0 @ c1_25__catalg_1 ) ) ) & ( r2_hidden @ C @ ( k10_xtuple_0 @ E ) ) ) ) ) => ( = @ A @ B ) ) ),file(catalg_1,e1_25_1_2__catalg_1)).
