% Mizar problem: e2_87_1,funct_2,1234,26 
include('Axioms/SET010^0.ax').
thf(f1_s5_funct_2_type,type,( f1_s5_funct_2: $i )).
thf(f3_s5_funct_2_type,type,( f3_s5_funct_2: $i > $i )).
thf(f4_s5_funct_2_type,type,( f4_s5_funct_2: $i > $i )).
thf(k1_funct_1_type,type,( k1_funct_1: $i > $i > $i )).
thf(k9_xtuple_0_type,type,( k9_xtuple_0: $i > $i )).
thf(p1_s5_funct_2_type,type,( p1_s5_funct_2: $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(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_k9_xtuple_0,axiom,( $true ),file(xtuple_0,k9_xtuple_0)).
thf(dt_f1_s5_funct_2,axiom,( $true ),file(funct_2,f1_s5_funct_2)).
thf(dt_f3_s5_funct_2,axiom,( $true ),file(funct_2,f3_s5_funct_2)).
thf(dt_f4_s5_funct_2,axiom,( $true ),file(funct_2,f4_s5_funct_2)).
thf(rc1_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ),file(funct_1,rc1_funct_1)).
thf(s1_partfun1,axiom,( ! [A: $i > $i] : ! [B: $i > $i] : ! [C: $i > $o] : ! [D: $i] : ? [E: $i] : ( ( v1_relat_1 @ E ) & ( v1_funct_1 @ E ) & ( = @ ( k9_xtuple_0 @ E ) @ D ) & ! [F: $i] : ( ( r2_hidden @ F @ D ) => ( ( ( C @ F ) => ( = @ ( k1_funct_1 @ E @ F ) @ ( B @ F ) ) ) & ( ~ ( C @ F ) => ( = @ ( k1_funct_1 @ E @ F ) @ ( A @ F ) ) ) ) ) ) ),file(partfun1,s1_partfun1)).
thf(e2_87_1__funct_2,conjecture,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( = @ ( k9_xtuple_0 @ A ) @ f1_s5_funct_2 ) & ! [B: $i] : ( ( r2_hidden @ B @ f1_s5_funct_2 ) => ( ( ( p1_s5_funct_2 @ B ) => ( = @ ( k1_funct_1 @ A @ B ) @ ( f3_s5_funct_2 @ B ) ) ) & ( ~ ( p1_s5_funct_2 @ B ) => ( = @ ( k1_funct_1 @ A @ B ) @ ( f4_s5_funct_2 @ B ) ) ) ) ) ) ),file(funct_2,e2_87_1__funct_2)).
