% Mizar problem: e3_75_1,ordinal2,2086,25 
include('Axioms/SET010^0.ax').
thf(c1_75_type,type,( c1_75__ordinal2: $i )).
thf(c2_75_type,type,( c2_75__ordinal2: $i )).
thf(k11_ordinal2_type,type,( k11_ordinal2: $i > $i > $i )).
thf(r1_ordinal1_type,type,( r1_ordinal1: $i > $i > $o )).
thf(r1_tarski_type,type,( r1_tarski: $i > $i > $o )).
thf(v1_ordinal1_type,type,( v1_ordinal1: $i > $o )).
thf(v2_ordinal1_type,type,( v2_ordinal1: $i > $o )).
thf(v3_ordinal1_type,type,( v3_ordinal1: $i > $o )).
thf(reflexivity_r1_tarski,axiom,( ! [A: $i] : ! [B: $i] : ( r1_tarski @ A @ A ) ),file(tarski,r1_tarski)).
thf(cc2_ordinal1,axiom,( ! [A: $i] : ( ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc2_ordinal1)).
thf(reflexivity_r1_ordinal1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v3_ordinal1 @ A ) & ( v3_ordinal1 @ B ) ) => ( r1_ordinal1 @ A @ A ) ) ),file(ordinal1,r1_ordinal1)).
thf(connectedness_r1_ordinal1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v3_ordinal1 @ A ) & ( v3_ordinal1 @ B ) ) => ( ( r1_ordinal1 @ A @ B ) | ( r1_ordinal1 @ B @ A ) ) ) ),file(ordinal1,r1_ordinal1)).
thf(antisymmetry_r2_hidden,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ~ ( r2_hidden @ B @ A ) ) ),file(hidden,r2_hidden)).
thf(redefinition_r1_ordinal1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v3_ordinal1 @ A ) & ( v3_ordinal1 @ B ) ) => ( ( r1_ordinal1 @ A @ B ) <=> ( r1_tarski @ A @ B ) ) ) ),file(ordinal1,r1_ordinal1)).
thf(dt_k11_ordinal2,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v3_ordinal1 @ A ) & ( v3_ordinal1 @ B ) ) => ( v3_ordinal1 @ ( k11_ordinal2 @ A @ B ) ) ) ),file(ordinal2,k11_ordinal2)).
thf(dt_c1_75__ordinal2,axiom,( v3_ordinal1 @ c1_75__ordinal2 ),file(ordinal2,c1_75__ordinal2)).
thf(dt_c2_75__ordinal2,axiom,( v3_ordinal1 @ c2_75__ordinal2 ),file(ordinal2,c2_75__ordinal2)).
thf(cc1_ordinal1,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) ) ),file(ordinal1,cc1_ordinal1)).
thf(rc1_ordinal1,axiom,( ? [A: $i] : ( v3_ordinal1 @ A ) ),file(ordinal1,rc1_ordinal1)).
thf(e2_75_1__ordinal2,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ( ! [B: $i] : ( ( v3_ordinal1 @ B ) => ( ( r2_hidden @ B @ A ) => ( r1_ordinal1 @ ( k11_ordinal2 @ B @ c1_75__ordinal2 ) @ ( k11_ordinal2 @ B @ c2_75__ordinal2 ) ) ) ) => ( r1_ordinal1 @ ( k11_ordinal2 @ A @ c1_75__ordinal2 ) @ ( k11_ordinal2 @ A @ c2_75__ordinal2 ) ) ) ) ),file(ordinal2,e2_75_1__ordinal2)).
thf(s2_ordinal1,axiom,( ! [A: $i > $o] : ( ! [B: $i] : ( ( v3_ordinal1 @ B ) => ( ! [C: $i] : ( ( v3_ordinal1 @ C ) => ( ( r2_hidden @ C @ B ) => ( A @ C ) ) ) => ( A @ B ) ) ) => ! [B: $i] : ( ( v3_ordinal1 @ B ) => ( A @ B ) ) ) ),file(ordinal1,s2_ordinal1)).
thf(e3_75_1__ordinal2,conjecture,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ( r1_ordinal1 @ ( k11_ordinal2 @ A @ c1_75__ordinal2 ) @ ( k11_ordinal2 @ A @ c2_75__ordinal2 ) ) ) ),file(ordinal2,e3_75_1__ordinal2)).
