% Mizar problem: e14_56,ordinal1,994,43 
include('Axioms/SET010^0.ax').
thf(c3_56_type,type,( c3_56__ordinal1: $i )).
thf(k10_xtuple_0_type,type,( k10_xtuple_0: $i > $i )).
thf(r1_ordinal1_type,type,( r1_ordinal1: $i > $i > $o )).
thf(r1_tarski_type,type,( r1_tarski: $i > $i > $o )).
thf(v1_funct_1_type,type,( v1_funct_1: $i > $o )).
thf(v1_ordinal1_type,type,( v1_ordinal1: $i > $o )).
thf(v1_relat_1_type,type,( v1_relat_1: $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_k10_xtuple_0,axiom,( $true ),file(xtuple_0,k10_xtuple_0)).
thf(dt_c3_56__ordinal1,axiom,( ( v1_relat_1 @ c3_56__ordinal1 ) & ( v1_funct_1 @ c3_56__ordinal1 ) ),file(ordinal1,c3_56__ordinal1)).
thf(cc1_ordinal1,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) ) ),file(ordinal1,cc1_ordinal1)).
thf(rc1_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ),file(funct_1,rc1_funct_1)).
thf(rc1_ordinal1,axiom,( ? [A: $i] : ( v3_ordinal1 @ A ) ),file(ordinal1,rc1_ordinal1)).
thf(e13_56__ordinal1,axiom,( ? [A: $i] : ( ( v3_ordinal1 @ A ) & ! [B: $i] : ( ( v3_ordinal1 @ B ) => ( ( r2_hidden @ B @ ( k10_xtuple_0 @ c3_56__ordinal1 ) ) => ( r1_ordinal1 @ B @ A ) ) ) ) ),file(ordinal1,e13_56__ordinal1)).
thf(s1_ordinal1,axiom,( ! [A: $i > $o] : ( ? [B: $i] : ( ( v3_ordinal1 @ B ) & ( A @ B ) ) => ? [B: $i] : ( ( v3_ordinal1 @ B ) & ( A @ B ) & ! [C: $i] : ( ( v3_ordinal1 @ C ) => ( ( A @ C ) => ( r1_ordinal1 @ B @ C ) ) ) ) ) ),file(ordinal1,s1_ordinal1)).
thf(e14_56__ordinal1,conjecture,( ? [A: $i] : ( ( v3_ordinal1 @ A ) & ! [B: $i] : ( ( v3_ordinal1 @ B ) => ( ( r2_hidden @ B @ ( k10_xtuple_0 @ c3_56__ordinal1 ) ) => ( r1_ordinal1 @ B @ A ) ) ) & ! [B: $i] : ( ( v3_ordinal1 @ B ) => ( ! [C: $i] : ( ( v3_ordinal1 @ C ) => ( ( r2_hidden @ C @ ( k10_xtuple_0 @ c3_56__ordinal1 ) ) => ( r1_ordinal1 @ C @ B ) ) ) => ( r1_ordinal1 @ A @ B ) ) ) ) ),file(ordinal1,e14_56__ordinal1)).
