% Mizar problem: e12_58_1_1_1,ordinal1,1125,16 
include('Axioms/SET010^0.ax').
thf(c4_58_1_1_1_type,type,( c4_58_1_1_1__ordinal1: $i )).
thf(c5_58_1_1_1_type,type,( c5_58_1_1_1__ordinal1: $i )).
thf(c6_58_1_1_1_type,type,( c6_58_1_1_1__ordinal1: $i )).
thf(f2_s4_ordinal1_type,type,( f2_s4_ordinal1: $i > $i )).
thf(k10_xtuple_0_type,type,( k10_xtuple_0: $i > $i )).
thf(k1_funct_1_type,type,( k1_funct_1: $i > $i > $i )).
thf(k5_relat_1_type,type,( k5_relat_1: $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_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(v5_ordinal1_type,type,( v5_ordinal1: $i > $o )).
thf(v5_relat_1_type,type,( v5_relat_1: $i > $i > $o )).
thf(dt_k10_xtuple_0,axiom,( $true ),file(xtuple_0,k10_xtuple_0)).
thf(cc2_ordinal1,axiom,( ! [A: $i] : ( ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc2_ordinal1)).
thf(fc26_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_relat_1 @ C ) & ( v5_relat_1 @ C @ B ) ) => ( ( v1_relat_1 @ ( k5_relat_1 @ C @ A ) ) & ( v5_relat_1 @ ( k5_relat_1 @ C @ A ) @ B ) ) ) ),file(relat_1,fc26_relat_1)).
thf(rc3_ordinal1,axiom,( ! [A: $i] : ? [B: $i] : ( ( v1_relat_1 @ B ) & ( v5_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v5_ordinal1 @ B ) ) ),file(ordinal1,rc3_ordinal1)).
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_k5_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_relat_1 @ A ) => ( v1_relat_1 @ ( k5_relat_1 @ A @ B ) ) ) ),file(relat_1,k5_relat_1)).
thf(dt_k9_xtuple_0,axiom,( $true ),file(xtuple_0,k9_xtuple_0)).
thf(dt_c4_58_1_1_1__ordinal1,axiom,( ( v1_relat_1 @ c4_58_1_1_1__ordinal1 ) & ( v1_funct_1 @ c4_58_1_1_1__ordinal1 ) & ( v5_ordinal1 @ c4_58_1_1_1__ordinal1 ) ),file(ordinal1,c4_58_1_1_1__ordinal1)).
thf(dt_c5_58_1_1_1__ordinal1,axiom,( v3_ordinal1 @ c5_58_1_1_1__ordinal1 ),file(ordinal1,c5_58_1_1_1__ordinal1)).
thf(dt_c6_58_1_1_1__ordinal1,axiom,( ( v1_relat_1 @ c6_58_1_1_1__ordinal1 ) & ( v1_funct_1 @ c6_58_1_1_1__ordinal1 ) & ( v5_ordinal1 @ c6_58_1_1_1__ordinal1 ) ),file(ordinal1,c6_58_1_1_1__ordinal1)).
thf(dt_f2_s4_ordinal1,axiom,( $true ),file(ordinal1,f2_s4_ordinal1)).
thf(cc1_ordinal1,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) ) ),file(ordinal1,cc1_ordinal1)).
thf(fc4_ordinal1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v5_ordinal1 @ A ) ) => ( v3_ordinal1 @ ( k9_xtuple_0 @ A ) ) ) ),file(ordinal1,fc4_ordinal1)).
thf(fc5_ordinal1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v5_ordinal1 @ A ) & ( v3_ordinal1 @ B ) ) => ( ( v1_relat_1 @ ( k5_relat_1 @ A @ B ) ) & ( v5_relat_1 @ ( k5_relat_1 @ A @ B ) @ ( k10_xtuple_0 @ A ) ) & ( v5_ordinal1 @ ( k5_relat_1 @ A @ B ) ) ) ) ),file(ordinal1,fc5_ordinal1)).
thf(fc8_funct_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) => ( ( v1_relat_1 @ ( k5_relat_1 @ A @ B ) ) & ( v1_funct_1 @ ( k5_relat_1 @ A @ B ) ) ) ) ),file(funct_1,fc8_funct_1)).
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(rd4_relat_1,axiom,( ! [A: $i] : ( ( v1_relat_1 @ A ) => ( = @ ( k5_relat_1 @ A @ ( k9_xtuple_0 @ A ) ) @ A ) ) ),file(relat_1,rd4_relat_1)).
thf(rd5_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( v1_relat_1 @ A ) => ( = @ ( k5_relat_1 @ ( k5_relat_1 @ A @ B ) @ B ) @ ( k5_relat_1 @ A @ B ) ) ) ),file(relat_1,rd5_relat_1)).
thf(e11_58_1_1_1__ordinal1,axiom,( ( = @ ( k9_xtuple_0 @ c6_58_1_1_1__ordinal1 ) @ c5_58_1_1_1__ordinal1 ) & ! [A: $i] : ( ( v3_ordinal1 @ A ) => ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) & ( v5_ordinal1 @ B ) ) => ( ( ( r2_hidden @ A @ c5_58_1_1_1__ordinal1 ) & ( = @ B @ ( k5_relat_1 @ c6_58_1_1_1__ordinal1 @ A ) ) ) => ( = @ ( k1_funct_1 @ c6_58_1_1_1__ordinal1 @ A ) @ ( f2_s4_ordinal1 @ B ) ) ) ) ) ),file(ordinal1,e11_58_1_1_1__ordinal1)).
thf(e9_58_1_1_1__ordinal1,axiom,( ( = @ ( k9_xtuple_0 @ c4_58_1_1_1__ordinal1 ) @ c5_58_1_1_1__ordinal1 ) & ! [A: $i] : ( ( v3_ordinal1 @ A ) => ! [B: $i] : ( ( ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) & ( v5_ordinal1 @ B ) ) => ( ( ( r2_hidden @ A @ c5_58_1_1_1__ordinal1 ) & ( = @ B @ ( k5_relat_1 @ c4_58_1_1_1__ordinal1 @ A ) ) ) => ( = @ ( k1_funct_1 @ c4_58_1_1_1__ordinal1 @ A ) @ ( f2_s4_ordinal1 @ B ) ) ) ) ) ),file(ordinal1,e9_58_1_1_1__ordinal1)).
thf(s3_ordinal1,axiom,( ! [A: $i > $i] : ! [B: $i] : ! [C: $i] : ! [D: $i] : ( ( ( v3_ordinal1 @ D ) & ( v1_relat_1 @ C ) & ( v1_funct_1 @ C ) & ( v5_ordinal1 @ C ) & ( v1_relat_1 @ B ) & ( v1_funct_1 @ B ) & ( v5_ordinal1 @ B ) ) => ( ( ( = @ ( k9_xtuple_0 @ C ) @ D ) & ! [E: $i] : ( ( v3_ordinal1 @ E ) => ! [F: $i] : ( ( ( v1_relat_1 @ F ) & ( v1_funct_1 @ F ) & ( v5_ordinal1 @ F ) ) => ( ( ( r2_hidden @ E @ D ) & ( = @ F @ ( k5_relat_1 @ C @ E ) ) ) => ( = @ ( k1_funct_1 @ C @ E ) @ ( A @ F ) ) ) ) ) & ( = @ ( k9_xtuple_0 @ B ) @ D ) & ! [E: $i] : ( ( v3_ordinal1 @ E ) => ! [F: $i] : ( ( ( v1_relat_1 @ F ) & ( v1_funct_1 @ F ) & ( v5_ordinal1 @ F ) ) => ( ( ( r2_hidden @ E @ D ) & ( = @ F @ ( k5_relat_1 @ B @ E ) ) ) => ( = @ ( k1_funct_1 @ B @ E ) @ ( A @ F ) ) ) ) ) ) => ( = @ C @ B ) ) ) ),file(ordinal1,s3_ordinal1)).
thf(e12_58_1_1_1__ordinal1,conjecture,( = @ c6_58_1_1_1__ordinal1 @ c4_58_1_1_1__ordinal1 ),file(ordinal1,e12_58_1_1_1__ordinal1)).
