% Mizar problem: e6_45,funct_6,1196,44 
include('Axioms/SET010^0.ax').
thf(c1_45_type,type,( c1_45__funct_6: $i )).
thf(c3_45_type,type,( c3_45__funct_6: $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(k1_funct_6_type,type,( k1_funct_6: $i > $i )).
thf(k2_funct_6_type,type,( k2_funct_6: $i > $i )).
thf(k8_relat_1_type,type,( k8_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_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_k10_xtuple_0,axiom,( $true ),file(xtuple_0,k10_xtuple_0)).
thf(dt_k1_funct_1,axiom,( $true ),file(funct_1,k1_funct_1)).
thf(dt_k1_funct_6,axiom,( $true ),file(funct_6,k1_funct_6)).
thf(dt_k2_funct_6,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) => ( ( v1_relat_1 @ ( k2_funct_6 @ A ) ) & ( v1_funct_1 @ ( k2_funct_6 @ A ) ) ) ) ),file(funct_6,k2_funct_6)).
thf(dt_k8_relat_1,axiom,( $true ),file(relat_1,k8_relat_1)).
thf(dt_k9_xtuple_0,axiom,( $true ),file(xtuple_0,k9_xtuple_0)).
thf(dt_c1_45__funct_6,axiom,( ( v1_relat_1 @ c1_45__funct_6 ) & ( v1_funct_1 @ c1_45__funct_6 ) ),file(funct_6,c1_45__funct_6)).
thf(dt_c3_45__funct_6,axiom,( ( v1_relat_1 @ c3_45__funct_6 ) & ( v1_funct_1 @ c3_45__funct_6 ) ),file(funct_6,c3_45__funct_6)).
thf(rc1_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ),file(funct_1,rc1_funct_1)).
thf(s2_card_3,axiom,( ! [A: $i > $i > $o] : ! [B: $i > $i] : ! [C: $i] : ? [D: $i] : ( ( v1_relat_1 @ D ) & ( v1_funct_1 @ D ) & ( = @ ( k9_xtuple_0 @ D ) @ C ) & ! [E: $i] : ( ( r2_hidden @ E @ C ) => ! [F: $i] : ( ( r2_hidden @ F @ ( k1_funct_1 @ D @ E ) ) <=> ( ( r2_hidden @ F @ ( B @ E ) ) & ( A @ E @ F ) ) ) ) ) ),file(card_3,s2_card_3)).
thf(e6_45__funct_6,conjecture,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( = @ ( k9_xtuple_0 @ A ) @ ( k8_relat_1 @ c1_45__funct_6 @ ( k1_funct_6 @ ( k10_xtuple_0 @ c1_45__funct_6 ) ) ) ) & ! [B: $i] : ( ( r2_hidden @ B @ ( k8_relat_1 @ c1_45__funct_6 @ ( k1_funct_6 @ ( k10_xtuple_0 @ c1_45__funct_6 ) ) ) ) => ! [C: $i] : ( ( r2_hidden @ C @ ( k1_funct_1 @ A @ B ) ) <=> ( ( r2_hidden @ C @ ( k1_funct_1 @ ( k2_funct_6 @ c1_45__funct_6 ) @ B ) ) & ? [D: $i] : ( ( v1_relat_1 @ D ) & ( v1_funct_1 @ D ) & ( = @ D @ ( k1_funct_1 @ c1_45__funct_6 @ B ) ) & ( = @ ( k1_funct_1 @ D @ C ) @ ( k1_funct_1 @ c3_45__funct_6 @ B ) ) ) ) ) ) ) ),file(funct_6,e6_45__funct_6)).
