% Mizar problem: e4_26,funct_5,540,39 
include('Axioms/SET010^0.ax').
thf(c1_26_type,type,( c1_26__funct_5: $i )).
thf(c3_26_type,type,( c3_26__funct_5: $i )).
thf(k1_funct_1_type,type,( k1_funct_1: $i > $i > $i )).
thf(k2_funct_5_type,type,( k2_funct_5: $i > $i )).
thf(k2_zfmisc_1_type,type,( k2_zfmisc_1: $i > $i > $i )).
thf(k4_tarski_type,type,( k4_tarski: $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(v1_xtuple_0_type,type,( v1_xtuple_0: $i > $o )).
thf(rc1_xtuple_0,axiom,( ? [A: $i] : ( v1_xtuple_0 @ A ) ),file(xtuple_0,rc1_xtuple_0)).
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_k2_funct_5,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) => ( ( v1_relat_1 @ ( k2_funct_5 @ A ) ) & ( v1_funct_1 @ ( k2_funct_5 @ A ) ) ) ) ),file(funct_5,k2_funct_5)).
thf(dt_k2_zfmisc_1,axiom,( $true ),file(zfmisc_1,k2_zfmisc_1)).
thf(dt_k4_tarski,axiom,( $true ),file(tarski,k4_tarski)).
thf(dt_k9_xtuple_0,axiom,( $true ),file(xtuple_0,k9_xtuple_0)).
thf(dt_c1_26__funct_5,axiom,( $true ),file(funct_5,c1_26__funct_5)).
thf(dt_c3_26__funct_5,axiom,( ( v1_relat_1 @ c3_26__funct_5 ) & ( v1_funct_1 @ c3_26__funct_5 ) ),file(funct_5,c3_26__funct_5)).
thf(fc1_xtuple_0,axiom,( ! [A: $i] : ! [B: $i] : ( v1_xtuple_0 @ ( k4_tarski @ A @ B ) ) ),file(xtuple_0,fc1_xtuple_0)).
thf(fc6_relat_1,axiom,( ! [A: $i] : ! [B: $i] : ( v1_relat_1 @ ( k2_zfmisc_1 @ A @ B ) ) ),file(relat_1,fc6_relat_1)).
thf(rc1_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ),file(funct_1,rc1_funct_1)).
thf(e3_26__funct_5,axiom,( ! [A: $i] : ( ( r2_hidden @ A @ ( k9_xtuple_0 @ ( k2_funct_5 @ c3_26__funct_5 ) ) ) <=> ? [B: $i] : ? [C: $i] : ( ( v1_relat_1 @ C ) & ( v1_funct_1 @ C ) & ? [D: $i] : ( ( = @ A @ ( k4_tarski @ B @ D ) ) & ( r2_hidden @ B @ ( k9_xtuple_0 @ c3_26__funct_5 ) ) & ( = @ C @ ( k1_funct_1 @ c3_26__funct_5 @ B ) ) & ( r2_hidden @ D @ ( k9_xtuple_0 @ C ) ) ) ) ) ),file(funct_5,e3_26__funct_5)).
thf(e2_26__funct_5,axiom,( ! [A: $i] : ( ( r2_hidden @ A @ ( k2_zfmisc_1 @ ( k9_xtuple_0 @ c3_26__funct_5 ) @ c1_26__funct_5 ) ) <=> ? [B: $i] : ? [C: $i] : ( ( v1_relat_1 @ C ) & ( v1_funct_1 @ C ) & ? [D: $i] : ( ( = @ A @ ( k4_tarski @ B @ D ) ) & ( r2_hidden @ B @ ( k9_xtuple_0 @ c3_26__funct_5 ) ) & ( = @ C @ ( k1_funct_1 @ c3_26__funct_5 @ B ) ) & ( r2_hidden @ D @ ( k9_xtuple_0 @ C ) ) ) ) ) ),file(funct_5,e2_26__funct_5)).
thf(s2_xboole_0,axiom,( ! [A: $i] : ! [B: $i > $o] : ! [C: $i] : ( ( ! [D: $i] : ( ( r2_hidden @ D @ C ) <=> ( B @ D ) ) & ! [D: $i] : ( ( r2_hidden @ D @ A ) <=> ( B @ D ) ) ) => ( = @ C @ A ) ) ),file(xboole_0,s2_xboole_0)).
thf(e4_26__funct_5,conjecture,( = @ ( k9_xtuple_0 @ ( k2_funct_5 @ c3_26__funct_5 ) ) @ ( k2_zfmisc_1 @ ( k9_xtuple_0 @ c3_26__funct_5 ) @ c1_26__funct_5 ) ),file(funct_5,e4_26__funct_5)).
