% Mizar problem: e9_1_1_1,simplex1,89,57 
include('Axioms/SET010^0.ax').
thf(c1_1_type,type,( c1_1__simplex1: $i )).
thf(c2_1_type,type,( c2_1__simplex1: $i )).
thf(c3_1_1_1_type,type,( c3_1_1_1__simplex1: $i )).
thf(k1_funct_1_type,type,( k1_funct_1: $i > $i > $i )).
thf(k1_xtuple_0_type,type,( k1_xtuple_0: $i > $i )).
thf(k2_xtuple_0_type,type,( k2_xtuple_0: $i > $i )).
thf(k4_tarski_type,type,( k4_tarski: $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_funcop_1_type,type,( v1_funcop_1: $i > $o )).
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(v2_funcop_1_type,type,( v2_funcop_1: $i > $o )).
thf(rc1_xtuple_0,axiom,( ? [A: $i] : ( v1_xtuple_0 @ A ) ),file(xtuple_0,rc1_xtuple_0)).
thf(rd3_xtuple_0,axiom,( ! [A: $i] : ( ( v1_xtuple_0 @ A ) => ( = @ ( k4_tarski @ ( k1_xtuple_0 @ A ) @ ( k2_xtuple_0 @ A ) ) @ A ) ) ),file(xtuple_0,rd3_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_k1_xtuple_0,axiom,( $true ),file(xtuple_0,k1_xtuple_0)).
thf(dt_k2_xtuple_0,axiom,( $true ),file(xtuple_0,k2_xtuple_0)).
thf(dt_k4_tarski,axiom,( $true ),file(tarski,k4_tarski)).
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_c1_1__simplex1,axiom,( $true ),file(simplex1,c1_1__simplex1)).
thf(dt_c2_1__simplex1,axiom,( v1_relat_1 @ c2_1__simplex1 ),file(simplex1,c2_1__simplex1)).
thf(dt_c3_1_1_1__simplex1,axiom,( ( v1_relat_1 @ c3_1_1_1__simplex1 ) & ( v1_funct_1 @ c3_1_1_1__simplex1 ) & ( v1_funcop_1 @ c3_1_1_1__simplex1 ) ),file(simplex1,c3_1_1_1__simplex1)).
thf(cc2_funcop_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_funcop_1 @ A ) ) => ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v2_funcop_1 @ A ) ) ) ),file(funcop_1,cc2_funcop_1)).
thf(fc13_funcop_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_funcop_1 @ A ) ) => ( ( v1_relat_1 @ ( k5_relat_1 @ A @ B ) ) & ( v1_funcop_1 @ ( k5_relat_1 @ A @ B ) ) ) ) ),file(funcop_1,fc13_funcop_1)).
thf(fc1_xtuple_0,axiom,( ! [A: $i] : ! [B: $i] : ( v1_xtuple_0 @ ( k4_tarski @ A @ B ) ) ),file(xtuple_0,fc1_xtuple_0)).
thf(fc8_funcop_1,axiom,( ! [A: $i] : ! [B: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_funcop_1 @ A ) ) => ( ( v1_relat_1 @ ( k1_funct_1 @ A @ B ) ) & ( v1_funct_1 @ ( k1_funct_1 @ A @ B ) ) ) ) ),file(funcop_1,fc8_funcop_1)).
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_funcop_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( v1_funcop_1 @ A ) ) ),file(funcop_1,rc1_funcop_1)).
thf(rc1_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ),file(funct_1,rc1_funct_1)).
thf(rd1_xtuple_0,axiom,( ! [A: $i] : ! [B: $i] : ( = @ ( k1_xtuple_0 @ ( k4_tarski @ A @ B ) ) @ A ) ),file(xtuple_0,rd1_xtuple_0)).
thf(rd2_xtuple_0,axiom,( ! [A: $i] : ! [B: $i] : ( = @ ( k2_xtuple_0 @ ( k4_tarski @ A @ B ) ) @ B ) ),file(xtuple_0,rd2_xtuple_0)).
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(s3_funct_1,axiom,( ! [A: $i > $i] : ! [B: $i] : ? [C: $i] : ( ( v1_relat_1 @ C ) & ( v1_funct_1 @ C ) & ( = @ ( k9_xtuple_0 @ C ) @ B ) & ! [D: $i] : ( ( r2_hidden @ D @ B ) => ( = @ ( k1_funct_1 @ C @ D ) @ ( A @ D ) ) ) ) ),file(funct_1,s3_funct_1)).
thf(e9_1_1_1__simplex1,conjecture,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) & ( = @ ( k9_xtuple_0 @ A ) @ ( k5_relat_1 @ c2_1__simplex1 @ c1_1__simplex1 ) ) & ! [B: $i] : ( ( r2_hidden @ B @ ( k5_relat_1 @ c2_1__simplex1 @ c1_1__simplex1 ) ) => ( = @ ( k1_funct_1 @ A @ B ) @ ( k4_tarski @ ( k1_xtuple_0 @ B ) @ ( k1_funct_1 @ ( k1_funct_1 @ c3_1_1_1__simplex1 @ ( k1_xtuple_0 @ B ) ) @ ( k2_xtuple_0 @ B ) ) ) ) ) ) ),file(simplex1,e9_1_1_1__simplex1)).
