% Mizar problem: e1_7_1_1,equation,235,13 
include('Axioms/SET010^0.ax').
thf(c1_7_type,type,( c1_7__equation: $i )).
thf(c2_7_type,type,( c2_7__equation: $i )).
thf(c3_7_type,type,( c3_7__equation: $i )).
thf(k1_funct_1_type,type,( k1_funct_1: $i > $i > $i )).
thf(k8_relat_1_type,type,( k8_relat_1: $i > $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_partfun1_type,type,( v1_partfun1: $i > $i > $o )).
thf(v1_relat_1_type,type,( v1_relat_1: $i > $o )).
thf(v2_funcop_1_type,type,( v2_funcop_1: $i > $o )).
thf(v4_relat_1_type,type,( v4_relat_1: $i > $i > $o )).
thf(rc1_msualg_4,axiom,( ! [A: $i] : ? [B: $i] : ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ( v2_funcop_1 @ B ) ) ),file(msualg_4,rc1_msualg_4)).
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_k8_relat_1,axiom,( $true ),file(relat_1,k8_relat_1)).
thf(dt_c1_7__equation,axiom,( $true ),file(equation,c1_7__equation)).
thf(dt_c2_7__equation,axiom,( ( v1_relat_1 @ c2_7__equation ) & ( v4_relat_1 @ c2_7__equation @ c1_7__equation ) & ( v1_funct_1 @ c2_7__equation ) & ( v1_partfun1 @ c2_7__equation @ c1_7__equation ) ),file(equation,c2_7__equation)).
thf(dt_c3_7__equation,axiom,( ( v1_relat_1 @ c3_7__equation ) & ( v4_relat_1 @ c3_7__equation @ c1_7__equation ) & ( v1_funct_1 @ c3_7__equation ) & ( v1_partfun1 @ c3_7__equation @ c1_7__equation ) & ( v1_funcop_1 @ c3_7__equation ) ),file(equation,c3_7__equation)).
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(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(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(rc1_pboole,axiom,( ! [A: $i] : ? [B: $i] : ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) ),file(pboole,rc1_pboole)).
thf(rc4_pboole,axiom,( ! [A: $i] : ? [B: $i] : ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ( v1_funcop_1 @ B ) ) ),file(pboole,rc4_pboole)).
thf(s4_pboole,axiom,( ! [A: $i > $i] : ! [B: $i] : ? [C: $i] : ( ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ B ) & ( v1_funct_1 @ C ) & ( v1_partfun1 @ C @ B ) & ! [D: $i] : ( ( r2_hidden @ D @ B ) => ( = @ ( k1_funct_1 @ C @ D ) @ ( A @ D ) ) ) ) ),file(pboole,s4_pboole)).
thf(e1_7_1_1__equation,conjecture,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v4_relat_1 @ A @ c1_7__equation ) & ( v1_funct_1 @ A ) & ( v1_partfun1 @ A @ c1_7__equation ) & ! [B: $i] : ( ( r2_hidden @ B @ c1_7__equation ) => ( = @ ( k1_funct_1 @ A @ B ) @ ( k8_relat_1 @ ( k1_funct_1 @ c3_7__equation @ B ) @ ( k1_funct_1 @ c2_7__equation @ B ) ) ) ) ) ),file(equation,e1_7_1_1__equation)).
