% Mizar problem: e1_27_2_1,msualg_9,710,49 
include('Axioms/SET010^0.ax').
thf(c1_27_type,type,( c1_27__msualg_9: $i )).
thf(c2_27_type,type,( c2_27__msualg_9: $i )).
thf(c3_27_type,type,( c3_27__msualg_9: $i )).
thf(c4_27_type,type,( c4_27__msualg_9: $i )).
thf(c5_27_type,type,( c5_27__msualg_9: $i )).
thf(k12_mcart_1_type,type,( k12_mcart_1: $i > $i )).
thf(k1_funct_1_type,type,( k1_funct_1: $i > $i > $i )).
thf(k6_pboole_type,type,( k6_pboole: $i > $i > $i > $i )).
thf(m2_pboole_type,type,( m2_pboole: $i > $i > $i > $i > $o )).
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(v2_relat_1_type,type,( v2_relat_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(dt_c2_27__msualg_9,axiom,( ( v1_relat_1 @ c2_27__msualg_9 ) & ( v4_relat_1 @ c2_27__msualg_9 @ c1_27__msualg_9 ) & ( v1_funct_1 @ c2_27__msualg_9 ) & ( v1_partfun1 @ c2_27__msualg_9 @ c1_27__msualg_9 ) ),file(msualg_9,c2_27__msualg_9)).
thf(dt_c3_27__msualg_9,axiom,( ( v1_relat_1 @ c3_27__msualg_9 ) & ( v2_relat_1 @ c3_27__msualg_9 ) & ( v4_relat_1 @ c3_27__msualg_9 @ c1_27__msualg_9 ) & ( v1_funct_1 @ c3_27__msualg_9 ) & ( v1_partfun1 @ c3_27__msualg_9 @ c1_27__msualg_9 ) ),file(msualg_9,c3_27__msualg_9)).
thf(dt_c4_27__msualg_9,axiom,( ( v1_relat_1 @ c4_27__msualg_9 ) & ( v2_relat_1 @ c4_27__msualg_9 ) & ( v4_relat_1 @ c4_27__msualg_9 @ c1_27__msualg_9 ) & ( v1_funct_1 @ c4_27__msualg_9 ) & ( v1_partfun1 @ c4_27__msualg_9 @ c1_27__msualg_9 ) ),file(msualg_9,c4_27__msualg_9)).
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(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(antisymmetry_r2_hidden,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ~ ( r2_hidden @ B @ A ) ) ),file(hidden,r2_hidden)).
thf(dt_k12_mcart_1,axiom,( ! [A: $i] : ( ( ( v1_relat_1 @ A ) & ( v1_funct_1 @ A ) ) => ( ( v1_relat_1 @ ( k12_mcart_1 @ A ) ) & ( v1_funct_1 @ ( k12_mcart_1 @ A ) ) ) ) ),file(mcart_1,k12_mcart_1)).
thf(dt_k1_funct_1,axiom,( $true ),file(funct_1,k1_funct_1)).
thf(dt_k6_pboole,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v1_funct_1 @ C ) & ( v1_partfun1 @ C @ A ) ) => ( ( v1_relat_1 @ ( k6_pboole @ A @ B @ C ) ) & ( v4_relat_1 @ ( k6_pboole @ A @ B @ C ) @ A ) & ( v1_funct_1 @ ( k6_pboole @ A @ B @ C ) ) & ( v1_partfun1 @ ( k6_pboole @ A @ B @ C ) @ A ) ) ) ),file(pboole,k6_pboole)).
thf(dt_m2_pboole,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v1_funct_1 @ C ) & ( v1_partfun1 @ C @ A ) ) => ! [D: $i] : ( ( m2_pboole @ D @ A @ B @ C ) => ( ( v1_relat_1 @ D ) & ( v4_relat_1 @ D @ A ) & ( v1_funct_1 @ D ) & ( v1_partfun1 @ D @ A ) ) ) ) ),file(pboole,m2_pboole)).
thf(dt_c1_27__msualg_9,axiom,( $true ),file(msualg_9,c1_27__msualg_9)).
thf(dt_c5_27__msualg_9,axiom,( m2_pboole @ c5_27__msualg_9 @ c1_27__msualg_9 @ c2_27__msualg_9 @ ( k6_pboole @ c1_27__msualg_9 @ c3_27__msualg_9 @ c4_27__msualg_9 ) ),file(msualg_9,c5_27__msualg_9)).
thf(cc3_pboole,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ( v1_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v1_funct_1 @ C ) & ( v1_partfun1 @ C @ A ) ) => ! [D: $i] : ( ( m2_pboole @ D @ A @ B @ C ) => ( v1_funcop_1 @ D ) ) ) ),file(pboole,cc3_pboole)).
thf(fc1_pralg_2,axiom,( ! [A: $i] : ! [B: $i] : ! [C: $i] : ( ( ( v1_relat_1 @ B ) & ( v2_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) & ( v1_relat_1 @ C ) & ( v2_relat_1 @ C ) & ( v4_relat_1 @ C @ A ) & ( v1_funct_1 @ C ) & ( v1_partfun1 @ C @ A ) ) => ( ( v1_relat_1 @ ( k6_pboole @ A @ B @ C ) ) & ( v2_relat_1 @ ( k6_pboole @ A @ B @ C ) ) & ( v4_relat_1 @ ( k6_pboole @ A @ B @ C ) @ A ) & ( v1_funct_1 @ ( k6_pboole @ A @ B @ C ) ) & ( v1_partfun1 @ ( k6_pboole @ A @ B @ C ) @ A ) ) ) ),file(pralg_2,fc1_pralg_2)).
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(rc2_relat_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v2_relat_1 @ A ) ) ),file(relat_1,rc2_relat_1)).
thf(rc3_funct_1,axiom,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v2_relat_1 @ A ) & ( v1_funct_1 @ A ) ) ),file(funct_1,rc3_funct_1)).
thf(rc3_pboole,axiom,( ! [A: $i] : ? [B: $i] : ( ( v1_relat_1 @ B ) & ( v2_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) ),file(pboole,rc3_pboole)).
thf(rc4_funcop_1,axiom,( ! [A: $i] : ? [B: $i] : ( ( v1_relat_1 @ B ) & ( v2_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) & ( v1_partfun1 @ B @ A ) ) ),file(funcop_1,rc4_funcop_1)).
thf(rc9_funct_1,axiom,( ! [A: $i] : ? [B: $i] : ( ( v1_relat_1 @ B ) & ( v2_relat_1 @ B ) & ( v4_relat_1 @ B @ A ) & ( v1_funct_1 @ B ) ) ),file(funct_1,rc9_funct_1)).
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_27_2_1__msualg_9,conjecture,( ? [A: $i] : ( ( v1_relat_1 @ A ) & ( v4_relat_1 @ A @ c1_27__msualg_9 ) & ( v1_funct_1 @ A ) & ( v1_partfun1 @ A @ c1_27__msualg_9 ) & ! [B: $i] : ( ( r2_hidden @ B @ c1_27__msualg_9 ) => ( = @ ( k1_funct_1 @ A @ B ) @ ( k12_mcart_1 @ ( k1_funct_1 @ c5_27__msualg_9 @ B ) ) ) ) ) ),file(msualg_9,e1_27_2_1__msualg_9)).
