% Mizar ND problem: t2_group_6,group_6,71,54 fof(dh_c1_4__group_6,definition, ( ( ( ~ v3_struct_0(c1_4__group_6) & v3_group_1(c1_4__group_6) & v4_group_1(c1_4__group_6) & l1_group_1(c1_4__group_6) ) => ! [A] : ( m1_group_2(A,c1_4__group_6) => ! [B] : ( m1_subset_1(B,u1_struct_0(c1_4__group_6)) => ! [C] : ( m1_group_6(C,c1_4__group_6,A) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( D = B => ( k12_group_2(A,C,D) = k12_group_2(c1_4__group_6,C,B) & k13_group_2(A,C,D) = k13_group_2(c1_4__group_6,C,B) ) ) ) ) ) ) ) => ! [E] : ( ( ~ v3_struct_0(E) & v3_group_1(E) & v4_group_1(E) & l1_group_1(E) ) => ! [F] : ( m1_group_2(F,E) => ! [G] : ( m1_subset_1(G,u1_struct_0(E)) => ! [H] : ( m1_group_6(H,E,F) => ! [I] : ( m1_subset_1(I,u1_struct_0(F)) => ( I = G => ( k12_group_2(F,H,I) = k12_group_2(E,H,G) & k13_group_2(F,H,I) = k13_group_2(E,H,G) ) ) ) ) ) ) ) ), introduced(definition,[new_symbol(c1_4__group_6),file(group_6,c1_4__group_6)]), [interesting(0.8),axiom,file(group_6,c1_4__group_6)]). fof(dh_c2_4__group_6,definition, ( ( m1_group_2(c2_4__group_6,c1_4__group_6) => ! [A] : ( m1_subset_1(A,u1_struct_0(c1_4__group_6)) => ! [B] : ( m1_group_6(B,c1_4__group_6,c2_4__group_6) => ! [C] : ( m1_subset_1(C,u1_struct_0(c2_4__group_6)) => ( C = A => ( k12_group_2(c2_4__group_6,B,C) = k12_group_2(c1_4__group_6,B,A) & k13_group_2(c2_4__group_6,B,C) = k13_group_2(c1_4__group_6,B,A) ) ) ) ) ) ) => ! [D] : ( m1_group_2(D,c1_4__group_6) => ! [E] : ( m1_subset_1(E,u1_struct_0(c1_4__group_6)) => ! [F] : ( m1_group_6(F,c1_4__group_6,D) => ! [G] : ( m1_subset_1(G,u1_struct_0(D)) => ( G = E => ( k12_group_2(D,F,G) = k12_group_2(c1_4__group_6,F,E) & k13_group_2(D,F,G) = k13_group_2(c1_4__group_6,F,E) ) ) ) ) ) ) ), introduced(definition,[new_symbol(c2_4__group_6),file(group_6,c2_4__group_6)]), [interesting(0.8),axiom,file(group_6,c2_4__group_6)]). fof(dh_c3_4__group_6,definition, ( ( m1_subset_1(c3_4__group_6,u1_struct_0(c1_4__group_6)) => ! [A] : ( m1_group_6(A,c1_4__group_6,c2_4__group_6) => ! [B] : ( m1_subset_1(B,u1_struct_0(c2_4__group_6)) => ( B = c3_4__group_6 => ( k12_group_2(c2_4__group_6,A,B) = k12_group_2(c1_4__group_6,A,c3_4__group_6) & k13_group_2(c2_4__group_6,A,B) = k13_group_2(c1_4__group_6,A,c3_4__group_6) ) ) ) ) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(c1_4__group_6)) => ! [D] : ( m1_group_6(D,c1_4__group_6,c2_4__group_6) => ! [E] : ( m1_subset_1(E,u1_struct_0(c2_4__group_6)) => ( E = C => ( k12_group_2(c2_4__group_6,D,E) = k12_group_2(c1_4__group_6,D,C) & k13_group_2(c2_4__group_6,D,E) = k13_group_2(c1_4__group_6,D,C) ) ) ) ) ) ), introduced(definition,[new_symbol(c3_4__group_6),file(group_6,c3_4__group_6)]), [interesting(0.8),axiom,file(group_6,c3_4__group_6)]). fof(dh_c4_4__group_6,definition, ( ( m1_group_6(c4_4__group_6,c1_4__group_6,c2_4__group_6) => ! [A] : ( m1_subset_1(A,u1_struct_0(c2_4__group_6)) => ( A = c3_4__group_6 => ( k12_group_2(c2_4__group_6,c4_4__group_6,A) = k12_group_2(c1_4__group_6,c4_4__group_6,c3_4__group_6) & k13_group_2(c2_4__group_6,c4_4__group_6,A) = k13_group_2(c1_4__group_6,c4_4__group_6,c3_4__group_6) ) ) ) ) => ! [B] : ( m1_group_6(B,c1_4__group_6,c2_4__group_6) => ! [C] : ( m1_subset_1(C,u1_struct_0(c2_4__group_6)) => ( C = c3_4__group_6 => ( k12_group_2(c2_4__group_6,B,C) = k12_group_2(c1_4__group_6,B,c3_4__group_6) & k13_group_2(c2_4__group_6,B,C) = k13_group_2(c1_4__group_6,B,c3_4__group_6) ) ) ) ) ), introduced(definition,[new_symbol(c4_4__group_6),file(group_6,c4_4__group_6)]), [interesting(0.8),axiom,file(group_6,c4_4__group_6)]). fof(dh_c5_4__group_6,definition, ( ( m1_subset_1(c5_4__group_6,u1_struct_0(c2_4__group_6)) => ( c5_4__group_6 = c3_4__group_6 => ( k12_group_2(c2_4__group_6,c4_4__group_6,c5_4__group_6) = k12_group_2(c1_4__group_6,c4_4__group_6,c3_4__group_6) & k13_group_2(c2_4__group_6,c4_4__group_6,c5_4__group_6) = k13_group_2(c1_4__group_6,c4_4__group_6,c3_4__group_6) ) ) ) => ! [A] : ( m1_subset_1(A,u1_struct_0(c2_4__group_6)) => ( A = c3_4__group_6 => ( k12_group_2(c2_4__group_6,c4_4__group_6,A) = k12_group_2(c1_4__group_6,c4_4__group_6,c3_4__group_6) & k13_group_2(c2_4__group_6,c4_4__group_6,A) = k13_group_2(c1_4__group_6,c4_4__group_6,c3_4__group_6) ) ) ) ), introduced(definition,[new_symbol(c5_4__group_6),file(group_6,c5_4__group_6)]), [interesting(0.8),axiom,file(group_6,c5_4__group_6)]). fof(e1_4__group_6,assumption,( c5_4__group_6 = c3_4__group_6 ), introduced(assumption,[file(group_6,e1_4__group_6)]), [interesting(0.8),axiom,file(group_6,e1_4__group_6)]). fof(cc2_finset_1,theorem,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v1_finset_1(B) ) ) ), file(finset_1,cc2_finset_1), [interesting(0.9),axiom,file(finset_1,cc2_finset_1)]). fof(rc1_finset_1,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v1_finset_1(A) ) ), file(finset_1,rc1_finset_1), [interesting(0.9),axiom,file(finset_1,rc1_finset_1)]). fof(rc3_finset_1,theorem,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) & v1_finset_1(B) ) ) ), file(finset_1,rc3_finset_1), [interesting(0.9),axiom,file(finset_1,rc3_finset_1)]). fof(rc4_finset_1,theorem,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) & v1_finset_1(B) ) ) ), file(finset_1,rc4_finset_1), [interesting(0.9),axiom,file(finset_1,rc4_finset_1)]). fof(cc1_finset_1,theorem,( ! [A] : ( v1_xboole_0(A) => v1_finset_1(A) ) ), file(finset_1,cc1_finset_1), [interesting(0.9),axiom,file(finset_1,cc1_finset_1)]). fof(rc1_xboole_0,theorem,( ? [A] : v1_xboole_0(A) ), file(xboole_0,rc1_xboole_0), [interesting(0.9),axiom,file(xboole_0,rc1_xboole_0)]). fof(rc2_xboole_0,theorem,( ? [A] : ~ v1_xboole_0(A) ), file(xboole_0,rc2_xboole_0), [interesting(0.9),axiom,file(xboole_0,rc2_xboole_0)]). fof(rc5_struct_0,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) ) ) ), file(struct_0,rc5_struct_0), [interesting(0.9),axiom,file(struct_0,rc5_struct_0)]). fof(dt_l1_struct_0,axiom,( $true ), file(struct_0,l1_struct_0), [interesting(0.9),axiom,file(struct_0,l1_struct_0)]). fof(fc1_struct_0,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ~ v1_xboole_0(u1_struct_0(A)) ) ), file(struct_0,fc1_struct_0), [interesting(0.9),axiom,file(struct_0,fc1_struct_0)]). fof(rc3_struct_0,theorem,( ? [A] : ( l1_struct_0(A) & ~ v3_struct_0(A) ) ), file(struct_0,rc3_struct_0), [interesting(0.9),axiom,file(struct_0,rc3_struct_0)]). fof(redefinition_m1_group_6,definition,( ! [A,B] : ( ( ~ v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B,A) ) => ! [C] : ( m1_group_6(C,A,B) <=> m1_group_2(C,B) ) ) ), file(group_6,m1_group_6), [interesting(0.9),axiom,file(group_6,m1_group_6)]). fof(dt_k1_zfmisc_1,axiom,( $true ), file(zfmisc_1,k1_zfmisc_1), [interesting(0.9),axiom,file(zfmisc_1,k1_zfmisc_1)]). fof(dt_l1_group_1,axiom,( ! [A] : ( l1_group_1(A) => l1_struct_0(A) ) ), file(group_1,l1_group_1), [interesting(0.9),axiom,file(group_1,l1_group_1)]). fof(dt_m1_group_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) ) => ! [B] : ( m1_group_2(B,A) => ( ~ v3_struct_0(B) & v3_group_1(B) & l1_group_1(B) ) ) ) ), file(group_2,m1_group_2), [interesting(0.9),axiom,file(group_2,m1_group_2)]). fof(dt_m1_group_6,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B,A) ) => ! [C] : ( m1_group_6(C,A,B) => m1_group_2(C,A) ) ) ), file(group_6,m1_group_6), [interesting(0.9),axiom,file(group_6,m1_group_6)]). fof(dt_m1_subset_1,axiom,( $true ), file(subset_1,m1_subset_1), [interesting(0.9),axiom,file(subset_1,m1_subset_1)]). fof(dt_u1_struct_0,axiom,( $true ), file(struct_0,u1_struct_0), [interesting(0.9),axiom,file(struct_0,u1_struct_0)]). fof(cc1_group_1,theorem,( ! [A] : ( l1_group_1(A) => ( ( ~ v3_struct_0(A) & v3_group_1(A) ) => ( ~ v3_struct_0(A) & v2_group_1(A) ) ) ) ), file(group_1,cc1_group_1), [interesting(0.9),axiom,file(group_1,cc1_group_1)]). fof(cc1_group_2,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) ) => ! [B] : ( m1_group_2(B,A) => v4_group_1(B) ) ) ), file(group_2,cc1_group_2), [interesting(0.9),axiom,file(group_2,cc1_group_2)]). fof(reflexivity_r1_tarski,theorem,( ! [A,B] : r1_tarski(A,A) ), file(tarski,r1_tarski), [interesting(0.9),axiom,file(tarski,r1_tarski)]). fof(dt_k12_group_2,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B,A) & m1_subset_1(C,u1_struct_0(A)) ) => m1_subset_1(k12_group_2(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) ), file(group_2,k12_group_2), [interesting(0.9),axiom,file(group_2,k12_group_2)]). fof(dt_k13_group_2,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B,A) & m1_subset_1(C,u1_struct_0(A)) ) => m1_subset_1(k13_group_2(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) ), file(group_2,k13_group_2), [interesting(0.9),axiom,file(group_2,k13_group_2)]). fof(dt_c1_4__group_6,assumption, ( ~ v3_struct_0(c1_4__group_6) & v3_group_1(c1_4__group_6) & v4_group_1(c1_4__group_6) & l1_group_1(c1_4__group_6) ), introduced(assumption,[file(group_6,c1_4__group_6)]), [interesting(0.8),axiom,file(group_6,c1_4__group_6)]). fof(dt_c2_4__group_6,assumption,( m1_group_2(c2_4__group_6,c1_4__group_6) ), introduced(assumption,[file(group_6,c2_4__group_6)]), [interesting(0.8),axiom,file(group_6,c2_4__group_6)]). fof(dt_c3_4__group_6,assumption,( m1_subset_1(c3_4__group_6,u1_struct_0(c1_4__group_6)) ), introduced(assumption,[file(group_6,c3_4__group_6)]), [interesting(0.8),axiom,file(group_6,c3_4__group_6)]). fof(dt_c4_4__group_6,assumption,( m1_group_6(c4_4__group_6,c1_4__group_6,c2_4__group_6) ), introduced(assumption,[file(group_6,c4_4__group_6)]), [interesting(0.8),axiom,file(group_6,c4_4__group_6)]). fof(dt_c5_4__group_6,assumption,( m1_subset_1(c5_4__group_6,u1_struct_0(c2_4__group_6)) ), introduced(assumption,[file(group_6,c5_4__group_6)]), [interesting(0.8),axiom,file(group_6,c5_4__group_6)]). fof(d10_xboole_0,definition,( ! [A,B] : ( A = B <=> ( r1_tarski(A,B) & r1_tarski(B,A) ) ) ), file(xboole_0,d10_xboole_0), [interesting(0.9),axiom,file(xboole_0,d10_xboole_0)]). fof(antisymmetry_r2_hidden,theorem,( ! [A,B] : ( r2_hidden(A,B) => ~ r2_hidden(B,A) ) ), file(hidden,r2_hidden), [interesting(0.9),axiom,file(hidden,r2_hidden)]). fof(dt_c1_4_1__group_6,assumption,( $true ), introduced(assumption,[file(group_6,c1_4_1__group_6)]), [interesting(0.65),axiom,file(group_6,c1_4_1__group_6)]). fof(d3_tarski,definition,( ! [A,B] : ( r1_tarski(A,B) <=> ! [C] : ( r2_hidden(C,A) => r2_hidden(C,B) ) ) ), file(tarski,d3_tarski), [interesting(0.9),axiom,file(tarski,d3_tarski)]). fof(dh_c1_4_1__group_6,definition, ( ~ ( r2_hidden(c1_4_1__group_6,k12_group_2(c2_4__group_6,c4_4__group_6,c5_4__group_6)) & ~ r2_hidden(c1_4_1__group_6,k12_group_2(c1_4__group_6,c4_4__group_6,c3_4__group_6)) ) => ! [A] : ~ ( r2_hidden(A,k12_group_2(c2_4__group_6,c4_4__group_6,c5_4__group_6)) & ~ r2_hidden(A,k12_group_2(c1_4__group_6,c4_4__group_6,c3_4__group_6)) ) ), introduced(definition,[new_symbol(c1_4_1__group_6),file(group_6,c1_4_1__group_6)]), [interesting(0.65),axiom,file(group_6,c1_4_1__group_6)]). fof(e1_4_1__group_6,assumption,( r2_hidden(c1_4_1__group_6,k12_group_2(c2_4__group_6,c4_4__group_6,c5_4__group_6)) ), introduced(assumption,[file(group_6,e1_4_1__group_6)]), [interesting(0.65),axiom,file(group_6,e1_4_1__group_6)]). fof(commutativity_k2_tarski,theorem,( ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ), file(tarski,k2_tarski), [interesting(0.9),axiom,file(tarski,k2_tarski)]). fof(dt_k2_tarski,axiom,( $true ), file(tarski,k2_tarski), [interesting(0.9),axiom,file(tarski,k2_tarski)]). fof(fc2_finset_1,theorem,( ! [A,B] : ( ~ v1_xboole_0(k2_tarski(A,B)) & v1_finset_1(k2_tarski(A,B)) ) ), file(finset_1,fc2_finset_1), [interesting(0.9),axiom,file(finset_1,fc2_finset_1)]). fof(dt_k1_funct_1,axiom,( $true ), file(funct_1,k1_funct_1), [interesting(0.9),axiom,file(funct_1,k1_funct_1)]). fof(dt_k1_tarski,axiom,( $true ), file(tarski,k1_tarski), [interesting(0.9),axiom,file(tarski,k1_tarski)]). fof(dt_k4_tarski,axiom,( $true ), file(tarski,k4_tarski), [interesting(0.9),axiom,file(tarski,k4_tarski)]). fof(cc1_funct_2,theorem,( ! [A,B,C] : ( m1_relset_1(C,A,B) => ( ( v1_funct_1(C) & v1_partfun1(C,A,B) ) => ( v1_funct_1(C) & v1_funct_2(C,A,B) ) ) ) ), file(funct_2,cc1_funct_2), [interesting(0.9),axiom,file(funct_2,cc1_funct_2)]). fof(fc1_finset_1,theorem,( ! [A] : ( ~ v1_xboole_0(k1_tarski(A)) & v1_finset_1(k1_tarski(A)) ) ), file(finset_1,fc1_finset_1), [interesting(0.9),axiom,file(finset_1,fc1_finset_1)]). fof(rc1_funct_2,theorem,( ! [A,B] : ? [C] : ( m1_relset_1(C,A,B) & v1_relat_1(C) & v1_funct_1(C) & v1_funct_2(C,A,B) ) ), file(funct_2,rc1_funct_2), [interesting(0.9),axiom,file(funct_2,rc1_funct_2)]). fof(rc2_partfun1,theorem,( ! [A,B] : ? [C] : ( m1_relset_1(C,A,B) & v1_relat_1(C) & v1_funct_1(C) ) ), file(partfun1,rc2_partfun1), [interesting(0.9),axiom,file(partfun1,rc2_partfun1)]). fof(t2_tarski,theorem,( ! [A,B] : ( ! [C] : ( r2_hidden(C,A) <=> r2_hidden(C,B) ) => A = B ) ), file(tarski,t2_tarski), [interesting(0.9),axiom,file(tarski,t2_tarski)]). fof(fraenkel_a_3_0_group_2,definition,( ! [A,B,C,D] : ( ( ~ v3_struct_0(B) & l1_group_1(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_0_group_2(B,C,D)) <=> ? [E,F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k1_group_1(B,E,F) & r2_hidden(E,C) & r2_hidden(F,D) ) ) ) ), file(group_2,a_3_0_group_2), [interesting(0.9),axiom,file(group_2,a_3_0_group_2)]). fof(d5_tarski,definition,( ! [A,B] : k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A)) ), file(tarski,d5_tarski), [interesting(0.9),axiom,file(tarski,d5_tarski)]). fof(existence_m1_relset_1,axiom,( ! [A,B] : ? [C] : m1_relset_1(C,A,B) ), file(relset_1,m1_relset_1), [interesting(0.9),axiom,file(relset_1,m1_relset_1)]). fof(existence_m2_relset_1,axiom,( ! [A,B] : ? [C] : m2_relset_1(C,A,B) ), file(relset_1,m2_relset_1), [interesting(0.9),axiom,file(relset_1,m2_relset_1)]). fof(redefinition_k6_domain_1,definition,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => k6_domain_1(A,B) = k1_tarski(B) ) ), file(domain_1,k6_domain_1), [interesting(0.9),axiom,file(domain_1,k6_domain_1)]). fof(redefinition_m2_relset_1,definition,( ! [A,B,C] : ( m2_relset_1(C,A,B) <=> m1_relset_1(C,A,B) ) ), file(relset_1,m2_relset_1), [interesting(0.9),axiom,file(relset_1,m2_relset_1)]). fof(dt_k1_binop_1,axiom,( $true ), file(binop_1,k1_binop_1), [interesting(0.9),axiom,file(binop_1,k1_binop_1)]). fof(dt_k1_xboole_0,axiom,( $true ), file(xboole_0,k1_xboole_0), [interesting(0.9),axiom,file(xboole_0,k1_xboole_0)]). fof(dt_k2_group_2,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l1_group_1(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => m1_subset_1(k2_group_2(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) ), file(group_2,k2_group_2), [interesting(0.9),axiom,file(group_2,k2_group_2)]). fof(dt_k2_zfmisc_1,axiom,( $true ), file(zfmisc_1,k2_zfmisc_1), [interesting(0.9),axiom,file(zfmisc_1,k2_zfmisc_1)]). fof(dt_k6_domain_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => m1_subset_1(k6_domain_1(A,B),k1_zfmisc_1(A)) ) ), file(domain_1,k6_domain_1), [interesting(0.9),axiom,file(domain_1,k6_domain_1)]). fof(dt_m1_relset_1,axiom,( $true ), file(relset_1,m1_relset_1), [interesting(0.9),axiom,file(relset_1,m1_relset_1)]). fof(dt_m2_relset_1,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ), file(relset_1,m2_relset_1), [interesting(0.9),axiom,file(relset_1,m2_relset_1)]). fof(cc1_relset_1,theorem,( ! [A,B,C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => v1_relat_1(C) ) ), file(relset_1,cc1_relset_1), [interesting(0.9),axiom,file(relset_1,cc1_relset_1)]). fof(cc5_funct_2,theorem,( ! [A,B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_relset_1(C,A,B) => ( ( v1_funct_1(C) & v1_funct_2(C,A,B) ) => ( v1_funct_1(C) & v1_partfun1(C,A,B) & v1_funct_2(C,A,B) ) ) ) ) ), file(funct_2,cc5_funct_2), [interesting(0.9),axiom,file(funct_2,cc5_funct_2)]). fof(cc6_funct_2,theorem,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ! [C] : ( m1_relset_1(C,A,B) => ( ( v1_funct_1(C) & v1_funct_2(C,A,B) ) => ( v1_funct_1(C) & ~ v1_xboole_0(C) & v1_partfun1(C,A,B) & v1_funct_2(C,A,B) ) ) ) ) ), file(funct_2,cc6_funct_2), [interesting(0.9),axiom,file(funct_2,cc6_funct_2)]). fof(fc14_finset_1,theorem,( ! [A,B] : ( ( v1_finset_1(A) & v1_finset_1(B) ) => v1_finset_1(k2_zfmisc_1(A,B)) ) ), file(finset_1,fc14_finset_1), [interesting(0.9),axiom,file(finset_1,fc14_finset_1)]). fof(fc1_xboole_0,theorem,( v1_xboole_0(k1_xboole_0) ), file(xboole_0,fc1_xboole_0), [interesting(0.9),axiom,file(xboole_0,fc1_xboole_0)]). fof(d1_binop_1,definition,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B,C] : k1_binop_1(A,B,C) = k1_funct_1(A,k4_tarski(B,C)) ) ), file(binop_1,d1_binop_1), [interesting(0.9),axiom,file(binop_1,d1_binop_1)]). fof(d2_group_2,definition,( ! [A] : ( ( ~ v3_struct_0(A) & l1_group_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => k2_group_2(A,B,C) = a_3_0_group_2(A,B,C) ) ) ) ), file(group_2,d2_group_2), [interesting(0.9),axiom,file(group_2,d2_group_2)]). fof(existence_l1_struct_0,axiom,( ? [A] : l1_struct_0(A) ), file(struct_0,l1_struct_0), [interesting(0.9),axiom,file(struct_0,l1_struct_0)]). fof(existence_m1_group_6,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B,A) ) => ? [C] : m1_group_6(C,A,B) ) ), file(group_6,m1_group_6), [interesting(0.9),axiom,file(group_6,m1_group_6)]). fof(redefinition_k2_binop_1,definition,( ! [A,B,C,D,E,F] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(A,B),C) & m1_relset_1(D,k2_zfmisc_1(A,B),C) & m1_subset_1(E,A) & m1_subset_1(F,B) ) => k2_binop_1(A,B,C,D,E,F) = k1_binop_1(D,E,F) ) ), file(binop_1,k2_binop_1), [interesting(0.9),axiom,file(binop_1,k2_binop_1)]). fof(dt_k2_binop_1,axiom,( ! [A,B,C,D,E,F] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(A,B),C) & m1_relset_1(D,k2_zfmisc_1(A,B),C) & m1_subset_1(E,A) & m1_subset_1(F,B) ) => m1_subset_1(k2_binop_1(A,B,C,D,E,F),C) ) ), file(binop_1,k2_binop_1), [interesting(0.9),axiom,file(binop_1,k2_binop_1)]). fof(dt_k3_group_2,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l1_group_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => m1_subset_1(k3_group_2(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) ), file(group_2,k3_group_2), [interesting(0.9),axiom,file(group_2,k3_group_2)]). fof(dt_k7_group_2,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B,A) ) => m1_subset_1(k7_group_2(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ), file(group_2,k7_group_2), [interesting(0.9),axiom,file(group_2,k7_group_2)]). fof(dt_u1_group_1,axiom,( ! [A] : ( l1_group_1(A) => ( v1_funct_1(u1_group_1(A)) & v1_funct_2(u1_group_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & m2_relset_1(u1_group_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) ) ) ), file(group_1,u1_group_1), [interesting(0.9),axiom,file(group_1,u1_group_1)]). fof(t2_subset,theorem,( ! [A,B] : ( m1_subset_1(A,B) => ( v1_xboole_0(B) | r2_hidden(A,B) ) ) ), file(subset,t2_subset), [interesting(0.9),axiom,file(subset,t2_subset)]). fof(t3_subset,theorem,( ! [A,B] : ( m1_subset_1(A,k1_zfmisc_1(B)) <=> r1_tarski(A,B) ) ), file(subset,t3_subset), [interesting(0.9),axiom,file(subset,t3_subset)]). fof(t4_subset,theorem,( ! [A,B,C] : ( ( r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) ) => m1_subset_1(A,C) ) ), file(subset,t4_subset), [interesting(0.9),axiom,file(subset,t4_subset)]). fof(t5_subset,theorem,( ! [A,B,C] : ~ ( r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) & v1_xboole_0(C) ) ), file(subset,t5_subset), [interesting(0.9),axiom,file(subset,t5_subset)]). fof(t6_boole,theorem,( ! [A] : ( v1_xboole_0(A) => A = k1_xboole_0 ) ), file(boole,t6_boole), [interesting(0.9),axiom,file(boole,t6_boole)]). fof(t8_boole,theorem,( ! [A,B] : ~ ( v1_xboole_0(A) & A != B & v1_xboole_0(B) ) ), file(boole,t8_boole), [interesting(0.9),axiom,file(boole,t8_boole)]). fof(d3_group_2,definition,( ! [A] : ( ( ~ v3_struct_0(A) & l1_group_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => k3_group_2(A,B,C) = k2_group_2(A,k6_domain_1(u1_struct_0(A),B),C) ) ) ) ), file(group_2,d3_group_2), [interesting(0.9),axiom,file(group_2,d3_group_2)]). fof(d9_group_2,definition,( ! [A] : ( ( ~ v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) ) => ! [B] : ( m1_group_2(B,A) => k7_group_2(A,B) = u1_struct_0(B) ) ) ), file(group_2,d9_group_2), [interesting(0.9),axiom,file(group_2,d9_group_2)]). fof(existence_l1_group_1,axiom,( ? [A] : l1_group_1(A) ), file(group_1,l1_group_1), [interesting(0.9),axiom,file(group_1,l1_group_1)]). fof(existence_m1_group_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) ) => ? [B] : m1_group_2(B,A) ) ), file(group_2,m1_group_2), [interesting(0.9),axiom,file(group_2,m1_group_2)]). fof(existence_m1_subset_1,axiom,( ! [A] : ? [B] : m1_subset_1(B,A) ), file(subset_1,m1_subset_1), [interesting(0.9),axiom,file(subset_1,m1_subset_1)]). fof(dt_k1_group_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l1_group_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => m1_subset_1(k1_group_1(A,B,C),u1_struct_0(A)) ) ), file(group_1,k1_group_1), [interesting(0.9),axiom,file(group_1,k1_group_1)]). fof(dh_c2_4_1__group_6,definition, ( ? [A] : ( m1_subset_1(A,u1_struct_0(c2_4__group_6)) & c1_4_1__group_6 = k1_group_1(c2_4__group_6,c5_4__group_6,A) & r1_rlvect_1(c4_4__group_6,A) ) => ( m1_subset_1(c2_4_1__group_6,u1_struct_0(c2_4__group_6)) & c1_4_1__group_6 = k1_group_1(c2_4__group_6,c5_4__group_6,c2_4_1__group_6) & r1_rlvect_1(c4_4__group_6,c2_4_1__group_6) ) ), introduced(definition,[new_symbol(c2_4_1__group_6),file(group_6,c2_4_1__group_6)]), [interesting(0.65),axiom,file(group_6,c2_4_1__group_6)]). fof(t1_subset,theorem,( ! [A,B] : ( r2_hidden(A,B) => m1_subset_1(A,B) ) ), file(subset,t1_subset), [interesting(0.9),axiom,file(subset,t1_subset)]). fof(t7_boole,theorem,( ! [A,B] : ~ ( r2_hidden(A,B) & v1_xboole_0(B) ) ), file(boole,t7_boole), [interesting(0.9),axiom,file(boole,t7_boole)]). fof(d13_group_2,definition,( ! [A] : ( ( ~ v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k12_group_2(A,B,C) = k3_group_2(A,C,k7_group_2(A,B)) ) ) ) ), file(group_2,d13_group_2), [interesting(0.9),axiom,file(group_2,d13_group_2)]). fof(d1_group_1,definition,( ! [A] : ( ( ~ v3_struct_0(A) & l1_group_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k1_group_1(A,B,C) = k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),u1_group_1(A),B,C) ) ) ) ), file(group_1,d1_group_1), [interesting(0.9),axiom,file(group_1,d1_group_1)]). fof(t125_group_2,theorem,( ! [A,B] : ( ( ~ v3_struct_0(B) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_group_2(D,B) => ( r2_hidden(A,k12_group_2(B,D,C)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k1_group_1(B,C,E) & r1_rlvect_1(D,E) ) ) ) ) ) ), file(group_2,t125_group_2), [interesting(0.9),axiom,file(group_2,t125_group_2)]). fof(e2_4_1__group_6,plain,( ? [A] : ( m1_subset_1(A,u1_struct_0(c2_4__group_6)) & c1_4_1__group_6 = k1_group_1(c2_4__group_6,c5_4__group_6,A) & r1_rlvect_1(c4_4__group_6,A) ) ), inference(mizar_by,[status(thm),assumptions([dt_c1_4__group_6,dt_c1_4_1__group_6,dt_c2_4__group_6,dt_c4_4__group_6,dt_c5_4__group_6,e1_4_1__group_6])],[commutativity_k2_tarski,dt_k2_tarski,fc2_finset_1,dt_k1_funct_1,dt_k1_tarski,dt_k4_tarski,cc1_funct_2,fc1_finset_1,rc1_funct_2,rc2_partfun1,t2_tarski,fraenkel_a_3_0_group_2,d5_tarski,reflexivity_r1_tarski,existence_m1_relset_1,existence_m2_relset_1,redefinition_k6_domain_1,redefinition_m2_relset_1,dt_k1_binop_1,dt_k1_xboole_0,dt_k2_group_2,dt_k2_zfmisc_1,dt_k6_domain_1,dt_m1_relset_1,dt_m2_relset_1,cc1_relset_1,cc2_finset_1,cc5_funct_2,cc6_funct_2,fc14_finset_1,fc1_xboole_0,rc1_finset_1,rc3_finset_1,rc4_finset_1,d1_binop_1,d2_group_2,existence_l1_struct_0,existence_m1_group_6,redefinition_k2_binop_1,redefinition_m1_group_6,dt_k1_zfmisc_1,dt_k2_binop_1,dt_k3_group_2,dt_k7_group_2,dt_l1_struct_0,dt_m1_group_6,dt_u1_group_1,dt_c1_4__group_6,cc1_finset_1,fc1_struct_0,rc1_xboole_0,rc2_xboole_0,rc3_struct_0,rc5_struct_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,d3_group_2,d9_group_2,antisymmetry_r2_hidden,existence_l1_group_1,existence_m1_group_2,existence_m1_subset_1,dt_k12_group_2,dt_k1_group_1,dt_l1_group_1,dt_m1_group_2,dt_m1_subset_1,dt_u1_struct_0,dt_c1_4_1__group_6,dt_c2_4__group_6,dt_c4_4__group_6,dt_c5_4__group_6,cc1_group_1,cc1_group_2,t1_subset,t7_boole,d13_group_2,d1_group_1,e1_4_1__group_6,t125_group_2]), [interesting(0.65),file(group_6,e2_4_1__group_6),[file(group_6,e2_4_1__group_6)]]). fof(dt_c2_4_1__group_6,plain,( m1_subset_1(c2_4_1__group_6,u1_struct_0(c2_4__group_6)) ), inference(consider,[status(thm),assumptions([dt_c1_4__group_6,dt_c1_4_1__group_6,dt_c2_4__group_6,dt_c4_4__group_6,dt_c5_4__group_6,e1_4_1__group_6])],[dh_c2_4_1__group_6,e2_4_1__group_6]), [interesting(0.65),file(group_6,c2_4_1__group_6),[file(group_6,c2_4_1__group_6)]]). fof(de_c3_4_1__group_6,definition,( c3_4_1__group_6 = c2_4_1__group_6 ), introduced(definition,[new_symbol(c3_4_1__group_6),file(group_6,c3_4_1__group_6)]), [interesting(0.65),axiom,file(group_6,c3_4_1__group_6)]). fof(t51_group_2,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => m1_subset_1(C,u1_struct_0(A)) ) ) ) ), file(group_2,t51_group_2), [interesting(0.9),axiom,file(group_2,t51_group_2)]). fof(e4_4_1__group_6,plain,( m1_subset_1(c2_4_1__group_6,u1_struct_0(c1_4__group_6)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_4__group_6,dt_c1_4_1__group_6,dt_c2_4__group_6,dt_c4_4__group_6,dt_c5_4__group_6,e1_4_1__group_6])],[antisymmetry_r2_hidden,dt_k1_xboole_0,fc1_xboole_0,rc1_finset_1,t1_subset,t8_boole,cc1_finset_1,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t7_boole,existence_l1_struct_0,dt_l1_struct_0,dt_c2_4__group_6,cc1_group_2,fc1_struct_0,rc3_struct_0,existence_l1_group_1,existence_m1_group_2,existence_m1_subset_1,dt_l1_group_1,dt_m1_group_2,dt_m1_subset_1,dt_u1_struct_0,dt_c1_4__group_6,dt_c2_4_1__group_6,cc1_group_1,t51_group_2]), [interesting(0.65),file(group_6,e4_4_1__group_6),[file(group_6,e4_4_1__group_6)]]). fof(dt_c3_4_1__group_6,plain,( m1_subset_1(c3_4_1__group_6,u1_struct_0(c1_4__group_6)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_4__group_6,dt_c1_4_1__group_6,dt_c2_4__group_6,dt_c4_4__group_6,dt_c5_4__group_6,e1_4_1__group_6])],[antisymmetry_r2_hidden,dt_k1_xboole_0,fc1_xboole_0,rc1_finset_1,t1_subset,existence_m1_group_2,dt_m1_group_2,cc1_finset_1,cc1_group_2,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t7_boole,t8_boole,existence_l1_group_1,existence_l1_struct_0,dt_l1_group_1,dt_l1_struct_0,dt_c2_4__group_6,cc1_group_1,fc1_struct_0,rc3_struct_0,existence_m1_subset_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_4__group_6,dt_c2_4_1__group_6,de_c3_4_1__group_6,e4_4_1__group_6]), [interesting(0.65),file(group_6,c3_4_1__group_6),[file(group_6,c3_4_1__group_6)]]). fof(t52_group_2,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_group_2(D,A) => ! [E] : ( m1_subset_1(E,u1_struct_0(D)) => ! [F] : ( m1_subset_1(F,u1_struct_0(D)) => ( ( E = B & F = C ) => k1_group_1(D,E,F) = k1_group_1(A,B,C) ) ) ) ) ) ) ) ), file(group_2,t52_group_2), [interesting(0.9),axiom,file(group_2,t52_group_2)]). fof(e5_4_1__group_6,plain,( k1_group_1(c1_4__group_6,c3_4__group_6,c3_4_1__group_6) = k1_group_1(c2_4__group_6,c5_4__group_6,c2_4_1__group_6) ), inference(mizar_by,[status(thm),assumptions([dt_c3_4__group_6,dt_c1_4__group_6,dt_c1_4_1__group_6,dt_c2_4__group_6,dt_c4_4__group_6,e1_4_1__group_6,dt_c5_4__group_6,e1_4__group_6])],[commutativity_k2_tarski,reflexivity_r1_tarski,dt_k1_tarski,dt_k2_tarski,fc1_finset_1,fc2_finset_1,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k4_tarski,cc1_funct_2,cc1_relset_1,cc2_finset_1,fc14_finset_1,fc1_xboole_0,rc1_finset_1,rc1_funct_2,rc2_partfun1,rc3_finset_1,rc4_finset_1,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,d5_tarski,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_binop_1,dt_k2_zfmisc_1,dt_m1_relset_1,dt_m2_relset_1,cc1_finset_1,cc5_funct_2,cc6_funct_2,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t7_boole,t8_boole,d1_binop_1,existence_l1_struct_0,redefinition_k2_binop_1,dt_k2_binop_1,dt_l1_struct_0,dt_u1_group_1,cc1_group_2,fc1_struct_0,rc3_struct_0,existence_l1_group_1,existence_m1_group_2,existence_m1_subset_1,dt_k1_group_1,dt_l1_group_1,dt_m1_group_2,dt_m1_subset_1,dt_u1_struct_0,dt_c1_4__group_6,dt_c2_4__group_6,dt_c2_4_1__group_6,dt_c3_4__group_6,dt_c3_4_1__group_6,dt_c5_4__group_6,de_c3_4_1__group_6,cc1_group_1,d1_group_1,e1_4__group_6,t52_group_2]), [interesting(0.65),file(group_6,e5_4_1__group_6),[file(group_6,e5_4_1__group_6)]]). fof(e3_4_1__group_6,plain, ( c1_4_1__group_6 = k1_group_1(c2_4__group_6,c5_4__group_6,c2_4_1__group_6) & r1_rlvect_1(c4_4__group_6,c2_4_1__group_6) ), inference(consider,[status(thm),assumptions([dt_c1_4__group_6,dt_c1_4_1__group_6,dt_c2_4__group_6,dt_c4_4__group_6,dt_c5_4__group_6,e1_4_1__group_6])],[dh_c2_4_1__group_6,e2_4_1__group_6]), [interesting(0.65),file(group_6,e3_4_1__group_6),[file(group_6,e3_4_1__group_6)]]). fof(e6_4_1__group_6,plain,( r2_hidden(c1_4_1__group_6,k12_group_2(c1_4__group_6,c4_4__group_6,c3_4__group_6)) ), inference(mizar_by,[status(thm),assumptions([dt_c3_4__group_6,e1_4__group_6,dt_c1_4__group_6,dt_c1_4_1__group_6,dt_c2_4__group_6,dt_c4_4__group_6,dt_c5_4__group_6,e1_4_1__group_6])],[commutativity_k2_tarski,dt_k2_tarski,fc2_finset_1,dt_k1_funct_1,dt_k1_tarski,dt_k4_tarski,cc1_funct_2,fc1_finset_1,rc1_funct_2,rc2_partfun1,t2_tarski,fraenkel_a_3_0_group_2,d5_tarski,reflexivity_r1_tarski,existence_m1_relset_1,existence_m2_relset_1,redefinition_k6_domain_1,redefinition_m2_relset_1,dt_k1_binop_1,dt_k1_xboole_0,dt_k2_group_2,dt_k2_zfmisc_1,dt_k6_domain_1,dt_m1_relset_1,dt_m2_relset_1,cc1_relset_1,cc2_finset_1,cc5_funct_2,cc6_funct_2,fc14_finset_1,fc1_xboole_0,rc1_finset_1,rc3_finset_1,rc4_finset_1,d1_binop_1,d2_group_2,existence_l1_struct_0,existence_m1_group_6,redefinition_k2_binop_1,redefinition_m1_group_6,dt_k1_zfmisc_1,dt_k2_binop_1,dt_k3_group_2,dt_k7_group_2,dt_l1_struct_0,dt_m1_group_6,dt_u1_group_1,cc1_finset_1,fc1_struct_0,rc1_xboole_0,rc2_xboole_0,rc3_struct_0,rc5_struct_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,d3_group_2,d9_group_2,antisymmetry_r2_hidden,existence_l1_group_1,existence_m1_group_2,existence_m1_subset_1,dt_k12_group_2,dt_k1_group_1,dt_l1_group_1,dt_m1_group_2,dt_m1_subset_1,dt_u1_struct_0,dt_c1_4__group_6,dt_c1_4_1__group_6,dt_c2_4__group_6,dt_c2_4_1__group_6,dt_c3_4__group_6,dt_c3_4_1__group_6,dt_c4_4__group_6,dt_c5_4__group_6,de_c3_4_1__group_6,cc1_group_1,cc1_group_2,t1_subset,t7_boole,d13_group_2,d1_group_1,e5_4_1__group_6,e3_4_1__group_6,t125_group_2]), [interesting(0.65),file(group_6,e6_4_1__group_6),[file(group_6,e6_4_1__group_6)]]). fof(i3_4_1__group_6,theorem,( $true ), introduced(tautology,[file(group_6,i3_4_1__group_6)]), [interesting(0.65),trivial,file(group_6,i3_4_1__group_6)]). fof(i2_4_1__group_6,plain,( r2_hidden(c1_4_1__group_6,k12_group_2(c1_4__group_6,c4_4__group_6,c3_4__group_6)) ), inference(conclusion,[status(thm),assumptions([dt_c3_4__group_6,e1_4__group_6,dt_c1_4__group_6,dt_c1_4_1__group_6,dt_c2_4__group_6,dt_c4_4__group_6,dt_c5_4__group_6,e1_4_1__group_6])],[e6_4_1__group_6,i3_4_1__group_6]), [interesting(0.65),file(group_6,i2_4_1__group_6),[file(group_6,i2_4_1__group_6)]]). fof(i1_4_1__group_6,plain,( ~ ( r2_hidden(c1_4_1__group_6,k12_group_2(c2_4__group_6,c4_4__group_6,c5_4__group_6)) & ~ r2_hidden(c1_4_1__group_6,k12_group_2(c1_4__group_6,c4_4__group_6,c3_4__group_6)) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c3_4__group_6,e1_4__group_6,dt_c1_4__group_6,dt_c1_4_1__group_6,dt_c2_4__group_6,dt_c4_4__group_6,dt_c5_4__group_6]),discharge_asm(discharge,[e1_4_1__group_6])],[e1_4_1__group_6,i2_4_1__group_6]), [interesting(0.65),file(group_6,i1_4_1__group_6),[file(group_6,i1_4_1__group_6)]]). fof(i1_4_1_tmp__group_6,plain,( ~ ( r2_hidden(c1_4_1__group_6,k12_group_2(c2_4__group_6,c4_4__group_6,c5_4__group_6)) & ~ r2_hidden(c1_4_1__group_6,k12_group_2(c1_4__group_6,c4_4__group_6,c3_4__group_6)) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c3_4__group_6,e1_4__group_6,dt_c1_4__group_6,dt_c2_4__group_6,dt_c4_4__group_6,dt_c5_4__group_6]),discharge_asm(discharge,[dt_c1_4_1__group_6])],[dt_c1_4_1__group_6,i1_4_1__group_6]), [interesting(0.8),e2_4__group_6]). fof(e2_4__group_6,plain,( r1_tarski(k12_group_2(c2_4__group_6,c4_4__group_6,c5_4__group_6),k12_group_2(c1_4__group_6,c4_4__group_6,c3_4__group_6)) ), inference(let,[status(thm),assumptions([dt_c3_4__group_6,e1_4__group_6,dt_c1_4__group_6,dt_c2_4__group_6,dt_c4_4__group_6,dt_c5_4__group_6])],[i1_4_1_tmp__group_6,cc2_finset_1,rc1_finset_1,rc3_finset_1,rc4_finset_1,cc1_finset_1,rc1_xboole_0,rc2_xboole_0,rc5_struct_0,dt_l1_struct_0,fc1_struct_0,rc3_struct_0,redefinition_m1_group_6,dt_k1_zfmisc_1,dt_l1_group_1,dt_m1_group_2,dt_m1_group_6,dt_m1_subset_1,dt_u1_struct_0,cc1_group_1,cc1_group_2,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k12_group_2,dt_c1_4__group_6,dt_c2_4__group_6,dt_c3_4__group_6,dt_c4_4__group_6,dt_c5_4__group_6,d3_tarski,dh_c1_4_1__group_6]), [interesting(0.8),file(group_6,e2_4__group_6),[file(group_6,e2_4__group_6)]]). fof(dt_c1_4_2__group_6,assumption,( $true ), introduced(assumption,[file(group_6,c1_4_2__group_6)]), [interesting(0.65),axiom,file(group_6,c1_4_2__group_6)]). fof(dh_c1_4_2__group_6,definition, ( ~ ( r2_hidden(c1_4_2__group_6,k12_group_2(c1_4__group_6,c4_4__group_6,c3_4__group_6)) & ~ r2_hidden(c1_4_2__group_6,k12_group_2(c2_4__group_6,c4_4__group_6,c5_4__group_6)) ) => ! [A] : ~ ( r2_hidden(A,k12_group_2(c1_4__group_6,c4_4__group_6,c3_4__group_6)) & ~ r2_hidden(A,k12_group_2(c2_4__group_6,c4_4__group_6,c5_4__group_6)) ) ), introduced(definition,[new_symbol(c1_4_2__group_6),file(group_6,c1_4_2__group_6)]), [interesting(0.65),axiom,file(group_6,c1_4_2__group_6)]). fof(e1_4_2__group_6,assumption,( r2_hidden(c1_4_2__group_6,k12_group_2(c1_4__group_6,c4_4__group_6,c3_4__group_6)) ), introduced(assumption,[file(group_6,e1_4_2__group_6)]), [interesting(0.65),axiom,file(group_6,e1_4_2__group_6)]). fof(dh_c2_4_2__group_6,definition, ( ? [A] : ( m1_subset_1(A,u1_struct_0(c1_4__group_6)) & c1_4_2__group_6 = k1_group_1(c1_4__group_6,c3_4__group_6,A) & r1_rlvect_1(c4_4__group_6,A) ) => ( m1_subset_1(c2_4_2__group_6,u1_struct_0(c1_4__group_6)) & c1_4_2__group_6 = k1_group_1(c1_4__group_6,c3_4__group_6,c2_4_2__group_6) & r1_rlvect_1(c4_4__group_6,c2_4_2__group_6) ) ), introduced(definition,[new_symbol(c2_4_2__group_6),file(group_6,c2_4_2__group_6)]), [interesting(0.65),axiom,file(group_6,c2_4_2__group_6)]). fof(e2_4_2__group_6,plain,( ? [A] : ( m1_subset_1(A,u1_struct_0(c1_4__group_6)) & c1_4_2__group_6 = k1_group_1(c1_4__group_6,c3_4__group_6,A) & r1_rlvect_1(c4_4__group_6,A) ) ), inference(mizar_by,[status(thm),assumptions([dt_c2_4__group_6,dt_c1_4__group_6,dt_c1_4_2__group_6,dt_c3_4__group_6,dt_c4_4__group_6,e1_4_2__group_6])],[commutativity_k2_tarski,dt_k2_tarski,fc2_finset_1,dt_k1_funct_1,dt_k1_tarski,dt_k4_tarski,cc1_funct_2,fc1_finset_1,rc1_funct_2,rc2_partfun1,t2_tarski,fraenkel_a_3_0_group_2,d5_tarski,reflexivity_r1_tarski,existence_m1_relset_1,existence_m2_relset_1,redefinition_k6_domain_1,redefinition_m2_relset_1,dt_k1_binop_1,dt_k1_xboole_0,dt_k2_group_2,dt_k2_zfmisc_1,dt_k6_domain_1,dt_m1_relset_1,dt_m2_relset_1,cc1_relset_1,cc2_finset_1,cc5_funct_2,cc6_funct_2,fc14_finset_1,fc1_xboole_0,rc1_finset_1,rc3_finset_1,rc4_finset_1,d1_binop_1,d2_group_2,existence_l1_struct_0,existence_m1_group_6,redefinition_k2_binop_1,redefinition_m1_group_6,dt_k1_zfmisc_1,dt_k2_binop_1,dt_k3_group_2,dt_k7_group_2,dt_l1_struct_0,dt_m1_group_6,dt_u1_group_1,dt_c2_4__group_6,cc1_finset_1,fc1_struct_0,rc1_xboole_0,rc2_xboole_0,rc3_struct_0,rc5_struct_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,d3_group_2,d9_group_2,antisymmetry_r2_hidden,existence_l1_group_1,existence_m1_group_2,existence_m1_subset_1,dt_k12_group_2,dt_k1_group_1,dt_l1_group_1,dt_m1_group_2,dt_m1_subset_1,dt_u1_struct_0,dt_c1_4__group_6,dt_c1_4_2__group_6,dt_c3_4__group_6,dt_c4_4__group_6,cc1_group_1,cc1_group_2,t1_subset,t7_boole,d13_group_2,d1_group_1,e1_4_2__group_6,t125_group_2]), [interesting(0.65),file(group_6,e2_4_2__group_6),[file(group_6,e2_4_2__group_6)]]). fof(dt_c2_4_2__group_6,plain,( m1_subset_1(c2_4_2__group_6,u1_struct_0(c1_4__group_6)) ), inference(consider,[status(thm),assumptions([dt_c2_4__group_6,dt_c1_4__group_6,dt_c1_4_2__group_6,dt_c3_4__group_6,dt_c4_4__group_6,e1_4_2__group_6])],[dh_c2_4_2__group_6,e2_4_2__group_6]), [interesting(0.65),file(group_6,c2_4_2__group_6),[file(group_6,c2_4_2__group_6)]]). fof(de_c3_4_2__group_6,definition,( c3_4_2__group_6 = c2_4_2__group_6 ), introduced(definition,[new_symbol(c3_4_2__group_6),file(group_6,c3_4_2__group_6)]), [interesting(0.65),axiom,file(group_6,c3_4_2__group_6)]). fof(e3_4_2__group_6,plain, ( c1_4_2__group_6 = k1_group_1(c1_4__group_6,c3_4__group_6,c2_4_2__group_6) & r1_rlvect_1(c4_4__group_6,c2_4_2__group_6) ), inference(consider,[status(thm),assumptions([dt_c2_4__group_6,dt_c1_4__group_6,dt_c1_4_2__group_6,dt_c3_4__group_6,dt_c4_4__group_6,e1_4_2__group_6])],[dh_c2_4_2__group_6,e2_4_2__group_6]), [interesting(0.65),file(group_6,e3_4_2__group_6),[file(group_6,e3_4_2__group_6)]]). fof(d1_rlvect_1,definition,( ! [A] : ( l1_struct_0(A) => ! [B] : ( r1_rlvect_1(A,B) <=> r2_hidden(B,u1_struct_0(A)) ) ) ), file(rlvect_1,d1_rlvect_1), [interesting(0.9),axiom,file(rlvect_1,d1_rlvect_1)]). fof(e4_4_2__group_6,plain,( m1_subset_1(c2_4_2__group_6,u1_struct_0(c4_4__group_6)) ), inference(mizar_by,[status(thm),assumptions([dt_c2_4__group_6,dt_c1_4__group_6,dt_c1_4_2__group_6,dt_c3_4__group_6,dt_c4_4__group_6,e1_4_2__group_6])],[commutativity_k2_tarski,reflexivity_r1_tarski,dt_k1_tarski,dt_k2_tarski,fc1_finset_1,fc2_finset_1,dt_k1_funct_1,dt_k1_zfmisc_1,dt_k4_tarski,cc1_funct_2,cc1_relset_1,cc2_finset_1,rc1_funct_2,rc2_partfun1,rc3_finset_1,rc4_finset_1,rc5_struct_0,t3_subset,t4_subset,t5_subset,d5_tarski,existence_m1_group_2,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_binop_1,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_m1_group_2,dt_m1_relset_1,dt_m2_relset_1,cc1_group_2,cc5_funct_2,cc6_funct_2,fc14_finset_1,fc1_xboole_0,rc1_finset_1,d1_binop_1,existence_l1_group_1,existence_m1_group_6,redefinition_k2_binop_1,redefinition_m1_group_6,dt_k2_binop_1,dt_l1_group_1,dt_m1_group_6,dt_u1_group_1,dt_c2_4__group_6,cc1_finset_1,cc1_group_1,fc1_struct_0,rc1_xboole_0,rc2_xboole_0,rc3_struct_0,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,existence_l1_struct_0,existence_m1_subset_1,dt_k1_group_1,dt_l1_struct_0,dt_m1_subset_1,dt_u1_struct_0,dt_c1_4__group_6,dt_c1_4_2__group_6,dt_c2_4_2__group_6,dt_c3_4__group_6,dt_c4_4__group_6,t1_subset,t7_boole,d1_group_1,e3_4_2__group_6,d1_rlvect_1]), [interesting(0.65),file(group_6,e4_4_2__group_6),[file(group_6,e4_4_2__group_6)]]). fof(dt_c3_4_2__group_6,plain,( m1_subset_1(c3_4_2__group_6,u1_struct_0(c4_4__group_6)) ), inference(mizar_by,[status(thm),assumptions([dt_c2_4__group_6,dt_c1_4__group_6,dt_c1_4_2__group_6,dt_c3_4__group_6,dt_c4_4__group_6,e1_4_2__group_6])],[antisymmetry_r2_hidden,dt_k1_xboole_0,fc1_xboole_0,rc1_finset_1,t1_subset,cc1_finset_1,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t7_boole,t8_boole,existence_l1_group_1,existence_m1_group_2,dt_l1_group_1,dt_m1_group_2,cc1_group_1,cc1_group_2,fc1_struct_0,rc3_struct_0,existence_l1_struct_0,existence_m1_group_6,redefinition_m1_group_6,dt_l1_struct_0,dt_m1_group_6,dt_c1_4__group_6,dt_c2_4__group_6,existence_m1_subset_1,dt_m1_subset_1,dt_u1_struct_0,dt_c2_4_2__group_6,dt_c4_4__group_6,de_c3_4_2__group_6,e4_4_2__group_6]), [interesting(0.65),file(group_6,c3_4_2__group_6),[file(group_6,c3_4_2__group_6)]]). fof(de_c4_4_2__group_6,definition,( c4_4_2__group_6 = c3_4_2__group_6 ), introduced(definition,[new_symbol(c4_4_2__group_6),file(group_6,c4_4_2__group_6)]), [interesting(0.65),axiom,file(group_6,c4_4_2__group_6)]). fof(e5_4_2__group_6,plain,( m1_subset_1(c3_4_2__group_6,u1_struct_0(c2_4__group_6)) ), inference(mizar_by,[status(thm),assumptions([dt_c2_4__group_6,dt_c1_4__group_6,dt_c1_4_2__group_6,dt_c3_4__group_6,dt_c4_4__group_6,e1_4_2__group_6])],[antisymmetry_r2_hidden,dt_k1_xboole_0,fc1_xboole_0,rc1_finset_1,t1_subset,existence_m1_group_6,redefinition_m1_group_6,dt_m1_group_6,cc1_finset_1,cc1_group_2,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t7_boole,t8_boole,existence_l1_struct_0,dt_l1_struct_0,dt_c1_4__group_6,dt_c2_4_2__group_6,dt_c4_4__group_6,fc1_struct_0,rc3_struct_0,existence_l1_group_1,existence_m1_group_2,existence_m1_subset_1,dt_l1_group_1,dt_m1_group_2,dt_m1_subset_1,dt_u1_struct_0,dt_c2_4__group_6,dt_c3_4_2__group_6,de_c3_4_2__group_6,cc1_group_1,t51_group_2]), [interesting(0.65),file(group_6,e5_4_2__group_6),[file(group_6,e5_4_2__group_6)]]). fof(dt_c4_4_2__group_6,plain,( m1_subset_1(c4_4_2__group_6,u1_struct_0(c2_4__group_6)) ), inference(mizar_by,[status(thm),assumptions([dt_c2_4__group_6,dt_c1_4__group_6,dt_c1_4_2__group_6,dt_c3_4__group_6,dt_c4_4__group_6,e1_4_2__group_6])],[antisymmetry_r2_hidden,dt_k1_xboole_0,fc1_xboole_0,rc1_finset_1,t1_subset,cc1_finset_1,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t7_boole,t8_boole,existence_l1_group_1,existence_m1_group_6,redefinition_m1_group_6,dt_l1_group_1,dt_m1_group_6,cc1_group_1,cc1_group_2,fc1_struct_0,rc3_struct_0,existence_l1_struct_0,existence_m1_group_2,dt_l1_struct_0,dt_m1_group_2,dt_c1_4__group_6,dt_c2_4_2__group_6,dt_c4_4__group_6,existence_m1_subset_1,dt_m1_subset_1,dt_u1_struct_0,dt_c2_4__group_6,dt_c3_4_2__group_6,de_c3_4_2__group_6,de_c4_4_2__group_6,e5_4_2__group_6]), [interesting(0.65),file(group_6,c4_4_2__group_6),[file(group_6,c4_4_2__group_6)]]). fof(e6_4_2__group_6,plain,( k1_group_1(c1_4__group_6,c3_4__group_6,c2_4_2__group_6) = k1_group_1(c2_4__group_6,c5_4__group_6,c4_4_2__group_6) ), inference(mizar_by,[status(thm),assumptions([dt_c2_4__group_6,dt_c1_4__group_6,dt_c1_4_2__group_6,dt_c3_4__group_6,dt_c4_4__group_6,e1_4_2__group_6,dt_c5_4__group_6,e1_4__group_6])],[commutativity_k2_tarski,reflexivity_r1_tarski,dt_k1_tarski,dt_k2_tarski,fc1_finset_1,fc2_finset_1,antisymmetry_r2_hidden,existence_m1_group_6,redefinition_m1_group_6,dt_k1_funct_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k4_tarski,dt_m1_group_6,cc1_funct_2,cc1_relset_1,cc2_finset_1,fc14_finset_1,fc1_xboole_0,rc1_finset_1,rc1_funct_2,rc2_partfun1,rc3_finset_1,rc4_finset_1,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,d5_tarski,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_binop_1,dt_k2_zfmisc_1,dt_m1_relset_1,dt_m2_relset_1,dt_c4_4__group_6,cc1_finset_1,cc5_funct_2,cc6_funct_2,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t7_boole,t8_boole,d1_binop_1,existence_l1_struct_0,redefinition_k2_binop_1,dt_k2_binop_1,dt_l1_struct_0,dt_u1_group_1,dt_c3_4_2__group_6,de_c3_4_2__group_6,cc1_group_2,fc1_struct_0,rc3_struct_0,existence_l1_group_1,existence_m1_group_2,existence_m1_subset_1,dt_k1_group_1,dt_l1_group_1,dt_m1_group_2,dt_m1_subset_1,dt_u1_struct_0,dt_c1_4__group_6,dt_c2_4__group_6,dt_c2_4_2__group_6,dt_c3_4__group_6,dt_c4_4_2__group_6,dt_c5_4__group_6,de_c4_4_2__group_6,cc1_group_1,d1_group_1,e1_4__group_6,t52_group_2]), [interesting(0.65),file(group_6,e6_4_2__group_6),[file(group_6,e6_4_2__group_6)]]). fof(e7_4_2__group_6,plain,( r2_hidden(c1_4_2__group_6,k12_group_2(c2_4__group_6,c4_4__group_6,c5_4__group_6)) ), inference(mizar_by,[status(thm),assumptions([dt_c5_4__group_6,e1_4__group_6,dt_c2_4__group_6,dt_c1_4__group_6,dt_c1_4_2__group_6,dt_c3_4__group_6,dt_c4_4__group_6,e1_4_2__group_6])],[commutativity_k2_tarski,dt_k2_tarski,fc2_finset_1,dt_k1_funct_1,dt_k1_tarski,dt_k4_tarski,cc1_funct_2,fc1_finset_1,rc1_funct_2,rc2_partfun1,t2_tarski,fraenkel_a_3_0_group_2,d5_tarski,reflexivity_r1_tarski,existence_m1_relset_1,existence_m2_relset_1,redefinition_k6_domain_1,redefinition_m2_relset_1,dt_k1_binop_1,dt_k1_xboole_0,dt_k2_group_2,dt_k2_zfmisc_1,dt_k6_domain_1,dt_m1_relset_1,dt_m2_relset_1,cc1_relset_1,cc2_finset_1,cc5_funct_2,cc6_funct_2,fc14_finset_1,fc1_xboole_0,rc1_finset_1,rc3_finset_1,rc4_finset_1,d1_binop_1,d2_group_2,existence_l1_struct_0,existence_m1_group_6,redefinition_k2_binop_1,redefinition_m1_group_6,dt_k1_zfmisc_1,dt_k2_binop_1,dt_k3_group_2,dt_k7_group_2,dt_l1_struct_0,dt_m1_group_6,dt_u1_group_1,dt_c3_4_2__group_6,de_c3_4_2__group_6,cc1_finset_1,fc1_struct_0,rc1_xboole_0,rc2_xboole_0,rc3_struct_0,rc5_struct_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,d3_group_2,d9_group_2,antisymmetry_r2_hidden,existence_l1_group_1,existence_m1_group_2,existence_m1_subset_1,dt_k12_group_2,dt_k1_group_1,dt_l1_group_1,dt_m1_group_2,dt_m1_subset_1,dt_u1_struct_0,dt_c1_4__group_6,dt_c1_4_2__group_6,dt_c2_4__group_6,dt_c2_4_2__group_6,dt_c3_4__group_6,dt_c4_4__group_6,dt_c4_4_2__group_6,dt_c5_4__group_6,de_c4_4_2__group_6,cc1_group_1,cc1_group_2,t1_subset,t7_boole,d13_group_2,d1_group_1,e6_4_2__group_6,e3_4_2__group_6,t125_group_2]), [interesting(0.65),file(group_6,e7_4_2__group_6),[file(group_6,e7_4_2__group_6)]]). fof(i3_4_2__group_6,theorem,( $true ), introduced(tautology,[file(group_6,i3_4_2__group_6)]), [interesting(0.65),trivial,file(group_6,i3_4_2__group_6)]). fof(i2_4_2__group_6,plain,( r2_hidden(c1_4_2__group_6,k12_group_2(c2_4__group_6,c4_4__group_6,c5_4__group_6)) ), inference(conclusion,[status(thm),assumptions([dt_c5_4__group_6,e1_4__group_6,dt_c2_4__group_6,dt_c1_4__group_6,dt_c1_4_2__group_6,dt_c3_4__group_6,dt_c4_4__group_6,e1_4_2__group_6])],[e7_4_2__group_6,i3_4_2__group_6]), [interesting(0.65),file(group_6,i2_4_2__group_6),[file(group_6,i2_4_2__group_6)]]). fof(i1_4_2__group_6,plain,( ~ ( r2_hidden(c1_4_2__group_6,k12_group_2(c1_4__group_6,c4_4__group_6,c3_4__group_6)) & ~ r2_hidden(c1_4_2__group_6,k12_group_2(c2_4__group_6,c4_4__group_6,c5_4__group_6)) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c5_4__group_6,e1_4__group_6,dt_c2_4__group_6,dt_c1_4__group_6,dt_c1_4_2__group_6,dt_c3_4__group_6,dt_c4_4__group_6]),discharge_asm(discharge,[e1_4_2__group_6])],[e1_4_2__group_6,i2_4_2__group_6]), [interesting(0.65),file(group_6,i1_4_2__group_6),[file(group_6,i1_4_2__group_6)]]). fof(i1_4_2_tmp__group_6,plain,( ~ ( r2_hidden(c1_4_2__group_6,k12_group_2(c1_4__group_6,c4_4__group_6,c3_4__group_6)) & ~ r2_hidden(c1_4_2__group_6,k12_group_2(c2_4__group_6,c4_4__group_6,c5_4__group_6)) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c5_4__group_6,e1_4__group_6,dt_c2_4__group_6,dt_c1_4__group_6,dt_c3_4__group_6,dt_c4_4__group_6]),discharge_asm(discharge,[dt_c1_4_2__group_6])],[dt_c1_4_2__group_6,i1_4_2__group_6]), [interesting(0.8),e3_4__group_6]). fof(e3_4__group_6,plain,( r1_tarski(k12_group_2(c1_4__group_6,c4_4__group_6,c3_4__group_6),k12_group_2(c2_4__group_6,c4_4__group_6,c5_4__group_6)) ), inference(let,[status(thm),assumptions([dt_c5_4__group_6,e1_4__group_6,dt_c2_4__group_6,dt_c1_4__group_6,dt_c3_4__group_6,dt_c4_4__group_6])],[i1_4_2_tmp__group_6,cc2_finset_1,rc1_finset_1,rc3_finset_1,rc4_finset_1,cc1_finset_1,rc1_xboole_0,rc2_xboole_0,rc5_struct_0,dt_l1_struct_0,fc1_struct_0,rc3_struct_0,redefinition_m1_group_6,dt_k1_zfmisc_1,dt_l1_group_1,dt_m1_group_2,dt_m1_group_6,dt_m1_subset_1,dt_u1_struct_0,cc1_group_1,cc1_group_2,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k12_group_2,dt_c1_4__group_6,dt_c2_4__group_6,dt_c3_4__group_6,dt_c4_4__group_6,dt_c5_4__group_6,d3_tarski,dh_c1_4_2__group_6]), [interesting(0.8),file(group_6,e3_4__group_6),[file(group_6,e3_4__group_6)]]). fof(dt_c1_4_3__group_6,assumption,( $true ), introduced(assumption,[file(group_6,c1_4_3__group_6)]), [interesting(0.65),axiom,file(group_6,c1_4_3__group_6)]). fof(dh_c1_4_3__group_6,definition, ( ~ ( r2_hidden(c1_4_3__group_6,k13_group_2(c2_4__group_6,c4_4__group_6,c5_4__group_6)) & ~ r2_hidden(c1_4_3__group_6,k13_group_2(c1_4__group_6,c4_4__group_6,c3_4__group_6)) ) => ! [A] : ~ ( r2_hidden(A,k13_group_2(c2_4__group_6,c4_4__group_6,c5_4__group_6)) & ~ r2_hidden(A,k13_group_2(c1_4__group_6,c4_4__group_6,c3_4__group_6)) ) ), introduced(definition,[new_symbol(c1_4_3__group_6),file(group_6,c1_4_3__group_6)]), [interesting(0.65),axiom,file(group_6,c1_4_3__group_6)]). fof(e1_4_3__group_6,assumption,( r2_hidden(c1_4_3__group_6,k13_group_2(c2_4__group_6,c4_4__group_6,c5_4__group_6)) ), introduced(assumption,[file(group_6,e1_4_3__group_6)]), [interesting(0.65),axiom,file(group_6,e1_4_3__group_6)]). fof(dt_k4_group_2,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l1_group_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => m1_subset_1(k4_group_2(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) ), file(group_2,k4_group_2), [interesting(0.9),axiom,file(group_2,k4_group_2)]). fof(d4_group_2,definition,( ! [A] : ( ( ~ v3_struct_0(A) & l1_group_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => k4_group_2(A,B,C) = k2_group_2(A,C,k6_domain_1(u1_struct_0(A),B)) ) ) ) ), file(group_2,d4_group_2), [interesting(0.9),axiom,file(group_2,d4_group_2)]). fof(dh_c2_4_3__group_6,definition, ( ? [A] : ( m1_subset_1(A,u1_struct_0(c2_4__group_6)) & c1_4_3__group_6 = k1_group_1(c2_4__group_6,A,c5_4__group_6) & r1_rlvect_1(c4_4__group_6,A) ) => ( m1_subset_1(c2_4_3__group_6,u1_struct_0(c2_4__group_6)) & c1_4_3__group_6 = k1_group_1(c2_4__group_6,c2_4_3__group_6,c5_4__group_6) & r1_rlvect_1(c4_4__group_6,c2_4_3__group_6) ) ), introduced(definition,[new_symbol(c2_4_3__group_6),file(group_6,c2_4_3__group_6)]), [interesting(0.65),axiom,file(group_6,c2_4_3__group_6)]). fof(d14_group_2,definition,( ! [A] : ( ( ~ v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k13_group_2(A,B,C) = k4_group_2(A,C,k7_group_2(A,B)) ) ) ) ), file(group_2,d14_group_2), [interesting(0.9),axiom,file(group_2,d14_group_2)]). fof(t126_group_2,theorem,( ! [A,B] : ( ( ~ v3_struct_0(B) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_group_2(D,B) => ( r2_hidden(A,k13_group_2(B,D,C)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k1_group_1(B,E,C) & r1_rlvect_1(D,E) ) ) ) ) ) ), file(group_2,t126_group_2), [interesting(0.9),axiom,file(group_2,t126_group_2)]). fof(e2_4_3__group_6,plain,( ? [A] : ( m1_subset_1(A,u1_struct_0(c2_4__group_6)) & c1_4_3__group_6 = k1_group_1(c2_4__group_6,A,c5_4__group_6) & r1_rlvect_1(c4_4__group_6,A) ) ), inference(mizar_by,[status(thm),assumptions([dt_c1_4__group_6,dt_c1_4_3__group_6,dt_c2_4__group_6,dt_c4_4__group_6,dt_c5_4__group_6,e1_4_3__group_6])],[commutativity_k2_tarski,dt_k2_tarski,fc2_finset_1,dt_k1_funct_1,dt_k1_tarski,dt_k4_tarski,cc1_funct_2,fc1_finset_1,rc1_funct_2,rc2_partfun1,t2_tarski,fraenkel_a_3_0_group_2,d5_tarski,reflexivity_r1_tarski,existence_m1_relset_1,existence_m2_relset_1,redefinition_k6_domain_1,redefinition_m2_relset_1,dt_k1_binop_1,dt_k1_xboole_0,dt_k2_group_2,dt_k2_zfmisc_1,dt_k6_domain_1,dt_m1_relset_1,dt_m2_relset_1,cc1_relset_1,cc2_finset_1,cc5_funct_2,cc6_funct_2,fc14_finset_1,fc1_xboole_0,rc1_finset_1,rc3_finset_1,rc4_finset_1,d1_binop_1,d2_group_2,existence_l1_struct_0,existence_m1_group_6,redefinition_k2_binop_1,redefinition_m1_group_6,dt_k1_zfmisc_1,dt_k2_binop_1,dt_k4_group_2,dt_k7_group_2,dt_l1_struct_0,dt_m1_group_6,dt_u1_group_1,dt_c1_4__group_6,cc1_finset_1,fc1_struct_0,rc1_xboole_0,rc2_xboole_0,rc3_struct_0,rc5_struct_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,d4_group_2,d9_group_2,antisymmetry_r2_hidden,existence_l1_group_1,existence_m1_group_2,existence_m1_subset_1,dt_k13_group_2,dt_k1_group_1,dt_l1_group_1,dt_m1_group_2,dt_m1_subset_1,dt_u1_struct_0,dt_c1_4_3__group_6,dt_c2_4__group_6,dt_c4_4__group_6,dt_c5_4__group_6,cc1_group_1,cc1_group_2,t1_subset,t7_boole,d14_group_2,d1_group_1,e1_4_3__group_6,t126_group_2]), [interesting(0.65),file(group_6,e2_4_3__group_6),[file(group_6,e2_4_3__group_6)]]). fof(dt_c2_4_3__group_6,plain,( m1_subset_1(c2_4_3__group_6,u1_struct_0(c2_4__group_6)) ), inference(consider,[status(thm),assumptions([dt_c1_4__group_6,dt_c1_4_3__group_6,dt_c2_4__group_6,dt_c4_4__group_6,dt_c5_4__group_6,e1_4_3__group_6])],[dh_c2_4_3__group_6,e2_4_3__group_6]), [interesting(0.65),file(group_6,c2_4_3__group_6),[file(group_6,c2_4_3__group_6)]]). fof(de_c3_4_3__group_6,definition,( c3_4_3__group_6 = c2_4_3__group_6 ), introduced(definition,[new_symbol(c3_4_3__group_6),file(group_6,c3_4_3__group_6)]), [interesting(0.65),axiom,file(group_6,c3_4_3__group_6)]). fof(e4_4_3__group_6,plain,( m1_subset_1(c2_4_3__group_6,u1_struct_0(c1_4__group_6)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_4__group_6,dt_c1_4_3__group_6,dt_c2_4__group_6,dt_c4_4__group_6,dt_c5_4__group_6,e1_4_3__group_6])],[antisymmetry_r2_hidden,dt_k1_xboole_0,fc1_xboole_0,rc1_finset_1,t1_subset,t8_boole,cc1_finset_1,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t7_boole,existence_l1_struct_0,dt_l1_struct_0,dt_c2_4__group_6,cc1_group_2,fc1_struct_0,rc3_struct_0,existence_l1_group_1,existence_m1_group_2,existence_m1_subset_1,dt_l1_group_1,dt_m1_group_2,dt_m1_subset_1,dt_u1_struct_0,dt_c1_4__group_6,dt_c2_4_3__group_6,cc1_group_1,t51_group_2]), [interesting(0.65),file(group_6,e4_4_3__group_6),[file(group_6,e4_4_3__group_6)]]). fof(dt_c3_4_3__group_6,plain,( m1_subset_1(c3_4_3__group_6,u1_struct_0(c1_4__group_6)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_4__group_6,dt_c1_4_3__group_6,dt_c2_4__group_6,dt_c4_4__group_6,dt_c5_4__group_6,e1_4_3__group_6])],[antisymmetry_r2_hidden,dt_k1_xboole_0,fc1_xboole_0,rc1_finset_1,t1_subset,existence_m1_group_2,dt_m1_group_2,cc1_finset_1,cc1_group_2,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t7_boole,t8_boole,existence_l1_group_1,existence_l1_struct_0,dt_l1_group_1,dt_l1_struct_0,dt_c2_4__group_6,cc1_group_1,fc1_struct_0,rc3_struct_0,existence_m1_subset_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_4__group_6,dt_c2_4_3__group_6,de_c3_4_3__group_6,e4_4_3__group_6]), [interesting(0.65),file(group_6,c3_4_3__group_6),[file(group_6,c3_4_3__group_6)]]). fof(e5_4_3__group_6,plain,( k1_group_1(c1_4__group_6,c3_4_3__group_6,c3_4__group_6) = k1_group_1(c2_4__group_6,c2_4_3__group_6,c5_4__group_6) ), inference(mizar_by,[status(thm),assumptions([dt_c3_4__group_6,dt_c1_4__group_6,dt_c1_4_3__group_6,dt_c2_4__group_6,dt_c4_4__group_6,e1_4_3__group_6,dt_c5_4__group_6,e1_4__group_6])],[commutativity_k2_tarski,reflexivity_r1_tarski,dt_k1_tarski,dt_k2_tarski,fc1_finset_1,fc2_finset_1,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k4_tarski,cc1_funct_2,cc1_relset_1,cc2_finset_1,fc14_finset_1,fc1_xboole_0,rc1_finset_1,rc1_funct_2,rc2_partfun1,rc3_finset_1,rc4_finset_1,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,d5_tarski,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_binop_1,dt_k2_zfmisc_1,dt_m1_relset_1,dt_m2_relset_1,cc1_finset_1,cc5_funct_2,cc6_funct_2,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t7_boole,t8_boole,d1_binop_1,existence_l1_struct_0,redefinition_k2_binop_1,dt_k2_binop_1,dt_l1_struct_0,dt_u1_group_1,cc1_group_2,fc1_struct_0,rc3_struct_0,existence_l1_group_1,existence_m1_group_2,existence_m1_subset_1,dt_k1_group_1,dt_l1_group_1,dt_m1_group_2,dt_m1_subset_1,dt_u1_struct_0,dt_c1_4__group_6,dt_c2_4__group_6,dt_c2_4_3__group_6,dt_c3_4__group_6,dt_c3_4_3__group_6,dt_c5_4__group_6,de_c3_4_3__group_6,cc1_group_1,d1_group_1,e1_4__group_6,t52_group_2]), [interesting(0.65),file(group_6,e5_4_3__group_6),[file(group_6,e5_4_3__group_6)]]). fof(e3_4_3__group_6,plain, ( c1_4_3__group_6 = k1_group_1(c2_4__group_6,c2_4_3__group_6,c5_4__group_6) & r1_rlvect_1(c4_4__group_6,c2_4_3__group_6) ), inference(consider,[status(thm),assumptions([dt_c1_4__group_6,dt_c1_4_3__group_6,dt_c2_4__group_6,dt_c4_4__group_6,dt_c5_4__group_6,e1_4_3__group_6])],[dh_c2_4_3__group_6,e2_4_3__group_6]), [interesting(0.65),file(group_6,e3_4_3__group_6),[file(group_6,e3_4_3__group_6)]]). fof(e6_4_3__group_6,plain,( r2_hidden(c1_4_3__group_6,k13_group_2(c1_4__group_6,c4_4__group_6,c3_4__group_6)) ), inference(mizar_by,[status(thm),assumptions([dt_c3_4__group_6,e1_4__group_6,dt_c1_4__group_6,dt_c1_4_3__group_6,dt_c2_4__group_6,dt_c4_4__group_6,dt_c5_4__group_6,e1_4_3__group_6])],[commutativity_k2_tarski,dt_k2_tarski,fc2_finset_1,dt_k1_funct_1,dt_k1_tarski,dt_k4_tarski,cc1_funct_2,fc1_finset_1,rc1_funct_2,rc2_partfun1,t2_tarski,fraenkel_a_3_0_group_2,d5_tarski,reflexivity_r1_tarski,existence_m1_relset_1,existence_m2_relset_1,redefinition_k6_domain_1,redefinition_m2_relset_1,dt_k1_binop_1,dt_k1_xboole_0,dt_k2_group_2,dt_k2_zfmisc_1,dt_k6_domain_1,dt_m1_relset_1,dt_m2_relset_1,cc1_relset_1,cc2_finset_1,cc5_funct_2,cc6_funct_2,fc14_finset_1,fc1_xboole_0,rc1_finset_1,rc3_finset_1,rc4_finset_1,d1_binop_1,d2_group_2,existence_l1_struct_0,existence_m1_group_6,redefinition_k2_binop_1,redefinition_m1_group_6,dt_k1_zfmisc_1,dt_k2_binop_1,dt_k4_group_2,dt_k7_group_2,dt_l1_struct_0,dt_m1_group_6,dt_u1_group_1,cc1_finset_1,fc1_struct_0,rc1_xboole_0,rc2_xboole_0,rc3_struct_0,rc5_struct_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,d4_group_2,d9_group_2,antisymmetry_r2_hidden,existence_l1_group_1,existence_m1_group_2,existence_m1_subset_1,dt_k13_group_2,dt_k1_group_1,dt_l1_group_1,dt_m1_group_2,dt_m1_subset_1,dt_u1_struct_0,dt_c1_4__group_6,dt_c1_4_3__group_6,dt_c2_4__group_6,dt_c2_4_3__group_6,dt_c3_4__group_6,dt_c3_4_3__group_6,dt_c4_4__group_6,dt_c5_4__group_6,de_c3_4_3__group_6,cc1_group_1,cc1_group_2,t1_subset,t7_boole,d14_group_2,d1_group_1,e5_4_3__group_6,e3_4_3__group_6,t126_group_2]), [interesting(0.65),file(group_6,e6_4_3__group_6),[file(group_6,e6_4_3__group_6)]]). fof(i3_4_3__group_6,theorem,( $true ), introduced(tautology,[file(group_6,i3_4_3__group_6)]), [interesting(0.65),trivial,file(group_6,i3_4_3__group_6)]). fof(i2_4_3__group_6,plain,( r2_hidden(c1_4_3__group_6,k13_group_2(c1_4__group_6,c4_4__group_6,c3_4__group_6)) ), inference(conclusion,[status(thm),assumptions([dt_c3_4__group_6,e1_4__group_6,dt_c1_4__group_6,dt_c1_4_3__group_6,dt_c2_4__group_6,dt_c4_4__group_6,dt_c5_4__group_6,e1_4_3__group_6])],[e6_4_3__group_6,i3_4_3__group_6]), [interesting(0.65),file(group_6,i2_4_3__group_6),[file(group_6,i2_4_3__group_6)]]). fof(i1_4_3__group_6,plain,( ~ ( r2_hidden(c1_4_3__group_6,k13_group_2(c2_4__group_6,c4_4__group_6,c5_4__group_6)) & ~ r2_hidden(c1_4_3__group_6,k13_group_2(c1_4__group_6,c4_4__group_6,c3_4__group_6)) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c3_4__group_6,e1_4__group_6,dt_c1_4__group_6,dt_c1_4_3__group_6,dt_c2_4__group_6,dt_c4_4__group_6,dt_c5_4__group_6]),discharge_asm(discharge,[e1_4_3__group_6])],[e1_4_3__group_6,i2_4_3__group_6]), [interesting(0.65),file(group_6,i1_4_3__group_6),[file(group_6,i1_4_3__group_6)]]). fof(i1_4_3_tmp__group_6,plain,( ~ ( r2_hidden(c1_4_3__group_6,k13_group_2(c2_4__group_6,c4_4__group_6,c5_4__group_6)) & ~ r2_hidden(c1_4_3__group_6,k13_group_2(c1_4__group_6,c4_4__group_6,c3_4__group_6)) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c3_4__group_6,e1_4__group_6,dt_c1_4__group_6,dt_c2_4__group_6,dt_c4_4__group_6,dt_c5_4__group_6]),discharge_asm(discharge,[dt_c1_4_3__group_6])],[dt_c1_4_3__group_6,i1_4_3__group_6]), [interesting(0.8),e4_4__group_6]). fof(e4_4__group_6,plain,( r1_tarski(k13_group_2(c2_4__group_6,c4_4__group_6,c5_4__group_6),k13_group_2(c1_4__group_6,c4_4__group_6,c3_4__group_6)) ), inference(let,[status(thm),assumptions([dt_c3_4__group_6,e1_4__group_6,dt_c1_4__group_6,dt_c2_4__group_6,dt_c4_4__group_6,dt_c5_4__group_6])],[i1_4_3_tmp__group_6,cc2_finset_1,rc1_finset_1,rc3_finset_1,rc4_finset_1,cc1_finset_1,rc1_xboole_0,rc2_xboole_0,rc5_struct_0,dt_l1_struct_0,fc1_struct_0,rc3_struct_0,redefinition_m1_group_6,dt_k1_zfmisc_1,dt_l1_group_1,dt_m1_group_2,dt_m1_group_6,dt_m1_subset_1,dt_u1_struct_0,cc1_group_1,cc1_group_2,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k13_group_2,dt_c1_4__group_6,dt_c2_4__group_6,dt_c3_4__group_6,dt_c4_4__group_6,dt_c5_4__group_6,d3_tarski,dh_c1_4_3__group_6]), [interesting(0.8),file(group_6,e4_4__group_6),[file(group_6,e4_4__group_6)]]). fof(dt_c1_4_4__group_6,assumption,( $true ), introduced(assumption,[file(group_6,c1_4_4__group_6)]), [interesting(0.65),axiom,file(group_6,c1_4_4__group_6)]). fof(dh_c1_4_4__group_6,definition, ( ~ ( r2_hidden(c1_4_4__group_6,k13_group_2(c1_4__group_6,c4_4__group_6,c3_4__group_6)) & ~ r2_hidden(c1_4_4__group_6,k13_group_2(c2_4__group_6,c4_4__group_6,c5_4__group_6)) ) => ! [A] : ~ ( r2_hidden(A,k13_group_2(c1_4__group_6,c4_4__group_6,c3_4__group_6)) & ~ r2_hidden(A,k13_group_2(c2_4__group_6,c4_4__group_6,c5_4__group_6)) ) ), introduced(definition,[new_symbol(c1_4_4__group_6),file(group_6,c1_4_4__group_6)]), [interesting(0.65),axiom,file(group_6,c1_4_4__group_6)]). fof(e1_4_4__group_6,assumption,( r2_hidden(c1_4_4__group_6,k13_group_2(c1_4__group_6,c4_4__group_6,c3_4__group_6)) ), introduced(assumption,[file(group_6,e1_4_4__group_6)]), [interesting(0.65),axiom,file(group_6,e1_4_4__group_6)]). fof(dh_c2_4_4__group_6,definition, ( ? [A] : ( m1_subset_1(A,u1_struct_0(c1_4__group_6)) & c1_4_4__group_6 = k1_group_1(c1_4__group_6,A,c3_4__group_6) & r1_rlvect_1(c4_4__group_6,A) ) => ( m1_subset_1(c2_4_4__group_6,u1_struct_0(c1_4__group_6)) & c1_4_4__group_6 = k1_group_1(c1_4__group_6,c2_4_4__group_6,c3_4__group_6) & r1_rlvect_1(c4_4__group_6,c2_4_4__group_6) ) ), introduced(definition,[new_symbol(c2_4_4__group_6),file(group_6,c2_4_4__group_6)]), [interesting(0.65),axiom,file(group_6,c2_4_4__group_6)]). fof(e2_4_4__group_6,plain,( ? [A] : ( m1_subset_1(A,u1_struct_0(c1_4__group_6)) & c1_4_4__group_6 = k1_group_1(c1_4__group_6,A,c3_4__group_6) & r1_rlvect_1(c4_4__group_6,A) ) ), inference(mizar_by,[status(thm),assumptions([dt_c2_4__group_6,dt_c1_4__group_6,dt_c1_4_4__group_6,dt_c3_4__group_6,dt_c4_4__group_6,e1_4_4__group_6])],[commutativity_k2_tarski,dt_k2_tarski,fc2_finset_1,dt_k1_funct_1,dt_k1_tarski,dt_k4_tarski,cc1_funct_2,fc1_finset_1,rc1_funct_2,rc2_partfun1,t2_tarski,fraenkel_a_3_0_group_2,d5_tarski,reflexivity_r1_tarski,existence_m1_relset_1,existence_m2_relset_1,redefinition_k6_domain_1,redefinition_m2_relset_1,dt_k1_binop_1,dt_k1_xboole_0,dt_k2_group_2,dt_k2_zfmisc_1,dt_k6_domain_1,dt_m1_relset_1,dt_m2_relset_1,cc1_relset_1,cc2_finset_1,cc5_funct_2,cc6_funct_2,fc14_finset_1,fc1_xboole_0,rc1_finset_1,rc3_finset_1,rc4_finset_1,d1_binop_1,d2_group_2,existence_l1_struct_0,existence_m1_group_6,redefinition_k2_binop_1,redefinition_m1_group_6,dt_k1_zfmisc_1,dt_k2_binop_1,dt_k4_group_2,dt_k7_group_2,dt_l1_struct_0,dt_m1_group_6,dt_u1_group_1,dt_c2_4__group_6,cc1_finset_1,fc1_struct_0,rc1_xboole_0,rc2_xboole_0,rc3_struct_0,rc5_struct_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,d4_group_2,d9_group_2,antisymmetry_r2_hidden,existence_l1_group_1,existence_m1_group_2,existence_m1_subset_1,dt_k13_group_2,dt_k1_group_1,dt_l1_group_1,dt_m1_group_2,dt_m1_subset_1,dt_u1_struct_0,dt_c1_4__group_6,dt_c1_4_4__group_6,dt_c3_4__group_6,dt_c4_4__group_6,cc1_group_1,cc1_group_2,t1_subset,t7_boole,d14_group_2,d1_group_1,e1_4_4__group_6,t126_group_2]), [interesting(0.65),file(group_6,e2_4_4__group_6),[file(group_6,e2_4_4__group_6)]]). fof(dt_c2_4_4__group_6,plain,( m1_subset_1(c2_4_4__group_6,u1_struct_0(c1_4__group_6)) ), inference(consider,[status(thm),assumptions([dt_c2_4__group_6,dt_c1_4__group_6,dt_c1_4_4__group_6,dt_c3_4__group_6,dt_c4_4__group_6,e1_4_4__group_6])],[dh_c2_4_4__group_6,e2_4_4__group_6]), [interesting(0.65),file(group_6,c2_4_4__group_6),[file(group_6,c2_4_4__group_6)]]). fof(de_c3_4_4__group_6,definition,( c3_4_4__group_6 = c2_4_4__group_6 ), introduced(definition,[new_symbol(c3_4_4__group_6),file(group_6,c3_4_4__group_6)]), [interesting(0.65),axiom,file(group_6,c3_4_4__group_6)]). fof(e3_4_4__group_6,plain, ( c1_4_4__group_6 = k1_group_1(c1_4__group_6,c2_4_4__group_6,c3_4__group_6) & r1_rlvect_1(c4_4__group_6,c2_4_4__group_6) ), inference(consider,[status(thm),assumptions([dt_c2_4__group_6,dt_c1_4__group_6,dt_c1_4_4__group_6,dt_c3_4__group_6,dt_c4_4__group_6,e1_4_4__group_6])],[dh_c2_4_4__group_6,e2_4_4__group_6]), [interesting(0.65),file(group_6,e3_4_4__group_6),[file(group_6,e3_4_4__group_6)]]). fof(e4_4_4__group_6,plain,( m1_subset_1(c2_4_4__group_6,u1_struct_0(c4_4__group_6)) ), inference(mizar_by,[status(thm),assumptions([dt_c2_4__group_6,dt_c1_4__group_6,dt_c1_4_4__group_6,dt_c3_4__group_6,dt_c4_4__group_6,e1_4_4__group_6])],[commutativity_k2_tarski,reflexivity_r1_tarski,dt_k1_tarski,dt_k2_tarski,fc1_finset_1,fc2_finset_1,dt_k1_funct_1,dt_k1_zfmisc_1,dt_k4_tarski,cc1_funct_2,cc1_relset_1,cc2_finset_1,rc1_funct_2,rc2_partfun1,rc3_finset_1,rc4_finset_1,rc5_struct_0,t3_subset,t4_subset,t5_subset,d5_tarski,existence_m1_group_2,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_binop_1,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_m1_group_2,dt_m1_relset_1,dt_m2_relset_1,cc1_group_2,cc5_funct_2,cc6_funct_2,fc14_finset_1,fc1_xboole_0,rc1_finset_1,d1_binop_1,existence_l1_group_1,existence_m1_group_6,redefinition_k2_binop_1,redefinition_m1_group_6,dt_k2_binop_1,dt_l1_group_1,dt_m1_group_6,dt_u1_group_1,dt_c2_4__group_6,cc1_finset_1,cc1_group_1,fc1_struct_0,rc1_xboole_0,rc2_xboole_0,rc3_struct_0,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,existence_l1_struct_0,existence_m1_subset_1,dt_k1_group_1,dt_l1_struct_0,dt_m1_subset_1,dt_u1_struct_0,dt_c1_4__group_6,dt_c1_4_4__group_6,dt_c2_4_4__group_6,dt_c3_4__group_6,dt_c4_4__group_6,t1_subset,t7_boole,d1_group_1,e3_4_4__group_6,d1_rlvect_1]), [interesting(0.65),file(group_6,e4_4_4__group_6),[file(group_6,e4_4_4__group_6)]]). fof(dt_c3_4_4__group_6,plain,( m1_subset_1(c3_4_4__group_6,u1_struct_0(c4_4__group_6)) ), inference(mizar_by,[status(thm),assumptions([dt_c2_4__group_6,dt_c1_4__group_6,dt_c1_4_4__group_6,dt_c3_4__group_6,dt_c4_4__group_6,e1_4_4__group_6])],[antisymmetry_r2_hidden,dt_k1_xboole_0,fc1_xboole_0,rc1_finset_1,t1_subset,cc1_finset_1,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t7_boole,t8_boole,existence_l1_group_1,existence_m1_group_2,dt_l1_group_1,dt_m1_group_2,cc1_group_1,cc1_group_2,fc1_struct_0,rc3_struct_0,existence_l1_struct_0,existence_m1_group_6,redefinition_m1_group_6,dt_l1_struct_0,dt_m1_group_6,dt_c1_4__group_6,dt_c2_4__group_6,existence_m1_subset_1,dt_m1_subset_1,dt_u1_struct_0,dt_c2_4_4__group_6,dt_c4_4__group_6,de_c3_4_4__group_6,e4_4_4__group_6]), [interesting(0.65),file(group_6,c3_4_4__group_6),[file(group_6,c3_4_4__group_6)]]). fof(de_c4_4_4__group_6,definition,( c4_4_4__group_6 = c3_4_4__group_6 ), introduced(definition,[new_symbol(c4_4_4__group_6),file(group_6,c4_4_4__group_6)]), [interesting(0.65),axiom,file(group_6,c4_4_4__group_6)]). fof(e5_4_4__group_6,plain,( m1_subset_1(c3_4_4__group_6,u1_struct_0(c2_4__group_6)) ), inference(mizar_by,[status(thm),assumptions([dt_c2_4__group_6,dt_c1_4__group_6,dt_c1_4_4__group_6,dt_c3_4__group_6,dt_c4_4__group_6,e1_4_4__group_6])],[antisymmetry_r2_hidden,dt_k1_xboole_0,fc1_xboole_0,rc1_finset_1,t1_subset,existence_m1_group_6,redefinition_m1_group_6,dt_m1_group_6,cc1_finset_1,cc1_group_2,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t7_boole,t8_boole,existence_l1_struct_0,dt_l1_struct_0,dt_c1_4__group_6,dt_c2_4_4__group_6,dt_c4_4__group_6,fc1_struct_0,rc3_struct_0,existence_l1_group_1,existence_m1_group_2,existence_m1_subset_1,dt_l1_group_1,dt_m1_group_2,dt_m1_subset_1,dt_u1_struct_0,dt_c2_4__group_6,dt_c3_4_4__group_6,de_c3_4_4__group_6,cc1_group_1,t51_group_2]), [interesting(0.65),file(group_6,e5_4_4__group_6),[file(group_6,e5_4_4__group_6)]]). fof(dt_c4_4_4__group_6,plain,( m1_subset_1(c4_4_4__group_6,u1_struct_0(c2_4__group_6)) ), inference(mizar_by,[status(thm),assumptions([dt_c2_4__group_6,dt_c1_4__group_6,dt_c1_4_4__group_6,dt_c3_4__group_6,dt_c4_4__group_6,e1_4_4__group_6])],[antisymmetry_r2_hidden,dt_k1_xboole_0,fc1_xboole_0,rc1_finset_1,t1_subset,cc1_finset_1,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t7_boole,t8_boole,existence_l1_group_1,existence_m1_group_6,redefinition_m1_group_6,dt_l1_group_1,dt_m1_group_6,cc1_group_1,cc1_group_2,fc1_struct_0,rc3_struct_0,existence_l1_struct_0,existence_m1_group_2,dt_l1_struct_0,dt_m1_group_2,dt_c1_4__group_6,dt_c2_4_4__group_6,dt_c4_4__group_6,existence_m1_subset_1,dt_m1_subset_1,dt_u1_struct_0,dt_c2_4__group_6,dt_c3_4_4__group_6,de_c3_4_4__group_6,de_c4_4_4__group_6,e5_4_4__group_6]), [interesting(0.65),file(group_6,c4_4_4__group_6),[file(group_6,c4_4_4__group_6)]]). fof(e6_4_4__group_6,plain,( k1_group_1(c1_4__group_6,c2_4_4__group_6,c3_4__group_6) = k1_group_1(c2_4__group_6,c4_4_4__group_6,c5_4__group_6) ), inference(mizar_by,[status(thm),assumptions([dt_c2_4__group_6,dt_c1_4__group_6,dt_c1_4_4__group_6,dt_c3_4__group_6,dt_c4_4__group_6,e1_4_4__group_6,dt_c5_4__group_6,e1_4__group_6])],[commutativity_k2_tarski,reflexivity_r1_tarski,dt_k1_tarski,dt_k2_tarski,fc1_finset_1,fc2_finset_1,antisymmetry_r2_hidden,existence_m1_group_6,redefinition_m1_group_6,dt_k1_funct_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k4_tarski,dt_m1_group_6,cc1_funct_2,cc1_relset_1,cc2_finset_1,fc14_finset_1,fc1_xboole_0,rc1_finset_1,rc1_funct_2,rc2_partfun1,rc3_finset_1,rc4_finset_1,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,d5_tarski,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_binop_1,dt_k2_zfmisc_1,dt_m1_relset_1,dt_m2_relset_1,dt_c4_4__group_6,cc1_finset_1,cc5_funct_2,cc6_funct_2,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t7_boole,t8_boole,d1_binop_1,existence_l1_struct_0,redefinition_k2_binop_1,dt_k2_binop_1,dt_l1_struct_0,dt_u1_group_1,dt_c3_4_4__group_6,de_c3_4_4__group_6,cc1_group_2,fc1_struct_0,rc3_struct_0,existence_l1_group_1,existence_m1_group_2,existence_m1_subset_1,dt_k1_group_1,dt_l1_group_1,dt_m1_group_2,dt_m1_subset_1,dt_u1_struct_0,dt_c1_4__group_6,dt_c2_4__group_6,dt_c2_4_4__group_6,dt_c3_4__group_6,dt_c4_4_4__group_6,dt_c5_4__group_6,de_c4_4_4__group_6,cc1_group_1,d1_group_1,e1_4__group_6,t52_group_2]), [interesting(0.65),file(group_6,e6_4_4__group_6),[file(group_6,e6_4_4__group_6)]]). fof(e7_4_4__group_6,plain,( r2_hidden(c1_4_4__group_6,k13_group_2(c2_4__group_6,c4_4__group_6,c5_4__group_6)) ), inference(mizar_by,[status(thm),assumptions([dt_c5_4__group_6,e1_4__group_6,dt_c2_4__group_6,dt_c1_4__group_6,dt_c1_4_4__group_6,dt_c3_4__group_6,dt_c4_4__group_6,e1_4_4__group_6])],[commutativity_k2_tarski,dt_k2_tarski,fc2_finset_1,dt_k1_funct_1,dt_k1_tarski,dt_k4_tarski,cc1_funct_2,fc1_finset_1,rc1_funct_2,rc2_partfun1,t2_tarski,fraenkel_a_3_0_group_2,d5_tarski,reflexivity_r1_tarski,existence_m1_relset_1,existence_m2_relset_1,redefinition_k6_domain_1,redefinition_m2_relset_1,dt_k1_binop_1,dt_k1_xboole_0,dt_k2_group_2,dt_k2_zfmisc_1,dt_k6_domain_1,dt_m1_relset_1,dt_m2_relset_1,cc1_relset_1,cc2_finset_1,cc5_funct_2,cc6_funct_2,fc14_finset_1,fc1_xboole_0,rc1_finset_1,rc3_finset_1,rc4_finset_1,d1_binop_1,d2_group_2,existence_l1_struct_0,existence_m1_group_6,redefinition_k2_binop_1,redefinition_m1_group_6,dt_k1_zfmisc_1,dt_k2_binop_1,dt_k4_group_2,dt_k7_group_2,dt_l1_struct_0,dt_m1_group_6,dt_u1_group_1,dt_c3_4_4__group_6,de_c3_4_4__group_6,cc1_finset_1,fc1_struct_0,rc1_xboole_0,rc2_xboole_0,rc3_struct_0,rc5_struct_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,d4_group_2,d9_group_2,antisymmetry_r2_hidden,existence_l1_group_1,existence_m1_group_2,existence_m1_subset_1,dt_k13_group_2,dt_k1_group_1,dt_l1_group_1,dt_m1_group_2,dt_m1_subset_1,dt_u1_struct_0,dt_c1_4__group_6,dt_c1_4_4__group_6,dt_c2_4__group_6,dt_c2_4_4__group_6,dt_c3_4__group_6,dt_c4_4__group_6,dt_c4_4_4__group_6,dt_c5_4__group_6,de_c4_4_4__group_6,cc1_group_1,cc1_group_2,t1_subset,t7_boole,d14_group_2,d1_group_1,e6_4_4__group_6,e3_4_4__group_6,t126_group_2]), [interesting(0.65),file(group_6,e7_4_4__group_6),[file(group_6,e7_4_4__group_6)]]). fof(i3_4_4__group_6,theorem,( $true ), introduced(tautology,[file(group_6,i3_4_4__group_6)]), [interesting(0.65),trivial,file(group_6,i3_4_4__group_6)]). fof(i2_4_4__group_6,plain,( r2_hidden(c1_4_4__group_6,k13_group_2(c2_4__group_6,c4_4__group_6,c5_4__group_6)) ), inference(conclusion,[status(thm),assumptions([dt_c5_4__group_6,e1_4__group_6,dt_c2_4__group_6,dt_c1_4__group_6,dt_c1_4_4__group_6,dt_c3_4__group_6,dt_c4_4__group_6,e1_4_4__group_6])],[e7_4_4__group_6,i3_4_4__group_6]), [interesting(0.65),file(group_6,i2_4_4__group_6),[file(group_6,i2_4_4__group_6)]]). fof(i1_4_4__group_6,plain,( ~ ( r2_hidden(c1_4_4__group_6,k13_group_2(c1_4__group_6,c4_4__group_6,c3_4__group_6)) & ~ r2_hidden(c1_4_4__group_6,k13_group_2(c2_4__group_6,c4_4__group_6,c5_4__group_6)) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c5_4__group_6,e1_4__group_6,dt_c2_4__group_6,dt_c1_4__group_6,dt_c1_4_4__group_6,dt_c3_4__group_6,dt_c4_4__group_6]),discharge_asm(discharge,[e1_4_4__group_6])],[e1_4_4__group_6,i2_4_4__group_6]), [interesting(0.65),file(group_6,i1_4_4__group_6),[file(group_6,i1_4_4__group_6)]]). fof(i1_4_4_tmp__group_6,plain,( ~ ( r2_hidden(c1_4_4__group_6,k13_group_2(c1_4__group_6,c4_4__group_6,c3_4__group_6)) & ~ r2_hidden(c1_4_4__group_6,k13_group_2(c2_4__group_6,c4_4__group_6,c5_4__group_6)) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c5_4__group_6,e1_4__group_6,dt_c2_4__group_6,dt_c1_4__group_6,dt_c3_4__group_6,dt_c4_4__group_6]),discharge_asm(discharge,[dt_c1_4_4__group_6])],[dt_c1_4_4__group_6,i1_4_4__group_6]), [interesting(0.8),e5_4__group_6]). fof(e5_4__group_6,plain,( r1_tarski(k13_group_2(c1_4__group_6,c4_4__group_6,c3_4__group_6),k13_group_2(c2_4__group_6,c4_4__group_6,c5_4__group_6)) ), inference(let,[status(thm),assumptions([dt_c5_4__group_6,e1_4__group_6,dt_c2_4__group_6,dt_c1_4__group_6,dt_c3_4__group_6,dt_c4_4__group_6])],[i1_4_4_tmp__group_6,cc2_finset_1,rc1_finset_1,rc3_finset_1,rc4_finset_1,cc1_finset_1,rc1_xboole_0,rc2_xboole_0,rc5_struct_0,dt_l1_struct_0,fc1_struct_0,rc3_struct_0,redefinition_m1_group_6,dt_k1_zfmisc_1,dt_l1_group_1,dt_m1_group_2,dt_m1_group_6,dt_m1_subset_1,dt_u1_struct_0,cc1_group_1,cc1_group_2,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k13_group_2,dt_c1_4__group_6,dt_c2_4__group_6,dt_c3_4__group_6,dt_c4_4__group_6,dt_c5_4__group_6,d3_tarski,dh_c1_4_4__group_6]), [interesting(0.8),file(group_6,e5_4__group_6),[file(group_6,e5_4__group_6)]]). fof(i10_4__group_6,theorem,( $true ), introduced(tautology,[file(group_6,i10_4__group_6)]), [interesting(0.8),trivial,file(group_6,i10_4__group_6)]). fof(i9_4__group_6,plain,( r1_tarski(k13_group_2(c1_4__group_6,c4_4__group_6,c3_4__group_6),k13_group_2(c2_4__group_6,c4_4__group_6,c5_4__group_6)) ), inference(conclusion,[status(thm),assumptions([dt_c5_4__group_6,e1_4__group_6,dt_c2_4__group_6,dt_c1_4__group_6,dt_c3_4__group_6,dt_c4_4__group_6])],[e5_4__group_6,i10_4__group_6]), [interesting(0.8),file(group_6,i9_4__group_6),[file(group_6,i9_4__group_6)]]). fof(i8_4__group_6,plain,( k13_group_2(c2_4__group_6,c4_4__group_6,c5_4__group_6) = k13_group_2(c1_4__group_6,c4_4__group_6,c3_4__group_6) ), inference(conclusion,[status(thm),assumptions([dt_c5_4__group_6,e1_4__group_6,dt_c2_4__group_6,dt_c1_4__group_6,dt_c3_4__group_6,dt_c4_4__group_6])],[cc2_finset_1,rc1_finset_1,rc3_finset_1,rc4_finset_1,cc1_finset_1,rc1_xboole_0,rc2_xboole_0,rc5_struct_0,dt_l1_struct_0,fc1_struct_0,rc3_struct_0,redefinition_m1_group_6,dt_k1_zfmisc_1,dt_l1_group_1,dt_m1_group_2,dt_m1_group_6,dt_m1_subset_1,dt_u1_struct_0,cc1_group_1,cc1_group_2,reflexivity_r1_tarski,dt_k13_group_2,dt_c1_4__group_6,dt_c2_4__group_6,dt_c3_4__group_6,dt_c4_4__group_6,dt_c5_4__group_6,d10_xboole_0,e4_4__group_6,i9_4__group_6]), [interesting(0.8),file(group_6,i8_4__group_6),[file(group_6,i8_4__group_6)]]). fof(i7_4__group_6,plain, ( r1_tarski(k12_group_2(c1_4__group_6,c4_4__group_6,c3_4__group_6),k12_group_2(c2_4__group_6,c4_4__group_6,c5_4__group_6)) & k13_group_2(c2_4__group_6,c4_4__group_6,c5_4__group_6) = k13_group_2(c1_4__group_6,c4_4__group_6,c3_4__group_6) ), inference(conclusion,[status(thm),assumptions([dt_c5_4__group_6,e1_4__group_6,dt_c2_4__group_6,dt_c1_4__group_6,dt_c3_4__group_6,dt_c4_4__group_6])],[e3_4__group_6,i8_4__group_6]), [interesting(0.8),file(group_6,i7_4__group_6),[file(group_6,i7_4__group_6)]]). fof(i6_4__group_6,plain, ( k12_group_2(c2_4__group_6,c4_4__group_6,c5_4__group_6) = k12_group_2(c1_4__group_6,c4_4__group_6,c3_4__group_6) & k13_group_2(c2_4__group_6,c4_4__group_6,c5_4__group_6) = k13_group_2(c1_4__group_6,c4_4__group_6,c3_4__group_6) ), inference(conclusion,[status(thm),assumptions([dt_c5_4__group_6,e1_4__group_6,dt_c2_4__group_6,dt_c1_4__group_6,dt_c3_4__group_6,dt_c4_4__group_6])],[cc2_finset_1,rc1_finset_1,rc3_finset_1,rc4_finset_1,cc1_finset_1,rc1_xboole_0,rc2_xboole_0,rc5_struct_0,dt_l1_struct_0,fc1_struct_0,rc3_struct_0,redefinition_m1_group_6,dt_k1_zfmisc_1,dt_l1_group_1,dt_m1_group_2,dt_m1_group_6,dt_m1_subset_1,dt_u1_struct_0,cc1_group_1,cc1_group_2,reflexivity_r1_tarski,dt_k12_group_2,dt_k13_group_2,dt_c1_4__group_6,dt_c2_4__group_6,dt_c3_4__group_6,dt_c4_4__group_6,dt_c5_4__group_6,d10_xboole_0,e2_4__group_6,i7_4__group_6]), [interesting(0.8),file(group_6,i6_4__group_6),[file(group_6,i6_4__group_6)]]). fof(i5_4__group_6,plain, ( c5_4__group_6 = c3_4__group_6 => ( k12_group_2(c2_4__group_6,c4_4__group_6,c5_4__group_6) = k12_group_2(c1_4__group_6,c4_4__group_6,c3_4__group_6) & k13_group_2(c2_4__group_6,c4_4__group_6,c5_4__group_6) = k13_group_2(c1_4__group_6,c4_4__group_6,c3_4__group_6) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c5_4__group_6,dt_c2_4__group_6,dt_c1_4__group_6,dt_c3_4__group_6,dt_c4_4__group_6]),discharge_asm(discharge,[e1_4__group_6])],[e1_4__group_6,i6_4__group_6]), [interesting(0.8),file(group_6,i5_4__group_6),[file(group_6,i5_4__group_6)]]). fof(i5_4_tmp__group_6,plain, ( m1_subset_1(c5_4__group_6,u1_struct_0(c2_4__group_6)) => ( c5_4__group_6 = c3_4__group_6 => ( k12_group_2(c2_4__group_6,c4_4__group_6,c5_4__group_6) = k12_group_2(c1_4__group_6,c4_4__group_6,c3_4__group_6) & k13_group_2(c2_4__group_6,c4_4__group_6,c5_4__group_6) = k13_group_2(c1_4__group_6,c4_4__group_6,c3_4__group_6) ) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c2_4__group_6,dt_c1_4__group_6,dt_c3_4__group_6,dt_c4_4__group_6]),discharge_asm(discharge,[dt_c5_4__group_6])],[dt_c5_4__group_6,i5_4__group_6]), [interesting(0.8),i4_4__group_6]). fof(i4_4__group_6,plain,( ! [A] : ( m1_subset_1(A,u1_struct_0(c2_4__group_6)) => ( A = c3_4__group_6 => ( k12_group_2(c2_4__group_6,c4_4__group_6,A) = k12_group_2(c1_4__group_6,c4_4__group_6,c3_4__group_6) & k13_group_2(c2_4__group_6,c4_4__group_6,A) = k13_group_2(c1_4__group_6,c4_4__group_6,c3_4__group_6) ) ) ) ), inference(let,[status(thm),assumptions([dt_c2_4__group_6,dt_c1_4__group_6,dt_c3_4__group_6,dt_c4_4__group_6])],[i5_4_tmp__group_6,dh_c5_4__group_6]), [interesting(0.8),file(group_6,i4_4__group_6),[file(group_6,i4_4__group_6)]]). fof(i4_4_tmp__group_6,plain, ( m1_group_6(c4_4__group_6,c1_4__group_6,c2_4__group_6) => ! [A] : ( m1_subset_1(A,u1_struct_0(c2_4__group_6)) => ( A = c3_4__group_6 => ( k12_group_2(c2_4__group_6,c4_4__group_6,A) = k12_group_2(c1_4__group_6,c4_4__group_6,c3_4__group_6) & k13_group_2(c2_4__group_6,c4_4__group_6,A) = k13_group_2(c1_4__group_6,c4_4__group_6,c3_4__group_6) ) ) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c2_4__group_6,dt_c1_4__group_6,dt_c3_4__group_6]),discharge_asm(discharge,[dt_c4_4__group_6])],[dt_c4_4__group_6,i4_4__group_6]), [interesting(0.8),i3_4__group_6]). fof(i3_4__group_6,plain,( ! [A] : ( m1_group_6(A,c1_4__group_6,c2_4__group_6) => ! [B] : ( m1_subset_1(B,u1_struct_0(c2_4__group_6)) => ( B = c3_4__group_6 => ( k12_group_2(c2_4__group_6,A,B) = k12_group_2(c1_4__group_6,A,c3_4__group_6) & k13_group_2(c2_4__group_6,A,B) = k13_group_2(c1_4__group_6,A,c3_4__group_6) ) ) ) ) ), inference(let,[status(thm),assumptions([dt_c2_4__group_6,dt_c1_4__group_6,dt_c3_4__group_6])],[i4_4_tmp__group_6,dh_c4_4__group_6]), [interesting(0.8),file(group_6,i3_4__group_6),[file(group_6,i3_4__group_6)]]). fof(i3_4_tmp__group_6,plain, ( m1_subset_1(c3_4__group_6,u1_struct_0(c1_4__group_6)) => ! [A] : ( m1_group_6(A,c1_4__group_6,c2_4__group_6) => ! [B] : ( m1_subset_1(B,u1_struct_0(c2_4__group_6)) => ( B = c3_4__group_6 => ( k12_group_2(c2_4__group_6,A,B) = k12_group_2(c1_4__group_6,A,c3_4__group_6) & k13_group_2(c2_4__group_6,A,B) = k13_group_2(c1_4__group_6,A,c3_4__group_6) ) ) ) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c2_4__group_6,dt_c1_4__group_6]),discharge_asm(discharge,[dt_c3_4__group_6])],[dt_c3_4__group_6,i3_4__group_6]), [interesting(0.8),i2_4__group_6]). fof(i2_4__group_6,plain,( ! [A] : ( m1_subset_1(A,u1_struct_0(c1_4__group_6)) => ! [B] : ( m1_group_6(B,c1_4__group_6,c2_4__group_6) => ! [C] : ( m1_subset_1(C,u1_struct_0(c2_4__group_6)) => ( C = A => ( k12_group_2(c2_4__group_6,B,C) = k12_group_2(c1_4__group_6,B,A) & k13_group_2(c2_4__group_6,B,C) = k13_group_2(c1_4__group_6,B,A) ) ) ) ) ) ), inference(let,[status(thm),assumptions([dt_c2_4__group_6,dt_c1_4__group_6])],[i3_4_tmp__group_6,dh_c3_4__group_6]), [interesting(0.8),file(group_6,i2_4__group_6),[file(group_6,i2_4__group_6)]]). fof(i2_4_tmp__group_6,plain, ( m1_group_2(c2_4__group_6,c1_4__group_6) => ! [A] : ( m1_subset_1(A,u1_struct_0(c1_4__group_6)) => ! [B] : ( m1_group_6(B,c1_4__group_6,c2_4__group_6) => ! [C] : ( m1_subset_1(C,u1_struct_0(c2_4__group_6)) => ( C = A => ( k12_group_2(c2_4__group_6,B,C) = k12_group_2(c1_4__group_6,B,A) & k13_group_2(c2_4__group_6,B,C) = k13_group_2(c1_4__group_6,B,A) ) ) ) ) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_4__group_6]),discharge_asm(discharge,[dt_c2_4__group_6])],[dt_c2_4__group_6,i2_4__group_6]), [interesting(0.8),i1_4__group_6]). fof(i1_4__group_6,plain,( ! [A] : ( m1_group_2(A,c1_4__group_6) => ! [B] : ( m1_subset_1(B,u1_struct_0(c1_4__group_6)) => ! [C] : ( m1_group_6(C,c1_4__group_6,A) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( D = B => ( k12_group_2(A,C,D) = k12_group_2(c1_4__group_6,C,B) & k13_group_2(A,C,D) = k13_group_2(c1_4__group_6,C,B) ) ) ) ) ) ) ), inference(let,[status(thm),assumptions([dt_c1_4__group_6])],[i2_4_tmp__group_6,dh_c2_4__group_6]), [interesting(0.8),file(group_6,i1_4__group_6),[file(group_6,i1_4__group_6)]]). fof(i1_4_tmp__group_6,plain, ( ( ~ v3_struct_0(c1_4__group_6) & v3_group_1(c1_4__group_6) & v4_group_1(c1_4__group_6) & l1_group_1(c1_4__group_6) ) => ! [A] : ( m1_group_2(A,c1_4__group_6) => ! [B] : ( m1_subset_1(B,u1_struct_0(c1_4__group_6)) => ! [C] : ( m1_group_6(C,c1_4__group_6,A) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( D = B => ( k12_group_2(A,C,D) = k12_group_2(c1_4__group_6,C,B) & k13_group_2(A,C,D) = k13_group_2(c1_4__group_6,C,B) ) ) ) ) ) ) ), inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_4__group_6])],[dt_c1_4__group_6,i1_4__group_6]), [interesting(1),t2_group_6]). fof(t2_group_6,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_group_6(D,A,B) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ( E = C => ( k12_group_2(B,D,E) = k12_group_2(A,D,C) & k13_group_2(B,D,E) = k13_group_2(A,D,C) ) ) ) ) ) ) ) ), inference(let,[status(thm),assumptions([])],[i1_4_tmp__group_6,dh_c1_4__group_6]), [interesting(1),file(group_6,t2_group_6),[file(group_6,t2_group_6)]]).