% Mizar ND problem: t2_armstrng,armstrng,105,55 fof(dh_c1_4__armstrng,definition, ( ( ( v1_relat_1(c1_4__armstrng) & ~ v1_xboole_0(c1_4__armstrng) & v4_relat_2(c1_4__armstrng) & v8_relat_2(c1_4__armstrng) ) => ! [A] : ( ( v1_finset_1(A) & m1_subset_1(A,k1_zfmisc_1(k3_relat_1(c1_4__armstrng))) ) => ~ ( A != k1_xboole_0 & ! [B] : ( m1_subset_1(B,A) => ~ r2_waybel_4(A,B,c1_4__armstrng) ) ) ) ) => ! [C] : ( ( v1_relat_1(C) & ~ v1_xboole_0(C) & v4_relat_2(C) & v8_relat_2(C) ) => ! [D] : ( ( v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(k3_relat_1(C))) ) => ~ ( D != k1_xboole_0 & ! [E] : ( m1_subset_1(E,D) => ~ r2_waybel_4(D,E,C) ) ) ) ) ), introduced(definition,[new_symbol(c1_4__armstrng),file(armstrng,c1_4__armstrng)]), [interesting(0.8),axiom,file(armstrng,c1_4__armstrng)]). fof(dh_c2_4__armstrng,definition, ( ( ( v1_finset_1(c2_4__armstrng) & m1_subset_1(c2_4__armstrng,k1_zfmisc_1(k3_relat_1(c1_4__armstrng))) ) => ~ ( c2_4__armstrng != k1_xboole_0 & ! [A] : ( m1_subset_1(A,c2_4__armstrng) => ~ r2_waybel_4(c2_4__armstrng,A,c1_4__armstrng) ) ) ) => ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(k3_relat_1(c1_4__armstrng))) ) => ~ ( B != k1_xboole_0 & ! [C] : ( m1_subset_1(C,B) => ~ r2_waybel_4(B,C,c1_4__armstrng) ) ) ) ), introduced(definition,[new_symbol(c2_4__armstrng),file(armstrng,c2_4__armstrng)]), [interesting(0.8),axiom,file(armstrng,c2_4__armstrng)]). fof(e1_4__armstrng,assumption,( c2_4__armstrng != k1_xboole_0 ), introduced(assumption,[file(armstrng,e1_4__armstrng)]), [interesting(0.8),axiom,file(armstrng,e1_4__armstrng)]). fof(rc3_funct_1,theorem,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) ) ), file(funct_1,rc3_funct_1), [interesting(0.9),axiom,file(funct_1,rc3_funct_1)]). fof(rc6_finseq_1,theorem,( ? [A] : ( v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_finset_1(A) ) ), file(finseq_1,rc6_finseq_1), [interesting(0.9),axiom,file(finseq_1,rc6_finseq_1)]). fof(cc2_funct_1,theorem,( ! [A] : ( ( v1_relat_1(A) & v1_xboole_0(A) & v1_funct_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) ) ) ), file(funct_1,cc2_funct_1), [interesting(0.9),axiom,file(funct_1,cc2_funct_1)]). fof(rc1_funct_1,theorem,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) ) ), file(funct_1,rc1_funct_1), [interesting(0.9),axiom,file(funct_1,rc1_funct_1)]). fof(rc2_funct_1,theorem,( ? [A] : ( v1_relat_1(A) & v1_xboole_0(A) & v1_funct_1(A) ) ), file(funct_1,rc2_funct_1), [interesting(0.9),axiom,file(funct_1,rc2_funct_1)]). fof(rc7_finseq_1,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) ), file(finseq_1,rc7_finseq_1), [interesting(0.9),axiom,file(finseq_1,rc7_finseq_1)]). 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_k3_relat_1,axiom,( $true ), file(relat_1,k3_relat_1), [interesting(0.9),axiom,file(relat_1,k3_relat_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(cc1_funct_1,theorem,( ! [A] : ( v1_xboole_0(A) => v1_funct_1(A) ) ), file(funct_1,cc1_funct_1), [interesting(0.9),axiom,file(funct_1,cc1_funct_1)]). 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(fc1_subset_1,theorem,( ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ), file(subset_1,fc1_subset_1), [interesting(0.9),axiom,file(subset_1,fc1_subset_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(rc1_subset_1,theorem,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) ) ) ), file(subset_1,rc1_subset_1), [interesting(0.9),axiom,file(subset_1,rc1_subset_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_subset_1,theorem,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & v1_xboole_0(B) ) ), file(subset_1,rc2_subset_1), [interesting(0.9),axiom,file(subset_1,rc2_subset_1)]). 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(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(dt_m1_subset_1,axiom,( $true ), file(subset_1,m1_subset_1), [interesting(0.9),axiom,file(subset_1,m1_subset_1)]). 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_u1_orders_2,axiom,( ! [A] : ( l1_orders_2(A) => m2_relset_1(u1_orders_2(A),u1_struct_0(A),u1_struct_0(A)) ) ), file(orders_2,u1_orders_2), [interesting(0.9),axiom,file(orders_2,u1_orders_2)]). fof(cc1_finseq_1,theorem,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) ) ), file(finseq_1,cc1_finseq_1), [interesting(0.9),axiom,file(finseq_1,cc1_finseq_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(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(fc4_subset_1,theorem,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) ), file(subset_1,fc4_subset_1), [interesting(0.9),axiom,file(subset_1,fc4_subset_1)]). fof(rc1_finseq_1,theorem,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) ), file(finseq_1,rc1_finseq_1), [interesting(0.9),axiom,file(finseq_1,rc1_finseq_1)]). fof(rc1_margrel1,theorem,( ? [A] : v1_margrel1(A) ), file(margrel1,rc1_margrel1), [interesting(0.9),axiom,file(margrel1,rc1_margrel1)]). fof(rc1_pboole,theorem,( ? [A] : ( v1_relat_1(A) & v3_relat_1(A) & v1_funct_1(A) ) ), file(pboole,rc1_pboole), [interesting(0.9),axiom,file(pboole,rc1_pboole)]). fof(rc3_finseq_1,theorem,( ? [A] : ( v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) ) ), file(finseq_1,rc3_finseq_1), [interesting(0.9),axiom,file(finseq_1,rc3_finseq_1)]). fof(rc4_funct_1,theorem,( ? [A] : ( v1_relat_1(A) & v3_relat_1(A) & v1_funct_1(A) ) ), file(funct_1,rc4_funct_1), [interesting(0.9),axiom,file(funct_1,rc4_funct_1)]). fof(rc8_finseq_1,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) ) ), file(finseq_1,rc8_finseq_1), [interesting(0.9),axiom,file(finseq_1,rc8_finseq_1)]). 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(abstractness_v1_orders_2,theorem,( ! [A] : ( l1_orders_2(A) => ( v1_orders_2(A) => A = g1_orders_2(u1_struct_0(A),u1_orders_2(A)) ) ) ), file(orders_2,v1_orders_2), [interesting(0.9),axiom,file(orders_2,v1_orders_2)]). 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_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_xboole_0,axiom,( $true ), file(xboole_0,k1_xboole_0), [interesting(0.9),axiom,file(xboole_0,k1_xboole_0)]). 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(fc1_margrel1,theorem, ( v1_xboole_0(k1_xboole_0) & v1_margrel1(k1_xboole_0) ), file(margrel1,fc1_margrel1), [interesting(0.9),axiom,file(margrel1,fc1_margrel1)]). fof(fc1_orders_2,theorem,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_relset_1(B,A,A) ) => ( ~ v3_struct_0(g1_orders_2(A,B)) & v1_orders_2(g1_orders_2(A,B)) ) ) ), file(orders_2,fc1_orders_2), [interesting(0.9),axiom,file(orders_2,fc1_orders_2)]). 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(fc2_finseq_1,theorem, ( v1_xboole_0(k1_xboole_0) & v1_relat_1(k1_xboole_0) & v3_relat_1(k1_xboole_0) & v1_funct_1(k1_xboole_0) & v2_funct_1(k1_xboole_0) & v1_finset_1(k1_xboole_0) & v1_finseq_1(k1_xboole_0) ), file(finseq_1,fc2_finseq_1), [interesting(0.9),axiom,file(finseq_1,fc2_finseq_1)]). fof(rc1_orders_2,theorem,( ? [A] : ( l1_orders_2(A) & v1_orders_2(A) ) ), file(orders_2,rc1_orders_2), [interesting(0.9),axiom,file(orders_2,rc1_orders_2)]). 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(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(free_g1_orders_2,definition,( ! [A,B] : ( m1_relset_1(B,A,A) => ! [C,D] : ( g1_orders_2(A,B) = g1_orders_2(C,D) => ( A = C & B = D ) ) ) ), file(orders_2,g1_orders_2), [interesting(0.9),axiom,file(orders_2,g1_orders_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(existence_l1_orders_2,axiom,( ? [A] : l1_orders_2(A) ), file(orders_2,l1_orders_2), [interesting(0.9),axiom,file(orders_2,l1_orders_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(dt_g1_orders_2,axiom,( ! [A,B] : ( m1_relset_1(B,A,A) => ( v1_orders_2(g1_orders_2(A,B)) & l1_orders_2(g1_orders_2(A,B)) ) ) ), file(orders_2,g1_orders_2), [interesting(0.9),axiom,file(orders_2,g1_orders_2)]). fof(dt_l1_orders_2,axiom,( ! [A] : ( l1_orders_2(A) => l1_struct_0(A) ) ), file(orders_2,l1_orders_2), [interesting(0.9),axiom,file(orders_2,l1_orders_2)]). fof(dt_l1_struct_0,axiom,( $true ), file(struct_0,l1_struct_0), [interesting(0.9),axiom,file(struct_0,l1_struct_0)]). 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(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(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(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(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(dt_c1_4__armstrng,assumption, ( v1_relat_1(c1_4__armstrng) & ~ v1_xboole_0(c1_4__armstrng) & v4_relat_2(c1_4__armstrng) & v8_relat_2(c1_4__armstrng) ), introduced(assumption,[file(armstrng,c1_4__armstrng)]), [interesting(0.8),axiom,file(armstrng,c1_4__armstrng)]). fof(de_c3_4__armstrng,definition,( c3_4__armstrng = c1_4__armstrng ), introduced(definition,[new_symbol(c3_4__armstrng),file(armstrng,c3_4__armstrng)]), [interesting(0.8),axiom,file(armstrng,c3_4__armstrng)]). fof(t4_polynom1,theorem,( ! [A,B] : ( v1_relat_1(B) => ( r1_tarski(k3_relat_1(B),A) => m2_relset_1(B,A,A) ) ) ), file(polynom1,t4_polynom1), [interesting(0.9),axiom,file(polynom1,t4_polynom1)]). fof(e2_4__armstrng,plain,( m2_relset_1(c1_4__armstrng,k3_relat_1(c1_4__armstrng),k3_relat_1(c1_4__armstrng)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_4__armstrng])],[cc1_finseq_1,rc1_finseq_1,rc1_margrel1,rc1_pboole,rc3_finseq_1,rc3_funct_1,rc4_funct_1,rc6_finseq_1,rc8_finseq_1,antisymmetry_r2_hidden,dt_k1_xboole_0,cc2_finset_1,cc2_funct_1,fc14_finset_1,fc1_margrel1,fc1_xboole_0,fc2_finseq_1,rc1_finset_1,rc1_funct_1,rc2_funct_1,rc3_finset_1,rc4_finset_1,rc7_finseq_1,t1_subset,t4_subset,t5_subset,t8_boole,existence_m1_relset_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_m1_relset_1,dt_m1_subset_1,cc1_finset_1,cc1_funct_1,cc1_relset_1,fc1_subset_1,fc4_subset_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,t2_subset,t6_boole,t7_boole,reflexivity_r1_tarski,existence_m2_relset_1,redefinition_m2_relset_1,dt_k3_relat_1,dt_m2_relset_1,dt_c1_4__armstrng,t3_subset,t4_polynom1]), [interesting(0.8),file(armstrng,e2_4__armstrng),[file(armstrng,e2_4__armstrng)]]). fof(dt_c3_4__armstrng,plain,( m2_relset_1(c3_4__armstrng,k3_relat_1(c1_4__armstrng),k3_relat_1(c1_4__armstrng)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_4__armstrng])],[cc1_finseq_1,rc1_finseq_1,rc1_margrel1,rc1_pboole,rc3_finseq_1,rc3_funct_1,rc4_funct_1,rc6_finseq_1,rc8_finseq_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,cc2_finset_1,cc2_funct_1,fc14_finset_1,fc1_margrel1,fc1_xboole_0,fc2_finseq_1,rc1_finset_1,rc1_funct_1,rc2_funct_1,rc3_finset_1,rc4_finset_1,rc7_finseq_1,t1_subset,t4_subset,t5_subset,existence_m1_relset_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_m1_relset_1,dt_m1_subset_1,cc1_finset_1,cc1_funct_1,cc1_relset_1,fc1_subset_1,fc4_subset_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,existence_m2_relset_1,redefinition_m2_relset_1,dt_k3_relat_1,dt_m2_relset_1,dt_c1_4__armstrng,de_c3_4__armstrng,e2_4__armstrng]), [interesting(0.8),file(armstrng,c3_4__armstrng),[file(armstrng,c3_4__armstrng)]]). fof(dt_u1_struct_0,axiom,( $true ), file(struct_0,u1_struct_0), [interesting(0.9),axiom,file(struct_0,u1_struct_0)]). fof(de_c7_4__armstrng,definition,( c7_4__armstrng = g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng) ), introduced(definition,[new_symbol(c7_4__armstrng),file(armstrng,c7_4__armstrng)]), [interesting(0.8),axiom,file(armstrng,c7_4__armstrng)]). fof(dt_c1_4_2__armstrng,assumption,( m1_subset_1(c1_4_2__armstrng,u1_struct_0(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng))) ), introduced(assumption,[file(armstrng,c1_4_2__armstrng)]), [interesting(0.65),axiom,file(armstrng,c1_4_2__armstrng)]). fof(dt_c2_4_2__armstrng,assumption,( m1_subset_1(c2_4_2__armstrng,u1_struct_0(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng))) ), introduced(assumption,[file(armstrng,c2_4_2__armstrng)]), [interesting(0.65),axiom,file(armstrng,c2_4_2__armstrng)]). fof(dt_c3_4_2__armstrng,assumption,( m1_subset_1(c3_4_2__armstrng,u1_struct_0(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng))) ), introduced(assumption,[file(armstrng,c3_4_2__armstrng)]), [interesting(0.65),axiom,file(armstrng,c3_4_2__armstrng)]). fof(d2_yellow_0,definition,( ! [A] : ( l1_orders_2(A) => ( v3_orders_2(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( r1_orders_2(A,B,C) & r1_orders_2(A,C,D) ) => r1_orders_2(A,B,D) ) ) ) ) ) ) ), file(yellow_0,d2_yellow_0), [interesting(0.9),axiom,file(yellow_0,d2_yellow_0)]). fof(dh_c1_4_2__armstrng,definition, ( ( m1_subset_1(c1_4_2__armstrng,u1_struct_0(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng))) => ! [A] : ( m1_subset_1(A,u1_struct_0(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng))) => ! [B] : ( m1_subset_1(B,u1_struct_0(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng))) => ~ ( r1_orders_2(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng),c1_4_2__armstrng,A) & r1_orders_2(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng),A,B) & ~ r1_orders_2(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng),c1_4_2__armstrng,B) ) ) ) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng))) => ! [D] : ( m1_subset_1(D,u1_struct_0(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng))) => ! [E] : ( m1_subset_1(E,u1_struct_0(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng))) => ~ ( r1_orders_2(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng),C,D) & r1_orders_2(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng),D,E) & ~ r1_orders_2(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng),C,E) ) ) ) ) ), introduced(definition,[new_symbol(c1_4_2__armstrng),file(armstrng,c1_4_2__armstrng)]), [interesting(0.65),axiom,file(armstrng,c1_4_2__armstrng)]). fof(dh_c2_4_2__armstrng,definition, ( ( m1_subset_1(c2_4_2__armstrng,u1_struct_0(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng))) => ! [A] : ( m1_subset_1(A,u1_struct_0(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng))) => ~ ( r1_orders_2(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng),c1_4_2__armstrng,c2_4_2__armstrng) & r1_orders_2(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng),c2_4_2__armstrng,A) & ~ r1_orders_2(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng),c1_4_2__armstrng,A) ) ) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng))) => ! [C] : ( m1_subset_1(C,u1_struct_0(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng))) => ~ ( r1_orders_2(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng),c1_4_2__armstrng,B) & r1_orders_2(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng),B,C) & ~ r1_orders_2(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng),c1_4_2__armstrng,C) ) ) ) ), introduced(definition,[new_symbol(c2_4_2__armstrng),file(armstrng,c2_4_2__armstrng)]), [interesting(0.65),axiom,file(armstrng,c2_4_2__armstrng)]). fof(dh_c3_4_2__armstrng,definition, ( ( m1_subset_1(c3_4_2__armstrng,u1_struct_0(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng))) => ~ ( r1_orders_2(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng),c1_4_2__armstrng,c2_4_2__armstrng) & r1_orders_2(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng),c2_4_2__armstrng,c3_4_2__armstrng) & ~ r1_orders_2(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng),c1_4_2__armstrng,c3_4_2__armstrng) ) ) => ! [A] : ( m1_subset_1(A,u1_struct_0(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng))) => ~ ( r1_orders_2(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng),c1_4_2__armstrng,c2_4_2__armstrng) & r1_orders_2(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng),c2_4_2__armstrng,A) & ~ r1_orders_2(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng),c1_4_2__armstrng,A) ) ) ), introduced(definition,[new_symbol(c3_4_2__armstrng),file(armstrng,c3_4_2__armstrng)]), [interesting(0.65),axiom,file(armstrng,c3_4_2__armstrng)]). fof(e1_4_2__armstrng,assumption, ( r1_orders_2(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng),c1_4_2__armstrng,c2_4_2__armstrng) & r1_orders_2(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng),c2_4_2__armstrng,c3_4_2__armstrng) ), introduced(assumption,[file(armstrng,e1_4_2__armstrng)]), [interesting(0.65),axiom,file(armstrng,e1_4_2__armstrng)]). fof(cc1_altcat_1,theorem,( ! [A] : ( v1_fraenkel(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v1_fraenkel(B) ) ) ), file(altcat_1,cc1_altcat_1), [interesting(0.9),axiom,file(altcat_1,cc1_altcat_1)]). fof(cc1_fraenkel,theorem,( ! [A] : ( v1_fraenkel(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_relat_1(B) & v1_funct_1(B) ) ) ) ), file(fraenkel,cc1_fraenkel), [interesting(0.9),axiom,file(fraenkel,cc1_fraenkel)]). fof(rc1_fraenkel,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v1_fraenkel(A) ) ), file(fraenkel,rc1_fraenkel), [interesting(0.9),axiom,file(fraenkel,rc1_fraenkel)]). fof(fc2_altcat_1,theorem,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( ~ v1_xboole_0(k1_tarski(A)) & v1_finset_1(k1_tarski(A)) & v1_fraenkel(k1_tarski(A)) & v1_realset1(k1_tarski(A)) ) ) ), file(altcat_1,fc2_altcat_1), [interesting(0.9),axiom,file(altcat_1,fc2_altcat_1)]). 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_k1_tarski,axiom,( $true ), file(tarski,k1_tarski), [interesting(0.9),axiom,file(tarski,k1_tarski)]). fof(dt_k2_tarski,axiom,( $true ), file(tarski,k2_tarski), [interesting(0.9),axiom,file(tarski,k2_tarski)]). 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(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(fc2_subset_1,theorem,( ! [A] : ~ v1_xboole_0(k1_tarski(A)) ), file(subset_1,fc2_subset_1), [interesting(0.9),axiom,file(subset_1,fc2_subset_1)]). fof(fc3_subset_1,theorem,( ! [A,B] : ~ v1_xboole_0(k2_tarski(A,B)) ), file(subset_1,fc3_subset_1), [interesting(0.9),axiom,file(subset_1,fc3_subset_1)]). fof(dt_k4_tarski,axiom,( $true ), file(tarski,k4_tarski), [interesting(0.9),axiom,file(tarski,k4_tarski)]). 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(d9_orders_2,definition,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_orders_2(A,B,C) <=> r2_hidden(k4_tarski(B,C),u1_orders_2(A)) ) ) ) ) ), file(orders_2,d9_orders_2), [interesting(0.9),axiom,file(orders_2,d9_orders_2)]). fof(e2_4_2__armstrng,plain, ( r2_hidden(k4_tarski(c1_4_2__armstrng,c2_4_2__armstrng),u1_orders_2(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng))) & r2_hidden(k4_tarski(c2_4_2__armstrng,c3_4_2__armstrng),u1_orders_2(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng))) ), inference(mizar_by,[status(thm),assumptions([dt_c1_4_2__armstrng,dt_c2_4_2__armstrng,dt_c1_4__armstrng,dt_c3_4_2__armstrng,e1_4_2__armstrng])],[reflexivity_r1_tarski,cc1_altcat_1,cc1_finseq_1,cc1_fraenkel,rc1_finseq_1,rc1_fraenkel,rc1_margrel1,rc1_pboole,rc3_finseq_1,rc3_funct_1,rc4_funct_1,rc6_finseq_1,rc8_finseq_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_zfmisc_1,cc1_relset_1,cc2_finset_1,cc2_funct_1,fc14_finset_1,fc1_margrel1,fc1_subset_1,fc1_xboole_0,fc2_altcat_1,fc2_finseq_1,fc4_subset_1,rc1_finset_1,rc1_funct_1,rc1_subset_1,rc2_funct_1,rc2_subset_1,rc3_finset_1,rc4_finset_1,rc7_finseq_1,t3_subset,t4_subset,t5_subset,commutativity_k2_tarski,abstractness_v1_orders_2,existence_l1_struct_0,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_tarski,dt_k2_tarski,dt_l1_struct_0,dt_m1_relset_1,dt_m2_relset_1,cc1_finset_1,cc1_funct_1,fc1_finset_1,fc1_orders_2,fc2_finset_1,fc2_subset_1,fc3_subset_1,rc1_orders_2,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t8_boole,free_g1_orders_2,antisymmetry_r2_hidden,existence_l1_orders_2,existence_m1_subset_1,dt_g1_orders_2,dt_k3_relat_1,dt_k4_tarski,dt_l1_orders_2,dt_m1_subset_1,dt_u1_orders_2,dt_u1_struct_0,dt_c1_4__armstrng,dt_c1_4_2__armstrng,dt_c2_4_2__armstrng,dt_c3_4__armstrng,dt_c3_4_2__armstrng,de_c3_4__armstrng,t1_subset,t7_boole,d5_tarski,e1_4_2__armstrng,d9_orders_2]), [interesting(0.65),file(armstrng,e2_4_2__armstrng),[file(armstrng,e2_4_2__armstrng)]]). fof(dt_c2_4__armstrng,assumption, ( v1_finset_1(c2_4__armstrng) & m1_subset_1(c2_4__armstrng,k1_zfmisc_1(k3_relat_1(c1_4__armstrng))) ), introduced(assumption,[file(armstrng,c2_4__armstrng)]), [interesting(0.8),axiom,file(armstrng,c2_4__armstrng)]). fof(t3_xboole_1,theorem,( ! [A] : ( r1_tarski(A,k1_xboole_0) => A = k1_xboole_0 ) ), file(xboole_1,t3_xboole_1), [interesting(0.9),axiom,file(xboole_1,t3_xboole_1)]). fof(e3_4__armstrng,plain,( ~ v1_xboole_0(u1_struct_0(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng))) ), inference(mizar_by,[status(thm),assumptions([dt_c2_4__armstrng,dt_c1_4__armstrng,e1_4__armstrng])],[dt_k2_zfmisc_1,dt_u1_orders_2,cc1_relset_1,fc14_finset_1,fc4_subset_1,antisymmetry_r2_hidden,abstractness_v1_orders_2,existence_l1_orders_2,existence_l1_struct_0,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_zfmisc_1,dt_l1_orders_2,dt_l1_struct_0,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,cc1_finseq_1,cc2_finset_1,cc2_funct_1,fc1_orders_2,fc1_subset_1,rc1_finseq_1,rc1_finset_1,rc1_funct_1,rc1_margrel1,rc1_orders_2,rc1_pboole,rc1_subset_1,rc2_funct_1,rc2_subset_1,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc4_finset_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t1_subset,t2_subset,t4_subset,t5_subset,free_g1_orders_2,reflexivity_r1_tarski,dt_g1_orders_2,dt_k1_xboole_0,dt_k3_relat_1,dt_u1_struct_0,dt_c1_4__armstrng,dt_c2_4__armstrng,dt_c3_4__armstrng,de_c3_4__armstrng,cc1_finset_1,cc1_funct_1,fc1_margrel1,fc1_xboole_0,fc2_finseq_1,rc1_xboole_0,rc2_xboole_0,t3_subset,t6_boole,t7_boole,t8_boole,e1_4__armstrng,t3_xboole_1]), [interesting(0.8),file(armstrng,e3_4__armstrng),[file(armstrng,e3_4__armstrng)]]). fof(d16_relat_2,definition,( ! [A] : ( v1_relat_1(A) => ( v8_relat_2(A) <=> r8_relat_2(A,k3_relat_1(A)) ) ) ), file(relat_2,d16_relat_2), [interesting(0.9),axiom,file(relat_2,d16_relat_2)]). fof(e6_4__armstrng,plain,( r8_relat_2(c1_4__armstrng,k3_relat_1(c1_4__armstrng)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_4__armstrng])],[existence_m1_subset_1,dt_m1_subset_1,cc1_finseq_1,rc1_finseq_1,rc1_margrel1,rc1_pboole,rc3_finseq_1,rc3_funct_1,rc4_funct_1,rc6_finseq_1,rc8_finseq_1,t2_subset,antisymmetry_r2_hidden,dt_k1_xboole_0,cc2_funct_1,fc1_margrel1,fc1_xboole_0,fc2_finseq_1,rc1_finset_1,rc1_funct_1,rc2_funct_1,rc7_finseq_1,t1_subset,t8_boole,cc1_finset_1,cc1_funct_1,rc1_xboole_0,rc2_xboole_0,t6_boole,t7_boole,dt_k3_relat_1,dt_c1_4__armstrng,d16_relat_2]), [interesting(0.8),file(armstrng,e6_4__armstrng),[file(armstrng,e6_4__armstrng)]]). fof(d8_relat_2,definition,( ! [A] : ( v1_relat_1(A) => ! [B] : ( r8_relat_2(A,B) <=> ! [C,D,E] : ( ( r2_hidden(C,B) & r2_hidden(D,B) & r2_hidden(E,B) & r2_hidden(k4_tarski(C,D),A) & r2_hidden(k4_tarski(D,E),A) ) => r2_hidden(k4_tarski(C,E),A) ) ) ) ), file(relat_2,d8_relat_2), [interesting(0.9),axiom,file(relat_2,d8_relat_2)]). fof(e3_4_2__armstrng,plain,( r2_hidden(k4_tarski(c1_4_2__armstrng,c3_4_2__armstrng),u1_orders_2(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng))) ), inference(mizar_by,[status(thm),assumptions([dt_c1_4_2__armstrng,dt_c2_4_2__armstrng,dt_c3_4_2__armstrng,e1_4_2__armstrng,dt_c2_4__armstrng,e1_4__armstrng,dt_c1_4__armstrng])],[reflexivity_r1_tarski,dt_k1_zfmisc_1,dt_k2_zfmisc_1,cc1_altcat_1,cc1_finseq_1,cc1_fraenkel,cc1_relset_1,cc2_finset_1,fc14_finset_1,fc1_subset_1,fc4_subset_1,rc1_finseq_1,rc1_fraenkel,rc1_margrel1,rc1_pboole,rc1_subset_1,rc2_subset_1,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc4_finset_1,rc4_funct_1,rc6_finseq_1,rc8_finseq_1,t3_subset,t4_subset,t5_subset,commutativity_k2_tarski,abstractness_v1_orders_2,existence_l1_orders_2,existence_l1_struct_0,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_tarski,dt_k1_xboole_0,dt_k2_tarski,dt_l1_orders_2,dt_l1_struct_0,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,cc2_funct_1,fc1_finset_1,fc1_margrel1,fc1_orders_2,fc1_xboole_0,fc2_altcat_1,fc2_finseq_1,fc2_finset_1,fc2_subset_1,fc3_subset_1,rc1_finset_1,rc1_funct_1,rc1_orders_2,rc2_funct_1,rc7_finseq_1,t2_subset,t8_boole,free_g1_orders_2,antisymmetry_r2_hidden,dt_g1_orders_2,dt_k3_relat_1,dt_k4_tarski,dt_u1_orders_2,dt_u1_struct_0,dt_c1_4__armstrng,dt_c1_4_2__armstrng,dt_c2_4_2__armstrng,dt_c3_4__armstrng,dt_c3_4_2__armstrng,de_c3_4__armstrng,cc1_finset_1,cc1_funct_1,rc1_xboole_0,rc2_xboole_0,t1_subset,t6_boole,t7_boole,d5_tarski,e2_4_2__armstrng,e3_4__armstrng,e6_4__armstrng,d8_relat_2]), [interesting(0.65),file(armstrng,e3_4_2__armstrng),[file(armstrng,e3_4_2__armstrng)]]). fof(e4_4_2__armstrng,plain,( r1_orders_2(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng),c1_4_2__armstrng,c3_4_2__armstrng) ), inference(mizar_by,[status(thm),assumptions([dt_c1_4_2__armstrng,dt_c2_4_2__armstrng,dt_c3_4_2__armstrng,e1_4_2__armstrng,dt_c2_4__armstrng,e1_4__armstrng,dt_c1_4__armstrng])],[reflexivity_r1_tarski,cc1_altcat_1,cc1_finseq_1,cc1_fraenkel,rc1_finseq_1,rc1_fraenkel,rc1_margrel1,rc1_pboole,rc3_finseq_1,rc3_funct_1,rc4_funct_1,rc6_finseq_1,rc8_finseq_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_zfmisc_1,cc1_relset_1,cc2_finset_1,cc2_funct_1,fc14_finset_1,fc1_margrel1,fc1_subset_1,fc1_xboole_0,fc2_altcat_1,fc2_finseq_1,fc4_subset_1,rc1_finset_1,rc1_funct_1,rc1_subset_1,rc2_funct_1,rc2_subset_1,rc3_finset_1,rc4_finset_1,rc7_finseq_1,t3_subset,t4_subset,t5_subset,commutativity_k2_tarski,abstractness_v1_orders_2,existence_l1_struct_0,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_tarski,dt_k2_tarski,dt_l1_struct_0,dt_m1_relset_1,dt_m2_relset_1,cc1_finset_1,cc1_funct_1,fc1_finset_1,fc1_orders_2,fc2_finset_1,fc2_subset_1,fc3_subset_1,rc1_orders_2,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t8_boole,free_g1_orders_2,antisymmetry_r2_hidden,existence_l1_orders_2,existence_m1_subset_1,dt_g1_orders_2,dt_k3_relat_1,dt_k4_tarski,dt_l1_orders_2,dt_m1_subset_1,dt_u1_orders_2,dt_u1_struct_0,dt_c1_4__armstrng,dt_c1_4_2__armstrng,dt_c3_4__armstrng,dt_c3_4_2__armstrng,de_c3_4__armstrng,t1_subset,t7_boole,d5_tarski,e3_4_2__armstrng,d9_orders_2]), [interesting(0.65),file(armstrng,e4_4_2__armstrng),[file(armstrng,e4_4_2__armstrng)]]). fof(i3_4_2__armstrng,theorem,( $true ), introduced(tautology,[file(armstrng,i3_4_2__armstrng)]), [interesting(0.65),trivial,file(armstrng,i3_4_2__armstrng)]). fof(i2_4_2__armstrng,plain,( r1_orders_2(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng),c1_4_2__armstrng,c3_4_2__armstrng) ), inference(conclusion,[status(thm),assumptions([dt_c1_4_2__armstrng,dt_c2_4_2__armstrng,dt_c3_4_2__armstrng,e1_4_2__armstrng,dt_c2_4__armstrng,e1_4__armstrng,dt_c1_4__armstrng])],[e4_4_2__armstrng,i3_4_2__armstrng]), [interesting(0.65),file(armstrng,i2_4_2__armstrng),[file(armstrng,i2_4_2__armstrng)]]). fof(i1_4_2__armstrng,plain,( ~ ( r1_orders_2(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng),c1_4_2__armstrng,c2_4_2__armstrng) & r1_orders_2(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng),c2_4_2__armstrng,c3_4_2__armstrng) & ~ r1_orders_2(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng),c1_4_2__armstrng,c3_4_2__armstrng) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_4_2__armstrng,dt_c2_4_2__armstrng,dt_c3_4_2__armstrng,dt_c2_4__armstrng,e1_4__armstrng,dt_c1_4__armstrng]),discharge_asm(discharge,[e1_4_2__armstrng])],[e1_4_2__armstrng,i2_4_2__armstrng]), [interesting(0.65),file(armstrng,i1_4_2__armstrng),[file(armstrng,i1_4_2__armstrng)]]). fof(i1_4_2_tmp__armstrng,plain, ( ( m1_subset_1(c1_4_2__armstrng,u1_struct_0(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng))) & m1_subset_1(c2_4_2__armstrng,u1_struct_0(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng))) & m1_subset_1(c3_4_2__armstrng,u1_struct_0(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng))) ) => ~ ( r1_orders_2(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng),c1_4_2__armstrng,c2_4_2__armstrng) & r1_orders_2(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng),c2_4_2__armstrng,c3_4_2__armstrng) & ~ r1_orders_2(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng),c1_4_2__armstrng,c3_4_2__armstrng) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c2_4__armstrng,e1_4__armstrng,dt_c1_4__armstrng]),discharge_asm(discharge,[dt_c1_4_2__armstrng,dt_c2_4_2__armstrng,dt_c3_4_2__armstrng])],[dt_c1_4_2__armstrng,dt_c2_4_2__armstrng,dt_c3_4_2__armstrng,i1_4_2__armstrng]), [interesting(0.8),e7_4__armstrng]). fof(e7_4__armstrng,plain,( v3_orders_2(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng)) ), inference(let,[status(thm),assumptions([dt_c2_4__armstrng,e1_4__armstrng,dt_c1_4__armstrng])],[i1_4_2_tmp__armstrng,rc3_funct_1,rc6_finseq_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_u1_orders_2,cc1_relset_1,cc2_finset_1,cc2_funct_1,fc14_finset_1,fc1_subset_1,fc4_subset_1,rc1_finset_1,rc1_funct_1,rc1_subset_1,rc2_funct_1,rc2_subset_1,rc3_finset_1,rc4_finset_1,rc7_finseq_1,abstractness_v1_orders_2,redefinition_m2_relset_1,dt_l1_struct_0,dt_m1_relset_1,dt_m2_relset_1,cc1_finset_1,cc1_funct_1,fc1_orders_2,rc1_orders_2,rc1_xboole_0,rc2_xboole_0,free_g1_orders_2,dt_g1_orders_2,dt_k3_relat_1,dt_l1_orders_2,dt_m1_subset_1,dt_u1_struct_0,dt_c1_4__armstrng,dt_c3_4__armstrng,d2_yellow_0,dh_c1_4_2__armstrng,dh_c2_4_2__armstrng,dh_c3_4_2__armstrng]), [interesting(0.8),file(armstrng,e7_4__armstrng),[file(armstrng,e7_4__armstrng)]]). fof(dt_c1_4_1__armstrng,assumption,( m1_subset_1(c1_4_1__armstrng,u1_struct_0(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng))) ), introduced(assumption,[file(armstrng,c1_4_1__armstrng)]), [interesting(0.65),axiom,file(armstrng,c1_4_1__armstrng)]). fof(dt_c2_4_1__armstrng,assumption,( m1_subset_1(c2_4_1__armstrng,u1_struct_0(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng))) ), introduced(assumption,[file(armstrng,c2_4_1__armstrng)]), [interesting(0.65),axiom,file(armstrng,c2_4_1__armstrng)]). fof(d3_yellow_0,definition,( ! [A] : ( l1_orders_2(A) => ( v4_orders_2(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ( r1_orders_2(A,B,C) & r1_orders_2(A,C,B) ) => B = C ) ) ) ) ) ), file(yellow_0,d3_yellow_0), [interesting(0.9),axiom,file(yellow_0,d3_yellow_0)]). fof(dh_c1_4_1__armstrng,definition, ( ( m1_subset_1(c1_4_1__armstrng,u1_struct_0(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng))) => ! [A] : ( m1_subset_1(A,u1_struct_0(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng))) => ~ ( r1_orders_2(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng),c1_4_1__armstrng,A) & r1_orders_2(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng),A,c1_4_1__armstrng) & c1_4_1__armstrng != A ) ) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng))) => ! [C] : ( m1_subset_1(C,u1_struct_0(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng))) => ~ ( r1_orders_2(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng),B,C) & r1_orders_2(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng),C,B) & B != C ) ) ) ), introduced(definition,[new_symbol(c1_4_1__armstrng),file(armstrng,c1_4_1__armstrng)]), [interesting(0.65),axiom,file(armstrng,c1_4_1__armstrng)]). fof(dh_c2_4_1__armstrng,definition, ( ( m1_subset_1(c2_4_1__armstrng,u1_struct_0(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng))) => ~ ( r1_orders_2(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng),c1_4_1__armstrng,c2_4_1__armstrng) & r1_orders_2(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng),c2_4_1__armstrng,c1_4_1__armstrng) & c1_4_1__armstrng != c2_4_1__armstrng ) ) => ! [A] : ( m1_subset_1(A,u1_struct_0(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng))) => ~ ( r1_orders_2(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng),c1_4_1__armstrng,A) & r1_orders_2(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng),A,c1_4_1__armstrng) & c1_4_1__armstrng != A ) ) ), introduced(definition,[new_symbol(c2_4_1__armstrng),file(armstrng,c2_4_1__armstrng)]), [interesting(0.65),axiom,file(armstrng,c2_4_1__armstrng)]). fof(e1_4_1__armstrng,assumption, ( r1_orders_2(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng),c1_4_1__armstrng,c2_4_1__armstrng) & r1_orders_2(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng),c2_4_1__armstrng,c1_4_1__armstrng) ), introduced(assumption,[file(armstrng,e1_4_1__armstrng)]), [interesting(0.65),axiom,file(armstrng,e1_4_1__armstrng)]). fof(e2_4_1__armstrng,plain, ( r2_hidden(k4_tarski(c1_4_1__armstrng,c2_4_1__armstrng),u1_orders_2(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng))) & r2_hidden(k4_tarski(c2_4_1__armstrng,c1_4_1__armstrng),u1_orders_2(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng))) ), inference(mizar_by,[status(thm),assumptions([dt_c1_4_1__armstrng,dt_c2_4_1__armstrng,dt_c1_4__armstrng,e1_4_1__armstrng])],[reflexivity_r1_tarski,cc1_altcat_1,cc1_finseq_1,cc1_fraenkel,rc1_finseq_1,rc1_fraenkel,rc1_margrel1,rc1_pboole,rc3_finseq_1,rc3_funct_1,rc4_funct_1,rc6_finseq_1,rc8_finseq_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_zfmisc_1,cc1_relset_1,cc2_finset_1,cc2_funct_1,fc14_finset_1,fc1_margrel1,fc1_subset_1,fc1_xboole_0,fc2_altcat_1,fc2_finseq_1,fc4_subset_1,rc1_finset_1,rc1_funct_1,rc1_subset_1,rc2_funct_1,rc2_subset_1,rc3_finset_1,rc4_finset_1,rc7_finseq_1,t3_subset,t4_subset,t5_subset,commutativity_k2_tarski,abstractness_v1_orders_2,existence_l1_struct_0,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_tarski,dt_k2_tarski,dt_l1_struct_0,dt_m1_relset_1,dt_m2_relset_1,cc1_finset_1,cc1_funct_1,fc1_finset_1,fc1_orders_2,fc2_finset_1,fc2_subset_1,fc3_subset_1,rc1_orders_2,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t8_boole,free_g1_orders_2,antisymmetry_r2_hidden,existence_l1_orders_2,existence_m1_subset_1,dt_g1_orders_2,dt_k3_relat_1,dt_k4_tarski,dt_l1_orders_2,dt_m1_subset_1,dt_u1_orders_2,dt_u1_struct_0,dt_c1_4__armstrng,dt_c1_4_1__armstrng,dt_c2_4_1__armstrng,dt_c3_4__armstrng,de_c3_4__armstrng,t1_subset,t7_boole,d5_tarski,e1_4_1__armstrng,d9_orders_2]), [interesting(0.65),file(armstrng,e2_4_1__armstrng),[file(armstrng,e2_4_1__armstrng)]]). fof(d12_relat_2,definition,( ! [A] : ( v1_relat_1(A) => ( v4_relat_2(A) <=> r4_relat_2(A,k3_relat_1(A)) ) ) ), file(relat_2,d12_relat_2), [interesting(0.9),axiom,file(relat_2,d12_relat_2)]). fof(e4_4__armstrng,plain,( r4_relat_2(c1_4__armstrng,k3_relat_1(c1_4__armstrng)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_4__armstrng])],[existence_m1_subset_1,dt_m1_subset_1,cc1_finseq_1,rc1_finseq_1,rc1_margrel1,rc1_pboole,rc3_finseq_1,rc3_funct_1,rc4_funct_1,rc6_finseq_1,rc8_finseq_1,t2_subset,antisymmetry_r2_hidden,dt_k1_xboole_0,cc2_funct_1,fc1_margrel1,fc1_xboole_0,fc2_finseq_1,rc1_finset_1,rc1_funct_1,rc2_funct_1,rc7_finseq_1,t1_subset,t8_boole,cc1_finset_1,cc1_funct_1,rc1_xboole_0,rc2_xboole_0,t6_boole,t7_boole,dt_k3_relat_1,dt_c1_4__armstrng,d12_relat_2]), [interesting(0.8),file(armstrng,e4_4__armstrng),[file(armstrng,e4_4__armstrng)]]). fof(d4_relat_2,definition,( ! [A] : ( v1_relat_1(A) => ! [B] : ( r4_relat_2(A,B) <=> ! [C,D] : ( ( r2_hidden(C,B) & r2_hidden(D,B) & r2_hidden(k4_tarski(C,D),A) & r2_hidden(k4_tarski(D,C),A) ) => C = D ) ) ) ), file(relat_2,d4_relat_2), [interesting(0.9),axiom,file(relat_2,d4_relat_2)]). fof(e3_4_1__armstrng,plain,( c1_4_1__armstrng = c2_4_1__armstrng ), inference(mizar_by,[status(thm),assumptions([dt_c1_4_1__armstrng,dt_c2_4_1__armstrng,e1_4_1__armstrng,dt_c2_4__armstrng,e1_4__armstrng,dt_c1_4__armstrng])],[reflexivity_r1_tarski,dt_k1_zfmisc_1,dt_k2_zfmisc_1,cc1_altcat_1,cc1_finseq_1,cc1_fraenkel,cc1_relset_1,cc2_finset_1,fc14_finset_1,fc1_subset_1,fc4_subset_1,rc1_finseq_1,rc1_fraenkel,rc1_margrel1,rc1_pboole,rc1_subset_1,rc2_subset_1,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc4_finset_1,rc4_funct_1,rc6_finseq_1,rc8_finseq_1,t3_subset,t4_subset,t5_subset,commutativity_k2_tarski,abstractness_v1_orders_2,existence_l1_orders_2,existence_l1_struct_0,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_tarski,dt_k1_xboole_0,dt_k2_tarski,dt_l1_orders_2,dt_l1_struct_0,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,cc2_funct_1,fc1_finset_1,fc1_margrel1,fc1_orders_2,fc1_xboole_0,fc2_altcat_1,fc2_finseq_1,fc2_finset_1,fc2_subset_1,fc3_subset_1,rc1_finset_1,rc1_funct_1,rc1_orders_2,rc2_funct_1,rc7_finseq_1,t2_subset,free_g1_orders_2,antisymmetry_r2_hidden,dt_g1_orders_2,dt_k3_relat_1,dt_k4_tarski,dt_u1_orders_2,dt_u1_struct_0,dt_c1_4__armstrng,dt_c1_4_1__armstrng,dt_c2_4_1__armstrng,dt_c3_4__armstrng,de_c3_4__armstrng,cc1_finset_1,cc1_funct_1,rc1_xboole_0,rc2_xboole_0,t1_subset,t6_boole,t7_boole,t8_boole,d5_tarski,e2_4_1__armstrng,e3_4__armstrng,e4_4__armstrng,d4_relat_2]), [interesting(0.65),file(armstrng,e3_4_1__armstrng),[file(armstrng,e3_4_1__armstrng)]]). fof(i3_4_1__armstrng,theorem,( $true ), introduced(tautology,[file(armstrng,i3_4_1__armstrng)]), [interesting(0.65),trivial,file(armstrng,i3_4_1__armstrng)]). fof(i2_4_1__armstrng,plain,( c1_4_1__armstrng = c2_4_1__armstrng ), inference(conclusion,[status(thm),assumptions([dt_c1_4_1__armstrng,dt_c2_4_1__armstrng,e1_4_1__armstrng,dt_c2_4__armstrng,e1_4__armstrng,dt_c1_4__armstrng])],[e3_4_1__armstrng,i3_4_1__armstrng]), [interesting(0.65),file(armstrng,i2_4_1__armstrng),[file(armstrng,i2_4_1__armstrng)]]). fof(i1_4_1__armstrng,plain,( ~ ( r1_orders_2(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng),c1_4_1__armstrng,c2_4_1__armstrng) & r1_orders_2(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng),c2_4_1__armstrng,c1_4_1__armstrng) & c1_4_1__armstrng != c2_4_1__armstrng ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_4_1__armstrng,dt_c2_4_1__armstrng,dt_c2_4__armstrng,e1_4__armstrng,dt_c1_4__armstrng]),discharge_asm(discharge,[e1_4_1__armstrng])],[e1_4_1__armstrng,i2_4_1__armstrng]), [interesting(0.65),file(armstrng,i1_4_1__armstrng),[file(armstrng,i1_4_1__armstrng)]]). fof(i1_4_1_tmp__armstrng,plain, ( ( m1_subset_1(c1_4_1__armstrng,u1_struct_0(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng))) & m1_subset_1(c2_4_1__armstrng,u1_struct_0(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng))) ) => ~ ( r1_orders_2(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng),c1_4_1__armstrng,c2_4_1__armstrng) & r1_orders_2(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng),c2_4_1__armstrng,c1_4_1__armstrng) & c1_4_1__armstrng != c2_4_1__armstrng ) ), inference(discharge_asm,[status(thm),assumptions([dt_c2_4__armstrng,e1_4__armstrng,dt_c1_4__armstrng]),discharge_asm(discharge,[dt_c1_4_1__armstrng,dt_c2_4_1__armstrng])],[dt_c1_4_1__armstrng,dt_c2_4_1__armstrng,i1_4_1__armstrng]), [interesting(0.8),e5_4__armstrng]). fof(e5_4__armstrng,plain,( v4_orders_2(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng)) ), inference(let,[status(thm),assumptions([dt_c2_4__armstrng,e1_4__armstrng,dt_c1_4__armstrng])],[i1_4_1_tmp__armstrng,rc3_funct_1,rc6_finseq_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_u1_orders_2,cc1_relset_1,cc2_finset_1,cc2_funct_1,fc14_finset_1,fc1_subset_1,fc4_subset_1,rc1_finset_1,rc1_funct_1,rc1_subset_1,rc2_funct_1,rc2_subset_1,rc3_finset_1,rc4_finset_1,rc7_finseq_1,abstractness_v1_orders_2,redefinition_m2_relset_1,dt_l1_struct_0,dt_m1_relset_1,dt_m2_relset_1,cc1_finset_1,cc1_funct_1,fc1_orders_2,rc1_orders_2,rc1_xboole_0,rc2_xboole_0,free_g1_orders_2,dt_g1_orders_2,dt_k3_relat_1,dt_l1_orders_2,dt_m1_subset_1,dt_u1_struct_0,dt_c1_4__armstrng,dt_c3_4__armstrng,d3_yellow_0,dh_c1_4_1__armstrng,dh_c2_4_1__armstrng]), [interesting(0.8),file(armstrng,e5_4__armstrng),[file(armstrng,e5_4__armstrng)]]). fof(d1_struct_0,definition,( ! [A] : ( l1_struct_0(A) => ( v3_struct_0(A) <=> v1_xboole_0(u1_struct_0(A)) ) ) ), file(struct_0,d1_struct_0), [interesting(0.9),axiom,file(struct_0,d1_struct_0)]). fof(e8_4__armstrng,plain, ( ~ v3_struct_0(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng)) & v3_orders_2(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng)) & v4_orders_2(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng)) & l1_orders_2(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng)) ), inference(mizar_by,[status(thm),assumptions([dt_c2_4__armstrng,e1_4__armstrng,dt_c1_4__armstrng])],[reflexivity_r1_tarski,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_m1_subset_1,dt_u1_orders_2,cc1_finseq_1,cc1_relset_1,cc2_finset_1,fc14_finset_1,fc1_subset_1,fc4_subset_1,rc1_finseq_1,rc1_margrel1,rc1_pboole,rc1_subset_1,rc2_subset_1,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc4_finset_1,rc4_funct_1,rc6_finseq_1,rc8_finseq_1,t2_subset,t3_subset,t4_subset,t5_subset,antisymmetry_r2_hidden,abstractness_v1_orders_2,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_m1_relset_1,dt_m2_relset_1,cc2_funct_1,fc1_margrel1,fc1_orders_2,fc1_xboole_0,fc2_finseq_1,rc1_finset_1,rc1_funct_1,rc1_orders_2,rc2_funct_1,rc7_finseq_1,t1_subset,t8_boole,free_g1_orders_2,existence_l1_orders_2,existence_l1_struct_0,dt_g1_orders_2,dt_k3_relat_1,dt_l1_orders_2,dt_l1_struct_0,dt_u1_struct_0,dt_c1_4__armstrng,dt_c3_4__armstrng,de_c3_4__armstrng,cc1_finset_1,cc1_funct_1,rc1_xboole_0,rc2_xboole_0,t6_boole,t7_boole,e7_4__armstrng,e3_4__armstrng,e5_4__armstrng,d1_struct_0]), [interesting(0.8),file(armstrng,e8_4__armstrng),[file(armstrng,e8_4__armstrng)]]). fof(dt_c7_4__armstrng,plain, ( ~ v3_struct_0(c7_4__armstrng) & v3_orders_2(c7_4__armstrng) & v4_orders_2(c7_4__armstrng) & l1_orders_2(c7_4__armstrng) ), inference(mizar_by,[status(thm),assumptions([dt_c2_4__armstrng,e1_4__armstrng,dt_c1_4__armstrng])],[reflexivity_r1_tarski,cc1_finseq_1,rc1_finseq_1,rc1_margrel1,rc1_pboole,rc3_finseq_1,rc3_funct_1,rc4_funct_1,rc6_finseq_1,rc8_finseq_1,antisymmetry_r2_hidden,existence_m1_subset_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_m1_subset_1,dt_u1_orders_2,dt_u1_struct_0,cc1_relset_1,cc2_finset_1,cc2_funct_1,fc14_finset_1,fc1_margrel1,fc1_subset_1,fc1_xboole_0,fc2_finseq_1,fc4_subset_1,rc1_finset_1,rc1_funct_1,rc1_subset_1,rc2_funct_1,rc2_subset_1,rc3_finset_1,rc4_finset_1,rc7_finseq_1,t1_subset,t2_subset,t3_subset,t4_subset,t5_subset,abstractness_v1_orders_2,existence_l1_struct_0,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_l1_struct_0,dt_m1_relset_1,dt_m2_relset_1,cc1_finset_1,cc1_funct_1,fc1_orders_2,rc1_orders_2,rc1_xboole_0,rc2_xboole_0,t6_boole,t7_boole,t8_boole,free_g1_orders_2,existence_l1_orders_2,dt_g1_orders_2,dt_k3_relat_1,dt_l1_orders_2,dt_c1_4__armstrng,dt_c3_4__armstrng,de_c3_4__armstrng,de_c7_4__armstrng,e8_4__armstrng]), [interesting(0.8),file(armstrng,c7_4__armstrng),[file(armstrng,c7_4__armstrng)]]). fof(dh_c9_4__armstrng,definition, ( ? [A] : ( m1_subset_1(A,u1_struct_0(c7_4__armstrng)) & r2_hidden(A,c8_4__armstrng) & r2_waybel_4(c8_4__armstrng,A,u1_orders_2(c7_4__armstrng)) ) => ( m1_subset_1(c9_4__armstrng,u1_struct_0(c7_4__armstrng)) & r2_hidden(c9_4__armstrng,c8_4__armstrng) & r2_waybel_4(c8_4__armstrng,c9_4__armstrng,u1_orders_2(c7_4__armstrng)) ) ), introduced(definition,[new_symbol(c9_4__armstrng),file(armstrng,c9_4__armstrng)]), [interesting(0.8),axiom,file(armstrng,c9_4__armstrng)]). fof(de_c8_4__armstrng,definition,( c8_4__armstrng = c2_4__armstrng ), introduced(definition,[new_symbol(c8_4__armstrng),file(armstrng,c8_4__armstrng)]), [interesting(0.8),axiom,file(armstrng,c8_4__armstrng)]). fof(e9_4__armstrng,plain, ( v1_finset_1(c2_4__armstrng) & m1_subset_1(c2_4__armstrng,k1_zfmisc_1(u1_struct_0(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng)))) ), inference(mizar_by,[status(thm),assumptions([dt_c2_4__armstrng,dt_c1_4__armstrng])],[cc1_finseq_1,rc1_finseq_1,rc1_margrel1,rc1_pboole,rc3_finseq_1,rc3_funct_1,rc4_funct_1,rc6_finseq_1,rc8_finseq_1,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_u1_orders_2,cc1_relset_1,cc2_funct_1,fc14_finset_1,fc1_margrel1,fc1_xboole_0,fc2_finseq_1,fc4_subset_1,rc1_funct_1,rc2_funct_1,rc7_finseq_1,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,abstractness_v1_orders_2,existence_l1_orders_2,existence_l1_struct_0,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_l1_orders_2,dt_l1_struct_0,dt_m1_relset_1,dt_m2_relset_1,cc1_finset_1,cc1_funct_1,fc1_orders_2,rc1_finset_1,rc1_orders_2,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,rc3_finset_1,rc4_finset_1,t2_subset,t6_boole,t7_boole,t8_boole,free_g1_orders_2,existence_m1_subset_1,dt_g1_orders_2,dt_k1_zfmisc_1,dt_k3_relat_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_4__armstrng,dt_c2_4__armstrng,dt_c3_4__armstrng,de_c3_4__armstrng,cc2_finset_1,fc1_subset_1,t3_subset]), [interesting(0.8),file(armstrng,e9_4__armstrng),[file(armstrng,e9_4__armstrng)]]). fof(dt_c8_4__armstrng,plain, ( v1_finset_1(c8_4__armstrng) & m1_subset_1(c8_4__armstrng,k1_zfmisc_1(u1_struct_0(g1_orders_2(k3_relat_1(c1_4__armstrng),c3_4__armstrng)))) ), inference(mizar_by,[status(thm),assumptions([dt_c2_4__armstrng,dt_c1_4__armstrng])],[cc1_finseq_1,rc1_finseq_1,rc1_margrel1,rc1_pboole,rc3_finseq_1,rc3_funct_1,rc4_funct_1,rc6_finseq_1,rc8_finseq_1,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_u1_orders_2,cc1_relset_1,cc2_funct_1,fc14_finset_1,fc1_margrel1,fc1_xboole_0,fc2_finseq_1,fc4_subset_1,rc1_funct_1,rc2_funct_1,rc7_finseq_1,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,abstractness_v1_orders_2,existence_l1_orders_2,existence_l1_struct_0,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_l1_orders_2,dt_l1_struct_0,dt_m1_relset_1,dt_m2_relset_1,cc1_finset_1,cc1_funct_1,fc1_orders_2,rc1_finset_1,rc1_orders_2,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,rc3_finset_1,rc4_finset_1,t2_subset,t6_boole,t7_boole,t8_boole,free_g1_orders_2,existence_m1_subset_1,dt_g1_orders_2,dt_k1_zfmisc_1,dt_k3_relat_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_4__armstrng,dt_c2_4__armstrng,dt_c3_4__armstrng,de_c3_4__armstrng,cc2_finset_1,fc1_subset_1,t3_subset,de_c8_4__armstrng,e9_4__armstrng]), [interesting(0.8),file(armstrng,c8_4__armstrng),[file(armstrng,c8_4__armstrng)]]). fof(t7_bagorder,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ~ ( B != k1_xboole_0 & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( r2_hidden(C,B) & r2_waybel_4(B,C,u1_orders_2(A)) ) ) ) ) ) ), file(bagorder,t7_bagorder), [interesting(0.9),axiom,file(bagorder,t7_bagorder)]). fof(e10_4__armstrng,plain,( ? [A] : ( m1_subset_1(A,u1_struct_0(c7_4__armstrng)) & r2_hidden(A,c8_4__armstrng) & r2_waybel_4(c8_4__armstrng,A,u1_orders_2(c7_4__armstrng)) ) ), inference(mizar_by,[status(thm),assumptions([dt_c2_4__armstrng,dt_c1_4__armstrng,e1_4__armstrng])],[abstractness_v1_orders_2,existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc14_finset_1,fc1_orders_2,fc4_subset_1,rc1_orders_2,free_g1_orders_2,reflexivity_r1_tarski,existence_l1_struct_0,existence_m2_relset_1,redefinition_m2_relset_1,dt_g1_orders_2,dt_k3_relat_1,dt_l1_struct_0,dt_m2_relset_1,dt_c1_4__armstrng,dt_c3_4__armstrng,de_c3_4__armstrng,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc2_funct_1,rc1_finseq_1,rc1_finset_1,rc1_funct_1,rc1_margrel1,rc1_pboole,rc1_subset_1,rc1_xboole_0,rc2_funct_1,rc2_subset_1,rc2_xboole_0,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc4_finset_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t5_subset,t8_boole,antisymmetry_r2_hidden,existence_l1_orders_2,existence_m1_subset_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_l1_orders_2,dt_m1_subset_1,dt_u1_orders_2,dt_u1_struct_0,dt_c2_4__armstrng,dt_c7_4__armstrng,dt_c8_4__armstrng,de_c7_4__armstrng,de_c8_4__armstrng,cc2_finset_1,fc1_margrel1,fc1_subset_1,fc1_xboole_0,fc2_finseq_1,t1_subset,t3_subset,t4_subset,t6_boole,t7_boole,e1_4__armstrng,t7_bagorder]), [interesting(0.8),file(armstrng,e10_4__armstrng),[file(armstrng,e10_4__armstrng)]]). fof(dt_c9_4__armstrng,plain,( m1_subset_1(c9_4__armstrng,u1_struct_0(c7_4__armstrng)) ), inference(consider,[status(thm),assumptions([dt_c2_4__armstrng,dt_c1_4__armstrng,e1_4__armstrng])],[dh_c9_4__armstrng,e10_4__armstrng]), [interesting(0.8),file(armstrng,c9_4__armstrng),[file(armstrng,c9_4__armstrng)]]). fof(de_c10_4__armstrng,definition,( c10_4__armstrng = c9_4__armstrng ), introduced(definition,[new_symbol(c10_4__armstrng),file(armstrng,c10_4__armstrng)]), [interesting(0.8),axiom,file(armstrng,c10_4__armstrng)]). fof(e11_4__armstrng,plain, ( r2_hidden(c9_4__armstrng,c8_4__armstrng) & r2_waybel_4(c8_4__armstrng,c9_4__armstrng,u1_orders_2(c7_4__armstrng)) ), inference(consider,[status(thm),assumptions([dt_c2_4__armstrng,dt_c1_4__armstrng,e1_4__armstrng])],[dh_c9_4__armstrng,e10_4__armstrng]), [interesting(0.8),file(armstrng,e11_4__armstrng),[file(armstrng,e11_4__armstrng)]]). fof(e12_4__armstrng,plain,( m1_subset_1(c9_4__armstrng,c2_4__armstrng) ), inference(mizar_by,[status(thm),assumptions([dt_c2_4__armstrng,dt_c1_4__armstrng,e1_4__armstrng])],[cc1_finseq_1,rc1_finseq_1,rc1_margrel1,rc1_pboole,rc3_finseq_1,rc3_funct_1,rc4_funct_1,rc6_finseq_1,rc8_finseq_1,reflexivity_r1_tarski,abstractness_v1_orders_2,existence_l1_struct_0,existence_m1_relset_1,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_l1_struct_0,dt_m1_relset_1,cc1_relset_1,cc2_funct_1,fc14_finset_1,fc1_margrel1,fc1_orders_2,fc1_xboole_0,fc2_finseq_1,fc4_subset_1,rc1_funct_1,rc1_orders_2,rc2_funct_1,rc7_finseq_1,free_g1_orders_2,existence_l1_orders_2,existence_m2_relset_1,redefinition_m2_relset_1,dt_g1_orders_2,dt_k1_zfmisc_1,dt_k3_relat_1,dt_l1_orders_2,dt_m2_relset_1,dt_u1_struct_0,dt_c1_4__armstrng,dt_c3_4__armstrng,de_c3_4__armstrng,cc1_finset_1,cc1_funct_1,cc2_finset_1,fc1_subset_1,rc1_finset_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,rc3_finset_1,rc4_finset_1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,existence_m1_subset_1,dt_m1_subset_1,dt_u1_orders_2,dt_c2_4__armstrng,dt_c7_4__armstrng,dt_c8_4__armstrng,dt_c9_4__armstrng,de_c7_4__armstrng,de_c8_4__armstrng,t1_subset,t7_boole,e11_4__armstrng]), [interesting(0.8),file(armstrng,e12_4__armstrng),[file(armstrng,e12_4__armstrng)]]). fof(dt_c10_4__armstrng,plain,( m1_subset_1(c10_4__armstrng,c2_4__armstrng) ), inference(mizar_by,[status(thm),assumptions([dt_c2_4__armstrng,dt_c1_4__armstrng,e1_4__armstrng])],[dt_k2_zfmisc_1,dt_u1_orders_2,cc1_finseq_1,cc1_relset_1,fc14_finset_1,fc4_subset_1,rc1_finseq_1,rc1_margrel1,rc1_pboole,rc3_finseq_1,rc3_funct_1,rc4_funct_1,rc6_finseq_1,rc8_finseq_1,antisymmetry_r2_hidden,abstractness_v1_orders_2,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_m1_relset_1,dt_m2_relset_1,cc2_funct_1,fc1_margrel1,fc1_orders_2,fc1_xboole_0,fc2_finseq_1,rc1_funct_1,rc1_orders_2,rc2_funct_1,rc7_finseq_1,t1_subset,t4_subset,t5_subset,free_g1_orders_2,reflexivity_r1_tarski,existence_l1_orders_2,existence_l1_struct_0,dt_g1_orders_2,dt_l1_orders_2,dt_l1_struct_0,dt_c3_4__armstrng,de_c3_4__armstrng,cc1_finset_1,cc1_funct_1,rc1_finset_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,rc3_finset_1,rc4_finset_1,t2_subset,t6_boole,t7_boole,t8_boole,dt_k1_zfmisc_1,dt_k3_relat_1,dt_u1_struct_0,dt_c1_4__armstrng,dt_c7_4__armstrng,de_c7_4__armstrng,cc2_finset_1,fc1_subset_1,t3_subset,existence_m1_subset_1,dt_m1_subset_1,dt_c2_4__armstrng,dt_c9_4__armstrng,de_c10_4__armstrng,e12_4__armstrng]), [interesting(0.8),file(armstrng,c10_4__armstrng),[file(armstrng,c10_4__armstrng)]]). fof(d24_waybel_4,definition,( ! [A,B,C] : ( v1_relat_1(C) => ( r2_waybel_4(A,B,C) <=> ( r2_hidden(B,A) & ! [D] : ~ ( r2_hidden(D,A) & D != B & r2_hidden(k4_tarski(B,D),C) ) ) ) ) ), file(waybel_4,d24_waybel_4), [interesting(0.9),axiom,file(waybel_4,d24_waybel_4)]). fof(e13_4__armstrng,plain,( r2_hidden(c10_4__armstrng,c2_4__armstrng) ), inference(mizar_by,[status(thm),assumptions([dt_c2_4__armstrng,dt_c1_4__armstrng,e1_4__armstrng])],[cc1_finseq_1,rc1_finseq_1,rc1_margrel1,rc1_pboole,rc3_finseq_1,rc3_funct_1,rc4_funct_1,rc6_finseq_1,rc8_finseq_1,reflexivity_r1_tarski,abstractness_v1_orders_2,existence_l1_struct_0,existence_m1_relset_1,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_l1_struct_0,dt_m1_relset_1,cc1_relset_1,cc2_funct_1,fc14_finset_1,fc1_margrel1,fc1_orders_2,fc1_xboole_0,fc2_finseq_1,fc4_subset_1,rc1_funct_1,rc1_orders_2,rc2_funct_1,rc7_finseq_1,free_g1_orders_2,existence_l1_orders_2,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_g1_orders_2,dt_k1_zfmisc_1,dt_k3_relat_1,dt_l1_orders_2,dt_m1_subset_1,dt_m2_relset_1,dt_u1_struct_0,dt_c1_4__armstrng,dt_c3_4__armstrng,de_c3_4__armstrng,cc1_finset_1,cc1_funct_1,cc2_finset_1,fc1_subset_1,rc1_finset_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,rc3_finset_1,rc4_finset_1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_u1_orders_2,dt_c10_4__armstrng,dt_c2_4__armstrng,dt_c7_4__armstrng,dt_c8_4__armstrng,dt_c9_4__armstrng,de_c10_4__armstrng,de_c7_4__armstrng,de_c8_4__armstrng,t1_subset,t7_boole,e11_4__armstrng]), [interesting(0.8),file(armstrng,e13_4__armstrng),[file(armstrng,e13_4__armstrng)]]). fof(e14_4__armstrng,assumption,( ? [A] : ( r2_hidden(A,c2_4__armstrng) & A != c10_4__armstrng & r2_hidden(k4_tarski(c10_4__armstrng,A),c1_4__armstrng) ) ), introduced(assumption,[file(armstrng,e14_4__armstrng)]), [interesting(0.8),axiom,file(armstrng,e14_4__armstrng)]). fof(dh_c11_4__armstrng,definition, ( ? [A] : ( r2_hidden(A,c2_4__armstrng) & A != c10_4__armstrng & r2_hidden(k4_tarski(c10_4__armstrng,A),c1_4__armstrng) ) => ( r2_hidden(c11_4__armstrng,c2_4__armstrng) & c11_4__armstrng != c10_4__armstrng & r2_hidden(k4_tarski(c10_4__armstrng,c11_4__armstrng),c1_4__armstrng) ) ), introduced(definition,[new_symbol(c11_4__armstrng),file(armstrng,c11_4__armstrng)]), [interesting(0.8),axiom,file(armstrng,c11_4__armstrng)]). fof(dt_c11_4__armstrng,plain,( $true ), inference(consider,[status(thm),assumptions([e14_4__armstrng])],[dh_c11_4__armstrng,e14_4__armstrng]), [interesting(0.8),file(armstrng,c11_4__armstrng),[file(armstrng,c11_4__armstrng)]]). fof(e15_4__armstrng,plain, ( r2_hidden(c11_4__armstrng,c2_4__armstrng) & c11_4__armstrng != c10_4__armstrng & r2_hidden(k4_tarski(c10_4__armstrng,c11_4__armstrng),c1_4__armstrng) ), inference(consider,[status(thm),assumptions([e14_4__armstrng])],[dh_c11_4__armstrng,e14_4__armstrng]), [interesting(0.8),file(armstrng,e15_4__armstrng),[file(armstrng,e15_4__armstrng)]]). fof(e16_4__armstrng,plain,( ~ $true ), inference(mizar_by,[status(thm),assumptions([dt_c2_4__armstrng,dt_c1_4__armstrng,e1_4__armstrng,e14_4__armstrng])],[cc1_altcat_1,cc1_finseq_1,cc1_fraenkel,rc1_finseq_1,rc1_fraenkel,rc1_margrel1,rc1_pboole,rc3_finseq_1,rc3_funct_1,rc4_funct_1,rc6_finseq_1,rc8_finseq_1,reflexivity_r1_tarski,abstractness_v1_orders_2,existence_l1_struct_0,existence_m1_relset_1,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_l1_struct_0,dt_m1_relset_1,cc1_relset_1,cc2_funct_1,fc14_finset_1,fc1_margrel1,fc1_orders_2,fc1_xboole_0,fc2_altcat_1,fc2_finseq_1,fc4_subset_1,rc1_funct_1,rc1_orders_2,rc2_funct_1,rc7_finseq_1,free_g1_orders_2,commutativity_k2_tarski,existence_l1_orders_2,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_g1_orders_2,dt_k1_tarski,dt_k1_zfmisc_1,dt_k2_tarski,dt_k3_relat_1,dt_l1_orders_2,dt_m1_subset_1,dt_m2_relset_1,dt_u1_struct_0,dt_c3_4__armstrng,de_c3_4__armstrng,cc1_finset_1,cc1_funct_1,cc2_finset_1,fc1_finset_1,fc1_subset_1,fc2_finset_1,fc2_subset_1,fc3_subset_1,rc1_finset_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,rc3_finset_1,rc4_finset_1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k4_tarski,dt_u1_orders_2,dt_c10_4__armstrng,dt_c11_4__armstrng,dt_c1_4__armstrng,dt_c2_4__armstrng,dt_c7_4__armstrng,dt_c8_4__armstrng,dt_c9_4__armstrng,de_c10_4__armstrng,de_c7_4__armstrng,de_c8_4__armstrng,t1_subset,t7_boole,d5_tarski,e11_4__armstrng,e15_4__armstrng,d24_waybel_4]), [interesting(0.8),file(armstrng,e16_4__armstrng),[file(armstrng,e16_4__armstrng)]]). fof(i7_4__armstrng,theorem,( $true ), introduced(tautology,[file(armstrng,i7_4__armstrng)]), [interesting(0.8),trivial,file(armstrng,i7_4__armstrng)]). fof(i6_4__armstrng,plain,( ~ $true ), inference(conclusion,[status(thm),assumptions([dt_c2_4__armstrng,dt_c1_4__armstrng,e1_4__armstrng,e14_4__armstrng])],[e16_4__armstrng,i7_4__armstrng]), [interesting(0.8),file(armstrng,i6_4__armstrng),[file(armstrng,i6_4__armstrng)]]). fof(i5_4__armstrng,plain,( ! [A] : ~ ( r2_hidden(A,c2_4__armstrng) & A != c10_4__armstrng & r2_hidden(k4_tarski(c10_4__armstrng,A),c1_4__armstrng) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c2_4__armstrng,dt_c1_4__armstrng,e1_4__armstrng]),discharge_asm(discharge,[e14_4__armstrng])],[e14_4__armstrng,i6_4__armstrng]), [interesting(0.8),file(armstrng,i5_4__armstrng),[file(armstrng,i5_4__armstrng)]]). fof(i4_4__armstrng,plain,( r2_waybel_4(c2_4__armstrng,c10_4__armstrng,c1_4__armstrng) ), inference(conclusion,[status(thm),assumptions([dt_c2_4__armstrng,dt_c1_4__armstrng,e1_4__armstrng])],[rc3_funct_1,rc6_finseq_1,cc2_funct_1,rc1_funct_1,rc2_funct_1,rc7_finseq_1,dt_k1_zfmisc_1,dt_k3_relat_1,dt_m1_subset_1,cc1_finset_1,cc1_funct_1,cc2_finset_1,fc1_subset_1,rc1_finset_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,rc3_finset_1,rc4_finset_1,antisymmetry_r2_hidden,dt_k4_tarski,dt_c10_4__armstrng,dt_c1_4__armstrng,dt_c2_4__armstrng,d24_waybel_4,e13_4__armstrng,i5_4__armstrng]), [interesting(0.8),file(armstrng,i4_4__armstrng),[file(armstrng,i4_4__armstrng)]]). fof(i3_4__armstrng,plain,( ? [A] : ( m1_subset_1(A,c2_4__armstrng) & r2_waybel_4(c2_4__armstrng,A,c1_4__armstrng) ) ), inference(take,[status(thm),assumptions([dt_c2_4__armstrng,dt_c1_4__armstrng,e1_4__armstrng])],[rc3_funct_1,rc6_finseq_1,cc2_funct_1,rc1_funct_1,rc2_funct_1,rc7_finseq_1,dt_k1_zfmisc_1,dt_k3_relat_1,cc1_finset_1,cc1_funct_1,cc2_finset_1,fc1_subset_1,rc1_finset_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,rc3_finset_1,rc4_finset_1,dt_m1_subset_1,dt_c10_4__armstrng,dt_c1_4__armstrng,dt_c2_4__armstrng,i4_4__armstrng]), [interesting(0.8),file(armstrng,i3_4__armstrng),[file(armstrng,i3_4__armstrng)]]). fof(i2_4__armstrng,plain,( ~ ( c2_4__armstrng != k1_xboole_0 & ! [A] : ( m1_subset_1(A,c2_4__armstrng) => ~ r2_waybel_4(c2_4__armstrng,A,c1_4__armstrng) ) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c2_4__armstrng,dt_c1_4__armstrng]),discharge_asm(discharge,[e1_4__armstrng])],[e1_4__armstrng,i3_4__armstrng]), [interesting(0.8),file(armstrng,i2_4__armstrng),[file(armstrng,i2_4__armstrng)]]). fof(i2_4_tmp__armstrng,plain, ( ( v1_finset_1(c2_4__armstrng) & m1_subset_1(c2_4__armstrng,k1_zfmisc_1(k3_relat_1(c1_4__armstrng))) ) => ~ ( c2_4__armstrng != k1_xboole_0 & ! [A] : ( m1_subset_1(A,c2_4__armstrng) => ~ r2_waybel_4(c2_4__armstrng,A,c1_4__armstrng) ) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_4__armstrng]),discharge_asm(discharge,[dt_c2_4__armstrng])],[dt_c2_4__armstrng,i2_4__armstrng]), [interesting(0.8),i1_4__armstrng]). fof(i1_4__armstrng,plain,( ! [A] : ( ( v1_finset_1(A) & m1_subset_1(A,k1_zfmisc_1(k3_relat_1(c1_4__armstrng))) ) => ~ ( A != k1_xboole_0 & ! [B] : ( m1_subset_1(B,A) => ~ r2_waybel_4(A,B,c1_4__armstrng) ) ) ) ), inference(let,[status(thm),assumptions([dt_c1_4__armstrng])],[i2_4_tmp__armstrng,dh_c2_4__armstrng]), [interesting(0.8),file(armstrng,i1_4__armstrng),[file(armstrng,i1_4__armstrng)]]). fof(i1_4_tmp__armstrng,plain, ( ( v1_relat_1(c1_4__armstrng) & ~ v1_xboole_0(c1_4__armstrng) & v4_relat_2(c1_4__armstrng) & v8_relat_2(c1_4__armstrng) ) => ! [A] : ( ( v1_finset_1(A) & m1_subset_1(A,k1_zfmisc_1(k3_relat_1(c1_4__armstrng))) ) => ~ ( A != k1_xboole_0 & ! [B] : ( m1_subset_1(B,A) => ~ r2_waybel_4(A,B,c1_4__armstrng) ) ) ) ), inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_4__armstrng])],[dt_c1_4__armstrng,i1_4__armstrng]), [interesting(1),t2_armstrng]). fof(t2_armstrng,theorem,( ! [A] : ( ( v1_relat_1(A) & ~ v1_xboole_0(A) & v4_relat_2(A) & v8_relat_2(A) ) => ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(k3_relat_1(A))) ) => ~ ( B != k1_xboole_0 & ! [C] : ( m1_subset_1(C,B) => ~ r2_waybel_4(B,C,A) ) ) ) ) ), inference(let,[status(thm),assumptions([])],[i1_4_tmp__armstrng,dh_c1_4__armstrng]), [interesting(1),file(armstrng,t2_armstrng),[file(armstrng,t2_armstrng)]]).