% Mizar ND problem: t179_orders_1,orders_1,1999,47 fof(dh_c1_95__orders_1,definition, ( ( v1_relat_1(c1_95__orders_1) => ! [A] : ~ ( r2_orders_1(c1_95__orders_1,A) & k3_relat_1(c1_95__orders_1) = A & ! [B] : ( v1_relat_1(B) => ~ ( r1_tarski(c1_95__orders_1,B) & r3_orders_1(B,A) & k3_relat_1(B) = A ) ) ) ) => ! [C] : ( v1_relat_1(C) => ! [D] : ~ ( r2_orders_1(C,D) & k3_relat_1(C) = D & ! [E] : ( v1_relat_1(E) => ~ ( r1_tarski(C,E) & r3_orders_1(E,D) & k3_relat_1(E) = D ) ) ) ) ), introduced(definition,[new_symbol(c1_95__orders_1),file(orders_1,c1_95__orders_1)]), [interesting(0.8),axiom,file(orders_1,c1_95__orders_1)]). fof(dh_c2_95__orders_1,definition, ( ~ ( r2_orders_1(c1_95__orders_1,c2_95__orders_1) & k3_relat_1(c1_95__orders_1) = c2_95__orders_1 & ! [A] : ( v1_relat_1(A) => ~ ( r1_tarski(c1_95__orders_1,A) & r3_orders_1(A,c2_95__orders_1) & k3_relat_1(A) = c2_95__orders_1 ) ) ) => ! [B] : ~ ( r2_orders_1(c1_95__orders_1,B) & k3_relat_1(c1_95__orders_1) = B & ! [C] : ( v1_relat_1(C) => ~ ( r1_tarski(c1_95__orders_1,C) & r3_orders_1(C,B) & k3_relat_1(C) = B ) ) ) ), introduced(definition,[new_symbol(c2_95__orders_1),file(orders_1,c2_95__orders_1)]), [interesting(0.8),axiom,file(orders_1,c2_95__orders_1)]). fof(e1_95__orders_1,assumption, ( r2_orders_1(c1_95__orders_1,c2_95__orders_1) & k3_relat_1(c1_95__orders_1) = c2_95__orders_1 ), introduced(assumption,[file(orders_1,e1_95__orders_1)]), [interesting(0.8),axiom,file(orders_1,e1_95__orders_1)]). 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_k3_relat_1,axiom,( $true ), file(relat_1,k3_relat_1), [interesting(0.9),axiom,file(relat_1,k3_relat_1)]). fof(dt_c1_95__orders_1,assumption,( v1_relat_1(c1_95__orders_1) ), introduced(assumption,[file(orders_1,c1_95__orders_1)]), [interesting(0.8),axiom,file(orders_1,c1_95__orders_1)]). fof(dt_c2_95__orders_1,assumption,( $true ), introduced(assumption,[file(orders_1,c2_95__orders_1)]), [interesting(0.8),axiom,file(orders_1,c2_95__orders_1)]). fof(dh_c5_95__orders_1,definition, ( ? [A] : ( v1_relat_1(A) & c4_95__orders_1 = A & r1_tarski(c1_95__orders_1,A) & r2_orders_1(A,c2_95__orders_1) & k3_relat_1(A) = c2_95__orders_1 ) => ( v1_relat_1(c5_95__orders_1) & c4_95__orders_1 = c5_95__orders_1 & r1_tarski(c1_95__orders_1,c5_95__orders_1) & r2_orders_1(c5_95__orders_1,c2_95__orders_1) & k3_relat_1(c5_95__orders_1) = c2_95__orders_1 ) ), introduced(definition,[new_symbol(c5_95__orders_1),file(orders_1,c5_95__orders_1)]), [interesting(0.8),axiom,file(orders_1,c5_95__orders_1)]). fof(rc1_partfun1,theorem,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_xboole_0(A) ) ), file(partfun1,rc1_partfun1), [interesting(0.9),axiom,file(partfun1,rc1_partfun1)]). fof(rc2_ordinal1,theorem,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_xboole_0(A) & v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) ) ), file(ordinal1,rc2_ordinal1), [interesting(0.9),axiom,file(ordinal1,rc2_ordinal1)]). fof(dt_k1_xboole_0,axiom,( $true ), file(xboole_0,k1_xboole_0), [interesting(0.9),axiom,file(xboole_0,k1_xboole_0)]). fof(cc1_ordinal1,theorem,( ! [A] : ( v3_ordinal1(A) => ( v1_ordinal1(A) & v2_ordinal1(A) ) ) ), file(ordinal1,cc1_ordinal1), [interesting(0.9),axiom,file(ordinal1,cc1_ordinal1)]). 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(cc2_ordinal1,theorem,( ! [A] : ( ( v1_ordinal1(A) & v2_ordinal1(A) ) => v3_ordinal1(A) ) ), file(ordinal1,cc2_ordinal1), [interesting(0.9),axiom,file(ordinal1,cc2_ordinal1)]). 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(fc2_ordinal1,theorem, ( 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_xboole_0(k1_xboole_0) & v1_ordinal1(k1_xboole_0) & v2_ordinal1(k1_xboole_0) & v3_ordinal1(k1_xboole_0) ), file(ordinal1,fc2_ordinal1), [interesting(0.9),axiom,file(ordinal1,fc2_ordinal1)]). fof(fc9_finset_1,theorem,( ! [A,B] : ( ( v1_finset_1(A) & v1_finset_1(B) ) => v1_finset_1(k2_xboole_0(A,B)) ) ), file(finset_1,fc9_finset_1), [interesting(0.9),axiom,file(finset_1,fc9_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(rc1_ordinal1,theorem,( ? [A] : ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) ) ), file(ordinal1,rc1_ordinal1), [interesting(0.9),axiom,file(ordinal1,rc1_ordinal1)]). 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(rc3_ordinal1,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) ) ), file(ordinal1,rc3_ordinal1), [interesting(0.9),axiom,file(ordinal1,rc3_ordinal1)]). 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(t1_boole,theorem,( ! [A] : k2_xboole_0(A,k1_xboole_0) = A ), file(boole,t1_boole), [interesting(0.9),axiom,file(boole,t1_boole)]). fof(commutativity_k2_xboole_0,theorem,( ! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A) ), file(xboole_0,k2_xboole_0), [interesting(0.9),axiom,file(xboole_0,k2_xboole_0)]). fof(idempotence_k2_xboole_0,theorem,( ! [A,B] : k2_xboole_0(A,A) = A ), file(xboole_0,k2_xboole_0), [interesting(0.9),axiom,file(xboole_0,k2_xboole_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(dt_k1_relat_1,axiom,( $true ), file(relat_1,k1_relat_1), [interesting(0.9),axiom,file(relat_1,k1_relat_1)]). fof(dt_k2_relat_1,axiom,( $true ), file(relat_1,k2_relat_1), [interesting(0.9),axiom,file(relat_1,k2_relat_1)]). fof(dt_k2_xboole_0,axiom,( $true ), file(xboole_0,k2_xboole_0), [interesting(0.9),axiom,file(xboole_0,k2_xboole_0)]). fof(dt_m1_subset_1,axiom,( $true ), file(subset_1,m1_subset_1), [interesting(0.9),axiom,file(subset_1,m1_subset_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_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(cc3_ordinal1,theorem,( ! [A] : ( v1_xboole_0(A) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) ) ) ), file(ordinal1,cc3_ordinal1), [interesting(0.9),axiom,file(ordinal1,cc3_ordinal1)]). 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_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(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(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(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(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_k1_zfmisc_1,axiom,( $true ), file(zfmisc_1,k1_zfmisc_1), [interesting(0.9),axiom,file(zfmisc_1,k1_zfmisc_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(dh_c3_95__orders_1,definition, ( ? [A] : ! [B] : ( r2_hidden(B,A) <=> ( r2_hidden(B,k1_zfmisc_1(k2_zfmisc_1(c2_95__orders_1,c2_95__orders_1))) & ? [C] : ( v1_relat_1(C) & B = C & r1_tarski(c1_95__orders_1,C) & r2_orders_1(C,c2_95__orders_1) & k3_relat_1(C) = c2_95__orders_1 ) ) ) => ! [D] : ( r2_hidden(D,c3_95__orders_1) <=> ( r2_hidden(D,k1_zfmisc_1(k2_zfmisc_1(c2_95__orders_1,c2_95__orders_1))) & ? [E] : ( v1_relat_1(E) & D = E & r1_tarski(c1_95__orders_1,E) & r2_orders_1(E,c2_95__orders_1) & k3_relat_1(E) = c2_95__orders_1 ) ) ) ), introduced(definition,[new_symbol(c3_95__orders_1),file(orders_1,c3_95__orders_1)]), [interesting(0.8),axiom,file(orders_1,c3_95__orders_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(s1_xboole_0__e2_95__orders_1,theorem,( ! [A,B] : ( v1_relat_1(A) => ? [C] : ! [D] : ( r2_hidden(D,C) <=> ( r2_hidden(D,k1_zfmisc_1(k2_zfmisc_1(B,B))) & ? [E] : ( v1_relat_1(E) & D = E & r1_tarski(A,E) & r2_orders_1(E,B) & k3_relat_1(E) = B ) ) ) ) ), file(orders_1,s1_xboole_0__e2_95__orders_1), [interesting(0.9),axiom,file(orders_1,s1_xboole_0__e2_95__orders_1)]). fof(e2_95__orders_1,plain,( ? [A] : ! [B] : ( r2_hidden(B,A) <=> ( r2_hidden(B,k1_zfmisc_1(k2_zfmisc_1(c2_95__orders_1,c2_95__orders_1))) & ? [C] : ( v1_relat_1(C) & B = C & r1_tarski(c1_95__orders_1,C) & r2_orders_1(C,c2_95__orders_1) & k3_relat_1(C) = c2_95__orders_1 ) ) ) ), inference(mizar_from,[status(thm),assumptions([dt_c1_95__orders_1,dt_c2_95__orders_1])],[cc1_ordinal1,cc2_ordinal1,fc14_finset_1,rc1_finset_1,rc1_ordinal1,rc3_ordinal1,cc1_finset_1,cc3_ordinal1,fc4_subset_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k3_relat_1,dt_c1_95__orders_1,dt_c2_95__orders_1,fc1_subset_1,s1_xboole_0__e2_95__orders_1]), [interesting(0.8),file(orders_1,e2_95__orders_1),[file(orders_1,e2_95__orders_1)]]). fof(dt_c3_95__orders_1,plain,( $true ), inference(consider,[status(thm),assumptions([dt_c1_95__orders_1,dt_c2_95__orders_1])],[dh_c3_95__orders_1,e2_95__orders_1]), [interesting(0.8),file(orders_1,c3_95__orders_1),[file(orders_1,c3_95__orders_1)]]). fof(dh_c4_95__orders_1,definition, ( ? [A] : ( r2_hidden(A,c3_95__orders_1) & ! [B] : ~ ( r2_hidden(B,c3_95__orders_1) & B != A & r1_tarski(A,B) ) ) => ( r2_hidden(c4_95__orders_1,c3_95__orders_1) & ! [C] : ~ ( r2_hidden(C,c3_95__orders_1) & C != c4_95__orders_1 & r1_tarski(c4_95__orders_1,C) ) ) ), introduced(definition,[new_symbol(c4_95__orders_1),file(orders_1,c4_95__orders_1)]), [interesting(0.8),axiom,file(orders_1,c4_95__orders_1)]). fof(fc4_ordinal1,theorem,( ! [A] : ( v3_ordinal1(A) => ( v1_ordinal1(k3_tarski(A)) & v2_ordinal1(k3_tarski(A)) & v3_ordinal1(k3_tarski(A)) ) ) ), file(ordinal1,fc4_ordinal1), [interesting(0.9),axiom,file(ordinal1,fc4_ordinal1)]). fof(dt_k3_tarski,axiom,( $true ), file(tarski,k3_tarski), [interesting(0.9),axiom,file(tarski,k3_tarski)]). 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(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(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(dh_c1_95_1__orders_1,definition, ( ( ( r1_tarski(c1_95_1__orders_1,c3_95__orders_1) & v6_ordinal1(c1_95_1__orders_1) ) => ( c1_95_1__orders_1 = k1_xboole_0 | r2_hidden(k3_tarski(c1_95_1__orders_1),c3_95__orders_1) ) ) => ! [A] : ( ( r1_tarski(A,c3_95__orders_1) & v6_ordinal1(A) ) => ( A = k1_xboole_0 | r2_hidden(k3_tarski(A),c3_95__orders_1) ) ) ), introduced(definition,[new_symbol(c1_95_1__orders_1),file(orders_1,c1_95_1__orders_1)]), [interesting(0.65),axiom,file(orders_1,c1_95_1__orders_1)]). fof(e1_95_1__orders_1,assumption, ( c1_95_1__orders_1 != k1_xboole_0 & r1_tarski(c1_95_1__orders_1,c3_95__orders_1) ), introduced(assumption,[file(orders_1,e1_95_1__orders_1)]), [interesting(0.65),axiom,file(orders_1,e1_95_1__orders_1)]). fof(e2_95_1__orders_1,assumption,( v6_ordinal1(c1_95_1__orders_1) ), introduced(assumption,[file(orders_1,e2_95_1__orders_1)]), [interesting(0.65),axiom,file(orders_1,e2_95_1__orders_1)]). fof(dt_c1_95_1__orders_1,assumption,( $true ), introduced(assumption,[file(orders_1,c1_95_1__orders_1)]), [interesting(0.65),axiom,file(orders_1,c1_95_1__orders_1)]). fof(de_c2_95_1__orders_1,definition,( c2_95_1__orders_1 = k2_zfmisc_1(c2_95__orders_1,c2_95__orders_1) ), introduced(definition,[new_symbol(c2_95_1__orders_1),file(orders_1,c2_95_1__orders_1)]), [interesting(0.65),axiom,file(orders_1,c2_95_1__orders_1)]). fof(t6_relat_1,theorem,( ! [A,B] : v1_relat_1(k2_zfmisc_1(A,B)) ), file(relat_1,t6_relat_1), [interesting(0.9),axiom,file(relat_1,t6_relat_1)]). fof(e3_95_1__orders_1,plain,( v1_relat_1(k2_zfmisc_1(c2_95__orders_1,c2_95__orders_1)) ), inference(mizar_by,[status(thm),assumptions([dt_c2_95__orders_1])],[dt_k2_zfmisc_1,dt_c2_95__orders_1,t6_relat_1]), [interesting(0.65),file(orders_1,e3_95_1__orders_1),[file(orders_1,e3_95_1__orders_1)]]). fof(dt_c2_95_1__orders_1,plain,( v1_relat_1(c2_95_1__orders_1) ), inference(mizar_by,[status(thm),assumptions([dt_c2_95__orders_1])],[dt_k2_zfmisc_1,dt_c2_95__orders_1,de_c2_95_1__orders_1,e3_95_1__orders_1]), [interesting(0.65),file(orders_1,c2_95_1__orders_1),[file(orders_1,c2_95_1__orders_1)]]). fof(de_c3_95_1__orders_1,definition,( c3_95_1__orders_1 = k3_tarski(c1_95_1__orders_1) ), introduced(definition,[new_symbol(c3_95_1__orders_1),file(orders_1,c3_95_1__orders_1)]), [interesting(0.65),axiom,file(orders_1,c3_95_1__orders_1)]). fof(dt_c1_95_1_1__orders_1,assumption,( $true ), introduced(assumption,[file(orders_1,c1_95_1_1__orders_1)]), [interesting(0.5),axiom,file(orders_1,c1_95_1_1__orders_1)]). 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_95_1_1__orders_1,definition, ( ~ ( r2_hidden(c1_95_1_1__orders_1,c1_95_1__orders_1) & ~ r2_hidden(c1_95_1_1__orders_1,k1_zfmisc_1(k2_zfmisc_1(c2_95__orders_1,c2_95__orders_1))) ) => ! [A] : ~ ( r2_hidden(A,c1_95_1__orders_1) & ~ r2_hidden(A,k1_zfmisc_1(k2_zfmisc_1(c2_95__orders_1,c2_95__orders_1))) ) ), introduced(definition,[new_symbol(c1_95_1_1__orders_1),file(orders_1,c1_95_1_1__orders_1)]), [interesting(0.5),axiom,file(orders_1,c1_95_1_1__orders_1)]). fof(e1_95_1_1__orders_1,assumption,( r2_hidden(c1_95_1_1__orders_1,c1_95_1__orders_1) ), introduced(assumption,[file(orders_1,e1_95_1_1__orders_1)]), [interesting(0.5),axiom,file(orders_1,e1_95_1_1__orders_1)]). fof(d6_relat_1,definition,( ! [A] : ( v1_relat_1(A) => k3_relat_1(A) = k2_xboole_0(k1_relat_1(A),k2_relat_1(A)) ) ), file(relat_1,d6_relat_1), [interesting(0.9),axiom,file(relat_1,d6_relat_1)]). fof(e3_95__orders_1,plain,( ! [A] : ( r2_hidden(A,c3_95__orders_1) <=> ( r2_hidden(A,k1_zfmisc_1(k2_zfmisc_1(c2_95__orders_1,c2_95__orders_1))) & ? [B] : ( v1_relat_1(B) & A = B & r1_tarski(c1_95__orders_1,B) & r2_orders_1(B,c2_95__orders_1) & k3_relat_1(B) = c2_95__orders_1 ) ) ) ), inference(consider,[status(thm),assumptions([dt_c1_95__orders_1,dt_c2_95__orders_1])],[dh_c3_95__orders_1,e2_95__orders_1]), [interesting(0.8),file(orders_1,e3_95__orders_1),[file(orders_1,e3_95__orders_1)]]). fof(e2_95_1_1__orders_1,plain,( r2_hidden(c1_95_1_1__orders_1,k1_zfmisc_1(k2_zfmisc_1(c2_95__orders_1,c2_95__orders_1))) ), inference(mizar_by,[status(thm),assumptions([dt_c1_95_1__orders_1,dt_c1_95_1_1__orders_1,e1_95_1_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1])],[cc2_finset_1,fc14_finset_1,fc9_finset_1,rc1_finset_1,rc3_finset_1,rc4_finset_1,commutativity_k2_xboole_0,idempotence_k2_xboole_0,existence_m1_subset_1,dt_k1_relat_1,dt_k2_relat_1,dt_k2_xboole_0,dt_m1_subset_1,cc1_finset_1,cc1_ordinal1,cc1_relset_1,cc2_ordinal1,cc3_ordinal1,fc4_subset_1,rc1_ordinal1,rc1_partfun1,rc1_subset_1,rc2_ordinal1,rc2_subset_1,rc3_ordinal1,t1_boole,t2_subset,t4_subset,t5_subset,t8_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k3_relat_1,dt_c1_95__orders_1,dt_c1_95_1__orders_1,dt_c1_95_1_1__orders_1,dt_c2_95__orders_1,dt_c3_95__orders_1,fc1_subset_1,fc2_ordinal1,t1_subset,t3_subset,t6_boole,t7_boole,d6_relat_1,e1_95_1_1__orders_1,e3_95__orders_1,e1_95_1__orders_1]), [interesting(0.5),file(orders_1,e2_95_1_1__orders_1),[file(orders_1,e2_95_1_1__orders_1)]]). fof(i3_95_1_1__orders_1,theorem,( $true ), introduced(tautology,[file(orders_1,i3_95_1_1__orders_1)]), [interesting(0.5),trivial,file(orders_1,i3_95_1_1__orders_1)]). fof(i2_95_1_1__orders_1,plain,( r2_hidden(c1_95_1_1__orders_1,k1_zfmisc_1(k2_zfmisc_1(c2_95__orders_1,c2_95__orders_1))) ), inference(conclusion,[status(thm),assumptions([dt_c1_95_1__orders_1,dt_c1_95_1_1__orders_1,e1_95_1_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1])],[e2_95_1_1__orders_1,i3_95_1_1__orders_1]), [interesting(0.5),file(orders_1,i2_95_1_1__orders_1),[file(orders_1,i2_95_1_1__orders_1)]]). fof(i1_95_1_1__orders_1,plain,( ~ ( r2_hidden(c1_95_1_1__orders_1,c1_95_1__orders_1) & ~ r2_hidden(c1_95_1_1__orders_1,k1_zfmisc_1(k2_zfmisc_1(c2_95__orders_1,c2_95__orders_1))) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_95_1__orders_1,dt_c1_95_1_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1]),discharge_asm(discharge,[e1_95_1_1__orders_1])],[e1_95_1_1__orders_1,i2_95_1_1__orders_1]), [interesting(0.5),file(orders_1,i1_95_1_1__orders_1),[file(orders_1,i1_95_1_1__orders_1)]]). fof(i1_95_1_1_tmp__orders_1,plain,( ~ ( r2_hidden(c1_95_1_1__orders_1,c1_95_1__orders_1) & ~ r2_hidden(c1_95_1_1__orders_1,k1_zfmisc_1(k2_zfmisc_1(c2_95__orders_1,c2_95__orders_1))) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1]),discharge_asm(discharge,[dt_c1_95_1_1__orders_1])],[dt_c1_95_1_1__orders_1,i1_95_1_1__orders_1]), [interesting(0.65),e4_95_1__orders_1]). fof(e4_95_1__orders_1,plain,( r1_tarski(c1_95_1__orders_1,k1_zfmisc_1(k2_zfmisc_1(c2_95__orders_1,c2_95__orders_1))) ), inference(let,[status(thm),assumptions([dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1])],[i1_95_1_1_tmp__orders_1,cc1_ordinal1,cc2_ordinal1,fc14_finset_1,rc1_finset_1,rc1_ordinal1,rc3_ordinal1,cc1_finset_1,cc3_ordinal1,fc4_subset_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_c1_95_1__orders_1,dt_c2_95__orders_1,fc1_subset_1,d3_tarski,dh_c1_95_1_1__orders_1]), [interesting(0.65),file(orders_1,e4_95_1__orders_1),[file(orders_1,e4_95_1__orders_1)]]). fof(t95_zfmisc_1,theorem,( ! [A,B] : ( r1_tarski(A,B) => r1_tarski(k3_tarski(A),k3_tarski(B)) ) ), file(zfmisc_1,t95_zfmisc_1), [interesting(0.9),axiom,file(zfmisc_1,t95_zfmisc_1)]). fof(t99_zfmisc_1,theorem,( ! [A] : k3_tarski(k1_zfmisc_1(A)) = A ), file(zfmisc_1,t99_zfmisc_1), [interesting(0.9),axiom,file(zfmisc_1,t99_zfmisc_1)]). fof(e5_95_1__orders_1,plain, ( r1_tarski(k3_tarski(c1_95_1__orders_1),k3_tarski(k1_zfmisc_1(k2_zfmisc_1(c2_95__orders_1,c2_95__orders_1)))) & k3_tarski(k1_zfmisc_1(k2_zfmisc_1(c2_95__orders_1,c2_95__orders_1))) = c2_95_1__orders_1 ), inference(mizar_by,[status(thm),assumptions([dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1])],[rc1_partfun1,rc2_ordinal1,antisymmetry_r2_hidden,dt_k1_xboole_0,cc1_ordinal1,cc2_finset_1,cc2_ordinal1,fc14_finset_1,fc2_ordinal1,fc4_ordinal1,rc1_finset_1,rc1_ordinal1,rc3_finset_1,rc3_ordinal1,rc4_finset_1,t1_subset,t4_subset,t5_subset,existence_m1_subset_1,dt_m1_subset_1,cc1_finset_1,cc1_relset_1,cc3_ordinal1,fc4_subset_1,rc1_subset_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,t8_boole,reflexivity_r1_tarski,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k3_tarski,dt_c1_95_1__orders_1,dt_c2_95__orders_1,dt_c2_95_1__orders_1,de_c2_95_1__orders_1,fc1_subset_1,t3_subset,e4_95_1__orders_1,t95_zfmisc_1,t99_zfmisc_1]), [interesting(0.65),file(orders_1,e5_95_1__orders_1),[file(orders_1,e5_95_1__orders_1)]]). fof(t3_relat_1,theorem,( ! [A,B] : ( v1_relat_1(B) => ( r1_tarski(A,B) => v1_relat_1(A) ) ) ), file(relat_1,t3_relat_1), [interesting(0.9),axiom,file(relat_1,t3_relat_1)]). fof(e6_95_1__orders_1,plain,( v1_relat_1(k3_tarski(c1_95_1__orders_1)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1])],[rc1_partfun1,rc2_ordinal1,antisymmetry_r2_hidden,dt_k1_xboole_0,cc1_ordinal1,cc2_finset_1,cc2_ordinal1,fc14_finset_1,fc2_ordinal1,fc4_ordinal1,rc1_finset_1,rc1_ordinal1,rc3_finset_1,rc3_ordinal1,rc4_finset_1,t1_subset,t4_subset,t5_subset,existence_m1_subset_1,dt_m1_subset_1,cc1_finset_1,cc1_relset_1,cc3_ordinal1,fc4_subset_1,rc1_subset_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,t8_boole,reflexivity_r1_tarski,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k3_tarski,dt_c1_95_1__orders_1,dt_c2_95__orders_1,dt_c2_95_1__orders_1,de_c2_95_1__orders_1,fc1_subset_1,t3_subset,e5_95_1__orders_1,t3_relat_1]), [interesting(0.65),file(orders_1,e6_95_1__orders_1),[file(orders_1,e6_95_1__orders_1)]]). fof(dt_c3_95_1__orders_1,plain,( v1_relat_1(c3_95_1__orders_1) ), inference(mizar_by,[status(thm),assumptions([dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1])],[dt_k3_tarski,dt_c1_95_1__orders_1,de_c3_95_1__orders_1,e6_95_1__orders_1]), [interesting(0.65),file(orders_1,c3_95_1__orders_1),[file(orders_1,c3_95_1__orders_1)]]). fof(d7_orders_1,definition,( ! [A] : ( v1_relat_1(A) => ! [B] : ( r2_orders_1(A,B) <=> ( r1_relat_2(A,B) & r8_relat_2(A,B) & r4_relat_2(A,B) ) ) ) ), file(orders_1,d7_orders_1), [interesting(0.9),axiom,file(orders_1,d7_orders_1)]). fof(dt_k4_tarski,axiom,( $true ), file(tarski,k4_tarski), [interesting(0.9),axiom,file(tarski,k4_tarski)]). fof(dt_c1_95_1_4_1__orders_1,assumption,( $true ), introduced(assumption,[file(orders_1,c1_95_1_4_1__orders_1)]), [interesting(0.35),axiom,file(orders_1,c1_95_1_4_1__orders_1)]). fof(d1_relat_2,definition,( ! [A] : ( v1_relat_1(A) => ! [B] : ( r1_relat_2(A,B) <=> ! [C] : ( r2_hidden(C,B) => r2_hidden(k4_tarski(C,C),A) ) ) ) ), file(relat_2,d1_relat_2), [interesting(0.9),axiom,file(relat_2,d1_relat_2)]). fof(dh_c1_95_1_4_1__orders_1,definition, ( ~ ( r2_hidden(c1_95_1_4_1__orders_1,c2_95__orders_1) & ~ r2_hidden(k4_tarski(c1_95_1_4_1__orders_1,c1_95_1_4_1__orders_1),c3_95_1__orders_1) ) => ! [A] : ~ ( r2_hidden(A,c2_95__orders_1) & ~ r2_hidden(k4_tarski(A,A),c3_95_1__orders_1) ) ), introduced(definition,[new_symbol(c1_95_1_4_1__orders_1),file(orders_1,c1_95_1_4_1__orders_1)]), [interesting(0.35),axiom,file(orders_1,c1_95_1_4_1__orders_1)]). fof(e1_95_1_4_1__orders_1,assumption,( r2_hidden(c1_95_1_4_1__orders_1,c2_95__orders_1) ), introduced(assumption,[file(orders_1,e1_95_1_4_1__orders_1)]), [interesting(0.35),axiom,file(orders_1,e1_95_1_4_1__orders_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(dh_c4_95_1__orders_1,definition, ( ? [A] : m1_subset_1(A,c1_95_1__orders_1) => m1_subset_1(c4_95_1__orders_1,c1_95_1__orders_1) ), introduced(definition,[new_symbol(c4_95_1__orders_1),file(orders_1,c4_95_1__orders_1)]), [interesting(0.65),axiom,file(orders_1,c4_95_1__orders_1)]). fof(e7_95_1__orders_1,plain,( ? [A] : m1_subset_1(A,c1_95_1__orders_1) ), inference(mizar_by,[status(thm),assumptions([dt_c1_95_1__orders_1])],[existence_m1_subset_1,dt_m1_subset_1,dt_c1_95_1__orders_1]), [interesting(0.65),file(orders_1,e7_95_1__orders_1),[file(orders_1,e7_95_1__orders_1)]]). fof(dt_c4_95_1__orders_1,plain,( m1_subset_1(c4_95_1__orders_1,c1_95_1__orders_1) ), inference(consider,[status(thm),assumptions([dt_c1_95_1__orders_1])],[dh_c4_95_1__orders_1,e7_95_1__orders_1]), [interesting(0.65),file(orders_1,c4_95_1__orders_1),[file(orders_1,c4_95_1__orders_1)]]). fof(dh_c5_95_1__orders_1,definition, ( ? [A] : ( v1_relat_1(A) & c4_95_1__orders_1 = A & r1_tarski(c1_95__orders_1,A) & r2_orders_1(A,c2_95__orders_1) & k3_relat_1(A) = c2_95__orders_1 ) => ( v1_relat_1(c5_95_1__orders_1) & c4_95_1__orders_1 = c5_95_1__orders_1 & r1_tarski(c1_95__orders_1,c5_95_1__orders_1) & r2_orders_1(c5_95_1__orders_1,c2_95__orders_1) & k3_relat_1(c5_95_1__orders_1) = c2_95__orders_1 ) ), introduced(definition,[new_symbol(c5_95_1__orders_1),file(orders_1,c5_95_1__orders_1)]), [interesting(0.65),axiom,file(orders_1,c5_95_1__orders_1)]). fof(e8_95_1__orders_1,plain,( r2_hidden(c4_95_1__orders_1,c3_95__orders_1) ), inference(mizar_by,[status(thm),assumptions([dt_c1_95__orders_1,dt_c2_95__orders_1,dt_c1_95_1__orders_1,e1_95_1__orders_1])],[cc2_finset_1,rc1_finset_1,rc3_finset_1,rc4_finset_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,cc1_finset_1,cc1_ordinal1,cc2_ordinal1,cc3_ordinal1,fc1_subset_1,rc1_ordinal1,rc1_partfun1,rc1_subset_1,rc2_ordinal1,rc2_subset_1,rc3_ordinal1,t2_subset,t4_subset,t5_subset,t8_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_c1_95_1__orders_1,dt_c3_95__orders_1,dt_c4_95_1__orders_1,fc2_ordinal1,t1_subset,t3_subset,t6_boole,t7_boole,e1_95_1__orders_1,d3_tarski]), [interesting(0.65),file(orders_1,e8_95_1__orders_1),[file(orders_1,e8_95_1__orders_1)]]). fof(e9_95_1__orders_1,plain,( ? [A] : ( v1_relat_1(A) & c4_95_1__orders_1 = A & r1_tarski(c1_95__orders_1,A) & r2_orders_1(A,c2_95__orders_1) & k3_relat_1(A) = c2_95__orders_1 ) ), inference(mizar_by,[status(thm),assumptions([dt_c1_95_1__orders_1,e1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1])],[rc1_partfun1,rc2_ordinal1,dt_k1_xboole_0,cc1_ordinal1,cc2_finset_1,cc2_ordinal1,fc14_finset_1,fc2_ordinal1,fc9_finset_1,rc1_finset_1,rc1_ordinal1,rc3_finset_1,rc3_ordinal1,rc4_finset_1,t1_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,existence_m1_subset_1,dt_k1_relat_1,dt_k2_relat_1,dt_k2_xboole_0,dt_m1_subset_1,dt_c1_95_1__orders_1,cc1_finset_1,cc1_relset_1,cc3_ordinal1,fc4_subset_1,rc1_subset_1,rc2_subset_1,t2_subset,t4_subset,t5_subset,t6_boole,t8_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k3_relat_1,dt_c1_95__orders_1,dt_c2_95__orders_1,dt_c3_95__orders_1,dt_c4_95_1__orders_1,fc1_subset_1,t1_subset,t3_subset,t7_boole,d6_relat_1,e8_95_1__orders_1,e3_95__orders_1]), [interesting(0.65),file(orders_1,e9_95_1__orders_1),[file(orders_1,e9_95_1__orders_1)]]). fof(dt_c5_95_1__orders_1,plain,( v1_relat_1(c5_95_1__orders_1) ), inference(consider,[status(thm),assumptions([dt_c1_95_1__orders_1,e1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1])],[dh_c5_95_1__orders_1,e9_95_1__orders_1]), [interesting(0.65),file(orders_1,c5_95_1__orders_1),[file(orders_1,c5_95_1__orders_1)]]). 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(e10_95_1__orders_1,plain, ( c4_95_1__orders_1 = c5_95_1__orders_1 & r1_tarski(c1_95__orders_1,c5_95_1__orders_1) & r2_orders_1(c5_95_1__orders_1,c2_95__orders_1) & k3_relat_1(c5_95_1__orders_1) = c2_95__orders_1 ), inference(consider,[status(thm),assumptions([dt_c1_95_1__orders_1,e1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1])],[dh_c5_95_1__orders_1,e9_95_1__orders_1]), [interesting(0.65),file(orders_1,e10_95_1__orders_1),[file(orders_1,e10_95_1__orders_1)]]). fof(e11_95_1__orders_1,plain,( r1_relat_2(c5_95_1__orders_1,c2_95__orders_1) ), inference(mizar_by,[status(thm),assumptions([dt_c1_95_1__orders_1,e1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1])],[rc1_partfun1,rc2_ordinal1,antisymmetry_r2_hidden,dt_k1_xboole_0,cc1_ordinal1,cc2_finset_1,cc2_ordinal1,fc2_ordinal1,fc9_finset_1,rc1_finset_1,rc1_ordinal1,rc3_finset_1,rc3_ordinal1,rc4_finset_1,t1_boole,t1_subset,t4_subset,t5_subset,cc1_finset_1,cc3_ordinal1,rc1_subset_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,existence_m1_subset_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k2_relat_1,dt_k2_xboole_0,dt_m1_subset_1,dt_c1_95_1__orders_1,fc1_subset_1,reflexivity_r1_tarski,dt_k3_relat_1,dt_c1_95__orders_1,dt_c2_95__orders_1,dt_c4_95_1__orders_1,dt_c5_95_1__orders_1,t3_subset,d6_relat_1,e10_95_1__orders_1,d7_orders_1]), [interesting(0.65),file(orders_1,e11_95_1__orders_1),[file(orders_1,e11_95_1__orders_1)]]). fof(e2_95_1_4_1__orders_1,plain,( r2_hidden(k4_tarski(c1_95_1_4_1__orders_1,c1_95_1_4_1__orders_1),c5_95_1__orders_1) ), inference(mizar_by,[status(thm),assumptions([dt_c1_95_1_4_1__orders_1,e1_95_1_4_1__orders_1,dt_c1_95_1__orders_1,e1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1])],[rc1_partfun1,rc2_ordinal1,dt_k1_xboole_0,cc1_ordinal1,cc2_ordinal1,fc2_ordinal1,rc1_finset_1,rc1_ordinal1,rc3_ordinal1,commutativity_k2_tarski,existence_m1_subset_1,dt_k1_tarski,dt_k2_tarski,dt_m1_subset_1,cc1_finset_1,cc3_ordinal1,fc1_finset_1,fc2_finset_1,fc2_subset_1,fc3_subset_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k4_tarski,dt_c1_95_1_4_1__orders_1,dt_c2_95__orders_1,dt_c5_95_1__orders_1,t1_subset,t7_boole,d5_tarski,e1_95_1_4_1__orders_1,e11_95_1__orders_1,d1_relat_2]), [interesting(0.35),file(orders_1,e2_95_1_4_1__orders_1),[file(orders_1,e2_95_1_4_1__orders_1)]]). fof(d4_tarski,definition,( ! [A,B] : ( B = k3_tarski(A) <=> ! [C] : ( r2_hidden(C,B) <=> ? [D] : ( r2_hidden(C,D) & r2_hidden(D,A) ) ) ) ), file(tarski,d4_tarski), [interesting(0.9),axiom,file(tarski,d4_tarski)]). fof(e3_95_1_4_1__orders_1,plain,( r2_hidden(k4_tarski(c1_95_1_4_1__orders_1,c1_95_1_4_1__orders_1),c3_95_1__orders_1) ), inference(mizar_by,[status(thm),assumptions([dt_c1_95_1_4_1__orders_1,e1_95_1_4_1__orders_1,dt_c1_95_1__orders_1,e1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1])],[cc2_finset_1,fc9_finset_1,rc1_finset_1,rc3_finset_1,rc4_finset_1,commutativity_k2_tarski,commutativity_k2_xboole_0,idempotence_k2_xboole_0,existence_m1_subset_1,dt_k1_relat_1,dt_k1_tarski,dt_k1_zfmisc_1,dt_k2_relat_1,dt_k2_tarski,dt_k2_xboole_0,dt_m1_subset_1,cc1_finset_1,cc1_ordinal1,cc2_ordinal1,cc3_ordinal1,fc1_finset_1,fc1_subset_1,fc2_finset_1,fc2_subset_1,fc3_subset_1,fc4_ordinal1,rc1_ordinal1,rc1_partfun1,rc1_subset_1,rc2_ordinal1,rc2_subset_1,rc3_ordinal1,t1_boole,t2_subset,t4_subset,t5_subset,t8_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k3_relat_1,dt_k3_tarski,dt_k4_tarski,dt_c1_95__orders_1,dt_c1_95_1__orders_1,dt_c1_95_1_4_1__orders_1,dt_c2_95__orders_1,dt_c3_95__orders_1,dt_c3_95_1__orders_1,dt_c4_95_1__orders_1,dt_c5_95_1__orders_1,de_c3_95_1__orders_1,fc2_ordinal1,t1_subset,t3_subset,t6_boole,t7_boole,d6_relat_1,d5_tarski,e2_95_1_4_1__orders_1,e1_95_1__orders_1,e10_95_1__orders_1,d4_tarski]), [interesting(0.35),file(orders_1,e3_95_1_4_1__orders_1),[file(orders_1,e3_95_1_4_1__orders_1)]]). fof(i3_95_1_4_1__orders_1,theorem,( $true ), introduced(tautology,[file(orders_1,i3_95_1_4_1__orders_1)]), [interesting(0.35),trivial,file(orders_1,i3_95_1_4_1__orders_1)]). fof(i2_95_1_4_1__orders_1,plain,( r2_hidden(k4_tarski(c1_95_1_4_1__orders_1,c1_95_1_4_1__orders_1),c3_95_1__orders_1) ), inference(conclusion,[status(thm),assumptions([dt_c1_95_1_4_1__orders_1,e1_95_1_4_1__orders_1,dt_c1_95_1__orders_1,e1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1])],[e3_95_1_4_1__orders_1,i3_95_1_4_1__orders_1]), [interesting(0.35),file(orders_1,i2_95_1_4_1__orders_1),[file(orders_1,i2_95_1_4_1__orders_1)]]). fof(i1_95_1_4_1__orders_1,plain,( ~ ( r2_hidden(c1_95_1_4_1__orders_1,c2_95__orders_1) & ~ r2_hidden(k4_tarski(c1_95_1_4_1__orders_1,c1_95_1_4_1__orders_1),c3_95_1__orders_1) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_95_1_4_1__orders_1,dt_c1_95_1__orders_1,e1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1]),discharge_asm(discharge,[e1_95_1_4_1__orders_1])],[e1_95_1_4_1__orders_1,i2_95_1_4_1__orders_1]), [interesting(0.35),file(orders_1,i1_95_1_4_1__orders_1),[file(orders_1,i1_95_1_4_1__orders_1)]]). fof(i1_95_1_4_1_tmp__orders_1,plain,( ~ ( r2_hidden(c1_95_1_4_1__orders_1,c2_95__orders_1) & ~ r2_hidden(k4_tarski(c1_95_1_4_1__orders_1,c1_95_1_4_1__orders_1),c3_95_1__orders_1) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_95_1__orders_1,e1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1]),discharge_asm(discharge,[dt_c1_95_1_4_1__orders_1])],[dt_c1_95_1_4_1__orders_1,i1_95_1_4_1__orders_1]), [interesting(0.5),e1_95_1_4__orders_1]). fof(e1_95_1_4__orders_1,plain,( r1_relat_2(c3_95_1__orders_1,c2_95__orders_1) ), inference(let,[status(thm),assumptions([dt_c1_95_1__orders_1,e1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1])],[i1_95_1_4_1_tmp__orders_1,antisymmetry_r2_hidden,dt_k4_tarski,dt_c2_95__orders_1,dt_c3_95_1__orders_1,d1_relat_2,dh_c1_95_1_4_1__orders_1]), [interesting(0.5),file(orders_1,e1_95_1_4__orders_1),[file(orders_1,e1_95_1_4__orders_1)]]). fof(dt_c1_95_1_4_2__orders_1,assumption,( $true ), introduced(assumption,[file(orders_1,c1_95_1_4_2__orders_1)]), [interesting(0.35),axiom,file(orders_1,c1_95_1_4_2__orders_1)]). 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(dh_c1_95_1_4_2__orders_1,definition, ( ! [A,B] : ~ ( r2_hidden(c1_95_1_4_2__orders_1,c2_95__orders_1) & r2_hidden(A,c2_95__orders_1) & r2_hidden(B,c2_95__orders_1) & r2_hidden(k4_tarski(c1_95_1_4_2__orders_1,A),c3_95_1__orders_1) & r2_hidden(k4_tarski(A,B),c3_95_1__orders_1) & ~ r2_hidden(k4_tarski(c1_95_1_4_2__orders_1,B),c3_95_1__orders_1) ) => ! [C,D,E] : ~ ( r2_hidden(C,c2_95__orders_1) & r2_hidden(D,c2_95__orders_1) & r2_hidden(E,c2_95__orders_1) & r2_hidden(k4_tarski(C,D),c3_95_1__orders_1) & r2_hidden(k4_tarski(D,E),c3_95_1__orders_1) & ~ r2_hidden(k4_tarski(C,E),c3_95_1__orders_1) ) ), introduced(definition,[new_symbol(c1_95_1_4_2__orders_1),file(orders_1,c1_95_1_4_2__orders_1)]), [interesting(0.35),axiom,file(orders_1,c1_95_1_4_2__orders_1)]). fof(dh_c2_95_1_4_2__orders_1,definition, ( ! [A] : ~ ( r2_hidden(c1_95_1_4_2__orders_1,c2_95__orders_1) & r2_hidden(c2_95_1_4_2__orders_1,c2_95__orders_1) & r2_hidden(A,c2_95__orders_1) & r2_hidden(k4_tarski(c1_95_1_4_2__orders_1,c2_95_1_4_2__orders_1),c3_95_1__orders_1) & r2_hidden(k4_tarski(c2_95_1_4_2__orders_1,A),c3_95_1__orders_1) & ~ r2_hidden(k4_tarski(c1_95_1_4_2__orders_1,A),c3_95_1__orders_1) ) => ! [B,C] : ~ ( r2_hidden(c1_95_1_4_2__orders_1,c2_95__orders_1) & r2_hidden(B,c2_95__orders_1) & r2_hidden(C,c2_95__orders_1) & r2_hidden(k4_tarski(c1_95_1_4_2__orders_1,B),c3_95_1__orders_1) & r2_hidden(k4_tarski(B,C),c3_95_1__orders_1) & ~ r2_hidden(k4_tarski(c1_95_1_4_2__orders_1,C),c3_95_1__orders_1) ) ), introduced(definition,[new_symbol(c2_95_1_4_2__orders_1),file(orders_1,c2_95_1_4_2__orders_1)]), [interesting(0.35),axiom,file(orders_1,c2_95_1_4_2__orders_1)]). fof(dh_c3_95_1_4_2__orders_1,definition, ( ~ ( r2_hidden(c1_95_1_4_2__orders_1,c2_95__orders_1) & r2_hidden(c2_95_1_4_2__orders_1,c2_95__orders_1) & r2_hidden(c3_95_1_4_2__orders_1,c2_95__orders_1) & r2_hidden(k4_tarski(c1_95_1_4_2__orders_1,c2_95_1_4_2__orders_1),c3_95_1__orders_1) & r2_hidden(k4_tarski(c2_95_1_4_2__orders_1,c3_95_1_4_2__orders_1),c3_95_1__orders_1) & ~ r2_hidden(k4_tarski(c1_95_1_4_2__orders_1,c3_95_1_4_2__orders_1),c3_95_1__orders_1) ) => ! [A] : ~ ( r2_hidden(c1_95_1_4_2__orders_1,c2_95__orders_1) & r2_hidden(c2_95_1_4_2__orders_1,c2_95__orders_1) & r2_hidden(A,c2_95__orders_1) & r2_hidden(k4_tarski(c1_95_1_4_2__orders_1,c2_95_1_4_2__orders_1),c3_95_1__orders_1) & r2_hidden(k4_tarski(c2_95_1_4_2__orders_1,A),c3_95_1__orders_1) & ~ r2_hidden(k4_tarski(c1_95_1_4_2__orders_1,A),c3_95_1__orders_1) ) ), introduced(definition,[new_symbol(c3_95_1_4_2__orders_1),file(orders_1,c3_95_1_4_2__orders_1)]), [interesting(0.35),axiom,file(orders_1,c3_95_1_4_2__orders_1)]). fof(e1_95_1_4_2__orders_1,assumption, ( r2_hidden(c1_95_1_4_2__orders_1,c2_95__orders_1) & r2_hidden(c2_95_1_4_2__orders_1,c2_95__orders_1) & r2_hidden(c3_95_1_4_2__orders_1,c2_95__orders_1) & r2_hidden(k4_tarski(c1_95_1_4_2__orders_1,c2_95_1_4_2__orders_1),c3_95_1__orders_1) & r2_hidden(k4_tarski(c2_95_1_4_2__orders_1,c3_95_1_4_2__orders_1),c3_95_1__orders_1) ), introduced(assumption,[file(orders_1,e1_95_1_4_2__orders_1)]), [interesting(0.35),axiom,file(orders_1,e1_95_1_4_2__orders_1)]). fof(dt_c2_95_1_4_2__orders_1,assumption,( $true ), introduced(assumption,[file(orders_1,c2_95_1_4_2__orders_1)]), [interesting(0.35),axiom,file(orders_1,c2_95_1_4_2__orders_1)]). fof(dt_c3_95_1_4_2__orders_1,assumption,( $true ), introduced(assumption,[file(orders_1,c3_95_1_4_2__orders_1)]), [interesting(0.35),axiom,file(orders_1,c3_95_1_4_2__orders_1)]). fof(dh_c4_95_1_4_2__orders_1,definition, ( ? [A] : ( r2_hidden(k4_tarski(c1_95_1_4_2__orders_1,c2_95_1_4_2__orders_1),A) & r2_hidden(A,c1_95_1__orders_1) ) => ( r2_hidden(k4_tarski(c1_95_1_4_2__orders_1,c2_95_1_4_2__orders_1),c4_95_1_4_2__orders_1) & r2_hidden(c4_95_1_4_2__orders_1,c1_95_1__orders_1) ) ), introduced(definition,[new_symbol(c4_95_1_4_2__orders_1),file(orders_1,c4_95_1_4_2__orders_1)]), [interesting(0.35),axiom,file(orders_1,c4_95_1_4_2__orders_1)]). fof(e2_95_1_4_2__orders_1,plain,( ? [A] : ( r2_hidden(k4_tarski(c1_95_1_4_2__orders_1,c2_95_1_4_2__orders_1),A) & r2_hidden(A,c1_95_1__orders_1) ) ), inference(mizar_by,[status(thm),assumptions([dt_c1_95_1_4_2__orders_1,dt_c2_95_1_4_2__orders_1,dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1,dt_c3_95_1_4_2__orders_1,e1_95_1_4_2__orders_1])],[rc1_partfun1,rc2_ordinal1,dt_k1_xboole_0,cc1_ordinal1,cc2_ordinal1,fc2_ordinal1,fc4_ordinal1,rc1_finset_1,rc1_ordinal1,rc3_ordinal1,commutativity_k2_tarski,existence_m1_subset_1,dt_k1_tarski,dt_k2_tarski,dt_m1_subset_1,cc1_finset_1,cc3_ordinal1,fc1_finset_1,fc2_finset_1,fc2_subset_1,fc3_subset_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k3_tarski,dt_k4_tarski,dt_c1_95_1__orders_1,dt_c1_95_1_4_2__orders_1,dt_c2_95__orders_1,dt_c2_95_1_4_2__orders_1,dt_c3_95_1__orders_1,dt_c3_95_1_4_2__orders_1,de_c3_95_1__orders_1,t1_subset,t7_boole,d5_tarski,e1_95_1_4_2__orders_1,d4_tarski]), [interesting(0.35),file(orders_1,e2_95_1_4_2__orders_1),[file(orders_1,e2_95_1_4_2__orders_1)]]). fof(dt_c4_95_1_4_2__orders_1,plain,( $true ), inference(consider,[status(thm),assumptions([dt_c1_95_1_4_2__orders_1,dt_c2_95_1_4_2__orders_1,dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1,dt_c3_95_1_4_2__orders_1,e1_95_1_4_2__orders_1])],[dh_c4_95_1_4_2__orders_1,e2_95_1_4_2__orders_1]), [interesting(0.35),file(orders_1,c4_95_1_4_2__orders_1),[file(orders_1,c4_95_1_4_2__orders_1)]]). fof(dh_c5_95_1_4_2__orders_1,definition, ( ? [A] : ( r2_hidden(k4_tarski(c2_95_1_4_2__orders_1,c3_95_1_4_2__orders_1),A) & r2_hidden(A,c1_95_1__orders_1) ) => ( r2_hidden(k4_tarski(c2_95_1_4_2__orders_1,c3_95_1_4_2__orders_1),c5_95_1_4_2__orders_1) & r2_hidden(c5_95_1_4_2__orders_1,c1_95_1__orders_1) ) ), introduced(definition,[new_symbol(c5_95_1_4_2__orders_1),file(orders_1,c5_95_1_4_2__orders_1)]), [interesting(0.35),axiom,file(orders_1,c5_95_1_4_2__orders_1)]). fof(e4_95_1_4_2__orders_1,plain,( ? [A] : ( r2_hidden(k4_tarski(c2_95_1_4_2__orders_1,c3_95_1_4_2__orders_1),A) & r2_hidden(A,c1_95_1__orders_1) ) ), inference(mizar_by,[status(thm),assumptions([dt_c1_95_1_4_2__orders_1,dt_c2_95_1_4_2__orders_1,dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1,dt_c3_95_1_4_2__orders_1,e1_95_1_4_2__orders_1])],[rc1_partfun1,rc2_ordinal1,dt_k1_xboole_0,cc1_ordinal1,cc2_ordinal1,fc2_ordinal1,fc4_ordinal1,rc1_finset_1,rc1_ordinal1,rc3_ordinal1,commutativity_k2_tarski,existence_m1_subset_1,dt_k1_tarski,dt_k2_tarski,dt_m1_subset_1,cc1_finset_1,cc3_ordinal1,fc1_finset_1,fc2_finset_1,fc2_subset_1,fc3_subset_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k3_tarski,dt_k4_tarski,dt_c1_95_1__orders_1,dt_c1_95_1_4_2__orders_1,dt_c2_95__orders_1,dt_c2_95_1_4_2__orders_1,dt_c3_95_1__orders_1,dt_c3_95_1_4_2__orders_1,de_c3_95_1__orders_1,t1_subset,t7_boole,d5_tarski,e1_95_1_4_2__orders_1,d4_tarski]), [interesting(0.35),file(orders_1,e4_95_1_4_2__orders_1),[file(orders_1,e4_95_1_4_2__orders_1)]]). fof(dt_c5_95_1_4_2__orders_1,plain,( $true ), inference(consider,[status(thm),assumptions([dt_c1_95_1_4_2__orders_1,dt_c2_95_1_4_2__orders_1,dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1,dt_c3_95_1_4_2__orders_1,e1_95_1_4_2__orders_1])],[dh_c5_95_1_4_2__orders_1,e4_95_1_4_2__orders_1]), [interesting(0.35),file(orders_1,c5_95_1_4_2__orders_1),[file(orders_1,c5_95_1_4_2__orders_1)]]). fof(dh_c6_95_1_4_2__orders_1,definition, ( ? [A] : ( v1_relat_1(A) & c4_95_1_4_2__orders_1 = A & r1_tarski(c1_95__orders_1,A) & r2_orders_1(A,c2_95__orders_1) & k3_relat_1(A) = c2_95__orders_1 ) => ( v1_relat_1(c6_95_1_4_2__orders_1) & c4_95_1_4_2__orders_1 = c6_95_1_4_2__orders_1 & r1_tarski(c1_95__orders_1,c6_95_1_4_2__orders_1) & r2_orders_1(c6_95_1_4_2__orders_1,c2_95__orders_1) & k3_relat_1(c6_95_1_4_2__orders_1) = c2_95__orders_1 ) ), introduced(definition,[new_symbol(c6_95_1_4_2__orders_1),file(orders_1,c6_95_1_4_2__orders_1)]), [interesting(0.35),axiom,file(orders_1,c6_95_1_4_2__orders_1)]). fof(e3_95_1_4_2__orders_1,plain, ( r2_hidden(k4_tarski(c1_95_1_4_2__orders_1,c2_95_1_4_2__orders_1),c4_95_1_4_2__orders_1) & r2_hidden(c4_95_1_4_2__orders_1,c1_95_1__orders_1) ), inference(consider,[status(thm),assumptions([dt_c1_95_1_4_2__orders_1,dt_c2_95_1_4_2__orders_1,dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1,dt_c3_95_1_4_2__orders_1,e1_95_1_4_2__orders_1])],[dh_c4_95_1_4_2__orders_1,e2_95_1_4_2__orders_1]), [interesting(0.35),file(orders_1,e3_95_1_4_2__orders_1),[file(orders_1,e3_95_1_4_2__orders_1)]]). fof(e8_95_1_4_2__orders_1,plain,( ? [A] : ( v1_relat_1(A) & c4_95_1_4_2__orders_1 = A & r1_tarski(c1_95__orders_1,A) & r2_orders_1(A,c2_95__orders_1) & k3_relat_1(A) = c2_95__orders_1 ) ), inference(mizar_by,[status(thm),assumptions([dt_c1_95_1_4_2__orders_1,dt_c2_95_1_4_2__orders_1,dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1,dt_c3_95_1_4_2__orders_1,e1_95_1_4_2__orders_1])],[cc2_finset_1,fc14_finset_1,fc9_finset_1,rc1_finset_1,rc3_finset_1,rc4_finset_1,commutativity_k2_tarski,commutativity_k2_xboole_0,idempotence_k2_xboole_0,existence_m1_subset_1,dt_k1_relat_1,dt_k1_tarski,dt_k2_relat_1,dt_k2_tarski,dt_k2_xboole_0,dt_m1_subset_1,cc1_finset_1,cc1_ordinal1,cc1_relset_1,cc2_ordinal1,cc3_ordinal1,fc1_finset_1,fc2_finset_1,fc2_subset_1,fc3_subset_1,fc4_subset_1,rc1_ordinal1,rc1_partfun1,rc1_subset_1,rc2_ordinal1,rc2_subset_1,rc3_ordinal1,t1_boole,t2_subset,t4_subset,t5_subset,t8_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k3_relat_1,dt_k4_tarski,dt_c1_95__orders_1,dt_c1_95_1__orders_1,dt_c1_95_1_4_2__orders_1,dt_c2_95__orders_1,dt_c2_95_1_4_2__orders_1,dt_c3_95__orders_1,dt_c4_95_1_4_2__orders_1,fc1_subset_1,fc2_ordinal1,t1_subset,t3_subset,t6_boole,t7_boole,d6_relat_1,d5_tarski,e3_95__orders_1,e1_95_1__orders_1,e3_95_1_4_2__orders_1]), [interesting(0.35),file(orders_1,e8_95_1_4_2__orders_1),[file(orders_1,e8_95_1_4_2__orders_1)]]). fof(dt_c6_95_1_4_2__orders_1,plain,( v1_relat_1(c6_95_1_4_2__orders_1) ), inference(consider,[status(thm),assumptions([dt_c1_95_1_4_2__orders_1,dt_c2_95_1_4_2__orders_1,dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1,dt_c3_95_1_4_2__orders_1,e1_95_1_4_2__orders_1])],[dh_c6_95_1_4_2__orders_1,e8_95_1_4_2__orders_1]), [interesting(0.35),file(orders_1,c6_95_1_4_2__orders_1),[file(orders_1,c6_95_1_4_2__orders_1)]]). fof(dh_c7_95_1_4_2__orders_1,definition, ( ? [A] : ( v1_relat_1(A) & c5_95_1_4_2__orders_1 = A & r1_tarski(c1_95__orders_1,A) & r2_orders_1(A,c2_95__orders_1) & k3_relat_1(A) = c2_95__orders_1 ) => ( v1_relat_1(c7_95_1_4_2__orders_1) & c5_95_1_4_2__orders_1 = c7_95_1_4_2__orders_1 & r1_tarski(c1_95__orders_1,c7_95_1_4_2__orders_1) & r2_orders_1(c7_95_1_4_2__orders_1,c2_95__orders_1) & k3_relat_1(c7_95_1_4_2__orders_1) = c2_95__orders_1 ) ), introduced(definition,[new_symbol(c7_95_1_4_2__orders_1),file(orders_1,c7_95_1_4_2__orders_1)]), [interesting(0.35),axiom,file(orders_1,c7_95_1_4_2__orders_1)]). fof(e5_95_1_4_2__orders_1,plain, ( r2_hidden(k4_tarski(c2_95_1_4_2__orders_1,c3_95_1_4_2__orders_1),c5_95_1_4_2__orders_1) & r2_hidden(c5_95_1_4_2__orders_1,c1_95_1__orders_1) ), inference(consider,[status(thm),assumptions([dt_c1_95_1_4_2__orders_1,dt_c2_95_1_4_2__orders_1,dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1,dt_c3_95_1_4_2__orders_1,e1_95_1_4_2__orders_1])],[dh_c5_95_1_4_2__orders_1,e4_95_1_4_2__orders_1]), [interesting(0.35),file(orders_1,e5_95_1_4_2__orders_1),[file(orders_1,e5_95_1_4_2__orders_1)]]). fof(e10_95_1_4_2__orders_1,plain,( ? [A] : ( v1_relat_1(A) & c5_95_1_4_2__orders_1 = A & r1_tarski(c1_95__orders_1,A) & r2_orders_1(A,c2_95__orders_1) & k3_relat_1(A) = c2_95__orders_1 ) ), inference(mizar_by,[status(thm),assumptions([dt_c1_95_1_4_2__orders_1,dt_c2_95_1_4_2__orders_1,dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1,dt_c3_95_1_4_2__orders_1,e1_95_1_4_2__orders_1])],[cc2_finset_1,fc14_finset_1,fc9_finset_1,rc1_finset_1,rc3_finset_1,rc4_finset_1,commutativity_k2_tarski,commutativity_k2_xboole_0,idempotence_k2_xboole_0,existence_m1_subset_1,dt_k1_relat_1,dt_k1_tarski,dt_k2_relat_1,dt_k2_tarski,dt_k2_xboole_0,dt_m1_subset_1,cc1_finset_1,cc1_ordinal1,cc1_relset_1,cc2_ordinal1,cc3_ordinal1,fc1_finset_1,fc2_finset_1,fc2_subset_1,fc3_subset_1,fc4_subset_1,rc1_ordinal1,rc1_partfun1,rc1_subset_1,rc2_ordinal1,rc2_subset_1,rc3_ordinal1,t1_boole,t2_subset,t4_subset,t5_subset,t8_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k3_relat_1,dt_k4_tarski,dt_c1_95__orders_1,dt_c1_95_1__orders_1,dt_c2_95__orders_1,dt_c2_95_1_4_2__orders_1,dt_c3_95__orders_1,dt_c3_95_1_4_2__orders_1,dt_c5_95_1_4_2__orders_1,fc1_subset_1,fc2_ordinal1,t1_subset,t3_subset,t6_boole,t7_boole,d6_relat_1,d5_tarski,e3_95__orders_1,e1_95_1__orders_1,e5_95_1_4_2__orders_1]), [interesting(0.35),file(orders_1,e10_95_1_4_2__orders_1),[file(orders_1,e10_95_1_4_2__orders_1)]]). fof(dt_c7_95_1_4_2__orders_1,plain,( v1_relat_1(c7_95_1_4_2__orders_1) ), inference(consider,[status(thm),assumptions([dt_c1_95_1_4_2__orders_1,dt_c2_95_1_4_2__orders_1,dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1,dt_c3_95_1_4_2__orders_1,e1_95_1_4_2__orders_1])],[dh_c7_95_1_4_2__orders_1,e10_95_1_4_2__orders_1]), [interesting(0.35),file(orders_1,c7_95_1_4_2__orders_1),[file(orders_1,c7_95_1_4_2__orders_1)]]). fof(e9_95_1_4_2__orders_1,plain, ( c4_95_1_4_2__orders_1 = c6_95_1_4_2__orders_1 & r1_tarski(c1_95__orders_1,c6_95_1_4_2__orders_1) & r2_orders_1(c6_95_1_4_2__orders_1,c2_95__orders_1) & k3_relat_1(c6_95_1_4_2__orders_1) = c2_95__orders_1 ), inference(consider,[status(thm),assumptions([dt_c1_95_1_4_2__orders_1,dt_c2_95_1_4_2__orders_1,dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1,dt_c3_95_1_4_2__orders_1,e1_95_1_4_2__orders_1])],[dh_c6_95_1_4_2__orders_1,e8_95_1_4_2__orders_1]), [interesting(0.35),file(orders_1,e9_95_1_4_2__orders_1),[file(orders_1,e9_95_1_4_2__orders_1)]]). fof(e11_95_1_4_2__orders_1,plain, ( c5_95_1_4_2__orders_1 = c7_95_1_4_2__orders_1 & r1_tarski(c1_95__orders_1,c7_95_1_4_2__orders_1) & r2_orders_1(c7_95_1_4_2__orders_1,c2_95__orders_1) & k3_relat_1(c7_95_1_4_2__orders_1) = c2_95__orders_1 ), inference(consider,[status(thm),assumptions([dt_c1_95_1_4_2__orders_1,dt_c2_95_1_4_2__orders_1,dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1,dt_c3_95_1_4_2__orders_1,e1_95_1_4_2__orders_1])],[dh_c7_95_1_4_2__orders_1,e10_95_1_4_2__orders_1]), [interesting(0.35),file(orders_1,e11_95_1_4_2__orders_1),[file(orders_1,e11_95_1_4_2__orders_1)]]). fof(e12_95_1_4_2__orders_1,plain, ( r8_relat_2(c6_95_1_4_2__orders_1,c2_95__orders_1) & r8_relat_2(c7_95_1_4_2__orders_1,c2_95__orders_1) ), inference(mizar_by,[status(thm),assumptions([dt_c1_95_1_4_2__orders_1,dt_c2_95_1_4_2__orders_1,dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1,dt_c3_95_1_4_2__orders_1,e1_95_1_4_2__orders_1])],[rc1_partfun1,rc2_ordinal1,antisymmetry_r2_hidden,dt_k1_xboole_0,cc1_ordinal1,cc2_finset_1,cc2_ordinal1,fc2_ordinal1,fc9_finset_1,rc1_finset_1,rc1_ordinal1,rc3_finset_1,rc3_ordinal1,rc4_finset_1,t1_boole,t1_subset,t4_subset,t5_subset,cc1_finset_1,cc3_ordinal1,rc1_subset_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,existence_m1_subset_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k2_relat_1,dt_k2_xboole_0,dt_m1_subset_1,fc1_subset_1,reflexivity_r1_tarski,dt_k3_relat_1,dt_c1_95__orders_1,dt_c2_95__orders_1,dt_c4_95_1_4_2__orders_1,dt_c5_95_1_4_2__orders_1,dt_c6_95_1_4_2__orders_1,dt_c7_95_1_4_2__orders_1,t3_subset,d6_relat_1,e9_95_1_4_2__orders_1,e11_95_1_4_2__orders_1,d7_orders_1]), [interesting(0.35),file(orders_1,e12_95_1_4_2__orders_1),[file(orders_1,e12_95_1_4_2__orders_1)]]). fof(symmetry_r3_xboole_0,theorem,( ! [A,B] : ( r3_xboole_0(A,B) => r3_xboole_0(B,A) ) ), file(xboole_0,r3_xboole_0), [interesting(0.9),axiom,file(xboole_0,r3_xboole_0)]). fof(reflexivity_r3_xboole_0,theorem,( ! [A,B] : r3_xboole_0(A,A) ), file(xboole_0,r3_xboole_0), [interesting(0.9),axiom,file(xboole_0,r3_xboole_0)]). fof(d9_ordinal1,definition,( ! [A] : ( v6_ordinal1(A) <=> ! [B,C] : ( ( r2_hidden(B,A) & r2_hidden(C,A) ) => r3_xboole_0(B,C) ) ) ), file(ordinal1,d9_ordinal1), [interesting(0.9),axiom,file(ordinal1,d9_ordinal1)]). fof(e6_95_1_4_2__orders_1,plain,( r3_xboole_0(c4_95_1_4_2__orders_1,c5_95_1_4_2__orders_1) ), inference(mizar_by,[status(thm),assumptions([e2_95_1__orders_1,dt_c1_95_1_4_2__orders_1,dt_c2_95_1_4_2__orders_1,dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1,dt_c3_95_1_4_2__orders_1,e1_95_1_4_2__orders_1])],[rc1_partfun1,rc2_ordinal1,dt_k1_xboole_0,cc1_ordinal1,cc2_ordinal1,fc2_ordinal1,rc1_finset_1,rc1_ordinal1,rc3_ordinal1,commutativity_k2_tarski,existence_m1_subset_1,dt_k1_tarski,dt_k2_tarski,dt_m1_subset_1,cc1_finset_1,cc3_ordinal1,fc1_finset_1,fc2_finset_1,fc2_subset_1,fc3_subset_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,symmetry_r3_xboole_0,reflexivity_r3_xboole_0,dt_k4_tarski,dt_c1_95_1__orders_1,dt_c1_95_1_4_2__orders_1,dt_c2_95_1_4_2__orders_1,dt_c3_95_1_4_2__orders_1,dt_c4_95_1_4_2__orders_1,dt_c5_95_1_4_2__orders_1,t1_subset,t7_boole,d5_tarski,e2_95_1__orders_1,e3_95_1_4_2__orders_1,e5_95_1_4_2__orders_1,d9_ordinal1]), [interesting(0.35),file(orders_1,e6_95_1_4_2__orders_1),[file(orders_1,e6_95_1_4_2__orders_1)]]). fof(d9_xboole_0,definition,( ! [A,B] : ( r3_xboole_0(A,B) <=> ( r1_tarski(A,B) | r1_tarski(B,A) ) ) ), file(xboole_0,d9_xboole_0), [interesting(0.9),axiom,file(xboole_0,d9_xboole_0)]). fof(e7_95_1_4_2__orders_1,plain, ( r1_tarski(c4_95_1_4_2__orders_1,c5_95_1_4_2__orders_1) | r1_tarski(c5_95_1_4_2__orders_1,c4_95_1_4_2__orders_1) ), inference(mizar_by,[status(thm),assumptions([e2_95_1__orders_1,dt_c1_95_1_4_2__orders_1,dt_c2_95_1_4_2__orders_1,dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1,dt_c3_95_1_4_2__orders_1,e1_95_1_4_2__orders_1])],[rc1_partfun1,rc2_ordinal1,antisymmetry_r2_hidden,dt_k1_xboole_0,cc1_ordinal1,cc2_finset_1,cc2_ordinal1,fc2_ordinal1,rc1_finset_1,rc1_ordinal1,rc3_finset_1,rc3_ordinal1,rc4_finset_1,t1_subset,t4_subset,t5_subset,t8_boole,cc1_finset_1,cc3_ordinal1,rc1_subset_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,fc1_subset_1,reflexivity_r1_tarski,symmetry_r3_xboole_0,reflexivity_r3_xboole_0,dt_c4_95_1_4_2__orders_1,dt_c5_95_1_4_2__orders_1,t3_subset,e6_95_1_4_2__orders_1,d9_xboole_0]), [interesting(0.35),file(orders_1,e7_95_1_4_2__orders_1),[file(orders_1,e7_95_1_4_2__orders_1)]]). fof(e13_95_1_4_2__orders_1,plain, ( r2_hidden(k4_tarski(c1_95_1_4_2__orders_1,c3_95_1_4_2__orders_1),c6_95_1_4_2__orders_1) | r2_hidden(k4_tarski(c1_95_1_4_2__orders_1,c3_95_1_4_2__orders_1),c7_95_1_4_2__orders_1) ), inference(mizar_by,[status(thm),assumptions([e2_95_1__orders_1,dt_c1_95_1_4_2__orders_1,dt_c2_95_1_4_2__orders_1,dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1,dt_c3_95_1_4_2__orders_1,e1_95_1_4_2__orders_1])],[rc1_partfun1,rc2_ordinal1,dt_k1_xboole_0,cc1_ordinal1,cc2_finset_1,cc2_ordinal1,fc2_ordinal1,fc4_ordinal1,fc9_finset_1,rc1_finset_1,rc1_ordinal1,rc3_finset_1,rc3_ordinal1,rc4_finset_1,t1_boole,commutativity_k2_tarski,commutativity_k2_xboole_0,idempotence_k2_xboole_0,existence_m1_subset_1,dt_k1_relat_1,dt_k1_tarski,dt_k1_zfmisc_1,dt_k2_relat_1,dt_k2_tarski,dt_k2_xboole_0,dt_k3_tarski,dt_m1_subset_1,cc1_finset_1,cc3_ordinal1,fc1_finset_1,fc1_subset_1,fc2_finset_1,fc2_subset_1,fc3_subset_1,rc1_subset_1,rc2_subset_1,t2_subset,t4_subset,t5_subset,t6_boole,t8_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k3_relat_1,dt_k4_tarski,dt_c1_95__orders_1,dt_c1_95_1__orders_1,dt_c1_95_1_4_2__orders_1,dt_c2_95__orders_1,dt_c2_95_1_4_2__orders_1,dt_c3_95_1__orders_1,dt_c3_95_1_4_2__orders_1,dt_c4_95_1_4_2__orders_1,dt_c5_95_1_4_2__orders_1,dt_c6_95_1_4_2__orders_1,dt_c7_95_1_4_2__orders_1,de_c3_95_1__orders_1,t1_subset,t3_subset,t7_boole,d6_relat_1,d5_tarski,e12_95_1_4_2__orders_1,e1_95_1_4_2__orders_1,e3_95_1_4_2__orders_1,e5_95_1_4_2__orders_1,e7_95_1_4_2__orders_1,e9_95_1_4_2__orders_1,e11_95_1_4_2__orders_1,d8_relat_2]), [interesting(0.35),file(orders_1,e13_95_1_4_2__orders_1),[file(orders_1,e13_95_1_4_2__orders_1)]]). fof(e14_95_1_4_2__orders_1,plain,( r2_hidden(k4_tarski(c1_95_1_4_2__orders_1,c3_95_1_4_2__orders_1),c3_95_1__orders_1) ), inference(mizar_by,[status(thm),assumptions([e2_95_1__orders_1,dt_c1_95_1_4_2__orders_1,dt_c2_95_1_4_2__orders_1,dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1,dt_c3_95_1_4_2__orders_1,e1_95_1_4_2__orders_1])],[rc1_partfun1,rc2_ordinal1,dt_k1_xboole_0,cc1_ordinal1,cc2_finset_1,cc2_ordinal1,fc2_ordinal1,fc4_ordinal1,fc9_finset_1,rc1_finset_1,rc1_ordinal1,rc3_finset_1,rc3_ordinal1,rc4_finset_1,t1_boole,commutativity_k2_tarski,commutativity_k2_xboole_0,idempotence_k2_xboole_0,existence_m1_subset_1,dt_k1_relat_1,dt_k1_tarski,dt_k1_zfmisc_1,dt_k2_relat_1,dt_k2_tarski,dt_k2_xboole_0,dt_m1_subset_1,cc1_finset_1,cc3_ordinal1,fc1_finset_1,fc1_subset_1,fc2_finset_1,fc2_subset_1,fc3_subset_1,rc1_subset_1,rc2_subset_1,t2_subset,t4_subset,t5_subset,t6_boole,t8_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k3_relat_1,dt_k3_tarski,dt_k4_tarski,dt_c1_95__orders_1,dt_c1_95_1__orders_1,dt_c1_95_1_4_2__orders_1,dt_c2_95__orders_1,dt_c2_95_1_4_2__orders_1,dt_c3_95_1__orders_1,dt_c3_95_1_4_2__orders_1,dt_c4_95_1_4_2__orders_1,dt_c5_95_1_4_2__orders_1,dt_c6_95_1_4_2__orders_1,dt_c7_95_1_4_2__orders_1,de_c3_95_1__orders_1,t1_subset,t3_subset,t7_boole,d6_relat_1,d5_tarski,e13_95_1_4_2__orders_1,e3_95_1_4_2__orders_1,e5_95_1_4_2__orders_1,e9_95_1_4_2__orders_1,e11_95_1_4_2__orders_1,d4_tarski]), [interesting(0.35),file(orders_1,e14_95_1_4_2__orders_1),[file(orders_1,e14_95_1_4_2__orders_1)]]). fof(i5_95_1_4_2__orders_1,theorem,( $true ), introduced(tautology,[file(orders_1,i5_95_1_4_2__orders_1)]), [interesting(0.35),trivial,file(orders_1,i5_95_1_4_2__orders_1)]). fof(i4_95_1_4_2__orders_1,plain,( r2_hidden(k4_tarski(c1_95_1_4_2__orders_1,c3_95_1_4_2__orders_1),c3_95_1__orders_1) ), inference(conclusion,[status(thm),assumptions([e2_95_1__orders_1,dt_c1_95_1_4_2__orders_1,dt_c2_95_1_4_2__orders_1,dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1,dt_c3_95_1_4_2__orders_1,e1_95_1_4_2__orders_1])],[e14_95_1_4_2__orders_1,i5_95_1_4_2__orders_1]), [interesting(0.35),file(orders_1,i4_95_1_4_2__orders_1),[file(orders_1,i4_95_1_4_2__orders_1)]]). fof(i3_95_1_4_2__orders_1,plain,( ~ ( r2_hidden(c1_95_1_4_2__orders_1,c2_95__orders_1) & r2_hidden(c2_95_1_4_2__orders_1,c2_95__orders_1) & r2_hidden(c3_95_1_4_2__orders_1,c2_95__orders_1) & r2_hidden(k4_tarski(c1_95_1_4_2__orders_1,c2_95_1_4_2__orders_1),c3_95_1__orders_1) & r2_hidden(k4_tarski(c2_95_1_4_2__orders_1,c3_95_1_4_2__orders_1),c3_95_1__orders_1) & ~ r2_hidden(k4_tarski(c1_95_1_4_2__orders_1,c3_95_1_4_2__orders_1),c3_95_1__orders_1) ) ), inference(discharge_asm,[status(thm),assumptions([e2_95_1__orders_1,dt_c1_95_1_4_2__orders_1,dt_c2_95_1_4_2__orders_1,dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1,dt_c3_95_1_4_2__orders_1]),discharge_asm(discharge,[e1_95_1_4_2__orders_1])],[e1_95_1_4_2__orders_1,i4_95_1_4_2__orders_1]), [interesting(0.35),file(orders_1,i3_95_1_4_2__orders_1),[file(orders_1,i3_95_1_4_2__orders_1)]]). fof(i3_95_1_4_2_tmp__orders_1,plain,( ~ ( r2_hidden(c1_95_1_4_2__orders_1,c2_95__orders_1) & r2_hidden(c2_95_1_4_2__orders_1,c2_95__orders_1) & r2_hidden(c3_95_1_4_2__orders_1,c2_95__orders_1) & r2_hidden(k4_tarski(c1_95_1_4_2__orders_1,c2_95_1_4_2__orders_1),c3_95_1__orders_1) & r2_hidden(k4_tarski(c2_95_1_4_2__orders_1,c3_95_1_4_2__orders_1),c3_95_1__orders_1) & ~ r2_hidden(k4_tarski(c1_95_1_4_2__orders_1,c3_95_1_4_2__orders_1),c3_95_1__orders_1) ) ), inference(discharge_asm,[status(thm),assumptions([e2_95_1__orders_1,dt_c1_95_1_4_2__orders_1,dt_c2_95_1_4_2__orders_1,dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1]),discharge_asm(discharge,[dt_c3_95_1_4_2__orders_1])],[dt_c3_95_1_4_2__orders_1,i3_95_1_4_2__orders_1]), [interesting(0.35),i2_95_1_4_2__orders_1]). fof(i2_95_1_4_2__orders_1,plain,( ! [A] : ~ ( r2_hidden(c1_95_1_4_2__orders_1,c2_95__orders_1) & r2_hidden(c2_95_1_4_2__orders_1,c2_95__orders_1) & r2_hidden(A,c2_95__orders_1) & r2_hidden(k4_tarski(c1_95_1_4_2__orders_1,c2_95_1_4_2__orders_1),c3_95_1__orders_1) & r2_hidden(k4_tarski(c2_95_1_4_2__orders_1,A),c3_95_1__orders_1) & ~ r2_hidden(k4_tarski(c1_95_1_4_2__orders_1,A),c3_95_1__orders_1) ) ), inference(let,[status(thm),assumptions([e2_95_1__orders_1,dt_c1_95_1_4_2__orders_1,dt_c2_95_1_4_2__orders_1,dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1])],[i3_95_1_4_2_tmp__orders_1,dh_c3_95_1_4_2__orders_1]), [interesting(0.35),file(orders_1,i2_95_1_4_2__orders_1),[file(orders_1,i2_95_1_4_2__orders_1)]]). fof(i2_95_1_4_2_tmp__orders_1,plain,( ! [A] : ~ ( r2_hidden(c1_95_1_4_2__orders_1,c2_95__orders_1) & r2_hidden(c2_95_1_4_2__orders_1,c2_95__orders_1) & r2_hidden(A,c2_95__orders_1) & r2_hidden(k4_tarski(c1_95_1_4_2__orders_1,c2_95_1_4_2__orders_1),c3_95_1__orders_1) & r2_hidden(k4_tarski(c2_95_1_4_2__orders_1,A),c3_95_1__orders_1) & ~ r2_hidden(k4_tarski(c1_95_1_4_2__orders_1,A),c3_95_1__orders_1) ) ), inference(discharge_asm,[status(thm),assumptions([e2_95_1__orders_1,dt_c1_95_1_4_2__orders_1,dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1]),discharge_asm(discharge,[dt_c2_95_1_4_2__orders_1])],[dt_c2_95_1_4_2__orders_1,i2_95_1_4_2__orders_1]), [interesting(0.35),i1_95_1_4_2__orders_1]). fof(i1_95_1_4_2__orders_1,plain,( ! [A,B] : ~ ( r2_hidden(c1_95_1_4_2__orders_1,c2_95__orders_1) & r2_hidden(A,c2_95__orders_1) & r2_hidden(B,c2_95__orders_1) & r2_hidden(k4_tarski(c1_95_1_4_2__orders_1,A),c3_95_1__orders_1) & r2_hidden(k4_tarski(A,B),c3_95_1__orders_1) & ~ r2_hidden(k4_tarski(c1_95_1_4_2__orders_1,B),c3_95_1__orders_1) ) ), inference(let,[status(thm),assumptions([e2_95_1__orders_1,dt_c1_95_1_4_2__orders_1,dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1])],[i2_95_1_4_2_tmp__orders_1,dh_c2_95_1_4_2__orders_1]), [interesting(0.35),file(orders_1,i1_95_1_4_2__orders_1),[file(orders_1,i1_95_1_4_2__orders_1)]]). fof(i1_95_1_4_2_tmp__orders_1,plain,( ! [A,B] : ~ ( r2_hidden(c1_95_1_4_2__orders_1,c2_95__orders_1) & r2_hidden(A,c2_95__orders_1) & r2_hidden(B,c2_95__orders_1) & r2_hidden(k4_tarski(c1_95_1_4_2__orders_1,A),c3_95_1__orders_1) & r2_hidden(k4_tarski(A,B),c3_95_1__orders_1) & ~ r2_hidden(k4_tarski(c1_95_1_4_2__orders_1,B),c3_95_1__orders_1) ) ), inference(discharge_asm,[status(thm),assumptions([e2_95_1__orders_1,dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1]),discharge_asm(discharge,[dt_c1_95_1_4_2__orders_1])],[dt_c1_95_1_4_2__orders_1,i1_95_1_4_2__orders_1]), [interesting(0.5),e2_95_1_4__orders_1]). fof(e2_95_1_4__orders_1,plain,( r8_relat_2(c3_95_1__orders_1,c2_95__orders_1) ), inference(let,[status(thm),assumptions([e2_95_1__orders_1,dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1])],[i1_95_1_4_2_tmp__orders_1,antisymmetry_r2_hidden,dt_k4_tarski,dt_c2_95__orders_1,dt_c3_95_1__orders_1,d8_relat_2,dh_c1_95_1_4_2__orders_1]), [interesting(0.5),file(orders_1,e2_95_1_4__orders_1),[file(orders_1,e2_95_1_4__orders_1)]]). fof(dt_c1_95_1_4_3__orders_1,assumption,( $true ), introduced(assumption,[file(orders_1,c1_95_1_4_3__orders_1)]), [interesting(0.35),axiom,file(orders_1,c1_95_1_4_3__orders_1)]). 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(dh_c1_95_1_4_3__orders_1,definition, ( ! [A] : ~ ( r2_hidden(c1_95_1_4_3__orders_1,c2_95__orders_1) & r2_hidden(A,c2_95__orders_1) & r2_hidden(k4_tarski(c1_95_1_4_3__orders_1,A),c3_95_1__orders_1) & r2_hidden(k4_tarski(A,c1_95_1_4_3__orders_1),c3_95_1__orders_1) & c1_95_1_4_3__orders_1 != A ) => ! [B,C] : ~ ( r2_hidden(B,c2_95__orders_1) & r2_hidden(C,c2_95__orders_1) & r2_hidden(k4_tarski(B,C),c3_95_1__orders_1) & r2_hidden(k4_tarski(C,B),c3_95_1__orders_1) & B != C ) ), introduced(definition,[new_symbol(c1_95_1_4_3__orders_1),file(orders_1,c1_95_1_4_3__orders_1)]), [interesting(0.35),axiom,file(orders_1,c1_95_1_4_3__orders_1)]). fof(dh_c2_95_1_4_3__orders_1,definition, ( ~ ( r2_hidden(c1_95_1_4_3__orders_1,c2_95__orders_1) & r2_hidden(c2_95_1_4_3__orders_1,c2_95__orders_1) & r2_hidden(k4_tarski(c1_95_1_4_3__orders_1,c2_95_1_4_3__orders_1),c3_95_1__orders_1) & r2_hidden(k4_tarski(c2_95_1_4_3__orders_1,c1_95_1_4_3__orders_1),c3_95_1__orders_1) & c1_95_1_4_3__orders_1 != c2_95_1_4_3__orders_1 ) => ! [A] : ~ ( r2_hidden(c1_95_1_4_3__orders_1,c2_95__orders_1) & r2_hidden(A,c2_95__orders_1) & r2_hidden(k4_tarski(c1_95_1_4_3__orders_1,A),c3_95_1__orders_1) & r2_hidden(k4_tarski(A,c1_95_1_4_3__orders_1),c3_95_1__orders_1) & c1_95_1_4_3__orders_1 != A ) ), introduced(definition,[new_symbol(c2_95_1_4_3__orders_1),file(orders_1,c2_95_1_4_3__orders_1)]), [interesting(0.35),axiom,file(orders_1,c2_95_1_4_3__orders_1)]). fof(e1_95_1_4_3__orders_1,assumption, ( r2_hidden(c1_95_1_4_3__orders_1,c2_95__orders_1) & r2_hidden(c2_95_1_4_3__orders_1,c2_95__orders_1) & r2_hidden(k4_tarski(c1_95_1_4_3__orders_1,c2_95_1_4_3__orders_1),c3_95_1__orders_1) & r2_hidden(k4_tarski(c2_95_1_4_3__orders_1,c1_95_1_4_3__orders_1),c3_95_1__orders_1) ), introduced(assumption,[file(orders_1,e1_95_1_4_3__orders_1)]), [interesting(0.35),axiom,file(orders_1,e1_95_1_4_3__orders_1)]). fof(dt_c2_95_1_4_3__orders_1,assumption,( $true ), introduced(assumption,[file(orders_1,c2_95_1_4_3__orders_1)]), [interesting(0.35),axiom,file(orders_1,c2_95_1_4_3__orders_1)]). fof(dh_c3_95_1_4_3__orders_1,definition, ( ? [A] : ( r2_hidden(k4_tarski(c1_95_1_4_3__orders_1,c2_95_1_4_3__orders_1),A) & r2_hidden(A,c1_95_1__orders_1) ) => ( r2_hidden(k4_tarski(c1_95_1_4_3__orders_1,c2_95_1_4_3__orders_1),c3_95_1_4_3__orders_1) & r2_hidden(c3_95_1_4_3__orders_1,c1_95_1__orders_1) ) ), introduced(definition,[new_symbol(c3_95_1_4_3__orders_1),file(orders_1,c3_95_1_4_3__orders_1)]), [interesting(0.35),axiom,file(orders_1,c3_95_1_4_3__orders_1)]). fof(e2_95_1_4_3__orders_1,plain,( ? [A] : ( r2_hidden(k4_tarski(c1_95_1_4_3__orders_1,c2_95_1_4_3__orders_1),A) & r2_hidden(A,c1_95_1__orders_1) ) ), inference(mizar_by,[status(thm),assumptions([dt_c1_95_1_4_3__orders_1,dt_c2_95_1_4_3__orders_1,dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1,e1_95_1_4_3__orders_1])],[rc1_partfun1,rc2_ordinal1,dt_k1_xboole_0,cc1_ordinal1,cc2_ordinal1,fc2_ordinal1,fc4_ordinal1,rc1_finset_1,rc1_ordinal1,rc3_ordinal1,commutativity_k2_tarski,existence_m1_subset_1,dt_k1_tarski,dt_k2_tarski,dt_m1_subset_1,cc1_finset_1,cc3_ordinal1,fc1_finset_1,fc2_finset_1,fc2_subset_1,fc3_subset_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k3_tarski,dt_k4_tarski,dt_c1_95_1__orders_1,dt_c1_95_1_4_3__orders_1,dt_c2_95__orders_1,dt_c2_95_1_4_3__orders_1,dt_c3_95_1__orders_1,de_c3_95_1__orders_1,t1_subset,t7_boole,d5_tarski,e1_95_1_4_3__orders_1,d4_tarski]), [interesting(0.35),file(orders_1,e2_95_1_4_3__orders_1),[file(orders_1,e2_95_1_4_3__orders_1)]]). fof(dt_c3_95_1_4_3__orders_1,plain,( $true ), inference(consider,[status(thm),assumptions([dt_c1_95_1_4_3__orders_1,dt_c2_95_1_4_3__orders_1,dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1,e1_95_1_4_3__orders_1])],[dh_c3_95_1_4_3__orders_1,e2_95_1_4_3__orders_1]), [interesting(0.35),file(orders_1,c3_95_1_4_3__orders_1),[file(orders_1,c3_95_1_4_3__orders_1)]]). fof(dh_c4_95_1_4_3__orders_1,definition, ( ? [A] : ( r2_hidden(k4_tarski(c2_95_1_4_3__orders_1,c1_95_1_4_3__orders_1),A) & r2_hidden(A,c1_95_1__orders_1) ) => ( r2_hidden(k4_tarski(c2_95_1_4_3__orders_1,c1_95_1_4_3__orders_1),c4_95_1_4_3__orders_1) & r2_hidden(c4_95_1_4_3__orders_1,c1_95_1__orders_1) ) ), introduced(definition,[new_symbol(c4_95_1_4_3__orders_1),file(orders_1,c4_95_1_4_3__orders_1)]), [interesting(0.35),axiom,file(orders_1,c4_95_1_4_3__orders_1)]). fof(e4_95_1_4_3__orders_1,plain,( ? [A] : ( r2_hidden(k4_tarski(c2_95_1_4_3__orders_1,c1_95_1_4_3__orders_1),A) & r2_hidden(A,c1_95_1__orders_1) ) ), inference(mizar_by,[status(thm),assumptions([dt_c1_95_1_4_3__orders_1,dt_c2_95_1_4_3__orders_1,dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1,e1_95_1_4_3__orders_1])],[rc1_partfun1,rc2_ordinal1,dt_k1_xboole_0,cc1_ordinal1,cc2_ordinal1,fc2_ordinal1,fc4_ordinal1,rc1_finset_1,rc1_ordinal1,rc3_ordinal1,commutativity_k2_tarski,existence_m1_subset_1,dt_k1_tarski,dt_k2_tarski,dt_m1_subset_1,cc1_finset_1,cc3_ordinal1,fc1_finset_1,fc2_finset_1,fc2_subset_1,fc3_subset_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k3_tarski,dt_k4_tarski,dt_c1_95_1__orders_1,dt_c1_95_1_4_3__orders_1,dt_c2_95__orders_1,dt_c2_95_1_4_3__orders_1,dt_c3_95_1__orders_1,de_c3_95_1__orders_1,t1_subset,t7_boole,d5_tarski,e1_95_1_4_3__orders_1,d4_tarski]), [interesting(0.35),file(orders_1,e4_95_1_4_3__orders_1),[file(orders_1,e4_95_1_4_3__orders_1)]]). fof(dt_c4_95_1_4_3__orders_1,plain,( $true ), inference(consider,[status(thm),assumptions([dt_c1_95_1_4_3__orders_1,dt_c2_95_1_4_3__orders_1,dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1,e1_95_1_4_3__orders_1])],[dh_c4_95_1_4_3__orders_1,e4_95_1_4_3__orders_1]), [interesting(0.35),file(orders_1,c4_95_1_4_3__orders_1),[file(orders_1,c4_95_1_4_3__orders_1)]]). fof(dh_c5_95_1_4_3__orders_1,definition, ( ? [A] : ( v1_relat_1(A) & c3_95_1_4_3__orders_1 = A & r1_tarski(c1_95__orders_1,A) & r2_orders_1(A,c2_95__orders_1) & k3_relat_1(A) = c2_95__orders_1 ) => ( v1_relat_1(c5_95_1_4_3__orders_1) & c3_95_1_4_3__orders_1 = c5_95_1_4_3__orders_1 & r1_tarski(c1_95__orders_1,c5_95_1_4_3__orders_1) & r2_orders_1(c5_95_1_4_3__orders_1,c2_95__orders_1) & k3_relat_1(c5_95_1_4_3__orders_1) = c2_95__orders_1 ) ), introduced(definition,[new_symbol(c5_95_1_4_3__orders_1),file(orders_1,c5_95_1_4_3__orders_1)]), [interesting(0.35),axiom,file(orders_1,c5_95_1_4_3__orders_1)]). fof(e3_95_1_4_3__orders_1,plain, ( r2_hidden(k4_tarski(c1_95_1_4_3__orders_1,c2_95_1_4_3__orders_1),c3_95_1_4_3__orders_1) & r2_hidden(c3_95_1_4_3__orders_1,c1_95_1__orders_1) ), inference(consider,[status(thm),assumptions([dt_c1_95_1_4_3__orders_1,dt_c2_95_1_4_3__orders_1,dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1,e1_95_1_4_3__orders_1])],[dh_c3_95_1_4_3__orders_1,e2_95_1_4_3__orders_1]), [interesting(0.35),file(orders_1,e3_95_1_4_3__orders_1),[file(orders_1,e3_95_1_4_3__orders_1)]]). fof(e8_95_1_4_3__orders_1,plain,( ? [A] : ( v1_relat_1(A) & c3_95_1_4_3__orders_1 = A & r1_tarski(c1_95__orders_1,A) & r2_orders_1(A,c2_95__orders_1) & k3_relat_1(A) = c2_95__orders_1 ) ), inference(mizar_by,[status(thm),assumptions([dt_c1_95_1_4_3__orders_1,dt_c2_95_1_4_3__orders_1,dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1,e1_95_1_4_3__orders_1])],[cc2_finset_1,fc14_finset_1,fc9_finset_1,rc1_finset_1,rc3_finset_1,rc4_finset_1,commutativity_k2_tarski,commutativity_k2_xboole_0,idempotence_k2_xboole_0,existence_m1_subset_1,dt_k1_relat_1,dt_k1_tarski,dt_k2_relat_1,dt_k2_tarski,dt_k2_xboole_0,dt_m1_subset_1,cc1_finset_1,cc1_ordinal1,cc1_relset_1,cc2_ordinal1,cc3_ordinal1,fc1_finset_1,fc2_finset_1,fc2_subset_1,fc3_subset_1,fc4_subset_1,rc1_ordinal1,rc1_partfun1,rc1_subset_1,rc2_ordinal1,rc2_subset_1,rc3_ordinal1,t1_boole,t2_subset,t4_subset,t5_subset,t8_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k3_relat_1,dt_k4_tarski,dt_c1_95__orders_1,dt_c1_95_1__orders_1,dt_c1_95_1_4_3__orders_1,dt_c2_95__orders_1,dt_c2_95_1_4_3__orders_1,dt_c3_95__orders_1,dt_c3_95_1_4_3__orders_1,fc1_subset_1,fc2_ordinal1,t1_subset,t3_subset,t6_boole,t7_boole,d6_relat_1,d5_tarski,e3_95__orders_1,e1_95_1__orders_1,e3_95_1_4_3__orders_1]), [interesting(0.35),file(orders_1,e8_95_1_4_3__orders_1),[file(orders_1,e8_95_1_4_3__orders_1)]]). fof(dt_c5_95_1_4_3__orders_1,plain,( v1_relat_1(c5_95_1_4_3__orders_1) ), inference(consider,[status(thm),assumptions([dt_c1_95_1_4_3__orders_1,dt_c2_95_1_4_3__orders_1,dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1,e1_95_1_4_3__orders_1])],[dh_c5_95_1_4_3__orders_1,e8_95_1_4_3__orders_1]), [interesting(0.35),file(orders_1,c5_95_1_4_3__orders_1),[file(orders_1,c5_95_1_4_3__orders_1)]]). fof(dh_c6_95_1_4_3__orders_1,definition, ( ? [A] : ( v1_relat_1(A) & c4_95_1_4_3__orders_1 = A & r1_tarski(c1_95__orders_1,A) & r2_orders_1(A,c2_95__orders_1) & k3_relat_1(A) = c2_95__orders_1 ) => ( v1_relat_1(c6_95_1_4_3__orders_1) & c4_95_1_4_3__orders_1 = c6_95_1_4_3__orders_1 & r1_tarski(c1_95__orders_1,c6_95_1_4_3__orders_1) & r2_orders_1(c6_95_1_4_3__orders_1,c2_95__orders_1) & k3_relat_1(c6_95_1_4_3__orders_1) = c2_95__orders_1 ) ), introduced(definition,[new_symbol(c6_95_1_4_3__orders_1),file(orders_1,c6_95_1_4_3__orders_1)]), [interesting(0.35),axiom,file(orders_1,c6_95_1_4_3__orders_1)]). fof(e5_95_1_4_3__orders_1,plain, ( r2_hidden(k4_tarski(c2_95_1_4_3__orders_1,c1_95_1_4_3__orders_1),c4_95_1_4_3__orders_1) & r2_hidden(c4_95_1_4_3__orders_1,c1_95_1__orders_1) ), inference(consider,[status(thm),assumptions([dt_c1_95_1_4_3__orders_1,dt_c2_95_1_4_3__orders_1,dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1,e1_95_1_4_3__orders_1])],[dh_c4_95_1_4_3__orders_1,e4_95_1_4_3__orders_1]), [interesting(0.35),file(orders_1,e5_95_1_4_3__orders_1),[file(orders_1,e5_95_1_4_3__orders_1)]]). fof(e10_95_1_4_3__orders_1,plain,( ? [A] : ( v1_relat_1(A) & c4_95_1_4_3__orders_1 = A & r1_tarski(c1_95__orders_1,A) & r2_orders_1(A,c2_95__orders_1) & k3_relat_1(A) = c2_95__orders_1 ) ), inference(mizar_by,[status(thm),assumptions([dt_c1_95_1_4_3__orders_1,dt_c2_95_1_4_3__orders_1,dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1,e1_95_1_4_3__orders_1])],[cc2_finset_1,fc14_finset_1,fc9_finset_1,rc1_finset_1,rc3_finset_1,rc4_finset_1,commutativity_k2_tarski,commutativity_k2_xboole_0,idempotence_k2_xboole_0,existence_m1_subset_1,dt_k1_relat_1,dt_k1_tarski,dt_k2_relat_1,dt_k2_tarski,dt_k2_xboole_0,dt_m1_subset_1,cc1_finset_1,cc1_ordinal1,cc1_relset_1,cc2_ordinal1,cc3_ordinal1,fc1_finset_1,fc2_finset_1,fc2_subset_1,fc3_subset_1,fc4_subset_1,rc1_ordinal1,rc1_partfun1,rc1_subset_1,rc2_ordinal1,rc2_subset_1,rc3_ordinal1,t1_boole,t2_subset,t4_subset,t5_subset,t8_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k3_relat_1,dt_k4_tarski,dt_c1_95__orders_1,dt_c1_95_1__orders_1,dt_c1_95_1_4_3__orders_1,dt_c2_95__orders_1,dt_c2_95_1_4_3__orders_1,dt_c3_95__orders_1,dt_c4_95_1_4_3__orders_1,fc1_subset_1,fc2_ordinal1,t1_subset,t3_subset,t6_boole,t7_boole,d6_relat_1,d5_tarski,e3_95__orders_1,e1_95_1__orders_1,e5_95_1_4_3__orders_1]), [interesting(0.35),file(orders_1,e10_95_1_4_3__orders_1),[file(orders_1,e10_95_1_4_3__orders_1)]]). fof(dt_c6_95_1_4_3__orders_1,plain,( v1_relat_1(c6_95_1_4_3__orders_1) ), inference(consider,[status(thm),assumptions([dt_c1_95_1_4_3__orders_1,dt_c2_95_1_4_3__orders_1,dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1,e1_95_1_4_3__orders_1])],[dh_c6_95_1_4_3__orders_1,e10_95_1_4_3__orders_1]), [interesting(0.35),file(orders_1,c6_95_1_4_3__orders_1),[file(orders_1,c6_95_1_4_3__orders_1)]]). fof(e9_95_1_4_3__orders_1,plain, ( c3_95_1_4_3__orders_1 = c5_95_1_4_3__orders_1 & r1_tarski(c1_95__orders_1,c5_95_1_4_3__orders_1) & r2_orders_1(c5_95_1_4_3__orders_1,c2_95__orders_1) & k3_relat_1(c5_95_1_4_3__orders_1) = c2_95__orders_1 ), inference(consider,[status(thm),assumptions([dt_c1_95_1_4_3__orders_1,dt_c2_95_1_4_3__orders_1,dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1,e1_95_1_4_3__orders_1])],[dh_c5_95_1_4_3__orders_1,e8_95_1_4_3__orders_1]), [interesting(0.35),file(orders_1,e9_95_1_4_3__orders_1),[file(orders_1,e9_95_1_4_3__orders_1)]]). fof(e11_95_1_4_3__orders_1,plain, ( c4_95_1_4_3__orders_1 = c6_95_1_4_3__orders_1 & r1_tarski(c1_95__orders_1,c6_95_1_4_3__orders_1) & r2_orders_1(c6_95_1_4_3__orders_1,c2_95__orders_1) & k3_relat_1(c6_95_1_4_3__orders_1) = c2_95__orders_1 ), inference(consider,[status(thm),assumptions([dt_c1_95_1_4_3__orders_1,dt_c2_95_1_4_3__orders_1,dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1,e1_95_1_4_3__orders_1])],[dh_c6_95_1_4_3__orders_1,e10_95_1_4_3__orders_1]), [interesting(0.35),file(orders_1,e11_95_1_4_3__orders_1),[file(orders_1,e11_95_1_4_3__orders_1)]]). fof(e12_95_1_4_3__orders_1,plain, ( r4_relat_2(c5_95_1_4_3__orders_1,c2_95__orders_1) & r4_relat_2(c6_95_1_4_3__orders_1,c2_95__orders_1) ), inference(mizar_by,[status(thm),assumptions([dt_c1_95_1_4_3__orders_1,dt_c2_95_1_4_3__orders_1,dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1,e1_95_1_4_3__orders_1])],[rc1_partfun1,rc2_ordinal1,antisymmetry_r2_hidden,dt_k1_xboole_0,cc1_ordinal1,cc2_finset_1,cc2_ordinal1,fc2_ordinal1,fc9_finset_1,rc1_finset_1,rc1_ordinal1,rc3_finset_1,rc3_ordinal1,rc4_finset_1,t1_boole,t1_subset,t4_subset,t5_subset,cc1_finset_1,cc3_ordinal1,rc1_subset_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,existence_m1_subset_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k2_relat_1,dt_k2_xboole_0,dt_m1_subset_1,fc1_subset_1,reflexivity_r1_tarski,dt_k3_relat_1,dt_c1_95__orders_1,dt_c2_95__orders_1,dt_c3_95_1_4_3__orders_1,dt_c4_95_1_4_3__orders_1,dt_c5_95_1_4_3__orders_1,dt_c6_95_1_4_3__orders_1,t3_subset,d6_relat_1,e9_95_1_4_3__orders_1,e11_95_1_4_3__orders_1,d7_orders_1]), [interesting(0.35),file(orders_1,e12_95_1_4_3__orders_1),[file(orders_1,e12_95_1_4_3__orders_1)]]). fof(e6_95_1_4_3__orders_1,plain,( r3_xboole_0(c3_95_1_4_3__orders_1,c4_95_1_4_3__orders_1) ), inference(mizar_by,[status(thm),assumptions([e2_95_1__orders_1,dt_c1_95_1_4_3__orders_1,dt_c2_95_1_4_3__orders_1,dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1,e1_95_1_4_3__orders_1])],[rc1_partfun1,rc2_ordinal1,dt_k1_xboole_0,cc1_ordinal1,cc2_ordinal1,fc2_ordinal1,rc1_finset_1,rc1_ordinal1,rc3_ordinal1,commutativity_k2_tarski,existence_m1_subset_1,dt_k1_tarski,dt_k2_tarski,dt_m1_subset_1,cc1_finset_1,cc3_ordinal1,fc1_finset_1,fc2_finset_1,fc2_subset_1,fc3_subset_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,symmetry_r3_xboole_0,reflexivity_r3_xboole_0,dt_k4_tarski,dt_c1_95_1__orders_1,dt_c1_95_1_4_3__orders_1,dt_c2_95_1_4_3__orders_1,dt_c3_95_1_4_3__orders_1,dt_c4_95_1_4_3__orders_1,t1_subset,t7_boole,d5_tarski,e2_95_1__orders_1,e3_95_1_4_3__orders_1,e5_95_1_4_3__orders_1,d9_ordinal1]), [interesting(0.35),file(orders_1,e6_95_1_4_3__orders_1),[file(orders_1,e6_95_1_4_3__orders_1)]]). fof(e7_95_1_4_3__orders_1,plain, ( r1_tarski(c3_95_1_4_3__orders_1,c4_95_1_4_3__orders_1) | r1_tarski(c4_95_1_4_3__orders_1,c3_95_1_4_3__orders_1) ), inference(mizar_by,[status(thm),assumptions([e2_95_1__orders_1,dt_c1_95_1_4_3__orders_1,dt_c2_95_1_4_3__orders_1,dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1,e1_95_1_4_3__orders_1])],[rc1_partfun1,rc2_ordinal1,antisymmetry_r2_hidden,dt_k1_xboole_0,cc1_ordinal1,cc2_finset_1,cc2_ordinal1,fc2_ordinal1,rc1_finset_1,rc1_ordinal1,rc3_finset_1,rc3_ordinal1,rc4_finset_1,t1_subset,t4_subset,t5_subset,t8_boole,cc1_finset_1,cc3_ordinal1,rc1_subset_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,fc1_subset_1,reflexivity_r1_tarski,symmetry_r3_xboole_0,reflexivity_r3_xboole_0,dt_c3_95_1_4_3__orders_1,dt_c4_95_1_4_3__orders_1,t3_subset,e6_95_1_4_3__orders_1,d9_xboole_0]), [interesting(0.35),file(orders_1,e7_95_1_4_3__orders_1),[file(orders_1,e7_95_1_4_3__orders_1)]]). fof(e13_95_1_4_3__orders_1,plain,( c1_95_1_4_3__orders_1 = c2_95_1_4_3__orders_1 ), inference(mizar_by,[status(thm),assumptions([e2_95_1__orders_1,dt_c1_95_1_4_3__orders_1,dt_c2_95_1_4_3__orders_1,dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1,e1_95_1_4_3__orders_1])],[rc1_partfun1,rc2_ordinal1,dt_k1_xboole_0,cc1_ordinal1,cc2_finset_1,cc2_ordinal1,fc2_ordinal1,fc4_ordinal1,fc9_finset_1,rc1_finset_1,rc1_ordinal1,rc3_finset_1,rc3_ordinal1,rc4_finset_1,t1_boole,commutativity_k2_tarski,commutativity_k2_xboole_0,idempotence_k2_xboole_0,existence_m1_subset_1,dt_k1_relat_1,dt_k1_tarski,dt_k1_zfmisc_1,dt_k2_relat_1,dt_k2_tarski,dt_k2_xboole_0,dt_k3_tarski,dt_m1_subset_1,cc1_finset_1,cc3_ordinal1,fc1_finset_1,fc1_subset_1,fc2_finset_1,fc2_subset_1,fc3_subset_1,rc1_subset_1,rc2_subset_1,t2_subset,t4_subset,t5_subset,t6_boole,t8_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k3_relat_1,dt_k4_tarski,dt_c1_95__orders_1,dt_c1_95_1__orders_1,dt_c1_95_1_4_3__orders_1,dt_c2_95__orders_1,dt_c2_95_1_4_3__orders_1,dt_c3_95_1__orders_1,dt_c3_95_1_4_3__orders_1,dt_c4_95_1_4_3__orders_1,dt_c5_95_1_4_3__orders_1,dt_c6_95_1_4_3__orders_1,de_c3_95_1__orders_1,t1_subset,t3_subset,t7_boole,d6_relat_1,d5_tarski,e12_95_1_4_3__orders_1,e1_95_1_4_3__orders_1,e3_95_1_4_3__orders_1,e5_95_1_4_3__orders_1,e7_95_1_4_3__orders_1,e9_95_1_4_3__orders_1,e11_95_1_4_3__orders_1,d4_relat_2]), [interesting(0.35),file(orders_1,e13_95_1_4_3__orders_1),[file(orders_1,e13_95_1_4_3__orders_1)]]). fof(i4_95_1_4_3__orders_1,theorem,( $true ), introduced(tautology,[file(orders_1,i4_95_1_4_3__orders_1)]), [interesting(0.35),trivial,file(orders_1,i4_95_1_4_3__orders_1)]). fof(i3_95_1_4_3__orders_1,plain,( c1_95_1_4_3__orders_1 = c2_95_1_4_3__orders_1 ), inference(conclusion,[status(thm),assumptions([e2_95_1__orders_1,dt_c1_95_1_4_3__orders_1,dt_c2_95_1_4_3__orders_1,dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1,e1_95_1_4_3__orders_1])],[e13_95_1_4_3__orders_1,i4_95_1_4_3__orders_1]), [interesting(0.35),file(orders_1,i3_95_1_4_3__orders_1),[file(orders_1,i3_95_1_4_3__orders_1)]]). fof(i2_95_1_4_3__orders_1,plain,( ~ ( r2_hidden(c1_95_1_4_3__orders_1,c2_95__orders_1) & r2_hidden(c2_95_1_4_3__orders_1,c2_95__orders_1) & r2_hidden(k4_tarski(c1_95_1_4_3__orders_1,c2_95_1_4_3__orders_1),c3_95_1__orders_1) & r2_hidden(k4_tarski(c2_95_1_4_3__orders_1,c1_95_1_4_3__orders_1),c3_95_1__orders_1) & c1_95_1_4_3__orders_1 != c2_95_1_4_3__orders_1 ) ), inference(discharge_asm,[status(thm),assumptions([e2_95_1__orders_1,dt_c1_95_1_4_3__orders_1,dt_c2_95_1_4_3__orders_1,dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1]),discharge_asm(discharge,[e1_95_1_4_3__orders_1])],[e1_95_1_4_3__orders_1,i3_95_1_4_3__orders_1]), [interesting(0.35),file(orders_1,i2_95_1_4_3__orders_1),[file(orders_1,i2_95_1_4_3__orders_1)]]). fof(i2_95_1_4_3_tmp__orders_1,plain,( ~ ( r2_hidden(c1_95_1_4_3__orders_1,c2_95__orders_1) & r2_hidden(c2_95_1_4_3__orders_1,c2_95__orders_1) & r2_hidden(k4_tarski(c1_95_1_4_3__orders_1,c2_95_1_4_3__orders_1),c3_95_1__orders_1) & r2_hidden(k4_tarski(c2_95_1_4_3__orders_1,c1_95_1_4_3__orders_1),c3_95_1__orders_1) & c1_95_1_4_3__orders_1 != c2_95_1_4_3__orders_1 ) ), inference(discharge_asm,[status(thm),assumptions([e2_95_1__orders_1,dt_c1_95_1_4_3__orders_1,dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1]),discharge_asm(discharge,[dt_c2_95_1_4_3__orders_1])],[dt_c2_95_1_4_3__orders_1,i2_95_1_4_3__orders_1]), [interesting(0.35),i1_95_1_4_3__orders_1]). fof(i1_95_1_4_3__orders_1,plain,( ! [A] : ~ ( r2_hidden(c1_95_1_4_3__orders_1,c2_95__orders_1) & r2_hidden(A,c2_95__orders_1) & r2_hidden(k4_tarski(c1_95_1_4_3__orders_1,A),c3_95_1__orders_1) & r2_hidden(k4_tarski(A,c1_95_1_4_3__orders_1),c3_95_1__orders_1) & c1_95_1_4_3__orders_1 != A ) ), inference(let,[status(thm),assumptions([e2_95_1__orders_1,dt_c1_95_1_4_3__orders_1,dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1])],[i2_95_1_4_3_tmp__orders_1,dh_c2_95_1_4_3__orders_1]), [interesting(0.35),file(orders_1,i1_95_1_4_3__orders_1),[file(orders_1,i1_95_1_4_3__orders_1)]]). fof(i1_95_1_4_3_tmp__orders_1,plain,( ! [A] : ~ ( r2_hidden(c1_95_1_4_3__orders_1,c2_95__orders_1) & r2_hidden(A,c2_95__orders_1) & r2_hidden(k4_tarski(c1_95_1_4_3__orders_1,A),c3_95_1__orders_1) & r2_hidden(k4_tarski(A,c1_95_1_4_3__orders_1),c3_95_1__orders_1) & c1_95_1_4_3__orders_1 != A ) ), inference(discharge_asm,[status(thm),assumptions([e2_95_1__orders_1,dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1]),discharge_asm(discharge,[dt_c1_95_1_4_3__orders_1])],[dt_c1_95_1_4_3__orders_1,i1_95_1_4_3__orders_1]), [interesting(0.5),e3_95_1_4__orders_1]). fof(e3_95_1_4__orders_1,plain,( r4_relat_2(c3_95_1__orders_1,c2_95__orders_1) ), inference(let,[status(thm),assumptions([e2_95_1__orders_1,dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1])],[i1_95_1_4_3_tmp__orders_1,antisymmetry_r2_hidden,dt_k4_tarski,dt_c2_95__orders_1,dt_c3_95_1__orders_1,d4_relat_2,dh_c1_95_1_4_3__orders_1]), [interesting(0.5),file(orders_1,e3_95_1_4__orders_1),[file(orders_1,e3_95_1_4__orders_1)]]). fof(i3_95_1_4__orders_1,theorem,( $true ), introduced(tautology,[file(orders_1,i3_95_1_4__orders_1)]), [interesting(0.5),trivial,file(orders_1,i3_95_1_4__orders_1)]). fof(i2_95_1_4__orders_1,plain,( r4_relat_2(c3_95_1__orders_1,c2_95__orders_1) ), inference(conclusion,[status(thm),assumptions([e2_95_1__orders_1,dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1])],[e3_95_1_4__orders_1,i3_95_1_4__orders_1]), [interesting(0.5),file(orders_1,i2_95_1_4__orders_1),[file(orders_1,i2_95_1_4__orders_1)]]). fof(i1_95_1_4__orders_1,plain, ( r8_relat_2(c3_95_1__orders_1,c2_95__orders_1) & r4_relat_2(c3_95_1__orders_1,c2_95__orders_1) ), inference(conclusion,[status(thm),assumptions([e2_95_1__orders_1,dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1])],[e2_95_1_4__orders_1,i2_95_1_4__orders_1]), [interesting(0.5),file(orders_1,i1_95_1_4__orders_1),[file(orders_1,i1_95_1_4__orders_1)]]). fof(e14_95_1__orders_1,plain,( r2_orders_1(c3_95_1__orders_1,c2_95__orders_1) ), inference(conclusion,[status(thm),assumptions([e2_95_1__orders_1,dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1])],[dt_c2_95__orders_1,dt_c3_95_1__orders_1,d7_orders_1,e1_95_1_4__orders_1,i1_95_1_4__orders_1]), [interesting(0.65),file(orders_1,e14_95_1__orders_1),[file(orders_1,e14_95_1__orders_1)]]). fof(dt_c1_95_1_2__orders_1,assumption,( $true ), introduced(assumption,[file(orders_1,c1_95_1_2__orders_1)]), [interesting(0.5),axiom,file(orders_1,c1_95_1_2__orders_1)]). fof(d3_relat_1,definition,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => ( r1_tarski(A,B) <=> ! [C,D] : ( r2_hidden(k4_tarski(C,D),A) => r2_hidden(k4_tarski(C,D),B) ) ) ) ) ), file(relat_1,d3_relat_1), [interesting(0.9),axiom,file(relat_1,d3_relat_1)]). fof(dh_c1_95_1_2__orders_1,definition, ( ! [A] : ~ ( r2_hidden(k4_tarski(c1_95_1_2__orders_1,A),c1_95__orders_1) & ~ r2_hidden(k4_tarski(c1_95_1_2__orders_1,A),c3_95_1__orders_1) ) => ! [B,C] : ~ ( r2_hidden(k4_tarski(B,C),c1_95__orders_1) & ~ r2_hidden(k4_tarski(B,C),c3_95_1__orders_1) ) ), introduced(definition,[new_symbol(c1_95_1_2__orders_1),file(orders_1,c1_95_1_2__orders_1)]), [interesting(0.5),axiom,file(orders_1,c1_95_1_2__orders_1)]). fof(dh_c2_95_1_2__orders_1,definition, ( ~ ( r2_hidden(k4_tarski(c1_95_1_2__orders_1,c2_95_1_2__orders_1),c1_95__orders_1) & ~ r2_hidden(k4_tarski(c1_95_1_2__orders_1,c2_95_1_2__orders_1),c3_95_1__orders_1) ) => ! [A] : ~ ( r2_hidden(k4_tarski(c1_95_1_2__orders_1,A),c1_95__orders_1) & ~ r2_hidden(k4_tarski(c1_95_1_2__orders_1,A),c3_95_1__orders_1) ) ), introduced(definition,[new_symbol(c2_95_1_2__orders_1),file(orders_1,c2_95_1_2__orders_1)]), [interesting(0.5),axiom,file(orders_1,c2_95_1_2__orders_1)]). fof(e1_95_1_2__orders_1,assumption,( r2_hidden(k4_tarski(c1_95_1_2__orders_1,c2_95_1_2__orders_1),c1_95__orders_1) ), introduced(assumption,[file(orders_1,e1_95_1_2__orders_1)]), [interesting(0.5),axiom,file(orders_1,e1_95_1_2__orders_1)]). fof(dt_c2_95_1_2__orders_1,assumption,( $true ), introduced(assumption,[file(orders_1,c2_95_1_2__orders_1)]), [interesting(0.5),axiom,file(orders_1,c2_95_1_2__orders_1)]). fof(e2_95_1_2__orders_1,plain,( r2_hidden(k4_tarski(c1_95_1_2__orders_1,c2_95_1_2__orders_1),c3_95_1__orders_1) ), inference(mizar_by,[status(thm),assumptions([dt_c1_95_1_2__orders_1,dt_c2_95_1_2__orders_1,e1_95_1_2__orders_1,dt_c1_95_1__orders_1,e1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1])],[cc2_finset_1,fc9_finset_1,rc1_finset_1,rc3_finset_1,rc4_finset_1,commutativity_k2_tarski,commutativity_k2_xboole_0,idempotence_k2_xboole_0,existence_m1_subset_1,dt_k1_relat_1,dt_k1_tarski,dt_k1_zfmisc_1,dt_k2_relat_1,dt_k2_tarski,dt_k2_xboole_0,dt_m1_subset_1,cc1_finset_1,cc1_ordinal1,cc2_ordinal1,cc3_ordinal1,fc1_finset_1,fc1_subset_1,fc2_finset_1,fc2_subset_1,fc3_subset_1,fc4_ordinal1,rc1_ordinal1,rc1_partfun1,rc1_subset_1,rc2_ordinal1,rc2_subset_1,rc3_ordinal1,t1_boole,t2_subset,t4_subset,t5_subset,t8_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k3_relat_1,dt_k3_tarski,dt_k4_tarski,dt_c1_95__orders_1,dt_c1_95_1__orders_1,dt_c1_95_1_2__orders_1,dt_c2_95__orders_1,dt_c2_95_1_2__orders_1,dt_c3_95__orders_1,dt_c3_95_1__orders_1,dt_c4_95_1__orders_1,dt_c5_95_1__orders_1,de_c3_95_1__orders_1,fc2_ordinal1,t1_subset,t3_subset,t6_boole,t7_boole,d6_relat_1,d5_tarski,e1_95_1_2__orders_1,e1_95_1__orders_1,e10_95_1__orders_1,d4_tarski]), [interesting(0.5),file(orders_1,e2_95_1_2__orders_1),[file(orders_1,e2_95_1_2__orders_1)]]). fof(i4_95_1_2__orders_1,theorem,( $true ), introduced(tautology,[file(orders_1,i4_95_1_2__orders_1)]), [interesting(0.5),trivial,file(orders_1,i4_95_1_2__orders_1)]). fof(i3_95_1_2__orders_1,plain,( r2_hidden(k4_tarski(c1_95_1_2__orders_1,c2_95_1_2__orders_1),c3_95_1__orders_1) ), inference(conclusion,[status(thm),assumptions([dt_c1_95_1_2__orders_1,dt_c2_95_1_2__orders_1,e1_95_1_2__orders_1,dt_c1_95_1__orders_1,e1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1])],[e2_95_1_2__orders_1,i4_95_1_2__orders_1]), [interesting(0.5),file(orders_1,i3_95_1_2__orders_1),[file(orders_1,i3_95_1_2__orders_1)]]). fof(i2_95_1_2__orders_1,plain,( ~ ( r2_hidden(k4_tarski(c1_95_1_2__orders_1,c2_95_1_2__orders_1),c1_95__orders_1) & ~ r2_hidden(k4_tarski(c1_95_1_2__orders_1,c2_95_1_2__orders_1),c3_95_1__orders_1) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_95_1_2__orders_1,dt_c2_95_1_2__orders_1,dt_c1_95_1__orders_1,e1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1]),discharge_asm(discharge,[e1_95_1_2__orders_1])],[e1_95_1_2__orders_1,i3_95_1_2__orders_1]), [interesting(0.5),file(orders_1,i2_95_1_2__orders_1),[file(orders_1,i2_95_1_2__orders_1)]]). fof(i2_95_1_2_tmp__orders_1,plain,( ~ ( r2_hidden(k4_tarski(c1_95_1_2__orders_1,c2_95_1_2__orders_1),c1_95__orders_1) & ~ r2_hidden(k4_tarski(c1_95_1_2__orders_1,c2_95_1_2__orders_1),c3_95_1__orders_1) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_95_1_2__orders_1,dt_c1_95_1__orders_1,e1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1]),discharge_asm(discharge,[dt_c2_95_1_2__orders_1])],[dt_c2_95_1_2__orders_1,i2_95_1_2__orders_1]), [interesting(0.5),i1_95_1_2__orders_1]). fof(i1_95_1_2__orders_1,plain,( ! [A] : ~ ( r2_hidden(k4_tarski(c1_95_1_2__orders_1,A),c1_95__orders_1) & ~ r2_hidden(k4_tarski(c1_95_1_2__orders_1,A),c3_95_1__orders_1) ) ), inference(let,[status(thm),assumptions([dt_c1_95_1_2__orders_1,dt_c1_95_1__orders_1,e1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1])],[i2_95_1_2_tmp__orders_1,dh_c2_95_1_2__orders_1]), [interesting(0.5),file(orders_1,i1_95_1_2__orders_1),[file(orders_1,i1_95_1_2__orders_1)]]). fof(i1_95_1_2_tmp__orders_1,plain,( ! [A] : ~ ( r2_hidden(k4_tarski(c1_95_1_2__orders_1,A),c1_95__orders_1) & ~ r2_hidden(k4_tarski(c1_95_1_2__orders_1,A),c3_95_1__orders_1) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_95_1__orders_1,e1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1]),discharge_asm(discharge,[dt_c1_95_1_2__orders_1])],[dt_c1_95_1_2__orders_1,i1_95_1_2__orders_1]), [interesting(0.65),e12_95_1__orders_1]). fof(e12_95_1__orders_1,plain,( r1_tarski(c1_95__orders_1,c3_95_1__orders_1) ), inference(let,[status(thm),assumptions([dt_c1_95_1__orders_1,e1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1])],[i1_95_1_2_tmp__orders_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k4_tarski,dt_c1_95__orders_1,dt_c3_95_1__orders_1,d3_relat_1,dh_c1_95_1_2__orders_1]), [interesting(0.65),file(orders_1,e12_95_1__orders_1),[file(orders_1,e12_95_1__orders_1)]]). 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(dt_c1_95_1_3_1__orders_1,assumption,( $true ), introduced(assumption,[file(orders_1,c1_95_1_3_1__orders_1)]), [interesting(0.35),axiom,file(orders_1,c1_95_1_3_1__orders_1)]). fof(dh_c1_95_1_3_1__orders_1,definition, ( ~ ( r2_hidden(c1_95_1_3_1__orders_1,k3_relat_1(c3_95_1__orders_1)) & ~ r2_hidden(c1_95_1_3_1__orders_1,c2_95__orders_1) ) => ! [A] : ~ ( r2_hidden(A,k3_relat_1(c3_95_1__orders_1)) & ~ r2_hidden(A,c2_95__orders_1) ) ), introduced(definition,[new_symbol(c1_95_1_3_1__orders_1),file(orders_1,c1_95_1_3_1__orders_1)]), [interesting(0.35),axiom,file(orders_1,c1_95_1_3_1__orders_1)]). fof(e1_95_1_3_1__orders_1,assumption,( r2_hidden(c1_95_1_3_1__orders_1,k3_relat_1(c3_95_1__orders_1)) ), introduced(assumption,[file(orders_1,e1_95_1_3_1__orders_1)]), [interesting(0.35),axiom,file(orders_1,e1_95_1_3_1__orders_1)]). fof(e1_95_1_3_1_2__orders_1,assumption,( r2_hidden(c1_95_1_3_1__orders_1,k2_relat_1(c3_95_1__orders_1)) ), introduced(assumption,[file(orders_1,e1_95_1_3_1_2__orders_1)]), [interesting(0.2),axiom,file(orders_1,e1_95_1_3_1_2__orders_1)]). fof(dh_c1_95_1_3_1_2__orders_1,definition, ( ? [A] : r2_hidden(k4_tarski(A,c1_95_1_3_1__orders_1),c3_95_1__orders_1) => r2_hidden(k4_tarski(c1_95_1_3_1_2__orders_1,c1_95_1_3_1__orders_1),c3_95_1__orders_1) ), introduced(definition,[new_symbol(c1_95_1_3_1_2__orders_1),file(orders_1,c1_95_1_3_1_2__orders_1)]), [interesting(0.2),axiom,file(orders_1,c1_95_1_3_1_2__orders_1)]). fof(d5_relat_1,definition,( ! [A] : ( v1_relat_1(A) => ! [B] : ( B = k2_relat_1(A) <=> ! [C] : ( r2_hidden(C,B) <=> ? [D] : r2_hidden(k4_tarski(D,C),A) ) ) ) ), file(relat_1,d5_relat_1), [interesting(0.9),axiom,file(relat_1,d5_relat_1)]). fof(e2_95_1_3_1_2__orders_1,plain,( ? [A] : r2_hidden(k4_tarski(A,c1_95_1_3_1__orders_1),c3_95_1__orders_1) ), inference(mizar_by,[status(thm),assumptions([dt_c1_95_1_3_1__orders_1,dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1,e1_95_1_3_1_2__orders_1])],[rc1_partfun1,rc2_ordinal1,dt_k1_xboole_0,cc1_ordinal1,cc2_ordinal1,fc2_ordinal1,fc4_ordinal1,rc1_finset_1,rc1_ordinal1,rc3_ordinal1,commutativity_k2_tarski,existence_m1_subset_1,dt_k1_tarski,dt_k2_tarski,dt_k3_tarski,dt_m1_subset_1,dt_c1_95_1__orders_1,cc1_finset_1,cc3_ordinal1,fc1_finset_1,fc2_finset_1,fc2_subset_1,fc3_subset_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k2_relat_1,dt_k4_tarski,dt_c1_95_1_3_1__orders_1,dt_c3_95_1__orders_1,de_c3_95_1__orders_1,t1_subset,t7_boole,d5_tarski,e1_95_1_3_1_2__orders_1,d5_relat_1]), [interesting(0.2),file(orders_1,e2_95_1_3_1_2__orders_1),[file(orders_1,e2_95_1_3_1_2__orders_1)]]). fof(dt_c1_95_1_3_1_2__orders_1,plain,( $true ), inference(consider,[status(thm),assumptions([dt_c1_95_1_3_1__orders_1,dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1,e1_95_1_3_1_2__orders_1])],[dh_c1_95_1_3_1_2__orders_1,e2_95_1_3_1_2__orders_1]), [interesting(0.2),file(orders_1,c1_95_1_3_1_2__orders_1),[file(orders_1,c1_95_1_3_1_2__orders_1)]]). fof(dh_c2_95_1_3_1_2__orders_1,definition, ( ? [A] : ( r2_hidden(k4_tarski(c1_95_1_3_1_2__orders_1,c1_95_1_3_1__orders_1),A) & r2_hidden(A,c1_95_1__orders_1) ) => ( r2_hidden(k4_tarski(c1_95_1_3_1_2__orders_1,c1_95_1_3_1__orders_1),c2_95_1_3_1_2__orders_1) & r2_hidden(c2_95_1_3_1_2__orders_1,c1_95_1__orders_1) ) ), introduced(definition,[new_symbol(c2_95_1_3_1_2__orders_1),file(orders_1,c2_95_1_3_1_2__orders_1)]), [interesting(0.2),axiom,file(orders_1,c2_95_1_3_1_2__orders_1)]). fof(e3_95_1_3_1_2__orders_1,plain,( r2_hidden(k4_tarski(c1_95_1_3_1_2__orders_1,c1_95_1_3_1__orders_1),c3_95_1__orders_1) ), inference(consider,[status(thm),assumptions([dt_c1_95_1_3_1__orders_1,dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1,e1_95_1_3_1_2__orders_1])],[dh_c1_95_1_3_1_2__orders_1,e2_95_1_3_1_2__orders_1]), [interesting(0.2),file(orders_1,e3_95_1_3_1_2__orders_1),[file(orders_1,e3_95_1_3_1_2__orders_1)]]). fof(e4_95_1_3_1_2__orders_1,plain,( ? [A] : ( r2_hidden(k4_tarski(c1_95_1_3_1_2__orders_1,c1_95_1_3_1__orders_1),A) & r2_hidden(A,c1_95_1__orders_1) ) ), inference(mizar_by,[status(thm),assumptions([dt_c1_95_1_3_1__orders_1,dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1,e1_95_1_3_1_2__orders_1])],[rc1_partfun1,rc2_ordinal1,dt_k1_xboole_0,cc1_ordinal1,cc2_ordinal1,fc2_ordinal1,fc4_ordinal1,rc1_finset_1,rc1_ordinal1,rc3_ordinal1,commutativity_k2_tarski,existence_m1_subset_1,dt_k1_tarski,dt_k2_tarski,dt_m1_subset_1,cc1_finset_1,cc3_ordinal1,fc1_finset_1,fc2_finset_1,fc2_subset_1,fc3_subset_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k3_tarski,dt_k4_tarski,dt_c1_95_1__orders_1,dt_c1_95_1_3_1__orders_1,dt_c1_95_1_3_1_2__orders_1,dt_c3_95_1__orders_1,de_c3_95_1__orders_1,t1_subset,t7_boole,d5_tarski,e3_95_1_3_1_2__orders_1,d4_tarski]), [interesting(0.2),file(orders_1,e4_95_1_3_1_2__orders_1),[file(orders_1,e4_95_1_3_1_2__orders_1)]]). fof(dt_c2_95_1_3_1_2__orders_1,plain,( $true ), inference(consider,[status(thm),assumptions([dt_c1_95_1_3_1__orders_1,dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1,e1_95_1_3_1_2__orders_1])],[dh_c2_95_1_3_1_2__orders_1,e4_95_1_3_1_2__orders_1]), [interesting(0.2),file(orders_1,c2_95_1_3_1_2__orders_1),[file(orders_1,c2_95_1_3_1_2__orders_1)]]). fof(e5_95_1_3_1_2__orders_1,plain, ( r2_hidden(k4_tarski(c1_95_1_3_1_2__orders_1,c1_95_1_3_1__orders_1),c2_95_1_3_1_2__orders_1) & r2_hidden(c2_95_1_3_1_2__orders_1,c1_95_1__orders_1) ), inference(consider,[status(thm),assumptions([dt_c1_95_1_3_1__orders_1,dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1,e1_95_1_3_1_2__orders_1])],[dh_c2_95_1_3_1_2__orders_1,e4_95_1_3_1_2__orders_1]), [interesting(0.2),file(orders_1,e5_95_1_3_1_2__orders_1),[file(orders_1,e5_95_1_3_1_2__orders_1)]]). fof(e6_95_1_3_1_2__orders_1,plain,( ? [A] : ( v1_relat_1(A) & c2_95_1_3_1_2__orders_1 = A & r1_tarski(c1_95__orders_1,A) & r2_orders_1(A,c2_95__orders_1) & k3_relat_1(A) = c2_95__orders_1 ) ), inference(mizar_by,[status(thm),assumptions([dt_c1_95_1_3_1__orders_1,dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1,e1_95_1_3_1_2__orders_1])],[cc2_finset_1,fc14_finset_1,fc9_finset_1,rc1_finset_1,rc3_finset_1,rc4_finset_1,commutativity_k2_tarski,commutativity_k2_xboole_0,idempotence_k2_xboole_0,existence_m1_subset_1,dt_k1_relat_1,dt_k1_tarski,dt_k2_relat_1,dt_k2_tarski,dt_k2_xboole_0,dt_m1_subset_1,cc1_finset_1,cc1_ordinal1,cc1_relset_1,cc2_ordinal1,cc3_ordinal1,fc1_finset_1,fc2_finset_1,fc2_subset_1,fc3_subset_1,fc4_subset_1,rc1_ordinal1,rc1_partfun1,rc1_subset_1,rc2_ordinal1,rc2_subset_1,rc3_ordinal1,t1_boole,t2_subset,t4_subset,t5_subset,t8_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k3_relat_1,dt_k4_tarski,dt_c1_95__orders_1,dt_c1_95_1__orders_1,dt_c1_95_1_3_1__orders_1,dt_c1_95_1_3_1_2__orders_1,dt_c2_95__orders_1,dt_c2_95_1_3_1_2__orders_1,dt_c3_95__orders_1,fc1_subset_1,fc2_ordinal1,t1_subset,t3_subset,t6_boole,t7_boole,d6_relat_1,d5_tarski,e3_95__orders_1,e1_95_1__orders_1,e5_95_1_3_1_2__orders_1]), [interesting(0.2),file(orders_1,e6_95_1_3_1_2__orders_1),[file(orders_1,e6_95_1_3_1_2__orders_1)]]). fof(t30_relat_1,theorem,( ! [A,B,C] : ( v1_relat_1(C) => ( r2_hidden(k4_tarski(A,B),C) => ( r2_hidden(A,k3_relat_1(C)) & r2_hidden(B,k3_relat_1(C)) ) ) ) ), file(relat_1,t30_relat_1), [interesting(0.9),axiom,file(relat_1,t30_relat_1)]). fof(e7_95_1_3_1_2__orders_1,plain,( r2_hidden(c1_95_1_3_1__orders_1,c2_95__orders_1) ), inference(mizar_by,[status(thm),assumptions([dt_c1_95_1_3_1__orders_1,dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1,e1_95_1_3_1_2__orders_1])],[rc1_partfun1,rc2_ordinal1,dt_k1_xboole_0,cc1_ordinal1,cc2_finset_1,cc2_ordinal1,fc2_ordinal1,fc9_finset_1,rc1_finset_1,rc1_ordinal1,rc3_finset_1,rc3_ordinal1,rc4_finset_1,t1_boole,commutativity_k2_tarski,commutativity_k2_xboole_0,idempotence_k2_xboole_0,existence_m1_subset_1,dt_k1_relat_1,dt_k1_tarski,dt_k1_zfmisc_1,dt_k2_relat_1,dt_k2_tarski,dt_k2_xboole_0,dt_m1_subset_1,cc1_finset_1,cc3_ordinal1,fc1_finset_1,fc1_subset_1,fc2_finset_1,fc2_subset_1,fc3_subset_1,rc1_subset_1,rc2_subset_1,t2_subset,t4_subset,t5_subset,t6_boole,t8_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k3_relat_1,dt_k4_tarski,dt_c1_95__orders_1,dt_c1_95_1__orders_1,dt_c1_95_1_3_1__orders_1,dt_c1_95_1_3_1_2__orders_1,dt_c2_95__orders_1,dt_c2_95_1_3_1_2__orders_1,t1_subset,t3_subset,t7_boole,d6_relat_1,d5_tarski,e6_95_1_3_1_2__orders_1,e5_95_1_3_1_2__orders_1,t30_relat_1]), [interesting(0.2),file(orders_1,e7_95_1_3_1_2__orders_1),[file(orders_1,e7_95_1_3_1_2__orders_1)]]). fof(i2_95_1_3_1_2__orders_1,theorem,( $true ), introduced(tautology,[file(orders_1,i2_95_1_3_1_2__orders_1)]), [interesting(0.2),trivial,file(orders_1,i2_95_1_3_1_2__orders_1)]). fof(i1_95_1_3_1_2__orders_1,plain,( r2_hidden(c1_95_1_3_1__orders_1,c2_95__orders_1) ), inference(conclusion,[status(thm),assumptions([dt_c1_95_1_3_1__orders_1,dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1,e1_95_1_3_1_2__orders_1])],[e7_95_1_3_1_2__orders_1,i2_95_1_3_1_2__orders_1]), [interesting(0.2),file(orders_1,i1_95_1_3_1_2__orders_1),[file(orders_1,i1_95_1_3_1_2__orders_1)]]). fof(e4_95_1_3_1__orders_1,plain, ( r2_hidden(c1_95_1_3_1__orders_1,k2_relat_1(c3_95_1__orders_1)) => r2_hidden(c1_95_1_3_1__orders_1,c2_95__orders_1) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_95_1_3_1__orders_1,dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1]),discharge_asm(discharge,[e1_95_1_3_1_2__orders_1])],[e1_95_1_3_1_2__orders_1,i1_95_1_3_1_2__orders_1]), [interesting(0.35),file(orders_1,e4_95_1_3_1__orders_1),[file(orders_1,e4_95_1_3_1__orders_1)]]). fof(e2_95_1_3_1__orders_1,plain,( r2_hidden(c1_95_1_3_1__orders_1,k2_xboole_0(k1_relat_1(c3_95_1__orders_1),k2_relat_1(c3_95_1__orders_1))) ), inference(mizar_by,[status(thm),assumptions([dt_c1_95_1_3_1__orders_1,dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1,e1_95_1_3_1__orders_1])],[rc1_partfun1,rc2_ordinal1,dt_k1_xboole_0,cc1_ordinal1,cc2_ordinal1,fc2_ordinal1,fc4_ordinal1,fc9_finset_1,rc1_finset_1,rc1_ordinal1,rc3_ordinal1,t1_boole,existence_m1_subset_1,dt_k3_tarski,dt_m1_subset_1,dt_c1_95_1__orders_1,cc1_finset_1,cc3_ordinal1,t2_subset,t6_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,antisymmetry_r2_hidden,dt_k1_relat_1,dt_k2_relat_1,dt_k2_xboole_0,dt_k3_relat_1,dt_c1_95_1_3_1__orders_1,dt_c3_95_1__orders_1,de_c3_95_1__orders_1,t1_subset,t7_boole,d6_relat_1,e1_95_1_3_1__orders_1]), [interesting(0.35),file(orders_1,e2_95_1_3_1__orders_1),[file(orders_1,e2_95_1_3_1__orders_1)]]). fof(e1_95_1_3_1_1__orders_1,assumption,( r2_hidden(c1_95_1_3_1__orders_1,k1_relat_1(c3_95_1__orders_1)) ), introduced(assumption,[file(orders_1,e1_95_1_3_1_1__orders_1)]), [interesting(0.2),axiom,file(orders_1,e1_95_1_3_1_1__orders_1)]). fof(dh_c1_95_1_3_1_1__orders_1,definition, ( ? [A] : r2_hidden(k4_tarski(c1_95_1_3_1__orders_1,A),c3_95_1__orders_1) => r2_hidden(k4_tarski(c1_95_1_3_1__orders_1,c1_95_1_3_1_1__orders_1),c3_95_1__orders_1) ), introduced(definition,[new_symbol(c1_95_1_3_1_1__orders_1),file(orders_1,c1_95_1_3_1_1__orders_1)]), [interesting(0.2),axiom,file(orders_1,c1_95_1_3_1_1__orders_1)]). fof(d4_relat_1,definition,( ! [A] : ( v1_relat_1(A) => ! [B] : ( B = k1_relat_1(A) <=> ! [C] : ( r2_hidden(C,B) <=> ? [D] : r2_hidden(k4_tarski(C,D),A) ) ) ) ), file(relat_1,d4_relat_1), [interesting(0.9),axiom,file(relat_1,d4_relat_1)]). fof(e2_95_1_3_1_1__orders_1,plain,( ? [A] : r2_hidden(k4_tarski(c1_95_1_3_1__orders_1,A),c3_95_1__orders_1) ), inference(mizar_by,[status(thm),assumptions([dt_c1_95_1_3_1__orders_1,dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1,e1_95_1_3_1_1__orders_1])],[rc1_partfun1,rc2_ordinal1,dt_k1_xboole_0,cc1_ordinal1,cc2_ordinal1,fc2_ordinal1,fc4_ordinal1,rc1_finset_1,rc1_ordinal1,rc3_ordinal1,commutativity_k2_tarski,existence_m1_subset_1,dt_k1_tarski,dt_k2_tarski,dt_k3_tarski,dt_m1_subset_1,dt_c1_95_1__orders_1,cc1_finset_1,cc3_ordinal1,fc1_finset_1,fc2_finset_1,fc2_subset_1,fc3_subset_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_relat_1,dt_k4_tarski,dt_c1_95_1_3_1__orders_1,dt_c3_95_1__orders_1,de_c3_95_1__orders_1,t1_subset,t7_boole,d5_tarski,e1_95_1_3_1_1__orders_1,d4_relat_1]), [interesting(0.2),file(orders_1,e2_95_1_3_1_1__orders_1),[file(orders_1,e2_95_1_3_1_1__orders_1)]]). fof(dt_c1_95_1_3_1_1__orders_1,plain,( $true ), inference(consider,[status(thm),assumptions([dt_c1_95_1_3_1__orders_1,dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1,e1_95_1_3_1_1__orders_1])],[dh_c1_95_1_3_1_1__orders_1,e2_95_1_3_1_1__orders_1]), [interesting(0.2),file(orders_1,c1_95_1_3_1_1__orders_1),[file(orders_1,c1_95_1_3_1_1__orders_1)]]). fof(dh_c2_95_1_3_1_1__orders_1,definition, ( ? [A] : ( r2_hidden(k4_tarski(c1_95_1_3_1__orders_1,c1_95_1_3_1_1__orders_1),A) & r2_hidden(A,c1_95_1__orders_1) ) => ( r2_hidden(k4_tarski(c1_95_1_3_1__orders_1,c1_95_1_3_1_1__orders_1),c2_95_1_3_1_1__orders_1) & r2_hidden(c2_95_1_3_1_1__orders_1,c1_95_1__orders_1) ) ), introduced(definition,[new_symbol(c2_95_1_3_1_1__orders_1),file(orders_1,c2_95_1_3_1_1__orders_1)]), [interesting(0.2),axiom,file(orders_1,c2_95_1_3_1_1__orders_1)]). fof(e3_95_1_3_1_1__orders_1,plain,( r2_hidden(k4_tarski(c1_95_1_3_1__orders_1,c1_95_1_3_1_1__orders_1),c3_95_1__orders_1) ), inference(consider,[status(thm),assumptions([dt_c1_95_1_3_1__orders_1,dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1,e1_95_1_3_1_1__orders_1])],[dh_c1_95_1_3_1_1__orders_1,e2_95_1_3_1_1__orders_1]), [interesting(0.2),file(orders_1,e3_95_1_3_1_1__orders_1),[file(orders_1,e3_95_1_3_1_1__orders_1)]]). fof(e4_95_1_3_1_1__orders_1,plain,( ? [A] : ( r2_hidden(k4_tarski(c1_95_1_3_1__orders_1,c1_95_1_3_1_1__orders_1),A) & r2_hidden(A,c1_95_1__orders_1) ) ), inference(mizar_by,[status(thm),assumptions([dt_c1_95_1_3_1__orders_1,dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1,e1_95_1_3_1_1__orders_1])],[rc1_partfun1,rc2_ordinal1,dt_k1_xboole_0,cc1_ordinal1,cc2_ordinal1,fc2_ordinal1,fc4_ordinal1,rc1_finset_1,rc1_ordinal1,rc3_ordinal1,commutativity_k2_tarski,existence_m1_subset_1,dt_k1_tarski,dt_k2_tarski,dt_m1_subset_1,cc1_finset_1,cc3_ordinal1,fc1_finset_1,fc2_finset_1,fc2_subset_1,fc3_subset_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k3_tarski,dt_k4_tarski,dt_c1_95_1__orders_1,dt_c1_95_1_3_1__orders_1,dt_c1_95_1_3_1_1__orders_1,dt_c3_95_1__orders_1,de_c3_95_1__orders_1,t1_subset,t7_boole,d5_tarski,e3_95_1_3_1_1__orders_1,d4_tarski]), [interesting(0.2),file(orders_1,e4_95_1_3_1_1__orders_1),[file(orders_1,e4_95_1_3_1_1__orders_1)]]). fof(dt_c2_95_1_3_1_1__orders_1,plain,( $true ), inference(consider,[status(thm),assumptions([dt_c1_95_1_3_1__orders_1,dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1,e1_95_1_3_1_1__orders_1])],[dh_c2_95_1_3_1_1__orders_1,e4_95_1_3_1_1__orders_1]), [interesting(0.2),file(orders_1,c2_95_1_3_1_1__orders_1),[file(orders_1,c2_95_1_3_1_1__orders_1)]]). fof(e5_95_1_3_1_1__orders_1,plain, ( r2_hidden(k4_tarski(c1_95_1_3_1__orders_1,c1_95_1_3_1_1__orders_1),c2_95_1_3_1_1__orders_1) & r2_hidden(c2_95_1_3_1_1__orders_1,c1_95_1__orders_1) ), inference(consider,[status(thm),assumptions([dt_c1_95_1_3_1__orders_1,dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1,e1_95_1_3_1_1__orders_1])],[dh_c2_95_1_3_1_1__orders_1,e4_95_1_3_1_1__orders_1]), [interesting(0.2),file(orders_1,e5_95_1_3_1_1__orders_1),[file(orders_1,e5_95_1_3_1_1__orders_1)]]). fof(e6_95_1_3_1_1__orders_1,plain,( ? [A] : ( v1_relat_1(A) & c2_95_1_3_1_1__orders_1 = A & r1_tarski(c1_95__orders_1,A) & r2_orders_1(A,c2_95__orders_1) & k3_relat_1(A) = c2_95__orders_1 ) ), inference(mizar_by,[status(thm),assumptions([dt_c1_95_1_3_1__orders_1,dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1,e1_95_1_3_1_1__orders_1])],[cc2_finset_1,fc14_finset_1,fc9_finset_1,rc1_finset_1,rc3_finset_1,rc4_finset_1,commutativity_k2_tarski,commutativity_k2_xboole_0,idempotence_k2_xboole_0,existence_m1_subset_1,dt_k1_relat_1,dt_k1_tarski,dt_k2_relat_1,dt_k2_tarski,dt_k2_xboole_0,dt_m1_subset_1,cc1_finset_1,cc1_ordinal1,cc1_relset_1,cc2_ordinal1,cc3_ordinal1,fc1_finset_1,fc2_finset_1,fc2_subset_1,fc3_subset_1,fc4_subset_1,rc1_ordinal1,rc1_partfun1,rc1_subset_1,rc2_ordinal1,rc2_subset_1,rc3_ordinal1,t1_boole,t2_subset,t4_subset,t5_subset,t8_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k3_relat_1,dt_k4_tarski,dt_c1_95__orders_1,dt_c1_95_1__orders_1,dt_c1_95_1_3_1__orders_1,dt_c1_95_1_3_1_1__orders_1,dt_c2_95__orders_1,dt_c2_95_1_3_1_1__orders_1,dt_c3_95__orders_1,fc1_subset_1,fc2_ordinal1,t1_subset,t3_subset,t6_boole,t7_boole,d6_relat_1,d5_tarski,e3_95__orders_1,e1_95_1__orders_1,e5_95_1_3_1_1__orders_1]), [interesting(0.2),file(orders_1,e6_95_1_3_1_1__orders_1),[file(orders_1,e6_95_1_3_1_1__orders_1)]]). fof(e7_95_1_3_1_1__orders_1,plain,( r2_hidden(c1_95_1_3_1__orders_1,c2_95__orders_1) ), inference(mizar_by,[status(thm),assumptions([dt_c1_95_1_3_1__orders_1,dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1,e1_95_1_3_1_1__orders_1])],[rc1_partfun1,rc2_ordinal1,dt_k1_xboole_0,cc1_ordinal1,cc2_finset_1,cc2_ordinal1,fc2_ordinal1,fc9_finset_1,rc1_finset_1,rc1_ordinal1,rc3_finset_1,rc3_ordinal1,rc4_finset_1,t1_boole,commutativity_k2_tarski,commutativity_k2_xboole_0,idempotence_k2_xboole_0,existence_m1_subset_1,dt_k1_relat_1,dt_k1_tarski,dt_k1_zfmisc_1,dt_k2_relat_1,dt_k2_tarski,dt_k2_xboole_0,dt_m1_subset_1,cc1_finset_1,cc3_ordinal1,fc1_finset_1,fc1_subset_1,fc2_finset_1,fc2_subset_1,fc3_subset_1,rc1_subset_1,rc2_subset_1,t2_subset,t4_subset,t5_subset,t6_boole,t8_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k3_relat_1,dt_k4_tarski,dt_c1_95__orders_1,dt_c1_95_1__orders_1,dt_c1_95_1_3_1__orders_1,dt_c1_95_1_3_1_1__orders_1,dt_c2_95__orders_1,dt_c2_95_1_3_1_1__orders_1,t1_subset,t3_subset,t7_boole,d6_relat_1,d5_tarski,e6_95_1_3_1_1__orders_1,e5_95_1_3_1_1__orders_1,t30_relat_1]), [interesting(0.2),file(orders_1,e7_95_1_3_1_1__orders_1),[file(orders_1,e7_95_1_3_1_1__orders_1)]]). fof(i2_95_1_3_1_1__orders_1,theorem,( $true ), introduced(tautology,[file(orders_1,i2_95_1_3_1_1__orders_1)]), [interesting(0.2),trivial,file(orders_1,i2_95_1_3_1_1__orders_1)]). fof(i1_95_1_3_1_1__orders_1,plain,( r2_hidden(c1_95_1_3_1__orders_1,c2_95__orders_1) ), inference(conclusion,[status(thm),assumptions([dt_c1_95_1_3_1__orders_1,dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1,e1_95_1_3_1_1__orders_1])],[e7_95_1_3_1_1__orders_1,i2_95_1_3_1_1__orders_1]), [interesting(0.2),file(orders_1,i1_95_1_3_1_1__orders_1),[file(orders_1,i1_95_1_3_1_1__orders_1)]]). fof(e3_95_1_3_1__orders_1,plain, ( r2_hidden(c1_95_1_3_1__orders_1,k1_relat_1(c3_95_1__orders_1)) => r2_hidden(c1_95_1_3_1__orders_1,c2_95__orders_1) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_95_1_3_1__orders_1,dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1]),discharge_asm(discharge,[e1_95_1_3_1_1__orders_1])],[e1_95_1_3_1_1__orders_1,i1_95_1_3_1_1__orders_1]), [interesting(0.35),file(orders_1,e3_95_1_3_1__orders_1),[file(orders_1,e3_95_1_3_1__orders_1)]]). fof(d2_xboole_0,definition,( ! [A,B,C] : ( C = k2_xboole_0(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( r2_hidden(D,A) | r2_hidden(D,B) ) ) ) ), file(xboole_0,d2_xboole_0), [interesting(0.9),axiom,file(xboole_0,d2_xboole_0)]). fof(e5_95_1_3_1__orders_1,plain,( r2_hidden(c1_95_1_3_1__orders_1,c2_95__orders_1) ), inference(mizar_by,[status(thm),assumptions([e1_95_1_3_1__orders_1,dt_c1_95_1_3_1__orders_1,dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1])],[rc1_partfun1,rc2_ordinal1,dt_k1_xboole_0,cc1_ordinal1,cc2_ordinal1,fc2_ordinal1,fc4_ordinal1,fc9_finset_1,rc1_finset_1,rc1_ordinal1,rc3_ordinal1,t1_boole,existence_m1_subset_1,dt_k3_tarski,dt_m1_subset_1,dt_c1_95_1__orders_1,cc1_finset_1,cc3_ordinal1,t2_subset,t6_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,antisymmetry_r2_hidden,dt_k1_relat_1,dt_k2_relat_1,dt_k2_xboole_0,dt_c1_95_1_3_1__orders_1,dt_c2_95__orders_1,dt_c3_95_1__orders_1,de_c3_95_1__orders_1,t1_subset,t7_boole,e4_95_1_3_1__orders_1,e2_95_1_3_1__orders_1,e3_95_1_3_1__orders_1,d2_xboole_0]), [interesting(0.35),file(orders_1,e5_95_1_3_1__orders_1),[file(orders_1,e5_95_1_3_1__orders_1)]]). fof(i3_95_1_3_1__orders_1,theorem,( $true ), introduced(tautology,[file(orders_1,i3_95_1_3_1__orders_1)]), [interesting(0.35),trivial,file(orders_1,i3_95_1_3_1__orders_1)]). fof(i2_95_1_3_1__orders_1,plain,( r2_hidden(c1_95_1_3_1__orders_1,c2_95__orders_1) ), inference(conclusion,[status(thm),assumptions([e1_95_1_3_1__orders_1,dt_c1_95_1_3_1__orders_1,dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1])],[e5_95_1_3_1__orders_1,i3_95_1_3_1__orders_1]), [interesting(0.35),file(orders_1,i2_95_1_3_1__orders_1),[file(orders_1,i2_95_1_3_1__orders_1)]]). fof(i1_95_1_3_1__orders_1,plain,( ~ ( r2_hidden(c1_95_1_3_1__orders_1,k3_relat_1(c3_95_1__orders_1)) & ~ r2_hidden(c1_95_1_3_1__orders_1,c2_95__orders_1) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_95_1_3_1__orders_1,dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1]),discharge_asm(discharge,[e1_95_1_3_1__orders_1])],[e1_95_1_3_1__orders_1,i2_95_1_3_1__orders_1]), [interesting(0.35),file(orders_1,i1_95_1_3_1__orders_1),[file(orders_1,i1_95_1_3_1__orders_1)]]). fof(i1_95_1_3_1_tmp__orders_1,plain,( ~ ( r2_hidden(c1_95_1_3_1__orders_1,k3_relat_1(c3_95_1__orders_1)) & ~ r2_hidden(c1_95_1_3_1__orders_1,c2_95__orders_1) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1]),discharge_asm(discharge,[dt_c1_95_1_3_1__orders_1])],[dt_c1_95_1_3_1__orders_1,i1_95_1_3_1__orders_1]), [interesting(0.5),e1_95_1_3__orders_1]). fof(e1_95_1_3__orders_1,plain,( r1_tarski(k3_relat_1(c3_95_1__orders_1),c2_95__orders_1) ), inference(let,[status(thm),assumptions([dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_1__orders_1])],[i1_95_1_3_1_tmp__orders_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k3_relat_1,dt_c2_95__orders_1,dt_c3_95_1__orders_1,d3_tarski,dh_c1_95_1_3_1__orders_1]), [interesting(0.5),file(orders_1,e1_95_1_3__orders_1),[file(orders_1,e1_95_1_3__orders_1)]]). fof(t31_relat_1,theorem,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => ( r1_tarski(A,B) => r1_tarski(k3_relat_1(A),k3_relat_1(B)) ) ) ) ), file(relat_1,t31_relat_1), [interesting(0.9),axiom,file(relat_1,t31_relat_1)]). fof(e2_95_1_3__orders_1,plain,( r1_tarski(c2_95__orders_1,k3_relat_1(c3_95_1__orders_1)) ), inference(mizar_by,[status(thm),assumptions([e1_95__orders_1,dt_c1_95_1__orders_1,e1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1])],[rc1_partfun1,rc2_ordinal1,antisymmetry_r2_hidden,dt_k1_xboole_0,cc1_ordinal1,cc2_finset_1,cc2_ordinal1,fc2_ordinal1,fc4_ordinal1,fc9_finset_1,rc1_finset_1,rc1_ordinal1,rc3_finset_1,rc3_ordinal1,rc4_finset_1,t1_boole,t1_subset,t4_subset,t5_subset,cc1_finset_1,cc3_ordinal1,rc1_subset_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,existence_m1_subset_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k2_relat_1,dt_k2_xboole_0,dt_k3_tarski,dt_m1_subset_1,dt_c1_95_1__orders_1,fc1_subset_1,reflexivity_r1_tarski,dt_k3_relat_1,dt_c1_95__orders_1,dt_c2_95__orders_1,dt_c3_95_1__orders_1,de_c3_95_1__orders_1,t3_subset,d6_relat_1,e1_95__orders_1,e12_95_1__orders_1,t31_relat_1]), [interesting(0.5),file(orders_1,e2_95_1_3__orders_1),[file(orders_1,e2_95_1_3__orders_1)]]). fof(i2_95_1_3__orders_1,theorem,( $true ), introduced(tautology,[file(orders_1,i2_95_1_3__orders_1)]), [interesting(0.5),trivial,file(orders_1,i2_95_1_3__orders_1)]). fof(i1_95_1_3__orders_1,plain,( r1_tarski(c2_95__orders_1,k3_relat_1(c3_95_1__orders_1)) ), inference(conclusion,[status(thm),assumptions([e1_95__orders_1,dt_c1_95_1__orders_1,e1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1])],[e2_95_1_3__orders_1,i2_95_1_3__orders_1]), [interesting(0.5),file(orders_1,i1_95_1_3__orders_1),[file(orders_1,i1_95_1_3__orders_1)]]). fof(e13_95_1__orders_1,plain,( k3_relat_1(c3_95_1__orders_1) = c2_95__orders_1 ), inference(conclusion,[status(thm),assumptions([e1_95__orders_1,dt_c1_95_1__orders_1,e1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1])],[reflexivity_r1_tarski,dt_k3_relat_1,dt_c2_95__orders_1,dt_c3_95_1__orders_1,d10_xboole_0,e1_95_1_3__orders_1,i1_95_1_3__orders_1]), [interesting(0.65),file(orders_1,e13_95_1__orders_1),[file(orders_1,e13_95_1__orders_1)]]). fof(e15_95_1__orders_1,plain,( r2_hidden(k3_tarski(c1_95_1__orders_1),c3_95__orders_1) ), inference(mizar_by,[status(thm),assumptions([e2_95_1__orders_1,e1_95__orders_1,dt_c1_95_1__orders_1,e1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1])],[rc1_partfun1,rc2_ordinal1,dt_k1_xboole_0,cc1_ordinal1,cc2_finset_1,cc2_ordinal1,fc14_finset_1,fc2_ordinal1,fc4_ordinal1,fc9_finset_1,rc1_finset_1,rc1_ordinal1,rc3_finset_1,rc3_ordinal1,rc4_finset_1,t1_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,existence_m1_subset_1,dt_k1_relat_1,dt_k2_relat_1,dt_k2_xboole_0,dt_m1_subset_1,cc1_finset_1,cc1_relset_1,cc3_ordinal1,fc4_subset_1,rc1_subset_1,rc2_subset_1,t2_subset,t4_subset,t5_subset,t6_boole,t8_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k3_relat_1,dt_k3_tarski,dt_c1_95__orders_1,dt_c1_95_1__orders_1,dt_c2_95__orders_1,dt_c2_95_1__orders_1,dt_c3_95__orders_1,dt_c3_95_1__orders_1,de_c2_95_1__orders_1,de_c3_95_1__orders_1,fc1_subset_1,t1_subset,t3_subset,t7_boole,d6_relat_1,e14_95_1__orders_1,e3_95__orders_1,e5_95_1__orders_1,e12_95_1__orders_1,e13_95_1__orders_1]), [interesting(0.65),file(orders_1,e15_95_1__orders_1),[file(orders_1,e15_95_1__orders_1)]]). fof(i3_95_1__orders_1,theorem,( $true ), introduced(tautology,[file(orders_1,i3_95_1__orders_1)]), [interesting(0.65),trivial,file(orders_1,i3_95_1__orders_1)]). fof(i2_95_1__orders_1,plain,( r2_hidden(k3_tarski(c1_95_1__orders_1),c3_95__orders_1) ), inference(conclusion,[status(thm),assumptions([e2_95_1__orders_1,e1_95__orders_1,dt_c1_95_1__orders_1,e1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1])],[e15_95_1__orders_1,i3_95_1__orders_1]), [interesting(0.65),file(orders_1,i2_95_1__orders_1),[file(orders_1,i2_95_1__orders_1)]]). fof(i1_95_1__orders_1,plain, ( ( r1_tarski(c1_95_1__orders_1,c3_95__orders_1) & v6_ordinal1(c1_95_1__orders_1) ) => ( c1_95_1__orders_1 = k1_xboole_0 | r2_hidden(k3_tarski(c1_95_1__orders_1),c3_95__orders_1) ) ), inference(discharge_asm,[status(thm),assumptions([e1_95__orders_1,dt_c1_95_1__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1]),discharge_asm(discharge,[e1_95_1__orders_1,e2_95_1__orders_1])],[e1_95_1__orders_1,e2_95_1__orders_1,i2_95_1__orders_1]), [interesting(0.65),file(orders_1,i1_95_1__orders_1),[file(orders_1,i1_95_1__orders_1)]]). fof(i1_95_1_tmp__orders_1,plain, ( ( r1_tarski(c1_95_1__orders_1,c3_95__orders_1) & v6_ordinal1(c1_95_1__orders_1) ) => ( c1_95_1__orders_1 = k1_xboole_0 | r2_hidden(k3_tarski(c1_95_1__orders_1),c3_95__orders_1) ) ), inference(discharge_asm,[status(thm),assumptions([e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1]),discharge_asm(discharge,[dt_c1_95_1__orders_1])],[dt_c1_95_1__orders_1,i1_95_1__orders_1]), [interesting(0.8),e6_95__orders_1]). fof(e6_95__orders_1,plain,( ! [A] : ( ( r1_tarski(A,c3_95__orders_1) & v6_ordinal1(A) ) => ( A = k1_xboole_0 | r2_hidden(k3_tarski(A),c3_95__orders_1) ) ) ), inference(let,[status(thm),assumptions([e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1])],[i1_95_1_tmp__orders_1,dh_c1_95_1__orders_1]), [interesting(0.8),file(orders_1,e6_95__orders_1),[file(orders_1,e6_95__orders_1)]]). fof(l121_orders_1,plain,( ! [A] : ( v1_relat_1(A) => r1_tarski(A,k2_zfmisc_1(k3_relat_1(A),k3_relat_1(A))) ) ), file(orders_1,l121_orders_1), [interesting(0.9),axiom,file(orders_1,l121_orders_1)]). fof(e4_95__orders_1,plain,( r1_tarski(c1_95__orders_1,k2_zfmisc_1(c2_95__orders_1,c2_95__orders_1)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95__orders_1])],[rc1_partfun1,rc2_ordinal1,antisymmetry_r2_hidden,dt_k1_xboole_0,cc1_ordinal1,cc2_finset_1,cc2_ordinal1,fc14_finset_1,fc2_ordinal1,fc9_finset_1,rc1_finset_1,rc1_ordinal1,rc3_finset_1,rc3_ordinal1,rc4_finset_1,t1_boole,t1_subset,t4_subset,t5_subset,cc1_finset_1,cc3_ordinal1,fc4_subset_1,rc1_subset_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,existence_m1_subset_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k2_relat_1,dt_k2_xboole_0,dt_m1_subset_1,cc1_relset_1,fc1_subset_1,reflexivity_r1_tarski,dt_k2_zfmisc_1,dt_k3_relat_1,dt_c1_95__orders_1,dt_c2_95__orders_1,t3_subset,d6_relat_1,e1_95__orders_1,l121_orders_1]), [interesting(0.8),file(orders_1,e4_95__orders_1),[file(orders_1,e4_95__orders_1)]]). fof(e5_95__orders_1,plain,( c3_95__orders_1 != k1_xboole_0 ), inference(mizar_by,[status(thm),assumptions([e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1])],[cc2_finset_1,fc14_finset_1,fc9_finset_1,rc1_finset_1,rc3_finset_1,rc4_finset_1,commutativity_k2_xboole_0,idempotence_k2_xboole_0,existence_m1_subset_1,dt_k1_relat_1,dt_k2_relat_1,dt_k2_xboole_0,dt_m1_subset_1,cc1_finset_1,cc1_ordinal1,cc1_relset_1,cc2_ordinal1,cc3_ordinal1,fc4_subset_1,rc1_ordinal1,rc1_partfun1,rc1_subset_1,rc2_ordinal1,rc2_subset_1,rc3_ordinal1,t1_boole,t2_subset,t4_subset,t5_subset,t8_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k3_relat_1,dt_c1_95__orders_1,dt_c2_95__orders_1,dt_c3_95__orders_1,fc1_subset_1,fc2_ordinal1,t1_subset,t3_subset,t6_boole,t7_boole,d6_relat_1,e4_95__orders_1,e1_95__orders_1,e3_95__orders_1]), [interesting(0.8),file(orders_1,e5_95__orders_1),[file(orders_1,e5_95__orders_1)]]). fof(t177_orders_1,theorem,( ! [A] : ~ ( A != k1_xboole_0 & ! [B] : ( ( r1_tarski(B,A) & v6_ordinal1(B) ) => ( B = k1_xboole_0 | r2_hidden(k3_tarski(B),A) ) ) & ! [B] : ~ ( r2_hidden(B,A) & ! [C] : ~ ( r2_hidden(C,A) & C != B & r1_tarski(B,C) ) ) ) ), file(orders_1,t177_orders_1), [interesting(0.9),axiom,file(orders_1,t177_orders_1)]). fof(e7_95__orders_1,plain,( ? [A] : ( r2_hidden(A,c3_95__orders_1) & ! [B] : ~ ( r2_hidden(B,c3_95__orders_1) & B != A & r1_tarski(A,B) ) ) ), inference(mizar_by,[status(thm),assumptions([e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1])],[cc2_finset_1,rc1_finset_1,rc3_finset_1,rc4_finset_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,cc1_finset_1,cc1_ordinal1,cc2_ordinal1,cc3_ordinal1,fc1_subset_1,fc4_ordinal1,rc1_ordinal1,rc1_partfun1,rc1_subset_1,rc2_ordinal1,rc2_subset_1,rc3_ordinal1,t2_subset,t4_subset,t5_subset,t8_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k3_tarski,dt_c3_95__orders_1,fc2_ordinal1,t1_subset,t3_subset,t6_boole,t7_boole,e6_95__orders_1,e5_95__orders_1,t177_orders_1]), [interesting(0.8),file(orders_1,e7_95__orders_1),[file(orders_1,e7_95__orders_1)]]). fof(dt_c4_95__orders_1,plain,( $true ), inference(consider,[status(thm),assumptions([e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1])],[dh_c4_95__orders_1,e7_95__orders_1]), [interesting(0.8),file(orders_1,c4_95__orders_1),[file(orders_1,c4_95__orders_1)]]). fof(e8_95__orders_1,plain, ( r2_hidden(c4_95__orders_1,c3_95__orders_1) & ! [A] : ~ ( r2_hidden(A,c3_95__orders_1) & A != c4_95__orders_1 & r1_tarski(c4_95__orders_1,A) ) ), inference(consider,[status(thm),assumptions([e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1])],[dh_c4_95__orders_1,e7_95__orders_1]), [interesting(0.8),file(orders_1,e8_95__orders_1),[file(orders_1,e8_95__orders_1)]]). fof(e9_95__orders_1,plain,( ? [A] : ( v1_relat_1(A) & c4_95__orders_1 = A & r1_tarski(c1_95__orders_1,A) & r2_orders_1(A,c2_95__orders_1) & k3_relat_1(A) = c2_95__orders_1 ) ), inference(mizar_by,[status(thm),assumptions([e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1])],[rc1_partfun1,rc2_ordinal1,dt_k1_xboole_0,cc1_ordinal1,cc2_finset_1,cc2_ordinal1,fc14_finset_1,fc2_ordinal1,fc9_finset_1,rc1_finset_1,rc1_ordinal1,rc3_finset_1,rc3_ordinal1,rc4_finset_1,t1_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,existence_m1_subset_1,dt_k1_relat_1,dt_k2_relat_1,dt_k2_xboole_0,dt_m1_subset_1,cc1_finset_1,cc1_relset_1,cc3_ordinal1,fc4_subset_1,rc1_subset_1,rc2_subset_1,t2_subset,t4_subset,t5_subset,t6_boole,t8_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k3_relat_1,dt_c1_95__orders_1,dt_c2_95__orders_1,dt_c3_95__orders_1,dt_c4_95__orders_1,fc1_subset_1,t1_subset,t3_subset,t7_boole,d6_relat_1,e3_95__orders_1,e8_95__orders_1]), [interesting(0.8),file(orders_1,e9_95__orders_1),[file(orders_1,e9_95__orders_1)]]). fof(dt_c5_95__orders_1,plain,( v1_relat_1(c5_95__orders_1) ), inference(consider,[status(thm),assumptions([e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1])],[dh_c5_95__orders_1,e9_95__orders_1]), [interesting(0.8),file(orders_1,c5_95__orders_1),[file(orders_1,c5_95__orders_1)]]). fof(e10_95__orders_1,plain, ( c4_95__orders_1 = c5_95__orders_1 & r1_tarski(c1_95__orders_1,c5_95__orders_1) & r2_orders_1(c5_95__orders_1,c2_95__orders_1) & k3_relat_1(c5_95__orders_1) = c2_95__orders_1 ), inference(consider,[status(thm),assumptions([e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1])],[dh_c5_95__orders_1,e9_95__orders_1]), [interesting(0.8),file(orders_1,e10_95__orders_1),[file(orders_1,e10_95__orders_1)]]). fof(e11_95__orders_1,plain,( r1_tarski(c1_95__orders_1,c5_95__orders_1) ), inference(mizar_by,[status(thm),assumptions([e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1])],[rc1_partfun1,rc2_ordinal1,antisymmetry_r2_hidden,dt_k1_xboole_0,cc1_ordinal1,cc2_finset_1,cc2_ordinal1,fc2_ordinal1,fc9_finset_1,rc1_finset_1,rc1_ordinal1,rc3_finset_1,rc3_ordinal1,rc4_finset_1,t1_boole,t1_subset,t4_subset,t5_subset,cc1_finset_1,cc3_ordinal1,rc1_subset_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,existence_m1_subset_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k2_relat_1,dt_k2_xboole_0,dt_m1_subset_1,fc1_subset_1,reflexivity_r1_tarski,dt_k3_relat_1,dt_c1_95__orders_1,dt_c2_95__orders_1,dt_c4_95__orders_1,dt_c5_95__orders_1,t3_subset,d6_relat_1,e10_95__orders_1]), [interesting(0.8),file(orders_1,e11_95__orders_1),[file(orders_1,e11_95__orders_1)]]). fof(d8_orders_1,definition,( ! [A] : ( v1_relat_1(A) => ! [B] : ( r3_orders_1(A,B) <=> ( r1_relat_2(A,B) & r8_relat_2(A,B) & r4_relat_2(A,B) & r6_relat_2(A,B) ) ) ) ), file(orders_1,d8_orders_1), [interesting(0.9),axiom,file(orders_1,d8_orders_1)]). fof(e12_95__orders_1,plain, ( r1_relat_2(c5_95__orders_1,c2_95__orders_1) & r8_relat_2(c5_95__orders_1,c2_95__orders_1) & r4_relat_2(c5_95__orders_1,c2_95__orders_1) ), inference(mizar_by,[status(thm),assumptions([e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1])],[rc1_partfun1,rc2_ordinal1,antisymmetry_r2_hidden,dt_k1_xboole_0,cc1_ordinal1,cc2_finset_1,cc2_ordinal1,fc2_ordinal1,fc9_finset_1,rc1_finset_1,rc1_ordinal1,rc3_finset_1,rc3_ordinal1,rc4_finset_1,t1_boole,t1_subset,t4_subset,t5_subset,cc1_finset_1,cc3_ordinal1,rc1_subset_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,existence_m1_subset_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k2_relat_1,dt_k2_xboole_0,dt_m1_subset_1,fc1_subset_1,reflexivity_r1_tarski,dt_k3_relat_1,dt_c1_95__orders_1,dt_c2_95__orders_1,dt_c4_95__orders_1,dt_c5_95__orders_1,t3_subset,d6_relat_1,e10_95__orders_1,d7_orders_1]), [interesting(0.8),file(orders_1,e12_95__orders_1),[file(orders_1,e12_95__orders_1)]]). fof(dt_c1_95_2__orders_1,assumption,( $true ), introduced(assumption,[file(orders_1,c1_95_2__orders_1)]), [interesting(0.65),axiom,file(orders_1,c1_95_2__orders_1)]). fof(d6_relat_2,definition,( ! [A] : ( v1_relat_1(A) => ! [B] : ( r6_relat_2(A,B) <=> ! [C,D] : ~ ( r2_hidden(C,B) & r2_hidden(D,B) & C != D & ~ r2_hidden(k4_tarski(C,D),A) & ~ r2_hidden(k4_tarski(D,C),A) ) ) ) ), file(relat_2,d6_relat_2), [interesting(0.9),axiom,file(relat_2,d6_relat_2)]). fof(dh_c1_95_2__orders_1,definition, ( ! [A] : ~ ( r2_hidden(c1_95_2__orders_1,c2_95__orders_1) & r2_hidden(A,c2_95__orders_1) & c1_95_2__orders_1 != A & ~ r2_hidden(k4_tarski(c1_95_2__orders_1,A),c5_95__orders_1) & ~ r2_hidden(k4_tarski(A,c1_95_2__orders_1),c5_95__orders_1) ) => ! [B,C] : ~ ( r2_hidden(B,c2_95__orders_1) & r2_hidden(C,c2_95__orders_1) & B != C & ~ r2_hidden(k4_tarski(B,C),c5_95__orders_1) & ~ r2_hidden(k4_tarski(C,B),c5_95__orders_1) ) ), introduced(definition,[new_symbol(c1_95_2__orders_1),file(orders_1,c1_95_2__orders_1)]), [interesting(0.65),axiom,file(orders_1,c1_95_2__orders_1)]). fof(dh_c2_95_2__orders_1,definition, ( ~ ( r2_hidden(c1_95_2__orders_1,c2_95__orders_1) & r2_hidden(c2_95_2__orders_1,c2_95__orders_1) & c1_95_2__orders_1 != c2_95_2__orders_1 & ~ r2_hidden(k4_tarski(c1_95_2__orders_1,c2_95_2__orders_1),c5_95__orders_1) & ~ r2_hidden(k4_tarski(c2_95_2__orders_1,c1_95_2__orders_1),c5_95__orders_1) ) => ! [A] : ~ ( r2_hidden(c1_95_2__orders_1,c2_95__orders_1) & r2_hidden(A,c2_95__orders_1) & c1_95_2__orders_1 != A & ~ r2_hidden(k4_tarski(c1_95_2__orders_1,A),c5_95__orders_1) & ~ r2_hidden(k4_tarski(A,c1_95_2__orders_1),c5_95__orders_1) ) ), introduced(definition,[new_symbol(c2_95_2__orders_1),file(orders_1,c2_95_2__orders_1)]), [interesting(0.65),axiom,file(orders_1,c2_95_2__orders_1)]). fof(e1_95_2__orders_1,assumption, ( r2_hidden(c1_95_2__orders_1,c2_95__orders_1) & r2_hidden(c2_95_2__orders_1,c2_95__orders_1) & c1_95_2__orders_1 != c2_95_2__orders_1 & ~ r2_hidden(k4_tarski(c1_95_2__orders_1,c2_95_2__orders_1),c5_95__orders_1) & ~ r2_hidden(k4_tarski(c2_95_2__orders_1,c1_95_2__orders_1),c5_95__orders_1) ), introduced(assumption,[file(orders_1,e1_95_2__orders_1)]), [interesting(0.65),axiom,file(orders_1,e1_95_2__orders_1)]). fof(dt_c2_95_2__orders_1,assumption,( $true ), introduced(assumption,[file(orders_1,c2_95_2__orders_1)]), [interesting(0.65),axiom,file(orders_1,c2_95_2__orders_1)]). fof(dh_c3_95_2__orders_1,definition, ( ? [A] : ( v1_relat_1(A) & ! [B,C] : ( r2_hidden(k4_tarski(B,C),A) <=> ( r2_hidden(B,c2_95__orders_1) & r2_hidden(C,c2_95__orders_1) & ( r2_hidden(k4_tarski(B,C),c5_95__orders_1) | ( r2_hidden(k4_tarski(B,c1_95_2__orders_1),c5_95__orders_1) & r2_hidden(k4_tarski(c2_95_2__orders_1,C),c5_95__orders_1) ) ) ) ) ) => ( v1_relat_1(c3_95_2__orders_1) & ! [D,E] : ( r2_hidden(k4_tarski(D,E),c3_95_2__orders_1) <=> ( r2_hidden(D,c2_95__orders_1) & r2_hidden(E,c2_95__orders_1) & ( r2_hidden(k4_tarski(D,E),c5_95__orders_1) | ( r2_hidden(k4_tarski(D,c1_95_2__orders_1),c5_95__orders_1) & r2_hidden(k4_tarski(c2_95_2__orders_1,E),c5_95__orders_1) ) ) ) ) ) ), introduced(definition,[new_symbol(c3_95_2__orders_1),file(orders_1,c3_95_2__orders_1)]), [interesting(0.65),axiom,file(orders_1,c3_95_2__orders_1)]). fof(s1_relat_1__e2_95_2__orders_1,theorem,( ! [A,B,C,D] : ( v1_relat_1(B) => ? [E] : ( v1_relat_1(E) & ! [F,G] : ( r2_hidden(k4_tarski(F,G),E) <=> ( r2_hidden(F,A) & r2_hidden(G,A) & ( r2_hidden(k4_tarski(F,G),B) | ( r2_hidden(k4_tarski(F,C),B) & r2_hidden(k4_tarski(D,G),B) ) ) ) ) ) ) ), file(orders_1,s1_relat_1__e2_95_2__orders_1), [interesting(0.9),axiom,file(orders_1,s1_relat_1__e2_95_2__orders_1)]). fof(e2_95_2__orders_1,plain,( ? [A] : ( v1_relat_1(A) & ! [B,C] : ( r2_hidden(k4_tarski(B,C),A) <=> ( r2_hidden(B,c2_95__orders_1) & r2_hidden(C,c2_95__orders_1) & ( r2_hidden(k4_tarski(B,C),c5_95__orders_1) | ( r2_hidden(k4_tarski(B,c1_95_2__orders_1),c5_95__orders_1) & r2_hidden(k4_tarski(c2_95_2__orders_1,C),c5_95__orders_1) ) ) ) ) ) ), inference(mizar_from,[status(thm),assumptions([dt_c1_95_2__orders_1,dt_c2_95_2__orders_1,e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1])],[antisymmetry_r2_hidden,dt_k4_tarski,dt_c1_95_2__orders_1,dt_c2_95__orders_1,dt_c2_95_2__orders_1,dt_c5_95__orders_1,s1_relat_1__e2_95_2__orders_1]), [interesting(0.65),file(orders_1,e2_95_2__orders_1),[file(orders_1,e2_95_2__orders_1)]]). fof(dt_c3_95_2__orders_1,plain,( v1_relat_1(c3_95_2__orders_1) ), inference(consider,[status(thm),assumptions([dt_c1_95_2__orders_1,dt_c2_95_2__orders_1,e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1])],[dh_c3_95_2__orders_1,e2_95_2__orders_1]), [interesting(0.65),file(orders_1,c3_95_2__orders_1),[file(orders_1,c3_95_2__orders_1)]]). fof(e11_95_2__orders_1,plain, ( r2_hidden(k4_tarski(c1_95_2__orders_1,c1_95_2__orders_1),c5_95__orders_1) & r2_hidden(k4_tarski(c2_95_2__orders_1,c2_95_2__orders_1),c5_95__orders_1) & r2_hidden(c1_95_2__orders_1,c2_95__orders_1) & r2_hidden(c2_95_2__orders_1,c2_95__orders_1) ), inference(mizar_by,[status(thm),assumptions([dt_c1_95_2__orders_1,dt_c2_95_2__orders_1,e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_2__orders_1])],[rc1_partfun1,rc2_ordinal1,dt_k1_xboole_0,cc1_ordinal1,cc2_ordinal1,fc2_ordinal1,rc1_finset_1,rc1_ordinal1,rc3_ordinal1,commutativity_k2_tarski,existence_m1_subset_1,dt_k1_tarski,dt_k2_tarski,dt_m1_subset_1,cc1_finset_1,cc3_ordinal1,fc1_finset_1,fc2_finset_1,fc2_subset_1,fc3_subset_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k4_tarski,dt_c1_95_2__orders_1,dt_c2_95__orders_1,dt_c2_95_2__orders_1,dt_c5_95__orders_1,t1_subset,t7_boole,d5_tarski,e12_95__orders_1,e1_95_2__orders_1,d1_relat_2]), [interesting(0.65),file(orders_1,e11_95_2__orders_1),[file(orders_1,e11_95_2__orders_1)]]). fof(e3_95_2__orders_1,plain,( ! [A,B] : ( r2_hidden(k4_tarski(A,B),c3_95_2__orders_1) <=> ( r2_hidden(A,c2_95__orders_1) & r2_hidden(B,c2_95__orders_1) & ( r2_hidden(k4_tarski(A,B),c5_95__orders_1) | ( r2_hidden(k4_tarski(A,c1_95_2__orders_1),c5_95__orders_1) & r2_hidden(k4_tarski(c2_95_2__orders_1,B),c5_95__orders_1) ) ) ) ) ), inference(consider,[status(thm),assumptions([dt_c1_95_2__orders_1,dt_c2_95_2__orders_1,e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1])],[dh_c3_95_2__orders_1,e2_95_2__orders_1]), [interesting(0.65),file(orders_1,e3_95_2__orders_1),[file(orders_1,e3_95_2__orders_1)]]). fof(dt_c1_95_2_4_1__orders_1,assumption,( $true ), introduced(assumption,[file(orders_1,c1_95_2_4_1__orders_1)]), [interesting(0.35),axiom,file(orders_1,c1_95_2_4_1__orders_1)]). fof(dh_c1_95_2_4_1__orders_1,definition, ( ~ ( r2_hidden(c1_95_2_4_1__orders_1,c2_95__orders_1) & ~ r2_hidden(k4_tarski(c1_95_2_4_1__orders_1,c1_95_2_4_1__orders_1),c3_95_2__orders_1) ) => ! [A] : ~ ( r2_hidden(A,c2_95__orders_1) & ~ r2_hidden(k4_tarski(A,A),c3_95_2__orders_1) ) ), introduced(definition,[new_symbol(c1_95_2_4_1__orders_1),file(orders_1,c1_95_2_4_1__orders_1)]), [interesting(0.35),axiom,file(orders_1,c1_95_2_4_1__orders_1)]). fof(e1_95_2_4_1__orders_1,assumption,( r2_hidden(c1_95_2_4_1__orders_1,c2_95__orders_1) ), introduced(assumption,[file(orders_1,e1_95_2_4_1__orders_1)]), [interesting(0.35),axiom,file(orders_1,e1_95_2_4_1__orders_1)]). fof(e2_95_2_4_1__orders_1,plain,( r2_hidden(k4_tarski(c1_95_2_4_1__orders_1,c1_95_2_4_1__orders_1),c5_95__orders_1) ), inference(mizar_by,[status(thm),assumptions([dt_c1_95_2_4_1__orders_1,e1_95_2_4_1__orders_1,e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1])],[rc1_partfun1,rc2_ordinal1,dt_k1_xboole_0,cc1_ordinal1,cc2_ordinal1,fc2_ordinal1,rc1_finset_1,rc1_ordinal1,rc3_ordinal1,commutativity_k2_tarski,existence_m1_subset_1,dt_k1_tarski,dt_k2_tarski,dt_m1_subset_1,cc1_finset_1,cc3_ordinal1,fc1_finset_1,fc2_finset_1,fc2_subset_1,fc3_subset_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k4_tarski,dt_c1_95_2_4_1__orders_1,dt_c2_95__orders_1,dt_c5_95__orders_1,t1_subset,t7_boole,d5_tarski,e1_95_2_4_1__orders_1,e12_95__orders_1,d1_relat_2]), [interesting(0.35),file(orders_1,e2_95_2_4_1__orders_1),[file(orders_1,e2_95_2_4_1__orders_1)]]). fof(e3_95_2_4_1__orders_1,plain,( r2_hidden(k4_tarski(c1_95_2_4_1__orders_1,c1_95_2_4_1__orders_1),c3_95_2__orders_1) ), inference(mizar_by,[status(thm),assumptions([dt_c1_95_2_4_1__orders_1,dt_c1_95_2__orders_1,dt_c2_95_2__orders_1,e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_2_4_1__orders_1])],[rc1_partfun1,rc2_ordinal1,dt_k1_xboole_0,cc1_ordinal1,cc2_ordinal1,fc2_ordinal1,rc1_finset_1,rc1_ordinal1,rc3_ordinal1,commutativity_k2_tarski,existence_m1_subset_1,dt_k1_tarski,dt_k2_tarski,dt_m1_subset_1,cc1_finset_1,cc3_ordinal1,fc1_finset_1,fc2_finset_1,fc2_subset_1,fc3_subset_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k4_tarski,dt_c1_95_2__orders_1,dt_c1_95_2_4_1__orders_1,dt_c2_95__orders_1,dt_c2_95_2__orders_1,dt_c3_95_2__orders_1,dt_c5_95__orders_1,t1_subset,t7_boole,d5_tarski,e2_95_2_4_1__orders_1,e3_95_2__orders_1,e1_95_2_4_1__orders_1]), [interesting(0.35),file(orders_1,e3_95_2_4_1__orders_1),[file(orders_1,e3_95_2_4_1__orders_1)]]). fof(i3_95_2_4_1__orders_1,theorem,( $true ), introduced(tautology,[file(orders_1,i3_95_2_4_1__orders_1)]), [interesting(0.35),trivial,file(orders_1,i3_95_2_4_1__orders_1)]). fof(i2_95_2_4_1__orders_1,plain,( r2_hidden(k4_tarski(c1_95_2_4_1__orders_1,c1_95_2_4_1__orders_1),c3_95_2__orders_1) ), inference(conclusion,[status(thm),assumptions([dt_c1_95_2_4_1__orders_1,dt_c1_95_2__orders_1,dt_c2_95_2__orders_1,e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_2_4_1__orders_1])],[e3_95_2_4_1__orders_1,i3_95_2_4_1__orders_1]), [interesting(0.35),file(orders_1,i2_95_2_4_1__orders_1),[file(orders_1,i2_95_2_4_1__orders_1)]]). fof(i1_95_2_4_1__orders_1,plain,( ~ ( r2_hidden(c1_95_2_4_1__orders_1,c2_95__orders_1) & ~ r2_hidden(k4_tarski(c1_95_2_4_1__orders_1,c1_95_2_4_1__orders_1),c3_95_2__orders_1) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_95_2_4_1__orders_1,dt_c1_95_2__orders_1,dt_c2_95_2__orders_1,e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1]),discharge_asm(discharge,[e1_95_2_4_1__orders_1])],[e1_95_2_4_1__orders_1,i2_95_2_4_1__orders_1]), [interesting(0.35),file(orders_1,i1_95_2_4_1__orders_1),[file(orders_1,i1_95_2_4_1__orders_1)]]). fof(i1_95_2_4_1_tmp__orders_1,plain,( ~ ( r2_hidden(c1_95_2_4_1__orders_1,c2_95__orders_1) & ~ r2_hidden(k4_tarski(c1_95_2_4_1__orders_1,c1_95_2_4_1__orders_1),c3_95_2__orders_1) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_95_2__orders_1,dt_c2_95_2__orders_1,e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1]),discharge_asm(discharge,[dt_c1_95_2_4_1__orders_1])],[dt_c1_95_2_4_1__orders_1,i1_95_2_4_1__orders_1]), [interesting(0.5),e1_95_2_4__orders_1]). fof(e1_95_2_4__orders_1,plain,( r1_relat_2(c3_95_2__orders_1,c2_95__orders_1) ), inference(let,[status(thm),assumptions([dt_c1_95_2__orders_1,dt_c2_95_2__orders_1,e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1])],[i1_95_2_4_1_tmp__orders_1,antisymmetry_r2_hidden,dt_k4_tarski,dt_c2_95__orders_1,dt_c3_95_2__orders_1,d1_relat_2,dh_c1_95_2_4_1__orders_1]), [interesting(0.5),file(orders_1,e1_95_2_4__orders_1),[file(orders_1,e1_95_2_4__orders_1)]]). fof(dt_c1_95_2_4_2__orders_1,assumption,( $true ), introduced(assumption,[file(orders_1,c1_95_2_4_2__orders_1)]), [interesting(0.35),axiom,file(orders_1,c1_95_2_4_2__orders_1)]). fof(dt_c2_95_2_4_2__orders_1,assumption,( $true ), introduced(assumption,[file(orders_1,c2_95_2_4_2__orders_1)]), [interesting(0.35),axiom,file(orders_1,c2_95_2_4_2__orders_1)]). fof(dt_c3_95_2_4_2__orders_1,assumption,( $true ), introduced(assumption,[file(orders_1,c3_95_2_4_2__orders_1)]), [interesting(0.35),axiom,file(orders_1,c3_95_2_4_2__orders_1)]). fof(dh_c1_95_2_4_2__orders_1,definition, ( ! [A,B] : ~ ( r2_hidden(c1_95_2_4_2__orders_1,c2_95__orders_1) & r2_hidden(A,c2_95__orders_1) & r2_hidden(B,c2_95__orders_1) & r2_hidden(k4_tarski(c1_95_2_4_2__orders_1,A),c3_95_2__orders_1) & r2_hidden(k4_tarski(A,B),c3_95_2__orders_1) & ~ r2_hidden(k4_tarski(c1_95_2_4_2__orders_1,B),c3_95_2__orders_1) ) => ! [C,D,E] : ~ ( r2_hidden(C,c2_95__orders_1) & r2_hidden(D,c2_95__orders_1) & r2_hidden(E,c2_95__orders_1) & r2_hidden(k4_tarski(C,D),c3_95_2__orders_1) & r2_hidden(k4_tarski(D,E),c3_95_2__orders_1) & ~ r2_hidden(k4_tarski(C,E),c3_95_2__orders_1) ) ), introduced(definition,[new_symbol(c1_95_2_4_2__orders_1),file(orders_1,c1_95_2_4_2__orders_1)]), [interesting(0.35),axiom,file(orders_1,c1_95_2_4_2__orders_1)]). fof(dh_c2_95_2_4_2__orders_1,definition, ( ! [A] : ~ ( r2_hidden(c1_95_2_4_2__orders_1,c2_95__orders_1) & r2_hidden(c2_95_2_4_2__orders_1,c2_95__orders_1) & r2_hidden(A,c2_95__orders_1) & r2_hidden(k4_tarski(c1_95_2_4_2__orders_1,c2_95_2_4_2__orders_1),c3_95_2__orders_1) & r2_hidden(k4_tarski(c2_95_2_4_2__orders_1,A),c3_95_2__orders_1) & ~ r2_hidden(k4_tarski(c1_95_2_4_2__orders_1,A),c3_95_2__orders_1) ) => ! [B,C] : ~ ( r2_hidden(c1_95_2_4_2__orders_1,c2_95__orders_1) & r2_hidden(B,c2_95__orders_1) & r2_hidden(C,c2_95__orders_1) & r2_hidden(k4_tarski(c1_95_2_4_2__orders_1,B),c3_95_2__orders_1) & r2_hidden(k4_tarski(B,C),c3_95_2__orders_1) & ~ r2_hidden(k4_tarski(c1_95_2_4_2__orders_1,C),c3_95_2__orders_1) ) ), introduced(definition,[new_symbol(c2_95_2_4_2__orders_1),file(orders_1,c2_95_2_4_2__orders_1)]), [interesting(0.35),axiom,file(orders_1,c2_95_2_4_2__orders_1)]). fof(dh_c3_95_2_4_2__orders_1,definition, ( ~ ( r2_hidden(c1_95_2_4_2__orders_1,c2_95__orders_1) & r2_hidden(c2_95_2_4_2__orders_1,c2_95__orders_1) & r2_hidden(c3_95_2_4_2__orders_1,c2_95__orders_1) & r2_hidden(k4_tarski(c1_95_2_4_2__orders_1,c2_95_2_4_2__orders_1),c3_95_2__orders_1) & r2_hidden(k4_tarski(c2_95_2_4_2__orders_1,c3_95_2_4_2__orders_1),c3_95_2__orders_1) & ~ r2_hidden(k4_tarski(c1_95_2_4_2__orders_1,c3_95_2_4_2__orders_1),c3_95_2__orders_1) ) => ! [A] : ~ ( r2_hidden(c1_95_2_4_2__orders_1,c2_95__orders_1) & r2_hidden(c2_95_2_4_2__orders_1,c2_95__orders_1) & r2_hidden(A,c2_95__orders_1) & r2_hidden(k4_tarski(c1_95_2_4_2__orders_1,c2_95_2_4_2__orders_1),c3_95_2__orders_1) & r2_hidden(k4_tarski(c2_95_2_4_2__orders_1,A),c3_95_2__orders_1) & ~ r2_hidden(k4_tarski(c1_95_2_4_2__orders_1,A),c3_95_2__orders_1) ) ), introduced(definition,[new_symbol(c3_95_2_4_2__orders_1),file(orders_1,c3_95_2_4_2__orders_1)]), [interesting(0.35),axiom,file(orders_1,c3_95_2_4_2__orders_1)]). fof(e1_95_2_4_2__orders_1,assumption, ( r2_hidden(c1_95_2_4_2__orders_1,c2_95__orders_1) & r2_hidden(c2_95_2_4_2__orders_1,c2_95__orders_1) & r2_hidden(c3_95_2_4_2__orders_1,c2_95__orders_1) & r2_hidden(k4_tarski(c1_95_2_4_2__orders_1,c2_95_2_4_2__orders_1),c3_95_2__orders_1) & r2_hidden(k4_tarski(c2_95_2_4_2__orders_1,c3_95_2_4_2__orders_1),c3_95_2__orders_1) ), introduced(assumption,[file(orders_1,e1_95_2_4_2__orders_1)]), [interesting(0.35),axiom,file(orders_1,e1_95_2_4_2__orders_1)]). fof(e2_95_2_4_2__orders_1,plain, ( ( r2_hidden(k4_tarski(c1_95_2_4_2__orders_1,c2_95_2_4_2__orders_1),c5_95__orders_1) | ( r2_hidden(k4_tarski(c1_95_2_4_2__orders_1,c1_95_2__orders_1),c5_95__orders_1) & r2_hidden(k4_tarski(c2_95_2__orders_1,c2_95_2_4_2__orders_1),c5_95__orders_1) ) ) & ( r2_hidden(k4_tarski(c2_95_2_4_2__orders_1,c3_95_2_4_2__orders_1),c5_95__orders_1) | ( r2_hidden(k4_tarski(c2_95_2_4_2__orders_1,c1_95_2__orders_1),c5_95__orders_1) & r2_hidden(k4_tarski(c2_95_2__orders_1,c3_95_2_4_2__orders_1),c5_95__orders_1) ) ) ), inference(mizar_by,[status(thm),assumptions([dt_c1_95_2_4_2__orders_1,dt_c2_95_2_4_2__orders_1,dt_c3_95_2_4_2__orders_1,e1_95_2_4_2__orders_1,dt_c1_95_2__orders_1,dt_c2_95_2__orders_1,e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1])],[rc1_partfun1,rc2_ordinal1,dt_k1_xboole_0,cc1_ordinal1,cc2_ordinal1,fc2_ordinal1,rc1_finset_1,rc1_ordinal1,rc3_ordinal1,commutativity_k2_tarski,existence_m1_subset_1,dt_k1_tarski,dt_k2_tarski,dt_m1_subset_1,cc1_finset_1,cc3_ordinal1,fc1_finset_1,fc2_finset_1,fc2_subset_1,fc3_subset_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k4_tarski,dt_c1_95_2__orders_1,dt_c1_95_2_4_2__orders_1,dt_c2_95__orders_1,dt_c2_95_2__orders_1,dt_c2_95_2_4_2__orders_1,dt_c3_95_2__orders_1,dt_c3_95_2_4_2__orders_1,dt_c5_95__orders_1,t1_subset,t7_boole,d5_tarski,e1_95_2_4_2__orders_1,e3_95_2__orders_1]), [interesting(0.35),file(orders_1,e2_95_2_4_2__orders_1),[file(orders_1,e2_95_2_4_2__orders_1)]]). fof(e3_95_2_4_2__orders_1,plain,( ~ ( ~ r2_hidden(k4_tarski(c1_95_2_4_2__orders_1,c3_95_2_4_2__orders_1),c5_95__orders_1) & ~ ( r2_hidden(k4_tarski(c1_95_2_4_2__orders_1,c1_95_2__orders_1),c5_95__orders_1) & r2_hidden(k4_tarski(c2_95_2__orders_1,c3_95_2_4_2__orders_1),c5_95__orders_1) ) & ~ ( r2_hidden(k4_tarski(c1_95_2_4_2__orders_1,c1_95_2__orders_1),c5_95__orders_1) & r2_hidden(k4_tarski(c2_95_2__orders_1,c3_95_2_4_2__orders_1),c5_95__orders_1) ) & ~ r2_hidden(k4_tarski(c2_95_2__orders_1,c1_95_2__orders_1),c5_95__orders_1) ) ), inference(mizar_by,[status(thm),assumptions([dt_c1_95_2_4_2__orders_1,dt_c2_95_2_4_2__orders_1,dt_c3_95_2_4_2__orders_1,dt_c1_95_2__orders_1,dt_c2_95_2__orders_1,e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_2__orders_1,e1_95_2_4_2__orders_1])],[rc1_partfun1,rc2_ordinal1,dt_k1_xboole_0,cc1_ordinal1,cc2_ordinal1,fc2_ordinal1,rc1_finset_1,rc1_ordinal1,rc3_ordinal1,commutativity_k2_tarski,existence_m1_subset_1,dt_k1_tarski,dt_k2_tarski,dt_m1_subset_1,cc1_finset_1,cc3_ordinal1,fc1_finset_1,fc2_finset_1,fc2_subset_1,fc3_subset_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k4_tarski,dt_c1_95_2__orders_1,dt_c1_95_2_4_2__orders_1,dt_c2_95__orders_1,dt_c2_95_2__orders_1,dt_c2_95_2_4_2__orders_1,dt_c3_95_2__orders_1,dt_c3_95_2_4_2__orders_1,dt_c5_95__orders_1,t1_subset,t7_boole,d5_tarski,e2_95_2_4_2__orders_1,e12_95__orders_1,e1_95_2__orders_1,e1_95_2_4_2__orders_1,d8_relat_2]), [interesting(0.35),file(orders_1,e3_95_2_4_2__orders_1),[file(orders_1,e3_95_2_4_2__orders_1)]]). fof(e4_95_2_4_2__orders_1,plain,( r2_hidden(k4_tarski(c1_95_2_4_2__orders_1,c3_95_2_4_2__orders_1),c3_95_2__orders_1) ), inference(mizar_by,[status(thm),assumptions([dt_c1_95_2_4_2__orders_1,dt_c2_95_2_4_2__orders_1,dt_c3_95_2_4_2__orders_1,e1_95_2__orders_1,dt_c1_95_2__orders_1,dt_c2_95_2__orders_1,e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_2_4_2__orders_1])],[rc1_partfun1,rc2_ordinal1,dt_k1_xboole_0,cc1_ordinal1,cc2_ordinal1,fc2_ordinal1,rc1_finset_1,rc1_ordinal1,rc3_ordinal1,commutativity_k2_tarski,existence_m1_subset_1,dt_k1_tarski,dt_k2_tarski,dt_m1_subset_1,cc1_finset_1,cc3_ordinal1,fc1_finset_1,fc2_finset_1,fc2_subset_1,fc3_subset_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k4_tarski,dt_c1_95_2__orders_1,dt_c1_95_2_4_2__orders_1,dt_c2_95__orders_1,dt_c2_95_2__orders_1,dt_c2_95_2_4_2__orders_1,dt_c3_95_2__orders_1,dt_c3_95_2_4_2__orders_1,dt_c5_95__orders_1,t1_subset,t7_boole,d5_tarski,e3_95_2_4_2__orders_1,e1_95_2__orders_1,e3_95_2__orders_1,e1_95_2_4_2__orders_1]), [interesting(0.35),file(orders_1,e4_95_2_4_2__orders_1),[file(orders_1,e4_95_2_4_2__orders_1)]]). fof(i3_95_2_4_2__orders_1,theorem,( $true ), introduced(tautology,[file(orders_1,i3_95_2_4_2__orders_1)]), [interesting(0.35),trivial,file(orders_1,i3_95_2_4_2__orders_1)]). fof(i2_95_2_4_2__orders_1,plain,( r2_hidden(k4_tarski(c1_95_2_4_2__orders_1,c3_95_2_4_2__orders_1),c3_95_2__orders_1) ), inference(conclusion,[status(thm),assumptions([dt_c1_95_2_4_2__orders_1,dt_c2_95_2_4_2__orders_1,dt_c3_95_2_4_2__orders_1,e1_95_2__orders_1,dt_c1_95_2__orders_1,dt_c2_95_2__orders_1,e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_2_4_2__orders_1])],[e4_95_2_4_2__orders_1,i3_95_2_4_2__orders_1]), [interesting(0.35),file(orders_1,i2_95_2_4_2__orders_1),[file(orders_1,i2_95_2_4_2__orders_1)]]). fof(i1_95_2_4_2__orders_1,plain,( ~ ( r2_hidden(c1_95_2_4_2__orders_1,c2_95__orders_1) & r2_hidden(c2_95_2_4_2__orders_1,c2_95__orders_1) & r2_hidden(c3_95_2_4_2__orders_1,c2_95__orders_1) & r2_hidden(k4_tarski(c1_95_2_4_2__orders_1,c2_95_2_4_2__orders_1),c3_95_2__orders_1) & r2_hidden(k4_tarski(c2_95_2_4_2__orders_1,c3_95_2_4_2__orders_1),c3_95_2__orders_1) & ~ r2_hidden(k4_tarski(c1_95_2_4_2__orders_1,c3_95_2_4_2__orders_1),c3_95_2__orders_1) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_95_2_4_2__orders_1,dt_c2_95_2_4_2__orders_1,dt_c3_95_2_4_2__orders_1,e1_95_2__orders_1,dt_c1_95_2__orders_1,dt_c2_95_2__orders_1,e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1]),discharge_asm(discharge,[e1_95_2_4_2__orders_1])],[e1_95_2_4_2__orders_1,i2_95_2_4_2__orders_1]), [interesting(0.35),file(orders_1,i1_95_2_4_2__orders_1),[file(orders_1,i1_95_2_4_2__orders_1)]]). fof(i1_95_2_4_2_tmp__orders_1,plain,( ~ ( r2_hidden(c1_95_2_4_2__orders_1,c2_95__orders_1) & r2_hidden(c2_95_2_4_2__orders_1,c2_95__orders_1) & r2_hidden(c3_95_2_4_2__orders_1,c2_95__orders_1) & r2_hidden(k4_tarski(c1_95_2_4_2__orders_1,c2_95_2_4_2__orders_1),c3_95_2__orders_1) & r2_hidden(k4_tarski(c2_95_2_4_2__orders_1,c3_95_2_4_2__orders_1),c3_95_2__orders_1) & ~ r2_hidden(k4_tarski(c1_95_2_4_2__orders_1,c3_95_2_4_2__orders_1),c3_95_2__orders_1) ) ), inference(discharge_asm,[status(thm),assumptions([e1_95_2__orders_1,dt_c1_95_2__orders_1,dt_c2_95_2__orders_1,e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1]),discharge_asm(discharge,[dt_c1_95_2_4_2__orders_1,dt_c2_95_2_4_2__orders_1,dt_c3_95_2_4_2__orders_1])],[dt_c1_95_2_4_2__orders_1,dt_c2_95_2_4_2__orders_1,dt_c3_95_2_4_2__orders_1,i1_95_2_4_2__orders_1]), [interesting(0.5),e2_95_2_4__orders_1]). fof(e2_95_2_4__orders_1,plain,( r8_relat_2(c3_95_2__orders_1,c2_95__orders_1) ), inference(let,[status(thm),assumptions([e1_95_2__orders_1,dt_c1_95_2__orders_1,dt_c2_95_2__orders_1,e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1])],[i1_95_2_4_2_tmp__orders_1,antisymmetry_r2_hidden,dt_k4_tarski,dt_c2_95__orders_1,dt_c3_95_2__orders_1,d8_relat_2,dh_c1_95_2_4_2__orders_1,dh_c2_95_2_4_2__orders_1,dh_c3_95_2_4_2__orders_1]), [interesting(0.5),file(orders_1,e2_95_2_4__orders_1),[file(orders_1,e2_95_2_4__orders_1)]]). fof(dt_c1_95_2_4_3__orders_1,assumption,( $true ), introduced(assumption,[file(orders_1,c1_95_2_4_3__orders_1)]), [interesting(0.35),axiom,file(orders_1,c1_95_2_4_3__orders_1)]). fof(dt_c2_95_2_4_3__orders_1,assumption,( $true ), introduced(assumption,[file(orders_1,c2_95_2_4_3__orders_1)]), [interesting(0.35),axiom,file(orders_1,c2_95_2_4_3__orders_1)]). fof(dh_c1_95_2_4_3__orders_1,definition, ( ! [A] : ~ ( r2_hidden(c1_95_2_4_3__orders_1,c2_95__orders_1) & r2_hidden(A,c2_95__orders_1) & r2_hidden(k4_tarski(c1_95_2_4_3__orders_1,A),c3_95_2__orders_1) & r2_hidden(k4_tarski(A,c1_95_2_4_3__orders_1),c3_95_2__orders_1) & c1_95_2_4_3__orders_1 != A ) => ! [B,C] : ~ ( r2_hidden(B,c2_95__orders_1) & r2_hidden(C,c2_95__orders_1) & r2_hidden(k4_tarski(B,C),c3_95_2__orders_1) & r2_hidden(k4_tarski(C,B),c3_95_2__orders_1) & B != C ) ), introduced(definition,[new_symbol(c1_95_2_4_3__orders_1),file(orders_1,c1_95_2_4_3__orders_1)]), [interesting(0.35),axiom,file(orders_1,c1_95_2_4_3__orders_1)]). fof(dh_c2_95_2_4_3__orders_1,definition, ( ~ ( r2_hidden(c1_95_2_4_3__orders_1,c2_95__orders_1) & r2_hidden(c2_95_2_4_3__orders_1,c2_95__orders_1) & r2_hidden(k4_tarski(c1_95_2_4_3__orders_1,c2_95_2_4_3__orders_1),c3_95_2__orders_1) & r2_hidden(k4_tarski(c2_95_2_4_3__orders_1,c1_95_2_4_3__orders_1),c3_95_2__orders_1) & c1_95_2_4_3__orders_1 != c2_95_2_4_3__orders_1 ) => ! [A] : ~ ( r2_hidden(c1_95_2_4_3__orders_1,c2_95__orders_1) & r2_hidden(A,c2_95__orders_1) & r2_hidden(k4_tarski(c1_95_2_4_3__orders_1,A),c3_95_2__orders_1) & r2_hidden(k4_tarski(A,c1_95_2_4_3__orders_1),c3_95_2__orders_1) & c1_95_2_4_3__orders_1 != A ) ), introduced(definition,[new_symbol(c2_95_2_4_3__orders_1),file(orders_1,c2_95_2_4_3__orders_1)]), [interesting(0.35),axiom,file(orders_1,c2_95_2_4_3__orders_1)]). fof(e1_95_2_4_3__orders_1,assumption, ( r2_hidden(c1_95_2_4_3__orders_1,c2_95__orders_1) & r2_hidden(c2_95_2_4_3__orders_1,c2_95__orders_1) & r2_hidden(k4_tarski(c1_95_2_4_3__orders_1,c2_95_2_4_3__orders_1),c3_95_2__orders_1) & r2_hidden(k4_tarski(c2_95_2_4_3__orders_1,c1_95_2_4_3__orders_1),c3_95_2__orders_1) ), introduced(assumption,[file(orders_1,e1_95_2_4_3__orders_1)]), [interesting(0.35),axiom,file(orders_1,e1_95_2_4_3__orders_1)]). fof(e2_95_2_4_3__orders_1,plain, ( ( r2_hidden(k4_tarski(c1_95_2_4_3__orders_1,c2_95_2_4_3__orders_1),c5_95__orders_1) | ( r2_hidden(k4_tarski(c1_95_2_4_3__orders_1,c1_95_2__orders_1),c5_95__orders_1) & r2_hidden(k4_tarski(c2_95_2__orders_1,c2_95_2_4_3__orders_1),c5_95__orders_1) ) ) & ( r2_hidden(k4_tarski(c2_95_2_4_3__orders_1,c1_95_2_4_3__orders_1),c5_95__orders_1) | ( r2_hidden(k4_tarski(c2_95_2_4_3__orders_1,c1_95_2__orders_1),c5_95__orders_1) & r2_hidden(k4_tarski(c2_95_2__orders_1,c1_95_2_4_3__orders_1),c5_95__orders_1) ) ) ), inference(mizar_by,[status(thm),assumptions([dt_c1_95_2_4_3__orders_1,dt_c2_95_2_4_3__orders_1,e1_95_2_4_3__orders_1,dt_c1_95_2__orders_1,dt_c2_95_2__orders_1,e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1])],[rc1_partfun1,rc2_ordinal1,dt_k1_xboole_0,cc1_ordinal1,cc2_ordinal1,fc2_ordinal1,rc1_finset_1,rc1_ordinal1,rc3_ordinal1,commutativity_k2_tarski,existence_m1_subset_1,dt_k1_tarski,dt_k2_tarski,dt_m1_subset_1,cc1_finset_1,cc3_ordinal1,fc1_finset_1,fc2_finset_1,fc2_subset_1,fc3_subset_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k4_tarski,dt_c1_95_2__orders_1,dt_c1_95_2_4_3__orders_1,dt_c2_95__orders_1,dt_c2_95_2__orders_1,dt_c2_95_2_4_3__orders_1,dt_c3_95_2__orders_1,dt_c5_95__orders_1,t1_subset,t7_boole,d5_tarski,e1_95_2_4_3__orders_1,e3_95_2__orders_1]), [interesting(0.35),file(orders_1,e2_95_2_4_3__orders_1),[file(orders_1,e2_95_2_4_3__orders_1)]]). fof(e3_95_2_4_3__orders_1,plain,( ~ ( c1_95_2_4_3__orders_1 != c2_95_2_4_3__orders_1 & ~ ( r2_hidden(k4_tarski(c1_95_2_4_3__orders_1,c1_95_2__orders_1),c5_95__orders_1) & r2_hidden(k4_tarski(c2_95_2__orders_1,c1_95_2_4_3__orders_1),c5_95__orders_1) ) & ~ r2_hidden(k4_tarski(c2_95_2__orders_1,c1_95_2__orders_1),c5_95__orders_1) ) ), inference(mizar_by,[status(thm),assumptions([dt_c1_95_2_4_3__orders_1,dt_c2_95_2_4_3__orders_1,dt_c1_95_2__orders_1,dt_c2_95_2__orders_1,e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_2__orders_1,e1_95_2_4_3__orders_1])],[rc1_partfun1,rc2_ordinal1,dt_k1_xboole_0,cc1_ordinal1,cc2_ordinal1,fc2_ordinal1,rc1_finset_1,rc1_ordinal1,rc3_ordinal1,commutativity_k2_tarski,existence_m1_subset_1,dt_k1_tarski,dt_k2_tarski,dt_m1_subset_1,cc1_finset_1,cc3_ordinal1,fc1_finset_1,fc2_finset_1,fc2_subset_1,fc3_subset_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k4_tarski,dt_c1_95_2__orders_1,dt_c1_95_2_4_3__orders_1,dt_c2_95__orders_1,dt_c2_95_2__orders_1,dt_c2_95_2_4_3__orders_1,dt_c3_95_2__orders_1,dt_c5_95__orders_1,t1_subset,t7_boole,d5_tarski,e2_95_2_4_3__orders_1,e12_95__orders_1,e1_95_2__orders_1,e1_95_2_4_3__orders_1,d4_relat_2,d8_relat_2]), [interesting(0.35),file(orders_1,e3_95_2_4_3__orders_1),[file(orders_1,e3_95_2_4_3__orders_1)]]). fof(e4_95_2_4_3__orders_1,plain,( c1_95_2_4_3__orders_1 = c2_95_2_4_3__orders_1 ), inference(mizar_by,[status(thm),assumptions([dt_c1_95_2_4_3__orders_1,dt_c2_95_2_4_3__orders_1,dt_c1_95_2__orders_1,dt_c2_95_2__orders_1,e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_2__orders_1,e1_95_2_4_3__orders_1])],[rc1_partfun1,rc2_ordinal1,dt_k1_xboole_0,cc1_ordinal1,cc2_ordinal1,fc2_ordinal1,rc1_finset_1,rc1_ordinal1,rc3_ordinal1,commutativity_k2_tarski,existence_m1_subset_1,dt_k1_tarski,dt_k2_tarski,dt_m1_subset_1,cc1_finset_1,cc3_ordinal1,fc1_finset_1,fc2_finset_1,fc2_subset_1,fc3_subset_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k4_tarski,dt_c1_95_2__orders_1,dt_c1_95_2_4_3__orders_1,dt_c2_95__orders_1,dt_c2_95_2__orders_1,dt_c2_95_2_4_3__orders_1,dt_c3_95_2__orders_1,dt_c5_95__orders_1,t1_subset,t7_boole,d5_tarski,e3_95_2_4_3__orders_1,e12_95__orders_1,e1_95_2__orders_1,e1_95_2_4_3__orders_1,d8_relat_2]), [interesting(0.35),file(orders_1,e4_95_2_4_3__orders_1),[file(orders_1,e4_95_2_4_3__orders_1)]]). fof(i3_95_2_4_3__orders_1,theorem,( $true ), introduced(tautology,[file(orders_1,i3_95_2_4_3__orders_1)]), [interesting(0.35),trivial,file(orders_1,i3_95_2_4_3__orders_1)]). fof(i2_95_2_4_3__orders_1,plain,( c1_95_2_4_3__orders_1 = c2_95_2_4_3__orders_1 ), inference(conclusion,[status(thm),assumptions([dt_c1_95_2_4_3__orders_1,dt_c2_95_2_4_3__orders_1,dt_c1_95_2__orders_1,dt_c2_95_2__orders_1,e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_2__orders_1,e1_95_2_4_3__orders_1])],[e4_95_2_4_3__orders_1,i3_95_2_4_3__orders_1]), [interesting(0.35),file(orders_1,i2_95_2_4_3__orders_1),[file(orders_1,i2_95_2_4_3__orders_1)]]). fof(i1_95_2_4_3__orders_1,plain,( ~ ( r2_hidden(c1_95_2_4_3__orders_1,c2_95__orders_1) & r2_hidden(c2_95_2_4_3__orders_1,c2_95__orders_1) & r2_hidden(k4_tarski(c1_95_2_4_3__orders_1,c2_95_2_4_3__orders_1),c3_95_2__orders_1) & r2_hidden(k4_tarski(c2_95_2_4_3__orders_1,c1_95_2_4_3__orders_1),c3_95_2__orders_1) & c1_95_2_4_3__orders_1 != c2_95_2_4_3__orders_1 ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_95_2_4_3__orders_1,dt_c2_95_2_4_3__orders_1,dt_c1_95_2__orders_1,dt_c2_95_2__orders_1,e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_2__orders_1]),discharge_asm(discharge,[e1_95_2_4_3__orders_1])],[e1_95_2_4_3__orders_1,i2_95_2_4_3__orders_1]), [interesting(0.35),file(orders_1,i1_95_2_4_3__orders_1),[file(orders_1,i1_95_2_4_3__orders_1)]]). fof(i1_95_2_4_3_tmp__orders_1,plain,( ~ ( r2_hidden(c1_95_2_4_3__orders_1,c2_95__orders_1) & r2_hidden(c2_95_2_4_3__orders_1,c2_95__orders_1) & r2_hidden(k4_tarski(c1_95_2_4_3__orders_1,c2_95_2_4_3__orders_1),c3_95_2__orders_1) & r2_hidden(k4_tarski(c2_95_2_4_3__orders_1,c1_95_2_4_3__orders_1),c3_95_2__orders_1) & c1_95_2_4_3__orders_1 != c2_95_2_4_3__orders_1 ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_95_2__orders_1,dt_c2_95_2__orders_1,e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_2__orders_1]),discharge_asm(discharge,[dt_c1_95_2_4_3__orders_1,dt_c2_95_2_4_3__orders_1])],[dt_c1_95_2_4_3__orders_1,dt_c2_95_2_4_3__orders_1,i1_95_2_4_3__orders_1]), [interesting(0.5),e3_95_2_4__orders_1]). fof(e3_95_2_4__orders_1,plain,( r4_relat_2(c3_95_2__orders_1,c2_95__orders_1) ), inference(let,[status(thm),assumptions([dt_c1_95_2__orders_1,dt_c2_95_2__orders_1,e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_2__orders_1])],[i1_95_2_4_3_tmp__orders_1,antisymmetry_r2_hidden,dt_k4_tarski,dt_c2_95__orders_1,dt_c3_95_2__orders_1,d4_relat_2,dh_c1_95_2_4_3__orders_1,dh_c2_95_2_4_3__orders_1]), [interesting(0.5),file(orders_1,e3_95_2_4__orders_1),[file(orders_1,e3_95_2_4__orders_1)]]). fof(i3_95_2_4__orders_1,theorem,( $true ), introduced(tautology,[file(orders_1,i3_95_2_4__orders_1)]), [interesting(0.5),trivial,file(orders_1,i3_95_2_4__orders_1)]). fof(i2_95_2_4__orders_1,plain,( r4_relat_2(c3_95_2__orders_1,c2_95__orders_1) ), inference(conclusion,[status(thm),assumptions([dt_c1_95_2__orders_1,dt_c2_95_2__orders_1,e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_2__orders_1])],[e3_95_2_4__orders_1,i3_95_2_4__orders_1]), [interesting(0.5),file(orders_1,i2_95_2_4__orders_1),[file(orders_1,i2_95_2_4__orders_1)]]). fof(i1_95_2_4__orders_1,plain, ( r8_relat_2(c3_95_2__orders_1,c2_95__orders_1) & r4_relat_2(c3_95_2__orders_1,c2_95__orders_1) ), inference(conclusion,[status(thm),assumptions([dt_c1_95_2__orders_1,dt_c2_95_2__orders_1,e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_2__orders_1])],[e2_95_2_4__orders_1,i2_95_2_4__orders_1]), [interesting(0.5),file(orders_1,i1_95_2_4__orders_1),[file(orders_1,i1_95_2_4__orders_1)]]). fof(e8_95_2__orders_1,plain,( r2_orders_1(c3_95_2__orders_1,c2_95__orders_1) ), inference(conclusion,[status(thm),assumptions([dt_c1_95_2__orders_1,dt_c2_95_2__orders_1,e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_2__orders_1])],[dt_c2_95__orders_1,dt_c3_95_2__orders_1,d7_orders_1,e1_95_2_4__orders_1,i1_95_2_4__orders_1]), [interesting(0.65),file(orders_1,e8_95_2__orders_1),[file(orders_1,e8_95_2__orders_1)]]). fof(dt_c1_95_2_1__orders_1,assumption,( $true ), introduced(assumption,[file(orders_1,c1_95_2_1__orders_1)]), [interesting(0.5),axiom,file(orders_1,c1_95_2_1__orders_1)]). fof(dh_c1_95_2_1__orders_1,definition, ( ! [A] : ~ ( r2_hidden(k4_tarski(c1_95_2_1__orders_1,A),c5_95__orders_1) & ~ r2_hidden(k4_tarski(c1_95_2_1__orders_1,A),c3_95_2__orders_1) ) => ! [B,C] : ~ ( r2_hidden(k4_tarski(B,C),c5_95__orders_1) & ~ r2_hidden(k4_tarski(B,C),c3_95_2__orders_1) ) ), introduced(definition,[new_symbol(c1_95_2_1__orders_1),file(orders_1,c1_95_2_1__orders_1)]), [interesting(0.5),axiom,file(orders_1,c1_95_2_1__orders_1)]). fof(dh_c2_95_2_1__orders_1,definition, ( ~ ( r2_hidden(k4_tarski(c1_95_2_1__orders_1,c2_95_2_1__orders_1),c5_95__orders_1) & ~ r2_hidden(k4_tarski(c1_95_2_1__orders_1,c2_95_2_1__orders_1),c3_95_2__orders_1) ) => ! [A] : ~ ( r2_hidden(k4_tarski(c1_95_2_1__orders_1,A),c5_95__orders_1) & ~ r2_hidden(k4_tarski(c1_95_2_1__orders_1,A),c3_95_2__orders_1) ) ), introduced(definition,[new_symbol(c2_95_2_1__orders_1),file(orders_1,c2_95_2_1__orders_1)]), [interesting(0.5),axiom,file(orders_1,c2_95_2_1__orders_1)]). fof(e1_95_2_1__orders_1,assumption,( r2_hidden(k4_tarski(c1_95_2_1__orders_1,c2_95_2_1__orders_1),c5_95__orders_1) ), introduced(assumption,[file(orders_1,e1_95_2_1__orders_1)]), [interesting(0.5),axiom,file(orders_1,e1_95_2_1__orders_1)]). fof(dt_c2_95_2_1__orders_1,assumption,( $true ), introduced(assumption,[file(orders_1,c2_95_2_1__orders_1)]), [interesting(0.5),axiom,file(orders_1,c2_95_2_1__orders_1)]). fof(e2_95_2_1__orders_1,plain, ( r2_hidden(c1_95_2_1__orders_1,k3_relat_1(c5_95__orders_1)) & r2_hidden(c2_95_2_1__orders_1,k3_relat_1(c5_95__orders_1)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_95_2_1__orders_1,dt_c2_95_2_1__orders_1,e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_2_1__orders_1])],[rc1_partfun1,rc2_ordinal1,dt_k1_xboole_0,cc1_ordinal1,cc2_ordinal1,fc2_ordinal1,fc9_finset_1,rc1_finset_1,rc1_ordinal1,rc3_ordinal1,t1_boole,commutativity_k2_tarski,commutativity_k2_xboole_0,idempotence_k2_xboole_0,existence_m1_subset_1,dt_k1_relat_1,dt_k1_tarski,dt_k2_relat_1,dt_k2_tarski,dt_k2_xboole_0,dt_m1_subset_1,cc1_finset_1,cc3_ordinal1,fc1_finset_1,fc2_finset_1,fc2_subset_1,fc3_subset_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k3_relat_1,dt_k4_tarski,dt_c1_95_2_1__orders_1,dt_c2_95_2_1__orders_1,dt_c5_95__orders_1,t1_subset,t7_boole,d6_relat_1,d5_tarski,e1_95_2_1__orders_1,t30_relat_1]), [interesting(0.5),file(orders_1,e2_95_2_1__orders_1),[file(orders_1,e2_95_2_1__orders_1)]]). fof(e3_95_2_1__orders_1,plain,( r2_hidden(k4_tarski(c1_95_2_1__orders_1,c2_95_2_1__orders_1),c3_95_2__orders_1) ), inference(mizar_by,[status(thm),assumptions([dt_c1_95_2_1__orders_1,dt_c2_95_2_1__orders_1,dt_c1_95_2__orders_1,dt_c2_95_2__orders_1,e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_2_1__orders_1])],[rc1_partfun1,rc2_ordinal1,dt_k1_xboole_0,cc1_ordinal1,cc2_finset_1,cc2_ordinal1,fc2_ordinal1,fc9_finset_1,rc1_finset_1,rc1_ordinal1,rc3_finset_1,rc3_ordinal1,rc4_finset_1,t1_boole,commutativity_k2_tarski,commutativity_k2_xboole_0,idempotence_k2_xboole_0,existence_m1_subset_1,dt_k1_relat_1,dt_k1_tarski,dt_k1_zfmisc_1,dt_k2_relat_1,dt_k2_tarski,dt_k2_xboole_0,dt_m1_subset_1,cc1_finset_1,cc3_ordinal1,fc1_finset_1,fc1_subset_1,fc2_finset_1,fc2_subset_1,fc3_subset_1,rc1_subset_1,rc2_subset_1,t2_subset,t4_subset,t5_subset,t6_boole,t8_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k3_relat_1,dt_k4_tarski,dt_c1_95__orders_1,dt_c1_95_2__orders_1,dt_c1_95_2_1__orders_1,dt_c2_95__orders_1,dt_c2_95_2__orders_1,dt_c2_95_2_1__orders_1,dt_c3_95_2__orders_1,dt_c4_95__orders_1,dt_c5_95__orders_1,t1_subset,t3_subset,t7_boole,d6_relat_1,d5_tarski,e2_95_2_1__orders_1,e10_95__orders_1,e3_95_2__orders_1,e1_95_2_1__orders_1]), [interesting(0.5),file(orders_1,e3_95_2_1__orders_1),[file(orders_1,e3_95_2_1__orders_1)]]). fof(i4_95_2_1__orders_1,theorem,( $true ), introduced(tautology,[file(orders_1,i4_95_2_1__orders_1)]), [interesting(0.5),trivial,file(orders_1,i4_95_2_1__orders_1)]). fof(i3_95_2_1__orders_1,plain,( r2_hidden(k4_tarski(c1_95_2_1__orders_1,c2_95_2_1__orders_1),c3_95_2__orders_1) ), inference(conclusion,[status(thm),assumptions([dt_c1_95_2_1__orders_1,dt_c2_95_2_1__orders_1,dt_c1_95_2__orders_1,dt_c2_95_2__orders_1,e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_2_1__orders_1])],[e3_95_2_1__orders_1,i4_95_2_1__orders_1]), [interesting(0.5),file(orders_1,i3_95_2_1__orders_1),[file(orders_1,i3_95_2_1__orders_1)]]). fof(i2_95_2_1__orders_1,plain,( ~ ( r2_hidden(k4_tarski(c1_95_2_1__orders_1,c2_95_2_1__orders_1),c5_95__orders_1) & ~ r2_hidden(k4_tarski(c1_95_2_1__orders_1,c2_95_2_1__orders_1),c3_95_2__orders_1) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_95_2_1__orders_1,dt_c2_95_2_1__orders_1,dt_c1_95_2__orders_1,dt_c2_95_2__orders_1,e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1]),discharge_asm(discharge,[e1_95_2_1__orders_1])],[e1_95_2_1__orders_1,i3_95_2_1__orders_1]), [interesting(0.5),file(orders_1,i2_95_2_1__orders_1),[file(orders_1,i2_95_2_1__orders_1)]]). fof(i2_95_2_1_tmp__orders_1,plain,( ~ ( r2_hidden(k4_tarski(c1_95_2_1__orders_1,c2_95_2_1__orders_1),c5_95__orders_1) & ~ r2_hidden(k4_tarski(c1_95_2_1__orders_1,c2_95_2_1__orders_1),c3_95_2__orders_1) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_95_2_1__orders_1,dt_c1_95_2__orders_1,dt_c2_95_2__orders_1,e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1]),discharge_asm(discharge,[dt_c2_95_2_1__orders_1])],[dt_c2_95_2_1__orders_1,i2_95_2_1__orders_1]), [interesting(0.5),i1_95_2_1__orders_1]). fof(i1_95_2_1__orders_1,plain,( ! [A] : ~ ( r2_hidden(k4_tarski(c1_95_2_1__orders_1,A),c5_95__orders_1) & ~ r2_hidden(k4_tarski(c1_95_2_1__orders_1,A),c3_95_2__orders_1) ) ), inference(let,[status(thm),assumptions([dt_c1_95_2_1__orders_1,dt_c1_95_2__orders_1,dt_c2_95_2__orders_1,e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1])],[i2_95_2_1_tmp__orders_1,dh_c2_95_2_1__orders_1]), [interesting(0.5),file(orders_1,i1_95_2_1__orders_1),[file(orders_1,i1_95_2_1__orders_1)]]). fof(i1_95_2_1_tmp__orders_1,plain,( ! [A] : ~ ( r2_hidden(k4_tarski(c1_95_2_1__orders_1,A),c5_95__orders_1) & ~ r2_hidden(k4_tarski(c1_95_2_1__orders_1,A),c3_95_2__orders_1) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_95_2__orders_1,dt_c2_95_2__orders_1,e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1]),discharge_asm(discharge,[dt_c1_95_2_1__orders_1])],[dt_c1_95_2_1__orders_1,i1_95_2_1__orders_1]), [interesting(0.65),e4_95_2__orders_1]). fof(e4_95_2__orders_1,plain,( r1_tarski(c5_95__orders_1,c3_95_2__orders_1) ), inference(let,[status(thm),assumptions([dt_c1_95_2__orders_1,dt_c2_95_2__orders_1,e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1])],[i1_95_2_1_tmp__orders_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k4_tarski,dt_c3_95_2__orders_1,dt_c5_95__orders_1,d3_relat_1,dh_c1_95_2_1__orders_1]), [interesting(0.65),file(orders_1,e4_95_2__orders_1),[file(orders_1,e4_95_2__orders_1)]]). fof(t1_xboole_1,theorem,( ! [A,B,C] : ( ( r1_tarski(A,B) & r1_tarski(B,C) ) => r1_tarski(A,C) ) ), file(xboole_1,t1_xboole_1), [interesting(0.9),axiom,file(xboole_1,t1_xboole_1)]). fof(e5_95_2__orders_1,plain,( r1_tarski(c1_95__orders_1,c3_95_2__orders_1) ), inference(mizar_by,[status(thm),assumptions([dt_c1_95_2__orders_1,dt_c2_95_2__orders_1,e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1])],[rc1_partfun1,rc2_ordinal1,antisymmetry_r2_hidden,dt_k1_xboole_0,cc1_ordinal1,cc2_finset_1,cc2_ordinal1,fc2_ordinal1,fc9_finset_1,rc1_finset_1,rc1_ordinal1,rc3_finset_1,rc3_ordinal1,rc4_finset_1,t1_boole,t1_subset,t4_subset,t5_subset,cc1_finset_1,cc3_ordinal1,rc1_subset_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,existence_m1_subset_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k2_relat_1,dt_k2_xboole_0,dt_m1_subset_1,fc1_subset_1,reflexivity_r1_tarski,dt_k3_relat_1,dt_c1_95__orders_1,dt_c2_95__orders_1,dt_c3_95_2__orders_1,dt_c4_95__orders_1,dt_c5_95__orders_1,t3_subset,d6_relat_1,e4_95_2__orders_1,e10_95__orders_1,t1_xboole_1]), [interesting(0.65),file(orders_1,e5_95_2__orders_1),[file(orders_1,e5_95_2__orders_1)]]). fof(dt_c1_95_2_2__orders_1,assumption,( $true ), introduced(assumption,[file(orders_1,c1_95_2_2__orders_1)]), [interesting(0.5),axiom,file(orders_1,c1_95_2_2__orders_1)]). fof(dh_c1_95_2_2__orders_1,definition, ( ~ ( r2_hidden(c1_95_2_2__orders_1,c3_95_2__orders_1) & ~ r2_hidden(c1_95_2_2__orders_1,k2_zfmisc_1(c2_95__orders_1,c2_95__orders_1)) ) => ! [A] : ~ ( r2_hidden(A,c3_95_2__orders_1) & ~ r2_hidden(A,k2_zfmisc_1(c2_95__orders_1,c2_95__orders_1)) ) ), introduced(definition,[new_symbol(c1_95_2_2__orders_1),file(orders_1,c1_95_2_2__orders_1)]), [interesting(0.5),axiom,file(orders_1,c1_95_2_2__orders_1)]). fof(e1_95_2_2__orders_1,assumption,( r2_hidden(c1_95_2_2__orders_1,c3_95_2__orders_1) ), introduced(assumption,[file(orders_1,e1_95_2_2__orders_1)]), [interesting(0.5),axiom,file(orders_1,e1_95_2_2__orders_1)]). fof(dh_c2_95_2_2__orders_1,definition, ( ? [A,B] : c1_95_2_2__orders_1 = k4_tarski(A,B) => ? [C] : c1_95_2_2__orders_1 = k4_tarski(c2_95_2_2__orders_1,C) ), introduced(definition,[new_symbol(c2_95_2_2__orders_1),file(orders_1,c2_95_2_2__orders_1)]), [interesting(0.5),axiom,file(orders_1,c2_95_2_2__orders_1)]). fof(d1_relat_1,definition,( ! [A] : ( v1_relat_1(A) <=> ! [B] : ~ ( r2_hidden(B,A) & ! [C,D] : B != k4_tarski(C,D) ) ) ), file(relat_1,d1_relat_1), [interesting(0.9),axiom,file(relat_1,d1_relat_1)]). fof(e2_95_2_2__orders_1,plain,( ? [A,B] : c1_95_2_2__orders_1 = k4_tarski(A,B) ), inference(mizar_by,[status(thm),assumptions([dt_c1_95_2_2__orders_1,dt_c1_95_2__orders_1,dt_c2_95_2__orders_1,e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_2_2__orders_1])],[rc1_partfun1,rc2_ordinal1,dt_k1_xboole_0,cc1_ordinal1,cc2_ordinal1,fc2_ordinal1,rc1_finset_1,rc1_ordinal1,rc3_ordinal1,commutativity_k2_tarski,existence_m1_subset_1,dt_k1_tarski,dt_k2_tarski,dt_m1_subset_1,cc1_finset_1,cc3_ordinal1,fc1_finset_1,fc2_finset_1,fc2_subset_1,fc3_subset_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k4_tarski,dt_c1_95_2_2__orders_1,dt_c3_95_2__orders_1,t1_subset,t7_boole,d5_tarski,e1_95_2_2__orders_1,d1_relat_1]), [interesting(0.5),file(orders_1,e2_95_2_2__orders_1),[file(orders_1,e2_95_2_2__orders_1)]]). fof(dt_c2_95_2_2__orders_1,plain,( $true ), inference(consider,[status(thm),assumptions([dt_c1_95_2_2__orders_1,dt_c1_95_2__orders_1,dt_c2_95_2__orders_1,e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_2_2__orders_1])],[dh_c2_95_2_2__orders_1,e2_95_2_2__orders_1]), [interesting(0.5),file(orders_1,c2_95_2_2__orders_1),[file(orders_1,c2_95_2_2__orders_1)]]). fof(dh_c3_95_2_2__orders_1,definition, ( ? [A] : c1_95_2_2__orders_1 = k4_tarski(c2_95_2_2__orders_1,A) => c1_95_2_2__orders_1 = k4_tarski(c2_95_2_2__orders_1,c3_95_2_2__orders_1) ), introduced(definition,[new_symbol(c3_95_2_2__orders_1),file(orders_1,c3_95_2_2__orders_1)]), [interesting(0.5),axiom,file(orders_1,c3_95_2_2__orders_1)]). fof(dt_c3_95_2_2__orders_1,plain,( $true ), inference(consider,[status(thm),assumptions([dt_c1_95_2_2__orders_1,dt_c1_95_2__orders_1,dt_c2_95_2__orders_1,e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_2_2__orders_1])],[dh_c2_95_2_2__orders_1,dh_c3_95_2_2__orders_1,e2_95_2_2__orders_1]), [interesting(0.5),file(orders_1,c3_95_2_2__orders_1),[file(orders_1,c3_95_2_2__orders_1)]]). fof(e3_95_2_2__orders_1,plain,( c1_95_2_2__orders_1 = k4_tarski(c2_95_2_2__orders_1,c3_95_2_2__orders_1) ), inference(consider,[status(thm),assumptions([dt_c1_95_2_2__orders_1,dt_c1_95_2__orders_1,dt_c2_95_2__orders_1,e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_2_2__orders_1])],[dh_c2_95_2_2__orders_1,dh_c3_95_2_2__orders_1,e2_95_2_2__orders_1]), [interesting(0.5),file(orders_1,e3_95_2_2__orders_1),[file(orders_1,e3_95_2_2__orders_1)]]). fof(e4_95_2_2__orders_1,plain, ( r2_hidden(c2_95_2_2__orders_1,c2_95__orders_1) & r2_hidden(c3_95_2_2__orders_1,c2_95__orders_1) ), inference(mizar_by,[status(thm),assumptions([dt_c1_95_2_2__orders_1,dt_c1_95_2__orders_1,dt_c2_95_2__orders_1,e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_2_2__orders_1])],[rc1_partfun1,rc2_ordinal1,dt_k1_xboole_0,cc1_ordinal1,cc2_ordinal1,fc2_ordinal1,rc1_finset_1,rc1_ordinal1,rc3_ordinal1,commutativity_k2_tarski,existence_m1_subset_1,dt_k1_tarski,dt_k2_tarski,dt_m1_subset_1,cc1_finset_1,cc3_ordinal1,fc1_finset_1,fc2_finset_1,fc2_subset_1,fc3_subset_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k4_tarski,dt_c1_95_2__orders_1,dt_c1_95_2_2__orders_1,dt_c2_95__orders_1,dt_c2_95_2__orders_1,dt_c2_95_2_2__orders_1,dt_c3_95_2__orders_1,dt_c3_95_2_2__orders_1,dt_c5_95__orders_1,t1_subset,t7_boole,d5_tarski,e3_95_2__orders_1,e1_95_2_2__orders_1,e3_95_2_2__orders_1]), [interesting(0.5),file(orders_1,e4_95_2_2__orders_1),[file(orders_1,e4_95_2_2__orders_1)]]). fof(t106_zfmisc_1,theorem,( ! [A,B,C,D] : ( r2_hidden(k4_tarski(A,B),k2_zfmisc_1(C,D)) <=> ( r2_hidden(A,C) & r2_hidden(B,D) ) ) ), file(zfmisc_1,t106_zfmisc_1), [interesting(0.9),axiom,file(zfmisc_1,t106_zfmisc_1)]). fof(e5_95_2_2__orders_1,plain,( r2_hidden(c1_95_2_2__orders_1,k2_zfmisc_1(c2_95__orders_1,c2_95__orders_1)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_95_2_2__orders_1,dt_c1_95_2__orders_1,dt_c2_95_2__orders_1,e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_2_2__orders_1])],[rc1_partfun1,rc2_ordinal1,dt_k1_xboole_0,cc1_ordinal1,cc2_ordinal1,fc14_finset_1,fc2_ordinal1,rc1_finset_1,rc1_ordinal1,rc3_ordinal1,commutativity_k2_tarski,existence_m1_subset_1,dt_k1_tarski,dt_k2_tarski,dt_m1_subset_1,cc1_finset_1,cc3_ordinal1,fc1_finset_1,fc2_finset_1,fc2_subset_1,fc3_subset_1,fc4_subset_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k2_zfmisc_1,dt_k4_tarski,dt_c1_95_2_2__orders_1,dt_c2_95__orders_1,dt_c2_95_2_2__orders_1,dt_c3_95_2_2__orders_1,t1_subset,t7_boole,d5_tarski,e4_95_2_2__orders_1,e3_95_2_2__orders_1,t106_zfmisc_1]), [interesting(0.5),file(orders_1,e5_95_2_2__orders_1),[file(orders_1,e5_95_2_2__orders_1)]]). fof(i3_95_2_2__orders_1,theorem,( $true ), introduced(tautology,[file(orders_1,i3_95_2_2__orders_1)]), [interesting(0.5),trivial,file(orders_1,i3_95_2_2__orders_1)]). fof(i2_95_2_2__orders_1,plain,( r2_hidden(c1_95_2_2__orders_1,k2_zfmisc_1(c2_95__orders_1,c2_95__orders_1)) ), inference(conclusion,[status(thm),assumptions([dt_c1_95_2_2__orders_1,dt_c1_95_2__orders_1,dt_c2_95_2__orders_1,e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_2_2__orders_1])],[e5_95_2_2__orders_1,i3_95_2_2__orders_1]), [interesting(0.5),file(orders_1,i2_95_2_2__orders_1),[file(orders_1,i2_95_2_2__orders_1)]]). fof(i1_95_2_2__orders_1,plain,( ~ ( r2_hidden(c1_95_2_2__orders_1,c3_95_2__orders_1) & ~ r2_hidden(c1_95_2_2__orders_1,k2_zfmisc_1(c2_95__orders_1,c2_95__orders_1)) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_95_2_2__orders_1,dt_c1_95_2__orders_1,dt_c2_95_2__orders_1,e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1]),discharge_asm(discharge,[e1_95_2_2__orders_1])],[e1_95_2_2__orders_1,i2_95_2_2__orders_1]), [interesting(0.5),file(orders_1,i1_95_2_2__orders_1),[file(orders_1,i1_95_2_2__orders_1)]]). fof(i1_95_2_2_tmp__orders_1,plain,( ~ ( r2_hidden(c1_95_2_2__orders_1,c3_95_2__orders_1) & ~ r2_hidden(c1_95_2_2__orders_1,k2_zfmisc_1(c2_95__orders_1,c2_95__orders_1)) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_95_2__orders_1,dt_c2_95_2__orders_1,e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1]),discharge_asm(discharge,[dt_c1_95_2_2__orders_1])],[dt_c1_95_2_2__orders_1,i1_95_2_2__orders_1]), [interesting(0.65),e6_95_2__orders_1]). fof(e6_95_2__orders_1,plain,( r1_tarski(c3_95_2__orders_1,k2_zfmisc_1(c2_95__orders_1,c2_95__orders_1)) ), inference(let,[status(thm),assumptions([dt_c1_95_2__orders_1,dt_c2_95_2__orders_1,e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1])],[i1_95_2_2_tmp__orders_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k2_zfmisc_1,dt_c2_95__orders_1,dt_c3_95_2__orders_1,d3_tarski,dh_c1_95_2_2__orders_1]), [interesting(0.65),file(orders_1,e6_95_2__orders_1),[file(orders_1,e6_95_2__orders_1)]]). fof(dt_c1_95_2_3_1__orders_1,assumption,( $true ), introduced(assumption,[file(orders_1,c1_95_2_3_1__orders_1)]), [interesting(0.35),axiom,file(orders_1,c1_95_2_3_1__orders_1)]). fof(dh_c1_95_2_3_1__orders_1,definition, ( ~ ( r2_hidden(c1_95_2_3_1__orders_1,k3_relat_1(c3_95_2__orders_1)) & ~ r2_hidden(c1_95_2_3_1__orders_1,c2_95__orders_1) ) => ! [A] : ~ ( r2_hidden(A,k3_relat_1(c3_95_2__orders_1)) & ~ r2_hidden(A,c2_95__orders_1) ) ), introduced(definition,[new_symbol(c1_95_2_3_1__orders_1),file(orders_1,c1_95_2_3_1__orders_1)]), [interesting(0.35),axiom,file(orders_1,c1_95_2_3_1__orders_1)]). fof(e1_95_2_3_1__orders_1,assumption,( r2_hidden(c1_95_2_3_1__orders_1,k3_relat_1(c3_95_2__orders_1)) ), introduced(assumption,[file(orders_1,e1_95_2_3_1__orders_1)]), [interesting(0.35),axiom,file(orders_1,e1_95_2_3_1__orders_1)]). fof(e1_95_2_3_1_2__orders_1,assumption,( r2_hidden(c1_95_2_3_1__orders_1,k2_relat_1(c3_95_2__orders_1)) ), introduced(assumption,[file(orders_1,e1_95_2_3_1_2__orders_1)]), [interesting(0.2),axiom,file(orders_1,e1_95_2_3_1_2__orders_1)]). fof(e2_95_2_3_1_2__orders_1,plain,( ? [A] : r2_hidden(k4_tarski(A,c1_95_2_3_1__orders_1),c3_95_2__orders_1) ), inference(mizar_by,[status(thm),assumptions([dt_c1_95_2_3_1__orders_1,dt_c1_95_2__orders_1,dt_c2_95_2__orders_1,e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_2_3_1_2__orders_1])],[rc1_partfun1,rc2_ordinal1,dt_k1_xboole_0,cc1_ordinal1,cc2_ordinal1,fc2_ordinal1,rc1_finset_1,rc1_ordinal1,rc3_ordinal1,commutativity_k2_tarski,existence_m1_subset_1,dt_k1_tarski,dt_k2_tarski,dt_m1_subset_1,cc1_finset_1,cc3_ordinal1,fc1_finset_1,fc2_finset_1,fc2_subset_1,fc3_subset_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k2_relat_1,dt_k4_tarski,dt_c1_95_2_3_1__orders_1,dt_c3_95_2__orders_1,t1_subset,t7_boole,d5_tarski,e1_95_2_3_1_2__orders_1,d5_relat_1]), [interesting(0.2),file(orders_1,e2_95_2_3_1_2__orders_1),[file(orders_1,e2_95_2_3_1_2__orders_1)]]). fof(e3_95_2_3_1_2__orders_1,plain,( r2_hidden(c1_95_2_3_1__orders_1,c2_95__orders_1) ), inference(mizar_by,[status(thm),assumptions([dt_c1_95_2_3_1__orders_1,e1_95_2_3_1_2__orders_1,dt_c1_95_2__orders_1,dt_c2_95_2__orders_1,e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1])],[rc1_partfun1,rc2_ordinal1,dt_k1_xboole_0,cc1_ordinal1,cc2_ordinal1,fc2_ordinal1,rc1_finset_1,rc1_ordinal1,rc3_ordinal1,commutativity_k2_tarski,existence_m1_subset_1,dt_k1_tarski,dt_k2_tarski,dt_m1_subset_1,cc1_finset_1,cc3_ordinal1,fc1_finset_1,fc2_finset_1,fc2_subset_1,fc3_subset_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k4_tarski,dt_c1_95_2__orders_1,dt_c1_95_2_3_1__orders_1,dt_c2_95__orders_1,dt_c2_95_2__orders_1,dt_c3_95_2__orders_1,dt_c5_95__orders_1,t1_subset,t7_boole,d5_tarski,e2_95_2_3_1_2__orders_1,e3_95_2__orders_1]), [interesting(0.2),file(orders_1,e3_95_2_3_1_2__orders_1),[file(orders_1,e3_95_2_3_1_2__orders_1)]]). fof(i2_95_2_3_1_2__orders_1,theorem,( $true ), introduced(tautology,[file(orders_1,i2_95_2_3_1_2__orders_1)]), [interesting(0.2),trivial,file(orders_1,i2_95_2_3_1_2__orders_1)]). fof(i1_95_2_3_1_2__orders_1,plain,( r2_hidden(c1_95_2_3_1__orders_1,c2_95__orders_1) ), inference(conclusion,[status(thm),assumptions([dt_c1_95_2_3_1__orders_1,e1_95_2_3_1_2__orders_1,dt_c1_95_2__orders_1,dt_c2_95_2__orders_1,e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1])],[e3_95_2_3_1_2__orders_1,i2_95_2_3_1_2__orders_1]), [interesting(0.2),file(orders_1,i1_95_2_3_1_2__orders_1),[file(orders_1,i1_95_2_3_1_2__orders_1)]]). fof(e4_95_2_3_1__orders_1,plain, ( r2_hidden(c1_95_2_3_1__orders_1,k2_relat_1(c3_95_2__orders_1)) => r2_hidden(c1_95_2_3_1__orders_1,c2_95__orders_1) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_95_2_3_1__orders_1,dt_c1_95_2__orders_1,dt_c2_95_2__orders_1,e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1]),discharge_asm(discharge,[e1_95_2_3_1_2__orders_1])],[e1_95_2_3_1_2__orders_1,i1_95_2_3_1_2__orders_1]), [interesting(0.35),file(orders_1,e4_95_2_3_1__orders_1),[file(orders_1,e4_95_2_3_1__orders_1)]]). fof(e2_95_2_3_1__orders_1,plain,( r2_hidden(c1_95_2_3_1__orders_1,k2_xboole_0(k1_relat_1(c3_95_2__orders_1),k2_relat_1(c3_95_2__orders_1))) ), inference(mizar_by,[status(thm),assumptions([dt_c1_95_2_3_1__orders_1,dt_c1_95_2__orders_1,dt_c2_95_2__orders_1,e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_2_3_1__orders_1])],[rc1_partfun1,rc2_ordinal1,dt_k1_xboole_0,cc1_ordinal1,cc2_ordinal1,fc2_ordinal1,fc9_finset_1,rc1_finset_1,rc1_ordinal1,rc3_ordinal1,t1_boole,existence_m1_subset_1,dt_m1_subset_1,cc1_finset_1,cc3_ordinal1,t2_subset,t6_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,antisymmetry_r2_hidden,dt_k1_relat_1,dt_k2_relat_1,dt_k2_xboole_0,dt_k3_relat_1,dt_c1_95_2_3_1__orders_1,dt_c3_95_2__orders_1,t1_subset,t7_boole,d6_relat_1,e1_95_2_3_1__orders_1]), [interesting(0.35),file(orders_1,e2_95_2_3_1__orders_1),[file(orders_1,e2_95_2_3_1__orders_1)]]). fof(e1_95_2_3_1_1__orders_1,assumption,( r2_hidden(c1_95_2_3_1__orders_1,k1_relat_1(c3_95_2__orders_1)) ), introduced(assumption,[file(orders_1,e1_95_2_3_1_1__orders_1)]), [interesting(0.2),axiom,file(orders_1,e1_95_2_3_1_1__orders_1)]). fof(e2_95_2_3_1_1__orders_1,plain,( ? [A] : r2_hidden(k4_tarski(c1_95_2_3_1__orders_1,A),c3_95_2__orders_1) ), inference(mizar_by,[status(thm),assumptions([dt_c1_95_2_3_1__orders_1,dt_c1_95_2__orders_1,dt_c2_95_2__orders_1,e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1,e1_95_2_3_1_1__orders_1])],[rc1_partfun1,rc2_ordinal1,dt_k1_xboole_0,cc1_ordinal1,cc2_ordinal1,fc2_ordinal1,rc1_finset_1,rc1_ordinal1,rc3_ordinal1,commutativity_k2_tarski,existence_m1_subset_1,dt_k1_tarski,dt_k2_tarski,dt_m1_subset_1,cc1_finset_1,cc3_ordinal1,fc1_finset_1,fc2_finset_1,fc2_subset_1,fc3_subset_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_relat_1,dt_k4_tarski,dt_c1_95_2_3_1__orders_1,dt_c3_95_2__orders_1,t1_subset,t7_boole,d5_tarski,e1_95_2_3_1_1__orders_1,d4_relat_1]), [interesting(0.2),file(orders_1,e2_95_2_3_1_1__orders_1),[file(orders_1,e2_95_2_3_1_1__orders_1)]]). fof(e3_95_2_3_1_1__orders_1,plain,( r2_hidden(c1_95_2_3_1__orders_1,c2_95__orders_1) ), inference(mizar_by,[status(thm),assumptions([dt_c1_95_2_3_1__orders_1,e1_95_2_3_1_1__orders_1,dt_c1_95_2__orders_1,dt_c2_95_2__orders_1,e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1])],[rc1_partfun1,rc2_ordinal1,dt_k1_xboole_0,cc1_ordinal1,cc2_ordinal1,fc2_ordinal1,rc1_finset_1,rc1_ordinal1,rc3_ordinal1,commutativity_k2_tarski,existence_m1_subset_1,dt_k1_tarski,dt_k2_tarski,dt_m1_subset_1,cc1_finset_1,cc3_ordinal1,fc1_finset_1,fc2_finset_1,fc2_subset_1,fc3_subset_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k4_tarski,dt_c1_95_2__orders_1,dt_c1_95_2_3_1__orders_1,dt_c2_95__orders_1,dt_c2_95_2__orders_1,dt_c3_95_2__orders_1,dt_c5_95__orders_1,t1_subset,t7_boole,d5_tarski,e2_95_2_3_1_1__orders_1,e3_95_2__orders_1]), [interesting(0.2),file(orders_1,e3_95_2_3_1_1__orders_1),[file(orders_1,e3_95_2_3_1_1__orders_1)]]). fof(i2_95_2_3_1_1__orders_1,theorem,( $true ), introduced(tautology,[file(orders_1,i2_95_2_3_1_1__orders_1)]), [interesting(0.2),trivial,file(orders_1,i2_95_2_3_1_1__orders_1)]). fof(i1_95_2_3_1_1__orders_1,plain,( r2_hidden(c1_95_2_3_1__orders_1,c2_95__orders_1) ), inference(conclusion,[status(thm),assumptions([dt_c1_95_2_3_1__orders_1,e1_95_2_3_1_1__orders_1,dt_c1_95_2__orders_1,dt_c2_95_2__orders_1,e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1])],[e3_95_2_3_1_1__orders_1,i2_95_2_3_1_1__orders_1]), [interesting(0.2),file(orders_1,i1_95_2_3_1_1__orders_1),[file(orders_1,i1_95_2_3_1_1__orders_1)]]). fof(e3_95_2_3_1__orders_1,plain, ( r2_hidden(c1_95_2_3_1__orders_1,k1_relat_1(c3_95_2__orders_1)) => r2_hidden(c1_95_2_3_1__orders_1,c2_95__orders_1) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_95_2_3_1__orders_1,dt_c1_95_2__orders_1,dt_c2_95_2__orders_1,e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1]),discharge_asm(discharge,[e1_95_2_3_1_1__orders_1])],[e1_95_2_3_1_1__orders_1,i1_95_2_3_1_1__orders_1]), [interesting(0.35),file(orders_1,e3_95_2_3_1__orders_1),[file(orders_1,e3_95_2_3_1__orders_1)]]). fof(e5_95_2_3_1__orders_1,plain,( r2_hidden(c1_95_2_3_1__orders_1,c2_95__orders_1) ), inference(mizar_by,[status(thm),assumptions([e1_95_2_3_1__orders_1,dt_c1_95_2_3_1__orders_1,dt_c1_95_2__orders_1,dt_c2_95_2__orders_1,e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1])],[rc1_partfun1,rc2_ordinal1,dt_k1_xboole_0,cc1_ordinal1,cc2_ordinal1,fc2_ordinal1,fc9_finset_1,rc1_finset_1,rc1_ordinal1,rc3_ordinal1,t1_boole,existence_m1_subset_1,dt_m1_subset_1,cc1_finset_1,cc3_ordinal1,t2_subset,t6_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,antisymmetry_r2_hidden,dt_k1_relat_1,dt_k2_relat_1,dt_k2_xboole_0,dt_c1_95_2_3_1__orders_1,dt_c2_95__orders_1,dt_c3_95_2__orders_1,t1_subset,t7_boole,e4_95_2_3_1__orders_1,e2_95_2_3_1__orders_1,e3_95_2_3_1__orders_1,d2_xboole_0]), [interesting(0.35),file(orders_1,e5_95_2_3_1__orders_1),[file(orders_1,e5_95_2_3_1__orders_1)]]). fof(i3_95_2_3_1__orders_1,theorem,( $true ), introduced(tautology,[file(orders_1,i3_95_2_3_1__orders_1)]), [interesting(0.35),trivial,file(orders_1,i3_95_2_3_1__orders_1)]). fof(i2_95_2_3_1__orders_1,plain,( r2_hidden(c1_95_2_3_1__orders_1,c2_95__orders_1) ), inference(conclusion,[status(thm),assumptions([e1_95_2_3_1__orders_1,dt_c1_95_2_3_1__orders_1,dt_c1_95_2__orders_1,dt_c2_95_2__orders_1,e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1])],[e5_95_2_3_1__orders_1,i3_95_2_3_1__orders_1]), [interesting(0.35),file(orders_1,i2_95_2_3_1__orders_1),[file(orders_1,i2_95_2_3_1__orders_1)]]). fof(i1_95_2_3_1__orders_1,plain,( ~ ( r2_hidden(c1_95_2_3_1__orders_1,k3_relat_1(c3_95_2__orders_1)) & ~ r2_hidden(c1_95_2_3_1__orders_1,c2_95__orders_1) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_95_2_3_1__orders_1,dt_c1_95_2__orders_1,dt_c2_95_2__orders_1,e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1]),discharge_asm(discharge,[e1_95_2_3_1__orders_1])],[e1_95_2_3_1__orders_1,i2_95_2_3_1__orders_1]), [interesting(0.35),file(orders_1,i1_95_2_3_1__orders_1),[file(orders_1,i1_95_2_3_1__orders_1)]]). fof(i1_95_2_3_1_tmp__orders_1,plain,( ~ ( r2_hidden(c1_95_2_3_1__orders_1,k3_relat_1(c3_95_2__orders_1)) & ~ r2_hidden(c1_95_2_3_1__orders_1,c2_95__orders_1) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_95_2__orders_1,dt_c2_95_2__orders_1,e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1]),discharge_asm(discharge,[dt_c1_95_2_3_1__orders_1])],[dt_c1_95_2_3_1__orders_1,i1_95_2_3_1__orders_1]), [interesting(0.5),e1_95_2_3__orders_1]). fof(e1_95_2_3__orders_1,plain,( r1_tarski(k3_relat_1(c3_95_2__orders_1),c2_95__orders_1) ), inference(let,[status(thm),assumptions([dt_c1_95_2__orders_1,dt_c2_95_2__orders_1,e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1])],[i1_95_2_3_1_tmp__orders_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k3_relat_1,dt_c2_95__orders_1,dt_c3_95_2__orders_1,d3_tarski,dh_c1_95_2_3_1__orders_1]), [interesting(0.5),file(orders_1,e1_95_2_3__orders_1),[file(orders_1,e1_95_2_3__orders_1)]]). fof(e2_95_2_3__orders_1,plain,( r1_tarski(c2_95__orders_1,k3_relat_1(c3_95_2__orders_1)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_95_2__orders_1,dt_c2_95_2__orders_1,e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1])],[rc1_partfun1,rc2_ordinal1,antisymmetry_r2_hidden,dt_k1_xboole_0,cc1_ordinal1,cc2_finset_1,cc2_ordinal1,fc2_ordinal1,fc9_finset_1,rc1_finset_1,rc1_ordinal1,rc3_finset_1,rc3_ordinal1,rc4_finset_1,t1_boole,t1_subset,t4_subset,t5_subset,cc1_finset_1,cc3_ordinal1,rc1_subset_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,existence_m1_subset_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k2_relat_1,dt_k2_xboole_0,dt_m1_subset_1,fc1_subset_1,reflexivity_r1_tarski,dt_k3_relat_1,dt_c1_95__orders_1,dt_c2_95__orders_1,dt_c3_95_2__orders_1,dt_c4_95__orders_1,dt_c5_95__orders_1,t3_subset,d6_relat_1,e10_95__orders_1,e4_95_2__orders_1,t31_relat_1]), [interesting(0.5),file(orders_1,e2_95_2_3__orders_1),[file(orders_1,e2_95_2_3__orders_1)]]). fof(i2_95_2_3__orders_1,theorem,( $true ), introduced(tautology,[file(orders_1,i2_95_2_3__orders_1)]), [interesting(0.5),trivial,file(orders_1,i2_95_2_3__orders_1)]). fof(i1_95_2_3__orders_1,plain,( r1_tarski(c2_95__orders_1,k3_relat_1(c3_95_2__orders_1)) ), inference(conclusion,[status(thm),assumptions([dt_c1_95_2__orders_1,dt_c2_95_2__orders_1,e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1])],[e2_95_2_3__orders_1,i2_95_2_3__orders_1]), [interesting(0.5),file(orders_1,i1_95_2_3__orders_1),[file(orders_1,i1_95_2_3__orders_1)]]). fof(e7_95_2__orders_1,plain,( k3_relat_1(c3_95_2__orders_1) = c2_95__orders_1 ), inference(conclusion,[status(thm),assumptions([dt_c1_95_2__orders_1,dt_c2_95_2__orders_1,e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1])],[reflexivity_r1_tarski,dt_k3_relat_1,dt_c2_95__orders_1,dt_c3_95_2__orders_1,d10_xboole_0,e1_95_2_3__orders_1,i1_95_2_3__orders_1]), [interesting(0.65),file(orders_1,e7_95_2__orders_1),[file(orders_1,e7_95_2__orders_1)]]). fof(e9_95_2__orders_1,plain,( r2_hidden(c3_95_2__orders_1,c3_95__orders_1) ), inference(mizar_by,[status(thm),assumptions([e1_95_2__orders_1,dt_c1_95_2__orders_1,dt_c2_95_2__orders_1,e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1])],[rc1_partfun1,rc2_ordinal1,dt_k1_xboole_0,cc1_ordinal1,cc2_finset_1,cc2_ordinal1,fc14_finset_1,fc2_ordinal1,fc9_finset_1,rc1_finset_1,rc1_ordinal1,rc3_finset_1,rc3_ordinal1,rc4_finset_1,t1_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,existence_m1_subset_1,dt_k1_relat_1,dt_k2_relat_1,dt_k2_xboole_0,dt_m1_subset_1,cc1_finset_1,cc1_relset_1,cc3_ordinal1,fc4_subset_1,rc1_subset_1,rc2_subset_1,t2_subset,t4_subset,t5_subset,t6_boole,t8_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k3_relat_1,dt_c1_95__orders_1,dt_c2_95__orders_1,dt_c3_95__orders_1,dt_c3_95_2__orders_1,fc1_subset_1,t1_subset,t3_subset,t7_boole,d6_relat_1,e8_95_2__orders_1,e3_95__orders_1,e5_95_2__orders_1,e6_95_2__orders_1,e7_95_2__orders_1]), [interesting(0.65),file(orders_1,e9_95_2__orders_1),[file(orders_1,e9_95_2__orders_1)]]). fof(e10_95_2__orders_1,plain,( c3_95_2__orders_1 = c5_95__orders_1 ), inference(mizar_by,[status(thm),assumptions([e1_95_2__orders_1,dt_c1_95_2__orders_1,dt_c2_95_2__orders_1,e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1])],[rc1_partfun1,rc2_ordinal1,dt_k1_xboole_0,cc1_ordinal1,cc2_finset_1,cc2_ordinal1,fc2_ordinal1,fc9_finset_1,rc1_finset_1,rc1_ordinal1,rc3_finset_1,rc3_ordinal1,rc4_finset_1,t1_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,existence_m1_subset_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k2_relat_1,dt_k2_xboole_0,dt_m1_subset_1,cc1_finset_1,cc3_ordinal1,fc1_subset_1,rc1_subset_1,rc2_subset_1,t2_subset,t4_subset,t5_subset,t6_boole,t8_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k3_relat_1,dt_c1_95__orders_1,dt_c2_95__orders_1,dt_c3_95__orders_1,dt_c3_95_2__orders_1,dt_c4_95__orders_1,dt_c5_95__orders_1,t1_subset,t3_subset,t7_boole,d6_relat_1,e9_95_2__orders_1,e8_95__orders_1,e10_95__orders_1,e4_95_2__orders_1]), [interesting(0.65),file(orders_1,e10_95_2__orders_1),[file(orders_1,e10_95_2__orders_1)]]). fof(e12_95_2__orders_1,plain,( ~ $true ), inference(mizar_by,[status(thm),assumptions([e1_95_2__orders_1,dt_c1_95_2__orders_1,dt_c2_95_2__orders_1,e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1])],[rc1_partfun1,rc2_ordinal1,dt_k1_xboole_0,cc1_ordinal1,cc2_ordinal1,fc2_ordinal1,rc1_finset_1,rc1_ordinal1,rc3_ordinal1,commutativity_k2_tarski,existence_m1_subset_1,dt_k1_tarski,dt_k2_tarski,dt_m1_subset_1,cc1_finset_1,cc3_ordinal1,fc1_finset_1,fc2_finset_1,fc2_subset_1,fc3_subset_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k4_tarski,dt_c1_95_2__orders_1,dt_c2_95__orders_1,dt_c2_95_2__orders_1,dt_c3_95_2__orders_1,dt_c5_95__orders_1,t1_subset,t7_boole,d5_tarski,e11_95_2__orders_1,e1_95_2__orders_1,e3_95_2__orders_1,e10_95_2__orders_1]), [interesting(0.65),file(orders_1,e12_95_2__orders_1),[file(orders_1,e12_95_2__orders_1)]]). fof(i4_95_2__orders_1,theorem,( $true ), introduced(tautology,[file(orders_1,i4_95_2__orders_1)]), [interesting(0.65),trivial,file(orders_1,i4_95_2__orders_1)]). fof(i3_95_2__orders_1,plain,( ~ $true ), inference(conclusion,[status(thm),assumptions([e1_95_2__orders_1,dt_c1_95_2__orders_1,dt_c2_95_2__orders_1,e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1])],[e12_95_2__orders_1,i4_95_2__orders_1]), [interesting(0.65),file(orders_1,i3_95_2__orders_1),[file(orders_1,i3_95_2__orders_1)]]). fof(i2_95_2__orders_1,plain,( ~ ( r2_hidden(c1_95_2__orders_1,c2_95__orders_1) & r2_hidden(c2_95_2__orders_1,c2_95__orders_1) & c1_95_2__orders_1 != c2_95_2__orders_1 & ~ r2_hidden(k4_tarski(c1_95_2__orders_1,c2_95_2__orders_1),c5_95__orders_1) & ~ r2_hidden(k4_tarski(c2_95_2__orders_1,c1_95_2__orders_1),c5_95__orders_1) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_95_2__orders_1,dt_c2_95_2__orders_1,e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1]),discharge_asm(discharge,[e1_95_2__orders_1])],[e1_95_2__orders_1,i3_95_2__orders_1]), [interesting(0.65),file(orders_1,i2_95_2__orders_1),[file(orders_1,i2_95_2__orders_1)]]). fof(i2_95_2_tmp__orders_1,plain,( ~ ( r2_hidden(c1_95_2__orders_1,c2_95__orders_1) & r2_hidden(c2_95_2__orders_1,c2_95__orders_1) & c1_95_2__orders_1 != c2_95_2__orders_1 & ~ r2_hidden(k4_tarski(c1_95_2__orders_1,c2_95_2__orders_1),c5_95__orders_1) & ~ r2_hidden(k4_tarski(c2_95_2__orders_1,c1_95_2__orders_1),c5_95__orders_1) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_95_2__orders_1,e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1]),discharge_asm(discharge,[dt_c2_95_2__orders_1])],[dt_c2_95_2__orders_1,i2_95_2__orders_1]), [interesting(0.65),i1_95_2__orders_1]). fof(i1_95_2__orders_1,plain,( ! [A] : ~ ( r2_hidden(c1_95_2__orders_1,c2_95__orders_1) & r2_hidden(A,c2_95__orders_1) & c1_95_2__orders_1 != A & ~ r2_hidden(k4_tarski(c1_95_2__orders_1,A),c5_95__orders_1) & ~ r2_hidden(k4_tarski(A,c1_95_2__orders_1),c5_95__orders_1) ) ), inference(let,[status(thm),assumptions([dt_c1_95_2__orders_1,e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1])],[i2_95_2_tmp__orders_1,dh_c2_95_2__orders_1]), [interesting(0.65),file(orders_1,i1_95_2__orders_1),[file(orders_1,i1_95_2__orders_1)]]). fof(i1_95_2_tmp__orders_1,plain,( ! [A] : ~ ( r2_hidden(c1_95_2__orders_1,c2_95__orders_1) & r2_hidden(A,c2_95__orders_1) & c1_95_2__orders_1 != A & ~ r2_hidden(k4_tarski(c1_95_2__orders_1,A),c5_95__orders_1) & ~ r2_hidden(k4_tarski(A,c1_95_2__orders_1),c5_95__orders_1) ) ), inference(discharge_asm,[status(thm),assumptions([e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1]),discharge_asm(discharge,[dt_c1_95_2__orders_1])],[dt_c1_95_2__orders_1,i1_95_2__orders_1]), [interesting(0.8),e13_95__orders_1]). fof(e13_95__orders_1,plain,( r6_relat_2(c5_95__orders_1,c2_95__orders_1) ), inference(let,[status(thm),assumptions([e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1])],[i1_95_2_tmp__orders_1,antisymmetry_r2_hidden,dt_k4_tarski,dt_c2_95__orders_1,dt_c5_95__orders_1,d6_relat_2,dh_c1_95_2__orders_1]), [interesting(0.8),file(orders_1,e13_95__orders_1),[file(orders_1,e13_95__orders_1)]]). fof(e14_95__orders_1,plain,( k3_relat_1(c5_95__orders_1) = c2_95__orders_1 ), inference(mizar_by,[status(thm),assumptions([e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1])],[rc1_partfun1,rc2_ordinal1,antisymmetry_r2_hidden,dt_k1_xboole_0,cc1_ordinal1,cc2_finset_1,cc2_ordinal1,fc2_ordinal1,fc9_finset_1,rc1_finset_1,rc1_ordinal1,rc3_finset_1,rc3_ordinal1,rc4_finset_1,t1_boole,t1_subset,t4_subset,t5_subset,cc1_finset_1,cc3_ordinal1,rc1_subset_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,existence_m1_subset_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k2_relat_1,dt_k2_xboole_0,dt_m1_subset_1,fc1_subset_1,reflexivity_r1_tarski,dt_k3_relat_1,dt_c1_95__orders_1,dt_c2_95__orders_1,dt_c4_95__orders_1,dt_c5_95__orders_1,t3_subset,d6_relat_1,e10_95__orders_1]), [interesting(0.8),file(orders_1,e14_95__orders_1),[file(orders_1,e14_95__orders_1)]]). fof(i8_95__orders_1,theorem,( $true ), introduced(tautology,[file(orders_1,i8_95__orders_1)]), [interesting(0.8),trivial,file(orders_1,i8_95__orders_1)]). fof(i7_95__orders_1,plain,( k3_relat_1(c5_95__orders_1) = c2_95__orders_1 ), inference(conclusion,[status(thm),assumptions([e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1])],[e14_95__orders_1,i8_95__orders_1]), [interesting(0.8),file(orders_1,i7_95__orders_1),[file(orders_1,i7_95__orders_1)]]). fof(i6_95__orders_1,plain, ( r6_relat_2(c5_95__orders_1,c2_95__orders_1) & k3_relat_1(c5_95__orders_1) = c2_95__orders_1 ), inference(conclusion,[status(thm),assumptions([e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1])],[e13_95__orders_1,i7_95__orders_1]), [interesting(0.8),file(orders_1,i6_95__orders_1),[file(orders_1,i6_95__orders_1)]]). fof(i5_95__orders_1,plain, ( r3_orders_1(c5_95__orders_1,c2_95__orders_1) & k3_relat_1(c5_95__orders_1) = c2_95__orders_1 ), inference(conclusion,[status(thm),assumptions([e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1])],[dt_k3_relat_1,dt_c2_95__orders_1,dt_c5_95__orders_1,d8_orders_1,e12_95__orders_1,i6_95__orders_1]), [interesting(0.8),file(orders_1,i5_95__orders_1),[file(orders_1,i5_95__orders_1)]]). fof(i4_95__orders_1,plain, ( r1_tarski(c1_95__orders_1,c5_95__orders_1) & r3_orders_1(c5_95__orders_1,c2_95__orders_1) & k3_relat_1(c5_95__orders_1) = c2_95__orders_1 ), inference(conclusion,[status(thm),assumptions([e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1])],[e11_95__orders_1,i5_95__orders_1]), [interesting(0.8),file(orders_1,i4_95__orders_1),[file(orders_1,i4_95__orders_1)]]). fof(i3_95__orders_1,plain,( ? [A] : ( v1_relat_1(A) & r1_tarski(c1_95__orders_1,A) & r3_orders_1(A,c2_95__orders_1) & k3_relat_1(A) = c2_95__orders_1 ) ), inference(take,[status(thm),assumptions([e1_95__orders_1,dt_c1_95__orders_1,dt_c2_95__orders_1])],[reflexivity_r1_tarski,dt_k3_relat_1,dt_c1_95__orders_1,dt_c2_95__orders_1,dt_c5_95__orders_1,i4_95__orders_1]), [interesting(0.8),file(orders_1,i3_95__orders_1),[file(orders_1,i3_95__orders_1)]]). fof(i2_95__orders_1,plain,( ~ ( r2_orders_1(c1_95__orders_1,c2_95__orders_1) & k3_relat_1(c1_95__orders_1) = c2_95__orders_1 & ! [A] : ( v1_relat_1(A) => ~ ( r1_tarski(c1_95__orders_1,A) & r3_orders_1(A,c2_95__orders_1) & k3_relat_1(A) = c2_95__orders_1 ) ) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_95__orders_1,dt_c2_95__orders_1]),discharge_asm(discharge,[e1_95__orders_1])],[e1_95__orders_1,i3_95__orders_1]), [interesting(0.8),file(orders_1,i2_95__orders_1),[file(orders_1,i2_95__orders_1)]]). fof(i2_95_tmp__orders_1,plain,( ~ ( r2_orders_1(c1_95__orders_1,c2_95__orders_1) & k3_relat_1(c1_95__orders_1) = c2_95__orders_1 & ! [A] : ( v1_relat_1(A) => ~ ( r1_tarski(c1_95__orders_1,A) & r3_orders_1(A,c2_95__orders_1) & k3_relat_1(A) = c2_95__orders_1 ) ) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_95__orders_1]),discharge_asm(discharge,[dt_c2_95__orders_1])],[dt_c2_95__orders_1,i2_95__orders_1]), [interesting(0.8),i1_95__orders_1]). fof(i1_95__orders_1,plain,( ! [A] : ~ ( r2_orders_1(c1_95__orders_1,A) & k3_relat_1(c1_95__orders_1) = A & ! [B] : ( v1_relat_1(B) => ~ ( r1_tarski(c1_95__orders_1,B) & r3_orders_1(B,A) & k3_relat_1(B) = A ) ) ) ), inference(let,[status(thm),assumptions([dt_c1_95__orders_1])],[i2_95_tmp__orders_1,dh_c2_95__orders_1]), [interesting(0.8),file(orders_1,i1_95__orders_1),[file(orders_1,i1_95__orders_1)]]). fof(i1_95_tmp__orders_1,plain, ( v1_relat_1(c1_95__orders_1) => ! [A] : ~ ( r2_orders_1(c1_95__orders_1,A) & k3_relat_1(c1_95__orders_1) = A & ! [B] : ( v1_relat_1(B) => ~ ( r1_tarski(c1_95__orders_1,B) & r3_orders_1(B,A) & k3_relat_1(B) = A ) ) ) ), inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_95__orders_1])],[dt_c1_95__orders_1,i1_95__orders_1]), [interesting(1),t179_orders_1]). fof(t179_orders_1,theorem,( ! [A] : ( v1_relat_1(A) => ! [B] : ~ ( r2_orders_1(A,B) & k3_relat_1(A) = B & ! [C] : ( v1_relat_1(C) => ~ ( r1_tarski(A,C) & r3_orders_1(C,B) & k3_relat_1(C) = B ) ) ) ) ), inference(let,[status(thm),assumptions([])],[i1_95_tmp__orders_1,dh_c1_95__orders_1]), [interesting(1),file(orders_1,t179_orders_1),[file(orders_1,t179_orders_1)]]).