% Mizar ND problem: t2_bvfunc14,bvfunc14,73,15 fof(dh_c1_2__bvfunc14,definition, ( ( ~ v1_xboole_0(c1_2__bvfunc14) => ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_bvfunc_2(c1_2__bvfunc14))) => ! [B] : ( m1_eqrel_1(B,c1_2__bvfunc14) => ! [C] : ( m1_eqrel_1(C,c1_2__bvfunc14) => ( A = k2_tarski(B,C) => ( B = C | k2_bvfunc_2(c1_2__bvfunc14,A) = k2_partit1(c1_2__bvfunc14,B,C) ) ) ) ) ) ) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(k1_bvfunc_2(D))) => ! [F] : ( m1_eqrel_1(F,D) => ! [G] : ( m1_eqrel_1(G,D) => ( E = k2_tarski(F,G) => ( F = G | k2_bvfunc_2(D,E) = k2_partit1(D,F,G) ) ) ) ) ) ) ), introduced(definition,[new_symbol(c1_2__bvfunc14),file(bvfunc14,c1_2__bvfunc14)]), [interesting(0.8),axiom,file(bvfunc14,c1_2__bvfunc14)]). fof(dh_c2_2__bvfunc14,definition, ( ( m1_subset_1(c2_2__bvfunc14,k1_zfmisc_1(k1_bvfunc_2(c1_2__bvfunc14))) => ! [A] : ( m1_eqrel_1(A,c1_2__bvfunc14) => ! [B] : ( m1_eqrel_1(B,c1_2__bvfunc14) => ( c2_2__bvfunc14 = k2_tarski(A,B) => ( A = B | k2_bvfunc_2(c1_2__bvfunc14,c2_2__bvfunc14) = k2_partit1(c1_2__bvfunc14,A,B) ) ) ) ) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(c1_2__bvfunc14))) => ! [D] : ( m1_eqrel_1(D,c1_2__bvfunc14) => ! [E] : ( m1_eqrel_1(E,c1_2__bvfunc14) => ( C = k2_tarski(D,E) => ( D = E | k2_bvfunc_2(c1_2__bvfunc14,C) = k2_partit1(c1_2__bvfunc14,D,E) ) ) ) ) ) ), introduced(definition,[new_symbol(c2_2__bvfunc14),file(bvfunc14,c2_2__bvfunc14)]), [interesting(0.8),axiom,file(bvfunc14,c2_2__bvfunc14)]). fof(dh_c3_2__bvfunc14,definition, ( ( m1_eqrel_1(c3_2__bvfunc14,c1_2__bvfunc14) => ! [A] : ( m1_eqrel_1(A,c1_2__bvfunc14) => ( c2_2__bvfunc14 = k2_tarski(c3_2__bvfunc14,A) => ( c3_2__bvfunc14 = A | k2_bvfunc_2(c1_2__bvfunc14,c2_2__bvfunc14) = k2_partit1(c1_2__bvfunc14,c3_2__bvfunc14,A) ) ) ) ) => ! [B] : ( m1_eqrel_1(B,c1_2__bvfunc14) => ! [C] : ( m1_eqrel_1(C,c1_2__bvfunc14) => ( c2_2__bvfunc14 = k2_tarski(B,C) => ( B = C | k2_bvfunc_2(c1_2__bvfunc14,c2_2__bvfunc14) = k2_partit1(c1_2__bvfunc14,B,C) ) ) ) ) ), introduced(definition,[new_symbol(c3_2__bvfunc14),file(bvfunc14,c3_2__bvfunc14)]), [interesting(0.8),axiom,file(bvfunc14,c3_2__bvfunc14)]). fof(dh_c4_2__bvfunc14,definition, ( ( m1_eqrel_1(c4_2__bvfunc14,c1_2__bvfunc14) => ( c2_2__bvfunc14 = k2_tarski(c3_2__bvfunc14,c4_2__bvfunc14) => ( c3_2__bvfunc14 = c4_2__bvfunc14 | k2_bvfunc_2(c1_2__bvfunc14,c2_2__bvfunc14) = k2_partit1(c1_2__bvfunc14,c3_2__bvfunc14,c4_2__bvfunc14) ) ) ) => ! [A] : ( m1_eqrel_1(A,c1_2__bvfunc14) => ( c2_2__bvfunc14 = k2_tarski(c3_2__bvfunc14,A) => ( c3_2__bvfunc14 = A | k2_bvfunc_2(c1_2__bvfunc14,c2_2__bvfunc14) = k2_partit1(c1_2__bvfunc14,c3_2__bvfunc14,A) ) ) ) ), introduced(definition,[new_symbol(c4_2__bvfunc14),file(bvfunc14,c4_2__bvfunc14)]), [interesting(0.8),axiom,file(bvfunc14,c4_2__bvfunc14)]). fof(e1_2__bvfunc14,assumption, ( c2_2__bvfunc14 = k2_tarski(c3_2__bvfunc14,c4_2__bvfunc14) & c3_2__bvfunc14 != c4_2__bvfunc14 ), introduced(assumption,[file(bvfunc14,e1_2__bvfunc14)]), [interesting(0.8),axiom,file(bvfunc14,e1_2__bvfunc14)]). 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(existence_m1_t_1topsp,axiom,( ! [A] : ? [B] : m1_t_1topsp(B,A) ), file(t_1topsp,m1_t_1topsp), [interesting(0.9),axiom,file(t_1topsp,m1_t_1topsp)]). fof(dt_k1_partit1,axiom,( $true ), file(partit1,k1_partit1), [interesting(0.9),axiom,file(partit1,k1_partit1)]). fof(dt_k1_xboole_0,axiom,( $true ), file(xboole_0,k1_xboole_0), [interesting(0.9),axiom,file(xboole_0,k1_xboole_0)]). fof(dt_m1_t_1topsp,axiom,( $true ), file(t_1topsp,m1_t_1topsp), [interesting(0.9),axiom,file(t_1topsp,m1_t_1topsp)]). fof(fc1_xboole_0,theorem,( v1_xboole_0(k1_xboole_0) ), file(xboole_0,fc1_xboole_0), [interesting(0.9),axiom,file(xboole_0,fc1_xboole_0)]). fof(t1_subset,theorem,( ! [A,B] : ( r2_hidden(A,B) => m1_subset_1(A,B) ) ), file(subset,t1_subset), [interesting(0.9),axiom,file(subset,t1_subset)]). fof(t4_subset,theorem,( ! [A,B,C] : ( ( r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) ) => m1_subset_1(A,C) ) ), file(subset,t4_subset), [interesting(0.9),axiom,file(subset,t4_subset)]). fof(t5_subset,theorem,( ! [A,B,C] : ~ ( r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) & v1_xboole_0(C) ) ), file(subset,t5_subset), [interesting(0.9),axiom,file(subset,t5_subset)]). fof(existence_m1_eqrel_1,axiom,( ! [A] : ? [B] : m1_eqrel_1(B,A) ), file(eqrel_1,m1_eqrel_1), [interesting(0.9),axiom,file(eqrel_1,m1_eqrel_1)]). 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(redefinition_k1_bvfunc_2,definition,( ! [A] : k1_bvfunc_2(A) = k1_partit1(A) ), file(bvfunc_2,k1_bvfunc_2), [interesting(0.9),axiom,file(bvfunc_2,k1_bvfunc_2)]). fof(dt_k1_bvfunc_2,axiom,( ! [A] : ( v1_t_1topsp(k1_bvfunc_2(A),A) & m1_t_1topsp(k1_bvfunc_2(A),A) ) ), file(bvfunc_2,k1_bvfunc_2), [interesting(0.9),axiom,file(bvfunc_2,k1_bvfunc_2)]). 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_m1_eqrel_1,axiom,( ! [A,B] : ( m1_eqrel_1(B,A) => m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) ) ), file(eqrel_1,m1_eqrel_1), [interesting(0.9),axiom,file(eqrel_1,m1_eqrel_1)]). fof(dt_m1_subset_1,axiom,( $true ), file(subset_1,m1_subset_1), [interesting(0.9),axiom,file(subset_1,m1_subset_1)]). fof(cc1_eqrel_1,theorem,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_eqrel_1(B,A) => ~ v1_xboole_0(B) ) ) ), file(eqrel_1,cc1_eqrel_1), [interesting(0.9),axiom,file(eqrel_1,cc1_eqrel_1)]). fof(cc2_eqrel_1,theorem,( ! [A,B] : ( m1_eqrel_1(B,A) => v1_setfam_1(B) ) ), file(eqrel_1,cc2_eqrel_1), [interesting(0.9),axiom,file(eqrel_1,cc2_eqrel_1)]). fof(fc1_subset_1,theorem,( ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ), file(subset_1,fc1_subset_1), [interesting(0.9),axiom,file(subset_1,fc1_subset_1)]). fof(rc1_subset_1,theorem,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) ) ) ), file(subset_1,rc1_subset_1), [interesting(0.9),axiom,file(subset_1,rc1_subset_1)]). fof(rc1_xboole_0,theorem,( ? [A] : v1_xboole_0(A) ), file(xboole_0,rc1_xboole_0), [interesting(0.9),axiom,file(xboole_0,rc1_xboole_0)]). fof(rc2_subset_1,theorem,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & v1_xboole_0(B) ) ), file(subset_1,rc2_subset_1), [interesting(0.9),axiom,file(subset_1,rc2_subset_1)]). fof(rc2_xboole_0,theorem,( ? [A] : ~ v1_xboole_0(A) ), file(xboole_0,rc2_xboole_0), [interesting(0.9),axiom,file(xboole_0,rc2_xboole_0)]). fof(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(t6_boole,theorem,( ! [A] : ( v1_xboole_0(A) => A = k1_xboole_0 ) ), file(boole,t6_boole), [interesting(0.9),axiom,file(boole,t6_boole)]). fof(t7_boole,theorem,( ! [A,B] : ~ ( r2_hidden(A,B) & v1_xboole_0(B) ) ), file(boole,t7_boole), [interesting(0.9),axiom,file(boole,t7_boole)]). fof(t8_boole,theorem,( ! [A,B] : ~ ( v1_xboole_0(A) & A != B & v1_xboole_0(B) ) ), file(boole,t8_boole), [interesting(0.9),axiom,file(boole,t8_boole)]). fof(commutativity_k2_partit1,theorem,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & m1_eqrel_1(B,A) & m1_eqrel_1(C,A) ) => k2_partit1(A,B,C) = k2_partit1(A,C,B) ) ), file(partit1,k2_partit1), [interesting(0.9),axiom,file(partit1,k2_partit1)]). 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_k2_bvfunc_2,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) ) => m1_eqrel_1(k2_bvfunc_2(A,B),A) ) ), file(bvfunc_2,k2_bvfunc_2), [interesting(0.9),axiom,file(bvfunc_2,k2_bvfunc_2)]). fof(dt_k2_partit1,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & m1_eqrel_1(B,A) & m1_eqrel_1(C,A) ) => m1_eqrel_1(k2_partit1(A,B,C),A) ) ), file(partit1,k2_partit1), [interesting(0.9),axiom,file(partit1,k2_partit1)]). fof(dt_c1_2__bvfunc14,assumption,( ~ v1_xboole_0(c1_2__bvfunc14) ), introduced(assumption,[file(bvfunc14,c1_2__bvfunc14)]), [interesting(0.8),axiom,file(bvfunc14,c1_2__bvfunc14)]). fof(dt_c2_2__bvfunc14,assumption,( m1_subset_1(c2_2__bvfunc14,k1_zfmisc_1(k1_bvfunc_2(c1_2__bvfunc14))) ), introduced(assumption,[file(bvfunc14,c2_2__bvfunc14)]), [interesting(0.8),axiom,file(bvfunc14,c2_2__bvfunc14)]). fof(dt_c3_2__bvfunc14,assumption,( m1_eqrel_1(c3_2__bvfunc14,c1_2__bvfunc14) ), introduced(assumption,[file(bvfunc14,c3_2__bvfunc14)]), [interesting(0.8),axiom,file(bvfunc14,c3_2__bvfunc14)]). fof(dt_c4_2__bvfunc14,assumption,( m1_eqrel_1(c4_2__bvfunc14,c1_2__bvfunc14) ), introduced(assumption,[file(bvfunc14,c4_2__bvfunc14)]), [interesting(0.8),axiom,file(bvfunc14,c4_2__bvfunc14)]). 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(dt_c1_2_2__bvfunc14,assumption,( $true ), introduced(assumption,[file(bvfunc14,c1_2_2__bvfunc14)]), [interesting(0.65),axiom,file(bvfunc14,c1_2_2__bvfunc14)]). 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_2_2__bvfunc14,definition, ( ~ ( r2_hidden(c1_2_2__bvfunc14,k2_bvfunc_2(c1_2__bvfunc14,c2_2__bvfunc14)) & ~ r2_hidden(c1_2_2__bvfunc14,k2_partit1(c1_2__bvfunc14,c3_2__bvfunc14,c4_2__bvfunc14)) ) => ! [A] : ~ ( r2_hidden(A,k2_bvfunc_2(c1_2__bvfunc14,c2_2__bvfunc14)) & ~ r2_hidden(A,k2_partit1(c1_2__bvfunc14,c3_2__bvfunc14,c4_2__bvfunc14)) ) ), introduced(definition,[new_symbol(c1_2_2__bvfunc14),file(bvfunc14,c1_2_2__bvfunc14)]), [interesting(0.65),axiom,file(bvfunc14,c1_2_2__bvfunc14)]). fof(e1_2_2__bvfunc14,assumption,( r2_hidden(c1_2_2__bvfunc14,k2_bvfunc_2(c1_2__bvfunc14,c2_2__bvfunc14)) ), introduced(assumption,[file(bvfunc14,e1_2_2__bvfunc14)]), [interesting(0.65),axiom,file(bvfunc14,e1_2_2__bvfunc14)]). fof(commutativity_k3_setfam_1,theorem,( ! [A,B] : k3_setfam_1(A,B) = k3_setfam_1(B,A) ), file(setfam_1,k3_setfam_1), [interesting(0.9),axiom,file(setfam_1,k3_setfam_1)]). fof(dt_k1_tarski,axiom,( $true ), file(tarski,k1_tarski), [interesting(0.9),axiom,file(tarski,k1_tarski)]). fof(dt_k3_setfam_1,axiom,( $true ), file(setfam_1,k3_setfam_1), [interesting(0.9),axiom,file(setfam_1,k3_setfam_1)]). fof(dt_k4_xboole_0,axiom,( $true ), file(xboole_0,k4_xboole_0), [interesting(0.9),axiom,file(xboole_0,k4_xboole_0)]). 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(t3_boole,theorem,( ! [A] : k4_xboole_0(A,k1_xboole_0) = A ), file(boole,t3_boole), [interesting(0.9),axiom,file(boole,t3_boole)]). fof(t4_boole,theorem,( ! [A] : k4_xboole_0(k1_xboole_0,A) = k1_xboole_0 ), file(boole,t4_boole), [interesting(0.9),axiom,file(boole,t4_boole)]). fof(t2_boole,theorem,( ! [A] : k3_xboole_0(A,k1_xboole_0) = k1_xboole_0 ), file(boole,t2_boole), [interesting(0.9),axiom,file(boole,t2_boole)]). fof(commutativity_k3_xboole_0,theorem,( ! [A,B] : k3_xboole_0(A,B) = k3_xboole_0(B,A) ), file(xboole_0,k3_xboole_0), [interesting(0.9),axiom,file(xboole_0,k3_xboole_0)]). fof(idempotence_k3_xboole_0,theorem,( ! [A,B] : k3_xboole_0(A,A) = A ), file(xboole_0,k3_xboole_0), [interesting(0.9),axiom,file(xboole_0,k3_xboole_0)]). fof(dt_k1_funct_1,axiom,( $true ), file(funct_1,k1_funct_1), [interesting(0.9),axiom,file(funct_1,k1_funct_1)]). fof(dt_k3_xboole_0,axiom,( $true ), file(xboole_0,k3_xboole_0), [interesting(0.9),axiom,file(xboole_0,k3_xboole_0)]). fof(dh_c2_2_2__bvfunc14,definition, ( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(c1_2__bvfunc14))) & k1_relat_1(A) = c2_2__bvfunc14 & k2_relat_1(A) = B & ! [C] : ( r2_hidden(C,c2_2__bvfunc14) => r2_hidden(k1_funct_1(A,C),C) ) & c1_2_2__bvfunc14 = k8_setfam_1(c1_2__bvfunc14,B) & c1_2_2__bvfunc14 != k1_xboole_0 ) ) => ( v1_relat_1(c2_2_2__bvfunc14) & v1_funct_1(c2_2_2__bvfunc14) & ? [D] : ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(c1_2__bvfunc14))) & k1_relat_1(c2_2_2__bvfunc14) = c2_2__bvfunc14 & k2_relat_1(c2_2_2__bvfunc14) = D & ! [E] : ( r2_hidden(E,c2_2__bvfunc14) => r2_hidden(k1_funct_1(c2_2_2__bvfunc14,E),E) ) & c1_2_2__bvfunc14 = k8_setfam_1(c1_2__bvfunc14,D) & c1_2_2__bvfunc14 != k1_xboole_0 ) ) ), introduced(definition,[new_symbol(c2_2_2__bvfunc14),file(bvfunc14,c2_2_2__bvfunc14)]), [interesting(0.65),axiom,file(bvfunc14,c2_2_2__bvfunc14)]). 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_k8_setfam_1,axiom,( ! [A,B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => m1_subset_1(k8_setfam_1(A,B),k1_zfmisc_1(A)) ) ), file(setfam_1,k8_setfam_1), [interesting(0.9),axiom,file(setfam_1,k8_setfam_1)]). fof(d1_bvfunc_2,definition,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( m1_eqrel_1(C,A) => ( C = k2_bvfunc_2(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ? [E] : ( v1_relat_1(E) & v1_funct_1(E) & ? [F] : ( m1_subset_1(F,k1_zfmisc_1(k1_zfmisc_1(A))) & k1_relat_1(E) = B & k2_relat_1(E) = F & ! [G] : ( r2_hidden(G,B) => r2_hidden(k1_funct_1(E,G),G) ) & D = k8_setfam_1(A,F) & D != k1_xboole_0 ) ) ) ) ) ) ) ), file(bvfunc_2,d1_bvfunc_2), [interesting(0.9),axiom,file(bvfunc_2,d1_bvfunc_2)]). fof(e2_2_2__bvfunc14,plain,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(c1_2__bvfunc14))) & k1_relat_1(A) = c2_2__bvfunc14 & k2_relat_1(A) = B & ! [C] : ( r2_hidden(C,c2_2__bvfunc14) => r2_hidden(k1_funct_1(A,C),C) ) & c1_2_2__bvfunc14 = k8_setfam_1(c1_2__bvfunc14,B) & c1_2_2__bvfunc14 != k1_xboole_0 ) ) ), inference(mizar_by,[status(thm),assumptions([dt_c1_2__bvfunc14,dt_c1_2_2__bvfunc14,dt_c2_2__bvfunc14,e1_2_2__bvfunc14])],[reflexivity_r1_tarski,existence_m1_t_1topsp,dt_k1_partit1,dt_m1_t_1topsp,antisymmetry_r2_hidden,existence_m1_eqrel_1,existence_m1_subset_1,redefinition_k1_bvfunc_2,dt_k1_bvfunc_2,dt_k1_funct_1,dt_k1_relat_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_bvfunc_2,dt_k2_relat_1,dt_k8_setfam_1,dt_m1_eqrel_1,dt_m1_subset_1,dt_c1_2__bvfunc14,dt_c1_2_2__bvfunc14,dt_c2_2__bvfunc14,cc1_eqrel_1,cc2_eqrel_1,fc1_subset_1,fc1_xboole_0,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,t1_subset,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole,e1_2_2__bvfunc14,d1_bvfunc_2]), [interesting(0.65),file(bvfunc14,e2_2_2__bvfunc14),[file(bvfunc14,e2_2_2__bvfunc14)]]). fof(dt_c2_2_2__bvfunc14,plain, ( v1_relat_1(c2_2_2__bvfunc14) & v1_funct_1(c2_2_2__bvfunc14) ), inference(consider,[status(thm),assumptions([dt_c1_2__bvfunc14,dt_c1_2_2__bvfunc14,dt_c2_2__bvfunc14,e1_2_2__bvfunc14])],[dh_c2_2_2__bvfunc14,e2_2_2__bvfunc14]), [interesting(0.65),file(bvfunc14,c2_2_2__bvfunc14),[file(bvfunc14,c2_2_2__bvfunc14)]]). fof(dt_c1_2_2_2__bvfunc14,assumption,( $true ), introduced(assumption,[file(bvfunc14,c1_2_2_2__bvfunc14)]), [interesting(0.5),axiom,file(bvfunc14,c1_2_2_2__bvfunc14)]). fof(dh_c1_2_2_2__bvfunc14,definition, ( ~ ( r2_hidden(c1_2_2_2__bvfunc14,c1_2_2__bvfunc14) & ~ r2_hidden(c1_2_2_2__bvfunc14,k3_xboole_0(k1_funct_1(c2_2_2__bvfunc14,c3_2__bvfunc14),k1_funct_1(c2_2_2__bvfunc14,c4_2__bvfunc14))) ) => ! [A] : ~ ( r2_hidden(A,c1_2_2__bvfunc14) & ~ r2_hidden(A,k3_xboole_0(k1_funct_1(c2_2_2__bvfunc14,c3_2__bvfunc14),k1_funct_1(c2_2_2__bvfunc14,c4_2__bvfunc14))) ) ), introduced(definition,[new_symbol(c1_2_2_2__bvfunc14),file(bvfunc14,c1_2_2_2__bvfunc14)]), [interesting(0.5),axiom,file(bvfunc14,c1_2_2_2__bvfunc14)]). fof(e1_2_2_2__bvfunc14,assumption,( r2_hidden(c1_2_2_2__bvfunc14,c1_2_2__bvfunc14) ), introduced(assumption,[file(bvfunc14,e1_2_2_2__bvfunc14)]), [interesting(0.5),axiom,file(bvfunc14,e1_2_2_2__bvfunc14)]). fof(dt_k1_setfam_1,axiom,( $true ), file(setfam_1,k1_setfam_1), [interesting(0.9),axiom,file(setfam_1,k1_setfam_1)]). fof(redefinition_k6_setfam_1,definition,( ! [A,B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => k6_setfam_1(A,B) = k1_setfam_1(B) ) ), file(setfam_1,k6_setfam_1), [interesting(0.9),axiom,file(setfam_1,k6_setfam_1)]). fof(dt_k6_setfam_1,axiom,( ! [A,B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => m1_subset_1(k6_setfam_1(A,B),k1_zfmisc_1(A)) ) ), file(setfam_1,k6_setfam_1), [interesting(0.9),axiom,file(setfam_1,k6_setfam_1)]). fof(dh_c3_2_2__bvfunc14,definition, ( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(c1_2__bvfunc14))) & k1_relat_1(c2_2_2__bvfunc14) = c2_2__bvfunc14 & k2_relat_1(c2_2_2__bvfunc14) = A & ! [B] : ( r2_hidden(B,c2_2__bvfunc14) => r2_hidden(k1_funct_1(c2_2_2__bvfunc14,B),B) ) & c1_2_2__bvfunc14 = k8_setfam_1(c1_2__bvfunc14,A) & c1_2_2__bvfunc14 != k1_xboole_0 ) => ( m1_subset_1(c3_2_2__bvfunc14,k1_zfmisc_1(k1_zfmisc_1(c1_2__bvfunc14))) & k1_relat_1(c2_2_2__bvfunc14) = c2_2__bvfunc14 & k2_relat_1(c2_2_2__bvfunc14) = c3_2_2__bvfunc14 & ! [C] : ( r2_hidden(C,c2_2__bvfunc14) => r2_hidden(k1_funct_1(c2_2_2__bvfunc14,C),C) ) & c1_2_2__bvfunc14 = k8_setfam_1(c1_2__bvfunc14,c3_2_2__bvfunc14) & c1_2_2__bvfunc14 != k1_xboole_0 ) ), introduced(definition,[new_symbol(c3_2_2__bvfunc14),file(bvfunc14,c3_2_2__bvfunc14)]), [interesting(0.65),axiom,file(bvfunc14,c3_2_2__bvfunc14)]). fof(dt_c3_2_2__bvfunc14,plain,( m1_subset_1(c3_2_2__bvfunc14,k1_zfmisc_1(k1_zfmisc_1(c1_2__bvfunc14))) ), inference(consider,[status(thm),assumptions([dt_c1_2__bvfunc14,dt_c1_2_2__bvfunc14,dt_c2_2__bvfunc14,e1_2_2__bvfunc14])],[dh_c2_2_2__bvfunc14,dh_c3_2_2__bvfunc14,e2_2_2__bvfunc14]), [interesting(0.65),file(bvfunc14,c3_2_2__bvfunc14),[file(bvfunc14,c3_2_2__bvfunc14)]]). fof(e3_2_2__bvfunc14,plain, ( k1_relat_1(c2_2_2__bvfunc14) = c2_2__bvfunc14 & k2_relat_1(c2_2_2__bvfunc14) = c3_2_2__bvfunc14 & ! [A] : ( r2_hidden(A,c2_2__bvfunc14) => r2_hidden(k1_funct_1(c2_2_2__bvfunc14,A),A) ) & c1_2_2__bvfunc14 = k8_setfam_1(c1_2__bvfunc14,c3_2_2__bvfunc14) & c1_2_2__bvfunc14 != k1_xboole_0 ), inference(consider,[status(thm),assumptions([dt_c1_2__bvfunc14,dt_c1_2_2__bvfunc14,dt_c2_2__bvfunc14,e1_2_2__bvfunc14])],[dh_c2_2_2__bvfunc14,dh_c3_2_2__bvfunc14,e2_2_2__bvfunc14]), [interesting(0.65),file(bvfunc14,e3_2_2__bvfunc14),[file(bvfunc14,e3_2_2__bvfunc14)]]). fof(commutativity_k2_tarski,theorem,( ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ), file(tarski,k2_tarski), [interesting(0.9),axiom,file(tarski,k2_tarski)]). fof(dt_k2_tarski,axiom,( $true ), file(tarski,k2_tarski), [interesting(0.9),axiom,file(tarski,k2_tarski)]). fof(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(d2_tarski,definition,( ! [A,B,C] : ( C = k2_tarski(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( D = A | D = B ) ) ) ), file(tarski,d2_tarski), [interesting(0.9),axiom,file(tarski,d2_tarski)]). fof(e6_2_2__bvfunc14,plain, ( r2_hidden(c3_2__bvfunc14,k1_relat_1(c2_2_2__bvfunc14)) & r2_hidden(c4_2__bvfunc14,k1_relat_1(c2_2_2__bvfunc14)) ), inference(mizar_by,[status(thm),assumptions([dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_2__bvfunc14,dt_c2_2__bvfunc14,e1_2_2__bvfunc14])],[reflexivity_r1_tarski,existence_m1_t_1topsp,dt_k1_partit1,dt_m1_t_1topsp,existence_m1_eqrel_1,existence_m1_subset_1,redefinition_k1_bvfunc_2,dt_k1_bvfunc_2,dt_k1_zfmisc_1,dt_m1_eqrel_1,dt_m1_subset_1,cc1_eqrel_1,cc2_eqrel_1,fc1_subset_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,t2_subset,t3_subset,t4_subset,t5_subset,t8_boole,commutativity_k2_tarski,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k1_xboole_0,dt_k2_relat_1,dt_k2_tarski,dt_k8_setfam_1,dt_c1_2__bvfunc14,dt_c1_2_2__bvfunc14,dt_c2_2__bvfunc14,dt_c2_2_2__bvfunc14,dt_c3_2__bvfunc14,dt_c3_2_2__bvfunc14,dt_c4_2__bvfunc14,fc1_xboole_0,fc3_subset_1,t1_subset,t6_boole,t7_boole,e1_2__bvfunc14,e3_2_2__bvfunc14,d2_tarski]), [interesting(0.65),file(bvfunc14,e6_2_2__bvfunc14),[file(bvfunc14,e6_2_2__bvfunc14)]]). fof(d5_funct_1,definition,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( B = k2_relat_1(A) <=> ! [C] : ( r2_hidden(C,B) <=> ? [D] : ( r2_hidden(D,k1_relat_1(A)) & C = k1_funct_1(A,D) ) ) ) ) ), file(funct_1,d5_funct_1), [interesting(0.9),axiom,file(funct_1,d5_funct_1)]). fof(e7_2_2__bvfunc14,plain, ( r2_hidden(k1_funct_1(c2_2_2__bvfunc14,c3_2__bvfunc14),k2_relat_1(c2_2_2__bvfunc14)) & r2_hidden(k1_funct_1(c2_2_2__bvfunc14,c4_2__bvfunc14),k2_relat_1(c2_2_2__bvfunc14)) ), inference(mizar_by,[status(thm),assumptions([dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_2__bvfunc14,dt_c2_2__bvfunc14,e1_2_2__bvfunc14])],[reflexivity_r1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,fc1_subset_1,fc1_xboole_0,rc1_subset_1,rc2_subset_1,t3_subset,t4_subset,t5_subset,existence_m1_eqrel_1,existence_m1_subset_1,dt_m1_eqrel_1,dt_m1_subset_1,dt_c1_2__bvfunc14,cc1_eqrel_1,cc2_eqrel_1,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k2_relat_1,dt_c2_2_2__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,t1_subset,t7_boole,e6_2_2__bvfunc14,d5_funct_1]), [interesting(0.65),file(bvfunc14,e7_2_2__bvfunc14),[file(bvfunc14,e7_2_2__bvfunc14)]]). fof(d10_setfam_1,definition,( ! [A,B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ( ( B != k1_xboole_0 => k8_setfam_1(A,B) = k6_setfam_1(A,B) ) & ( B = k1_xboole_0 => k8_setfam_1(A,B) = A ) ) ) ), file(setfam_1,d10_setfam_1), [interesting(0.9),axiom,file(setfam_1,d10_setfam_1)]). fof(e2_2_2_2__bvfunc14,plain,( r2_hidden(c1_2_2_2__bvfunc14,k1_setfam_1(k2_relat_1(c2_2_2__bvfunc14))) ), inference(mizar_by,[status(thm),assumptions([dt_c1_2_2_2__bvfunc14,e1_2_2_2__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_2__bvfunc14,dt_c2_2__bvfunc14,e1_2_2__bvfunc14])],[existence_m1_t_1topsp,dt_k1_partit1,dt_m1_t_1topsp,reflexivity_r1_tarski,existence_m1_eqrel_1,redefinition_k1_bvfunc_2,dt_k1_bvfunc_2,dt_m1_eqrel_1,cc1_eqrel_1,cc2_eqrel_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,t2_subset,t5_subset,t8_boole,antisymmetry_r2_hidden,existence_m1_subset_1,redefinition_k6_setfam_1,dt_k1_funct_1,dt_k1_relat_1,dt_k1_setfam_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_relat_1,dt_k6_setfam_1,dt_k8_setfam_1,dt_m1_subset_1,dt_c1_2__bvfunc14,dt_c1_2_2__bvfunc14,dt_c1_2_2_2__bvfunc14,dt_c2_2__bvfunc14,dt_c2_2_2__bvfunc14,dt_c3_2__bvfunc14,dt_c3_2_2__bvfunc14,dt_c4_2__bvfunc14,fc1_subset_1,fc1_xboole_0,t1_subset,t3_subset,t4_subset,t6_boole,t7_boole,e1_2_2_2__bvfunc14,e3_2_2__bvfunc14,e7_2_2__bvfunc14,d10_setfam_1]), [interesting(0.5),file(bvfunc14,e2_2_2_2__bvfunc14),[file(bvfunc14,e2_2_2_2__bvfunc14)]]). fof(d1_setfam_1,definition,( ! [A,B] : ( ( A != k1_xboole_0 => ( B = k1_setfam_1(A) <=> ! [C] : ( r2_hidden(C,B) <=> ! [D] : ( r2_hidden(D,A) => r2_hidden(C,D) ) ) ) ) & ( A = k1_xboole_0 => ( B = k1_setfam_1(A) <=> B = k1_xboole_0 ) ) ) ), file(setfam_1,d1_setfam_1), [interesting(0.9),axiom,file(setfam_1,d1_setfam_1)]). fof(e3_2_2_2__bvfunc14,plain, ( r2_hidden(c1_2_2_2__bvfunc14,k1_funct_1(c2_2_2__bvfunc14,c3_2__bvfunc14)) & r2_hidden(c1_2_2_2__bvfunc14,k1_funct_1(c2_2_2__bvfunc14,c4_2__bvfunc14)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_2_2_2__bvfunc14,e1_2_2_2__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_2__bvfunc14,dt_c2_2__bvfunc14,e1_2_2__bvfunc14])],[reflexivity_r1_tarski,dt_k1_zfmisc_1,fc1_subset_1,rc1_subset_1,rc2_subset_1,t3_subset,t4_subset,t5_subset,existence_m1_eqrel_1,existence_m1_subset_1,dt_m1_eqrel_1,dt_m1_subset_1,dt_c1_2__bvfunc14,cc1_eqrel_1,cc2_eqrel_1,rc1_xboole_0,rc2_xboole_0,t2_subset,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_setfam_1,dt_k1_xboole_0,dt_k2_relat_1,dt_c1_2_2_2__bvfunc14,dt_c2_2_2__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,fc1_xboole_0,t1_subset,t6_boole,t7_boole,e2_2_2_2__bvfunc14,e7_2_2__bvfunc14,d1_setfam_1]), [interesting(0.5),file(bvfunc14,e3_2_2_2__bvfunc14),[file(bvfunc14,e3_2_2_2__bvfunc14)]]). fof(d3_xboole_0,definition,( ! [A,B,C] : ( C = k3_xboole_0(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( r2_hidden(D,A) & r2_hidden(D,B) ) ) ) ), file(xboole_0,d3_xboole_0), [interesting(0.9),axiom,file(xboole_0,d3_xboole_0)]). fof(e4_2_2_2__bvfunc14,plain,( r2_hidden(c1_2_2_2__bvfunc14,k3_xboole_0(k1_funct_1(c2_2_2__bvfunc14,c3_2__bvfunc14),k1_funct_1(c2_2_2__bvfunc14,c4_2__bvfunc14))) ), inference(mizar_by,[status(thm),assumptions([dt_c1_2_2_2__bvfunc14,e1_2_2_2__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_2__bvfunc14,dt_c2_2__bvfunc14,e1_2_2__bvfunc14])],[reflexivity_r1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,fc1_subset_1,fc1_xboole_0,rc1_subset_1,rc2_subset_1,t2_boole,t3_subset,t4_subset,t5_subset,existence_m1_eqrel_1,existence_m1_subset_1,dt_m1_eqrel_1,dt_m1_subset_1,dt_c1_2__bvfunc14,cc1_eqrel_1,cc2_eqrel_1,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t8_boole,commutativity_k3_xboole_0,idempotence_k3_xboole_0,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k3_xboole_0,dt_c1_2_2_2__bvfunc14,dt_c2_2_2__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,t1_subset,t7_boole,e3_2_2_2__bvfunc14,d3_xboole_0]), [interesting(0.5),file(bvfunc14,e4_2_2_2__bvfunc14),[file(bvfunc14,e4_2_2_2__bvfunc14)]]). fof(i3_2_2_2__bvfunc14,theorem,( $true ), introduced(tautology,[file(bvfunc14,i3_2_2_2__bvfunc14)]), [interesting(0.5),trivial,file(bvfunc14,i3_2_2_2__bvfunc14)]). fof(i2_2_2_2__bvfunc14,plain,( r2_hidden(c1_2_2_2__bvfunc14,k3_xboole_0(k1_funct_1(c2_2_2__bvfunc14,c3_2__bvfunc14),k1_funct_1(c2_2_2__bvfunc14,c4_2__bvfunc14))) ), inference(conclusion,[status(thm),assumptions([dt_c1_2_2_2__bvfunc14,e1_2_2_2__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_2__bvfunc14,dt_c2_2__bvfunc14,e1_2_2__bvfunc14])],[e4_2_2_2__bvfunc14,i3_2_2_2__bvfunc14]), [interesting(0.5),file(bvfunc14,i2_2_2_2__bvfunc14),[file(bvfunc14,i2_2_2_2__bvfunc14)]]). fof(i1_2_2_2__bvfunc14,plain,( ~ ( r2_hidden(c1_2_2_2__bvfunc14,c1_2_2__bvfunc14) & ~ r2_hidden(c1_2_2_2__bvfunc14,k3_xboole_0(k1_funct_1(c2_2_2__bvfunc14,c3_2__bvfunc14),k1_funct_1(c2_2_2__bvfunc14,c4_2__bvfunc14))) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_2_2_2__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_2__bvfunc14,dt_c2_2__bvfunc14,e1_2_2__bvfunc14]),discharge_asm(discharge,[e1_2_2_2__bvfunc14])],[e1_2_2_2__bvfunc14,i2_2_2_2__bvfunc14]), [interesting(0.5),file(bvfunc14,i1_2_2_2__bvfunc14),[file(bvfunc14,i1_2_2_2__bvfunc14)]]). fof(i1_2_2_2_tmp__bvfunc14,plain,( ~ ( r2_hidden(c1_2_2_2__bvfunc14,c1_2_2__bvfunc14) & ~ r2_hidden(c1_2_2_2__bvfunc14,k3_xboole_0(k1_funct_1(c2_2_2__bvfunc14,c3_2__bvfunc14),k1_funct_1(c2_2_2__bvfunc14,c4_2__bvfunc14))) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_2__bvfunc14,dt_c2_2__bvfunc14,e1_2_2__bvfunc14]),discharge_asm(discharge,[dt_c1_2_2_2__bvfunc14])],[dt_c1_2_2_2__bvfunc14,i1_2_2_2__bvfunc14]), [interesting(0.65),e10_2_2__bvfunc14]). fof(e10_2_2__bvfunc14,plain,( r1_tarski(c1_2_2__bvfunc14,k3_xboole_0(k1_funct_1(c2_2_2__bvfunc14,c3_2__bvfunc14),k1_funct_1(c2_2_2__bvfunc14,c4_2__bvfunc14))) ), inference(let,[status(thm),assumptions([dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_2__bvfunc14,dt_c2_2__bvfunc14,e1_2_2__bvfunc14])],[i1_2_2_2_tmp__bvfunc14,dt_k1_zfmisc_1,dt_m1_subset_1,cc1_eqrel_1,fc1_subset_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,dt_m1_eqrel_1,dt_c1_2__bvfunc14,cc2_eqrel_1,commutativity_k3_xboole_0,idempotence_k3_xboole_0,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k3_xboole_0,dt_c1_2_2__bvfunc14,dt_c2_2_2__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,d3_tarski,dh_c1_2_2_2__bvfunc14]), [interesting(0.65),file(bvfunc14,e10_2_2__bvfunc14),[file(bvfunc14,e10_2_2__bvfunc14)]]). fof(dt_c1_2_2_1__bvfunc14,assumption,( $true ), introduced(assumption,[file(bvfunc14,c1_2_2_1__bvfunc14)]), [interesting(0.5),axiom,file(bvfunc14,c1_2_2_1__bvfunc14)]). fof(dh_c1_2_2_1__bvfunc14,definition, ( ~ ( r2_hidden(c1_2_2_1__bvfunc14,k3_xboole_0(k1_funct_1(c2_2_2__bvfunc14,c3_2__bvfunc14),k1_funct_1(c2_2_2__bvfunc14,c4_2__bvfunc14))) & ~ r2_hidden(c1_2_2_1__bvfunc14,c1_2_2__bvfunc14) ) => ! [A] : ~ ( r2_hidden(A,k3_xboole_0(k1_funct_1(c2_2_2__bvfunc14,c3_2__bvfunc14),k1_funct_1(c2_2_2__bvfunc14,c4_2__bvfunc14))) & ~ r2_hidden(A,c1_2_2__bvfunc14) ) ), introduced(definition,[new_symbol(c1_2_2_1__bvfunc14),file(bvfunc14,c1_2_2_1__bvfunc14)]), [interesting(0.5),axiom,file(bvfunc14,c1_2_2_1__bvfunc14)]). fof(e1_2_2_1__bvfunc14,assumption,( r2_hidden(c1_2_2_1__bvfunc14,k3_xboole_0(k1_funct_1(c2_2_2__bvfunc14,c3_2__bvfunc14),k1_funct_1(c2_2_2__bvfunc14,c4_2__bvfunc14))) ), introduced(assumption,[file(bvfunc14,e1_2_2_1__bvfunc14)]), [interesting(0.5),axiom,file(bvfunc14,e1_2_2_1__bvfunc14)]). fof(dh_c1_2_2_1_2__bvfunc14,definition, ( ( r2_hidden(c1_2_2_1_2__bvfunc14,k2_relat_1(c2_2_2__bvfunc14)) => r2_hidden(c1_2_2_1__bvfunc14,c1_2_2_1_2__bvfunc14) ) => ! [A] : ( r2_hidden(A,k2_relat_1(c2_2_2__bvfunc14)) => r2_hidden(c1_2_2_1__bvfunc14,A) ) ), introduced(definition,[new_symbol(c1_2_2_1_2__bvfunc14),file(bvfunc14,c1_2_2_1_2__bvfunc14)]), [interesting(0.35),axiom,file(bvfunc14,c1_2_2_1_2__bvfunc14)]). fof(e1_2_2_1_2__bvfunc14,assumption,( r2_hidden(c1_2_2_1_2__bvfunc14,k2_relat_1(c2_2_2__bvfunc14)) ), introduced(assumption,[file(bvfunc14,e1_2_2_1_2__bvfunc14)]), [interesting(0.35),axiom,file(bvfunc14,e1_2_2_1_2__bvfunc14)]). fof(dt_c1_2_2_1_2__bvfunc14,assumption,( $true ), introduced(assumption,[file(bvfunc14,c1_2_2_1_2__bvfunc14)]), [interesting(0.35),axiom,file(bvfunc14,c1_2_2_1_2__bvfunc14)]). fof(e1_2_2_1_2_1_1_1__bvfunc14,assumption,( c1_2_2_1_2__bvfunc14 = k1_funct_1(c2_2_2__bvfunc14,c3_2__bvfunc14) ), introduced(assumption,[file(bvfunc14,e1_2_2_1_2_1_1_1__bvfunc14)]), [interesting(0.02),axiom,file(bvfunc14,e1_2_2_1_2_1_1_1__bvfunc14)]). fof(e2_2_2_1_2_1_1_1__bvfunc14,plain,( r2_hidden(c1_2_2_1__bvfunc14,c1_2_2_1_2__bvfunc14) ), inference(mizar_by,[status(thm),assumptions([dt_c1_2_2_1__bvfunc14,dt_c1_2_2_1_2__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_2__bvfunc14,dt_c2_2__bvfunc14,e1_2_2__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2_2_1_2_1_1_1__bvfunc14,e1_2_2_1__bvfunc14])],[reflexivity_r1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,fc1_subset_1,fc1_xboole_0,rc1_subset_1,rc2_subset_1,t2_boole,t3_subset,t4_subset,t5_subset,existence_m1_eqrel_1,existence_m1_subset_1,dt_m1_eqrel_1,dt_m1_subset_1,dt_c1_2__bvfunc14,cc1_eqrel_1,cc2_eqrel_1,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t8_boole,commutativity_k3_xboole_0,idempotence_k3_xboole_0,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k3_xboole_0,dt_c1_2_2_1__bvfunc14,dt_c1_2_2_1_2__bvfunc14,dt_c2_2_2__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,t1_subset,t7_boole,e1_2_2_1_2_1_1_1__bvfunc14,e1_2_2_1__bvfunc14,d3_xboole_0]), [interesting(0.02),file(bvfunc14,e2_2_2_1_2_1_1_1__bvfunc14),[file(bvfunc14,e2_2_2_1_2_1_1_1__bvfunc14)]]). fof(i2_2_2_1_2_1_1_1__bvfunc14,theorem,( $true ), introduced(tautology,[file(bvfunc14,i2_2_2_1_2_1_1_1__bvfunc14)]), [interesting(0.02),trivial,file(bvfunc14,i2_2_2_1_2_1_1_1__bvfunc14)]). fof(i1_2_2_1_2_1_1_1__bvfunc14,plain,( r2_hidden(c1_2_2_1__bvfunc14,c1_2_2_1_2__bvfunc14) ), inference(conclusion,[status(thm),assumptions([dt_c1_2_2_1__bvfunc14,dt_c1_2_2_1_2__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_2__bvfunc14,dt_c2_2__bvfunc14,e1_2_2__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2_2_1_2_1_1_1__bvfunc14,e1_2_2_1__bvfunc14])],[e2_2_2_1_2_1_1_1__bvfunc14,i2_2_2_1_2_1_1_1__bvfunc14]), [interesting(0.02),file(bvfunc14,i1_2_2_1_2_1_1_1__bvfunc14),[file(bvfunc14,i1_2_2_1_2_1_1_1__bvfunc14)]]). fof(i1_2_2_1_2_1_1__bvfunc14,plain, ( c1_2_2_1_2__bvfunc14 = k1_funct_1(c2_2_2__bvfunc14,c3_2__bvfunc14) => ( c1_2_2_1_2__bvfunc14 = k1_funct_1(c2_2_2__bvfunc14,c3_2__bvfunc14) & r2_hidden(c1_2_2_1__bvfunc14,c1_2_2_1_2__bvfunc14) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_2_2_1__bvfunc14,dt_c1_2_2_1_2__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_2__bvfunc14,dt_c2_2__bvfunc14,e1_2_2__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2_2_1__bvfunc14]),discharge_asm(discharge,[e1_2_2_1_2_1_1_1__bvfunc14])],[e1_2_2_1_2_1_1_1__bvfunc14,i1_2_2_1_2_1_1_1__bvfunc14]), [interesting(0.05),file(bvfunc14,i1_2_2_1_2_1_1__bvfunc14),[file(bvfunc14,i1_2_2_1_2_1_1__bvfunc14)]]). fof(e1_2_2_1_2_1_1_2__bvfunc14,assumption,( c1_2_2_1_2__bvfunc14 = k1_funct_1(c2_2_2__bvfunc14,c4_2__bvfunc14) ), introduced(assumption,[file(bvfunc14,e1_2_2_1_2_1_1_2__bvfunc14)]), [interesting(0.02),axiom,file(bvfunc14,e1_2_2_1_2_1_1_2__bvfunc14)]). fof(e2_2_2_1_2_1_1_2__bvfunc14,plain,( r2_hidden(c1_2_2_1__bvfunc14,c1_2_2_1_2__bvfunc14) ), inference(mizar_by,[status(thm),assumptions([dt_c1_2_2_1__bvfunc14,dt_c1_2_2_1_2__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_2__bvfunc14,dt_c2_2__bvfunc14,e1_2_2__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2_2_1_2_1_1_2__bvfunc14,e1_2_2_1__bvfunc14])],[reflexivity_r1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,fc1_subset_1,fc1_xboole_0,rc1_subset_1,rc2_subset_1,t2_boole,t3_subset,t4_subset,t5_subset,existence_m1_eqrel_1,existence_m1_subset_1,dt_m1_eqrel_1,dt_m1_subset_1,dt_c1_2__bvfunc14,cc1_eqrel_1,cc2_eqrel_1,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t8_boole,commutativity_k3_xboole_0,idempotence_k3_xboole_0,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k3_xboole_0,dt_c1_2_2_1__bvfunc14,dt_c1_2_2_1_2__bvfunc14,dt_c2_2_2__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,t1_subset,t7_boole,e1_2_2_1_2_1_1_2__bvfunc14,e1_2_2_1__bvfunc14,d3_xboole_0]), [interesting(0.02),file(bvfunc14,e2_2_2_1_2_1_1_2__bvfunc14),[file(bvfunc14,e2_2_2_1_2_1_1_2__bvfunc14)]]). fof(i2_2_2_1_2_1_1_2__bvfunc14,theorem,( $true ), introduced(tautology,[file(bvfunc14,i2_2_2_1_2_1_1_2__bvfunc14)]), [interesting(0.02),trivial,file(bvfunc14,i2_2_2_1_2_1_1_2__bvfunc14)]). fof(i1_2_2_1_2_1_1_2__bvfunc14,plain,( r2_hidden(c1_2_2_1__bvfunc14,c1_2_2_1_2__bvfunc14) ), inference(conclusion,[status(thm),assumptions([dt_c1_2_2_1__bvfunc14,dt_c1_2_2_1_2__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_2__bvfunc14,dt_c2_2__bvfunc14,e1_2_2__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2_2_1_2_1_1_2__bvfunc14,e1_2_2_1__bvfunc14])],[e2_2_2_1_2_1_1_2__bvfunc14,i2_2_2_1_2_1_1_2__bvfunc14]), [interesting(0.02),file(bvfunc14,i1_2_2_1_2_1_1_2__bvfunc14),[file(bvfunc14,i1_2_2_1_2_1_1_2__bvfunc14)]]). fof(i2_2_2_1_2_1_1__bvfunc14,plain, ( c1_2_2_1_2__bvfunc14 = k1_funct_1(c2_2_2__bvfunc14,c4_2__bvfunc14) => ( c1_2_2_1_2__bvfunc14 = k1_funct_1(c2_2_2__bvfunc14,c4_2__bvfunc14) & r2_hidden(c1_2_2_1__bvfunc14,c1_2_2_1_2__bvfunc14) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_2_2_1__bvfunc14,dt_c1_2_2_1_2__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_2__bvfunc14,dt_c2_2__bvfunc14,e1_2_2__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2_2_1__bvfunc14]),discharge_asm(discharge,[e1_2_2_1_2_1_1_2__bvfunc14])],[e1_2_2_1_2_1_1_2__bvfunc14,i1_2_2_1_2_1_1_2__bvfunc14]), [interesting(0.05),file(bvfunc14,i2_2_2_1_2_1_1__bvfunc14),[file(bvfunc14,i2_2_2_1_2_1_1__bvfunc14)]]). fof(dt_c1_2_2_1_1__bvfunc14,assumption,( $true ), introduced(assumption,[file(bvfunc14,c1_2_2_1_1__bvfunc14)]), [interesting(0.35),axiom,file(bvfunc14,c1_2_2_1_1__bvfunc14)]). fof(dh_c1_2_2_1_1__bvfunc14,definition, ( ~ ( r2_hidden(c1_2_2_1_1__bvfunc14,k2_relat_1(c2_2_2__bvfunc14)) & ~ r2_hidden(c1_2_2_1_1__bvfunc14,k2_tarski(k1_funct_1(c2_2_2__bvfunc14,c3_2__bvfunc14),k1_funct_1(c2_2_2__bvfunc14,c4_2__bvfunc14))) ) => ! [A] : ~ ( r2_hidden(A,k2_relat_1(c2_2_2__bvfunc14)) & ~ r2_hidden(A,k2_tarski(k1_funct_1(c2_2_2__bvfunc14,c3_2__bvfunc14),k1_funct_1(c2_2_2__bvfunc14,c4_2__bvfunc14))) ) ), introduced(definition,[new_symbol(c1_2_2_1_1__bvfunc14),file(bvfunc14,c1_2_2_1_1__bvfunc14)]), [interesting(0.35),axiom,file(bvfunc14,c1_2_2_1_1__bvfunc14)]). fof(e1_2_2_1_1__bvfunc14,assumption,( r2_hidden(c1_2_2_1_1__bvfunc14,k2_relat_1(c2_2_2__bvfunc14)) ), introduced(assumption,[file(bvfunc14,e1_2_2_1_1__bvfunc14)]), [interesting(0.35),axiom,file(bvfunc14,e1_2_2_1_1__bvfunc14)]). fof(dh_c2_2_2_1_1__bvfunc14,definition, ( ? [A] : ( r2_hidden(A,k1_relat_1(c2_2_2__bvfunc14)) & c1_2_2_1_1__bvfunc14 = k1_funct_1(c2_2_2__bvfunc14,A) ) => ( r2_hidden(c2_2_2_1_1__bvfunc14,k1_relat_1(c2_2_2__bvfunc14)) & c1_2_2_1_1__bvfunc14 = k1_funct_1(c2_2_2__bvfunc14,c2_2_2_1_1__bvfunc14) ) ), introduced(definition,[new_symbol(c2_2_2_1_1__bvfunc14),file(bvfunc14,c2_2_2_1_1__bvfunc14)]), [interesting(0.35),axiom,file(bvfunc14,c2_2_2_1_1__bvfunc14)]). fof(e2_2_2_1_1__bvfunc14,plain,( ? [A] : ( r2_hidden(A,k1_relat_1(c2_2_2__bvfunc14)) & c1_2_2_1_1__bvfunc14 = k1_funct_1(c2_2_2__bvfunc14,A) ) ), inference(mizar_by,[status(thm),assumptions([dt_c1_2_2_1_1__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_2__bvfunc14,dt_c2_2__bvfunc14,e1_2_2__bvfunc14,e1_2_2_1_1__bvfunc14])],[dt_k1_xboole_0,fc1_xboole_0,existence_m1_subset_1,dt_m1_subset_1,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k2_relat_1,dt_c1_2_2_1_1__bvfunc14,dt_c2_2_2__bvfunc14,t1_subset,t7_boole,e1_2_2_1_1__bvfunc14,d5_funct_1]), [interesting(0.35),file(bvfunc14,e2_2_2_1_1__bvfunc14),[file(bvfunc14,e2_2_2_1_1__bvfunc14)]]). fof(dt_c2_2_2_1_1__bvfunc14,plain,( $true ), inference(consider,[status(thm),assumptions([dt_c1_2_2_1_1__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_2__bvfunc14,dt_c2_2__bvfunc14,e1_2_2__bvfunc14,e1_2_2_1_1__bvfunc14])],[dh_c2_2_2_1_1__bvfunc14,e2_2_2_1_1__bvfunc14]), [interesting(0.35),file(bvfunc14,c2_2_2_1_1__bvfunc14),[file(bvfunc14,c2_2_2_1_1__bvfunc14)]]). fof(e1_2_2_1_1_1_1_1__bvfunc14,assumption,( c2_2_2_1_1__bvfunc14 = c3_2__bvfunc14 ), introduced(assumption,[file(bvfunc14,e1_2_2_1_1_1_1_1__bvfunc14)]), [interesting(0.02),axiom,file(bvfunc14,e1_2_2_1_1_1_1_1__bvfunc14)]). fof(e3_2_2_1_1__bvfunc14,plain, ( r2_hidden(c2_2_2_1_1__bvfunc14,k1_relat_1(c2_2_2__bvfunc14)) & c1_2_2_1_1__bvfunc14 = k1_funct_1(c2_2_2__bvfunc14,c2_2_2_1_1__bvfunc14) ), inference(consider,[status(thm),assumptions([dt_c1_2_2_1_1__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_2__bvfunc14,dt_c2_2__bvfunc14,e1_2_2__bvfunc14,e1_2_2_1_1__bvfunc14])],[dh_c2_2_2_1_1__bvfunc14,e2_2_2_1_1__bvfunc14]), [interesting(0.35),file(bvfunc14,e3_2_2_1_1__bvfunc14),[file(bvfunc14,e3_2_2_1_1__bvfunc14)]]). fof(e2_2_2_1_1_1_1_1__bvfunc14,plain,( r2_hidden(c1_2_2_1_1__bvfunc14,k2_tarski(k1_funct_1(c2_2_2__bvfunc14,c3_2__bvfunc14),k1_funct_1(c2_2_2__bvfunc14,c4_2__bvfunc14))) ), inference(mizar_by,[status(thm),assumptions([dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2_2_1_1_1_1_1__bvfunc14,dt_c1_2_2_1_1__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_2__bvfunc14,dt_c2_2__bvfunc14,e1_2_2__bvfunc14,e1_2_2_1_1__bvfunc14])],[reflexivity_r1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,fc1_subset_1,fc1_xboole_0,rc1_subset_1,rc2_subset_1,t3_subset,t4_subset,t5_subset,existence_m1_eqrel_1,existence_m1_subset_1,dt_m1_eqrel_1,dt_m1_subset_1,dt_c1_2__bvfunc14,cc1_eqrel_1,cc2_eqrel_1,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t8_boole,commutativity_k2_tarski,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k2_tarski,dt_c1_2_2_1_1__bvfunc14,dt_c2_2_2__bvfunc14,dt_c2_2_2_1_1__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,fc3_subset_1,t1_subset,t7_boole,e1_2_2_1_1_1_1_1__bvfunc14,e3_2_2_1_1__bvfunc14,d2_tarski]), [interesting(0.02),file(bvfunc14,e2_2_2_1_1_1_1_1__bvfunc14),[file(bvfunc14,e2_2_2_1_1_1_1_1__bvfunc14)]]). fof(i2_2_2_1_1_1_1_1__bvfunc14,theorem,( $true ), introduced(tautology,[file(bvfunc14,i2_2_2_1_1_1_1_1__bvfunc14)]), [interesting(0.02),trivial,file(bvfunc14,i2_2_2_1_1_1_1_1__bvfunc14)]). fof(i1_2_2_1_1_1_1_1__bvfunc14,plain,( r2_hidden(c1_2_2_1_1__bvfunc14,k2_tarski(k1_funct_1(c2_2_2__bvfunc14,c3_2__bvfunc14),k1_funct_1(c2_2_2__bvfunc14,c4_2__bvfunc14))) ), inference(conclusion,[status(thm),assumptions([dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2_2_1_1_1_1_1__bvfunc14,dt_c1_2_2_1_1__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_2__bvfunc14,dt_c2_2__bvfunc14,e1_2_2__bvfunc14,e1_2_2_1_1__bvfunc14])],[e2_2_2_1_1_1_1_1__bvfunc14,i2_2_2_1_1_1_1_1__bvfunc14]), [interesting(0.02),file(bvfunc14,i1_2_2_1_1_1_1_1__bvfunc14),[file(bvfunc14,i1_2_2_1_1_1_1_1__bvfunc14)]]). fof(i1_2_2_1_1_1_1__bvfunc14,plain, ( c2_2_2_1_1__bvfunc14 = c3_2__bvfunc14 => ( c2_2_2_1_1__bvfunc14 = c3_2__bvfunc14 & r2_hidden(c1_2_2_1_1__bvfunc14,k2_tarski(k1_funct_1(c2_2_2__bvfunc14,c3_2__bvfunc14),k1_funct_1(c2_2_2__bvfunc14,c4_2__bvfunc14))) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,dt_c1_2_2_1_1__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_2__bvfunc14,dt_c2_2__bvfunc14,e1_2_2__bvfunc14,e1_2_2_1_1__bvfunc14]),discharge_asm(discharge,[e1_2_2_1_1_1_1_1__bvfunc14])],[e1_2_2_1_1_1_1_1__bvfunc14,i1_2_2_1_1_1_1_1__bvfunc14]), [interesting(0.05),file(bvfunc14,i1_2_2_1_1_1_1__bvfunc14),[file(bvfunc14,i1_2_2_1_1_1_1__bvfunc14)]]). fof(e1_2_2_1_1_1_1_2__bvfunc14,assumption,( c2_2_2_1_1__bvfunc14 = c4_2__bvfunc14 ), introduced(assumption,[file(bvfunc14,e1_2_2_1_1_1_1_2__bvfunc14)]), [interesting(0.02),axiom,file(bvfunc14,e1_2_2_1_1_1_1_2__bvfunc14)]). fof(e2_2_2_1_1_1_1_2__bvfunc14,plain,( r2_hidden(c1_2_2_1_1__bvfunc14,k2_tarski(k1_funct_1(c2_2_2__bvfunc14,c3_2__bvfunc14),k1_funct_1(c2_2_2__bvfunc14,c4_2__bvfunc14))) ), inference(mizar_by,[status(thm),assumptions([dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2_2_1_1_1_1_2__bvfunc14,dt_c1_2_2_1_1__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_2__bvfunc14,dt_c2_2__bvfunc14,e1_2_2__bvfunc14,e1_2_2_1_1__bvfunc14])],[reflexivity_r1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,fc1_subset_1,fc1_xboole_0,rc1_subset_1,rc2_subset_1,t3_subset,t4_subset,t5_subset,existence_m1_eqrel_1,existence_m1_subset_1,dt_m1_eqrel_1,dt_m1_subset_1,dt_c1_2__bvfunc14,cc1_eqrel_1,cc2_eqrel_1,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t8_boole,commutativity_k2_tarski,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k2_tarski,dt_c1_2_2_1_1__bvfunc14,dt_c2_2_2__bvfunc14,dt_c2_2_2_1_1__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,fc3_subset_1,t1_subset,t7_boole,e1_2_2_1_1_1_1_2__bvfunc14,e3_2_2_1_1__bvfunc14,d2_tarski]), [interesting(0.02),file(bvfunc14,e2_2_2_1_1_1_1_2__bvfunc14),[file(bvfunc14,e2_2_2_1_1_1_1_2__bvfunc14)]]). fof(i2_2_2_1_1_1_1_2__bvfunc14,theorem,( $true ), introduced(tautology,[file(bvfunc14,i2_2_2_1_1_1_1_2__bvfunc14)]), [interesting(0.02),trivial,file(bvfunc14,i2_2_2_1_1_1_1_2__bvfunc14)]). fof(i1_2_2_1_1_1_1_2__bvfunc14,plain,( r2_hidden(c1_2_2_1_1__bvfunc14,k2_tarski(k1_funct_1(c2_2_2__bvfunc14,c3_2__bvfunc14),k1_funct_1(c2_2_2__bvfunc14,c4_2__bvfunc14))) ), inference(conclusion,[status(thm),assumptions([dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2_2_1_1_1_1_2__bvfunc14,dt_c1_2_2_1_1__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_2__bvfunc14,dt_c2_2__bvfunc14,e1_2_2__bvfunc14,e1_2_2_1_1__bvfunc14])],[e2_2_2_1_1_1_1_2__bvfunc14,i2_2_2_1_1_1_1_2__bvfunc14]), [interesting(0.02),file(bvfunc14,i1_2_2_1_1_1_1_2__bvfunc14),[file(bvfunc14,i1_2_2_1_1_1_1_2__bvfunc14)]]). fof(i2_2_2_1_1_1_1__bvfunc14,plain, ( c2_2_2_1_1__bvfunc14 = c4_2__bvfunc14 => ( c2_2_2_1_1__bvfunc14 = c4_2__bvfunc14 & r2_hidden(c1_2_2_1_1__bvfunc14,k2_tarski(k1_funct_1(c2_2_2__bvfunc14,c3_2__bvfunc14),k1_funct_1(c2_2_2__bvfunc14,c4_2__bvfunc14))) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,dt_c1_2_2_1_1__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_2__bvfunc14,dt_c2_2__bvfunc14,e1_2_2__bvfunc14,e1_2_2_1_1__bvfunc14]),discharge_asm(discharge,[e1_2_2_1_1_1_1_2__bvfunc14])],[e1_2_2_1_1_1_1_2__bvfunc14,i1_2_2_1_1_1_1_2__bvfunc14]), [interesting(0.05),file(bvfunc14,i2_2_2_1_1_1_1__bvfunc14),[file(bvfunc14,i2_2_2_1_1_1_1__bvfunc14)]]). fof(e1_2_2_1_1_1_1__bvfunc14,plain, ( c2_2_2_1_1__bvfunc14 = c3_2__bvfunc14 | c2_2_2_1_1__bvfunc14 = c4_2__bvfunc14 ), inference(mizar_by,[status(thm),assumptions([dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2__bvfunc14,dt_c1_2_2_1_1__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_2__bvfunc14,dt_c2_2__bvfunc14,e1_2_2__bvfunc14,e1_2_2_1_1__bvfunc14])],[reflexivity_r1_tarski,existence_m1_t_1topsp,dt_k1_partit1,dt_m1_t_1topsp,existence_m1_eqrel_1,existence_m1_subset_1,redefinition_k1_bvfunc_2,dt_k1_bvfunc_2,dt_k1_zfmisc_1,dt_m1_eqrel_1,dt_m1_subset_1,cc1_eqrel_1,cc2_eqrel_1,fc1_subset_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,t2_subset,t3_subset,t4_subset,t5_subset,t8_boole,commutativity_k2_tarski,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k1_xboole_0,dt_k2_relat_1,dt_k2_tarski,dt_k8_setfam_1,dt_c1_2__bvfunc14,dt_c1_2_2__bvfunc14,dt_c1_2_2_1_1__bvfunc14,dt_c2_2__bvfunc14,dt_c2_2_2__bvfunc14,dt_c2_2_2_1_1__bvfunc14,dt_c3_2__bvfunc14,dt_c3_2_2__bvfunc14,dt_c4_2__bvfunc14,fc1_xboole_0,fc3_subset_1,t1_subset,t6_boole,t7_boole,e1_2__bvfunc14,e3_2_2__bvfunc14,e3_2_2_1_1__bvfunc14,d2_tarski]), [interesting(0.05),file(bvfunc14,e1_2_2_1_1_1_1__bvfunc14),[file(bvfunc14,e1_2_2_1_1_1_1__bvfunc14)]]). fof(e4_2_2_1_1__bvfunc14,plain, ( ( c2_2_2_1_1__bvfunc14 = c3_2__bvfunc14 & r2_hidden(c1_2_2_1_1__bvfunc14,k2_tarski(k1_funct_1(c2_2_2__bvfunc14,c3_2__bvfunc14),k1_funct_1(c2_2_2__bvfunc14,c4_2__bvfunc14))) ) | ( c2_2_2_1_1__bvfunc14 = c4_2__bvfunc14 & r2_hidden(c1_2_2_1_1__bvfunc14,k2_tarski(k1_funct_1(c2_2_2__bvfunc14,c3_2__bvfunc14),k1_funct_1(c2_2_2__bvfunc14,c4_2__bvfunc14))) ) ), inference(percases,[status(thm),assumptions([dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2__bvfunc14,dt_c1_2_2_1_1__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_2__bvfunc14,dt_c2_2__bvfunc14,e1_2_2__bvfunc14,e1_2_2_1_1__bvfunc14])],[i1_2_2_1_1_1_1__bvfunc14,i2_2_2_1_1_1_1__bvfunc14,e1_2_2_1_1_1_1__bvfunc14]), [interesting(0.35),file(bvfunc14,e4_2_2_1_1__bvfunc14),[file(bvfunc14,e4_2_2_1_1__bvfunc14)]]). fof(e5_2_2_1_1__bvfunc14,plain,( r2_hidden(c1_2_2_1_1__bvfunc14,k2_tarski(k1_funct_1(c2_2_2__bvfunc14,c3_2__bvfunc14),k1_funct_1(c2_2_2__bvfunc14,c4_2__bvfunc14))) ), inference(mizar_by,[status(thm),assumptions([dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2__bvfunc14,dt_c1_2_2_1_1__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_2__bvfunc14,dt_c2_2__bvfunc14,e1_2_2__bvfunc14,e1_2_2_1_1__bvfunc14])],[reflexivity_r1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,fc1_subset_1,fc1_xboole_0,rc1_subset_1,rc2_subset_1,t3_subset,t4_subset,t5_subset,existence_m1_eqrel_1,existence_m1_subset_1,dt_m1_eqrel_1,dt_m1_subset_1,dt_c1_2__bvfunc14,cc1_eqrel_1,cc2_eqrel_1,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t8_boole,commutativity_k2_tarski,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k2_tarski,dt_c1_2_2_1_1__bvfunc14,dt_c2_2_2__bvfunc14,dt_c2_2_2_1_1__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,fc3_subset_1,t1_subset,t7_boole,e4_2_2_1_1__bvfunc14]), [interesting(0.35),file(bvfunc14,e5_2_2_1_1__bvfunc14),[file(bvfunc14,e5_2_2_1_1__bvfunc14)]]). fof(i3_2_2_1_1__bvfunc14,theorem,( $true ), introduced(tautology,[file(bvfunc14,i3_2_2_1_1__bvfunc14)]), [interesting(0.35),trivial,file(bvfunc14,i3_2_2_1_1__bvfunc14)]). fof(i2_2_2_1_1__bvfunc14,plain,( r2_hidden(c1_2_2_1_1__bvfunc14,k2_tarski(k1_funct_1(c2_2_2__bvfunc14,c3_2__bvfunc14),k1_funct_1(c2_2_2__bvfunc14,c4_2__bvfunc14))) ), inference(conclusion,[status(thm),assumptions([dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2__bvfunc14,dt_c1_2_2_1_1__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_2__bvfunc14,dt_c2_2__bvfunc14,e1_2_2__bvfunc14,e1_2_2_1_1__bvfunc14])],[e5_2_2_1_1__bvfunc14,i3_2_2_1_1__bvfunc14]), [interesting(0.35),file(bvfunc14,i2_2_2_1_1__bvfunc14),[file(bvfunc14,i2_2_2_1_1__bvfunc14)]]). fof(i1_2_2_1_1__bvfunc14,plain,( ~ ( r2_hidden(c1_2_2_1_1__bvfunc14,k2_relat_1(c2_2_2__bvfunc14)) & ~ r2_hidden(c1_2_2_1_1__bvfunc14,k2_tarski(k1_funct_1(c2_2_2__bvfunc14,c3_2__bvfunc14),k1_funct_1(c2_2_2__bvfunc14,c4_2__bvfunc14))) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2__bvfunc14,dt_c1_2_2_1_1__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_2__bvfunc14,dt_c2_2__bvfunc14,e1_2_2__bvfunc14]),discharge_asm(discharge,[e1_2_2_1_1__bvfunc14])],[e1_2_2_1_1__bvfunc14,i2_2_2_1_1__bvfunc14]), [interesting(0.35),file(bvfunc14,i1_2_2_1_1__bvfunc14),[file(bvfunc14,i1_2_2_1_1__bvfunc14)]]). fof(i1_2_2_1_1_tmp__bvfunc14,plain,( ~ ( r2_hidden(c1_2_2_1_1__bvfunc14,k2_relat_1(c2_2_2__bvfunc14)) & ~ r2_hidden(c1_2_2_1_1__bvfunc14,k2_tarski(k1_funct_1(c2_2_2__bvfunc14,c3_2__bvfunc14),k1_funct_1(c2_2_2__bvfunc14,c4_2__bvfunc14))) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_2__bvfunc14,dt_c2_2__bvfunc14,e1_2_2__bvfunc14]),discharge_asm(discharge,[dt_c1_2_2_1_1__bvfunc14])],[dt_c1_2_2_1_1__bvfunc14,i1_2_2_1_1__bvfunc14]), [interesting(0.5),e2_2_2_1__bvfunc14]). fof(e2_2_2_1__bvfunc14,plain,( r1_tarski(k2_relat_1(c2_2_2__bvfunc14),k2_tarski(k1_funct_1(c2_2_2__bvfunc14,c3_2__bvfunc14),k1_funct_1(c2_2_2__bvfunc14,c4_2__bvfunc14))) ), inference(let,[status(thm),assumptions([dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_2__bvfunc14,dt_c2_2__bvfunc14,e1_2_2__bvfunc14])],[i1_2_2_1_1_tmp__bvfunc14,dt_k1_zfmisc_1,dt_m1_subset_1,fc1_subset_1,rc1_subset_1,rc2_subset_1,dt_m1_eqrel_1,dt_c1_2__bvfunc14,cc1_eqrel_1,cc2_eqrel_1,rc1_xboole_0,rc2_xboole_0,commutativity_k2_tarski,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k2_relat_1,dt_k2_tarski,dt_c2_2_2__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,fc3_subset_1,d3_tarski,dh_c1_2_2_1_1__bvfunc14]), [interesting(0.5),file(bvfunc14,e2_2_2_1__bvfunc14),[file(bvfunc14,e2_2_2_1__bvfunc14)]]). fof(e1_2_2_1_2_1_1__bvfunc14,plain, ( c1_2_2_1_2__bvfunc14 = k1_funct_1(c2_2_2__bvfunc14,c3_2__bvfunc14) | c1_2_2_1_2__bvfunc14 = k1_funct_1(c2_2_2__bvfunc14,c4_2__bvfunc14) ), inference(mizar_by,[status(thm),assumptions([dt_c1_2_2_1_2__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_2__bvfunc14,dt_c2_2__bvfunc14,e1_2_2__bvfunc14,e1_2_2_1_2__bvfunc14])],[dt_k1_xboole_0,fc1_xboole_0,existence_m1_eqrel_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_eqrel_1,dt_m1_subset_1,dt_c1_2__bvfunc14,cc1_eqrel_1,cc2_eqrel_1,fc1_subset_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,t2_subset,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k2_tarski,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k2_relat_1,dt_k2_tarski,dt_c1_2_2_1_2__bvfunc14,dt_c2_2_2__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,fc3_subset_1,t1_subset,t3_subset,t7_boole,e2_2_2_1__bvfunc14,e1_2_2_1_2__bvfunc14,d2_tarski]), [interesting(0.05),file(bvfunc14,e1_2_2_1_2_1_1__bvfunc14),[file(bvfunc14,e1_2_2_1_2_1_1__bvfunc14)]]). fof(e2_2_2_1_2__bvfunc14,plain, ( ( c1_2_2_1_2__bvfunc14 = k1_funct_1(c2_2_2__bvfunc14,c3_2__bvfunc14) & r2_hidden(c1_2_2_1__bvfunc14,c1_2_2_1_2__bvfunc14) ) | ( c1_2_2_1_2__bvfunc14 = k1_funct_1(c2_2_2__bvfunc14,c4_2__bvfunc14) & r2_hidden(c1_2_2_1__bvfunc14,c1_2_2_1_2__bvfunc14) ) ), inference(percases,[status(thm),assumptions([dt_c1_2_2_1__bvfunc14,e1_2_2_1__bvfunc14,dt_c1_2_2_1_2__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_2__bvfunc14,dt_c2_2__bvfunc14,e1_2_2__bvfunc14,e1_2_2_1_2__bvfunc14])],[i1_2_2_1_2_1_1__bvfunc14,i2_2_2_1_2_1_1__bvfunc14,e1_2_2_1_2_1_1__bvfunc14]), [interesting(0.35),file(bvfunc14,e2_2_2_1_2__bvfunc14),[file(bvfunc14,e2_2_2_1_2__bvfunc14)]]). fof(e3_2_2_1_2__bvfunc14,plain,( r2_hidden(c1_2_2_1__bvfunc14,c1_2_2_1_2__bvfunc14) ), inference(mizar_by,[status(thm),assumptions([dt_c1_2_2_1__bvfunc14,e1_2_2_1__bvfunc14,dt_c1_2_2_1_2__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_2__bvfunc14,dt_c2_2__bvfunc14,e1_2_2__bvfunc14,e1_2_2_1_2__bvfunc14])],[reflexivity_r1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,fc1_subset_1,fc1_xboole_0,rc1_subset_1,rc2_subset_1,t3_subset,t4_subset,t5_subset,existence_m1_eqrel_1,existence_m1_subset_1,dt_m1_eqrel_1,dt_m1_subset_1,dt_c1_2__bvfunc14,cc1_eqrel_1,cc2_eqrel_1,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_c1_2_2_1__bvfunc14,dt_c1_2_2_1_2__bvfunc14,dt_c2_2_2__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,t1_subset,t7_boole,e2_2_2_1_2__bvfunc14]), [interesting(0.35),file(bvfunc14,e3_2_2_1_2__bvfunc14),[file(bvfunc14,e3_2_2_1_2__bvfunc14)]]). fof(i3_2_2_1_2__bvfunc14,theorem,( $true ), introduced(tautology,[file(bvfunc14,i3_2_2_1_2__bvfunc14)]), [interesting(0.35),trivial,file(bvfunc14,i3_2_2_1_2__bvfunc14)]). fof(i2_2_2_1_2__bvfunc14,plain,( r2_hidden(c1_2_2_1__bvfunc14,c1_2_2_1_2__bvfunc14) ), inference(conclusion,[status(thm),assumptions([dt_c1_2_2_1__bvfunc14,e1_2_2_1__bvfunc14,dt_c1_2_2_1_2__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_2__bvfunc14,dt_c2_2__bvfunc14,e1_2_2__bvfunc14,e1_2_2_1_2__bvfunc14])],[e3_2_2_1_2__bvfunc14,i3_2_2_1_2__bvfunc14]), [interesting(0.35),file(bvfunc14,i2_2_2_1_2__bvfunc14),[file(bvfunc14,i2_2_2_1_2__bvfunc14)]]). fof(i1_2_2_1_2__bvfunc14,plain, ( r2_hidden(c1_2_2_1_2__bvfunc14,k2_relat_1(c2_2_2__bvfunc14)) => r2_hidden(c1_2_2_1__bvfunc14,c1_2_2_1_2__bvfunc14) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_2_2_1__bvfunc14,e1_2_2_1__bvfunc14,dt_c1_2_2_1_2__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_2__bvfunc14,dt_c2_2__bvfunc14,e1_2_2__bvfunc14]),discharge_asm(discharge,[e1_2_2_1_2__bvfunc14])],[e1_2_2_1_2__bvfunc14,i2_2_2_1_2__bvfunc14]), [interesting(0.35),file(bvfunc14,i1_2_2_1_2__bvfunc14),[file(bvfunc14,i1_2_2_1_2__bvfunc14)]]). fof(i1_2_2_1_2_tmp__bvfunc14,plain, ( r2_hidden(c1_2_2_1_2__bvfunc14,k2_relat_1(c2_2_2__bvfunc14)) => r2_hidden(c1_2_2_1__bvfunc14,c1_2_2_1_2__bvfunc14) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_2_2_1__bvfunc14,e1_2_2_1__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_2__bvfunc14,dt_c2_2__bvfunc14,e1_2_2__bvfunc14]),discharge_asm(discharge,[dt_c1_2_2_1_2__bvfunc14])],[dt_c1_2_2_1_2__bvfunc14,i1_2_2_1_2__bvfunc14]), [interesting(0.5),e3_2_2_1__bvfunc14]). fof(e3_2_2_1__bvfunc14,plain,( ! [A] : ( r2_hidden(A,k2_relat_1(c2_2_2__bvfunc14)) => r2_hidden(c1_2_2_1__bvfunc14,A) ) ), inference(let,[status(thm),assumptions([dt_c1_2_2_1__bvfunc14,e1_2_2_1__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_2__bvfunc14,dt_c2_2__bvfunc14,e1_2_2__bvfunc14])],[i1_2_2_1_2_tmp__bvfunc14,dh_c1_2_2_1_2__bvfunc14]), [interesting(0.5),file(bvfunc14,e3_2_2_1__bvfunc14),[file(bvfunc14,e3_2_2_1__bvfunc14)]]). fof(e4_2_2_1__bvfunc14,plain,( r2_hidden(c1_2_2_1__bvfunc14,k1_setfam_1(k2_relat_1(c2_2_2__bvfunc14))) ), inference(mizar_by,[status(thm),assumptions([dt_c1_2_2_1__bvfunc14,e1_2_2_1__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_2__bvfunc14,dt_c2_2__bvfunc14,e1_2_2__bvfunc14])],[reflexivity_r1_tarski,dt_k1_zfmisc_1,fc1_subset_1,rc1_subset_1,rc2_subset_1,t3_subset,t4_subset,t5_subset,existence_m1_eqrel_1,existence_m1_subset_1,dt_m1_eqrel_1,dt_m1_subset_1,dt_c1_2__bvfunc14,cc1_eqrel_1,cc2_eqrel_1,rc1_xboole_0,rc2_xboole_0,t2_subset,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_setfam_1,dt_k1_xboole_0,dt_k2_relat_1,dt_c1_2_2_1__bvfunc14,dt_c2_2_2__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,fc1_xboole_0,t1_subset,t6_boole,t7_boole,e3_2_2_1__bvfunc14,e7_2_2__bvfunc14,d1_setfam_1]), [interesting(0.5),file(bvfunc14,e4_2_2_1__bvfunc14),[file(bvfunc14,e4_2_2_1__bvfunc14)]]). fof(e5_2_2_1__bvfunc14,plain,( r2_hidden(c1_2_2_1__bvfunc14,c1_2_2__bvfunc14) ), inference(mizar_by,[status(thm),assumptions([dt_c1_2_2_1__bvfunc14,e1_2_2_1__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_2__bvfunc14,dt_c2_2__bvfunc14,e1_2_2__bvfunc14])],[existence_m1_t_1topsp,dt_k1_partit1,dt_m1_t_1topsp,reflexivity_r1_tarski,existence_m1_eqrel_1,redefinition_k1_bvfunc_2,dt_k1_bvfunc_2,dt_m1_eqrel_1,cc1_eqrel_1,cc2_eqrel_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,t2_subset,t5_subset,t8_boole,antisymmetry_r2_hidden,existence_m1_subset_1,redefinition_k6_setfam_1,dt_k1_funct_1,dt_k1_relat_1,dt_k1_setfam_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_relat_1,dt_k6_setfam_1,dt_k8_setfam_1,dt_m1_subset_1,dt_c1_2__bvfunc14,dt_c1_2_2__bvfunc14,dt_c1_2_2_1__bvfunc14,dt_c2_2__bvfunc14,dt_c2_2_2__bvfunc14,dt_c3_2__bvfunc14,dt_c3_2_2__bvfunc14,dt_c4_2__bvfunc14,fc1_subset_1,fc1_xboole_0,t1_subset,t3_subset,t4_subset,t6_boole,t7_boole,e4_2_2_1__bvfunc14,e3_2_2__bvfunc14,e7_2_2__bvfunc14,d10_setfam_1]), [interesting(0.5),file(bvfunc14,e5_2_2_1__bvfunc14),[file(bvfunc14,e5_2_2_1__bvfunc14)]]). fof(i3_2_2_1__bvfunc14,theorem,( $true ), introduced(tautology,[file(bvfunc14,i3_2_2_1__bvfunc14)]), [interesting(0.5),trivial,file(bvfunc14,i3_2_2_1__bvfunc14)]). fof(i2_2_2_1__bvfunc14,plain,( r2_hidden(c1_2_2_1__bvfunc14,c1_2_2__bvfunc14) ), inference(conclusion,[status(thm),assumptions([dt_c1_2_2_1__bvfunc14,e1_2_2_1__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_2__bvfunc14,dt_c2_2__bvfunc14,e1_2_2__bvfunc14])],[e5_2_2_1__bvfunc14,i3_2_2_1__bvfunc14]), [interesting(0.5),file(bvfunc14,i2_2_2_1__bvfunc14),[file(bvfunc14,i2_2_2_1__bvfunc14)]]). fof(i1_2_2_1__bvfunc14,plain,( ~ ( r2_hidden(c1_2_2_1__bvfunc14,k3_xboole_0(k1_funct_1(c2_2_2__bvfunc14,c3_2__bvfunc14),k1_funct_1(c2_2_2__bvfunc14,c4_2__bvfunc14))) & ~ r2_hidden(c1_2_2_1__bvfunc14,c1_2_2__bvfunc14) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_2_2_1__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_2__bvfunc14,dt_c2_2__bvfunc14,e1_2_2__bvfunc14]),discharge_asm(discharge,[e1_2_2_1__bvfunc14])],[e1_2_2_1__bvfunc14,i2_2_2_1__bvfunc14]), [interesting(0.5),file(bvfunc14,i1_2_2_1__bvfunc14),[file(bvfunc14,i1_2_2_1__bvfunc14)]]). fof(i1_2_2_1_tmp__bvfunc14,plain,( ~ ( r2_hidden(c1_2_2_1__bvfunc14,k3_xboole_0(k1_funct_1(c2_2_2__bvfunc14,c3_2__bvfunc14),k1_funct_1(c2_2_2__bvfunc14,c4_2__bvfunc14))) & ~ r2_hidden(c1_2_2_1__bvfunc14,c1_2_2__bvfunc14) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_2__bvfunc14,dt_c2_2__bvfunc14,e1_2_2__bvfunc14]),discharge_asm(discharge,[dt_c1_2_2_1__bvfunc14])],[dt_c1_2_2_1__bvfunc14,i1_2_2_1__bvfunc14]), [interesting(0.65),e9_2_2__bvfunc14]). fof(e9_2_2__bvfunc14,plain,( r1_tarski(k3_xboole_0(k1_funct_1(c2_2_2__bvfunc14,c3_2__bvfunc14),k1_funct_1(c2_2_2__bvfunc14,c4_2__bvfunc14)),c1_2_2__bvfunc14) ), inference(let,[status(thm),assumptions([dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_2__bvfunc14,dt_c2_2__bvfunc14,e1_2_2__bvfunc14])],[i1_2_2_1_tmp__bvfunc14,dt_k1_zfmisc_1,dt_m1_subset_1,cc1_eqrel_1,fc1_subset_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,dt_m1_eqrel_1,dt_c1_2__bvfunc14,cc2_eqrel_1,commutativity_k3_xboole_0,idempotence_k3_xboole_0,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k3_xboole_0,dt_c1_2_2__bvfunc14,dt_c2_2_2__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,d3_tarski,dh_c1_2_2_1__bvfunc14]), [interesting(0.65),file(bvfunc14,e9_2_2__bvfunc14),[file(bvfunc14,e9_2_2__bvfunc14)]]). 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(e11_2_2__bvfunc14,plain,( k3_xboole_0(k1_funct_1(c2_2_2__bvfunc14,c3_2__bvfunc14),k1_funct_1(c2_2_2__bvfunc14,c4_2__bvfunc14)) = c1_2_2__bvfunc14 ), inference(mizar_by,[status(thm),assumptions([dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_2__bvfunc14,dt_c2_2__bvfunc14,e1_2_2__bvfunc14])],[antisymmetry_r2_hidden,dt_k1_xboole_0,fc1_xboole_0,t1_subset,t2_boole,t4_subset,t5_subset,cc1_eqrel_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_eqrel_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_eqrel_1,dt_m1_subset_1,dt_c1_2__bvfunc14,cc2_eqrel_1,fc1_subset_1,commutativity_k3_xboole_0,idempotence_k3_xboole_0,reflexivity_r1_tarski,dt_k1_funct_1,dt_k3_xboole_0,dt_c1_2_2__bvfunc14,dt_c2_2_2__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,t3_subset,e10_2_2__bvfunc14,e9_2_2__bvfunc14,d10_xboole_0]), [interesting(0.65),file(bvfunc14,e11_2_2__bvfunc14),[file(bvfunc14,e11_2_2__bvfunc14)]]). fof(e4_2_2__bvfunc14,plain, ( r2_hidden(c3_2__bvfunc14,c2_2__bvfunc14) & r2_hidden(c4_2__bvfunc14,c2_2__bvfunc14) ), inference(mizar_by,[status(thm),assumptions([dt_c1_2__bvfunc14,dt_c2_2__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2__bvfunc14])],[reflexivity_r1_tarski,existence_m1_t_1topsp,dt_k1_partit1,dt_k1_xboole_0,dt_m1_t_1topsp,fc1_xboole_0,existence_m1_eqrel_1,existence_m1_subset_1,redefinition_k1_bvfunc_2,dt_k1_bvfunc_2,dt_k1_zfmisc_1,dt_m1_eqrel_1,dt_m1_subset_1,dt_c1_2__bvfunc14,cc1_eqrel_1,cc2_eqrel_1,fc1_subset_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k2_tarski,antisymmetry_r2_hidden,dt_k2_tarski,dt_c2_2__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,fc3_subset_1,t1_subset,t7_boole,e1_2__bvfunc14,d2_tarski]), [interesting(0.65),file(bvfunc14,e4_2_2__bvfunc14),[file(bvfunc14,e4_2_2__bvfunc14)]]). fof(e5_2_2__bvfunc14,plain, ( r2_hidden(k1_funct_1(c2_2_2__bvfunc14,c3_2__bvfunc14),c3_2__bvfunc14) & r2_hidden(k1_funct_1(c2_2_2__bvfunc14,c4_2__bvfunc14),c4_2__bvfunc14) ), inference(mizar_by,[status(thm),assumptions([dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_2__bvfunc14,dt_c2_2__bvfunc14,e1_2_2__bvfunc14])],[reflexivity_r1_tarski,existence_m1_t_1topsp,dt_k1_partit1,dt_m1_t_1topsp,existence_m1_eqrel_1,existence_m1_subset_1,redefinition_k1_bvfunc_2,dt_k1_bvfunc_2,dt_k1_zfmisc_1,dt_m1_eqrel_1,dt_m1_subset_1,cc1_eqrel_1,cc2_eqrel_1,fc1_subset_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,t2_subset,t3_subset,t4_subset,t5_subset,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k1_xboole_0,dt_k2_relat_1,dt_k8_setfam_1,dt_c1_2__bvfunc14,dt_c1_2_2__bvfunc14,dt_c2_2__bvfunc14,dt_c2_2_2__bvfunc14,dt_c3_2__bvfunc14,dt_c3_2_2__bvfunc14,dt_c4_2__bvfunc14,fc1_xboole_0,t1_subset,t6_boole,t7_boole,e4_2_2__bvfunc14,e3_2_2__bvfunc14]), [interesting(0.65),file(bvfunc14,e5_2_2__bvfunc14),[file(bvfunc14,e5_2_2__bvfunc14)]]). fof(d5_setfam_1,definition,( ! [A,B,C] : ( C = k3_setfam_1(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ? [E,F] : ( r2_hidden(E,A) & r2_hidden(F,B) & D = k3_xboole_0(E,F) ) ) ) ), file(setfam_1,d5_setfam_1), [interesting(0.9),axiom,file(setfam_1,d5_setfam_1)]). fof(e12_2_2__bvfunc14,plain,( r2_hidden(c1_2_2__bvfunc14,k3_setfam_1(c3_2__bvfunc14,c4_2__bvfunc14)) ), inference(mizar_by,[status(thm),assumptions([dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_2__bvfunc14,dt_c2_2__bvfunc14,e1_2_2__bvfunc14])],[reflexivity_r1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,fc1_subset_1,fc1_xboole_0,rc1_subset_1,rc2_subset_1,t2_boole,t3_subset,t4_subset,t5_subset,existence_m1_eqrel_1,existence_m1_subset_1,dt_m1_eqrel_1,dt_m1_subset_1,dt_c1_2__bvfunc14,cc1_eqrel_1,cc2_eqrel_1,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t8_boole,commutativity_k3_setfam_1,commutativity_k3_xboole_0,idempotence_k3_xboole_0,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k3_setfam_1,dt_k3_xboole_0,dt_c1_2_2__bvfunc14,dt_c2_2_2__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,t1_subset,t7_boole,e11_2_2__bvfunc14,e5_2_2__bvfunc14,d5_setfam_1]), [interesting(0.65),file(bvfunc14,e12_2_2__bvfunc14),[file(bvfunc14,e12_2_2__bvfunc14)]]). fof(d1_tarski,definition,( ! [A,B] : ( B = k1_tarski(A) <=> ! [C] : ( r2_hidden(C,B) <=> C = A ) ) ), file(tarski,d1_tarski), [interesting(0.9),axiom,file(tarski,d1_tarski)]). fof(e8_2_2__bvfunc14,plain,( ~ r2_hidden(c1_2_2__bvfunc14,k1_tarski(k1_xboole_0)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_2__bvfunc14,dt_c1_2_2__bvfunc14,dt_c2_2__bvfunc14,e1_2_2__bvfunc14])],[reflexivity_r1_tarski,existence_m1_t_1topsp,dt_k1_partit1,dt_m1_t_1topsp,existence_m1_subset_1,redefinition_k1_bvfunc_2,dt_k1_bvfunc_2,dt_k1_zfmisc_1,dt_m1_subset_1,fc1_subset_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,t2_subset,t3_subset,t4_subset,t5_subset,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k1_tarski,dt_k1_xboole_0,dt_k2_relat_1,dt_k8_setfam_1,dt_c1_2__bvfunc14,dt_c1_2_2__bvfunc14,dt_c2_2__bvfunc14,dt_c2_2_2__bvfunc14,dt_c3_2_2__bvfunc14,fc1_xboole_0,fc2_subset_1,t1_subset,t6_boole,t7_boole,e3_2_2__bvfunc14,d1_tarski]), [interesting(0.65),file(bvfunc14,e8_2_2__bvfunc14),[file(bvfunc14,e8_2_2__bvfunc14)]]). fof(d4_xboole_0,definition,( ! [A,B,C] : ( C = k4_xboole_0(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( r2_hidden(D,A) & ~ r2_hidden(D,B) ) ) ) ), file(xboole_0,d4_xboole_0), [interesting(0.9),axiom,file(xboole_0,d4_xboole_0)]). fof(e13_2_2__bvfunc14,plain,( r2_hidden(c1_2_2__bvfunc14,k4_xboole_0(k3_setfam_1(c3_2__bvfunc14,c4_2__bvfunc14),k1_tarski(k1_xboole_0))) ), inference(mizar_by,[status(thm),assumptions([dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_2__bvfunc14,dt_c2_2__bvfunc14,e1_2_2__bvfunc14])],[reflexivity_r1_tarski,dt_k1_zfmisc_1,fc1_subset_1,rc1_subset_1,rc2_subset_1,t3_subset,t4_subset,t5_subset,existence_m1_eqrel_1,existence_m1_subset_1,dt_m1_eqrel_1,dt_m1_subset_1,dt_c1_2__bvfunc14,cc1_eqrel_1,cc2_eqrel_1,rc1_xboole_0,rc2_xboole_0,t2_subset,t8_boole,commutativity_k3_setfam_1,antisymmetry_r2_hidden,dt_k1_tarski,dt_k1_xboole_0,dt_k3_setfam_1,dt_k4_xboole_0,dt_c1_2_2__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,fc1_xboole_0,fc2_subset_1,t1_subset,t3_boole,t4_boole,t6_boole,t7_boole,e12_2_2__bvfunc14,e8_2_2__bvfunc14,d4_xboole_0]), [interesting(0.65),file(bvfunc14,e13_2_2__bvfunc14),[file(bvfunc14,e13_2_2__bvfunc14)]]). fof(d4_partit1,definition,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_eqrel_1(B,A) => ! [C] : ( m1_eqrel_1(C,A) => k2_partit1(A,B,C) = k4_xboole_0(k3_setfam_1(B,C),k1_tarski(k1_xboole_0)) ) ) ) ), file(partit1,d4_partit1), [interesting(0.9),axiom,file(partit1,d4_partit1)]). fof(e14_2_2__bvfunc14,plain,( r2_hidden(c1_2_2__bvfunc14,k2_partit1(c1_2__bvfunc14,c3_2__bvfunc14,c4_2__bvfunc14)) ), inference(mizar_by,[status(thm),assumptions([dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_2__bvfunc14,dt_c2_2__bvfunc14,e1_2_2__bvfunc14])],[reflexivity_r1_tarski,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,fc1_subset_1,rc1_subset_1,rc2_subset_1,t2_subset,t3_subset,t4_subset,t5_subset,commutativity_k2_partit1,commutativity_k3_setfam_1,antisymmetry_r2_hidden,existence_m1_eqrel_1,dt_k1_tarski,dt_k1_xboole_0,dt_k2_partit1,dt_k3_setfam_1,dt_k4_xboole_0,dt_m1_eqrel_1,dt_c1_2__bvfunc14,dt_c1_2_2__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,cc1_eqrel_1,cc2_eqrel_1,fc1_xboole_0,fc2_subset_1,rc1_xboole_0,rc2_xboole_0,t1_subset,t3_boole,t4_boole,t6_boole,t7_boole,t8_boole,e13_2_2__bvfunc14,d4_partit1]), [interesting(0.65),file(bvfunc14,e14_2_2__bvfunc14),[file(bvfunc14,e14_2_2__bvfunc14)]]). fof(i3_2_2__bvfunc14,theorem,( $true ), introduced(tautology,[file(bvfunc14,i3_2_2__bvfunc14)]), [interesting(0.65),trivial,file(bvfunc14,i3_2_2__bvfunc14)]). fof(i2_2_2__bvfunc14,plain,( r2_hidden(c1_2_2__bvfunc14,k2_partit1(c1_2__bvfunc14,c3_2__bvfunc14,c4_2__bvfunc14)) ), inference(conclusion,[status(thm),assumptions([dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_2__bvfunc14,dt_c2_2__bvfunc14,e1_2_2__bvfunc14])],[e14_2_2__bvfunc14,i3_2_2__bvfunc14]), [interesting(0.65),file(bvfunc14,i2_2_2__bvfunc14),[file(bvfunc14,i2_2_2__bvfunc14)]]). fof(i1_2_2__bvfunc14,plain,( ~ ( r2_hidden(c1_2_2__bvfunc14,k2_bvfunc_2(c1_2__bvfunc14,c2_2__bvfunc14)) & ~ r2_hidden(c1_2_2__bvfunc14,k2_partit1(c1_2__bvfunc14,c3_2__bvfunc14,c4_2__bvfunc14)) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_2__bvfunc14,dt_c2_2__bvfunc14]),discharge_asm(discharge,[e1_2_2__bvfunc14])],[e1_2_2__bvfunc14,i2_2_2__bvfunc14]), [interesting(0.65),file(bvfunc14,i1_2_2__bvfunc14),[file(bvfunc14,i1_2_2__bvfunc14)]]). fof(i1_2_2_tmp__bvfunc14,plain,( ~ ( r2_hidden(c1_2_2__bvfunc14,k2_bvfunc_2(c1_2__bvfunc14,c2_2__bvfunc14)) & ~ r2_hidden(c1_2_2__bvfunc14,k2_partit1(c1_2__bvfunc14,c3_2__bvfunc14,c4_2__bvfunc14)) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2__bvfunc14,dt_c1_2__bvfunc14,dt_c2_2__bvfunc14]),discharge_asm(discharge,[dt_c1_2_2__bvfunc14])],[dt_c1_2_2__bvfunc14,i1_2_2__bvfunc14]), [interesting(0.8),e3_2__bvfunc14]). fof(e3_2__bvfunc14,plain,( r1_tarski(k2_bvfunc_2(c1_2__bvfunc14,c2_2__bvfunc14),k2_partit1(c1_2__bvfunc14,c3_2__bvfunc14,c4_2__bvfunc14)) ), inference(let,[status(thm),assumptions([dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2__bvfunc14,dt_c1_2__bvfunc14,dt_c2_2__bvfunc14])],[i1_2_2_tmp__bvfunc14,dt_k1_partit1,dt_m1_t_1topsp,redefinition_k1_bvfunc_2,dt_k1_bvfunc_2,dt_k1_zfmisc_1,dt_m1_eqrel_1,dt_m1_subset_1,cc1_eqrel_1,cc2_eqrel_1,fc1_subset_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,commutativity_k2_partit1,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k2_bvfunc_2,dt_k2_partit1,dt_c1_2__bvfunc14,dt_c2_2__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,d3_tarski,dh_c1_2_2__bvfunc14]), [interesting(0.8),file(bvfunc14,e3_2__bvfunc14),[file(bvfunc14,e3_2__bvfunc14)]]). fof(dt_c1_2_1__bvfunc14,assumption,( $true ), introduced(assumption,[file(bvfunc14,c1_2_1__bvfunc14)]), [interesting(0.65),axiom,file(bvfunc14,c1_2_1__bvfunc14)]). fof(dh_c1_2_1__bvfunc14,definition, ( ~ ( r2_hidden(c1_2_1__bvfunc14,k2_partit1(c1_2__bvfunc14,c3_2__bvfunc14,c4_2__bvfunc14)) & ~ r2_hidden(c1_2_1__bvfunc14,k2_bvfunc_2(c1_2__bvfunc14,c2_2__bvfunc14)) ) => ! [A] : ~ ( r2_hidden(A,k2_partit1(c1_2__bvfunc14,c3_2__bvfunc14,c4_2__bvfunc14)) & ~ r2_hidden(A,k2_bvfunc_2(c1_2__bvfunc14,c2_2__bvfunc14)) ) ), introduced(definition,[new_symbol(c1_2_1__bvfunc14),file(bvfunc14,c1_2_1__bvfunc14)]), [interesting(0.65),axiom,file(bvfunc14,c1_2_1__bvfunc14)]). fof(e1_2_1__bvfunc14,assumption,( r2_hidden(c1_2_1__bvfunc14,k2_partit1(c1_2__bvfunc14,c3_2__bvfunc14,c4_2__bvfunc14)) ), introduced(assumption,[file(bvfunc14,e1_2_1__bvfunc14)]), [interesting(0.65),axiom,file(bvfunc14,e1_2_1__bvfunc14)]). fof(dt_k4_funct_4,axiom,( $true ), file(funct_4,k4_funct_4), [interesting(0.9),axiom,file(funct_4,k4_funct_4)]). fof(dh_c2_2_1__bvfunc14,definition, ( ? [A,B] : ( r2_hidden(A,c3_2__bvfunc14) & r2_hidden(B,c4_2__bvfunc14) & c1_2_1__bvfunc14 = k3_xboole_0(A,B) ) => ? [C] : ( r2_hidden(c2_2_1__bvfunc14,c3_2__bvfunc14) & r2_hidden(C,c4_2__bvfunc14) & c1_2_1__bvfunc14 = k3_xboole_0(c2_2_1__bvfunc14,C) ) ), introduced(definition,[new_symbol(c2_2_1__bvfunc14),file(bvfunc14,c2_2_1__bvfunc14)]), [interesting(0.65),axiom,file(bvfunc14,c2_2_1__bvfunc14)]). fof(e2_2_1__bvfunc14,plain,( r2_hidden(c1_2_1__bvfunc14,k4_xboole_0(k3_setfam_1(c3_2__bvfunc14,c4_2__bvfunc14),k1_tarski(k1_xboole_0))) ), inference(mizar_by,[status(thm),assumptions([dt_c1_2__bvfunc14,dt_c1_2_1__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2_1__bvfunc14])],[reflexivity_r1_tarski,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,fc1_subset_1,rc1_subset_1,rc2_subset_1,t2_subset,t3_subset,t4_subset,t5_subset,commutativity_k2_partit1,commutativity_k3_setfam_1,antisymmetry_r2_hidden,existence_m1_eqrel_1,dt_k1_tarski,dt_k1_xboole_0,dt_k2_partit1,dt_k3_setfam_1,dt_k4_xboole_0,dt_m1_eqrel_1,dt_c1_2__bvfunc14,dt_c1_2_1__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,cc1_eqrel_1,cc2_eqrel_1,fc1_xboole_0,fc2_subset_1,rc1_xboole_0,rc2_xboole_0,t1_subset,t3_boole,t4_boole,t6_boole,t7_boole,t8_boole,e1_2_1__bvfunc14,d4_partit1]), [interesting(0.65),file(bvfunc14,e2_2_1__bvfunc14),[file(bvfunc14,e2_2_1__bvfunc14)]]). fof(e3_2_1__bvfunc14,plain, ( r2_hidden(c1_2_1__bvfunc14,k3_setfam_1(c3_2__bvfunc14,c4_2__bvfunc14)) & ~ r2_hidden(c1_2_1__bvfunc14,k1_tarski(k1_xboole_0)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_2__bvfunc14,dt_c1_2_1__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2_1__bvfunc14])],[reflexivity_r1_tarski,dt_k1_zfmisc_1,fc1_subset_1,rc1_subset_1,rc2_subset_1,t3_subset,t4_subset,t5_subset,existence_m1_eqrel_1,existence_m1_subset_1,dt_m1_eqrel_1,dt_m1_subset_1,dt_c1_2__bvfunc14,cc1_eqrel_1,cc2_eqrel_1,rc1_xboole_0,rc2_xboole_0,t2_subset,t8_boole,commutativity_k3_setfam_1,antisymmetry_r2_hidden,dt_k1_tarski,dt_k1_xboole_0,dt_k3_setfam_1,dt_k4_xboole_0,dt_c1_2_1__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,fc1_xboole_0,fc2_subset_1,t1_subset,t3_boole,t4_boole,t6_boole,t7_boole,e2_2_1__bvfunc14,d4_xboole_0]), [interesting(0.65),file(bvfunc14,e3_2_1__bvfunc14),[file(bvfunc14,e3_2_1__bvfunc14)]]). fof(e4_2_1__bvfunc14,plain,( ? [A,B] : ( r2_hidden(A,c3_2__bvfunc14) & r2_hidden(B,c4_2__bvfunc14) & c1_2_1__bvfunc14 = k3_xboole_0(A,B) ) ), inference(mizar_by,[status(thm),assumptions([dt_c1_2__bvfunc14,dt_c1_2_1__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2_1__bvfunc14])],[reflexivity_r1_tarski,dt_k1_zfmisc_1,fc1_subset_1,rc1_subset_1,rc2_subset_1,t3_subset,t4_subset,t5_subset,existence_m1_eqrel_1,existence_m1_subset_1,dt_m1_eqrel_1,dt_m1_subset_1,dt_c1_2__bvfunc14,cc1_eqrel_1,cc2_eqrel_1,rc1_xboole_0,rc2_xboole_0,t2_subset,t8_boole,commutativity_k3_setfam_1,commutativity_k3_xboole_0,idempotence_k3_xboole_0,antisymmetry_r2_hidden,dt_k1_tarski,dt_k1_xboole_0,dt_k3_setfam_1,dt_k3_xboole_0,dt_c1_2_1__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,fc1_xboole_0,fc2_subset_1,t1_subset,t2_boole,t6_boole,t7_boole,e3_2_1__bvfunc14,d5_setfam_1]), [interesting(0.65),file(bvfunc14,e4_2_1__bvfunc14),[file(bvfunc14,e4_2_1__bvfunc14)]]). fof(dt_c2_2_1__bvfunc14,plain,( $true ), inference(consider,[status(thm),assumptions([dt_c1_2__bvfunc14,dt_c1_2_1__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2_1__bvfunc14])],[dh_c2_2_1__bvfunc14,e4_2_1__bvfunc14]), [interesting(0.65),file(bvfunc14,c2_2_1__bvfunc14),[file(bvfunc14,c2_2_1__bvfunc14)]]). fof(dh_c3_2_1__bvfunc14,definition, ( ? [A] : ( r2_hidden(c2_2_1__bvfunc14,c3_2__bvfunc14) & r2_hidden(A,c4_2__bvfunc14) & c1_2_1__bvfunc14 = k3_xboole_0(c2_2_1__bvfunc14,A) ) => ( r2_hidden(c2_2_1__bvfunc14,c3_2__bvfunc14) & r2_hidden(c3_2_1__bvfunc14,c4_2__bvfunc14) & c1_2_1__bvfunc14 = k3_xboole_0(c2_2_1__bvfunc14,c3_2_1__bvfunc14) ) ), introduced(definition,[new_symbol(c3_2_1__bvfunc14),file(bvfunc14,c3_2_1__bvfunc14)]), [interesting(0.65),axiom,file(bvfunc14,c3_2_1__bvfunc14)]). fof(dt_c3_2_1__bvfunc14,plain,( $true ), inference(consider,[status(thm),assumptions([dt_c1_2__bvfunc14,dt_c1_2_1__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2_1__bvfunc14])],[dh_c2_2_1__bvfunc14,dh_c3_2_1__bvfunc14,e4_2_1__bvfunc14]), [interesting(0.65),file(bvfunc14,c3_2_1__bvfunc14),[file(bvfunc14,c3_2_1__bvfunc14)]]). fof(fc1_funct_4,theorem,( ! [A,B,C,D] : ( v1_relat_1(k4_funct_4(A,B,C,D)) & v1_funct_1(k4_funct_4(A,B,C,D)) ) ), file(funct_4,fc1_funct_4), [interesting(0.9),axiom,file(funct_4,fc1_funct_4)]). fof(de_c5_2_1__bvfunc14,definition,( c5_2_1__bvfunc14 = k2_relat_1(k4_funct_4(c3_2__bvfunc14,c4_2__bvfunc14,c2_2_1__bvfunc14,c3_2_1__bvfunc14)) ), introduced(definition,[new_symbol(c5_2_1__bvfunc14),file(bvfunc14,c5_2_1__bvfunc14)]), [interesting(0.65),axiom,file(bvfunc14,c5_2_1__bvfunc14)]). fof(dt_c1_2_1_1__bvfunc14,assumption,( $true ), introduced(assumption,[file(bvfunc14,c1_2_1_1__bvfunc14)]), [interesting(0.5),axiom,file(bvfunc14,c1_2_1_1__bvfunc14)]). fof(dh_c1_2_1_1__bvfunc14,definition, ( ~ ( r2_hidden(c1_2_1_1__bvfunc14,k2_relat_1(k4_funct_4(c3_2__bvfunc14,c4_2__bvfunc14,c2_2_1__bvfunc14,c3_2_1__bvfunc14))) & ~ r2_hidden(c1_2_1_1__bvfunc14,k1_zfmisc_1(c1_2__bvfunc14)) ) => ! [A] : ~ ( r2_hidden(A,k2_relat_1(k4_funct_4(c3_2__bvfunc14,c4_2__bvfunc14,c2_2_1__bvfunc14,c3_2_1__bvfunc14))) & ~ r2_hidden(A,k1_zfmisc_1(c1_2__bvfunc14)) ) ), introduced(definition,[new_symbol(c1_2_1_1__bvfunc14),file(bvfunc14,c1_2_1_1__bvfunc14)]), [interesting(0.5),axiom,file(bvfunc14,c1_2_1_1__bvfunc14)]). fof(e1_2_1_1__bvfunc14,assumption,( r2_hidden(c1_2_1_1__bvfunc14,k2_relat_1(k4_funct_4(c3_2__bvfunc14,c4_2__bvfunc14,c2_2_1__bvfunc14,c3_2_1__bvfunc14))) ), introduced(assumption,[file(bvfunc14,e1_2_1_1__bvfunc14)]), [interesting(0.5),axiom,file(bvfunc14,e1_2_1_1__bvfunc14)]). fof(e1_2_1_1_1_1_1__bvfunc14,assumption,( c1_2_1_1__bvfunc14 = c2_2_1__bvfunc14 ), introduced(assumption,[file(bvfunc14,e1_2_1_1_1_1_1__bvfunc14)]), [interesting(0.05),axiom,file(bvfunc14,e1_2_1_1_1_1_1__bvfunc14)]). fof(e5_2_1__bvfunc14,plain, ( r2_hidden(c2_2_1__bvfunc14,c3_2__bvfunc14) & r2_hidden(c3_2_1__bvfunc14,c4_2__bvfunc14) & c1_2_1__bvfunc14 = k3_xboole_0(c2_2_1__bvfunc14,c3_2_1__bvfunc14) ), inference(consider,[status(thm),assumptions([dt_c1_2__bvfunc14,dt_c1_2_1__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2_1__bvfunc14])],[dh_c2_2_1__bvfunc14,dh_c3_2_1__bvfunc14,e4_2_1__bvfunc14]), [interesting(0.65),file(bvfunc14,e5_2_1__bvfunc14),[file(bvfunc14,e5_2_1__bvfunc14)]]). fof(e2_2_1_1_1_1_1__bvfunc14,plain,( r2_hidden(c1_2_1_1__bvfunc14,k1_zfmisc_1(c1_2__bvfunc14)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_2_1_1__bvfunc14,e1_2_1_1_1_1_1__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_1__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2_1__bvfunc14])],[reflexivity_r1_tarski,dt_k1_xboole_0,fc1_xboole_0,t2_boole,existence_m1_eqrel_1,existence_m1_subset_1,dt_m1_eqrel_1,dt_m1_subset_1,cc1_eqrel_1,cc2_eqrel_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k3_xboole_0,idempotence_k3_xboole_0,antisymmetry_r2_hidden,dt_k1_zfmisc_1,dt_k3_xboole_0,dt_c1_2__bvfunc14,dt_c1_2_1__bvfunc14,dt_c1_2_1_1__bvfunc14,dt_c2_2_1__bvfunc14,dt_c3_2__bvfunc14,dt_c3_2_1__bvfunc14,dt_c4_2__bvfunc14,fc1_subset_1,t1_subset,t7_boole,e1_2_1_1_1_1_1__bvfunc14,e5_2_1__bvfunc14]), [interesting(0.05),file(bvfunc14,e2_2_1_1_1_1_1__bvfunc14),[file(bvfunc14,e2_2_1_1_1_1_1__bvfunc14)]]). fof(i2_2_1_1_1_1_1__bvfunc14,theorem,( $true ), introduced(tautology,[file(bvfunc14,i2_2_1_1_1_1_1__bvfunc14)]), [interesting(0.05),trivial,file(bvfunc14,i2_2_1_1_1_1_1__bvfunc14)]). fof(i1_2_1_1_1_1_1__bvfunc14,plain,( r2_hidden(c1_2_1_1__bvfunc14,k1_zfmisc_1(c1_2__bvfunc14)) ), inference(conclusion,[status(thm),assumptions([dt_c1_2_1_1__bvfunc14,e1_2_1_1_1_1_1__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_1__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2_1__bvfunc14])],[e2_2_1_1_1_1_1__bvfunc14,i2_2_1_1_1_1_1__bvfunc14]), [interesting(0.05),file(bvfunc14,i1_2_1_1_1_1_1__bvfunc14),[file(bvfunc14,i1_2_1_1_1_1_1__bvfunc14)]]). fof(i1_2_1_1_1_1__bvfunc14,plain, ( c1_2_1_1__bvfunc14 = c2_2_1__bvfunc14 => ( c1_2_1_1__bvfunc14 = c2_2_1__bvfunc14 & r2_hidden(c1_2_1_1__bvfunc14,k1_zfmisc_1(c1_2__bvfunc14)) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_2_1_1__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_1__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2_1__bvfunc14]),discharge_asm(discharge,[e1_2_1_1_1_1_1__bvfunc14])],[e1_2_1_1_1_1_1__bvfunc14,i1_2_1_1_1_1_1__bvfunc14]), [interesting(0.2),file(bvfunc14,i1_2_1_1_1_1__bvfunc14),[file(bvfunc14,i1_2_1_1_1_1__bvfunc14)]]). fof(e1_2_1_1_1_1_2__bvfunc14,assumption,( c1_2_1_1__bvfunc14 = c3_2_1__bvfunc14 ), introduced(assumption,[file(bvfunc14,e1_2_1_1_1_1_2__bvfunc14)]), [interesting(0.05),axiom,file(bvfunc14,e1_2_1_1_1_1_2__bvfunc14)]). fof(e2_2_1_1_1_1_2__bvfunc14,plain,( r2_hidden(c1_2_1_1__bvfunc14,k1_zfmisc_1(c1_2__bvfunc14)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_2_1_1__bvfunc14,e1_2_1_1_1_1_2__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_1__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2_1__bvfunc14])],[reflexivity_r1_tarski,dt_k1_xboole_0,fc1_xboole_0,t2_boole,existence_m1_eqrel_1,existence_m1_subset_1,dt_m1_eqrel_1,dt_m1_subset_1,cc1_eqrel_1,cc2_eqrel_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k3_xboole_0,idempotence_k3_xboole_0,antisymmetry_r2_hidden,dt_k1_zfmisc_1,dt_k3_xboole_0,dt_c1_2__bvfunc14,dt_c1_2_1__bvfunc14,dt_c1_2_1_1__bvfunc14,dt_c2_2_1__bvfunc14,dt_c3_2__bvfunc14,dt_c3_2_1__bvfunc14,dt_c4_2__bvfunc14,fc1_subset_1,t1_subset,t7_boole,e1_2_1_1_1_1_2__bvfunc14,e5_2_1__bvfunc14]), [interesting(0.05),file(bvfunc14,e2_2_1_1_1_1_2__bvfunc14),[file(bvfunc14,e2_2_1_1_1_1_2__bvfunc14)]]). fof(i2_2_1_1_1_1_2__bvfunc14,theorem,( $true ), introduced(tautology,[file(bvfunc14,i2_2_1_1_1_1_2__bvfunc14)]), [interesting(0.05),trivial,file(bvfunc14,i2_2_1_1_1_1_2__bvfunc14)]). fof(i1_2_1_1_1_1_2__bvfunc14,plain,( r2_hidden(c1_2_1_1__bvfunc14,k1_zfmisc_1(c1_2__bvfunc14)) ), inference(conclusion,[status(thm),assumptions([dt_c1_2_1_1__bvfunc14,e1_2_1_1_1_1_2__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_1__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2_1__bvfunc14])],[e2_2_1_1_1_1_2__bvfunc14,i2_2_1_1_1_1_2__bvfunc14]), [interesting(0.05),file(bvfunc14,i1_2_1_1_1_1_2__bvfunc14),[file(bvfunc14,i1_2_1_1_1_1_2__bvfunc14)]]). fof(i2_2_1_1_1_1__bvfunc14,plain, ( c1_2_1_1__bvfunc14 = c3_2_1__bvfunc14 => ( c1_2_1_1__bvfunc14 = c3_2_1__bvfunc14 & r2_hidden(c1_2_1_1__bvfunc14,k1_zfmisc_1(c1_2__bvfunc14)) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_2_1_1__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_1__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2_1__bvfunc14]),discharge_asm(discharge,[e1_2_1_1_1_1_2__bvfunc14])],[e1_2_1_1_1_1_2__bvfunc14,i1_2_1_1_1_1_2__bvfunc14]), [interesting(0.2),file(bvfunc14,i2_2_1_1_1_1__bvfunc14),[file(bvfunc14,i2_2_1_1_1_1__bvfunc14)]]). fof(t67_funct_4,theorem,( ! [A,B,C,D] : ( A != B => k2_relat_1(k4_funct_4(A,B,C,D)) = k2_tarski(C,D) ) ), file(funct_4,t67_funct_4), [interesting(0.9),axiom,file(funct_4,t67_funct_4)]). fof(e7_2_1__bvfunc14,plain,( k2_relat_1(k4_funct_4(c3_2__bvfunc14,c4_2__bvfunc14,c2_2_1__bvfunc14,c3_2_1__bvfunc14)) = k2_tarski(c2_2_1__bvfunc14,c3_2_1__bvfunc14) ), inference(mizar_by,[status(thm),assumptions([dt_c2_2__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_1__bvfunc14,dt_c3_2__bvfunc14,e1_2_1__bvfunc14,dt_c4_2__bvfunc14,e1_2__bvfunc14])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_m1_t_1topsp,dt_k1_partit1,dt_k1_xboole_0,dt_m1_t_1topsp,fc1_xboole_0,t1_subset,t4_subset,t5_subset,existence_m1_eqrel_1,existence_m1_subset_1,redefinition_k1_bvfunc_2,dt_k1_bvfunc_2,dt_k1_zfmisc_1,dt_m1_eqrel_1,dt_m1_subset_1,dt_c1_2__bvfunc14,cc1_eqrel_1,cc2_eqrel_1,fc1_subset_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,commutativity_k2_tarski,dt_k2_relat_1,dt_k2_tarski,dt_k4_funct_4,dt_c2_2__bvfunc14,dt_c2_2_1__bvfunc14,dt_c3_2__bvfunc14,dt_c3_2_1__bvfunc14,dt_c4_2__bvfunc14,fc1_funct_4,fc3_subset_1,e1_2__bvfunc14,t67_funct_4]), [interesting(0.65),file(bvfunc14,e7_2_1__bvfunc14),[file(bvfunc14,e7_2_1__bvfunc14)]]). fof(e1_2_1_1_1_1__bvfunc14,plain, ( c1_2_1_1__bvfunc14 = c2_2_1__bvfunc14 | c1_2_1_1__bvfunc14 = c3_2_1__bvfunc14 ), inference(mizar_by,[status(thm),assumptions([dt_c1_2_1_1__bvfunc14,dt_c2_2__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_1__bvfunc14,dt_c3_2__bvfunc14,e1_2_1__bvfunc14,dt_c4_2__bvfunc14,e1_2__bvfunc14,e1_2_1_1__bvfunc14])],[reflexivity_r1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,fc1_subset_1,fc1_xboole_0,rc1_subset_1,rc2_subset_1,t3_subset,t4_subset,t5_subset,existence_m1_eqrel_1,existence_m1_subset_1,dt_m1_eqrel_1,dt_m1_subset_1,dt_c1_2__bvfunc14,cc1_eqrel_1,cc2_eqrel_1,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t8_boole,commutativity_k2_tarski,antisymmetry_r2_hidden,dt_k2_relat_1,dt_k2_tarski,dt_k4_funct_4,dt_c1_2_1_1__bvfunc14,dt_c2_2_1__bvfunc14,dt_c3_2__bvfunc14,dt_c3_2_1__bvfunc14,dt_c4_2__bvfunc14,fc1_funct_4,fc3_subset_1,t1_subset,t7_boole,e7_2_1__bvfunc14,e1_2_1_1__bvfunc14,d2_tarski]), [interesting(0.2),file(bvfunc14,e1_2_1_1_1_1__bvfunc14),[file(bvfunc14,e1_2_1_1_1_1__bvfunc14)]]). fof(e2_2_1_1__bvfunc14,plain, ( ( c1_2_1_1__bvfunc14 = c2_2_1__bvfunc14 & r2_hidden(c1_2_1_1__bvfunc14,k1_zfmisc_1(c1_2__bvfunc14)) ) | ( c1_2_1_1__bvfunc14 = c3_2_1__bvfunc14 & r2_hidden(c1_2_1_1__bvfunc14,k1_zfmisc_1(c1_2__bvfunc14)) ) ), inference(percases,[status(thm),assumptions([dt_c1_2_1_1__bvfunc14,dt_c2_2__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_1__bvfunc14,dt_c3_2__bvfunc14,e1_2_1__bvfunc14,dt_c4_2__bvfunc14,e1_2__bvfunc14,e1_2_1_1__bvfunc14])],[i1_2_1_1_1_1__bvfunc14,i2_2_1_1_1_1__bvfunc14,e1_2_1_1_1_1__bvfunc14]), [interesting(0.5),file(bvfunc14,e2_2_1_1__bvfunc14),[file(bvfunc14,e2_2_1_1__bvfunc14)]]). fof(e3_2_1_1__bvfunc14,plain,( r2_hidden(c1_2_1_1__bvfunc14,k1_zfmisc_1(c1_2__bvfunc14)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_2_1_1__bvfunc14,dt_c2_2__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_1__bvfunc14,dt_c3_2__bvfunc14,e1_2_1__bvfunc14,dt_c4_2__bvfunc14,e1_2__bvfunc14,e1_2_1_1__bvfunc14])],[reflexivity_r1_tarski,dt_k1_xboole_0,fc1_xboole_0,existence_m1_subset_1,dt_m1_subset_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_zfmisc_1,dt_c1_2__bvfunc14,dt_c1_2_1_1__bvfunc14,dt_c2_2_1__bvfunc14,dt_c3_2_1__bvfunc14,fc1_subset_1,t1_subset,t7_boole,e2_2_1_1__bvfunc14]), [interesting(0.5),file(bvfunc14,e3_2_1_1__bvfunc14),[file(bvfunc14,e3_2_1_1__bvfunc14)]]). fof(i3_2_1_1__bvfunc14,theorem,( $true ), introduced(tautology,[file(bvfunc14,i3_2_1_1__bvfunc14)]), [interesting(0.5),trivial,file(bvfunc14,i3_2_1_1__bvfunc14)]). fof(i2_2_1_1__bvfunc14,plain,( r2_hidden(c1_2_1_1__bvfunc14,k1_zfmisc_1(c1_2__bvfunc14)) ), inference(conclusion,[status(thm),assumptions([dt_c1_2_1_1__bvfunc14,dt_c2_2__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_1__bvfunc14,dt_c3_2__bvfunc14,e1_2_1__bvfunc14,dt_c4_2__bvfunc14,e1_2__bvfunc14,e1_2_1_1__bvfunc14])],[e3_2_1_1__bvfunc14,i3_2_1_1__bvfunc14]), [interesting(0.5),file(bvfunc14,i2_2_1_1__bvfunc14),[file(bvfunc14,i2_2_1_1__bvfunc14)]]). fof(i1_2_1_1__bvfunc14,plain,( ~ ( r2_hidden(c1_2_1_1__bvfunc14,k2_relat_1(k4_funct_4(c3_2__bvfunc14,c4_2__bvfunc14,c2_2_1__bvfunc14,c3_2_1__bvfunc14))) & ~ r2_hidden(c1_2_1_1__bvfunc14,k1_zfmisc_1(c1_2__bvfunc14)) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_2_1_1__bvfunc14,dt_c2_2__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_1__bvfunc14,dt_c3_2__bvfunc14,e1_2_1__bvfunc14,dt_c4_2__bvfunc14,e1_2__bvfunc14]),discharge_asm(discharge,[e1_2_1_1__bvfunc14])],[e1_2_1_1__bvfunc14,i2_2_1_1__bvfunc14]), [interesting(0.5),file(bvfunc14,i1_2_1_1__bvfunc14),[file(bvfunc14,i1_2_1_1__bvfunc14)]]). fof(i1_2_1_1_tmp__bvfunc14,plain,( ~ ( r2_hidden(c1_2_1_1__bvfunc14,k2_relat_1(k4_funct_4(c3_2__bvfunc14,c4_2__bvfunc14,c2_2_1__bvfunc14,c3_2_1__bvfunc14))) & ~ r2_hidden(c1_2_1_1__bvfunc14,k1_zfmisc_1(c1_2__bvfunc14)) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c2_2__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_1__bvfunc14,dt_c3_2__bvfunc14,e1_2_1__bvfunc14,dt_c4_2__bvfunc14,e1_2__bvfunc14]),discharge_asm(discharge,[dt_c1_2_1_1__bvfunc14])],[dt_c1_2_1_1__bvfunc14,i1_2_1_1__bvfunc14]), [interesting(0.65),e9_2_1__bvfunc14]). fof(e9_2_1__bvfunc14,plain,( r1_tarski(k2_relat_1(k4_funct_4(c3_2__bvfunc14,c4_2__bvfunc14,c2_2_1__bvfunc14,c3_2_1__bvfunc14)),k1_zfmisc_1(c1_2__bvfunc14)) ), inference(let,[status(thm),assumptions([dt_c2_2__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_1__bvfunc14,dt_c3_2__bvfunc14,e1_2_1__bvfunc14,dt_c4_2__bvfunc14,e1_2__bvfunc14])],[i1_2_1_1_tmp__bvfunc14,dt_m1_subset_1,rc1_subset_1,rc2_subset_1,dt_m1_eqrel_1,cc1_eqrel_1,cc2_eqrel_1,rc1_xboole_0,rc2_xboole_0,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_zfmisc_1,dt_k2_relat_1,dt_k4_funct_4,dt_c1_2__bvfunc14,dt_c2_2_1__bvfunc14,dt_c3_2__bvfunc14,dt_c3_2_1__bvfunc14,dt_c4_2__bvfunc14,fc1_funct_4,fc1_subset_1,d3_tarski,dh_c1_2_1_1__bvfunc14]), [interesting(0.65),file(bvfunc14,e9_2_1__bvfunc14),[file(bvfunc14,e9_2_1__bvfunc14)]]). fof(e10_2_1__bvfunc14,plain,( m1_subset_1(k2_relat_1(k4_funct_4(c3_2__bvfunc14,c4_2__bvfunc14,c2_2_1__bvfunc14,c3_2_1__bvfunc14)),k1_zfmisc_1(k1_zfmisc_1(c1_2__bvfunc14))) ), inference(mizar_by,[status(thm),assumptions([dt_c2_2__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_1__bvfunc14,dt_c3_2__bvfunc14,e1_2_1__bvfunc14,dt_c4_2__bvfunc14,e1_2__bvfunc14])],[antisymmetry_r2_hidden,dt_k1_xboole_0,fc1_xboole_0,t1_subset,t4_subset,t5_subset,t8_boole,existence_m1_eqrel_1,dt_m1_eqrel_1,cc1_eqrel_1,cc2_eqrel_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,t2_subset,t6_boole,t7_boole,reflexivity_r1_tarski,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_relat_1,dt_k4_funct_4,dt_m1_subset_1,dt_c1_2__bvfunc14,dt_c2_2_1__bvfunc14,dt_c3_2__bvfunc14,dt_c3_2_1__bvfunc14,dt_c4_2__bvfunc14,fc1_funct_4,fc1_subset_1,t3_subset,e9_2_1__bvfunc14]), [interesting(0.65),file(bvfunc14,e10_2_1__bvfunc14),[file(bvfunc14,e10_2_1__bvfunc14)]]). fof(dt_c5_2_1__bvfunc14,plain,( m1_subset_1(c5_2_1__bvfunc14,k1_zfmisc_1(k1_zfmisc_1(c1_2__bvfunc14))) ), inference(mizar_by,[status(thm),assumptions([dt_c2_2__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_1__bvfunc14,dt_c3_2__bvfunc14,e1_2_1__bvfunc14,dt_c4_2__bvfunc14,e1_2__bvfunc14])],[antisymmetry_r2_hidden,dt_k1_xboole_0,fc1_xboole_0,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,existence_m1_eqrel_1,dt_m1_eqrel_1,cc1_eqrel_1,cc2_eqrel_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_relat_1,dt_k4_funct_4,dt_m1_subset_1,dt_c1_2__bvfunc14,dt_c2_2_1__bvfunc14,dt_c3_2__bvfunc14,dt_c3_2_1__bvfunc14,dt_c4_2__bvfunc14,fc1_funct_4,fc1_subset_1,t3_subset,de_c5_2_1__bvfunc14,e10_2_1__bvfunc14]), [interesting(0.65),file(bvfunc14,c5_2_1__bvfunc14),[file(bvfunc14,c5_2_1__bvfunc14)]]). fof(dt_k3_tarski,axiom,( $true ), file(tarski,k3_tarski), [interesting(0.9),axiom,file(tarski,k3_tarski)]). fof(symmetry_r1_xboole_0,theorem,( ! [A,B] : ( r1_xboole_0(A,B) => r1_xboole_0(B,A) ) ), file(xboole_0,r1_xboole_0), [interesting(0.9),axiom,file(xboole_0,r1_xboole_0)]). fof(redefinition_k5_setfam_1,definition,( ! [A,B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => k5_setfam_1(A,B) = k3_tarski(B) ) ), file(setfam_1,k5_setfam_1), [interesting(0.9),axiom,file(setfam_1,k5_setfam_1)]). fof(dt_k5_setfam_1,axiom,( ! [A,B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => m1_subset_1(k5_setfam_1(A,B),k1_zfmisc_1(A)) ) ), file(setfam_1,k5_setfam_1), [interesting(0.9),axiom,file(setfam_1,k5_setfam_1)]). fof(d6_eqrel_1,definition,( ! [A,B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ( ( A != k1_xboole_0 => ( m1_eqrel_1(B,A) <=> ( k5_setfam_1(A,B) = A & ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ( r2_hidden(C,B) => ( C != k1_xboole_0 & ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ~ ( r2_hidden(D,B) & C != D & ~ r1_xboole_0(C,D) ) ) ) ) ) ) ) ) & ( A = k1_xboole_0 => ( m1_eqrel_1(B,A) <=> B = k1_xboole_0 ) ) ) ) ), file(eqrel_1,d6_eqrel_1), [interesting(0.9),axiom,file(eqrel_1,d6_eqrel_1)]). fof(e15_2_1__bvfunc14,plain,( c1_2_1__bvfunc14 != k1_xboole_0 ), inference(mizar_by,[status(thm),assumptions([dt_c1_2__bvfunc14,dt_c1_2_1__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2_1__bvfunc14])],[reflexivity_r1_tarski,dt_k3_tarski,cc1_eqrel_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,t2_subset,t5_subset,t8_boole,commutativity_k2_partit1,symmetry_r1_xboole_0,antisymmetry_r2_hidden,existence_m1_eqrel_1,existence_m1_subset_1,redefinition_k5_setfam_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_partit1,dt_k5_setfam_1,dt_m1_eqrel_1,dt_m1_subset_1,dt_c1_2__bvfunc14,dt_c1_2_1__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,cc2_eqrel_1,fc1_subset_1,fc1_xboole_0,t1_subset,t3_subset,t4_subset,t6_boole,t7_boole,e1_2_1__bvfunc14,d6_eqrel_1]), [interesting(0.65),file(bvfunc14,e15_2_1__bvfunc14),[file(bvfunc14,e15_2_1__bvfunc14)]]). fof(t65_funct_4,theorem,( ! [A,B,C,D] : ( k1_relat_1(k4_funct_4(A,B,C,D)) = k2_tarski(A,B) & r1_tarski(k2_relat_1(k4_funct_4(A,B,C,D)),k2_tarski(C,D)) ) ), file(funct_4,t65_funct_4), [interesting(0.9),axiom,file(funct_4,t65_funct_4)]). fof(e6_2_1__bvfunc14,plain,( k1_relat_1(k4_funct_4(c3_2__bvfunc14,c4_2__bvfunc14,c2_2_1__bvfunc14,c3_2_1__bvfunc14)) = k2_tarski(c3_2__bvfunc14,c4_2__bvfunc14) ), inference(mizar_by,[status(thm),assumptions([dt_c1_2__bvfunc14,dt_c1_2_1__bvfunc14,dt_c3_2__bvfunc14,e1_2_1__bvfunc14,dt_c4_2__bvfunc14])],[antisymmetry_r2_hidden,dt_k1_xboole_0,fc1_xboole_0,t1_subset,t4_subset,t5_subset,existence_m1_eqrel_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_eqrel_1,dt_m1_subset_1,dt_c1_2__bvfunc14,cc1_eqrel_1,cc2_eqrel_1,fc1_subset_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k2_tarski,reflexivity_r1_tarski,dt_k1_relat_1,dt_k2_relat_1,dt_k2_tarski,dt_k4_funct_4,dt_c2_2_1__bvfunc14,dt_c3_2__bvfunc14,dt_c3_2_1__bvfunc14,dt_c4_2__bvfunc14,fc1_funct_4,fc3_subset_1,t3_subset,t65_funct_4]), [interesting(0.65),file(bvfunc14,e6_2_1__bvfunc14),[file(bvfunc14,e6_2_1__bvfunc14)]]). fof(dh_c1_2_1_2__bvfunc14,definition, ( ( r2_hidden(c1_2_1_2__bvfunc14,c2_2__bvfunc14) => r2_hidden(k1_funct_1(k4_funct_4(c3_2__bvfunc14,c4_2__bvfunc14,c2_2_1__bvfunc14,c3_2_1__bvfunc14),c1_2_1_2__bvfunc14),c1_2_1_2__bvfunc14) ) => ! [A] : ( r2_hidden(A,c2_2__bvfunc14) => r2_hidden(k1_funct_1(k4_funct_4(c3_2__bvfunc14,c4_2__bvfunc14,c2_2_1__bvfunc14,c3_2_1__bvfunc14),A),A) ) ), introduced(definition,[new_symbol(c1_2_1_2__bvfunc14),file(bvfunc14,c1_2_1_2__bvfunc14)]), [interesting(0.5),axiom,file(bvfunc14,c1_2_1_2__bvfunc14)]). fof(e1_2_1_2__bvfunc14,assumption,( r2_hidden(c1_2_1_2__bvfunc14,c2_2__bvfunc14) ), introduced(assumption,[file(bvfunc14,e1_2_1_2__bvfunc14)]), [interesting(0.5),axiom,file(bvfunc14,e1_2_1_2__bvfunc14)]). fof(dt_c1_2_1_2__bvfunc14,assumption,( $true ), introduced(assumption,[file(bvfunc14,c1_2_1_2__bvfunc14)]), [interesting(0.5),axiom,file(bvfunc14,c1_2_1_2__bvfunc14)]). fof(e1_2_1_2_1_1_1__bvfunc14,assumption,( c1_2_1_2__bvfunc14 = c3_2__bvfunc14 ), introduced(assumption,[file(bvfunc14,e1_2_1_2_1_1_1__bvfunc14)]), [interesting(0.05),axiom,file(bvfunc14,e1_2_1_2_1_1_1__bvfunc14)]). fof(t66_funct_4,theorem,( ! [A,B,C,D] : ( A != B => ( k1_funct_1(k4_funct_4(A,B,C,D),A) = C & k1_funct_1(k4_funct_4(A,B,C,D),B) = D ) ) ), file(funct_4,t66_funct_4), [interesting(0.9),axiom,file(funct_4,t66_funct_4)]). fof(e2_2_1_2_1_1_1__bvfunc14,plain,( r2_hidden(k1_funct_1(k4_funct_4(c3_2__bvfunc14,c4_2__bvfunc14,c2_2_1__bvfunc14,c3_2_1__bvfunc14),c1_2_1_2__bvfunc14),c1_2_1_2__bvfunc14) ), inference(mizar_by,[status(thm),assumptions([dt_c1_2_1_2__bvfunc14,dt_c2_2__bvfunc14,e1_2_1_2_1_1_1__bvfunc14,e1_2__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_1__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2_1__bvfunc14])],[reflexivity_r1_tarski,existence_m1_t_1topsp,dt_k1_partit1,dt_k1_xboole_0,dt_m1_t_1topsp,fc1_xboole_0,t2_boole,existence_m1_eqrel_1,existence_m1_subset_1,redefinition_k1_bvfunc_2,dt_k1_bvfunc_2,dt_k1_zfmisc_1,dt_m1_eqrel_1,dt_m1_subset_1,dt_c1_2__bvfunc14,cc1_eqrel_1,cc2_eqrel_1,fc1_subset_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k2_tarski,commutativity_k3_xboole_0,idempotence_k3_xboole_0,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k2_tarski,dt_k3_xboole_0,dt_k4_funct_4,dt_c1_2_1__bvfunc14,dt_c1_2_1_2__bvfunc14,dt_c2_2__bvfunc14,dt_c2_2_1__bvfunc14,dt_c3_2__bvfunc14,dt_c3_2_1__bvfunc14,dt_c4_2__bvfunc14,fc1_funct_4,fc3_subset_1,t1_subset,t7_boole,e1_2_1_2_1_1_1__bvfunc14,e1_2__bvfunc14,e5_2_1__bvfunc14,t66_funct_4]), [interesting(0.05),file(bvfunc14,e2_2_1_2_1_1_1__bvfunc14),[file(bvfunc14,e2_2_1_2_1_1_1__bvfunc14)]]). fof(i2_2_1_2_1_1_1__bvfunc14,theorem,( $true ), introduced(tautology,[file(bvfunc14,i2_2_1_2_1_1_1__bvfunc14)]), [interesting(0.05),trivial,file(bvfunc14,i2_2_1_2_1_1_1__bvfunc14)]). fof(i1_2_1_2_1_1_1__bvfunc14,plain,( r2_hidden(k1_funct_1(k4_funct_4(c3_2__bvfunc14,c4_2__bvfunc14,c2_2_1__bvfunc14,c3_2_1__bvfunc14),c1_2_1_2__bvfunc14),c1_2_1_2__bvfunc14) ), inference(conclusion,[status(thm),assumptions([dt_c1_2_1_2__bvfunc14,dt_c2_2__bvfunc14,e1_2_1_2_1_1_1__bvfunc14,e1_2__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_1__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2_1__bvfunc14])],[e2_2_1_2_1_1_1__bvfunc14,i2_2_1_2_1_1_1__bvfunc14]), [interesting(0.05),file(bvfunc14,i1_2_1_2_1_1_1__bvfunc14),[file(bvfunc14,i1_2_1_2_1_1_1__bvfunc14)]]). fof(i1_2_1_2_1_1__bvfunc14,plain, ( c1_2_1_2__bvfunc14 = c3_2__bvfunc14 => ( c1_2_1_2__bvfunc14 = c3_2__bvfunc14 & r2_hidden(k1_funct_1(k4_funct_4(c3_2__bvfunc14,c4_2__bvfunc14,c2_2_1__bvfunc14,c3_2_1__bvfunc14),c1_2_1_2__bvfunc14),c1_2_1_2__bvfunc14) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_2_1_2__bvfunc14,dt_c2_2__bvfunc14,e1_2__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_1__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2_1__bvfunc14]),discharge_asm(discharge,[e1_2_1_2_1_1_1__bvfunc14])],[e1_2_1_2_1_1_1__bvfunc14,i1_2_1_2_1_1_1__bvfunc14]), [interesting(0.2),file(bvfunc14,i1_2_1_2_1_1__bvfunc14),[file(bvfunc14,i1_2_1_2_1_1__bvfunc14)]]). fof(e1_2_1_2_1_1_2__bvfunc14,assumption,( c1_2_1_2__bvfunc14 = c4_2__bvfunc14 ), introduced(assumption,[file(bvfunc14,e1_2_1_2_1_1_2__bvfunc14)]), [interesting(0.05),axiom,file(bvfunc14,e1_2_1_2_1_1_2__bvfunc14)]). fof(e2_2_1_2_1_1_2__bvfunc14,plain,( r2_hidden(k1_funct_1(k4_funct_4(c3_2__bvfunc14,c4_2__bvfunc14,c2_2_1__bvfunc14,c3_2_1__bvfunc14),c1_2_1_2__bvfunc14),c1_2_1_2__bvfunc14) ), inference(mizar_by,[status(thm),assumptions([dt_c1_2_1_2__bvfunc14,dt_c2_2__bvfunc14,e1_2_1_2_1_1_2__bvfunc14,e1_2__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_1__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2_1__bvfunc14])],[reflexivity_r1_tarski,existence_m1_t_1topsp,dt_k1_partit1,dt_k1_xboole_0,dt_m1_t_1topsp,fc1_xboole_0,t2_boole,existence_m1_eqrel_1,existence_m1_subset_1,redefinition_k1_bvfunc_2,dt_k1_bvfunc_2,dt_k1_zfmisc_1,dt_m1_eqrel_1,dt_m1_subset_1,dt_c1_2__bvfunc14,cc1_eqrel_1,cc2_eqrel_1,fc1_subset_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k2_tarski,commutativity_k3_xboole_0,idempotence_k3_xboole_0,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k2_tarski,dt_k3_xboole_0,dt_k4_funct_4,dt_c1_2_1__bvfunc14,dt_c1_2_1_2__bvfunc14,dt_c2_2__bvfunc14,dt_c2_2_1__bvfunc14,dt_c3_2__bvfunc14,dt_c3_2_1__bvfunc14,dt_c4_2__bvfunc14,fc1_funct_4,fc3_subset_1,t1_subset,t7_boole,e1_2_1_2_1_1_2__bvfunc14,e1_2__bvfunc14,e5_2_1__bvfunc14,t66_funct_4]), [interesting(0.05),file(bvfunc14,e2_2_1_2_1_1_2__bvfunc14),[file(bvfunc14,e2_2_1_2_1_1_2__bvfunc14)]]). fof(i2_2_1_2_1_1_2__bvfunc14,theorem,( $true ), introduced(tautology,[file(bvfunc14,i2_2_1_2_1_1_2__bvfunc14)]), [interesting(0.05),trivial,file(bvfunc14,i2_2_1_2_1_1_2__bvfunc14)]). fof(i1_2_1_2_1_1_2__bvfunc14,plain,( r2_hidden(k1_funct_1(k4_funct_4(c3_2__bvfunc14,c4_2__bvfunc14,c2_2_1__bvfunc14,c3_2_1__bvfunc14),c1_2_1_2__bvfunc14),c1_2_1_2__bvfunc14) ), inference(conclusion,[status(thm),assumptions([dt_c1_2_1_2__bvfunc14,dt_c2_2__bvfunc14,e1_2_1_2_1_1_2__bvfunc14,e1_2__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_1__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2_1__bvfunc14])],[e2_2_1_2_1_1_2__bvfunc14,i2_2_1_2_1_1_2__bvfunc14]), [interesting(0.05),file(bvfunc14,i1_2_1_2_1_1_2__bvfunc14),[file(bvfunc14,i1_2_1_2_1_1_2__bvfunc14)]]). fof(i2_2_1_2_1_1__bvfunc14,plain, ( c1_2_1_2__bvfunc14 = c4_2__bvfunc14 => ( c1_2_1_2__bvfunc14 = c4_2__bvfunc14 & r2_hidden(k1_funct_1(k4_funct_4(c3_2__bvfunc14,c4_2__bvfunc14,c2_2_1__bvfunc14,c3_2_1__bvfunc14),c1_2_1_2__bvfunc14),c1_2_1_2__bvfunc14) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_2_1_2__bvfunc14,dt_c2_2__bvfunc14,e1_2__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_1__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2_1__bvfunc14]),discharge_asm(discharge,[e1_2_1_2_1_1_2__bvfunc14])],[e1_2_1_2_1_1_2__bvfunc14,i1_2_1_2_1_1_2__bvfunc14]), [interesting(0.2),file(bvfunc14,i2_2_1_2_1_1__bvfunc14),[file(bvfunc14,i2_2_1_2_1_1__bvfunc14)]]). fof(e1_2_1_2_1_1__bvfunc14,plain, ( c1_2_1_2__bvfunc14 = c3_2__bvfunc14 | c1_2_1_2__bvfunc14 = c4_2__bvfunc14 ), inference(mizar_by,[status(thm),assumptions([dt_c1_2__bvfunc14,dt_c1_2_1_2__bvfunc14,dt_c2_2__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2__bvfunc14,e1_2_1_2__bvfunc14])],[reflexivity_r1_tarski,existence_m1_t_1topsp,dt_k1_partit1,dt_k1_xboole_0,dt_m1_t_1topsp,fc1_xboole_0,existence_m1_eqrel_1,existence_m1_subset_1,redefinition_k1_bvfunc_2,dt_k1_bvfunc_2,dt_k1_zfmisc_1,dt_m1_eqrel_1,dt_m1_subset_1,dt_c1_2__bvfunc14,cc1_eqrel_1,cc2_eqrel_1,fc1_subset_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k2_tarski,antisymmetry_r2_hidden,dt_k2_tarski,dt_c1_2_1_2__bvfunc14,dt_c2_2__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,fc3_subset_1,t1_subset,t7_boole,e1_2__bvfunc14,e1_2_1_2__bvfunc14,d2_tarski]), [interesting(0.2),file(bvfunc14,e1_2_1_2_1_1__bvfunc14),[file(bvfunc14,e1_2_1_2_1_1__bvfunc14)]]). fof(e2_2_1_2__bvfunc14,plain, ( ( c1_2_1_2__bvfunc14 = c3_2__bvfunc14 & r2_hidden(k1_funct_1(k4_funct_4(c3_2__bvfunc14,c4_2__bvfunc14,c2_2_1__bvfunc14,c3_2_1__bvfunc14),c1_2_1_2__bvfunc14),c1_2_1_2__bvfunc14) ) | ( c1_2_1_2__bvfunc14 = c4_2__bvfunc14 & r2_hidden(k1_funct_1(k4_funct_4(c3_2__bvfunc14,c4_2__bvfunc14,c2_2_1__bvfunc14,c3_2_1__bvfunc14),c1_2_1_2__bvfunc14),c1_2_1_2__bvfunc14) ) ), inference(percases,[status(thm),assumptions([dt_c1_2_1__bvfunc14,e1_2_1__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_1_2__bvfunc14,dt_c2_2__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2__bvfunc14,e1_2_1_2__bvfunc14])],[i1_2_1_2_1_1__bvfunc14,i2_2_1_2_1_1__bvfunc14,e1_2_1_2_1_1__bvfunc14]), [interesting(0.5),file(bvfunc14,e2_2_1_2__bvfunc14),[file(bvfunc14,e2_2_1_2__bvfunc14)]]). fof(e3_2_1_2__bvfunc14,plain,( r2_hidden(k1_funct_1(k4_funct_4(c3_2__bvfunc14,c4_2__bvfunc14,c2_2_1__bvfunc14,c3_2_1__bvfunc14),c1_2_1_2__bvfunc14),c1_2_1_2__bvfunc14) ), inference(mizar_by,[status(thm),assumptions([dt_c1_2_1__bvfunc14,e1_2_1__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_1_2__bvfunc14,dt_c2_2__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2__bvfunc14,e1_2_1_2__bvfunc14])],[reflexivity_r1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,fc1_subset_1,fc1_xboole_0,rc1_subset_1,rc2_subset_1,t3_subset,t4_subset,t5_subset,existence_m1_eqrel_1,existence_m1_subset_1,dt_m1_eqrel_1,dt_m1_subset_1,dt_c1_2__bvfunc14,cc1_eqrel_1,cc2_eqrel_1,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k4_funct_4,dt_c1_2_1_2__bvfunc14,dt_c2_2_1__bvfunc14,dt_c3_2__bvfunc14,dt_c3_2_1__bvfunc14,dt_c4_2__bvfunc14,fc1_funct_4,t1_subset,t7_boole,e2_2_1_2__bvfunc14]), [interesting(0.5),file(bvfunc14,e3_2_1_2__bvfunc14),[file(bvfunc14,e3_2_1_2__bvfunc14)]]). fof(i3_2_1_2__bvfunc14,theorem,( $true ), introduced(tautology,[file(bvfunc14,i3_2_1_2__bvfunc14)]), [interesting(0.5),trivial,file(bvfunc14,i3_2_1_2__bvfunc14)]). fof(i2_2_1_2__bvfunc14,plain,( r2_hidden(k1_funct_1(k4_funct_4(c3_2__bvfunc14,c4_2__bvfunc14,c2_2_1__bvfunc14,c3_2_1__bvfunc14),c1_2_1_2__bvfunc14),c1_2_1_2__bvfunc14) ), inference(conclusion,[status(thm),assumptions([dt_c1_2_1__bvfunc14,e1_2_1__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_1_2__bvfunc14,dt_c2_2__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2__bvfunc14,e1_2_1_2__bvfunc14])],[e3_2_1_2__bvfunc14,i3_2_1_2__bvfunc14]), [interesting(0.5),file(bvfunc14,i2_2_1_2__bvfunc14),[file(bvfunc14,i2_2_1_2__bvfunc14)]]). fof(i1_2_1_2__bvfunc14,plain, ( r2_hidden(c1_2_1_2__bvfunc14,c2_2__bvfunc14) => r2_hidden(k1_funct_1(k4_funct_4(c3_2__bvfunc14,c4_2__bvfunc14,c2_2_1__bvfunc14,c3_2_1__bvfunc14),c1_2_1_2__bvfunc14),c1_2_1_2__bvfunc14) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_2_1__bvfunc14,e1_2_1__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_1_2__bvfunc14,dt_c2_2__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2__bvfunc14]),discharge_asm(discharge,[e1_2_1_2__bvfunc14])],[e1_2_1_2__bvfunc14,i2_2_1_2__bvfunc14]), [interesting(0.5),file(bvfunc14,i1_2_1_2__bvfunc14),[file(bvfunc14,i1_2_1_2__bvfunc14)]]). fof(i1_2_1_2_tmp__bvfunc14,plain, ( r2_hidden(c1_2_1_2__bvfunc14,c2_2__bvfunc14) => r2_hidden(k1_funct_1(k4_funct_4(c3_2__bvfunc14,c4_2__bvfunc14,c2_2_1__bvfunc14,c3_2_1__bvfunc14),c1_2_1_2__bvfunc14),c1_2_1_2__bvfunc14) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_2_1__bvfunc14,e1_2_1__bvfunc14,dt_c1_2__bvfunc14,dt_c2_2__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2__bvfunc14]),discharge_asm(discharge,[dt_c1_2_1_2__bvfunc14])],[dt_c1_2_1_2__bvfunc14,i1_2_1_2__bvfunc14]), [interesting(0.65),e11_2_1__bvfunc14]). fof(e11_2_1__bvfunc14,plain,( ! [A] : ( r2_hidden(A,c2_2__bvfunc14) => r2_hidden(k1_funct_1(k4_funct_4(c3_2__bvfunc14,c4_2__bvfunc14,c2_2_1__bvfunc14,c3_2_1__bvfunc14),A),A) ) ), inference(let,[status(thm),assumptions([dt_c1_2_1__bvfunc14,e1_2_1__bvfunc14,dt_c1_2__bvfunc14,dt_c2_2__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2__bvfunc14])],[i1_2_1_2_tmp__bvfunc14,dh_c1_2_1_2__bvfunc14]), [interesting(0.65),file(bvfunc14,e11_2_1__bvfunc14),[file(bvfunc14,e11_2_1__bvfunc14)]]). fof(dt_c1_2_1_4__bvfunc14,assumption,( $true ), introduced(assumption,[file(bvfunc14,c1_2_1_4__bvfunc14)]), [interesting(0.5),axiom,file(bvfunc14,c1_2_1_4__bvfunc14)]). fof(dh_c1_2_1_4__bvfunc14,definition, ( ~ ( r2_hidden(c1_2_1_4__bvfunc14,k8_setfam_1(c1_2__bvfunc14,c5_2_1__bvfunc14)) & ~ r2_hidden(c1_2_1_4__bvfunc14,c1_2_1__bvfunc14) ) => ! [A] : ~ ( r2_hidden(A,k8_setfam_1(c1_2__bvfunc14,c5_2_1__bvfunc14)) & ~ r2_hidden(A,c1_2_1__bvfunc14) ) ), introduced(definition,[new_symbol(c1_2_1_4__bvfunc14),file(bvfunc14,c1_2_1_4__bvfunc14)]), [interesting(0.5),axiom,file(bvfunc14,c1_2_1_4__bvfunc14)]). fof(e1_2_1_4__bvfunc14,assumption,( r2_hidden(c1_2_1_4__bvfunc14,k8_setfam_1(c1_2__bvfunc14,c5_2_1__bvfunc14)) ), introduced(assumption,[file(bvfunc14,e1_2_1_4__bvfunc14)]), [interesting(0.5),axiom,file(bvfunc14,e1_2_1_4__bvfunc14)]). fof(e2_2_1_4__bvfunc14,plain, ( r2_hidden(c2_2_1__bvfunc14,k2_tarski(c2_2_1__bvfunc14,c3_2_1__bvfunc14)) & r2_hidden(c3_2_1__bvfunc14,k2_tarski(c2_2_1__bvfunc14,c3_2_1__bvfunc14)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_2__bvfunc14,dt_c1_2_1__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2_1__bvfunc14])],[dt_k1_xboole_0,fc1_xboole_0,existence_m1_subset_1,dt_m1_subset_1,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t8_boole,commutativity_k2_tarski,antisymmetry_r2_hidden,dt_k2_tarski,dt_c2_2_1__bvfunc14,dt_c3_2_1__bvfunc14,fc3_subset_1,t1_subset,t7_boole,d2_tarski]), [interesting(0.5),file(bvfunc14,e2_2_1_4__bvfunc14),[file(bvfunc14,e2_2_1_4__bvfunc14)]]). fof(e3_2_1_4__bvfunc14,plain, ( r2_hidden(c2_2_1__bvfunc14,c5_2_1__bvfunc14) & r2_hidden(c3_2_1__bvfunc14,c5_2_1__bvfunc14) ), inference(mizar_by,[status(thm),assumptions([dt_c2_2__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_1__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2_1__bvfunc14,e1_2__bvfunc14])],[reflexivity_r1_tarski,existence_m1_t_1topsp,dt_k1_partit1,dt_k1_xboole_0,dt_m1_t_1topsp,fc1_xboole_0,existence_m1_eqrel_1,existence_m1_subset_1,redefinition_k1_bvfunc_2,dt_k1_bvfunc_2,dt_k1_zfmisc_1,dt_m1_eqrel_1,dt_m1_subset_1,dt_c1_2__bvfunc14,cc1_eqrel_1,cc2_eqrel_1,fc1_subset_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k2_tarski,antisymmetry_r2_hidden,dt_k2_relat_1,dt_k2_tarski,dt_k4_funct_4,dt_c2_2__bvfunc14,dt_c2_2_1__bvfunc14,dt_c3_2__bvfunc14,dt_c3_2_1__bvfunc14,dt_c4_2__bvfunc14,dt_c5_2_1__bvfunc14,de_c5_2_1__bvfunc14,fc1_funct_4,fc3_subset_1,t1_subset,t7_boole,e2_2_1_4__bvfunc14,e1_2__bvfunc14,t67_funct_4]), [interesting(0.5),file(bvfunc14,e3_2_1_4__bvfunc14),[file(bvfunc14,e3_2_1_4__bvfunc14)]]). fof(e4_2_1_4__bvfunc14,plain,( k8_setfam_1(c1_2__bvfunc14,c5_2_1__bvfunc14) = k6_setfam_1(c1_2__bvfunc14,c5_2_1__bvfunc14) ), inference(mizar_by,[status(thm),assumptions([dt_c2_2__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_1__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2_1__bvfunc14,e1_2__bvfunc14])],[existence_m1_eqrel_1,dt_m1_eqrel_1,cc1_eqrel_1,cc2_eqrel_1,reflexivity_r1_tarski,dt_k1_setfam_1,dt_k2_relat_1,dt_k4_funct_4,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,fc1_funct_4,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,t2_subset,t5_subset,t8_boole,antisymmetry_r2_hidden,existence_m1_subset_1,redefinition_k6_setfam_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k6_setfam_1,dt_k8_setfam_1,dt_m1_subset_1,dt_c1_2__bvfunc14,dt_c2_2_1__bvfunc14,dt_c3_2_1__bvfunc14,dt_c5_2_1__bvfunc14,de_c5_2_1__bvfunc14,fc1_subset_1,fc1_xboole_0,t1_subset,t3_subset,t4_subset,t6_boole,t7_boole,e3_2_1_4__bvfunc14,d10_setfam_1]), [interesting(0.5),file(bvfunc14,e4_2_1_4__bvfunc14),[file(bvfunc14,e4_2_1_4__bvfunc14)]]). fof(e8_2_1__bvfunc14,plain,( k2_relat_1(k4_funct_4(c3_2__bvfunc14,c4_2__bvfunc14,c2_2_1__bvfunc14,c3_2_1__bvfunc14)) = k2_tarski(c2_2_1__bvfunc14,c3_2_1__bvfunc14) ), inference(mizar_by,[status(thm),assumptions([dt_c2_2__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_1__bvfunc14,dt_c3_2__bvfunc14,e1_2_1__bvfunc14,dt_c4_2__bvfunc14,e1_2__bvfunc14])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_m1_t_1topsp,dt_k1_partit1,dt_k1_xboole_0,dt_m1_t_1topsp,fc1_xboole_0,t1_subset,t4_subset,t5_subset,existence_m1_eqrel_1,existence_m1_subset_1,redefinition_k1_bvfunc_2,dt_k1_bvfunc_2,dt_k1_zfmisc_1,dt_m1_eqrel_1,dt_m1_subset_1,dt_c1_2__bvfunc14,cc1_eqrel_1,cc2_eqrel_1,fc1_subset_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,commutativity_k2_tarski,dt_k2_relat_1,dt_k2_tarski,dt_k4_funct_4,dt_c2_2__bvfunc14,dt_c2_2_1__bvfunc14,dt_c3_2__bvfunc14,dt_c3_2_1__bvfunc14,dt_c4_2__bvfunc14,fc1_funct_4,fc3_subset_1,e1_2__bvfunc14,t67_funct_4]), [interesting(0.65),file(bvfunc14,e8_2_1__bvfunc14),[file(bvfunc14,e8_2_1__bvfunc14)]]). fof(e5_2_1_4__bvfunc14,plain, ( r2_hidden(c1_2_1_4__bvfunc14,c2_2_1__bvfunc14) & r2_hidden(c1_2_1_4__bvfunc14,c3_2_1__bvfunc14) ), inference(mizar_by,[status(thm),assumptions([dt_c1_2_1_4__bvfunc14,dt_c2_2__bvfunc14,e1_2__bvfunc14,e1_2_1_4__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_1__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2_1__bvfunc14])],[reflexivity_r1_tarski,existence_m1_eqrel_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_eqrel_1,dt_m1_subset_1,cc1_eqrel_1,cc2_eqrel_1,fc1_subset_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,t2_subset,t3_subset,t4_subset,t5_subset,t8_boole,commutativity_k2_tarski,antisymmetry_r2_hidden,redefinition_k6_setfam_1,dt_k1_setfam_1,dt_k1_xboole_0,dt_k2_relat_1,dt_k2_tarski,dt_k4_funct_4,dt_k6_setfam_1,dt_k8_setfam_1,dt_c1_2__bvfunc14,dt_c1_2_1_4__bvfunc14,dt_c2_2_1__bvfunc14,dt_c3_2__bvfunc14,dt_c3_2_1__bvfunc14,dt_c4_2__bvfunc14,dt_c5_2_1__bvfunc14,de_c5_2_1__bvfunc14,fc1_funct_4,fc1_xboole_0,fc3_subset_1,t1_subset,t6_boole,t7_boole,e4_2_1_4__bvfunc14,e8_2_1__bvfunc14,e1_2_1_4__bvfunc14,e2_2_1_4__bvfunc14,d1_setfam_1]), [interesting(0.5),file(bvfunc14,e5_2_1_4__bvfunc14),[file(bvfunc14,e5_2_1_4__bvfunc14)]]). fof(e6_2_1_4__bvfunc14,plain,( r2_hidden(c1_2_1_4__bvfunc14,c1_2_1__bvfunc14) ), inference(mizar_by,[status(thm),assumptions([dt_c1_2_1_4__bvfunc14,dt_c2_2__bvfunc14,e1_2__bvfunc14,e1_2_1_4__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_1__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2_1__bvfunc14])],[reflexivity_r1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,fc1_subset_1,fc1_xboole_0,rc1_subset_1,rc2_subset_1,t2_boole,t3_subset,t4_subset,t5_subset,existence_m1_eqrel_1,existence_m1_subset_1,dt_m1_eqrel_1,dt_m1_subset_1,dt_c1_2__bvfunc14,cc1_eqrel_1,cc2_eqrel_1,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t8_boole,commutativity_k3_xboole_0,idempotence_k3_xboole_0,antisymmetry_r2_hidden,dt_k3_xboole_0,dt_c1_2_1__bvfunc14,dt_c1_2_1_4__bvfunc14,dt_c2_2_1__bvfunc14,dt_c3_2__bvfunc14,dt_c3_2_1__bvfunc14,dt_c4_2__bvfunc14,t1_subset,t7_boole,e5_2_1_4__bvfunc14,e5_2_1__bvfunc14,d3_xboole_0]), [interesting(0.5),file(bvfunc14,e6_2_1_4__bvfunc14),[file(bvfunc14,e6_2_1_4__bvfunc14)]]). fof(i3_2_1_4__bvfunc14,theorem,( $true ), introduced(tautology,[file(bvfunc14,i3_2_1_4__bvfunc14)]), [interesting(0.5),trivial,file(bvfunc14,i3_2_1_4__bvfunc14)]). fof(i2_2_1_4__bvfunc14,plain,( r2_hidden(c1_2_1_4__bvfunc14,c1_2_1__bvfunc14) ), inference(conclusion,[status(thm),assumptions([dt_c1_2_1_4__bvfunc14,dt_c2_2__bvfunc14,e1_2__bvfunc14,e1_2_1_4__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_1__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2_1__bvfunc14])],[e6_2_1_4__bvfunc14,i3_2_1_4__bvfunc14]), [interesting(0.5),file(bvfunc14,i2_2_1_4__bvfunc14),[file(bvfunc14,i2_2_1_4__bvfunc14)]]). fof(i1_2_1_4__bvfunc14,plain,( ~ ( r2_hidden(c1_2_1_4__bvfunc14,k8_setfam_1(c1_2__bvfunc14,c5_2_1__bvfunc14)) & ~ r2_hidden(c1_2_1_4__bvfunc14,c1_2_1__bvfunc14) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_2_1_4__bvfunc14,dt_c2_2__bvfunc14,e1_2__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_1__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2_1__bvfunc14]),discharge_asm(discharge,[e1_2_1_4__bvfunc14])],[e1_2_1_4__bvfunc14,i2_2_1_4__bvfunc14]), [interesting(0.5),file(bvfunc14,i1_2_1_4__bvfunc14),[file(bvfunc14,i1_2_1_4__bvfunc14)]]). fof(i1_2_1_4_tmp__bvfunc14,plain,( ~ ( r2_hidden(c1_2_1_4__bvfunc14,k8_setfam_1(c1_2__bvfunc14,c5_2_1__bvfunc14)) & ~ r2_hidden(c1_2_1_4__bvfunc14,c1_2_1__bvfunc14) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c2_2__bvfunc14,e1_2__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_1__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2_1__bvfunc14]),discharge_asm(discharge,[dt_c1_2_1_4__bvfunc14])],[dt_c1_2_1_4__bvfunc14,i1_2_1_4__bvfunc14]), [interesting(0.65),e13_2_1__bvfunc14]). fof(e13_2_1__bvfunc14,plain,( r1_tarski(k8_setfam_1(c1_2__bvfunc14,c5_2_1__bvfunc14),c1_2_1__bvfunc14) ), inference(let,[status(thm),assumptions([dt_c2_2__bvfunc14,e1_2__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_1__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2_1__bvfunc14])],[i1_2_1_4_tmp__bvfunc14,dt_k1_zfmisc_1,dt_m1_subset_1,fc1_subset_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k8_setfam_1,dt_c1_2__bvfunc14,dt_c1_2_1__bvfunc14,dt_c5_2_1__bvfunc14,d3_tarski,dh_c1_2_1_4__bvfunc14]), [interesting(0.65),file(bvfunc14,e13_2_1__bvfunc14),[file(bvfunc14,e13_2_1__bvfunc14)]]). fof(dt_c1_2_1_3__bvfunc14,assumption,( $true ), introduced(assumption,[file(bvfunc14,c1_2_1_3__bvfunc14)]), [interesting(0.5),axiom,file(bvfunc14,c1_2_1_3__bvfunc14)]). fof(dh_c1_2_1_3__bvfunc14,definition, ( ~ ( r2_hidden(c1_2_1_3__bvfunc14,c1_2_1__bvfunc14) & ~ r2_hidden(c1_2_1_3__bvfunc14,k8_setfam_1(c1_2__bvfunc14,c5_2_1__bvfunc14)) ) => ! [A] : ~ ( r2_hidden(A,c1_2_1__bvfunc14) & ~ r2_hidden(A,k8_setfam_1(c1_2__bvfunc14,c5_2_1__bvfunc14)) ) ), introduced(definition,[new_symbol(c1_2_1_3__bvfunc14),file(bvfunc14,c1_2_1_3__bvfunc14)]), [interesting(0.5),axiom,file(bvfunc14,c1_2_1_3__bvfunc14)]). fof(e1_2_1_3__bvfunc14,assumption,( r2_hidden(c1_2_1_3__bvfunc14,c1_2_1__bvfunc14) ), introduced(assumption,[file(bvfunc14,e1_2_1_3__bvfunc14)]), [interesting(0.5),axiom,file(bvfunc14,e1_2_1_3__bvfunc14)]). fof(dh_c1_2_1_3_1__bvfunc14,definition, ( ( r2_hidden(c1_2_1_3_1__bvfunc14,c5_2_1__bvfunc14) => r2_hidden(c1_2_1_3__bvfunc14,c1_2_1_3_1__bvfunc14) ) => ! [A] : ( r2_hidden(A,c5_2_1__bvfunc14) => r2_hidden(c1_2_1_3__bvfunc14,A) ) ), introduced(definition,[new_symbol(c1_2_1_3_1__bvfunc14),file(bvfunc14,c1_2_1_3_1__bvfunc14)]), [interesting(0.35),axiom,file(bvfunc14,c1_2_1_3_1__bvfunc14)]). fof(e1_2_1_3_1__bvfunc14,assumption,( r2_hidden(c1_2_1_3_1__bvfunc14,c5_2_1__bvfunc14) ), introduced(assumption,[file(bvfunc14,e1_2_1_3_1__bvfunc14)]), [interesting(0.35),axiom,file(bvfunc14,e1_2_1_3_1__bvfunc14)]). fof(dt_c1_2_1_3_1__bvfunc14,assumption,( $true ), introduced(assumption,[file(bvfunc14,c1_2_1_3_1__bvfunc14)]), [interesting(0.35),axiom,file(bvfunc14,c1_2_1_3_1__bvfunc14)]). fof(e1_2_1_3_1_1_1_1__bvfunc14,assumption,( c1_2_1_3_1__bvfunc14 = c2_2_1__bvfunc14 ), introduced(assumption,[file(bvfunc14,e1_2_1_3_1_1_1_1__bvfunc14)]), [interesting(0.02),axiom,file(bvfunc14,e1_2_1_3_1_1_1_1__bvfunc14)]). fof(e2_2_1_3_1_1_1_1__bvfunc14,plain,( r2_hidden(c1_2_1_3__bvfunc14,c1_2_1_3_1__bvfunc14) ), inference(mizar_by,[status(thm),assumptions([dt_c1_2_1_3__bvfunc14,dt_c1_2_1_3_1__bvfunc14,e1_2_1_3_1_1_1_1__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_1__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2_1__bvfunc14,e1_2_1_3__bvfunc14])],[reflexivity_r1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,fc1_subset_1,fc1_xboole_0,rc1_subset_1,rc2_subset_1,t2_boole,t3_subset,t4_subset,t5_subset,existence_m1_eqrel_1,existence_m1_subset_1,dt_m1_eqrel_1,dt_m1_subset_1,dt_c1_2__bvfunc14,cc1_eqrel_1,cc2_eqrel_1,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t8_boole,commutativity_k3_xboole_0,idempotence_k3_xboole_0,antisymmetry_r2_hidden,dt_k3_xboole_0,dt_c1_2_1__bvfunc14,dt_c1_2_1_3__bvfunc14,dt_c1_2_1_3_1__bvfunc14,dt_c2_2_1__bvfunc14,dt_c3_2__bvfunc14,dt_c3_2_1__bvfunc14,dt_c4_2__bvfunc14,t1_subset,t7_boole,e1_2_1_3_1_1_1_1__bvfunc14,e5_2_1__bvfunc14,e1_2_1_3__bvfunc14,d3_xboole_0]), [interesting(0.02),file(bvfunc14,e2_2_1_3_1_1_1_1__bvfunc14),[file(bvfunc14,e2_2_1_3_1_1_1_1__bvfunc14)]]). fof(i2_2_1_3_1_1_1_1__bvfunc14,theorem,( $true ), introduced(tautology,[file(bvfunc14,i2_2_1_3_1_1_1_1__bvfunc14)]), [interesting(0.02),trivial,file(bvfunc14,i2_2_1_3_1_1_1_1__bvfunc14)]). fof(i1_2_1_3_1_1_1_1__bvfunc14,plain,( r2_hidden(c1_2_1_3__bvfunc14,c1_2_1_3_1__bvfunc14) ), inference(conclusion,[status(thm),assumptions([dt_c1_2_1_3__bvfunc14,dt_c1_2_1_3_1__bvfunc14,e1_2_1_3_1_1_1_1__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_1__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2_1__bvfunc14,e1_2_1_3__bvfunc14])],[e2_2_1_3_1_1_1_1__bvfunc14,i2_2_1_3_1_1_1_1__bvfunc14]), [interesting(0.02),file(bvfunc14,i1_2_1_3_1_1_1_1__bvfunc14),[file(bvfunc14,i1_2_1_3_1_1_1_1__bvfunc14)]]). fof(i1_2_1_3_1_1_1__bvfunc14,plain, ( c1_2_1_3_1__bvfunc14 = c2_2_1__bvfunc14 => ( c1_2_1_3_1__bvfunc14 = c2_2_1__bvfunc14 & r2_hidden(c1_2_1_3__bvfunc14,c1_2_1_3_1__bvfunc14) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_2_1_3__bvfunc14,dt_c1_2_1_3_1__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_1__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2_1__bvfunc14,e1_2_1_3__bvfunc14]),discharge_asm(discharge,[e1_2_1_3_1_1_1_1__bvfunc14])],[e1_2_1_3_1_1_1_1__bvfunc14,i1_2_1_3_1_1_1_1__bvfunc14]), [interesting(0.05),file(bvfunc14,i1_2_1_3_1_1_1__bvfunc14),[file(bvfunc14,i1_2_1_3_1_1_1__bvfunc14)]]). fof(e1_2_1_3_1_1_1_2__bvfunc14,assumption,( c1_2_1_3_1__bvfunc14 = c3_2_1__bvfunc14 ), introduced(assumption,[file(bvfunc14,e1_2_1_3_1_1_1_2__bvfunc14)]), [interesting(0.02),axiom,file(bvfunc14,e1_2_1_3_1_1_1_2__bvfunc14)]). fof(e2_2_1_3_1_1_1_2__bvfunc14,plain,( r2_hidden(c1_2_1_3__bvfunc14,c1_2_1_3_1__bvfunc14) ), inference(mizar_by,[status(thm),assumptions([dt_c1_2_1_3__bvfunc14,dt_c1_2_1_3_1__bvfunc14,e1_2_1_3_1_1_1_2__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_1__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2_1__bvfunc14,e1_2_1_3__bvfunc14])],[reflexivity_r1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,fc1_subset_1,fc1_xboole_0,rc1_subset_1,rc2_subset_1,t2_boole,t3_subset,t4_subset,t5_subset,existence_m1_eqrel_1,existence_m1_subset_1,dt_m1_eqrel_1,dt_m1_subset_1,dt_c1_2__bvfunc14,cc1_eqrel_1,cc2_eqrel_1,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t8_boole,commutativity_k3_xboole_0,idempotence_k3_xboole_0,antisymmetry_r2_hidden,dt_k3_xboole_0,dt_c1_2_1__bvfunc14,dt_c1_2_1_3__bvfunc14,dt_c1_2_1_3_1__bvfunc14,dt_c2_2_1__bvfunc14,dt_c3_2__bvfunc14,dt_c3_2_1__bvfunc14,dt_c4_2__bvfunc14,t1_subset,t7_boole,e1_2_1_3_1_1_1_2__bvfunc14,e5_2_1__bvfunc14,e1_2_1_3__bvfunc14,d3_xboole_0]), [interesting(0.02),file(bvfunc14,e2_2_1_3_1_1_1_2__bvfunc14),[file(bvfunc14,e2_2_1_3_1_1_1_2__bvfunc14)]]). fof(i2_2_1_3_1_1_1_2__bvfunc14,theorem,( $true ), introduced(tautology,[file(bvfunc14,i2_2_1_3_1_1_1_2__bvfunc14)]), [interesting(0.02),trivial,file(bvfunc14,i2_2_1_3_1_1_1_2__bvfunc14)]). fof(i1_2_1_3_1_1_1_2__bvfunc14,plain,( r2_hidden(c1_2_1_3__bvfunc14,c1_2_1_3_1__bvfunc14) ), inference(conclusion,[status(thm),assumptions([dt_c1_2_1_3__bvfunc14,dt_c1_2_1_3_1__bvfunc14,e1_2_1_3_1_1_1_2__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_1__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2_1__bvfunc14,e1_2_1_3__bvfunc14])],[e2_2_1_3_1_1_1_2__bvfunc14,i2_2_1_3_1_1_1_2__bvfunc14]), [interesting(0.02),file(bvfunc14,i1_2_1_3_1_1_1_2__bvfunc14),[file(bvfunc14,i1_2_1_3_1_1_1_2__bvfunc14)]]). fof(i2_2_1_3_1_1_1__bvfunc14,plain, ( c1_2_1_3_1__bvfunc14 = c3_2_1__bvfunc14 => ( c1_2_1_3_1__bvfunc14 = c3_2_1__bvfunc14 & r2_hidden(c1_2_1_3__bvfunc14,c1_2_1_3_1__bvfunc14) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_2_1_3__bvfunc14,dt_c1_2_1_3_1__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_1__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2_1__bvfunc14,e1_2_1_3__bvfunc14]),discharge_asm(discharge,[e1_2_1_3_1_1_1_2__bvfunc14])],[e1_2_1_3_1_1_1_2__bvfunc14,i1_2_1_3_1_1_1_2__bvfunc14]), [interesting(0.05),file(bvfunc14,i2_2_1_3_1_1_1__bvfunc14),[file(bvfunc14,i2_2_1_3_1_1_1__bvfunc14)]]). fof(e1_2_1_3_1_1_1__bvfunc14,plain, ( c1_2_1_3_1__bvfunc14 = c2_2_1__bvfunc14 | c1_2_1_3_1__bvfunc14 = c3_2_1__bvfunc14 ), inference(mizar_by,[status(thm),assumptions([dt_c1_2_1_3_1__bvfunc14,dt_c2_2__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_1__bvfunc14,dt_c3_2__bvfunc14,e1_2_1__bvfunc14,dt_c4_2__bvfunc14,e1_2__bvfunc14,e1_2_1_3_1__bvfunc14])],[reflexivity_r1_tarski,dt_k1_xboole_0,fc1_xboole_0,existence_m1_eqrel_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_eqrel_1,dt_m1_subset_1,dt_c1_2__bvfunc14,cc1_eqrel_1,cc2_eqrel_1,fc1_subset_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k2_tarski,antisymmetry_r2_hidden,dt_k2_relat_1,dt_k2_tarski,dt_k4_funct_4,dt_c1_2_1_3_1__bvfunc14,dt_c2_2_1__bvfunc14,dt_c3_2__bvfunc14,dt_c3_2_1__bvfunc14,dt_c4_2__bvfunc14,dt_c5_2_1__bvfunc14,de_c5_2_1__bvfunc14,fc1_funct_4,fc3_subset_1,t1_subset,t7_boole,e7_2_1__bvfunc14,e1_2_1_3_1__bvfunc14,d2_tarski]), [interesting(0.05),file(bvfunc14,e1_2_1_3_1_1_1__bvfunc14),[file(bvfunc14,e1_2_1_3_1_1_1__bvfunc14)]]). fof(e2_2_1_3_1__bvfunc14,plain, ( ( c1_2_1_3_1__bvfunc14 = c2_2_1__bvfunc14 & r2_hidden(c1_2_1_3__bvfunc14,c1_2_1_3_1__bvfunc14) ) | ( c1_2_1_3_1__bvfunc14 = c3_2_1__bvfunc14 & r2_hidden(c1_2_1_3__bvfunc14,c1_2_1_3_1__bvfunc14) ) ), inference(percases,[status(thm),assumptions([dt_c1_2_1_3__bvfunc14,e1_2_1_3__bvfunc14,dt_c1_2_1_3_1__bvfunc14,dt_c2_2__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_1__bvfunc14,dt_c3_2__bvfunc14,e1_2_1__bvfunc14,dt_c4_2__bvfunc14,e1_2__bvfunc14,e1_2_1_3_1__bvfunc14])],[i1_2_1_3_1_1_1__bvfunc14,i2_2_1_3_1_1_1__bvfunc14,e1_2_1_3_1_1_1__bvfunc14]), [interesting(0.35),file(bvfunc14,e2_2_1_3_1__bvfunc14),[file(bvfunc14,e2_2_1_3_1__bvfunc14)]]). fof(e3_2_1_3_1__bvfunc14,plain,( r2_hidden(c1_2_1_3__bvfunc14,c1_2_1_3_1__bvfunc14) ), inference(mizar_by,[status(thm),assumptions([dt_c1_2_1_3__bvfunc14,e1_2_1_3__bvfunc14,dt_c1_2_1_3_1__bvfunc14,dt_c2_2__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_1__bvfunc14,dt_c3_2__bvfunc14,e1_2_1__bvfunc14,dt_c4_2__bvfunc14,e1_2__bvfunc14,e1_2_1_3_1__bvfunc14])],[dt_k1_xboole_0,fc1_xboole_0,existence_m1_subset_1,dt_m1_subset_1,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_c1_2_1_3__bvfunc14,dt_c1_2_1_3_1__bvfunc14,dt_c2_2_1__bvfunc14,dt_c3_2_1__bvfunc14,t1_subset,t7_boole,e2_2_1_3_1__bvfunc14]), [interesting(0.35),file(bvfunc14,e3_2_1_3_1__bvfunc14),[file(bvfunc14,e3_2_1_3_1__bvfunc14)]]). fof(i3_2_1_3_1__bvfunc14,theorem,( $true ), introduced(tautology,[file(bvfunc14,i3_2_1_3_1__bvfunc14)]), [interesting(0.35),trivial,file(bvfunc14,i3_2_1_3_1__bvfunc14)]). fof(i2_2_1_3_1__bvfunc14,plain,( r2_hidden(c1_2_1_3__bvfunc14,c1_2_1_3_1__bvfunc14) ), inference(conclusion,[status(thm),assumptions([dt_c1_2_1_3__bvfunc14,e1_2_1_3__bvfunc14,dt_c1_2_1_3_1__bvfunc14,dt_c2_2__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_1__bvfunc14,dt_c3_2__bvfunc14,e1_2_1__bvfunc14,dt_c4_2__bvfunc14,e1_2__bvfunc14,e1_2_1_3_1__bvfunc14])],[e3_2_1_3_1__bvfunc14,i3_2_1_3_1__bvfunc14]), [interesting(0.35),file(bvfunc14,i2_2_1_3_1__bvfunc14),[file(bvfunc14,i2_2_1_3_1__bvfunc14)]]). fof(i1_2_1_3_1__bvfunc14,plain, ( r2_hidden(c1_2_1_3_1__bvfunc14,c5_2_1__bvfunc14) => r2_hidden(c1_2_1_3__bvfunc14,c1_2_1_3_1__bvfunc14) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_2_1_3__bvfunc14,e1_2_1_3__bvfunc14,dt_c1_2_1_3_1__bvfunc14,dt_c2_2__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_1__bvfunc14,dt_c3_2__bvfunc14,e1_2_1__bvfunc14,dt_c4_2__bvfunc14,e1_2__bvfunc14]),discharge_asm(discharge,[e1_2_1_3_1__bvfunc14])],[e1_2_1_3_1__bvfunc14,i2_2_1_3_1__bvfunc14]), [interesting(0.35),file(bvfunc14,i1_2_1_3_1__bvfunc14),[file(bvfunc14,i1_2_1_3_1__bvfunc14)]]). fof(i1_2_1_3_1_tmp__bvfunc14,plain, ( r2_hidden(c1_2_1_3_1__bvfunc14,c5_2_1__bvfunc14) => r2_hidden(c1_2_1_3__bvfunc14,c1_2_1_3_1__bvfunc14) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_2_1_3__bvfunc14,e1_2_1_3__bvfunc14,dt_c2_2__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_1__bvfunc14,dt_c3_2__bvfunc14,e1_2_1__bvfunc14,dt_c4_2__bvfunc14,e1_2__bvfunc14]),discharge_asm(discharge,[dt_c1_2_1_3_1__bvfunc14])],[dt_c1_2_1_3_1__bvfunc14,i1_2_1_3_1__bvfunc14]), [interesting(0.5),e2_2_1_3__bvfunc14]). fof(e2_2_1_3__bvfunc14,plain,( ! [A] : ( r2_hidden(A,c5_2_1__bvfunc14) => r2_hidden(c1_2_1_3__bvfunc14,A) ) ), inference(let,[status(thm),assumptions([dt_c1_2_1_3__bvfunc14,e1_2_1_3__bvfunc14,dt_c2_2__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_1__bvfunc14,dt_c3_2__bvfunc14,e1_2_1__bvfunc14,dt_c4_2__bvfunc14,e1_2__bvfunc14])],[i1_2_1_3_1_tmp__bvfunc14,dh_c1_2_1_3_1__bvfunc14]), [interesting(0.5),file(bvfunc14,e2_2_1_3__bvfunc14),[file(bvfunc14,e2_2_1_3__bvfunc14)]]). fof(e3_2_1_3__bvfunc14,plain,( r2_hidden(c1_2_1_3__bvfunc14,k6_setfam_1(c1_2__bvfunc14,c5_2_1__bvfunc14)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_2_1_3__bvfunc14,e1_2_1_3__bvfunc14,dt_c2_2__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_1__bvfunc14,dt_c3_2__bvfunc14,e1_2_1__bvfunc14,dt_c4_2__bvfunc14,e1_2__bvfunc14])],[reflexivity_r1_tarski,existence_m1_eqrel_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_eqrel_1,dt_m1_subset_1,cc1_eqrel_1,cc2_eqrel_1,fc1_subset_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,t2_subset,t3_subset,t4_subset,t5_subset,t8_boole,commutativity_k2_tarski,antisymmetry_r2_hidden,redefinition_k6_setfam_1,dt_k1_setfam_1,dt_k1_xboole_0,dt_k2_relat_1,dt_k2_tarski,dt_k4_funct_4,dt_k6_setfam_1,dt_c1_2__bvfunc14,dt_c1_2_1_3__bvfunc14,dt_c2_2_1__bvfunc14,dt_c3_2__bvfunc14,dt_c3_2_1__bvfunc14,dt_c4_2__bvfunc14,dt_c5_2_1__bvfunc14,de_c5_2_1__bvfunc14,fc1_funct_4,fc1_xboole_0,fc3_subset_1,t1_subset,t6_boole,t7_boole,e2_2_1_3__bvfunc14,e7_2_1__bvfunc14,d1_setfam_1]), [interesting(0.5),file(bvfunc14,e3_2_1_3__bvfunc14),[file(bvfunc14,e3_2_1_3__bvfunc14)]]). fof(e4_2_1_3__bvfunc14,plain,( r2_hidden(c1_2_1_3__bvfunc14,k8_setfam_1(c1_2__bvfunc14,c5_2_1__bvfunc14)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_2_1_3__bvfunc14,e1_2_1_3__bvfunc14,dt_c2_2__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_1__bvfunc14,dt_c3_2__bvfunc14,e1_2_1__bvfunc14,dt_c4_2__bvfunc14,e1_2__bvfunc14])],[reflexivity_r1_tarski,existence_m1_eqrel_1,dt_k1_setfam_1,dt_m1_eqrel_1,cc1_eqrel_1,cc2_eqrel_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,t2_subset,t5_subset,t8_boole,commutativity_k2_tarski,antisymmetry_r2_hidden,existence_m1_subset_1,redefinition_k6_setfam_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_relat_1,dt_k2_tarski,dt_k4_funct_4,dt_k6_setfam_1,dt_k8_setfam_1,dt_m1_subset_1,dt_c1_2__bvfunc14,dt_c1_2_1_3__bvfunc14,dt_c2_2_1__bvfunc14,dt_c3_2__bvfunc14,dt_c3_2_1__bvfunc14,dt_c4_2__bvfunc14,dt_c5_2_1__bvfunc14,de_c5_2_1__bvfunc14,fc1_funct_4,fc1_subset_1,fc1_xboole_0,fc3_subset_1,t1_subset,t3_subset,t4_subset,t6_boole,t7_boole,e3_2_1_3__bvfunc14,e7_2_1__bvfunc14,d10_setfam_1]), [interesting(0.5),file(bvfunc14,e4_2_1_3__bvfunc14),[file(bvfunc14,e4_2_1_3__bvfunc14)]]). fof(i3_2_1_3__bvfunc14,theorem,( $true ), introduced(tautology,[file(bvfunc14,i3_2_1_3__bvfunc14)]), [interesting(0.5),trivial,file(bvfunc14,i3_2_1_3__bvfunc14)]). fof(i2_2_1_3__bvfunc14,plain,( r2_hidden(c1_2_1_3__bvfunc14,k8_setfam_1(c1_2__bvfunc14,c5_2_1__bvfunc14)) ), inference(conclusion,[status(thm),assumptions([dt_c1_2_1_3__bvfunc14,e1_2_1_3__bvfunc14,dt_c2_2__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_1__bvfunc14,dt_c3_2__bvfunc14,e1_2_1__bvfunc14,dt_c4_2__bvfunc14,e1_2__bvfunc14])],[e4_2_1_3__bvfunc14,i3_2_1_3__bvfunc14]), [interesting(0.5),file(bvfunc14,i2_2_1_3__bvfunc14),[file(bvfunc14,i2_2_1_3__bvfunc14)]]). fof(i1_2_1_3__bvfunc14,plain,( ~ ( r2_hidden(c1_2_1_3__bvfunc14,c1_2_1__bvfunc14) & ~ r2_hidden(c1_2_1_3__bvfunc14,k8_setfam_1(c1_2__bvfunc14,c5_2_1__bvfunc14)) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_2_1_3__bvfunc14,dt_c2_2__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_1__bvfunc14,dt_c3_2__bvfunc14,e1_2_1__bvfunc14,dt_c4_2__bvfunc14,e1_2__bvfunc14]),discharge_asm(discharge,[e1_2_1_3__bvfunc14])],[e1_2_1_3__bvfunc14,i2_2_1_3__bvfunc14]), [interesting(0.5),file(bvfunc14,i1_2_1_3__bvfunc14),[file(bvfunc14,i1_2_1_3__bvfunc14)]]). fof(i1_2_1_3_tmp__bvfunc14,plain,( ~ ( r2_hidden(c1_2_1_3__bvfunc14,c1_2_1__bvfunc14) & ~ r2_hidden(c1_2_1_3__bvfunc14,k8_setfam_1(c1_2__bvfunc14,c5_2_1__bvfunc14)) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c2_2__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_1__bvfunc14,dt_c3_2__bvfunc14,e1_2_1__bvfunc14,dt_c4_2__bvfunc14,e1_2__bvfunc14]),discharge_asm(discharge,[dt_c1_2_1_3__bvfunc14])],[dt_c1_2_1_3__bvfunc14,i1_2_1_3__bvfunc14]), [interesting(0.65),e12_2_1__bvfunc14]). fof(e12_2_1__bvfunc14,plain,( r1_tarski(c1_2_1__bvfunc14,k8_setfam_1(c1_2__bvfunc14,c5_2_1__bvfunc14)) ), inference(let,[status(thm),assumptions([dt_c2_2__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_1__bvfunc14,dt_c3_2__bvfunc14,e1_2_1__bvfunc14,dt_c4_2__bvfunc14,e1_2__bvfunc14])],[i1_2_1_3_tmp__bvfunc14,dt_k1_zfmisc_1,dt_m1_subset_1,fc1_subset_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k8_setfam_1,dt_c1_2__bvfunc14,dt_c1_2_1__bvfunc14,dt_c5_2_1__bvfunc14,d3_tarski,dh_c1_2_1_3__bvfunc14]), [interesting(0.65),file(bvfunc14,e12_2_1__bvfunc14),[file(bvfunc14,e12_2_1__bvfunc14)]]). fof(e14_2_1__bvfunc14,plain,( c1_2_1__bvfunc14 = k8_setfam_1(c1_2__bvfunc14,c5_2_1__bvfunc14) ), inference(mizar_by,[status(thm),assumptions([dt_c2_2__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_1__bvfunc14,dt_c3_2__bvfunc14,e1_2_1__bvfunc14,dt_c4_2__bvfunc14,e1_2__bvfunc14])],[antisymmetry_r2_hidden,existence_m1_eqrel_1,dt_k1_xboole_0,dt_m1_eqrel_1,cc1_eqrel_1,cc2_eqrel_1,fc1_xboole_0,t1_subset,t4_subset,t5_subset,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_relat_1,dt_k4_funct_4,dt_m1_subset_1,dt_c2_2_1__bvfunc14,dt_c3_2__bvfunc14,dt_c3_2_1__bvfunc14,dt_c4_2__bvfunc14,fc1_funct_4,fc1_subset_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,t2_subset,t6_boole,t7_boole,t8_boole,reflexivity_r1_tarski,dt_k8_setfam_1,dt_c1_2__bvfunc14,dt_c1_2_1__bvfunc14,dt_c5_2_1__bvfunc14,de_c5_2_1__bvfunc14,t3_subset,e13_2_1__bvfunc14,e12_2_1__bvfunc14,d10_xboole_0]), [interesting(0.65),file(bvfunc14,e14_2_1__bvfunc14),[file(bvfunc14,e14_2_1__bvfunc14)]]). fof(e16_2_1__bvfunc14,plain,( r2_hidden(c1_2_1__bvfunc14,k2_bvfunc_2(c1_2__bvfunc14,c2_2__bvfunc14)) ), inference(mizar_by,[status(thm),assumptions([dt_c2_2__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_1__bvfunc14,dt_c3_2__bvfunc14,e1_2_1__bvfunc14,dt_c4_2__bvfunc14,e1_2__bvfunc14])],[reflexivity_r1_tarski,existence_m1_t_1topsp,dt_k1_partit1,dt_m1_t_1topsp,commutativity_k2_tarski,antisymmetry_r2_hidden,existence_m1_eqrel_1,existence_m1_subset_1,redefinition_k1_bvfunc_2,dt_k1_bvfunc_2,dt_k1_funct_1,dt_k1_relat_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_bvfunc_2,dt_k2_relat_1,dt_k2_tarski,dt_k4_funct_4,dt_k8_setfam_1,dt_m1_eqrel_1,dt_m1_subset_1,dt_c1_2__bvfunc14,dt_c1_2_1__bvfunc14,dt_c2_2__bvfunc14,dt_c2_2_1__bvfunc14,dt_c3_2__bvfunc14,dt_c3_2_1__bvfunc14,dt_c4_2__bvfunc14,dt_c5_2_1__bvfunc14,de_c5_2_1__bvfunc14,cc1_eqrel_1,cc2_eqrel_1,fc1_funct_4,fc1_subset_1,fc1_xboole_0,fc3_subset_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,t1_subset,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole,e15_2_1__bvfunc14,e1_2__bvfunc14,e6_2_1__bvfunc14,e11_2_1__bvfunc14,e14_2_1__bvfunc14,d1_bvfunc_2]), [interesting(0.65),file(bvfunc14,e16_2_1__bvfunc14),[file(bvfunc14,e16_2_1__bvfunc14)]]). fof(i3_2_1__bvfunc14,theorem,( $true ), introduced(tautology,[file(bvfunc14,i3_2_1__bvfunc14)]), [interesting(0.65),trivial,file(bvfunc14,i3_2_1__bvfunc14)]). fof(i2_2_1__bvfunc14,plain,( r2_hidden(c1_2_1__bvfunc14,k2_bvfunc_2(c1_2__bvfunc14,c2_2__bvfunc14)) ), inference(conclusion,[status(thm),assumptions([dt_c2_2__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_1__bvfunc14,dt_c3_2__bvfunc14,e1_2_1__bvfunc14,dt_c4_2__bvfunc14,e1_2__bvfunc14])],[e16_2_1__bvfunc14,i3_2_1__bvfunc14]), [interesting(0.65),file(bvfunc14,i2_2_1__bvfunc14),[file(bvfunc14,i2_2_1__bvfunc14)]]). fof(i1_2_1__bvfunc14,plain,( ~ ( r2_hidden(c1_2_1__bvfunc14,k2_partit1(c1_2__bvfunc14,c3_2__bvfunc14,c4_2__bvfunc14)) & ~ r2_hidden(c1_2_1__bvfunc14,k2_bvfunc_2(c1_2__bvfunc14,c2_2__bvfunc14)) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c2_2__bvfunc14,dt_c1_2__bvfunc14,dt_c1_2_1__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2__bvfunc14]),discharge_asm(discharge,[e1_2_1__bvfunc14])],[e1_2_1__bvfunc14,i2_2_1__bvfunc14]), [interesting(0.65),file(bvfunc14,i1_2_1__bvfunc14),[file(bvfunc14,i1_2_1__bvfunc14)]]). fof(i1_2_1_tmp__bvfunc14,plain,( ~ ( r2_hidden(c1_2_1__bvfunc14,k2_partit1(c1_2__bvfunc14,c3_2__bvfunc14,c4_2__bvfunc14)) & ~ r2_hidden(c1_2_1__bvfunc14,k2_bvfunc_2(c1_2__bvfunc14,c2_2__bvfunc14)) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c2_2__bvfunc14,dt_c1_2__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2__bvfunc14]),discharge_asm(discharge,[dt_c1_2_1__bvfunc14])],[dt_c1_2_1__bvfunc14,i1_2_1__bvfunc14]), [interesting(0.8),e2_2__bvfunc14]). fof(e2_2__bvfunc14,plain,( r1_tarski(k2_partit1(c1_2__bvfunc14,c3_2__bvfunc14,c4_2__bvfunc14),k2_bvfunc_2(c1_2__bvfunc14,c2_2__bvfunc14)) ), inference(let,[status(thm),assumptions([dt_c2_2__bvfunc14,dt_c1_2__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2__bvfunc14])],[i1_2_1_tmp__bvfunc14,dt_k1_partit1,dt_m1_t_1topsp,redefinition_k1_bvfunc_2,dt_k1_bvfunc_2,dt_k1_zfmisc_1,dt_m1_eqrel_1,dt_m1_subset_1,cc1_eqrel_1,cc2_eqrel_1,fc1_subset_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,commutativity_k2_partit1,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k2_bvfunc_2,dt_k2_partit1,dt_c1_2__bvfunc14,dt_c2_2__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,d3_tarski,dh_c1_2_1__bvfunc14]), [interesting(0.8),file(bvfunc14,e2_2__bvfunc14),[file(bvfunc14,e2_2__bvfunc14)]]). fof(e4_2__bvfunc14,plain,( k2_bvfunc_2(c1_2__bvfunc14,c2_2__bvfunc14) = k2_partit1(c1_2__bvfunc14,c3_2__bvfunc14,c4_2__bvfunc14) ), inference(mizar_by,[status(thm),assumptions([dt_c2_2__bvfunc14,dt_c1_2__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2__bvfunc14])],[antisymmetry_r2_hidden,existence_m1_t_1topsp,dt_k1_partit1,dt_k1_xboole_0,dt_m1_t_1topsp,fc1_xboole_0,t1_subset,t4_subset,t5_subset,existence_m1_eqrel_1,existence_m1_subset_1,redefinition_k1_bvfunc_2,dt_k1_bvfunc_2,dt_k1_zfmisc_1,dt_m1_eqrel_1,dt_m1_subset_1,cc1_eqrel_1,cc2_eqrel_1,fc1_subset_1,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k2_partit1,reflexivity_r1_tarski,dt_k2_bvfunc_2,dt_k2_partit1,dt_c1_2__bvfunc14,dt_c2_2__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,t3_subset,e3_2__bvfunc14,e2_2__bvfunc14,d10_xboole_0]), [interesting(0.8),file(bvfunc14,e4_2__bvfunc14),[file(bvfunc14,e4_2__bvfunc14)]]). fof(i6_2__bvfunc14,theorem,( $true ), introduced(tautology,[file(bvfunc14,i6_2__bvfunc14)]), [interesting(0.8),trivial,file(bvfunc14,i6_2__bvfunc14)]). fof(i5_2__bvfunc14,plain,( k2_bvfunc_2(c1_2__bvfunc14,c2_2__bvfunc14) = k2_partit1(c1_2__bvfunc14,c3_2__bvfunc14,c4_2__bvfunc14) ), inference(conclusion,[status(thm),assumptions([dt_c2_2__bvfunc14,dt_c1_2__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14,e1_2__bvfunc14])],[e4_2__bvfunc14,i6_2__bvfunc14]), [interesting(0.8),file(bvfunc14,i5_2__bvfunc14),[file(bvfunc14,i5_2__bvfunc14)]]). fof(i4_2__bvfunc14,plain, ( c2_2__bvfunc14 = k2_tarski(c3_2__bvfunc14,c4_2__bvfunc14) => ( c3_2__bvfunc14 = c4_2__bvfunc14 | k2_bvfunc_2(c1_2__bvfunc14,c2_2__bvfunc14) = k2_partit1(c1_2__bvfunc14,c3_2__bvfunc14,c4_2__bvfunc14) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c2_2__bvfunc14,dt_c1_2__bvfunc14,dt_c3_2__bvfunc14,dt_c4_2__bvfunc14]),discharge_asm(discharge,[e1_2__bvfunc14])],[e1_2__bvfunc14,i5_2__bvfunc14]), [interesting(0.8),file(bvfunc14,i4_2__bvfunc14),[file(bvfunc14,i4_2__bvfunc14)]]). fof(i4_2_tmp__bvfunc14,plain, ( m1_eqrel_1(c4_2__bvfunc14,c1_2__bvfunc14) => ( c2_2__bvfunc14 = k2_tarski(c3_2__bvfunc14,c4_2__bvfunc14) => ( c3_2__bvfunc14 = c4_2__bvfunc14 | k2_bvfunc_2(c1_2__bvfunc14,c2_2__bvfunc14) = k2_partit1(c1_2__bvfunc14,c3_2__bvfunc14,c4_2__bvfunc14) ) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c2_2__bvfunc14,dt_c1_2__bvfunc14,dt_c3_2__bvfunc14]),discharge_asm(discharge,[dt_c4_2__bvfunc14])],[dt_c4_2__bvfunc14,i4_2__bvfunc14]), [interesting(0.8),i3_2__bvfunc14]). fof(i3_2__bvfunc14,plain,( ! [A] : ( m1_eqrel_1(A,c1_2__bvfunc14) => ( c2_2__bvfunc14 = k2_tarski(c3_2__bvfunc14,A) => ( c3_2__bvfunc14 = A | k2_bvfunc_2(c1_2__bvfunc14,c2_2__bvfunc14) = k2_partit1(c1_2__bvfunc14,c3_2__bvfunc14,A) ) ) ) ), inference(let,[status(thm),assumptions([dt_c2_2__bvfunc14,dt_c1_2__bvfunc14,dt_c3_2__bvfunc14])],[i4_2_tmp__bvfunc14,dh_c4_2__bvfunc14]), [interesting(0.8),file(bvfunc14,i3_2__bvfunc14),[file(bvfunc14,i3_2__bvfunc14)]]). fof(i3_2_tmp__bvfunc14,plain, ( m1_eqrel_1(c3_2__bvfunc14,c1_2__bvfunc14) => ! [A] : ( m1_eqrel_1(A,c1_2__bvfunc14) => ( c2_2__bvfunc14 = k2_tarski(c3_2__bvfunc14,A) => ( c3_2__bvfunc14 = A | k2_bvfunc_2(c1_2__bvfunc14,c2_2__bvfunc14) = k2_partit1(c1_2__bvfunc14,c3_2__bvfunc14,A) ) ) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c2_2__bvfunc14,dt_c1_2__bvfunc14]),discharge_asm(discharge,[dt_c3_2__bvfunc14])],[dt_c3_2__bvfunc14,i3_2__bvfunc14]), [interesting(0.8),i2_2__bvfunc14]). fof(i2_2__bvfunc14,plain,( ! [A] : ( m1_eqrel_1(A,c1_2__bvfunc14) => ! [B] : ( m1_eqrel_1(B,c1_2__bvfunc14) => ( c2_2__bvfunc14 = k2_tarski(A,B) => ( A = B | k2_bvfunc_2(c1_2__bvfunc14,c2_2__bvfunc14) = k2_partit1(c1_2__bvfunc14,A,B) ) ) ) ) ), inference(let,[status(thm),assumptions([dt_c2_2__bvfunc14,dt_c1_2__bvfunc14])],[i3_2_tmp__bvfunc14,dh_c3_2__bvfunc14]), [interesting(0.8),file(bvfunc14,i2_2__bvfunc14),[file(bvfunc14,i2_2__bvfunc14)]]). fof(i2_2_tmp__bvfunc14,plain, ( m1_subset_1(c2_2__bvfunc14,k1_zfmisc_1(k1_bvfunc_2(c1_2__bvfunc14))) => ! [A] : ( m1_eqrel_1(A,c1_2__bvfunc14) => ! [B] : ( m1_eqrel_1(B,c1_2__bvfunc14) => ( c2_2__bvfunc14 = k2_tarski(A,B) => ( A = B | k2_bvfunc_2(c1_2__bvfunc14,c2_2__bvfunc14) = k2_partit1(c1_2__bvfunc14,A,B) ) ) ) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_2__bvfunc14]),discharge_asm(discharge,[dt_c2_2__bvfunc14])],[dt_c2_2__bvfunc14,i2_2__bvfunc14]), [interesting(0.8),i1_2__bvfunc14]). fof(i1_2__bvfunc14,plain,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_bvfunc_2(c1_2__bvfunc14))) => ! [B] : ( m1_eqrel_1(B,c1_2__bvfunc14) => ! [C] : ( m1_eqrel_1(C,c1_2__bvfunc14) => ( A = k2_tarski(B,C) => ( B = C | k2_bvfunc_2(c1_2__bvfunc14,A) = k2_partit1(c1_2__bvfunc14,B,C) ) ) ) ) ) ), inference(let,[status(thm),assumptions([dt_c1_2__bvfunc14])],[i2_2_tmp__bvfunc14,dh_c2_2__bvfunc14]), [interesting(0.8),file(bvfunc14,i1_2__bvfunc14),[file(bvfunc14,i1_2__bvfunc14)]]). fof(i1_2_tmp__bvfunc14,plain, ( ~ v1_xboole_0(c1_2__bvfunc14) => ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_bvfunc_2(c1_2__bvfunc14))) => ! [B] : ( m1_eqrel_1(B,c1_2__bvfunc14) => ! [C] : ( m1_eqrel_1(C,c1_2__bvfunc14) => ( A = k2_tarski(B,C) => ( B = C | k2_bvfunc_2(c1_2__bvfunc14,A) = k2_partit1(c1_2__bvfunc14,B,C) ) ) ) ) ) ), inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_2__bvfunc14])],[dt_c1_2__bvfunc14,i1_2__bvfunc14]), [interesting(1),t2_bvfunc14]). fof(t2_bvfunc14,theorem,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( m1_eqrel_1(D,A) => ( B = k2_tarski(C,D) => ( C = D | k2_bvfunc_2(A,B) = k2_partit1(A,C,D) ) ) ) ) ) ) ), inference(let,[status(thm),assumptions([])],[i1_2_tmp__bvfunc14,dh_c1_2__bvfunc14]), [interesting(1),file(bvfunc14,t2_bvfunc14),[file(bvfunc14,t2_bvfunc14)]]).