% Mizar ND problem: t19_trees_4,trees_4,498,33 fof(dh_c1_30__trees_4,definition, ( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v6_trees_3(A) ) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ( r2_hidden(k7_finseq_1(k12_finseq_1(k5_numbers,B),C),k1_relat_1(k4_trees_4(c1_30__trees_4,A))) => k1_funct_1(k4_trees_4(c1_30__trees_4,A),k7_finseq_1(k12_finseq_1(k5_numbers,B),C)) = k5_funct_6(A,k1_nat_1(B,1),C) ) ) ) ) => ! [D,E] : ( ( v1_relat_1(E) & v1_funct_1(E) & v1_finseq_1(E) & v6_trees_3(E) ) => ! [F] : ( m2_subset_1(F,k1_numbers,k5_numbers) => ! [G] : ( ( v1_relat_1(G) & v1_funct_1(G) & v1_finseq_1(G) ) => ( r2_hidden(k7_finseq_1(k12_finseq_1(k5_numbers,F),G),k1_relat_1(k4_trees_4(D,E))) => k1_funct_1(k4_trees_4(D,E),k7_finseq_1(k12_finseq_1(k5_numbers,F),G)) = k5_funct_6(E,k1_nat_1(F,1),G) ) ) ) ) ), introduced(definition,[new_symbol(c1_30__trees_4),file(trees_4,c1_30__trees_4)]), [interesting(0.8),axiom,file(trees_4,c1_30__trees_4)]). fof(dh_c2_30__trees_4,definition, ( ( ( v1_relat_1(c2_30__trees_4) & v1_funct_1(c2_30__trees_4) & v1_finseq_1(c2_30__trees_4) & v6_trees_3(c2_30__trees_4) ) => ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( r2_hidden(k7_finseq_1(k12_finseq_1(k5_numbers,A),B),k1_relat_1(k4_trees_4(c1_30__trees_4,c2_30__trees_4))) => k1_funct_1(k4_trees_4(c1_30__trees_4,c2_30__trees_4),k7_finseq_1(k12_finseq_1(k5_numbers,A),B)) = k5_funct_6(c2_30__trees_4,k1_nat_1(A,1),B) ) ) ) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) & v6_trees_3(C) ) => ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) & v1_finseq_1(E) ) => ( r2_hidden(k7_finseq_1(k12_finseq_1(k5_numbers,D),E),k1_relat_1(k4_trees_4(c1_30__trees_4,C))) => k1_funct_1(k4_trees_4(c1_30__trees_4,C),k7_finseq_1(k12_finseq_1(k5_numbers,D),E)) = k5_funct_6(C,k1_nat_1(D,1),E) ) ) ) ) ), introduced(definition,[new_symbol(c2_30__trees_4),file(trees_4,c2_30__trees_4)]), [interesting(0.8),axiom,file(trees_4,c2_30__trees_4)]). fof(dh_c3_30__trees_4,definition, ( ( m2_subset_1(c3_30__trees_4,k1_numbers,k5_numbers) => ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( r2_hidden(k7_finseq_1(k12_finseq_1(k5_numbers,c3_30__trees_4),A),k1_relat_1(k4_trees_4(c1_30__trees_4,c2_30__trees_4))) => k1_funct_1(k4_trees_4(c1_30__trees_4,c2_30__trees_4),k7_finseq_1(k12_finseq_1(k5_numbers,c3_30__trees_4),A)) = k5_funct_6(c2_30__trees_4,k1_nat_1(c3_30__trees_4,1),A) ) ) ) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ( r2_hidden(k7_finseq_1(k12_finseq_1(k5_numbers,B),C),k1_relat_1(k4_trees_4(c1_30__trees_4,c2_30__trees_4))) => k1_funct_1(k4_trees_4(c1_30__trees_4,c2_30__trees_4),k7_finseq_1(k12_finseq_1(k5_numbers,B),C)) = k5_funct_6(c2_30__trees_4,k1_nat_1(B,1),C) ) ) ) ), introduced(definition,[new_symbol(c3_30__trees_4),file(trees_4,c3_30__trees_4)]), [interesting(0.8),axiom,file(trees_4,c3_30__trees_4)]). fof(dh_c4_30__trees_4,definition, ( ( ( v1_relat_1(c4_30__trees_4) & v1_funct_1(c4_30__trees_4) & v1_finseq_1(c4_30__trees_4) ) => ( r2_hidden(k7_finseq_1(k12_finseq_1(k5_numbers,c3_30__trees_4),c4_30__trees_4),k1_relat_1(k4_trees_4(c1_30__trees_4,c2_30__trees_4))) => k1_funct_1(k4_trees_4(c1_30__trees_4,c2_30__trees_4),k7_finseq_1(k12_finseq_1(k5_numbers,c3_30__trees_4),c4_30__trees_4)) = k5_funct_6(c2_30__trees_4,k1_nat_1(c3_30__trees_4,1),c4_30__trees_4) ) ) => ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( r2_hidden(k7_finseq_1(k12_finseq_1(k5_numbers,c3_30__trees_4),A),k1_relat_1(k4_trees_4(c1_30__trees_4,c2_30__trees_4))) => k1_funct_1(k4_trees_4(c1_30__trees_4,c2_30__trees_4),k7_finseq_1(k12_finseq_1(k5_numbers,c3_30__trees_4),A)) = k5_funct_6(c2_30__trees_4,k1_nat_1(c3_30__trees_4,1),A) ) ) ), introduced(definition,[new_symbol(c4_30__trees_4),file(trees_4,c4_30__trees_4)]), [interesting(0.8),axiom,file(trees_4,c4_30__trees_4)]). fof(e1_30__trees_4,assumption,( r2_hidden(k7_finseq_1(k12_finseq_1(k5_numbers,c3_30__trees_4),c4_30__trees_4),k1_relat_1(k4_trees_4(c1_30__trees_4,c2_30__trees_4))) ), introduced(assumption,[file(trees_4,e1_30__trees_4)]), [interesting(0.8),axiom,file(trees_4,e1_30__trees_4)]). 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(existence_m1_relset_1,axiom,( ! [A,B] : ? [C] : m1_relset_1(C,A,B) ), file(relset_1,m1_relset_1), [interesting(0.9),axiom,file(relset_1,m1_relset_1)]). fof(dt_k2_tarski,axiom,( $true ), file(tarski,k2_tarski), [interesting(0.9),axiom,file(tarski,k2_tarski)]). fof(dt_k2_zfmisc_1,axiom,( $true ), file(zfmisc_1,k2_zfmisc_1), [interesting(0.9),axiom,file(zfmisc_1,k2_zfmisc_1)]). fof(dt_m1_relset_1,axiom,( $true ), file(relset_1,m1_relset_1), [interesting(0.9),axiom,file(relset_1,m1_relset_1)]). fof(cc1_relset_1,theorem,( ! [A,B,C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => v1_relat_1(C) ) ), file(relset_1,cc1_relset_1), [interesting(0.9),axiom,file(relset_1,cc1_relset_1)]). fof(cc7_trees_3,theorem,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v5_trees_3(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v4_trees_3(A) ) ) ), file(trees_3,cc7_trees_3), [interesting(0.9),axiom,file(trees_3,cc7_trees_3)]). fof(fc10_membered,theorem,( ! [A] : ( v1_int_1(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) & v4_membered(k1_tarski(A)) ) ) ), file(membered,fc10_membered), [interesting(0.9),axiom,file(membered,fc10_membered)]). fof(fc12_membered,theorem,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => v1_membered(k2_tarski(A,B)) ) ), file(membered,fc12_membered), [interesting(0.9),axiom,file(membered,fc12_membered)]). fof(fc13_membered,theorem,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) ) ) ), file(membered,fc13_membered), [interesting(0.9),axiom,file(membered,fc13_membered)]). fof(fc14_membered,theorem,( ! [A,B] : ( ( v1_rat_1(A) & v1_rat_1(B) ) => ( v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) & v3_membered(k2_tarski(A,B)) ) ) ), file(membered,fc14_membered), [interesting(0.9),axiom,file(membered,fc14_membered)]). fof(fc15_membered,theorem,( ! [A,B] : ( ( v1_int_1(A) & v1_int_1(B) ) => ( v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) & v3_membered(k2_tarski(A,B)) & v4_membered(k2_tarski(A,B)) ) ) ), file(membered,fc15_membered), [interesting(0.9),axiom,file(membered,fc15_membered)]). fof(fc16_membered,theorem,( ! [A,B] : ( ( v4_ordinal2(A) & v4_ordinal2(B) ) => ( v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) & v3_membered(k2_tarski(A,B)) & v4_membered(k2_tarski(A,B)) & v5_membered(k2_tarski(A,B)) ) ) ), file(membered,fc16_membered), [interesting(0.9),axiom,file(membered,fc16_membered)]). 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(fc4_subset_1,theorem,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) ), file(subset_1,fc4_subset_1), [interesting(0.9),axiom,file(subset_1,fc4_subset_1)]). fof(fc8_trees_3,theorem,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v5_trees_3(A) & v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v5_trees_3(B) ) => ( v1_relat_1(k7_finseq_1(A,B)) & v1_funct_1(k7_finseq_1(A,B)) & v1_finset_1(k7_finseq_1(A,B)) & v1_finseq_1(k7_finseq_1(A,B)) & v4_trees_3(k7_finseq_1(A,B)) & v5_trees_3(k7_finseq_1(A,B)) ) ) ), file(trees_3,fc8_trees_3), [interesting(0.9),axiom,file(trees_3,fc8_trees_3)]). fof(fc9_membered,theorem,( ! [A] : ( v1_rat_1(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) ) ) ), file(membered,fc9_membered), [interesting(0.9),axiom,file(membered,fc9_membered)]). fof(rc2_finseq_1,theorem,( ! [A] : ? [B] : ( m1_relset_1(B,k5_numbers,A) & v1_relat_1(B) & v1_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) ) ), file(finseq_1,rc2_finseq_1), [interesting(0.9),axiom,file(finseq_1,rc2_finseq_1)]). fof(rc3_finseq_1,theorem,( ? [A] : ( v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) ) ), file(finseq_1,rc3_finseq_1), [interesting(0.9),axiom,file(finseq_1,rc3_finseq_1)]). fof(rc4_finseq_1,theorem,( ! [A] : ? [B] : ( m1_finseq_1(B,A) & v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v2_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) ) ), file(finseq_1,rc4_finseq_1), [interesting(0.9),axiom,file(finseq_1,rc4_finseq_1)]). fof(rc5_trees_3,theorem,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finset_1(A) & v1_finseq_1(A) & v4_trees_3(A) & v5_trees_3(A) ) ), file(trees_3,rc5_trees_3), [interesting(0.9),axiom,file(trees_3,rc5_trees_3)]). fof(rc6_finseq_1,theorem,( ? [A] : ( v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_finset_1(A) ) ), file(finseq_1,rc6_finseq_1), [interesting(0.9),axiom,file(finseq_1,rc6_finseq_1)]). fof(rc7_trees_3,theorem,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v4_trees_3(A) & v5_trees_3(A) ) ), file(trees_3,rc7_trees_3), [interesting(0.9),axiom,file(trees_3,rc7_trees_3)]). fof(rc9_trees_2,theorem,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ? [C] : ( m1_relset_1(C,A,B) & v1_relat_1(C) & ~ v1_xboole_0(C) ) ) ), file(trees_2,rc9_trees_2), [interesting(0.9),axiom,file(trees_2,rc9_trees_2)]). fof(reflexivity_r1_tarski,theorem,( ! [A,B] : r1_tarski(A,A) ), file(tarski,r1_tarski), [interesting(0.9),axiom,file(tarski,r1_tarski)]). fof(existence_m2_relset_1,axiom,( ! [A,B] : ? [C] : m2_relset_1(C,A,B) ), file(relset_1,m2_relset_1), [interesting(0.9),axiom,file(relset_1,m2_relset_1)]). fof(redefinition_m2_relset_1,definition,( ! [A,B,C] : ( m2_relset_1(C,A,B) <=> m1_relset_1(C,A,B) ) ), file(relset_1,m2_relset_1), [interesting(0.9),axiom,file(relset_1,m2_relset_1)]). fof(dt_k1_tarski,axiom,( $true ), file(tarski,k1_tarski), [interesting(0.9),axiom,file(tarski,k1_tarski)]). 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_k4_tarski,axiom,( $true ), file(tarski,k4_tarski), [interesting(0.9),axiom,file(tarski,k4_tarski)]). fof(dt_m2_relset_1,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ), file(relset_1,m2_relset_1), [interesting(0.9),axiom,file(relset_1,m2_relset_1)]). fof(cc10_membered,theorem,( ! [A] : ( v1_membered(A) => ! [B] : ( m1_subset_1(B,A) => v1_xcmplx_0(B) ) ) ), file(membered,cc10_membered), [interesting(0.9),axiom,file(membered,cc10_membered)]). fof(cc11_membered,theorem,( ! [A] : ( v2_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v1_xreal_0(B) ) ) ) ), file(membered,cc11_membered), [interesting(0.9),axiom,file(membered,cc11_membered)]). fof(cc12_membered,theorem,( ! [A] : ( v3_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v1_xreal_0(B) & v1_rat_1(B) ) ) ) ), file(membered,cc12_membered), [interesting(0.9),axiom,file(membered,cc12_membered)]). fof(cc13_membered,theorem,( ! [A] : ( v4_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v1_xreal_0(B) & v1_int_1(B) & v1_rat_1(B) ) ) ) ), file(membered,cc13_membered), [interesting(0.9),axiom,file(membered,cc13_membered)]). fof(cc14_membered,theorem,( ! [A] : ( v5_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v4_ordinal2(B) & v1_xreal_0(B) & v1_int_1(B) & v1_rat_1(B) ) ) ) ), file(membered,cc14_membered), [interesting(0.9),axiom,file(membered,cc14_membered)]). fof(cc16_membered,theorem,( ! [A] : ( v1_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v1_membered(B) ) ) ), file(membered,cc16_membered), [interesting(0.9),axiom,file(membered,cc16_membered)]). fof(cc17_membered,theorem,( ! [A] : ( v2_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) ) ) ) ), file(membered,cc17_membered), [interesting(0.9),axiom,file(membered,cc17_membered)]). fof(cc18_membered,theorem,( ! [A] : ( v3_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) & v3_membered(B) ) ) ) ), file(membered,cc18_membered), [interesting(0.9),axiom,file(membered,cc18_membered)]). fof(cc19_membered,theorem,( ! [A] : ( v4_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) ) ) ) ), file(membered,cc19_membered), [interesting(0.9),axiom,file(membered,cc19_membered)]). fof(cc1_arytm_3,theorem,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_ordinal1(B) & v2_ordinal1(B) & v3_ordinal1(B) ) ) ) ), file(arytm_3,cc1_arytm_3), [interesting(0.9),axiom,file(arytm_3,cc1_arytm_3)]). fof(cc1_membered,theorem,( ! [A] : ( v5_membered(A) => v4_membered(A) ) ), file(membered,cc1_membered), [interesting(0.9),axiom,file(membered,cc1_membered)]). fof(cc20_membered,theorem,( ! [A] : ( v5_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B) ) ) ) ), file(membered,cc20_membered), [interesting(0.9),axiom,file(membered,cc20_membered)]). fof(cc2_arytm_3,theorem,( ! [A] : ( ( v1_xboole_0(A) & v3_ordinal1(A) ) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) ) ) ), file(arytm_3,cc2_arytm_3), [interesting(0.9),axiom,file(arytm_3,cc2_arytm_3)]). fof(cc2_membered,theorem,( ! [A] : ( v4_membered(A) => v3_membered(A) ) ), file(membered,cc2_membered), [interesting(0.9),axiom,file(membered,cc2_membered)]). fof(cc3_membered,theorem,( ! [A] : ( v3_membered(A) => v2_membered(A) ) ), file(membered,cc3_membered), [interesting(0.9),axiom,file(membered,cc3_membered)]). fof(cc4_membered,theorem,( ! [A] : ( v2_membered(A) => v1_membered(A) ) ), file(membered,cc4_membered), [interesting(0.9),axiom,file(membered,cc4_membered)]). fof(fc11_membered,theorem,( ! [A] : ( v4_ordinal2(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) & v4_membered(k1_tarski(A)) & v5_membered(k1_tarski(A)) ) ) ), file(membered,fc11_membered), [interesting(0.9),axiom,file(membered,fc11_membered)]). fof(fc13_trees_3,theorem,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_trees_1(A) ) => ( v1_relat_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A)) & ~ v1_xboole_0(k5_finseq_1(A)) & v1_finset_1(k5_finseq_1(A)) & v1_finseq_1(k5_finseq_1(A)) & v4_trees_3(k5_finseq_1(A)) & v5_trees_3(k5_finseq_1(A)) ) ) ), file(trees_3,fc13_trees_3), [interesting(0.9),axiom,file(trees_3,fc13_trees_3)]). fof(fc17_finseq_1,theorem,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) => v1_finset_1(k1_relat_1(A)) ) ), file(finseq_1,fc17_finseq_1), [interesting(0.9),axiom,file(finseq_1,fc17_finseq_1)]). fof(fc2_finseq_1,theorem, ( v1_xboole_0(k1_xboole_0) & v1_relat_1(k1_xboole_0) & v3_relat_1(k1_xboole_0) & v1_funct_1(k1_xboole_0) & v2_funct_1(k1_xboole_0) & v1_finset_1(k1_xboole_0) & v1_finseq_1(k1_xboole_0) ), file(finseq_1,fc2_finseq_1), [interesting(0.9),axiom,file(finseq_1,fc2_finseq_1)]). fof(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(fc5_trees_2,theorem,( ! [A] : ( ( v1_relat_1(A) & v1_finset_1(A) ) => v1_finset_1(k1_relat_1(A)) ) ), file(trees_2,fc5_trees_2), [interesting(0.9),axiom,file(trees_2,fc5_trees_2)]). fof(fc6_membered,theorem, ( v1_xboole_0(k1_xboole_0) & v1_membered(k1_xboole_0) & v2_membered(k1_xboole_0) & v3_membered(k1_xboole_0) & v4_membered(k1_xboole_0) & v5_membered(k1_xboole_0) ), file(membered,fc6_membered), [interesting(0.9),axiom,file(membered,fc6_membered)]). fof(fc7_membered,theorem,( ! [A] : ( v1_xcmplx_0(A) => v1_membered(k1_tarski(A)) ) ), file(membered,fc7_membered), [interesting(0.9),axiom,file(membered,fc7_membered)]). fof(fc7_trees_3,theorem,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v4_trees_3(A) & v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v4_trees_3(B) ) => ( v1_relat_1(k7_finseq_1(A,B)) & v1_funct_1(k7_finseq_1(A,B)) & v1_finset_1(k7_finseq_1(A,B)) & v1_finseq_1(k7_finseq_1(A,B)) & v4_trees_3(k7_finseq_1(A,B)) ) ) ), file(trees_3,fc7_trees_3), [interesting(0.9),axiom,file(trees_3,fc7_trees_3)]). fof(fc8_membered,theorem,( ! [A] : ( v1_xreal_0(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) ) ) ), file(membered,fc8_membered), [interesting(0.9),axiom,file(membered,fc8_membered)]). fof(rc1_arytm_3,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) ) ), file(arytm_3,rc1_arytm_3), [interesting(0.9),axiom,file(arytm_3,rc1_arytm_3)]). fof(rc1_membered,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ), file(membered,rc1_membered), [interesting(0.9),axiom,file(membered,rc1_membered)]). fof(rc6_trees_3,theorem,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finset_1(A) & v1_finseq_1(A) & v6_trees_3(A) ) ), file(trees_3,rc6_trees_3), [interesting(0.9),axiom,file(trees_3,rc6_trees_3)]). fof(rc7_finseq_1,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) ), file(finseq_1,rc7_finseq_1), [interesting(0.9),axiom,file(finseq_1,rc7_finseq_1)]). fof(rc7_trees_2,theorem,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v3_trees_2(A) ) ), file(trees_2,rc7_trees_2), [interesting(0.9),axiom,file(trees_2,rc7_trees_2)]). fof(rc8_finseq_1,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) ) ), file(finseq_1,rc8_finseq_1), [interesting(0.9),axiom,file(finseq_1,rc8_finseq_1)]). fof(spc6_arithm,theorem,( ! [A,B,C] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) & v1_xcmplx_0(C) ) => k2_xcmplx_0(k2_xcmplx_0(A,B),C) = k2_xcmplx_0(A,k2_xcmplx_0(B,C)) ) ), file(arithm,spc6_arithm), [interesting(0.9),axiom,file(arithm,spc6_arithm)]). fof(d5_tarski,definition,( ! [A,B] : k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A)) ), file(tarski,d5_tarski), [interesting(0.9),axiom,file(tarski,d5_tarski)]). fof(commutativity_k2_xcmplx_0,theorem,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => k2_xcmplx_0(A,B) = k2_xcmplx_0(B,A) ) ), file(xcmplx_0,k2_xcmplx_0), [interesting(0.9),axiom,file(xcmplx_0,k2_xcmplx_0)]). fof(existence_m1_finseq_1,axiom,( ! [A] : ? [B] : m1_finseq_1(B,A) ), file(finseq_1,m1_finseq_1), [interesting(0.9),axiom,file(finseq_1,m1_finseq_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(existence_m2_finseq_1,axiom,( ! [A] : ? [B] : m2_finseq_1(B,A) ), file(finseq_1,m2_finseq_1), [interesting(0.9),axiom,file(finseq_1,m2_finseq_1)]). fof(existence_m2_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ? [C] : m2_subset_1(C,A,B) ) ), file(subset_1,m2_subset_1), [interesting(0.9),axiom,file(subset_1,m2_subset_1)]). fof(redefinition_m2_finseq_1,definition,( ! [A,B] : ( m2_finseq_1(B,A) <=> m1_finseq_1(B,A) ) ), file(finseq_1,m2_finseq_1), [interesting(0.9),axiom,file(finseq_1,m2_finseq_1)]). fof(redefinition_m2_subset_1,definition,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m2_subset_1(C,A,B) <=> m1_subset_1(C,B) ) ) ), file(subset_1,m2_subset_1), [interesting(0.9),axiom,file(subset_1,m2_subset_1)]). fof(dt_k1_card_1,axiom,( ! [A] : v1_card_1(k1_card_1(A)) ), file(card_1,k1_card_1), [interesting(0.9),axiom,file(card_1,k1_card_1)]). fof(dt_k1_numbers,axiom,( $true ), file(numbers,k1_numbers), [interesting(0.9),axiom,file(numbers,k1_numbers)]). fof(dt_k1_zfmisc_1,axiom,( $true ), file(zfmisc_1,k1_zfmisc_1), [interesting(0.9),axiom,file(zfmisc_1,k1_zfmisc_1)]). fof(dt_k2_xcmplx_0,axiom,( $true ), file(xcmplx_0,k2_xcmplx_0), [interesting(0.9),axiom,file(xcmplx_0,k2_xcmplx_0)]). fof(dt_k5_finseq_1,axiom,( $true ), file(finseq_1,k5_finseq_1), [interesting(0.9),axiom,file(finseq_1,k5_finseq_1)]). fof(dt_k5_ordinal2,axiom,( $true ), file(ordinal2,k5_ordinal2), [interesting(0.9),axiom,file(ordinal2,k5_ordinal2)]). fof(dt_m1_finseq_1,axiom,( ! [A,B] : ( m1_finseq_1(B,A) => ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) ) ), file(finseq_1,m1_finseq_1), [interesting(0.9),axiom,file(finseq_1,m1_finseq_1)]). fof(dt_m1_subset_1,axiom,( $true ), file(subset_1,m1_subset_1), [interesting(0.9),axiom,file(subset_1,m1_subset_1)]). fof(dt_m2_finseq_1,axiom,( ! [A,B] : ( m2_finseq_1(B,A) => ( v1_funct_1(B) & v1_finseq_1(B) & m2_relset_1(B,k5_numbers,A) ) ) ), file(finseq_1,m2_finseq_1), [interesting(0.9),axiom,file(finseq_1,m2_finseq_1)]). fof(dt_m2_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m2_subset_1(C,A,B) => m1_subset_1(C,A) ) ) ), file(subset_1,m2_subset_1), [interesting(0.9),axiom,file(subset_1,m2_subset_1)]). fof(cc15_membered,theorem,( ! [A] : ( v1_xboole_0(A) => ( v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ) ), file(membered,cc15_membered), [interesting(0.9),axiom,file(membered,cc15_membered)]). fof(cc1_finseq_1,theorem,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) ) ), file(finseq_1,cc1_finseq_1), [interesting(0.9),axiom,file(finseq_1,cc1_finseq_1)]). fof(cc3_arytm_3,theorem,( ! [A] : ( m1_subset_1(A,k5_ordinal2) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) ) ) ), file(arytm_3,cc3_arytm_3), [interesting(0.9),axiom,file(arytm_3,cc3_arytm_3)]). fof(cc6_membered,theorem,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( v1_membered(A) & v2_membered(A) ) ) ), file(membered,cc6_membered), [interesting(0.9),axiom,file(membered,cc6_membered)]). fof(cc9_membered,theorem,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k5_numbers)) => ( v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ) ), file(membered,cc9_membered), [interesting(0.9),axiom,file(membered,cc9_membered)]). fof(fc10_trees_3,theorem,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ( v1_relat_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A)) & ~ v1_xboole_0(k5_finseq_1(A)) & v1_finset_1(k5_finseq_1(A)) & v1_finseq_1(k5_finseq_1(A)) & v4_trees_3(k5_finseq_1(A)) ) ) ), file(trees_3,fc10_trees_3), [interesting(0.9),axiom,file(trees_3,fc10_trees_3)]). fof(fc12_finseq_1,theorem,( ! [A] : ( ~ v1_xboole_0(k5_finseq_1(A)) & v1_relat_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A)) & v1_finset_1(k5_finseq_1(A)) & v1_finseq_1(k5_finseq_1(A)) ) ), file(finseq_1,fc12_finseq_1), [interesting(0.9),axiom,file(finseq_1,fc12_finseq_1)]). fof(fc13_finseq_1,theorem,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & ~ v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( ~ v1_xboole_0(k7_finseq_1(A,B)) & v1_relat_1(k7_finseq_1(A,B)) & v1_funct_1(k7_finseq_1(A,B)) & v1_finset_1(k7_finseq_1(A,B)) & v1_finseq_1(k7_finseq_1(A,B)) ) ) ), file(finseq_1,fc13_finseq_1), [interesting(0.9),axiom,file(finseq_1,fc13_finseq_1)]). fof(fc14_finseq_1,theorem,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & ~ v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( ~ v1_xboole_0(k7_finseq_1(B,A)) & v1_relat_1(k7_finseq_1(B,A)) & v1_funct_1(k7_finseq_1(B,A)) & v1_finset_1(k7_finseq_1(B,A)) & v1_finseq_1(k7_finseq_1(B,A)) ) ) ), file(finseq_1,fc14_finseq_1), [interesting(0.9),axiom,file(finseq_1,fc14_finseq_1)]). fof(fc16_trees_3,theorem,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) ) => ( v1_relat_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A)) & ~ v1_xboole_0(k5_finseq_1(A)) & v1_finset_1(k5_finseq_1(A)) & v1_finseq_1(k5_finseq_1(A)) & v6_trees_3(k5_finseq_1(A)) ) ) ), file(trees_3,fc16_trees_3), [interesting(0.9),axiom,file(trees_3,fc16_trees_3)]). fof(fc1_ordinal2,theorem, ( v1_ordinal1(k5_ordinal2) & v2_ordinal1(k5_ordinal2) & v3_ordinal1(k5_ordinal2) & ~ v1_xboole_0(k5_ordinal2) ), file(ordinal2,fc1_ordinal2), [interesting(0.9),axiom,file(ordinal2,fc1_ordinal2)]). 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(fc2_membered,theorem, ( ~ v1_xboole_0(k1_numbers) & v1_membered(k1_numbers) & v2_membered(k1_numbers) ), file(membered,fc2_membered), [interesting(0.9),axiom,file(membered,fc2_membered)]). fof(fc2_trees_2,theorem,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) ) => ( ~ v1_xboole_0(k1_relat_1(A)) & v1_trees_1(k1_relat_1(A)) ) ) ), file(trees_2,fc2_trees_2), [interesting(0.9),axiom,file(trees_2,fc2_trees_2)]). fof(fc3_finseq_1,theorem,( ! [A] : ( v1_relat_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A)) ) ), file(finseq_1,fc3_finseq_1), [interesting(0.9),axiom,file(finseq_1,fc3_finseq_1)]). fof(fc4_finseq_1,theorem,( ! [A] : ( v1_relat_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A)) & v1_finset_1(k5_finseq_1(A)) & v1_finseq_1(k5_finseq_1(A)) ) ), file(finseq_1,fc4_finseq_1), [interesting(0.9),axiom,file(finseq_1,fc4_finseq_1)]). fof(fc5_membered,theorem, ( v1_membered(k5_ordinal2) & v2_membered(k5_ordinal2) & v3_membered(k5_ordinal2) & v4_membered(k5_ordinal2) & v5_membered(k5_ordinal2) ), file(membered,fc5_membered), [interesting(0.9),axiom,file(membered,fc5_membered)]). fof(fc9_trees_3,theorem,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v6_trees_3(A) & v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v6_trees_3(B) ) => ( v1_relat_1(k7_finseq_1(A,B)) & v1_funct_1(k7_finseq_1(A,B)) & v1_finset_1(k7_finseq_1(A,B)) & v1_finseq_1(k7_finseq_1(A,B)) & v6_trees_3(k7_finseq_1(A,B)) ) ) ), file(trees_3,fc9_trees_3), [interesting(0.9),axiom,file(trees_3,fc9_trees_3)]). fof(rc1_finseq_1,theorem,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) ), file(finseq_1,rc1_finseq_1), [interesting(0.9),axiom,file(finseq_1,rc1_finseq_1)]). fof(rc1_subset_1,theorem,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) ) ) ), file(subset_1,rc1_subset_1), [interesting(0.9),axiom,file(subset_1,rc1_subset_1)]). fof(rc2_subset_1,theorem,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & v1_xboole_0(B) ) ), file(subset_1,rc2_subset_1), [interesting(0.9),axiom,file(subset_1,rc2_subset_1)]). fof(rc5_trees_2,theorem,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) ) ), file(trees_2,rc5_trees_2), [interesting(0.9),axiom,file(trees_2,rc5_trees_2)]). fof(rc8_trees_3,theorem,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v6_trees_3(A) ) ), file(trees_3,rc8_trees_3), [interesting(0.9),axiom,file(trees_3,rc8_trees_3)]). fof(t1_real,theorem,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xreal_0(A,B) & v2_xreal_0(A) ) => v2_xreal_0(B) ) ) ) ), file(real,t1_real), [interesting(0.9),axiom,file(real,t1_real)]). fof(t2_subset,theorem,( ! [A,B] : ( m1_subset_1(A,B) => ( v1_xboole_0(B) | r2_hidden(A,B) ) ) ), file(subset,t2_subset), [interesting(0.9),axiom,file(subset,t2_subset)]). fof(t3_subset,theorem,( ! [A,B] : ( m1_subset_1(A,k1_zfmisc_1(B)) <=> r1_tarski(A,B) ) ), file(subset,t3_subset), [interesting(0.9),axiom,file(subset,t3_subset)]). fof(t4_real,theorem,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( r1_xreal_0(A,B) & ~ v2_xreal_0(B) & v2_xreal_0(A) ) ) ) ), file(real,t4_real), [interesting(0.9),axiom,file(real,t4_real)]). fof(t4_subset,theorem,( ! [A,B,C] : ( ( r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) ) => m1_subset_1(A,C) ) ), file(subset,t4_subset), [interesting(0.9),axiom,file(subset,t4_subset)]). fof(t5_subset,theorem,( ! [A,B,C] : ~ ( r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) & v1_xboole_0(C) ) ), file(subset,t5_subset), [interesting(0.9),axiom,file(subset,t5_subset)]). fof(t6_boole,theorem,( ! [A] : ( v1_xboole_0(A) => A = k1_xboole_0 ) ), file(boole,t6_boole), [interesting(0.9),axiom,file(boole,t6_boole)]). fof(t8_boole,theorem,( ! [A,B] : ~ ( v1_xboole_0(A) & A != B & v1_xboole_0(B) ) ), file(boole,t8_boole), [interesting(0.9),axiom,file(boole,t8_boole)]). fof(d5_finseq_1,definition,( ! [A] : k5_finseq_1(A) = k1_tarski(k4_tarski(1,A)) ), file(finseq_1,d5_finseq_1), [interesting(0.9),axiom,file(finseq_1,d5_finseq_1)]). fof(commutativity_k1_nat_1,theorem,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => k1_nat_1(A,B) = k1_nat_1(B,A) ) ), file(nat_1,k1_nat_1), [interesting(0.9),axiom,file(nat_1,k1_nat_1)]). fof(reflexivity_r1_xreal_0,theorem,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => r1_xreal_0(A,A) ) ), file(xreal_0,r1_xreal_0), [interesting(0.9),axiom,file(xreal_0,r1_xreal_0)]). fof(connectedness_r1_xreal_0,theorem,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( r1_xreal_0(A,B) | r1_xreal_0(B,A) ) ) ), file(xreal_0,r1_xreal_0), [interesting(0.9),axiom,file(xreal_0,r1_xreal_0)]). fof(antisymmetry_r2_hidden,theorem,( ! [A,B] : ( r2_hidden(A,B) => ~ r2_hidden(B,A) ) ), file(hidden,r2_hidden), [interesting(0.9),axiom,file(hidden,r2_hidden)]). fof(redefinition_k12_finseq_1,definition,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => k12_finseq_1(A,B) = k5_finseq_1(B) ) ), file(finseq_1,k12_finseq_1), [interesting(0.9),axiom,file(finseq_1,k12_finseq_1)]). fof(redefinition_k1_nat_1,definition,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => k1_nat_1(A,B) = k2_xcmplx_0(A,B) ) ), file(nat_1,k1_nat_1), [interesting(0.9),axiom,file(nat_1,k1_nat_1)]). fof(redefinition_k3_finseq_1,definition,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => k3_finseq_1(A) = k1_card_1(A) ) ), file(finseq_1,k3_finseq_1), [interesting(0.9),axiom,file(finseq_1,k3_finseq_1)]). fof(redefinition_k4_finseq_1,definition,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => k4_finseq_1(A) = k1_relat_1(A) ) ), file(finseq_1,k4_finseq_1), [interesting(0.9),axiom,file(finseq_1,k4_finseq_1)]). fof(redefinition_k5_numbers,definition,( k5_numbers = k5_ordinal2 ), file(numbers,k5_numbers), [interesting(0.9),axiom,file(numbers,k5_numbers)]). fof(dt_k12_finseq_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => m2_finseq_1(k12_finseq_1(A,B),A) ) ), file(finseq_1,k12_finseq_1), [interesting(0.9),axiom,file(finseq_1,k12_finseq_1)]). fof(dt_k1_funct_1,axiom,( $true ), file(funct_1,k1_funct_1), [interesting(0.9),axiom,file(funct_1,k1_funct_1)]). fof(dt_k1_nat_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => m2_subset_1(k1_nat_1(A,B),k1_numbers,k5_numbers) ) ), file(nat_1,k1_nat_1), [interesting(0.9),axiom,file(nat_1,k1_nat_1)]). fof(dt_k1_relat_1,axiom,( $true ), file(relat_1,k1_relat_1), [interesting(0.9),axiom,file(relat_1,k1_relat_1)]). fof(dt_k3_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => m2_subset_1(k3_finseq_1(A),k1_numbers,k5_numbers) ) ), file(finseq_1,k3_finseq_1), [interesting(0.9),axiom,file(finseq_1,k3_finseq_1)]). fof(dt_k4_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => m1_subset_1(k4_finseq_1(A),k1_zfmisc_1(k5_numbers)) ) ), file(finseq_1,k4_finseq_1), [interesting(0.9),axiom,file(finseq_1,k4_finseq_1)]). fof(dt_k4_trees_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) & m1_finseq_1(B,k5_numbers) ) => ( ~ v1_xboole_0(k4_trees_1(A,B)) & v1_trees_1(k4_trees_1(A,B)) ) ) ), file(trees_1,k4_trees_1), [interesting(0.9),axiom,file(trees_1,k4_trees_1)]). fof(dt_k4_trees_4,axiom,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( v1_relat_1(k4_trees_4(A,B)) & v1_funct_1(k4_trees_4(A,B)) & v3_trees_2(k4_trees_4(A,B)) ) ) ), file(trees_4,k4_trees_4), [interesting(0.9),axiom,file(trees_4,k4_trees_4)]). fof(dt_k5_funct_6,axiom,( $true ), file(funct_6,k5_funct_6), [interesting(0.9),axiom,file(funct_6,k5_funct_6)]). fof(dt_k5_numbers,axiom,( m1_subset_1(k5_numbers,k1_zfmisc_1(k1_numbers)) ), file(numbers,k5_numbers), [interesting(0.9),axiom,file(numbers,k5_numbers)]). fof(dt_k5_trees_2,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) & m1_finseq_1(B,k5_numbers) ) => ( v1_relat_1(k5_trees_2(A,B)) & v1_funct_1(k5_trees_2(A,B)) & v3_trees_2(k5_trees_2(A,B)) ) ) ), file(trees_2,k5_trees_2), [interesting(0.9),axiom,file(trees_2,k5_trees_2)]). fof(dt_k7_finseq_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( v1_relat_1(k7_finseq_1(A,B)) & v1_funct_1(k7_finseq_1(A,B)) & v1_finseq_1(k7_finseq_1(A,B)) ) ) ), file(finseq_1,k7_finseq_1), [interesting(0.9),axiom,file(finseq_1,k7_finseq_1)]). fof(dt_c1_30__trees_4,assumption,( $true ), introduced(assumption,[file(trees_4,c1_30__trees_4)]), [interesting(0.8),axiom,file(trees_4,c1_30__trees_4)]). fof(dt_c2_30__trees_4,assumption, ( v1_relat_1(c2_30__trees_4) & v1_funct_1(c2_30__trees_4) & v1_finseq_1(c2_30__trees_4) & v6_trees_3(c2_30__trees_4) ), introduced(assumption,[file(trees_4,c2_30__trees_4)]), [interesting(0.8),axiom,file(trees_4,c2_30__trees_4)]). fof(dt_c3_30__trees_4,assumption,( m2_subset_1(c3_30__trees_4,k1_numbers,k5_numbers) ), introduced(assumption,[file(trees_4,c3_30__trees_4)]), [interesting(0.8),axiom,file(trees_4,c3_30__trees_4)]). fof(dt_c4_30__trees_4,assumption, ( v1_relat_1(c4_30__trees_4) & v1_funct_1(c4_30__trees_4) & v1_finseq_1(c4_30__trees_4) ), introduced(assumption,[file(trees_4,c4_30__trees_4)]), [interesting(0.8),axiom,file(trees_4,c4_30__trees_4)]). fof(t1_subset,theorem,( ! [A,B] : ( r2_hidden(A,B) => m1_subset_1(A,B) ) ), file(subset,t1_subset), [interesting(0.9),axiom,file(subset,t1_subset)]). fof(t7_boole,theorem,( ! [A,B] : ~ ( r2_hidden(A,B) & v1_xboole_0(B) ) ), file(boole,t7_boole), [interesting(0.9),axiom,file(boole,t7_boole)]). fof(de_c5_30__trees_4,definition,( c5_30__trees_4 = c4_30__trees_4 ), introduced(definition,[new_symbol(c5_30__trees_4),file(trees_4,c5_30__trees_4)]), [interesting(0.8),axiom,file(trees_4,c5_30__trees_4)]). fof(spc1_boole,theorem,( ~ v1_xboole_0(1) ), file(boole,spc1_boole), [interesting(0.9),axiom,file(boole,spc1_boole)]). fof(spc1_numerals,theorem, ( v2_xreal_0(1) & m2_subset_1(1,k1_numbers,k5_numbers) & m1_subset_1(1,k5_numbers) & m1_subset_1(1,k1_numbers) ), file(numerals,spc1_numerals), [interesting(0.9),axiom,file(numerals,spc1_numerals)]). fof(existence_m1_trees_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ? [B] : m1_trees_1(B,A) ) ), file(trees_1,m1_trees_1), [interesting(0.9),axiom,file(trees_1,m1_trees_1)]). fof(redefinition_m1_trees_1,definition,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( m1_trees_1(B,A) <=> m1_subset_1(B,A) ) ) ), file(trees_1,m1_trees_1), [interesting(0.9),axiom,file(trees_1,m1_trees_1)]). fof(dt_m1_trees_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( m1_trees_1(B,A) => m2_finseq_1(B,k5_numbers) ) ) ), file(trees_1,m1_trees_1), [interesting(0.9),axiom,file(trees_1,m1_trees_1)]). fof(e2_30__trees_4,plain,( m1_trees_1(k7_finseq_1(k12_finseq_1(k5_numbers,c3_30__trees_4),c4_30__trees_4),k1_relat_1(k4_trees_4(c1_30__trees_4,c2_30__trees_4))) ), inference(mizar_by,[status(thm),assumptions([dt_c1_30__trees_4,dt_c2_30__trees_4,dt_c3_30__trees_4,dt_c4_30__trees_4,e1_30__trees_4])],[commutativity_k2_tarski,existence_m1_relset_1,dt_k2_tarski,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,cc7_trees_3,fc10_membered,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,fc3_subset_1,fc4_subset_1,fc7_membered,fc8_membered,fc8_trees_3,fc9_membered,rc2_finseq_1,rc3_finseq_1,rc4_finseq_1,rc5_trees_3,rc6_finseq_1,rc7_trees_3,rc9_trees_2,reflexivity_r1_tarski,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_tarski,dt_k1_xboole_0,dt_k4_tarski,dt_m1_finseq_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_arytm_3,cc1_membered,cc20_membered,cc2_arytm_3,cc2_membered,cc3_membered,cc4_membered,fc11_membered,fc13_trees_3,fc17_finseq_1,fc2_finseq_1,fc2_subset_1,fc5_trees_2,fc6_membered,fc7_trees_3,rc1_arytm_3,rc1_membered,rc6_trees_3,rc7_finseq_1,rc7_trees_2,rc8_finseq_1,spc1_boole,d5_tarski,spc1_numerals,spc1_boole,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_subset_1,redefinition_m2_finseq_1,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k5_finseq_1,dt_k5_ordinal2,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_subset_1,cc15_membered,cc1_finseq_1,cc3_arytm_3,cc6_membered,cc9_membered,fc10_trees_3,fc12_finseq_1,fc13_finseq_1,fc14_finseq_1,fc16_trees_3,fc1_ordinal2,fc1_subset_1,fc2_membered,fc2_trees_2,fc3_finseq_1,fc4_finseq_1,fc5_membered,fc9_trees_3,rc1_finseq_1,rc1_subset_1,rc2_subset_1,rc5_trees_2,rc8_trees_3,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,d5_finseq_1,antisymmetry_r2_hidden,existence_m1_trees_1,redefinition_k12_finseq_1,redefinition_k5_numbers,redefinition_m1_trees_1,dt_k12_finseq_1,dt_k1_relat_1,dt_k4_trees_4,dt_k5_numbers,dt_k7_finseq_1,dt_m1_trees_1,dt_c1_30__trees_4,dt_c2_30__trees_4,dt_c3_30__trees_4,dt_c4_30__trees_4,t1_subset,t7_boole,e1_30__trees_4]), [interesting(0.8),file(trees_4,e2_30__trees_4),[file(trees_4,e2_30__trees_4)]]). fof(t50_finseq_1,theorem,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( m2_finseq_1(k7_finseq_1(A,B),C) => ( m2_finseq_1(A,C) & m2_finseq_1(B,C) ) ) ) ) ), file(finseq_1,t50_finseq_1), [interesting(0.9),axiom,file(finseq_1,t50_finseq_1)]). fof(e3_30__trees_4,plain,( m2_finseq_1(c4_30__trees_4,k5_numbers) ), inference(mizar_by,[status(thm),assumptions([dt_c1_30__trees_4,dt_c2_30__trees_4,dt_c3_30__trees_4,dt_c4_30__trees_4,e1_30__trees_4])],[commutativity_k2_tarski,dt_k2_tarski,fc10_membered,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,fc3_subset_1,fc7_membered,fc8_membered,fc9_membered,rc3_finseq_1,rc4_finseq_1,rc6_finseq_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_m1_relset_1,dt_k1_tarski,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_k4_tarski,dt_m1_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_arytm_3,cc1_membered,cc1_relset_1,cc20_membered,cc2_arytm_3,cc2_membered,cc3_membered,cc4_membered,cc7_trees_3,fc11_membered,fc2_finseq_1,fc2_subset_1,fc4_subset_1,fc6_membered,fc7_trees_3,fc8_trees_3,rc1_arytm_3,rc1_membered,rc2_finseq_1,rc5_trees_3,rc7_trees_3,rc9_trees_2,spc1_boole,t1_subset,t4_subset,t5_subset,d5_tarski,spc1_numerals,spc1_boole,existence_m1_finseq_1,existence_m1_subset_1,existence_m2_relset_1,existence_m2_subset_1,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k5_finseq_1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m1_subset_1,dt_m2_relset_1,dt_m2_subset_1,cc15_membered,cc3_arytm_3,cc6_membered,cc9_membered,fc10_trees_3,fc12_finseq_1,fc13_finseq_1,fc13_trees_3,fc14_finseq_1,fc16_trees_3,fc17_finseq_1,fc1_ordinal2,fc1_subset_1,fc2_membered,fc2_trees_2,fc3_finseq_1,fc4_finseq_1,fc5_membered,fc5_trees_2,fc9_trees_3,rc1_subset_1,rc2_subset_1,rc5_trees_2,rc6_trees_3,rc7_finseq_1,rc7_trees_2,rc8_finseq_1,rc8_trees_3,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,d5_finseq_1,existence_m1_trees_1,existence_m2_finseq_1,redefinition_k12_finseq_1,redefinition_k5_numbers,redefinition_m1_trees_1,redefinition_m2_finseq_1,dt_k12_finseq_1,dt_k1_relat_1,dt_k4_trees_4,dt_k5_numbers,dt_k7_finseq_1,dt_m1_trees_1,dt_m2_finseq_1,dt_c1_30__trees_4,dt_c2_30__trees_4,dt_c3_30__trees_4,dt_c4_30__trees_4,cc1_finseq_1,rc1_finseq_1,e2_30__trees_4,t50_finseq_1]), [interesting(0.8),file(trees_4,e3_30__trees_4),[file(trees_4,e3_30__trees_4)]]). fof(dt_c5_30__trees_4,plain,( m2_finseq_1(c5_30__trees_4,k5_numbers) ), inference(mizar_by,[status(thm),assumptions([dt_c1_30__trees_4,dt_c2_30__trees_4,dt_c3_30__trees_4,dt_c4_30__trees_4,e1_30__trees_4])],[rc3_finseq_1,rc4_finseq_1,rc6_finseq_1,antisymmetry_r2_hidden,dt_k1_xboole_0,fc2_finseq_1,fc6_membered,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_arytm_3,cc1_membered,cc1_relset_1,cc20_membered,cc2_arytm_3,cc2_membered,cc3_membered,cc4_membered,fc4_subset_1,rc1_arytm_3,rc1_membered,rc1_subset_1,rc2_finseq_1,rc2_subset_1,rc7_finseq_1,rc8_finseq_1,rc9_trees_2,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_finseq_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m1_subset_1,dt_m2_relset_1,cc1_finseq_1,cc3_arytm_3,cc6_membered,cc9_membered,fc1_ordinal2,fc1_subset_1,fc2_membered,fc5_membered,rc1_finseq_1,t3_subset,existence_m2_finseq_1,redefinition_k5_numbers,redefinition_m2_finseq_1,dt_k5_numbers,dt_m2_finseq_1,dt_c4_30__trees_4,de_c5_30__trees_4,e3_30__trees_4]), [interesting(0.8),file(trees_4,c5_30__trees_4),[file(trees_4,c5_30__trees_4)]]). fof(rqLessOrEqual__r1_xreal_0__r1_r1,theorem,( r1_xreal_0(1,1) ), file(arithm,rqLessOrEqual__r1_xreal_0__r1_r1), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r1_r1)]). fof(fc23_trees_3,theorem,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v5_trees_3(A) ) => ( ~ v1_xboole_0(k13_trees_3(A)) & v1_finset_1(k13_trees_3(A)) & v1_trees_1(k13_trees_3(A)) ) ) ), file(trees_3,fc23_trees_3), [interesting(0.9),axiom,file(trees_3,fc23_trees_3)]). fof(fc11_finseq_1,theorem,( ! [A] : ( ( v1_relat_1(A) & v1_finset_1(A) ) => v1_finset_1(k2_relat_1(A)) ) ), file(finseq_1,fc11_finseq_1), [interesting(0.9),axiom,file(finseq_1,fc11_finseq_1)]). fof(redefinition_k8_finseq_1,definition,( ! [A,B,C] : ( ( m1_finseq_1(B,A) & m1_finseq_1(C,A) ) => k8_finseq_1(A,B,C) = k7_finseq_1(B,C) ) ), file(finseq_1,k8_finseq_1), [interesting(0.9),axiom,file(finseq_1,k8_finseq_1)]). fof(dt_k13_trees_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( ~ v1_xboole_0(k13_trees_3(A)) & v1_trees_1(k13_trees_3(A)) ) ) ), file(trees_3,k13_trees_3), [interesting(0.9),axiom,file(trees_3,k13_trees_3)]). fof(dt_k2_funct_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_relat_1(k2_funct_6(A)) & v1_funct_1(k2_funct_6(A)) ) ) ), file(funct_6,k2_funct_6), [interesting(0.9),axiom,file(funct_6,k2_funct_6)]). 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_finseq_1,axiom,( ! [A,B,C] : ( ( m1_finseq_1(B,A) & m1_finseq_1(C,A) ) => m2_finseq_1(k8_finseq_1(A,B,C),A) ) ), file(finseq_1,k8_finseq_1), [interesting(0.9),axiom,file(finseq_1,k8_finseq_1)]). fof(fc19_trees_3,theorem,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v6_trees_3(A) ) => ( v1_relat_1(k2_funct_6(A)) & v1_funct_1(k2_funct_6(A)) & v1_finset_1(k2_funct_6(A)) & v1_finseq_1(k2_funct_6(A)) & v4_trees_3(k2_funct_6(A)) ) ) ), file(trees_3,fc19_trees_3), [interesting(0.9),axiom,file(trees_3,fc19_trees_3)]). fof(t10_trees_4,theorem,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v6_trees_3(B) ) => k1_relat_1(k4_trees_4(A,B)) = k13_trees_3(k2_funct_6(B)) ) ), file(trees_4,t10_trees_4), [interesting(0.9),axiom,file(trees_4,t10_trees_4)]). fof(t46_trees_1,theorem,( ! [A] : ( m2_finseq_1(A,k5_numbers) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_trees_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ( r2_hidden(k7_finseq_1(A,C),B) => r2_hidden(A,B) ) ) ) ) ), file(trees_1,t46_trees_1), [interesting(0.9),axiom,file(trees_1,t46_trees_1)]). fof(t40_trees_3,theorem,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v6_trees_3(A) ) => k3_finseq_1(k2_funct_6(A)) = k3_finseq_1(A) ) ), file(trees_3,t40_trees_3), [interesting(0.9),axiom,file(trees_3,t40_trees_3)]). fof(e4_30__trees_4,plain, ( r2_hidden(k12_finseq_1(k5_numbers,c3_30__trees_4),k1_relat_1(k4_trees_4(c1_30__trees_4,c2_30__trees_4))) & r2_hidden(k7_finseq_1(k12_finseq_1(k5_numbers,c3_30__trees_4),c4_30__trees_4),k13_trees_3(k2_funct_6(c2_30__trees_4))) & k3_finseq_1(k2_funct_6(c2_30__trees_4)) = k3_finseq_1(c2_30__trees_4) ), inference(mizar_by,[status(thm),assumptions([dt_c1_30__trees_4,dt_c2_30__trees_4,dt_c3_30__trees_4,dt_c4_30__trees_4,e1_30__trees_4])],[commutativity_k2_tarski,dt_k2_tarski,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,fc3_subset_1,reflexivity_r1_tarski,existence_m1_relset_1,dt_k1_tarski,dt_k2_zfmisc_1,dt_k4_tarski,dt_m1_relset_1,cc1_arytm_3,cc1_relset_1,cc2_arytm_3,cc7_trees_3,fc10_membered,fc11_membered,fc23_trees_3,fc2_subset_1,fc4_subset_1,fc7_membered,fc8_membered,fc8_trees_3,fc9_membered,rc1_arytm_3,rc2_finseq_1,rc3_finseq_1,rc4_finseq_1,rc5_trees_3,rc6_finseq_1,rc7_trees_3,rc9_trees_2,spc1_boole,d5_tarski,spc1_numerals,spc1_boole,existence_m1_finseq_1,existence_m1_subset_1,existence_m2_relset_1,existence_m2_subset_1,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k1_card_1,dt_k1_numbers,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_finseq_1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m1_subset_1,dt_m2_relset_1,dt_m2_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_arytm_3,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc10_trees_3,fc12_finseq_1,fc13_trees_3,fc16_trees_3,fc17_finseq_1,fc1_ordinal2,fc1_subset_1,fc2_finseq_1,fc2_membered,fc2_trees_2,fc3_finseq_1,fc4_finseq_1,fc5_membered,fc5_trees_2,fc6_membered,fc7_trees_3,rc1_membered,rc1_subset_1,rc2_subset_1,rc5_trees_2,rc6_trees_3,rc7_finseq_1,rc7_trees_2,rc8_finseq_1,t2_subset,t3_subset,t4_subset,t5_subset,d5_finseq_1,antisymmetry_r2_hidden,existence_m2_finseq_1,redefinition_k12_finseq_1,redefinition_k3_finseq_1,redefinition_k5_numbers,redefinition_m2_finseq_1,dt_k12_finseq_1,dt_k13_trees_3,dt_k1_relat_1,dt_k2_funct_6,dt_k3_finseq_1,dt_k4_trees_4,dt_k5_numbers,dt_k7_finseq_1,dt_m2_finseq_1,dt_c1_30__trees_4,dt_c2_30__trees_4,dt_c3_30__trees_4,dt_c4_30__trees_4,cc15_membered,cc1_finseq_1,fc13_finseq_1,fc14_finseq_1,fc19_trees_3,fc9_trees_3,rc1_finseq_1,rc8_trees_3,t1_subset,t6_boole,t7_boole,t8_boole,e1_30__trees_4,t10_trees_4,t46_trees_1,t40_trees_3]), [interesting(0.8),file(trees_4,e4_30__trees_4),[file(trees_4,e4_30__trees_4)]]). fof(d9_trees_1,definition,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( m2_finseq_1(B,k5_numbers) => ( r2_hidden(B,A) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_trees_1(C) ) => ( C = k4_trees_1(A,B) <=> ! [D] : ( m2_finseq_1(D,k5_numbers) => ( r2_hidden(D,C) <=> r2_hidden(k8_finseq_1(k5_numbers,B,D),A) ) ) ) ) ) ) ) ), file(trees_1,d9_trees_1), [interesting(0.9),axiom,file(trees_1,d9_trees_1)]). fof(t51_trees_3,theorem,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ( v4_trees_3(B) => ( r2_hidden(k7_finseq_1(k12_finseq_1(k5_numbers,A),C),k13_trees_3(B)) <=> ( ~ r1_xreal_0(k3_finseq_1(B),A) & r2_hidden(C,k1_funct_1(B,k1_nat_1(A,1))) ) ) ) ) ) ) ), file(trees_3,t51_trees_3), [interesting(0.9),axiom,file(trees_3,t51_trees_3)]). fof(e5_30__trees_4,plain, ( r2_hidden(c5_30__trees_4,k4_trees_1(k1_relat_1(k4_trees_4(c1_30__trees_4,c2_30__trees_4)),k12_finseq_1(k5_numbers,c3_30__trees_4))) & ~ r1_xreal_0(k3_finseq_1(c2_30__trees_4),c3_30__trees_4) ), inference(mizar_by,[status(thm),assumptions([dt_c1_30__trees_4,dt_c2_30__trees_4,dt_c3_30__trees_4,dt_c4_30__trees_4,e1_30__trees_4])],[commutativity_k2_tarski,dt_k2_tarski,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,fc3_subset_1,reflexivity_r1_tarski,existence_m1_relset_1,dt_k1_tarski,dt_k2_zfmisc_1,dt_k4_tarski,dt_m1_relset_1,cc1_arytm_3,cc1_relset_1,cc2_arytm_3,cc7_trees_3,fc10_membered,fc11_membered,fc23_trees_3,fc2_subset_1,fc4_subset_1,fc7_membered,fc8_membered,fc8_trees_3,fc9_membered,rc1_arytm_3,rc2_finseq_1,rc3_finseq_1,rc4_finseq_1,rc5_trees_3,rc6_finseq_1,rc7_trees_3,rc9_trees_2,spc6_arithm,d5_tarski,commutativity_k2_xcmplx_0,existence_m1_finseq_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_card_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_xcmplx_0,dt_k5_finseq_1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m1_subset_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_arytm_3,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc10_trees_3,fc12_finseq_1,fc13_trees_3,fc16_trees_3,fc17_finseq_1,fc19_trees_3,fc1_ordinal2,fc1_subset_1,fc2_finseq_1,fc2_trees_2,fc3_finseq_1,fc4_finseq_1,fc5_membered,fc5_trees_2,fc6_membered,fc9_trees_3,rc1_membered,rc1_subset_1,rc2_subset_1,rc5_trees_2,rc6_trees_3,rc7_finseq_1,rc7_trees_2,rc8_finseq_1,rc8_trees_3,t1_real,t2_subset,t3_subset,t4_real,t4_subset,t5_subset,d5_finseq_1,commutativity_k1_nat_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,existence_m2_finseq_1,existence_m2_subset_1,redefinition_k12_finseq_1,redefinition_k1_nat_1,redefinition_k3_finseq_1,redefinition_k5_numbers,redefinition_k8_finseq_1,redefinition_m2_finseq_1,redefinition_m2_subset_1,dt_k12_finseq_1,dt_k13_trees_3,dt_k1_funct_1,dt_k1_nat_1,dt_k1_numbers,dt_k1_relat_1,dt_k2_funct_6,dt_k3_finseq_1,dt_k4_trees_1,dt_k4_trees_4,dt_k5_numbers,dt_k7_finseq_1,dt_k8_finseq_1,dt_m2_finseq_1,dt_m2_subset_1,dt_c1_30__trees_4,dt_c2_30__trees_4,dt_c3_30__trees_4,dt_c4_30__trees_4,dt_c5_30__trees_4,de_c5_30__trees_4,cc15_membered,cc1_finseq_1,fc13_finseq_1,fc14_finseq_1,fc2_membered,fc7_trees_3,rc1_finseq_1,rqLessOrEqual__r1_xreal_0__r1_r1,spc1_boole,t1_subset,t6_boole,t7_boole,t8_boole,spc1_numerals,spc1_boole,e4_30__trees_4,e1_30__trees_4,d9_trees_1,t51_trees_3]), [interesting(0.8),file(trees_4,e5_30__trees_4),[file(trees_4,e5_30__trees_4)]]). fof(d4_trees_4,definition,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( v6_trees_3(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v3_trees_2(C) ) => ( C = k4_trees_4(A,B) <=> ( ? [D] : ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) & v6_trees_3(D) & B = D & k1_relat_1(C) = k13_trees_3(k2_funct_6(D)) ) & k1_funct_1(C,k1_xboole_0) = A & ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ( ~ r1_xreal_0(k3_finseq_1(B),D) => k5_trees_2(C,k12_finseq_1(k5_numbers,D)) = k1_funct_1(B,k1_nat_1(D,1)) ) ) ) ) ) ) ) ), file(trees_4,d4_trees_4), [interesting(0.9),axiom,file(trees_4,d4_trees_4)]). fof(l5_trees_4,plain,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( ~ r1_xreal_0(k3_finseq_1(B),A) => ( r2_hidden(k1_nat_1(A,1),k4_finseq_1(B)) & r2_hidden(k1_funct_1(B,k1_nat_1(A,1)),k2_relat_1(B)) ) ) ) ) ), file(trees_4,l5_trees_4), [interesting(0.9),axiom,file(trees_4,l5_trees_4)]). fof(d11_trees_2,definition,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) ) => ! [B] : ( m2_finseq_1(B,k5_numbers) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v3_trees_2(C) ) => ( C = k5_trees_2(A,B) <=> ( k1_relat_1(C) = k4_trees_1(k1_relat_1(A),B) & ! [D] : ( m2_finseq_1(D,k5_numbers) => ( r2_hidden(D,k4_trees_1(k1_relat_1(A),B)) => k1_funct_1(C,D) = k1_funct_1(A,k8_finseq_1(k5_numbers,B,D)) ) ) ) ) ) ) ) ), file(trees_2,d11_trees_2), [interesting(0.9),axiom,file(trees_2,d11_trees_2)]). fof(e6_30__trees_4,plain, ( k1_relat_1(k5_trees_2(k4_trees_4(c1_30__trees_4,c2_30__trees_4),k12_finseq_1(k5_numbers,c3_30__trees_4))) = k4_trees_1(k1_relat_1(k4_trees_4(c1_30__trees_4,c2_30__trees_4)),k12_finseq_1(k5_numbers,c3_30__trees_4)) & r2_hidden(k1_nat_1(c3_30__trees_4,1),k4_finseq_1(c2_30__trees_4)) & k1_funct_1(k5_trees_2(k4_trees_4(c1_30__trees_4,c2_30__trees_4),k12_finseq_1(k5_numbers,c3_30__trees_4)),c5_30__trees_4) = k1_funct_1(k4_trees_4(c1_30__trees_4,c2_30__trees_4),k7_finseq_1(k12_finseq_1(k5_numbers,c3_30__trees_4),c4_30__trees_4)) & k1_funct_1(c2_30__trees_4,k1_nat_1(c3_30__trees_4,1)) = k5_trees_2(k4_trees_4(c1_30__trees_4,c2_30__trees_4),k12_finseq_1(k5_numbers,c3_30__trees_4)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_30__trees_4,dt_c2_30__trees_4,dt_c3_30__trees_4,dt_c4_30__trees_4,e1_30__trees_4])],[commutativity_k2_tarski,dt_k2_tarski,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,fc3_subset_1,reflexivity_r1_tarski,existence_m1_relset_1,dt_k1_tarski,dt_k2_zfmisc_1,dt_k4_tarski,dt_m1_relset_1,cc1_arytm_3,cc1_relset_1,cc2_arytm_3,cc7_trees_3,fc10_membered,fc11_membered,fc23_trees_3,fc2_subset_1,fc4_subset_1,fc7_membered,fc8_membered,fc8_trees_3,fc9_membered,rc1_arytm_3,rc2_finseq_1,rc5_trees_3,rc7_trees_3,rc9_trees_2,spc6_arithm,d5_tarski,commutativity_k2_xcmplx_0,existence_m1_finseq_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_card_1,dt_k1_zfmisc_1,dt_k2_xcmplx_0,dt_k5_finseq_1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m1_subset_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_arytm_3,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc10_trees_3,fc11_finseq_1,fc12_finseq_1,fc13_finseq_1,fc13_trees_3,fc14_finseq_1,fc16_trees_3,fc17_finseq_1,fc1_ordinal2,fc1_subset_1,fc3_finseq_1,fc4_finseq_1,fc5_membered,fc5_trees_2,fc7_trees_3,rc1_membered,rc1_subset_1,rc2_subset_1,rc3_finseq_1,rc4_finseq_1,rc6_finseq_1,rc6_trees_3,rc7_finseq_1,rc7_trees_2,rc8_finseq_1,rc8_trees_3,t1_real,t2_subset,t3_subset,t4_real,t4_subset,t5_subset,t8_boole,d5_finseq_1,commutativity_k1_nat_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,existence_m2_finseq_1,existence_m2_subset_1,redefinition_k12_finseq_1,redefinition_k1_nat_1,redefinition_k3_finseq_1,redefinition_k4_finseq_1,redefinition_k5_numbers,redefinition_k8_finseq_1,redefinition_m2_finseq_1,redefinition_m2_subset_1,dt_k12_finseq_1,dt_k13_trees_3,dt_k1_funct_1,dt_k1_nat_1,dt_k1_numbers,dt_k1_relat_1,dt_k1_xboole_0,dt_k2_funct_6,dt_k2_relat_1,dt_k3_finseq_1,dt_k4_finseq_1,dt_k4_trees_1,dt_k4_trees_4,dt_k5_numbers,dt_k5_trees_2,dt_k7_finseq_1,dt_k8_finseq_1,dt_m2_finseq_1,dt_m2_subset_1,dt_c1_30__trees_4,dt_c2_30__trees_4,dt_c3_30__trees_4,dt_c4_30__trees_4,dt_c5_30__trees_4,de_c5_30__trees_4,cc1_finseq_1,fc19_trees_3,fc2_finseq_1,fc2_membered,fc2_trees_2,fc6_membered,fc9_trees_3,rc1_finseq_1,rc5_trees_2,rqLessOrEqual__r1_xreal_0__r1_r1,t1_subset,t6_boole,t7_boole,spc1_numerals,spc1_boole,e5_30__trees_4,d4_trees_4,l5_trees_4,d11_trees_2]), [interesting(0.8),file(trees_4,e6_30__trees_4),[file(trees_4,e6_30__trees_4)]]). fof(t44_funct_6,theorem,( ! [A,B,C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ( ( r2_hidden(A,k1_relat_1(C)) & D = k1_funct_1(C,A) & r2_hidden(B,k1_relat_1(D)) ) => k5_funct_6(C,A,B) = k1_funct_1(D,B) ) ) ) ), file(funct_6,t44_funct_6), [interesting(0.9),axiom,file(funct_6,t44_funct_6)]). fof(e7_30__trees_4,plain,( k1_funct_1(k4_trees_4(c1_30__trees_4,c2_30__trees_4),k7_finseq_1(k12_finseq_1(k5_numbers,c3_30__trees_4),c4_30__trees_4)) = k5_funct_6(c2_30__trees_4,k1_nat_1(c3_30__trees_4,1),c4_30__trees_4) ), inference(mizar_by,[status(thm),assumptions([dt_c1_30__trees_4,dt_c2_30__trees_4,dt_c3_30__trees_4,dt_c4_30__trees_4,e1_30__trees_4])],[commutativity_k2_tarski,existence_m1_relset_1,dt_k2_tarski,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,cc7_trees_3,fc10_membered,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,fc3_subset_1,fc4_subset_1,fc8_trees_3,fc9_membered,rc2_finseq_1,rc3_finseq_1,rc4_finseq_1,rc5_trees_3,rc6_finseq_1,rc7_trees_3,rc9_trees_2,reflexivity_r1_tarski,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_tarski,dt_k1_xboole_0,dt_k4_tarski,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_arytm_3,cc1_membered,cc20_membered,cc2_arytm_3,cc2_membered,cc3_membered,cc4_membered,fc11_membered,fc13_trees_3,fc17_finseq_1,fc2_finseq_1,fc2_subset_1,fc5_trees_2,fc6_membered,fc7_membered,fc7_trees_3,fc8_membered,rc1_arytm_3,rc1_membered,rc6_trees_3,rc7_finseq_1,rc7_trees_2,rc8_finseq_1,spc6_arithm,d5_tarski,commutativity_k2_xcmplx_0,existence_m1_finseq_1,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_subset_1,redefinition_m2_finseq_1,redefinition_m2_subset_1,dt_k1_card_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k2_xcmplx_0,dt_k5_finseq_1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_subset_1,cc15_membered,cc1_finseq_1,cc3_arytm_3,cc6_membered,cc9_membered,fc10_trees_3,fc12_finseq_1,fc13_finseq_1,fc14_finseq_1,fc16_trees_3,fc1_ordinal2,fc1_subset_1,fc2_membered,fc2_trees_2,fc3_finseq_1,fc4_finseq_1,fc5_membered,fc9_trees_3,rc1_finseq_1,rc1_subset_1,rc2_subset_1,rc5_trees_2,rc8_trees_3,t1_real,t2_subset,t3_subset,t4_real,t4_subset,t5_subset,t6_boole,t8_boole,d5_finseq_1,commutativity_k1_nat_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,redefinition_k12_finseq_1,redefinition_k1_nat_1,redefinition_k3_finseq_1,redefinition_k4_finseq_1,redefinition_k5_numbers,dt_k12_finseq_1,dt_k1_funct_1,dt_k1_nat_1,dt_k1_relat_1,dt_k3_finseq_1,dt_k4_finseq_1,dt_k4_trees_1,dt_k4_trees_4,dt_k5_funct_6,dt_k5_numbers,dt_k5_trees_2,dt_k7_finseq_1,dt_c1_30__trees_4,dt_c2_30__trees_4,dt_c3_30__trees_4,dt_c4_30__trees_4,dt_c5_30__trees_4,de_c5_30__trees_4,rqLessOrEqual__r1_xreal_0__r1_r1,t1_subset,t7_boole,spc1_numerals,spc1_boole,e6_30__trees_4,e5_30__trees_4,t44_funct_6]), [interesting(0.8),file(trees_4,e7_30__trees_4),[file(trees_4,e7_30__trees_4)]]). fof(i6_30__trees_4,theorem,( $true ), introduced(tautology,[file(trees_4,i6_30__trees_4)]), [interesting(0.8),trivial,file(trees_4,i6_30__trees_4)]). fof(i5_30__trees_4,plain,( k1_funct_1(k4_trees_4(c1_30__trees_4,c2_30__trees_4),k7_finseq_1(k12_finseq_1(k5_numbers,c3_30__trees_4),c4_30__trees_4)) = k5_funct_6(c2_30__trees_4,k1_nat_1(c3_30__trees_4,1),c4_30__trees_4) ), inference(conclusion,[status(thm),assumptions([dt_c1_30__trees_4,dt_c2_30__trees_4,dt_c3_30__trees_4,dt_c4_30__trees_4,e1_30__trees_4])],[e7_30__trees_4,i6_30__trees_4]), [interesting(0.8),file(trees_4,i5_30__trees_4),[file(trees_4,i5_30__trees_4)]]). fof(i4_30__trees_4,plain, ( r2_hidden(k7_finseq_1(k12_finseq_1(k5_numbers,c3_30__trees_4),c4_30__trees_4),k1_relat_1(k4_trees_4(c1_30__trees_4,c2_30__trees_4))) => k1_funct_1(k4_trees_4(c1_30__trees_4,c2_30__trees_4),k7_finseq_1(k12_finseq_1(k5_numbers,c3_30__trees_4),c4_30__trees_4)) = k5_funct_6(c2_30__trees_4,k1_nat_1(c3_30__trees_4,1),c4_30__trees_4) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_30__trees_4,dt_c2_30__trees_4,dt_c3_30__trees_4,dt_c4_30__trees_4]),discharge_asm(discharge,[e1_30__trees_4])],[e1_30__trees_4,i5_30__trees_4]), [interesting(0.8),file(trees_4,i4_30__trees_4),[file(trees_4,i4_30__trees_4)]]). fof(i4_30_tmp__trees_4,plain, ( ( v1_relat_1(c4_30__trees_4) & v1_funct_1(c4_30__trees_4) & v1_finseq_1(c4_30__trees_4) ) => ( r2_hidden(k7_finseq_1(k12_finseq_1(k5_numbers,c3_30__trees_4),c4_30__trees_4),k1_relat_1(k4_trees_4(c1_30__trees_4,c2_30__trees_4))) => k1_funct_1(k4_trees_4(c1_30__trees_4,c2_30__trees_4),k7_finseq_1(k12_finseq_1(k5_numbers,c3_30__trees_4),c4_30__trees_4)) = k5_funct_6(c2_30__trees_4,k1_nat_1(c3_30__trees_4,1),c4_30__trees_4) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_30__trees_4,dt_c2_30__trees_4,dt_c3_30__trees_4]),discharge_asm(discharge,[dt_c4_30__trees_4])],[dt_c4_30__trees_4,i4_30__trees_4]), [interesting(0.8),i3_30__trees_4]). fof(i3_30__trees_4,plain,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( r2_hidden(k7_finseq_1(k12_finseq_1(k5_numbers,c3_30__trees_4),A),k1_relat_1(k4_trees_4(c1_30__trees_4,c2_30__trees_4))) => k1_funct_1(k4_trees_4(c1_30__trees_4,c2_30__trees_4),k7_finseq_1(k12_finseq_1(k5_numbers,c3_30__trees_4),A)) = k5_funct_6(c2_30__trees_4,k1_nat_1(c3_30__trees_4,1),A) ) ) ), inference(let,[status(thm),assumptions([dt_c1_30__trees_4,dt_c2_30__trees_4,dt_c3_30__trees_4])],[i4_30_tmp__trees_4,dh_c4_30__trees_4]), [interesting(0.8),file(trees_4,i3_30__trees_4),[file(trees_4,i3_30__trees_4)]]). fof(i3_30_tmp__trees_4,plain, ( m2_subset_1(c3_30__trees_4,k1_numbers,k5_numbers) => ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( r2_hidden(k7_finseq_1(k12_finseq_1(k5_numbers,c3_30__trees_4),A),k1_relat_1(k4_trees_4(c1_30__trees_4,c2_30__trees_4))) => k1_funct_1(k4_trees_4(c1_30__trees_4,c2_30__trees_4),k7_finseq_1(k12_finseq_1(k5_numbers,c3_30__trees_4),A)) = k5_funct_6(c2_30__trees_4,k1_nat_1(c3_30__trees_4,1),A) ) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_30__trees_4,dt_c2_30__trees_4]),discharge_asm(discharge,[dt_c3_30__trees_4])],[dt_c3_30__trees_4,i3_30__trees_4]), [interesting(0.8),i2_30__trees_4]). fof(i2_30__trees_4,plain,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( r2_hidden(k7_finseq_1(k12_finseq_1(k5_numbers,A),B),k1_relat_1(k4_trees_4(c1_30__trees_4,c2_30__trees_4))) => k1_funct_1(k4_trees_4(c1_30__trees_4,c2_30__trees_4),k7_finseq_1(k12_finseq_1(k5_numbers,A),B)) = k5_funct_6(c2_30__trees_4,k1_nat_1(A,1),B) ) ) ) ), inference(let,[status(thm),assumptions([dt_c1_30__trees_4,dt_c2_30__trees_4])],[i3_30_tmp__trees_4,dh_c3_30__trees_4]), [interesting(0.8),file(trees_4,i2_30__trees_4),[file(trees_4,i2_30__trees_4)]]). fof(i2_30_tmp__trees_4,plain, ( ( v1_relat_1(c2_30__trees_4) & v1_funct_1(c2_30__trees_4) & v1_finseq_1(c2_30__trees_4) & v6_trees_3(c2_30__trees_4) ) => ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( r2_hidden(k7_finseq_1(k12_finseq_1(k5_numbers,A),B),k1_relat_1(k4_trees_4(c1_30__trees_4,c2_30__trees_4))) => k1_funct_1(k4_trees_4(c1_30__trees_4,c2_30__trees_4),k7_finseq_1(k12_finseq_1(k5_numbers,A),B)) = k5_funct_6(c2_30__trees_4,k1_nat_1(A,1),B) ) ) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_30__trees_4]),discharge_asm(discharge,[dt_c2_30__trees_4])],[dt_c2_30__trees_4,i2_30__trees_4]), [interesting(0.8),i1_30__trees_4]). fof(i1_30__trees_4,plain,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v6_trees_3(A) ) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ( r2_hidden(k7_finseq_1(k12_finseq_1(k5_numbers,B),C),k1_relat_1(k4_trees_4(c1_30__trees_4,A))) => k1_funct_1(k4_trees_4(c1_30__trees_4,A),k7_finseq_1(k12_finseq_1(k5_numbers,B),C)) = k5_funct_6(A,k1_nat_1(B,1),C) ) ) ) ) ), inference(let,[status(thm),assumptions([dt_c1_30__trees_4])],[i2_30_tmp__trees_4,dh_c2_30__trees_4]), [interesting(0.8),file(trees_4,i1_30__trees_4),[file(trees_4,i1_30__trees_4)]]). fof(i1_30_tmp__trees_4,plain,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v6_trees_3(A) ) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ( r2_hidden(k7_finseq_1(k12_finseq_1(k5_numbers,B),C),k1_relat_1(k4_trees_4(c1_30__trees_4,A))) => k1_funct_1(k4_trees_4(c1_30__trees_4,A),k7_finseq_1(k12_finseq_1(k5_numbers,B),C)) = k5_funct_6(A,k1_nat_1(B,1),C) ) ) ) ) ), inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_30__trees_4])],[dt_c1_30__trees_4,i1_30__trees_4]), [interesting(1),t19_trees_4]). fof(t19_trees_4,theorem,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v6_trees_3(B) ) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) => ( r2_hidden(k7_finseq_1(k12_finseq_1(k5_numbers,C),D),k1_relat_1(k4_trees_4(A,B))) => k1_funct_1(k4_trees_4(A,B),k7_finseq_1(k12_finseq_1(k5_numbers,C),D)) = k5_funct_6(B,k1_nat_1(C,1),D) ) ) ) ) ), inference(let,[status(thm),assumptions([])],[i1_30_tmp__trees_4,dh_c1_30__trees_4]), [interesting(1),file(trees_4,t19_trees_4),[file(trees_4,t19_trees_4)]]).