% Mizar problem: t47_msualg_6,msualg_6,2314,39 fof(t47_msualg_6,conjecture,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v5_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v3_msualg_6(C,A,B) & m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,k1_funct_1(u4_msualg_1(A,B),D)) => ! [G] : ( m1_subset_1(G,k1_funct_1(u4_msualg_1(A,B),D)) => ( r2_rewrite1(k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),C,D),F,G) => ! [H] : ( ( v1_relat_1(H) & v1_funct_1(H) ) => ( r1_msualg_6(A,D,E,B,H) => r2_rewrite1(k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),C,E),k1_funct_1(H,F),k1_funct_1(H,G)) ) ) ) ) ) ) ) ) ) ) ), inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc10_rewrite1,cc11_rewrite1,cc12_rewrite1,cc13_rewrite1,cc14_rewrite1,cc15_rewrite1,cc1_altcat_1,cc1_arytm_3,cc1_finseq_1,cc1_fraenkel,cc1_funct_1,cc1_funct_7,cc1_msualg_4,cc1_msualg_6,cc1_pboole,cc1_relset_1,cc1_rewrite1,cc1_xreal_0,cc2_arytm_3,cc2_funct_1,cc2_funct_7,cc2_pboole,cc2_rewrite1,cc2_xreal_0,cc3_arytm_3,cc3_rewrite1,cc3_xreal_0,cc4_rewrite1,cc4_xreal_0,cc5_rewrite1,cc5_xreal_0,cc6_rewrite1,cc6_xreal_0,cc7_rewrite1,cc7_xreal_0,cc8_rewrite1,cc8_xreal_0,cc9_rewrite1,commutativity_k1_nat_1,commutativity_k1_relset_1,commutativity_k2_tarski,commutativity_k2_xboole_0,commutativity_k2_xcmplx_0,connectedness_r1_xreal_0,d2_rewrite1,d2_xboole_0,d3_rewrite1,d4_rewrite1,d5_tarski,d7_relat_1,d8_msualg_6,dt_k1_card_1,dt_k1_funct_1,dt_k1_msualg_4,dt_k1_nat_1,dt_k1_numbers,dt_k1_relat_1,dt_k1_relset_1,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_tarski,dt_k2_xboole_0,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k3_finseq_1,dt_k4_finseq_1,dt_k4_relat_1,dt_k4_tarski,dt_k5_numbers,dt_k5_ordinal2,dt_k6_relset_1,dt_l1_msualg_1,dt_l1_struct_0,dt_l2_msualg_1,dt_l3_msualg_1,dt_m1_msualg_4,dt_m1_pboole,dt_m1_relset_1,dt_m1_rewrite1,dt_m1_subset_1,dt_m2_relset_1,dt_m2_subset_1,dt_u1_struct_0,dt_u4_msualg_1,existence_l1_msualg_1,existence_l1_struct_0,existence_l2_msualg_1,existence_l3_msualg_1,existence_m1_msualg_4,existence_m1_pboole,existence_m1_relset_1,existence_m1_rewrite1,existence_m1_subset_1,existence_m2_relset_1,existence_m2_subset_1,fc10_xreal_0,fc11_xreal_0,fc12_xreal_0,fc17_finseq_1,fc1_msualg_1,fc1_struct_0,fc2_altcat_1,fc2_finseq_1,fc2_pboole,fc3_funct_1,fc3_funct_7,fc3_xreal_0,fc7_funcop_1,fc7_xreal_0,fc8_xreal_0,fc9_xreal_0,idempotence_k1_relset_1,idempotence_k2_xboole_0,involutiveness_k4_relat_1,involutiveness_k6_relset_1,rc1_arytm_3,rc1_finseq_1,rc1_fraenkel,rc1_funcop_1,rc1_funct_1,rc1_funct_7,rc1_msualg_4,rc1_msualg_6,rc1_partfun1,rc1_pboole,rc1_rewrite1,rc1_xreal_0,rc2_finseq_1,rc2_funct_1,rc2_funct_7,rc2_partfun1,rc2_pboole,rc2_rewrite1,rc2_xreal_0,rc3_finseq_1,rc3_funct_1,rc3_pboole,rc3_rewrite1,rc3_struct_0,rc3_xreal_0,rc4_funct_1,rc4_pboole,rc4_rewrite1,rc4_xreal_0,rc5_funct_1,rc5_struct_0,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,redefinition_k1_msualg_4,redefinition_k1_nat_1,redefinition_k1_relset_1,redefinition_k3_finseq_1,redefinition_k4_finseq_1,redefinition_k5_numbers,redefinition_k6_relset_1,redefinition_m2_relset_1,redefinition_m2_subset_1,reflexivity_r1_tarski,reflexivity_r1_xreal_0,s1_nat_1__e7_75__msualg_6,spc0_boole,spc1_boole,spc1_numerals,t106_zfmisc_1,t19_nat_1,t1_arithm,t1_boole,t1_numerals,t1_real,t1_subset,t27_finseq_3,t27_rewrite1,t29_nat_1,t2_real,t2_subset,t2_xreal_1,t30_rewrite1,t31_rewrite1,t32_rewrite1,t38_nat_1,t3_real,t3_subset,t4_real,t4_subset,t5_real,t5_subset,t6_boole,t6_finseq_5,t6_real,t7_boole,t7_real,t8_boole,t8_real]), [file(msualg_6,t47_msualg_6)]). fof(antisymmetry_r2_hidden,axiom,( ! [A,B] : ( r2_hidden(A,B) => ~ r2_hidden(B,A) ) ), file(hidden,r2_hidden), []). fof(cc10_rewrite1,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_rewrite1(A) ) => ( v1_relat_1(A) & v4_rewrite1(A) ) ) ), file(rewrite1,cc10_rewrite1), []). fof(cc11_rewrite1,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_rewrite1(A) & v4_rewrite1(A) ) => ( v1_relat_1(A) & v8_rewrite1(A) ) ) ), file(rewrite1,cc11_rewrite1), []). fof(cc12_rewrite1,axiom,( ! [A] : ( ( v1_xboole_0(A) & v1_relat_1(A) ) => ( v1_relat_1(A) & v4_rewrite1(A) & v5_rewrite1(A) & v6_rewrite1(A) & v7_rewrite1(A) & v8_rewrite1(A) & v9_rewrite1(A) ) ) ), file(rewrite1,cc12_rewrite1), []). fof(cc13_rewrite1,axiom,( ! [A] : ( ( v1_relat_1(A) & v3_rewrite1(A) & v9_rewrite1(A) ) => ( v1_relat_1(A) & v4_rewrite1(A) & v5_rewrite1(A) & v7_rewrite1(A) & v8_rewrite1(A) & v9_rewrite1(A) ) ) ), file(rewrite1,cc13_rewrite1), []). fof(cc14_rewrite1,axiom,( ! [A] : ( ( v1_relat_1(A) & v10_rewrite1(A) ) => ( v1_relat_1(A) & v2_relat_2(A) & v1_rewrite1(A) & v2_rewrite1(A) & v3_rewrite1(A) & v4_rewrite1(A) & v5_rewrite1(A) & v7_rewrite1(A) & v8_rewrite1(A) & v9_rewrite1(A) ) ) ), file(rewrite1,cc14_rewrite1), []). fof(cc15_rewrite1,axiom,( ! [A] : ( ( v1_relat_1(A) & v3_rewrite1(A) & v7_rewrite1(A) ) => ( v1_relat_1(A) & v10_rewrite1(A) ) ) ), file(rewrite1,cc15_rewrite1), []). fof(cc1_altcat_1,axiom,( ! [A] : ( v1_fraenkel(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v1_fraenkel(B) ) ) ), file(altcat_1,cc1_altcat_1), []). fof(cc1_arytm_3,axiom,( ! [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), []). fof(cc1_finseq_1,axiom,( ! [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), []). fof(cc1_fraenkel,axiom,( ! [A] : ( v1_fraenkel(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_relat_1(B) & v1_funct_1(B) ) ) ) ), file(fraenkel,cc1_fraenkel), []). fof(cc1_funct_1,axiom,( ! [A] : ( v1_xboole_0(A) => v1_funct_1(A) ) ), file(funct_1,cc1_funct_1), []). fof(cc1_funct_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_funct_7(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v1_funcop_1(A) ) ) ), file(funct_7,cc1_funct_7), []). fof(cc1_msualg_4,axiom,( ! [A,B,C] : ( ( m1_pboole(B,A) & m1_pboole(C,A) ) => ! [D] : ( m1_msualg_4(D,A,B,C) => v1_msualg_4(D) ) ) ), file(msualg_4,cc1_msualg_4), []). fof(cc1_msualg_6,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ( v5_msualg_1(B,A) => v1_msualg_6(B,A) ) ) ) ), file(msualg_6,cc1_msualg_6), []). fof(cc1_pboole,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_pboole(B,A) => ( v2_relat_1(B) => ~ v3_relat_1(B) ) ) ) ), file(pboole,cc1_pboole), []). fof(cc1_relset_1,axiom,( ! [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), []). fof(cc1_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( m1_rewrite1(B,A) => ~ v1_xboole_0(B) ) ) ), file(rewrite1,cc1_rewrite1), []). fof(cc1_xreal_0,axiom,( ! [A] : ( v4_ordinal2(A) => v1_xreal_0(A) ) ), file(xreal_0,cc1_xreal_0), []). fof(cc2_arytm_3,axiom,( ! [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), []). fof(cc2_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_xboole_0(A) & v1_funct_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) ) ) ), file(funct_1,cc2_funct_1), []). fof(cc2_funct_7,axiom,( ! [A] : ( ( v1_xboole_0(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) & v1_finseq_1(A) & v1_funcop_1(A) & v1_funct_7(A) ) ) ), file(funct_7,cc2_funct_7), []). fof(cc2_pboole,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_pboole(B,A) => ( v3_relat_1(B) => ~ v2_relat_1(B) ) ) ) ), file(pboole,cc2_pboole), []). fof(cc2_rewrite1,axiom,( ! [A] : ( ( v1_relat_1(A) & v3_rewrite1(A) ) => ( v1_relat_1(A) & v2_relat_2(A) & v1_rewrite1(A) ) ) ), file(rewrite1,cc2_rewrite1), []). fof(cc2_xreal_0,axiom,( ! [A] : ( v1_xreal_0(A) => v1_xcmplx_0(A) ) ), file(xreal_0,cc2_xreal_0), []). fof(cc3_arytm_3,axiom,( ! [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), []). fof(cc3_rewrite1,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_relat_2(A) & v1_rewrite1(A) ) => ( v1_relat_1(A) & v3_rewrite1(A) ) ) ), file(rewrite1,cc3_rewrite1), []). fof(cc3_xreal_0,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xreal_0(A) ) => ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) ) ) ), file(xreal_0,cc3_xreal_0), []). fof(cc4_rewrite1,axiom,( ! [A] : ( ( v1_xboole_0(A) & v1_relat_1(A) ) => ( v1_relat_1(A) & v2_relat_2(A) & v1_rewrite1(A) & v2_rewrite1(A) & v3_rewrite1(A) ) ) ), file(rewrite1,cc4_rewrite1), []). fof(cc4_xreal_0,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) ) => ( v1_xcmplx_0(A) & v1_xreal_0(A) & v2_xreal_0(A) ) ) ), file(xreal_0,cc4_xreal_0), []). fof(cc5_rewrite1,axiom,( ! [A] : ( ( v1_relat_1(A) & v3_rewrite1(A) ) => ( v1_relat_1(A) & v2_rewrite1(A) ) ) ), file(rewrite1,cc5_rewrite1), []). fof(cc5_xreal_0,axiom,( ! [A] : ( ( v1_xreal_0(A) & v3_xreal_0(A) ) => ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) ) ) ), file(xreal_0,cc5_xreal_0), []). fof(cc6_rewrite1,axiom,( ! [A] : ( ( v1_relat_1(A) & v8_rewrite1(A) ) => ( v1_relat_1(A) & v7_rewrite1(A) ) ) ), file(rewrite1,cc6_rewrite1), []). fof(cc6_xreal_0,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) ) => ( v1_xcmplx_0(A) & v1_xreal_0(A) & v3_xreal_0(A) ) ) ), file(xreal_0,cc6_xreal_0), []). fof(cc7_rewrite1,axiom,( ! [A] : ( ( v1_relat_1(A) & v7_rewrite1(A) ) => ( v1_relat_1(A) & v8_rewrite1(A) & v9_rewrite1(A) ) ) ), file(rewrite1,cc7_rewrite1), []). fof(cc7_xreal_0,axiom,( ! [A] : ( ( v1_xboole_0(A) & v1_xreal_0(A) ) => ( v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) & ~ v3_xreal_0(A) ) ) ), file(xreal_0,cc7_xreal_0), []). fof(cc8_rewrite1,axiom,( ! [A] : ( ( v1_relat_1(A) & v6_rewrite1(A) ) => ( v1_relat_1(A) & v7_rewrite1(A) ) ) ), file(rewrite1,cc8_rewrite1), []). fof(cc8_xreal_0,axiom,( ! [A] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) & ~ v3_xreal_0(A) ) => ( v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) ) ) ), file(xreal_0,cc8_xreal_0), []). fof(cc9_rewrite1,axiom,( ! [A] : ( ( v1_relat_1(A) & v8_rewrite1(A) ) => ( v1_relat_1(A) & v5_rewrite1(A) ) ) ), file(rewrite1,cc9_rewrite1), []). fof(commutativity_k1_nat_1,axiom,( ! [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), []). fof(commutativity_k1_relset_1,axiom,( ! [A,B,C,D] : ( ( m1_relset_1(C,A,B) & m1_relset_1(D,A,B) ) => k1_relset_1(A,B,C,D) = k1_relset_1(A,B,D,C) ) ), file(relset_1,k1_relset_1), []). fof(commutativity_k2_tarski,axiom,( ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ), file(tarski,k2_tarski), []). fof(commutativity_k2_xboole_0,axiom,( ! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A) ), file(xboole_0,k2_xboole_0), []). fof(commutativity_k2_xcmplx_0,axiom,( ! [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), []). fof(connectedness_r1_xreal_0,axiom,( ! [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), []). fof(d2_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( m1_rewrite1(B,A) <=> ( ~ r1_xreal_0(k3_finseq_1(B),0) & ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ( ( r2_hidden(C,k4_finseq_1(B)) & r2_hidden(k1_nat_1(C,1),k4_finseq_1(B)) ) => r2_hidden(k4_tarski(k1_funct_1(B,C),k1_funct_1(B,k1_nat_1(C,1))),A) ) ) ) ) ) ) ), file(rewrite1,d2_rewrite1), []). fof(d2_xboole_0,axiom,( ! [A,B,C] : ( C = k2_xboole_0(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( r2_hidden(D,A) | r2_hidden(D,B) ) ) ) ), file(xboole_0,d2_xboole_0), []). fof(d3_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B,C] : ( r1_rewrite1(A,B,C) <=> ? [D] : ( m1_rewrite1(D,A) & k1_funct_1(D,1) = B & k1_funct_1(D,k3_finseq_1(D)) = C ) ) ) ), file(rewrite1,d3_rewrite1), []). fof(d4_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B,C] : ( r2_rewrite1(A,B,C) <=> r1_rewrite1(k2_xboole_0(A,k4_relat_1(A)),B,C) ) ) ), file(rewrite1,d4_rewrite1), []). fof(d5_tarski,axiom,( ! [A,B] : k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A)) ), file(tarski,d5_tarski), []). fof(d7_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => ( B = k4_relat_1(A) <=> ! [C,D] : ( r2_hidden(k4_tarski(C,D),B) <=> r2_hidden(k4_tarski(D,C),A) ) ) ) ) ), file(relat_1,d7_relat_1), []). fof(d8_msualg_6,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) => ( v3_msualg_6(C,A,B) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( ( v1_relat_1(F) & v1_funct_1(F) ) => ( r1_msualg_6(A,D,E,B,F) => ! [G,H] : ( r2_hidden(k4_tarski(G,H),k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),C,D)) => r2_hidden(k4_tarski(k1_funct_1(F,G),k1_funct_1(F,H)),k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),C,E)) ) ) ) ) ) ) ) ) ) ), file(msualg_6,d8_msualg_6), []). fof(dt_k1_card_1,axiom,( ! [A] : v1_card_1(k1_card_1(A)) ), file(card_1,k1_card_1), []). fof(dt_k1_funct_1,axiom,( $true ), file(funct_1,k1_funct_1), []). fof(dt_k1_msualg_4,axiom,( ! [A,B,C,D,E] : ( ( ~ v1_xboole_0(A) & m1_pboole(B,A) & m1_pboole(C,A) & m1_msualg_4(D,A,B,C) & m1_subset_1(E,A) ) => m2_relset_1(k1_msualg_4(A,B,C,D,E),k1_funct_1(B,E),k1_funct_1(C,E)) ) ), file(msualg_4,k1_msualg_4), []). 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), []). fof(dt_k1_numbers,axiom,( $true ), file(numbers,k1_numbers), []). fof(dt_k1_relat_1,axiom,( $true ), file(relat_1,k1_relat_1), []). fof(dt_k1_relset_1,axiom,( ! [A,B,C,D] : ( ( m1_relset_1(C,A,B) & m1_relset_1(D,A,B) ) => m2_relset_1(k1_relset_1(A,B,C,D),A,B) ) ), file(relset_1,k1_relset_1), []). fof(dt_k1_tarski,axiom,( $true ), file(tarski,k1_tarski), []). fof(dt_k1_xboole_0,axiom,( $true ), file(xboole_0,k1_xboole_0), []). fof(dt_k1_zfmisc_1,axiom,( $true ), file(zfmisc_1,k1_zfmisc_1), []). fof(dt_k2_tarski,axiom,( $true ), file(tarski,k2_tarski), []). fof(dt_k2_xboole_0,axiom,( $true ), file(xboole_0,k2_xboole_0), []). fof(dt_k2_xcmplx_0,axiom,( $true ), file(xcmplx_0,k2_xcmplx_0), []). fof(dt_k2_zfmisc_1,axiom,( $true ), file(zfmisc_1,k2_zfmisc_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), []). 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), []). fof(dt_k4_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => v1_relat_1(k4_relat_1(A)) ) ), file(relat_1,k4_relat_1), []). fof(dt_k4_tarski,axiom,( $true ), file(tarski,k4_tarski), []). fof(dt_k5_numbers,axiom,( m1_subset_1(k5_numbers,k1_zfmisc_1(k1_numbers)) ), file(numbers,k5_numbers), []). fof(dt_k5_ordinal2,axiom,( $true ), file(ordinal2,k5_ordinal2), []). fof(dt_k6_relset_1,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => m2_relset_1(k6_relset_1(A,B,C),B,A) ) ), file(relset_1,k6_relset_1), []). fof(dt_l1_msualg_1,axiom,( ! [A] : ( l1_msualg_1(A) => l1_struct_0(A) ) ), file(msualg_1,l1_msualg_1), []). fof(dt_l1_struct_0,axiom,( $true ), file(struct_0,l1_struct_0), []). fof(dt_l2_msualg_1,axiom,( $true ), file(msualg_1,l2_msualg_1), []). fof(dt_l3_msualg_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => l2_msualg_1(B,A) ) ) ), file(msualg_1,l3_msualg_1), []). fof(dt_m1_msualg_4,axiom,( ! [A,B,C] : ( ( m1_pboole(B,A) & m1_pboole(C,A) ) => ! [D] : ( m1_msualg_4(D,A,B,C) => m1_pboole(D,A) ) ) ), file(msualg_4,m1_msualg_4), []). fof(dt_m1_pboole,axiom,( ! [A,B] : ( m1_pboole(B,A) => ( v1_relat_1(B) & v1_funct_1(B) ) ) ), file(pboole,m1_pboole), []). fof(dt_m1_relset_1,axiom,( $true ), file(relset_1,m1_relset_1), []). fof(dt_m1_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( m1_rewrite1(B,A) => ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) ) ) ), file(rewrite1,m1_rewrite1), []). fof(dt_m1_subset_1,axiom,( $true ), file(subset_1,m1_subset_1), []). fof(dt_m2_relset_1,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ), file(relset_1,m2_relset_1), []). 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), []). fof(dt_u1_struct_0,axiom,( $true ), file(struct_0,u1_struct_0), []). fof(dt_u4_msualg_1,axiom,( ! [A,B] : ( ( l1_struct_0(A) & l2_msualg_1(B,A) ) => m1_pboole(u4_msualg_1(A,B),u1_struct_0(A)) ) ), file(msualg_1,u4_msualg_1), []). fof(existence_l1_msualg_1,axiom,( ? [A] : l1_msualg_1(A) ), file(msualg_1,l1_msualg_1), []). fof(existence_l1_struct_0,axiom,( ? [A] : l1_struct_0(A) ), file(struct_0,l1_struct_0), []). fof(existence_l2_msualg_1,axiom,( ! [A] : ( l1_struct_0(A) => ? [B] : l2_msualg_1(B,A) ) ), file(msualg_1,l2_msualg_1), []). fof(existence_l3_msualg_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_msualg_1(A) ) => ? [B] : l3_msualg_1(B,A) ) ), file(msualg_1,l3_msualg_1), []). fof(existence_m1_msualg_4,axiom,( ! [A,B,C] : ( ( m1_pboole(B,A) & m1_pboole(C,A) ) => ? [D] : m1_msualg_4(D,A,B,C) ) ), file(msualg_4,m1_msualg_4), []). fof(existence_m1_pboole,axiom,( ! [A] : ? [B] : m1_pboole(B,A) ), file(pboole,m1_pboole), []). fof(existence_m1_relset_1,axiom,( ! [A,B] : ? [C] : m1_relset_1(C,A,B) ), file(relset_1,m1_relset_1), []). fof(existence_m1_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ? [B] : m1_rewrite1(B,A) ) ), file(rewrite1,m1_rewrite1), []). fof(existence_m1_subset_1,axiom,( ! [A] : ? [B] : m1_subset_1(B,A) ), file(subset_1,m1_subset_1), []). fof(existence_m2_relset_1,axiom,( ! [A,B] : ? [C] : m2_relset_1(C,A,B) ), file(relset_1,m2_relset_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), []). fof(fc10_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v2_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(B,A)) & v1_xcmplx_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) & v2_xreal_0(k2_xcmplx_0(B,A)) & ~ v3_xreal_0(k2_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc10_xreal_0), []). fof(fc11_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v3_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & ~ v2_xreal_0(k2_xcmplx_0(A,B)) & v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc11_xreal_0), []). fof(fc12_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v3_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(B,A)) & v1_xcmplx_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) & ~ v2_xreal_0(k2_xcmplx_0(B,A)) & v3_xreal_0(k2_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc12_xreal_0), []). fof(fc17_finseq_1,axiom,( ! [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), []). fof(fc1_msualg_1,axiom,( ! [A,B] : ( ( l1_struct_0(A) & v5_msualg_1(B,A) & l2_msualg_1(B,A) ) => ( v1_relat_1(u4_msualg_1(A,B)) & v2_relat_1(u4_msualg_1(A,B)) & v1_funct_1(u4_msualg_1(A,B)) ) ) ), file(msualg_1,fc1_msualg_1), []). fof(fc1_struct_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ~ v1_xboole_0(u1_struct_0(A)) ) ), file(struct_0,fc1_struct_0), []). fof(fc2_altcat_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( ~ v1_xboole_0(k1_tarski(A)) & v1_finset_1(k1_tarski(A)) & v1_fraenkel(k1_tarski(A)) & v1_realset1(k1_tarski(A)) ) ) ), file(altcat_1,fc2_altcat_1), []). fof(fc2_finseq_1,axiom, ( 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), []). fof(fc2_pboole,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & v2_relat_1(B) & m1_pboole(B,A) & m1_subset_1(C,A) ) => ~ v1_xboole_0(k1_funct_1(B,C)) ) ), file(pboole,fc2_pboole), []). fof(fc3_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) ) => ( v1_relat_1(k4_relat_1(A)) & v1_funct_1(k4_relat_1(A)) ) ) ), file(funct_1,fc3_funct_1), []). fof(fc3_funct_7,axiom, ( 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) & v1_funcop_1(k1_xboole_0) ), file(funct_7,fc3_funct_7), []). fof(fc3_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc3_xreal_0), []). fof(fc7_funcop_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) ) => ( v1_relat_1(k1_funct_1(A,B)) & v1_funct_1(k1_funct_1(A,B)) ) ) ), file(funcop_1,fc7_funcop_1), []). fof(fc7_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & ~ v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc7_xreal_0), []). fof(fc8_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & ~ v2_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc8_xreal_0), []). fof(fc9_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v2_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & v2_xreal_0(k2_xcmplx_0(A,B)) & ~ v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc9_xreal_0), []). fof(idempotence_k1_relset_1,axiom,( ! [A,B,C,D] : ( ( m1_relset_1(C,A,B) & m1_relset_1(D,A,B) ) => k1_relset_1(A,B,C,C) = C ) ), file(relset_1,k1_relset_1), []). fof(idempotence_k2_xboole_0,axiom,( ! [A,B] : k2_xboole_0(A,A) = A ), file(xboole_0,k2_xboole_0), []). fof(involutiveness_k4_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => k4_relat_1(k4_relat_1(A)) = A ) ), file(relat_1,k4_relat_1), []). fof(involutiveness_k6_relset_1,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => k6_relset_1(A,B,k6_relset_1(A,B,C)) = C ) ), file(relset_1,k6_relset_1), []). fof(rc1_arytm_3,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) ) ), file(arytm_3,rc1_arytm_3), []). fof(rc1_finseq_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) ), file(finseq_1,rc1_finseq_1), []). fof(rc1_fraenkel,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_fraenkel(A) ) ), file(fraenkel,rc1_fraenkel), []). fof(rc1_funcop_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) ) ), file(funcop_1,rc1_funcop_1), []). fof(rc1_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) ) ), file(funct_1,rc1_funct_1), []). fof(rc1_funct_7,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v1_funcop_1(A) ) ), file(funct_7,rc1_funct_7), []). fof(rc1_msualg_4,axiom,( ! [A] : ? [B] : ( m1_pboole(B,A) & v1_relat_1(B) & v1_funct_1(B) & v1_msualg_4(B) ) ), file(msualg_4,rc1_msualg_4), []). fof(rc1_msualg_6,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ? [B] : ( l3_msualg_1(B,A) & v5_msualg_1(B,A) & v1_msualg_6(B,A) ) ) ), file(msualg_6,rc1_msualg_6), []). fof(rc1_partfun1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_xboole_0(A) ) ), file(partfun1,rc1_partfun1), []). fof(rc1_pboole,axiom,( ? [A] : ( v1_relat_1(A) & v3_relat_1(A) & v1_funct_1(A) ) ), file(pboole,rc1_pboole), []). fof(rc1_rewrite1,axiom,( ? [A] : ( v1_xboole_0(A) & v1_relat_1(A) & v2_relat_2(A) & v1_rewrite1(A) & v2_rewrite1(A) & v3_rewrite1(A) ) ), file(rewrite1,rc1_rewrite1), []). fof(rc1_xreal_0,axiom,( ? [A] : ( v1_xcmplx_0(A) & v1_xreal_0(A) ) ), file(xreal_0,rc1_xreal_0), []). fof(rc2_finseq_1,axiom,( ! [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), []). fof(rc2_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_xboole_0(A) & v1_funct_1(A) ) ), file(funct_1,rc2_funct_1), []). fof(rc2_funct_7,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v1_funcop_1(A) & v1_funct_7(A) ) ), file(funct_7,rc2_funct_7), []). fof(rc2_partfun1,axiom,( ! [A,B] : ? [C] : ( m1_relset_1(C,A,B) & v1_relat_1(C) & v1_funct_1(C) ) ), file(partfun1,rc2_partfun1), []). fof(rc2_pboole,axiom,( ! [A] : ? [B] : ( m1_pboole(B,A) & v1_relat_1(B) & v3_relat_1(B) & v1_funct_1(B) ) ), file(pboole,rc2_pboole), []). fof(rc2_rewrite1,axiom,( ? [A] : ( v1_xboole_0(A) & v1_relat_1(A) & v2_relat_2(A) & v1_rewrite1(A) & v2_rewrite1(A) & v3_rewrite1(A) & v4_rewrite1(A) & v5_rewrite1(A) & v6_rewrite1(A) & v7_rewrite1(A) & v8_rewrite1(A) & v9_rewrite1(A) ) ), file(rewrite1,rc2_rewrite1), []). fof(rc2_xreal_0,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & v2_xreal_0(A) & ~ v3_xreal_0(A) ) ), file(xreal_0,rc2_xreal_0), []). fof(rc3_finseq_1,axiom,( ? [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), []). fof(rc3_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) ) ), file(funct_1,rc3_funct_1), []). fof(rc3_pboole,axiom,( ! [A] : ? [B] : ( m1_pboole(B,A) & v1_relat_1(B) & v2_relat_1(B) & v1_funct_1(B) ) ), file(pboole,rc3_pboole), []). fof(rc3_rewrite1,axiom,( ? [A] : ( v1_xboole_0(A) & v1_relat_1(A) & v2_relat_2(A) & v1_rewrite1(A) & v2_rewrite1(A) & v3_rewrite1(A) & v4_rewrite1(A) & v5_rewrite1(A) & v6_rewrite1(A) & v7_rewrite1(A) & v8_rewrite1(A) & v9_rewrite1(A) & v10_rewrite1(A) ) ), file(rewrite1,rc3_rewrite1), []). fof(rc3_struct_0,axiom,( ? [A] : ( l1_struct_0(A) & ~ v3_struct_0(A) ) ), file(struct_0,rc3_struct_0), []). fof(rc3_xreal_0,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) & v3_xreal_0(A) ) ), file(xreal_0,rc3_xreal_0), []). fof(rc4_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v3_relat_1(A) & v1_funct_1(A) ) ), file(funct_1,rc4_funct_1), []). fof(rc4_pboole,axiom,( ! [A] : ? [B] : ( m1_pboole(B,A) & v1_relat_1(B) & v1_funct_1(B) & v1_funcop_1(B) ) ), file(pboole,rc4_pboole), []). fof(rc4_rewrite1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v2_relat_2(A) & v1_rewrite1(A) & v2_rewrite1(A) & v3_rewrite1(A) & v4_rewrite1(A) & v5_rewrite1(A) & v7_rewrite1(A) & v8_rewrite1(A) & v9_rewrite1(A) & v10_rewrite1(A) ) ), file(rewrite1,rc4_rewrite1), []). fof(rc4_xreal_0,axiom,( ? [A] : ( v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) & ~ v3_xreal_0(A) ) ), file(xreal_0,rc4_xreal_0), []). fof(rc5_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) ) ), file(funct_1,rc5_funct_1), []). fof(rc5_struct_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) ) ) ), file(struct_0,rc5_struct_0), []). fof(rc6_finseq_1,axiom,( ? [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), []). fof(rc7_finseq_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) ), file(finseq_1,rc7_finseq_1), []). fof(rc8_finseq_1,axiom,( ? [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), []). fof(redefinition_k1_msualg_4,axiom,( ! [A,B,C,D,E] : ( ( ~ v1_xboole_0(A) & m1_pboole(B,A) & m1_pboole(C,A) & m1_msualg_4(D,A,B,C) & m1_subset_1(E,A) ) => k1_msualg_4(A,B,C,D,E) = k1_funct_1(D,E) ) ), file(msualg_4,k1_msualg_4), []). fof(redefinition_k1_nat_1,axiom,( ! [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), []). fof(redefinition_k1_relset_1,axiom,( ! [A,B,C,D] : ( ( m1_relset_1(C,A,B) & m1_relset_1(D,A,B) ) => k1_relset_1(A,B,C,D) = k2_xboole_0(C,D) ) ), file(relset_1,k1_relset_1), []). fof(redefinition_k3_finseq_1,axiom,( ! [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), []). fof(redefinition_k4_finseq_1,axiom,( ! [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), []). fof(redefinition_k5_numbers,axiom,( k5_numbers = k5_ordinal2 ), file(numbers,k5_numbers), []). fof(redefinition_k6_relset_1,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => k6_relset_1(A,B,C) = k4_relat_1(C) ) ), file(relset_1,k6_relset_1), []). fof(redefinition_m2_relset_1,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) <=> m1_relset_1(C,A,B) ) ), file(relset_1,m2_relset_1), []). fof(redefinition_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,B) ) ) ), file(subset_1,m2_subset_1), []). fof(reflexivity_r1_tarski,axiom,( ! [A,B] : r1_tarski(A,A) ), file(tarski,r1_tarski), []). fof(reflexivity_r1_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => r1_xreal_0(A,A) ) ), file(xreal_0,r1_xreal_0), []). fof(s1_nat_1__e7_75__msualg_6,axiom,( ! [A,B,C,D,E,F,G,H] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v5_msualg_1(B,A) & l3_msualg_1(B,A) & v3_msualg_6(C,A,B) & m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) & m1_subset_1(D,u1_struct_0(A)) & m1_subset_1(E,u1_struct_0(A)) & m1_subset_1(F,k1_funct_1(u4_msualg_1(A,B),D)) & m1_rewrite1(G,k1_relset_1(k1_funct_1(u4_msualg_1(A,B),D),k1_funct_1(u4_msualg_1(A,B),D),k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),C,D),k6_relset_1(k1_funct_1(u4_msualg_1(A,B),D),k1_funct_1(u4_msualg_1(A,B),D),k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),C,D)))) & v1_relat_1(H) & v1_funct_1(H) ) => ( ( ( r2_hidden(0,k4_finseq_1(G)) => r2_rewrite1(k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),C,E),k1_funct_1(H,F),k1_funct_1(H,k1_funct_1(G,0))) ) & ! [I] : ( m2_subset_1(I,k1_numbers,k5_numbers) => ( ( r2_hidden(I,k4_finseq_1(G)) => r2_rewrite1(k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),C,E),k1_funct_1(H,F),k1_funct_1(H,k1_funct_1(G,I))) ) => ( r2_hidden(k1_nat_1(I,1),k4_finseq_1(G)) => r2_rewrite1(k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),C,E),k1_funct_1(H,F),k1_funct_1(H,k1_funct_1(G,k1_nat_1(I,1)))) ) ) ) ) => ! [I] : ( m2_subset_1(I,k1_numbers,k5_numbers) => ( r2_hidden(I,k4_finseq_1(G)) => r2_rewrite1(k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),C,E),k1_funct_1(H,F),k1_funct_1(H,k1_funct_1(G,I))) ) ) ) ) ), file(msualg_6,s1_nat_1__e7_75__msualg_6), []). fof(spc0_boole,axiom,( v1_xboole_0(0) ), file(boole,spc0_boole), []). fof(spc1_boole,axiom,( ~ v1_xboole_0(1) ), file(boole,spc1_boole), []). fof(spc1_numerals,axiom, ( v2_xreal_0(1) & m1_subset_1(1,k5_numbers) ), file(numerals,spc1_numerals), []). fof(t106_zfmisc_1,axiom,( ! [A,B,C,D] : ( r2_hidden(k4_tarski(A,B),k2_zfmisc_1(C,D)) <=> ( r2_hidden(A,C) & r2_hidden(B,D) ) ) ), file(zfmisc_1,t106_zfmisc_1), []). fof(t19_nat_1,axiom,( ! [A] : ( v4_ordinal2(A) => ~ ( 0 != A & r1_xreal_0(A,0) ) ) ), file(nat_1,t19_nat_1), []). fof(t1_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k2_xcmplx_0(A,0) = A ) ), file(arithm,t1_arithm), []). fof(t1_boole,axiom,( ! [A] : k2_xboole_0(A,k1_xboole_0) = A ), file(boole,t1_boole), []). fof(t1_numerals,axiom,( m1_subset_1(0,k5_numbers) ), file(numerals,t1_numerals), []). fof(t1_real,axiom,( ! [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), []). fof(t1_subset,axiom,( ! [A,B] : ( r2_hidden(A,B) => m1_subset_1(A,B) ) ), file(subset,t1_subset), []). fof(t27_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( v4_ordinal2(B) => ( r2_hidden(B,k4_finseq_1(A)) <=> ( r1_xreal_0(1,B) & r1_xreal_0(B,k3_finseq_1(A)) ) ) ) ) ), file(finseq_3,t27_finseq_3), []). fof(t27_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : r2_rewrite1(A,B,B) ) ), file(rewrite1,t27_rewrite1), []). fof(t29_nat_1,axiom,( ! [A] : ( v4_ordinal2(A) => ! [B] : ( v4_ordinal2(B) => r1_xreal_0(A,k2_xcmplx_0(A,B)) ) ) ), file(nat_1,t29_nat_1), []). fof(t2_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xreal_0(A,B) & v3_xreal_0(B) ) => v3_xreal_0(A) ) ) ) ), file(real,t2_real), []). fof(t2_subset,axiom,( ! [A,B] : ( m1_subset_1(A,B) => ( v1_xboole_0(B) | r2_hidden(A,B) ) ) ), file(subset,t2_subset), []). fof(t2_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ( r1_xreal_0(A,B) & r1_xreal_0(B,C) ) => r1_xreal_0(A,C) ) ) ) ) ), file(xreal_1,t2_xreal_1), []). fof(t30_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B,C] : ( r2_hidden(k4_tarski(B,C),A) => r2_rewrite1(A,B,C) ) ) ), file(rewrite1,t30_rewrite1), []). fof(t31_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B,C,D] : ( ( r2_rewrite1(A,B,C) & r2_rewrite1(A,C,D) ) => r2_rewrite1(A,B,D) ) ) ), file(rewrite1,t31_rewrite1), []). fof(t32_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B,C] : ( r2_rewrite1(A,B,C) => r2_rewrite1(A,C,B) ) ) ), file(rewrite1,t32_rewrite1), []). fof(t38_nat_1,axiom,( ! [A] : ( v4_ordinal2(A) => ! [B] : ( v4_ordinal2(B) => ( ~ r1_xreal_0(k2_xcmplx_0(B,1),A) <=> r1_xreal_0(A,B) ) ) ) ), file(nat_1,t38_nat_1), []). fof(t3_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( r1_xreal_0(A,B) & ~ v3_xreal_0(A) & v3_xreal_0(B) ) ) ) ), file(real,t3_real), []). fof(t3_subset,axiom,( ! [A,B] : ( m1_subset_1(A,k1_zfmisc_1(B)) <=> r1_tarski(A,B) ) ), file(subset,t3_subset), []). fof(t4_real,axiom,( ! [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), []). fof(t4_subset,axiom,( ! [A,B,C] : ( ( r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) ) => m1_subset_1(A,C) ) ), file(subset,t4_subset), []). fof(t5_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xreal_0(A,B) => ( v1_xboole_0(B) | v3_xreal_0(A) | v2_xreal_0(B) ) ) ) ) ), file(real,t5_real), []). fof(t5_subset,axiom,( ! [A,B,C] : ~ ( r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) & v1_xboole_0(C) ) ), file(subset,t5_subset), []). fof(t6_boole,axiom,( ! [A] : ( v1_xboole_0(A) => A = k1_xboole_0 ) ), file(boole,t6_boole), []). fof(t6_finseq_5,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( r2_hidden(1,k4_finseq_1(A)) & r2_hidden(k3_finseq_1(A),k4_finseq_1(A)) ) ) ), file(finseq_5,t6_finseq_5), []). fof(t6_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xreal_0(A,B) => ( v1_xboole_0(A) | v2_xreal_0(B) | v3_xreal_0(A) ) ) ) ) ), file(real,t6_real), []). fof(t7_boole,axiom,( ! [A,B] : ~ ( r2_hidden(A,B) & v1_xboole_0(B) ) ), file(boole,t7_boole), []). fof(t7_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xreal_0(A,B) & ~ v2_xreal_0(A) & ~ v3_xreal_0(B) ) ) ) ), file(real,t7_real), []). fof(t8_boole,axiom,( ! [A,B] : ~ ( v1_xboole_0(A) & A != B & v1_xboole_0(B) ) ), file(boole,t8_boole), []). fof(t8_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xreal_0(A,B) & ~ v3_xreal_0(B) & ~ v2_xreal_0(A) ) ) ) ), file(real,t8_real), []).