% Mizar problem: t17_fscirc_1,fscirc_1,527,49 fof(t17_fscirc_1,conjecture,( ! [A] : ( ~ v1_facirc_1(A) => ! [B] : ( ~ v1_facirc_1(B) => ! [C] : ( ~ v1_facirc_1(C) => ! [D] : ( m1_subset_1(D,k4_card_3(u4_msualg_1(k4_fscirc_1(A,B,C),k7_fscirc_1(A,B,C)))) => ! [E] : ( m1_subset_1(E,k10_circcomb) => ! [F] : ( m1_subset_1(F,k10_circcomb) => ! [G] : ( m1_subset_1(G,k10_circcomb) => ( ( E = k1_funct_1(D,A) & F = k1_funct_1(D,B) & G = k1_funct_1(D,C) ) => k15_facirc_1(k4_fscirc_1(A,B,C),k7_fscirc_1(A,B,C),k9_facirc_1(k4_fscirc_1(A,B,C),k7_fscirc_1(A,B,C),D,2),k6_fscirc_1(A,B,C)) = k3_binarith(k3_binarith(k12_margrel1(k11_margrel1(E),F),k12_margrel1(F,G)),k12_margrel1(k11_margrel1(E),G)) ) ) ) ) ) ) ) ) ), inference(mizar_bg_added,[status(thm)],[dt_k13_finseq_1,dt_k5_relat_1,existence_m3_pboole,redefinition_k3_finseq_2,redefinition_k7_pboole,dt_k3_finseq_2,dt_k6_pboole,dt_k7_pboole,dt_m3_pboole,rc1_circcomb,rc4_facirc_1,rc5_facirc_1,free_g1_msualg_1,free_g3_msualg_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_m1_finseq_2,existence_m1_relset_1,dt_g1_msualg_1,dt_g3_msualg_1,dt_k10_facirc_1,dt_k11_finseq_1,dt_k1_numbers,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_k3_msafree2,dt_k5_ordinal2,dt_k9_circcomb,dt_m1_finseq_2,dt_m1_relset_1,dt_u1_msualg_1,dt_u2_msualg_1,dt_u3_msualg_1,dt_u5_msualg_1,cc1_relset_1,fc6_circcomb,fc7_circcomb,fc10_circcomb,fc11_circcomb,fc12_circcomb,rc3_circcomb,fc14_circcomb,rc4_circcomb,rc5_circcomb,rc6_circcomb,rc7_circcomb,fc16_circcomb,rc3_facirc_1,cc4_facirc_1,fc14_facirc_1,rc1_fraenkel,cc1_fraenkel,spc3_boole,spc3_numerals,t1_subset,t4_subset,t5_subset,d10_facirc_1,spc3_numerals,spc3_boole,commutativity_k10_margrel1,commutativity_k1_binarith,involutiveness_k9_margrel1,abstractness_v1_msualg_1,abstractness_v4_msualg_1,existence_l1_msualg_1,existence_l1_struct_0,existence_l2_msualg_1,existence_l3_msualg_1,existence_m1_circcomb,existence_m1_pboole,existence_m1_struct_0,existence_m2_relset_1,existence_m2_subset_1,redefinition_k4_msafree2,redefinition_k5_numbers,redefinition_k7_facirc_1,redefinition_m1_struct_0,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k10_finseq_1,dt_k10_margrel1,dt_k11_facirc_1,dt_k1_binarith,dt_k1_zfmisc_1,dt_k3_circcomb,dt_k3_fscirc_1,dt_k4_circcomb,dt_k4_facirc_1,dt_k4_finseq_2,dt_k4_msafree2,dt_k5_fscirc_1,dt_k5_numbers,dt_k6_margrel1,dt_k7_circcomb,dt_k7_facirc_1,dt_k9_margrel1,dt_l1_msualg_1,dt_l1_struct_0,dt_l2_msualg_1,dt_l3_msualg_1,dt_m1_circcomb,dt_m1_pboole,dt_m1_struct_0,dt_m2_relset_1,dt_m2_subset_1,dt_u1_struct_0,rc3_struct_0,fc1_struct_0,rc5_struct_0,fc3_circcomb,fc4_circcomb,cc1_circcomb,cc2_circcomb,rc2_circcomb,fc8_circcomb,fc9_circcomb,fc13_circcomb,cc3_circcomb,fc15_circcomb,rc1_facirc_1,cc2_facirc_1,cc3_facirc_1,fc13_facirc_1,fc3_card_3,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,d11_facirc_1,d3_fscirc_1,d5_fscirc_1,involutiveness_k11_margrel1,commutativity_k12_margrel1,commutativity_k3_binarith,existence_m1_subset_1,redefinition_k10_circcomb,redefinition_k11_margrel1,redefinition_k12_margrel1,redefinition_k15_facirc_1,redefinition_k3_binarith,redefinition_k6_facirc_1,dt_k10_circcomb,dt_k11_margrel1,dt_k12_margrel1,dt_k15_facirc_1,dt_k1_funct_1,dt_k2_twoscomp,dt_k3_binarith,dt_k3_twoscomp,dt_k4_card_3,dt_k4_fscirc_1,dt_k4_tarski,dt_k6_facirc_1,dt_k6_fscirc_1,dt_k7_fscirc_1,dt_k9_facirc_1,dt_m1_subset_1,dt_u4_msualg_1,cc1_facirc_1,fc1_facirc_1,rc2_facirc_1,d4_fscirc_1,d6_fscirc_1,d7_fscirc_1,spc2_numerals,spc2_boole,l22_fscirc_1]), [file(fscirc_1,t17_fscirc_1)]). fof(dt_k13_finseq_1,axiom,( $true ), file(finseq_1,k13_finseq_1), []). fof(dt_k5_relat_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_relat_1(B) ) => v1_relat_1(k5_relat_1(A,B)) ) ), file(relat_1,k5_relat_1), []). fof(existence_m3_pboole,axiom,( ! [A,B,C] : ( ( m1_pboole(B,A) & m1_pboole(C,A) ) => ? [D] : m3_pboole(D,A,B,C) ) ), file(pboole,m3_pboole), []). fof(redefinition_k3_finseq_2,axiom,( ! [A] : k3_finseq_2(A) = k13_finseq_1(A) ), file(finseq_2,k3_finseq_2), []). fof(redefinition_k7_pboole,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(B) & v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & m1_pboole(D,B) ) => k7_pboole(A,B,C,D) = k5_relat_1(C,D) ) ), file(pboole,k7_pboole), []). fof(dt_k3_finseq_2,axiom,( ! [A] : ( ~ v1_xboole_0(k3_finseq_2(A)) & m1_finseq_2(k3_finseq_2(A),A) ) ), file(finseq_2,k3_finseq_2), []). fof(dt_k6_pboole,axiom,( ! [A,B] : ( m1_pboole(B,A) => m1_pboole(k6_pboole(A,B),k3_finseq_2(A)) ) ), file(pboole,k6_pboole), []). fof(dt_k7_pboole,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(B) & v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & m1_pboole(D,B) ) => m1_pboole(k7_pboole(A,B,C,D),A) ) ), file(pboole,k7_pboole), []). fof(dt_m3_pboole,axiom,( ! [A,B,C] : ( ( m1_pboole(B,A) & m1_pboole(C,A) ) => ! [D] : ( m3_pboole(D,A,B,C) => m1_pboole(D,A) ) ) ), file(pboole,m3_pboole), []). fof(rc1_circcomb,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) ) ), file(circcomb,rc1_circcomb), []). fof(rc4_facirc_1,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ? [B] : ( m1_circcomb(B,A) & v1_relat_1(B) & v1_funct_1(B) & v2_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) & v3_facirc_1(B) ) ) ), file(facirc_1,rc4_facirc_1), []). fof(rc5_facirc_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v3_facirc_1(A) ) ), file(facirc_1,rc5_facirc_1), []). fof(free_g1_msualg_1,axiom,( ! [A,B,C,D] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k3_finseq_2(A)) & m1_relset_1(C,B,k3_finseq_2(A)) & v1_funct_1(D) & v1_funct_2(D,B,A) & m1_relset_1(D,B,A) ) => ! [E,F,G,H] : ( g1_msualg_1(A,B,C,D) = g1_msualg_1(E,F,G,H) => ( A = E & B = F & C = G & D = H ) ) ) ), file(msualg_1,g1_msualg_1), []). fof(free_g3_msualg_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l1_msualg_1(A) & m1_pboole(B,u1_struct_0(A)) & m3_pboole(C,u1_msualg_1(A),k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),B)),k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),B)) ) => ! [D,E,F] : ( g3_msualg_1(A,B,C) = g3_msualg_1(D,E,F) => ( A = D & B = E & C = F ) ) ) ), file(msualg_1,g3_msualg_1), []). fof(reflexivity_r1_tarski,axiom,( ! [A,B] : r1_tarski(A,A) ), file(tarski,r1_tarski), []). fof(antisymmetry_r2_hidden,axiom,( ! [A,B] : ( r2_hidden(A,B) => ~ r2_hidden(B,A) ) ), file(hidden,r2_hidden), []). fof(existence_m1_finseq_2,axiom,( ! [A] : ? [B] : m1_finseq_2(B,A) ), file(finseq_2,m1_finseq_2), []). fof(existence_m1_relset_1,axiom,( ! [A,B] : ? [C] : m1_relset_1(C,A,B) ), file(relset_1,m1_relset_1), []). fof(dt_g1_msualg_1,axiom,( ! [A,B,C,D] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k3_finseq_2(A)) & m1_relset_1(C,B,k3_finseq_2(A)) & v1_funct_1(D) & v1_funct_2(D,B,A) & m1_relset_1(D,B,A) ) => ( v1_msualg_1(g1_msualg_1(A,B,C,D)) & l1_msualg_1(g1_msualg_1(A,B,C,D)) ) ) ), file(msualg_1,g1_msualg_1), []). fof(dt_g3_msualg_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l1_msualg_1(A) & m1_pboole(B,u1_struct_0(A)) & m3_pboole(C,u1_msualg_1(A),k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),B)),k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),B)) ) => ( v4_msualg_1(g3_msualg_1(A,B,C),A) & l3_msualg_1(g3_msualg_1(A,B,C),A) ) ) ), file(msualg_1,g3_msualg_1), []). fof(dt_k10_facirc_1,axiom,( ! [A,B,C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_finseq_2(2,k10_circcomb),k10_circcomb) & m1_relset_1(C,k4_finseq_2(2,k10_circcomb),k10_circcomb) ) => ( v4_msualg_1(k10_facirc_1(A,B,C),k7_circcomb(C,k6_facirc_1(A,B))) & v4_msafree2(k10_facirc_1(A,B,C),k7_circcomb(C,k6_facirc_1(A,B))) & v4_circcomb(k10_facirc_1(A,B,C),k7_circcomb(C,k6_facirc_1(A,B))) & v6_circcomb(k10_facirc_1(A,B,C),k7_circcomb(C,k6_facirc_1(A,B))) & l3_msualg_1(k10_facirc_1(A,B,C),k7_circcomb(C,k6_facirc_1(A,B))) ) ) ), file(facirc_1,k10_facirc_1), []). fof(dt_k11_finseq_1,axiom,( $true ), file(finseq_1,k11_finseq_1), []). fof(dt_k1_numbers,axiom,( $true ), file(numbers,k1_numbers), []). fof(dt_k1_xboole_0,axiom,( $true ), file(xboole_0,k1_xboole_0), []). fof(dt_k2_zfmisc_1,axiom,( $true ), file(zfmisc_1,k2_zfmisc_1), []). fof(dt_k3_msafree2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_msualg_1(A) ) => m1_subset_1(k3_msafree2(A),k1_zfmisc_1(u1_struct_0(A))) ) ), file(msafree2,k3_msafree2), []). fof(dt_k5_ordinal2,axiom,( $true ), file(ordinal2,k5_ordinal2), []). fof(dt_k9_circcomb,axiom,( ! [A,B,C,D] : ( ( m1_subset_1(A,k5_numbers) & ~ v1_xboole_0(B) & v1_funct_1(C) & v1_funct_2(C,k4_finseq_2(A,B),B) & m1_relset_1(C,k4_finseq_2(A,B),B) & m1_circcomb(D,A) ) => ( v4_msualg_1(k9_circcomb(A,B,C,D),k7_circcomb(C,D)) & v5_msualg_1(k9_circcomb(A,B,C,D),k7_circcomb(C,D)) & l3_msualg_1(k9_circcomb(A,B,C,D),k7_circcomb(C,D)) ) ) ), file(circcomb,k9_circcomb), []). fof(dt_m1_finseq_2,axiom,( $true ), file(finseq_2,m1_finseq_2), []). fof(dt_m1_relset_1,axiom,( $true ), file(relset_1,m1_relset_1), []). fof(dt_u1_msualg_1,axiom,( $true ), file(msualg_1,u1_msualg_1), []). fof(dt_u2_msualg_1,axiom,( ! [A] : ( l1_msualg_1(A) => ( v1_funct_1(u2_msualg_1(A)) & v1_funct_2(u2_msualg_1(A),u1_msualg_1(A),k3_finseq_2(u1_struct_0(A))) & m2_relset_1(u2_msualg_1(A),u1_msualg_1(A),k3_finseq_2(u1_struct_0(A))) ) ) ), file(msualg_1,u2_msualg_1), []). fof(dt_u3_msualg_1,axiom,( ! [A] : ( l1_msualg_1(A) => ( v1_funct_1(u3_msualg_1(A)) & v1_funct_2(u3_msualg_1(A),u1_msualg_1(A),u1_struct_0(A)) & m2_relset_1(u3_msualg_1(A),u1_msualg_1(A),u1_struct_0(A)) ) ) ), file(msualg_1,u3_msualg_1), []). fof(dt_u5_msualg_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_msualg_1(A) & l3_msualg_1(B,A) ) => m3_pboole(u5_msualg_1(A,B),u1_msualg_1(A),k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),u4_msualg_1(A,B))),k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),u4_msualg_1(A,B))) ) ), file(msualg_1,u5_msualg_1), []). 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(fc6_circcomb,axiom,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( ~ v3_struct_0(k7_circcomb(A,B)) & v1_msualg_1(k7_circcomb(A,B)) & ~ v2_msualg_1(k7_circcomb(A,B)) ) ) ), file(circcomb,fc6_circcomb), []). fof(fc7_circcomb,axiom,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( ~ v3_struct_0(k7_circcomb(A,B)) & v1_msualg_1(k7_circcomb(A,B)) & ~ v2_msualg_1(k7_circcomb(A,B)) & v2_msafree2(k7_circcomb(A,B)) & v1_circcomb(k7_circcomb(A,B)) & v2_circcomb(k7_circcomb(A,B)) ) ) ), file(circcomb,fc7_circcomb), []). fof(fc10_circcomb,axiom,( ! [A,B,C,D] : ( ( m1_subset_1(A,k5_numbers) & ~ v1_xboole_0(B) & v1_funct_1(C) & v1_funct_2(C,k4_finseq_2(A,B),B) & m1_relset_1(C,k4_finseq_2(A,B),B) & m1_circcomb(D,A) ) => ( v4_msualg_1(k9_circcomb(A,B,C,D),k7_circcomb(C,D)) & v5_msualg_1(k9_circcomb(A,B,C,D),k7_circcomb(C,D)) & v4_circcomb(k9_circcomb(A,B,C,D),k7_circcomb(C,D)) ) ) ), file(circcomb,fc10_circcomb), []). fof(fc11_circcomb,axiom,( ! [A,B,C,D] : ( ( m1_subset_1(A,k5_numbers) & ~ v1_xboole_0(B) & v1_funct_1(C) & v1_funct_2(C,k4_finseq_2(A,B),B) & m1_relset_1(C,k4_finseq_2(A,B),B) & m1_circcomb(D,A) ) => ( ~ v3_struct_0(k7_circcomb(C,D)) & v1_msualg_1(k7_circcomb(C,D)) & ~ v2_msualg_1(k7_circcomb(C,D)) & v2_msafree2(k7_circcomb(C,D)) & v1_circcomb(k7_circcomb(C,D)) & v2_circcomb(k7_circcomb(C,D)) & v5_circcomb(k7_circcomb(C,D)) ) ) ), file(circcomb,fc11_circcomb), []). fof(fc12_circcomb,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k5_numbers) & v1_funct_1(B) & v1_funct_2(B,k4_finseq_2(A,k6_margrel1),k6_margrel1) & m1_relset_1(B,k4_finseq_2(A,k6_margrel1),k6_margrel1) & m1_circcomb(C,A) ) => ( ~ v3_struct_0(k7_circcomb(B,C)) & v1_msualg_1(k7_circcomb(B,C)) & ~ v2_msualg_1(k7_circcomb(B,C)) & v2_msafree2(k7_circcomb(B,C)) & v1_circcomb(k7_circcomb(B,C)) & v2_circcomb(k7_circcomb(B,C)) & v3_circcomb(k7_circcomb(B,C)) & v5_circcomb(k7_circcomb(B,C)) ) ) ), file(circcomb,fc12_circcomb), []). fof(rc3_circcomb,axiom,( ? [A] : ( l1_msualg_1(A) & ~ v3_struct_0(A) & v3_circcomb(A) & v5_circcomb(A) ) ), file(circcomb,rc3_circcomb), []). fof(fc14_circcomb,axiom,( ! [A,B,C,D] : ( ( m1_subset_1(A,k5_numbers) & ~ v1_xboole_0(B) & v1_finset_1(B) & v1_funct_1(C) & v1_funct_2(C,k4_finseq_2(A,B),B) & m1_relset_1(C,k4_finseq_2(A,B),B) & m1_circcomb(D,A) ) => ( v4_msualg_1(k9_circcomb(A,B,C,D),k7_circcomb(C,D)) & v5_msualg_1(k9_circcomb(A,B,C,D),k7_circcomb(C,D)) & v3_msafree2(k9_circcomb(A,B,C,D),k7_circcomb(C,D)) & v4_msafree2(k9_circcomb(A,B,C,D),k7_circcomb(C,D)) & v4_circcomb(k9_circcomb(A,B,C,D),k7_circcomb(C,D)) ) ) ), file(circcomb,fc14_circcomb), []). fof(rc4_circcomb,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_msualg_1(A) ) => ? [B] : ( l3_msualg_1(B,A) & v4_msualg_1(B,A) & v5_msualg_1(B,A) & v3_msafree2(B,A) & v4_msafree2(B,A) & v6_circcomb(B,A) ) ) ), file(circcomb,rc4_circcomb), []). fof(rc5_circcomb,axiom,( ? [A] : ( l1_msualg_1(A) & ~ v3_struct_0(A) & v1_msualg_1(A) & ~ v2_msualg_1(A) & v2_msafree2(A) & v1_circcomb(A) & v2_circcomb(A) & v3_circcomb(A) & v5_circcomb(A) ) ), file(circcomb,rc5_circcomb), []). fof(rc6_circcomb,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_circcomb(A) & l1_msualg_1(A) ) => ? [B] : ( l3_msualg_1(B,A) & v4_msualg_1(B,A) & v5_msualg_1(B,A) & v3_msafree2(B,A) & v4_msafree2(B,A) & v4_circcomb(B,A) & v6_circcomb(B,A) ) ) ), file(circcomb,rc6_circcomb), []). fof(rc7_circcomb,axiom,( ! [A,B,C,D] : ( ( m1_subset_1(A,k5_numbers) & ~ v1_xboole_0(B) & v1_finset_1(B) & v1_funct_1(C) & v1_funct_2(C,k4_finseq_2(A,B),B) & m1_relset_1(C,k4_finseq_2(A,B),B) & m1_circcomb(D,A) ) => ? [E] : ( l3_msualg_1(E,k7_circcomb(C,D)) & v4_msualg_1(E,k7_circcomb(C,D)) & v5_msualg_1(E,k7_circcomb(C,D)) & v3_msafree2(E,k7_circcomb(C,D)) & v4_msafree2(E,k7_circcomb(C,D)) & v4_circcomb(E,k7_circcomb(C,D)) ) ) ), file(circcomb,rc7_circcomb), []). fof(fc16_circcomb,axiom,( ! [A,B,C,D] : ( ( m1_subset_1(A,k5_numbers) & ~ v1_xboole_0(B) & v1_finset_1(B) & v1_funct_1(C) & v1_funct_2(C,k4_finseq_2(A,B),B) & m1_relset_1(C,k4_finseq_2(A,B),B) & m1_circcomb(D,A) ) => ( v4_msualg_1(k9_circcomb(A,B,C,D),k7_circcomb(C,D)) & v5_msualg_1(k9_circcomb(A,B,C,D),k7_circcomb(C,D)) & v3_msafree2(k9_circcomb(A,B,C,D),k7_circcomb(C,D)) & v4_msafree2(k9_circcomb(A,B,C,D),k7_circcomb(C,D)) & v4_circcomb(k9_circcomb(A,B,C,D),k7_circcomb(C,D)) ) ) ), file(circcomb,fc16_circcomb), []). fof(rc3_facirc_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & ~ v2_facirc_1(A) ) ), file(facirc_1,rc3_facirc_1), []). fof(cc4_facirc_1,axiom,( ! [A] : ( ( v1_relat_1(A) & ~ v2_facirc_1(A) ) => ( v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) & ~ v3_xreal_0(A) & ~ v2_facirc_1(A) ) ) ), file(facirc_1,cc4_facirc_1), []). fof(fc14_facirc_1,axiom,( ! [A,B,C] : ( ( ~ v1_facirc_1(A) & ~ v1_facirc_1(B) & ~ v1_facirc_1(C) ) => ( v1_relat_1(k11_finseq_1(A,B,C)) & v1_funct_1(k11_finseq_1(A,B,C)) & v1_finset_1(k11_finseq_1(A,B,C)) & v1_finseq_1(k11_finseq_1(A,B,C)) & v3_facirc_1(k11_finseq_1(A,B,C)) ) ) ), file(facirc_1,fc14_facirc_1), []). fof(rc1_fraenkel,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_fraenkel(A) ) ), file(fraenkel,rc1_fraenkel), []). 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(spc3_boole,axiom,( ~ v1_xboole_0(3) ), file(boole,spc3_boole), []). fof(spc3_numerals,axiom, ( v2_xreal_0(3) & m1_subset_1(3,k5_numbers) ), file(numerals,spc3_numerals), []). fof(t1_subset,axiom,( ! [A,B] : ( r2_hidden(A,B) => m1_subset_1(A,B) ) ), file(subset,t1_subset), []). 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_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(d10_facirc_1,axiom,( ! [A,B,C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_finseq_2(2,k10_circcomb),k10_circcomb) & m2_relset_1(C,k4_finseq_2(2,k10_circcomb),k10_circcomb) ) => k10_facirc_1(A,B,C) = k9_circcomb(2,k10_circcomb,C,k6_facirc_1(A,B)) ) ), file(facirc_1,d10_facirc_1), []). fof(spc3_numerals,axiom, ( v2_xreal_0(3) & m1_subset_1(3,k5_numbers) ), file(numerals,spc3_numerals), []). fof(spc3_boole,axiom,( ~ v1_xboole_0(3) ), file(boole,spc3_boole), []). fof(commutativity_k10_margrel1,axiom,( ! [A,B] : ( ( v2_margrel1(A) & v2_margrel1(B) ) => k10_margrel1(A,B) = k10_margrel1(B,A) ) ), file(margrel1,k10_margrel1), []). fof(commutativity_k1_binarith,axiom,( ! [A,B] : ( ( v2_margrel1(A) & v2_margrel1(B) ) => k1_binarith(A,B) = k1_binarith(B,A) ) ), file(binarith,k1_binarith), []). fof(involutiveness_k9_margrel1,axiom,( ! [A] : ( v2_margrel1(A) => k9_margrel1(k9_margrel1(A)) = A ) ), file(margrel1,k9_margrel1), []). fof(abstractness_v1_msualg_1,axiom,( ! [A] : ( l1_msualg_1(A) => ( v1_msualg_1(A) => A = g1_msualg_1(u1_struct_0(A),u1_msualg_1(A),u2_msualg_1(A),u3_msualg_1(A)) ) ) ), file(msualg_1,v1_msualg_1), []). fof(abstractness_v4_msualg_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_msualg_1(A) & l3_msualg_1(B,A) ) => ( v4_msualg_1(B,A) => B = g3_msualg_1(A,u4_msualg_1(A,B),u5_msualg_1(A,B)) ) ) ), file(msualg_1,v4_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_circcomb,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ? [B] : m1_circcomb(B,A) ) ), file(circcomb,m1_circcomb), []). fof(existence_m1_pboole,axiom,( ! [A] : ? [B] : m1_pboole(B,A) ), file(pboole,m1_pboole), []). fof(existence_m1_struct_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ? [C] : m1_struct_0(C,A,B) ) ), file(struct_0,m1_struct_0), []). 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(redefinition_k4_msafree2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => k4_msafree2(A) = k3_msafree2(A) ) ), file(msafree2,k4_msafree2), []). fof(redefinition_k5_numbers,axiom,( k5_numbers = k5_ordinal2 ), file(numbers,k5_numbers), []). fof(redefinition_k7_facirc_1,axiom,( ! [A,B,C] : k7_facirc_1(A,B,C) = k11_finseq_1(A,B,C) ), file(facirc_1,k7_facirc_1), []). fof(redefinition_m1_struct_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_struct_0(C,A,B) <=> m1_subset_1(C,B) ) ) ), file(struct_0,m1_struct_0), []). 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(dt_k10_finseq_1,axiom,( $true ), file(finseq_1,k10_finseq_1), []). fof(dt_k10_margrel1,axiom,( $true ), file(margrel1,k10_margrel1), []). fof(dt_k11_facirc_1,axiom,( ! [A,B,C,D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_finseq_2(3,k10_circcomb),k10_circcomb) & m1_relset_1(D,k4_finseq_2(3,k10_circcomb),k10_circcomb) ) => ( v4_msualg_1(k11_facirc_1(A,B,C,D),k7_circcomb(D,k7_facirc_1(A,B,C))) & v4_msafree2(k11_facirc_1(A,B,C,D),k7_circcomb(D,k7_facirc_1(A,B,C))) & v4_circcomb(k11_facirc_1(A,B,C,D),k7_circcomb(D,k7_facirc_1(A,B,C))) & v6_circcomb(k11_facirc_1(A,B,C,D),k7_circcomb(D,k7_facirc_1(A,B,C))) & l3_msualg_1(k11_facirc_1(A,B,C,D),k7_circcomb(D,k7_facirc_1(A,B,C))) ) ) ), file(facirc_1,k11_facirc_1), []). fof(dt_k1_binarith,axiom,( $true ), file(binarith,k1_binarith), []). fof(dt_k1_zfmisc_1,axiom,( $true ), file(zfmisc_1,k1_zfmisc_1), []). fof(dt_k3_circcomb,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_msualg_1(A) & ~ v3_struct_0(B) & l1_msualg_1(B) ) => ( ~ v3_struct_0(k3_circcomb(A,B)) & v1_msualg_1(k3_circcomb(A,B)) & l1_msualg_1(k3_circcomb(A,B)) ) ) ), file(circcomb,k3_circcomb), []). fof(dt_k3_fscirc_1,axiom,( ! [A,B,C] : ( ~ v3_struct_0(k3_fscirc_1(A,B,C)) & v1_msualg_1(k3_fscirc_1(A,B,C)) & ~ v2_msualg_1(k3_fscirc_1(A,B,C)) & v1_circcomb(k3_fscirc_1(A,B,C)) & v2_circcomb(k3_fscirc_1(A,B,C)) & v3_circcomb(k3_fscirc_1(A,B,C)) & l1_msualg_1(k3_fscirc_1(A,B,C)) ) ), file(fscirc_1,k3_fscirc_1), []). fof(dt_k4_circcomb,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(A) & l1_msualg_1(A) & ~ v3_struct_0(B) & l1_msualg_1(B) & v5_msualg_1(C,A) & l3_msualg_1(C,A) & v5_msualg_1(D,B) & l3_msualg_1(D,B) ) => ( v4_msualg_1(k4_circcomb(A,B,C,D),k3_circcomb(A,B)) & v5_msualg_1(k4_circcomb(A,B,C,D),k3_circcomb(A,B)) & l3_msualg_1(k4_circcomb(A,B,C,D),k3_circcomb(A,B)) ) ) ), file(circcomb,k4_circcomb), []). fof(dt_k4_facirc_1,axiom, ( v1_funct_1(k4_facirc_1) & v1_funct_2(k4_facirc_1,k4_finseq_2(3,k10_circcomb),k10_circcomb) & m2_relset_1(k4_facirc_1,k4_finseq_2(3,k10_circcomb),k10_circcomb) ), file(facirc_1,k4_facirc_1), []). fof(dt_k4_finseq_2,axiom,( ! [A,B] : ( v4_ordinal2(A) => m1_finseq_2(k4_finseq_2(A,B),B) ) ), file(finseq_2,k4_finseq_2), []). fof(dt_k4_msafree2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ( ~ v1_xboole_0(k4_msafree2(A)) & m1_subset_1(k4_msafree2(A),k1_zfmisc_1(u1_struct_0(A))) ) ) ), file(msafree2,k4_msafree2), []). fof(dt_k5_fscirc_1,axiom,( ! [A,B,C] : ( v4_msualg_1(k5_fscirc_1(A,B,C),k3_fscirc_1(A,B,C)) & v4_msafree2(k5_fscirc_1(A,B,C),k3_fscirc_1(A,B,C)) & v4_circcomb(k5_fscirc_1(A,B,C),k3_fscirc_1(A,B,C)) & v6_circcomb(k5_fscirc_1(A,B,C),k3_fscirc_1(A,B,C)) & l3_msualg_1(k5_fscirc_1(A,B,C),k3_fscirc_1(A,B,C)) ) ), file(fscirc_1,k5_fscirc_1), []). fof(dt_k5_numbers,axiom,( m1_subset_1(k5_numbers,k1_zfmisc_1(k1_numbers)) ), file(numbers,k5_numbers), []). fof(dt_k6_margrel1,axiom,( $true ), file(margrel1,k6_margrel1), []). fof(dt_k7_circcomb,axiom,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( v1_msualg_1(k7_circcomb(A,B)) & ~ v2_msualg_1(k7_circcomb(A,B)) & l1_msualg_1(k7_circcomb(A,B)) ) ) ), file(circcomb,k7_circcomb), []). fof(dt_k7_facirc_1,axiom,( ! [A,B,C] : m1_circcomb(k7_facirc_1(A,B,C),3) ), file(facirc_1,k7_facirc_1), []). fof(dt_k9_margrel1,axiom,( ! [A] : ( v2_margrel1(A) => v2_margrel1(k9_margrel1(A)) ) ), file(margrel1,k9_margrel1), []). 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_circcomb,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ! [B] : ( m1_circcomb(B,A) => ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) ) ) ), file(circcomb,m1_circcomb), []). 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_struct_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_struct_0(C,A,B) => m1_subset_1(C,u1_struct_0(A)) ) ) ), file(struct_0,m1_struct_0), []). 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(rc3_struct_0,axiom,( ? [A] : ( l1_struct_0(A) & ~ v3_struct_0(A) ) ), file(struct_0,rc3_struct_0), []). 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(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(fc3_circcomb,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & ~ v3_struct_0(B) & l1_msualg_1(B) ) => ( ~ v3_struct_0(k3_circcomb(A,B)) & v1_msualg_1(k3_circcomb(A,B)) & ~ v2_msualg_1(k3_circcomb(A,B)) ) ) ), file(circcomb,fc3_circcomb), []). fof(fc4_circcomb,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & ~ v3_struct_0(B) & l1_msualg_1(B) ) => ( ~ v3_struct_0(k3_circcomb(B,A)) & v1_msualg_1(k3_circcomb(B,A)) & ~ v2_msualg_1(k3_circcomb(B,A)) ) ) ), file(circcomb,fc4_circcomb), []). fof(cc1_circcomb,axiom,( ! [A] : ( l1_msualg_1(A) => ( ( ~ v3_struct_0(A) & v3_circcomb(A) ) => ( ~ v3_struct_0(A) & v5_circcomb(A) ) ) ) ), file(circcomb,cc1_circcomb), []). fof(cc2_circcomb,axiom,( ! [A] : ( l1_msualg_1(A) => ( ( ~ v3_struct_0(A) & v1_circcomb(A) ) => ( ~ v3_struct_0(A) & v2_msafree2(A) ) ) ) ), file(circcomb,cc2_circcomb), []). fof(rc2_circcomb,axiom,( ? [A] : ( l1_msualg_1(A) & ~ v3_struct_0(A) & v1_msualg_1(A) & ~ v2_msualg_1(A) & v2_msafree2(A) & v1_circcomb(A) & v2_circcomb(A) ) ), file(circcomb,rc2_circcomb), []). fof(fc8_circcomb,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v1_circcomb(A) & l1_msualg_1(A) & ~ v3_struct_0(B) & v1_circcomb(B) & l1_msualg_1(B) ) => ( ~ v3_struct_0(k3_circcomb(A,B)) & v1_msualg_1(k3_circcomb(A,B)) & v2_msafree2(k3_circcomb(A,B)) & v1_circcomb(k3_circcomb(A,B)) ) ) ), file(circcomb,fc8_circcomb), []). fof(fc9_circcomb,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_circcomb(A) & l1_msualg_1(A) & ~ v3_struct_0(B) & v2_circcomb(B) & l1_msualg_1(B) ) => ( ~ v3_struct_0(k3_circcomb(A,B)) & v1_msualg_1(k3_circcomb(A,B)) & v2_circcomb(k3_circcomb(A,B)) ) ) ), file(circcomb,fc9_circcomb), []). fof(fc13_circcomb,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v3_circcomb(A) & l1_msualg_1(A) & ~ v3_struct_0(B) & v3_circcomb(B) & l1_msualg_1(B) ) => ( ~ v3_struct_0(k3_circcomb(A,B)) & v1_msualg_1(k3_circcomb(A,B)) & v3_circcomb(k3_circcomb(A,B)) & v5_circcomb(k3_circcomb(A,B)) ) ) ), file(circcomb,fc13_circcomb), []). fof(cc3_circcomb,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ( v6_circcomb(B,A) => ( v5_msualg_1(B,A) & v3_msafree2(B,A) & v4_msafree2(B,A) ) ) ) ) ), file(circcomb,cc3_circcomb), []). fof(fc15_circcomb,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v1_circcomb(A) & v3_circcomb(A) & l1_msualg_1(A) & ~ v3_struct_0(B) & ~ v2_msualg_1(B) & v1_circcomb(B) & v3_circcomb(B) & l1_msualg_1(B) & v4_msafree2(C,A) & v4_circcomb(C,A) & v6_circcomb(C,A) & l3_msualg_1(C,A) & v4_msafree2(D,B) & v4_circcomb(D,B) & v6_circcomb(D,B) & l3_msualg_1(D,B) ) => ( v4_msualg_1(k4_circcomb(A,B,C,D),k3_circcomb(A,B)) & v5_msualg_1(k4_circcomb(A,B,C,D),k3_circcomb(A,B)) & v3_msafree2(k4_circcomb(A,B,C,D),k3_circcomb(A,B)) & v4_msafree2(k4_circcomb(A,B,C,D),k3_circcomb(A,B)) & v4_circcomb(k4_circcomb(A,B,C,D),k3_circcomb(A,B)) & v6_circcomb(k4_circcomb(A,B,C,D),k3_circcomb(A,B)) ) ) ), file(circcomb,fc15_circcomb), []). fof(rc1_facirc_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_facirc_1(A) ) ), file(facirc_1,rc1_facirc_1), []). fof(cc2_facirc_1,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v1_facirc_1(A) ) ) ), file(facirc_1,cc2_facirc_1), []). fof(cc3_facirc_1,axiom,( ! [A] : ( v1_xboole_0(A) => ~ v2_facirc_1(A) ) ), file(facirc_1,cc3_facirc_1), []). fof(fc13_facirc_1,axiom,( ! [A,B] : ( ( ~ v1_facirc_1(A) & ~ v1_facirc_1(B) ) => ( v1_relat_1(k10_finseq_1(A,B)) & v1_funct_1(k10_finseq_1(A,B)) & v1_finset_1(k10_finseq_1(A,B)) & v1_finseq_1(k10_finseq_1(A,B)) & v3_facirc_1(k10_finseq_1(A,B)) ) ) ), file(facirc_1,fc13_facirc_1), []). fof(fc3_card_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => v1_fraenkel(k4_card_3(A)) ) ), file(card_3,fc3_card_3), []). fof(t2_subset,axiom,( ! [A,B] : ( m1_subset_1(A,B) => ( v1_xboole_0(B) | r2_hidden(A,B) ) ) ), file(subset,t2_subset), []). fof(t3_subset,axiom,( ! [A,B] : ( m1_subset_1(A,k1_zfmisc_1(B)) <=> r1_tarski(A,B) ) ), file(subset,t3_subset), []). fof(t6_boole,axiom,( ! [A] : ( v1_xboole_0(A) => A = k1_xboole_0 ) ), file(boole,t6_boole), []). fof(t7_boole,axiom,( ! [A,B] : ~ ( r2_hidden(A,B) & v1_xboole_0(B) ) ), file(boole,t7_boole), []). fof(t8_boole,axiom,( ! [A,B] : ~ ( v1_xboole_0(A) & A != B & v1_xboole_0(B) ) ), file(boole,t8_boole), []). fof(d11_facirc_1,axiom,( ! [A,B,C,D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_finseq_2(3,k10_circcomb),k10_circcomb) & m2_relset_1(D,k4_finseq_2(3,k10_circcomb),k10_circcomb) ) => k11_facirc_1(A,B,C,D) = k9_circcomb(3,k10_circcomb,D,k7_facirc_1(A,B,C)) ) ), file(facirc_1,d11_facirc_1), []). fof(d3_fscirc_1,axiom,( ! [A,B,C] : k3_fscirc_1(A,B,C) = k3_circcomb(k3_circcomb(k7_circcomb(k3_twoscomp,k6_facirc_1(A,B)),k7_circcomb(k2_twoscomp,k6_facirc_1(B,C))),k7_circcomb(k3_twoscomp,k6_facirc_1(A,C))) ), file(fscirc_1,d3_fscirc_1), []). fof(d5_fscirc_1,axiom,( ! [A,B,C] : k5_fscirc_1(A,B,C) = k4_circcomb(k3_circcomb(k7_circcomb(k3_twoscomp,k6_facirc_1(A,B)),k7_circcomb(k2_twoscomp,k6_facirc_1(B,C))),k7_circcomb(k3_twoscomp,k6_facirc_1(A,C)),k4_circcomb(k7_circcomb(k3_twoscomp,k6_facirc_1(A,B)),k7_circcomb(k2_twoscomp,k6_facirc_1(B,C)),k10_facirc_1(A,B,k3_twoscomp),k10_facirc_1(B,C,k2_twoscomp)),k10_facirc_1(A,C,k3_twoscomp)) ), file(fscirc_1,d5_fscirc_1), []). fof(involutiveness_k11_margrel1,axiom,( ! [A] : ( m1_subset_1(A,k6_margrel1) => k11_margrel1(k11_margrel1(A)) = A ) ), file(margrel1,k11_margrel1), []). fof(commutativity_k12_margrel1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k6_margrel1) & m1_subset_1(B,k6_margrel1) ) => k12_margrel1(A,B) = k12_margrel1(B,A) ) ), file(margrel1,k12_margrel1), []). fof(commutativity_k3_binarith,axiom,( ! [A,B] : ( ( m1_subset_1(A,k6_margrel1) & m1_subset_1(B,k6_margrel1) ) => k3_binarith(A,B) = k3_binarith(B,A) ) ), file(binarith,k3_binarith), []). fof(existence_m1_subset_1,axiom,( ! [A] : ? [B] : m1_subset_1(B,A) ), file(subset_1,m1_subset_1), []). fof(redefinition_k10_circcomb,axiom,( k10_circcomb = k6_margrel1 ), file(circcomb,k10_circcomb), []). fof(redefinition_k11_margrel1,axiom,( ! [A] : ( m1_subset_1(A,k6_margrel1) => k11_margrel1(A) = k9_margrel1(A) ) ), file(margrel1,k11_margrel1), []). fof(redefinition_k12_margrel1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k6_margrel1) & m1_subset_1(B,k6_margrel1) ) => k12_margrel1(A,B) = k10_margrel1(A,B) ) ), file(margrel1,k12_margrel1), []). fof(redefinition_k15_facirc_1,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v1_circcomb(A) & l1_msualg_1(A) & v4_msafree2(B,A) & v6_circcomb(B,A) & l3_msualg_1(B,A) & m1_subset_1(C,k4_card_3(u4_msualg_1(A,B))) & m1_subset_1(D,u1_struct_0(A)) ) => k15_facirc_1(A,B,C,D) = k1_funct_1(C,D) ) ), file(facirc_1,k15_facirc_1), []). fof(redefinition_k3_binarith,axiom,( ! [A,B] : ( ( m1_subset_1(A,k6_margrel1) & m1_subset_1(B,k6_margrel1) ) => k3_binarith(A,B) = k1_binarith(A,B) ) ), file(binarith,k3_binarith), []). fof(redefinition_k6_facirc_1,axiom,( ! [A,B] : k6_facirc_1(A,B) = k10_finseq_1(A,B) ), file(facirc_1,k6_facirc_1), []). fof(dt_k10_circcomb,axiom, ( ~ v1_xboole_0(k10_circcomb) & v1_finset_1(k10_circcomb) & m1_subset_1(k10_circcomb,k1_zfmisc_1(k5_numbers)) ), file(circcomb,k10_circcomb), []). fof(dt_k11_margrel1,axiom,( ! [A] : ( m1_subset_1(A,k6_margrel1) => m1_subset_1(k11_margrel1(A),k6_margrel1) ) ), file(margrel1,k11_margrel1), []). fof(dt_k12_margrel1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k6_margrel1) & m1_subset_1(B,k6_margrel1) ) => m1_subset_1(k12_margrel1(A,B),k6_margrel1) ) ), file(margrel1,k12_margrel1), []). fof(dt_k15_facirc_1,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v1_circcomb(A) & l1_msualg_1(A) & v4_msafree2(B,A) & v6_circcomb(B,A) & l3_msualg_1(B,A) & m1_subset_1(C,k4_card_3(u4_msualg_1(A,B))) & m1_subset_1(D,u1_struct_0(A)) ) => m2_subset_1(k15_facirc_1(A,B,C,D),k5_numbers,k10_circcomb) ) ), file(facirc_1,k15_facirc_1), []). fof(dt_k1_funct_1,axiom,( $true ), file(funct_1,k1_funct_1), []). fof(dt_k2_twoscomp,axiom, ( v1_funct_1(k2_twoscomp) & v1_funct_2(k2_twoscomp,k4_finseq_2(2,k10_circcomb),k10_circcomb) & m2_relset_1(k2_twoscomp,k4_finseq_2(2,k10_circcomb),k10_circcomb) ), file(twoscomp,k2_twoscomp), []). fof(dt_k3_binarith,axiom,( ! [A,B] : ( ( m1_subset_1(A,k6_margrel1) & m1_subset_1(B,k6_margrel1) ) => m1_subset_1(k3_binarith(A,B),k6_margrel1) ) ), file(binarith,k3_binarith), []). fof(dt_k3_twoscomp,axiom, ( v1_funct_1(k3_twoscomp) & v1_funct_2(k3_twoscomp,k4_finseq_2(2,k10_circcomb),k10_circcomb) & m2_relset_1(k3_twoscomp,k4_finseq_2(2,k10_circcomb),k10_circcomb) ), file(twoscomp,k3_twoscomp), []). fof(dt_k4_card_3,axiom,( $true ), file(card_3,k4_card_3), []). fof(dt_k4_fscirc_1,axiom,( ! [A,B,C] : ( ~ v3_struct_0(k4_fscirc_1(A,B,C)) & v1_msualg_1(k4_fscirc_1(A,B,C)) & ~ v2_msualg_1(k4_fscirc_1(A,B,C)) & v1_circcomb(k4_fscirc_1(A,B,C)) & v2_circcomb(k4_fscirc_1(A,B,C)) & v3_circcomb(k4_fscirc_1(A,B,C)) & l1_msualg_1(k4_fscirc_1(A,B,C)) ) ), file(fscirc_1,k4_fscirc_1), []). fof(dt_k4_tarski,axiom,( $true ), file(tarski,k4_tarski), []). fof(dt_k6_facirc_1,axiom,( ! [A,B] : m1_circcomb(k6_facirc_1(A,B),2) ), file(facirc_1,k6_facirc_1), []). fof(dt_k6_fscirc_1,axiom,( ! [A,B,C] : m1_struct_0(k6_fscirc_1(A,B,C),k4_fscirc_1(A,B,C),k4_msafree2(k4_fscirc_1(A,B,C))) ), file(fscirc_1,k6_fscirc_1), []). fof(dt_k7_fscirc_1,axiom,( ! [A,B,C] : ( v4_msualg_1(k7_fscirc_1(A,B,C),k4_fscirc_1(A,B,C)) & v4_msafree2(k7_fscirc_1(A,B,C),k4_fscirc_1(A,B,C)) & v4_circcomb(k7_fscirc_1(A,B,C),k4_fscirc_1(A,B,C)) & v6_circcomb(k7_fscirc_1(A,B,C),k4_fscirc_1(A,B,C)) & l3_msualg_1(k7_fscirc_1(A,B,C),k4_fscirc_1(A,B,C)) ) ), file(fscirc_1,k7_fscirc_1), []). fof(dt_k9_facirc_1,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v2_msafree2(A) & l1_msualg_1(A) & v5_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) & m1_subset_1(C,k4_card_3(u4_msualg_1(A,B))) & m1_subset_1(D,k5_numbers) ) => m1_subset_1(k9_facirc_1(A,B,C,D),k4_card_3(u4_msualg_1(A,B))) ) ), file(facirc_1,k9_facirc_1), []). fof(dt_m1_subset_1,axiom,( $true ), file(subset_1,m1_subset_1), []). 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(cc1_facirc_1,axiom,( ! [A] : ( v1_facirc_1(A) => ~ v1_xboole_0(A) ) ), file(facirc_1,cc1_facirc_1), []). fof(fc1_facirc_1,axiom,( ! [A,B] : ( ~ v1_xboole_0(k4_tarski(A,B)) & v1_facirc_1(k4_tarski(A,B)) ) ), file(facirc_1,fc1_facirc_1), []). fof(rc2_facirc_1,axiom,( ? [A] : ~ v1_facirc_1(A) ), file(facirc_1,rc2_facirc_1), []). fof(d4_fscirc_1,axiom,( ! [A,B,C] : k4_fscirc_1(A,B,C) = k3_circcomb(k3_fscirc_1(A,B,C),k7_circcomb(k4_facirc_1,k7_facirc_1(k4_tarski(k6_facirc_1(A,B),k3_twoscomp),k4_tarski(k6_facirc_1(B,C),k2_twoscomp),k4_tarski(k6_facirc_1(A,C),k3_twoscomp)))) ), file(fscirc_1,d4_fscirc_1), []). fof(d6_fscirc_1,axiom,( ! [A,B,C] : k6_fscirc_1(A,B,C) = k4_tarski(k7_facirc_1(k4_tarski(k6_facirc_1(A,B),k3_twoscomp),k4_tarski(k6_facirc_1(B,C),k2_twoscomp),k4_tarski(k6_facirc_1(A,C),k3_twoscomp)),k4_facirc_1) ), file(fscirc_1,d6_fscirc_1), []). fof(d7_fscirc_1,axiom,( ! [A,B,C] : k7_fscirc_1(A,B,C) = k4_circcomb(k3_fscirc_1(A,B,C),k7_circcomb(k4_facirc_1,k7_facirc_1(k4_tarski(k6_facirc_1(A,B),k3_twoscomp),k4_tarski(k6_facirc_1(B,C),k2_twoscomp),k4_tarski(k6_facirc_1(A,C),k3_twoscomp))),k5_fscirc_1(A,B,C),k11_facirc_1(k4_tarski(k6_facirc_1(A,B),k3_twoscomp),k4_tarski(k6_facirc_1(B,C),k2_twoscomp),k4_tarski(k6_facirc_1(A,C),k3_twoscomp),k4_facirc_1)) ), file(fscirc_1,d7_fscirc_1), []). fof(spc2_numerals,axiom, ( v2_xreal_0(2) & m1_subset_1(2,k5_numbers) ), file(numerals,spc2_numerals), []). fof(spc2_boole,axiom,( ~ v1_xboole_0(2) ), file(boole,spc2_boole), []). fof(l22_fscirc_1,axiom,( ! [A] : ( ~ v1_facirc_1(A) => ! [B] : ( ~ v1_facirc_1(B) => ! [C] : ( ~ v1_facirc_1(C) => ! [D] : ( m1_subset_1(D,k4_card_3(u4_msualg_1(k4_fscirc_1(A,B,C),k7_fscirc_1(A,B,C)))) => ! [E] : ( m1_subset_1(E,k10_circcomb) => ! [F] : ( m1_subset_1(F,k10_circcomb) => ! [G] : ( m1_subset_1(G,k10_circcomb) => ( ( E = k1_funct_1(D,A) & F = k1_funct_1(D,B) & G = k1_funct_1(D,C) ) => ( k15_facirc_1(k4_fscirc_1(A,B,C),k7_fscirc_1(A,B,C),k9_facirc_1(k4_fscirc_1(A,B,C),k7_fscirc_1(A,B,C),D,2),k6_fscirc_1(A,B,C)) = k3_binarith(k3_binarith(k12_margrel1(k11_margrel1(E),F),k12_margrel1(F,G)),k12_margrel1(k11_margrel1(E),G)) & k1_funct_1(k9_facirc_1(k4_fscirc_1(A,B,C),k7_fscirc_1(A,B,C),D,2),k4_tarski(k6_facirc_1(A,B),k3_twoscomp)) = k12_margrel1(k11_margrel1(E),F) & k1_funct_1(k9_facirc_1(k4_fscirc_1(A,B,C),k7_fscirc_1(A,B,C),D,2),k4_tarski(k6_facirc_1(B,C),k2_twoscomp)) = k12_margrel1(F,G) & k1_funct_1(k9_facirc_1(k4_fscirc_1(A,B,C),k7_fscirc_1(A,B,C),D,2),k4_tarski(k6_facirc_1(A,C),k3_twoscomp)) = k12_margrel1(k11_margrel1(E),G) ) ) ) ) ) ) ) ) ) ), file(fscirc_1,l22_fscirc_1), []).