% Mizar problem: t29_equation,equation,1176,19 fof(t29_equation,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] : ( C = a_2_0_equation(A,B) => ! [D] : ( m2_pralg_2(D,C,A) => ~ ( ! [E] : ( r2_hidden(E,C) => E = k1_funct_1(D,E) ) & ! [E] : ( ( v4_msualg_1(E,A) & v5_msualg_1(E,A) & m1_msualg_2(E,A,k15_pralg_2(C,A,D)) ) => ! [F] : ( m3_pboole(F,u1_struct_0(A),u4_msualg_1(A,E),u4_msualg_1(A,B)) => ~ r2_msualg_3(A,E,B,F) ) ) ) ) ) ) ) ), inference(mizar_bg_added,[status(thm)],[abstractness_v4_msualg_1,antisymmetry_r2_hidden,cc1_closure2,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc1_msualg_1,cc1_msualg_6,cc1_msualg_9,cc1_pboole,cc1_relset_1,cc2_finset_1,cc2_funct_1,cc2_msualg_1,cc2_msualg_9,cc2_pboole,cc3_pboole,commutativity_k2_xboole_0,d10_msualg_1,d10_msualg_2,d10_msualg_3,d10_xboole_0,d11_msualg_1,d12_pralg_2,d16_msualg_2,d16_pboole,d16_pralg_2,d17_pralg_2,d18_msualg_2,d19_pboole,d1_funct_2,d1_funct_4,d1_pralg_3,d1_tarski,d1_xboole_0,d20_msualg_2,d21_pralg_2,d23_pboole,d2_equation,d3_msualg_3,d3_pboole,d3_pre_circ,d3_tarski,d4_finseq_4,d5_card_3,d5_funct_1,d5_pboole,d6_msualg_1,d6_msualg_2,d7_msualg_1,d7_msualg_2,d8_msualg_1,d8_msualg_3,d9_msualg_1,d9_msualg_3,dt_g3_msualg_1,dt_k10_funct_6,dt_k10_msualg_2,dt_k10_pralg_2,dt_k11_pralg_2,dt_k12_msualg_2,dt_k13_finseq_1,dt_k14_msualg_2,dt_k14_pralg_2,dt_k15_pralg_2,dt_k1_funct_1,dt_k1_funct_2,dt_k1_funct_4,dt_k1_msualg_1,dt_k1_msualg_3,dt_k1_numbers,dt_k1_relat_1,dt_k1_struct_0,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_equation,dt_k2_funcop_1,dt_k2_msualg_1,dt_k2_partfun1,dt_k2_pralg_3,dt_k2_pre_circ,dt_k2_relat_1,dt_k2_xboole_0,dt_k2_zfmisc_1,dt_k3_finseq_2,dt_k3_msualg_1,dt_k3_tarski,dt_k4_card_3,dt_k4_finseq_1,dt_k4_finseq_4,dt_k4_msualg_1,dt_k4_msualg_2,dt_k4_relset_1,dt_k5_msualg_1,dt_k5_msualg_3,dt_k5_numbers,dt_k5_ordinal2,dt_k5_relat_1,dt_k6_msualg_3,dt_k6_pboole,dt_k6_pralg_2,dt_k7_pboole,dt_k7_relat_1,dt_k8_funct_2,dt_k8_pboole,dt_l1_msualg_1,dt_l1_struct_0,dt_l2_msualg_1,dt_l3_msualg_1,dt_m1_finseq_1,dt_m1_finseq_2,dt_m1_msualg_2,dt_m1_pboole,dt_m1_relset_1,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_finseq_2,dt_m2_pralg_2,dt_m2_relset_1,dt_m2_subset_1,dt_m3_pboole,dt_m4_pboole,dt_u1_msualg_1,dt_u1_struct_0,dt_u2_msualg_1,dt_u3_msualg_1,dt_u4_msualg_1,dt_u5_msualg_1,existence_l1_msualg_1,existence_l1_struct_0,existence_l2_msualg_1,existence_l3_msualg_1,existence_m1_finseq_1,existence_m1_finseq_2,existence_m1_msualg_2,existence_m1_pboole,existence_m1_relset_1,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_finseq_2,existence_m2_pralg_2,existence_m2_relset_1,existence_m2_subset_1,existence_m3_pboole,existence_m4_pboole,fc10_msualg_2,fc11_finseq_1,fc11_msualg_2,fc14_finset_1,fc16_finseq_1,fc17_finseq_1,fc1_cantor_1,fc1_equation,fc1_finset_1,fc1_funcop_1,fc1_funct_1,fc1_msualg_1,fc1_ordinal2,fc1_pboole,fc1_pralg_2,fc1_pralg_3,fc1_struct_0,fc1_subset_1,fc2_equation,fc2_finseq_1,fc2_funcop_1,fc2_pboole,fc2_subset_1,fc3_funcop_1,fc3_msafree,fc3_pralg_3,fc4_funct_1,fc4_ordinal2,fc4_subset_1,fc6_funct_1,fc6_msualg_2,fc6_pralg_2,fc7_funcop_1,fc7_pralg_2,fc8_funcop_1,fc8_pralg_2,fc9_finseq_1,fc9_finset_1,fc9_funcop_1,fraenkel_a_2_0_equation,fraenkel_a_3_0_equation,fraenkel_a_3_1_pralg_3,free_g3_msualg_1,idempotence_k1_funct_4,idempotence_k2_xboole_0,rc1_closure2,rc1_finseq_1,rc1_finset_1,rc1_funcop_1,rc1_funct_1,rc1_msualg_6,rc1_pboole,rc1_pralg_2,rc1_subset_1,rc2_equation,rc2_finseq_1,rc2_funct_1,rc2_msualg_2,rc2_msualg_9,rc2_pboole,rc2_subset_1,rc3_equation,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc3_msualg_2,rc3_pboole,rc3_struct_0,rc4_finseq_1,rc4_finset_1,rc4_funct_1,rc4_pboole,rc5_funct_1,rc5_msualg_1,rc5_pboole,rc5_struct_0,rc6_finseq_1,rc6_msualg_1,rc7_finseq_1,rc8_finseq_1,redefinition_k1_msualg_3,redefinition_k1_struct_0,redefinition_k2_partfun1,redefinition_k2_pre_circ,redefinition_k3_finseq_2,redefinition_k4_finseq_1,redefinition_k4_relset_1,redefinition_k5_numbers,redefinition_k6_msualg_3,redefinition_k6_pralg_2,redefinition_k7_pboole,redefinition_k8_funct_2,redefinition_k8_pboole,redefinition_m2_finseq_1,redefinition_m2_finseq_2,redefinition_m2_relset_1,redefinition_m2_subset_1,redefinition_r6_pboole,reflexivity_r1_tarski,reflexivity_r2_pboole,reflexivity_r6_pboole,s1_mssubfam__e17_34__equation,s1_xboole_0__e51_34__equation,s1_xboole_0__e5_34_4_1__equation,s2_pboole__e7_34__equation,s3_funct_2__e4_34_7_1_2__equation,s3_funct_2__e8_34_3_1_1_2__equation,s3_pboole__e8_34_4_1__equation,symmetry_r6_pboole,t10_pralg_2,t10_pralg_3,t11_pralg_2,t12_funct_4,t12_pralg_3,t12_relset_1,t12_xboole_1,t13_funcop_1,t14_funct_4,t15_pralg_3,t169_funct_2,t18_card_3,t19_funcop_1,t19_msualg_9,t1_boole,t1_subset,t20_equation,t21_equation,t21_funct_2,t21_pralg_3,t22_equation,t22_pralg_3,t23_funct_1,t23_pralg_3,t26_finseq_1,t27_equation,t27_partfun1,t28_equation,t2_msualg_6,t2_subset,t2_tarski,t38_funct_2,t3_equation,t3_msualg_2,t3_subset,t46_zfmisc_1,t4_subset,t5_subset,t6_boole,t6_msualg_2,t6_msualg_3,t70_funct_1,t7_boole,t7_msualg_2,t8_boole,t9_funct_1]), [file(equation,t29_equation)]). 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(antisymmetry_r2_hidden,axiom,( ! [A,B] : ( r2_hidden(A,B) => ~ r2_hidden(B,A) ) ), file(hidden,r2_hidden), []). fof(cc1_closure2,axiom,( ! [A] : ( v1_xboole_0(A) => v1_fraenkel(A) ) ), file(closure2,cc1_closure2), []). 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_finset_1,axiom,( ! [A] : ( v1_xboole_0(A) => v1_finset_1(A) ) ), file(finset_1,cc1_finset_1), []). fof(cc1_funct_1,axiom,( ! [A] : ( v1_xboole_0(A) => v1_funct_1(A) ) ), file(funct_1,cc1_funct_1), []). fof(cc1_msualg_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_msualg_1(A) & v5_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,k2_relat_1(u4_msualg_1(A,B))) => ~ v1_xboole_0(C) ) ) ), file(msualg_1,cc1_msualg_1), []). 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_msualg_9,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v5_msualg_1(B,A) & l3_msualg_1(B,A) & m1_subset_1(C,u1_msualg_1(A)) ) => ! [D] : ( m1_subset_1(D,k3_msualg_1(A,C,B)) => ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) ) ) ), file(msualg_9,cc1_msualg_9), []). 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(cc2_finset_1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v1_finset_1(B) ) ) ), file(finset_1,cc2_finset_1), []). 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_msualg_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_msualg_1(A) & v5_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,k2_relat_1(k6_pboole(u1_struct_0(A),u4_msualg_1(A,B)))) => ~ v1_xboole_0(C) ) ) ), file(msualg_1,cc2_msualg_1), []). fof(cc2_msualg_9,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & m1_subset_1(C,u1_struct_0(A)) & m2_pralg_2(D,B,A) ) => ! [E] : ( m1_subset_1(E,k1_funct_1(k11_pralg_2(B,A,D),C)) => ( v1_relat_1(E) & v1_funct_1(E) ) ) ) ), file(msualg_9,cc2_msualg_9), []). 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(cc3_pboole,axiom,( ! [A,B,C] : ( ( m1_pboole(B,A) & m1_pboole(C,A) ) => ! [D] : ( m3_pboole(D,A,B,C) => v1_funcop_1(D) ) ) ), file(pboole,cc3_pboole), []). 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(d10_msualg_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_msualg_1(A)) => ! [C] : ( l3_msualg_1(C,A) => k4_msualg_1(A,B,C) = k1_funct_1(k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),u4_msualg_1(A,C)),B) ) ) ) ), file(msualg_1,d10_msualg_1), []). fof(d10_msualg_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( l3_msualg_1(C,A) => ( m1_msualg_2(C,A,B) <=> ( m4_pboole(u4_msualg_1(A,C),u1_struct_0(A),u4_msualg_1(A,B)) & ! [D] : ( m4_pboole(D,u1_struct_0(A),u4_msualg_1(A,B)) => ( r6_pboole(u1_struct_0(A),D,u4_msualg_1(A,C)) => ( v3_msualg_2(D,A,B) & r6_pboole(u1_msualg_1(A),u5_msualg_1(A,C),k4_msualg_2(A,B,D)) ) ) ) ) ) ) ) ) ), file(msualg_2,d10_msualg_2), []). fof(d10_msualg_3,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( l3_msualg_1(C,A) => ! [D] : ( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C)) => ( r2_msualg_3(A,B,C,D) <=> ( r1_msualg_3(A,B,C,D) & v2_msualg_3(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C)) ) ) ) ) ) ) ), file(msualg_3,d10_msualg_3), []). fof(d10_xboole_0,axiom,( ! [A,B] : ( A = B <=> ( r1_tarski(A,B) & r1_tarski(B,A) ) ) ), file(xboole_0,d10_xboole_0), []). fof(d11_msualg_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_msualg_1(A)) => ! [C] : ( l3_msualg_1(C,A) => k5_msualg_1(A,B,C) = k1_funct_1(u5_msualg_1(A,C),B) ) ) ) ), file(msualg_1,d11_msualg_1), []). fof(d12_pralg_2,axiom,( ! [A,B] : ( ( ~ v3_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( m1_pboole(C,A) => ( m2_pralg_2(C,A,B) <=> ! [D] : ( r2_hidden(D,A) => ( v5_msualg_1(k1_funct_1(C,D),B) & l3_msualg_1(k1_funct_1(C,D),B) ) ) ) ) ) ), file(pralg_2,d12_pralg_2), []). fof(d16_msualg_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) => ( v3_msualg_2(C,A,B) => k10_msualg_2(A,B,C) = g3_msualg_1(A,C,k4_msualg_2(A,B,C)) ) ) ) ) ), file(msualg_2,d16_msualg_2), []). fof(d16_pboole,axiom,( ! [A,B] : ( m1_pboole(B,A) => ( v2_relat_1(B) <=> ! [C] : ~ ( r2_hidden(C,A) & v1_xboole_0(k1_funct_1(B,C)) ) ) ) ), file(pboole,d16_pboole), []). fof(d16_pralg_2,axiom,( ! [A,B] : ( ( ~ v3_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m2_pralg_2(D,A,B) => ! [E] : ( m1_pboole(E,A) => ( ( A != k1_xboole_0 => ( E = k10_pralg_2(A,B,C,D) <=> ! [F] : ~ ( r2_hidden(F,A) & ! [G] : ( l3_msualg_1(G,B) => ~ ( G = k1_funct_1(D,F) & k1_funct_1(E,F) = k1_funct_1(u4_msualg_1(B,G),C) ) ) ) ) ) & ( A = k1_xboole_0 => ( E = k10_pralg_2(A,B,C,D) <=> E = k1_xboole_0 ) ) ) ) ) ) ) ), file(pralg_2,d16_pralg_2), []). fof(d17_pralg_2,axiom,( ! [A,B] : ( ( ~ v3_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( m2_pralg_2(C,A,B) => ! [D] : ( m1_pboole(D,u1_struct_0(B)) => ( D = k11_pralg_2(A,B,C) <=> ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => k1_funct_1(D,E) = k4_card_3(k10_pralg_2(A,B,E,C)) ) ) ) ) ) ), file(pralg_2,d17_pralg_2), []). fof(d18_msualg_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) => ! [D] : ( ( v4_msualg_1(D,A) & m1_msualg_2(D,A,B) ) => ( D = k12_msualg_2(A,B,C) <=> ( m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,D)) & ! [E] : ( m1_msualg_2(E,A,B) => ( m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,E)) => m1_msualg_2(D,A,E) ) ) ) ) ) ) ) ) ), file(msualg_2,d18_msualg_2), []). fof(d19_pboole,axiom,( ! [A,B] : ( m1_pboole(B,A) => ! [C] : ( m1_pboole(C,k3_finseq_2(A)) => ( C = k6_pboole(A,B) <=> ! [D] : ( m2_finseq_2(D,A,k3_finseq_2(A)) => k1_funct_1(C,D) = k4_card_3(k5_relat_1(D,B)) ) ) ) ) ), file(pboole,d19_pboole), []). fof(d1_funct_2,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) => ( ( ( B = k1_xboole_0 => A = k1_xboole_0 ) => ( v1_funct_2(C,A,B) <=> A = k4_relset_1(A,B,C) ) ) & ( B = k1_xboole_0 => ( A = k1_xboole_0 | ( v1_funct_2(C,A,B) <=> C = k1_xboole_0 ) ) ) ) ) ), file(funct_2,d1_funct_2), []). fof(d1_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( C = k1_funct_4(A,B) <=> ( k1_relat_1(C) = k2_xboole_0(k1_relat_1(A),k1_relat_1(B)) & ! [D] : ( r2_hidden(D,k2_xboole_0(k1_relat_1(A),k1_relat_1(B))) => ( ( r2_hidden(D,k1_relat_1(B)) => k1_funct_1(C,D) = k1_funct_1(B,D) ) & ( ~ r2_hidden(D,k1_relat_1(B)) => k1_funct_1(C,D) = k1_funct_1(A,D) ) ) ) ) ) ) ) ) ), file(funct_4,d1_funct_4), []). fof(d1_pralg_3,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( m1_subset_1(C,u1_msualg_1(A)) => k2_pralg_3(A,B,C) = k1_funct_1(k5_msualg_1(A,C,B),k1_xboole_0) ) ) ) ), file(pralg_3,d1_pralg_3), []). fof(d1_tarski,axiom,( ! [A,B] : ( B = k1_tarski(A) <=> ! [C] : ( r2_hidden(C,B) <=> C = A ) ) ), file(tarski,d1_tarski), []). fof(d1_xboole_0,axiom,( ! [A] : ( A = k1_xboole_0 <=> ! [B] : ~ r2_hidden(B,A) ) ), file(xboole_0,d1_xboole_0), []). fof(d20_msualg_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( C = k14_msualg_2(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( v4_msualg_1(D,A) & m1_msualg_2(D,A,B) ) ) ) ) ) ), file(msualg_2,d20_msualg_2), []). fof(d21_pralg_2,axiom,( ! [A,B] : ( ( ~ v3_struct_0(B) & ~ v2_msualg_1(B) & l1_msualg_1(B) ) => ! [C] : ( m2_pralg_2(C,A,B) => k15_pralg_2(A,B,C) = g3_msualg_1(B,k11_pralg_2(A,B,C),k14_pralg_2(A,B,C)) ) ) ), file(pralg_2,d21_pralg_2), []). fof(d23_pboole,axiom,( ! [A,B] : ( m1_pboole(B,A) => ! [C] : ( m1_pboole(C,A) => ( m4_pboole(C,A,B) <=> r2_pboole(A,C,B) ) ) ) ), file(pboole,d23_pboole), []). fof(d2_equation,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( m1_msualg_2(C,A,B) => ! [D] : ( D = k2_equation(A,B,C) <=> ! [E] : ( r2_hidden(E,D) <=> ? [F] : ( v4_msualg_1(F,A) & m1_msualg_2(F,A,B) & E = F & m1_msualg_2(C,A,F) ) ) ) ) ) ) ), file(equation,d2_equation), []). fof(d3_msualg_3,axiom,( ! [A,B] : ( m1_pboole(B,A) => ! [C] : ( m1_pboole(C,A) => ! [D] : ( m3_pboole(D,A,B,C) => ( v2_msualg_3(D,A,B,C) <=> ! [E] : ( r2_hidden(E,A) => k2_relat_1(k1_funct_1(D,E)) = k1_funct_1(C,E) ) ) ) ) ) ), file(msualg_3,d3_msualg_3), []). fof(d3_pboole,axiom,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( m1_pboole(B,A) <=> k1_relat_1(B) = A ) ) ), file(pboole,d3_pboole), []). fof(d3_pre_circ,axiom,( ! [A,B] : ( m1_pboole(B,A) => ( v1_pre_circ(B,A) <=> ! [C] : ( r2_hidden(C,A) => v1_finset_1(k1_funct_1(B,C)) ) ) ) ), file(pre_circ,d3_pre_circ), []). fof(d3_tarski,axiom,( ! [A,B] : ( r1_tarski(A,B) <=> ! [C] : ( r2_hidden(C,A) => r2_hidden(C,B) ) ) ), file(tarski,d3_tarski), []). fof(d4_finseq_4,axiom,( ! [A,B,C] : ( ( v1_funct_1(C) & m2_relset_1(C,A,B) ) => ! [D] : ( r2_hidden(D,k1_relat_1(C)) => k4_finseq_4(A,B,C,D) = k1_funct_1(C,D) ) ) ), file(finseq_4,d4_finseq_4), []). fof(d5_card_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( B = k4_card_3(A) <=> ! [C] : ( r2_hidden(C,B) <=> ? [D] : ( v1_relat_1(D) & v1_funct_1(D) & C = D & k1_relat_1(D) = k1_relat_1(A) & ! [E] : ( r2_hidden(E,k1_relat_1(A)) => r2_hidden(k1_funct_1(D,E),k1_funct_1(A,E)) ) ) ) ) ) ), file(card_3,d5_card_3), []). fof(d5_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( B = k2_relat_1(A) <=> ! [C] : ( r2_hidden(C,B) <=> ? [D] : ( r2_hidden(D,k1_relat_1(A)) & C = k1_funct_1(A,D) ) ) ) ) ), file(funct_1,d5_funct_1), []). fof(d5_pboole,axiom,( ! [A,B] : ( m1_pboole(B,A) => ! [C] : ( m1_pboole(C,A) => ( r2_pboole(A,B,C) <=> ! [D] : ( r2_hidden(D,A) => r1_tarski(k1_funct_1(B,D),k1_funct_1(C,D)) ) ) ) ) ), file(pboole,d5_pboole), []). fof(d6_msualg_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_msualg_1(A)) => k1_msualg_1(A,B) = k1_funct_1(u2_msualg_1(A),B) ) ) ), file(msualg_1,d6_msualg_1), []). fof(d6_msualg_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( m1_subset_1(C,u1_msualg_1(A)) => ! [D] : ( m4_pboole(D,u1_struct_0(A),u4_msualg_1(A,B)) => ( r1_msualg_2(A,B,C,D) <=> r1_tarski(k2_relat_1(k7_relat_1(k5_msualg_1(A,C,B),k1_funct_1(k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),D)),C))),k1_funct_1(k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),D),C)) ) ) ) ) ) ), file(msualg_2,d6_msualg_2), []). fof(d7_msualg_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_msualg_1(A)) => k2_msualg_1(A,B) = k1_funct_1(u3_msualg_1(A),B) ) ) ), file(msualg_1,d7_msualg_1), []). fof(d7_msualg_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) => ( v3_msualg_2(C,A,B) <=> ! [D] : ( m1_subset_1(D,u1_msualg_1(A)) => r1_msualg_2(A,B,D,C) ) ) ) ) ) ), file(msualg_2,d7_msualg_2), []). fof(d8_msualg_1,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( l2_msualg_1(B,A) => ( v5_msualg_1(B,A) <=> v2_relat_1(u4_msualg_1(A,B)) ) ) ) ), file(msualg_1,d8_msualg_1), []). fof(d8_msualg_3,axiom,( ! [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] : ( ( v5_msualg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( m1_subset_1(D,u1_msualg_1(A)) => ! [E] : ( m3_pboole(E,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C)) => ! [F] : ( m1_subset_1(F,k3_msualg_1(A,D,B)) => ! [G] : ( m1_subset_1(G,k3_msualg_1(A,D,C)) => ( G = k6_msualg_3(A,B,C,D,E,F) <=> ! [H] : ( m2_subset_1(H,k1_numbers,k5_numbers) => ( r2_hidden(H,k1_relat_1(F)) => k1_funct_1(G,H) = k1_funct_1(k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C),E,k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,D),H)),k1_funct_1(F,H)) ) ) ) ) ) ) ) ) ) ) ), file(msualg_3,d8_msualg_3), []). fof(d9_msualg_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_msualg_1(A)) => ! [C] : ( l3_msualg_1(C,A) => k3_msualg_1(A,B,C) = k1_funct_1(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,C))),B) ) ) ) ), file(msualg_1,d9_msualg_1), []). fof(d9_msualg_3,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( l3_msualg_1(C,A) => ! [D] : ( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C)) => ( r1_msualg_3(A,B,C,D) <=> ! [E] : ( m1_subset_1(E,u1_msualg_1(A)) => ( k3_msualg_1(A,E,B) != k1_xboole_0 => ! [F] : ( m1_subset_1(F,k3_msualg_1(A,E,B)) => k1_funct_1(k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C),D,k2_msualg_1(A,E)),k1_funct_1(k5_msualg_1(A,E,B),F)) = k1_funct_1(k5_msualg_1(A,E,C),k5_msualg_3(A,B,C,E,D,F)) ) ) ) ) ) ) ) ) ), file(msualg_3,d9_msualg_3), []). 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_funct_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_relat_1(k10_funct_6(A)) & v1_funct_1(k10_funct_6(A)) & v1_funcop_1(k10_funct_6(A)) ) ) ), file(funct_6,k10_funct_6), []). fof(dt_k10_msualg_2,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & l3_msualg_1(B,A) & m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) ) => ( v4_msualg_1(k10_msualg_2(A,B,C),A) & m1_msualg_2(k10_msualg_2(A,B,C),A,B) ) ) ), file(msualg_2,k10_msualg_2), []). fof(dt_k10_pralg_2,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(B) & l1_msualg_1(B) & m1_subset_1(C,u1_struct_0(B)) & m2_pralg_2(D,A,B) ) => m1_pboole(k10_pralg_2(A,B,C,D),A) ) ), file(pralg_2,k10_pralg_2), []). fof(dt_k11_pralg_2,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(B) & l1_msualg_1(B) & m2_pralg_2(C,A,B) ) => m1_pboole(k11_pralg_2(A,B,C),u1_struct_0(B)) ) ), file(pralg_2,k11_pralg_2), []). fof(dt_k12_msualg_2,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & l3_msualg_1(B,A) & m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) ) => ( v4_msualg_1(k12_msualg_2(A,B,C),A) & m1_msualg_2(k12_msualg_2(A,B,C),A,B) ) ) ), file(msualg_2,k12_msualg_2), []). fof(dt_k13_finseq_1,axiom,( $true ), file(finseq_1,k13_finseq_1), []). fof(dt_k14_msualg_2,axiom,( $true ), file(msualg_2,k14_msualg_2), []). fof(dt_k14_pralg_2,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(B) & ~ v2_msualg_1(B) & l1_msualg_1(B) & m2_pralg_2(C,A,B) ) => m3_pboole(k14_pralg_2(A,B,C),u1_msualg_1(B),k8_pboole(u1_msualg_1(B),k3_finseq_2(u1_struct_0(B)),u2_msualg_1(B),k6_pboole(u1_struct_0(B),k11_pralg_2(A,B,C))),k8_pboole(u1_msualg_1(B),u1_struct_0(B),u3_msualg_1(B),k11_pralg_2(A,B,C))) ) ), file(pralg_2,k14_pralg_2), []). fof(dt_k15_pralg_2,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(B) & ~ v2_msualg_1(B) & l1_msualg_1(B) & m2_pralg_2(C,A,B) ) => l3_msualg_1(k15_pralg_2(A,B,C),B) ) ), file(pralg_2,k15_pralg_2), []). fof(dt_k1_funct_1,axiom,( $true ), file(funct_1,k1_funct_1), []). fof(dt_k1_funct_2,axiom,( $true ), file(funct_2,k1_funct_2), []). fof(dt_k1_funct_4,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_relat_1(B) & v1_funct_1(B) ) => ( v1_relat_1(k1_funct_4(A,B)) & v1_funct_1(k1_funct_4(A,B)) ) ) ), file(funct_4,k1_funct_4), []). fof(dt_k1_msualg_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & m1_subset_1(B,u1_msualg_1(A)) ) => m2_finseq_2(k1_msualg_1(A,B),u1_struct_0(A),k3_finseq_2(u1_struct_0(A))) ) ), file(msualg_1,k1_msualg_1), []). fof(dt_k1_msualg_3,axiom,( ! [A,B,C,D,E] : ( ( ~ v1_xboole_0(A) & m1_pboole(B,A) & m1_pboole(C,A) & m3_pboole(D,A,B,C) & m1_subset_1(E,A) ) => ( v1_funct_1(k1_msualg_3(A,B,C,D,E)) & v1_funct_2(k1_msualg_3(A,B,C,D,E),k1_funct_1(B,E),k1_funct_1(C,E)) & m2_relset_1(k1_msualg_3(A,B,C,D,E),k1_funct_1(B,E),k1_funct_1(C,E)) ) ) ), file(msualg_3,k1_msualg_3), []). 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_struct_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) ) => m1_subset_1(k1_struct_0(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ), file(struct_0,k1_struct_0), []). 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_equation,axiom,( $true ), file(equation,k2_equation), []). fof(dt_k2_funcop_1,axiom,( $true ), file(funcop_1,k2_funcop_1), []). fof(dt_k2_msualg_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & m1_subset_1(B,u1_msualg_1(A)) ) => m1_subset_1(k2_msualg_1(A,B),u1_struct_0(A)) ) ), file(msualg_1,k2_msualg_1), []). fof(dt_k2_partfun1,axiom,( ! [A,B,C,D] : ( ( v1_funct_1(C) & m1_relset_1(C,A,B) ) => ( v1_funct_1(k2_partfun1(A,B,C,D)) & m2_relset_1(k2_partfun1(A,B,C,D),A,B) ) ) ), file(partfun1,k2_partfun1), []). fof(dt_k2_pralg_3,axiom,( $true ), file(pralg_3,k2_pralg_3), []). fof(dt_k2_pre_circ,axiom,( ! [A,B] : m1_pboole(k2_pre_circ(A,B),A) ), file(pre_circ,k2_pre_circ), []). fof(dt_k2_relat_1,axiom,( $true ), file(relat_1,k2_relat_1), []). fof(dt_k2_xboole_0,axiom,( $true ), file(xboole_0,k2_xboole_0), []). fof(dt_k2_zfmisc_1,axiom,( $true ), file(zfmisc_1,k2_zfmisc_1), []). 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_k3_msualg_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & m1_subset_1(B,u1_msualg_1(A)) & l3_msualg_1(C,A) ) => m1_subset_1(k3_msualg_1(A,B,C),k2_relat_1(k6_pboole(u1_struct_0(A),u4_msualg_1(A,C)))) ) ), file(msualg_1,k3_msualg_1), []). fof(dt_k3_tarski,axiom,( $true ), file(tarski,k3_tarski), []). fof(dt_k4_card_3,axiom,( $true ), file(card_3,k4_card_3), []). 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_finseq_4,axiom,( ! [A,B,C,D] : ( ( v1_funct_1(C) & m1_relset_1(C,A,B) ) => m1_subset_1(k4_finseq_4(A,B,C,D),B) ) ), file(finseq_4,k4_finseq_4), []). fof(dt_k4_msualg_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & m1_subset_1(B,u1_msualg_1(A)) & l3_msualg_1(C,A) ) => m1_subset_1(k4_msualg_1(A,B,C),k2_relat_1(u4_msualg_1(A,C))) ) ), file(msualg_1,k4_msualg_1), []). fof(dt_k4_msualg_2,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & l3_msualg_1(B,A) & m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) ) => m3_pboole(k4_msualg_2(A,B,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),C)),k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),C)) ) ), file(msualg_2,k4_msualg_2), []). fof(dt_k4_relset_1,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => m1_subset_1(k4_relset_1(A,B,C),k1_zfmisc_1(A)) ) ), file(relset_1,k4_relset_1), []). fof(dt_k5_msualg_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & m1_subset_1(B,u1_msualg_1(A)) & l3_msualg_1(C,A) ) => ( v1_funct_1(k5_msualg_1(A,B,C)) & v1_funct_2(k5_msualg_1(A,B,C),k3_msualg_1(A,B,C),k4_msualg_1(A,B,C)) & m2_relset_1(k5_msualg_1(A,B,C),k3_msualg_1(A,B,C),k4_msualg_1(A,B,C)) ) ) ), file(msualg_1,k5_msualg_1), []). fof(dt_k5_msualg_3,axiom,( ! [A,B,C,D,E,F] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & l3_msualg_1(B,A) & l3_msualg_1(C,A) & m1_subset_1(D,u1_msualg_1(A)) & m3_pboole(E,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C)) & m1_subset_1(F,k3_msualg_1(A,D,B)) ) => m1_subset_1(k5_msualg_3(A,B,C,D,E,F),k3_msualg_1(A,D,C)) ) ), file(msualg_3,k5_msualg_3), []). 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_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(dt_k6_msualg_3,axiom,( ! [A,B,C,D,E,F] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v5_msualg_1(B,A) & l3_msualg_1(B,A) & v5_msualg_1(C,A) & l3_msualg_1(C,A) & m1_subset_1(D,u1_msualg_1(A)) & m3_pboole(E,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C)) & m1_subset_1(F,k3_msualg_1(A,D,B)) ) => m1_subset_1(k6_msualg_3(A,B,C,D,E,F),k3_msualg_1(A,D,C)) ) ), file(msualg_3,k6_msualg_3), []). 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_k6_pralg_2,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & ~ v3_struct_0(B) & l1_msualg_1(B) & m2_pralg_2(C,A,B) & m1_subset_1(D,A) ) => ( v5_msualg_1(k6_pralg_2(A,B,C,D),B) & l3_msualg_1(k6_pralg_2(A,B,C,D),B) ) ) ), file(pralg_2,k6_pralg_2), []). 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_k7_relat_1,axiom,( ! [A,B] : ( v1_relat_1(A) => v1_relat_1(k7_relat_1(A,B)) ) ), file(relat_1,k7_relat_1), []). fof(dt_k8_funct_2,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & m1_subset_1(D,A) ) => m1_subset_1(k8_funct_2(A,B,C,D),B) ) ), file(funct_2,k8_funct_2), []). fof(dt_k8_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) & v2_relat_1(D) & m1_pboole(D,B) ) => ( v2_relat_1(k8_pboole(A,B,C,D)) & m1_pboole(k8_pboole(A,B,C,D),A) ) ) ), file(pboole,k8_pboole), []). 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_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), []). fof(dt_m1_finseq_2,axiom,( $true ), file(finseq_2,m1_finseq_2), []). fof(dt_m1_msualg_2,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_msualg_2(C,A,B) => l3_msualg_1(C,A) ) ) ), file(msualg_2,m1_msualg_2), []). 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_subset_1,axiom,( $true ), 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), []). fof(dt_m2_finseq_2,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(B) & m1_finseq_2(B,A) ) => ! [C] : ( m2_finseq_2(C,A,B) => m2_finseq_1(C,A) ) ) ), file(finseq_2,m2_finseq_2), []). fof(dt_m2_pralg_2,axiom,( ! [A,B] : ( ( ~ v3_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( m2_pralg_2(C,A,B) => m1_pboole(C,A) ) ) ), file(pralg_2,m2_pralg_2), []). 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_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(dt_m4_pboole,axiom,( ! [A,B] : ( m1_pboole(B,A) => ! [C] : ( m4_pboole(C,A,B) => m1_pboole(C,A) ) ) ), file(pboole,m4_pboole), []). fof(dt_u1_msualg_1,axiom,( $true ), file(msualg_1,u1_msualg_1), []). fof(dt_u1_struct_0,axiom,( $true ), file(struct_0,u1_struct_0), []). 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_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(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(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_finseq_1,axiom,( ! [A] : ? [B] : m1_finseq_1(B,A) ), file(finseq_1,m1_finseq_1), []). fof(existence_m1_finseq_2,axiom,( ! [A] : ? [B] : m1_finseq_2(B,A) ), file(finseq_2,m1_finseq_2), []). fof(existence_m1_msualg_2,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & l3_msualg_1(B,A) ) => ? [C] : m1_msualg_2(C,A,B) ) ), file(msualg_2,m1_msualg_2), []). 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_subset_1,axiom,( ! [A] : ? [B] : m1_subset_1(B,A) ), 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), []). fof(existence_m2_finseq_2,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(B) & m1_finseq_2(B,A) ) => ? [C] : m2_finseq_2(C,A,B) ) ), file(finseq_2,m2_finseq_2), []). fof(existence_m2_pralg_2,axiom,( ! [A,B] : ( ( ~ v3_struct_0(B) & l1_msualg_1(B) ) => ? [C] : m2_pralg_2(C,A,B) ) ), file(pralg_2,m2_pralg_2), []). 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(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(existence_m4_pboole,axiom,( ! [A,B] : ( m1_pboole(B,A) => ? [C] : m4_pboole(C,A,B) ) ), file(pboole,m4_pboole), []). fof(fc10_msualg_2,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v5_msualg_1(B,A) & l3_msualg_1(B,A) & v2_relat_1(C) & m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) ) => ( v4_msualg_1(k12_msualg_2(A,B,C),A) & v5_msualg_1(k12_msualg_2(A,B,C),A) ) ) ), file(msualg_2,fc10_msualg_2), []). fof(fc11_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_finset_1(A) ) => v1_finset_1(k2_relat_1(A)) ) ), file(finseq_1,fc11_finseq_1), []). fof(fc11_msualg_2,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & l3_msualg_1(B,A) ) => ~ v1_xboole_0(k14_msualg_2(A,B)) ) ), file(msualg_2,fc11_msualg_2), []). fof(fc14_finset_1,axiom,( ! [A,B] : ( ( v1_finset_1(A) & v1_finset_1(B) ) => v1_finset_1(k2_zfmisc_1(A,B)) ) ), file(finset_1,fc14_finset_1), []). fof(fc16_finseq_1,axiom,( ! [A] : ( ~ v1_xboole_0(k13_finseq_1(A)) & v1_fraenkel(k13_finseq_1(A)) ) ), file(finseq_1,fc16_finseq_1), []). 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_cantor_1,axiom,( ! [A,B] : ( ~ v1_xboole_0(B) => ( v1_relat_1(k2_funcop_1(A,B)) & v2_relat_1(k2_funcop_1(A,B)) & v1_funct_1(k2_funcop_1(A,B)) ) ) ), file(cantor_1,fc1_cantor_1), []). fof(fc1_equation,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & l3_msualg_1(B,A) & m1_msualg_2(C,A,B) ) => ~ v1_xboole_0(k2_equation(A,B,C)) ) ), file(equation,fc1_equation), []). fof(fc1_finset_1,axiom,( ! [A] : ( ~ v1_xboole_0(k1_tarski(A)) & v1_finset_1(k1_tarski(A)) ) ), file(finset_1,fc1_finset_1), []). fof(fc1_funcop_1,axiom,( ! [A,B] : ( v1_relat_1(k2_funcop_1(A,B)) & v1_funct_1(k2_funcop_1(A,B)) ) ), file(funcop_1,fc1_funcop_1), []). fof(fc1_funct_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_relat_1(B) & v1_funct_1(B) ) => ( v1_relat_1(k5_relat_1(A,B)) & v1_funct_1(k5_relat_1(A,B)) ) ) ), file(funct_1,fc1_funct_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_ordinal2,axiom, ( v1_ordinal1(k5_ordinal2) & v2_ordinal1(k5_ordinal2) & v3_ordinal1(k5_ordinal2) & ~ v1_xboole_0(k5_ordinal2) ), file(ordinal2,fc1_ordinal2), []). fof(fc1_pboole,axiom,( ! [A,B] : ( ( v2_relat_1(B) & m1_pboole(B,A) ) => ( v1_relat_1(k6_pboole(A,B)) & v2_relat_1(k6_pboole(A,B)) & ~ v3_relat_1(k6_pboole(A,B)) & v1_funct_1(k6_pboole(A,B)) ) ) ), file(pboole,fc1_pboole), []). fof(fc1_pralg_2,axiom,( ! [A,B] : ( ( v2_relat_1(B) & m1_pboole(B,A) ) => ( ~ v1_xboole_0(k4_card_3(B)) & v1_fraenkel(k4_card_3(B)) & v1_pralg_2(k4_card_3(B)) ) ) ), file(pralg_2,fc1_pralg_2), []). fof(fc1_pralg_3,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(B) & ~ v2_msualg_1(B) & l1_msualg_1(B) & m2_pralg_2(C,A,B) ) => ( v4_msualg_1(k15_pralg_2(A,B,C),B) & v5_msualg_1(k15_pralg_2(A,B,C),B) ) ) ), file(pralg_3,fc1_pralg_3), []). 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(fc1_subset_1,axiom,( ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ), file(subset_1,fc1_subset_1), []). fof(fc2_equation,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v5_msualg_1(B,A) & l3_msualg_1(B,A) & v2_relat_1(C) & v1_pre_circ(C,u1_struct_0(A)) & m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) ) => ( v4_msualg_1(k12_msualg_2(A,B,C),A) & v5_msualg_1(k12_msualg_2(A,B,C),A) & v3_msafree2(k12_msualg_2(A,B,C),A) & v1_msualg_6(k12_msualg_2(A,B,C),A) ) ) ), file(equation,fc2_equation), []). 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_funcop_1,axiom,( ! [A] : ( v1_xboole_0(k2_funcop_1(k1_xboole_0,A)) & v1_relat_1(k2_funcop_1(k1_xboole_0,A)) & v1_funct_1(k2_funcop_1(k1_xboole_0,A)) & v2_funct_1(k2_funcop_1(k1_xboole_0,A)) ) ), file(funcop_1,fc2_funcop_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(fc2_subset_1,axiom,( ! [A] : ~ v1_xboole_0(k1_tarski(A)) ), file(subset_1,fc2_subset_1), []). fof(fc3_funcop_1,axiom,( ! [A,B] : ( v1_xboole_0(B) => ( v1_xboole_0(k2_funcop_1(B,A)) & v1_relat_1(k2_funcop_1(B,A)) & v1_funct_1(k2_funcop_1(B,A)) & v2_funct_1(k2_funcop_1(B,A)) ) ) ), file(funcop_1,fc3_funcop_1), []). fof(fc3_msafree,axiom,( ! [A] : ( ( ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ~ v1_xboole_0(u1_msualg_1(A)) ) ), file(msafree,fc3_msafree), []). fof(fc3_pralg_3,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & ~ v1_xboole_0(B) & m1_subset_1(C,u1_msualg_1(A)) & m2_pralg_2(D,B,A) ) => ( v1_relat_1(k2_pralg_3(A,k15_pralg_2(B,A,D),C)) & v1_funct_1(k2_pralg_3(A,k15_pralg_2(B,A,D),C)) ) ) ), file(pralg_3,fc3_pralg_3), []). fof(fc4_funct_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_relat_1(k7_relat_1(A,B)) & v1_funct_1(k7_relat_1(A,B)) ) ) ), file(funct_1,fc4_funct_1), []). fof(fc4_ordinal2,axiom,( ! [A,B] : ( v3_ordinal1(B) => ( v1_relat_1(k2_funcop_1(A,B)) & v1_funct_1(k2_funcop_1(A,B)) & v1_ordinal2(k2_funcop_1(A,B)) ) ) ), file(ordinal2,fc4_ordinal2), []). fof(fc4_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) ), file(subset_1,fc4_subset_1), []). fof(fc6_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) ) => v1_setfam_1(k2_relat_1(A)) ) ), file(funct_1,fc6_funct_1), []). fof(fc6_msualg_2,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v5_msualg_1(B,A) & l3_msualg_1(B,A) ) => ( v4_msualg_1(g3_msualg_1(A,u4_msualg_1(A,B),u5_msualg_1(A,B)),A) & v5_msualg_1(g3_msualg_1(A,u4_msualg_1(A,B),u5_msualg_1(A,B)),A) ) ) ), file(msualg_2,fc6_msualg_2), []). fof(fc6_pralg_2,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(B) & l1_msualg_1(B) & m1_subset_1(C,u1_struct_0(B)) & m2_pralg_2(D,A,B) ) => ( v1_relat_1(k10_pralg_2(A,B,C,D)) & v2_relat_1(k10_pralg_2(A,B,C,D)) & v1_funct_1(k10_pralg_2(A,B,C,D)) ) ) ), file(pralg_2,fc6_pralg_2), []). 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_pralg_2,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(B) & l1_msualg_1(B) & m2_pralg_2(C,A,B) ) => ( v1_relat_1(k11_pralg_2(A,B,C)) & v2_relat_1(k11_pralg_2(A,B,C)) & ~ v3_relat_1(k11_pralg_2(A,B,C)) & v1_funct_1(k11_pralg_2(A,B,C)) ) ) ), file(pralg_2,fc7_pralg_2), []). fof(fc8_funcop_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) & v1_relat_1(B) & v1_funct_1(B) ) => ( v1_relat_1(k5_relat_1(B,A)) & v1_funct_1(k5_relat_1(B,A)) & v1_funcop_1(k5_relat_1(B,A)) ) ) ), file(funcop_1,fc8_funcop_1), []). fof(fc8_pralg_2,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(B) & ~ v2_msualg_1(B) & l1_msualg_1(B) & m2_pralg_2(C,A,B) ) => v4_msualg_1(k15_pralg_2(A,B,C),B) ) ), file(pralg_2,fc8_pralg_2), []). fof(fc9_finseq_1,axiom,( ! [A] : ~ v1_xboole_0(k13_finseq_1(A)) ), file(finseq_1,fc9_finseq_1), []). fof(fc9_finset_1,axiom,( ! [A,B] : ( ( v1_finset_1(A) & v1_finset_1(B) ) => v1_finset_1(k2_xboole_0(A,B)) ) ), file(finset_1,fc9_finset_1), []). fof(fc9_funcop_1,axiom,( ! [A,B] : ( ~ v1_xboole_0(B) => ( v1_relat_1(k2_funcop_1(A,B)) & v2_relat_1(k2_funcop_1(A,B)) & v1_funct_1(k2_funcop_1(A,B)) ) ) ), file(funcop_1,fc9_funcop_1), []). fof(fraenkel_a_2_0_equation,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(B) & ~ v2_msualg_1(B) & l1_msualg_1(B) & v5_msualg_1(C,B) & l3_msualg_1(C,B) ) => ( r2_hidden(A,a_2_0_equation(B,C)) <=> ? [D] : ( m1_subset_1(D,k14_msualg_2(B,C)) & A = D & ? [E] : ( v4_msualg_1(E,B) & v5_msualg_1(E,B) & v3_msafree2(E,B) & m1_msualg_2(E,B,C) & E = D ) ) ) ) ), file(equation,a_2_0_equation), []). fof(fraenkel_a_3_0_equation,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(B) & ~ v2_msualg_1(B) & l1_msualg_1(B) & ~ v1_xboole_0(C) & m2_pralg_2(D,C,B) ) => ( r2_hidden(A,a_3_0_equation(B,C,D)) <=> ? [E,F] : ( m1_subset_1(E,C) & m1_subset_1(F,u1_struct_0(B)) & A = k1_funct_1(u4_msualg_1(B,k6_pralg_2(C,B,D,E)),F) ) ) ) ), file(equation,a_3_0_equation), []). fof(fraenkel_a_3_1_pralg_3,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(B) & ~ v3_struct_0(C) & ~ v2_msualg_1(C) & l1_msualg_1(C) & m2_pralg_2(D,B,C) ) => ( r2_hidden(A,a_3_1_pralg_3(B,C,D)) <=> ? [E,F] : ( m1_subset_1(E,B) & m1_subset_1(F,u1_struct_0(C)) & A = k1_funct_1(u4_msualg_1(C,k6_pralg_2(B,C,D,E)),F) ) ) ) ), file(pralg_3,a_3_1_pralg_3), []). 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(idempotence_k1_funct_4,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_relat_1(B) & v1_funct_1(B) ) => k1_funct_4(A,A) = A ) ), file(funct_4,k1_funct_4), []). fof(idempotence_k2_xboole_0,axiom,( ! [A,B] : k2_xboole_0(A,A) = A ), file(xboole_0,k2_xboole_0), []). fof(rc1_closure2,axiom,( ? [A] : ( v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_finset_1(A) & v1_fraenkel(A) ) ), file(closure2,rc1_closure2), []). 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_finset_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_finset_1(A) ) ), file(finset_1,rc1_finset_1), []). 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_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_pboole,axiom,( ? [A] : ( v1_relat_1(A) & v3_relat_1(A) & v1_funct_1(A) ) ), file(pboole,rc1_pboole), []). fof(rc1_pralg_2,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_fraenkel(A) & v1_pralg_2(A) ) ), file(pralg_2,rc1_pralg_2), []). fof(rc1_subset_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) ) ) ), file(subset_1,rc1_subset_1), []). fof(rc2_equation,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v5_msualg_1(B,A) & l3_msualg_1(B,A) ) => ? [C] : ( m1_msualg_2(C,A,B) & v4_msualg_1(C,A) & v5_msualg_1(C,A) & v3_msafree2(C,A) & v1_msualg_6(C,A) ) ) ), file(equation,rc2_equation), []). 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_msualg_2,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & l3_msualg_1(B,A) ) => ? [C] : ( m1_msualg_2(C,A,B) & v4_msualg_1(C,A) ) ) ), file(msualg_2,rc2_msualg_2), []). fof(rc2_msualg_9,axiom,( ! [A,B] : ( ( v2_relat_1(B) & m1_pboole(B,A) ) => ? [C] : ( m4_pboole(C,A,B) & v1_relat_1(C) & v2_relat_1(C) & v1_funct_1(C) & v1_pre_circ(C,A) ) ) ), file(msualg_9,rc2_msualg_9), []). 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_subset_1,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & v1_xboole_0(B) ) ), file(subset_1,rc2_subset_1), []). fof(rc3_equation,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v1_msualg_6(B,A) & l3_msualg_1(B,A) ) => ? [C] : ( m1_msualg_2(C,A,B) & v1_msualg_6(C,A) ) ) ), file(equation,rc3_equation), []). 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_finset_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) & v1_finset_1(B) ) ) ), file(finset_1,rc3_finset_1), []). 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_msualg_2,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v5_msualg_1(B,A) & l3_msualg_1(B,A) ) => ? [C] : ( m1_msualg_2(C,A,B) & v4_msualg_1(C,A) & v5_msualg_1(C,A) ) ) ), file(msualg_2,rc3_msualg_2), []). 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_struct_0,axiom,( ? [A] : ( l1_struct_0(A) & ~ v3_struct_0(A) ) ), file(struct_0,rc3_struct_0), []). fof(rc4_finseq_1,axiom,( ! [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), []). fof(rc4_finset_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) & v1_finset_1(B) ) ) ), file(finset_1,rc4_finset_1), []). 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(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_msualg_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_msualg_1(A) ) => ? [B] : ( l3_msualg_1(B,A) & v4_msualg_1(B,A) ) ) ), file(msualg_1,rc5_msualg_1), []). fof(rc5_pboole,axiom,( ! [A,B] : ( ( v2_relat_1(B) & m1_pboole(B,A) ) => ? [C] : ( m4_pboole(C,A,B) & v1_relat_1(C) & v2_relat_1(C) & v1_funct_1(C) ) ) ), file(pboole,rc5_pboole), []). 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(rc6_msualg_1,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) ) ) ), file(msualg_1,rc6_msualg_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_3,axiom,( ! [A,B,C,D,E] : ( ( ~ v1_xboole_0(A) & m1_pboole(B,A) & m1_pboole(C,A) & m3_pboole(D,A,B,C) & m1_subset_1(E,A) ) => k1_msualg_3(A,B,C,D,E) = k1_funct_1(D,E) ) ), file(msualg_3,k1_msualg_3), []). fof(redefinition_k1_struct_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) ) => k1_struct_0(A,B) = k1_tarski(B) ) ), file(struct_0,k1_struct_0), []). fof(redefinition_k2_partfun1,axiom,( ! [A,B,C,D] : ( ( v1_funct_1(C) & m1_relset_1(C,A,B) ) => k2_partfun1(A,B,C,D) = k7_relat_1(C,D) ) ), file(partfun1,k2_partfun1), []). fof(redefinition_k2_pre_circ,axiom,( ! [A,B] : k2_pre_circ(A,B) = k2_funcop_1(A,B) ), file(pre_circ,k2_pre_circ), []). fof(redefinition_k3_finseq_2,axiom,( ! [A] : k3_finseq_2(A) = k13_finseq_1(A) ), file(finseq_2,k3_finseq_2), []). 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_k4_relset_1,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => k4_relset_1(A,B,C) = k1_relat_1(C) ) ), file(relset_1,k4_relset_1), []). fof(redefinition_k5_numbers,axiom,( k5_numbers = k5_ordinal2 ), file(numbers,k5_numbers), []). fof(redefinition_k6_msualg_3,axiom,( ! [A,B,C,D,E,F] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v5_msualg_1(B,A) & l3_msualg_1(B,A) & v5_msualg_1(C,A) & l3_msualg_1(C,A) & m1_subset_1(D,u1_msualg_1(A)) & m3_pboole(E,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C)) & m1_subset_1(F,k3_msualg_1(A,D,B)) ) => k6_msualg_3(A,B,C,D,E,F) = k5_msualg_3(A,B,C,D,E,F) ) ), file(msualg_3,k6_msualg_3), []). fof(redefinition_k6_pralg_2,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & ~ v3_struct_0(B) & l1_msualg_1(B) & m2_pralg_2(C,A,B) & m1_subset_1(D,A) ) => k6_pralg_2(A,B,C,D) = k1_funct_1(C,D) ) ), file(pralg_2,k6_pralg_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(redefinition_k8_funct_2,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & m1_subset_1(D,A) ) => k8_funct_2(A,B,C,D) = k1_funct_1(C,D) ) ), file(funct_2,k8_funct_2), []). fof(redefinition_k8_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) & v2_relat_1(D) & m1_pboole(D,B) ) => k8_pboole(A,B,C,D) = k5_relat_1(C,D) ) ), file(pboole,k8_pboole), []). fof(redefinition_m2_finseq_1,axiom,( ! [A,B] : ( m2_finseq_1(B,A) <=> m1_finseq_1(B,A) ) ), file(finseq_1,m2_finseq_1), []). fof(redefinition_m2_finseq_2,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(B) & m1_finseq_2(B,A) ) => ! [C] : ( m2_finseq_2(C,A,B) <=> m1_subset_1(C,B) ) ) ), file(finseq_2,m2_finseq_2), []). 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(redefinition_r6_pboole,axiom,( ! [A,B,C] : ( ( m1_pboole(B,A) & m1_pboole(C,A) ) => ( r6_pboole(A,B,C) <=> B = C ) ) ), file(pboole,r6_pboole), []). fof(reflexivity_r1_tarski,axiom,( ! [A,B] : r1_tarski(A,A) ), file(tarski,r1_tarski), []). fof(reflexivity_r2_pboole,axiom,( ! [A,B,C] : ( ( m1_pboole(B,A) & m1_pboole(C,A) ) => r2_pboole(A,B,B) ) ), file(pboole,r2_pboole), []). fof(reflexivity_r6_pboole,axiom,( ! [A,B,C] : ( ( m1_pboole(B,A) & m1_pboole(C,A) ) => r6_pboole(A,B,B) ) ), file(pboole,r6_pboole), []). fof(s1_mssubfam__e17_34__equation,axiom,( ! [A,B,C,D,E,F,G] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v5_msualg_1(B,A) & l3_msualg_1(B,A) & m2_pralg_2(D,C,A) & ~ v1_xboole_0(E) & m2_pralg_2(F,E,A) & v4_msualg_1(G,A) & v5_msualg_1(G,A) & m1_msualg_2(G,A,k15_pralg_2(C,A,D)) ) => ( ! [H] : ( r2_hidden(H,u1_struct_0(A)) => ! [I] : ~ ( r2_hidden(I,k1_funct_1(u4_msualg_1(A,G),H)) & ! [J] : ~ ( r2_hidden(J,k1_funct_1(u4_msualg_1(A,B),H)) & ? [K] : ( m1_subset_1(K,u1_struct_0(A)) & ? [L] : ( m1_subset_1(L,k1_funct_1(k11_pralg_2(E,A,F),K)) & ? [M] : ( v4_msualg_1(M,A) & v5_msualg_1(M,A) & v3_msafree2(M,A) & m1_msualg_2(M,A,B) & K = H & L = I & ! [N] : ( ( v4_msualg_1(N,A) & v5_msualg_1(N,A) & v3_msafree2(N,A) & m1_msualg_2(N,A,B) ) => ( m1_msualg_2(M,A,N) => k1_funct_1(L,M) = k1_funct_1(L,N) ) ) & J = k1_funct_1(L,M) ) ) ) ) ) ) => ? [H] : ( m3_pboole(H,u1_struct_0(A),u4_msualg_1(A,G),u4_msualg_1(A,B)) & ! [I] : ~ ( r2_hidden(I,u1_struct_0(A)) & ! [J] : ( ( v1_funct_1(J) & v1_funct_2(J,k1_funct_1(u4_msualg_1(A,G),I),k1_funct_1(u4_msualg_1(A,B),I)) & m2_relset_1(J,k1_funct_1(u4_msualg_1(A,G),I),k1_funct_1(u4_msualg_1(A,B),I)) ) => ~ ( J = k1_funct_1(H,I) & ! [O] : ( r2_hidden(O,k1_funct_1(u4_msualg_1(A,G),I)) => ? [P] : ( m1_subset_1(P,u1_struct_0(A)) & ? [Q] : ( m1_subset_1(Q,k1_funct_1(k11_pralg_2(E,A,F),P)) & ? [R] : ( v4_msualg_1(R,A) & v5_msualg_1(R,A) & v3_msafree2(R,A) & m1_msualg_2(R,A,B) & P = I & Q = O & ! [S] : ( ( v4_msualg_1(S,A) & v5_msualg_1(S,A) & v3_msafree2(S,A) & m1_msualg_2(S,A,B) ) => ( m1_msualg_2(R,A,S) => k1_funct_1(Q,R) = k1_funct_1(Q,S) ) ) & k1_funct_1(J,O) = k1_funct_1(Q,R) ) ) ) ) ) ) ) ) ) ) ), file(equation,s1_mssubfam__e17_34__equation), []). fof(s1_xboole_0__e51_34__equation,axiom,( ! [A,B,C,D,E] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v5_msualg_1(B,A) & l3_msualg_1(B,A) & ~ v1_xboole_0(C) & m1_subset_1(D,u1_struct_0(A)) ) => ? [F] : ! [G] : ( r2_hidden(G,F) <=> ( r2_hidden(G,C) & ? [H] : ( m1_msualg_2(H,A,B) & H = G & r2_hidden(E,k1_funct_1(u4_msualg_1(A,H),D)) ) ) ) ) ), file(equation,s1_xboole_0__e51_34__equation), []). fof(s1_xboole_0__e5_34_4_1__equation,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v5_msualg_1(B,A) & l3_msualg_1(B,A) & v4_msualg_1(C,A) & v5_msualg_1(C,A) & v3_msafree2(C,A) & m1_msualg_2(C,A,B) ) => ? [D] : ! [E] : ( r2_hidden(E,D) <=> ( r2_hidden(E,k2_equation(A,B,C)) & ? [F] : ( v4_msualg_1(F,A) & v5_msualg_1(F,A) & m1_msualg_2(F,A,B) & E = F & v3_msafree2(F,A) ) ) ) ) ), file(equation,s1_xboole_0__e5_34_4_1__equation), []). fof(s2_pboole__e7_34__equation,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v5_msualg_1(B,A) & l3_msualg_1(B,A) & ~ v1_xboole_0(C) & m2_pralg_2(D,C,A) ) => ? [E] : ( m1_pboole(E,u1_struct_0(A)) & ! [F] : ( r2_hidden(F,u1_struct_0(A)) => ! [G] : ( r2_hidden(G,k1_funct_1(E,F)) <=> ( r2_hidden(G,k1_funct_1(k11_pralg_2(C,A,D),F)) & ? [H] : ( m1_subset_1(H,u1_struct_0(A)) & ? [I] : ( m1_subset_1(I,k1_funct_1(k11_pralg_2(C,A,D),H)) & ? [J] : ( v4_msualg_1(J,A) & v5_msualg_1(J,A) & v3_msafree2(J,A) & m1_msualg_2(J,A,B) & H = F & I = G & ! [K] : ( ( v4_msualg_1(K,A) & v5_msualg_1(K,A) & v3_msafree2(K,A) & m1_msualg_2(K,A,B) ) => ( m1_msualg_2(J,A,K) => k1_funct_1(I,J) = k1_funct_1(I,K) ) ) ) ) ) ) ) ) ) ) ), file(equation,s2_pboole__e7_34__equation), []). fof(s3_funct_2__e4_34_7_1_2__equation,axiom,( ! [A,B,C,D,E,F,G,H,I] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v5_msualg_1(B,A) & l3_msualg_1(B,A) & m2_pralg_2(D,C,A) & v4_msualg_1(E,A) & v5_msualg_1(E,A) & m1_msualg_2(E,A,k15_pralg_2(C,A,D)) & m3_pboole(F,u1_struct_0(A),u4_msualg_1(A,E),u4_msualg_1(A,B)) & m1_subset_1(G,u1_msualg_1(A)) & m1_subset_1(H,k3_msualg_1(A,G,E)) & ~ v1_xboole_0(I) & v1_finset_1(I) ) => ( ! [J] : ( m1_subset_1(J,I) => ? [K] : ( m1_subset_1(K,k14_msualg_2(A,B)) & ? [L] : ( v1_relat_1(L) & v1_funct_1(L) & ? [M] : ( v4_msualg_1(M,A) & v5_msualg_1(M,A) & v3_msafree2(M,A) & m1_msualg_2(M,A,B) & L = k1_funct_1(H,J) & ! [N] : ( ( v4_msualg_1(N,A) & v5_msualg_1(N,A) & v3_msafree2(N,A) & m1_msualg_2(N,A,B) ) => ( m1_msualg_2(M,A,N) => k1_funct_1(L,M) = k1_funct_1(L,N) ) ) & k1_funct_1(k1_funct_1(F,k1_funct_1(k1_msualg_1(A,G),J)),L) = k1_funct_1(L,M) & K = M ) ) ) ) => ? [J] : ( v1_funct_1(J) & v1_funct_2(J,I,k14_msualg_2(A,B)) & m2_relset_1(J,I,k14_msualg_2(A,B)) & ! [K] : ( m1_subset_1(K,I) => ? [O] : ( v1_relat_1(O) & v1_funct_1(O) & ? [P] : ( v4_msualg_1(P,A) & v5_msualg_1(P,A) & v3_msafree2(P,A) & m1_msualg_2(P,A,B) & O = k1_funct_1(H,K) & ! [Q] : ( ( v4_msualg_1(Q,A) & v5_msualg_1(Q,A) & v3_msafree2(Q,A) & m1_msualg_2(Q,A,B) ) => ( m1_msualg_2(P,A,Q) => k1_funct_1(O,P) = k1_funct_1(O,Q) ) ) & k1_funct_1(k1_funct_1(F,k1_funct_1(k1_msualg_1(A,G),K)),O) = k1_funct_1(O,P) & k8_funct_2(I,k14_msualg_2(A,B),J,K) = P ) ) ) ) ) ) ), file(equation,s3_funct_2__e4_34_7_1_2__equation), []). fof(s3_funct_2__e8_34_3_1_1_2__equation,axiom,( ! [A,B,C,D,E,F,G] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v5_msualg_1(B,A) & l3_msualg_1(B,A) & ~ v1_xboole_0(C) & m2_pralg_2(D,C,A) & m1_subset_1(E,u1_msualg_1(A)) & m1_subset_1(F,k3_msualg_1(A,E,k15_pralg_2(C,A,D))) & ~ v1_xboole_0(G) & v1_finset_1(G) ) => ( ! [H] : ( m1_subset_1(H,G) => ? [I] : ( m1_subset_1(I,k14_msualg_2(A,B)) & ? [J] : ( v1_relat_1(J) & v1_funct_1(J) & ? [K] : ( v4_msualg_1(K,A) & v5_msualg_1(K,A) & v3_msafree2(K,A) & m1_msualg_2(K,A,B) & J = k1_funct_1(F,H) & ! [L] : ( ( v4_msualg_1(L,A) & v5_msualg_1(L,A) & v3_msafree2(L,A) & m1_msualg_2(L,A,B) ) => ( m1_msualg_2(K,A,L) => k1_funct_1(J,K) = k1_funct_1(J,L) ) ) & I = K ) ) ) ) => ? [H] : ( v1_funct_1(H) & v1_funct_2(H,G,k14_msualg_2(A,B)) & m2_relset_1(H,G,k14_msualg_2(A,B)) & ! [I] : ( m1_subset_1(I,G) => ? [M] : ( v1_relat_1(M) & v1_funct_1(M) & ? [N] : ( v4_msualg_1(N,A) & v5_msualg_1(N,A) & v3_msafree2(N,A) & m1_msualg_2(N,A,B) & M = k1_funct_1(F,I) & ! [O] : ( ( v4_msualg_1(O,A) & v5_msualg_1(O,A) & v3_msafree2(O,A) & m1_msualg_2(O,A,B) ) => ( m1_msualg_2(N,A,O) => k1_funct_1(M,N) = k1_funct_1(M,O) ) ) & k8_funct_2(G,k14_msualg_2(A,B),H,I) = N ) ) ) ) ) ) ), file(equation,s3_funct_2__e8_34_3_1_1_2__equation), []). fof(s3_pboole__e8_34_4_1__equation,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v5_msualg_1(B,A) & l3_msualg_1(B,A) & ~ v1_xboole_0(C) ) => ( ! [E] : ~ ( r2_hidden(E,C) & ! [F] : ~ ? [G] : ( m1_msualg_2(G,A,B) & ? [H] : ( E = G & r2_hidden(H,k1_funct_1(u4_msualg_1(A,G),D)) & F = H ) ) ) => ? [E] : ( m1_pboole(E,C) & ! [F] : ( r2_hidden(F,C) => ? [I] : ( m1_msualg_2(I,A,B) & ? [J] : ( F = I & r2_hidden(J,k1_funct_1(u4_msualg_1(A,I),D)) & k1_funct_1(E,F) = J ) ) ) ) ) ) ), file(equation,s3_pboole__e8_34_4_1__equation), []). fof(symmetry_r6_pboole,axiom,( ! [A,B,C] : ( ( m1_pboole(B,A) & m1_pboole(C,A) ) => ( r6_pboole(A,B,C) => r6_pboole(A,C,B) ) ) ), file(pboole,r6_pboole), []). fof(t10_pralg_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( m1_subset_1(C,u1_msualg_1(A)) => ( k3_msualg_1(A,C,B) = k4_card_3(k5_relat_1(k1_msualg_1(A,C),u4_msualg_1(A,B))) & k1_relat_1(k5_relat_1(k1_msualg_1(A,C),u4_msualg_1(A,B))) = k1_relat_1(k1_msualg_1(A,C)) & k4_msualg_1(A,C,B) = k1_funct_1(u4_msualg_1(A,B),k2_msualg_1(A,C)) ) ) ) ) ), file(pralg_2,t10_pralg_2), []). fof(t10_pralg_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v3_struct_0(B) & ~ v2_msualg_1(B) & l1_msualg_1(B) ) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m2_pralg_2(D,A,B) => ! [E] : ( m1_subset_1(E,u1_msualg_1(B)) => ( k1_msualg_1(B,E) = k1_xboole_0 => k1_funct_1(k2_pralg_3(B,k15_pralg_2(A,B,D),E),C) = k2_pralg_3(B,k6_pralg_2(A,B,D,C),E) ) ) ) ) ) ) ), file(pralg_3,t10_pralg_3), []). fof(t11_pralg_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( m1_subset_1(C,u1_msualg_1(A)) => ( k1_msualg_1(A,C) = k1_xboole_0 => k3_msualg_1(A,C,B) = k1_tarski(k1_xboole_0) ) ) ) ) ), file(pralg_2,t11_pralg_2), []). fof(t12_funct_4,axiom,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( ~ r2_hidden(A,k1_relat_1(B)) => k1_funct_1(k1_funct_4(C,B),A) = k1_funct_1(C,A) ) ) ) ), file(funct_4,t12_funct_4), []). fof(t12_pralg_3,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( l3_msualg_1(C,A) => ! [D] : ( m1_subset_1(D,u1_msualg_1(A)) => ! [E] : ( m1_subset_1(E,k3_msualg_1(A,D,B)) => ( ( E = k1_xboole_0 & k1_msualg_1(A,D) = k1_xboole_0 ) => ( k3_msualg_1(A,D,B) = k1_xboole_0 | k3_msualg_1(A,D,C) = k1_xboole_0 | ! [F] : ( m3_pboole(F,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C)) => k5_msualg_3(A,B,C,D,F,E) = k1_xboole_0 ) ) ) ) ) ) ) ) ), file(pralg_3,t12_pralg_3), []). fof(t12_relset_1,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) => ( r1_tarski(k1_relat_1(C),A) & r1_tarski(k2_relat_1(C),B) ) ) ), file(relset_1,t12_relset_1), []). fof(t12_xboole_1,axiom,( ! [A,B] : ( r1_tarski(A,B) => k2_xboole_0(A,B) = B ) ), file(xboole_1,t12_xboole_1), []). fof(t13_funcop_1,axiom,( ! [A,B,C] : ( r2_hidden(B,A) => k1_funct_1(k2_funcop_1(A,C),B) = C ) ), file(funcop_1,t13_funcop_1), []). fof(t14_funct_4,axiom,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( r2_hidden(A,k1_relat_1(B)) => k1_funct_1(k1_funct_4(C,B),A) = k1_funct_1(B,A) ) ) ) ), file(funct_4,t14_funct_4), []). fof(t15_pralg_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v3_struct_0(B) & ~ v2_msualg_1(B) & l1_msualg_1(B) ) => ! [C] : ( m2_pralg_2(C,A,B) => ! [D] : ( m1_subset_1(D,u1_msualg_1(B)) => ! [E] : ( m1_subset_1(E,k3_msualg_1(B,D,k15_pralg_2(A,B,C))) => r2_hidden(E,k1_funct_2(k4_finseq_1(k1_msualg_1(B,D)),k1_funct_2(A,k3_tarski(a_3_1_pralg_3(A,B,C))))) ) ) ) ) ) ), file(pralg_3,t15_pralg_3), []). fof(t169_funct_2,axiom,( ! [A,B,C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( r2_hidden(C,k1_funct_2(A,B)) => ( k1_relat_1(C) = A & r1_tarski(k2_relat_1(C),B) ) ) ) ), file(funct_2,t169_funct_2), []). fof(t18_card_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r2_hidden(A,k4_card_3(B)) <=> ( k1_relat_1(A) = k1_relat_1(B) & ! [C] : ( r2_hidden(C,k1_relat_1(B)) => r2_hidden(k1_funct_1(A,C),k1_funct_1(B,C)) ) ) ) ) ) ), file(card_3,t18_card_3), []). fof(t19_funcop_1,axiom,( ! [A,B] : ( k1_relat_1(k2_funcop_1(A,B)) = A & r1_tarski(k2_relat_1(k2_funcop_1(A,B)),k1_tarski(B)) ) ), file(funcop_1,t19_funcop_1), []). fof(t19_msualg_9,axiom,( ! [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] : ( m1_subset_1(C,u1_msualg_1(A)) => ! [D] : ( m1_subset_1(D,k3_msualg_1(A,C,B)) => r2_hidden(k8_funct_2(k3_msualg_1(A,C,B),k4_msualg_1(A,C,B),k5_msualg_1(A,C,B),D),k1_funct_1(u4_msualg_1(A,B),k2_msualg_1(A,C))) ) ) ) ) ), file(msualg_9,t19_msualg_9), []). fof(t1_boole,axiom,( ! [A] : k2_xboole_0(A,k1_xboole_0) = A ), file(boole,t1_boole), []). fof(t1_subset,axiom,( ! [A,B] : ( r2_hidden(A,B) => m1_subset_1(A,B) ) ), file(subset,t1_subset), []). fof(t20_equation,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( m1_msualg_2(C,A,B) => ! [D] : ( m1_subset_1(D,u1_msualg_1(A)) => ! [E] : ( r2_hidden(E,k3_msualg_1(A,D,C)) => r2_hidden(E,k3_msualg_1(A,D,B)) ) ) ) ) ) ), file(equation,t20_equation), []). fof(t21_equation,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( m1_msualg_2(C,A,B) => ! [D] : ( m1_subset_1(D,u1_msualg_1(A)) => ! [E] : ( r2_hidden(E,k3_msualg_1(A,D,C)) => k1_funct_1(k5_msualg_1(A,D,C),E) = k1_funct_1(k5_msualg_1(A,D,B),E) ) ) ) ) ) ), file(equation,t21_equation), []). fof(t21_funct_2,axiom,( ! [A,B,C,D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) ) => ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) ) => ( r2_hidden(C,A) => ( B = k1_xboole_0 | k1_funct_1(k5_relat_1(D,E),C) = k1_funct_1(E,k1_funct_1(D,C)) ) ) ) ) ), file(funct_2,t21_funct_2), []). fof(t21_pralg_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v3_struct_0(B) & ~ v2_msualg_1(B) & l1_msualg_1(B) ) => ! [C] : ( m2_pralg_2(C,A,B) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,u1_msualg_1(B)) => ( k1_msualg_1(B,E) != k1_xboole_0 => ! [F] : ( ( v5_msualg_1(F,B) & l3_msualg_1(F,B) ) => ! [G] : ( m1_subset_1(G,k3_msualg_1(B,E,k15_pralg_2(A,B,C))) => m1_subset_1(k1_funct_1(k10_funct_6(G),D),k3_msualg_1(B,E,k6_pralg_2(A,B,C,D))) ) ) ) ) ) ) ) ) ), file(pralg_3,t21_pralg_3), []). fof(t22_equation,axiom,( ! [A,B] : ( ( ~ v3_struct_0(B) & ~ v2_msualg_1(B) & l1_msualg_1(B) ) => ! [C] : ( m2_pralg_2(C,A,B) => ! [D] : ( m1_msualg_2(D,B,k15_pralg_2(A,B,C)) => ! [E] : ( m1_subset_1(E,u1_msualg_1(B)) => ! [F] : ( r2_hidden(F,k3_msualg_1(B,E,D)) => ( v1_relat_1(k1_funct_1(k5_msualg_1(B,E,D),F)) & v1_funct_1(k1_funct_1(k5_msualg_1(B,E,D),F)) & v1_relat_1(k1_funct_1(k5_msualg_1(B,E,k15_pralg_2(A,B,C)),F)) & v1_funct_1(k1_funct_1(k5_msualg_1(B,E,k15_pralg_2(A,B,C)),F)) ) ) ) ) ) ) ), file(equation,t22_equation), []). fof(t22_pralg_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v3_struct_0(B) & ~ v2_msualg_1(B) & l1_msualg_1(B) ) => ! [C] : ( m2_pralg_2(C,A,B) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,u1_msualg_1(B)) => ! [F] : ( m1_subset_1(F,k3_msualg_1(B,E,k15_pralg_2(A,B,C))) => ! [G] : ( r2_hidden(G,k4_finseq_1(k1_msualg_1(B,E))) => ! [H] : ( ( v1_relat_1(H) & v1_funct_1(H) ) => ( H = k1_funct_1(F,G) => k1_funct_1(k1_funct_1(k10_funct_6(F),D),G) = k1_funct_1(H,D) ) ) ) ) ) ) ) ) ) ), file(pralg_3,t22_pralg_3), []). fof(t23_funct_1,axiom,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( r2_hidden(A,k1_relat_1(B)) => k1_funct_1(k5_relat_1(B,C),A) = k1_funct_1(C,k1_funct_1(B,A)) ) ) ) ), file(funct_1,t23_funct_1), []). fof(t23_pralg_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v3_struct_0(B) & ~ v2_msualg_1(B) & l1_msualg_1(B) ) => ! [C] : ( m2_pralg_2(C,A,B) => ! [D] : ( m1_subset_1(D,u1_msualg_1(B)) => ( k1_msualg_1(B,D) != k1_xboole_0 => ! [E] : ( m1_subset_1(E,k3_msualg_1(B,D,k15_pralg_2(A,B,C))) => ! [F] : ( m1_subset_1(F,A) => ! [G] : ( ( v1_relat_1(G) & v1_funct_1(G) ) => ( G = k8_funct_2(k3_msualg_1(B,D,k15_pralg_2(A,B,C)),k4_msualg_1(B,D,k15_pralg_2(A,B,C)),k5_msualg_1(B,D,k15_pralg_2(A,B,C)),E) => k1_funct_1(G,F) = k1_funct_1(k5_msualg_1(B,D,k6_pralg_2(A,B,C,F)),k1_funct_1(k10_funct_6(E),F)) ) ) ) ) ) ) ) ) ) ), file(pralg_3,t23_pralg_3), []). fof(t26_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( A = k1_xboole_0 <=> k4_finseq_1(A) = k1_xboole_0 ) ) ), file(finseq_1,t26_finseq_1), []). fof(t27_equation,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) ) => ! [C] : ( ( v5_msualg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( m2_pralg_2(D,B,A) => ~ ( ! [E] : ( m1_subset_1(E,B) => ? [F] : ( v4_msualg_1(F,A) & v5_msualg_1(F,A) & v3_msafree2(F,A) & m1_msualg_2(F,A,C) & F = k6_pralg_2(B,A,D,E) ) ) & ! [E] : ( ( v4_msualg_1(E,A) & v5_msualg_1(E,A) & v3_msafree2(E,A) & m1_msualg_2(E,A,C) ) => ~ ! [F] : ( m1_subset_1(F,B) => m1_msualg_2(k6_pralg_2(B,A,D,F),A,E) ) ) ) ) ) ) ) ), file(equation,t27_equation), []). fof(t27_partfun1,axiom,( ! [A,B,C,D] : ( ( v1_funct_1(D) & m2_relset_1(D,A,B) ) => ( r2_hidden(C,k4_relset_1(A,B,D)) => r2_hidden(k1_funct_1(D,C),B) ) ) ), file(partfun1,t27_partfun1), []). fof(t28_equation,axiom,( ! [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] : ( ( v4_msualg_1(C,A) & v5_msualg_1(C,A) & v3_msafree2(C,A) & m1_msualg_2(C,A,B) ) => ! [D] : ( ( v4_msualg_1(D,A) & v5_msualg_1(D,A) & v3_msafree2(D,A) & m1_msualg_2(D,A,B) ) => ? [E] : ( v4_msualg_1(E,A) & v5_msualg_1(E,A) & v3_msafree2(E,A) & m1_msualg_2(E,A,B) & m1_msualg_2(C,A,E) & m1_msualg_2(D,A,E) ) ) ) ) ) ), file(equation,t28_equation), []). fof(t2_msualg_6,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( m1_subset_1(C,u1_msualg_1(A)) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ( r2_hidden(D,k3_msualg_1(A,C,B)) => ( k1_relat_1(D) = k4_finseq_1(k1_msualg_1(A,C)) & ! [E] : ( r2_hidden(E,k4_finseq_1(k1_msualg_1(A,C))) => r2_hidden(k1_funct_1(D,E),k1_funct_1(u4_msualg_1(A,B),k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,C),E))) ) ) ) ) ) ) ) ), file(msualg_6,t2_msualg_6), []). 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_tarski,axiom,( ! [A,B] : ( ! [C] : ( r2_hidden(C,A) <=> r2_hidden(C,B) ) => A = B ) ), file(tarski,t2_tarski), []). fof(t38_funct_2,axiom,( ! [A,B,C,D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) ) => ( r1_tarski(C,A) => ( ( B = k1_xboole_0 & A != k1_xboole_0 ) | ( v1_funct_1(k2_partfun1(A,B,D,C)) & v1_funct_2(k2_partfun1(A,B,D,C),C,B) & m2_relset_1(k2_partfun1(A,B,D,C),C,B) ) ) ) ) ), file(funct_2,t38_funct_2), []). fof(t3_equation,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C,D,E] : ( ( v1_relat_1(E) & v1_funct_1(E) ) => ( ( r2_hidden(E,k1_funct_2(A,k1_funct_2(B,C))) & r2_hidden(D,B) ) => ( k1_relat_1(k1_funct_1(k10_funct_6(E),D)) = A & r1_tarski(k2_relat_1(k1_funct_1(k10_funct_6(E),D)),C) ) ) ) ) ) ), file(equation,t3_equation), []). fof(t3_msualg_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_msualg_1(A)) => ! [C] : ( l3_msualg_1(C,A) => ! [D] : ( m4_pboole(D,u1_struct_0(A),u4_msualg_1(A,C)) => ! [E] : ( m4_pboole(E,u1_struct_0(A),u4_msualg_1(A,C)) => ( r2_pboole(u1_struct_0(A),D,E) => r1_tarski(k1_funct_1(k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),D)),B),k1_funct_1(k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),E)),B)) ) ) ) ) ) ) ), file(msualg_2,t3_msualg_2), []). fof(t3_subset,axiom,( ! [A,B] : ( m1_subset_1(A,k1_zfmisc_1(B)) <=> r1_tarski(A,B) ) ), file(subset,t3_subset), []). fof(t46_zfmisc_1,axiom,( ! [A,B] : ( r2_hidden(A,B) => k2_xboole_0(k1_tarski(A),B) = B ) ), file(zfmisc_1,t46_zfmisc_1), []). 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(t6_boole,axiom,( ! [A] : ( v1_xboole_0(A) => A = k1_xboole_0 ) ), file(boole,t6_boole), []). fof(t6_msualg_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => m1_msualg_2(B,A,B) ) ) ), file(msualg_2,t6_msualg_2), []). fof(t6_msualg_3,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_msualg_1(A)) => ! [C] : ( l3_msualg_1(C,A) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ( r2_hidden(D,k3_msualg_1(A,B,C)) => ( k1_relat_1(D) = k4_finseq_1(k1_msualg_1(A,B)) & ! [E] : ( r2_hidden(E,k1_relat_1(k5_relat_1(k1_msualg_1(A,B),u4_msualg_1(A,C)))) => r2_hidden(k1_funct_1(D,E),k1_funct_1(k5_relat_1(k1_msualg_1(A,B),u4_msualg_1(A,C)),E)) ) ) ) ) ) ) ) ), file(msualg_3,t6_msualg_3), []). fof(t70_funct_1,axiom,( ! [A,B,C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( r2_hidden(B,k1_relat_1(k7_relat_1(C,A))) => k1_funct_1(k7_relat_1(C,A),B) = k1_funct_1(C,B) ) ) ), file(funct_1,t70_funct_1), []). fof(t7_boole,axiom,( ! [A,B] : ~ ( r2_hidden(A,B) & v1_xboole_0(B) ) ), file(boole,t7_boole), []). fof(t7_msualg_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( l3_msualg_1(C,A) => ! [D] : ( l3_msualg_1(D,A) => ( ( m1_msualg_2(B,A,C) & m1_msualg_2(C,A,D) ) => m1_msualg_2(B,A,D) ) ) ) ) ) ), file(msualg_2,t7_msualg_2), []). fof(t8_boole,axiom,( ! [A,B] : ~ ( v1_xboole_0(A) & A != B & v1_xboole_0(B) ) ), file(boole,t8_boole), []). fof(t9_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( ( k1_relat_1(A) = k1_relat_1(B) & ! [C] : ( r2_hidden(C,k1_relat_1(A)) => k1_funct_1(A,C) = k1_funct_1(B,C) ) ) => A = B ) ) ) ), file(funct_1,t9_funct_1), []).