% Mizar problem: t53_graphsp,graphsp,3342,61 fof(t53_graphsp,conjecture,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( m2_finseq_2(C,k1_numbers,k3_finseq_2(k1_numbers)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k3_finseq_2(k1_numbers)) => ! [E] : ( ( v2_graph_1(E) & v3_graph_1(E) & v7_graph_1(E) & l1_graph_1(E) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,u2_graph_1(E),k8_graph_5) & m2_relset_1(F,u2_graph_1(E),k8_graph_5) ) => ! [G] : ( m1_subset_1(G,u1_graph_1(E)) => ! [H] : ( m1_subset_1(H,u1_graph_1(E)) => ( ( r6_graphsp(C,E,A,F) & G = 1 & H = B & r1_xreal_0(1,A) & D = k8_graphsp(k22_graphsp(A),C) ) => ( 1 = H | ( u1_graph_1(E) = k4_subset_1(k5_numbers,k16_graphsp(D,A),k15_graphsp(D,A)) & ~ ( r2_hidden(H,k16_graphsp(D,A)) & ! [I] : ( m2_finseq_1(I,k5_numbers) => ! [J] : ( ( v8_graph_1(J,E) & m2_graph_1(J,E) ) => ~ ( r4_graphsp(I,D,B,A) & r5_graphsp(E,J,I) & r7_graph_5(E,G,H,J,F) & k10_graph_5(E,J,F) = k1_goboard1(D,k1_nat_1(k2_nat_1(2,A),B)) ) ) ) ) & ( r2_hidden(H,k15_graphsp(D,A)) => ! [I] : ( ( v8_graph_1(I,E) & m2_graph_1(I,E) ) => ~ r1_graph_5(E,I,G,H) ) ) ) ) ) ) ) ) ) ) ) ) ) ), inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_finseq_1,cc1_finset_1,cc1_fraenkel,cc1_funct_2,cc1_graph_4,cc1_membered,cc1_relset_1,cc1_xreal_0,cc20_membered,cc2_finset_1,cc2_int_1,cc2_membered,cc2_xreal_0,cc3_int_1,cc3_membered,cc3_xreal_0,cc4_int_1,cc4_membered,cc4_xreal_0,cc5_funct_2,cc5_xreal_0,cc6_funct_2,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,cc9_membered,commutativity_k1_nat_1,commutativity_k2_nat_1,commutativity_k2_xboole_0,commutativity_k2_xcmplx_0,commutativity_k3_xcmplx_0,commutativity_k4_subset_1,connectedness_r1_xreal_0,d10_xboole_0,d1_tarski,d20_graphsp,d21_graphsp,d2_xboole_0,d3_graphsp,d3_tarski,d4_graphsp,d5_graphsp,d5_real_1,d8_graphsp,d9_graphsp,dt_k10_graph_5,dt_k10_graphsp,dt_k11_graphsp,dt_k13_finseq_1,dt_k13_graphsp,dt_k14_graphsp,dt_k15_graphsp,dt_k16_graphsp,dt_k17_graphsp,dt_k18_graphsp,dt_k1_card_1,dt_k1_finseq_1,dt_k1_funct_1,dt_k1_funct_2,dt_k1_goboard1,dt_k1_nat_1,dt_k1_numbers,dt_k1_real_1,dt_k1_relat_1,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k21_graphsp,dt_k22_graphsp,dt_k2_finseq_1,dt_k2_nat_1,dt_k2_xboole_0,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k3_finseq_1,dt_k3_finseq_2,dt_k3_xcmplx_0,dt_k4_finseq_1,dt_k4_subset_1,dt_k4_xcmplx_0,dt_k5_graphsp,dt_k5_numbers,dt_k5_ordinal2,dt_k5_relat_1,dt_k6_domain_1,dt_k6_graphsp,dt_k7_graphsp,dt_k8_funct_2,dt_k8_graph_5,dt_k8_graphsp,dt_k9_graphsp,dt_l1_graph_1,dt_m1_finseq_1,dt_m1_finseq_2,dt_m1_graph_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_finseq_2,dt_m2_graph_1,dt_m2_relset_1,dt_m2_subset_1,dt_u1_graph_1,dt_u2_graph_1,existence_l1_graph_1,existence_m1_finseq_1,existence_m1_finseq_2,existence_m1_graph_1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_finseq_2,existence_m2_graph_1,existence_m2_relset_1,existence_m2_subset_1,fc10_membered,fc10_xreal_0,fc11_membered,fc11_xreal_0,fc12_xreal_0,fc13_xreal_0,fc14_finset_1,fc14_xreal_0,fc16_finseq_1,fc17_finseq_1,fc1_finseq_1,fc1_finset_1,fc1_fraenkel,fc1_funct_2,fc1_graph_5,fc1_graphsp,fc1_int_1,fc1_ordinal2,fc1_xreal_0,fc21_xreal_0,fc22_membered,fc22_xreal_0,fc23_membered,fc23_xreal_0,fc24_membered,fc24_xreal_0,fc25_membered,fc26_membered,fc2_finseq_1,fc2_fraenkel,fc2_funct_2,fc2_graphsp,fc2_int_1,fc2_membered,fc3_int_1,fc3_xreal_0,fc4_xreal_0,fc5_int_1,fc5_membered,fc6_int_1,fc6_membered,fc7_int_1,fc7_membered,fc7_xreal_0,fc8_membered,fc8_xreal_0,fc9_finseq_1,fc9_finset_1,fc9_membered,fc9_xreal_0,fraenkel_a_2_0_graphsp,fraenkel_a_2_1_graphsp,fraenkel_a_2_2_graphsp,fraenkel_a_2_3_graphsp,fraenkel_a_2_4_graphsp,fraenkel_a_2_5_graphsp,idempotence_k2_xboole_0,idempotence_k4_subset_1,involutiveness_k1_real_1,involutiveness_k4_xcmplx_0,l52_graphsp,l88_graphsp,l93_graphsp,rc1_finseq_1,rc1_finset_1,rc1_fraenkel,rc1_funct_2,rc1_graph_4,rc1_int_1,rc1_membered,rc1_partfun1,rc1_xreal_0,rc2_finseq_1,rc2_finset_1,rc2_int_1,rc2_partfun1,rc2_xreal_0,rc3_finseq_1,rc3_finset_1,rc3_graph_1,rc3_xreal_0,rc4_finseq_1,rc4_finset_1,rc4_xreal_0,rc5_graph_1,rc6_finseq_1,rc6_graph_1,rc7_finseq_1,rc7_graph_1,rc8_finseq_1,redefinition_k14_graphsp,redefinition_k1_goboard1,redefinition_k1_nat_1,redefinition_k1_real_1,redefinition_k2_finseq_1,redefinition_k2_nat_1,redefinition_k3_finseq_1,redefinition_k3_finseq_2,redefinition_k4_finseq_1,redefinition_k4_subset_1,redefinition_k5_graphsp,redefinition_k5_numbers,redefinition_k6_domain_1,redefinition_k6_graphsp,redefinition_k8_funct_2,redefinition_k8_graphsp,redefinition_m2_finseq_1,redefinition_m2_finseq_2,redefinition_m2_graph_1,redefinition_m2_relset_1,redefinition_m2_subset_1,reflexivity_r1_tarski,reflexivity_r1_xreal_0,s1_nat_1__e13_102__graphsp,spc0_boole,spc1_boole,spc1_numerals,spc2_boole,spc2_numerals,spc3_boole,spc3_numerals,t11_graphsp,t16_graphsp,t1_arithm,t1_boole,t1_numerals,t1_real,t1_subset,t20_int_1,t22_graphsp,t24_graphsp,t27_finseq_3,t2_arithm,t2_real,t2_subset,t2_tarski,t2_xreal_1,t37_nat_1,t38_nat_1,t3_arithm,t3_finseq_1,t3_real,t3_subset,t41_graphsp,t42_graphsp,t48_graphsp,t49_graphsp,t4_real,t4_subset,t5_real,t5_subset,t6_boole,t6_real,t7_boole,t7_real,t8_boole,t8_real]), [file(graphsp,t53_graphsp)]). fof(antisymmetry_r2_hidden,axiom,( ! [A,B] : ( r2_hidden(A,B) => ~ r2_hidden(B,A) ) ), file(hidden,r2_hidden), []). fof(cc10_membered,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( m1_subset_1(B,A) => v1_xcmplx_0(B) ) ) ), file(membered,cc10_membered), []). fof(cc11_membered,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v1_xreal_0(B) ) ) ) ), file(membered,cc11_membered), []). fof(cc12_membered,axiom,( ! [A] : ( v3_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v1_xreal_0(B) & v1_rat_1(B) ) ) ) ), file(membered,cc12_membered), []). fof(cc13_membered,axiom,( ! [A] : ( v4_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v1_xreal_0(B) & v1_int_1(B) & v1_rat_1(B) ) ) ) ), file(membered,cc13_membered), []). fof(cc14_membered,axiom,( ! [A] : ( v5_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v4_ordinal2(B) & v1_xreal_0(B) & v1_int_1(B) & v1_rat_1(B) ) ) ) ), file(membered,cc14_membered), []). fof(cc15_membered,axiom,( ! [A] : ( v1_xboole_0(A) => ( v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ) ), file(membered,cc15_membered), []). fof(cc16_membered,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v1_membered(B) ) ) ), file(membered,cc16_membered), []). fof(cc17_membered,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) ) ) ) ), file(membered,cc17_membered), []). fof(cc18_membered,axiom,( ! [A] : ( v3_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) & v3_membered(B) ) ) ) ), file(membered,cc18_membered), []). fof(cc19_membered,axiom,( ! [A] : ( v4_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) ) ) ) ), file(membered,cc19_membered), []). 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_fraenkel,axiom,( ! [A] : ( v1_fraenkel(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_relat_1(B) & v1_funct_1(B) ) ) ) ), file(fraenkel,cc1_fraenkel), []). fof(cc1_funct_2,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => ( ( v1_funct_1(C) & v1_partfun1(C,A,B) ) => ( v1_funct_1(C) & v1_funct_2(C,A,B) ) ) ) ), file(funct_2,cc1_funct_2), []). fof(cc1_graph_4,axiom,( ! [A] : ( ( v2_graph_1(A) & l1_graph_1(A) ) => ! [B] : ( m1_graph_1(B,A) => ( ( v1_xboole_0(B) & v8_graph_1(B,A) ) => ( v2_funct_1(B) & v8_graph_1(B,A) ) ) ) ) ), file(graph_4,cc1_graph_4), []). fof(cc1_membered,axiom,( ! [A] : ( v5_membered(A) => v4_membered(A) ) ), file(membered,cc1_membered), []). fof(cc1_relset_1,axiom,( ! [A,B,C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => v1_relat_1(C) ) ), file(relset_1,cc1_relset_1), []). fof(cc1_xreal_0,axiom,( ! [A] : ( v4_ordinal2(A) => v1_xreal_0(A) ) ), file(xreal_0,cc1_xreal_0), []). fof(cc20_membered,axiom,( ! [A] : ( v5_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B) ) ) ) ), file(membered,cc20_membered), []). 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_int_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) & ~ v3_xreal_0(A) & v1_int_1(A) ) ) ), file(int_1,cc2_int_1), []). fof(cc2_membered,axiom,( ! [A] : ( v4_membered(A) => v3_membered(A) ) ), file(membered,cc2_membered), []). fof(cc2_xreal_0,axiom,( ! [A] : ( v1_xreal_0(A) => v1_xcmplx_0(A) ) ), file(xreal_0,cc2_xreal_0), []). fof(cc3_int_1,axiom,( ! [A] : ( v4_ordinal2(A) => v1_int_1(A) ) ), file(int_1,cc3_int_1), []). fof(cc3_membered,axiom,( ! [A] : ( v3_membered(A) => v2_membered(A) ) ), file(membered,cc3_membered), []). fof(cc3_xreal_0,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xreal_0(A) ) => ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) ) ) ), file(xreal_0,cc3_xreal_0), []). fof(cc4_int_1,axiom,( ! [A] : ( v1_int_1(A) => ( v1_xcmplx_0(A) & v1_xreal_0(A) ) ) ), file(int_1,cc4_int_1), []). fof(cc4_membered,axiom,( ! [A] : ( v2_membered(A) => v1_membered(A) ) ), file(membered,cc4_membered), []). fof(cc4_xreal_0,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) ) => ( v1_xcmplx_0(A) & v1_xreal_0(A) & v2_xreal_0(A) ) ) ), file(xreal_0,cc4_xreal_0), []). fof(cc5_funct_2,axiom,( ! [A,B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_relset_1(C,A,B) => ( ( v1_funct_1(C) & v1_funct_2(C,A,B) ) => ( v1_funct_1(C) & v1_partfun1(C,A,B) & v1_funct_2(C,A,B) ) ) ) ) ), file(funct_2,cc5_funct_2), []). fof(cc5_xreal_0,axiom,( ! [A] : ( ( v1_xreal_0(A) & v3_xreal_0(A) ) => ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) ) ) ), file(xreal_0,cc5_xreal_0), []). fof(cc6_funct_2,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ! [C] : ( m1_relset_1(C,A,B) => ( ( v1_funct_1(C) & v1_funct_2(C,A,B) ) => ( v1_funct_1(C) & ~ v1_xboole_0(C) & v1_partfun1(C,A,B) & v1_funct_2(C,A,B) ) ) ) ) ), file(funct_2,cc6_funct_2), []). fof(cc6_membered,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( v1_membered(A) & v2_membered(A) ) ) ), file(membered,cc6_membered), []). fof(cc6_xreal_0,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) ) => ( v1_xcmplx_0(A) & v1_xreal_0(A) & v3_xreal_0(A) ) ) ), file(xreal_0,cc6_xreal_0), []). fof(cc7_xreal_0,axiom,( ! [A] : ( ( v1_xboole_0(A) & v1_xreal_0(A) ) => ( v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) & ~ v3_xreal_0(A) ) ) ), file(xreal_0,cc7_xreal_0), []). fof(cc8_xreal_0,axiom,( ! [A] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) & ~ v3_xreal_0(A) ) => ( v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) ) ) ), file(xreal_0,cc8_xreal_0), []). fof(cc9_membered,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k5_numbers)) => ( v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ) ), file(membered,cc9_membered), []). fof(commutativity_k1_nat_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => k1_nat_1(A,B) = k1_nat_1(B,A) ) ), file(nat_1,k1_nat_1), []). fof(commutativity_k2_nat_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => k2_nat_1(A,B) = k2_nat_1(B,A) ) ), file(nat_1,k2_nat_1), []). fof(commutativity_k2_xboole_0,axiom,( ! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A) ), file(xboole_0,k2_xboole_0), []). fof(commutativity_k2_xcmplx_0,axiom,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => k2_xcmplx_0(A,B) = k2_xcmplx_0(B,A) ) ), file(xcmplx_0,k2_xcmplx_0), []). fof(commutativity_k3_xcmplx_0,axiom,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => k3_xcmplx_0(A,B) = k3_xcmplx_0(B,A) ) ), file(xcmplx_0,k3_xcmplx_0), []). fof(commutativity_k4_subset_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => k4_subset_1(A,B,C) = k4_subset_1(A,C,B) ) ), file(subset_1,k4_subset_1), []). fof(connectedness_r1_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( r1_xreal_0(A,B) | r1_xreal_0(B,A) ) ) ), file(xreal_0,r1_xreal_0), []). fof(d10_xboole_0,axiom,( ! [A,B] : ( A = B <=> ( r1_tarski(A,B) & r1_tarski(B,A) ) ) ), file(xboole_0,d10_xboole_0), []). fof(d1_tarski,axiom,( ! [A,B] : ( B = k1_tarski(A) <=> ! [C] : ( r2_hidden(C,B) <=> C = A ) ) ), file(tarski,d1_tarski), []). fof(d20_graphsp,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k3_finseq_2(k1_numbers)) => ! [B] : ( ( v2_graph_1(B) & v3_graph_1(B) & l1_graph_1(B) ) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,u2_graph_1(B),k8_graph_5) & m2_relset_1(D,u2_graph_1(B),k8_graph_5) ) => ( r6_graphsp(A,B,C,D) <=> ( k3_finseq_1(A) = k1_nat_1(k1_nat_1(k2_nat_1(C,C),k2_nat_1(3,C)),1) & k2_finseq_1(C) = u1_graph_1(B) & ! [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) => ( ( r1_xreal_0(1,E) & r1_xreal_0(E,C) ) => ( k1_goboard1(A,E) = 1 & k1_goboard1(A,k1_nat_1(k2_nat_1(2,C),E)) = 0 ) ) ) & k1_goboard1(A,k1_nat_1(C,1)) = 0 & ! [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) => ( ( r1_xreal_0(2,E) & r1_xreal_0(E,C) ) => k1_goboard1(A,k1_nat_1(C,E)) = k1_real_1(1) ) ) & ! [E] : ( m1_subset_1(E,u1_graph_1(B)) => ! [F] : ( m1_subset_1(F,u1_graph_1(B)) => ! [G] : ( m2_subset_1(G,k1_numbers,k5_numbers) => ! [H] : ( m2_subset_1(H,k1_numbers,k5_numbers) => ( ( G = E & H = F ) => k1_goboard1(A,k1_nat_1(k1_nat_1(k2_nat_1(2,C),k2_nat_1(C,G)),H)) = k14_graphsp(B,E,F,D) ) ) ) ) ) ) ) ) ) ) ) ), file(graphsp,d20_graphsp), []). fof(d21_graphsp,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => k22_graphsp(A) = k11_graphsp(k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A)),A) ) ), file(graphsp,d21_graphsp), []). fof(d2_xboole_0,axiom,( ! [A,B,C] : ( C = k2_xboole_0(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( r2_hidden(D,A) | r2_hidden(D,B) ) ) ) ), file(xboole_0,d2_xboole_0), []). fof(d3_graphsp,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k3_finseq_2(k1_numbers)) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => k9_graphsp(A,B) = a_2_0_graphsp(A,B) ) ) ), file(graphsp,d3_graphsp), []). 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_graphsp,axiom,( ! [A] : ( m1_subset_1(A,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers))) => ! [B] : ( m2_finseq_2(B,k1_numbers,k3_finseq_2(k1_numbers)) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ( ? [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) & k9_graphsp(k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),A),D),B),C) = k1_xboole_0 ) => ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ( D = k10_graphsp(A,B,C) <=> ( k9_graphsp(k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),A),D),B),C) = k1_xboole_0 & ! [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) => ( k9_graphsp(k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),A),E),B),C) = k1_xboole_0 => r1_xreal_0(D,E) ) ) ) ) ) ) ) ) ) ), file(graphsp,d4_graphsp), []). fof(d5_graphsp,axiom,( ! [A] : ( m1_subset_1(A,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers))) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( m1_subset_1(C,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers))) => ( C = k11_graphsp(A,B) <=> ( k1_relat_1(C) = k3_finseq_2(k1_numbers) & ! [D] : ( m2_finseq_2(D,k1_numbers,k3_finseq_2(k1_numbers)) => k8_graphsp(C,D) = k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),A),k10_graphsp(A,D,B)),D) ) ) ) ) ) ) ), file(graphsp,d5_graphsp), []). fof(d5_real_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xreal_0(A,B) <=> ~ ( r1_xreal_0(B,A) & B != A ) ) ) ) ), file(real_1,d5_real_1), []). fof(d8_graphsp,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k3_finseq_2(k1_numbers)) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => k15_graphsp(A,B) = a_2_1_graphsp(A,B) ) ) ), file(graphsp,d8_graphsp), []). fof(d9_graphsp,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k3_finseq_2(k1_numbers)) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => k16_graphsp(A,B) = a_2_2_graphsp(A,B) ) ) ), file(graphsp,d9_graphsp), []). fof(dt_k10_graph_5,axiom,( ! [A,B,C] : ( ( v2_graph_1(A) & l1_graph_1(A) & m1_finseq_1(B,u2_graph_1(A)) & v1_relat_1(C) & v1_funct_1(C) ) => m1_subset_1(k10_graph_5(A,B,C),k1_numbers) ) ), file(graph_5,k10_graph_5), []). fof(dt_k10_graphsp,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers))) & m1_subset_1(B,k3_finseq_2(k1_numbers)) & m1_subset_1(C,k5_numbers) ) => m2_subset_1(k10_graphsp(A,B,C),k1_numbers,k5_numbers) ) ), file(graphsp,k10_graphsp), []). fof(dt_k11_graphsp,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers))) & m1_subset_1(B,k5_numbers) ) => m1_subset_1(k11_graphsp(A,B),k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers))) ) ), file(graphsp,k11_graphsp), []). fof(dt_k13_finseq_1,axiom,( $true ), file(finseq_1,k13_finseq_1), []). fof(dt_k13_graphsp,axiom,( $true ), file(graphsp,k13_graphsp), []). fof(dt_k14_graphsp,axiom,( ! [A,B,C,D] : ( ( v2_graph_1(A) & v3_graph_1(A) & l1_graph_1(A) & m1_subset_1(B,u1_graph_1(A)) & m1_subset_1(C,u1_graph_1(A)) & v1_funct_1(D) & v1_funct_2(D,u2_graph_1(A),k8_graph_5) & m1_relset_1(D,u2_graph_1(A),k8_graph_5) ) => m1_subset_1(k14_graphsp(A,B,C,D),k1_numbers) ) ), file(graphsp,k14_graphsp), []). fof(dt_k15_graphsp,axiom,( ! [A,B] : ( ( m1_subset_1(A,k3_finseq_2(k1_numbers)) & m1_subset_1(B,k5_numbers) ) => m1_subset_1(k15_graphsp(A,B),k1_zfmisc_1(k5_numbers)) ) ), file(graphsp,k15_graphsp), []). fof(dt_k16_graphsp,axiom,( ! [A,B] : ( ( m1_subset_1(A,k3_finseq_2(k1_numbers)) & m1_subset_1(B,k5_numbers) ) => m1_subset_1(k16_graphsp(A,B),k1_zfmisc_1(k5_numbers)) ) ), file(graphsp,k16_graphsp), []). fof(dt_k17_graphsp,axiom,( ! [A,B,C] : ( ( v1_finset_1(A) & m1_subset_1(A,k1_zfmisc_1(k5_numbers)) & m1_subset_1(B,k3_finseq_2(k1_numbers)) & m1_subset_1(C,k5_numbers) ) => m2_subset_1(k17_graphsp(A,B,C),k1_numbers,k5_numbers) ) ), file(graphsp,k17_graphsp), []). fof(dt_k18_graphsp,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => m1_subset_1(k18_graphsp(A),k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers))) ) ), file(graphsp,k18_graphsp), []). fof(dt_k1_card_1,axiom,( ! [A] : v1_card_1(k1_card_1(A)) ), file(card_1,k1_card_1), []). fof(dt_k1_finseq_1,axiom,( $true ), file(finseq_1,k1_finseq_1), []). 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_goboard1,axiom,( ! [A,B] : ( ( m1_finseq_1(A,k1_numbers) & m1_subset_1(B,k5_numbers) ) => m1_subset_1(k1_goboard1(A,B),k1_numbers) ) ), file(goboard1,k1_goboard1), []). fof(dt_k1_nat_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => m2_subset_1(k1_nat_1(A,B),k1_numbers,k5_numbers) ) ), file(nat_1,k1_nat_1), []). fof(dt_k1_numbers,axiom,( $true ), file(numbers,k1_numbers), []). fof(dt_k1_real_1,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => m1_subset_1(k1_real_1(A),k1_numbers) ) ), file(real_1,k1_real_1), []). fof(dt_k1_relat_1,axiom,( $true ), file(relat_1,k1_relat_1), []). fof(dt_k1_tarski,axiom,( $true ), file(tarski,k1_tarski), []). fof(dt_k1_xboole_0,axiom,( $true ), file(xboole_0,k1_xboole_0), []). fof(dt_k1_zfmisc_1,axiom,( $true ), file(zfmisc_1,k1_zfmisc_1), []). fof(dt_k21_graphsp,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => m1_subset_1(k21_graphsp(A),k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers))) ) ), file(graphsp,k21_graphsp), []). fof(dt_k22_graphsp,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => m1_subset_1(k22_graphsp(A),k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers))) ) ), file(graphsp,k22_graphsp), []). fof(dt_k2_finseq_1,axiom,( ! [A] : ( v4_ordinal2(A) => m1_subset_1(k2_finseq_1(A),k1_zfmisc_1(k5_numbers)) ) ), file(finseq_1,k2_finseq_1), []). fof(dt_k2_nat_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => m2_subset_1(k2_nat_1(A,B),k1_numbers,k5_numbers) ) ), file(nat_1,k2_nat_1), []). fof(dt_k2_xboole_0,axiom,( $true ), file(xboole_0,k2_xboole_0), []). fof(dt_k2_xcmplx_0,axiom,( $true ), file(xcmplx_0,k2_xcmplx_0), []). fof(dt_k2_zfmisc_1,axiom,( $true ), file(zfmisc_1,k2_zfmisc_1), []). fof(dt_k3_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => m2_subset_1(k3_finseq_1(A),k1_numbers,k5_numbers) ) ), file(finseq_1,k3_finseq_1), []). fof(dt_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_xcmplx_0,axiom,( $true ), file(xcmplx_0,k3_xcmplx_0), []). 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_subset_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => m1_subset_1(k4_subset_1(A,B,C),k1_zfmisc_1(A)) ) ), file(subset_1,k4_subset_1), []). fof(dt_k4_xcmplx_0,axiom,( ! [A] : ( v1_xcmplx_0(A) => v1_xcmplx_0(k4_xcmplx_0(A)) ) ), file(xcmplx_0,k4_xcmplx_0), []). fof(dt_k5_graphsp,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k1_funct_2(A,A)) & m1_subset_1(C,k1_funct_2(A,A)) ) => m1_subset_1(k5_graphsp(A,B,C),k1_funct_2(A,A)) ) ), file(graphsp,k5_graphsp), []). 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_domain_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => m1_subset_1(k6_domain_1(A,B),k1_zfmisc_1(A)) ) ), file(domain_1,k6_domain_1), []). fof(dt_k6_graphsp,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k1_funct_2(A,A)) & m1_subset_1(C,A) ) => m1_subset_1(k6_graphsp(A,B,C),A) ) ), file(graphsp,k6_graphsp), []). fof(dt_k7_graphsp,axiom,( ! [A,B] : ( m1_subset_1(B,k1_funct_2(A,A)) => ( v1_funct_1(k7_graphsp(A,B)) & v1_funct_2(k7_graphsp(A,B),k5_numbers,k1_funct_2(A,A)) & m2_relset_1(k7_graphsp(A,B),k5_numbers,k1_funct_2(A,A)) ) ) ), file(graphsp,k7_graphsp), []). 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_graph_5,axiom,( m1_subset_1(k8_graph_5,k1_zfmisc_1(k1_numbers)) ), file(graph_5,k8_graph_5), []). fof(dt_k8_graphsp,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers))) & m1_subset_1(B,k3_finseq_2(k1_numbers)) ) => m2_finseq_2(k8_graphsp(A,B),k1_numbers,k3_finseq_2(k1_numbers)) ) ), file(graphsp,k8_graphsp), []). fof(dt_k9_graphsp,axiom,( ! [A,B] : ( ( m1_subset_1(A,k3_finseq_2(k1_numbers)) & m1_subset_1(B,k5_numbers) ) => m1_subset_1(k9_graphsp(A,B),k1_zfmisc_1(k5_numbers)) ) ), file(graphsp,k9_graphsp), []). fof(dt_l1_graph_1,axiom,( $true ), file(graph_1,l1_graph_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_graph_1,axiom,( ! [A] : ( ( v2_graph_1(A) & l1_graph_1(A) ) => ! [B] : ( m1_graph_1(B,A) => ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) ) ) ), file(graph_1,m1_graph_1), []). 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_graph_1,axiom,( ! [A] : ( ( v2_graph_1(A) & l1_graph_1(A) ) => ! [B] : ( m2_graph_1(B,A) => m2_finseq_1(B,u2_graph_1(A)) ) ) ), file(graph_1,m2_graph_1), []). fof(dt_m2_relset_1,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ), file(relset_1,m2_relset_1), []). fof(dt_m2_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m2_subset_1(C,A,B) => m1_subset_1(C,A) ) ) ), file(subset_1,m2_subset_1), []). fof(dt_u1_graph_1,axiom,( $true ), file(graph_1,u1_graph_1), []). fof(dt_u2_graph_1,axiom,( $true ), file(graph_1,u2_graph_1), []). fof(existence_l1_graph_1,axiom,( ? [A] : l1_graph_1(A) ), file(graph_1,l1_graph_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_graph_1,axiom,( ! [A] : ( ( v2_graph_1(A) & l1_graph_1(A) ) => ? [B] : m1_graph_1(B,A) ) ), file(graph_1,m1_graph_1), []). 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_graph_1,axiom,( ! [A] : ( ( v2_graph_1(A) & l1_graph_1(A) ) => ? [B] : m2_graph_1(B,A) ) ), file(graph_1,m2_graph_1), []). fof(existence_m2_relset_1,axiom,( ! [A,B] : ? [C] : m2_relset_1(C,A,B) ), file(relset_1,m2_relset_1), []). fof(existence_m2_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ? [C] : m2_subset_1(C,A,B) ) ), file(subset_1,m2_subset_1), []). fof(fc10_membered,axiom,( ! [A] : ( v1_int_1(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) & v4_membered(k1_tarski(A)) ) ) ), file(membered,fc10_membered), []). fof(fc10_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v2_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(B,A)) & v1_xcmplx_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) & v2_xreal_0(k2_xcmplx_0(B,A)) & ~ v3_xreal_0(k2_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc10_xreal_0), []). fof(fc11_membered,axiom,( ! [A] : ( v4_ordinal2(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) & v4_membered(k1_tarski(A)) & v5_membered(k1_tarski(A)) ) ) ), file(membered,fc11_membered), []). fof(fc11_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v3_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & ~ v2_xreal_0(k2_xcmplx_0(A,B)) & v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc11_xreal_0), []). fof(fc12_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v3_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(B,A)) & v1_xcmplx_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) & ~ v2_xreal_0(k2_xcmplx_0(B,A)) & v3_xreal_0(k2_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc12_xreal_0), []). fof(fc13_xreal_0,axiom,( ! [A] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) ) => ( v1_xcmplx_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)) & ~ v3_xreal_0(k4_xcmplx_0(A)) ) ) ), file(xreal_0,fc13_xreal_0), []). 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(fc14_xreal_0,axiom,( ! [A] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) ) => ( v1_xcmplx_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)) & ~ v2_xreal_0(k4_xcmplx_0(A)) ) ) ), file(xreal_0,fc14_xreal_0), []). 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_finseq_1,axiom,( ! [A] : ( v4_ordinal2(A) => v1_finset_1(k1_finseq_1(A)) ) ), file(finseq_1,fc1_finseq_1), []). 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_fraenkel,axiom,( ! [A,B] : v1_fraenkel(k1_funct_2(A,B)) ), file(fraenkel,fc1_fraenkel), []). fof(fc1_funct_2,axiom,( ! [A,B] : ( ~ v1_xboole_0(B) => ~ v1_xboole_0(k1_funct_2(A,B)) ) ), file(funct_2,fc1_funct_2), []). fof(fc1_graph_5,axiom, ( ~ v1_xboole_0(k8_graph_5) & v1_membered(k8_graph_5) & v2_membered(k8_graph_5) ), file(graph_5,fc1_graph_5), []). fof(fc1_graphsp,axiom,( ! [A,B] : ( ( m1_subset_1(A,k3_finseq_2(k1_numbers)) & m1_subset_1(B,k5_numbers) ) => ( v1_finset_1(k15_graphsp(A,B)) & v1_membered(k15_graphsp(A,B)) & v2_membered(k15_graphsp(A,B)) & v3_membered(k15_graphsp(A,B)) & v4_membered(k15_graphsp(A,B)) & v5_membered(k15_graphsp(A,B)) ) ) ), file(graphsp,fc1_graphsp), []). fof(fc1_int_1,axiom,( ! [A,B] : ( ( v1_int_1(A) & v1_int_1(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & v1_int_1(k2_xcmplx_0(A,B)) ) ) ), file(int_1,fc1_int_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_xreal_0,axiom,( ! [A] : ( v1_xreal_0(A) => ( v1_xcmplx_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)) ) ) ), file(xreal_0,fc1_xreal_0), []). fof(fc21_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & ~ v2_xreal_0(k3_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc21_xreal_0), []). fof(fc22_membered,axiom,( ! [A,B] : ( ( v1_membered(A) & v1_membered(B) ) => v1_membered(k2_xboole_0(A,B)) ) ), file(membered,fc22_membered), []). fof(fc22_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( v1_xcmplx_0(k3_xcmplx_0(B,A)) & v1_xreal_0(k3_xcmplx_0(B,A)) & ~ v2_xreal_0(k3_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc22_xreal_0), []). fof(fc23_membered,axiom,( ! [A,B] : ( ( v2_membered(A) & v2_membered(B) ) => ( v1_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)) ) ) ), file(membered,fc23_membered), []). fof(fc23_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & ~ v3_xreal_0(k3_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc23_xreal_0), []). fof(fc24_membered,axiom,( ! [A,B] : ( ( v3_membered(A) & v3_membered(B) ) => ( v1_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)) & v3_membered(k2_xboole_0(A,B)) ) ) ), file(membered,fc24_membered), []). fof(fc24_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & ~ v3_xreal_0(k3_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc24_xreal_0), []). fof(fc25_membered,axiom,( ! [A,B] : ( ( v4_membered(A) & v4_membered(B) ) => ( v1_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)) & v3_membered(k2_xboole_0(A,B)) & v4_membered(k2_xboole_0(A,B)) ) ) ), file(membered,fc25_membered), []). fof(fc26_membered,axiom,( ! [A,B] : ( ( v5_membered(A) & v5_membered(B) ) => ( v1_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)) & v3_membered(k2_xboole_0(A,B)) & v4_membered(k2_xboole_0(A,B)) & v5_membered(k2_xboole_0(A,B)) ) ) ), file(membered,fc26_membered), []). 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_fraenkel,axiom,( ! [A,B] : ( ( v1_finset_1(A) & v1_finset_1(B) ) => ( v1_finset_1(k1_funct_2(A,B)) & v1_fraenkel(k1_funct_2(A,B)) ) ) ), file(fraenkel,fc2_fraenkel), []). fof(fc2_funct_2,axiom,( ! [A] : ~ v1_xboole_0(k1_funct_2(A,A)) ), file(funct_2,fc2_funct_2), []). fof(fc2_graphsp,axiom,( ! [A,B] : ( ( m1_subset_1(A,k3_finseq_2(k1_numbers)) & m1_subset_1(B,k5_numbers) ) => ( v1_finset_1(k9_graphsp(A,B)) & v1_membered(k9_graphsp(A,B)) & v2_membered(k9_graphsp(A,B)) & v3_membered(k9_graphsp(A,B)) & v4_membered(k9_graphsp(A,B)) & v5_membered(k9_graphsp(A,B)) ) ) ), file(graphsp,fc2_graphsp), []). fof(fc2_int_1,axiom,( ! [A,B] : ( ( v1_int_1(A) & v1_int_1(B) ) => ( v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & v1_int_1(k3_xcmplx_0(A,B)) ) ) ), file(int_1,fc2_int_1), []). fof(fc2_membered,axiom, ( ~ v1_xboole_0(k1_numbers) & v1_membered(k1_numbers) & v2_membered(k1_numbers) ), file(membered,fc2_membered), []). fof(fc3_int_1,axiom,( ! [A] : ( v1_int_1(A) => ( v1_xcmplx_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)) & v1_int_1(k4_xcmplx_0(A)) ) ) ), file(int_1,fc3_int_1), []). fof(fc3_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc3_xreal_0), []). fof(fc4_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc4_xreal_0), []). fof(fc5_int_1,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ( v1_xcmplx_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)) & ~ v2_xreal_0(k4_xcmplx_0(A)) & v1_int_1(k4_xcmplx_0(A)) ) ) ), file(int_1,fc5_int_1), []). fof(fc5_membered,axiom, ( v1_membered(k5_ordinal2) & v2_membered(k5_ordinal2) & v3_membered(k5_ordinal2) & v4_membered(k5_ordinal2) & v5_membered(k5_ordinal2) ), file(membered,fc5_membered), []). fof(fc6_int_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & v1_int_1(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) & v1_int_1(k2_xcmplx_0(B,A)) ) ) ), file(int_1,fc6_int_1), []). fof(fc6_membered,axiom, ( v1_xboole_0(k1_xboole_0) & v1_membered(k1_xboole_0) & v2_membered(k1_xboole_0) & v3_membered(k1_xboole_0) & v4_membered(k1_xboole_0) & v5_membered(k1_xboole_0) ), file(membered,fc6_membered), []). fof(fc7_int_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & v1_int_1(B) ) => ( v1_xcmplx_0(k3_xcmplx_0(B,A)) & v1_xreal_0(k3_xcmplx_0(B,A)) & v1_int_1(k3_xcmplx_0(B,A)) ) ) ), file(int_1,fc7_int_1), []). fof(fc7_membered,axiom,( ! [A] : ( v1_xcmplx_0(A) => v1_membered(k1_tarski(A)) ) ), file(membered,fc7_membered), []). fof(fc7_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & ~ v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc7_xreal_0), []). fof(fc8_membered,axiom,( ! [A] : ( v1_xreal_0(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) ) ) ), file(membered,fc8_membered), []). fof(fc8_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & ~ v2_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc8_xreal_0), []). fof(fc9_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_membered,axiom,( ! [A] : ( v1_rat_1(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) ) ) ), file(membered,fc9_membered), []). fof(fc9_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v2_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & v2_xreal_0(k2_xcmplx_0(A,B)) & ~ v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc9_xreal_0), []). fof(fraenkel_a_2_0_graphsp,axiom,( ! [A,B,C] : ( ( m2_finseq_2(B,k1_numbers,k3_finseq_2(k1_numbers)) & m2_subset_1(C,k1_numbers,k5_numbers) ) => ( r2_hidden(A,a_2_0_graphsp(B,C)) <=> ? [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) & A = D & r2_hidden(D,k4_finseq_1(B)) & r1_xreal_0(1,D) & r1_xreal_0(D,C) & k1_goboard1(B,D) != k1_real_1(1) & k1_goboard1(B,k1_nat_1(C,D)) != k1_real_1(1) ) ) ) ), file(graphsp,a_2_0_graphsp), []). fof(fraenkel_a_2_1_graphsp,axiom,( ! [A,B,C] : ( ( m2_finseq_2(B,k1_numbers,k3_finseq_2(k1_numbers)) & m2_subset_1(C,k1_numbers,k5_numbers) ) => ( r2_hidden(A,a_2_1_graphsp(B,C)) <=> ? [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) & A = D & r2_hidden(D,k4_finseq_1(B)) & r1_xreal_0(1,D) & r1_xreal_0(D,C) & k1_goboard1(B,D) != k1_real_1(1) ) ) ) ), file(graphsp,a_2_1_graphsp), []). fof(fraenkel_a_2_2_graphsp,axiom,( ! [A,B,C] : ( ( m2_finseq_2(B,k1_numbers,k3_finseq_2(k1_numbers)) & m2_subset_1(C,k1_numbers,k5_numbers) ) => ( r2_hidden(A,a_2_2_graphsp(B,C)) <=> ? [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) & A = D & r2_hidden(D,k4_finseq_1(B)) & r1_xreal_0(1,D) & r1_xreal_0(D,C) & k1_goboard1(B,D) = k1_real_1(1) ) ) ) ), file(graphsp,a_2_2_graphsp), []). fof(fraenkel_a_2_3_graphsp,axiom,( ! [A,B,C] : ( ( m2_subset_1(B,k1_numbers,k5_numbers) & m2_finseq_2(C,k1_numbers,k3_finseq_2(k1_numbers)) ) => ( r2_hidden(A,a_2_3_graphsp(B,C)) <=> ? [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) & A = D & r2_hidden(D,k4_finseq_1(C)) & r1_xreal_0(1,D) & r1_xreal_0(D,B) & k1_goboard1(C,D) != k1_real_1(1) ) ) ) ), file(graphsp,a_2_3_graphsp), []). fof(fraenkel_a_2_4_graphsp,axiom,( ! [A,B,C] : ( ( m2_subset_1(B,k1_numbers,k5_numbers) & m2_finseq_2(C,k1_numbers,k3_finseq_2(k1_numbers)) ) => ( r2_hidden(A,a_2_4_graphsp(B,C)) <=> ? [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) & A = D & r2_hidden(D,k4_finseq_1(C)) & r1_xreal_0(1,D) & r1_xreal_0(D,B) & k1_goboard1(C,D) != k1_real_1(1) & k1_goboard1(C,k1_nat_1(B,D)) != k1_real_1(1) ) ) ) ), file(graphsp,a_2_4_graphsp), []). fof(fraenkel_a_2_5_graphsp,axiom,( ! [A,B,C] : ( ( m2_subset_1(B,k1_numbers,k5_numbers) & m2_finseq_2(C,k1_numbers,k3_finseq_2(k1_numbers)) ) => ( r2_hidden(A,a_2_5_graphsp(B,C)) <=> ? [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) & A = D & r2_hidden(D,k4_finseq_1(C)) & r1_xreal_0(1,D) & r1_xreal_0(D,B) & k1_goboard1(C,D) = k1_real_1(1) ) ) ) ), file(graphsp,a_2_5_graphsp), []). fof(idempotence_k2_xboole_0,axiom,( ! [A,B] : k2_xboole_0(A,A) = A ), file(xboole_0,k2_xboole_0), []). fof(idempotence_k4_subset_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => k4_subset_1(A,B,B) = B ) ), file(subset_1,k4_subset_1), []). fof(involutiveness_k1_real_1,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => k1_real_1(k1_real_1(A)) = A ) ), file(real_1,k1_real_1), []). fof(involutiveness_k4_xcmplx_0,axiom,( ! [A] : ( v1_xcmplx_0(A) => k4_xcmplx_0(k4_xcmplx_0(A)) = A ) ), file(xcmplx_0,k4_xcmplx_0), []). fof(l52_graphsp,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ( ~ r1_xreal_0(k1_nat_1(k1_nat_1(k2_nat_1(A,A),k2_nat_1(3,A)),1),k2_nat_1(3,A)) & ~ r1_xreal_0(k1_nat_1(k1_nat_1(k2_nat_1(A,A),k2_nat_1(3,A)),1),A) & ~ r1_xreal_0(k1_nat_1(k1_nat_1(k2_nat_1(A,A),k2_nat_1(3,A)),1),k2_nat_1(2,A)) ) ) ), file(graphsp,l52_graphsp), []). fof(l88_graphsp,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m2_finseq_2(B,k1_numbers,k3_finseq_2(k1_numbers)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k3_finseq_2(k1_numbers)) => ! [D] : ( ( v2_graph_1(D) & v3_graph_1(D) & v7_graph_1(D) & l1_graph_1(D) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,u2_graph_1(D),k8_graph_5) & m2_relset_1(E,u2_graph_1(D),k8_graph_5) ) => ! [F] : ( m1_subset_1(F,u1_graph_1(D)) => ( ( r6_graphsp(B,D,A,E) & F = 1 & r1_xreal_0(1,A) & C = k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),1),B) ) => ( ! [G] : ( m1_subset_1(G,u1_graph_1(D)) => ! [H] : ( m2_subset_1(H,k1_numbers,k5_numbers) => ~ ( G != F & G = H & k1_goboard1(C,k1_nat_1(A,H)) != k1_real_1(1) & ! [I] : ( m2_finseq_1(I,k5_numbers) => ! [J] : ( ( v8_graph_1(J,D) & m2_graph_1(J,D) ) => ~ ( r4_graphsp(I,C,H,A) & ! [K] : ( m2_subset_1(K,k1_numbers,k5_numbers) => ( r1_xreal_0(1,K) => ( r1_xreal_0(k3_finseq_1(I),K) | r2_hidden(k1_funct_1(I,K),k16_graphsp(C,A)) ) ) ) & r5_graphsp(D,J,I) & r8_graph_5(D,F,G,J,k16_graphsp(C,A),E) & k10_graph_5(D,J,E) = k1_goboard1(C,k1_nat_1(k2_nat_1(2,A),H)) & ( ~ r2_hidden(G,k16_graphsp(C,A)) => r9_graph_5(D,J,k16_graphsp(C,A),F,E) ) ) ) ) ) ) ) & ! [G] : ( m2_subset_1(G,k1_numbers,k5_numbers) => ! [H] : ( m2_subset_1(H,k1_numbers,k5_numbers) => ( ( k1_goboard1(C,k1_nat_1(A,H)) = k1_real_1(1) & r1_xreal_0(1,H) & r1_xreal_0(H,A) & r2_hidden(G,k16_graphsp(C,A)) ) => k1_goboard1(B,k1_nat_1(k1_nat_1(k2_nat_1(2,A),k2_nat_1(A,G)),H)) = k1_real_1(1) ) ) ) & ! [G] : ( m2_subset_1(G,k1_numbers,k5_numbers) => ~ ( r2_hidden(G,k16_graphsp(C,A)) & k1_goboard1(C,k1_nat_1(A,G)) = k1_real_1(1) ) ) ) ) ) ) ) ) ) ) ), file(graphsp,l88_graphsp), []). fof(l93_graphsp,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( m2_finseq_2(C,k1_numbers,k3_finseq_2(k1_numbers)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k3_finseq_2(k1_numbers)) => ! [E] : ( m2_finseq_2(E,k1_numbers,k3_finseq_2(k1_numbers)) => ! [F] : ( ( v2_graph_1(F) & v3_graph_1(F) & v7_graph_1(F) & l1_graph_1(F) ) => ! [G] : ( ( v1_funct_1(G) & v1_funct_2(G,u2_graph_1(F),k8_graph_5) & m2_relset_1(G,u2_graph_1(F),k8_graph_5) ) => ! [H] : ( m1_subset_1(H,u1_graph_1(F)) => ( ( r6_graphsp(C,F,A,G) & H = 1 & r1_xreal_0(1,A) & D = k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),B),C) & E = k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),k1_nat_1(B,1)),C) & r1_xreal_0(1,B) & r2_hidden(1,k16_graphsp(D,A)) & ! [I] : ( m1_subset_1(I,u1_graph_1(F)) => ! [J] : ( m2_subset_1(J,k1_numbers,k5_numbers) => ~ ( I != H & I = J & k1_goboard1(D,k1_nat_1(A,J)) != k1_real_1(1) & ! [K] : ( m2_finseq_1(K,k5_numbers) => ! [L] : ( ( v8_graph_1(L,F) & m2_graph_1(L,F) ) => ~ ( r4_graphsp(K,D,J,A) & ! [M] : ( m2_subset_1(M,k1_numbers,k5_numbers) => ( r1_xreal_0(1,M) => ( r1_xreal_0(k3_finseq_1(K),M) | r2_hidden(k1_funct_1(K,M),k16_graphsp(D,A)) ) ) ) & r5_graphsp(F,L,K) & r8_graph_5(F,H,I,L,k16_graphsp(D,A),G) & k10_graph_5(F,L,G) = k1_goboard1(D,k1_nat_1(k2_nat_1(2,A),J)) & ( ~ r2_hidden(I,k16_graphsp(D,A)) => r9_graph_5(F,L,k16_graphsp(D,A),H,G) ) ) ) ) ) ) ) & ! [I] : ( m2_subset_1(I,k1_numbers,k5_numbers) => ! [J] : ( m2_subset_1(J,k1_numbers,k5_numbers) => ( ( k1_goboard1(D,k1_nat_1(A,J)) = k1_real_1(1) & r1_xreal_0(1,J) & r1_xreal_0(J,A) & r2_hidden(I,k16_graphsp(D,A)) ) => k1_goboard1(C,k1_nat_1(k1_nat_1(k2_nat_1(2,A),k2_nat_1(A,I)),J)) = k1_real_1(1) ) ) ) & ! [I] : ( m2_subset_1(I,k1_numbers,k5_numbers) => ~ ( r2_hidden(I,k16_graphsp(D,A)) & k1_goboard1(D,k1_nat_1(A,I)) = k1_real_1(1) ) ) ) => ( k9_graphsp(D,A) = k1_xboole_0 | ( ! [I] : ( m1_subset_1(I,u1_graph_1(F)) => ! [J] : ( m2_subset_1(J,k1_numbers,k5_numbers) => ~ ( I != H & I = J & k1_goboard1(E,k1_nat_1(A,J)) != k1_real_1(1) & ! [K] : ( m2_finseq_1(K,k5_numbers) => ! [L] : ( ( v8_graph_1(L,F) & m2_graph_1(L,F) ) => ~ ( r4_graphsp(K,E,J,A) & ! [M] : ( m2_subset_1(M,k1_numbers,k5_numbers) => ( r1_xreal_0(1,M) => ( r1_xreal_0(k3_finseq_1(K),M) | r2_hidden(k1_funct_1(K,M),k16_graphsp(E,A)) ) ) ) & r5_graphsp(F,L,K) & r8_graph_5(F,H,I,L,k16_graphsp(E,A),G) & k10_graph_5(F,L,G) = k1_goboard1(E,k1_nat_1(k2_nat_1(2,A),J)) & ( ~ r2_hidden(I,k16_graphsp(E,A)) => r9_graph_5(F,L,k16_graphsp(E,A),H,G) ) ) ) ) ) ) ) & ! [I] : ( m2_subset_1(I,k1_numbers,k5_numbers) => ! [J] : ( m2_subset_1(J,k1_numbers,k5_numbers) => ( ( k1_goboard1(E,k1_nat_1(A,J)) = k1_real_1(1) & r1_xreal_0(1,J) & r1_xreal_0(J,A) & r2_hidden(I,k16_graphsp(E,A)) ) => k1_goboard1(C,k1_nat_1(k1_nat_1(k2_nat_1(2,A),k2_nat_1(A,I)),J)) = k1_real_1(1) ) ) ) & ! [I] : ( m2_subset_1(I,k1_numbers,k5_numbers) => ~ ( r2_hidden(I,k16_graphsp(E,A)) & k1_goboard1(E,k1_nat_1(A,I)) = k1_real_1(1) ) ) ) ) ) ) ) ) ) ) ) ) ) ), file(graphsp,l93_graphsp), []). 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_fraenkel,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_fraenkel(A) ) ), file(fraenkel,rc1_fraenkel), []). fof(rc1_funct_2,axiom,( ! [A,B] : ? [C] : ( m1_relset_1(C,A,B) & v1_relat_1(C) & v1_funct_1(C) & v1_funct_2(C,A,B) ) ), file(funct_2,rc1_funct_2), []). fof(rc1_graph_4,axiom,( ! [A] : ( ( v2_graph_1(A) & l1_graph_1(A) ) => ? [B] : ( m1_graph_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) & v8_graph_1(B,A) & v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B) ) ) ), file(graph_4,rc1_graph_4), []). fof(rc1_int_1,axiom,( ? [A] : ( m1_subset_1(A,k1_numbers) & v1_xcmplx_0(A) & v1_xreal_0(A) & v1_int_1(A) ) ), file(int_1,rc1_int_1), []). fof(rc1_membered,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ), file(membered,rc1_membered), []). fof(rc1_partfun1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_xboole_0(A) ) ), file(partfun1,rc1_partfun1), []). fof(rc1_xreal_0,axiom,( ? [A] : ( v1_xcmplx_0(A) & v1_xreal_0(A) ) ), file(xreal_0,rc1_xreal_0), []). fof(rc2_finseq_1,axiom,( ! [A] : ? [B] : ( m1_relset_1(B,k5_numbers,A) & v1_relat_1(B) & v1_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) ) ), file(finseq_1,rc2_finseq_1), []). fof(rc2_finset_1,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v2_funct_1(B) & v1_ordinal1(B) & v2_ordinal1(B) & v3_ordinal1(B) & v4_ordinal2(B) & v1_finset_1(B) ) ), file(finset_1,rc2_finset_1), []). fof(rc2_int_1,axiom,( ? [A] : v1_int_1(A) ), file(int_1,rc2_int_1), []). fof(rc2_partfun1,axiom,( ! [A,B] : ? [C] : ( m1_relset_1(C,A,B) & v1_relat_1(C) & v1_funct_1(C) ) ), file(partfun1,rc2_partfun1), []). fof(rc2_xreal_0,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & v2_xreal_0(A) & ~ v3_xreal_0(A) ) ), file(xreal_0,rc2_xreal_0), []). fof(rc3_finseq_1,axiom,( ? [A] : ( v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) ) ), file(finseq_1,rc3_finseq_1), []). fof(rc3_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_graph_1,axiom,( ? [A] : ( l1_graph_1(A) & v7_graph_1(A) ) ), file(graph_1,rc3_graph_1), []). fof(rc3_xreal_0,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) & v3_xreal_0(A) ) ), file(xreal_0,rc3_xreal_0), []). fof(rc4_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_xreal_0,axiom,( ? [A] : ( v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) & ~ v3_xreal_0(A) ) ), file(xreal_0,rc4_xreal_0), []). fof(rc5_graph_1,axiom,( ! [A] : ( ( v2_graph_1(A) & l1_graph_1(A) ) => ? [B] : ( m1_graph_1(B,A) & v1_relat_1(B) & v1_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) & v8_graph_1(B,A) ) ) ), file(graph_1,rc5_graph_1), []). 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_graph_1,axiom,( ! [A] : ( ( v2_graph_1(A) & l1_graph_1(A) ) => ? [B] : ( m1_graph_1(B,A) & v1_relat_1(B) & v1_funct_1(B) & v2_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) ) ) ), file(graph_1,rc6_graph_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(rc7_graph_1,axiom,( ! [A] : ( ( v2_graph_1(A) & l1_graph_1(A) ) => ? [B] : ( m1_graph_1(B,A) & v1_relat_1(B) & v1_funct_1(B) & v2_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) & v8_graph_1(B,A) ) ) ), file(graph_1,rc7_graph_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_k14_graphsp,axiom,( ! [A,B,C,D] : ( ( v2_graph_1(A) & v3_graph_1(A) & l1_graph_1(A) & m1_subset_1(B,u1_graph_1(A)) & m1_subset_1(C,u1_graph_1(A)) & v1_funct_1(D) & v1_funct_2(D,u2_graph_1(A),k8_graph_5) & m1_relset_1(D,u2_graph_1(A),k8_graph_5) ) => k14_graphsp(A,B,C,D) = k13_graphsp(A,B,C,D) ) ), file(graphsp,k14_graphsp), []). fof(redefinition_k1_goboard1,axiom,( ! [A,B] : ( ( m1_finseq_1(A,k1_numbers) & m1_subset_1(B,k5_numbers) ) => k1_goboard1(A,B) = k1_funct_1(A,B) ) ), file(goboard1,k1_goboard1), []). fof(redefinition_k1_nat_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => k1_nat_1(A,B) = k2_xcmplx_0(A,B) ) ), file(nat_1,k1_nat_1), []). fof(redefinition_k1_real_1,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => k1_real_1(A) = k4_xcmplx_0(A) ) ), file(real_1,k1_real_1), []). fof(redefinition_k2_finseq_1,axiom,( ! [A] : ( v4_ordinal2(A) => k2_finseq_1(A) = k1_finseq_1(A) ) ), file(finseq_1,k2_finseq_1), []). fof(redefinition_k2_nat_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => k2_nat_1(A,B) = k3_xcmplx_0(A,B) ) ), file(nat_1,k2_nat_1), []). fof(redefinition_k3_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => k3_finseq_1(A) = k1_card_1(A) ) ), file(finseq_1,k3_finseq_1), []). fof(redefinition_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_subset_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => k4_subset_1(A,B,C) = k2_xboole_0(B,C) ) ), file(subset_1,k4_subset_1), []). fof(redefinition_k5_graphsp,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k1_funct_2(A,A)) & m1_subset_1(C,k1_funct_2(A,A)) ) => k5_graphsp(A,B,C) = k5_relat_1(B,C) ) ), file(graphsp,k5_graphsp), []). fof(redefinition_k5_numbers,axiom,( k5_numbers = k5_ordinal2 ), file(numbers,k5_numbers), []). fof(redefinition_k6_domain_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => k6_domain_1(A,B) = k1_tarski(B) ) ), file(domain_1,k6_domain_1), []). fof(redefinition_k6_graphsp,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k1_funct_2(A,A)) & m1_subset_1(C,A) ) => k6_graphsp(A,B,C) = k1_funct_1(B,C) ) ), file(graphsp,k6_graphsp), []). 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_graphsp,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers))) & m1_subset_1(B,k3_finseq_2(k1_numbers)) ) => k8_graphsp(A,B) = k1_funct_1(A,B) ) ), file(graphsp,k8_graphsp), []). 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_graph_1,axiom,( ! [A] : ( ( v2_graph_1(A) & l1_graph_1(A) ) => ! [B] : ( m2_graph_1(B,A) <=> m1_graph_1(B,A) ) ) ), file(graph_1,m2_graph_1), []). fof(redefinition_m2_relset_1,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) <=> m1_relset_1(C,A,B) ) ), file(relset_1,m2_relset_1), []). fof(redefinition_m2_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m2_subset_1(C,A,B) <=> m1_subset_1(C,B) ) ) ), file(subset_1,m2_subset_1), []). fof(reflexivity_r1_tarski,axiom,( ! [A,B] : r1_tarski(A,A) ), file(tarski,r1_tarski), []). fof(reflexivity_r1_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => r1_xreal_0(A,A) ) ), file(xreal_0,r1_xreal_0), []). fof(s1_nat_1__e13_102__graphsp,axiom,( ! [A,B,C,D,E] : ( ( m2_subset_1(A,k1_numbers,k5_numbers) & m2_finseq_2(B,k1_numbers,k3_finseq_2(k1_numbers)) & v2_graph_1(C) & v3_graph_1(C) & v7_graph_1(C) & l1_graph_1(C) & v1_funct_1(D) & v1_funct_2(D,u2_graph_1(C),k8_graph_5) & m2_relset_1(D,u2_graph_1(C),k8_graph_5) & m1_subset_1(E,u1_graph_1(C)) ) => ( ( ( r1_xreal_0(0,k10_graphsp(k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A)),B,A)) => ( ! [F] : ( m1_subset_1(F,u1_graph_1(C)) => ! [G] : ( m2_subset_1(G,k1_numbers,k5_numbers) => ~ ( F != E & F = G & k1_goboard1(k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),0),B),k1_nat_1(A,G)) != k1_real_1(1) & ! [H] : ( m2_finseq_1(H,k5_numbers) => ! [I] : ( ( v8_graph_1(I,C) & m2_graph_1(I,C) ) => ~ ( r4_graphsp(H,k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),0),B),G,A) & ! [J] : ( m2_subset_1(J,k1_numbers,k5_numbers) => ( r1_xreal_0(1,J) => ( r1_xreal_0(k3_finseq_1(H),J) | r2_hidden(k1_funct_1(H,J),k16_graphsp(k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),0),B),A)) ) ) ) & r5_graphsp(C,I,H) & r8_graph_5(C,E,F,I,k16_graphsp(k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),0),B),A),D) & k10_graph_5(C,I,D) = k1_goboard1(k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),0),B),k1_nat_1(k2_nat_1(2,A),G)) & ( ~ r2_hidden(F,k16_graphsp(k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),0),B),A)) => r9_graph_5(C,I,k16_graphsp(k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),0),B),A),E,D) ) ) ) ) ) ) ) & ! [F] : ( m2_subset_1(F,k1_numbers,k5_numbers) => ! [G] : ( m2_subset_1(G,k1_numbers,k5_numbers) => ( ( k1_goboard1(k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),0),B),k1_nat_1(A,G)) = k1_real_1(1) & r1_xreal_0(1,G) & r1_xreal_0(G,A) & r2_hidden(F,k16_graphsp(k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),0),B),A)) ) => k1_goboard1(B,k1_nat_1(k1_nat_1(k2_nat_1(2,A),k2_nat_1(A,F)),G)) = k1_real_1(1) ) ) ) & ! [F] : ( m2_subset_1(F,k1_numbers,k5_numbers) => ~ ( r2_hidden(F,k16_graphsp(k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),0),B),A)) & k1_goboard1(k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),0),B),k1_nat_1(A,F)) = k1_real_1(1) ) ) ) ) & ! [K] : ( m2_subset_1(K,k1_numbers,k5_numbers) => ( ( r1_xreal_0(K,k10_graphsp(k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A)),B,A)) => ( ! [L] : ( m1_subset_1(L,u1_graph_1(C)) => ! [M] : ( m2_subset_1(M,k1_numbers,k5_numbers) => ~ ( L != E & L = M & k1_goboard1(k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),K),B),k1_nat_1(A,M)) != k1_real_1(1) & ! [N] : ( m2_finseq_1(N,k5_numbers) => ! [O] : ( ( v8_graph_1(O,C) & m2_graph_1(O,C) ) => ~ ( r4_graphsp(N,k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),K),B),M,A) & ! [P] : ( m2_subset_1(P,k1_numbers,k5_numbers) => ( r1_xreal_0(1,P) => ( r1_xreal_0(k3_finseq_1(N),P) | r2_hidden(k1_funct_1(N,P),k16_graphsp(k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),K),B),A)) ) ) ) & r5_graphsp(C,O,N) & r8_graph_5(C,E,L,O,k16_graphsp(k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),K),B),A),D) & k10_graph_5(C,O,D) = k1_goboard1(k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),K),B),k1_nat_1(k2_nat_1(2,A),M)) & ( ~ r2_hidden(L,k16_graphsp(k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),K),B),A)) => r9_graph_5(C,O,k16_graphsp(k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),K),B),A),E,D) ) ) ) ) ) ) ) & ! [L] : ( m2_subset_1(L,k1_numbers,k5_numbers) => ! [M] : ( m2_subset_1(M,k1_numbers,k5_numbers) => ( ( k1_goboard1(k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),K),B),k1_nat_1(A,M)) = k1_real_1(1) & r1_xreal_0(1,M) & r1_xreal_0(M,A) & r2_hidden(L,k16_graphsp(k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),K),B),A)) ) => k1_goboard1(B,k1_nat_1(k1_nat_1(k2_nat_1(2,A),k2_nat_1(A,L)),M)) = k1_real_1(1) ) ) ) & ! [L] : ( m2_subset_1(L,k1_numbers,k5_numbers) => ~ ( r2_hidden(L,k16_graphsp(k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),K),B),A)) & k1_goboard1(k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),K),B),k1_nat_1(A,L)) = k1_real_1(1) ) ) ) ) => ( r1_xreal_0(k1_nat_1(K,1),k10_graphsp(k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A)),B,A)) => ( ! [Q] : ( m1_subset_1(Q,u1_graph_1(C)) => ! [R] : ( m2_subset_1(R,k1_numbers,k5_numbers) => ~ ( Q != E & Q = R & k1_goboard1(k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),k1_nat_1(K,1)),B),k1_nat_1(A,R)) != k1_real_1(1) & ! [S] : ( m2_finseq_1(S,k5_numbers) => ! [T] : ( ( v8_graph_1(T,C) & m2_graph_1(T,C) ) => ~ ( r4_graphsp(S,k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),k1_nat_1(K,1)),B),R,A) & ! [U] : ( m2_subset_1(U,k1_numbers,k5_numbers) => ( r1_xreal_0(1,U) => ( r1_xreal_0(k3_finseq_1(S),U) | r2_hidden(k1_funct_1(S,U),k16_graphsp(k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),k1_nat_1(K,1)),B),A)) ) ) ) & r5_graphsp(C,T,S) & r8_graph_5(C,E,Q,T,k16_graphsp(k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),k1_nat_1(K,1)),B),A),D) & k10_graph_5(C,T,D) = k1_goboard1(k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),k1_nat_1(K,1)),B),k1_nat_1(k2_nat_1(2,A),R)) & ( ~ r2_hidden(Q,k16_graphsp(k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),k1_nat_1(K,1)),B),A)) => r9_graph_5(C,T,k16_graphsp(k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),k1_nat_1(K,1)),B),A),E,D) ) ) ) ) ) ) ) & ! [Q] : ( m2_subset_1(Q,k1_numbers,k5_numbers) => ! [R] : ( m2_subset_1(R,k1_numbers,k5_numbers) => ( ( k1_goboard1(k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),k1_nat_1(K,1)),B),k1_nat_1(A,R)) = k1_real_1(1) & r1_xreal_0(1,R) & r1_xreal_0(R,A) & r2_hidden(Q,k16_graphsp(k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),k1_nat_1(K,1)),B),A)) ) => k1_goboard1(B,k1_nat_1(k1_nat_1(k2_nat_1(2,A),k2_nat_1(A,Q)),R)) = k1_real_1(1) ) ) ) & ! [Q] : ( m2_subset_1(Q,k1_numbers,k5_numbers) => ~ ( r2_hidden(Q,k16_graphsp(k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),k1_nat_1(K,1)),B),A)) & k1_goboard1(k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),k1_nat_1(K,1)),B),k1_nat_1(A,Q)) = k1_real_1(1) ) ) ) ) ) ) ) => ! [K] : ( m2_subset_1(K,k1_numbers,k5_numbers) => ( r1_xreal_0(K,k10_graphsp(k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A)),B,A)) => ( ! [V] : ( m1_subset_1(V,u1_graph_1(C)) => ! [W] : ( m2_subset_1(W,k1_numbers,k5_numbers) => ~ ( V != E & V = W & k1_goboard1(k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),K),B),k1_nat_1(A,W)) != k1_real_1(1) & ! [X] : ( m2_finseq_1(X,k5_numbers) => ! [Y] : ( ( v8_graph_1(Y,C) & m2_graph_1(Y,C) ) => ~ ( r4_graphsp(X,k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),K),B),W,A) & ! [Z] : ( m2_subset_1(Z,k1_numbers,k5_numbers) => ( r1_xreal_0(1,Z) => ( r1_xreal_0(k3_finseq_1(X),Z) | r2_hidden(k1_funct_1(X,Z),k16_graphsp(k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),K),B),A)) ) ) ) & r5_graphsp(C,Y,X) & r8_graph_5(C,E,V,Y,k16_graphsp(k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),K),B),A),D) & k10_graph_5(C,Y,D) = k1_goboard1(k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),K),B),k1_nat_1(k2_nat_1(2,A),W)) & ( ~ r2_hidden(V,k16_graphsp(k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),K),B),A)) => r9_graph_5(C,Y,k16_graphsp(k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),K),B),A),E,D) ) ) ) ) ) ) ) & ! [V] : ( m2_subset_1(V,k1_numbers,k5_numbers) => ! [W] : ( m2_subset_1(W,k1_numbers,k5_numbers) => ( ( k1_goboard1(k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),K),B),k1_nat_1(A,W)) = k1_real_1(1) & r1_xreal_0(1,W) & r1_xreal_0(W,A) & r2_hidden(V,k16_graphsp(k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),K),B),A)) ) => k1_goboard1(B,k1_nat_1(k1_nat_1(k2_nat_1(2,A),k2_nat_1(A,V)),W)) = k1_real_1(1) ) ) ) & ! [V] : ( m2_subset_1(V,k1_numbers,k5_numbers) => ~ ( r2_hidden(V,k16_graphsp(k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),K),B),A)) & k1_goboard1(k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),K),B),k1_nat_1(A,V)) = k1_real_1(1) ) ) ) ) ) ) ) ), file(graphsp,s1_nat_1__e13_102__graphsp), []). fof(spc0_boole,axiom,( v1_xboole_0(0) ), file(boole,spc0_boole), []). fof(spc1_boole,axiom,( ~ v1_xboole_0(1) ), file(boole,spc1_boole), []). fof(spc1_numerals,axiom, ( v2_xreal_0(1) & m1_subset_1(1,k5_numbers) ), file(numerals,spc1_numerals), []). fof(spc2_boole,axiom,( ~ v1_xboole_0(2) ), file(boole,spc2_boole), []). fof(spc2_numerals,axiom, ( v2_xreal_0(2) & m1_subset_1(2,k5_numbers) ), file(numerals,spc2_numerals), []). 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(t11_graphsp,axiom,( ! [A] : ( ( v2_graph_1(A) & l1_graph_1(A) ) => ! [B,C,D] : ( m1_subset_1(D,u1_graph_1(A)) => ! [E] : ( m1_subset_1(E,u1_graph_1(A)) => ( ( u1_graph_1(A) = k2_xboole_0(B,C) & r2_hidden(D,B) & r2_hidden(E,C) & ! [F] : ( m1_subset_1(F,u1_graph_1(A)) => ! [G] : ( m1_subset_1(G,u1_graph_1(A)) => ( ( r2_hidden(F,B) & r2_hidden(G,C) ) => ! [H] : ~ ( r2_hidden(H,u2_graph_1(A)) & r1_graph_4(A,F,G,H) ) ) ) ) ) => ! [F] : ( ( v8_graph_1(F,A) & m2_graph_1(F,A) ) => ~ r1_graph_5(A,F,D,E) ) ) ) ) ) ), file(graphsp,t11_graphsp), []). fof(t16_graphsp,axiom,( ! [A,B,C] : ( ( v2_graph_1(C) & v3_graph_1(C) & v7_graph_1(C) & l1_graph_1(C) ) => ! [D] : ( ( v8_graph_1(D,C) & m2_graph_1(D,C) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,u2_graph_1(C),k8_graph_5) & m2_relset_1(E,u2_graph_1(C),k8_graph_5) ) => ! [F] : ( m1_subset_1(F,u1_graph_1(C)) => ! [G] : ( m1_subset_1(G,u1_graph_1(C)) => ( ( u1_graph_1(C) = k2_xboole_0(A,B) & r2_hidden(F,A) & ! [H] : ( m1_subset_1(H,u1_graph_1(C)) => ! [I] : ( m1_subset_1(I,u1_graph_1(C)) => ( ( r2_hidden(H,A) & r2_hidden(I,B) ) => ! [J] : ~ ( r2_hidden(J,u2_graph_1(C)) & r1_graph_4(C,H,I,J) ) ) ) ) ) => ( r8_graph_5(C,F,G,D,A,E) <=> r7_graph_5(C,F,G,D,E) ) ) ) ) ) ) ) ), file(graphsp,t16_graphsp), []). fof(t1_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k2_xcmplx_0(A,0) = A ) ), file(arithm,t1_arithm), []). fof(t1_boole,axiom,( ! [A] : k2_xboole_0(A,k1_xboole_0) = A ), file(boole,t1_boole), []). fof(t1_numerals,axiom,( m1_subset_1(0,k5_numbers) ), file(numerals,t1_numerals), []). fof(t1_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xreal_0(A,B) & v2_xreal_0(A) ) => v2_xreal_0(B) ) ) ) ), file(real,t1_real), []). fof(t1_subset,axiom,( ! [A,B] : ( r2_hidden(A,B) => m1_subset_1(A,B) ) ), file(subset,t1_subset), []). fof(t20_int_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ( ~ r1_xreal_0(B,A) => r1_xreal_0(k2_xcmplx_0(A,1),B) ) ) ) ), file(int_1,t20_int_1), []). fof(t22_graphsp,axiom,( ! [A] : ( m1_subset_1(A,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers))) => ! [B] : ( m2_finseq_2(B,k1_numbers,k3_finseq_2(k1_numbers)) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => k6_graphsp(k3_finseq_2(k1_numbers),k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),A),0),B) = B ) ) ) ) ), file(graphsp,t22_graphsp), []). fof(t24_graphsp,axiom,( ! [A] : ( ( v2_graph_1(A) & v3_graph_1(A) & l1_graph_1(A) ) => ! [B] : ( m1_subset_1(B,u1_graph_1(A)) => ! [C] : ( m1_subset_1(C,u1_graph_1(A)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,u2_graph_1(A),k8_graph_5) & m2_relset_1(D,u2_graph_1(A),k8_graph_5) ) => ( r1_xreal_0(0,k14_graphsp(A,B,C,D)) <=> ? [E] : ( r2_hidden(E,u2_graph_1(A)) & r1_graph_4(A,B,C,E) ) ) ) ) ) ) ), file(graphsp,t24_graphsp), []). fof(t27_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( v4_ordinal2(B) => ( r2_hidden(B,k4_finseq_1(A)) <=> ( r1_xreal_0(1,B) & r1_xreal_0(B,k3_finseq_1(A)) ) ) ) ) ), file(finseq_3,t27_finseq_3), []). fof(t2_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k3_xcmplx_0(A,0) = 0 ) ), file(arithm,t2_arithm), []). fof(t2_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xreal_0(A,B) & v3_xreal_0(B) ) => v3_xreal_0(A) ) ) ) ), file(real,t2_real), []). fof(t2_subset,axiom,( ! [A,B] : ( m1_subset_1(A,B) => ( v1_xboole_0(B) | r2_hidden(A,B) ) ) ), file(subset,t2_subset), []). fof(t2_tarski,axiom,( ! [A,B] : ( ! [C] : ( r2_hidden(C,A) <=> r2_hidden(C,B) ) => A = B ) ), file(tarski,t2_tarski), []). fof(t2_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ( r1_xreal_0(A,B) & r1_xreal_0(B,C) ) => r1_xreal_0(A,C) ) ) ) ) ), file(xreal_1,t2_xreal_1), []). fof(t37_nat_1,axiom,( ! [A] : ( v4_ordinal2(A) => ! [B] : ( v4_ordinal2(B) => ! [C] : ( v4_ordinal2(C) => ( r1_xreal_0(A,B) => r1_xreal_0(A,k2_xcmplx_0(B,C)) ) ) ) ) ), file(nat_1,t37_nat_1), []). fof(t38_nat_1,axiom,( ! [A] : ( v4_ordinal2(A) => ! [B] : ( v4_ordinal2(B) => ( ~ r1_xreal_0(k2_xcmplx_0(B,1),A) <=> r1_xreal_0(A,B) ) ) ) ), file(nat_1,t38_nat_1), []). fof(t3_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k3_xcmplx_0(1,A) = A ) ), file(arithm,t3_arithm), []). fof(t3_finseq_1,axiom,( ! [A] : ( v4_ordinal2(A) => ! [B] : ( v4_ordinal2(B) => ( r2_hidden(A,k2_finseq_1(B)) <=> ( r1_xreal_0(1,A) & r1_xreal_0(A,B) ) ) ) ) ), file(finseq_1,t3_finseq_1), []). fof(t3_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( r1_xreal_0(A,B) & ~ v3_xreal_0(A) & v3_xreal_0(B) ) ) ) ), file(real,t3_real), []). fof(t3_subset,axiom,( ! [A,B] : ( m1_subset_1(A,k1_zfmisc_1(B)) <=> r1_tarski(A,B) ) ), file(subset,t3_subset), []). fof(t41_graphsp,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m2_finseq_2(B,k1_numbers,k3_finseq_2(k1_numbers)) => ? [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) & r1_xreal_0(C,A) & k9_graphsp(k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),C),B),A) = k1_xboole_0 ) ) ) ), file(graphsp,t41_graphsp), []). fof(t42_graphsp,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( m2_finseq_2(C,k1_numbers,k3_finseq_2(k1_numbers)) => k4_finseq_1(C) = k4_finseq_1(k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),B),C)) ) ) ) ), file(graphsp,t42_graphsp), []). fof(t48_graphsp,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m2_finseq_2(B,k1_numbers,k3_finseq_2(k1_numbers)) => ( ( r1_xreal_0(1,A) & r2_hidden(1,k4_finseq_1(B)) & ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ( ( r1_xreal_0(1,C) & r1_xreal_0(C,A) ) => k1_goboard1(B,C) = 1 ) ) & ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ( ( r1_xreal_0(2,C) & r1_xreal_0(C,A) ) => k1_goboard1(B,k1_nat_1(A,C)) = k1_real_1(1) ) ) ) => ( k1_goboard1(B,k1_nat_1(A,1)) = k1_real_1(1) | ( 1 = k17_graphsp(k9_graphsp(B,A),B,A) & k16_graphsp(B,A) = k1_xboole_0 & k6_domain_1(k5_numbers,1) = k16_graphsp(k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),1),B),A) ) ) ) ) ) ), file(graphsp,t48_graphsp), []). fof(t49_graphsp,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ! [D] : ( m2_finseq_2(D,k1_numbers,k3_finseq_2(k1_numbers)) => ! [E] : ( m2_finseq_2(E,k1_numbers,k3_finseq_2(k1_numbers)) => ! [F] : ( m2_finseq_2(F,k1_numbers,k3_finseq_2(k1_numbers)) => ( ( D = k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),1),E) & F = k8_graphsp(k8_funct_2(k5_numbers,k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k7_graphsp(k3_finseq_2(k1_numbers),k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A))),B),E) & r1_xreal_0(1,B) & r1_xreal_0(B,k10_graphsp(k5_graphsp(k3_finseq_2(k1_numbers),k18_graphsp(A),k21_graphsp(A)),E,A)) & r2_hidden(C,k16_graphsp(D,A)) ) => r2_hidden(C,k16_graphsp(F,A)) ) ) ) ) ) ) ) ), file(graphsp,t49_graphsp), []). fof(t4_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( r1_xreal_0(A,B) & ~ v2_xreal_0(B) & v2_xreal_0(A) ) ) ) ), file(real,t4_real), []). fof(t4_subset,axiom,( ! [A,B,C] : ( ( r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) ) => m1_subset_1(A,C) ) ), file(subset,t4_subset), []). fof(t5_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xreal_0(A,B) => ( v1_xboole_0(B) | v3_xreal_0(A) | v2_xreal_0(B) ) ) ) ) ), file(real,t5_real), []). fof(t5_subset,axiom,( ! [A,B,C] : ~ ( r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) & v1_xboole_0(C) ) ), file(subset,t5_subset), []). fof(t6_boole,axiom,( ! [A] : ( v1_xboole_0(A) => A = k1_xboole_0 ) ), file(boole,t6_boole), []). fof(t6_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xreal_0(A,B) => ( v1_xboole_0(A) | v2_xreal_0(B) | v3_xreal_0(A) ) ) ) ) ), file(real,t6_real), []). fof(t7_boole,axiom,( ! [A,B] : ~ ( r2_hidden(A,B) & v1_xboole_0(B) ) ), file(boole,t7_boole), []). fof(t7_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xreal_0(A,B) & ~ v2_xreal_0(A) & ~ v3_xreal_0(B) ) ) ) ), file(real,t7_real), []). fof(t8_boole,axiom,( ! [A,B] : ~ ( v1_xboole_0(A) & A != B & v1_xboole_0(B) ) ), file(boole,t8_boole), []). fof(t8_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xreal_0(A,B) & ~ v3_xreal_0(B) & ~ v2_xreal_0(A) ) ) ) ), file(real,t8_real), []).