% Mizar problem: t25_substut1,substut1,1784,42 fof(t25_substut1,conjecture,( ! [A] : ( m1_subset_1(A,k16_substut1) => ( ( v2_substut1(A) => k1_mcart_1(k1_funct_1(k10_qc_lang1(k18_substut1(A)),1)) = 0 ) & ~ ( v4_substut1(A) & ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ~ m2_subset_1(k1_funct_1(k10_qc_lang1(k18_substut1(A)),1),k5_qc_lang1,k7_qc_lang1(B)) ) ) & ( v5_substut1(A) => k1_mcart_1(k1_funct_1(k10_qc_lang1(k18_substut1(A)),1)) = 1 ) & ( v6_substut1(A) => k1_mcart_1(k1_funct_1(k10_qc_lang1(k18_substut1(A)),1)) = 2 ) & ( v7_substut1(A) => k1_mcart_1(k1_funct_1(k10_qc_lang1(k18_substut1(A)),1)) = 3 ) ) ) ), 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_arytm_3,cc1_finseq_1,cc1_finset_1,cc1_fraenkel,cc1_funct_1,cc1_membered,cc1_relset_1,cc20_membered,cc2_arytm_3,cc2_finset_1,cc2_funct_1,cc2_membered,cc3_arytm_3,cc3_membered,cc4_membered,cc6_membered,cc9_membered,commutativity_k2_tarski,d12_qc_lang1,d13_qc_lang1,d14_qc_lang1,d15_qc_lang1,d16_qc_lang1,d19_substut1,d1_substut1,d20_substut1,d21_substut1,d24_substut1,d25_substut1,d26_substut1,d27_substut1,d28_substut1,d5_tarski,d8_finseq_1,dt_k10_qc_lang1,dt_k11_qc_lang1,dt_k12_finseq_1,dt_k12_mcart_1,dt_k12_qc_lang1,dt_k13_qc_lang1,dt_k14_qc_lang1,dt_k16_substut1,dt_k17_substut1,dt_k18_substut1,dt_k19_substut1,dt_k1_domain_1,dt_k1_finseq_1,dt_k1_funct_1,dt_k1_mcart_1,dt_k1_numbers,dt_k1_qc_lang1,dt_k1_relat_1,dt_k1_substut1,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k20_substut1,dt_k21_substut1,dt_k22_substut1,dt_k23_substut1,dt_k24_substut1,dt_k2_finseq_1,dt_k2_mcart_1,dt_k2_qc_lang1,dt_k2_tarski,dt_k2_zfmisc_1,dt_k4_partfun1,dt_k4_tarski,dt_k5_finseq_1,dt_k5_numbers,dt_k5_ordinal2,dt_k5_qc_lang1,dt_k7_cqc_lang,dt_k7_finseq_1,dt_k7_qc_lang1,dt_k8_finseq_1,dt_k8_qc_lang1,dt_k9_cqc_lang,dt_k9_finseq_1,dt_k9_qc_lang1,dt_m1_finseq_1,dt_m1_qc_lang1,dt_m1_relset_1,dt_m1_subset_1,dt_m1_substut1,dt_m2_finseq_1,dt_m2_relset_1,dt_m2_subset_1,existence_m1_finseq_1,existence_m1_qc_lang1,existence_m1_relset_1,existence_m1_subset_1,existence_m1_substut1,existence_m2_finseq_1,existence_m2_relset_1,existence_m2_subset_1,fc10_membered,fc11_membered,fc12_finseq_1,fc12_membered,fc13_finseq_1,fc13_membered,fc14_finseq_1,fc14_finset_1,fc14_membered,fc15_membered,fc16_membered,fc17_finseq_1,fc1_finseq_1,fc1_finset_1,fc1_ordinal2,fc1_qc_lang1,fc1_subset_1,fc1_substut1,fc1_wellfnd1,fc2_cqc_lang,fc2_finseq_1,fc2_finset_1,fc2_membered,fc2_qc_lang1,fc2_subset_1,fc2_substut1,fc3_finseq_1,fc3_subset_1,fc4_finseq_1,fc4_subset_1,fc4_substut1,fc5_membered,fc5_qc_lang1,fc5_substut1,fc6_membered,fc6_qc_lang1,fc6_substut1,fc7_membered,fc8_membered,fc9_membered,rc1_arytm_3,rc1_finseq_1,rc1_finset_1,rc1_fraenkel,rc1_funct_1,rc1_membered,rc1_subset_1,rc1_substut1,rc2_finseq_1,rc2_finset_1,rc2_funct_1,rc2_subset_1,rc2_substut1,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc4_finseq_1,rc4_finset_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,redefinition_k12_finseq_1,redefinition_k12_mcart_1,redefinition_k18_substut1,redefinition_k19_substut1,redefinition_k1_domain_1,redefinition_k22_substut1,redefinition_k23_substut1,redefinition_k2_finseq_1,redefinition_k5_numbers,redefinition_k8_finseq_1,redefinition_k9_cqc_lang,redefinition_k9_finseq_1,redefinition_m2_finseq_1,redefinition_m2_relset_1,redefinition_m2_subset_1,reflexivity_r1_tarski,spc0_boole,spc1_boole,spc1_numerals,spc2_boole,spc2_numerals,spc3_boole,spc3_numerals,t1_numerals,t1_subset,t23_qc_lang1,t2_subset,t3_subset,t45_finseq_1,t4_subset,t58_finseq_1,t5_subset,t6_boole,t7_boole,t7_mcart_1,t8_boole,t9_substut1]), [file(substut1,t25_substut1)]). 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_arytm_3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_ordinal1(B) & v2_ordinal1(B) & v3_ordinal1(B) ) ) ) ), file(arytm_3,cc1_arytm_3), []). fof(cc1_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) ) ), file(finseq_1,cc1_finseq_1), []). fof(cc1_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_1,axiom,( ! [A] : ( v1_xboole_0(A) => v1_funct_1(A) ) ), file(funct_1,cc1_funct_1), []). 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(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_arytm_3,axiom,( ! [A] : ( ( v1_xboole_0(A) & v3_ordinal1(A) ) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) ) ) ), file(arytm_3,cc2_arytm_3), []). fof(cc2_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_membered,axiom,( ! [A] : ( v4_membered(A) => v3_membered(A) ) ), file(membered,cc2_membered), []). fof(cc3_arytm_3,axiom,( ! [A] : ( m1_subset_1(A,k5_ordinal2) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) ) ) ), file(arytm_3,cc3_arytm_3), []). fof(cc3_membered,axiom,( ! [A] : ( v3_membered(A) => v2_membered(A) ) ), file(membered,cc3_membered), []). fof(cc4_membered,axiom,( ! [A] : ( v2_membered(A) => v1_membered(A) ) ), file(membered,cc4_membered), []). 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(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_k2_tarski,axiom,( ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ), file(tarski,k2_tarski), []). fof(d12_qc_lang1,axiom,( ! [A] : ( m1_subset_1(A,k8_qc_lang1) => k10_qc_lang1(A) = A ) ), file(qc_lang1,d12_qc_lang1), []). fof(d13_qc_lang1,axiom,( k11_qc_lang1 = k9_finseq_1(k4_tarski(0,0)) ), file(qc_lang1,d13_qc_lang1), []). fof(d14_qc_lang1,axiom,( ! [A] : ( m1_subset_1(A,k8_qc_lang1) => k12_qc_lang1(A) = k7_finseq_1(k9_finseq_1(k4_tarski(1,0)),k10_qc_lang1(A)) ) ), file(qc_lang1,d14_qc_lang1), []). fof(d15_qc_lang1,axiom,( ! [A] : ( m1_subset_1(A,k8_qc_lang1) => ! [B] : ( m1_subset_1(B,k8_qc_lang1) => k13_qc_lang1(A,B) = k7_finseq_1(k7_finseq_1(k9_finseq_1(k4_tarski(2,0)),k10_qc_lang1(A)),k10_qc_lang1(B)) ) ) ), file(qc_lang1,d15_qc_lang1), []). fof(d16_qc_lang1,axiom,( ! [A] : ( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) => ! [B] : ( m1_subset_1(B,k8_qc_lang1) => k14_qc_lang1(A,B) = k7_finseq_1(k7_finseq_1(k9_finseq_1(k4_tarski(3,0)),k12_finseq_1(k2_qc_lang1,A)),k10_qc_lang1(B)) ) ) ), file(qc_lang1,d16_qc_lang1), []). fof(d19_substut1,axiom,( ! [A] : ( m1_subset_1(A,k16_substut1) => ( v2_substut1(A) <=> ? [B] : ( m1_subset_1(B,k1_substut1) & A = k1_domain_1(k7_cqc_lang,k1_substut1,k9_cqc_lang,B) ) ) ) ), file(substut1,d19_substut1), []). fof(d1_substut1,axiom,( k1_substut1 = k4_partfun1(k2_qc_lang1,k2_qc_lang1) ), file(substut1,d1_substut1), []). fof(d20_substut1,axiom,( ! [A] : ( m1_subset_1(A,k16_substut1) => k20_substut1(A) = k1_domain_1(k8_qc_lang1,k1_substut1,k12_qc_lang1(k18_substut1(A)),k19_substut1(A)) ) ), file(substut1,d20_substut1), []). fof(d21_substut1,axiom,( ! [A] : ( m1_subset_1(A,k16_substut1) => ! [B] : ( m1_subset_1(B,k16_substut1) => ( k19_substut1(A) = k19_substut1(B) => k21_substut1(A,B) = k1_domain_1(k8_qc_lang1,k1_substut1,k13_qc_lang1(k18_substut1(A),k18_substut1(B)),k19_substut1(A)) ) ) ) ), file(substut1,d21_substut1), []). fof(d24_substut1,axiom,( ! [A] : ( m1_subset_1(A,k2_zfmisc_1(k16_substut1,k2_qc_lang1)) => ! [B] : ( m1_substut1(B,A) => ( v3_substut1(A) => k24_substut1(A,B) = k1_domain_1(k8_qc_lang1,k1_substut1,k14_qc_lang1(k23_substut1(A),k18_substut1(k22_substut1(A))),B) ) ) ) ), file(substut1,d24_substut1), []). fof(d25_substut1,axiom,( ! [A] : ( m1_subset_1(A,k16_substut1) => ( v4_substut1(A) <=> ? [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) & ? [C] : ( m2_subset_1(C,k5_qc_lang1,k7_qc_lang1(B)) & ? [D] : ( m1_qc_lang1(D,B) & ? [E] : ( m1_subset_1(E,k1_substut1) & A = k17_substut1(C,D,E) ) ) ) ) ) ) ), file(substut1,d25_substut1), []). fof(d26_substut1,axiom,( ! [A] : ( m1_subset_1(A,k16_substut1) => ( v5_substut1(A) <=> ? [B] : ( m1_subset_1(B,k16_substut1) & A = k20_substut1(B) ) ) ) ), file(substut1,d26_substut1), []). fof(d27_substut1,axiom,( ! [A] : ( m1_subset_1(A,k16_substut1) => ( v6_substut1(A) <=> ? [B] : ( m1_subset_1(B,k16_substut1) & ? [C] : ( m1_subset_1(C,k16_substut1) & A = k21_substut1(B,C) & k19_substut1(B) = k19_substut1(C) ) ) ) ) ), file(substut1,d27_substut1), []). fof(d28_substut1,axiom,( ! [A] : ( v7_substut1(A) <=> ? [B] : ( m1_subset_1(B,k2_zfmisc_1(k16_substut1,k2_qc_lang1)) & ? [C] : ( m1_substut1(C,B) & A = k24_substut1(B,C) & v3_substut1(B) ) ) ) ), file(substut1,d28_substut1), []). fof(d5_tarski,axiom,( ! [A,B] : k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A)) ), file(tarski,d5_tarski), []). fof(d8_finseq_1,axiom,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( B = k9_finseq_1(A) <=> ( k1_relat_1(B) = k2_finseq_1(1) & k1_funct_1(B,1) = A ) ) ) ), file(finseq_1,d8_finseq_1), []). fof(dt_k10_qc_lang1,axiom,( ! [A] : ( m1_subset_1(A,k8_qc_lang1) => m2_finseq_1(k10_qc_lang1(A),k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers)) ) ), file(qc_lang1,k10_qc_lang1), []). fof(dt_k11_qc_lang1,axiom,( m1_subset_1(k11_qc_lang1,k8_qc_lang1) ), file(qc_lang1,k11_qc_lang1), []). fof(dt_k12_finseq_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => m2_finseq_1(k12_finseq_1(A,B),A) ) ), file(finseq_1,k12_finseq_1), []). fof(dt_k12_mcart_1,axiom,( ! [A,B,C,D] : ( ( m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(D,k1_zfmisc_1(B)) ) => m1_subset_1(k12_mcart_1(A,B,C,D),k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ), file(mcart_1,k12_mcart_1), []). fof(dt_k12_qc_lang1,axiom,( ! [A] : ( m1_subset_1(A,k8_qc_lang1) => m1_subset_1(k12_qc_lang1(A),k8_qc_lang1) ) ), file(qc_lang1,k12_qc_lang1), []). fof(dt_k13_qc_lang1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k8_qc_lang1) & m1_subset_1(B,k8_qc_lang1) ) => m1_subset_1(k13_qc_lang1(A,B),k8_qc_lang1) ) ), file(qc_lang1,k13_qc_lang1), []). fof(dt_k14_qc_lang1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k2_qc_lang1) & m1_subset_1(B,k8_qc_lang1) ) => m1_subset_1(k14_qc_lang1(A,B),k8_qc_lang1) ) ), file(qc_lang1,k14_qc_lang1), []). fof(dt_k16_substut1,axiom,( ~ v1_xboole_0(k16_substut1) ), file(substut1,k16_substut1), []). fof(dt_k17_substut1,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k5_qc_lang1) & m1_finseq_1(B,k1_qc_lang1) & m1_subset_1(C,k1_substut1) ) => m1_subset_1(k17_substut1(A,B,C),k16_substut1) ) ), file(substut1,k17_substut1), []). fof(dt_k18_substut1,axiom,( ! [A] : ( m1_subset_1(A,k16_substut1) => m1_subset_1(k18_substut1(A),k8_qc_lang1) ) ), file(substut1,k18_substut1), []). fof(dt_k19_substut1,axiom,( ! [A] : ( m1_subset_1(A,k16_substut1) => m1_subset_1(k19_substut1(A),k1_substut1) ) ), file(substut1,k19_substut1), []). fof(dt_k1_domain_1,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(C,A) & m1_subset_1(D,B) ) => m1_subset_1(k1_domain_1(A,B,C,D),k2_zfmisc_1(A,B)) ) ), file(domain_1,k1_domain_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_mcart_1,axiom,( $true ), file(mcart_1,k1_mcart_1), []). fof(dt_k1_numbers,axiom,( $true ), file(numbers,k1_numbers), []). fof(dt_k1_qc_lang1,axiom,( $true ), file(qc_lang1,k1_qc_lang1), []). fof(dt_k1_relat_1,axiom,( $true ), file(relat_1,k1_relat_1), []). fof(dt_k1_substut1,axiom,( $true ), file(substut1,k1_substut1), []). 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_k20_substut1,axiom,( ! [A] : ( m1_subset_1(A,k16_substut1) => m1_subset_1(k20_substut1(A),k16_substut1) ) ), file(substut1,k20_substut1), []). fof(dt_k21_substut1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k16_substut1) & m1_subset_1(B,k16_substut1) ) => m1_subset_1(k21_substut1(A,B),k16_substut1) ) ), file(substut1,k21_substut1), []). fof(dt_k22_substut1,axiom,( ! [A] : ( m1_subset_1(A,k2_zfmisc_1(k16_substut1,k2_qc_lang1)) => m1_subset_1(k22_substut1(A),k16_substut1) ) ), file(substut1,k22_substut1), []). fof(dt_k23_substut1,axiom,( ! [A] : ( m1_subset_1(A,k2_zfmisc_1(k16_substut1,k2_qc_lang1)) => m2_subset_1(k23_substut1(A),k1_qc_lang1,k2_qc_lang1) ) ), file(substut1,k23_substut1), []). fof(dt_k24_substut1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k2_zfmisc_1(k16_substut1,k2_qc_lang1)) & m1_substut1(B,A) ) => m1_subset_1(k24_substut1(A,B),k16_substut1) ) ), file(substut1,k24_substut1), []). 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_mcart_1,axiom,( $true ), file(mcart_1,k2_mcart_1), []). fof(dt_k2_qc_lang1,axiom,( m1_subset_1(k2_qc_lang1,k1_zfmisc_1(k1_qc_lang1)) ), file(qc_lang1,k2_qc_lang1), []). fof(dt_k2_tarski,axiom,( $true ), file(tarski,k2_tarski), []). fof(dt_k2_zfmisc_1,axiom,( $true ), file(zfmisc_1,k2_zfmisc_1), []). fof(dt_k4_partfun1,axiom,( $true ), file(partfun1,k4_partfun1), []). fof(dt_k4_tarski,axiom,( $true ), file(tarski,k4_tarski), []). fof(dt_k5_finseq_1,axiom,( $true ), file(finseq_1,k5_finseq_1), []). 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_qc_lang1,axiom,( $true ), file(qc_lang1,k5_qc_lang1), []). fof(dt_k7_cqc_lang,axiom,( m1_subset_1(k7_cqc_lang,k1_zfmisc_1(k8_qc_lang1)) ), file(cqc_lang,k7_cqc_lang), []). fof(dt_k7_finseq_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( v1_relat_1(k7_finseq_1(A,B)) & v1_funct_1(k7_finseq_1(A,B)) & v1_finseq_1(k7_finseq_1(A,B)) ) ) ), file(finseq_1,k7_finseq_1), []). fof(dt_k7_qc_lang1,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => m1_subset_1(k7_qc_lang1(A),k1_zfmisc_1(k5_qc_lang1)) ) ), file(qc_lang1,k7_qc_lang1), []). fof(dt_k8_finseq_1,axiom,( ! [A,B,C] : ( ( m1_finseq_1(B,A) & m1_finseq_1(C,A) ) => m2_finseq_1(k8_finseq_1(A,B,C),A) ) ), file(finseq_1,k8_finseq_1), []). fof(dt_k8_qc_lang1,axiom,( ~ v1_xboole_0(k8_qc_lang1) ), file(qc_lang1,k8_qc_lang1), []). fof(dt_k9_cqc_lang,axiom,( m2_subset_1(k9_cqc_lang,k8_qc_lang1,k7_cqc_lang) ), file(cqc_lang,k9_cqc_lang), []). fof(dt_k9_finseq_1,axiom,( ! [A] : ( v1_relat_1(k9_finseq_1(A)) & v1_funct_1(k9_finseq_1(A)) ) ), file(finseq_1,k9_finseq_1), []). fof(dt_k9_qc_lang1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_qc_lang1) & m1_finseq_1(B,k1_qc_lang1) ) => m1_subset_1(k9_qc_lang1(A,B),k8_qc_lang1) ) ), file(qc_lang1,k9_qc_lang1), []). 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_qc_lang1,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ! [B] : ( m1_qc_lang1(B,A) => m2_finseq_1(B,k1_qc_lang1) ) ) ), file(qc_lang1,m1_qc_lang1), []). 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_m1_substut1,axiom,( ! [A] : ( m1_subset_1(A,k2_zfmisc_1(k16_substut1,k2_qc_lang1)) => ! [B] : ( m1_substut1(B,A) => m1_subset_1(B,k1_substut1) ) ) ), file(substut1,m1_substut1), []). 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_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(existence_m1_finseq_1,axiom,( ! [A] : ? [B] : m1_finseq_1(B,A) ), file(finseq_1,m1_finseq_1), []). fof(existence_m1_qc_lang1,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ? [B] : m1_qc_lang1(B,A) ) ), file(qc_lang1,m1_qc_lang1), []). 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_m1_substut1,axiom,( ! [A] : ( m1_subset_1(A,k2_zfmisc_1(k16_substut1,k2_qc_lang1)) => ? [B] : m1_substut1(B,A) ) ), file(substut1,m1_substut1), []). fof(existence_m2_finseq_1,axiom,( ! [A] : ? [B] : m2_finseq_1(B,A) ), file(finseq_1,m2_finseq_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(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(fc12_finseq_1,axiom,( ! [A] : ( ~ v1_xboole_0(k5_finseq_1(A)) & v1_relat_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A)) & v1_finset_1(k5_finseq_1(A)) & v1_finseq_1(k5_finseq_1(A)) ) ), file(finseq_1,fc12_finseq_1), []). fof(fc12_membered,axiom,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => v1_membered(k2_tarski(A,B)) ) ), file(membered,fc12_membered), []). fof(fc13_finseq_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & ~ v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( ~ v1_xboole_0(k7_finseq_1(A,B)) & v1_relat_1(k7_finseq_1(A,B)) & v1_funct_1(k7_finseq_1(A,B)) & v1_finset_1(k7_finseq_1(A,B)) & v1_finseq_1(k7_finseq_1(A,B)) ) ) ), file(finseq_1,fc13_finseq_1), []). fof(fc13_membered,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) ) ) ), file(membered,fc13_membered), []). fof(fc14_finseq_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & ~ v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( ~ v1_xboole_0(k7_finseq_1(B,A)) & v1_relat_1(k7_finseq_1(B,A)) & v1_funct_1(k7_finseq_1(B,A)) & v1_finset_1(k7_finseq_1(B,A)) & v1_finseq_1(k7_finseq_1(B,A)) ) ) ), file(finseq_1,fc14_finseq_1), []). 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_membered,axiom,( ! [A,B] : ( ( v1_rat_1(A) & v1_rat_1(B) ) => ( v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) & v3_membered(k2_tarski(A,B)) ) ) ), file(membered,fc14_membered), []). fof(fc15_membered,axiom,( ! [A,B] : ( ( v1_int_1(A) & v1_int_1(B) ) => ( v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) & v3_membered(k2_tarski(A,B)) & v4_membered(k2_tarski(A,B)) ) ) ), file(membered,fc15_membered), []). fof(fc16_membered,axiom,( ! [A,B] : ( ( v4_ordinal2(A) & v4_ordinal2(B) ) => ( v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) & v3_membered(k2_tarski(A,B)) & v4_membered(k2_tarski(A,B)) & v5_membered(k2_tarski(A,B)) ) ) ), file(membered,fc16_membered), []). 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_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_qc_lang1,axiom,( ~ v1_xboole_0(k1_qc_lang1) ), file(qc_lang1,fc1_qc_lang1), []). fof(fc1_subset_1,axiom,( ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ), file(subset_1,fc1_subset_1), []). fof(fc1_substut1,axiom,( ~ v1_xboole_0(k1_substut1) ), file(substut1,fc1_substut1), []). fof(fc1_wellfnd1,axiom,( ! [A,B] : ( ~ v1_xboole_0(k4_partfun1(A,B)) & v1_fraenkel(k4_partfun1(A,B)) ) ), file(wellfnd1,fc1_wellfnd1), []). fof(fc2_cqc_lang,axiom,( ~ v1_xboole_0(k7_cqc_lang) ), file(cqc_lang,fc2_cqc_lang), []). 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_finset_1,axiom,( ! [A,B] : ( ~ v1_xboole_0(k2_tarski(A,B)) & v1_finset_1(k2_tarski(A,B)) ) ), file(finset_1,fc2_finset_1), []). fof(fc2_membered,axiom, ( ~ v1_xboole_0(k1_numbers) & v1_membered(k1_numbers) & v2_membered(k1_numbers) ), file(membered,fc2_membered), []). fof(fc2_qc_lang1,axiom,( ~ v1_xboole_0(k2_qc_lang1) ), file(qc_lang1,fc2_qc_lang1), []). fof(fc2_subset_1,axiom,( ! [A] : ~ v1_xboole_0(k1_tarski(A)) ), file(subset_1,fc2_subset_1), []). fof(fc2_substut1,axiom, ( ~ v1_xboole_0(k1_substut1) & v1_fraenkel(k1_substut1) ), file(substut1,fc2_substut1), []). fof(fc3_finseq_1,axiom,( ! [A] : ( v1_relat_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A)) ) ), file(finseq_1,fc3_finseq_1), []). fof(fc3_subset_1,axiom,( ! [A,B] : ~ v1_xboole_0(k2_tarski(A,B)) ), file(subset_1,fc3_subset_1), []). fof(fc4_finseq_1,axiom,( ! [A] : ( v1_relat_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A)) & v1_finset_1(k5_finseq_1(A)) & v1_finseq_1(k5_finseq_1(A)) ) ), file(finseq_1,fc4_finseq_1), []). 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(fc4_substut1,axiom, ( ~ v1_xboole_0(k16_substut1) & v1_substut1(k16_substut1) ), file(substut1,fc4_substut1), []). 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(fc5_qc_lang1,axiom,( ~ v1_xboole_0(k5_qc_lang1) ), file(qc_lang1,fc5_qc_lang1), []). fof(fc5_substut1,axiom,( ! [A,B,C,D] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k7_qc_lang1(A)) & m1_qc_lang1(C,A) & m1_subset_1(D,k1_substut1) ) => v4_substut1(k17_substut1(B,C,D)) ) ), file(substut1,fc5_substut1), []). 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(fc6_qc_lang1,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ~ v1_xboole_0(k7_qc_lang1(A)) ) ), file(qc_lang1,fc6_qc_lang1), []). fof(fc6_substut1,axiom,( ! [A] : ( m1_subset_1(A,k16_substut1) => v5_substut1(k20_substut1(A)) ) ), file(substut1,fc6_substut1), []). fof(fc7_membered,axiom,( ! [A] : ( v1_xcmplx_0(A) => v1_membered(k1_tarski(A)) ) ), file(membered,fc7_membered), []). fof(fc8_membered,axiom,( ! [A] : ( v1_xreal_0(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) ) ) ), file(membered,fc8_membered), []). 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(rc1_arytm_3,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) ) ), file(arytm_3,rc1_arytm_3), []). fof(rc1_finseq_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) ), file(finseq_1,rc1_finseq_1), []). fof(rc1_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_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) ) ), file(funct_1,rc1_funct_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_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(rc1_substut1,axiom,( ? [A] : ( m1_subset_1(A,k1_substut1) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) ), file(substut1,rc1_substut1), []). 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_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_xboole_0(A) & v1_funct_1(A) ) ), file(funct_1,rc2_funct_1), []). 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(rc2_substut1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_substut1(A) ) ), file(substut1,rc2_substut1), []). 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(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(rc6_finseq_1,axiom,( ? [A] : ( v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_finset_1(A) ) ), file(finseq_1,rc6_finseq_1), []). fof(rc7_finseq_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) ), file(finseq_1,rc7_finseq_1), []). fof(rc8_finseq_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) ) ), file(finseq_1,rc8_finseq_1), []). fof(redefinition_k12_finseq_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => k12_finseq_1(A,B) = k5_finseq_1(B) ) ), file(finseq_1,k12_finseq_1), []). fof(redefinition_k12_mcart_1,axiom,( ! [A,B,C,D] : ( ( m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(D,k1_zfmisc_1(B)) ) => k12_mcart_1(A,B,C,D) = k2_zfmisc_1(C,D) ) ), file(mcart_1,k12_mcart_1), []). fof(redefinition_k18_substut1,axiom,( ! [A] : ( m1_subset_1(A,k16_substut1) => k18_substut1(A) = k1_mcart_1(A) ) ), file(substut1,k18_substut1), []). fof(redefinition_k19_substut1,axiom,( ! [A] : ( m1_subset_1(A,k16_substut1) => k19_substut1(A) = k2_mcart_1(A) ) ), file(substut1,k19_substut1), []). fof(redefinition_k1_domain_1,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(C,A) & m1_subset_1(D,B) ) => k1_domain_1(A,B,C,D) = k4_tarski(C,D) ) ), file(domain_1,k1_domain_1), []). fof(redefinition_k22_substut1,axiom,( ! [A] : ( m1_subset_1(A,k2_zfmisc_1(k16_substut1,k2_qc_lang1)) => k22_substut1(A) = k1_mcart_1(A) ) ), file(substut1,k22_substut1), []). fof(redefinition_k23_substut1,axiom,( ! [A] : ( m1_subset_1(A,k2_zfmisc_1(k16_substut1,k2_qc_lang1)) => k23_substut1(A) = k2_mcart_1(A) ) ), file(substut1,k23_substut1), []). 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_k5_numbers,axiom,( k5_numbers = k5_ordinal2 ), file(numbers,k5_numbers), []). fof(redefinition_k8_finseq_1,axiom,( ! [A,B,C] : ( ( m1_finseq_1(B,A) & m1_finseq_1(C,A) ) => k8_finseq_1(A,B,C) = k7_finseq_1(B,C) ) ), file(finseq_1,k8_finseq_1), []). fof(redefinition_k9_cqc_lang,axiom,( k9_cqc_lang = k11_qc_lang1 ), file(cqc_lang,k9_cqc_lang), []). fof(redefinition_k9_finseq_1,axiom,( ! [A] : k9_finseq_1(A) = k5_finseq_1(A) ), file(finseq_1,k9_finseq_1), []). 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_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(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(t1_numerals,axiom,( m1_subset_1(0,k5_numbers) ), file(numerals,t1_numerals), []). fof(t1_subset,axiom,( ! [A,B] : ( r2_hidden(A,B) => m1_subset_1(A,B) ) ), file(subset,t1_subset), []). fof(t23_qc_lang1,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m2_subset_1(B,k5_qc_lang1,k7_qc_lang1(A)) => ! [C] : ( m1_qc_lang1(C,A) => k9_qc_lang1(B,C) = k7_finseq_1(k12_finseq_1(k7_qc_lang1(A),B),C) ) ) ) ), file(qc_lang1,t23_qc_lang1), []). fof(t2_subset,axiom,( ! [A,B] : ( m1_subset_1(A,B) => ( v1_xboole_0(B) | r2_hidden(A,B) ) ) ), file(subset,t2_subset), []). fof(t3_subset,axiom,( ! [A,B] : ( m1_subset_1(A,k1_zfmisc_1(B)) <=> r1_tarski(A,B) ) ), file(subset,t3_subset), []). fof(t45_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => k7_finseq_1(k7_finseq_1(A,B),C) = k7_finseq_1(A,k7_finseq_1(B,C)) ) ) ) ), file(finseq_1,t45_finseq_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(t58_finseq_1,axiom,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => k1_funct_1(k7_finseq_1(k9_finseq_1(A),B),1) = A ) ), file(finseq_1,t58_finseq_1), []). 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(t7_boole,axiom,( ! [A,B] : ~ ( r2_hidden(A,B) & v1_xboole_0(B) ) ), file(boole,t7_boole), []). fof(t7_mcart_1,axiom,( ! [A,B] : ( k1_mcart_1(k4_tarski(A,B)) = A & k2_mcart_1(k4_tarski(A,B)) = B ) ), file(mcart_1,t7_mcart_1), []). fof(t8_boole,axiom,( ! [A,B] : ~ ( v1_xboole_0(A) & A != B & v1_xboole_0(B) ) ), file(boole,t8_boole), []). fof(t9_substut1,axiom,( ! [A] : ( m1_subset_1(A,k1_substut1) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( m2_subset_1(C,k5_qc_lang1,k7_qc_lang1(B)) => ! [D] : ( m1_qc_lang1(D,B) => k17_substut1(C,D,A) = k1_domain_1(k8_qc_lang1,k1_substut1,k9_qc_lang1(C,D),A) ) ) ) ) ), file(substut1,t9_substut1), []).