% Mizar problem: t7_qmax_1,qmax_1,447,2 
fof(t7_qmax_1, conjecture,  (! [A] :  ( (v2_qmax_1(A) & l1_qmax_1(A))  =>  (! [B] :  (m1_subset_1(B, k5_qmax_1(A)) =>  (! [C] :  (m1_subset_1(C, k5_qmax_1(A)) =>  (! [D] :  (m1_subset_1(D, k5_qmax_1(A)) =>  ( (r4_qmax_1(A, B, C) & r4_qmax_1(A, C, D))  => r4_qmax_1(A, B, D)) ) ) ) ) ) ) ) ) ).
fof(cc13_ordinal1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  ~ (v8_ordinal1(A)) ) ) ).
fof(cc5_subset_1, axiom,  (! [A] :  (v1_zfmisc_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_zfmisc_1(B)) ) ) ) ).
fof(cc6_funct_1, axiom,  (! [A] :  ( (v1_zfmisc_1(A) &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v3_funct_1(A)) ) ) ) ).
fof(rc1_xtuple_0, axiom,  (? [A] : v1_xtuple_0(A)) ).
fof(rc5_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ( ~ (v1_xboole_0(B))  & v1_zfmisc_1(B)) ) ) ) ) ).
fof(rc6_subset_1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_zfmisc_1(B)) ) ) ) ) ).
fof(rd3_xtuple_0, axiom,  (! [A] :  (v1_xtuple_0(A) => k4_tarski(k1_xtuple_0(A), k2_xtuple_0(A))=A) ) ).
fof(reflexivity_r1_tarski, axiom,  (! [A, B] : r1_tarski(A, A)) ).
fof(antisymmetry_r2_hidden, axiom,  (! [A, B] :  (r2_hidden(A, B) =>  ~ (r2_hidden(B, A)) ) ) ).
fof(dt_k1_qmax_1, axiom, $true).
fof(dt_k4_tarski, axiom, $true).
fof(cc11_ordinal1, axiom,  (! [A] :  (v8_ordinal1(A) => v7_ordinal1(A)) ) ).
fof(cc12_ordinal1, axiom,  (! [A] :  (v8_ordinal1(A) => v1_zfmisc_1(A)) ) ).
fof(cc19_ordinal1, axiom,  (! [A] :  (v1_setfam_1(A) =>  ~ (v10_ordinal1(A)) ) ) ).
fof(cc20_ordinal1, axiom,  (! [A] :  ( ~ (v1_setfam_1(A))  => v10_ordinal1(A)) ) ).
fof(cc2_ordinal1, axiom,  (! [A] :  ( (v1_ordinal1(A) & v2_ordinal1(A))  => v3_ordinal1(A)) ) ).
fof(cc2_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) =>  ( ~ (v1_subset_1(B, A))  =>  ~ (v1_xboole_0(B)) ) ) ) ) ) ).
fof(cc5_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  ~ (v3_funct_1(A)) ) )  =>  ( ~ (v1_zfmisc_1(A))  &  (v1_relat_1(A) & v1_funct_1(A)) ) ) ) ).
fof(fc19_funct_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v3_relat_1(A) & v1_funct_1(A)) )  => v1_xboole_0(k1_funct_1(A, B))) ) ).
fof(fc1_qmax_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  (v1_prob_1(B, A) &  (v4_prob_1(B, A) & m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) ) ) )  =>  ~ (v1_xboole_0(k1_qmax_1(A, B))) ) ) ).
fof(fc1_xtuple_0, axiom,  (! [A, B] : v1_xtuple_0(k4_tarski(A, B))) ).
fof(rc10_ordinal1, axiom,  (? [A] :  ~ (v8_ordinal1(A)) ) ).
fof(rc12_ordinal1, axiom,  (? [A] :  (v1_relat_1(A) & v9_ordinal1(A)) ) ).
fof(rc13_ordinal1, axiom,  (? [A] :  (v1_relat_1(A) &  ~ (v9_ordinal1(A)) ) ) ).
fof(rc1_ordinal1, axiom,  (? [A] :  (v1_ordinal1(A) & v2_ordinal1(A)) ) ).
fof(rc1_prob_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A))) &  ( ~ (v1_xboole_0(B))  &  (v2_finsub_1(B) & v1_prob_1(B, A)) ) ) ) ) ).
fof(rc2_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v2_funct_1(A)) ) ) ).
fof(rc2_relat_1, axiom,  (? [A] :  (v1_relat_1(A) & v2_relat_1(A)) ) ).
fof(rc3_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v2_relat_1(A) & v1_funct_1(A)) ) ) ).
fof(rc3_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_ordinal1(A) &  (v2_ordinal1(A) & v3_ordinal1(A)) ) ) ) ).
fof(rc3_subset_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_subset_1(B, A)) ) ) ) ).
fof(rc4_funct_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) &  (v2_relat_1(A) & v1_funct_1(A)) ) ) ) ).
fof(rc4_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_subset_1(B, A)) ) ) ) ).
fof(rc5_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) &  ~ (v3_funct_1(A)) ) ) ) ).
fof(rc5_xreal_0, axiom,  (? [A] :  (v8_ordinal1(A) &  (v1_xcmplx_0(A) &  (v1_xxreal_0(A) & v1_xreal_0(A)) ) ) ) ).
fof(rc8_ordinal1, axiom,  (? [A] : v8_ordinal1(A)) ).
fof(rc9_ordinal1, axiom,  (? [A] : v8_ordinal1(A)) ).
fof(rd1_xtuple_0, axiom,  (! [A, B] : k1_xtuple_0(k4_tarski(A, B))=A) ).
fof(rd2_xtuple_0, axiom,  (! [A, B] : k2_xtuple_0(k4_tarski(A, B))=B) ).
fof(asymmetry_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) =>  ~ (r2_tarski(B, A)) ) ) ).
fof(existence_m1_prob_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(B))  &  (v1_prob_1(B, A) &  (v4_prob_1(B, A) & m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) ) )  =>  (? [C] : m1_prob_1(C, A, B)) ) ) ).
fof(existence_m2_prob_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  (v1_prob_1(B, A) &  (v4_prob_1(B, A) & m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) ) ) )  =>  (? [C] : m2_prob_1(C, A, B)) ) ) ).
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)) ) ).
fof(redefinition_m1_prob_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(B))  &  (v1_prob_1(B, A) &  (v4_prob_1(B, A) & m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) ) )  =>  (! [C] :  (m1_prob_1(C, A, B) <=> m1_subset_1(C, B)) ) ) ) ).
fof(redefinition_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) <=> r2_hidden(A, B)) ) ).
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))) ) ).
fof(dt_k1_funct_1, axiom, $true).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k1_xtuple_0, axiom, $true).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k2_xtuple_0, axiom, $true).
fof(dt_m1_prob_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(B))  &  (v1_prob_1(B, A) &  (v4_prob_1(B, A) & m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) ) )  =>  (! [C] :  (m1_prob_1(C, A, B) => m1_subset_1(C, k1_zfmisc_1(A))) ) ) ) ).
fof(dt_m2_prob_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  (v1_prob_1(B, A) &  (v4_prob_1(B, A) & m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) ) ) )  =>  (! [C] :  (m2_prob_1(C, A, B) =>  (v1_funct_1(C) &  (v1_funct_2(C, B, k1_numbers) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, k1_numbers)))) ) ) ) ) ) ).
fof(dt_u1_qmax_1, axiom,  (! [A] :  (l1_qmax_1(A) =>  ~ (v1_xboole_0(u1_qmax_1(A))) ) ) ).
fof(dt_u2_qmax_1, axiom,  (! [A] :  (l1_qmax_1(A) =>  ~ (v1_xboole_0(u2_qmax_1(A))) ) ) ).
fof(dt_u3_qmax_1, axiom,  (! [A] :  (l1_qmax_1(A) =>  (v1_funct_1(u3_qmax_1(A)) &  (v1_funct_2(u3_qmax_1(A), k2_zfmisc_1(u1_qmax_1(A), u2_qmax_1(A)), k1_qmax_1(k1_numbers, k12_prob_1)) & m1_subset_1(u3_qmax_1(A), k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_qmax_1(A), u2_qmax_1(A)), k1_qmax_1(k1_numbers, k12_prob_1))))) ) ) ) ).
fof(cc10_ordinal1, axiom,  (! [A] :  (v6_ordinal1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v6_ordinal1(B)) ) ) ) ).
fof(cc15_ordinal1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v9_ordinal1(A)) ) ) ).
fof(cc16_ordinal1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v10_ordinal1(A)) )  =>  (! [B] :  (m1_subset_1(B, A) =>  ~ (v8_ordinal1(B)) ) ) ) ) ).
fof(cc17_ordinal1, axiom,  (! [A] :  ( ~ (v10_ordinal1(A))  => v1_setfam_1(A)) ) ).
fof(cc18_ordinal1, axiom,  (! [A] :  (v10_ordinal1(A) =>  ~ (v1_setfam_1(A)) ) ) ).
fof(cc1_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) =>  (v1_ordinal1(A) & v2_ordinal1(A)) ) ) ).
fof(cc1_partfun1, axiom,  (! [A, B] :  (v1_xboole_0(A) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_partfun1(C, A)) ) ) ) ).
fof(cc1_prob_1, axiom,  (! [A] :  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A))) =>  ( ( ~ (v1_xboole_0(B))  &  (v1_prob_1(B, A) & v4_prob_1(B, A)) )  =>  ( ~ (v1_xboole_0(B))  &  (v2_finsub_1(B) &  (v1_prob_1(B, A) & v4_prob_1(B, A)) ) ) ) ) ) ) ).
fof(cc1_subset_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_xboole_0(B)) ) ) ) ).
fof(cc2_funct_1, axiom,  (! [A] :  ( (v1_xboole_0(A) &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v2_funct_1(A)) ) ) ) ).
fof(cc2_partfun1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  & v1_xboole_0(B))  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  ~ (v1_partfun1(C, A)) ) ) ) ) ).
fof(cc2_prob_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  (v1_prob_1(B, A) &  (v4_prob_1(B, A) & m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) ) ) )  =>  (! [C] :  (m2_prob_1(C, A, B) => v12_valued_0(C)) ) ) ) ).
fof(cc2_relat_1, axiom,  (! [A] :  (v1_relat_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_relat_1(B)) ) ) ) ).
fof(cc2_xreal_0, axiom,  (! [A] :  (v7_ordinal1(A) => v1_xreal_0(A)) ) ).
fof(cc3_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_funct_1(B)) ) ) ) ).
fof(cc3_relat_1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v3_relat_1(A)) ) ) ).
fof(cc3_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) =>  (v1_xboole_0(B) => v1_subset_1(B, A)) ) ) ) ) ).
fof(cc3_xreal_0, axiom,  (! [A] :  (v1_xreal_0(A) => v1_xcmplx_0(A)) ) ).
fof(cc4_funct_1, axiom,  (! [A] :  ( (v1_xboole_0(A) &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v3_funct_1(A)) ) ) ) ).
fof(cc4_relat_1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v2_relat_1(A)) ) ) ).
fof(cc4_subset_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) =>  ~ (v1_subset_1(B, A)) ) ) ) ) ).
fof(cc4_xreal_0, axiom,  (! [A] :  (v1_xreal_0(A) => v1_xxreal_0(A)) ) ).
fof(cc5_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  (m1_subset_1(B, A) => v3_ordinal1(B)) ) ) ) ).
fof(cc6_ordinal1, axiom,  (! [A] :  (v7_ordinal1(A) => v3_ordinal1(A)) ) ).
fof(cc8_funct_1, axiom,  (! [A] :  (v4_funct_1(A) =>  (! [B] :  (m1_subset_1(B, A) =>  (v1_relat_1(B) & v1_funct_1(B)) ) ) ) ) ).
fof(cc9_funct_1, axiom,  (! [A] :  (v4_funct_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v4_funct_1(B)) ) ) ) ).
fof(fc1_prob_1, axiom,  (! [A] : v2_finsub_1(k1_zfmisc_1(A))) ).
fof(fc1_subset_1, axiom,  (! [A] :  ~ (v1_xboole_0(k1_zfmisc_1(A))) ) ).
fof(fc1_xboole_0, axiom, v1_xboole_0(k1_xboole_0)).
fof(fc2_prob_1, axiom,  (! [A] : v1_prob_1(k1_zfmisc_1(A), A)) ).
fof(fc4_prob_1, axiom,  (! [A] : v4_prob_1(k1_zfmisc_1(A), A)) ).
fof(rc11_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  ~ (v10_ordinal1(A)) ) ) ).
fof(rc1_funct_1, axiom,  (? [A] :  (v1_relat_1(A) & v1_funct_1(A)) ) ).
fof(rc1_relat_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v1_relat_1(A)) ) ).
fof(rc1_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_xboole_0(B)) ) ) ) ) ).
fof(rc1_xreal_0, axiom,  (? [A] : v1_xreal_0(A)) ).
fof(rc2_ordinal1, axiom,  (? [A] : v3_ordinal1(A)) ).
fof(rc2_prob_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A))) &  ( ~ (v1_xboole_0(B))  &  (v1_prob_1(B, A) & v4_prob_1(B, A)) ) ) ) ) ).
fof(rc2_subset_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_xboole_0(B)) ) ) ).
fof(rc2_xreal_0, axiom,  (? [A] : v1_xreal_0(A)) ).
fof(rc4_prob_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(B))  &  (v1_prob_1(B, A) &  (v4_prob_1(B, A) & m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) ) )  =>  (? [C] :  (m1_subset_1(C, B) & v1_xboole_0(C)) ) ) ) ).
fof(rc5_ordinal1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc6_ordinal1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc7_funct_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v4_funct_1(A)) ) ).
fof(rc7_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v7_ordinal1(A)) ) ).
fof(t1_subset, axiom,  (! [A] :  (! [B] :  (r2_tarski(A, B) => m1_subset_1(A, B)) ) ) ).
fof(t3_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) ) ) ).
fof(t4_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ( (r2_tarski(A, B) & m1_subset_1(B, k1_zfmisc_1(C)))  => m1_subset_1(A, C)) ) ) ) ).
fof(t5_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ~ ( (r2_tarski(A, B) &  (m1_subset_1(B, k1_zfmisc_1(C)) & v1_xboole_0(C)) ) ) ) ) ) ).
fof(reflexivity_r1_xxreal_0, axiom,  (! [A, B] :  ( (v1_xxreal_0(A) & v1_xxreal_0(B))  => r1_xxreal_0(A, A)) ) ).
fof(connectedness_r1_xxreal_0, axiom,  (! [A, B] :  ( (v1_xxreal_0(A) & v1_xxreal_0(B))  =>  (r1_xxreal_0(A, B) | r1_xxreal_0(B, A)) ) ) ).
fof(redefinition_k3_funct_2, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_funct_1(C) &  (v1_funct_2(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  & m1_subset_1(D, A)) )  => k3_funct_2(A, B, C, D)=k1_funct_1(C, D)) ) ).
fof(redefinition_k6_qmax_1, axiom,  (! [A, B] :  ( ( (v2_qmax_1(A) & l1_qmax_1(A))  & m1_subset_1(B, k5_qmax_1(A)))  => k6_qmax_1(A, B)=k1_xtuple_0(B)) ) ).
fof(redefinition_k7_qmax_1, axiom,  (! [A, B] :  ( ( (v2_qmax_1(A) & l1_qmax_1(A))  & m1_subset_1(B, k5_qmax_1(A)))  => k7_qmax_1(A, B)=k2_xtuple_0(B)) ) ).
fof(dt_k12_prob_1, axiom,  ( ~ (v1_xboole_0(k12_prob_1))  &  (v1_prob_1(k12_prob_1, k1_numbers) &  (v4_prob_1(k12_prob_1, k1_numbers) & m1_subset_1(k12_prob_1, k1_zfmisc_1(k1_zfmisc_1(k1_numbers)))) ) ) ).
fof(dt_k1_numbers, axiom, $true).
fof(dt_k2_qmax_1, axiom, $true).
fof(dt_k2_zfmisc_1, axiom, $true).
fof(dt_k3_funct_2, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_funct_1(C) &  (v1_funct_2(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  & m1_subset_1(D, A)) )  => m1_subset_1(k3_funct_2(A, B, C, D), B)) ) ).
fof(dt_k3_qmax_1, axiom, $true).
fof(dt_k4_qmax_1, axiom,  (! [A, B, C] :  ( (l1_qmax_1(A) &  (m1_subset_1(B, k2_qmax_1(A)) & m1_subset_1(C, k3_qmax_1(A))) )  => m2_prob_1(k4_qmax_1(A, B, C), k1_numbers, k12_prob_1)) ) ).
fof(dt_k6_qmax_1, axiom,  (! [A, B] :  ( ( (v2_qmax_1(A) & l1_qmax_1(A))  & m1_subset_1(B, k5_qmax_1(A)))  => m1_subset_1(k6_qmax_1(A, B), k2_qmax_1(A))) ) ).
fof(dt_k7_qmax_1, axiom,  (! [A, B] :  ( ( (v2_qmax_1(A) & l1_qmax_1(A))  & m1_subset_1(B, k5_qmax_1(A)))  => m1_prob_1(k7_qmax_1(A, B), k1_numbers, k12_prob_1)) ) ).
fof(cc14_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) =>  ~ (v10_ordinal1(A)) ) ) ).
fof(cc1_funct_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_funct_1(A)) ) ).
fof(cc1_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_relat_1(A)) ) ).
fof(cc1_xreal_0, axiom,  (! [A] :  (m1_subset_1(A, k1_numbers) => v1_xreal_0(A)) ) ).
fof(cc3_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v3_ordinal1(A)) ) ).
fof(cc4_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v5_ordinal1(A)) ) ).
fof(cc7_funct_1, axiom,  (! [A] :  (v1_xboole_0(A) => v4_funct_1(A)) ) ).
fof(cc7_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v7_ordinal1(A)) ) ).
fof(cc9_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v6_ordinal1(A)) ) ).
fof(fc10_subset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v1_xboole_0(B)) )  =>  ~ (v1_xboole_0(k2_zfmisc_1(A, B))) ) ) ).
fof(fc1_numbers, axiom,  ~ (v1_xboole_0(k1_numbers)) ).
fof(fc2_qmax_1, axiom,  (! [A] :  (l1_qmax_1(A) =>  ~ (v1_xboole_0(k2_qmax_1(A))) ) ) ).
fof(fc3_qmax_1, axiom,  (! [A] :  (l1_qmax_1(A) =>  ~ (v1_xboole_0(k3_qmax_1(A))) ) ) ).
fof(fc6_relat_1, axiom,  (! [A, B] : v1_relat_1(k2_zfmisc_1(A, B))) ).
fof(fc8_numbers, axiom,  ~ (v1_finset_1(k1_numbers)) ).
fof(rc1_xboole_0, axiom,  (? [A] : v1_xboole_0(A)) ).
fof(rc2_xboole_0, axiom,  (? [A] :  ~ (v1_xboole_0(A)) ) ).
fof(t2_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, B) =>  (v1_xboole_0(B) | r2_tarski(A, B)) ) ) ) ).
fof(t6_boole, axiom,  (! [A] :  (v1_xboole_0(A) => A=k1_xboole_0) ) ).
fof(t7_boole, axiom,  (! [A] :  (! [B] :  ~ ( (r2_tarski(A, B) & v1_xboole_0(B)) ) ) ) ).
fof(t8_boole, axiom,  (! [A] :  (! [B] :  ~ ( (v1_xboole_0(A) &  ( ~ (A=B)  & v1_xboole_0(B)) ) ) ) ) ).
fof(d2_qmax_1, axiom,  (! [A] :  (l1_qmax_1(A) => k2_qmax_1(A)=u1_qmax_1(A)) ) ).
fof(d3_qmax_1, axiom,  (! [A] :  (l1_qmax_1(A) => k3_qmax_1(A)=u2_qmax_1(A)) ) ).
fof(d4_qmax_1, axiom,  (! [A] :  (l1_qmax_1(A) =>  (! [B] :  (m1_subset_1(B, k2_qmax_1(A)) =>  (! [C] :  (m1_subset_1(C, k3_qmax_1(A)) => k4_qmax_1(A, B, C)=k1_funct_1(u3_qmax_1(A), k1_domain_1(k2_qmax_1(A), k3_qmax_1(A), B, C))) ) ) ) ) ) ).
fof(reflexivity_r3_qmax_1, axiom,  (! [A, B, C] :  ( ( (v2_qmax_1(A) & l1_qmax_1(A))  &  (m1_subset_1(B, k5_qmax_1(A)) & m1_subset_1(C, k5_qmax_1(A))) )  => r3_qmax_1(A, B, B)) ) ).
fof(symmetry_r4_qmax_1, axiom,  (! [A, B, C] :  ( ( (v2_qmax_1(A) & l1_qmax_1(A))  &  (m1_subset_1(B, k5_qmax_1(A)) & m1_subset_1(C, k5_qmax_1(A))) )  =>  (r4_qmax_1(A, B, C) => r4_qmax_1(A, C, B)) ) ) ).
fof(reflexivity_r4_qmax_1, axiom,  (! [A, B, C] :  ( ( (v2_qmax_1(A) & l1_qmax_1(A))  &  (m1_subset_1(B, k5_qmax_1(A)) & m1_subset_1(C, k5_qmax_1(A))) )  => r4_qmax_1(A, B, B)) ) ).
fof(existence_l1_qmax_1, axiom,  (? [A] : l1_qmax_1(A)) ).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(dt_k5_qmax_1, axiom, $true).
fof(dt_l1_qmax_1, axiom, $true).
fof(dt_m1_subset_1, axiom, $true).
fof(fc4_qmax_1, axiom,  (! [A] :  ( (v2_qmax_1(A) & l1_qmax_1(A))  =>  ~ (v1_xboole_0(k5_qmax_1(A))) ) ) ).
fof(d8_qmax_1, axiom,  (! [A] :  ( (v2_qmax_1(A) & l1_qmax_1(A))  => k5_qmax_1(A)=k2_zfmisc_1(k2_qmax_1(A), k12_prob_1)) ) ).
fof(d10_qmax_1, axiom,  (! [A] :  ( (v2_qmax_1(A) & l1_qmax_1(A))  =>  (! [B] :  (m1_subset_1(B, k5_qmax_1(A)) =>  (! [C] :  (m1_subset_1(C, k5_qmax_1(A)) =>  (r3_qmax_1(A, B, C) <=>  (! [D] :  (m1_subset_1(D, k3_qmax_1(A)) => r1_xxreal_0(k3_funct_2(k12_prob_1, k1_numbers, k4_qmax_1(A, k6_qmax_1(A, B), D), k7_qmax_1(A, B)), k3_funct_2(k12_prob_1, k1_numbers, k4_qmax_1(A, k6_qmax_1(A, C), D), k7_qmax_1(A, C)))) ) ) ) ) ) ) ) ) ).
fof(d11_qmax_1, axiom,  (! [A] :  ( (v2_qmax_1(A) & l1_qmax_1(A))  =>  (! [B] :  (m1_subset_1(B, k5_qmax_1(A)) =>  (! [C] :  (m1_subset_1(C, k5_qmax_1(A)) =>  (r4_qmax_1(A, B, C) <=>  (r3_qmax_1(A, B, C) & r3_qmax_1(A, C, B)) ) ) ) ) ) ) ) ).
fof(t4_qmax_1, axiom,  (! [A] :  ( (v2_qmax_1(A) & l1_qmax_1(A))  =>  (! [B] :  (m1_subset_1(B, k5_qmax_1(A)) =>  (! [C] :  (m1_subset_1(C, k5_qmax_1(A)) =>  (! [D] :  (m1_subset_1(D, k5_qmax_1(A)) =>  ( (r3_qmax_1(A, B, C) & r3_qmax_1(A, C, D))  => r3_qmax_1(A, B, D)) ) ) ) ) ) ) ) ) ).
