% Mizar problem: t15_surreals,surreals,1033,5 
fof(t15_surreals, conjecture,  (! [A] :  (v2_surreal0(A) => k8_surreals(A)=k4_tarski(k3_card_3(k4_surreals(k9_surreals(A), A)), k3_card_3(k5_surreals(k9_surreals(A), A)))) ) ).
fof(antisymmetry_r2_hidden, axiom,  (! [A, B] :  (r2_hidden(A, B) =>  ~ (r2_hidden(B, A)) ) ) ).
fof(asymmetry_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) =>  ~ (r2_tarski(B, A)) ) ) ).
fof(cc10_ordinal1, axiom,  (! [A] :  (v6_ordinal1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v6_ordinal1(B)) ) ) ) ).
fof(cc11_ordinal1, axiom,  (! [A] :  (v8_ordinal1(A) => v7_ordinal1(A)) ) ).
fof(cc12_ordinal1, axiom,  (! [A] :  (v8_ordinal1(A) => v1_zfmisc_1(A)) ) ).
fof(cc13_ordinal1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  ~ (v8_ordinal1(A)) ) ) ).
fof(cc14_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) =>  ~ (v10_ordinal1(A)) ) ) ).
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(cc19_ordinal1, axiom,  (! [A] :  (v1_setfam_1(A) =>  ~ (v10_ordinal1(A)) ) ) ).
fof(cc1_funcop_1, axiom,  (! [A] :  (v4_funct_1(A) =>  (! [B] :  ( (v1_relat_1(B) &  (v5_relat_1(B, A) & v1_funct_1(B)) )  =>  (v1_relat_1(B) &  (v1_funct_1(B) & v1_funcop_1(B)) ) ) ) ) ) ).
fof(cc1_funct_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_funct_1(A)) ) ).
fof(cc1_nat_1, axiom,  (! [A] :  (v7_ordinal1(A) =>  (v3_ordinal1(A) & v7_ordinal1(A)) ) ) ).
fof(cc1_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) =>  (v1_ordinal1(A) & v2_ordinal1(A)) ) ) ).
fof(cc1_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_relat_1(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(cc1_surreal0, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  (m1_subset_1(B, k10_surreal0(A)) => v2_surreal0(B)) ) ) ) ).
fof(cc20_ordinal1, axiom,  (! [A] :  ( ~ (v1_setfam_1(A))  => v10_ordinal1(A)) ) ).
fof(cc2_funcop_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v2_funcop_1(A)) ) ) ) ).
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_nat_1, axiom,  (! [A] :  (v7_ordinal1(A) =>  (v7_ordinal1(A) &  ~ (v3_xxreal_0(A)) ) ) ) ).
fof(cc2_ordinal1, axiom,  (! [A] :  ( (v1_ordinal1(A) & v2_ordinal1(A))  => v3_ordinal1(A)) ) ).
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_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(cc2_surreal0, axiom,  (! [A] :  (v2_surreal0(A) =>  (v1_xtuple_0(A) & v2_surreal0(A)) ) ) ).
fof(cc2_xreal_0, axiom,  (! [A] :  (v7_ordinal1(A) => v1_xreal_0(A)) ) ).
fof(cc3_funcop_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_xboole_0(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(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_nat_1, axiom,  (! [A] :  (v7_ordinal1(A) =>  (v7_ordinal1(A) &  ~ (v3_xxreal_0(A)) ) ) ) ).
fof(cc3_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v3_ordinal1(A)) ) ).
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_surreal0, axiom,  (! [A] :  (v2_surreal0(A) =>  ~ (v1_xboole_0(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_nat_1, axiom,  (! [A] :  ( (v7_ordinal1(A) & v8_ordinal1(A))  =>  (v7_ordinal1(A) &  ~ (v2_xxreal_0(A)) ) ) ) ).
fof(cc4_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v5_ordinal1(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_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(cc5_nat_1, axiom,  (! [A] :  (v1_xboole_0(A) => v8_ordinal1(A)) ) ).
fof(cc5_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  (m1_subset_1(B, A) => v3_ordinal1(B)) ) ) ) ).
fof(cc5_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v4_relat_1(B, A))  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(B)) => v4_relat_1(C, 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(cc6_nat_1, axiom,  (! [A] :  ( ~ (v8_ordinal1(A))  =>  ~ (v1_xboole_0(A)) ) ) ).
fof(cc6_ordinal1, axiom,  (! [A] :  (v7_ordinal1(A) => v3_ordinal1(A)) ) ).
fof(cc6_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(B)) => v5_relat_1(C, 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(cc7_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  ( (v1_relat_1(B) & v4_relat_1(B, A))  =>  (v1_xboole_0(B) &  (v1_relat_1(B) & v4_relat_1(B, 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(cc8_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (v1_xboole_0(B) &  (v1_relat_1(B) & v5_relat_1(B, A)) ) ) ) ) ) ).
fof(cc9_funct_1, axiom,  (! [A] :  (v4_funct_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v4_funct_1(B)) ) ) ) ).
fof(cc9_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v6_ordinal1(A)) ) ).
fof(commutativity_k2_xboole_0, axiom,  (! [A, B] : k2_xboole_0(A, B)=k2_xboole_0(B, A)) ).
fof(connectedness_r1_ordinal1, axiom,  (! [A, B] :  ( (v3_ordinal1(A) & v3_ordinal1(B))  =>  (r1_ordinal1(A, B) | r1_ordinal1(B, A)) ) ) ).
fof(connectedness_r1_surrealo, axiom,  (! [A, B] :  ( (v2_surreal0(A) & v2_surreal0(B))  =>  (r1_surrealo(A, B) | r1_surrealo(B, A)) ) ) ).
fof(d10_xboole_0, axiom,  (! [A] :  (! [B] :  (A=B <=>  (r1_tarski(A, B) & r1_tarski(B, A)) ) ) ) ).
fof(d13_surreal0, axiom,  (! [A] :  (v3_ordinal1(A) => k10_surreal0(A)=k5_surreal0(A, k9_surreal0(A))) ) ).
fof(d15_surreal0, axiom, k11_surreal0=k4_tarski(k1_xboole_0, k1_xboole_0)).
fof(d16_surreal0, axiom,  (! [A] :  (v3_surreal0(A) <=>  (! [B] :  (r2_hidden(B, A) => v2_surreal0(B)) ) ) ) ).
fof(d18_surreal0, axiom,  (! [A] :  (v2_surreal0(A) =>  (! [B] :  (v3_ordinal1(B) =>  (B=k12_surreal0(A) <=>  (r2_tarski(A, k10_surreal0(B)) &  (! [C] :  (v3_ordinal1(C) =>  (r2_tarski(A, k10_surreal0(C)) => r1_ordinal1(B, C)) ) ) ) ) ) ) ) ) ).
fof(d2_partfun1, axiom,  (! [A] :  (! [B] :  ( (v1_relat_1(B) & v4_relat_1(B, A))  =>  (v1_partfun1(B, A) <=> k1_relset_1(A, B)=A) ) ) ) ).
fof(d3_tarski, axiom,  (! [A] :  (! [B] :  (r1_tarski(A, B) <=>  (! [C] :  (r2_hidden(C, A) => r2_hidden(C, B)) ) ) ) ) ).
fof(d3_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)) ) ) ) ) ) ) ).
fof(d6_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (! [B] :  (! [C] :  (C=k7_relat_1(A, B) <=>  (! [D] :  (r2_hidden(D, C) <=>  (? [E] :  (r2_hidden(E, k9_xtuple_0(A)) &  (r2_hidden(E, B) & D=k1_funct_1(A, E)) ) ) ) ) ) ) ) ) ) ).
fof(d6_surreals, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, k10_surreal0(A)) &  (v1_funct_1(B) & v1_partfun1(B, k10_surreal0(A))) ) )  =>  (B=k6_surreals(A) <=>  (? [C] :  ( (v1_relat_1(C) &  (v1_funct_1(C) &  (v5_ordinal1(C) &  (v6_cohsp_1(C) & v1_funcop_1(C)) ) ) )  &  (k9_xtuple_0(C)=k1_ordinal1(A) &  (B=k1_funct_1(C, A) &  (! [D] :  (v3_ordinal1(D) =>  ~ ( (r2_tarski(D, k1_ordinal1(A)) &  (! [E] :  ( (v1_relat_1(E) &  (v4_relat_1(E, k10_surreal0(D)) &  (v1_funct_1(E) & v1_partfun1(E, k10_surreal0(D))) ) )  =>  ~ ( (k1_funct_1(C, D)=E &  (! [F] :  (r2_hidden(F, k10_surreal0(D)) => k1_funct_1(E, F)=k4_tarski(k3_card_3(k4_surreals(k4_tarski(k7_relat_1(k3_tarski(k10_xtuple_0(k5_relat_1(C, D))), k1_surreal0(k1_surreals(F))), k7_relat_1(k3_tarski(k10_xtuple_0(k5_relat_1(C, D))), k2_surreal0(k1_surreals(F)))), F)), k3_card_3(k5_surreals(k4_tarski(k7_relat_1(k3_tarski(k10_xtuple_0(k5_relat_1(C, D))), k1_surreal0(k1_surreals(F))), k7_relat_1(k3_tarski(k10_xtuple_0(k5_relat_1(C, D))), k2_surreal0(k1_surreals(F)))), F)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d8_surreals, axiom,  (! [A] :  (v2_surreal0(A) => k8_surreals(A)=k1_funct_1(k6_surreals(k12_surreal0(A)), A)) ) ).
fof(d9_surreals, axiom,  (! [A] :  (! [B] :  (v1_xtuple_0(B) =>  (B=k9_surreals(A) <=>  (! [C] :  ( ~ ( (r2_hidden(C, k1_surreal0(B)) &  (! [D] :  (v2_surreal0(D) =>  ~ ( (C=k8_surreals(D) & r2_tarski(D, k1_surreal0(k1_surreals(A)))) ) ) ) ) )  &  ( ( (? [D] :  (v2_surreal0(D) &  (C=k8_surreals(D) & r2_tarski(D, k1_surreal0(k1_surreals(A)))) ) )  => r2_hidden(C, k1_surreal0(B)))  &  ( ~ ( (r2_hidden(C, k2_surreal0(B)) &  (! [D] :  (v2_surreal0(D) =>  ~ ( (C=k8_surreals(D) & r2_tarski(D, k2_surreal0(k1_surreals(A)))) ) ) ) ) )  &  ( (? [D] :  (v2_surreal0(D) &  (C=k8_surreals(D) & r2_tarski(D, k2_surreal0(k1_surreals(A)))) ) )  => r2_hidden(C, k2_surreal0(B))) ) ) ) ) ) ) ) ) ).
fof(dt_k10_surreal0, axiom,  (! [A] :  (v3_ordinal1(A) =>  ( ~ (v1_xboole_0(k10_surreal0(A)))  & m1_subset_1(k10_surreal0(A), k1_zfmisc_1(k3_surreal0(A)))) ) ) ).
fof(dt_k10_xtuple_0, axiom, $true).
fof(dt_k11_surreal0, axiom, v2_surreal0(k11_surreal0)).
fof(dt_k12_surreal0, axiom,  (! [A] :  (v2_surreal0(A) => v3_ordinal1(k12_surreal0(A))) ) ).
fof(dt_k1_funct_1, axiom, $true).
fof(dt_k1_ordinal1, axiom, $true).
fof(dt_k1_relset_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v4_relat_1(B, A))  => m1_subset_1(k1_relset_1(A, B), k1_zfmisc_1(A))) ) ).
fof(dt_k1_surreal0, axiom, $true).
fof(dt_k1_surreals, axiom,  (! [A] : v1_xtuple_0(k1_surreals(A))) ).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k1_xtuple_0, axiom, $true).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k2_relset_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  => m1_subset_1(k2_relset_1(A, B), k1_zfmisc_1(A))) ) ).
fof(dt_k2_surreal0, axiom, $true).
fof(dt_k2_xboole_0, axiom, $true).
fof(dt_k2_xtuple_0, axiom, $true).
fof(dt_k3_card_3, axiom, $true).
fof(dt_k3_surreal0, axiom, $true).
fof(dt_k3_tarski, axiom, $true).
fof(dt_k4_surreals, axiom,  (! [A, B] :  (v1_xtuple_0(A) =>  (v1_relat_1(k4_surreals(A, B)) & v1_funct_1(k4_surreals(A, B))) ) ) ).
fof(dt_k4_tarski, axiom, $true).
fof(dt_k5_relat_1, axiom,  (! [A, B] :  (v1_relat_1(A) => v1_relat_1(k5_relat_1(A, B))) ) ).
fof(dt_k5_surreal0, axiom,  (! [A, B] :  ( (v3_ordinal1(A) & v1_relat_1(B))  => m1_subset_1(k5_surreal0(A, B), k1_zfmisc_1(k3_surreal0(A)))) ) ).
fof(dt_k5_surreals, axiom,  (! [A, B] :  (v1_xtuple_0(A) =>  (v1_relat_1(k5_surreals(A, B)) & v1_funct_1(k5_surreals(A, B))) ) ) ).
fof(dt_k6_surreals, axiom,  (! [A] :  (v3_ordinal1(A) =>  (v1_relat_1(k6_surreals(A)) &  (v4_relat_1(k6_surreals(A), k10_surreal0(A)) &  (v1_funct_1(k6_surreals(A)) & v1_partfun1(k6_surreals(A), k10_surreal0(A))) ) ) ) ) ).
fof(dt_k7_relat_1, axiom, $true).
fof(dt_k7_surreals, axiom, $true).
fof(dt_k8_surreals, axiom, $true).
fof(dt_k9_surreal0, axiom,  (! [A] :  (v3_ordinal1(A) => v1_relat_1(k9_surreal0(A))) ) ).
fof(dt_k9_surreals, axiom,  (! [A] : v1_xtuple_0(k9_surreals(A))) ).
fof(dt_k9_xtuple_0, axiom, $true).
fof(dt_m1_subset_1, axiom, $true).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(fc10_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v2_relat_1(A) & v1_funct_1(A)) )  => v1_setfam_1(k10_xtuple_0(A))) ) ).
fof(fc10_ordinal1, axiom,  (! [A] :  ( (v1_relat_1(A) & v9_ordinal1(A))  =>  ~ (v10_ordinal1(k10_xtuple_0(A))) ) ) ).
fof(fc10_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_xboole_0(k9_xtuple_0(A))) ) ).
fof(fc11_funct_1, axiom,  (! [A, B] :  ( ( ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) &  (v2_relat_1(A) & v1_funct_1(A)) ) )  & m1_subset_1(B, k9_xtuple_0(A)))  =>  ~ (v1_xboole_0(k1_funct_1(A, B))) ) ) ).
fof(fc11_ordinal1, axiom,  (! [A] :  ( (v1_relat_1(A) &  ~ (v9_ordinal1(A)) )  => v10_ordinal1(k10_xtuple_0(A))) ) ).
fof(fc11_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_xboole_0(k10_xtuple_0(A))) ) ).
fof(fc12_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v3_funct_1(A)) )  => v1_zfmisc_1(k10_xtuple_0(A))) ) ).
fof(fc13_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  ~ (v3_funct_1(A)) ) )  =>  ~ (v1_zfmisc_1(k10_xtuple_0(A))) ) ) ).
fof(fc14_funcop_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) )  =>  (v1_relat_1(k5_relat_1(A, B)) & v1_funcop_1(k5_relat_1(A, B))) ) ) ).
fof(fc16_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v1_xboole_0(B))  =>  (v1_xboole_0(k5_relat_1(A, B)) & v1_relat_1(k5_relat_1(A, B))) ) ) ).
fof(fc17_funcop_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v3_funct_1(A)) )  =>  (v1_relat_1(k5_relat_1(A, B)) & v3_funct_1(k5_relat_1(A, B))) ) ) ).
fof(fc17_funct_1, axiom,  (! [A, B, C] :  ( (v4_funct_1(A) &  (v1_relat_1(C) &  (v5_relat_1(C, A) & v1_funct_1(C)) ) )  =>  (v1_relat_1(k1_funct_1(C, B)) & v1_funct_1(k1_funct_1(C, B))) ) ) ).
fof(fc17_relat_1, axiom,  (! [A, B] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_xboole_0(k5_relat_1(A, B)) & v1_relat_1(k5_relat_1(A, B))) ) ) ).
fof(fc18_funct_1, axiom,  (! [A] :  ( ( ~ (v1_zfmisc_1(A))  &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  ~ (v1_zfmisc_1(k9_xtuple_0(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(fc19_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v1_xboole_0(B))  => v1_xboole_0(k7_relat_1(A, B))) ) ).
fof(fc1_ordinal1, axiom,  (! [A] :  ~ (v1_xboole_0(k1_ordinal1(A))) ) ).
fof(fc1_subset_1, axiom,  (! [A] :  ~ (v1_xboole_0(k1_zfmisc_1(A))) ) ).
fof(fc1_surreal0, axiom,  (! [A] :  (v3_ordinal1(A) =>  ( ~ (v1_xboole_0(k3_surreal0(A)))  & v1_relat_1(k3_surreal0(A))) ) ) ).
fof(fc1_surrealr, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v6_cohsp_1(A)) )  =>  (v1_relat_1(k5_relat_1(A, B)) & v6_cohsp_1(k5_relat_1(A, B))) ) ) ).
fof(fc1_surreals, axiom,  (! [A] : v3_surreal0(k1_xtuple_0(k1_surreals(A)))) ).
fof(fc1_xboole_0, axiom, v1_xboole_0(k1_xboole_0)).
fof(fc1_xtuple_0, axiom,  (! [A, B] : v1_xtuple_0(k4_tarski(A, B))) ).
fof(fc20_relat_1, axiom,  (! [A, B] :  ( (v1_xboole_0(A) & v1_relat_1(A))  => v1_xboole_0(k7_relat_1(A, B))) ) ).
fof(fc23_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v3_relat_1(A))  =>  (v1_relat_1(k5_relat_1(A, B)) & v3_relat_1(k5_relat_1(A, B))) ) ) ).
fof(fc24_relat_1, axiom,  (! [A] :  ( (v1_zfmisc_1(A) & v1_relat_1(A))  => v1_zfmisc_1(k9_xtuple_0(A))) ) ).
fof(fc25_relat_1, axiom,  (! [A] :  ( (v1_zfmisc_1(A) & v1_relat_1(A))  => v1_zfmisc_1(k10_xtuple_0(A))) ) ).
fof(fc26_relat_1, axiom,  (! [A, B, C] :  ( (v1_relat_1(C) & v5_relat_1(C, B))  =>  (v1_relat_1(k5_relat_1(C, A)) & v5_relat_1(k5_relat_1(C, A), B)) ) ) ).
fof(fc27_relat_1, axiom,  (! [A, B, C] :  ( (v1_relat_1(C) & v4_relat_1(C, B))  =>  (v1_relat_1(k5_relat_1(C, A)) &  (v4_relat_1(k5_relat_1(C, A), A) & v4_relat_1(k5_relat_1(C, A), B)) ) ) ) ).
fof(fc2_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) =>  ( ~ (v1_xboole_0(k1_ordinal1(A)))  & v3_ordinal1(k1_ordinal1(A))) ) ) ).
fof(fc2_surreal0, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v3_ordinal1(B))  =>  ~ (v1_xboole_0(k5_surreal0(B, A))) ) ) ).
fof(fc2_surrealr, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v1_funcop_1(A) &  (v5_ordinal1(A) & v6_cohsp_1(A)) ) ) )  =>  (v1_relat_1(k3_tarski(k10_xtuple_0(A))) & v1_funct_1(k3_tarski(k10_xtuple_0(A)))) ) ) ).
fof(fc2_surreals, axiom,  (! [A] : v3_surreal0(k2_xtuple_0(k1_surreals(A)))) ).
fof(fc33_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v2_relat_1(A))  =>  (v1_relat_1(k5_relat_1(A, B)) & v2_relat_1(k5_relat_1(A, B))) ) ) ).
fof(fc3_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) => v3_ordinal1(k3_tarski(A))) ) ).
fof(fc3_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v1_relat_1(B))  => v1_relat_1(k2_xboole_0(A, B))) ) ).
fof(fc3_surreal0, axiom,  (! [A] :  (v3_ordinal1(A) =>  (v1_relat_1(k9_surreal0(A)) & v1_surreal0(k9_surreal0(A))) ) ) ).
fof(fc3_surreals, axiom,  (! [A] :  (v2_surreal0(A) =>  (v1_xtuple_0(k1_surreals(A)) & v2_surreal0(k1_surreals(A))) ) ) ).
fof(fc4_ordinal1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v5_ordinal1(A)) )  => v3_ordinal1(k9_xtuple_0(A))) ) ).
fof(fc4_surreal0, axiom, v2_surreal0(k4_tarski(k1_xboole_0, k1_xboole_0))).
fof(fc4_xboole_0, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(A))  =>  ~ (v1_xboole_0(k2_xboole_0(A, B))) ) ) ).
fof(fc4_xtuple_0, axiom,  (! [A] :  (v1_xboole_0(A) => v1_xboole_0(k9_xtuple_0(A))) ) ).
fof(fc5_ordinal1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) & v5_ordinal1(A)) )  & v3_ordinal1(B))  =>  (v1_relat_1(k5_relat_1(A, B)) &  (v5_relat_1(k5_relat_1(A, B), k10_xtuple_0(A)) & v5_ordinal1(k5_relat_1(A, B))) ) ) ) ).
fof(fc5_xboole_0, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(A))  =>  ~ (v1_xboole_0(k2_xboole_0(B, A))) ) ) ).
fof(fc5_xtuple_0, axiom,  (! [A] :  (v1_xboole_0(A) => v1_xboole_0(k10_xtuple_0(A))) ) ).
fof(fc6_surreal0, axiom,  (! [A] :  (v2_surreal0(A) => v3_surreal0(k1_xtuple_0(A))) ) ).
fof(fc7_ordinal1, axiom,  (! [A] :  ( (v3_ordinal1(A) & v7_ordinal1(A))  => v7_ordinal1(k1_ordinal1(A))) ) ).
fof(fc7_surreal0, axiom,  (! [A] :  (v2_surreal0(A) => v3_surreal0(k2_xtuple_0(A))) ) ).
fof(fc8_funct_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (v1_relat_1(k5_relat_1(A, B)) & v1_funct_1(k5_relat_1(A, B))) ) ) ).
fof(fc8_relat_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_relat_1(A))  =>  ~ (v1_xboole_0(k9_xtuple_0(A))) ) ) ).
fof(fc8_surreal0, axiom,  (! [A, B] :  ( (v3_surreal0(A) & v3_surreal0(B))  => v3_surreal0(k2_xboole_0(A, B))) ) ).
fof(fc9_funcop_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) )  =>  (v1_relat_1(k1_funct_1(A, B)) & v1_funct_1(k1_funct_1(A, B))) ) ) ).
fof(fc9_relat_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_relat_1(A))  =>  ~ (v1_xboole_0(k10_xtuple_0(A))) ) ) ).
fof(idempotence_k2_xboole_0, axiom,  (! [A, B] : k2_xboole_0(A, A)=A) ).
fof(rc10_ordinal1, axiom,  (? [A] :  ~ (v8_ordinal1(A)) ) ).
fof(rc11_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  ~ (v10_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_funcop_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) ) ) ).
fof(rc1_funct_1, axiom,  (? [A] :  (v1_relat_1(A) & v1_funct_1(A)) ) ).
fof(rc1_nat_1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc1_ordinal1, axiom,  (? [A] :  (v1_ordinal1(A) & v2_ordinal1(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_surreal0, axiom,  (? [A] : v2_surreal0(A)) ).
fof(rc1_surrealr, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) &  (v1_funcop_1(A) &  (v5_ordinal1(A) & v6_cohsp_1(A)) ) ) ) ) ).
fof(rc1_xboole_0, axiom,  (? [A] : v1_xboole_0(A)) ).
fof(rc1_xreal_0, axiom,  (? [A] : v1_xreal_0(A)) ).
fof(rc1_xtuple_0, axiom,  (? [A] : v1_xtuple_0(A)) ).
fof(rc2_funcop_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) &  (v3_funct_1(A) &  ~ (v1_xboole_0(A)) ) ) ) ) ).
fof(rc2_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v2_funct_1(A)) ) ) ).
fof(rc2_nat_1, axiom,  (? [A] :  (v7_ordinal1(A) & v8_ordinal1(A)) ) ).
fof(rc2_ordinal1, axiom,  (? [A] : v3_ordinal1(A)) ).
fof(rc2_relat_1, axiom,  (? [A] :  (v1_relat_1(A) & v2_relat_1(A)) ) ).
fof(rc2_subset_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_xboole_0(B)) ) ) ).
fof(rc2_surreal0, axiom,  (? [A] : v3_surreal0(A)) ).
fof(rc2_xboole_0, axiom,  (? [A] :  ~ (v1_xboole_0(A)) ) ).
fof(rc2_xreal_0, axiom,  (? [A] : v1_xreal_0(A)) ).
fof(rc3_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v2_relat_1(A) & v1_funct_1(A)) ) ) ).
fof(rc3_nat_1, axiom,  (? [A] :  (v7_ordinal1(A) &  ~ (v8_ordinal1(A)) ) ) ).
fof(rc3_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_ordinal1(A) &  (v2_ordinal1(A) & v3_ordinal1(A)) ) ) ) ).
fof(rc3_relat_1, axiom,  (! [A, B] :  (? [C] :  (v1_relat_1(C) &  (v4_relat_1(C, A) & v5_relat_1(C, B)) ) ) ) ).
fof(rc3_subset_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_subset_1(B, A)) ) ) ) ).
fof(rc3_surreal0, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v3_surreal0(A)) ) ).
fof(rc3_xreal_0, axiom,  (? [A] :  (v1_xcmplx_0(A) &  (v1_xxreal_0(A) &  (v2_xxreal_0(A) & v1_xreal_0(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_ordinal1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v5_relat_1(B, A) &  (v1_funct_1(B) & v5_ordinal1(B)) ) ) ) ) ).
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(rc4_xreal_0, axiom,  (? [A] :  (v1_xcmplx_0(A) &  (v1_xxreal_0(A) &  (v3_xxreal_0(A) & v1_xreal_0(A)) ) ) ) ).
fof(rc5_funcop_1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v2_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) ) ) ) ) ).
fof(rc5_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) &  ~ (v3_funct_1(A)) ) ) ) ).
fof(rc5_ordinal1, axiom,  (? [A] : v7_ordinal1(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(rc5_xreal_0, axiom,  (? [A] :  (v8_ordinal1(A) &  (v1_xcmplx_0(A) &  (v1_xxreal_0(A) & v1_xreal_0(A)) ) ) ) ).
fof(rc6_funct_1, axiom,  (! [A, B] :  (? [C] :  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) & v1_funct_1(C)) ) ) ) ) ).
fof(rc6_ordinal1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc6_subset_1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_zfmisc_1(B)) ) ) ) ) ).
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(rc8_ordinal1, axiom,  (? [A] : v8_ordinal1(A)) ).
fof(rc9_funct_1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v2_relat_1(B) &  (v4_relat_1(B, A) & v1_funct_1(B)) ) ) ) ) ).
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(rd3_xtuple_0, axiom,  (! [A] :  (v1_xtuple_0(A) => k4_tarski(k1_xtuple_0(A), k2_xtuple_0(A))=A) ) ).
fof(rd4_relat_1, axiom,  (! [A] :  (v1_relat_1(A) => k5_relat_1(A, k9_xtuple_0(A))=A) ) ).
fof(rd5_relat_1, axiom,  (! [A, B] :  (v1_relat_1(A) => k5_relat_1(k5_relat_1(A, B), B)=k5_relat_1(A, B)) ) ).
fof(rd8_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v4_relat_1(B, A))  => k5_relat_1(B, A)=B) ) ).
fof(redefinition_k1_relset_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v4_relat_1(B, A))  => k1_relset_1(A, B)=k9_xtuple_0(B)) ) ).
fof(redefinition_k1_surreal0, axiom,  (! [A] : k1_surreal0(A)=k1_xtuple_0(A)) ).
fof(redefinition_k2_relset_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  => k2_relset_1(A, B)=k10_xtuple_0(B)) ) ).
fof(redefinition_k2_surreal0, axiom,  (! [A] : k2_surreal0(A)=k2_xtuple_0(A)) ).
fof(redefinition_k8_surreals, axiom,  (! [A] :  (v2_surreal0(A) => k8_surreals(A)=k7_surreals(A)) ) ).
fof(redefinition_r1_ordinal1, axiom,  (! [A, B] :  ( (v3_ordinal1(A) & v3_ordinal1(B))  =>  (r1_ordinal1(A, B) <=> r1_tarski(A, B)) ) ) ).
fof(redefinition_r1_surrealo, axiom,  (! [A, B] :  ( (v2_surreal0(A) & v2_surreal0(B))  =>  (r1_surrealo(A, B) <=> r5_surreal0(A, B)) ) ) ).
fof(redefinition_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) <=> r2_hidden(A, B)) ) ).
fof(reflexivity_r1_ordinal1, axiom,  (! [A, B] :  ( (v3_ordinal1(A) & v3_ordinal1(B))  => r1_ordinal1(A, A)) ) ).
fof(reflexivity_r1_surrealo, axiom,  (! [A, B] :  ( (v2_surreal0(A) & v2_surreal0(B))  => r1_surrealo(A, A)) ) ).
fof(reflexivity_r1_tarski, axiom,  (! [A, B] : r1_tarski(A, A)) ).
fof(t14_surreals, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v5_ordinal1(A) &  (v6_cohsp_1(A) & v1_funcop_1(A)) ) ) )  =>  ( (! [B] :  (v3_ordinal1(B) =>  ~ ( (r2_tarski(B, k9_xtuple_0(A)) &  (! [C] :  ( (v1_relat_1(C) &  (v4_relat_1(C, k10_surreal0(B)) &  (v1_funct_1(C) & v1_partfun1(C, k10_surreal0(B))) ) )  =>  ~ ( (k1_funct_1(A, B)=C &  (! [D] :  (r2_hidden(D, k10_surreal0(B)) => k1_funct_1(C, D)=k4_tarski(k3_card_3(k4_surreals(k4_tarski(k7_relat_1(k3_tarski(k10_xtuple_0(k5_relat_1(A, B))), k1_surreal0(k1_surreals(D))), k7_relat_1(k3_tarski(k10_xtuple_0(k5_relat_1(A, B))), k2_surreal0(k1_surreals(D)))), D)), k3_card_3(k5_surreals(k4_tarski(k7_relat_1(k3_tarski(k10_xtuple_0(k5_relat_1(A, B))), k1_surreal0(k1_surreals(D))), k7_relat_1(k3_tarski(k10_xtuple_0(k5_relat_1(A, B))), k2_surreal0(k1_surreals(D)))), D)))) ) ) ) ) ) ) ) ) )  =>  (! [B] :  (v3_ordinal1(B) =>  (r2_tarski(B, k9_xtuple_0(A)) => k6_surreals(B)=k1_funct_1(A, B)) ) ) ) ) ) ).
fof(t1_boole, axiom,  (! [A] : k2_xboole_0(A, k1_xboole_0)=A) ).
fof(t1_subset, axiom,  (! [A] :  (! [B] :  (r2_tarski(A, B) => m1_subset_1(A, B)) ) ) ).
fof(t1_surrealo, axiom,  (! [A] :  (v2_surreal0(A) =>  (! [B] :  (v2_surreal0(B) =>  (r2_tarski(B, k2_xboole_0(k1_surreal0(A), k2_surreal0(A))) => r2_tarski(k12_surreal0(B), k12_surreal0(A))) ) ) ) ) ).
fof(t2_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, B) =>  (v1_xboole_0(B) | r2_tarski(A, B)) ) ) ) ).
fof(t2_surrealr, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v1_funcop_1(A) &  (v5_ordinal1(A) & v6_cohsp_1(A)) ) ) )  =>  (! [B] :  (v3_ordinal1(B) =>  (r2_tarski(B, k9_xtuple_0(A)) =>  (r1_tarski(k9_xtuple_0(k1_funct_1(A, B)), k9_xtuple_0(k3_tarski(k10_xtuple_0(A)))) &  (! [C] :  (r2_hidden(C, k9_xtuple_0(k1_funct_1(A, B))) => k1_funct_1(k1_funct_1(A, B), C)=k1_funct_1(k3_tarski(k10_xtuple_0(A)), C)) ) ) ) ) ) ) ) ).
fof(t2_surreals, axiom,  (! [A] :  (! [B] :  (v2_surreal0(B) =>  ( (r2_tarski(B, k1_surreal0(k1_surreals(A))) =>  (r2_tarski(B, k1_surreal0(A)) & r1_surrealo(k11_surreal0, B)) )  &  ( ( (r2_tarski(B, k1_surreal0(A)) & r1_surrealo(k11_surreal0, B))  => r2_tarski(B, k1_surreal0(k1_surreals(A))))  &  ( (r2_tarski(B, k2_surreal0(k1_surreals(A))) =>  (r2_tarski(B, k2_surreal0(A)) & r1_surrealo(k11_surreal0, B)) )  &  ( (r2_tarski(B, k2_surreal0(A)) & r1_surrealo(k11_surreal0, B))  => r2_tarski(B, k2_surreal0(k1_surreals(A)))) ) ) ) ) ) ) ).
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(t5_surrealr, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  (v3_ordinal1(B) =>  (! [C] :  (! [D] :  ( (v1_relat_1(D) &  (v1_funct_1(D) &  (v1_funcop_1(D) &  (v5_ordinal1(D) & v6_cohsp_1(D)) ) ) )  =>  ( (r2_hidden(C, k9_xtuple_0(k1_funct_1(D, B))) & r2_tarski(B, A))  =>  (r2_hidden(C, k9_xtuple_0(k3_tarski(k2_relset_1(k10_xtuple_0(D), k5_relat_1(D, A))))) & k1_funct_1(k3_tarski(k2_relset_1(k10_xtuple_0(D), k5_relat_1(D, A))), C)=k1_funct_1(k3_tarski(k10_xtuple_0(D)), C)) ) ) ) ) ) ) ) ) ).
fof(t6_boole, axiom,  (! [A] :  (v1_xboole_0(A) => A=k1_xboole_0) ) ).
fof(t6_ordinal1, axiom,  (! [A] : r2_tarski(A, k1_ordinal1(A))) ).
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(t8_ordinal1, axiom,  (! [A] :  (! [B] :  (r2_hidden(B, k1_ordinal1(A)) <=>  (r2_hidden(B, A) | B=A) ) ) ) ).
