% Mizar problem: l45_surreali,surreali,1866,5 
fof(l45_surreali, conjecture,  (! [A] :  (v2_surreal0(A) =>  (v2_surreali(A) =>  (v2_surreal0(k10_surreali(A)) &  (! [B] :  (v2_surreal0(B) =>  (B=k10_surreali(A) => r2_surrealo(k16_surrealr(A, B), k1_surrealo)) ) ) ) ) ) ) ).
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_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_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_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(cc2_xxreal_0, axiom,  (! [A] :  (v7_ordinal1(A) => v1_xxreal_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_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(cc3_xxreal_0, axiom,  (! [A] :  ( (v1_xxreal_0(A) & v2_xxreal_0(A))  =>  ( ~ (v8_ordinal1(A))  &  (v1_xxreal_0(A) &  ~ (v3_xxreal_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_xreal_0, axiom,  (! [A] :  (v1_xreal_0(A) => v1_xxreal_0(A)) ) ).
fof(cc4_xxreal_0, axiom,  (! [A] :  ( ( ~ (v8_ordinal1(A))  &  (v1_xxreal_0(A) &  ~ (v3_xxreal_0(A)) ) )  =>  (v1_xxreal_0(A) & v2_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_xxreal_0, axiom,  (! [A] :  ( (v1_xxreal_0(A) & v3_xxreal_0(A))  =>  ( ~ (v8_ordinal1(A))  &  (v1_xxreal_0(A) &  ~ (v2_xxreal_0(A)) ) ) ) ) ).
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_xxreal_0, axiom,  (! [A] :  ( ( ~ (v8_ordinal1(A))  &  (v1_xxreal_0(A) &  ~ (v2_xxreal_0(A)) ) )  =>  (v1_xxreal_0(A) & v3_xxreal_0(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(cc7_xxreal_0, axiom,  (! [A] :  ( (v8_ordinal1(A) & v1_xxreal_0(A))  =>  (v1_xxreal_0(A) &  ( ~ (v2_xxreal_0(A))  &  ~ (v3_xxreal_0(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_ordinal1, axiom,  (! [A] :  (m1_subset_1(A, k4_ordinal1) => v7_ordinal1(A)) ) ).
fof(cc8_xxreal_0, axiom,  (! [A] :  ( (v1_xxreal_0(A) &  ( ~ (v2_xxreal_0(A))  &  ~ (v3_xxreal_0(A)) ) )  =>  (v8_ordinal1(A) & v1_xxreal_0(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_k16_surrealr, axiom,  (! [A, B] :  ( (v2_surreal0(A) & v2_surreal0(B))  => k16_surrealr(A, B)=k16_surrealr(B, A)) ) ).
fof(commutativity_k1_nat_1, axiom,  (! [A, B] :  ( (v7_ordinal1(A) & m1_subset_1(B, k4_ordinal1))  => k1_nat_1(A, B)=k1_nat_1(B, A)) ) ).
fof(commutativity_k2_xboole_0, axiom,  (! [A, B] : k2_xboole_0(A, B)=k2_xboole_0(B, A)) ).
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)) ) ).
fof(commutativity_k5_ordinal7, axiom,  (! [A, B] :  ( (v3_ordinal1(A) & v3_ordinal1(B))  => k5_ordinal7(A, B)=k5_ordinal7(B, A)) ) ).
fof(commutativity_k8_surrealr, axiom,  (! [A, B] :  ( (v2_surreal0(A) & v2_surreal0(B))  => k8_surrealr(A, B)=k8_surrealr(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(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(d12_surreali, axiom,  (! [A] :  (v2_surreal0(A) => k10_surreali(A)=k1_funct_1(k9_surreali(k12_surreal0(A)), A)) ) ).
fof(d13_surreal0, axiom,  (! [A] :  (v3_ordinal1(A) => k10_surreal0(A)=k5_surreal0(A, k9_surreal0(A))) ) ).
fof(d13_surreali, axiom,  (! [A] :  (v2_surreal0(A) =>  (! [B] :  ( (v1_relat_1(B) & v1_funct_1(B))  =>  (B=k11_surreali(A) <=>  (k9_xtuple_0(B)=k6_subset_1(k2_xboole_0(k1_surreal0(A), k2_surreal0(A)), k1_tarski(k11_surreal0)) &  (! [C] :  (v2_surreal0(C) =>  (r2_tarski(C, k6_subset_1(k2_xboole_0(k1_surreal0(A), k2_surreal0(A)), k1_tarski(k11_surreal0))) => k1_funct_1(B, C)=k10_surreali(C)) ) ) ) ) ) ) ) ) ).
fof(d13_surrealr, axiom,  (! [A] :  (v2_surreal0(A) =>  (! [B] :  (v2_surreal0(B) => k14_surrealr(A, B)=k1_funct_1(k13_surrealr(k5_ordinal7(k12_surreal0(A), k12_surreal0(B))), k4_tarski(A, B))) ) ) ) ).
fof(d14_surrealr, axiom,  (! [A] :  (v2_surreal0(A) =>  (! [B] :  (v2_surreal0(B) =>  (! [C] :  (! [D] :  (! [E] :  (E=k15_surrealr(A, B, C, D) <=>  (! [F] :  (r2_hidden(F, E) <=>  (? [G] :  (v2_surreal0(G) &  (? [H] :  (v2_surreal0(H) &  (F=k12_surrealr(k12_surrealr(k14_surrealr(G, B), k14_surrealr(A, H)), k11_surrealr(k14_surrealr(G, H))) &  (r2_tarski(G, C) & r2_tarski(H, D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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(d17_surreal0, axiom,  (! [A] :  (v2_surreal0(A) =>  (! [B] :  (v2_surreal0(B) =>  (r5_surreal0(A, B) <=>  (? [C] :  (v3_ordinal1(C) & r1_surreal0(A, B, k9_surreal0(C))) ) ) ) ) ) ) ).
fof(d1_surrealo, axiom, k1_surrealo=k4_tarski(k1_tarski(k11_surreal0), k1_xboole_0)).
fof(d1_tarski, axiom,  (! [A] :  (! [B] :  (B=k1_tarski(A) <=>  (! [C] :  (r2_hidden(C, B) <=> C=A) ) ) ) ) ).
fof(d20_surreal0, axiom,  (! [A] :  (! [B] :  (r7_surreal0(A, B) <=>  (! [C] :  (v2_surreal0(C) =>  (! [D] :  (v2_surreal0(D) =>  ~ ( (r2_tarski(C, A) &  (r2_tarski(D, B) & r5_surreal0(D, C)) ) ) ) ) ) ) ) ) ) ).
fof(d2_surreali, axiom,  (! [A] :  (! [B] :  (! [C] :  (! [D] :  ( (v1_relat_1(D) & v1_funct_1(D))  =>  (! [E] :  (E=k2_surreali(A, B, C, D) <=>  (! [F] :  (r2_hidden(F, E) <=>  (? [G] :  (r2_hidden(G, C) &  ( ~ (G=k11_surreal0)  & F=k1_surreali(k12_surrealr(k1_surrealo, k1_surreali(k12_surrealr(G, k11_surrealr(B)), A)), k1_funct_1(D, G))) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d2_surrealo, axiom,  (! [A] :  (v2_surreal0(A) =>  (! [B] :  (v2_surreal0(B) =>  (r2_surrealo(A, B) <=>  (r1_surrealo(A, B) & r1_surrealo(B, A)) ) ) ) ) ) ).
fof(d3_surreali, axiom,  (! [A] :  (! [B] :  (! [C] :  (! [D] :  ( (v1_relat_1(D) & v1_funct_1(D))  =>  (! [E] :  (E=k3_surreali(A, B, C, D) <=>  (! [F] :  (r2_hidden(F, E) <=>  (? [G] :  (r2_hidden(G, A) & r2_hidden(F, k2_surreali(G, B, C, D))) ) ) ) ) ) ) ) ) ) ) ).
fof(d3_surrealr, axiom,  (! [A] :  (v2_surreal0(A) => k2_surrealr(A)=k1_funct_1(k1_surrealr(k12_surreal0(A)), A)) ) ).
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(d5_surreali, axiom,  (! [A] :  (! [B] :  ( (v1_relat_1(B) & v1_funct_1(B))  =>  (! [C] :  ( (v1_relat_1(C) & v1_funct_1(C))  =>  (C=k5_surreali(A, B) <=>  (k9_xtuple_0(C)=k4_ordinal1 &  (! [D] :  (v7_ordinal1(D) => k1_funct_1(C, D)=k1_xtuple_0(k1_funct_1(k4_surreali(A, B), D))) ) ) ) ) ) ) ) ) ).
fof(d6_surreali, axiom,  (! [A] :  (! [B] :  ( (v1_relat_1(B) & v1_funct_1(B))  =>  (! [C] :  ( (v1_relat_1(C) & v1_funct_1(C))  =>  (C=k6_surreali(A, B) <=>  (k9_xtuple_0(C)=k4_ordinal1 &  (! [D] :  (v7_ordinal1(D) => k1_funct_1(C, D)=k2_xtuple_0(k1_funct_1(k4_surreali(A, B), D))) ) ) ) ) ) ) ) ) ).
fof(d7_surreali, axiom,  (! [A] :  (! [B] :  ( (v1_relat_1(B) & v1_funct_1(B))  =>  (v1_surreali(B, A) <=>  (! [C] :  (r2_hidden(C, A) => v2_surreal0(k1_funct_1(B, C))) ) ) ) ) ) ).
fof(d7_surrealr, axiom,  (! [A] :  (v2_surreal0(A) =>  (! [B] :  (v2_surreal0(B) => k6_surrealr(A, B)=k1_funct_1(k5_surrealr(k5_ordinal7(k12_surreal0(A), k12_surreal0(B))), k4_tarski(A, B))) ) ) ) ).
fof(d8_surreali, axiom,  (! [A] :  (v2_surreal0(A) =>  (v2_surreali(A) <=>  ~ (r5_surreal0(A, k11_surreal0)) ) ) ) ).
fof(d9_surreali, axiom,  (! [A] :  ( (v2_surreal0(A) & v2_surreali(A))  =>  (! [B] :  ( (v2_surreal0(B) & v2_surreali(B))  =>  (B=k7_surreali(A) <=>  (! [C] :  (v2_surreal0(C) =>  ( ~ ( (r2_tarski(C, k1_surreal0(B)) &  ( ~ (C=k11_surreal0)  &  ~ ( (r2_tarski(C, k1_surreal0(A)) & v2_surreali(C)) ) ) ) )  &  ( ( (C=k11_surreal0 |  (r2_tarski(C, k1_surreal0(A)) & v2_surreali(C)) )  => r2_tarski(C, k1_surreal0(B)))  &  ( (r2_tarski(C, k2_surreal0(B)) =>  (r2_tarski(C, k2_surreal0(A)) & v2_surreali(C)) )  &  ( (r2_tarski(C, k2_surreal0(A)) & v2_surreali(C))  => r2_tarski(C, k2_surreal0(B))) ) ) ) ) ) ) ) ) ) ) ).
fof(d9_surrealr, axiom,  (! [A] :  (v2_surreal0(A) =>  (! [B] :  (v2_surreal0(B) => k10_surrealr(A, B)=k8_surrealr(A, k2_surrealr(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_surreali, axiom, $true).
fof(dt_k10_surrealr, axiom,  (! [A, B] :  ( (v2_surreal0(A) & v2_surreal0(B))  => v2_surreal0(k10_surrealr(A, B))) ) ).
fof(dt_k11_surreal0, axiom, v2_surreal0(k11_surreal0)).
fof(dt_k11_surreali, axiom,  (! [A] :  (v2_surreal0(A) =>  (v1_relat_1(k11_surreali(A)) & v1_funct_1(k11_surreali(A))) ) ) ).
fof(dt_k11_surrealr, axiom,  (! [A] : v2_surreal0(k11_surrealr(A))) ).
fof(dt_k12_surreal0, axiom,  (! [A] :  (v2_surreal0(A) => v3_ordinal1(k12_surreal0(A))) ) ).
fof(dt_k12_surrealr, axiom,  (! [A, B] : v2_surreal0(k12_surrealr(A, B))) ).
fof(dt_k13_surrealr, axiom,  (! [A] :  (v3_ordinal1(A) =>  (v1_relat_1(k13_surrealr(A)) &  (v4_relat_1(k13_surrealr(A), k4_surrealr(A)) &  (v1_funct_1(k13_surrealr(A)) & v1_partfun1(k13_surrealr(A), k4_surrealr(A))) ) ) ) ) ).
fof(dt_k14_surrealr, axiom, $true).
fof(dt_k15_surrealr, axiom, $true).
fof(dt_k16_surrealr, axiom, $true).
fof(dt_k1_funct_1, axiom, $true).
fof(dt_k1_nat_1, axiom,  (! [A, B] :  ( (v7_ordinal1(A) & m1_subset_1(B, k4_ordinal1))  => m1_subset_1(k1_nat_1(A, B), k4_ordinal1)) ) ).
fof(dt_k1_surreal0, axiom, $true).
fof(dt_k1_surreali, axiom,  (! [A, B] : v2_surreal0(k1_surreali(A, B))) ).
fof(dt_k1_surrealo, axiom, v2_surreal0(k1_surrealo)).
fof(dt_k1_surrealr, axiom,  (! [A] :  (v3_ordinal1(A) =>  (v1_relat_1(k1_surrealr(A)) &  (v4_relat_1(k1_surrealr(A), k10_surreal0(A)) &  (v1_funct_1(k1_surrealr(A)) & v1_partfun1(k1_surrealr(A), k10_surreal0(A))) ) ) ) ) ).
fof(dt_k1_tarski, 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_surreal0, axiom, $true).
fof(dt_k2_surreali, axiom, $true).
fof(dt_k2_surrealr, axiom, $true).
fof(dt_k2_xboole_0, axiom, $true).
fof(dt_k2_xcmplx_0, axiom, $true).
fof(dt_k2_xtuple_0, axiom, $true).
fof(dt_k2_zfmisc_1, axiom, $true).
fof(dt_k3_card_3, axiom, $true).
fof(dt_k3_surreal0, axiom, $true).
fof(dt_k3_surreali, axiom, $true).
fof(dt_k4_ordinal1, axiom, $true).
fof(dt_k4_surreali, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v1_funct_1(B))  =>  (v1_relat_1(k4_surreali(A, B)) & v1_funct_1(k4_surreali(A, B))) ) ) ).
fof(dt_k4_surrealr, axiom,  (! [A] :  (v3_ordinal1(A) => m1_subset_1(k4_surrealr(A), k1_zfmisc_1(k2_zfmisc_1(k10_surreal0(A), k10_surreal0(A))))) ) ).
fof(dt_k4_tarski, axiom, $true).
fof(dt_k4_xboole_0, axiom, $true).
fof(dt_k4_xcmplx_0, axiom,  (! [A] :  (v1_xcmplx_0(A) => v1_xcmplx_0(k4_xcmplx_0(A))) ) ).
fof(dt_k5_numbers, axiom, m1_subset_1(k5_numbers, k4_ordinal1)).
fof(dt_k5_ordinal1, axiom, $true).
fof(dt_k5_ordinal7, axiom,  (! [A, B] :  ( (v3_ordinal1(A) & v3_ordinal1(B))  => v3_ordinal1(k5_ordinal7(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_surreali, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v1_funct_1(B))  =>  (v1_relat_1(k5_surreali(A, B)) & v1_funct_1(k5_surreali(A, B))) ) ) ).
fof(dt_k5_surrealr, axiom,  (! [A] :  (v3_ordinal1(A) =>  (v1_relat_1(k5_surrealr(A)) &  (v4_relat_1(k5_surrealr(A), k4_surrealr(A)) &  (v1_funct_1(k5_surrealr(A)) & v1_partfun1(k5_surrealr(A), k4_surrealr(A))) ) ) ) ) ).
fof(dt_k6_subset_1, axiom,  (! [A, B] : m1_subset_1(k6_subset_1(A, B), k1_zfmisc_1(A))) ).
fof(dt_k6_surreali, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v1_funct_1(B))  =>  (v1_relat_1(k6_surreali(A, B)) & v1_funct_1(k6_surreali(A, B))) ) ) ).
fof(dt_k6_surrealr, axiom, $true).
fof(dt_k6_xcmplx_0, axiom, $true).
fof(dt_k7_surreali, axiom,  (! [A] :  (v2_surreal0(k7_surreali(A)) & v2_surreali(k7_surreali(A))) ) ).
fof(dt_k7_xcmplx_0, axiom, $true).
fof(dt_k8_surreali, axiom,  (! [A] :  (v3_ordinal1(A) => m1_subset_1(k8_surreali(A), k1_zfmisc_1(k10_surreal0(A)))) ) ).
fof(dt_k8_surrealr, axiom, $true).
fof(dt_k9_surreal0, axiom,  (! [A] :  (v3_ordinal1(A) => v1_relat_1(k9_surreal0(A))) ) ).
fof(dt_k9_surreali, axiom,  (! [A] :  (v3_ordinal1(A) =>  (v1_relat_1(k9_surreali(A)) &  (v4_relat_1(k9_surreali(A), k8_surreali(A)) &  (v1_funct_1(k9_surreali(A)) & v1_partfun1(k9_surreali(A), k8_surreali(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_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_xboole_0(k9_xtuple_0(A))) ) ).
fof(fc10_xreal_0, axiom,  (! [A, B] :  ( ( ( ~ (v2_xxreal_0(A))  & v1_xreal_0(A))  &  ( ~ (v2_xxreal_0(B))  & v1_xreal_0(B)) )  =>  ~ (v2_xxreal_0(k2_xcmplx_0(A, B))) ) ) ).
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_nat_1, axiom,  (! [A] :  ( ~ (v8_ordinal1(A))  => v1_setfam_1(k1_tarski(A))) ) ).
fof(fc11_xreal_0, axiom,  (! [A, B] :  ( ( (v2_xxreal_0(A) & v1_xreal_0(A))  &  ( ~ (v3_xxreal_0(B))  & v1_xreal_0(B)) )  => v2_xxreal_0(k2_xcmplx_0(A, B))) ) ).
fof(fc12_xreal_0, axiom,  (! [A, B] :  ( ( (v2_xxreal_0(A) & v1_xreal_0(A))  &  ( ~ (v3_xxreal_0(B))  & v1_xreal_0(B)) )  => v2_xxreal_0(k2_xcmplx_0(B, A))) ) ).
fof(fc13_xreal_0, axiom,  (! [A, B] :  ( ( (v3_xxreal_0(A) & v1_xreal_0(A))  &  ( ~ (v2_xxreal_0(B))  & v1_xreal_0(B)) )  => v3_xxreal_0(k2_xcmplx_0(A, B))) ) ).
fof(fc14_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  => v4_funct_1(k1_tarski(A))) ) ).
fof(fc14_xreal_0, axiom,  (! [A, B] :  ( ( (v3_xxreal_0(A) & v1_xreal_0(A))  &  ( ~ (v2_xxreal_0(B))  & v1_xreal_0(B)) )  => v3_xxreal_0(k2_xcmplx_0(B, A))) ) ).
fof(fc15_xreal_0, axiom,  (! [A] :  ( ( ~ (v2_xxreal_0(A))  & v1_xreal_0(A))  =>  (v1_xcmplx_0(k4_xcmplx_0(A)) &  ~ (v3_xxreal_0(k4_xcmplx_0(A))) ) ) ) ).
fof(fc16_xreal_0, axiom,  (! [A] :  ( ( ~ (v3_xxreal_0(A))  & v1_xreal_0(A))  =>  (v1_xcmplx_0(k4_xcmplx_0(A)) &  ~ (v2_xxreal_0(k4_xcmplx_0(A))) ) ) ) ).
fof(fc17_xreal_0, axiom,  (! [A, B] :  ( ( ( ~ (v3_xxreal_0(A))  & v1_xreal_0(A))  &  ( ~ (v2_xxreal_0(B))  & v1_xreal_0(B)) )  =>  ~ (v3_xxreal_0(k6_xcmplx_0(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(fc18_xreal_0, axiom,  (! [A, B] :  ( ( ( ~ (v3_xxreal_0(A))  & v1_xreal_0(A))  &  ( ~ (v2_xxreal_0(B))  & v1_xreal_0(B)) )  =>  ~ (v2_xxreal_0(k6_xcmplx_0(B, 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_xreal_0, axiom,  (! [A, B] :  ( ( (v2_xxreal_0(A) & v1_xreal_0(A))  &  ( ~ (v2_xxreal_0(B))  & v1_xreal_0(B)) )  => v2_xxreal_0(k6_xcmplx_0(A, B))) ) ).
fof(fc1_funct_1, axiom,  (! [A, B] : v1_funct_1(k1_tarski(k4_tarski(A, B)))) ).
fof(fc1_nat_1, axiom,  (! [A, B] :  ( (v7_ordinal1(A) & v7_ordinal1(B))  => v7_ordinal1(k2_xcmplx_0(A, B))) ) ).
fof(fc1_surreal0, axiom,  (! [A] :  (v3_ordinal1(A) =>  ( ~ (v1_xboole_0(k3_surreal0(A)))  & v1_relat_1(k3_surreal0(A))) ) ) ).
fof(fc1_surreali, axiom,  (v2_surreal0(k1_surrealo) & v2_surreali(k1_surrealo)) ).
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_xreal_0, axiom,  (! [A, B] :  ( ( (v2_xxreal_0(A) & v1_xreal_0(A))  &  ( ~ (v2_xxreal_0(B))  & v1_xreal_0(B)) )  => v3_xxreal_0(k6_xcmplx_0(B, A))) ) ).
fof(fc21_xreal_0, axiom,  (! [A, B] :  ( ( (v3_xxreal_0(A) & v1_xreal_0(A))  &  ( ~ (v3_xxreal_0(B))  & v1_xreal_0(B)) )  => v3_xxreal_0(k6_xcmplx_0(A, B))) ) ).
fof(fc22_xreal_0, axiom,  (! [A, B] :  ( ( (v3_xxreal_0(A) & v1_xreal_0(A))  &  ( ~ (v3_xxreal_0(B))  & v1_xreal_0(B)) )  => v2_xxreal_0(k6_xcmplx_0(B, A))) ) ).
fof(fc24_relat_1, axiom,  (! [A] :  ( (v1_zfmisc_1(A) & v1_relat_1(A))  => v1_zfmisc_1(k9_xtuple_0(A))) ) ).
fof(fc2_relat_1, axiom,  (! [A, B] :  (v1_relat_1(A) => v1_relat_1(k4_xboole_0(A, B))) ) ).
fof(fc2_surreal0, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v3_ordinal1(B))  =>  ~ (v1_xboole_0(k5_surreal0(B, A))) ) ) ).
fof(fc2_surreali, axiom,  (! [A, B] :  ( ( (v2_surreal0(A) & v2_surreali(A))  &  (v2_surreal0(B) & v2_surreali(B)) )  => v2_surreali(k6_surrealr(A, B))) ) ).
fof(fc2_xboole_0, axiom,  (! [A] :  ~ (v1_xboole_0(k1_tarski(A))) ) ).
fof(fc31_xreal_0, axiom,  (! [A, B] :  ( ( ( ~ (v3_xxreal_0(A))  & v1_xreal_0(A))  &  ( ~ (v2_xxreal_0(B))  & v1_xreal_0(B)) )  =>  ~ (v2_xxreal_0(k7_xcmplx_0(A, B))) ) ) ).
fof(fc32_xreal_0, axiom,  (! [A, B] :  ( ( ( ~ (v3_xxreal_0(A))  & v1_xreal_0(A))  &  ( ~ (v2_xxreal_0(B))  & v1_xreal_0(B)) )  =>  ~ (v2_xxreal_0(k7_xcmplx_0(B, A))) ) ) ).
fof(fc33_xreal_0, axiom,  (! [A, B] :  ( ( ( ~ (v3_xxreal_0(A))  & v1_xreal_0(A))  &  ( ~ (v3_xxreal_0(B))  & v1_xreal_0(B)) )  =>  ~ (v3_xxreal_0(k7_xcmplx_0(A, B))) ) ) ).
fof(fc34_xreal_0, axiom,  (! [A, B] :  ( ( ( ~ (v2_xxreal_0(A))  & v1_xreal_0(A))  &  ( ~ (v2_xxreal_0(B))  & v1_xreal_0(B)) )  =>  ~ (v3_xxreal_0(k7_xcmplx_0(A, B))) ) ) ).
fof(fc3_nat_1, axiom,  (! [A, B] :  ( (v7_ordinal1(A) &  (v7_ordinal1(B) &  ~ (v8_ordinal1(B)) ) )  =>  ~ (v8_ordinal1(k2_xcmplx_0(A, B))) ) ) ).
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_surreali, axiom,  (! [A, B] :  ( ( (v2_surreal0(A) & v2_surreali(A))  &  (v2_surreal0(B) & v2_surreali(B)) )  => v2_surreali(k14_surrealr(A, B))) ) ).
fof(fc3_surrealr, axiom,  (! [A] :  (v2_surreal0(A) => v2_surreal0(k2_surrealr(A))) ) ).
fof(fc3_xreal_0, axiom,  (! [A] :  (v1_xreal_0(A) =>  (v1_xcmplx_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A))) ) ) ).
fof(fc4_nat_1, axiom,  (! [A, B] :  ( (v7_ordinal1(A) &  (v7_ordinal1(B) &  ~ (v8_ordinal1(B)) ) )  =>  ~ (v8_ordinal1(k2_xcmplx_0(B, 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_relat_1, axiom,  (! [A, B] : v1_relat_1(k1_tarski(k4_tarski(A, B)))) ).
fof(fc5_surreal0, axiom,  (! [A] :  (v2_surreal0(A) => v3_surreal0(k1_tarski(A))) ) ).
fof(fc5_surrealr, axiom,  (! [A] :  (v3_ordinal1(A) =>  ~ (v1_xboole_0(k4_surrealr(A))) ) ) ).
fof(fc5_xboole_0, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(A))  =>  ~ (v1_xboole_0(k2_xboole_0(B, A))) ) ) ).
fof(fc5_xreal_0, axiom,  (! [A, B] :  ( (v1_xreal_0(A) & v1_xreal_0(B))  => v1_xreal_0(k2_xcmplx_0(A, B))) ) ).
fof(fc6_ordinal1, axiom,  ( ~ (v1_xboole_0(k4_ordinal1))  & v3_ordinal1(k4_ordinal1)) ).
fof(fc6_relat_1, axiom,  (! [A, B] : v1_relat_1(k2_zfmisc_1(A, B))) ).
fof(fc6_surreal0, axiom,  (! [A] :  (v2_surreal0(A) => v3_surreal0(k1_xtuple_0(A))) ) ).
fof(fc6_surrealr, axiom,  (! [A, B] :  ( (v2_surreal0(A) & v2_surreal0(B))  => v2_surreal0(k6_surrealr(A, B))) ) ).
fof(fc7_surreal0, axiom,  (! [A] :  (v2_surreal0(A) => v3_surreal0(k2_xtuple_0(A))) ) ).
fof(fc7_xreal_0, axiom,  (! [A, B] :  ( (v1_xreal_0(A) & v1_xreal_0(B))  => v1_xreal_0(k6_xcmplx_0(A, B))) ) ).
fof(fc8_ordinal1, axiom, v7_ordinal1(k5_ordinal1)).
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(fc8_surrealr, axiom,  (! [A, B] :  ( (v2_surreal0(A) & v2_surreal0(B))  => v2_surreal0(k14_surrealr(A, B))) ) ).
fof(fc8_xreal_0, axiom,  (! [A, B] :  ( (v1_xreal_0(A) & v1_xreal_0(B))  => v1_xreal_0(k7_xcmplx_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_ordinal1, axiom, v8_ordinal1(k5_ordinal1)).
fof(fc9_surreal0, axiom,  (! [A, B] :  ( (v3_surreal0(A) & v3_surreal0(B))  => v3_surreal0(k4_xboole_0(A, B))) ) ).
fof(fc9_surrealr, axiom,  (! [A, B, C, D] :  ( (v2_surreal0(A) & v2_surreal0(B))  => v3_surreal0(k15_surrealr(A, B, C, D))) ) ).
fof(fc9_xreal_0, axiom,  (! [A, B] :  ( ( ( ~ (v3_xxreal_0(A))  & v1_xreal_0(A))  &  ( ~ (v3_xxreal_0(B))  & v1_xreal_0(B)) )  =>  ~ (v3_xxreal_0(k2_xcmplx_0(A, B))) ) ) ).
fof(idempotence_k2_xboole_0, axiom,  (! [A, B] : k2_xboole_0(A, A)=A) ).
fof(ie1_surreali, axiom,  (! [A, B, C, D] :  ( (v2_surreal0(A) & v2_surreal0(B))  =>  ( (A=C & B=D)  => k16_surrealr(A, B)=k1_surreali(C, D)) ) ) ).
fof(ie1_surrealr, axiom,  (! [A, B] :  (v2_surreal0(A) =>  (A=B => k2_surrealr(A)=k11_surrealr(B)) ) ) ).
fof(ie2_surrealr, axiom,  (! [A, B, C, D] :  ( (v2_surreal0(A) & v2_surreal0(B))  =>  ( (A=C & B=D)  => k8_surrealr(A, B)=k12_surrealr(C, D)) ) ) ).
fof(involutiveness_k4_xcmplx_0, axiom,  (! [A] :  (v1_xcmplx_0(A) => k4_xcmplx_0(k4_xcmplx_0(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_surreal0, axiom,  (? [A] : v2_surreal0(A)) ).
fof(rc1_surreali, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_xtuple_0(A) &  (v2_surreal0(A) & v2_surreali(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(rc1_xxreal_0, axiom,  (? [A] : v1_xxreal_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_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(rc2_xxreal_0, axiom,  (? [A] : v1_xxreal_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_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(rc3_xxreal_0, axiom,  (? [A] :  (v1_xxreal_0(A) & v2_xxreal_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_xreal_0, axiom,  (? [A] :  (v1_xcmplx_0(A) &  (v1_xxreal_0(A) &  (v3_xxreal_0(A) & v1_xreal_0(A)) ) ) ) ).
fof(rc4_xxreal_0, axiom,  (? [A] :  (v1_xxreal_0(A) & v3_xxreal_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_xreal_0, axiom,  (? [A] :  (v8_ordinal1(A) &  (v1_xcmplx_0(A) &  (v1_xxreal_0(A) & v1_xreal_0(A)) ) ) ) ).
fof(rc5_xxreal_0, axiom,  (? [A] :  (v8_ordinal1(A) & v1_xxreal_0(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(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_surrealr, axiom,  (! [A] :  (v2_surreal0(A) => k2_surrealr(k2_surrealr(A))=A) ) ).
fof(rd1_xtuple_0, axiom,  (! [A, B] : k1_xtuple_0(k4_tarski(A, B))=A) ).
fof(rd2_surrealr, axiom, k2_surrealr(k11_surreal0)=k11_surreal0).
fof(rd2_xtuple_0, axiom,  (! [A, B] : k2_xtuple_0(k4_tarski(A, B))=B) ).
fof(rd3_surrealr, axiom,  (! [A] :  (v2_surreal0(A) => k8_surrealr(A, k11_surreal0)=A) ) ).
fof(rd3_xtuple_0, axiom,  (! [A] :  (v1_xtuple_0(A) => k4_tarski(k1_xtuple_0(A), k2_xtuple_0(A))=A) ) ).
fof(rd4_surrealr, axiom,  (! [A] :  (v2_surreal0(A) => k16_surrealr(A, k11_surreal0)=k11_surreal0) ) ).
fof(rd5_surrealr, axiom,  (! [A] :  (v2_surreal0(A) => k16_surrealr(A, k1_surrealo)=A) ) ).
fof(redefinition_k16_surrealr, axiom,  (! [A, B] :  ( (v2_surreal0(A) & v2_surreal0(B))  => k16_surrealr(A, B)=k14_surrealr(A, B)) ) ).
fof(redefinition_k1_nat_1, axiom,  (! [A, B] :  ( (v7_ordinal1(A) & m1_subset_1(B, k4_ordinal1))  => k1_nat_1(A, B)=k2_xcmplx_0(A, B)) ) ).
fof(redefinition_k1_surreal0, axiom,  (! [A] : k1_surreal0(A)=k1_xtuple_0(A)) ).
fof(redefinition_k2_surreal0, axiom,  (! [A] : k2_surreal0(A)=k2_xtuple_0(A)) ).
fof(redefinition_k5_numbers, axiom, k5_numbers=k5_ordinal1).
fof(redefinition_k6_subset_1, axiom,  (! [A, B] : k6_subset_1(A, B)=k4_xboole_0(A, B)) ).
fof(redefinition_k8_surrealr, axiom,  (! [A, B] :  ( (v2_surreal0(A) & v2_surreal0(B))  => k8_surrealr(A, B)=k6_surrealr(A, B)) ) ).
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(reflexivity_r1_xxreal_0, axiom,  (! [A, B] :  ( (v1_xxreal_0(A) & v1_xxreal_0(B))  => r1_xxreal_0(A, A)) ) ).
fof(reflexivity_r2_surrealo, axiom,  (! [A, B] :  ( (v2_surreal0(A) & v2_surreal0(B))  => r2_surrealo(A, A)) ) ).
fof(rqLessOrEqual__r1_xxreal_0__r0_r0, axiom, r1_xxreal_0(0, 0)).
fof(rqLessOrEqual__r1_xxreal_0__r0_r1, axiom, r1_xxreal_0(0, 1)).
fof(rqLessOrEqual__r1_xxreal_0__r0_r2, axiom, r1_xxreal_0(0, 2)).
fof(rqLessOrEqual__r1_xxreal_0__r0_rm1, axiom,  ~ (r1_xxreal_0(0, k4_xcmplx_0(1))) ).
fof(rqLessOrEqual__r1_xxreal_0__r0_rm2, axiom,  ~ (r1_xxreal_0(0, k4_xcmplx_0(2))) ).
fof(rqLessOrEqual__r1_xxreal_0__r0_rn1d2, axiom, r1_xxreal_0(0, k7_xcmplx_0(1, 2))).
fof(rqLessOrEqual__r1_xxreal_0__r0_rnm1d2, axiom,  ~ (r1_xxreal_0(0, k7_xcmplx_0(k4_xcmplx_0(1), 2))) ).
fof(rqLessOrEqual__r1_xxreal_0__r1_r0, axiom,  ~ (r1_xxreal_0(1, 0)) ).
fof(rqLessOrEqual__r1_xxreal_0__r1_r1, axiom, r1_xxreal_0(1, 1)).
fof(rqLessOrEqual__r1_xxreal_0__r1_r2, axiom, r1_xxreal_0(1, 2)).
fof(rqLessOrEqual__r1_xxreal_0__r1_rm1, axiom,  ~ (r1_xxreal_0(1, k4_xcmplx_0(1))) ).
fof(rqLessOrEqual__r1_xxreal_0__r1_rm2, axiom,  ~ (r1_xxreal_0(1, k4_xcmplx_0(2))) ).
fof(rqLessOrEqual__r1_xxreal_0__r1_rn1d2, axiom,  ~ (r1_xxreal_0(1, k7_xcmplx_0(1, 2))) ).
fof(rqLessOrEqual__r1_xxreal_0__r1_rnm1d2, axiom,  ~ (r1_xxreal_0(1, k7_xcmplx_0(k4_xcmplx_0(1), 2))) ).
fof(rqLessOrEqual__r1_xxreal_0__r2_r0, axiom,  ~ (r1_xxreal_0(2, 0)) ).
fof(rqLessOrEqual__r1_xxreal_0__r2_r1, axiom,  ~ (r1_xxreal_0(2, 1)) ).
fof(rqLessOrEqual__r1_xxreal_0__r2_r2, axiom, r1_xxreal_0(2, 2)).
fof(rqLessOrEqual__r1_xxreal_0__r2_rm1, axiom,  ~ (r1_xxreal_0(2, k4_xcmplx_0(1))) ).
fof(rqLessOrEqual__r1_xxreal_0__r2_rm2, axiom,  ~ (r1_xxreal_0(2, k4_xcmplx_0(2))) ).
fof(rqLessOrEqual__r1_xxreal_0__r2_rn1d2, axiom,  ~ (r1_xxreal_0(2, k7_xcmplx_0(1, 2))) ).
fof(rqLessOrEqual__r1_xxreal_0__r2_rnm1d2, axiom,  ~ (r1_xxreal_0(2, k7_xcmplx_0(k4_xcmplx_0(1), 2))) ).
fof(rqLessOrEqual__r1_xxreal_0__rm1_r0, axiom, r1_xxreal_0(k4_xcmplx_0(1), 0)).
fof(rqLessOrEqual__r1_xxreal_0__rm1_r1, axiom, r1_xxreal_0(k4_xcmplx_0(1), 1)).
fof(rqLessOrEqual__r1_xxreal_0__rm1_r2, axiom, r1_xxreal_0(k4_xcmplx_0(1), 2)).
fof(rqLessOrEqual__r1_xxreal_0__rm1_rm1, axiom, r1_xxreal_0(k4_xcmplx_0(1), k4_xcmplx_0(1))).
fof(rqLessOrEqual__r1_xxreal_0__rm1_rm2, axiom,  ~ (r1_xxreal_0(k4_xcmplx_0(1), k4_xcmplx_0(2))) ).
fof(rqLessOrEqual__r1_xxreal_0__rm1_rn1d2, axiom, r1_xxreal_0(k4_xcmplx_0(1), k7_xcmplx_0(1, 2))).
fof(rqLessOrEqual__r1_xxreal_0__rm1_rnm1d2, axiom, r1_xxreal_0(k4_xcmplx_0(1), k7_xcmplx_0(k4_xcmplx_0(1), 2))).
fof(rqLessOrEqual__r1_xxreal_0__rm2_r0, axiom, r1_xxreal_0(k4_xcmplx_0(2), 0)).
fof(rqLessOrEqual__r1_xxreal_0__rm2_r1, axiom, r1_xxreal_0(k4_xcmplx_0(2), 1)).
fof(rqLessOrEqual__r1_xxreal_0__rm2_r2, axiom, r1_xxreal_0(k4_xcmplx_0(2), 2)).
fof(rqLessOrEqual__r1_xxreal_0__rm2_rm1, axiom, r1_xxreal_0(k4_xcmplx_0(2), k4_xcmplx_0(1))).
fof(rqLessOrEqual__r1_xxreal_0__rm2_rm2, axiom, r1_xxreal_0(k4_xcmplx_0(2), k4_xcmplx_0(2))).
fof(rqLessOrEqual__r1_xxreal_0__rm2_rn1d2, axiom, r1_xxreal_0(k4_xcmplx_0(2), k7_xcmplx_0(1, 2))).
fof(rqLessOrEqual__r1_xxreal_0__rn1d2_r0, axiom,  ~ (r1_xxreal_0(k7_xcmplx_0(1, 2), 0)) ).
fof(rqLessOrEqual__r1_xxreal_0__rn1d2_r1, axiom, r1_xxreal_0(k7_xcmplx_0(1, 2), 1)).
fof(rqLessOrEqual__r1_xxreal_0__rn1d2_r2, axiom, r1_xxreal_0(k7_xcmplx_0(1, 2), 2)).
fof(rqLessOrEqual__r1_xxreal_0__rn1d2_rm1, axiom,  ~ (r1_xxreal_0(k7_xcmplx_0(1, 2), k4_xcmplx_0(1))) ).
fof(rqLessOrEqual__r1_xxreal_0__rn1d2_rm2, axiom,  ~ (r1_xxreal_0(k7_xcmplx_0(1, 2), k4_xcmplx_0(2))) ).
fof(rqLessOrEqual__r1_xxreal_0__rn1d2_rn1d2, axiom, r1_xxreal_0(k7_xcmplx_0(1, 2), k7_xcmplx_0(1, 2))).
fof(rqLessOrEqual__r1_xxreal_0__rn1d2_rnm1d2, axiom,  ~ (r1_xxreal_0(k7_xcmplx_0(1, 2), k7_xcmplx_0(k4_xcmplx_0(1), 2))) ).
fof(rqLessOrEqual__r1_xxreal_0__rnm1d2_r0, axiom, r1_xxreal_0(k7_xcmplx_0(k4_xcmplx_0(1), 2), 0)).
fof(rqLessOrEqual__r1_xxreal_0__rnm1d2_r1, axiom, r1_xxreal_0(k7_xcmplx_0(k4_xcmplx_0(1), 2), 1)).
fof(rqLessOrEqual__r1_xxreal_0__rnm1d2_r2, axiom, r1_xxreal_0(k7_xcmplx_0(k4_xcmplx_0(1), 2), 2)).
fof(rqLessOrEqual__r1_xxreal_0__rnm1d2_rm1, axiom,  ~ (r1_xxreal_0(k7_xcmplx_0(k4_xcmplx_0(1), 2), k4_xcmplx_0(1))) ).
fof(rqLessOrEqual__r1_xxreal_0__rnm1d2_rn1d2, axiom, r1_xxreal_0(k7_xcmplx_0(k4_xcmplx_0(1), 2), k7_xcmplx_0(1, 2))).
fof(rqLessOrEqual__r1_xxreal_0__rnm1d2_rnm1d2, axiom, r1_xxreal_0(k7_xcmplx_0(k4_xcmplx_0(1), 2), k7_xcmplx_0(k4_xcmplx_0(1), 2))).
fof(rqRealAdd__k2_xcmplx_0__r0_r0_r0, axiom, k2_xcmplx_0(0, 0)=0).
fof(rqRealAdd__k2_xcmplx_0__r0_r1_r1, axiom, k2_xcmplx_0(0, 1)=1).
fof(rqRealAdd__k2_xcmplx_0__r0_r2_r2, axiom, k2_xcmplx_0(0, 2)=2).
fof(rqRealAdd__k2_xcmplx_0__r0_rm1_rm1, axiom, k2_xcmplx_0(0, k4_xcmplx_0(1))=k4_xcmplx_0(1)).
fof(rqRealAdd__k2_xcmplx_0__r0_rm2_rm2, axiom, k2_xcmplx_0(0, k4_xcmplx_0(2))=k4_xcmplx_0(2)).
fof(rqRealAdd__k2_xcmplx_0__r0_rn1d2_rn1d2, axiom, k2_xcmplx_0(0, k7_xcmplx_0(1, 2))=k7_xcmplx_0(1, 2)).
fof(rqRealAdd__k2_xcmplx_0__r0_rnm1d2_rnm1d2, axiom, k2_xcmplx_0(0, k7_xcmplx_0(k4_xcmplx_0(1), 2))=k7_xcmplx_0(k4_xcmplx_0(1), 2)).
fof(rqRealAdd__k2_xcmplx_0__r1_r0_r1, axiom, k2_xcmplx_0(1, 0)=1).
fof(rqRealAdd__k2_xcmplx_0__r1_r1_r2, axiom, k2_xcmplx_0(1, 1)=2).
fof(rqRealAdd__k2_xcmplx_0__r1_rm1_r0, axiom, k2_xcmplx_0(1, k4_xcmplx_0(1))=0).
fof(rqRealAdd__k2_xcmplx_0__r1_rm2_rm1, axiom, k2_xcmplx_0(1, k4_xcmplx_0(2))=k4_xcmplx_0(1)).
fof(rqRealAdd__k2_xcmplx_0__r1_rnm1d2_rn1d2, axiom, k2_xcmplx_0(1, k7_xcmplx_0(k4_xcmplx_0(1), 2))=k7_xcmplx_0(1, 2)).
fof(rqRealAdd__k2_xcmplx_0__r2_r0_r2, axiom, k2_xcmplx_0(2, 0)=2).
fof(rqRealAdd__k2_xcmplx_0__r2_rm1_r1, axiom, k2_xcmplx_0(2, k4_xcmplx_0(1))=1).
fof(rqRealAdd__k2_xcmplx_0__r2_rm2_r0, axiom, k2_xcmplx_0(2, k4_xcmplx_0(2))=0).
fof(rqRealAdd__k2_xcmplx_0__rm1_r0_rm1, axiom, k2_xcmplx_0(k4_xcmplx_0(1), 0)=k4_xcmplx_0(1)).
fof(rqRealAdd__k2_xcmplx_0__rm1_r1_r0, axiom, k2_xcmplx_0(k4_xcmplx_0(1), 1)=0).
fof(rqRealAdd__k2_xcmplx_0__rm1_r2_r1, axiom, k2_xcmplx_0(k4_xcmplx_0(1), 2)=1).
fof(rqRealAdd__k2_xcmplx_0__rm1_rm1_rm2, axiom, k2_xcmplx_0(k4_xcmplx_0(1), k4_xcmplx_0(1))=k4_xcmplx_0(2)).
fof(rqRealAdd__k2_xcmplx_0__rm1_rn1d2_rnm1d2, axiom, k2_xcmplx_0(k4_xcmplx_0(1), k7_xcmplx_0(1, 2))=k7_xcmplx_0(k4_xcmplx_0(1), 2)).
fof(rqRealAdd__k2_xcmplx_0__rm2_r0_rm2, axiom, k2_xcmplx_0(k4_xcmplx_0(2), 0)=k4_xcmplx_0(2)).
fof(rqRealAdd__k2_xcmplx_0__rm2_r1_rm1, axiom, k2_xcmplx_0(k4_xcmplx_0(2), 1)=k4_xcmplx_0(1)).
fof(rqRealAdd__k2_xcmplx_0__rm2_r2_r0, axiom, k2_xcmplx_0(k4_xcmplx_0(2), 2)=0).
fof(rqRealAdd__k2_xcmplx_0__rn1d2_r0_rn1d2, axiom, k2_xcmplx_0(k7_xcmplx_0(1, 2), 0)=k7_xcmplx_0(1, 2)).
fof(rqRealAdd__k2_xcmplx_0__rn1d2_rm1_rnm1d2, axiom, k2_xcmplx_0(k7_xcmplx_0(1, 2), k4_xcmplx_0(1))=k7_xcmplx_0(k4_xcmplx_0(1), 2)).
fof(rqRealAdd__k2_xcmplx_0__rn1d2_rn1d2_r1, axiom, k2_xcmplx_0(k7_xcmplx_0(1, 2), k7_xcmplx_0(1, 2))=1).
fof(rqRealAdd__k2_xcmplx_0__rn1d2_rnm1d2_r0, axiom, k2_xcmplx_0(k7_xcmplx_0(1, 2), k7_xcmplx_0(k4_xcmplx_0(1), 2))=0).
fof(rqRealAdd__k2_xcmplx_0__rnm1d2_r0_rnm1d2, axiom, k2_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1), 2), 0)=k7_xcmplx_0(k4_xcmplx_0(1), 2)).
fof(rqRealAdd__k2_xcmplx_0__rnm1d2_r1_rn1d2, axiom, k2_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1), 2), 1)=k7_xcmplx_0(1, 2)).
fof(rqRealAdd__k2_xcmplx_0__rnm1d2_rn1d2_r0, axiom, k2_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1), 2), k7_xcmplx_0(1, 2))=0).
fof(rqRealAdd__k2_xcmplx_0__rnm1d2_rnm1d2_rm1, axiom, k2_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1), 2), k7_xcmplx_0(k4_xcmplx_0(1), 2))=k4_xcmplx_0(1)).
fof(rqRealDiff__k6_xcmplx_0__r0_r0_r0, axiom, k6_xcmplx_0(0, 0)=0).
fof(rqRealDiff__k6_xcmplx_0__r0_r1_rm1, axiom, k6_xcmplx_0(0, 1)=k4_xcmplx_0(1)).
fof(rqRealDiff__k6_xcmplx_0__r0_r2_rm2, axiom, k6_xcmplx_0(0, 2)=k4_xcmplx_0(2)).
fof(rqRealDiff__k6_xcmplx_0__r0_rm1_r1, axiom, k6_xcmplx_0(0, k4_xcmplx_0(1))=1).
fof(rqRealDiff__k6_xcmplx_0__r0_rm2_r2, axiom, k6_xcmplx_0(0, k4_xcmplx_0(2))=2).
fof(rqRealDiff__k6_xcmplx_0__r0_rn1d2_rnm1d2, axiom, k6_xcmplx_0(0, k7_xcmplx_0(1, 2))=k7_xcmplx_0(k4_xcmplx_0(1), 2)).
fof(rqRealDiff__k6_xcmplx_0__r0_rnm1d2_rn1d2, axiom, k6_xcmplx_0(0, k7_xcmplx_0(k4_xcmplx_0(1), 2))=k7_xcmplx_0(1, 2)).
fof(rqRealDiff__k6_xcmplx_0__r1_r0_r1, axiom, k6_xcmplx_0(1, 0)=1).
fof(rqRealDiff__k6_xcmplx_0__r1_r1_r0, axiom, k6_xcmplx_0(1, 1)=0).
fof(rqRealDiff__k6_xcmplx_0__r1_r2_rm1, axiom, k6_xcmplx_0(1, 2)=k4_xcmplx_0(1)).
fof(rqRealDiff__k6_xcmplx_0__r1_rm1_r2, axiom, k6_xcmplx_0(1, k4_xcmplx_0(1))=2).
fof(rqRealDiff__k6_xcmplx_0__r1_rn1d2_rn1d2, axiom, k6_xcmplx_0(1, k7_xcmplx_0(1, 2))=k7_xcmplx_0(1, 2)).
fof(rqRealDiff__k6_xcmplx_0__r2_r0_r2, axiom, k6_xcmplx_0(2, 0)=2).
fof(rqRealDiff__k6_xcmplx_0__r2_r1_r1, axiom, k6_xcmplx_0(2, 1)=1).
fof(rqRealDiff__k6_xcmplx_0__r2_r2_r0, axiom, k6_xcmplx_0(2, 2)=0).
fof(rqRealDiff__k6_xcmplx_0__rm1_r0_rm1, axiom, k6_xcmplx_0(k4_xcmplx_0(1), 0)=k4_xcmplx_0(1)).
fof(rqRealDiff__k6_xcmplx_0__rm1_r1_rm2, axiom, k6_xcmplx_0(k4_xcmplx_0(1), 1)=k4_xcmplx_0(2)).
fof(rqRealDiff__k6_xcmplx_0__rm1_rm1_r0, axiom, k6_xcmplx_0(k4_xcmplx_0(1), k4_xcmplx_0(1))=0).
fof(rqRealDiff__k6_xcmplx_0__rm1_rm2_r1, axiom, k6_xcmplx_0(k4_xcmplx_0(1), k4_xcmplx_0(2))=1).
fof(rqRealDiff__k6_xcmplx_0__rm1_rnm1d2_rnm1d2, axiom, k6_xcmplx_0(k4_xcmplx_0(1), k7_xcmplx_0(k4_xcmplx_0(1), 2))=k7_xcmplx_0(k4_xcmplx_0(1), 2)).
fof(rqRealDiff__k6_xcmplx_0__rm2_r0_rm2, axiom, k6_xcmplx_0(k4_xcmplx_0(2), 0)=k4_xcmplx_0(2)).
fof(rqRealDiff__k6_xcmplx_0__rm2_rm1_rm1, axiom, k6_xcmplx_0(k4_xcmplx_0(2), k4_xcmplx_0(1))=k4_xcmplx_0(1)).
fof(rqRealDiff__k6_xcmplx_0__rm2_rm2_r0, axiom, k6_xcmplx_0(k4_xcmplx_0(2), k4_xcmplx_0(2))=0).
fof(rqRealDiff__k6_xcmplx_0__rn1d2_r0_rn1d2, axiom, k6_xcmplx_0(k7_xcmplx_0(1, 2), 0)=k7_xcmplx_0(1, 2)).
fof(rqRealDiff__k6_xcmplx_0__rn1d2_r1_rnm1d2, axiom, k6_xcmplx_0(k7_xcmplx_0(1, 2), 1)=k7_xcmplx_0(k4_xcmplx_0(1), 2)).
fof(rqRealDiff__k6_xcmplx_0__rn1d2_rn1d2_r0, axiom, k6_xcmplx_0(k7_xcmplx_0(1, 2), k7_xcmplx_0(1, 2))=0).
fof(rqRealDiff__k6_xcmplx_0__rn1d2_rnm1d2_r1, axiom, k6_xcmplx_0(k7_xcmplx_0(1, 2), k7_xcmplx_0(k4_xcmplx_0(1), 2))=1).
fof(rqRealDiff__k6_xcmplx_0__rnm1d2_r0_rnm1d2, axiom, k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1), 2), 0)=k7_xcmplx_0(k4_xcmplx_0(1), 2)).
fof(rqRealDiff__k6_xcmplx_0__rnm1d2_rm1_rn1d2, axiom, k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1), 2), k4_xcmplx_0(1))=k7_xcmplx_0(1, 2)).
fof(rqRealDiff__k6_xcmplx_0__rnm1d2_rn1d2_rm1, axiom, k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1), 2), k7_xcmplx_0(1, 2))=k4_xcmplx_0(1)).
fof(rqRealDiff__k6_xcmplx_0__rnm1d2_rnm1d2_r0, axiom, k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1), 2), k7_xcmplx_0(k4_xcmplx_0(1), 2))=0).
fof(rqRealDiv__k7_xcmplx_0__r1_r1_r1, axiom, k7_xcmplx_0(1, 1)=1).
fof(rqRealDiv__k7_xcmplx_0__r1_r2_rn1d2, axiom, k7_xcmplx_0(1, 2)=k7_xcmplx_0(1, 2)).
fof(rqRealDiv__k7_xcmplx_0__r1_rm1_rm1, axiom, k7_xcmplx_0(1, k4_xcmplx_0(1))=k4_xcmplx_0(1)).
fof(rqRealDiv__k7_xcmplx_0__r1_rm2_rnm1d2, axiom, k7_xcmplx_0(1, k4_xcmplx_0(2))=k7_xcmplx_0(k4_xcmplx_0(1), 2)).
fof(rqRealDiv__k7_xcmplx_0__r1_rn1d2_r2, axiom, k7_xcmplx_0(1, k7_xcmplx_0(1, 2))=2).
fof(rqRealDiv__k7_xcmplx_0__r1_rnm1d2_rm2, axiom, k7_xcmplx_0(1, k7_xcmplx_0(k4_xcmplx_0(1), 2))=k4_xcmplx_0(2)).
fof(rqRealDiv__k7_xcmplx_0__r2_r1_r2, axiom, k7_xcmplx_0(2, 1)=2).
fof(rqRealDiv__k7_xcmplx_0__r2_r2_r1, axiom, k7_xcmplx_0(2, 2)=1).
fof(rqRealDiv__k7_xcmplx_0__rm1_r1_rm1, axiom, k7_xcmplx_0(k4_xcmplx_0(1), 1)=k4_xcmplx_0(1)).
fof(rqRealDiv__k7_xcmplx_0__rm1_r2_rnm1d2, axiom, k7_xcmplx_0(k4_xcmplx_0(1), 2)=k7_xcmplx_0(k4_xcmplx_0(1), 2)).
fof(rqRealDiv__k7_xcmplx_0__rm2_r2_rm1, axiom, k7_xcmplx_0(k4_xcmplx_0(2), 2)=k4_xcmplx_0(1)).
fof(rqRealNeg__k4_xcmplx_0__r0_r0, axiom, k4_xcmplx_0(0)=0).
fof(rqRealNeg__k4_xcmplx_0__r1_rm1, axiom, k4_xcmplx_0(1)=k4_xcmplx_0(1)).
fof(rqRealNeg__k4_xcmplx_0__r2_rm2, axiom, k4_xcmplx_0(2)=k4_xcmplx_0(2)).
fof(rqRealNeg__k4_xcmplx_0__rm1_r1, axiom, k4_xcmplx_0(k4_xcmplx_0(1))=1).
fof(rqRealNeg__k4_xcmplx_0__rm2_r2, axiom, k4_xcmplx_0(k4_xcmplx_0(2))=2).
fof(rqRealNeg__k4_xcmplx_0__rn1d2_rnm1d2, axiom, k4_xcmplx_0(k7_xcmplx_0(1, 2))=k7_xcmplx_0(k4_xcmplx_0(1), 2)).
fof(rqRealNeg__k4_xcmplx_0__rnm1d2_rn1d2, axiom, k4_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1), 2))=k7_xcmplx_0(1, 2)).
fof(s2_nat_1__e8_48_1__surreali, axiom,  (! [A] :  (v2_surreal0(A) =>  ( ( ( (! [B] :  (v2_surreal0(B) =>  ~ ( (r2_tarski(B, k1_funct_1(k5_surreali(k7_surreali(A), k11_surreali(k7_surreali(A))), k5_numbers)) & r5_surreal0(k1_surrealo, k16_surrealr(k7_surreali(A), B))) ) ) )  &  (! [B] :  (v2_surreal0(B) =>  ~ ( (r2_tarski(B, k1_funct_1(k6_surreali(k7_surreali(A), k11_surreali(k7_surreali(A))), k5_numbers)) & r5_surreal0(k16_surrealr(k7_surreali(A), B), k1_surrealo)) ) ) ) )  &  (! [C] :  (v7_ordinal1(C) =>  ( ( (! [D] :  (v2_surreal0(D) =>  ~ ( (r2_tarski(D, k1_funct_1(k5_surreali(k7_surreali(A), k11_surreali(k7_surreali(A))), C)) & r5_surreal0(k1_surrealo, k16_surrealr(k7_surreali(A), D))) ) ) )  &  (! [D] :  (v2_surreal0(D) =>  ~ ( (r2_tarski(D, k1_funct_1(k6_surreali(k7_surreali(A), k11_surreali(k7_surreali(A))), C)) & r5_surreal0(k16_surrealr(k7_surreali(A), D), k1_surrealo)) ) ) ) )  =>  ( (! [E] :  (v2_surreal0(E) =>  ~ ( (r2_tarski(E, k1_funct_1(k5_surreali(k7_surreali(A), k11_surreali(k7_surreali(A))), k1_nat_1(C, 1))) & r5_surreal0(k1_surrealo, k16_surrealr(k7_surreali(A), E))) ) ) )  &  (! [E] :  (v2_surreal0(E) =>  ~ ( (r2_tarski(E, k1_funct_1(k6_surreali(k7_surreali(A), k11_surreali(k7_surreali(A))), k1_nat_1(C, 1))) & r5_surreal0(k16_surrealr(k7_surreali(A), E), k1_surrealo)) ) ) ) ) ) ) ) )  =>  (! [C] :  (v7_ordinal1(C) =>  ( (! [F] :  (v2_surreal0(F) =>  ~ ( (r2_tarski(F, k1_funct_1(k5_surreali(k7_surreali(A), k11_surreali(k7_surreali(A))), C)) & r5_surreal0(k1_surrealo, k16_surrealr(k7_surreali(A), F))) ) ) )  &  (! [F] :  (v2_surreal0(F) =>  ~ ( (r2_tarski(F, k1_funct_1(k6_surreali(k7_surreali(A), k11_surreali(k7_surreali(A))), C)) & r5_surreal0(k16_surrealr(k7_surreali(A), F), k1_surrealo)) ) ) ) ) ) ) ) ) ) ).
fof(s2_ordinal1__e2_48__surreali, axiom,  ( (! [A] :  (v3_ordinal1(A) =>  ( (! [B] :  (v3_ordinal1(B) =>  (r2_tarski(B, A) =>  (! [C] :  (v2_surreal0(C) =>  ( (k12_surreal0(C)=B & v2_surreali(C))  =>  (v2_surreal0(k10_surreali(C)) &  (! [D] :  (v2_surreal0(D) =>  (D=k10_surreali(C) => r2_surrealo(k16_surrealr(C, D), k1_surrealo)) ) ) ) ) ) ) ) ) )  =>  (! [E] :  (v2_surreal0(E) =>  ( (k12_surreal0(E)=A & v2_surreali(E))  =>  (v2_surreal0(k10_surreali(E)) &  (! [F] :  (v2_surreal0(F) =>  (F=k10_surreali(E) => r2_surrealo(k16_surrealr(E, F), k1_surrealo)) ) ) ) ) ) ) ) ) )  =>  (! [A] :  (v3_ordinal1(A) =>  (! [G] :  (v2_surreal0(G) =>  ( (k12_surreal0(G)=A & v2_surreali(G))  =>  (v2_surreal0(k10_surreali(G)) &  (! [H] :  (v2_surreal0(H) =>  (H=k10_surreali(G) => r2_surrealo(k16_surrealr(G, H), k1_surrealo)) ) ) ) ) ) ) ) ) ) ).
fof(spc0_boole, axiom, v1_xboole_0(0)).
fof(spc0_numerals, axiom, m1_subset_1(0, k4_ordinal1)).
fof(spc1_arithm, axiom,  (! [A, B] :  ( (v1_xcmplx_0(A) & v1_xcmplx_0(B))  => k2_xcmplx_0(A, k4_xcmplx_0(B))=k6_xcmplx_0(A, B)) ) ).
fof(spc1_boole, axiom,  ~ (v1_xboole_0(1)) ).
fof(spc1_numerals, axiom,  (v2_xxreal_0(1) & m1_subset_1(1, k4_ordinal1)) ).
fof(spc2_boole, axiom,  ~ (v1_xboole_0(2)) ).
fof(spc2_numerals, axiom,  (v2_xxreal_0(2) & m1_subset_1(2, k4_ordinal1)) ).
fof(spc6_arithm, axiom,  (! [A, B, C] :  ( (v1_xcmplx_0(A) &  (v1_xcmplx_0(B) & v1_xcmplx_0(C)) )  => k2_xcmplx_0(k2_xcmplx_0(A, B), C)=k2_xcmplx_0(A, k2_xcmplx_0(B, C))) ) ).
fof(spc8_arithm, axiom,  (! [A, B] :  ( (v1_xcmplx_0(A) & v1_xcmplx_0(B))  => k2_xcmplx_0(k4_xcmplx_0(A), k4_xcmplx_0(B))=k4_xcmplx_0(k2_xcmplx_0(A, B))) ) ).
fof(spc9_arithm, axiom,  (! [A, B] :  ( (v1_xcmplx_0(A) & v1_xcmplx_0(B))  => k6_xcmplx_0(k4_xcmplx_0(A), k4_xcmplx_0(B))=k6_xcmplx_0(B, A)) ) ).
fof(symmetry_r2_surrealo, axiom,  (! [A, B] :  ( (v2_surreal0(A) & v2_surreal0(B))  =>  (r2_surrealo(A, B) => r2_surrealo(B, A)) ) ) ).
fof(t10_surreali, axiom,  (! [A] :  (v2_surreal0(A) =>  (! [B] :  ( (v1_relat_1(B) & v1_funct_1(B))  =>  (v1_surreali(B, k6_subset_1(k2_xboole_0(k1_surreal0(A), k2_surreal0(A)), k1_tarski(k11_surreal0))) =>  (v3_surreal0(k3_card_3(k5_surreali(A, B))) & v3_surreal0(k3_card_3(k6_surreali(A, B)))) ) ) ) ) ) ).
fof(t11_surrealo, axiom,  (! [A] :  (v2_surreal0(A) =>  (r7_surreal0(k1_surreal0(A), k1_tarski(A)) & r7_surreal0(k1_tarski(A), k2_surreal0(A))) ) ) ).
fof(t12_surreali, axiom,  (! [A] :  (v2_surreal0(A) =>  (! [B] :  ( (v1_relat_1(B) & v1_funct_1(B))  => k3_card_3(k5_surreali(A, B))=k2_xboole_0(k2_xboole_0(k1_tarski(k11_surreal0), k3_surreali(k3_card_3(k5_surreali(A, B)), A, k2_surreal0(A), B)), k3_surreali(k3_card_3(k6_surreali(A, B)), A, k1_surreal0(A), B))) ) ) ) ).
fof(t13_nat_1, axiom,  (! [A] :  (v7_ordinal1(A) =>  (! [B] :  (v7_ordinal1(B) =>  ( ~ (r1_xxreal_0(k1_nat_1(B, 1), A))  <=> r1_xxreal_0(A, B)) ) ) ) ) ).
fof(t14_surrealo, axiom,  (! [A] :  (v2_surreal0(A) =>  (! [B] :  (v2_surreal0(B) =>  ( (r7_surreal0(k1_surreal0(B), k1_tarski(A)) & r7_surreal0(k1_tarski(A), k2_surreal0(B)))  => v2_surreal0(k4_tarski(k2_xboole_0(k1_surreal0(A), k1_surreal0(B)), k2_xboole_0(k2_surreal0(A), k2_surreal0(B))))) ) ) ) ) ).
fof(t15_surrealo, axiom,  (! [A] :  (v2_surreal0(A) =>  (! [B] :  (v2_surreal0(B) =>  (! [C] :  (v2_surreal0(C) =>  ( (r7_surreal0(k1_surreal0(B), k1_tarski(A)) &  (r7_surreal0(k1_tarski(A), k2_surreal0(B)) & C=k4_tarski(k2_xboole_0(k1_surreal0(A), k1_surreal0(B)), k2_xboole_0(k2_surreal0(A), k2_surreal0(B)))) )  => r2_surrealo(A, C)) ) ) ) ) ) ) ).
fof(t18_surreali, axiom,  (! [A] :  (v2_surreal0(A) =>  (v2_surreali(A) => r2_surrealo(A, k7_surreali(A))) ) ) ).
fof(t1_abcmiz_1, axiom,  (! [A] :  (! [B] :  ( (v1_relat_1(B) & v1_funct_1(B))  => r1_tarski(k1_funct_1(B, A), k3_card_3(B))) ) ) ).
fof(t1_arithm, axiom,  (! [A] :  (v1_xcmplx_0(A) => k2_xcmplx_0(A, k5_numbers)=A) ) ).
fof(t1_boole, axiom,  (! [A] : k2_xboole_0(A, k1_xboole_0)=A) ).
fof(t1_numerals, axiom, m1_subset_1(k1_xboole_0, k4_ordinal1)).
fof(t1_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  ( (r1_xxreal_0(A, B) & v2_xxreal_0(A))  => v2_xxreal_0(B)) ) ) ) ) ).
fof(t1_subset, axiom,  (! [A] :  (! [B] :  (r2_tarski(A, B) => m1_subset_1(A, B)) ) ) ).
fof(t1_surreali, axiom,  (! [A] :  (! [B] :  ( (v1_relat_1(B) & v1_funct_1(B))  =>  (k1_funct_1(k5_surreali(A, B), k5_numbers)=k1_tarski(k11_surreal0) & k1_funct_1(k6_surreali(A, B), k5_numbers)=k1_xboole_0) ) ) ) ).
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(t20_nat_1, axiom,  (! [A] :  (v7_ordinal1(A) =>  (! [B] :  (v7_ordinal1(B) =>  ( ~ (r1_xxreal_0(B, A))  => m1_subset_1(k6_xcmplx_0(B, 1), k4_ordinal1)) ) ) ) ) ).
fof(t20_surreali, axiom,  (! [A] :  (v2_surreal0(A) =>  (v2_surreali(A) => r1_tarski(k6_subset_1(k2_xboole_0(k1_surreal0(k7_surreali(A)), k2_surreal0(k7_surreali(A))), k1_tarski(k11_surreal0)), k2_xboole_0(k1_surreal0(A), k2_surreal0(A)))) ) ) ).
fof(t21_surreali, axiom,  (! [A] :  (v2_surreal0(A) =>  (! [B] :  (v2_surreal0(B) =>  ( (v2_surreali(A) & r2_tarski(B, k6_subset_1(k2_xboole_0(k1_surreal0(k7_surreali(A)), k2_surreal0(k7_surreali(A))), k1_tarski(k11_surreal0))))  => v2_surreali(B)) ) ) ) ) ).
fof(t22_surreali, axiom,  (! [A] :  (v2_surreal0(A) =>  (v2_surreali(A) => r1_ordinal1(k12_surreal0(k7_surreali(A)), k12_surreal0(A))) ) ) ).
fof(t23_surrealr, axiom, k2_surrealr(k11_surreal0)=k11_surreal0).
fof(t26_surreali, axiom,  (! [A] :  (v2_surreal0(A) =>  (! [B] :  ( (v1_relat_1(B) & v1_funct_1(B))  =>  ( (v2_surreali(A) & r1_tarski(k11_surreali(k7_surreali(A)), B))  => k10_surreali(A)=k4_tarski(k3_card_3(k5_surreali(k7_surreali(A), B)), k3_card_3(k6_surreali(k7_surreali(A), B)))) ) ) ) ) ).
fof(t27_surreali, axiom,  (! [A] :  (v2_surreal0(A) =>  (! [B] :  ( (v1_relat_1(B) & v1_funct_1(B))  =>  ~ ( (k9_xtuple_0(B)=k4_ordinal1 &  (r2_tarski(A, k3_card_3(B)) &  (! [C] :  (v7_ordinal1(C) =>  ~ ( (r2_tarski(A, k1_funct_1(B, C)) &  (! [D] :  (v7_ordinal1(D) =>  (r2_tarski(A, k1_funct_1(B, D)) => r1_xxreal_0(C, D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t28_surreali, axiom,  (! [A] :  (v2_surreal0(A) =>  (! [B] :  (v2_surreal0(B) =>  (! [C] :  (v2_surreal0(C) =>  (! [D] :  (v2_surreal0(D) =>  (! [E] :  (v2_surreal0(E) =>  (! [F] :  (v2_surreal0(F) =>  ~ ( ( ~ (r5_surreal0(C, k11_surreal0))  &  (r2_surrealo(k16_surrealr(C, D), k1_surrealo) &  ( ~ (r5_surreal0(E, k11_surreal0))  &  (r2_surrealo(k16_surrealr(E, F), k1_surrealo) &  ( ~ (r5_surreal0(k16_surrealr(B, C), k16_surrealr(A, E)))  & r5_surreal0(k16_surrealr(B, F), k16_surrealr(A, D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t29_surreali, axiom,  (! [A] :  (v2_surreal0(A) =>  (! [B] :  (v2_surreal0(B) =>  (! [C] :  (v2_surreal0(C) =>  (! [D] :  (v2_surreal0(D) =>  (! [E] :  (v2_surreal0(E) =>  (r2_surrealo(k8_surrealr(k16_surrealr(k8_surrealr(k1_surrealo, k16_surrealr(k10_surrealr(C, A), E)), B), k2_surrealr(k16_surrealr(k8_surrealr(k1_surrealo, k16_surrealr(k10_surrealr(B, A), D)), C))), k8_surrealr(k16_surrealr(k10_surrealr(B, C), k10_surrealr(k1_surrealo, k16_surrealr(A, D))), k16_surrealr(k16_surrealr(k10_surrealr(D, E), B), k10_surrealr(A, C)))) & r2_surrealo(k10_surrealr(k16_surrealr(k8_surrealr(k1_surrealo, k16_surrealr(k10_surrealr(C, A), E)), B), k16_surrealr(k8_surrealr(k1_surrealo, k16_surrealr(k10_surrealr(B, A), D)), C)), k8_surrealr(k16_surrealr(k10_surrealr(B, C), k10_surrealr(k1_surrealo, k16_surrealr(A, E))), k16_surrealr(k16_surrealr(k10_surrealr(E, D), C), k10_surrealr(B, A))))) ) ) ) ) ) ) ) ) ) ) ).
fof(t2_card_5, axiom,  (! [A] :  (! [B] :  ( (v1_relat_1(B) & v1_funct_1(B))  =>  (r2_hidden(A, k3_card_3(B)) <=>  (? [C] :  (r2_hidden(C, k9_xtuple_0(B)) & r2_hidden(A, k1_funct_1(B, C))) ) ) ) ) ) ).
fof(t2_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  ( (r1_xxreal_0(A, B) & v3_xxreal_0(B))  => v3_xxreal_0(A)) ) ) ) ) ).
fof(t2_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, B) =>  (v1_xboole_0(B) | r2_tarski(A, B)) ) ) ) ).
fof(t30_surreali, axiom,  (! [A] :  (v2_surreal0(A) =>  (! [B] :  (v2_surreal0(B) =>  (! [C] :  (v2_surreal0(C) =>  (! [D] :  (v2_surreal0(D) =>  (! [E] :  (v2_surreal0(E) =>  (r2_surrealo(k16_surrealr(C, E), k1_surrealo) => r2_surrealo(k10_surrealr(k8_surrealr(k16_surrealr(C, B), k16_surrealr(A, D)), k16_surrealr(C, D)), k8_surrealr(k1_surrealo, k16_surrealr(C, k10_surrealr(B, k16_surrealr(k8_surrealr(k1_surrealo, k16_surrealr(k10_surrealr(C, A), D)), E)))))) ) ) ) ) ) ) ) ) ) ) ).
fof(t32_surrealr, axiom,  (! [A] :  (v2_surreal0(A) =>  (! [B] :  (v2_surreal0(B) =>  (! [C] :  (v2_surreal0(C) =>  (r1_surrealo(A, B) <=> r1_surrealo(k8_surrealr(A, C), k8_surrealr(B, C))) ) ) ) ) ) ) ).
fof(t37_surrealr, axiom,  (! [A] :  (v2_surreal0(A) =>  (! [B] :  (v2_surreal0(B) =>  (! [C] :  (v2_surreal0(C) => k8_surrealr(k8_surrealr(A, B), C)=k8_surrealr(A, k8_surrealr(B, C))) ) ) ) ) ) ).
fof(t39_surrealr, axiom,  (! [A] :  (v2_surreal0(A) => r2_surrealo(k10_surrealr(A, A), k11_surreal0)) ) ).
fof(t3_boole, axiom,  (! [A] : k4_xboole_0(A, k1_xboole_0)=A) ).
fof(t3_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  ~ ( (r1_xxreal_0(A, B) &  ( ~ (v3_xxreal_0(A))  & v3_xxreal_0(B)) ) ) ) ) ) ) ).
fof(t3_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) ) ) ).
fof(t40_zfmisc_1, axiom,  (! [A] :  (! [B] :  (r2_hidden(A, B) => k2_xboole_0(k1_tarski(A), B)=B) ) ) ).
fof(t43_surrealr, axiom,  (! [A] :  (v2_surreal0(A) =>  (! [B] :  (v2_surreal0(B) =>  (! [C] :  (v2_surreal0(C) =>  (! [D] :  (v2_surreal0(D) =>  ( (r1_surrealo(A, B) & r1_surrealo(C, D))  => r1_surrealo(k8_surrealr(A, C), k8_surrealr(B, D))) ) ) ) ) ) ) ) ) ).
fof(t44_surrealr, axiom,  (! [A] :  (v2_surreal0(A) =>  (! [B] :  (v2_surreal0(B) =>  (! [C] :  (v2_surreal0(C) =>  (! [D] :  (v2_surreal0(D) =>  ~ ( (r1_surrealo(A, B) &  ( ~ (r5_surreal0(D, C))  & r5_surreal0(k8_surrealr(B, D), k8_surrealr(A, C))) ) ) ) ) ) ) ) ) ) ) ).
fof(t45_surreal0, axiom,  (! [A] :  (v2_surreal0(A) => r7_surreal0(k1_surreal0(A), k2_surreal0(A))) ) ).
fof(t45_surrealr, axiom,  (! [A] :  (v2_surreal0(A) =>  (! [B] :  (v2_surreal0(B) =>  ( ~ ( ( ~ (r5_surreal0(B, A))  & r5_surreal0(k10_surrealr(B, A), k11_surreal0)) )  &  ~ ( ( ~ (r5_surreal0(k10_surrealr(B, A), k11_surreal0))  & r5_surreal0(B, A)) ) ) ) ) ) ) ).
fof(t46_surreal0, axiom,  (! [A] :  (! [B] :  (! [C] :  (v3_ordinal1(C) =>  (r2_hidden(k4_tarski(A, B), k10_surreal0(C)) <=>  (r7_surreal0(A, B) &  (! [D] :  ~ ( (r2_hidden(D, k2_xboole_0(A, B)) &  (! [E] :  (v3_ordinal1(E) =>  ~ ( (r2_tarski(E, C) & r2_hidden(D, k10_surreal0(E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t46_surrealr, axiom,  (! [A] :  (v2_surreal0(A) =>  (! [B] :  (v2_surreal0(B) =>  ( ~ ( ( ~ (r5_surreal0(B, A))  & r5_surreal0(k11_surreal0, k10_surrealr(A, B))) )  &  ~ ( ( ~ (r5_surreal0(k11_surreal0, k10_surrealr(A, B)))  & r5_surreal0(B, A)) ) ) ) ) ) ) ).
fof(t47_surreal0, axiom,  (! [A] :  ~ ( (v3_surreal0(A) &  (! [B] :  (v3_ordinal1(B) =>  (? [C] :  (r2_hidden(C, A) &  (! [D] :  (v3_ordinal1(D) =>  ~ ( (r2_tarski(D, B) & r2_hidden(C, k10_surreal0(D))) ) ) ) ) ) ) ) ) ) ) ).
fof(t4_arithm, axiom,  (! [A] :  (v1_xcmplx_0(A) => k6_xcmplx_0(A, k5_numbers)=A) ) ).
fof(t4_boole, axiom,  (! [A] : k4_xboole_0(k1_xboole_0, A)=k1_xboole_0) ).
fof(t4_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  ~ ( (r1_xxreal_0(A, B) &  ( ~ (v2_xxreal_0(B))  & v2_xxreal_0(A)) ) ) ) ) ) ) ).
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(t4_surrealo, axiom,  (! [A] :  (v2_surreal0(A) =>  (! [B] :  (v2_surreal0(B) =>  (! [C] :  (v2_surreal0(C) =>  ( (r5_surreal0(A, B) & r5_surreal0(B, C))  => r5_surreal0(A, C)) ) ) ) ) ) ) ).
fof(t50_surrealr, axiom,  (! [A] :  (v2_surreal0(A) =>  (! [B] :  (v2_surreal0(B) => k14_surrealr(A, B)=k4_tarski(k2_xboole_0(k15_surrealr(A, B, k1_surreal0(A), k1_surreal0(B)), k15_surrealr(A, B, k2_surreal0(A), k2_surreal0(B))), k2_xboole_0(k15_surrealr(A, B, k1_surreal0(A), k2_surreal0(B)), k15_surrealr(A, B, k2_surreal0(A), k1_surreal0(B))))) ) ) ) ).
fof(t51_surrealr, axiom,  ( (! [A] :  (v2_surreal0(A) =>  (! [B] :  (v2_surreal0(B) => v2_surreal0(k14_surrealr(A, B))) ) ) )  &  ( (! [A] :  (v2_surreal0(A) =>  (! [B] :  (v2_surreal0(B) => k14_surrealr(A, B)=k14_surrealr(B, A)) ) ) )  &  ( (! [A] :  (v2_surreal0(A) =>  (! [B] :  (v2_surreal0(B) =>  (! [C] :  (v2_surreal0(C) =>  (! [D] :  (v2_surreal0(D) =>  (! [E] :  (v2_surreal0(E) =>  ( (r2_surrealo(A, B) &  (D=k14_surrealr(A, C) & E=k14_surrealr(B, C)) )  => r2_surrealo(D, E)) ) ) ) ) ) ) ) ) ) )  &  (! [A] :  (v2_surreal0(A) =>  (! [B] :  (v2_surreal0(B) =>  (! [C] :  (v2_surreal0(C) =>  (! [D] :  (v2_surreal0(D) =>  (! [E] :  (v2_surreal0(E) =>  (! [F] :  (v2_surreal0(F) =>  (! [G] :  (v2_surreal0(G) =>  (! [H] :  (v2_surreal0(H) =>  ~ ( (G=k14_surrealr(A, C) &  (E=k14_surrealr(A, D) &  (F=k14_surrealr(B, C) &  (H=k14_surrealr(B, D) &  ( ~ (r5_surreal0(B, A))  &  ( ~ (r5_surreal0(D, C))  & r5_surreal0(k8_surrealr(G, H), k8_surrealr(E, F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t56_zfmisc_1, axiom,  (! [A] :  (! [B] :  (! [C] :  (r2_hidden(B, k4_xboole_0(C, k1_tarski(A))) <=>  (r2_hidden(B, C) &  ~ (B=A) ) ) ) ) ) ).
fof(t58_surrealr, axiom,  (! [A] :  (v2_surreal0(A) =>  (! [B] :  (v2_surreal0(B) =>  (k16_surrealr(A, k2_surrealr(B))=k2_surrealr(k16_surrealr(A, B)) &  (k16_surrealr(k2_surrealr(A), B)=k2_surrealr(k16_surrealr(A, B)) & k16_surrealr(k2_surrealr(A), k2_surrealr(B))=k16_surrealr(A, B)) ) ) ) ) ) ).
fof(t5_arithm, axiom,  (! [A] :  (v1_xcmplx_0(A) => k7_xcmplx_0(k5_numbers, A)=k5_numbers) ) ).
fof(t5_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  (r1_xxreal_0(A, B) =>  (v8_ordinal1(B) |  (v3_xxreal_0(A) | v2_xxreal_0(B)) ) ) ) ) ) ) ).
fof(t5_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ~ ( (r2_tarski(A, B) &  (m1_subset_1(B, k1_zfmisc_1(C)) & v1_xboole_0(C)) ) ) ) ) ) ).
fof(t67_surrealr, axiom,  (! [A] :  (v2_surreal0(A) =>  (! [B] :  (v2_surreal0(B) =>  (! [C] :  (v2_surreal0(C) => r2_surrealo(k16_surrealr(A, k8_surrealr(B, C)), k8_surrealr(k16_surrealr(A, B), k16_surrealr(A, C)))) ) ) ) ) ) ).
fof(t69_surrealr, axiom,  (! [A] :  (v2_surreal0(A) =>  (! [B] :  (v2_surreal0(B) =>  (! [C] :  (v2_surreal0(C) => r2_surrealo(k16_surrealr(k16_surrealr(A, B), C), k16_surrealr(A, k16_surrealr(B, C)))) ) ) ) ) ) ).
fof(t6_arithm, axiom,  (! [A] :  (v1_xcmplx_0(A) => k7_xcmplx_0(A, 1)=A) ) ).
fof(t6_boole, axiom,  (! [A] :  (v1_xboole_0(A) => A=k1_xboole_0) ) ).
fof(t6_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  (r1_xxreal_0(A, B) =>  (v8_ordinal1(A) |  (v2_xxreal_0(B) | v3_xxreal_0(A)) ) ) ) ) ) ) ).
fof(t6_surreali, axiom,  (! [A] :  (v7_ordinal1(A) =>  (! [B] :  (! [C] :  ( (v1_relat_1(C) & v1_funct_1(C))  =>  (k1_funct_1(k5_surreali(B, C), k1_nat_1(A, 1))=k2_xboole_0(k2_xboole_0(k1_funct_1(k5_surreali(B, C), A), k3_surreali(k1_funct_1(k5_surreali(B, C), A), B, k2_surreal0(B), C)), k3_surreali(k1_funct_1(k6_surreali(B, C), A), B, k1_surreal0(B), C)) & k1_funct_1(k6_surreali(B, C), k1_nat_1(A, 1))=k2_xboole_0(k2_xboole_0(k1_funct_1(k6_surreali(B, C), A), k3_surreali(k1_funct_1(k5_surreali(B, C), A), B, k1_surreal0(B), C)), k3_surreali(k1_funct_1(k6_surreali(B, C), A), B, k2_surreal0(B), C))) ) ) ) ) ) ).
fof(t70_surrealr, axiom,  (! [A] :  (v2_surreal0(A) =>  (! [B] :  (v2_surreal0(B) =>  (! [C] :  (v2_surreal0(C) =>  ~ ( ( ~ (r5_surreal0(A, k11_surreal0))  &  ( ~ (r5_surreal0(C, B))  & r5_surreal0(k16_surrealr(C, A), k16_surrealr(B, A))) ) ) ) ) ) ) ) ) ).
fof(t71_surrealr, axiom,  (! [A] :  (v2_surreal0(A) =>  (! [B] :  (v2_surreal0(B) =>  (! [C] :  (v2_surreal0(C) =>  ~ ( ( ~ (r5_surreal0(k11_surreal0, A))  &  ( ~ (r5_surreal0(C, B))  & r5_surreal0(k16_surrealr(B, A), k16_surrealr(C, A))) ) ) ) ) ) ) ) ) ).
fof(t72_surrealr, axiom,  (! [A] :  (v2_surreal0(A) =>  (! [B] :  (v2_surreal0(B) =>  ( ~ ( ( ~ (r5_surreal0(k16_surrealr(A, B), k11_surreal0))  &  ( ~ ( ( ~ (r5_surreal0(k11_surreal0, A))  &  ~ (r5_surreal0(k11_surreal0, B)) ) )  &  ~ ( ( ~ (r5_surreal0(A, k11_surreal0))  &  ~ (r5_surreal0(B, k11_surreal0)) ) ) ) ) )  &  ~ ( ( ( ( ~ (r5_surreal0(k11_surreal0, A))  &  ~ (r5_surreal0(k11_surreal0, B)) )  |  ( ~ (r5_surreal0(A, k11_surreal0))  &  ~ (r5_surreal0(B, k11_surreal0)) ) )  & r5_surreal0(k16_surrealr(A, B), k11_surreal0)) ) ) ) ) ) ) ).
fof(t73_surrealr, axiom,  (! [A] :  (v2_surreal0(A) =>  (! [B] :  (v2_surreal0(B) =>  (! [C] :  (v2_surreal0(C) =>  ~ ( ( ~ (r5_surreal0(C, k11_surreal0))  &  ( ~ (r5_surreal0(k16_surrealr(B, C), k16_surrealr(A, C)))  & r5_surreal0(B, A)) ) ) ) ) ) ) ) ) ).
fof(t74_surrealr, axiom,  (! [A] :  (v2_surreal0(A) =>  (! [B] :  (v2_surreal0(B) =>  ( ~ ( ( ~ (r5_surreal0(k11_surreal0, k16_surrealr(A, B)))  &  ( ~ ( ( ~ (r5_surreal0(k11_surreal0, A))  &  ~ (r5_surreal0(B, k11_surreal0)) ) )  &  ~ ( ( ~ (r5_surreal0(A, k11_surreal0))  &  ~ (r5_surreal0(k11_surreal0, B)) ) ) ) ) )  &  ~ ( ( ( ( ~ (r5_surreal0(k11_surreal0, A))  &  ~ (r5_surreal0(B, k11_surreal0)) )  |  ( ~ (r5_surreal0(A, k11_surreal0))  &  ~ (r5_surreal0(k11_surreal0, B)) ) )  & r5_surreal0(k11_surreal0, k16_surrealr(A, B))) ) ) ) ) ) ) ).
fof(t7_boole, axiom,  (! [A] :  (! [B] :  ~ ( (r2_tarski(A, B) & v1_xboole_0(B)) ) ) ) ).
fof(t7_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  ~ ( ( ~ (r1_xxreal_0(A, B))  &  ( ~ (v2_xxreal_0(A))  &  ~ (v3_xxreal_0(B)) ) ) ) ) ) ) ) ).
fof(t8_boole, axiom,  (! [A] :  (! [B] :  ~ ( (v1_xboole_0(A) &  ( ~ (A=B)  & v1_xboole_0(B)) ) ) ) ) ).
fof(t8_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  ~ ( ( ~ (r1_xxreal_0(A, B))  &  ( ~ (v3_xxreal_0(B))  &  ~ (v2_xxreal_0(A)) ) ) ) ) ) ) ) ).
