% Mizar problem: t17_surreals,surreals,1187,5 
fof(t17_surreals, conjecture,  (! [A] :  (v2_surreal0(A) =>  (! [B] :  (v2_surreal0(B) =>  (! [C] :  (v2_surreal0(C) =>  (! [D] :  (v2_surreal0(D) =>  (C=k16_surrealr(A, k12_surreali(B)) =>  (r2_surrealo(B, k11_surreal0) |  ( ~ ( ( ~ (r5_surreal0(D, k16_surrealr(C, C)))  & r5_surreal0(k16_surrealr(D, k16_surrealr(B, B)), k16_surrealr(A, A))) )  &  ( ~ ( ( ~ (r5_surreal0(k16_surrealr(D, k16_surrealr(B, B)), k16_surrealr(A, A)))  & r5_surreal0(D, k16_surrealr(C, C))) )  &  ( ~ ( ( ~ (r5_surreal0(k16_surrealr(C, C), D))  & r5_surreal0(k16_surrealr(A, A), k16_surrealr(D, k16_surrealr(B, B)))) )  &  ~ ( ( ~ (r5_surreal0(k16_surrealr(A, A), k16_surrealr(D, k16_surrealr(B, B))))  & r5_surreal0(k16_surrealr(C, C), D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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_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(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(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_k5_ordinal7, axiom,  (! [A, B] :  ( (v3_ordinal1(A) & v3_ordinal1(B))  => k5_ordinal7(A, B)=k5_ordinal7(B, A)) ) ).
fof(connectedness_r1_surrealo, axiom,  (! [A, B] :  ( (v2_surreal0(A) & v2_surreal0(B))  =>  (r1_surrealo(A, B) | r1_surrealo(B, A)) ) ) ).
fof(d13_surreal0, axiom,  (! [A] :  (v3_ordinal1(A) => k10_surreal0(A)=k5_surreal0(A, k9_surreal0(A))) ) ).
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(d15_surreal0, axiom, k11_surreal0=k4_tarski(k1_xboole_0, k1_xboole_0)).
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(d2_surrealo, axiom,  (! [A] :  (v2_surreal0(A) =>  (! [B] :  (v2_surreal0(B) =>  (r2_surrealo(A, B) <=>  (r1_surrealo(A, B) & r1_surrealo(B, A)) ) ) ) ) ) ).
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_k11_surreal0, axiom, v2_surreal0(k11_surreal0)).
fof(dt_k12_surreal0, axiom,  (! [A] :  (v2_surreal0(A) => v3_ordinal1(k12_surreal0(A))) ) ).
fof(dt_k12_surreali, axiom,  (! [A] :  (v2_surreal0(A) => v2_surreal0(k12_surreali(A))) ) ).
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_k16_surrealr, axiom, $true).
fof(dt_k1_funct_1, 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_tarski, axiom, $true).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k2_zfmisc_1, axiom, $true).
fof(dt_k3_surreal0, axiom, $true).
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_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_k9_surreal0, axiom,  (! [A] :  (v3_ordinal1(A) => v1_relat_1(k9_surreal0(A))) ) ).
fof(dt_m1_subset_1, axiom, $true).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(fc10_subset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v1_xboole_0(B)) )  =>  ~ (v1_xboole_0(k2_zfmisc_1(A, B))) ) ) ).
fof(fc11_nat_1, axiom,  (! [A] :  ( ~ (v8_ordinal1(A))  => v1_setfam_1(k1_tarski(A))) ) ).
fof(fc14_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  => v4_funct_1(k1_tarski(A))) ) ).
fof(fc19_funct_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v3_relat_1(A) & v1_funct_1(A)) )  => v1_xboole_0(k1_funct_1(A, B))) ) ).
fof(fc1_funct_1, axiom,  (! [A, B] : v1_funct_1(k1_tarski(k4_tarski(A, B)))) ).
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_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(fc2_surreal0, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v3_ordinal1(B))  =>  ~ (v1_xboole_0(k5_surreal0(B, A))) ) ) ).
fof(fc2_xboole_0, axiom,  (! [A] :  ~ (v1_xboole_0(k1_tarski(A))) ) ).
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(fc4_surreal0, axiom, v2_surreal0(k4_tarski(k1_xboole_0, k1_xboole_0))).
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(fc6_relat_1, axiom,  (! [A, B] : v1_relat_1(k2_zfmisc_1(A, B))) ).
fof(fc6_surreali, axiom,  (! [A] :  ( (v2_surreal0(A) & v2_surreali(A))  =>  (v2_surreal0(k12_surreali(A)) & v2_surreali(k12_surreali(A))) ) ) ).
fof(fc8_surrealr, axiom,  (! [A, B] :  ( (v2_surreal0(A) & v2_surreal0(B))  => v2_surreal0(k14_surrealr(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(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(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_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(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_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_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_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(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_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_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_r2_surrealo, axiom,  (! [A, B] :  ( (v2_surreal0(A) & v2_surreal0(B))  => r2_surrealo(A, A)) ) ).
fof(symmetry_r2_surrealo, axiom,  (! [A, B] :  ( (v2_surreal0(A) & v2_surreal0(B))  =>  (r2_surrealo(A, B) => r2_surrealo(B, A)) ) ) ).
fof(t1_subset, axiom,  (! [A] :  (! [B] :  (r2_tarski(A, B) => m1_subset_1(A, B)) ) ) ).
fof(t2_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, B) =>  (v1_xboole_0(B) | r2_tarski(A, B)) ) ) ) ).
fof(t33_surreali, axiom,  (! [A] :  (v2_surreal0(A) =>  ( ~ (r2_surrealo(A, k11_surreal0))  => r2_surrealo(k16_surrealr(A, k12_surreali(A)), k1_surrealo)) ) ) ).
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(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(t54_surrealr, axiom,  (! [A] :  (v2_surreal0(A) =>  (! [B] :  (v2_surreal0(B) =>  (! [C] :  (v2_surreal0(C) =>  (r2_surrealo(A, B) => r2_surrealo(k16_surrealr(A, C), k16_surrealr(B, 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(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_boole, axiom,  (! [A] :  (v1_xboole_0(A) => A=k1_xboole_0) ) ).
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(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(t75_surrealr, axiom,  (! [A] :  (v2_surreal0(A) =>  (! [B] :  (v2_surreal0(B) =>  (! [C] :  (v2_surreal0(C) =>  ( (r1_surrealo(k11_surreal0, A) & r1_surrealo(B, C))  => r1_surrealo(k16_surrealr(B, A), k16_surrealr(C, 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)) ) ) ) ) ).
