% Mizar problem: t31_xprimes1,xprimes1,168,5 
fof(t31_xprimes1, conjecture, v1_int_2(31)).
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(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(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_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(cc20_ordinal1, axiom,  (! [A] :  ( ~ (v1_setfam_1(A))  => v10_ordinal1(A)) ) ).
fof(cc2_int_1, axiom,  (! [A] :  (v7_ordinal1(A) => v1_int_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_xxreal_0, axiom,  (! [A] :  (v7_ordinal1(A) => v1_xxreal_0(A)) ) ).
fof(cc3_int_1, axiom,  (! [A] :  (v1_int_1(A) => v1_xreal_0(A)) ) ).
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_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_int_1, axiom,  (! [A] :  (v7_ordinal1(A) => v2_int_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_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_int_1, axiom,  (! [A] :  (v2_int_1(A) => v1_int_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_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_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_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v7_ordinal1(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_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_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v6_ordinal1(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_nat_1, axiom,  (! [A, B] :  ( (m1_subset_1(A, k4_ordinal1) & m1_subset_1(B, k4_ordinal1))  => k2_nat_1(A, B)=k2_nat_1(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_k3_xcmplx_0, axiom,  (! [A, B] :  ( (v1_xcmplx_0(A) & v1_xcmplx_0(B))  => k3_xcmplx_0(A, B)=k3_xcmplx_0(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(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_k2_nat_1, axiom,  (! [A, B] :  ( (m1_subset_1(A, k4_ordinal1) & m1_subset_1(B, k4_ordinal1))  => m1_subset_1(k2_nat_1(A, B), k4_ordinal1)) ) ).
fof(dt_k2_xcmplx_0, axiom, $true).
fof(dt_k3_xcmplx_0, axiom, $true).
fof(dt_k4_ordinal1, axiom, $true).
fof(dt_k5_numbers, axiom, m1_subset_1(k5_numbers, k4_ordinal1)).
fof(dt_k5_ordinal1, axiom, $true).
fof(dt_m1_subset_1, axiom, $true).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(fc1_int_1, axiom,  (! [A, B] :  ( (v1_int_1(A) & v1_int_1(B))  => v1_int_1(k2_xcmplx_0(A, B))) ) ).
fof(fc1_nat_1, axiom,  (! [A, B] :  ( (v7_ordinal1(A) & v7_ordinal1(B))  => v7_ordinal1(k2_xcmplx_0(A, B))) ) ).
fof(fc2_int_1, axiom,  (! [A, B] :  ( (v1_int_1(A) & v1_int_1(B))  => v1_int_1(k3_xcmplx_0(A, B))) ) ).
fof(fc2_nat_1, axiom,  (! [A, B] :  ( (v7_ordinal1(A) & v7_ordinal1(B))  => v7_ordinal1(k3_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(fc4_nat_1, axiom,  (! [A, B] :  ( (v7_ordinal1(A) &  (v7_ordinal1(B) &  ~ (v8_ordinal1(B)) ) )  =>  ~ (v8_ordinal1(k2_xcmplx_0(B, A))) ) ) ).
fof(fc6_ordinal1, axiom,  ( ~ (v1_xboole_0(k4_ordinal1))  & v3_ordinal1(k4_ordinal1)) ).
fof(fc7_int_1, axiom,  (! [A] :  (v2_int_1(A) => v7_ordinal1(k2_xcmplx_0(A, 1))) ) ).
fof(fc8_int_1, axiom,  (! [A, B] :  ( (v2_int_1(A) &  (v7_ordinal1(B) &  ~ (v8_ordinal1(B)) ) )  => v7_ordinal1(k2_xcmplx_0(A, B))) ) ).
fof(fc8_ordinal1, axiom, v7_ordinal1(k5_ordinal1)).
fof(fc9_ordinal1, axiom, v8_ordinal1(k5_ordinal1)).
fof(rc10_ordinal1, axiom,  (? [A] :  ~ (v8_ordinal1(A)) ) ).
fof(rc11_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  ~ (v10_ordinal1(A)) ) ) ).
fof(rc1_int_1, axiom,  (? [A] :  (v1_xxreal_0(A) &  (v1_xcmplx_0(A) &  (v1_xreal_0(A) & v1_int_1(A)) ) ) ) ).
fof(rc1_nat_1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc1_ordinal1, axiom,  (? [A] :  (v1_ordinal1(A) & v2_ordinal1(A)) ) ).
fof(rc1_xxreal_0, axiom,  (? [A] : v1_xxreal_0(A)) ).
fof(rc2_int_1, axiom,  (? [A] : v1_int_1(A)) ).
fof(rc2_nat_1, axiom,  (? [A] :  (v7_ordinal1(A) & v8_ordinal1(A)) ) ).
fof(rc2_ordinal1, axiom,  (? [A] : v3_ordinal1(A)) ).
fof(rc2_xxreal_0, axiom,  (? [A] : v1_xxreal_0(A)) ).
fof(rc3_int_1, axiom,  (? [A] : v2_int_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_xxreal_0, axiom,  (? [A] :  (v1_xxreal_0(A) & v2_xxreal_0(A)) ) ).
fof(rc4_xxreal_0, axiom,  (? [A] :  (v1_xxreal_0(A) & v3_xxreal_0(A)) ) ).
fof(rc5_ordinal1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc5_xxreal_0, axiom,  (? [A] :  (v8_ordinal1(A) & v1_xxreal_0(A)) ) ).
fof(rc6_ordinal1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc7_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v7_ordinal1(A)) ) ).
fof(rc8_ordinal1, axiom,  (? [A] : v8_ordinal1(A)) ).
fof(rc9_ordinal1, axiom,  (? [A] : v8_ordinal1(A)) ).
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_k2_nat_1, axiom,  (! [A, B] :  ( (m1_subset_1(A, k4_ordinal1) & m1_subset_1(B, k4_ordinal1))  => k2_nat_1(A, B)=k3_xcmplx_0(A, B)) ) ).
fof(redefinition_k5_numbers, axiom, k5_numbers=k5_ordinal1).
fof(redefinition_r1_nat_d, axiom,  (! [A, B] :  ( (v7_ordinal1(A) & v7_ordinal1(B))  =>  (r1_nat_d(A, B) <=> r1_int_1(A, B)) ) ) ).
fof(redefinition_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) <=> r2_hidden(A, B)) ) ).
fof(reflexivity_r1_int_1, axiom,  (! [A, B] :  ( (v1_int_1(A) & v1_int_1(B))  => r1_int_1(A, A)) ) ).
fof(reflexivity_r1_nat_d, axiom,  (! [A, B] :  ( (v7_ordinal1(A) & v7_ordinal1(B))  => r1_nat_d(A, A)) ) ).
fof(reflexivity_r1_xxreal_0, axiom,  (! [A, B] :  ( (v1_xxreal_0(A) & v1_xxreal_0(B))  => r1_xxreal_0(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_r10, axiom, r1_xxreal_0(0, 10)).
fof(rqLessOrEqual__r1_xxreal_0__r0_r15, axiom, r1_xxreal_0(0, 15)).
fof(rqLessOrEqual__r1_xxreal_0__r0_r2, axiom, r1_xxreal_0(0, 2)).
fof(rqLessOrEqual__r1_xxreal_0__r0_r3, axiom, r1_xxreal_0(0, 3)).
fof(rqLessOrEqual__r1_xxreal_0__r0_r30, axiom, r1_xxreal_0(0, 30)).
fof(rqLessOrEqual__r1_xxreal_0__r0_r31, axiom, r1_xxreal_0(0, 31)).
fof(rqLessOrEqual__r1_xxreal_0__r0_r49, axiom, r1_xxreal_0(0, 49)).
fof(rqLessOrEqual__r1_xxreal_0__r0_r5, axiom, r1_xxreal_0(0, 5)).
fof(rqLessOrEqual__r1_xxreal_0__r0_r6, axiom, r1_xxreal_0(0, 6)).
fof(rqLessOrEqual__r1_xxreal_0__r10_r0, axiom,  ~ (r1_xxreal_0(10, 0)) ).
fof(rqLessOrEqual__r1_xxreal_0__r10_r1, axiom,  ~ (r1_xxreal_0(10, 1)) ).
fof(rqLessOrEqual__r1_xxreal_0__r10_r10, axiom, r1_xxreal_0(10, 10)).
fof(rqLessOrEqual__r1_xxreal_0__r10_r15, axiom, r1_xxreal_0(10, 15)).
fof(rqLessOrEqual__r1_xxreal_0__r10_r2, axiom,  ~ (r1_xxreal_0(10, 2)) ).
fof(rqLessOrEqual__r1_xxreal_0__r10_r3, axiom,  ~ (r1_xxreal_0(10, 3)) ).
fof(rqLessOrEqual__r1_xxreal_0__r10_r30, axiom, r1_xxreal_0(10, 30)).
fof(rqLessOrEqual__r1_xxreal_0__r10_r31, axiom, r1_xxreal_0(10, 31)).
fof(rqLessOrEqual__r1_xxreal_0__r10_r49, axiom, r1_xxreal_0(10, 49)).
fof(rqLessOrEqual__r1_xxreal_0__r10_r5, axiom,  ~ (r1_xxreal_0(10, 5)) ).
fof(rqLessOrEqual__r1_xxreal_0__r10_r6, axiom,  ~ (r1_xxreal_0(10, 6)) ).
fof(rqLessOrEqual__r1_xxreal_0__r15_r0, axiom,  ~ (r1_xxreal_0(15, 0)) ).
fof(rqLessOrEqual__r1_xxreal_0__r15_r1, axiom,  ~ (r1_xxreal_0(15, 1)) ).
fof(rqLessOrEqual__r1_xxreal_0__r15_r10, axiom,  ~ (r1_xxreal_0(15, 10)) ).
fof(rqLessOrEqual__r1_xxreal_0__r15_r15, axiom, r1_xxreal_0(15, 15)).
fof(rqLessOrEqual__r1_xxreal_0__r15_r2, axiom,  ~ (r1_xxreal_0(15, 2)) ).
fof(rqLessOrEqual__r1_xxreal_0__r15_r3, axiom,  ~ (r1_xxreal_0(15, 3)) ).
fof(rqLessOrEqual__r1_xxreal_0__r15_r30, axiom, r1_xxreal_0(15, 30)).
fof(rqLessOrEqual__r1_xxreal_0__r15_r31, axiom, r1_xxreal_0(15, 31)).
fof(rqLessOrEqual__r1_xxreal_0__r15_r49, axiom, r1_xxreal_0(15, 49)).
fof(rqLessOrEqual__r1_xxreal_0__r15_r5, axiom,  ~ (r1_xxreal_0(15, 5)) ).
fof(rqLessOrEqual__r1_xxreal_0__r15_r6, axiom,  ~ (r1_xxreal_0(15, 6)) ).
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_r10, axiom, r1_xxreal_0(1, 10)).
fof(rqLessOrEqual__r1_xxreal_0__r1_r15, axiom, r1_xxreal_0(1, 15)).
fof(rqLessOrEqual__r1_xxreal_0__r1_r2, axiom, r1_xxreal_0(1, 2)).
fof(rqLessOrEqual__r1_xxreal_0__r1_r3, axiom, r1_xxreal_0(1, 3)).
fof(rqLessOrEqual__r1_xxreal_0__r1_r30, axiom, r1_xxreal_0(1, 30)).
fof(rqLessOrEqual__r1_xxreal_0__r1_r31, axiom, r1_xxreal_0(1, 31)).
fof(rqLessOrEqual__r1_xxreal_0__r1_r49, axiom, r1_xxreal_0(1, 49)).
fof(rqLessOrEqual__r1_xxreal_0__r1_r5, axiom, r1_xxreal_0(1, 5)).
fof(rqLessOrEqual__r1_xxreal_0__r1_r6, axiom, r1_xxreal_0(1, 6)).
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_r10, axiom, r1_xxreal_0(2, 10)).
fof(rqLessOrEqual__r1_xxreal_0__r2_r15, axiom, r1_xxreal_0(2, 15)).
fof(rqLessOrEqual__r1_xxreal_0__r2_r2, axiom, r1_xxreal_0(2, 2)).
fof(rqLessOrEqual__r1_xxreal_0__r2_r3, axiom, r1_xxreal_0(2, 3)).
fof(rqLessOrEqual__r1_xxreal_0__r2_r30, axiom, r1_xxreal_0(2, 30)).
fof(rqLessOrEqual__r1_xxreal_0__r2_r31, axiom, r1_xxreal_0(2, 31)).
fof(rqLessOrEqual__r1_xxreal_0__r2_r49, axiom, r1_xxreal_0(2, 49)).
fof(rqLessOrEqual__r1_xxreal_0__r2_r5, axiom, r1_xxreal_0(2, 5)).
fof(rqLessOrEqual__r1_xxreal_0__r2_r6, axiom, r1_xxreal_0(2, 6)).
fof(rqLessOrEqual__r1_xxreal_0__r30_r0, axiom,  ~ (r1_xxreal_0(30, 0)) ).
fof(rqLessOrEqual__r1_xxreal_0__r30_r1, axiom,  ~ (r1_xxreal_0(30, 1)) ).
fof(rqLessOrEqual__r1_xxreal_0__r30_r10, axiom,  ~ (r1_xxreal_0(30, 10)) ).
fof(rqLessOrEqual__r1_xxreal_0__r30_r15, axiom,  ~ (r1_xxreal_0(30, 15)) ).
fof(rqLessOrEqual__r1_xxreal_0__r30_r2, axiom,  ~ (r1_xxreal_0(30, 2)) ).
fof(rqLessOrEqual__r1_xxreal_0__r30_r3, axiom,  ~ (r1_xxreal_0(30, 3)) ).
fof(rqLessOrEqual__r1_xxreal_0__r30_r30, axiom, r1_xxreal_0(30, 30)).
fof(rqLessOrEqual__r1_xxreal_0__r30_r31, axiom, r1_xxreal_0(30, 31)).
fof(rqLessOrEqual__r1_xxreal_0__r30_r49, axiom, r1_xxreal_0(30, 49)).
fof(rqLessOrEqual__r1_xxreal_0__r30_r5, axiom,  ~ (r1_xxreal_0(30, 5)) ).
fof(rqLessOrEqual__r1_xxreal_0__r30_r6, axiom,  ~ (r1_xxreal_0(30, 6)) ).
fof(rqLessOrEqual__r1_xxreal_0__r31_r0, axiom,  ~ (r1_xxreal_0(31, 0)) ).
fof(rqLessOrEqual__r1_xxreal_0__r31_r1, axiom,  ~ (r1_xxreal_0(31, 1)) ).
fof(rqLessOrEqual__r1_xxreal_0__r31_r10, axiom,  ~ (r1_xxreal_0(31, 10)) ).
fof(rqLessOrEqual__r1_xxreal_0__r31_r15, axiom,  ~ (r1_xxreal_0(31, 15)) ).
fof(rqLessOrEqual__r1_xxreal_0__r31_r2, axiom,  ~ (r1_xxreal_0(31, 2)) ).
fof(rqLessOrEqual__r1_xxreal_0__r31_r3, axiom,  ~ (r1_xxreal_0(31, 3)) ).
fof(rqLessOrEqual__r1_xxreal_0__r31_r30, axiom,  ~ (r1_xxreal_0(31, 30)) ).
fof(rqLessOrEqual__r1_xxreal_0__r31_r31, axiom, r1_xxreal_0(31, 31)).
fof(rqLessOrEqual__r1_xxreal_0__r31_r49, axiom, r1_xxreal_0(31, 49)).
fof(rqLessOrEqual__r1_xxreal_0__r31_r5, axiom,  ~ (r1_xxreal_0(31, 5)) ).
fof(rqLessOrEqual__r1_xxreal_0__r31_r6, axiom,  ~ (r1_xxreal_0(31, 6)) ).
fof(rqLessOrEqual__r1_xxreal_0__r3_r0, axiom,  ~ (r1_xxreal_0(3, 0)) ).
fof(rqLessOrEqual__r1_xxreal_0__r3_r1, axiom,  ~ (r1_xxreal_0(3, 1)) ).
fof(rqLessOrEqual__r1_xxreal_0__r3_r10, axiom, r1_xxreal_0(3, 10)).
fof(rqLessOrEqual__r1_xxreal_0__r3_r15, axiom, r1_xxreal_0(3, 15)).
fof(rqLessOrEqual__r1_xxreal_0__r3_r2, axiom,  ~ (r1_xxreal_0(3, 2)) ).
fof(rqLessOrEqual__r1_xxreal_0__r3_r3, axiom, r1_xxreal_0(3, 3)).
fof(rqLessOrEqual__r1_xxreal_0__r3_r30, axiom, r1_xxreal_0(3, 30)).
fof(rqLessOrEqual__r1_xxreal_0__r3_r31, axiom, r1_xxreal_0(3, 31)).
fof(rqLessOrEqual__r1_xxreal_0__r3_r49, axiom, r1_xxreal_0(3, 49)).
fof(rqLessOrEqual__r1_xxreal_0__r3_r5, axiom, r1_xxreal_0(3, 5)).
fof(rqLessOrEqual__r1_xxreal_0__r3_r6, axiom, r1_xxreal_0(3, 6)).
fof(rqLessOrEqual__r1_xxreal_0__r49_r0, axiom,  ~ (r1_xxreal_0(49, 0)) ).
fof(rqLessOrEqual__r1_xxreal_0__r49_r1, axiom,  ~ (r1_xxreal_0(49, 1)) ).
fof(rqLessOrEqual__r1_xxreal_0__r49_r10, axiom,  ~ (r1_xxreal_0(49, 10)) ).
fof(rqLessOrEqual__r1_xxreal_0__r49_r2, axiom,  ~ (r1_xxreal_0(49, 2)) ).
fof(rqLessOrEqual__r1_xxreal_0__r49_r3, axiom,  ~ (r1_xxreal_0(49, 3)) ).
fof(rqLessOrEqual__r1_xxreal_0__r49_r30, axiom,  ~ (r1_xxreal_0(49, 30)) ).
fof(rqLessOrEqual__r1_xxreal_0__r49_r31, axiom,  ~ (r1_xxreal_0(49, 31)) ).
fof(rqLessOrEqual__r1_xxreal_0__r49_r49, axiom, r1_xxreal_0(49, 49)).
fof(rqLessOrEqual__r1_xxreal_0__r49_r5, axiom,  ~ (r1_xxreal_0(49, 5)) ).
fof(rqLessOrEqual__r1_xxreal_0__r49_r6, axiom,  ~ (r1_xxreal_0(49, 6)) ).
fof(rqLessOrEqual__r1_xxreal_0__r5_r0, axiom,  ~ (r1_xxreal_0(5, 0)) ).
fof(rqLessOrEqual__r1_xxreal_0__r5_r1, axiom,  ~ (r1_xxreal_0(5, 1)) ).
fof(rqLessOrEqual__r1_xxreal_0__r5_r10, axiom, r1_xxreal_0(5, 10)).
fof(rqLessOrEqual__r1_xxreal_0__r5_r15, axiom, r1_xxreal_0(5, 15)).
fof(rqLessOrEqual__r1_xxreal_0__r5_r2, axiom,  ~ (r1_xxreal_0(5, 2)) ).
fof(rqLessOrEqual__r1_xxreal_0__r5_r3, axiom,  ~ (r1_xxreal_0(5, 3)) ).
fof(rqLessOrEqual__r1_xxreal_0__r5_r30, axiom, r1_xxreal_0(5, 30)).
fof(rqLessOrEqual__r1_xxreal_0__r5_r31, axiom, r1_xxreal_0(5, 31)).
fof(rqLessOrEqual__r1_xxreal_0__r5_r49, axiom, r1_xxreal_0(5, 49)).
fof(rqLessOrEqual__r1_xxreal_0__r5_r5, axiom, r1_xxreal_0(5, 5)).
fof(rqLessOrEqual__r1_xxreal_0__r5_r6, axiom, r1_xxreal_0(5, 6)).
fof(rqLessOrEqual__r1_xxreal_0__r6_r0, axiom,  ~ (r1_xxreal_0(6, 0)) ).
fof(rqLessOrEqual__r1_xxreal_0__r6_r1, axiom,  ~ (r1_xxreal_0(6, 1)) ).
fof(rqLessOrEqual__r1_xxreal_0__r6_r10, axiom, r1_xxreal_0(6, 10)).
fof(rqLessOrEqual__r1_xxreal_0__r6_r15, axiom, r1_xxreal_0(6, 15)).
fof(rqLessOrEqual__r1_xxreal_0__r6_r2, axiom,  ~ (r1_xxreal_0(6, 2)) ).
fof(rqLessOrEqual__r1_xxreal_0__r6_r3, axiom,  ~ (r1_xxreal_0(6, 3)) ).
fof(rqLessOrEqual__r1_xxreal_0__r6_r30, axiom, r1_xxreal_0(6, 30)).
fof(rqLessOrEqual__r1_xxreal_0__r6_r31, axiom, r1_xxreal_0(6, 31)).
fof(rqLessOrEqual__r1_xxreal_0__r6_r49, axiom, r1_xxreal_0(6, 49)).
fof(rqLessOrEqual__r1_xxreal_0__r6_r5, axiom,  ~ (r1_xxreal_0(6, 5)) ).
fof(rqLessOrEqual__r1_xxreal_0__r6_r6, axiom, r1_xxreal_0(6, 6)).
fof(rqRealAdd__k2_xcmplx_0__r0_r0_r0, axiom, k2_xcmplx_0(0, 0)=0).
fof(rqRealAdd__k2_xcmplx_0__r0_r10_r10, axiom, k2_xcmplx_0(0, 10)=10).
fof(rqRealAdd__k2_xcmplx_0__r0_r15_r15, axiom, k2_xcmplx_0(0, 15)=15).
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_r30_r30, axiom, k2_xcmplx_0(0, 30)=30).
fof(rqRealAdd__k2_xcmplx_0__r0_r3_r3, axiom, k2_xcmplx_0(0, 3)=3).
fof(rqRealAdd__k2_xcmplx_0__r0_r5_r5, axiom, k2_xcmplx_0(0, 5)=5).
fof(rqRealAdd__k2_xcmplx_0__r0_r6_r6, axiom, k2_xcmplx_0(0, 6)=6).
fof(rqRealAdd__k2_xcmplx_0__r10_r0_r10, axiom, k2_xcmplx_0(10, 0)=10).
fof(rqRealAdd__k2_xcmplx_0__r10_r5_r15, axiom, k2_xcmplx_0(10, 5)=15).
fof(rqRealAdd__k2_xcmplx_0__r15_r0_r15, axiom, k2_xcmplx_0(15, 0)=15).
fof(rqRealAdd__k2_xcmplx_0__r15_r15_r30, axiom, k2_xcmplx_0(15, 15)=30).
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_r2_r3, axiom, k2_xcmplx_0(1, 2)=3).
fof(rqRealAdd__k2_xcmplx_0__r1_r30_r31, axiom, k2_xcmplx_0(1, 30)=31).
fof(rqRealAdd__k2_xcmplx_0__r1_r5_r6, axiom, k2_xcmplx_0(1, 5)=6).
fof(rqRealAdd__k2_xcmplx_0__r2_r0_r2, axiom, k2_xcmplx_0(2, 0)=2).
fof(rqRealAdd__k2_xcmplx_0__r2_r1_r3, axiom, k2_xcmplx_0(2, 1)=3).
fof(rqRealAdd__k2_xcmplx_0__r2_r3_r5, axiom, k2_xcmplx_0(2, 3)=5).
fof(rqRealAdd__k2_xcmplx_0__r30_r0_r30, axiom, k2_xcmplx_0(30, 0)=30).
fof(rqRealAdd__k2_xcmplx_0__r30_r1_r31, axiom, k2_xcmplx_0(30, 1)=31).
fof(rqRealAdd__k2_xcmplx_0__r3_r0_r3, axiom, k2_xcmplx_0(3, 0)=3).
fof(rqRealAdd__k2_xcmplx_0__r3_r2_r5, axiom, k2_xcmplx_0(3, 2)=5).
fof(rqRealAdd__k2_xcmplx_0__r3_r3_r6, axiom, k2_xcmplx_0(3, 3)=6).
fof(rqRealAdd__k2_xcmplx_0__r5_r0_r5, axiom, k2_xcmplx_0(5, 0)=5).
fof(rqRealAdd__k2_xcmplx_0__r5_r10_r15, axiom, k2_xcmplx_0(5, 10)=15).
fof(rqRealAdd__k2_xcmplx_0__r5_r1_r6, axiom, k2_xcmplx_0(5, 1)=6).
fof(rqRealAdd__k2_xcmplx_0__r5_r5_r10, axiom, k2_xcmplx_0(5, 5)=10).
fof(rqRealAdd__k2_xcmplx_0__r6_r0_r6, axiom, k2_xcmplx_0(6, 0)=6).
fof(rqRealMult__k3_xcmplx_0__r0_r0_r0, axiom, k3_xcmplx_0(0, 0)=0).
fof(rqRealMult__k3_xcmplx_0__r0_r10_r0, axiom, k3_xcmplx_0(0, 10)=0).
fof(rqRealMult__k3_xcmplx_0__r0_r15_r0, axiom, k3_xcmplx_0(0, 15)=0).
fof(rqRealMult__k3_xcmplx_0__r0_r1_r0, axiom, k3_xcmplx_0(0, 1)=0).
fof(rqRealMult__k3_xcmplx_0__r0_r2_r0, axiom, k3_xcmplx_0(0, 2)=0).
fof(rqRealMult__k3_xcmplx_0__r0_r30_r0, axiom, k3_xcmplx_0(0, 30)=0).
fof(rqRealMult__k3_xcmplx_0__r0_r3_r0, axiom, k3_xcmplx_0(0, 3)=0).
fof(rqRealMult__k3_xcmplx_0__r0_r5_r0, axiom, k3_xcmplx_0(0, 5)=0).
fof(rqRealMult__k3_xcmplx_0__r0_r6_r0, axiom, k3_xcmplx_0(0, 6)=0).
fof(rqRealMult__k3_xcmplx_0__r10_r0_r0, axiom, k3_xcmplx_0(10, 0)=0).
fof(rqRealMult__k3_xcmplx_0__r10_r1_r10, axiom, k3_xcmplx_0(10, 1)=10).
fof(rqRealMult__k3_xcmplx_0__r10_r3_r30, axiom, k3_xcmplx_0(10, 3)=30).
fof(rqRealMult__k3_xcmplx_0__r15_r0_r0, axiom, k3_xcmplx_0(15, 0)=0).
fof(rqRealMult__k3_xcmplx_0__r15_r1_r15, axiom, k3_xcmplx_0(15, 1)=15).
fof(rqRealMult__k3_xcmplx_0__r15_r2_r30, axiom, k3_xcmplx_0(15, 2)=30).
fof(rqRealMult__k3_xcmplx_0__r1_r0_r0, axiom, k3_xcmplx_0(1, 0)=0).
fof(rqRealMult__k3_xcmplx_0__r1_r10_r10, axiom, k3_xcmplx_0(1, 10)=10).
fof(rqRealMult__k3_xcmplx_0__r1_r15_r15, axiom, k3_xcmplx_0(1, 15)=15).
fof(rqRealMult__k3_xcmplx_0__r1_r1_r1, axiom, k3_xcmplx_0(1, 1)=1).
fof(rqRealMult__k3_xcmplx_0__r1_r2_r2, axiom, k3_xcmplx_0(1, 2)=2).
fof(rqRealMult__k3_xcmplx_0__r1_r30_r30, axiom, k3_xcmplx_0(1, 30)=30).
fof(rqRealMult__k3_xcmplx_0__r1_r31_r31, axiom, k3_xcmplx_0(1, 31)=31).
fof(rqRealMult__k3_xcmplx_0__r1_r3_r3, axiom, k3_xcmplx_0(1, 3)=3).
fof(rqRealMult__k3_xcmplx_0__r1_r49_r49, axiom, k3_xcmplx_0(1, 49)=49).
fof(rqRealMult__k3_xcmplx_0__r1_r5_r5, axiom, k3_xcmplx_0(1, 5)=5).
fof(rqRealMult__k3_xcmplx_0__r1_r6_r6, axiom, k3_xcmplx_0(1, 6)=6).
fof(rqRealMult__k3_xcmplx_0__r2_r0_r0, axiom, k3_xcmplx_0(2, 0)=0).
fof(rqRealMult__k3_xcmplx_0__r2_r15_r30, axiom, k3_xcmplx_0(2, 15)=30).
fof(rqRealMult__k3_xcmplx_0__r2_r1_r2, axiom, k3_xcmplx_0(2, 1)=2).
fof(rqRealMult__k3_xcmplx_0__r2_r3_r6, axiom, k3_xcmplx_0(2, 3)=6).
fof(rqRealMult__k3_xcmplx_0__r2_r5_r10, axiom, k3_xcmplx_0(2, 5)=10).
fof(rqRealMult__k3_xcmplx_0__r30_r0_r0, axiom, k3_xcmplx_0(30, 0)=0).
fof(rqRealMult__k3_xcmplx_0__r30_r1_r30, axiom, k3_xcmplx_0(30, 1)=30).
fof(rqRealMult__k3_xcmplx_0__r31_r1_r31, axiom, k3_xcmplx_0(31, 1)=31).
fof(rqRealMult__k3_xcmplx_0__r3_r0_r0, axiom, k3_xcmplx_0(3, 0)=0).
fof(rqRealMult__k3_xcmplx_0__r3_r10_r30, axiom, k3_xcmplx_0(3, 10)=30).
fof(rqRealMult__k3_xcmplx_0__r3_r1_r3, axiom, k3_xcmplx_0(3, 1)=3).
fof(rqRealMult__k3_xcmplx_0__r3_r2_r6, axiom, k3_xcmplx_0(3, 2)=6).
fof(rqRealMult__k3_xcmplx_0__r3_r5_r15, axiom, k3_xcmplx_0(3, 5)=15).
fof(rqRealMult__k3_xcmplx_0__r49_r1_r49, axiom, k3_xcmplx_0(49, 1)=49).
fof(rqRealMult__k3_xcmplx_0__r5_r0_r0, axiom, k3_xcmplx_0(5, 0)=0).
fof(rqRealMult__k3_xcmplx_0__r5_r1_r5, axiom, k3_xcmplx_0(5, 1)=5).
fof(rqRealMult__k3_xcmplx_0__r5_r2_r10, axiom, k3_xcmplx_0(5, 2)=10).
fof(rqRealMult__k3_xcmplx_0__r5_r3_r15, axiom, k3_xcmplx_0(5, 3)=15).
fof(rqRealMult__k3_xcmplx_0__r5_r6_r30, axiom, k3_xcmplx_0(5, 6)=30).
fof(rqRealMult__k3_xcmplx_0__r6_r0_r0, axiom, k3_xcmplx_0(6, 0)=0).
fof(rqRealMult__k3_xcmplx_0__r6_r1_r6, axiom, k3_xcmplx_0(6, 1)=6).
fof(rqRealMult__k3_xcmplx_0__r6_r5_r30, axiom, k3_xcmplx_0(6, 5)=30).
fof(spc0_numerals, axiom, m1_subset_1(0, k4_ordinal1)).
fof(spc10_numerals, axiom,  (v2_xxreal_0(10) & m1_subset_1(10, k4_ordinal1)) ).
fof(spc15_numerals, axiom,  (v2_xxreal_0(15) & m1_subset_1(15, k4_ordinal1)) ).
fof(spc1_numerals, axiom,  (v2_xxreal_0(1) & m1_subset_1(1, k4_ordinal1)) ).
fof(spc2_numerals, axiom,  (v2_xxreal_0(2) & m1_subset_1(2, k4_ordinal1)) ).
fof(spc30_numerals, axiom,  (v2_xxreal_0(30) & m1_subset_1(30, k4_ordinal1)) ).
fof(spc31_numerals, axiom,  (v2_xxreal_0(31) & m1_subset_1(31, k4_ordinal1)) ).
fof(spc3_numerals, axiom,  (v2_xxreal_0(3) & m1_subset_1(3, k4_ordinal1)) ).
fof(spc49_numerals, axiom,  (v2_xxreal_0(49) & m1_subset_1(49, k4_ordinal1)) ).
fof(spc5_arithm, axiom,  (! [A, B, C] :  ( (v1_xcmplx_0(A) &  (v1_xcmplx_0(B) & v1_xcmplx_0(C)) )  => k3_xcmplx_0(k2_xcmplx_0(A, B), C)=k2_xcmplx_0(k3_xcmplx_0(A, C), k3_xcmplx_0(B, C))) ) ).
fof(spc5_numerals, axiom,  (v2_xxreal_0(5) & m1_subset_1(5, 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(spc6_numerals, axiom,  (v2_xxreal_0(6) & m1_subset_1(6, k4_ordinal1)) ).
fof(spc7_arithm, axiom,  (! [A, B, C] :  ( (v1_xcmplx_0(A) &  (v1_xcmplx_0(B) & v1_xcmplx_0(C)) )  => k3_xcmplx_0(k3_xcmplx_0(A, B), C)=k3_xcmplx_0(A, k3_xcmplx_0(B, C))) ) ).
fof(t14_nat_4, axiom,  (! [A] :  (v7_ordinal1(A) =>  (v1_int_2(A) <=>  ( ~ (r1_xxreal_0(A, 1))  &  (! [B] :  (m1_subset_1(B, k4_ordinal1) =>  ~ ( ( ~ (r1_xxreal_0(B, 1))  &  (r1_xxreal_0(k2_nat_1(B, B), A) &  (v1_int_2(B) & r1_nat_d(B, A)) ) ) ) ) ) ) ) ) ) ).
fof(t1_arithm, axiom,  (! [A] :  (v1_xcmplx_0(A) => k2_xcmplx_0(A, k5_numbers)=A) ) ).
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(t2_arithm, axiom,  (! [A] :  (v1_xcmplx_0(A) => k3_xcmplx_0(A, k5_numbers)=k5_numbers) ) ).
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(t3_arithm, axiom,  (! [A] :  (v1_xcmplx_0(A) => k3_xcmplx_0(1, A)=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(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(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(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_xprimet1, axiom,  (! [A] :  (v7_ordinal1(A) =>  (! [B] :  ( (v7_ordinal1(B) & v1_int_2(B))  =>  ~ ( (r1_xxreal_0(k3_xcmplx_0(B, B), A) &  ( ~ (r1_xxreal_0(49, A))  &  ( ~ (B=2)  &  ( ~ (B=3)  &  ~ (B=5) ) ) ) ) ) ) ) ) ) ).
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_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)) ) ) ) ) ) ) ) ).
fof(t9_nat_4, axiom,  (! [A] :  (v7_ordinal1(A) =>  (! [B] :  (v7_ordinal1(B) =>  (! [C] :  (v7_ordinal1(C) =>  ~ ( ( ~ (r1_xxreal_0(C, k5_numbers))  &  ( ~ (r1_xxreal_0(A, C))  & r1_nat_d(A, k2_xcmplx_0(k3_xcmplx_0(A, B), C))) ) ) ) ) ) ) ) ) ).
