% Mizar problem: t1681_xprimes0,xprimes0,11883,7 
fof(t1681_xprimes0, conjecture,  ~ (v1_int_2(1681)) ).
fof(cc10_membered, axiom,  (! [A] :  (v5_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_int_1(B)) ) ) ) ).
fof(cc11_membered, axiom,  (! [A] :  (v6_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v7_ordinal1(B)) ) ) ) ).
fof(cc1_membered, axiom,  (! [A] :  (v6_membered(A) => v5_membered(A)) ) ).
fof(cc2_membered, axiom,  (! [A] :  (v5_membered(A) => v4_membered(A)) ) ).
fof(cc3_membered, axiom,  (! [A] :  (v4_membered(A) => v3_membered(A)) ) ).
fof(cc4_membered, axiom,  (! [A] :  (v3_membered(A) => v2_membered(A)) ) ).
fof(cc5_membered, axiom,  (! [A] :  (v3_membered(A) => v1_membered(A)) ) ).
fof(cc6_membered, axiom,  (! [A] :  (v1_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_xcmplx_0(B)) ) ) ) ).
fof(cc7_membered, axiom,  (! [A] :  (v2_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_xxreal_0(B)) ) ) ) ).
fof(cc8_membered, axiom,  (! [A] :  (v3_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_xreal_0(B)) ) ) ) ).
fof(cc9_membered, axiom,  (! [A] :  (v4_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_rat_1(B)) ) ) ) ).
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(d3_nat_d, axiom,  (! [A] :  (v7_ordinal1(A) =>  (! [B] :  (v7_ordinal1(B) =>  (r1_nat_d(A, B) <=>  (? [C] :  (v7_ordinal1(C) & B=k3_xcmplx_0(A, C)) ) ) ) ) ) ) ).
fof(dt_k3_xcmplx_0, axiom, $true).
fof(dt_k4_ordinal1, axiom, $true).
fof(dt_k4_xcmplx_0, axiom,  (! [A] :  (v1_xcmplx_0(A) => v1_xcmplx_0(k4_xcmplx_0(A))) ) ).
fof(dt_k6_xcmplx_0, axiom, $true).
fof(dt_k7_xcmplx_0, axiom, $true).
fof(dt_m1_subset_1, axiom, $true).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(fc59_membered, axiom, v7_membered(k4_ordinal1)).
fof(fc6_membered, axiom, v6_membered(k4_ordinal1)).
fof(involutiveness_k4_xcmplx_0, axiom,  (! [A] :  (v1_xcmplx_0(A) => k4_xcmplx_0(k4_xcmplx_0(A))=A) ) ).
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(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(rqRealDiff__k6_xcmplx_0__r0_r0_r0, axiom, k6_xcmplx_0(0, 0)=0).
fof(rqRealDiff__k6_xcmplx_0__r0_r1680_rm1680, axiom, k6_xcmplx_0(0, 1680)=k4_xcmplx_0(1680)).
fof(rqRealDiff__k6_xcmplx_0__r0_r1681_rm1681, axiom, k6_xcmplx_0(0, 1681)=k4_xcmplx_0(1681)).
fof(rqRealDiff__k6_xcmplx_0__r0_r1_rm1, axiom, k6_xcmplx_0(0, 1)=k4_xcmplx_0(1)).
fof(rqRealDiff__k6_xcmplx_0__r0_r40_rm40, axiom, k6_xcmplx_0(0, 40)=k4_xcmplx_0(40)).
fof(rqRealDiff__k6_xcmplx_0__r0_r41_rm41, axiom, k6_xcmplx_0(0, 41)=k4_xcmplx_0(41)).
fof(rqRealDiff__k6_xcmplx_0__r0_rm1_r1, axiom, k6_xcmplx_0(0, k4_xcmplx_0(1))=1).
fof(rqRealDiff__k6_xcmplx_0__r1680_r0_r1680, axiom, k6_xcmplx_0(1680, 0)=1680).
fof(rqRealDiff__k6_xcmplx_0__r1680_r1680_r0, axiom, k6_xcmplx_0(1680, 1680)=0).
fof(rqRealDiff__k6_xcmplx_0__r1681_r1_r1680, axiom, k6_xcmplx_0(1681, 1)=1680).
fof(rqRealDiff__k6_xcmplx_0__r1681_r41_r1640, axiom, k6_xcmplx_0(1681, 41)=1640).
fof(rqRealDiff__k6_xcmplx_0__r1_r0_r1, axiom, k6_xcmplx_0(1, 0)=1).
fof(rqRealDiff__k6_xcmplx_0__r1_r1681_rm1680, axiom, k6_xcmplx_0(1, 1681)=k4_xcmplx_0(1680)).
fof(rqRealDiff__k6_xcmplx_0__r1_r1_r0, axiom, k6_xcmplx_0(1, 1)=0).
fof(rqRealDiff__k6_xcmplx_0__r1_r41_rm40, axiom, k6_xcmplx_0(1, 41)=k4_xcmplx_0(40)).
fof(rqRealDiff__k6_xcmplx_0__r1_rm1680_r1681, axiom, k6_xcmplx_0(1, k4_xcmplx_0(1680))=1681).
fof(rqRealDiff__k6_xcmplx_0__r1_rm40_r41, axiom, k6_xcmplx_0(1, k4_xcmplx_0(40))=41).
fof(rqRealDiff__k6_xcmplx_0__r40_r0_r40, axiom, k6_xcmplx_0(40, 0)=40).
fof(rqRealDiff__k6_xcmplx_0__r40_r1680_rm1640, axiom, k6_xcmplx_0(40, 1680)=k4_xcmplx_0(1640)).
fof(rqRealDiff__k6_xcmplx_0__r40_r40_r0, axiom, k6_xcmplx_0(40, 40)=0).
fof(rqRealDiff__k6_xcmplx_0__r40_rm1_r41, axiom, k6_xcmplx_0(40, k4_xcmplx_0(1))=41).
fof(rqRealDiff__k6_xcmplx_0__r41_r0_r41, axiom, k6_xcmplx_0(41, 0)=41).
fof(rqRealDiff__k6_xcmplx_0__r41_r1681_rm1640, axiom, k6_xcmplx_0(41, 1681)=k4_xcmplx_0(1640)).
fof(rqRealDiff__k6_xcmplx_0__r41_r1_r40, axiom, k6_xcmplx_0(41, 1)=40).
fof(rqRealDiff__k6_xcmplx_0__r41_r40_r1, axiom, k6_xcmplx_0(41, 40)=1).
fof(rqRealDiff__k6_xcmplx_0__r41_r41_r0, axiom, k6_xcmplx_0(41, 41)=0).
fof(rqRealDiff__k6_xcmplx_0__rm1680_rm1680_r0, axiom, k6_xcmplx_0(k4_xcmplx_0(1680), k4_xcmplx_0(1680))=0).
fof(rqRealDiff__k6_xcmplx_0__rm1681_rm1_rm1680, axiom, k6_xcmplx_0(k4_xcmplx_0(1681), k4_xcmplx_0(1))=k4_xcmplx_0(1680)).
fof(rqRealDiff__k6_xcmplx_0__rm1681_rm41_rm1640, axiom, k6_xcmplx_0(k4_xcmplx_0(1681), k4_xcmplx_0(41))=k4_xcmplx_0(1640)).
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_r40_rm41, axiom, k6_xcmplx_0(k4_xcmplx_0(1), 40)=k4_xcmplx_0(41)).
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_rm41_r40, axiom, k6_xcmplx_0(k4_xcmplx_0(1), k4_xcmplx_0(41))=40).
fof(rqRealDiff__k6_xcmplx_0__rm40_r0_rm40, axiom, k6_xcmplx_0(k4_xcmplx_0(40), 0)=k4_xcmplx_0(40)).
fof(rqRealDiff__k6_xcmplx_0__rm40_r1_rm41, axiom, k6_xcmplx_0(k4_xcmplx_0(40), 1)=k4_xcmplx_0(41)).
fof(rqRealDiff__k6_xcmplx_0__rm40_rm40_r0, axiom, k6_xcmplx_0(k4_xcmplx_0(40), k4_xcmplx_0(40))=0).
fof(rqRealDiff__k6_xcmplx_0__rm41_r0_rm41, axiom, k6_xcmplx_0(k4_xcmplx_0(41), 0)=k4_xcmplx_0(41)).
fof(rqRealDiff__k6_xcmplx_0__rm41_rm1_rm40, axiom, k6_xcmplx_0(k4_xcmplx_0(41), k4_xcmplx_0(1))=k4_xcmplx_0(40)).
fof(rqRealDiff__k6_xcmplx_0__rm41_rm40_rm1, axiom, k6_xcmplx_0(k4_xcmplx_0(41), k4_xcmplx_0(40))=k4_xcmplx_0(1)).
fof(rqRealDiff__k6_xcmplx_0__rm41_rm41_r0, axiom, k6_xcmplx_0(k4_xcmplx_0(41), k4_xcmplx_0(41))=0).
fof(rqRealDiv__k7_xcmplx_0__r1_r1_r1, axiom, k7_xcmplx_0(1, 1)=1).
fof(rqRealDiv__k7_xcmplx_0__r1_r41_rn1d41, axiom, k7_xcmplx_0(1, 41)=k7_xcmplx_0(1, 41)).
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_rm41_rnm1d41, axiom, k7_xcmplx_0(1, k4_xcmplx_0(41))=k7_xcmplx_0(k4_xcmplx_0(1), 41)).
fof(rqRealDiv__k7_xcmplx_0__rm1_r1_rm1, axiom, k7_xcmplx_0(k4_xcmplx_0(1), 1)=k4_xcmplx_0(1)).
fof(rqRealMult__k3_xcmplx_0__r0_r0_r0, axiom, k3_xcmplx_0(0, 0)=0).
fof(rqRealMult__k3_xcmplx_0__r0_r1_r0, axiom, k3_xcmplx_0(0, 1)=0).
fof(rqRealMult__k3_xcmplx_0__r1_r0_r0, axiom, k3_xcmplx_0(1, 0)=0).
fof(rqRealMult__k3_xcmplx_0__r1_r1_r1, axiom, k3_xcmplx_0(1, 1)=1).
fof(rqRealMult__k3_xcmplx_0__r1_r40_r40, axiom, k3_xcmplx_0(1, 40)=40).
fof(rqRealMult__k3_xcmplx_0__r1_r41_r41, axiom, k3_xcmplx_0(1, 41)=41).
fof(rqRealMult__k3_xcmplx_0__r1_rm40_rm40, axiom, k3_xcmplx_0(1, k4_xcmplx_0(40))=k4_xcmplx_0(40)).
fof(rqRealMult__k3_xcmplx_0__r40_r1_r40, axiom, k3_xcmplx_0(40, 1)=40).
fof(rqRealMult__k3_xcmplx_0__r40_rm41_rm1640, axiom, k3_xcmplx_0(40, k4_xcmplx_0(41))=k4_xcmplx_0(1640)).
fof(rqRealMult__k3_xcmplx_0__r41_r1_r41, axiom, k3_xcmplx_0(41, 1)=41).
fof(rqRealMult__k3_xcmplx_0__r41_r41_r1681, axiom, k3_xcmplx_0(41, 41)=1681).
fof(rqRealMult__k3_xcmplx_0__rm40_r1_rm40, axiom, k3_xcmplx_0(k4_xcmplx_0(40), 1)=k4_xcmplx_0(40)).
fof(rqRealMult__k3_xcmplx_0__rm41_r1_rm41, axiom, k3_xcmplx_0(k4_xcmplx_0(41), 1)=k4_xcmplx_0(41)).
fof(rqRealMult__k3_xcmplx_0__rm41_rm41_r1681, axiom, k3_xcmplx_0(k4_xcmplx_0(41), k4_xcmplx_0(41))=1681).
fof(rqRealMult__k3_xcmplx_0__rn1d41_r41_r1, axiom, k3_xcmplx_0(k7_xcmplx_0(1, 41), 41)=1).
fof(rqRealMult__k3_xcmplx_0__rnm1d41_r1681_rm41, axiom, k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1), 41), 1681)=k4_xcmplx_0(41)).
fof(rqRealMult__k3_xcmplx_0__rnm1d41_rm41_r1, axiom, k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1), 41), k4_xcmplx_0(41))=1).
fof(rqRealNeg__k4_xcmplx_0__r0_r0, axiom, k4_xcmplx_0(0)=0).
fof(rqRealNeg__k4_xcmplx_0__r1680_rm1680, axiom, k4_xcmplx_0(1680)=k4_xcmplx_0(1680)).
fof(rqRealNeg__k4_xcmplx_0__r1681_rm1681, axiom, k4_xcmplx_0(1681)=k4_xcmplx_0(1681)).
fof(rqRealNeg__k4_xcmplx_0__r1_rm1, axiom, k4_xcmplx_0(1)=k4_xcmplx_0(1)).
fof(rqRealNeg__k4_xcmplx_0__r40_rm40, axiom, k4_xcmplx_0(40)=k4_xcmplx_0(40)).
fof(rqRealNeg__k4_xcmplx_0__r41_rm41, axiom, k4_xcmplx_0(41)=k4_xcmplx_0(41)).
fof(rqRealNeg__k4_xcmplx_0__rm1640_r1640, axiom, k4_xcmplx_0(k4_xcmplx_0(1640))=1640).
fof(rqRealNeg__k4_xcmplx_0__rm1680_r1680, axiom, k4_xcmplx_0(k4_xcmplx_0(1680))=1680).
fof(rqRealNeg__k4_xcmplx_0__rm1_r1, axiom, k4_xcmplx_0(k4_xcmplx_0(1))=1).
fof(rqRealNeg__k4_xcmplx_0__rm40_r40, axiom, k4_xcmplx_0(k4_xcmplx_0(40))=40).
fof(rqRealNeg__k4_xcmplx_0__rm41_r41, axiom, k4_xcmplx_0(k4_xcmplx_0(41))=41).
fof(spc0_numerals, axiom, m1_subset_1(0, k4_ordinal1)).
fof(spc1640_numerals, axiom,  (v2_xxreal_0(1640) & m1_subset_1(1640, k4_ordinal1)) ).
fof(spc1680_numerals, axiom,  (v2_xxreal_0(1680) & m1_subset_1(1680, k4_ordinal1)) ).
fof(spc1681_numerals, axiom,  (v2_xxreal_0(1681) & m1_subset_1(1681, k4_ordinal1)) ).
fof(spc1_numerals, axiom,  (v2_xxreal_0(1) & m1_subset_1(1, k4_ordinal1)) ).
fof(spc2_arithm, axiom,  (! [A] :  (v1_xcmplx_0(A) => k3_xcmplx_0(A, k4_xcmplx_0(1))=k4_xcmplx_0(A)) ) ).
fof(spc40_numerals, axiom,  (v2_xxreal_0(40) & m1_subset_1(40, k4_ordinal1)) ).
fof(spc41_numerals, axiom,  (v2_xxreal_0(41) & m1_subset_1(41, k4_ordinal1)) ).
fof(spc4_arithm, axiom,  (! [A, B, C] :  ( (v1_xcmplx_0(A) &  (v1_xcmplx_0(B) & v1_xcmplx_0(C)) )  => k3_xcmplx_0(A, k7_xcmplx_0(B, C))=k7_xcmplx_0(k3_xcmplx_0(A, B), C)) ) ).
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(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(t3_arithm, axiom,  (! [A] :  (v1_xcmplx_0(A) => k3_xcmplx_0(1, A)=A) ) ).
fof(t6_arithm, axiom,  (! [A] :  (v1_xcmplx_0(A) => k7_xcmplx_0(A, 1)=A) ) ).
