% Mizar problem: t40_gtarski4,gtarski4,1513,7 
fof(t40_gtarski4, conjecture,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v9_gtarski1(A) &  (v1_gtarski2(A) & l1_gtarski1(A)) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(A)) =>  (! [F] :  (m1_subset_1(F, u1_struct_0(A)) =>  (! [G] :  (m1_subset_1(G, u1_struct_0(A)) =>  ~ ( (r6_gtarski4(A, D, B, B, C) &  (r6_gtarski4(A, E, C, B, C) &  (r6_gtarski1(A, B, C, G) &  (r1_gtarski1(A, D, G, E) &  (r1_gtarski1(A, C, F, E) &  (r2_gtarski1(A, B, D, C, F) &  (! [H] :  (m1_subset_1(H, u1_struct_0(A)) =>  ~ ( (r9_gtarski3(A, B, C, H) & r9_gtarski3(A, D, F, H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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(cc13_gtarski3, axiom,  (! [A] :  (l1_gtarski1(A) =>  (v2_gtarski1(A) => v2_gtarski3(A)) ) ) ).
fof(cc14_gtarski3, axiom,  (! [A] :  (l1_gtarski1(A) =>  (v3_gtarski1(A) => v3_gtarski3(A)) ) ) ).
fof(cc15_gtarski3, axiom,  (! [A] :  (l1_gtarski1(A) =>  (v4_gtarski1(A) => v4_gtarski3(A)) ) ) ).
fof(cc16_gtarski3, axiom,  (! [A] :  (l1_gtarski1(A) =>  (v5_gtarski1(A) => v5_gtarski3(A)) ) ) ).
fof(cc17_gtarski3, axiom,  (! [A] :  (l1_gtarski1(A) =>  (v7_gtarski1(A) => v7_gtarski3(A)) ) ) ).
fof(cc18_gtarski3, axiom,  (! [A] :  (l1_gtarski1(A) =>  (v8_gtarski1(A) => v8_gtarski3(A)) ) ) ).
fof(cc19_gtarski3, axiom,  (! [A] :  (l1_gtarski1(A) =>  (v1_gtarski2(A) => v9_gtarski3(A)) ) ) ).
fof(cc1_gtarski3, axiom,  (! [A] :  (l1_gtarski1(A) =>  ( (v2_gtarski1(A) &  (v3_gtarski1(A) & v1_gtarski3(A)) )  =>  (v2_gtarski1(A) &  (v3_gtarski1(A) & v6_gtarski1(A)) ) ) ) ) ).
fof(cc2_gtarski3, axiom,  (! [A] :  (l1_gtarski1(A) =>  ( (v2_gtarski1(A) &  (v3_gtarski1(A) & v6_gtarski1(A)) )  =>  (v2_gtarski1(A) &  (v3_gtarski1(A) & v1_gtarski3(A)) ) ) ) ) ).
fof(cc3_gtarski3, axiom,  (! [A] :  (l1_gtarski1(A) =>  (v2_gtarski3(A) => v2_gtarski1(A)) ) ) ).
fof(cc4_gtarski3, axiom,  (! [A] :  (l1_gtarski1(A) =>  (v3_gtarski3(A) => v3_gtarski1(A)) ) ) ).
fof(cc5_gtarski3, axiom,  (! [A] :  (l1_gtarski1(A) =>  (v4_gtarski3(A) => v4_gtarski1(A)) ) ) ).
fof(cc6_gtarski1, axiom,  (! [A] :  (l1_gtarski1(A) =>  ( (v2_gtarski1(A) &  (v3_gtarski1(A) &  (v4_gtarski1(A) &  (v5_gtarski1(A) &  (v6_gtarski1(A) &  (v7_gtarski1(A) & v8_gtarski1(A)) ) ) ) ) )  => v9_gtarski1(A)) ) ) ).
fof(cc6_gtarski3, axiom,  (! [A] :  (l1_gtarski1(A) =>  (v5_gtarski3(A) => v5_gtarski1(A)) ) ) ).
fof(cc7_gtarski1, axiom,  (! [A] :  (l1_gtarski1(A) =>  (v9_gtarski1(A) =>  (v2_gtarski1(A) &  (v3_gtarski1(A) &  (v4_gtarski1(A) &  (v5_gtarski1(A) &  (v6_gtarski1(A) &  (v7_gtarski1(A) & v8_gtarski1(A)) ) ) ) ) ) ) ) ) ).
fof(cc7_gtarski3, axiom,  (! [A] :  (l1_gtarski1(A) =>  (v7_gtarski3(A) => v7_gtarski1(A)) ) ) ).
fof(cc8_gtarski3, axiom,  (! [A] :  (l1_gtarski1(A) =>  (v8_gtarski3(A) => v8_gtarski1(A)) ) ) ).
fof(cc9_gtarski3, axiom,  (! [A] :  (l1_gtarski1(A) =>  (v9_gtarski3(A) => v1_gtarski2(A)) ) ) ).
fof(commutativity_k1_gtarski4, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v4_gtarski1(A) &  (v5_gtarski1(A) &  (v7_gtarski1(A) &  (v8_gtarski1(A) & l1_gtarski1(A)) ) ) ) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => k1_gtarski4(A, B, C)=k1_gtarski4(A, C, B)) ) ).
fof(d10_gtarski1, axiom,  (! [A] :  (l1_gtarski1(A) =>  (v7_gtarski1(A) <=>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (r1_gtarski1(A, B, C, B) => B=C) ) ) ) ) ) ) ) ).
fof(d11_gtarski1, axiom,  (! [A] :  (l1_gtarski1(A) =>  (v8_gtarski1(A) <=>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(A)) =>  (! [F] :  (m1_subset_1(F, u1_struct_0(A)) =>  ~ ( (r1_gtarski1(A, B, D, F) &  (r1_gtarski1(A, C, E, F) &  (! [G] :  (m1_subset_1(G, u1_struct_0(A)) =>  ~ ( (r1_gtarski1(A, D, G, C) & r1_gtarski1(A, E, G, B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d11_gtarski3, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_gtarski1(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) =>  (r8_gtarski3(A, B) <=>  (? [C] :  (m1_subset_1(C, u1_struct_0(A)) &  (? [D] :  (m1_subset_1(D, u1_struct_0(A)) &  ( ~ (C=D)  & B=k2_gtarski3(A, C, D)) ) ) ) ) ) ) ) ) ) ).
fof(d12_gtarski3, axiom,  (! [A] :  (l1_gtarski1(A) =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (r9_gtarski3(A, B, C, D) <=>  (r1_gtarski1(A, B, D, C) & r2_gtarski1(A, D, B, D, C)) ) ) ) ) ) ) ) ) ) ).
fof(d13_gtarski3, axiom,  (! [A] :  ( (v2_gtarski1(A) &  (v3_gtarski1(A) &  (v4_gtarski1(A) &  (v5_gtarski1(A) &  (v6_gtarski1(A) &  (v7_gtarski1(A) & l1_gtarski1(A)) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (D=k3_gtarski3(A, B, C) <=> r9_gtarski3(A, C, D, B)) ) ) ) ) ) ) ) ) ).
fof(d17_gtarski1, axiom,  (! [A] :  (l1_gtarski1(A) =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (r6_gtarski1(A, B, C, D) <=>  ~ ( ( ~ (r1_gtarski1(A, B, C, D))  &  ( ~ (r1_gtarski1(A, C, D, B))  &  ~ (r1_gtarski1(A, D, B, C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d1_gtarski4, axiom,  (! [A] :  ( (v2_gtarski1(A) &  (v3_gtarski1(A) &  (v4_gtarski1(A) &  (v5_gtarski1(A) &  (v6_gtarski1(A) &  (v7_gtarski1(A) & l1_gtarski1(A)) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (r1_gtarski4(A, B, C, D) <=> r2_gtarski1(A, B, D, B, k3_gtarski3(A, C, D))) ) ) ) ) ) ) ) ) ).
fof(d2_gtarski4, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v9_gtarski1(A) & l1_gtarski1(A)) )  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (r2_gtarski4(A, B, C, D) <=>  (r8_gtarski3(A, B) &  (r8_gtarski3(A, C) &  (r2_hidden(D, B) &  (r2_hidden(D, C) &  (! [E] :  (m1_subset_1(E, u1_struct_0(A)) =>  (! [F] :  (m1_subset_1(F, u1_struct_0(A)) =>  ( (r2_hidden(E, B) & r2_hidden(F, C))  => r1_gtarski4(A, E, D, F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d3_gtarski4, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v9_gtarski1(A) & l1_gtarski1(A)) )  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) =>  (r3_gtarski4(A, B, C) <=>  (? [D] :  (m1_subset_1(D, u1_struct_0(A)) & r2_gtarski4(A, B, C, D)) ) ) ) ) ) ) ) ) ).
fof(d5_gtarski3, axiom,  (! [A] :  (l1_gtarski1(A) =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(A)) =>  (! [F] :  (m1_subset_1(F, u1_struct_0(A)) =>  (! [G] :  (m1_subset_1(G, u1_struct_0(A)) =>  (! [H] :  (m1_subset_1(H, u1_struct_0(A)) =>  (! [I] :  (m1_subset_1(I, u1_struct_0(A)) =>  (r4_gtarski3(A, B, C, D, E, F, G, H, I) <=>  (r1_gtarski1(A, B, C, D) &  (r1_gtarski1(A, F, G, H) &  (r2_gtarski1(A, B, D, F, H) &  (r2_gtarski1(A, C, D, G, H) &  (r2_gtarski1(A, B, E, F, I) & r2_gtarski1(A, D, E, H, I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d6_gtarski4, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v9_gtarski1(A) & l1_gtarski1(A)) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(A)) =>  (r6_gtarski4(A, B, C, D, E) <=>  ( ~ (B=C)  &  ( ~ (D=E)  & r3_gtarski4(A, k1_gtarski4(A, B, C), k1_gtarski4(A, D, E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d7_gtarski1, axiom,  (! [A] :  (l1_gtarski1(A) =>  (v4_gtarski1(A) <=>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (r2_gtarski1(A, B, C, D, D) => B=C) ) ) ) ) ) ) ) ) ) ).
fof(d8_gtarski1, axiom,  (! [A] :  (l1_gtarski1(A) =>  (v5_gtarski1(A) <=>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(A)) =>  (? [F] :  (m1_subset_1(F, u1_struct_0(A)) &  (r1_gtarski1(A, C, B, F) & r2_gtarski1(A, B, F, D, E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d8_gtarski4, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v9_gtarski1(A) & l1_gtarski1(A)) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(A)) =>  (r8_gtarski4(A, B, C, D, E) <=>  (r6_gtarski1(A, B, C, E) & r6_gtarski4(A, B, C, D, E)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(dt_k1_gtarski4, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v4_gtarski1(A) &  (v5_gtarski1(A) &  (v7_gtarski1(A) &  (v8_gtarski1(A) & l1_gtarski1(A)) ) ) ) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => m1_subset_1(k1_gtarski4(A, B, C), k1_zfmisc_1(u1_struct_0(A)))) ) ).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k2_gtarski3, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  & l1_gtarski1(A))  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => m1_subset_1(k2_gtarski3(A, B, C), k1_zfmisc_1(u1_struct_0(A)))) ) ).
fof(dt_k3_gtarski3, axiom,  (! [A, B, C] :  ( ( (v2_gtarski1(A) &  (v3_gtarski1(A) &  (v4_gtarski1(A) &  (v5_gtarski1(A) &  (v6_gtarski1(A) &  (v7_gtarski1(A) & l1_gtarski1(A)) ) ) ) ) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => m1_subset_1(k3_gtarski3(A, B, C), u1_struct_0(A))) ) ).
fof(dt_l1_gtarski1, axiom,  (! [A] :  (l1_gtarski1(A) => l1_struct_0(A)) ) ).
fof(dt_l1_struct_0, axiom, $true).
fof(dt_m1_subset_1, axiom, $true).
fof(dt_u1_struct_0, axiom, $true).
fof(existence_l1_gtarski1, axiom,  (? [A] : l1_gtarski1(A)) ).
fof(existence_l1_struct_0, axiom,  (? [A] : l1_struct_0(A)) ).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(l1_gtarski4, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v9_gtarski1(A) & l1_gtarski1(A)) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (r6_gtarski1(A, B, C, D) => r2_hidden(D, k1_gtarski4(A, B, C))) ) ) ) ) ) ) ) ) ).
fof(l2_gtarski4, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v9_gtarski1(A) & l1_gtarski1(A)) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (r2_hidden(C, k1_gtarski4(A, B, D)) => r6_gtarski1(A, C, B, D)) ) ) ) ) ) ) ) ) ).
fof(l48_gtarski4, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v9_gtarski1(A) &  (v1_gtarski2(A) & l1_gtarski1(A)) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  ~ ( ( ~ (B=D)  & k3_gtarski3(A, B, D)=D) ) ) ) ) ) ) ) ) ) ).
fof(rc1_gtarski3, axiom,  (? [A] :  (l1_gtarski1(A) &  (v2_gtarski1(A) &  (v3_gtarski1(A) &  (v4_gtarski1(A) &  (v5_gtarski1(A) &  (v6_gtarski1(A) &  (v7_gtarski1(A) &  (v8_gtarski1(A) &  (v9_gtarski1(A) &  (v1_gtarski2(A) & v1_gtarski3(A)) ) ) ) ) ) ) ) ) ) ) ).
fof(rc2_gtarski3, axiom,  (? [A] :  (l1_gtarski1(A) &  ( ~ (v2_struct_0(A))  &  (v2_gtarski1(A) &  (v3_gtarski1(A) &  (v4_gtarski1(A) &  (v5_gtarski1(A) &  (v6_gtarski1(A) &  (v7_gtarski1(A) &  (v8_gtarski1(A) &  (v9_gtarski1(A) &  (v1_gtarski2(A) & v1_gtarski3(A)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc3_gtarski3, axiom,  (? [A] :  (l1_gtarski1(A) &  (v2_gtarski3(A) & v3_gtarski3(A)) ) ) ).
fof(rc5_gtarski1, axiom,  (? [A] :  (l1_gtarski1(A) &  ( ~ (v2_struct_0(A))  & v9_gtarski1(A)) ) ) ).
fof(rc5_gtarski3, axiom,  (? [A] :  (l1_gtarski1(A) &  (v3_gtarski3(A) & v5_gtarski3(A)) ) ) ).
fof(redefinition_k1_gtarski4, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v4_gtarski1(A) &  (v5_gtarski1(A) &  (v7_gtarski1(A) &  (v8_gtarski1(A) & l1_gtarski1(A)) ) ) ) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => k1_gtarski4(A, B, C)=k2_gtarski3(A, B, C)) ) ).
fof(redefinition_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) <=> r2_hidden(A, B)) ) ).
fof(t100_gtarski3, axiom,  (! [A] :  ( (v2_gtarski1(A) &  (v3_gtarski1(A) &  (v4_gtarski1(A) &  (v5_gtarski1(A) &  (v6_gtarski1(A) &  (v7_gtarski1(A) & l1_gtarski1(A)) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (k3_gtarski3(A, B, C)=D <=> r9_gtarski3(A, C, D, B)) ) ) ) ) ) ) ) ) ).
fof(t112_gtarski3, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v9_gtarski1(A) & l1_gtarski1(A)) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(A)) =>  (! [F] :  (m1_subset_1(F, u1_struct_0(A)) =>  ( (r2_gtarski1(A, B, C, D, E) &  (r2_gtarski1(A, C, D, E, B) &  (r6_gtarski1(A, B, F, D) & r6_gtarski1(A, C, F, E)) ) )  =>  (r6_gtarski1(A, B, C, D) |  (C=E |  (r9_gtarski3(A, B, D, F) & r9_gtarski3(A, C, E, F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t115_gtarski3, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v9_gtarski1(A) & l1_gtarski1(A)) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(A)) =>  (! [F] :  (m1_subset_1(F, u1_struct_0(A)) =>  (! [G] :  (m1_subset_1(G, u1_struct_0(A)) =>  (! [H] :  (m1_subset_1(H, u1_struct_0(A)) =>  ( (r1_gtarski1(A, C, B, D) &  (r1_gtarski1(A, E, B, F) &  (r2_gtarski1(A, B, C, B, E) &  (r2_gtarski1(A, B, D, B, F) &  (r9_gtarski3(A, C, E, G) & r9_gtarski3(A, D, F, H)) ) ) ) )  => r1_gtarski1(A, G, B, H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t117_gtarski3, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v9_gtarski1(A) &  (v1_gtarski2(A) & l1_gtarski1(A)) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  ~ ( (r2_gtarski1(A, D, B, D, C) &  (! [E] :  (m1_subset_1(E, u1_struct_0(A)) =>  ~ (r9_gtarski3(A, B, C, E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t11_gtarski3, axiom,  (! [A] :  ( (v2_gtarski1(A) &  (v3_gtarski1(A) &  (v4_gtarski1(A) &  (v5_gtarski1(A) &  (v6_gtarski1(A) & l1_gtarski1(A)) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(A)) =>  (! [F] :  (m1_subset_1(F, u1_struct_0(A)) =>  (! [G] :  (m1_subset_1(G, u1_struct_0(A)) =>  ( (r1_gtarski1(A, B, C, D) &  (r1_gtarski1(A, E, F, G) &  (r2_gtarski1(A, B, C, E, F) & r2_gtarski1(A, C, D, F, G)) ) )  => r2_gtarski1(A, B, D, E, G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t13_gtarski4, axiom,  (! [A] :  ( (v9_gtarski1(A) & l1_gtarski1(A))  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (r1_gtarski4(A, B, C, D) => r1_gtarski4(A, D, C, B)) ) ) ) ) ) ) ) ) ).
fof(t14_gtarski3, axiom,  (! [A] :  ( (v4_gtarski1(A) &  (v5_gtarski1(A) &  (v7_gtarski1(A) &  (v8_gtarski1(A) & l1_gtarski1(A)) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (r1_gtarski1(A, B, C, D) => r1_gtarski1(A, D, C, B)) ) ) ) ) ) ) ) ) ).
fof(t15_gtarski4, axiom,  (! [A] :  ( (v9_gtarski1(A) & l1_gtarski1(A))  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(A)) =>  ( (r1_gtarski4(A, B, D, E) & r6_gtarski1(A, D, B, C))  =>  (B=D | r1_gtarski4(A, C, D, E)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t1_gtarski3, axiom,  (! [A] :  ( (v2_gtarski1(A) &  (v3_gtarski1(A) & l1_gtarski1(A)) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) => r2_gtarski1(A, B, C, B, C)) ) ) ) ) ) ).
fof(t1_gtarski4, axiom,  (! [A] :  ( (v2_gtarski1(A) &  (v3_gtarski1(A) &  (v4_gtarski1(A) & l1_gtarski1(A)) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(A)) =>  (r2_gtarski1(A, B, C, D, E) =>  (r2_gtarski1(A, B, C, E, D) &  (r2_gtarski1(A, C, B, D, E) &  (r2_gtarski1(A, C, B, E, D) &  (r2_gtarski1(A, D, E, B, C) &  (r2_gtarski1(A, E, D, B, C) &  (r2_gtarski1(A, D, E, C, B) & r2_gtarski1(A, E, D, C, B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t20_gtarski4, axiom,  (! [A] :  ( (v9_gtarski1(A) & l1_gtarski1(A))  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (r1_gtarski4(A, B, C, B) => B=C) ) ) ) ) ) ) ).
fof(t21_gtarski4, axiom,  (! [A] :  ( (v9_gtarski1(A) & l1_gtarski1(A))  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  ~ ( (r1_gtarski4(A, B, C, D) &  (r6_gtarski1(A, B, C, D) &  ( ~ (B=C)  &  ~ (D=C) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t23_gtarski4, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v9_gtarski1(A) & l1_gtarski1(A)) )  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (r2_gtarski4(A, B, C, D) <=> r2_gtarski4(A, C, B, D)) ) ) ) ) ) ) ) ) ).
fof(t24_gtarski4, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v9_gtarski1(A) & l1_gtarski1(A)) )  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (r2_gtarski4(A, B, C, D) <=>  (r8_gtarski3(A, B) &  (r8_gtarski3(A, C) &  (r2_hidden(D, B) &  (r2_hidden(D, C) &  (? [E] :  (m1_subset_1(E, u1_struct_0(A)) &  (? [F] :  (m1_subset_1(F, u1_struct_0(A)) &  (r2_hidden(E, B) &  (r2_hidden(F, C) &  ( ~ (E=D)  &  ( ~ (F=D)  & r1_gtarski4(A, E, D, F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t31_gtarski4, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v9_gtarski1(A) & l1_gtarski1(A)) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(A)) =>  (! [F] :  (m1_subset_1(F, u1_struct_0(A)) =>  ( (r8_gtarski4(A, D, E, F, B) & r8_gtarski4(A, D, E, F, C))  => B=C) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t37_gtarski4, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v9_gtarski1(A) &  (v1_gtarski2(A) & l1_gtarski1(A)) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(A)) =>  ~ ( ( ~ (B=C)  &  ( ~ (B=D)  &  (r1_gtarski4(A, C, B, D) &  (r1_gtarski4(A, B, C, E) & r6_gtarski1(A, D, B, E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t3_gtarski4, axiom,  (! [A] :  ( (v2_gtarski1(A) &  (v3_gtarski1(A) &  (v4_gtarski1(A) & l1_gtarski1(A)) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(A)) =>  (! [F] :  (m1_subset_1(F, u1_struct_0(A)) =>  (! [G] :  (m1_subset_1(G, u1_struct_0(A)) =>  ~ ( ( ~ ( ( ~ (r2_gtarski1(A, B, C, D, E))  &  ( ~ (r2_gtarski1(A, B, C, E, D))  &  ( ~ (r2_gtarski1(A, C, B, D, E))  &  ( ~ (r2_gtarski1(A, C, B, E, D))  &  ( ~ (r2_gtarski1(A, D, E, B, C))  &  ( ~ (r2_gtarski1(A, E, D, B, C))  &  ( ~ (r2_gtarski1(A, D, E, C, B))  &  ~ (r2_gtarski1(A, E, D, C, B)) ) ) ) ) ) ) ) )  &  ( ~ ( ( ~ (r2_gtarski1(A, B, C, F, G))  &  ( ~ (r2_gtarski1(A, B, C, G, F))  &  ( ~ (r2_gtarski1(A, C, B, F, G))  &  ( ~ (r2_gtarski1(A, C, B, G, F))  &  ( ~ (r2_gtarski1(A, F, G, B, C))  &  ( ~ (r2_gtarski1(A, G, F, B, C))  &  ( ~ (r2_gtarski1(A, F, G, C, B))  &  ~ (r2_gtarski1(A, G, F, C, B)) ) ) ) ) ) ) ) )  &  ~ ( (r2_gtarski1(A, D, E, G, F) &  (r2_gtarski1(A, E, D, F, G) &  (r2_gtarski1(A, E, D, G, F) &  (r2_gtarski1(A, F, G, D, E) &  (r2_gtarski1(A, G, F, D, E) &  (r2_gtarski1(A, F, G, E, D) &  (r2_gtarski1(A, G, F, E, D) & r2_gtarski1(A, D, E, F, G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t41_gtarski3, axiom,  (! [A] :  ( (v9_gtarski1(A) & l1_gtarski1(A))  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(A)) =>  (! [F] :  (m1_subset_1(F, u1_struct_0(A)) =>  (! [G] :  (m1_subset_1(G, u1_struct_0(A)) =>  (! [H] :  (m1_subset_1(H, u1_struct_0(A)) =>  (! [I] :  (m1_subset_1(I, u1_struct_0(A)) =>  (r4_gtarski3(A, B, C, D, E, F, G, H, I) => r2_gtarski1(A, C, E, G, I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t45_gtarski3, axiom,  (! [A] :  ( (v4_gtarski1(A) &  (v5_gtarski1(A) &  (v7_gtarski1(A) &  (v8_gtarski1(A) & l1_gtarski1(A)) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (r6_gtarski1(A, B, C, D) =>  (r6_gtarski1(A, C, D, B) &  (r6_gtarski1(A, D, B, C) &  (r6_gtarski1(A, D, C, B) &  (r6_gtarski1(A, C, B, D) & r6_gtarski1(A, B, D, C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t46_gtarski3, axiom,  (! [A] :  ( (v4_gtarski1(A) &  (v5_gtarski1(A) & l1_gtarski1(A)) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) => r6_gtarski1(A, B, B, C)) ) ) ) ) ) ).
fof(t4_gtarski3, axiom,  (! [A] :  ( (v3_gtarski1(A) &  (v5_gtarski1(A) & l1_gtarski1(A)) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(A)) =>  (r2_gtarski1(A, B, C, D, E) => r2_gtarski1(A, D, E, B, C)) ) ) ) ) ) ) ) ) ) ) ).
fof(t4_gtarski4, axiom,  (! [A] :  ( (v4_gtarski1(A) &  (v5_gtarski1(A) &  (v7_gtarski1(A) &  (v8_gtarski1(A) & l1_gtarski1(A)) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (r6_gtarski1(A, B, C, C) &  (r6_gtarski1(A, C, C, B) & r6_gtarski1(A, C, B, C)) ) ) ) ) ) ) ) ).
fof(t5_gtarski1, axiom,  (! [A] :  ( (v9_gtarski1(A) & l1_gtarski1(A))  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (r2_gtarski1(A, B, C, D, D) => B=C) ) ) ) ) ) ) ) ) ).
fof(t5_gtarski4, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v9_gtarski1(A) & l1_gtarski1(A)) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  ~ ( ( ~ (B=C)  &  ( ~ (B=D)  &  ( ~ ( ( ~ (r6_gtarski1(A, B, C, D))  &  ( ~ (r6_gtarski1(A, C, D, B))  &  ( ~ (r6_gtarski1(A, D, B, C))  &  ( ~ (r6_gtarski1(A, B, D, C))  &  ( ~ (r6_gtarski1(A, C, B, D))  &  ~ (r6_gtarski1(A, D, C, B)) ) ) ) ) ) )  &  ~ ( (k1_gtarski4(A, B, C)=k1_gtarski4(A, B, D) &  (k1_gtarski4(A, B, C)=k1_gtarski4(A, D, B) &  (k1_gtarski4(A, C, B)=k1_gtarski4(A, B, D) & k1_gtarski4(A, C, B)=k1_gtarski4(A, D, B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t6_gtarski4, axiom,  (! [A] :  (l1_gtarski1(A) =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  ( (r9_gtarski3(A, B, D, C) | r1_gtarski1(A, B, C, D))  => r6_gtarski1(A, B, C, D)) ) ) ) ) ) ) ) ) ).
fof(t7_gtarski4, axiom,  (! [A] :  ( (v4_gtarski1(A) &  (v5_gtarski1(A) &  (v7_gtarski1(A) &  (v8_gtarski1(A) & l1_gtarski1(A)) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  ( (r9_gtarski3(A, B, D, C) | r1_gtarski1(A, B, C, D))  =>  (r6_gtarski1(A, B, C, D) &  (r6_gtarski1(A, C, D, B) &  (r6_gtarski1(A, D, B, C) &  (r6_gtarski1(A, D, C, B) &  (r6_gtarski1(A, C, B, D) & r6_gtarski1(A, B, D, C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t82_gtarski3, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v9_gtarski1(A) & l1_gtarski1(A)) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (r2_tarski(D, k2_gtarski3(A, B, C)) =>  (B=C |  (D=B | k2_gtarski3(A, B, C)=k2_gtarski3(A, B, D)) ) ) ) ) ) ) ) ) ) ) ).
fof(t83_gtarski3, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v4_gtarski1(A) &  (v5_gtarski1(A) &  (v7_gtarski1(A) &  (v8_gtarski1(A) & l1_gtarski1(A)) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (r2_tarski(B, k2_gtarski3(A, B, C)) &  (r2_tarski(C, k2_gtarski3(A, B, C)) & k2_gtarski3(A, B, C)=k2_gtarski3(A, C, B)) ) ) ) ) ) ) ) ).
fof(t8_gtarski1, axiom,  (! [A] :  ( (v9_gtarski1(A) & l1_gtarski1(A))  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (r1_gtarski1(A, B, C, B) => B=C) ) ) ) ) ) ) ).
fof(t8_gtarski4, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v9_gtarski1(A) & l1_gtarski1(A)) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(A)) =>  ( (r6_gtarski1(A, B, C, D) & r6_gtarski1(A, B, C, E))  =>  (B=C | r6_gtarski1(A, B, D, E)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t96_gtarski3, axiom,  (! [A] :  ( (v2_gtarski1(A) &  (v3_gtarski1(A) &  (v4_gtarski1(A) &  (v5_gtarski1(A) &  (v7_gtarski1(A) &  (v8_gtarski1(A) & l1_gtarski1(A)) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (r9_gtarski3(A, B, C, D) => r9_gtarski3(A, C, B, D)) ) ) ) ) ) ) ) ) ).
fof(t97_gtarski3, axiom,  (! [A] :  ( (v2_gtarski1(A) &  (v3_gtarski1(A) &  (v4_gtarski1(A) &  (v5_gtarski1(A) &  (v7_gtarski1(A) & l1_gtarski1(A)) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (r9_gtarski3(A, B, B, C) <=> C=B) ) ) ) ) ) ) ).
