% Mizar problem: t36_interva1,interva1,1201,7 
fof(t36_interva1, conjecture,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( ( ~ (v1_xboole_0(B))  & m1_interva1(B, A))  =>  (! [C] :  ( ( ~ (v1_xboole_0(C))  & m1_interva1(C, A))  => r1_interva1(A, k4_interva1(A, k3_interva1(A, B, C), C), C)) ) ) ) ) ) ).
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(cc1_subset_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_xboole_0(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(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(cc4_subset_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) =>  ~ (v1_subset_1(B, A)) ) ) ) ) ).
fof(commutativity_k2_setfam_1, axiom,  (! [A, B] : k2_setfam_1(A, B)=k2_setfam_1(B, A)) ).
fof(commutativity_k3_setfam_1, axiom,  (! [A, B] : k3_setfam_1(A, B)=k3_setfam_1(B, A)) ).
fof(d3_interva1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( ( ~ (v1_xboole_0(B))  & m1_interva1(B, A))  =>  (! [C] :  ( ( ~ (v1_xboole_0(C))  & m1_interva1(C, A))  => k3_interva1(A, B, C)=k3_setfam_1(B, C)) ) ) ) ) ) ).
fof(d4_interva1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( ( ~ (v1_xboole_0(B))  & m1_interva1(B, A))  =>  (! [C] :  ( ( ~ (v1_xboole_0(C))  & m1_interva1(C, A))  => k4_interva1(A, B, C)=k2_setfam_1(B, C)) ) ) ) ) ) ).
fof(d7_interva1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( ( ~ (v1_xboole_0(B))  & m1_interva1(B, A))  =>  (! [C] :  ( ( ~ (v1_xboole_0(C))  & m1_interva1(C, A))  =>  (r1_interva1(A, B, C) <=>  (k5_interva1(A, B)=k5_interva1(A, C) & k6_interva1(A, B)=k6_interva1(A, C)) ) ) ) ) ) ) ) ).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k2_setfam_1, axiom, $true).
fof(dt_k3_interva1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( ( ~ (v1_xboole_0(B))  & m1_interva1(B, A))  &  ( ~ (v1_xboole_0(C))  & m1_interva1(C, A)) ) )  => m1_interva1(k3_interva1(A, B, C), A)) ) ).
fof(dt_k3_setfam_1, axiom, $true).
fof(dt_k4_interva1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( ( ~ (v1_xboole_0(B))  & m1_interva1(B, A))  &  ( ~ (v1_xboole_0(C))  & m1_interva1(C, A)) ) )  => m1_interva1(k4_interva1(A, B, C), A)) ) ).
fof(dt_k5_interva1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  & m1_interva1(B, A)) )  => m1_subset_1(k5_interva1(A, B), k1_zfmisc_1(A))) ) ).
fof(dt_k6_interva1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  & m1_interva1(B, A)) )  => m1_subset_1(k6_interva1(A, B), k1_zfmisc_1(A))) ) ).
fof(dt_m1_interva1, axiom,  (! [A] :  (! [B] :  (m1_interva1(B, A) => m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) ) ) ).
fof(dt_m1_subset_1, axiom, $true).
fof(existence_m1_interva1, axiom,  (! [A] :  (? [B] : m1_interva1(B, A)) ) ).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(fc1_interva1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( ( ~ (v1_xboole_0(B))  & m1_interva1(B, A))  &  ( ~ (v1_xboole_0(C))  & m1_interva1(C, A)) ) )  =>  ~ (v1_xboole_0(k3_interva1(A, B, C))) ) ) ).
fof(fc1_subset_1, axiom,  (! [A] :  ~ (v1_xboole_0(k1_zfmisc_1(A))) ) ).
fof(fc1_xboole_0, axiom, v1_xboole_0(k1_xboole_0)).
fof(fc2_interva1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( ( ~ (v1_xboole_0(B))  & m1_interva1(B, A))  &  ( ~ (v1_xboole_0(C))  & m1_interva1(C, A)) ) )  =>  ~ (v1_xboole_0(k4_interva1(A, B, C))) ) ) ).
fof(l40_interva1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( ( ~ (v1_xboole_0(B))  & m1_interva1(B, A))  =>  ( ~ (v1_xboole_0(B))  &  (v1_interva1(B, A) & m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) ) ) ) ) ) ).
fof(rc1_interva1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_interva1(B, A) &  ~ (v1_xboole_0(B)) ) ) ) ) ).
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_xboole_0, axiom,  (? [A] : v1_xboole_0(A)) ).
fof(rc2_interva1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A))) &  ( ~ (v1_xboole_0(B))  & v1_interva1(B, A)) ) ) ) ).
fof(rc2_subset_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_xboole_0(B)) ) ) ).
fof(rc2_xboole_0, axiom,  (? [A] :  ~ (v1_xboole_0(A)) ) ).
fof(rc3_subset_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_subset_1(B, 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(redefinition_r1_interva1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( ( ~ (v1_xboole_0(B))  & m1_interva1(B, A))  &  ( ~ (v1_xboole_0(C))  & m1_interva1(C, A)) ) )  =>  (r1_interva1(A, B, C) <=> B=C) ) ) ).
fof(redefinition_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) <=> r2_hidden(A, B)) ) ).
fof(reflexivity_r1_interva1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( ( ~ (v1_xboole_0(B))  & m1_interva1(B, A))  &  ( ~ (v1_xboole_0(C))  & m1_interva1(C, A)) ) )  => r1_interva1(A, B, B)) ) ).
fof(reflexivity_r1_tarski, axiom,  (! [A, B] : r1_tarski(A, A)) ).
fof(symmetry_r1_interva1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( ( ~ (v1_xboole_0(B))  & m1_interva1(B, A))  &  ( ~ (v1_xboole_0(C))  & m1_interva1(C, A)) ) )  =>  (r1_interva1(A, B, C) => r1_interva1(A, C, B)) ) ) ).
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(t34_interva1, axiom,  (! [A] :  (! [B] :  ( ( ~ (v1_xboole_0(B))  &  (v1_interva1(B, A) & m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) )  =>  (! [C] :  ( ( ~ (v1_xboole_0(C))  &  (v1_interva1(C, A) & m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A)))) )  => k2_setfam_1(k3_setfam_1(B, C), C)=C) ) ) ) ) ).
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(t5_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ~ ( (r2_tarski(A, B) &  (m1_subset_1(B, k1_zfmisc_1(C)) & v1_xboole_0(C)) ) ) ) ) ) ).
fof(t6_boole, axiom,  (! [A] :  (v1_xboole_0(A) => A=k1_xboole_0) ) ).
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)) ) ) ) ) ).
