============================== FOF-Prover9 =========================== FOF-Prover9 (32) version 2009-11A, November 2009. Process 23974 was started by mccune on cleo, Tue Nov 3 16:59:17 2009 The command was "/home/mccune/LADR/bin/fof-prover9 -f SET660+3.in". ============================== end of head =========================== ============================== INPUT ================================= % Reading from file SET660+3.in assign(max_seconds,120). set(prolog_style_variables). formulas(assumptions). (all B (ilf_type(B,binary_relation_type) -> (all C (ilf_type(C,set_type) -> (member(C,range_of(B)) <-> (exists D (ilf_type(D,set_type) & member(ordered_pair(D,C),B)))))))). (all B (ilf_type(B,binary_relation_type) -> ilf_type(range_of(B),set_type))). (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,binary_relation_type) -> (member(ordered_pair(B,C),D) -> member(B,domain_of(D)) & member(C,range_of(D))))))))). (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> ((all D (ilf_type(D,set_type) -> (member(D,B) <-> member(D,C)))) -> B = C))))). (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,set_type) -> (all E (ilf_type(E,set_type) -> (all F (ilf_type(F,set_type) -> (F = ordered_pair(D,E) <-> F = unordered_pair(unordered_pair(D,E),singleton(D))))))))))))). (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> ilf_type(ordered_pair(B,C),set_type))))). (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,subset_type(cross_product(B,C))) -> ilf_type(D,relation_type(B,C)))) & (all E (ilf_type(E,relation_type(B,C)) -> ilf_type(E,subset_type(cross_product(B,C))))))))). (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (exists D ilf_type(D,relation_type(C,B))))))). (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (B = C <-> subset(B,C) & subset(C,B)))))). (all B (ilf_type(B,binary_relation_type) -> ilf_type(domain_of(B),set_type))). (all B (ilf_type(B,set_type) -> ilf_type(singleton(B),set_type))). (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> ilf_type(cross_product(B,C),set_type))))). (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> ilf_type(unordered_pair(B,C),set_type))))). (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> unordered_pair(B,C) = unordered_pair(C,B))))). (all B (ilf_type(B,set_type) -> (ilf_type(B,binary_relation_type) <-> relation_like(B) & ilf_type(B,set_type)))). (exists B ilf_type(B,binary_relation_type)). (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (ilf_type(C,subset_type(B)) <-> ilf_type(C,member_type(power_set(B)))))))). (all B (ilf_type(B,set_type) -> (exists C ilf_type(C,subset_type(B))))). (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (B = C <-> (all D (ilf_type(D,set_type) -> (member(D,B) <-> member(D,C))))))))). (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (subset(B,C) <-> (all D (ilf_type(D,set_type) -> (member(D,B) -> member(D,C))))))))). (all B (ilf_type(B,set_type) -> subset(B,B))). (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (member(B,power_set(C)) <-> (all D (ilf_type(D,set_type) -> (member(D,B) -> member(D,C))))))))). (all B (ilf_type(B,set_type) -> -empty(power_set(B)) & ilf_type(power_set(B),set_type))). (all B (ilf_type(B,set_type) -> (all C (-empty(C) & ilf_type(C,set_type) -> (ilf_type(B,member_type(C)) <-> member(B,C)))))). (all B (-empty(B) & ilf_type(B,set_type) -> (exists C ilf_type(C,member_type(B))))). (all B (ilf_type(B,set_type) -> (relation_like(B) <-> (all C (ilf_type(C,set_type) -> (member(C,B) -> (exists D (ilf_type(D,set_type) & (exists E (ilf_type(E,set_type) & C = ordered_pair(D,E))))))))))). (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,subset_type(cross_product(B,C))) -> relation_like(D))))))). (all B (ilf_type(B,set_type) -> (empty(B) <-> (all C (ilf_type(C,set_type) -> -member(C,B)))))). (all B (empty(B) & ilf_type(B,set_type) -> relation_like(B))). (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,relation_type(B,C)) -> domain(B,C,D) = domain_of(D))))))). (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,relation_type(B,C)) -> ilf_type(domain(B,C,D),subset_type(B)))))))). (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,relation_type(B,C)) -> range(B,C,D) = range_of(D))))))). (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,relation_type(B,C)) -> ilf_type(range(B,C,D),subset_type(C)))))))). (all B ilf_type(B,set_type)). -(all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,relation_type(B,C)) -> ((all E (ilf_type(E,set_type) -> (member(E,C) -> (exists F (ilf_type(F,set_type) & member(ordered_pair(F,E),D)))))) <-> range(B,C,D) = C))))))). end_of_list. ============================== end of input ========================== % clear(auto_denials), because it is incompatiable with FOF reduction. Attempting problem reduction; original problem has = <549,143>. Problem reduction (0.02 sec) gives 6 independent subproblems: ( <735,116> <734,117> <709,115> <708,116> <709,115> <708,116> ). Max nnf_size of subproblems is 735; max cnf_max is 117. ============================== FOF REDUCTION MULTISEARCH ============= Subproblem 1 of 6 (negated): ((all B (- ilf_type(B,binary_relation_type) | (all C (- ilf_type(C,set_type) | member(C,range_of(B)) | (all D (- ilf_type(D,set_type) | - member(ordered_pair(D,C),B))))))) & (all B (- ilf_type(B,binary_relation_type) | (all C (- ilf_type(C,set_type) | (exists D (ilf_type(D,set_type) & member(ordered_pair(D,C),B))) | - member(C,range_of(B)))))) & (all B (- ilf_type(B,binary_relation_type) | (all C (- ilf_type(C,set_type) | (exists D (ilf_type(D,set_type) & member(ordered_pair(D,C),B))) | (all D (- ilf_type(D,set_type) | - member(ordered_pair(D,C),B))))))) & (all B (- ilf_type(B,binary_relation_type) | ilf_type(range_of(B),set_type))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,binary_relation_type) | - member(ordered_pair(B,C),D) | member(B,domain_of(D)))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,binary_relation_type) | - member(ordered_pair(B,C),D) | member(C,range_of(D)))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (exists D (ilf_type(D,set_type) & member(D,B) & - member(D,C))) | (exists D (ilf_type(D,set_type) & - member(D,B) & member(D,C))) | =(C,B))))) & (all D (- ilf_type(D,set_type) | (all E (- ilf_type(E,set_type) | (all F (- ilf_type(F,set_type) | =(ordered_pair(D,E),F) | - =(unordered_pair(unordered_pair(D,E),singleton(D)),F))))))) & (all D (- ilf_type(D,set_type) | (all E (- ilf_type(E,set_type) | (all F (- ilf_type(F,set_type) | =(unordered_pair(unordered_pair(D,E),singleton(D)),F) | - =(ordered_pair(D,E),F))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | ilf_type(ordered_pair(B,C),set_type))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,subset_type(cross_product(B,C))) | ilf_type(D,relation_type(B,C)))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all E (- ilf_type(E,relation_type(B,C)) | ilf_type(E,subset_type(cross_product(B,C))))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (exists D ilf_type(D,relation_type(C,B))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | =(C,B) | - subset(B,C) | - subset(C,B))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | subset(B,C) | - =(C,B))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | subset(C,B) | - =(C,B))))) & (all B (- ilf_type(B,binary_relation_type) | ilf_type(domain_of(B),set_type))) & (all B (- ilf_type(B,set_type) | ilf_type(singleton(B),set_type))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | ilf_type(cross_product(B,C),set_type))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | ilf_type(unordered_pair(B,C),set_type))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | =(unordered_pair(C,B),unordered_pair(B,C)))))) & (all B (- ilf_type(B,set_type) | ilf_type(B,binary_relation_type) | - relation_like(B))) & (all B (- ilf_type(B,set_type) | relation_like(B) | - ilf_type(B,binary_relation_type))) & (exists B ilf_type(B,binary_relation_type)) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | ilf_type(C,subset_type(B)) | - ilf_type(C,member_type(power_set(B))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | ilf_type(C,member_type(power_set(B))) | - ilf_type(C,subset_type(B)))))) & (all B (- ilf_type(B,set_type) | (exists C ilf_type(C,subset_type(B))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | =(C,B) | (exists D (ilf_type(D,set_type) & member(D,B) & - member(D,C))) | (exists D (ilf_type(D,set_type) & - member(D,B) & member(D,C))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,set_type) | member(D,B) | - member(D,C))) | - =(C,B))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,set_type) | member(D,B) | - member(D,C))) | (exists D (ilf_type(D,set_type) & member(D,B) & - member(D,C))) | (exists D (ilf_type(D,set_type) & - member(D,B) & member(D,C))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,set_type) | member(D,C) | - member(D,B))) | - =(C,B))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,set_type) | member(D,C) | - member(D,B))) | (exists D (ilf_type(D,set_type) & member(D,B) & - member(D,C))) | (exists D (ilf_type(D,set_type) & - member(D,B) & member(D,C))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | subset(B,C) | (exists D (ilf_type(D,set_type) & member(D,B) & - member(D,C))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,set_type) | - member(D,B) | member(D,C))) | - subset(B,C))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,set_type) | - member(D,B) | member(D,C))) | (exists D (ilf_type(D,set_type) & member(D,B) & - member(D,C))))))) & (all B (- ilf_type(B,set_type) | subset(B,B))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | member(B,power_set(C)) | (exists D (ilf_type(D,set_type) & member(D,B) & - member(D,C))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,set_type) | - member(D,B) | member(D,C))) | - member(B,power_set(C)))))) & (all B (- ilf_type(B,set_type) | - empty(power_set(B)))) & (all B (- ilf_type(B,set_type) | ilf_type(power_set(B),set_type))) & (all B (- ilf_type(B,set_type) | (all C (empty(C) | - ilf_type(C,set_type) | ilf_type(B,member_type(C)) | - member(B,C))))) & (all B (- ilf_type(B,set_type) | (all C (empty(C) | - ilf_type(C,set_type) | member(B,C) | - ilf_type(B,member_type(C)))))) & (all B (empty(B) | - ilf_type(B,set_type) | (exists C ilf_type(C,member_type(B))))) & (all B (- ilf_type(B,set_type) | relation_like(B) | (exists C (ilf_type(C,set_type) & member(C,B) & (all D (- ilf_type(D,set_type) | (all E (- ilf_type(E,set_type) | - =(ordered_pair(D,E),C))))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | - member(C,B) | (exists D (ilf_type(D,set_type) & (exists E (ilf_type(E,set_type) & =(ordered_pair(D,E),C))))))) | - relation_like(B))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | - member(C,B) | (exists D (ilf_type(D,set_type) & (exists E (ilf_type(E,set_type) & =(ordered_pair(D,E),C))))))) | (exists C (ilf_type(C,set_type) & member(C,B) & (all D (- ilf_type(D,set_type) | (all E (- ilf_type(E,set_type) | - =(ordered_pair(D,E),C))))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,subset_type(cross_product(B,C))) | relation_like(D))))))) & (all B (- ilf_type(B,set_type) | empty(B) | (exists C (ilf_type(C,set_type) & member(C,B))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | - member(C,B))) | - empty(B))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | - member(C,B))) | (exists C (ilf_type(C,set_type) & member(C,B))))) & (all B (- empty(B) | - ilf_type(B,set_type) | relation_like(B))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,relation_type(B,C)) | =(domain(B,C,D),domain_of(D)))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,relation_type(B,C)) | ilf_type(domain(B,C,D),subset_type(B)))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,relation_type(B,C)) | =(range(B,C,D),range_of(D)))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,relation_type(B,C)) | ilf_type(range(B,C,D),subset_type(C)))))))) & (all B ilf_type(B,set_type)) & (exists B (ilf_type(B,set_type) & (exists C (ilf_type(C,set_type) & (exists D (ilf_type(D,relation_type(B,C)) & (all E (- ilf_type(E,set_type) | - member(E,C) | (exists F (ilf_type(F,set_type) & member(ordered_pair(F,E),D))))) & - =(range(B,C,D),C)))))))). Max_seconds is 120 for this subproblem. Child search process 23975 started. ============================== PROCESS INITIAL CLAUSES =============== % Clauses before input processing: formulas(usable). end_of_list. formulas(sos). -ilf_type(A,binary_relation_type) | -ilf_type(B,set_type) | member(B,range_of(A)) | -ilf_type(C,set_type) | -member(ordered_pair(C,B),A). [assumption]. -ilf_type(A,binary_relation_type) | -ilf_type(B,set_type) | ilf_type(f1(A,B),set_type) | -member(B,range_of(A)). [assumption]. -ilf_type(A,binary_relation_type) | -ilf_type(B,set_type) | member(ordered_pair(f1(A,B),B),A) | -member(B,range_of(A)). [assumption]. -ilf_type(A,binary_relation_type) | -ilf_type(B,set_type) | ilf_type(f2(A,B),set_type) | -ilf_type(C,set_type) | -member(ordered_pair(C,B),A). [assumption]. -ilf_type(A,binary_relation_type) | -ilf_type(B,set_type) | member(ordered_pair(f2(A,B),B),A) | -ilf_type(C,set_type) | -member(ordered_pair(C,B),A). [assumption]. -ilf_type(A,binary_relation_type) | ilf_type(range_of(A),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,binary_relation_type) | -member(ordered_pair(A,B),C) | member(A,domain_of(C)). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,binary_relation_type) | -member(ordered_pair(A,B),C) | member(B,range_of(C)). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(f3(A,B),set_type) | ilf_type(f4(A,B),set_type) | B = A. [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(f3(A,B),set_type) | -member(f4(A,B),A) | B = A. [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(f3(A,B),set_type) | member(f4(A,B),B) | B = A. [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(f3(A,B),A) | ilf_type(f4(A,B),set_type) | B = A. [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(f3(A,B),A) | -member(f4(A,B),A) | B = A. [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(f3(A,B),A) | member(f4(A,B),B) | B = A. [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(f3(A,B),B) | ilf_type(f4(A,B),set_type) | B = A. [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(f3(A,B),B) | -member(f4(A,B),A) | B = A. [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(f3(A,B),B) | member(f4(A,B),B) | B = A. [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | ordered_pair(A,B) = C | unordered_pair(unordered_pair(A,B),singleton(A)) != C. [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | unordered_pair(unordered_pair(A,B),singleton(A)) = C | ordered_pair(A,B) != C. [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(ordered_pair(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,subset_type(cross_product(A,B))) | ilf_type(C,relation_type(A,B)). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,relation_type(A,B)) | ilf_type(C,subset_type(cross_product(A,B))). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(f5(A,B),relation_type(B,A)). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | -subset(A,B) | -subset(B,A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(A,B) | B != A. [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(B,A) | B != A. [assumption]. -ilf_type(A,binary_relation_type) | ilf_type(domain_of(A),set_type). [assumption]. -ilf_type(A,set_type) | ilf_type(singleton(A),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(cross_product(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(unordered_pair(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | unordered_pair(B,A) = unordered_pair(A,B). [assumption]. -ilf_type(A,set_type) | ilf_type(A,binary_relation_type) | -relation_like(A). [assumption]. -ilf_type(A,set_type) | relation_like(A) | -ilf_type(A,binary_relation_type). [assumption]. ilf_type(c1,binary_relation_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(B,subset_type(A)) | -ilf_type(B,member_type(power_set(A))). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(B,member_type(power_set(A))) | -ilf_type(B,subset_type(A)). [assumption]. -ilf_type(A,set_type) | ilf_type(f6(A),subset_type(A)). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | ilf_type(f7(A,B),set_type) | ilf_type(f8(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | ilf_type(f7(A,B),set_type) | -member(f8(A,B),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | ilf_type(f7(A,B),set_type) | member(f8(A,B),B). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | member(f7(A,B),A) | ilf_type(f8(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | member(f7(A,B),A) | -member(f8(A,B),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | member(f7(A,B),A) | member(f8(A,B),B). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | -member(f7(A,B),B) | ilf_type(f8(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | -member(f7(A,B),B) | -member(f8(A,B),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | -member(f7(A,B),B) | member(f8(A,B),B). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,A) | -member(C,B) | B != A. [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,A) | -member(C,B) | ilf_type(f9(A,B),set_type) | ilf_type(f10(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,A) | -member(C,B) | ilf_type(f9(A,B),set_type) | -member(f10(A,B),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,A) | -member(C,B) | ilf_type(f9(A,B),set_type) | member(f10(A,B),B). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,A) | -member(C,B) | member(f9(A,B),A) | ilf_type(f10(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,A) | -member(C,B) | member(f9(A,B),A) | -member(f10(A,B),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,A) | -member(C,B) | member(f9(A,B),A) | member(f10(A,B),B). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,A) | -member(C,B) | -member(f9(A,B),B) | ilf_type(f10(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,A) | -member(C,B) | -member(f9(A,B),B) | -member(f10(A,B),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,A) | -member(C,B) | -member(f9(A,B),B) | member(f10(A,B),B). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,B) | -member(C,A) | B != A. [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,B) | -member(C,A) | ilf_type(f11(A,B),set_type) | ilf_type(f12(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,B) | -member(C,A) | ilf_type(f11(A,B),set_type) | -member(f12(A,B),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,B) | -member(C,A) | ilf_type(f11(A,B),set_type) | member(f12(A,B),B). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,B) | -member(C,A) | member(f11(A,B),A) | ilf_type(f12(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,B) | -member(C,A) | member(f11(A,B),A) | -member(f12(A,B),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,B) | -member(C,A) | member(f11(A,B),A) | member(f12(A,B),B). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,B) | -member(C,A) | -member(f11(A,B),B) | ilf_type(f12(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,B) | -member(C,A) | -member(f11(A,B),B) | -member(f12(A,B),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,B) | -member(C,A) | -member(f11(A,B),B) | member(f12(A,B),B). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(A,B) | ilf_type(f13(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(A,B) | member(f13(A,B),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(A,B) | -member(f13(A,B),B). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | -member(C,A) | member(C,B) | -subset(A,B). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | -member(C,A) | member(C,B) | ilf_type(f14(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | -member(C,A) | member(C,B) | member(f14(A,B),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | -member(C,A) | member(C,B) | -member(f14(A,B),B). [assumption]. -ilf_type(A,set_type) | subset(A,A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(A,power_set(B)) | ilf_type(f15(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(A,power_set(B)) | member(f15(A,B),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(A,power_set(B)) | -member(f15(A,B),B). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | -member(C,A) | member(C,B) | -member(A,power_set(B)). [assumption]. -ilf_type(A,set_type) | -empty(power_set(A)). [assumption]. -ilf_type(A,set_type) | ilf_type(power_set(A),set_type). [assumption]. -ilf_type(A,set_type) | empty(B) | -ilf_type(B,set_type) | ilf_type(A,member_type(B)) | -member(A,B). [assumption]. -ilf_type(A,set_type) | empty(B) | -ilf_type(B,set_type) | member(A,B) | -ilf_type(A,member_type(B)). [assumption]. empty(A) | -ilf_type(A,set_type) | ilf_type(f16(A),member_type(A)). [assumption]. -ilf_type(A,set_type) | relation_like(A) | ilf_type(f17(A),set_type). [assumption]. -ilf_type(A,set_type) | relation_like(A) | member(f17(A),A). [assumption]. -ilf_type(A,set_type) | relation_like(A) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | ordered_pair(B,C) != f17(A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f18(A,B),set_type) | -relation_like(A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f19(A,B),set_type) | -relation_like(A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f18(A,B),f19(A,B)) = B | -relation_like(A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f20(A,B),set_type) | ilf_type(f22(A),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f20(A,B),set_type) | member(f22(A),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f20(A,B),set_type) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | ordered_pair(C,D) != f22(A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f21(A,B),set_type) | ilf_type(f22(A),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f21(A,B),set_type) | member(f22(A),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f21(A,B),set_type) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | ordered_pair(C,D) != f22(A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f20(A,B),f21(A,B)) = B | ilf_type(f22(A),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f20(A,B),f21(A,B)) = B | member(f22(A),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f20(A,B),f21(A,B)) = B | -ilf_type(C,set_type) | -ilf_type(D,set_type) | ordered_pair(C,D) != f22(A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,subset_type(cross_product(A,B))) | relation_like(C). [assumption]. -ilf_type(A,set_type) | empty(A) | ilf_type(f23(A),set_type). [assumption]. -ilf_type(A,set_type) | empty(A) | member(f23(A),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | -empty(A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f24(A),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | member(f24(A),A). [assumption]. -empty(A) | -ilf_type(A,set_type) | relation_like(A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,relation_type(A,B)) | domain(A,B,C) = domain_of(C). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,relation_type(A,B)) | ilf_type(domain(A,B,C),subset_type(A)). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,relation_type(A,B)) | range(A,B,C) = range_of(C). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,relation_type(A,B)) | ilf_type(range(A,B,C),subset_type(B)). [assumption]. ilf_type(A,set_type). [assumption]. ilf_type(c2,set_type). [assumption]. ilf_type(c3,set_type). [assumption]. ilf_type(c4,relation_type(c2,c3)). [assumption]. -ilf_type(A,set_type) | -member(A,c3) | ilf_type(f25(A),set_type). [assumption]. -ilf_type(A,set_type) | -member(A,c3) | member(ordered_pair(f25(A),A),c4). [assumption]. range(c2,c3,c4) != c3. [assumption]. end_of_list. formulas(demodulators). end_of_list. ============================== PREDICATE ELIMINATION ================= Eliminating relation_like/1 1 -ilf_type(A,set_type) | relation_like(A) | -ilf_type(A,binary_relation_type). [assumption]. 2 -ilf_type(A,set_type) | ilf_type(A,binary_relation_type) | -relation_like(A). [assumption]. 3 -ilf_type(A,set_type) | relation_like(A) | ilf_type(f17(A),set_type). [assumption]. 4 -ilf_type(A,set_type) | relation_like(A) | member(f17(A),A). [assumption]. Derived: -ilf_type(A,set_type) | member(f17(A),A) | -ilf_type(A,set_type) | ilf_type(A,binary_relation_type). [resolve(4,b,2,c)]. 5 -ilf_type(A,set_type) | relation_like(A) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | ordered_pair(B,C) != f17(A). [assumption]. Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | ordered_pair(B,C) != f17(A) | -ilf_type(A,set_type) | ilf_type(A,binary_relation_type). [resolve(5,b,2,c)]. 6 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f18(A,B),set_type) | -relation_like(A). [assumption]. 7 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f19(A,B),set_type) | -relation_like(A). [assumption]. 8 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f18(A,B),f19(A,B)) = B | -relation_like(A). [assumption]. Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f18(A,B),f19(A,B)) = B | -ilf_type(A,set_type) | -ilf_type(A,binary_relation_type). [resolve(8,e,1,b)]. Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f18(A,B),f19(A,B)) = B | -ilf_type(A,set_type) | member(f17(A),A). [resolve(8,e,4,b)]. Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f18(A,B),f19(A,B)) = B | -ilf_type(A,set_type) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | ordered_pair(C,D) != f17(A). [resolve(8,e,5,b)]. 9 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,subset_type(cross_product(A,B))) | relation_like(C). [assumption]. Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,subset_type(cross_product(A,B))) | -ilf_type(C,set_type) | ilf_type(C,binary_relation_type). [resolve(9,d,2,c)]. Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,subset_type(cross_product(A,B))) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | -member(D,C) | ordered_pair(f18(C,D),f19(C,D)) = D. [resolve(9,d,8,e)]. 10 -empty(A) | -ilf_type(A,set_type) | relation_like(A). [assumption]. Derived: -empty(A) | -ilf_type(A,set_type) | -ilf_type(A,set_type) | ilf_type(A,binary_relation_type). [resolve(10,c,2,c)]. Derived: -empty(A) | -ilf_type(A,set_type) | -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f18(A,B),f19(A,B)) = B. [resolve(10,c,8,e)]. ============================== end predicate elimination ============= Term ordering decisions: Predicate symbol precedence: predicate_order([ =, empty, ilf_type, member, subset ]). Function symbol precedence: function_order([ set_type, binary_relation_type, c1, c2, c3, c4, ordered_pair, relation_type, unordered_pair, cross_product, f1, f2, f3, f4, f5, f7, f8, f9, f10, f11, f12, f13, f14, f15, f18, f19, f20, f21, subset_type, power_set, range_of, member_type, domain_of, singleton, f6, f16, f17, f22, f23, f24, f25, domain, range ]). After inverse_order: (no changes). Unfolding symbols: (none). Auto_inference settings: % set(paramodulation). % (positive equality literals) % set(binary_resolution). % (non-Horn) Auto_process settings: % set(factor). % (non-Horn) % set(unit_deletion). % (non-Horn) kept: 11 -ilf_type(A,binary_relation_type) | -ilf_type(B,set_type) | member(B,range_of(A)) | -ilf_type(C,set_type) | -member(ordered_pair(C,B),A). [assumption]. kept: 12 -ilf_type(A,binary_relation_type) | -ilf_type(B,set_type) | ilf_type(f1(A,B),set_type) | -member(B,range_of(A)). [assumption]. kept: 13 -ilf_type(A,binary_relation_type) | -ilf_type(B,set_type) | member(ordered_pair(f1(A,B),B),A) | -member(B,range_of(A)). [assumption]. kept: 14 -ilf_type(A,binary_relation_type) | -ilf_type(B,set_type) | ilf_type(f2(A,B),set_type) | -ilf_type(C,set_type) | -member(ordered_pair(C,B),A). [assumption]. kept: 15 -ilf_type(A,binary_relation_type) | -ilf_type(B,set_type) | member(ordered_pair(f2(A,B),B),A) | -ilf_type(C,set_type) | -member(ordered_pair(C,B),A). [assumption]. kept: 16 -ilf_type(A,binary_relation_type) | ilf_type(range_of(A),set_type). [assumption]. kept: 17 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,binary_relation_type) | -member(ordered_pair(A,B),C) | member(A,domain_of(C)). [assumption]. kept: 18 -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(f3(A,B),set_type) | ilf_type(f4(A,B),set_type) | B = A. [assumption]. kept: 19 -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(f3(A,B),set_type) | -member(f4(A,B),A) | B = A. [assumption]. kept: 20 -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(f3(A,B),set_type) | member(f4(A,B),B) | B = A. [assumption]. kept: 21 -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(f3(A,B),A) | ilf_type(f4(A,B),set_type) | B = A. [assumption]. kept: 22 -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(f3(A,B),A) | -member(f4(A,B),A) | B = A. [assumption]. kept: 23 -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(f3(A,B),A) | member(f4(A,B),B) | B = A. [assumption]. kept: 24 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(f3(A,B),B) | ilf_type(f4(A,B),set_type) | B = A. [assumption]. kept: 25 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(f3(A,B),B) | -member(f4(A,B),A) | B = A. [assumption]. kept: 26 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(f3(A,B),B) | member(f4(A,B),B) | B = A. [assumption]. kept: 27 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | ordered_pair(A,B) = C | unordered_pair(unordered_pair(A,B),singleton(A)) != C. [assumption]. kept: 28 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | unordered_pair(unordered_pair(A,B),singleton(A)) = C | ordered_pair(A,B) != C. [assumption]. kept: 29 -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(ordered_pair(A,B),set_type). [assumption]. kept: 30 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,subset_type(cross_product(A,B))) | ilf_type(C,relation_type(A,B)). [assumption]. kept: 31 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,relation_type(A,B)) | ilf_type(C,subset_type(cross_product(A,B))). [assumption]. kept: 32 -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(f5(A,B),relation_type(B,A)). [assumption]. kept: 33 -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | -subset(A,B) | -subset(B,A). [assumption]. kept: 34 -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(A,B) | B != A. [assumption]. kept: 35 -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(B,A) | B != A. [assumption]. kept: 36 -ilf_type(A,binary_relation_type) | ilf_type(domain_of(A),set_type). [assumption]. kept: 37 -ilf_type(A,set_type) | ilf_type(singleton(A),set_type). [assumption]. kept: 38 -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(cross_product(A,B),set_type). [assumption]. kept: 39 -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(unordered_pair(A,B),set_type). [assumption]. kept: 40 -ilf_type(A,set_type) | -ilf_type(B,set_type) | unordered_pair(B,A) = unordered_pair(A,B). [assumption]. kept: 41 ilf_type(c1,binary_relation_type). [assumption]. kept: 42 -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(B,subset_type(A)) | -ilf_type(B,member_type(power_set(A))). [assumption]. kept: 43 -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(B,member_type(power_set(A))) | -ilf_type(B,subset_type(A)). [assumption]. kept: 44 -ilf_type(A,set_type) | ilf_type(f6(A),subset_type(A)). [assumption]. kept: 45 -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | ilf_type(f7(A,B),set_type) | ilf_type(f8(A,B),set_type). [assumption]. kept: 46 -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | ilf_type(f7(A,B),set_type) | -member(f8(A,B),A). [assumption]. kept: 47 -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | ilf_type(f7(A,B),set_type) | member(f8(A,B),B). [assumption]. kept: 48 -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | member(f7(A,B),A) | ilf_type(f8(A,B),set_type). [assumption]. kept: 49 -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | member(f7(A,B),A) | -member(f8(A,B),A). [assumption]. kept: 50 -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | member(f7(A,B),A) | member(f8(A,B),B). [assumption]. kept: 51 -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | -member(f7(A,B),B) | ilf_type(f8(A,B),set_type). [assumption]. kept: 52 -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | -member(f7(A,B),B) | -member(f8(A,B),A). [assumption]. kept: 53 -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | -member(f7(A,B),B) | member(f8(A,B),B). [assumption]. kept: 54 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,A) | -member(C,B) | B != A. [assumption]. kept: 55 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,A) | -member(C,B) | ilf_type(f9(A,B),set_type) | ilf_type(f10(A,B),set_type). [assumption]. kept: 56 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,A) | -member(C,B) | ilf_type(f9(A,B),set_type) | -member(f10(A,B),A). [assumption]. kept: 57 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,A) | -member(C,B) | ilf_type(f9(A,B),set_type) | member(f10(A,B),B). [assumption]. kept: 58 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,A) | -member(C,B) | member(f9(A,B),A) | ilf_type(f10(A,B),set_type). [assumption]. kept: 59 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,A) | -member(C,B) | member(f9(A,B),A) | -member(f10(A,B),A). [assumption]. kept: 60 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,A) | -member(C,B) | member(f9(A,B),A) | member(f10(A,B),B). [assumption]. kept: 61 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,A) | -member(C,B) | -member(f9(A,B),B) | ilf_type(f10(A,B),set_type). [assumption]. kept: 62 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,A) | -member(C,B) | -member(f9(A,B),B) | -member(f10(A,B),A). [assumption]. kept: 63 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,A) | -member(C,B) | -member(f9(A,B),B) | member(f10(A,B),B). [assumption]. kept: 64 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,B) | -member(C,A) | B != A. [assumption]. kept: 65 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,B) | -member(C,A) | ilf_type(f11(A,B),set_type) | ilf_type(f12(A,B),set_type). [assumption]. kept: 66 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,B) | -member(C,A) | ilf_type(f11(A,B),set_type) | -member(f12(A,B),A). [assumption]. kept: 67 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,B) | -member(C,A) | ilf_type(f11(A,B),set_type) | member(f12(A,B),B). [assumption]. kept: 68 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,B) | -member(C,A) | member(f11(A,B),A) | ilf_type(f12(A,B),set_type). [assumption]. kept: 69 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,B) | -member(C,A) | member(f11(A,B),A) | -member(f12(A,B),A). [assumption]. kept: 70 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,B) | -member(C,A) | member(f11(A,B),A) | member(f12(A,B),B). [assumption]. kept: 71 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,B) | -member(C,A) | -member(f11(A,B),B) | ilf_type(f12(A,B),set_type). [assumption]. kept: 72 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,B) | -member(C,A) | -member(f11(A,B),B) | -member(f12(A,B),A). [assumption]. kept: 73 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,B) | -member(C,A) | -member(f11(A,B),B) | member(f12(A,B),B). [assumption]. kept: 74 -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(A,B) | ilf_type(f13(A,B),set_type). [assumption]. kept: 75 -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(A,B) | member(f13(A,B),A). [assumption]. kept: 76 -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(A,B) | -member(f13(A,B),B). [assumption]. kept: 77 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | -member(C,A) | member(C,B) | -subset(A,B). [assumption]. kept: 78 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | -member(C,A) | member(C,B) | ilf_type(f14(A,B),set_type). [assumption]. kept: 79 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | -member(C,A) | member(C,B) | member(f14(A,B),A). [assumption]. kept: 80 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | -member(C,A) | member(C,B) | -member(f14(A,B),B). [assumption]. kept: 81 -ilf_type(A,set_type) | subset(A,A). [assumption]. kept: 82 -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(A,power_set(B)) | ilf_type(f15(A,B),set_type). [assumption]. kept: 83 -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(A,power_set(B)) | member(f15(A,B),A). [assumption]. kept: 84 -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(A,power_set(B)) | -member(f15(A,B),B). [assumption]. kept: 85 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | -member(C,A) | member(C,B) | -member(A,power_set(B)). [assumption]. kept: 86 -ilf_type(A,set_type) | -empty(power_set(A)). [assumption]. kept: 87 -ilf_type(A,set_type) | ilf_type(power_set(A),set_type). [assumption]. kept: 88 -ilf_type(A,set_type) | empty(B) | -ilf_type(B,set_type) | ilf_type(A,member_type(B)) | -member(A,B). [assumption]. kept: 89 -ilf_type(A,set_type) | empty(B) | -ilf_type(B,set_type) | member(A,B) | -ilf_type(A,member_type(B)). [assumption]. kept: 90 empty(A) | -ilf_type(A,set_type) | ilf_type(f16(A),member_type(A)). [assumption]. kept: 91 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f20(A,B),set_type) | ilf_type(f22(A),set_type). [assumption]. kept: 92 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f20(A,B),set_type) | member(f22(A),A). [assumption]. 93 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f20(A,B),set_type) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | ordered_pair(C,D) != f22(A). [assumption]. kept: 94 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f20(A,B),set_type) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | f22(A) != ordered_pair(C,D). [copy(93),flip(g)]. kept: 95 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f21(A,B),set_type) | ilf_type(f22(A),set_type). [assumption]. kept: 96 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f21(A,B),set_type) | member(f22(A),A). [assumption]. 97 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f21(A,B),set_type) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | ordered_pair(C,D) != f22(A). [assumption]. kept: 98 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f21(A,B),set_type) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | f22(A) != ordered_pair(C,D). [copy(97),flip(g)]. kept: 99 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f20(A,B),f21(A,B)) = B | ilf_type(f22(A),set_type). [assumption]. kept: 100 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f20(A,B),f21(A,B)) = B | member(f22(A),A). [assumption]. 101 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f20(A,B),f21(A,B)) = B | -ilf_type(C,set_type) | -ilf_type(D,set_type) | ordered_pair(C,D) != f22(A). [assumption]. kept: 102 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f20(A,B),f21(A,B)) = B | -ilf_type(C,set_type) | -ilf_type(D,set_type) | f22(A) != ordered_pair(C,D). [copy(101),flip(g)]. kept: 103 -ilf_type(A,set_type) | empty(A) | ilf_type(f23(A),set_type). [assumption]. kept: 104 -ilf_type(A,set_type) | empty(A) | member(f23(A),A). [assumption]. kept: 105 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | -empty(A). [assumption]. kept: 106 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f24(A),set_type). [assumption]. kept: 107 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | member(f24(A),A). [assumption]. kept: 108 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,relation_type(A,B)) | domain(A,B,C) = domain_of(C). [assumption]. kept: 109 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,relation_type(A,B)) | ilf_type(domain(A,B,C),subset_type(A)). [assumption]. kept: 110 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,relation_type(A,B)) | range(A,B,C) = range_of(C). [assumption]. kept: 111 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,relation_type(A,B)) | ilf_type(range(A,B,C),subset_type(B)). [assumption]. kept: 112 ilf_type(A,set_type). [assumption]. kept: 113 ilf_type(c4,relation_type(c2,c3)). [assumption]. 114 -ilf_type(A,set_type) | -member(A,c3) | ilf_type(f25(A),set_type). [assumption]. 115 -ilf_type(A,set_type) | -member(A,c3) | member(ordered_pair(f25(A),A),c4). [assumption]. kept: 116 -member(A,c3) | member(ordered_pair(f25(A),A),c4). [copy(115),unit_del(a,112)]. kept: 117 range(c2,c3,c4) != c3. [assumption]. 118 -ilf_type(A,set_type) | member(f17(A),A) | -ilf_type(A,set_type) | ilf_type(A,binary_relation_type). [resolve(4,b,2,c)]. kept: 119 member(f17(A),A) | ilf_type(A,binary_relation_type). [copy(118),merge(c),unit_del(a,112)]. 120 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | ordered_pair(B,C) != f17(A) | -ilf_type(A,set_type) | ilf_type(A,binary_relation_type). [resolve(5,b,2,c)]. kept: 121 f17(A) != ordered_pair(B,C) | ilf_type(A,binary_relation_type). [copy(120),flip(d),merge(e),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. 122 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f18(A,B),f19(A,B)) = B | -ilf_type(A,set_type) | -ilf_type(A,binary_relation_type). [resolve(8,e,1,b)]. kept: 123 -member(A,B) | ordered_pair(f18(B,A),f19(B,A)) = A | -ilf_type(B,binary_relation_type). [copy(122),merge(e),unit_del(a,112),unit_del(b,112)]. 124 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f18(A,B),f19(A,B)) = B | -ilf_type(A,set_type) | member(f17(A),A). [resolve(8,e,4,b)]. kept: 125 -member(A,B) | ordered_pair(f18(B,A),f19(B,A)) = A | member(f17(B),B). [copy(124),merge(e),unit_del(a,112),unit_del(b,112)]. 126 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f18(A,B),f19(A,B)) = B | -ilf_type(A,set_type) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | ordered_pair(C,D) != f17(A). [resolve(8,e,5,b)]. kept: 127 -member(A,B) | ordered_pair(f18(B,A),f19(B,A)) = A | f17(B) != ordered_pair(C,D). [copy(126),flip(h),merge(e),unit_del(a,112),unit_del(b,112),unit_del(e,112),unit_del(f,112)]. 128 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,subset_type(cross_product(A,B))) | -ilf_type(C,set_type) | ilf_type(C,binary_relation_type). [resolve(9,d,2,c)]. kept: 129 -ilf_type(A,subset_type(cross_product(B,C))) | ilf_type(A,binary_relation_type). [copy(128),unit_del(a,112),unit_del(b,112),unit_del(d,112)]. 130 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,subset_type(cross_product(A,B))) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | -member(D,C) | ordered_pair(f18(C,D),f19(C,D)) = D. [resolve(9,d,8,e)]. kept: 131 -ilf_type(A,subset_type(cross_product(B,C))) | -member(D,A) | ordered_pair(f18(A,D),f19(A,D)) = D. [copy(130),unit_del(a,112),unit_del(b,112),unit_del(d,112),unit_del(e,112)]. 132 -empty(A) | -ilf_type(A,set_type) | -ilf_type(A,set_type) | ilf_type(A,binary_relation_type). [resolve(10,c,2,c)]. kept: 133 -empty(A) | ilf_type(A,binary_relation_type). [copy(132),merge(c),unit_del(b,112)]. 134 -empty(A) | -ilf_type(A,set_type) | -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f18(A,B),f19(A,B)) = B. [resolve(10,c,8,e)]. kept: 135 -empty(A) | -member(B,A) | ordered_pair(f18(A,B),f19(A,B)) = B. [copy(134),merge(c),unit_del(b,112),unit_del(c,112)]. kept: 136 -ilf_type(A,binary_relation_type) | member(B,range_of(A)) | -member(ordered_pair(B,B),A). [factor(11,b,d),unit_del(b,112)]. kept: 137 -ilf_type(A,binary_relation_type) | member(ordered_pair(f2(A,B),B),A) | -member(ordered_pair(B,B),A). [factor(15,b,d),unit_del(b,112)]. kept: 138 -ilf_type(A,binary_relation_type) | -member(ordered_pair(B,B),A) | member(B,domain_of(A)). [factor(17,a,b),unit_del(a,112)]. kept: 139 ordered_pair(A,A) = B | unordered_pair(unordered_pair(A,A),singleton(A)) != B. [factor(27,a,b),unit_del(a,112),unit_del(b,112)]. kept: 140 ordered_pair(A,B) = A | unordered_pair(unordered_pair(A,B),singleton(A)) != A. [factor(27,a,c),unit_del(a,112),unit_del(b,112)]. kept: 141 ordered_pair(A,B) = B | unordered_pair(unordered_pair(A,B),singleton(A)) != B. [factor(27,b,c),unit_del(a,112),unit_del(b,112)]. kept: 142 unordered_pair(unordered_pair(A,A),singleton(A)) = B | ordered_pair(A,A) != B. [factor(28,a,b),unit_del(a,112),unit_del(b,112)]. kept: 143 unordered_pair(unordered_pair(A,B),singleton(A)) = A | ordered_pair(A,B) != A. [factor(28,a,c),unit_del(a,112),unit_del(b,112)]. kept: 144 unordered_pair(unordered_pair(A,B),singleton(A)) = B | ordered_pair(A,B) != B. [factor(28,b,c),unit_del(a,112),unit_del(b,112)]. kept: 145 -ilf_type(A,subset_type(cross_product(B,B))) | ilf_type(A,relation_type(B,B)). [factor(30,a,b),unit_del(a,112)]. kept: 146 -ilf_type(A,relation_type(B,B)) | ilf_type(A,subset_type(cross_product(B,B))). [factor(31,a,b),unit_del(a,112)]. kept: 147 ilf_type(f5(A,A),relation_type(A,A)). [factor(32,a,b),unit_del(a,112)]. kept: 148 subset(A,A). [factor(34,a,b),xx(c),unit_del(a,112)]. kept: 149 ilf_type(A,subset_type(A)) | -ilf_type(A,member_type(power_set(A))). [factor(42,a,b),unit_del(a,112)]. kept: 150 ilf_type(A,member_type(power_set(A))) | -ilf_type(A,subset_type(A)). [factor(43,a,b),unit_del(a,112)]. kept: 151 member(A,A) | -member(A,B) | B != A. [factor(54,a,c),unit_del(a,112),unit_del(b,112)]. kept: 152 member(A,B) | -member(A,A) | A != B. [factor(54,b,c),unit_del(a,112),unit_del(b,112)]. kept: 153 member(A,A) | -member(A,B) | member(f9(A,B),A) | -member(f10(A,B),A). [factor(59,a,c),unit_del(a,112),unit_del(b,112)]. kept: 154 member(A,B) | -member(A,A) | member(f9(B,A),B) | -member(f10(B,A),B). [factor(59,b,c),unit_del(a,112),unit_del(b,112)]. kept: 155 member(f9(A,B),A) | -member(f9(A,B),B) | -member(f10(A,B),A). [factor(59,d,f),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. kept: 156 member(A,A) | -member(A,B) | member(f9(A,B),A) | member(f10(A,B),B). [factor(60,a,c),unit_del(a,112),unit_del(b,112)]. kept: 157 member(A,B) | -member(A,A) | member(f9(B,A),B) | member(f10(B,A),A). [factor(60,b,c),unit_del(a,112),unit_del(b,112)]. kept: 158 member(f9(A,B),A) | -member(f9(A,B),B) | member(f10(A,B),B). [factor(60,d,f),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. kept: 159 member(A,A) | -member(A,B) | -member(f9(A,B),B) | -member(f10(A,B),A). [factor(62,a,c),unit_del(a,112),unit_del(b,112)]. kept: 160 member(A,B) | -member(A,A) | -member(f9(B,A),A) | -member(f10(B,A),B). [factor(62,b,c),unit_del(a,112),unit_del(b,112)]. kept: 161 member(A,A) | -member(A,B) | -member(f9(A,B),B) | member(f10(A,B),B). [factor(63,a,c),unit_del(a,112),unit_del(b,112)]. kept: 162 member(A,B) | -member(A,A) | -member(f9(B,A),A) | member(f10(B,A),A). [factor(63,b,c),unit_del(a,112),unit_del(b,112)]. kept: 163 member(A,B) | -member(A,A) | B != A. [factor(64,a,c),unit_del(a,112),unit_del(b,112)]. kept: 164 member(A,A) | -member(A,B) | A != B. [factor(64,b,c),unit_del(a,112),unit_del(b,112)]. kept: 165 member(A,B) | -member(A,A) | member(f11(A,B),A) | -member(f12(A,B),A). [factor(69,a,c),unit_del(a,112),unit_del(b,112)]. kept: 166 member(A,A) | -member(A,B) | member(f11(B,A),B) | -member(f12(B,A),B). [factor(69,b,c),unit_del(a,112),unit_del(b,112)]. kept: 167 member(f12(A,B),B) | -member(f12(A,B),A) | member(f11(A,B),A). [factor(69,e,g),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. kept: 168 member(A,B) | -member(A,A) | member(f11(A,B),A) | member(f12(A,B),B). [factor(70,a,c),unit_del(a,112),unit_del(b,112)]. kept: 169 member(A,A) | -member(A,B) | member(f11(B,A),B) | member(f12(B,A),A). [factor(70,b,c),unit_del(a,112),unit_del(b,112)]. kept: 170 member(A,B) | -member(A,A) | -member(f11(A,B),B) | -member(f12(A,B),A). [factor(72,a,c),unit_del(a,112),unit_del(b,112)]. kept: 171 member(A,A) | -member(A,B) | -member(f11(B,A),A) | -member(f12(B,A),B). [factor(72,b,c),unit_del(a,112),unit_del(b,112)]. kept: 172 member(f12(A,B),B) | -member(f12(A,B),A) | -member(f11(A,B),B). [factor(72,e,g),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. kept: 173 member(A,B) | -member(A,A) | -member(f11(A,B),B) | member(f12(A,B),B). [factor(73,a,c),unit_del(a,112),unit_del(b,112)]. kept: 174 member(A,A) | -member(A,B) | -member(f11(B,A),A) | member(f12(B,A),A). [factor(73,b,c),unit_del(a,112),unit_del(b,112)]. kept: 175 -member(A,A) | member(A,B) | -subset(A,B). [factor(77,a,c),unit_del(a,112),unit_del(b,112)]. kept: 176 -member(A,B) | member(A,A) | -subset(B,A). [factor(77,b,c),unit_del(a,112),unit_del(b,112)]. kept: 177 -member(A,A) | member(A,B) | member(f14(A,B),A). [factor(79,a,c),unit_del(a,112),unit_del(b,112)]. kept: 178 -member(A,B) | member(A,A) | member(f14(B,A),B). [factor(79,b,c),unit_del(a,112),unit_del(b,112)]. kept: 179 -member(A,A) | member(A,B) | -member(f14(A,B),B). [factor(80,a,c),unit_del(a,112),unit_del(b,112)]. kept: 180 -member(A,B) | member(A,A) | -member(f14(B,A),A). [factor(80,b,c),unit_del(a,112),unit_del(b,112)]. kept: 181 member(A,power_set(A)) | member(f15(A,A),A). [factor(83,a,b),unit_del(a,112)]. kept: 182 member(A,power_set(A)) | -member(f15(A,A),A). [factor(84,a,b),unit_del(a,112)]. kept: 183 -member(A,A) | member(A,B) | -member(A,power_set(B)). [factor(85,a,c),unit_del(a,112),unit_del(b,112)]. kept: 184 -member(A,B) | member(A,A) | -member(B,power_set(A)). [factor(85,b,c),unit_del(a,112),unit_del(b,112)]. kept: 185 -member(power_set(A),power_set(A)) | member(power_set(A),A). [factor(85,d,f),merge(c),unit_del(a,112),unit_del(b,112)]. kept: 186 empty(A) | ilf_type(A,member_type(A)) | -member(A,A). [factor(88,a,c),unit_del(a,112)]. kept: 187 empty(A) | member(A,A) | -ilf_type(A,member_type(A)). [factor(89,a,c),unit_del(a,112)]. kept: 188 -member(A,A) | ordered_pair(f20(A,A),f21(A,A)) = A | member(f22(A),A). [factor(100,a,b),unit_del(a,112)]. kept: 189 -member(A,A) | ordered_pair(f20(A,A),f21(A,A)) = A | f22(A) != ordered_pair(B,C). [factor(102,a,b),unit_del(a,112),unit_del(d,112),unit_del(e,112)]. kept: 190 -member(A,B) | ordered_pair(f20(B,A),f21(B,A)) = A | f22(B) != ordered_pair(B,C). [factor(102,a,e),unit_del(a,112),unit_del(b,112),unit_del(e,112)]. kept: 191 -member(A,B) | ordered_pair(f20(B,A),f21(B,A)) = A | f22(B) != ordered_pair(C,B). [factor(102,a,f),unit_del(a,112),unit_del(b,112),unit_del(e,112)]. kept: 192 -member(A,B) | ordered_pair(f20(B,A),f21(B,A)) = A | f22(B) != ordered_pair(A,C). [factor(102,b,e),unit_del(a,112),unit_del(b,112),unit_del(e,112)]. kept: 193 -member(A,B) | ordered_pair(f20(B,A),f21(B,A)) = A | f22(B) != ordered_pair(C,A). [factor(102,b,f),unit_del(a,112),unit_del(b,112),unit_del(e,112)]. kept: 194 -member(A,B) | ordered_pair(f20(B,A),f21(B,A)) = A | f22(B) != ordered_pair(C,C). [factor(102,e,f),unit_del(a,112),unit_del(b,112),unit_del(e,112)]. kept: 195 -member(A,A) | -empty(A). [factor(105,a,b),unit_del(a,112)]. kept: 196 -member(A,A) | member(f24(A),A). [factor(107,a,b),unit_del(a,112)]. kept: 197 -ilf_type(A,relation_type(B,B)) | domain(B,B,A) = domain_of(A). [factor(108,a,b),unit_del(a,112)]. kept: 198 -ilf_type(A,relation_type(B,B)) | ilf_type(domain(B,B,A),subset_type(B)). [factor(109,a,b),unit_del(a,112)]. kept: 199 -ilf_type(A,relation_type(B,B)) | range(B,B,A) = range_of(A). [factor(110,a,b),unit_del(a,112)]. kept: 200 -ilf_type(A,relation_type(B,B)) | ilf_type(range(B,B,A),subset_type(B)). [factor(111,a,b),unit_del(a,112)]. kept: 201 -ilf_type(A,relation_type(B,C)) | ilf_type(range(B,C,A),subset_type(C)). [back_unit_del(111),unit_del(a,112),unit_del(b,112)]. kept: 202 -ilf_type(A,relation_type(B,C)) | range(B,C,A) = range_of(A). [back_unit_del(110),unit_del(a,112),unit_del(b,112)]. kept: 203 -ilf_type(A,relation_type(B,C)) | ilf_type(domain(B,C,A),subset_type(B)). [back_unit_del(109),unit_del(a,112),unit_del(b,112)]. kept: 204 -ilf_type(A,relation_type(B,C)) | domain(B,C,A) = domain_of(A). [back_unit_del(108),unit_del(a,112),unit_del(b,112)]. kept: 205 -member(A,B) | member(f24(B),B). [back_unit_del(107),unit_del(a,112),unit_del(b,112)]. kept: 206 -member(A,B) | -empty(B). [back_unit_del(105),unit_del(a,112),unit_del(b,112)]. kept: 207 empty(A) | member(f23(A),A). [back_unit_del(104),unit_del(a,112)]. kept: 208 -member(A,B) | ordered_pair(f20(B,A),f21(B,A)) = A | f22(B) != ordered_pair(C,D). [back_unit_del(102),unit_del(a,112),unit_del(b,112),unit_del(e,112),unit_del(f,112)]. kept: 209 -member(A,B) | ordered_pair(f20(B,A),f21(B,A)) = A | member(f22(B),B). [back_unit_del(100),unit_del(a,112),unit_del(b,112)]. kept: 210 empty(A) | ilf_type(f16(A),member_type(A)). [back_unit_del(90),unit_del(b,112)]. kept: 211 empty(A) | member(B,A) | -ilf_type(B,member_type(A)). [back_unit_del(89),unit_del(a,112),unit_del(c,112)]. kept: 212 empty(A) | ilf_type(B,member_type(A)) | -member(B,A). [back_unit_del(88),unit_del(a,112),unit_del(c,112)]. kept: 213 -empty(power_set(A)). [back_unit_del(86),unit_del(a,112)]. kept: 214 -member(A,B) | member(A,C) | -member(B,power_set(C)). [back_unit_del(85),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. kept: 215 member(A,power_set(B)) | -member(f15(A,B),B). [back_unit_del(84),unit_del(a,112),unit_del(b,112)]. kept: 216 member(A,power_set(B)) | member(f15(A,B),A). [back_unit_del(83),unit_del(a,112),unit_del(b,112)]. kept: 217 -member(A,B) | member(A,C) | -member(f14(B,C),C). [back_unit_del(80),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. kept: 218 -member(A,B) | member(A,C) | member(f14(B,C),B). [back_unit_del(79),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. kept: 219 -member(A,B) | member(A,C) | -subset(B,C). [back_unit_del(77),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. kept: 220 subset(A,B) | -member(f13(A,B),B). [back_unit_del(76),unit_del(a,112),unit_del(b,112)]. kept: 221 subset(A,B) | member(f13(A,B),A). [back_unit_del(75),unit_del(a,112),unit_del(b,112)]. kept: 222 member(A,B) | -member(A,C) | -member(f11(C,B),B) | member(f12(C,B),B). [back_unit_del(73),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. kept: 223 member(A,B) | -member(A,C) | -member(f11(C,B),B) | -member(f12(C,B),C). [back_unit_del(72),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. kept: 224 member(A,B) | -member(A,C) | member(f11(C,B),C) | member(f12(C,B),B). [back_unit_del(70),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. kept: 225 member(A,B) | -member(A,C) | member(f11(C,B),C) | -member(f12(C,B),C). [back_unit_del(69),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. kept: 226 member(A,B) | -member(A,C) | B != C. [back_unit_del(64),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. kept: 227 member(A,B) | -member(A,C) | -member(f9(B,C),C) | member(f10(B,C),C). [back_unit_del(63),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. kept: 228 member(A,B) | -member(A,C) | -member(f9(B,C),C) | -member(f10(B,C),B). [back_unit_del(62),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. kept: 229 member(A,B) | -member(A,C) | member(f9(B,C),B) | member(f10(B,C),C). [back_unit_del(60),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. kept: 230 member(A,B) | -member(A,C) | member(f9(B,C),B) | -member(f10(B,C),B). [back_unit_del(59),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. kept: 231 member(A,B) | -member(A,C) | C != B. [back_unit_del(54),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. kept: 232 A = B | -member(f7(B,A),A) | member(f8(B,A),A). [back_unit_del(53),unit_del(a,112),unit_del(b,112)]. kept: 233 A = B | -member(f7(B,A),A) | -member(f8(B,A),B). [back_unit_del(52),unit_del(a,112),unit_del(b,112)]. kept: 234 A = B | member(f7(B,A),B) | member(f8(B,A),A). [back_unit_del(50),unit_del(a,112),unit_del(b,112)]. kept: 235 A = B | member(f7(B,A),B) | -member(f8(B,A),B). [back_unit_del(49),unit_del(a,112),unit_del(b,112)]. kept: 236 ilf_type(f6(A),subset_type(A)). [back_unit_del(44),unit_del(a,112)]. kept: 237 ilf_type(A,member_type(power_set(B))) | -ilf_type(A,subset_type(B)). [back_unit_del(43),unit_del(a,112),unit_del(b,112)]. kept: 238 ilf_type(A,subset_type(B)) | -ilf_type(A,member_type(power_set(B))). [back_unit_del(42),unit_del(a,112),unit_del(b,112)]. % Operation unordered_pair is commutative; C redundancy checks enabled. kept: 239 unordered_pair(A,B) = unordered_pair(B,A). [back_unit_del(40),unit_del(a,112),unit_del(b,112)]. kept: 240 subset(A,B) | A != B. [back_unit_del(35),unit_del(a,112),unit_del(b,112)]. kept: 241 subset(A,B) | B != A. [back_unit_del(34),unit_del(a,112),unit_del(b,112)]. kept: 242 A = B | -subset(B,A) | -subset(A,B). [back_unit_del(33),unit_del(a,112),unit_del(b,112)]. kept: 243 ilf_type(f5(A,B),relation_type(B,A)). [back_unit_del(32),unit_del(a,112),unit_del(b,112)]. kept: 244 -ilf_type(A,relation_type(B,C)) | ilf_type(A,subset_type(cross_product(B,C))). [back_unit_del(31),unit_del(a,112),unit_del(b,112)]. kept: 245 -ilf_type(A,subset_type(cross_product(B,C))) | ilf_type(A,relation_type(B,C)). [back_unit_del(30),unit_del(a,112),unit_del(b,112)]. kept: 246 unordered_pair(unordered_pair(A,B),singleton(A)) = C | ordered_pair(A,B) != C. [back_unit_del(28),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. kept: 247 ordered_pair(A,B) = C | unordered_pair(unordered_pair(A,B),singleton(A)) != C. [back_unit_del(27),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. kept: 248 -member(f3(A,B),B) | member(f4(A,B),B) | B = A. [back_unit_del(26),unit_del(a,112),unit_del(b,112)]. kept: 249 -member(f3(A,B),B) | -member(f4(A,B),A) | B = A. [back_unit_del(25),unit_del(a,112),unit_del(b,112)]. kept: 250 member(f3(A,B),A) | member(f4(A,B),B) | B = A. [back_unit_del(23),unit_del(a,112),unit_del(b,112)]. kept: 251 member(f3(A,B),A) | -member(f4(A,B),A) | B = A. [back_unit_del(22),unit_del(a,112),unit_del(b,112)]. kept: 252 -ilf_type(A,binary_relation_type) | -member(ordered_pair(B,C),A) | member(B,domain_of(A)). [back_unit_del(17),unit_del(a,112),unit_del(b,112)]. kept: 253 -ilf_type(A,binary_relation_type) | member(ordered_pair(f2(A,B),B),A) | -member(ordered_pair(C,B),A). [back_unit_del(15),unit_del(b,112),unit_del(d,112)]. kept: 254 -ilf_type(A,binary_relation_type) | member(ordered_pair(f1(A,B),B),A) | -member(B,range_of(A)). [back_unit_del(13),unit_del(b,112)]. kept: 255 -ilf_type(A,binary_relation_type) | member(B,range_of(A)) | -member(ordered_pair(C,B),A). [back_unit_del(11),unit_del(b,112),unit_del(d,112)]. ============================== end of process initial clauses ======== ============================== CLAUSES FOR SEARCH ==================== % Clauses after input processing: formulas(usable). end_of_list. formulas(sos). 41 ilf_type(c1,binary_relation_type). [assumption]. 112 ilf_type(A,set_type). [assumption]. 113 ilf_type(c4,relation_type(c2,c3)). [assumption]. 116 -member(A,c3) | member(ordered_pair(f25(A),A),c4). [copy(115),unit_del(a,112)]. 117 range(c2,c3,c4) != c3. [assumption]. 119 member(f17(A),A) | ilf_type(A,binary_relation_type). [copy(118),merge(c),unit_del(a,112)]. 121 f17(A) != ordered_pair(B,C) | ilf_type(A,binary_relation_type). [copy(120),flip(d),merge(e),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. 123 -member(A,B) | ordered_pair(f18(B,A),f19(B,A)) = A | -ilf_type(B,binary_relation_type). [copy(122),merge(e),unit_del(a,112),unit_del(b,112)]. 125 -member(A,B) | ordered_pair(f18(B,A),f19(B,A)) = A | member(f17(B),B). [copy(124),merge(e),unit_del(a,112),unit_del(b,112)]. 127 -member(A,B) | ordered_pair(f18(B,A),f19(B,A)) = A | f17(B) != ordered_pair(C,D). [copy(126),flip(h),merge(e),unit_del(a,112),unit_del(b,112),unit_del(e,112),unit_del(f,112)]. 129 -ilf_type(A,subset_type(cross_product(B,C))) | ilf_type(A,binary_relation_type). [copy(128),unit_del(a,112),unit_del(b,112),unit_del(d,112)]. 131 -ilf_type(A,subset_type(cross_product(B,C))) | -member(D,A) | ordered_pair(f18(A,D),f19(A,D)) = D. [copy(130),unit_del(a,112),unit_del(b,112),unit_del(d,112),unit_del(e,112)]. 133 -empty(A) | ilf_type(A,binary_relation_type). [copy(132),merge(c),unit_del(b,112)]. 148 subset(A,A). [factor(34,a,b),xx(c),unit_del(a,112)]. 155 member(f9(A,B),A) | -member(f9(A,B),B) | -member(f10(A,B),A). [factor(59,d,f),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. 158 member(f9(A,B),A) | -member(f9(A,B),B) | member(f10(A,B),B). [factor(60,d,f),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. 167 member(f12(A,B),B) | -member(f12(A,B),A) | member(f11(A,B),A). [factor(69,e,g),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. 172 member(f12(A,B),B) | -member(f12(A,B),A) | -member(f11(A,B),B). [factor(72,e,g),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. 185 -member(power_set(A),power_set(A)) | member(power_set(A),A). [factor(85,d,f),merge(c),unit_del(a,112),unit_del(b,112)]. 201 -ilf_type(A,relation_type(B,C)) | ilf_type(range(B,C,A),subset_type(C)). [back_unit_del(111),unit_del(a,112),unit_del(b,112)]. 202 -ilf_type(A,relation_type(B,C)) | range(B,C,A) = range_of(A). [back_unit_del(110),unit_del(a,112),unit_del(b,112)]. 203 -ilf_type(A,relation_type(B,C)) | ilf_type(domain(B,C,A),subset_type(B)). [back_unit_del(109),unit_del(a,112),unit_del(b,112)]. 204 -ilf_type(A,relation_type(B,C)) | domain(B,C,A) = domain_of(A). [back_unit_del(108),unit_del(a,112),unit_del(b,112)]. 205 -member(A,B) | member(f24(B),B). [back_unit_del(107),unit_del(a,112),unit_del(b,112)]. 206 -member(A,B) | -empty(B). [back_unit_del(105),unit_del(a,112),unit_del(b,112)]. 207 empty(A) | member(f23(A),A). [back_unit_del(104),unit_del(a,112)]. 208 -member(A,B) | ordered_pair(f20(B,A),f21(B,A)) = A | f22(B) != ordered_pair(C,D). [back_unit_del(102),unit_del(a,112),unit_del(b,112),unit_del(e,112),unit_del(f,112)]. 209 -member(A,B) | ordered_pair(f20(B,A),f21(B,A)) = A | member(f22(B),B). [back_unit_del(100),unit_del(a,112),unit_del(b,112)]. 210 empty(A) | ilf_type(f16(A),member_type(A)). [back_unit_del(90),unit_del(b,112)]. 211 empty(A) | member(B,A) | -ilf_type(B,member_type(A)). [back_unit_del(89),unit_del(a,112),unit_del(c,112)]. 212 empty(A) | ilf_type(B,member_type(A)) | -member(B,A). [back_unit_del(88),unit_del(a,112),unit_del(c,112)]. 213 -empty(power_set(A)). [back_unit_del(86),unit_del(a,112)]. 214 -member(A,B) | member(A,C) | -member(B,power_set(C)). [back_unit_del(85),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. 215 member(A,power_set(B)) | -member(f15(A,B),B). [back_unit_del(84),unit_del(a,112),unit_del(b,112)]. 216 member(A,power_set(B)) | member(f15(A,B),A). [back_unit_del(83),unit_del(a,112),unit_del(b,112)]. 217 -member(A,B) | member(A,C) | -member(f14(B,C),C). [back_unit_del(80),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. 218 -member(A,B) | member(A,C) | member(f14(B,C),B). [back_unit_del(79),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. 219 -member(A,B) | member(A,C) | -subset(B,C). [back_unit_del(77),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. 220 subset(A,B) | -member(f13(A,B),B). [back_unit_del(76),unit_del(a,112),unit_del(b,112)]. 221 subset(A,B) | member(f13(A,B),A). [back_unit_del(75),unit_del(a,112),unit_del(b,112)]. 222 member(A,B) | -member(A,C) | -member(f11(C,B),B) | member(f12(C,B),B). [back_unit_del(73),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. 223 member(A,B) | -member(A,C) | -member(f11(C,B),B) | -member(f12(C,B),C). [back_unit_del(72),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. 224 member(A,B) | -member(A,C) | member(f11(C,B),C) | member(f12(C,B),B). [back_unit_del(70),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. 225 member(A,B) | -member(A,C) | member(f11(C,B),C) | -member(f12(C,B),C). [back_unit_del(69),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. 226 member(A,B) | -member(A,C) | B != C. [back_unit_del(64),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. 227 member(A,B) | -member(A,C) | -member(f9(B,C),C) | member(f10(B,C),C). [back_unit_del(63),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. 228 member(A,B) | -member(A,C) | -member(f9(B,C),C) | -member(f10(B,C),B). [back_unit_del(62),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. 229 member(A,B) | -member(A,C) | member(f9(B,C),B) | member(f10(B,C),C). [back_unit_del(60),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. 230 member(A,B) | -member(A,C) | member(f9(B,C),B) | -member(f10(B,C),B). [back_unit_del(59),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. 231 member(A,B) | -member(A,C) | C != B. [back_unit_del(54),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. 232 A = B | -member(f7(B,A),A) | member(f8(B,A),A). [back_unit_del(53),unit_del(a,112),unit_del(b,112)]. 233 A = B | -member(f7(B,A),A) | -member(f8(B,A),B). [back_unit_del(52),unit_del(a,112),unit_del(b,112)]. 234 A = B | member(f7(B,A),B) | member(f8(B,A),A). [back_unit_del(50),unit_del(a,112),unit_del(b,112)]. 235 A = B | member(f7(B,A),B) | -member(f8(B,A),B). [back_unit_del(49),unit_del(a,112),unit_del(b,112)]. 236 ilf_type(f6(A),subset_type(A)). [back_unit_del(44),unit_del(a,112)]. 237 ilf_type(A,member_type(power_set(B))) | -ilf_type(A,subset_type(B)). [back_unit_del(43),unit_del(a,112),unit_del(b,112)]. 238 ilf_type(A,subset_type(B)) | -ilf_type(A,member_type(power_set(B))). [back_unit_del(42),unit_del(a,112),unit_del(b,112)]. 239 unordered_pair(A,B) = unordered_pair(B,A). [back_unit_del(40),unit_del(a,112),unit_del(b,112)]. 240 subset(A,B) | A != B. [back_unit_del(35),unit_del(a,112),unit_del(b,112)]. 241 subset(A,B) | B != A. [back_unit_del(34),unit_del(a,112),unit_del(b,112)]. 242 A = B | -subset(B,A) | -subset(A,B). [back_unit_del(33),unit_del(a,112),unit_del(b,112)]. 243 ilf_type(f5(A,B),relation_type(B,A)). [back_unit_del(32),unit_del(a,112),unit_del(b,112)]. 244 -ilf_type(A,relation_type(B,C)) | ilf_type(A,subset_type(cross_product(B,C))). [back_unit_del(31),unit_del(a,112),unit_del(b,112)]. 245 -ilf_type(A,subset_type(cross_product(B,C))) | ilf_type(A,relation_type(B,C)). [back_unit_del(30),unit_del(a,112),unit_del(b,112)]. 246 unordered_pair(unordered_pair(A,B),singleton(A)) = C | ordered_pair(A,B) != C. [back_unit_del(28),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. 247 ordered_pair(A,B) = C | unordered_pair(unordered_pair(A,B),singleton(A)) != C. [back_unit_del(27),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. 248 -member(f3(A,B),B) | member(f4(A,B),B) | B = A. [back_unit_del(26),unit_del(a,112),unit_del(b,112)]. 249 -member(f3(A,B),B) | -member(f4(A,B),A) | B = A. [back_unit_del(25),unit_del(a,112),unit_del(b,112)]. 250 member(f3(A,B),A) | member(f4(A,B),B) | B = A. [back_unit_del(23),unit_del(a,112),unit_del(b,112)]. 251 member(f3(A,B),A) | -member(f4(A,B),A) | B = A. [back_unit_del(22),unit_del(a,112),unit_del(b,112)]. 252 -ilf_type(A,binary_relation_type) | -member(ordered_pair(B,C),A) | member(B,domain_of(A)). [back_unit_del(17),unit_del(a,112),unit_del(b,112)]. 253 -ilf_type(A,binary_relation_type) | member(ordered_pair(f2(A,B),B),A) | -member(ordered_pair(C,B),A). [back_unit_del(15),unit_del(b,112),unit_del(d,112)]. 254 -ilf_type(A,binary_relation_type) | member(ordered_pair(f1(A,B),B),A) | -member(B,range_of(A)). [back_unit_del(13),unit_del(b,112)]. 255 -ilf_type(A,binary_relation_type) | member(B,range_of(A)) | -member(ordered_pair(C,B),A). [back_unit_del(11),unit_del(b,112),unit_del(d,112)]. end_of_list. formulas(demodulators). 239 unordered_pair(A,B) = unordered_pair(B,A). [back_unit_del(40),unit_del(a,112),unit_del(b,112)]. % (lex-dep) end_of_list. ============================== end of clauses for search ============= ============================== SEARCH ================================ % Starting search at 0.03 seconds. given #1 (I,wt=3): 41 ilf_type(c1,binary_relation_type). [assumption]. given #2 (I,wt=3): 112 ilf_type(A,set_type). [assumption]. given #3 (I,wt=5): 113 ilf_type(c4,relation_type(c2,c3)). [assumption]. given #4 (I,wt=9): 116 -member(A,c3) | member(ordered_pair(f25(A),A),c4). [copy(115),unit_del(a,112)]. given #5 (I,wt=6): 117 range(c2,c3,c4) != c3. [assumption]. given #6 (I,wt=7): 119 member(f17(A),A) | ilf_type(A,binary_relation_type). [copy(118),merge(c),unit_del(a,112)]. given #7 (I,wt=9): 121 f17(A) != ordered_pair(B,C) | ilf_type(A,binary_relation_type). [copy(120),flip(d),merge(e),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. given #8 (I,wt=15): 123 -member(A,B) | ordered_pair(f18(B,A),f19(B,A)) = A | -ilf_type(B,binary_relation_type). [copy(122),merge(e),unit_del(a,112),unit_del(b,112)]. given #9 (I,wt=16): 125 -member(A,B) | ordered_pair(f18(B,A),f19(B,A)) = A | member(f17(B),B). [copy(124),merge(e),unit_del(a,112),unit_del(b,112)]. given #10 (I,wt=18): 127 -member(A,B) | ordered_pair(f18(B,A),f19(B,A)) = A | f17(B) != ordered_pair(C,D). [copy(126),flip(h),merge(e),unit_del(a,112),unit_del(b,112),unit_del(e,112),unit_del(f,112)]. given #11 (I,wt=9): 129 -ilf_type(A,subset_type(cross_product(B,C))) | ilf_type(A,binary_relation_type). [copy(128),unit_del(a,112),unit_del(b,112),unit_del(d,112)]. given #12 (I,wt=18): 131 -ilf_type(A,subset_type(cross_product(B,C))) | -member(D,A) | ordered_pair(f18(A,D),f19(A,D)) = D. [copy(130),unit_del(a,112),unit_del(b,112),unit_del(d,112),unit_del(e,112)]. given #13 (I,wt=5): 133 -empty(A) | ilf_type(A,binary_relation_type). [copy(132),merge(c),unit_del(b,112)]. given #14 (I,wt=3): 148 subset(A,A). [factor(34,a,b),xx(c),unit_del(a,112)]. given #15 (I,wt=15): 155 member(f9(A,B),A) | -member(f9(A,B),B) | -member(f10(A,B),A). [factor(59,d,f),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. given #16 (I,wt=15): 158 member(f9(A,B),A) | -member(f9(A,B),B) | member(f10(A,B),B). [factor(60,d,f),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. given #17 (I,wt=15): 167 member(f12(A,B),B) | -member(f12(A,B),A) | member(f11(A,B),A). [factor(69,e,g),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. given #18 (I,wt=15): 172 member(f12(A,B),B) | -member(f12(A,B),A) | -member(f11(A,B),B). [factor(72,e,g),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. given #19 (I,wt=9): 185 -member(power_set(A),power_set(A)) | member(power_set(A),A). [factor(85,d,f),merge(c),unit_del(a,112),unit_del(b,112)]. given #20 (I,wt=12): 201 -ilf_type(A,relation_type(B,C)) | ilf_type(range(B,C,A),subset_type(C)). [back_unit_del(111),unit_del(a,112),unit_del(b,112)]. given #21 (I,wt=12): 202 -ilf_type(A,relation_type(B,C)) | range(B,C,A) = range_of(A). [back_unit_del(110),unit_del(a,112),unit_del(b,112)]. given #22 (I,wt=12): 203 -ilf_type(A,relation_type(B,C)) | ilf_type(domain(B,C,A),subset_type(B)). [back_unit_del(109),unit_del(a,112),unit_del(b,112)]. given #23 (I,wt=12): 204 -ilf_type(A,relation_type(B,C)) | domain(B,C,A) = domain_of(A). [back_unit_del(108),unit_del(a,112),unit_del(b,112)]. given #24 (I,wt=7): 205 -member(A,B) | member(f24(B),B). [back_unit_del(107),unit_del(a,112),unit_del(b,112)]. given #25 (I,wt=5): 206 -member(A,B) | -empty(B). [back_unit_del(105),unit_del(a,112),unit_del(b,112)]. given #26 (I,wt=6): 207 empty(A) | member(f23(A),A). [back_unit_del(104),unit_del(a,112)]. given #27 (I,wt=18): 208 -member(A,B) | ordered_pair(f20(B,A),f21(B,A)) = A | f22(B) != ordered_pair(C,D). [back_unit_del(102),unit_del(a,112),unit_del(b,112),unit_del(e,112),unit_del(f,112)]. given #28 (I,wt=16): 209 -member(A,B) | ordered_pair(f20(B,A),f21(B,A)) = A | member(f22(B),B). [back_unit_del(100),unit_del(a,112),unit_del(b,112)]. given #29 (I,wt=7): 210 empty(A) | ilf_type(f16(A),member_type(A)). [back_unit_del(90),unit_del(b,112)]. given #30 (I,wt=9): 211 empty(A) | member(B,A) | -ilf_type(B,member_type(A)). [back_unit_del(89),unit_del(a,112),unit_del(c,112)]. given #31 (I,wt=9): 212 empty(A) | ilf_type(B,member_type(A)) | -member(B,A). [back_unit_del(88),unit_del(a,112),unit_del(c,112)]. given #32 (I,wt=3): 213 -empty(power_set(A)). [back_unit_del(86),unit_del(a,112)]. given #33 (I,wt=10): 214 -member(A,B) | member(A,C) | -member(B,power_set(C)). [back_unit_del(85),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. given #34 (I,wt=9): 215 member(A,power_set(B)) | -member(f15(A,B),B). [back_unit_del(84),unit_del(a,112),unit_del(b,112)]. given #35 (I,wt=9): 216 member(A,power_set(B)) | member(f15(A,B),A). [back_unit_del(83),unit_del(a,112),unit_del(b,112)]. given #36 (I,wt=11): 217 -member(A,B) | member(A,C) | -member(f14(B,C),C). [back_unit_del(80),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. given #37 (I,wt=11): 218 -member(A,B) | member(A,C) | member(f14(B,C),B). [back_unit_del(79),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. given #38 (I,wt=9): 219 -member(A,B) | member(A,C) | -subset(B,C). [back_unit_del(77),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. given #39 (I,wt=8): 220 subset(A,B) | -member(f13(A,B),B). [back_unit_del(76),unit_del(a,112),unit_del(b,112)]. given #40 (I,wt=8): 221 subset(A,B) | member(f13(A,B),A). [back_unit_del(75),unit_del(a,112),unit_del(b,112)]. given #41 (I,wt=16): 222 member(A,B) | -member(A,C) | -member(f11(C,B),B) | member(f12(C,B),B). [back_unit_del(73),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. given #42 (I,wt=16): 223 member(A,B) | -member(A,C) | -member(f11(C,B),B) | -member(f12(C,B),C). [back_unit_del(72),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. given #43 (I,wt=16): 224 member(A,B) | -member(A,C) | member(f11(C,B),C) | member(f12(C,B),B). [back_unit_del(70),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. given #44 (I,wt=16): 225 member(A,B) | -member(A,C) | member(f11(C,B),C) | -member(f12(C,B),C). [back_unit_del(69),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. given #45 (I,wt=9): 226 member(A,B) | -member(A,C) | B != C. [back_unit_del(64),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. given #46 (I,wt=16): 227 member(A,B) | -member(A,C) | -member(f9(B,C),C) | member(f10(B,C),C). [back_unit_del(63),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. given #47 (I,wt=16): 228 member(A,B) | -member(A,C) | -member(f9(B,C),C) | -member(f10(B,C),B). [back_unit_del(62),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. given #48 (I,wt=16): 229 member(A,B) | -member(A,C) | member(f9(B,C),B) | member(f10(B,C),C). [back_unit_del(60),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. given #49 (I,wt=16): 230 member(A,B) | -member(A,C) | member(f9(B,C),B) | -member(f10(B,C),B). [back_unit_del(59),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. given #50 (I,wt=9): 231 member(A,B) | -member(A,C) | C != B. [back_unit_del(54),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. given #51 (I,wt=13): 232 A = B | -member(f7(B,A),A) | member(f8(B,A),A). [back_unit_del(53),unit_del(a,112),unit_del(b,112)]. given #52 (I,wt=13): 233 A = B | -member(f7(B,A),A) | -member(f8(B,A),B). [back_unit_del(52),unit_del(a,112),unit_del(b,112)]. given #53 (I,wt=13): 234 A = B | member(f7(B,A),B) | member(f8(B,A),A). [back_unit_del(50),unit_del(a,112),unit_del(b,112)]. given #54 (I,wt=13): 235 A = B | member(f7(B,A),B) | -member(f8(B,A),B). [back_unit_del(49),unit_del(a,112),unit_del(b,112)]. given #55 (I,wt=5): 236 ilf_type(f6(A),subset_type(A)). [back_unit_del(44),unit_del(a,112)]. given #56 (I,wt=9): 237 ilf_type(A,member_type(power_set(B))) | -ilf_type(A,subset_type(B)). [back_unit_del(43),unit_del(a,112),unit_del(b,112)]. given #57 (I,wt=9): 238 ilf_type(A,subset_type(B)) | -ilf_type(A,member_type(power_set(B))). [back_unit_del(42),unit_del(a,112),unit_del(b,112)]. given #58 (I,wt=7): 239 unordered_pair(A,B) = unordered_pair(B,A). [back_unit_del(40),unit_del(a,112),unit_del(b,112)]. given #59 (I,wt=6): 240 subset(A,B) | A != B. [back_unit_del(35),unit_del(a,112),unit_del(b,112)]. given #60 (I,wt=6): 241 subset(A,B) | B != A. [back_unit_del(34),unit_del(a,112),unit_del(b,112)]. given #61 (I,wt=9): 242 A = B | -subset(B,A) | -subset(A,B). [back_unit_del(33),unit_del(a,112),unit_del(b,112)]. given #62 (I,wt=7): 243 ilf_type(f5(A,B),relation_type(B,A)). [back_unit_del(32),unit_del(a,112),unit_del(b,112)]. given #63 (I,wt=11): 244 -ilf_type(A,relation_type(B,C)) | ilf_type(A,subset_type(cross_product(B,C))). [back_unit_del(31),unit_del(a,112),unit_del(b,112)]. given #64 (I,wt=11): 245 -ilf_type(A,subset_type(cross_product(B,C))) | ilf_type(A,relation_type(B,C)). [back_unit_del(30),unit_del(a,112),unit_del(b,112)]. given #65 (I,wt=13): 246 unordered_pair(unordered_pair(A,B),singleton(A)) = C | ordered_pair(A,B) != C. [back_unit_del(28),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. given #66 (I,wt=13): 248 -member(f3(A,B),B) | member(f4(A,B),B) | B = A. [back_unit_del(26),unit_del(a,112),unit_del(b,112)]. given #67 (I,wt=13): 249 -member(f3(A,B),B) | -member(f4(A,B),A) | B = A. [back_unit_del(25),unit_del(a,112),unit_del(b,112)]. given #68 (I,wt=13): 250 member(f3(A,B),A) | member(f4(A,B),B) | B = A. [back_unit_del(23),unit_del(a,112),unit_del(b,112)]. given #69 (I,wt=13): 251 member(f3(A,B),A) | -member(f4(A,B),A) | B = A. [back_unit_del(22),unit_del(a,112),unit_del(b,112)]. given #70 (I,wt=12): 252 -ilf_type(A,binary_relation_type) | -member(ordered_pair(B,C),A) | member(B,domain_of(A)). [back_unit_del(17),unit_del(a,112),unit_del(b,112)]. given #71 (I,wt=15): 253 -ilf_type(A,binary_relation_type) | member(ordered_pair(f2(A,B),B),A) | -member(ordered_pair(C,B),A). [back_unit_del(15),unit_del(b,112),unit_del(d,112)]. given #72 (I,wt=14): 254 -ilf_type(A,binary_relation_type) | member(ordered_pair(f1(A,B),B),A) | -member(B,range_of(A)). [back_unit_del(13),unit_del(b,112)]. given #73 (I,wt=12): 255 -ilf_type(A,binary_relation_type) | member(B,range_of(A)) | -member(ordered_pair(C,B),A). [back_unit_del(11),unit_del(b,112),unit_del(d,112)]. given #74 (A,wt=11): 256 ilf_type(c3,binary_relation_type) | member(ordered_pair(f25(f17(c3)),f17(c3)),c4). [resolve(119,a,116,a)]. given #75 (F,wt=4): 260 range_of(c4) != c3. [back_rewrite(117),rewrite([258(4)])]. given #76 (T,wt=4): 282 member(A,power_set(A)). [resolve(216,b,215,b),merge(b)]. given #77 (T,wt=5): 259 ilf_type(range_of(c4),subset_type(c3)). [back_rewrite(257),rewrite([258(4)])]. given #78 (T,wt=5): 263 ilf_type(domain_of(c4),subset_type(c2)). [back_rewrite(261),rewrite([262(4)])]. given #79 (T,wt=5): 420 ilf_type(c3,binary_relation_type) | -empty(c4). [resolve(256,b,206,a)]. given #80 (A,wt=7): 258 range(c2,c3,c4) = range_of(c4). [resolve(202,a,113,a)]. given #81 (T,wt=5): 441 ilf_type(A,member_type(power_set(A))). [resolve(282,a,212,c),unit_del(a,213)]. given #82 (T,wt=4): 451 ilf_type(A,subset_type(A)). [resolve(441,a,238,b)]. given #83 (T,wt=5): 453 ilf_type(cross_product(A,B),binary_relation_type). [resolve(451,a,129,a)]. given #84 (T,wt=6): 265 empty(A) | member(f24(A),A). [resolve(207,b,205,a)]. given #85 (A,wt=7): 262 domain(c2,c3,c4) = domain_of(c4). [resolve(204,a,113,a)]. given #86 (T,wt=6): 275 empty(A) | member(f16(A),A). [resolve(211,c,210,b),merge(c)]. given #87 (T,wt=6): 288 member(A,power_set(B)) | -empty(A). [resolve(216,b,206,a)]. given #88 (T,wt=6): 358 ilf_type(f6(cross_product(A,B)),binary_relation_type). [resolve(236,a,129,a)]. given #89 (T,wt=6): 359 ilf_type(f6(A),member_type(power_set(A))). [resolve(237,b,236,a)]. given #90 (A,wt=7): 264 member(f24(A),A) | ilf_type(A,binary_relation_type). [resolve(205,a,119,a)]. given #91 (T,wt=5): 499 member(f6(A),power_set(A)). [resolve(359,a,211,c),unit_del(a,213)]. given #92 (T,wt=6): 360 ilf_type(f16(power_set(A)),subset_type(A)). [resolve(238,b,210,b),unit_del(b,213)]. given #93 (T,wt=6): 369 ilf_type(c4,subset_type(cross_product(c2,c3))). [resolve(244,a,113,a)]. given #94 (T,wt=3): 540 ilf_type(c4,binary_relation_type). [resolve(369,a,129,a)]. given #95 (A,wt=20): 266 empty(A) | -ilf_type(A,subset_type(cross_product(B,C))) | ordered_pair(f18(A,f23(A)),f19(A,f23(A))) = f23(A). [resolve(207,b,131,b)]. given #96 (T,wt=6): 444 member(f24(power_set(A)),power_set(A)). [resolve(282,a,205,a)]. given #97 (T,wt=6): 449 ilf_type(range_of(c4),member_type(power_set(c3))). [resolve(259,a,237,b)]. given #98 (T,wt=5): 568 member(range_of(c4),power_set(c3)). [resolve(449,a,211,c),unit_del(a,213)]. given #99 (T,wt=6): 450 ilf_type(domain_of(c4),member_type(power_set(c2))). [resolve(263,a,237,b)]. given #100 (A,wt=20): 267 empty(A) | ordered_pair(f18(A,f23(A)),f19(A,f23(A))) = f23(A) | f17(A) != ordered_pair(B,C). [resolve(207,b,127,a)]. given #101 (T,wt=5): 588 member(domain_of(c4),power_set(c2)). [resolve(450,a,211,c),unit_del(a,213)]. given #102 (T,wt=7): 276 empty(A) | ilf_type(f23(A),member_type(A)). [resolve(212,c,207,b),merge(c)]. given #103 (T,wt=6): 608 ilf_type(f23(power_set(A)),subset_type(A)). [resolve(276,b,238,b),unit_del(a,213)]. given #104 (T,wt=7): 361 subset(unordered_pair(A,B),unordered_pair(B,A)). [resolve(240,b,239,a)]. given #105 (A,wt=18): 268 empty(A) | ordered_pair(f18(A,f23(A)),f19(A,f23(A))) = f23(A) | member(f17(A),A). [resolve(207,b,125,a)]. given #106 (T,wt=7): 365 ilf_type(domain_of(f5(A,B)),subset_type(B)). [resolve(243,a,203,a),rewrite([364(2)])]. given #107 (T,wt=7): 367 ilf_type(range_of(f5(A,B)),subset_type(A)). [resolve(243,a,201,a),rewrite([366(2)])]. given #108 (T,wt=7): 421 ilf_type(c3,binary_relation_type) | member(f24(c4),c4). [resolve(256,b,205,a)]. given #109 (T,wt=7): 429 member(A,B) | power_set(A) != B. [resolve(282,a,231,b)]. given #110 (A,wt=17): 269 empty(A) | ordered_pair(f18(A,f23(A)),f19(A,f23(A))) = f23(A) | -ilf_type(A,binary_relation_type). [resolve(207,b,123,a)]. given #111 (T,wt=7): 452 ilf_type(cross_product(A,B),relation_type(A,B)). [resolve(451,a,245,a)]. given #112 (T,wt=7): 469 empty(A) | ilf_type(f24(A),member_type(A)). [resolve(265,b,212,c),merge(b)]. given #113 (T,wt=6): 664 ilf_type(f24(power_set(A)),subset_type(A)). [resolve(469,b,238,b),unit_del(a,213)]. given #114 (T,wt=7): 528 -member(A,f6(B)) | member(A,B). [resolve(499,a,214,c)]. given #115 (A,wt=10): 270 empty(c3) | member(ordered_pair(f25(f23(c3)),f23(c3)),c4). [resolve(207,b,116,a)]. given #116 (T,wt=4): 695 empty(c3) | -empty(c4). [resolve(270,b,206,a)]. given #117 (T,wt=6): 696 empty(c3) | member(f24(c4),c4). [resolve(270,b,205,a)]. given #118 (T,wt=7): 537 ilf_type(f16(power_set(A)),member_type(power_set(A))). [resolve(360,a,237,b)]. given #119 (T,wt=6): 719 member(f16(power_set(A)),power_set(A)). [resolve(537,a,211,c),unit_del(a,213)]. given #120 (A,wt=20): 271 ordered_pair(f20(A,f23(A)),f21(A,f23(A))) = f23(A) | f22(A) != ordered_pair(B,C) | empty(A). [resolve(208,a,207,b)]. given #121 (T,wt=7): 538 ilf_type(f16(power_set(cross_product(A,B))),binary_relation_type). [resolve(360,a,129,a)]. given #122 (T,wt=7): 539 ilf_type(c4,member_type(power_set(cross_product(c2,c3)))). [resolve(369,a,237,b)]. given #123 (T,wt=6): 738 member(c4,power_set(cross_product(c2,c3))). [resolve(539,a,211,c),unit_del(a,213)]. given #124 (T,wt=7): 561 ilf_type(f24(power_set(A)),member_type(power_set(A))). [resolve(444,a,212,c),unit_del(a,213)]. given #125 (A,wt=21): 272 ordered_pair(f20(A,f17(A)),f21(A,f17(A))) = f17(A) | f22(A) != ordered_pair(B,C) | ilf_type(A,binary_relation_type). [resolve(208,a,119,a)]. given #126 (T,wt=7): 580 -member(A,range_of(c4)) | member(A,c3). [resolve(568,a,214,c)]. given #127 (T,wt=7): 600 -member(A,domain_of(c4)) | member(A,c2). [resolve(588,a,214,c)]. given #128 (T,wt=7): 611 ilf_type(f23(power_set(A)),member_type(power_set(A))). [resolve(608,a,237,b)]. given #129 (T,wt=6): 776 member(f23(power_set(A)),power_set(A)). [resolve(611,a,211,c),unit_del(a,213)]. given #130 (A,wt=18): 273 ordered_pair(f20(A,f23(A)),f21(A,f23(A))) = f23(A) | member(f22(A),A) | empty(A). [resolve(209,a,207,b)]. given #131 (T,wt=7): 612 ilf_type(f23(power_set(cross_product(A,B))),binary_relation_type). [resolve(608,a,129,a)]. given #132 (T,wt=7): 661 ilf_type(domain_of(cross_product(A,B)),subset_type(A)). [resolve(452,a,203,a),rewrite([660(2)])]. given #133 (T,wt=7): 663 ilf_type(range_of(cross_product(A,B)),subset_type(B)). [resolve(452,a,201,a),rewrite([662(2)])]. given #134 (T,wt=7): 667 ilf_type(f24(power_set(cross_product(A,B))),binary_relation_type). [resolve(664,a,129,a)]. given #135 (A,wt=19): 274 ordered_pair(f20(A,f17(A)),f21(A,f17(A))) = f17(A) | member(f22(A),A) | ilf_type(A,binary_relation_type). [resolve(209,a,119,a)]. given #136 (T,wt=7): 677 empty(c3) | member(f23(c3),range_of(c4)). [resolve(270,b,255,c),unit_del(b,540)]. given #137 (T,wt=5): 863 empty(c3) | -empty(range_of(c4)). [resolve(677,b,206,a)]. given #138 (T,wt=8): 280 -member(A,f23(power_set(B))) | member(A,B). [resolve(214,c,207,b),unit_del(c,213)]. given #139 (T,wt=8): 289 member(A,power_set(B)) | member(f24(A),A). [resolve(216,b,205,a)]. given #140 (A,wt=10): 277 empty(A) | ilf_type(f17(A),member_type(A)) | ilf_type(A,binary_relation_type). [resolve(212,c,119,a)]. given #141 (T,wt=8): 368 ilf_type(f5(A,B),subset_type(cross_product(B,A))). [resolve(244,a,243,a)]. given #142 (T,wt=5): 951 ilf_type(f5(A,B),binary_relation_type). [resolve(368,a,129,a)]. given #143 (T,wt=8): 370 ilf_type(f6(cross_product(A,B)),relation_type(A,B)). [resolve(245,a,236,a)]. given #144 (T,wt=8): 440 member(A,B) | -member(power_set(A),power_set(B)). [resolve(282,a,214,a)]. given #145 (A,wt=10): 278 member(f23(A),B) | -member(A,power_set(B)) | empty(A). [resolve(214,a,207,b)]. given #146 (T,wt=8): 467 -member(A,f24(power_set(B))) | member(A,B). [resolve(265,b,214,c),unit_del(a,213)]. given #147 (T,wt=8): 490 -member(A,f16(power_set(B))) | member(A,B). [resolve(275,b,214,c),unit_del(a,213)]. given #148 (T,wt=8): 517 member(f6(A),B) | power_set(A) != B. [resolve(499,a,231,b)]. given #149 (T,wt=8): 544 ilf_type(c3,binary_relation_type) | member(f17(c3),range_of(c4)). [back_unit_del(402),unit_del(b,540)]. given #150 (A,wt=11): 279 member(f17(A),B) | -member(A,power_set(B)) | ilf_type(A,binary_relation_type). [resolve(214,a,119,a)]. given #151 (T,wt=6): 1004 ilf_type(c3,binary_relation_type) | -empty(range_of(c4)). [resolve(544,b,206,a)]. given #152 (T,wt=8): 569 member(range_of(c4),A) | power_set(c3) != A. [resolve(568,a,231,b)]. given #153 (T,wt=8): 589 member(domain_of(c4),A) | power_set(c2) != A. [resolve(588,a,231,b)]. given #154 (T,wt=8): 635 ilf_type(domain_of(f5(A,B)),member_type(power_set(B))). [resolve(365,a,237,b)]. given #155 (A,wt=12): 281 -member(A,f17(power_set(B))) | member(A,B) | ilf_type(power_set(B),binary_relation_type). [resolve(214,c,119,a)]. given #156 (T,wt=7): 1017 member(domain_of(f5(A,B)),power_set(B)). [resolve(635,a,211,c),unit_del(a,213)]. given #157 (T,wt=8): 636 ilf_type(domain_of(f5(A,cross_product(B,C))),binary_relation_type). [resolve(365,a,129,a)]. given #158 (T,wt=8): 639 ilf_type(range_of(f5(A,B)),member_type(power_set(A))). [resolve(367,a,237,b)]. given #159 (T,wt=7): 1049 member(range_of(f5(A,B)),power_set(A)). [resolve(639,a,211,c),unit_del(a,213)]. given #160 (A,wt=14): 283 member(power_set(A),power_set(B)) | -member(C,f15(power_set(A),B)) | member(C,A). [resolve(216,b,214,c)]. given #161 (T,wt=8): 640 ilf_type(range_of(f5(cross_product(A,B),C)),binary_relation_type). [resolve(367,a,129,a)]. given #162 (T,wt=8): 668 member(f16(f6(A)),A) | empty(f6(A)). [resolve(528,a,275,b)]. given #163 (T,wt=5): 1109 empty(f6(A)) | -empty(A). [resolve(668,a,206,a)]. given #164 (T,wt=7): 1110 empty(f6(A)) | member(f24(A),A). [resolve(668,a,205,a)]. given #165 (A,wt=13): 284 member(A,power_set(B)) | member(f15(A,B),C) | -member(A,power_set(C)). [resolve(216,b,214,a)]. given #166 (T,wt=8): 670 member(f24(f6(A)),A) | empty(f6(A)). [resolve(528,a,265,b)]. given #167 (T,wt=8): 675 member(f23(f6(A)),A) | empty(f6(A)). [resolve(528,a,207,b)]. given #168 (T,wt=8): 679 empty(c3) | member(f25(f23(c3)),domain_of(c4)). [resolve(270,b,252,b),unit_del(b,540)]. given #169 (T,wt=5): 1238 empty(c3) | -empty(domain_of(c4)). [resolve(679,b,206,a)]. given #170 (A,wt=12): 285 member(A,power_set(B)) | empty(A) | ilf_type(f15(A,B),member_type(A)). [resolve(216,b,212,c)]. given #171 (T,wt=7): 1222 empty(c3) | member(f25(f23(c3)),c2). [resolve(679,b,600,a)]. given #172 (T,wt=4): 1308 empty(c3) | -empty(c2). [resolve(1222,b,206,a)]. given #173 (T,wt=6): 1309 empty(c3) | member(f24(c2),c2). [resolve(1222,b,205,a)]. given #174 (T,wt=8): 750 -member(A,c4) | member(A,cross_product(c2,c3)). [resolve(738,a,214,c)]. given #175 (A,wt=23): 286 member(A,power_set(B)) | ordered_pair(f20(A,f15(A,B)),f21(A,f15(A,B))) = f15(A,B) | member(f22(A),A). [resolve(216,b,209,a)]. given #176 (T,wt=8): 758 member(f16(range_of(c4)),c3) | empty(range_of(c4)). [resolve(580,a,275,b)]. given #177 (T,wt=5): 1445 empty(range_of(c4)) | -empty(c3). [resolve(758,a,206,a)]. given #178 (T,wt=7): 1446 empty(range_of(c4)) | member(f24(c3),c3). [resolve(758,a,205,a)]. given #179 (T,wt=8): 760 member(f24(range_of(c4)),c3) | empty(range_of(c4)). [resolve(580,a,265,b)]. given #180 (A,wt=25): 287 member(A,power_set(B)) | ordered_pair(f20(A,f15(A,B)),f21(A,f15(A,B))) = f15(A,B) | f22(A) != ordered_pair(C,D). [resolve(216,b,208,a)]. given #181 (T,wt=8): 765 member(f23(range_of(c4)),c3) | empty(range_of(c4)). [resolve(580,a,207,b)]. given #182 (T,wt=8): 767 member(f16(domain_of(c4)),c2) | empty(domain_of(c4)). [resolve(600,a,275,b)]. given #183 (T,wt=5): 1526 empty(domain_of(c4)) | -empty(c2). [resolve(767,a,206,a)]. given #184 (T,wt=7): 1527 empty(domain_of(c4)) | member(f24(c2),c2). [resolve(767,a,205,a)]. given #185 (A,wt=25): 290 member(A,power_set(B)) | -ilf_type(A,subset_type(cross_product(C,D))) | ordered_pair(f18(A,f15(A,B)),f19(A,f15(A,B))) = f15(A,B). [resolve(216,b,131,b)]. given #186 (T,wt=8): 769 member(f24(domain_of(c4)),c2) | empty(domain_of(c4)). [resolve(600,a,265,b)]. given #187 (T,wt=8): 774 member(f23(domain_of(c4)),c2) | empty(domain_of(c4)). [resolve(600,a,207,b)]. given #188 (T,wt=8): 821 ilf_type(domain_of(cross_product(A,B)),member_type(power_set(A))). [resolve(661,a,237,b)]. given #189 (T,wt=7): 1599 member(domain_of(cross_product(A,B)),power_set(A)). [resolve(821,a,211,c),unit_del(a,213)]. given #190 (A,wt=25): 291 member(A,power_set(B)) | ordered_pair(f18(A,f15(A,B)),f19(A,f15(A,B))) = f15(A,B) | f17(A) != ordered_pair(C,D). [resolve(216,b,127,a)]. given #191 (T,wt=8): 822 ilf_type(domain_of(cross_product(cross_product(A,B),C)),binary_relation_type). [resolve(661,a,129,a)]. given #192 (T,wt=8): 825 ilf_type(range_of(cross_product(A,B)),member_type(power_set(B))). [resolve(663,a,237,b)]. given #193 (T,wt=7): 1622 member(range_of(cross_product(A,B)),power_set(B)). [resolve(825,a,211,c),unit_del(a,213)]. given #194 (T,wt=8): 826 ilf_type(range_of(cross_product(A,cross_product(B,C))),binary_relation_type). [resolve(663,a,129,a)]. given #195 (A,wt=23): 292 member(A,power_set(B)) | ordered_pair(f18(A,f15(A,B)),f19(A,f15(A,B))) = f15(A,B) | member(f17(A),A). [resolve(216,b,125,a)]. given #196 (T,wt=8): 864 empty(c3) | member(f24(range_of(c4)),range_of(c4)). [resolve(677,b,205,a)]. given #197 (T,wt=7): 1725 empty(c3) | member(f24(range_of(c4)),c3). [resolve(864,b,580,a)]. given #198 (T,wt=8): 953 ilf_type(domain_of(f6(cross_product(A,B))),subset_type(A)). [resolve(370,a,203,a),rewrite([952(3)])]. given #199 (T,wt=8): 955 ilf_type(range_of(f6(cross_product(A,B))),subset_type(B)). [resolve(370,a,201,a),rewrite([954(3)])]. given #200 (A,wt=22): 293 member(A,power_set(B)) | ordered_pair(f18(A,f15(A,B)),f19(A,f15(A,B))) = f15(A,B) | -ilf_type(A,binary_relation_type). [resolve(216,b,123,a)]. given #201 (T,wt=8): 956 member(f23(c4),cross_product(c2,c3)) | empty(c4). [resolve(278,b,738,a)]. given #202 (T,wt=6): 1791 empty(c4) | -empty(cross_product(c2,c3)). [resolve(956,a,206,a)]. given #203 (T,wt=8): 1239 empty(c3) | member(f24(domain_of(c4)),domain_of(c4)). [resolve(679,b,205,a)]. given #204 (T,wt=7): 1797 empty(c3) | member(f24(domain_of(c4)),c2). [resolve(1239,b,600,a)]. given #205 (A,wt=14): 294 member(c3,power_set(A)) | member(ordered_pair(f25(f15(c3,A)),f15(c3,A)),c4). [resolve(216,b,116,a)]. given #206 (T,wt=6): 1854 member(c3,power_set(A)) | -empty(c4). [resolve(294,b,206,a)]. given #207 (T,wt=8): 1333 member(f24(c4),cross_product(c2,c3)) | empty(c3). [resolve(750,a,696,b)]. given #208 (T,wt=6): 1875 empty(c3) | -empty(cross_product(c2,c3)). [resolve(1333,a,206,a)]. given #209 (T,wt=8): 1339 member(f16(c4),cross_product(c2,c3)) | empty(c4). [resolve(750,a,275,b)]. given #210 (A,wt=15): 295 member(power_set(power_set(A)),power_set(A)) | -member(power_set(power_set(A)),f15(power_set(power_set(A)),A)). [factor(283,a,c)]. given #211 (T,wt=8): 1342 member(f24(c4),cross_product(c2,c3)) | empty(c4). [resolve(750,a,265,b)]. given #212 (T,wt=8): 1757 empty(c3) | ilf_type(f24(range_of(c4)),member_type(c3)). [resolve(1725,b,212,c),merge(b)]. given #213 (T,wt=8): 1855 member(c3,power_set(A)) | member(f24(c4),c4). [resolve(294,b,205,a)]. given #214 (T,wt=8): 1958 member(f24(c4),c4) | -member(f24(c4),c3). [factor(1930,a,c)]. given #215 (A,wt=14): 296 member(f15(A,B),C) | -member(f14(A,C),C) | member(A,power_set(B)). [resolve(217,a,216,b)]. given #216 (T,wt=9): 316 member(f23(A),B) | B != A | empty(A). [resolve(226,b,207,b)]. given #217 (T,wt=9): 331 member(f23(A),B) | A != B | empty(A). [resolve(231,b,207,b)]. given #218 (T,wt=9): 439 member(A,B) | -member(f14(power_set(A),B),B). [resolve(282,a,217,a)]. given #219 (T,wt=9): 455 empty(A) | member(f24(A),B) | A != B. [resolve(265,b,231,b)]. given #220 (A,wt=11): 297 member(f23(A),B) | -member(f14(A,B),B) | empty(A). [resolve(217,a,207,b)]. given #221 (T,wt=9): 460 empty(A) | member(f24(A),B) | B != A. [resolve(265,b,226,b)]. given #222 (T,wt=9): 478 empty(A) | member(f16(A),B) | A != B. [resolve(275,b,231,b)]. given #223 (T,wt=9): 483 empty(A) | member(f16(A),B) | B != A. [resolve(275,b,226,b)]. given #224 (T,wt=9): 529 member(f6(A),B) | -member(power_set(A),power_set(B)). [resolve(499,a,214,a)]. given #225 (A,wt=12): 298 member(f17(A),B) | -member(f14(A,B),B) | ilf_type(A,binary_relation_type). [resolve(217,a,119,a)]. given #226 (T,wt=9): 536 ilf_type(f16(power_set(cross_product(A,B))),relation_type(A,B)). [resolve(360,a,245,a)]. given #227 (T,wt=9): 542 ilf_type(c3,binary_relation_type) | member(f25(f17(c3)),domain_of(c4)). [back_unit_del(404),unit_del(b,540)]. given #228 (T,wt=6): 2001 ilf_type(c3,binary_relation_type) | -empty(domain_of(c4)). [resolve(542,b,206,a)]. given #229 (T,wt=8): 1985 ilf_type(c3,binary_relation_type) | member(f25(f17(c3)),c2). [resolve(542,b,600,a)]. given #230 (A,wt=14): 299 member(f15(A,B),C) | member(f14(A,C),A) | member(A,power_set(B)). [resolve(218,a,216,b)]. given #231 (T,wt=5): 2022 ilf_type(c3,binary_relation_type) | -empty(c2). [resolve(1985,b,206,a)]. given #232 (T,wt=7): 2023 ilf_type(c3,binary_relation_type) | member(f24(c2),c2). [resolve(1985,b,205,a)]. given #233 (T,wt=9): 549 member(f24(power_set(A)),B) | power_set(A) != B. [resolve(444,a,231,b)]. given #234 (T,wt=9): 581 member(range_of(c4),A) | -member(power_set(c3),power_set(A)). [resolve(568,a,214,a)]. given #235 (A,wt=11): 300 member(f23(A),B) | member(f14(A,B),A) | empty(A). [resolve(218,a,207,b)]. given #236 (T,wt=9): 601 member(domain_of(c4),A) | -member(power_set(c2),power_set(A)). [resolve(588,a,214,a)]. given #237 (T,wt=9): 610 ilf_type(f23(power_set(cross_product(A,B))),relation_type(A,B)). [resolve(608,a,245,a)]. given #238 (T,wt=9): 666 ilf_type(f24(power_set(cross_product(A,B))),relation_type(A,B)). [resolve(664,a,245,a)]. given #239 (T,wt=9): 671 member(f24(f6(A)),A) | ilf_type(f6(A),binary_relation_type). [resolve(528,a,264,a)]. given #240 (A,wt=12): 301 member(f17(A),B) | member(f14(A,B),A) | ilf_type(A,binary_relation_type). [resolve(218,a,119,a)]. given #241 (T,wt=6): 2253 ilf_type(f6(A),binary_relation_type) | -empty(A). [resolve(671,a,206,a)]. given #242 (T,wt=8): 2254 ilf_type(f6(A),binary_relation_type) | member(f24(A),A). [resolve(671,a,205,a)]. given #243 (T,wt=9): 676 member(f17(f6(A)),A) | ilf_type(f6(A),binary_relation_type). [resolve(528,a,119,a)]. given #244 (T,wt=9): 701 empty(c3) | member(f24(c4),A) | c4 != A. [resolve(696,b,231,b)]. given #245 (A,wt=11): 302 member(f13(A,B),A) | -member(C,A) | member(C,B). [resolve(221,a,219,c)]. given #246 (T,wt=9): 720 member(f16(power_set(A)),B) | power_set(A) != B. [resolve(719,a,231,b)]. given #247 (T,wt=9): 739 member(c4,A) | power_set(cross_product(c2,c3)) != A. [resolve(738,a,231,b)]. given #248 (T,wt=9): 761 member(f24(range_of(c4)),c3) | ilf_type(range_of(c4),binary_relation_type). [resolve(580,a,264,a)]. given #249 (T,wt=6): 2485 ilf_type(range_of(c4),binary_relation_type) | -empty(c3). [resolve(761,a,206,a)]. given #250 (A,wt=19): 303 member(f15(A,B),C) | -member(f11(A,C),C) | member(f12(A,C),C) | member(A,power_set(B)). [resolve(222,b,216,b)]. given #251 (T,wt=8): 2486 ilf_type(range_of(c4),binary_relation_type) | member(f24(c3),c3). [resolve(761,a,205,a)]. given #252 (T,wt=9): 766 member(f17(range_of(c4)),c3) | ilf_type(range_of(c4),binary_relation_type). [resolve(580,a,119,a)]. given #253 (T,wt=9): 770 member(f24(domain_of(c4)),c2) | ilf_type(domain_of(c4),binary_relation_type). [resolve(600,a,264,a)]. given #254 (T,wt=6): 2553 ilf_type(domain_of(c4),binary_relation_type) | -empty(c2). [resolve(770,a,206,a)]. given #255 (A,wt=16): 304 member(f23(A),B) | -member(f11(A,B),B) | member(f12(A,B),B) | empty(A). [resolve(222,b,207,b)]. given #256 (T,wt=8): 2554 ilf_type(domain_of(c4),binary_relation_type) | member(f24(c2),c2). [resolve(770,a,205,a)]. given #257 (T,wt=9): 775 member(f17(domain_of(c4)),c2) | ilf_type(domain_of(c4),binary_relation_type). [resolve(600,a,119,a)]. given #258 (T,wt=9): 777 member(f23(power_set(A)),B) | power_set(A) != B. [resolve(776,a,231,b)]. given #259 (T,wt=9): 910 member(f24(A),A) | ilf_type(A,member_type(power_set(B))). [resolve(289,a,212,c),unit_del(b,213)]. given #260 (A,wt=17): 305 member(f17(A),B) | -member(f11(A,B),B) | member(f12(A,B),B) | ilf_type(A,binary_relation_type). [resolve(222,b,119,a)]. given #261 (T,wt=7): 2628 ilf_type(A,member_type(power_set(B))) | -empty(A). [resolve(910,a,206,a)]. given #262 (T,wt=9): 950 ilf_type(f5(A,B),member_type(power_set(cross_product(B,A)))). [resolve(368,a,237,b)]. given #263 (T,wt=8): 2638 member(f5(A,B),power_set(cross_product(B,A))). [resolve(950,a,211,c),unit_del(a,213)]. given #264 (T,wt=9): 1005 ilf_type(c3,binary_relation_type) | member(f24(range_of(c4)),range_of(c4)). [resolve(544,b,205,a)]. given #265 (A,wt=19): 306 member(f15(A,B),C) | -member(f11(A,C),C) | -member(f12(A,C),A) | member(A,power_set(B)). [resolve(223,b,216,b)]. given #266 (T,wt=8): 2661 ilf_type(c3,binary_relation_type) | member(f24(range_of(c4)),c3). [resolve(1005,b,580,a)]. given #267 (T,wt=9): 1041 -member(A,domain_of(f5(B,C))) | member(A,C). [resolve(1017,a,214,c)]. given #268 (T,wt=9): 1063 -member(A,range_of(f5(B,C))) | member(A,B). [resolve(1049,a,214,c)]. given #269 (T,wt=9): 1116 empty(f6(domain_of(c4))) | member(f24(domain_of(c4)),c2). [resolve(1110,b,600,a)]. given #270 (A,wt=16): 307 member(f23(A),B) | -member(f11(A,B),B) | -member(f12(A,B),A) | empty(A). [resolve(223,b,207,b)]. given #271 (T,wt=6): 2768 empty(f6(domain_of(c4))) | -empty(c2). [resolve(1116,b,206,a)]. given #272 (T,wt=8): 2769 empty(f6(domain_of(c4))) | member(f24(c2),c2). [resolve(1116,b,205,a)]. given #273 (T,wt=9): 1117 empty(f6(range_of(c4))) | member(f24(range_of(c4)),c3). [resolve(1110,b,580,a)]. given #274 (T,wt=6): 2812 empty(f6(range_of(c4))) | -empty(c3). [resolve(1117,b,206,a)]. given #275 (A,wt=17): 308 member(f17(A),B) | -member(f11(A,B),B) | -member(f12(A,B),A) | ilf_type(A,binary_relation_type). [resolve(223,b,119,a)]. given #276 (T,wt=8): 2813 empty(f6(range_of(c4))) | member(f24(c3),c3). [resolve(1117,b,205,a)]. given #277 (T,wt=9): 1118 empty(f6(f6(A))) | member(f24(f6(A)),A). [resolve(1110,b,528,a)]. given #278 (T,wt=6): 2876 empty(f6(f6(A))) | -empty(A). [resolve(1118,b,206,a)]. given #279 (T,wt=8): 2877 empty(f6(f6(A))) | member(f24(A),A). [resolve(1118,b,205,a)]. given #280 (A,wt=19): 309 member(f15(A,B),C) | member(f11(A,C),A) | member(f12(A,C),C) | member(A,power_set(B)). [resolve(224,b,216,b)]. given #281 (T,wt=9): 1314 empty(c3) | member(f24(c2),A) | c2 != A. [resolve(1309,b,231,b)]. given #282 (T,wt=9): 1332 member(f24(c4),cross_product(c2,c3)) | empty(f6(c4)). [resolve(750,a,1110,b)]. given #283 (T,wt=7): 3043 empty(f6(c4)) | -empty(cross_product(c2,c3)). [resolve(1332,a,206,a)]. given #284 (T,wt=9): 1337 member(f24(c4),cross_product(c2,c3)) | ilf_type(c3,binary_relation_type). [resolve(750,a,421,b)]. given #285 (A,wt=16): 310 member(f23(A),B) | member(f11(A,B),A) | member(f12(A,B),B) | empty(A). [resolve(224,b,207,b)]. given #286 (T,wt=7): 3065 ilf_type(c3,binary_relation_type) | -empty(cross_product(c2,c3)). [resolve(1337,a,206,a)]. given #287 (T,wt=9): 1614 -member(A,domain_of(cross_product(B,C))) | member(A,B). [resolve(1599,a,214,c)]. given #288 (T,wt=9): 1637 -member(A,range_of(cross_product(B,C))) | member(A,C). [resolve(1622,a,214,c)]. given #289 (T,wt=9): 1768 ilf_type(domain_of(f6(cross_product(A,B))),member_type(power_set(A))). [resolve(953,a,237,b)]. given #290 (A,wt=17): 311 member(f17(A),B) | member(f11(A,B),A) | member(f12(A,B),B) | ilf_type(A,binary_relation_type). [resolve(224,b,119,a)]. given #291 (T,wt=8): 3215 member(domain_of(f6(cross_product(A,B))),power_set(A)). [resolve(1768,a,211,c),unit_del(a,213)]. given #292 (T,wt=9): 1769 ilf_type(domain_of(f6(cross_product(cross_product(A,B),C))),binary_relation_type). [resolve(953,a,129,a)]. given #293 (T,wt=9): 1773 ilf_type(range_of(f6(cross_product(A,B))),member_type(power_set(B))). [resolve(955,a,237,b)]. given #294 (T,wt=8): 3327 member(range_of(f6(cross_product(A,B))),power_set(B)). [resolve(1773,a,211,c),unit_del(a,213)]. given #295 (A,wt=19): 312 member(f15(A,B),C) | member(f11(A,C),A) | -member(f12(A,C),A) | member(A,power_set(B)). [resolve(225,b,216,b)]. given #296 (T,wt=9): 1774 ilf_type(range_of(f6(cross_product(A,cross_product(B,C)))),binary_relation_type). [resolve(955,a,129,a)]. given #297 (T,wt=9): 1932 member(f24(c4),c4) | ilf_type(c3,member_type(power_set(A))). [resolve(1855,a,212,c),unit_del(b,213)]. given #298 (T,wt=7): 3371 ilf_type(c3,member_type(power_set(A))) | -empty(c4). [resolve(1932,a,206,a)]. given #299 (T,wt=9): 1982 ilf_type(domain_of(f16(power_set(cross_product(A,B)))),subset_type(A)). [resolve(536,a,203,a),rewrite([1981(4)])]. given #300 (A,wt=16): 313 member(f23(A),B) | member(f11(A,B),A) | -member(f12(A,B),A) | empty(A). [resolve(225,b,207,b)]. given #301 (T,wt=9): 1984 ilf_type(range_of(f16(power_set(cross_product(A,B)))),subset_type(B)). [resolve(536,a,201,a),rewrite([1983(4)])]. given #302 (T,wt=9): 2002 ilf_type(c3,binary_relation_type) | member(f24(domain_of(c4)),domain_of(c4)). [resolve(542,b,205,a)]. given #303 (T,wt=8): 3390 ilf_type(c3,binary_relation_type) | member(f24(domain_of(c4)),c2). [resolve(2002,b,600,a)]. given #304 (T,wt=9): 2053 member(f14(A,B),A) | member(A,power_set(B)). [resolve(299,a,215,b),merge(c)]. given #305 (A,wt=17): 314 member(f17(A),B) | member(f11(A,B),A) | -member(f12(A,B),A) | ilf_type(A,binary_relation_type). [resolve(225,b,119,a)]. given #306 (T,wt=9): 2168 member(f14(A,B),A) | empty(A) | -empty(B). [resolve(300,a,206,a)]. given #307 (T,wt=9): 2216 ilf_type(domain_of(f23(power_set(cross_product(A,B)))),subset_type(A)). [resolve(610,a,203,a),rewrite([2215(4)])]. given #308 (T,wt=9): 2218 ilf_type(range_of(f23(power_set(cross_product(A,B)))),subset_type(B)). [resolve(610,a,201,a),rewrite([2217(4)])]. given #309 (T,wt=9): 2220 ilf_type(domain_of(f24(power_set(cross_product(A,B)))),subset_type(A)). [resolve(666,a,203,a),rewrite([2219(4)])]. given #310 (A,wt=12): 315 member(f15(A,B),C) | C != A | member(A,power_set(B)). [resolve(226,b,216,b)]. given #311 (T,wt=9): 2222 ilf_type(range_of(f24(power_set(cross_product(A,B)))),subset_type(B)). [resolve(666,a,201,a),rewrite([2221(4)])]. given #312 (T,wt=10): 317 member(f17(A),B) | B != A | ilf_type(A,binary_relation_type). [resolve(226,b,119,a)]. given #313 (T,wt=10): 332 member(f17(A),B) | A != B | ilf_type(A,binary_relation_type). [resolve(231,b,119,a)]. given #314 (T,wt=10): 350 A = B | member(f7(B,A),B) | -empty(A). [resolve(234,c,206,a)]. given #315 (A,wt=19): 318 member(f15(A,B),C) | -member(f9(C,A),A) | member(f10(C,A),A) | member(A,power_set(B)). [resolve(227,b,216,b)]. given #316 (T,wt=10): 371 unordered_pair(unordered_pair(A,B),singleton(A)) = ordered_pair(A,B). [xx_res(246,b)]. given #317 (T,wt=10): 389 member(f3(A,B),A) | B = A | -empty(B). [resolve(250,b,206,a)]. given #318 (T,wt=10): 438 member(A,B) | member(f14(power_set(A),B),power_set(A)). [resolve(282,a,218,a)]. given #319 (T,wt=9): 3528 member(A,A) | -member(A,f14(power_set(A),A)). [factor(3519,a,c)]. given #320 (A,wt=16): 319 member(f23(A),B) | -member(f9(B,A),A) | member(f10(B,A),A) | empty(A). [resolve(227,b,207,b)]. given #321 (T,wt=10): 468 empty(A) | member(f24(A),B) | -member(A,power_set(B)). [resolve(265,b,214,a)]. given #322 (T,wt=10): 476 empty(c3) | member(ordered_pair(f25(f24(c3)),f24(c3)),c4). [resolve(265,b,116,a)]. given #323 (T,wt=7): 3574 empty(c3) | member(f24(c3),range_of(c4)). [resolve(476,b,255,c),unit_del(b,540)]. given #324 (T,wt=8): 3576 empty(c3) | member(f25(f24(c3)),domain_of(c4)). [resolve(476,b,252,b),unit_del(b,540)]. given #325 (A,wt=17): 320 member(f17(A),B) | -member(f9(B,A),A) | member(f10(B,A),A) | ilf_type(A,binary_relation_type). [resolve(227,b,119,a)]. given #326 (T,wt=7): 3617 empty(c3) | member(f25(f24(c3)),c2). [resolve(3576,b,600,a)]. given #327 (T,wt=10): 491 empty(A) | member(f16(A),B) | -member(A,power_set(B)). [resolve(275,b,214,a)]. given #328 (T,wt=10): 498 empty(c3) | member(ordered_pair(f25(f16(c3)),f16(c3)),c4). [resolve(275,b,116,a)]. given #329 (T,wt=7): 3697 empty(c3) | member(f16(c3),range_of(c4)). [resolve(498,b,255,c),unit_del(b,540)]. given #330 (A,wt=19): 321 member(f15(A,B),C) | -member(f9(C,A),A) | -member(f10(C,A),C) | member(A,power_set(B)). [resolve(228,b,216,b)]. given #331 (T,wt=8): 3699 empty(c3) | member(f25(f16(c3)),domain_of(c4)). [resolve(498,b,252,b),unit_del(b,540)]. given #332 (T,wt=7): 3744 empty(c3) | member(f25(f16(c3)),c2). [resolve(3699,b,600,a)]. given #333 (T,wt=10): 501 ilf_type(A,binary_relation_type) | member(f24(A),B) | A != B. [resolve(264,a,231,b)]. given #334 (T,wt=10): 506 ilf_type(A,binary_relation_type) | member(f24(A),B) | B != A. [resolve(264,a,226,b)]. given #335 (A,wt=16): 322 member(f23(A),B) | -member(f9(B,A),A) | -member(f10(B,A),B) | empty(A). [resolve(228,b,207,b)]. given #336 (T,wt=10): 527 member(f6(A),B) | -member(f14(power_set(A),B),B). [resolve(499,a,217,a)]. given #337 (T,wt=10): 560 member(f24(power_set(A)),B) | -member(power_set(A),power_set(B)). [resolve(444,a,214,a)]. given #338 (T,wt=10): 579 member(range_of(c4),A) | -member(f14(power_set(c3),A),A). [resolve(568,a,217,a)]. given #339 (T,wt=10): 599 member(domain_of(c4),A) | -member(f14(power_set(c2),A),A). [resolve(588,a,217,a)]. given #340 (A,wt=17): 323 member(f17(A),B) | -member(f9(B,A),A) | -member(f10(B,A),B) | ilf_type(A,binary_relation_type). [resolve(228,b,119,a)]. given #341 (T,wt=10): 613 -member(A,unordered_pair(B,C)) | member(A,unordered_pair(C,B)). [resolve(361,a,219,c)]. given #342 (T,wt=10): 634 ilf_type(domain_of(f5(A,cross_product(B,C))),relation_type(B,C)). [resolve(365,a,245,a)]. given #343 (T,wt=10): 638 ilf_type(range_of(f5(cross_product(A,B),C)),relation_type(A,B)). [resolve(367,a,245,a)]. given #344 (T,wt=10): 641 ilf_type(c3,binary_relation_type) | member(f24(c4),A) | c4 != A. [resolve(421,b,231,b)]. given #345 (A,wt=19): 324 member(f15(A,B),C) | member(f9(C,A),C) | member(f10(C,A),A) | member(A,power_set(B)). [resolve(229,b,216,b)]. given #346 (T,wt=10): 712 empty(c3) | member(f24(c4),A) | -member(c4,power_set(A)). [resolve(696,b,214,a)]. given #347 (T,wt=10): 731 member(f16(power_set(A)),B) | -member(power_set(A),power_set(B)). [resolve(719,a,214,a)]. given #348 (T,wt=10): 751 member(c4,A) | -member(power_set(cross_product(c2,c3)),power_set(A)). [resolve(738,a,214,a)]. given #349 (T,wt=10): 788 member(f23(power_set(A)),B) | -member(power_set(A),power_set(B)). [resolve(776,a,214,a)]. given #350 (A,wt=16): 325 member(f23(A),B) | member(f9(B,A),B) | member(f10(B,A),A) | empty(A). [resolve(229,b,207,b)]. given #351 (T,wt=10): 820 ilf_type(domain_of(cross_product(cross_product(A,B),C)),relation_type(A,B)). [resolve(661,a,245,a)]. given #352 (T,wt=10): 824 ilf_type(range_of(cross_product(A,cross_product(B,C))),relation_type(B,C)). [resolve(663,a,245,a)]. given #353 (T,wt=10): 848 empty(c3) | member(f23(c3),A) | range_of(c4) != A. [resolve(677,b,231,b)]. given #354 (T,wt=10): 869 member(f16(f23(power_set(A))),A) | empty(f23(power_set(A))). [resolve(280,a,275,b)]. given #355 (A,wt=17): 326 member(f17(A),B) | member(f9(B,A),B) | member(f10(B,A),A) | ilf_type(A,binary_relation_type). [resolve(229,b,119,a)]. given #356 (T,wt=6): 4105 empty(f23(power_set(A))) | -empty(A). [resolve(869,a,206,a)]. given #357 (T,wt=8): 4106 empty(f23(power_set(A))) | member(f24(A),A). [resolve(869,a,205,a)]. given #358 (T,wt=10): 873 member(f24(f23(power_set(A))),A) | empty(f23(power_set(A))). [resolve(280,a,265,b)]. given #359 (T,wt=10): 878 member(f23(f23(power_set(A))),A) | empty(f23(power_set(A))). [resolve(280,a,207,b)]. given #360 (A,wt=19): 327 member(f15(A,B),C) | member(f9(C,A),C) | -member(f10(C,A),C) | member(A,power_set(B)). [resolve(230,b,216,b)]. given #361 (T,wt=10): 921 member(domain_of(c4),power_set(A)) | member(f24(domain_of(c4)),c2). [resolve(289,b,600,a)]. given #362 (T,wt=7): 4362 member(domain_of(c4),power_set(A)) | -empty(c2). [resolve(921,b,206,a)]. given #363 (T,wt=9): 4363 member(domain_of(c4),power_set(A)) | member(f24(c2),c2). [resolve(921,b,205,a)]. given #364 (T,wt=10): 922 member(range_of(c4),power_set(A)) | member(f24(range_of(c4)),c3). [resolve(289,b,580,a)]. given #365 (A,wt=16): 328 member(f23(A),B) | member(f9(B,A),B) | -member(f10(B,A),B) | empty(A). [resolve(230,b,207,b)]. given #366 (T,wt=7): 4443 member(range_of(c4),power_set(A)) | -empty(c3). [resolve(922,b,206,a)]. given #367 (T,wt=9): 4444 member(range_of(c4),power_set(A)) | member(f24(c3),c3). [resolve(922,b,205,a)]. given #368 (T,wt=10): 923 member(f6(A),power_set(B)) | member(f24(f6(A)),A). [resolve(289,b,528,a)]. given #369 (T,wt=7): 4553 member(f6(A),power_set(B)) | -empty(A). [resolve(923,b,206,a)]. given #370 (A,wt=17): 329 member(f17(A),B) | member(f9(B,A),B) | -member(f10(B,A),B) | ilf_type(A,binary_relation_type). [resolve(230,b,119,a)]. given #371 (T,wt=9): 4554 member(f6(A),power_set(B)) | member(f24(A),A). [resolve(923,b,205,a)]. given #372 (T,wt=10): 948 ilf_type(power_set(A),binary_relation_type) | ilf_type(f17(power_set(A)),subset_type(A)). [resolve(277,b,238,b),unit_del(a,213)]. given #373 (T,wt=10): 957 member(f23(f16(power_set(A))),A) | empty(f16(power_set(A))). [resolve(278,b,719,a)]. given #374 (T,wt=6): 4665 empty(f16(power_set(A))) | -empty(A). [resolve(957,a,206,a)]. given #375 (A,wt=12): 330 member(f15(A,B),C) | A != C | member(A,power_set(B)). [resolve(231,b,216,b)]. given #376 (T,wt=8): 4666 empty(f16(power_set(A))) | member(f24(A),A). [resolve(957,a,205,a)]. given #377 (T,wt=10): 958 member(f23(f24(power_set(A))),A) | empty(f24(power_set(A))). [resolve(278,b,444,a)]. given #378 (T,wt=6): 4746 empty(f24(power_set(A))) | -empty(A). [resolve(958,a,206,a)]. given #379 (T,wt=8): 4747 empty(f24(power_set(A))) | member(f24(A),A). [resolve(958,a,205,a)]. given #380 (A,wt=16): 333 A = B | member(f7(B,A),B) | member(f8(B,A),C) | A != C. [resolve(234,c,231,b)]. given #381 (T,wt=10): 967 member(f16(f24(power_set(A))),A) | empty(f24(power_set(A))). [resolve(467,a,275,b)]. given #382 (T,wt=10): 971 member(f24(f24(power_set(A))),A) | empty(f24(power_set(A))). [resolve(467,a,265,b)]. given #383 (T,wt=10): 978 member(f16(f16(power_set(A))),A) | empty(f16(power_set(A))). [resolve(490,a,275,b)]. given #384 (T,wt=10): 982 member(f24(f16(power_set(A))),A) | empty(f16(power_set(A))). [resolve(490,a,265,b)]. given #385 (A,wt=23): 334 A = B | member(f7(B,A),B) | member(f8(B,A),C) | member(f9(C,A),C) | -member(f10(C,A),C). [resolve(234,c,230,b)]. given #386 (T,wt=10): 1030 member(domain_of(f5(A,B)),C) | power_set(B) != C. [resolve(1017,a,231,b)]. given #387 (T,wt=10): 1052 member(range_of(f5(A,B)),C) | power_set(A) != C. [resolve(1049,a,231,b)]. given #388 (T,wt=10): 1081 empty(f6(domain_of(c4))) | member(f16(f6(domain_of(c4))),c2). [resolve(668,a,600,a)]. given #389 (T,wt=10): 1082 empty(f6(range_of(c4))) | member(f16(f6(range_of(c4))),c3). [resolve(668,a,580,a)]. given #390 (A,wt=23): 335 A = B | member(f7(B,A),B) | member(f8(B,A),C) | member(f9(C,A),C) | member(f10(C,A),A). [resolve(234,c,229,b)]. given #391 (T,wt=10): 1083 empty(f6(f6(A))) | member(f16(f6(f6(A))),A). [resolve(668,a,528,a)]. given #392 (T,wt=10): 1125 empty(f6(A)) | member(f24(A),B) | A != B. [resolve(1110,b,231,b)]. given #393 (T,wt=10): 1130 empty(f6(A)) | member(f24(A),B) | B != A. [resolve(1110,b,226,b)]. given #394 (T,wt=10): 1154 empty(f6(domain_of(c4))) | member(f24(f6(domain_of(c4))),c2). [resolve(670,a,600,a)]. given #395 (A,wt=23): 336 A = B | member(f7(B,A),B) | member(f8(B,A),C) | -member(f9(C,A),A) | -member(f10(C,A),C). [resolve(234,c,228,b)]. given #396 (T,wt=10): 1155 empty(f6(range_of(c4))) | member(f24(f6(range_of(c4))),c3). [resolve(670,a,580,a)]. given #397 (T,wt=10): 1156 empty(f6(f6(A))) | member(f24(f6(f6(A))),A). [resolve(670,a,528,a)]. given #398 (T,wt=10): 1188 empty(f6(domain_of(c4))) | member(f23(f6(domain_of(c4))),c2). [resolve(675,a,600,a)]. given #399 (T,wt=10): 1189 empty(f6(range_of(c4))) | member(f23(f6(range_of(c4))),c3). [resolve(675,a,580,a)]. given #400 (A,wt=23): 337 A = B | member(f7(B,A),B) | member(f8(B,A),C) | -member(f9(C,A),A) | member(f10(C,A),A). [resolve(234,c,227,b)]. given #401 (T,wt=10): 1190 empty(f6(f6(A))) | member(f23(f6(f6(A))),A). [resolve(675,a,528,a)]. given #402 (T,wt=10): 1293 empty(c3) | member(f25(f23(c3)),A) | c2 != A. [resolve(1222,b,231,b)]. given #403 (T,wt=10): 1305 empty(c3) | empty(c2) | ilf_type(f25(f23(c3)),member_type(c2)). [resolve(1222,b,212,c)]. given #404 (T,wt=10): 1325 empty(c3) | member(f24(c2),A) | -member(c2,power_set(A)). [resolve(1309,b,214,a)]. given #405 (A,wt=16): 338 A = B | member(f7(B,A),B) | member(f8(B,A),C) | C != A. [resolve(234,c,226,b)]. given #406 (T,wt=10): 1334 member(f23(f6(c4)),cross_product(c2,c3)) | empty(f6(c4)). [resolve(750,a,675,a)]. given #407 (T,wt=10): 1335 member(f24(f6(c4)),cross_product(c2,c3)) | empty(f6(c4)). [resolve(750,a,670,a)]. given #408 (T,wt=10): 1336 member(f16(f6(c4)),cross_product(c2,c3)) | empty(f6(c4)). [resolve(750,a,668,a)]. given #409 (T,wt=10): 1338 member(f24(c4),cross_product(c2,c3)) | member(c4,power_set(A)). [resolve(750,a,289,b)]. given #410 (A,wt=23): 339 A = B | member(f7(B,A),B) | member(f8(B,A),C) | member(f11(A,C),A) | -member(f12(A,C),A). [resolve(234,c,225,b)]. given #411 (T,wt=8): 5398 member(c4,power_set(A)) | -empty(cross_product(c2,c3)). [resolve(1338,a,206,a)]. given #412 (T,wt=10): 1452 empty(range_of(c4)) | member(f24(c3),A) | c3 != A. [resolve(1446,b,231,b)]. given #413 (T,wt=10): 1532 empty(domain_of(c4)) | member(f24(c2),A) | c2 != A. [resolve(1527,b,231,b)]. given #414 (T,wt=10): 1603 member(domain_of(cross_product(A,B)),C) | power_set(A) != C. [resolve(1599,a,231,b)]. given #415 (A,wt=23): 340 A = B | member(f7(B,A),B) | member(f8(B,A),C) | member(f11(A,C),A) | member(f12(A,C),C). [resolve(234,c,224,b)]. given #416 (T,wt=10): 1626 member(range_of(cross_product(A,B)),C) | power_set(B) != C. [resolve(1622,a,231,b)]. given #417 (T,wt=10): 1745 empty(c3) | member(f24(range_of(c4)),A) | c3 != A. [resolve(1725,b,231,b)]. given #418 (T,wt=10): 1792 empty(c4) | member(f24(cross_product(c2,c3)),cross_product(c2,c3)). [resolve(956,a,205,a)]. given #419 (T,wt=10): 1816 empty(c3) | member(f24(domain_of(c4)),A) | c2 != A. [resolve(1797,b,231,b)]. given #420 (A,wt=23): 341 A = B | member(f7(B,A),B) | member(f8(B,A),C) | -member(f11(A,C),C) | -member(f12(A,C),A). [resolve(234,c,223,b)]. given #421 (T,wt=10): 1828 empty(c3) | empty(c2) | ilf_type(f24(domain_of(c4)),member_type(c2)). [resolve(1797,b,212,c)]. given #422 (T,wt=10): 1836 member(c3,power_set(A)) | member(f15(c3,A),range_of(c4)). [resolve(294,b,255,c),unit_del(b,540)]. given #423 (T,wt=5): 5560 member(c3,power_set(range_of(c4))). [resolve(1836,b,215,b),merge(b)]. given #424 (T,wt=6): 5585 ilf_type(c3,member_type(power_set(range_of(c4)))). [resolve(5560,a,212,c),unit_del(a,213)]. given #425 (A,wt=23): 342 A = B | member(f7(B,A),B) | member(f8(B,A),C) | -member(f11(A,C),C) | member(f12(A,C),C). [resolve(234,c,222,b)]. given #426 (T,wt=5): 5592 ilf_type(c3,subset_type(range_of(c4))). [resolve(5585,a,238,b)]. given #427 (T,wt=7): 5565 member(c3,power_set(A)) | -empty(range_of(c4)). [resolve(1836,b,206,a)]. given #428 (T,wt=7): 5583 -member(A,c3) | member(A,range_of(c4)). [resolve(5560,a,214,c)]. given #429 (T,wt=8): 5572 member(c3,A) | power_set(range_of(c4)) != A. [resolve(5560,a,231,b)]. given #430 (A,wt=18): 343 A = B | member(f7(B,A),B) | member(f8(B,A),C) | member(f14(A,C),A). [resolve(234,c,218,a)]. given #431 (T,wt=8): 5607 member(f24(c3),range_of(c4)) | empty(range_of(c4)). [resolve(5583,a,1446,b)]. given #432 (T,wt=8): 5611 member(f24(c3),range_of(c4)) | empty(f6(c3)). [resolve(5583,a,1110,b)]. given #433 (T,wt=6): 5793 empty(f6(c3)) | -empty(range_of(c4)). [resolve(5611,a,206,a)]. given #434 (T,wt=8): 5657 member(f24(c3),range_of(c4)) | ilf_type(c3,binary_relation_type). [resolve(5583,a,264,a)]. given #435 (A,wt=18): 344 A = B | member(f7(B,A),B) | member(f8(B,A),C) | -member(f14(A,C),C). [resolve(234,c,217,a)]. given #436 (T,wt=9): 5584 member(c3,A) | -member(power_set(range_of(c4)),power_set(A)). [resolve(5560,a,214,a)]. given #437 (T,wt=9): 5597 member(f24(c3),range_of(c4)) | empty(f24(power_set(c3))). [resolve(5583,a,4747,b)]. given #438 (T,wt=7): 5842 empty(f24(power_set(c3))) | -empty(range_of(c4)). [resolve(5597,a,206,a)]. given #439 (T,wt=9): 5598 member(f24(c3),range_of(c4)) | empty(f16(power_set(c3))). [resolve(5583,a,4666,b)]. given #440 (A,wt=19): 345 power_set(A) = B | member(f7(B,power_set(A)),B) | -member(C,f8(B,power_set(A))) | member(C,A). [resolve(234,c,214,c)]. given #441 (T,wt=7): 5864 empty(f16(power_set(c3))) | -empty(range_of(c4)). [resolve(5598,a,206,a)]. given #442 (T,wt=9): 5601 member(f24(c3),range_of(c4)) | empty(f23(power_set(c3))). [resolve(5583,a,4106,b)]. given #443 (T,wt=7): 5955 empty(f23(power_set(c3))) | -empty(range_of(c4)). [resolve(5601,a,206,a)]. given #444 (T,wt=9): 5602 member(f24(c3),range_of(c4)) | empty(f6(f6(c3))). [resolve(5583,a,2877,b)]. given #445 (A,wt=17): 346 A = B | member(f7(B,A),B) | member(f8(B,A),C) | -member(A,power_set(C)). [resolve(234,c,214,a)]. given #446 (T,wt=7): 5977 empty(f6(f6(c3))) | -empty(range_of(c4)). [resolve(5602,a,206,a)]. given #447 (T,wt=9): 5603 member(f24(c3),range_of(c4)) | empty(f6(range_of(c4))). [resolve(5583,a,2813,b)]. given #448 (T,wt=9): 5604 member(f24(c3),range_of(c4)) | ilf_type(range_of(c4),binary_relation_type). [resolve(5583,a,2486,b)]. given #449 (T,wt=9): 5605 member(f24(c3),range_of(c4)) | ilf_type(f6(c3),binary_relation_type). [resolve(5583,a,2254,b)]. given #450 (A,wt=16): 347 A = B | member(f7(B,A),B) | empty(A) | ilf_type(f8(B,A),member_type(A)). [resolve(234,c,212,c)]. given #451 (T,wt=7): 6100 ilf_type(f6(c3),binary_relation_type) | -empty(range_of(c4)). [resolve(5605,a,206,a)]. given #452 (T,wt=9): 5625 member(f23(f6(c3)),range_of(c4)) | empty(f6(c3)). [resolve(5583,a,675,a)]. given #453 (T,wt=9): 5627 member(f24(f6(c3)),range_of(c4)) | empty(f6(c3)). [resolve(5583,a,670,a)]. given #454 (T,wt=9): 5628 member(f16(f6(c3)),range_of(c4)) | empty(f6(c3)). [resolve(5583,a,668,a)]. given #455 (A,wt=27): 348 A = B | member(f7(B,A),B) | ordered_pair(f20(A,f8(B,A)),f21(A,f8(B,A))) = f8(B,A) | member(f22(A),A). [resolve(234,c,209,a)]. given #456 (T,wt=9): 5652 member(f24(c3),range_of(c4)) | member(c3,power_set(A)). [resolve(5583,a,289,b)]. given #457 (T,wt=9): 5770 empty(range_of(c4)) | ilf_type(f24(c3),member_type(range_of(c4))). [resolve(5607,a,212,c),merge(b)]. given #458 (T,wt=9): 5794 empty(f6(c3)) | member(f24(range_of(c4)),range_of(c4)). [resolve(5611,a,205,a)]. given #459 (T,wt=8): 6352 empty(f6(c3)) | member(f24(range_of(c4)),c3). [resolve(5794,b,580,a)]. given #460 (A,wt=29): 349 A = B | member(f7(B,A),B) | ordered_pair(f20(A,f8(B,A)),f21(A,f8(B,A))) = f8(B,A) | f22(A) != ordered_pair(C,D). [resolve(234,c,208,a)]. given #461 (T,wt=10): 1876 empty(c3) | member(f24(cross_product(c2,c3)),cross_product(c2,c3)). [resolve(1333,a,205,a)]. given #462 (T,wt=10): 1930 member(f24(c4),c4) | -member(A,c3) | member(A,B). [resolve(1855,a,214,c)]. given #463 (T,wt=10): 1939 member(c3,power_set(A)) | member(f24(c4),cross_product(c2,c3)). [resolve(1855,b,750,a)]. given #464 (T,wt=8): 6510 member(c3,power_set(A)) | -empty(cross_product(c2,c3)). [resolve(1939,b,206,a)]. given #465 (A,wt=12): 351 A = B | member(f7(B,A),B) | member(f24(A),A). [resolve(234,c,205,a)]. given #466 (T,wt=9): 6559 A = B | member(f24(A),A) | -empty(B). [resolve(351,b,206,a)]. given #467 (T,wt=10): 2117 ilf_type(c3,binary_relation_type) | member(f24(c2),A) | c2 != A. [resolve(2023,b,231,b)]. given #468 (T,wt=10): 2290 member(f14(A,B),A) | ilf_type(A,binary_relation_type) | -empty(B). [resolve(301,a,206,a)]. given #469 (T,wt=10): 2330 ilf_type(f6(c4),binary_relation_type) | member(f24(c4),cross_product(c2,c3)). [resolve(2254,b,750,a)]. given #470 (A,wt=29): 352 A = B | member(f7(B,A),B) | -ilf_type(A,subset_type(cross_product(C,D))) | ordered_pair(f18(A,f8(B,A)),f19(A,f8(B,A))) = f8(B,A). [resolve(234,c,131,b)]. given #471 (T,wt=8): 6623 ilf_type(f6(c4),binary_relation_type) | -empty(cross_product(c2,c3)). [resolve(2330,b,206,a)]. given #472 (T,wt=10): 2331 ilf_type(f6(domain_of(c4)),binary_relation_type) | member(f24(domain_of(c4)),c2). [resolve(2254,b,600,a)]. given #473 (T,wt=7): 6665 ilf_type(f6(domain_of(c4)),binary_relation_type) | -empty(c2). [resolve(2331,b,206,a)]. given #474 (T,wt=9): 6666 ilf_type(f6(domain_of(c4)),binary_relation_type) | member(f24(c2),c2). [resolve(2331,b,205,a)]. given #475 (A,wt=29): 353 A = B | member(f7(B,A),B) | ordered_pair(f18(A,f8(B,A)),f19(A,f8(B,A))) = f8(B,A) | f17(A) != ordered_pair(C,D). [resolve(234,c,127,a)]. given #476 (T,wt=10): 2332 ilf_type(f6(range_of(c4)),binary_relation_type) | member(f24(range_of(c4)),c3). [resolve(2254,b,580,a)]. given #477 (T,wt=7): 6706 ilf_type(f6(range_of(c4)),binary_relation_type) | -empty(c3). [resolve(2332,b,206,a)]. given #478 (T,wt=9): 6707 ilf_type(f6(range_of(c4)),binary_relation_type) | member(f24(c3),c3). [resolve(2332,b,205,a)]. given #479 (T,wt=10): 2333 ilf_type(f6(f6(A)),binary_relation_type) | member(f24(f6(A)),A). [resolve(2254,b,528,a)]. given #480 (A,wt=27): 354 A = B | member(f7(B,A),B) | ordered_pair(f18(A,f8(B,A)),f19(A,f8(B,A))) = f8(B,A) | member(f17(A),A). [resolve(234,c,125,a)]. given #481 (T,wt=7): 6777 ilf_type(f6(f6(A)),binary_relation_type) | -empty(A). [resolve(2333,b,206,a)]. given #482 (T,wt=9): 6778 ilf_type(f6(f6(A)),binary_relation_type) | member(f24(A),A). [resolve(2333,b,205,a)]. given #483 (T,wt=10): 2455 member(f13(power_set(A),B),power_set(A)) | member(A,B). [resolve(302,b,282,a)]. given #484 (T,wt=9): 6943 member(A,A) | -member(A,f13(power_set(A),A)). [factor(6934,a,c)]. given #485 (A,wt=26): 355 A = B | member(f7(B,A),B) | ordered_pair(f18(A,f8(B,A)),f19(A,f8(B,A))) = f8(B,A) | -ilf_type(A,binary_relation_type). [resolve(234,c,123,a)]. given #486 (T,wt=10): 2653 -member(A,f5(B,C)) | member(A,cross_product(C,B)). [resolve(2638,a,214,c)]. given #487 (T,wt=10): 2885 empty(f6(f6(c4))) | member(f24(c4),cross_product(c2,c3)). [resolve(2877,b,750,a)]. given #488 (T,wt=8): 7035 empty(f6(f6(c4))) | -empty(cross_product(c2,c3)). [resolve(2885,b,206,a)]. given #489 (T,wt=10): 2886 empty(f6(f6(domain_of(c4)))) | member(f24(domain_of(c4)),c2). [resolve(2877,b,600,a)]. given #490 (A,wt=18): 356 c3 = A | member(f7(A,c3),A) | member(ordered_pair(f25(f8(A,c3)),f8(A,c3)),c4). [resolve(234,c,116,a)]. given #491 (T,wt=7): 7057 empty(f6(f6(domain_of(c4)))) | -empty(c2). [resolve(2886,b,206,a)]. given #492 (T,wt=9): 7058 empty(f6(f6(domain_of(c4)))) | member(f24(c2),c2). [resolve(2886,b,205,a)]. given #493 (T,wt=10): 2887 empty(f6(f6(range_of(c4)))) | member(f24(range_of(c4)),c3). [resolve(2877,b,580,a)]. given #494 (T,wt=7): 7123 empty(f6(f6(range_of(c4)))) | -empty(c3). [resolve(2887,b,206,a)]. given #495 (A,wt=19): 357 power_set(A) = A | member(f7(A,power_set(A)),A) | -member(f7(A,power_set(A)),f8(A,power_set(A))). [factor(345,b,d)]. given #496 (T,wt=9): 7124 empty(f6(f6(range_of(c4)))) | member(f24(c3),c3). [resolve(2887,b,205,a)]. given #497 (T,wt=10): 2888 empty(f6(f6(f6(A)))) | member(f24(f6(A)),A). [resolve(2877,b,528,a)]. given #498 (T,wt=7): 7195 empty(f6(f6(f6(A)))) | -empty(A). [resolve(2888,b,206,a)]. given #499 (T,wt=9): 7196 empty(f6(f6(f6(A)))) | member(f24(A),A). [resolve(2888,b,205,a)]. NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 38 (0.00 of 0.94 sec). given #500 (A,wt=11): 362 A = B | -subset(A,B) | member(f13(B,A),B). [resolve(242,b,221,a)]. given #501 (T,wt=10): 3319 -member(A,domain_of(f6(cross_product(B,C)))) | member(A,B). [resolve(3215,a,214,c)]. given #502 (T,wt=10): 3343 -member(A,range_of(f6(cross_product(B,C)))) | member(A,C). [resolve(3327,a,214,c)]. given #503 (T,wt=10): 3379 ilf_type(domain_of(f16(power_set(cross_product(A,B)))),member_type(power_set(A))). [resolve(1982,a,237,b)]. given #504 (T,wt=9): 7385 member(domain_of(f16(power_set(cross_product(A,B)))),power_set(A)). [resolve(3379,a,211,c),unit_del(a,213)]. given #505 (A,wt=11): 363 A = B | -subset(B,A) | member(f13(A,B),A). [resolve(242,c,221,a)]. given #506 (T,wt=10): 3380 ilf_type(domain_of(f16(power_set(cross_product(cross_product(A,B),C)))),binary_relation_type). [resolve(1982,a,129,a)]. given #507 (T,wt=10): 3388 ilf_type(range_of(f16(power_set(cross_product(A,B)))),member_type(power_set(B))). [resolve(1984,a,237,b)]. given #508 (T,wt=9): 7412 member(range_of(f16(power_set(cross_product(A,B)))),power_set(B)). [resolve(3388,a,211,c),unit_del(a,213)]. given #509 (T,wt=10): 3389 ilf_type(range_of(f16(power_set(cross_product(A,cross_product(B,C))))),binary_relation_type). [resolve(1984,a,129,a)]. given #510 (A,wt=11): 364 domain(A,B,f5(B,A)) = domain_of(f5(B,A)). [resolve(243,a,204,a)]. given #511 (T,wt=10): 3478 ilf_type(domain_of(f23(power_set(cross_product(A,B)))),member_type(power_set(A))). [resolve(2216,a,237,b)]. given #512 (T,wt=9): 7439 member(domain_of(f23(power_set(cross_product(A,B)))),power_set(A)). [resolve(3478,a,211,c),unit_del(a,213)]. given #513 (T,wt=10): 3479 ilf_type(domain_of(f23(power_set(cross_product(cross_product(A,B),C)))),binary_relation_type). [resolve(2216,a,129,a)]. given #514 (T,wt=10): 3483 ilf_type(range_of(f23(power_set(cross_product(A,B)))),member_type(power_set(B))). [resolve(2218,a,237,b)]. given #515 (A,wt=11): 366 range(A,B,f5(B,A)) = range_of(f5(B,A)). [resolve(243,a,202,a)]. given #516 (T,wt=9): 7466 member(range_of(f23(power_set(cross_product(A,B)))),power_set(B)). [resolve(3483,a,211,c),unit_del(a,213)]. given #517 (T,wt=10): 3484 ilf_type(range_of(f23(power_set(cross_product(A,cross_product(B,C))))),binary_relation_type). [resolve(2218,a,129,a)]. given #518 (T,wt=10): 3488 ilf_type(domain_of(f24(power_set(cross_product(A,B)))),member_type(power_set(A))). [resolve(2220,a,237,b)]. given #519 (T,wt=9): 7493 member(domain_of(f24(power_set(cross_product(A,B)))),power_set(A)). [resolve(3488,a,211,c),unit_del(a,213)]. given #520 (A,wt=16): 372 member(f3(A,B),A) | B = A | member(f4(A,B),C) | B != C. [resolve(250,b,231,b)]. given #521 (T,wt=10): 3489 ilf_type(domain_of(f24(power_set(cross_product(cross_product(A,B),C)))),binary_relation_type). [resolve(2220,a,129,a)]. given #522 (T,wt=10): 3494 ilf_type(range_of(f24(power_set(cross_product(A,B)))),member_type(power_set(B))). [resolve(2222,a,237,b)]. given #523 (T,wt=9): 7520 member(range_of(f24(power_set(cross_product(A,B)))),power_set(B)). [resolve(3494,a,211,c),unit_del(a,213)]. given #524 (T,wt=10): 3495 ilf_type(range_of(f24(power_set(cross_product(A,cross_product(B,C))))),binary_relation_type). [resolve(2222,a,129,a)]. given #525 (A,wt=23): 373 member(f3(A,B),A) | B = A | member(f4(A,B),C) | member(f9(C,B),C) | -member(f10(C,B),C). [resolve(250,b,230,b)]. given #526 (T,wt=10): 3501 unordered_pair(singleton(A),unordered_pair(A,B)) = ordered_pair(A,B). [para(371(a,1),239(a,1)),flip(a)]. given #527 (T,wt=10): 3502 unordered_pair(unordered_pair(A,B),singleton(B)) = ordered_pair(B,A). [para(239(a,1),371(a,1,1))]. given #528 (T,wt=10): 3598 empty(c3) | member(f24(c3),A) | range_of(c4) != A. [resolve(3574,b,231,b)]. given #529 (T,wt=10): 3643 empty(c3) | member(f25(f24(c3)),A) | c2 != A. [resolve(3617,b,231,b)]. given #530 (A,wt=23): 374 member(f3(A,B),A) | B = A | member(f4(A,B),C) | member(f9(C,B),C) | member(f10(C,B),B). [resolve(250,b,229,b)]. given #531 (T,wt=10): 3655 empty(c3) | empty(c2) | ilf_type(f25(f24(c3)),member_type(c2)). [resolve(3617,b,212,c)]. given #532 (T,wt=10): 3721 empty(c3) | member(f16(c3),A) | range_of(c4) != A. [resolve(3697,b,231,b)]. given #533 (T,wt=10): 3766 empty(c3) | member(f25(f16(c3)),A) | c2 != A. [resolve(3744,b,231,b)]. given #534 (T,wt=10): 3778 empty(c3) | empty(c2) | ilf_type(f25(f16(c3)),member_type(c2)). [resolve(3744,b,212,c)]. given #535 (A,wt=23): 375 member(f3(A,B),A) | B = A | member(f4(A,B),C) | -member(f9(C,B),B) | -member(f10(C,B),C). [resolve(250,b,228,b)]. given #536 (T,wt=10): 3841 ilf_type(domain_of(domain_of(f5(A,cross_product(B,C)))),subset_type(B)). [resolve(634,a,203,a),rewrite([3840(4)])]. given #537 (T,wt=10): 3843 ilf_type(range_of(domain_of(f5(A,cross_product(B,C)))),subset_type(C)). [resolve(634,a,201,a),rewrite([3842(4)])]. given #538 (T,wt=10): 3845 ilf_type(domain_of(range_of(f5(cross_product(A,B),C))),subset_type(A)). [resolve(638,a,203,a),rewrite([3844(4)])]. given #539 (T,wt=10): 3847 ilf_type(range_of(range_of(f5(cross_product(A,B),C))),subset_type(B)). [resolve(638,a,201,a),rewrite([3846(4)])]. given #540 (A,wt=23): 376 member(f3(A,B),A) | B = A | member(f4(A,B),C) | -member(f9(C,B),B) | member(f10(C,B),B). [resolve(250,b,227,b)]. given #541 (T,wt=10): 4060 ilf_type(domain_of(domain_of(cross_product(cross_product(A,B),C))),subset_type(A)). [resolve(820,a,203,a),rewrite([4059(4)])]. given #542 (T,wt=10): 4062 ilf_type(range_of(domain_of(cross_product(cross_product(A,B),C))),subset_type(B)). [resolve(820,a,201,a),rewrite([4061(4)])]. given #543 (T,wt=10): 4064 ilf_type(domain_of(range_of(cross_product(A,cross_product(B,C)))),subset_type(B)). [resolve(824,a,203,a),rewrite([4063(4)])]. given #544 (T,wt=10): 4066 ilf_type(range_of(range_of(cross_product(A,cross_product(B,C)))),subset_type(C)). [resolve(824,a,201,a),rewrite([4065(4)])]. given #545 (A,wt=16): 377 member(f3(A,B),A) | B = A | member(f4(A,B),C) | C != B. [resolve(250,b,226,b)]. given #546 (T,wt=10): 4204 empty(f23(power_set(c4))) | member(f24(c4),cross_product(c2,c3)). [resolve(4106,b,750,a)]. given #547 (T,wt=8): 7737 empty(f23(power_set(c4))) | -empty(cross_product(c2,c3)). [resolve(4204,b,206,a)]. given #548 (T,wt=10): 4206 empty(f23(power_set(domain_of(c4)))) | member(f24(domain_of(c4)),c2). [resolve(4106,b,600,a)]. given #549 (T,wt=7): 7759 empty(f23(power_set(domain_of(c4)))) | -empty(c2). [resolve(4206,b,206,a)]. given #550 (A,wt=23): 378 member(f3(A,B),A) | B = A | member(f4(A,B),C) | member(f11(B,C),B) | -member(f12(B,C),B). [resolve(250,b,225,b)]. given #551 (T,wt=9): 7760 empty(f23(power_set(domain_of(c4)))) | member(f24(c2),c2). [resolve(4206,b,205,a)]. given #552 (T,wt=10): 4207 empty(f23(power_set(range_of(c4)))) | member(f24(range_of(c4)),c3). [resolve(4106,b,580,a)]. given #553 (T,wt=7): 7804 empty(f23(power_set(range_of(c4)))) | -empty(c3). [resolve(4207,b,206,a)]. given #554 (T,wt=9): 7805 empty(f23(power_set(range_of(c4)))) | member(f24(c3),c3). [resolve(4207,b,205,a)]. given #555 (A,wt=23): 379 member(f3(A,B),A) | B = A | member(f4(A,B),C) | member(f11(B,C),B) | member(f12(B,C),C). [resolve(250,b,224,b)]. given #556 (T,wt=10): 4208 empty(f23(power_set(f6(A)))) | member(f24(f6(A)),A). [resolve(4106,b,528,a)]. given #557 (T,wt=7): 7991 empty(f23(power_set(f6(A)))) | -empty(A). [resolve(4208,b,206,a)]. given #558 (T,wt=9): 7992 empty(f23(power_set(f6(A)))) | member(f24(A),A). [resolve(4208,b,205,a)]. given #559 (T,wt=10): 4382 member(f24(c2),c2) | ilf_type(domain_of(c4),member_type(power_set(A))). [resolve(4363,a,212,c),unit_del(b,213)]. given #560 (A,wt=23): 380 member(f3(A,B),A) | B = A | member(f4(A,B),C) | -member(f11(B,C),C) | -member(f12(B,C),B). [resolve(250,b,223,b)]. given #561 (T,wt=8): 8055 ilf_type(domain_of(c4),member_type(power_set(A))) | -empty(c2). [resolve(4382,a,206,a)]. given #562 (T,wt=10): 4468 member(f24(c3),c3) | ilf_type(range_of(c4),member_type(power_set(A))). [resolve(4444,a,212,c),unit_del(b,213)]. given #563 (T,wt=8): 8081 ilf_type(range_of(c4),member_type(power_set(A))) | -empty(c3). [resolve(4468,a,206,a)]. given #564 (T,wt=10): 4579 member(f24(A),A) | ilf_type(f6(A),member_type(power_set(B))). [resolve(4554,a,212,c),unit_del(b,213)]. given #565 (A,wt=23): 381 member(f3(A,B),A) | B = A | member(f4(A,B),C) | -member(f11(B,C),C) | member(f12(B,C),C). [resolve(250,b,222,b)]. given #566 (T,wt=8): 8124 ilf_type(f6(A),member_type(power_set(B))) | -empty(A). [resolve(4579,a,206,a)]. given #567 (T,wt=10): 4676 empty(f16(power_set(c4))) | member(f24(c4),cross_product(c2,c3)). [resolve(4666,b,750,a)]. given #568 (T,wt=8): 8150 empty(f16(power_set(c4))) | -empty(cross_product(c2,c3)). [resolve(4676,b,206,a)]. given #569 (T,wt=10): 4678 empty(f16(power_set(domain_of(c4)))) | member(f24(domain_of(c4)),c2). [resolve(4666,b,600,a)]. given #570 (A,wt=18): 382 member(f3(A,B),A) | B = A | member(f4(A,B),C) | member(f14(B,C),B). [resolve(250,b,218,a)]. given #571 (T,wt=7): 8172 empty(f16(power_set(domain_of(c4)))) | -empty(c2). [resolve(4678,b,206,a)]. given #572 (T,wt=9): 8173 empty(f16(power_set(domain_of(c4)))) | member(f24(c2),c2). [resolve(4678,b,205,a)]. given #573 (T,wt=10): 4679 empty(f16(power_set(range_of(c4)))) | member(f24(range_of(c4)),c3). [resolve(4666,b,580,a)]. given #574 (T,wt=7): 8322 empty(f16(power_set(range_of(c4)))) | -empty(c3). [resolve(4679,b,206,a)]. given #575 (A,wt=18): 383 member(f3(A,B),A) | B = A | member(f4(A,B),C) | -member(f14(B,C),C). [resolve(250,b,217,a)]. given #576 (T,wt=9): 8323 empty(f16(power_set(range_of(c4)))) | member(f24(c3),c3). [resolve(4679,b,205,a)]. given #577 (T,wt=10): 4680 empty(f16(power_set(f6(A)))) | member(f24(f6(A)),A). [resolve(4666,b,528,a)]. given #578 (T,wt=7): 8400 empty(f16(power_set(f6(A)))) | -empty(A). [resolve(4680,b,206,a)]. given #579 (T,wt=9): 8401 empty(f16(power_set(f6(A)))) | member(f24(A),A). [resolve(4680,b,205,a)]. given #580 (A,wt=19): 384 member(f3(A,power_set(B)),A) | power_set(B) = A | -member(C,f4(A,power_set(B))) | member(C,B). [resolve(250,b,214,c)]. given #581 (T,wt=10): 4757 empty(f24(power_set(c4))) | member(f24(c4),cross_product(c2,c3)). [resolve(4747,b,750,a)]. given #582 (T,wt=8): 8559 empty(f24(power_set(c4))) | -empty(cross_product(c2,c3)). [resolve(4757,b,206,a)]. given #583 (T,wt=10): 4759 empty(f24(power_set(domain_of(c4)))) | member(f24(domain_of(c4)),c2). [resolve(4747,b,600,a)]. given #584 (T,wt=7): 8581 empty(f24(power_set(domain_of(c4)))) | -empty(c2). [resolve(4759,b,206,a)]. given #585 (A,wt=17): 385 member(f3(A,B),A) | B = A | member(f4(A,B),C) | -member(B,power_set(C)). [resolve(250,b,214,a)]. given #586 (T,wt=9): 8582 empty(f24(power_set(domain_of(c4)))) | member(f24(c2),c2). [resolve(4759,b,205,a)]. given #587 (T,wt=10): 4760 empty(f24(power_set(range_of(c4)))) | member(f24(range_of(c4)),c3). [resolve(4747,b,580,a)]. given #588 (T,wt=7): 8707 empty(f24(power_set(range_of(c4)))) | -empty(c3). [resolve(4760,b,206,a)]. given #589 (T,wt=9): 8708 empty(f24(power_set(range_of(c4)))) | member(f24(c3),c3). [resolve(4760,b,205,a)]. given #590 (A,wt=16): 386 member(f3(A,B),A) | B = A | empty(B) | ilf_type(f4(A,B),member_type(B)). [resolve(250,b,212,c)]. given #591 (T,wt=10): 4761 empty(f24(power_set(f6(A)))) | member(f24(f6(A)),A). [resolve(4747,b,528,a)]. given #592 (T,wt=7): 8837 empty(f24(power_set(f6(A)))) | -empty(A). [resolve(4761,b,206,a)]. given #593 (T,wt=9): 8838 empty(f24(power_set(f6(A)))) | member(f24(A),A). [resolve(4761,b,205,a)]. given #594 (T,wt=10): 5566 member(c3,power_set(A)) | member(f24(range_of(c4)),range_of(c4)). [resolve(1836,b,205,a)]. given #595 (A,wt=27): 387 member(f3(A,B),A) | B = A | ordered_pair(f20(B,f4(A,B)),f21(B,f4(A,B))) = f4(A,B) | member(f22(B),B). [resolve(250,b,209,a)]. given #596 (T,wt=9): 8910 member(c3,power_set(A)) | member(f24(range_of(c4)),c3). [resolve(5566,b,580,a)]. given #597 (T,wt=10): 5582 member(c3,A) | -member(f14(power_set(range_of(c4)),A),A). [resolve(5560,a,217,a)]. given #598 (T,wt=10): 5599 member(f24(c3),range_of(c4)) | member(f6(c3),power_set(A)). [resolve(5583,a,4554,b)]. given #599 (T,wt=8): 9100 member(f6(c3),power_set(A)) | -empty(range_of(c4)). [resolve(5599,a,206,a)]. given #600 (A,wt=29): 388 member(f3(A,B),A) | B = A | ordered_pair(f20(B,f4(A,B)),f21(B,f4(A,B))) = f4(A,B) | f22(B) != ordered_pair(C,D). [resolve(250,b,208,a)]. given #601 (T,wt=10): 5600 member(f24(c3),range_of(c4)) | member(range_of(c4),power_set(A)). [resolve(5583,a,4444,b)]. given #602 (T,wt=10): 5606 member(f14(c3,A),range_of(c4)) | member(c3,power_set(A)). [resolve(5583,a,2053,a)]. given #603 (T,wt=10): 5610 member(f24(f6(c3)),range_of(c4)) | empty(f6(f6(c3))). [resolve(5583,a,1118,b)]. given #604 (T,wt=10): 5620 member(f24(c3),range_of(c4)) | ilf_type(c3,member_type(power_set(A))). [resolve(5583,a,910,a)]. given #605 (A,wt=12): 390 member(f3(A,B),A) | B = A | member(f24(B),B). [resolve(250,b,205,a)]. given #606 (T,wt=8): 9229 ilf_type(c3,member_type(power_set(A))) | -empty(range_of(c4)). [resolve(5620,a,206,a)]. given #607 (T,wt=10): 5624 member(f17(f6(c3)),range_of(c4)) | ilf_type(f6(c3),binary_relation_type). [resolve(5583,a,676,a)]. given #608 (T,wt=10): 5626 member(f24(f6(c3)),range_of(c4)) | ilf_type(f6(c3),binary_relation_type). [resolve(5583,a,671,a)]. given #609 (T,wt=10): 5843 empty(f24(power_set(c3))) | member(f24(range_of(c4)),range_of(c4)). [resolve(5597,a,205,a)]. given #610 (A,wt=29): 391 member(f3(A,B),A) | B = A | -ilf_type(B,subset_type(cross_product(C,D))) | ordered_pair(f18(B,f4(A,B)),f19(B,f4(A,B))) = f4(A,B). [resolve(250,b,131,b)]. given #611 (T,wt=9): 9373 empty(f24(power_set(c3))) | member(f24(range_of(c4)),c3). [resolve(5843,b,580,a)]. given #612 (T,wt=10): 5865 empty(f16(power_set(c3))) | member(f24(range_of(c4)),range_of(c4)). [resolve(5598,a,205,a)]. given #613 (T,wt=9): 9443 empty(f16(power_set(c3))) | member(f24(range_of(c4)),c3). [resolve(5865,b,580,a)]. given #614 (T,wt=10): 5956 empty(f23(power_set(c3))) | member(f24(range_of(c4)),range_of(c4)). [resolve(5601,a,205,a)]. given #615 (A,wt=29): 392 member(f3(A,B),A) | B = A | ordered_pair(f18(B,f4(A,B)),f19(B,f4(A,B))) = f4(A,B) | f17(B) != ordered_pair(C,D). [resolve(250,b,127,a)]. given #616 (T,wt=9): 9485 empty(f23(power_set(c3))) | member(f24(range_of(c4)),c3). [resolve(5956,b,580,a)]. given #617 (T,wt=10): 5978 empty(f6(f6(c3))) | member(f24(range_of(c4)),range_of(c4)). [resolve(5602,a,205,a)]. given #618 (T,wt=9): 9527 empty(f6(f6(c3))) | member(f24(range_of(c4)),c3). [resolve(5978,b,580,a)]. given #619 (T,wt=10): 6101 ilf_type(f6(c3),binary_relation_type) | member(f24(range_of(c4)),range_of(c4)). [resolve(5605,a,205,a)]. given #620 (A,wt=27): 393 member(f3(A,B),A) | B = A | ordered_pair(f18(B,f4(A,B)),f19(B,f4(A,B))) = f4(A,B) | member(f17(B),B). [resolve(250,b,125,a)]. given #621 (T,wt=9): 9569 ilf_type(f6(c3),binary_relation_type) | member(f24(range_of(c4)),c3). [resolve(6101,b,580,a)]. given #622 (T,wt=10): 6516 member(f24(c4),cross_product(c2,c3)) | -member(f24(c4),c3). [factor(6486,a,c)]. given #623 (T,wt=10): 6713 ilf_type(f6(range_of(c4)),binary_relation_type) | member(f24(c3),range_of(c4)). [resolve(6707,b,5583,a)]. given #624 (T,wt=10): 6877 ilf_type(f6(f6(c3)),binary_relation_type) | member(f24(c3),range_of(c4)). [resolve(6778,b,5583,a)]. given #625 (A,wt=26): 394 member(f3(A,B),A) | B = A | ordered_pair(f18(B,f4(A,B)),f19(B,f4(A,B))) = f4(A,B) | -ilf_type(B,binary_relation_type). [resolve(250,b,123,a)]. given #626 (T,wt=8): 9749 ilf_type(f6(f6(c3)),binary_relation_type) | -empty(range_of(c4)). [resolve(6877,b,206,a)]. given #627 (T,wt=10): 7082 c3 = A | member(f7(A,c3),A) | -empty(c4). [resolve(356,c,206,a)]. given #628 (T,wt=10): 7130 empty(f6(f6(range_of(c4)))) | member(f24(c3),range_of(c4)). [resolve(7124,b,5583,a)]. given #629 (T,wt=10): 7202 empty(f6(f6(f6(c3)))) | member(f24(c3),range_of(c4)). [resolve(7196,b,5583,a)]. given #630 (A,wt=18): 395 member(f3(A,c3),A) | c3 = A | member(ordered_pair(f25(f4(A,c3)),f4(A,c3)),c4). [resolve(250,b,116,a)]. given #631 (T,wt=8): 9792 empty(f6(f6(f6(c3)))) | -empty(range_of(c4)). [resolve(7202,b,206,a)]. given #632 (T,wt=10): 7551 unordered_pair(singleton(A),unordered_pair(B,A)) = ordered_pair(A,B). [para(239(a,1),3501(a,1,2))]. given #633 (T,wt=10): 7811 empty(f23(power_set(range_of(c4)))) | member(f24(c3),range_of(c4)). [resolve(7805,b,5583,a)]. given #634 (T,wt=10): 7998 empty(f23(power_set(f6(c3)))) | member(f24(c3),range_of(c4)). [resolve(7992,b,5583,a)]. given #635 (A,wt=19): 396 member(f3(A,power_set(A)),A) | power_set(A) = A | -member(f3(A,power_set(A)),f4(A,power_set(A))). [factor(384,a,d)]. given #636 (T,wt=8): 9859 empty(f23(power_set(f6(c3)))) | -empty(range_of(c4)). [resolve(7998,b,206,a)]. given #637 (T,wt=10): 8333 empty(f16(power_set(range_of(c4)))) | member(f24(c3),range_of(c4)). [resolve(8323,b,5583,a)]. given #638 (T,wt=10): 8407 empty(f16(power_set(f6(c3)))) | member(f24(c3),range_of(c4)). [resolve(8401,b,5583,a)]. given #639 (T,wt=8): 9901 empty(f16(power_set(f6(c3)))) | -empty(range_of(c4)). [resolve(8407,b,206,a)]. given #640 (A,wt=26): 397 -ilf_type(A,binary_relation_type) | member(ordered_pair(f1(A,f4(B,range_of(A))),f4(B,range_of(A))),A) | member(f3(B,range_of(A)),B) | range_of(A) = B. [resolve(254,c,250,b)]. given #641 (T,wt=10): 8714 empty(f24(power_set(range_of(c4)))) | member(f24(c3),range_of(c4)). [resolve(8708,b,5583,a)]. given #642 (T,wt=10): 8844 empty(f24(power_set(f6(c3)))) | member(f24(c3),range_of(c4)). [resolve(8838,b,5583,a)]. given #643 (T,wt=8): 9963 empty(f24(power_set(f6(c3)))) | -empty(range_of(c4)). [resolve(8844,b,206,a)]. given #644 (T,wt=10): 9053 member(f24(range_of(c4)),c3) | ilf_type(c3,member_type(power_set(A))). [resolve(8910,a,212,c),unit_del(b,213)]. given #645 (A,wt=26): 398 -ilf_type(A,binary_relation_type) | member(ordered_pair(f1(A,f8(B,range_of(A))),f8(B,range_of(A))),A) | range_of(A) = B | member(f7(B,range_of(A)),B). [resolve(254,c,234,c)]. given #646 (T,wt=10): 9128 member(f24(c3),range_of(c4)) | -member(f24(c3),f6(c3)). [factor(9120,a,c)]. given #647 (T,wt=10): 9817 member(f3(A,c3),A) | c3 = A | -empty(c4). [resolve(395,c,206,a)]. given #648 (T,wt=11): 465 empty(A) | member(f24(A),B) | member(f14(A,B),A). [resolve(265,b,218,a)]. given #649 (T,wt=11): 466 empty(A) | member(f24(A),B) | -member(f14(A,B),B). [resolve(265,b,217,a)]. given #650 (A,wt=21): 399 -ilf_type(A,binary_relation_type) | member(ordered_pair(f1(A,f15(range_of(A),B)),f15(range_of(A),B)),A) | member(range_of(A),power_set(B)). [resolve(254,c,216,b)]. given #651 (T,wt=11): 488 empty(A) | member(f16(A),B) | member(f14(A,B),A). [resolve(275,b,218,a)]. given #652 (T,wt=11): 489 empty(A) | member(f16(A),B) | -member(f14(A,B),B). [resolve(275,b,217,a)]. given #653 (T,wt=11): 513 ilf_type(A,binary_relation_type) | member(f24(A),B) | -member(A,power_set(B)). [resolve(264,a,214,a)]. given #654 (T,wt=11): 516 ilf_type(c3,binary_relation_type) | member(ordered_pair(f25(f24(c3)),f24(c3)),c4). [resolve(264,a,116,a)]. given #655 (A,wt=17): 400 -ilf_type(A,binary_relation_type) | member(ordered_pair(f1(A,f23(range_of(A))),f23(range_of(A))),A) | empty(range_of(A)). [resolve(254,c,207,b)]. given #656 (T,wt=9): 10339 ilf_type(c3,binary_relation_type) | member(f25(f24(c3)),domain_of(c4)). [resolve(516,b,252,b),unit_del(b,540)]. given #657 (T,wt=8): 10379 ilf_type(c3,binary_relation_type) | member(f25(f24(c3)),c2). [resolve(10339,b,600,a)]. given #658 (T,wt=11): 526 member(f6(A),B) | member(f14(power_set(A),B),power_set(A)). [resolve(499,a,218,a)]. given #659 (T,wt=9): 10470 member(f14(power_set(A),B),power_set(A)) | -empty(B). [resolve(526,a,206,a)]. given #660 (A,wt=18): 401 -ilf_type(A,binary_relation_type) | member(ordered_pair(f1(A,f17(range_of(A))),f17(range_of(A))),A) | ilf_type(range_of(A),binary_relation_type). [resolve(254,c,119,a)]. given #661 (T,wt=11): 559 member(f24(power_set(A)),B) | -member(f14(power_set(A),B),B). [resolve(444,a,217,a)]. given #662 (T,wt=11): 578 member(range_of(c4),A) | member(f14(power_set(c3),A),power_set(c3)). [resolve(568,a,218,a)]. given #663 (T,wt=11): 598 member(domain_of(c4),A) | member(f14(power_set(c2),A),power_set(c2)). [resolve(588,a,218,a)]. given #664 (T,wt=11): 652 ilf_type(c3,binary_relation_type) | member(f24(c4),A) | -member(c4,power_set(A)). [resolve(421,b,214,a)]. given #665 (A,wt=14): 405 ilf_type(c3,binary_relation_type) | member(ordered_pair(f25(f17(c3)),f17(c3)),A) | c4 != A. [resolve(256,b,231,b)]. given #666 (T,wt=11): 660 domain(A,B,cross_product(A,B)) = domain_of(cross_product(A,B)). [resolve(452,a,204,a)]. given #667 (T,wt=11): 662 range(A,B,cross_product(A,B)) = range_of(cross_product(A,B)). [resolve(452,a,202,a)]. given #668 (T,wt=11): 674 member(f15(f6(A),B),A) | member(f6(A),power_set(B)). [resolve(528,a,216,b)]. given #669 (T,wt=11): 678 empty(c3) | member(ordered_pair(f2(c4,f23(c3)),f23(c3)),c4). [resolve(270,b,253,c),unit_del(b,540)]. given #670 (A,wt=21): 406 ilf_type(c3,binary_relation_type) | member(ordered_pair(f25(f17(c3)),f17(c3)),A) | member(f9(A,c4),A) | -member(f10(A,c4),A). [resolve(256,b,230,b)]. given #671 (T,wt=9): 10762 empty(c3) | member(f2(c4,f23(c3)),domain_of(c4)). [resolve(678,b,252,b),unit_del(b,540)]. given #672 (T,wt=8): 10786 empty(c3) | member(f2(c4,f23(c3)),c2). [resolve(10762,b,600,a)]. given #673 (T,wt=11): 710 empty(c3) | member(f24(c4),A) | member(f14(c4,A),c4). [resolve(696,b,218,a)]. given #674 (T,wt=9): 10875 empty(c3) | member(f14(c4,A),c4) | -empty(A). [resolve(710,b,206,a)]. given #675 (A,wt=21): 407 ilf_type(c3,binary_relation_type) | member(ordered_pair(f25(f17(c3)),f17(c3)),A) | member(f9(A,c4),A) | member(f10(A,c4),c4). [resolve(256,b,229,b)]. given #676 (T,wt=11): 711 empty(c3) | member(f24(c4),A) | -member(f14(c4,A),A). [resolve(696,b,217,a)]. given #677 (T,wt=11): 730 member(f16(power_set(A)),B) | -member(f14(power_set(A),B),B). [resolve(719,a,217,a)]. given #678 (T,wt=11): 749 member(c4,A) | -member(f14(power_set(cross_product(c2,c3)),A),A). [resolve(738,a,217,a)]. given #679 (T,wt=11): 764 member(f15(range_of(c4),A),c3) | member(range_of(c4),power_set(A)). [resolve(580,a,216,b)]. given #680 (A,wt=21): 408 ilf_type(c3,binary_relation_type) | member(ordered_pair(f25(f17(c3)),f17(c3)),A) | -member(f9(A,c4),c4) | -member(f10(A,c4),A). [resolve(256,b,228,b)]. given #681 (T,wt=11): 773 member(f15(domain_of(c4),A),c2) | member(domain_of(c4),power_set(A)). [resolve(600,a,216,b)]. given #682 (T,wt=11): 787 member(f23(power_set(A)),B) | -member(f14(power_set(A),B),B). [resolve(776,a,217,a)]. given #683 (T,wt=11): 847 empty(c3) | member(ordered_pair(f1(c4,f23(c3)),f23(c3)),c4). [resolve(677,b,254,c),unit_del(b,540)]. given #684 (T,wt=9): 11048 empty(c3) | member(f1(c4,f23(c3)),domain_of(c4)). [resolve(847,b,252,b),unit_del(b,540)]. given #685 (A,wt=21): 409 ilf_type(c3,binary_relation_type) | member(ordered_pair(f25(f17(c3)),f17(c3)),A) | -member(f9(A,c4),c4) | member(f10(A,c4),c4). [resolve(256,b,227,b)]. given #686 (T,wt=8): 11068 empty(c3) | member(f1(c4,f23(c3)),c2). [resolve(11048,b,600,a)]. given #687 (T,wt=11): 859 empty(c3) | member(f23(c3),A) | -member(range_of(c4),power_set(A)). [resolve(677,b,214,a)]. given #688 (T,wt=11): 860 empty(c3) | empty(range_of(c4)) | ilf_type(f23(c3),member_type(range_of(c4))). [resolve(677,b,212,c)]. given #689 (T,wt=11): 874 member(f24(f23(power_set(A))),A) | ilf_type(f23(power_set(A)),binary_relation_type). [resolve(280,a,264,a)]. given #690 (A,wt=21): 410 ilf_type(c3,binary_relation_type) | member(ordered_pair(f25(f17(c3)),f17(c3)),A) | member(f11(c4,A),c4) | -member(f12(c4,A),c4). [resolve(256,b,225,b)]. given #691 (T,wt=7): 11161 ilf_type(f23(power_set(A)),binary_relation_type) | -empty(A). [resolve(874,a,206,a)]. given #692 (T,wt=9): 11162 ilf_type(f23(power_set(A)),binary_relation_type) | member(f24(A),A). [resolve(874,a,205,a)]. given #693 (T,wt=10): 11168 ilf_type(f23(power_set(c3)),binary_relation_type) | member(f24(c3),range_of(c4)). [resolve(11162,b,5583,a)]. given #694 (T,wt=8): 11227 ilf_type(f23(power_set(c3)),binary_relation_type) | -empty(range_of(c4)). [resolve(11168,b,206,a)]. given #695 (A,wt=21): 411 ilf_type(c3,binary_relation_type) | member(ordered_pair(f25(f17(c3)),f17(c3)),A) | member(f11(c4,A),c4) | member(f12(c4,A),A). [resolve(256,b,224,b)]. given #696 (T,wt=11): 879 member(f17(f23(power_set(A))),A) | ilf_type(f23(power_set(A)),binary_relation_type). [resolve(280,a,119,a)]. given #697 (T,wt=11): 889 member(f24(A),A) | member(A,B) | power_set(C) != B. [resolve(289,a,231,b)]. given #698 (T,wt=11): 926 member(A,power_set(B)) | member(f24(A),C) | A != C. [resolve(289,b,231,b)]. given #699 (T,wt=11): 931 member(A,power_set(B)) | member(f24(A),C) | C != A. [resolve(289,b,226,b)]. given #700 (A,wt=21): 412 ilf_type(c3,binary_relation_type) | member(ordered_pair(f25(f17(c3)),f17(c3)),A) | -member(f11(c4,A),A) | -member(f12(c4,A),c4). [resolve(256,b,223,b)]. given #701 (T,wt=11): 972 member(f24(f24(power_set(A))),A) | ilf_type(f24(power_set(A)),binary_relation_type). [resolve(467,a,264,a)]. given #702 (T,wt=7): 11447 ilf_type(f24(power_set(A)),binary_relation_type) | -empty(A). [resolve(972,a,206,a)]. given #703 (T,wt=9): 11448 ilf_type(f24(power_set(A)),binary_relation_type) | member(f24(A),A). [resolve(972,a,205,a)]. given #704 (T,wt=10): 11454 ilf_type(f24(power_set(c3)),binary_relation_type) | member(f24(c3),range_of(c4)). [resolve(11448,b,5583,a)]. given #705 (A,wt=21): 413 ilf_type(c3,binary_relation_type) | member(ordered_pair(f25(f17(c3)),f17(c3)),A) | -member(f11(c4,A),A) | member(f12(c4,A),A). [resolve(256,b,222,b)]. given #706 (T,wt=8): 11513 ilf_type(f24(power_set(c3)),binary_relation_type) | -empty(range_of(c4)). [resolve(11454,b,206,a)]. given #707 (T,wt=11): 976 member(f17(f24(power_set(A))),A) | ilf_type(f24(power_set(A)),binary_relation_type). [resolve(467,a,119,a)]. given #708 (T,wt=11): 983 member(f24(f16(power_set(A))),A) | ilf_type(f16(power_set(A)),binary_relation_type). [resolve(490,a,264,a)]. given #709 (T,wt=7): 11624 ilf_type(f16(power_set(A)),binary_relation_type) | -empty(A). [resolve(983,a,206,a)]. given #710 (A,wt=16): 414 ilf_type(c3,binary_relation_type) | member(ordered_pair(f25(f17(c3)),f17(c3)),A) | member(f14(c4,A),c4). [resolve(256,b,218,a)]. given #711 (T,wt=9): 11625 ilf_type(f16(power_set(A)),binary_relation_type) | member(f24(A),A). [resolve(983,a,205,a)]. given #712 (T,wt=10): 11682 ilf_type(c3,binary_relation_type) | member(f14(c4,A),c4) | -empty(A). [resolve(414,b,206,a)]. given #713 (T,wt=10): 11711 ilf_type(f16(power_set(c3)),binary_relation_type) | member(f24(c3),range_of(c4)). [resolve(11625,b,5583,a)]. given #714 (T,wt=8): 11770 ilf_type(f16(power_set(c3)),binary_relation_type) | -empty(range_of(c4)). [resolve(11711,b,206,a)]. given #715 (A,wt=16): 415 ilf_type(c3,binary_relation_type) | member(ordered_pair(f25(f17(c3)),f17(c3)),A) | -member(f14(c4,A),A). [resolve(256,b,217,a)]. given #716 (T,wt=11): 987 member(f17(f16(power_set(A))),A) | ilf_type(f16(power_set(A)),binary_relation_type). [resolve(490,a,119,a)]. given #717 (T,wt=11): 989 ilf_type(c3,binary_relation_type) | member(f17(c3),A) | range_of(c4) != A. [resolve(544,b,231,b)]. given #718 (T,wt=11): 1042 member(domain_of(f5(A,B)),C) | -member(power_set(B),power_set(C)). [resolve(1017,a,214,a)]. given #719 (T,wt=11): 1064 member(range_of(f5(A,B)),C) | -member(power_set(A),power_set(C)). [resolve(1049,a,214,a)]. given #720 (A,wt=15): 416 ilf_type(c3,binary_relation_type) | member(ordered_pair(f25(f17(c3)),f17(c3)),A) | -member(c4,power_set(A)). [resolve(256,b,214,a)]. given #721 (T,wt=11): 1092 empty(f6(A)) | member(f16(f6(A)),B) | A != B. [resolve(668,a,231,b)]. given #722 (T,wt=11): 1097 empty(f6(A)) | member(f16(f6(A)),B) | B != A. [resolve(668,a,226,b)]. given #723 (T,wt=11): 1106 empty(f6(A)) | empty(A) | ilf_type(f16(f6(A)),member_type(A)). [resolve(668,a,212,c)]. given #724 (T,wt=11): 1119 empty(f6(f16(power_set(A)))) | member(f24(f16(power_set(A))),A). [resolve(1110,b,490,a)]. given #725 (A,wt=14): 417 ilf_type(c3,binary_relation_type) | empty(c4) | ilf_type(ordered_pair(f25(f17(c3)),f17(c3)),member_type(c4)). [resolve(256,b,212,c)]. given #726 (T,wt=7): 11891 empty(f6(f16(power_set(A)))) | -empty(A). [resolve(1119,b,206,a)]. given #727 (T,wt=9): 11892 empty(f6(f16(power_set(A)))) | member(f24(A),A). [resolve(1119,b,205,a)]. given #728 (T,wt=10): 11898 empty(f6(f16(power_set(c3)))) | member(f24(c3),range_of(c4)). [resolve(11892,b,5583,a)]. given #729 (T,wt=8): 11957 empty(f6(f16(power_set(c3)))) | -empty(range_of(c4)). [resolve(11898,b,206,a)]. given #730 (A,wt=31): 418 ilf_type(c3,binary_relation_type) | ordered_pair(f20(c4,ordered_pair(f25(f17(c3)),f17(c3))),f21(c4,ordered_pair(f25(f17(c3)),f17(c3)))) = ordered_pair(f25(f17(c3)),f17(c3)) | member(f22(c4),c4). [resolve(256,b,209,a)]. given #731 (T,wt=11): 1120 empty(f6(f24(power_set(A)))) | member(f24(f24(power_set(A))),A). [resolve(1110,b,467,a)]. given #732 (T,wt=7): 12030 empty(f6(f24(power_set(A)))) | -empty(A). [resolve(1120,b,206,a)]. given #733 (T,wt=9): 12031 empty(f6(f24(power_set(A)))) | member(f24(A),A). [resolve(1120,b,205,a)]. given #734 (T,wt=10): 12037 empty(f6(f24(power_set(c3)))) | member(f24(c3),range_of(c4)). [resolve(12031,b,5583,a)]. given #735 (A,wt=33): 419 ilf_type(c3,binary_relation_type) | ordered_pair(f20(c4,ordered_pair(f25(f17(c3)),f17(c3))),f21(c4,ordered_pair(f25(f17(c3)),f17(c3)))) = ordered_pair(f25(f17(c3)),f17(c3)) | f22(c4) != ordered_pair(A,B). [resolve(256,b,208,a)]. given #736 (T,wt=8): 12096 empty(f6(f24(power_set(c3)))) | -empty(range_of(c4)). [resolve(12037,b,206,a)]. given #737 (T,wt=11): 1123 empty(f6(f23(power_set(A)))) | member(f24(f23(power_set(A))),A). [resolve(1110,b,280,a)]. given #738 (T,wt=7): 12150 empty(f6(f23(power_set(A)))) | -empty(A). [resolve(1123,b,206,a)]. given #739 (T,wt=9): 12151 empty(f6(f23(power_set(A)))) | member(f24(A),A). [resolve(1123,b,205,a)]. given #740 (A,wt=13): 426 -ilf_type(power_set(ordered_pair(A,B)),binary_relation_type) | member(B,range_of(power_set(ordered_pair(A,B)))). [resolve(282,a,255,c)]. given #741 (T,wt=10): 12157 empty(f6(f23(power_set(c3)))) | member(f24(c3),range_of(c4)). [resolve(12151,b,5583,a)]. given #742 (T,wt=8): 12216 empty(f6(f23(power_set(c3)))) | -empty(range_of(c4)). [resolve(12157,b,206,a)]. given #743 (T,wt=11): 1137 empty(f6(A)) | member(f24(A),B) | -member(A,power_set(B)). [resolve(1110,b,214,a)]. given #744 (T,wt=11): 1144 empty(f6(c3)) | member(ordered_pair(f25(f24(c3)),f24(c3)),c4). [resolve(1110,b,116,a)]. given #745 (A,wt=19): 427 -ilf_type(power_set(ordered_pair(A,B)),binary_relation_type) | member(ordered_pair(f2(power_set(ordered_pair(A,B)),B),B),power_set(ordered_pair(A,B))). [resolve(282,a,253,c)]. given #746 (T,wt=5): 12349 empty(f6(c3)) | -empty(c4). [resolve(1144,b,206,a)]. given #747 (T,wt=7): 12350 empty(f6(c3)) | member(f24(c4),c4). [resolve(1144,b,205,a)]. given #748 (T,wt=9): 12333 empty(f6(c3)) | member(f25(f24(c3)),domain_of(c4)). [resolve(1144,b,252,b),unit_del(b,540)]. given #749 (T,wt=6): 12392 empty(f6(c3)) | -empty(domain_of(c4)). [resolve(12333,b,206,a)]. given #750 (A,wt=13): 428 -ilf_type(power_set(ordered_pair(A,B)),binary_relation_type) | member(A,domain_of(power_set(ordered_pair(A,B)))). [resolve(282,a,252,b)]. given #751 (T,wt=8): 12375 empty(f6(c3)) | member(f25(f24(c3)),c2). [resolve(12333,b,600,a)]. given #752 (T,wt=5): 12414 empty(f6(c3)) | -empty(c2). [resolve(12375,b,206,a)]. given #753 (T,wt=7): 12415 empty(f6(c3)) | member(f24(c2),c2). [resolve(12375,b,205,a)]. given #754 (T,wt=9): 12355 empty(f6(c3)) | member(f24(c4),cross_product(c2,c3)). [resolve(12350,b,750,a)]. given #755 (A,wt=15): 430 member(A,B) | member(f9(B,power_set(A)),B) | -member(f10(B,power_set(A)),B). [resolve(282,a,230,b)]. Low Water (keep): wt=59.000, iters=7080 given #756 (T,wt=7): 12455 empty(f6(c3)) | -empty(cross_product(c2,c3)). [resolve(12355,b,206,a)]. given #757 (T,wt=9): 12393 empty(f6(c3)) | member(f24(domain_of(c4)),domain_of(c4)). [resolve(12333,b,205,a)]. given #758 (T,wt=8): 12463 empty(f6(c3)) | member(f24(domain_of(c4)),c2). [resolve(12393,b,600,a)]. given #759 (T,wt=10): 12357 empty(f6(c3)) | member(f24(c4),A) | c4 != A. [resolve(12350,b,231,b)]. given #760 (A,wt=16): 431 member(A,B) | member(f9(B,power_set(A)),B) | member(f10(B,power_set(A)),power_set(A)). [resolve(282,a,229,b)]. given #761 (T,wt=10): 12421 empty(f6(c3)) | member(f24(c2),A) | c2 != A. [resolve(12415,b,231,b)]. given #762 (T,wt=11): 1147 member(c4,power_set(A)) | member(f15(c4,A),cross_product(c2,c3)). [resolve(284,c,738,a)]. given #763 (T,wt=11): 1166 empty(f6(A)) | member(f24(f6(A)),B) | A != B. [resolve(670,a,231,b)]. given #764 (T,wt=11): 1171 empty(f6(A)) | member(f24(f6(A)),B) | B != A. [resolve(670,a,226,b)]. given #765 (A,wt=16): 432 member(A,B) | -member(f9(B,power_set(A)),power_set(A)) | -member(f10(B,power_set(A)),B). [resolve(282,a,228,b)]. given #766 (T,wt=11): 1180 empty(f6(A)) | empty(A) | ilf_type(f24(f6(A)),member_type(A)). [resolve(670,a,212,c)]. given #767 (T,wt=11): 1200 empty(f6(A)) | member(f23(f6(A)),B) | A != B. [resolve(675,a,231,b)]. given #768 (T,wt=11): 1205 empty(f6(A)) | member(f23(f6(A)),B) | B != A. [resolve(675,a,226,b)]. given #769 (T,wt=11): 1214 empty(f6(A)) | empty(A) | ilf_type(f23(f6(A)),member_type(A)). [resolve(675,a,212,c)]. given #770 (A,wt=17): 433 member(A,B) | -member(f9(B,power_set(A)),power_set(A)) | member(f10(B,power_set(A)),power_set(A)). [resolve(282,a,227,b)]. Low Water (keep): wt=50.000, iters=7014 given #771 (T,wt=11): 1223 empty(c3) | member(f25(f23(c3)),A) | domain_of(c4) != A. [resolve(679,b,231,b)]. given #772 (T,wt=11): 1244 ilf_type(f15(power_set(A),B),member_type(power_set(A))) | member(A,B). [resolve(285,a,440,b),unit_del(a,213)]. given #773 (T,wt=10): 12709 ilf_type(f15(power_set(A),B),member_type(power_set(A))) | -empty(B). [resolve(1244,b,206,a)]. given #774 (T,wt=11): 1304 empty(c3) | member(f25(f23(c3)),A) | -member(c2,power_set(A)). [resolve(1222,b,214,a)]. given #775 (A,wt=17): 434 member(A,B) | member(f11(power_set(A),B),power_set(A)) | -member(f12(power_set(A),B),power_set(A)). [resolve(282,a,225,b)]. given #776 (T,wt=11): 1323 empty(c3) | member(f24(c2),A) | member(f14(c2,A),c2). [resolve(1309,b,218,a)]. given #777 (T,wt=9): 12779 empty(c3) | member(f14(c2,A),c2) | -empty(A). [resolve(1323,b,206,a)]. given #778 (T,wt=11): 1324 empty(c3) | member(f24(c2),A) | -member(f14(c2,A),A). [resolve(1309,b,217,a)]. Low Water (keep): wt=47.000, iters=7125 given #779 (T,wt=11): 1430 empty(range_of(c4)) | member(f16(range_of(c4)),A) | c3 != A. [resolve(758,a,231,b)]. given #780 (A,wt=16): 435 member(A,B) | member(f11(power_set(A),B),power_set(A)) | member(f12(power_set(A),B),B). [resolve(282,a,224,b)]. Low Water (keep): wt=37.000, iters=6823 Low Water (keep): wt=35.000, iters=6699 given #781 (T,wt=11): 1442 empty(range_of(c4)) | empty(c3) | ilf_type(f16(range_of(c4)),member_type(c3)). [resolve(758,a,212,c)]. given #782 (T,wt=11): 1463 empty(range_of(c4)) | member(f24(c3),A) | -member(c3,power_set(A)). [resolve(1446,b,214,a)]. given #783 (T,wt=11): 1470 empty(range_of(c4)) | member(ordered_pair(f25(f24(c3)),f24(c3)),c4). [resolve(1446,b,116,a)]. given #784 (T,wt=5): 12895 empty(range_of(c4)) | -empty(c4). [resolve(1470,b,206,a)]. given #785 (A,wt=16): 436 member(A,B) | -member(f11(power_set(A),B),B) | -member(f12(power_set(A),B),power_set(A)). [resolve(282,a,223,b)]. given #786 (T,wt=7): 12896 empty(range_of(c4)) | member(f24(c4),c4). [resolve(1470,b,205,a)]. given #787 (T,wt=9): 12879 empty(range_of(c4)) | member(f25(f24(c3)),domain_of(c4)). [resolve(1470,b,252,b),unit_del(b,540)]. given #788 (T,wt=6): 12941 empty(range_of(c4)) | -empty(domain_of(c4)). [resolve(12879,b,206,a)]. given #789 (T,wt=8): 12924 empty(range_of(c4)) | member(f25(f24(c3)),c2). [resolve(12879,b,600,a)]. given #790 (A,wt=15): 437 member(A,B) | -member(f11(power_set(A),B),B) | member(f12(power_set(A),B),B). [resolve(282,a,222,b)]. given #791 (T,wt=5): 12963 empty(range_of(c4)) | -empty(c2). [resolve(12924,b,206,a)]. given #792 (T,wt=7): 12964 empty(range_of(c4)) | member(f24(c2),c2). [resolve(12924,b,205,a)]. given #793 (T,wt=9): 12904 empty(range_of(c4)) | member(f24(c4),cross_product(c2,c3)). [resolve(12896,b,750,a)]. given #794 (T,wt=7): 13007 empty(range_of(c4)) | -empty(cross_product(c2,c3)). [resolve(12904,b,206,a)]. given #795 (A,wt=17): 442 ordered_pair(f20(power_set(A),A),f21(power_set(A),A)) = A | member(f22(power_set(A)),power_set(A)). [resolve(282,a,209,a)]. Low Water (keep): wt=34.000, iters=6740 given #796 (T,wt=9): 12942 empty(range_of(c4)) | member(f24(domain_of(c4)),domain_of(c4)). [resolve(12879,b,205,a)]. given #797 (T,wt=8): 13038 empty(range_of(c4)) | member(f24(domain_of(c4)),c2). [resolve(12942,b,600,a)]. given #798 (T,wt=10): 12906 empty(range_of(c4)) | member(f24(c4),A) | c4 != A. [resolve(12896,b,231,b)]. given #799 (T,wt=10): 12973 empty(range_of(c4)) | member(f24(c2),A) | c2 != A. [resolve(12964,b,231,b)]. given #800 (A,wt=18): 443 ordered_pair(f20(power_set(A),A),f21(power_set(A),A)) = A | f22(power_set(A)) != ordered_pair(B,C). [resolve(282,a,208,a)]. given #801 (T,wt=11): 1471 empty(range_of(c4)) | member(f24(range_of(c4)),A) | c3 != A. [resolve(760,a,231,b)]. given #802 (T,wt=11): 1491 empty(range_of(c4)) | member(f23(range_of(c4)),A) | c3 != A. [resolve(765,a,231,b)]. given #803 (T,wt=11): 1503 empty(range_of(c4)) | empty(c3) | ilf_type(f23(range_of(c4)),member_type(c3)). [resolve(765,a,212,c)]. given #804 (T,wt=11): 1511 empty(domain_of(c4)) | member(f16(domain_of(c4)),A) | c2 != A. [resolve(767,a,231,b)]. given #805 (A,wt=18): 445 -ilf_type(power_set(A),subset_type(cross_product(B,C))) | ordered_pair(f18(power_set(A),A),f19(power_set(A),A)) = A. [resolve(282,a,131,b)]. given #806 (T,wt=11): 1523 empty(domain_of(c4)) | empty(c2) | ilf_type(f16(domain_of(c4)),member_type(c2)). [resolve(767,a,212,c)]. given #807 (T,wt=11): 1543 empty(domain_of(c4)) | member(f24(c2),A) | -member(c2,power_set(A)). [resolve(1527,b,214,a)]. given #808 (T,wt=11): 1561 empty(domain_of(c4)) | member(f24(domain_of(c4)),A) | c2 != A. [resolve(769,a,231,b)]. given #809 (T,wt=11): 1573 empty(domain_of(c4)) | empty(c2) | ilf_type(f24(domain_of(c4)),member_type(c2)). [resolve(769,a,212,c)]. given #810 (A,wt=18): 446 ordered_pair(f18(power_set(A),A),f19(power_set(A),A)) = A | f17(power_set(A)) != ordered_pair(B,C). [resolve(282,a,127,a)]. given #811 (T,wt=11): 1580 empty(domain_of(c4)) | member(f23(domain_of(c4)),A) | c2 != A. [resolve(774,a,231,b)]. given #812 (T,wt=11): 1592 empty(domain_of(c4)) | empty(c2) | ilf_type(f23(domain_of(c4)),member_type(c2)). [resolve(774,a,212,c)]. given #813 (T,wt=11): 1615 member(domain_of(cross_product(A,B)),C) | -member(power_set(A),power_set(C)). [resolve(1599,a,214,a)]. given #814 (T,wt=11): 1638 member(range_of(cross_product(A,B)),C) | -member(power_set(B),power_set(C)). [resolve(1622,a,214,a)]. given #815 (A,wt=17): 447 ordered_pair(f18(power_set(A),A),f19(power_set(A),A)) = A | member(f17(power_set(A)),power_set(A)). [resolve(282,a,125,a)]. given #816 (T,wt=11): 1727 empty(c3) | member(f24(range_of(c4)),A) | range_of(c4) != A. [resolve(864,b,231,b)]. given #817 (T,wt=11): 1756 empty(c3) | member(f24(range_of(c4)),A) | -member(c3,power_set(A)). [resolve(1725,b,214,a)]. given #818 (T,wt=11): 1767 ilf_type(domain_of(f6(cross_product(cross_product(A,B),C))),relation_type(A,B)). [resolve(953,a,245,a)]. given #819 (T,wt=11): 1772 ilf_type(range_of(f6(cross_product(A,cross_product(B,C)))),relation_type(B,C)). [resolve(955,a,245,a)]. given #820 (A,wt=15): 448 ordered_pair(f18(power_set(A),A),f19(power_set(A),A)) = A | -ilf_type(power_set(A),binary_relation_type). [resolve(282,a,123,a)]. given #821 (T,wt=11): 1776 empty(c4) | member(f23(c4),A) | cross_product(c2,c3) != A. [resolve(956,a,231,b)]. given #822 (T,wt=11): 1798 empty(c3) | member(f24(domain_of(c4)),A) | domain_of(c4) != A. [resolve(1239,b,231,b)]. given #823 (T,wt=11): 1827 empty(c3) | member(f24(domain_of(c4)),A) | -member(c2,power_set(A)). [resolve(1797,b,214,a)]. given #824 (T,wt=11): 1838 member(c3,power_set(A)) | member(f25(f15(c3,A)),domain_of(c4)). [resolve(294,b,252,b),unit_del(b,540)]. given #825 (A,wt=17): 454 empty(range_of(A)) | -ilf_type(A,binary_relation_type) | member(ordered_pair(f1(A,f24(range_of(A))),f24(range_of(A))),A). [resolve(265,b,254,c)]. given #826 (T,wt=7): 13146 member(c3,power_set(A)) | -empty(domain_of(c4)). [resolve(1838,b,206,a)]. given #827 (T,wt=10): 13129 member(c3,power_set(A)) | member(f25(f15(c3,A)),c2). [resolve(1838,b,600,a)]. given #828 (T,wt=6): 13173 member(c3,power_set(A)) | -empty(c2). [resolve(13129,b,206,a)]. given #829 (T,wt=8): 13174 member(c3,power_set(A)) | member(f24(c2),c2). [resolve(13129,b,205,a)]. given #830 (A,wt=16): 456 empty(A) | member(f24(A),B) | member(f9(B,A),B) | -member(f10(B,A),B). [resolve(265,b,230,b)]. given #831 (T,wt=8): 13221 member(f24(c2),c2) | -member(f24(c2),c3). [factor(13193,a,c)]. given #832 (T,wt=9): 13195 member(f24(c2),c2) | ilf_type(c3,member_type(power_set(A))). [resolve(13174,a,212,c),unit_del(b,213)]. given #833 (T,wt=7): 13241 ilf_type(c3,member_type(power_set(A))) | -empty(c2). [resolve(13195,a,206,a)]. given #834 (T,wt=10): 13147 member(c3,power_set(A)) | member(f24(domain_of(c4)),domain_of(c4)). [resolve(1838,b,205,a)]. given #835 (A,wt=16): 457 empty(A) | member(f24(A),B) | member(f9(B,A),B) | member(f10(B,A),A). [resolve(265,b,229,b)]. Low Water (keep): wt=32.000, iters=6723 given #836 (T,wt=9): 13269 member(c3,power_set(A)) | member(f24(domain_of(c4)),c2). [resolve(13147,b,600,a)]. given #837 (T,wt=10): 13193 member(f24(c2),c2) | -member(A,c3) | member(A,B). [resolve(13174,a,214,c)]. Low Water (keep): wt=31.000, iters=6691 given #838 (T,wt=10): 13404 member(f24(domain_of(c4)),c2) | ilf_type(c3,member_type(power_set(A))). [resolve(13269,a,212,c),unit_del(b,213)]. given #839 (T,wt=10): 13431 member(f24(domain_of(c4)),c2) | -member(f24(domain_of(c4)),c3). [factor(13402,a,c)]. given #840 (A,wt=16): 458 empty(A) | member(f24(A),B) | -member(f9(B,A),A) | -member(f10(B,A),B). [resolve(265,b,228,b)]. given #841 (T,wt=11): 1860 empty(c3) | member(f24(c4),A) | cross_product(c2,c3) != A. [resolve(1333,a,231,b)]. given #842 (T,wt=11): 1881 empty(c4) | member(f16(c4),A) | cross_product(c2,c3) != A. [resolve(1339,a,231,b)]. given #843 (T,wt=11): 1900 empty(c4) | member(f24(c4),A) | cross_product(c2,c3) != A. [resolve(1342,a,231,b)]. given #844 (T,wt=11): 1919 member(f24(c4),c4) | member(c3,A) | power_set(B) != A. [resolve(1855,a,231,b)]. given #845 (A,wt=16): 459 empty(A) | member(f24(A),B) | -member(f9(B,A),A) | member(f10(B,A),A). [resolve(265,b,227,b)]. given #846 (T,wt=11): 1940 member(c3,power_set(A)) | member(f24(c4),B) | c4 != B. [resolve(1855,b,231,b)]. given #847 (T,wt=11): 2007 ilf_type(c3,binary_relation_type) | member(f25(f17(c3)),A) | c2 != A. [resolve(1985,b,231,b)]. given #848 (T,wt=11): 2019 ilf_type(c3,binary_relation_type) | empty(c2) | ilf_type(f25(f17(c3)),member_type(c2)). [resolve(1985,b,212,c)]. given #849 (T,wt=11): 2059 member(f14(A,B),A) | member(A,power_set(C)) | -empty(B). [resolve(299,a,206,a)]. given #850 (A,wt=16): 461 empty(A) | member(f24(A),B) | member(f11(A,B),A) | -member(f12(A,B),A). [resolve(265,b,225,b)]. given #851 (T,wt=11): 2128 ilf_type(c3,binary_relation_type) | member(f24(c2),A) | -member(c2,power_set(A)). [resolve(2023,b,214,a)]. given #852 (T,wt=11): 2169 member(f14(A,B),A) | empty(A) | member(f24(B),B). [resolve(300,a,205,a)]. given #853 (T,wt=11): 2223 ilf_type(f6(c4),binary_relation_type) | member(f24(f6(c4)),cross_product(c2,c3)). [resolve(671,a,750,a)]. given #854 (T,wt=11): 2224 ilf_type(f6(domain_of(c4)),binary_relation_type) | member(f24(f6(domain_of(c4))),c2). [resolve(671,a,600,a)]. given #855 (A,wt=16): 462 empty(A) | member(f24(A),B) | member(f11(A,B),A) | member(f12(A,B),B). [resolve(265,b,224,b)]. Low Water (keep): wt=30.000, iters=6720 given #856 (T,wt=11): 2225 ilf_type(f6(range_of(c4)),binary_relation_type) | member(f24(f6(range_of(c4))),c3). [resolve(671,a,580,a)]. given #857 (T,wt=11): 2226 ilf_type(f6(f6(A)),binary_relation_type) | member(f24(f6(f6(A))),A). [resolve(671,a,528,a)]. given #858 (T,wt=11): 2340 ilf_type(f6(A),binary_relation_type) | member(f24(A),B) | A != B. [resolve(2254,b,231,b)]. given #859 (T,wt=11): 2345 ilf_type(f6(A),binary_relation_type) | member(f24(A),B) | B != A. [resolve(2254,b,226,b)]. given #860 (A,wt=16): 463 empty(A) | member(f24(A),B) | -member(f11(A,B),B) | -member(f12(A,B),A). [resolve(265,b,223,b)]. given #861 (T,wt=11): 2360 ilf_type(f6(c4),binary_relation_type) | member(f17(f6(c4)),cross_product(c2,c3)). [resolve(676,a,750,a)]. given #862 (T,wt=11): 2361 ilf_type(f6(domain_of(c4)),binary_relation_type) | member(f17(f6(domain_of(c4))),c2). [resolve(676,a,600,a)]. Low Water (keep): wt=29.000, iters=6698 given #863 (T,wt=11): 2362 ilf_type(f6(range_of(c4)),binary_relation_type) | member(f17(f6(range_of(c4))),c3). [resolve(676,a,580,a)]. given #864 (T,wt=11): 2363 ilf_type(f6(f6(A)),binary_relation_type) | member(f17(f6(f6(A))),A). [resolve(676,a,528,a)]. given #865 (A,wt=16): 464 empty(A) | member(f24(A),B) | -member(f11(A,B),B) | member(f12(A,B),B). [resolve(265,b,222,b)]. given #866 (T,wt=11): 2409 member(f13(c2,A),c2) | member(f24(c2),A) | empty(c3). [resolve(302,b,1309,b)]. given #867 (T,wt=9): 14058 member(f13(c2,A),c2) | empty(c3) | -empty(A). [resolve(2409,b,206,a)]. given #868 (T,wt=11): 2426 member(f13(c4,A),c4) | member(f24(c4),A) | empty(c3). [resolve(302,b,696,b)]. given #869 (T,wt=9): 14137 member(f13(c4,A),c4) | empty(c3) | -empty(A). [resolve(2426,b,206,a)]. given #870 (A,wt=18): 470 empty(A) | ordered_pair(f20(A,f24(A)),f21(A,f24(A))) = f24(A) | member(f22(A),A). [resolve(265,b,209,a)]. Low Water (keep): wt=28.000, iters=6705 given #871 (T,wt=11): 2434 member(f13(power_set(c2),A),power_set(c2)) | member(domain_of(c4),A). [resolve(302,b,588,a)]. given #872 (T,wt=9): 14239 member(f13(power_set(c2),A),power_set(c2)) | -empty(A). [resolve(2434,b,206,a)]. given #873 (T,wt=11): 2435 member(f13(power_set(c3),A),power_set(c3)) | member(range_of(c4),A). [resolve(302,b,568,a)]. given #874 (T,wt=9): 14325 member(f13(power_set(c3),A),power_set(c3)) | -empty(A). [resolve(2435,b,206,a)]. given #875 (A,wt=20): 471 empty(A) | ordered_pair(f20(A,f24(A)),f21(A,f24(A))) = f24(A) | f22(A) != ordered_pair(B,C). [resolve(265,b,208,a)]. given #876 (T,wt=11): 2438 member(f13(power_set(A),B),power_set(A)) | member(f6(A),B). [resolve(302,b,499,a)]. given #877 (T,wt=9): 14410 member(f13(power_set(A),B),power_set(A)) | -empty(B). [resolve(2438,b,206,a)]. given #878 (T,wt=11): 2456 member(f13(A,B),A) | member(f16(A),B) | empty(A). [resolve(302,b,275,b)]. given #879 (T,wt=9): 14522 member(f13(A,B),A) | empty(A) | -empty(B). [resolve(2456,b,206,a)]. given #880 (A,wt=20): 472 empty(A) | -ilf_type(A,subset_type(cross_product(B,C))) | ordered_pair(f18(A,f24(A)),f19(A,f24(A))) = f24(A). [resolve(265,b,131,b)]. given #881 (T,wt=11): 2461 member(f13(A,B),A) | member(f24(A),B) | empty(A). [resolve(302,b,265,b)]. Low Water (keep): wt=27.000, iters=6687 given #882 (T,wt=11): 2467 member(f13(A,B),A) | member(f23(A),B) | empty(A). [resolve(302,b,207,b)]. given #883 (T,wt=11): 2497 ilf_type(range_of(c4),binary_relation_type) | member(f24(c3),A) | c3 != A. [resolve(2486,b,231,b)]. given #884 (T,wt=11): 2564 ilf_type(domain_of(c4),binary_relation_type) | member(f24(c2),A) | c2 != A. [resolve(2554,b,231,b)]. given #885 (A,wt=20): 473 empty(A) | ordered_pair(f18(A,f24(A)),f19(A,f24(A))) = f24(A) | f17(A) != ordered_pair(B,C). [resolve(265,b,127,a)]. given #886 (T,wt=11): 2602 ilf_type(c4,member_type(power_set(A))) | member(f24(c4),cross_product(c2,c3)). [resolve(910,a,750,a)]. given #887 (T,wt=9): 14756 ilf_type(c4,member_type(power_set(A))) | -empty(cross_product(c2,c3)). [resolve(2602,b,206,a)]. given #888 (T,wt=11): 2603 ilf_type(domain_of(c4),member_type(power_set(A))) | member(f24(domain_of(c4)),c2). [resolve(910,a,600,a)]. given #889 (T,wt=11): 2604 ilf_type(range_of(c4),member_type(power_set(A))) | member(f24(range_of(c4)),c3). [resolve(910,a,580,a)]. given #890 (A,wt=18): 474 empty(A) | ordered_pair(f18(A,f24(A)),f19(A,f24(A))) = f24(A) | member(f17(A),A). [resolve(265,b,125,a)]. given #891 (T,wt=11): 2605 ilf_type(f6(A),member_type(power_set(B))) | member(f24(f6(A)),A). [resolve(910,a,528,a)]. given #892 (T,wt=11): 2642 member(f5(A,B),C) | power_set(cross_product(B,A)) != C. [resolve(2638,a,231,b)]. given #893 (T,wt=11): 2687 ilf_type(c3,binary_relation_type) | member(f24(range_of(c4)),A) | c3 != A. [resolve(2661,b,231,b)]. given #894 (T,wt=11): 2779 empty(f6(domain_of(c4))) | member(f24(c2),A) | c2 != A. [resolve(2769,b,231,b)]. given #895 (A,wt=17): 475 empty(A) | ordered_pair(f18(A,f24(A)),f19(A,f24(A))) = f24(A) | -ilf_type(A,binary_relation_type). [resolve(265,b,123,a)]. given #896 (T,wt=11): 2824 empty(f6(range_of(c4))) | member(f24(c3),A) | c3 != A. [resolve(2813,b,231,b)]. given #897 (T,wt=11): 2845 empty(f6(f6(c4))) | member(f24(f6(c4)),cross_product(c2,c3)). [resolve(1118,b,750,a)]. given #898 (T,wt=11): 2846 empty(f6(f6(domain_of(c4)))) | member(f24(f6(domain_of(c4))),c2). [resolve(1118,b,600,a)]. given #899 (T,wt=11): 2847 empty(f6(f6(range_of(c4)))) | member(f24(f6(range_of(c4))),c3). [resolve(1118,b,580,a)]. Low Water (keep): wt=26.000, iters=6670 given #900 (A,wt=17): 477 empty(range_of(A)) | -ilf_type(A,binary_relation_type) | member(ordered_pair(f1(A,f16(range_of(A))),f16(range_of(A))),A). [resolve(275,b,254,c)]. given #901 (T,wt=11): 2848 empty(f6(f6(f6(A)))) | member(f24(f6(f6(A))),A). [resolve(1118,b,528,a)]. given #902 (T,wt=11): 2896 empty(f6(f6(A))) | member(f24(A),B) | A != B. [resolve(2877,b,231,b)]. given #903 (T,wt=11): 2901 empty(f6(f6(A))) | member(f24(A),B) | B != A. [resolve(2877,b,226,b)]. given #904 (T,wt=11): 3044 empty(f6(c4)) | member(f24(cross_product(c2,c3)),cross_product(c2,c3)). [resolve(1332,a,205,a)]. given #905 (A,wt=16): 479 empty(A) | member(f16(A),B) | member(f9(B,A),B) | -member(f10(B,A),B). [resolve(275,b,230,b)]. given #906 (T,wt=11): 3066 ilf_type(c3,binary_relation_type) | member(f24(cross_product(c2,c3)),cross_product(c2,c3)). [resolve(1337,a,205,a)]. given #907 (T,wt=11): 3308 member(domain_of(f6(cross_product(A,B))),C) | power_set(A) != C. [resolve(3215,a,231,b)]. given #908 (T,wt=11): 3332 member(range_of(f6(cross_product(A,B))),C) | power_set(B) != C. [resolve(3327,a,231,b)]. given #909 (T,wt=11): 3355 ilf_type(c3,member_type(power_set(A))) | member(f24(c4),cross_product(c2,c3)). [resolve(1932,a,750,a)]. given #910 (A,wt=16): 480 empty(A) | member(f16(A),B) | member(f9(B,A),B) | member(f10(B,A),A). [resolve(275,b,229,b)]. given #911 (T,wt=9): 14989 ilf_type(c3,member_type(power_set(A))) | -empty(cross_product(c2,c3)). [resolve(3355,b,206,a)]. given #912 (T,wt=11): 3411 ilf_type(c3,binary_relation_type) | member(f24(domain_of(c4)),A) | c2 != A. [resolve(3390,b,231,b)]. given #913 (T,wt=11): 3423 ilf_type(c3,binary_relation_type) | empty(c2) | ilf_type(f24(domain_of(c4)),member_type(c2)). [resolve(3390,b,212,c)]. given #914 (T,wt=11): 3434 member(c4,power_set(A)) | member(f14(c4,A),cross_product(c2,c3)). [resolve(2053,a,750,a)]. given #915 (A,wt=16): 481 empty(A) | member(f16(A),B) | -member(f9(B,A),A) | -member(f10(B,A),B). [resolve(275,b,228,b)]. given #916 (T,wt=11): 3435 member(domain_of(c4),power_set(A)) | member(f14(domain_of(c4),A),c2). [resolve(2053,a,600,a)]. given #917 (T,wt=11): 3436 member(range_of(c4),power_set(A)) | member(f14(range_of(c4),A),c3). [resolve(2053,a,580,a)]. given #918 (T,wt=11): 3437 member(f6(A),power_set(B)) | member(f14(f6(A),B),A). [resolve(2053,a,528,a)]. given #919 (T,wt=11): 3521 member(A,B) | ilf_type(f14(power_set(A),B),member_type(power_set(A))). [resolve(438,b,212,c),unit_del(b,213)]. given #920 (A,wt=16): 482 empty(A) | member(f16(A),B) | -member(f9(B,A),A) | member(f10(B,A),A). [resolve(275,b,227,b)]. given #921 (T,wt=10): 15286 ilf_type(f14(power_set(A),B),member_type(power_set(A))) | -empty(B). [resolve(3521,a,206,a)]. given #922 (T,wt=11): 3575 empty(c3) | member(ordered_pair(f2(c4,f24(c3)),f24(c3)),c4). [resolve(476,b,253,c),unit_del(b,540)]. given #923 (T,wt=9): 15305 empty(c3) | member(f2(c4,f24(c3)),domain_of(c4)). [resolve(3575,b,252,b),unit_del(b,540)]. given #924 (T,wt=8): 15319 empty(c3) | member(f2(c4,f24(c3)),c2). [resolve(15305,b,600,a)]. given #925 (A,wt=16): 484 empty(A) | member(f16(A),B) | member(f11(A,B),A) | -member(f12(A,B),A). [resolve(275,b,225,b)]. given #926 (T,wt=11): 3597 empty(c3) | member(ordered_pair(f1(c4,f24(c3)),f24(c3)),c4). [resolve(3574,b,254,c),unit_del(b,540)]. given #927 (T,wt=9): 15356 empty(c3) | member(f1(c4,f24(c3)),domain_of(c4)). [resolve(3597,b,252,b),unit_del(b,540)]. given #928 (T,wt=8): 15370 empty(c3) | member(f1(c4,f24(c3)),c2). [resolve(15356,b,600,a)]. given #929 (T,wt=11): 3609 empty(c3) | member(f24(c3),A) | -member(range_of(c4),power_set(A)). [resolve(3574,b,214,a)]. given #930 (A,wt=16): 485 empty(A) | member(f16(A),B) | member(f11(A,B),A) | member(f12(A,B),B). [resolve(275,b,224,b)]. given #931 (T,wt=11): 3619 empty(c3) | member(f25(f24(c3)),A) | domain_of(c4) != A. [resolve(3576,b,231,b)]. given #932 (T,wt=11): 3654 empty(c3) | member(f25(f24(c3)),A) | -member(c2,power_set(A)). [resolve(3617,b,214,a)]. given #933 (T,wt=11): 3698 empty(c3) | member(ordered_pair(f2(c4,f16(c3)),f16(c3)),c4). [resolve(498,b,253,c),unit_del(b,540)]. given #934 (T,wt=9): 15475 empty(c3) | member(f2(c4,f16(c3)),domain_of(c4)). [resolve(3698,b,252,b),unit_del(b,540)]. given #935 (A,wt=16): 486 empty(A) | member(f16(A),B) | -member(f11(A,B),B) | -member(f12(A,B),A). [resolve(275,b,223,b)]. given #936 (T,wt=8): 15489 empty(c3) | member(f2(c4,f16(c3)),c2). [resolve(15475,b,600,a)]. given #937 (T,wt=11): 3720 empty(c3) | member(ordered_pair(f1(c4,f16(c3)),f16(c3)),c4). [resolve(3697,b,254,c),unit_del(b,540)]. given #938 (T,wt=9): 15526 empty(c3) | member(f1(c4,f16(c3)),domain_of(c4)). [resolve(3720,b,252,b),unit_del(b,540)]. given #939 (T,wt=8): 15540 empty(c3) | member(f1(c4,f16(c3)),c2). [resolve(15526,b,600,a)]. given #940 (A,wt=16): 487 empty(A) | member(f16(A),B) | -member(f11(A,B),B) | member(f12(A,B),B). [resolve(275,b,222,b)]. given #941 (T,wt=11): 3732 empty(c3) | member(f16(c3),A) | -member(range_of(c4),power_set(A)). [resolve(3697,b,214,a)]. given #942 (T,wt=11): 3733 empty(c3) | empty(range_of(c4)) | ilf_type(f16(c3),member_type(range_of(c4))). [resolve(3697,b,212,c)]. given #943 (T,wt=11): 3746 empty(c3) | member(f25(f16(c3)),A) | domain_of(c4) != A. [resolve(3699,b,231,b)]. given #944 (T,wt=11): 3777 empty(c3) | member(f25(f16(c3)),A) | -member(c2,power_set(A)). [resolve(3744,b,214,a)]. given #945 (A,wt=18): 492 empty(A) | ordered_pair(f20(A,f16(A)),f21(A,f16(A))) = f16(A) | member(f22(A),A). [resolve(275,b,209,a)]. Low Water (keep): wt=25.000, iters=6681 given #946 (T,wt=11): 4216 empty(f23(power_set(A))) | member(f24(A),B) | A != B. [resolve(4106,b,231,b)]. given #947 (T,wt=11): 4221 empty(f23(power_set(A))) | member(f24(A),B) | B != A. [resolve(4106,b,226,b)]. given #948 (T,wt=11): 4380 member(f24(c2),c2) | -member(A,domain_of(c4)) | member(A,B). [resolve(4363,a,214,c)]. given #949 (T,wt=11): 4466 member(f24(c3),c3) | -member(A,range_of(c4)) | member(A,B). [resolve(4444,a,214,c)]. given #950 (A,wt=20): 493 empty(A) | ordered_pair(f20(A,f16(A)),f21(A,f16(A))) = f16(A) | f22(A) != ordered_pair(B,C). [resolve(275,b,208,a)]. given #951 (T,wt=10): 15739 member(f24(c3),c3) | member(f3(range_of(c4),c3),A). [factor(15723,a,d),unit_del(c,260)]. given #952 (T,wt=4): 15779 member(f24(c3),c3). [factor(15776,a,b)]. Low Water (keep): wt=22.000, iters=10202 Low Water (keep): wt=19.000, iters=7112 given #953 (T,wt=4): 16800 member(f24(c2),c2). [back_unit_del(1309),unit_del(a,15798)]. given #954 (T,wt=4): 16878 member(f24(c4),c4). [back_unit_del(696),unit_del(a,15798)]. given #955 (A,wt=20): 494 empty(A) | -ilf_type(A,subset_type(cross_product(B,C))) | ordered_pair(f18(A,f16(A)),f19(A,f16(A))) = f16(A). [resolve(275,b,131,b)]. given #956 (F,wt=2): 15798 -empty(c3). [resolve(15779,a,206,a)]. given #957 (F,wt=2): 16801 -empty(c2). [back_unit_del(1308),unit_del(a,15798)]. given #958 (F,wt=2): 16879 -empty(c4). [back_unit_del(695),unit_del(a,15798)]. given #959 (F,wt=3): 16822 -empty(domain_of(c4)). [back_unit_del(1238),unit_del(a,15798)]. given #960 (T,wt=5): 15781 member(f24(c3),range_of(c4)). [resolve(15779,a,5583,a)]. given #961 (T,wt=5): 16545 member(f25(f16(c3)),c2). [back_unit_del(3744),unit_del(a,15798)]. given #962 (T,wt=5): 16583 member(f16(c3),range_of(c4)). [back_unit_del(3697),unit_del(a,15798)]. given #963 (T,wt=4): 17104 member(f16(c3),c3). [resolve(16583,a,580,a)]. given #964 (A,wt=20): 495 empty(A) | ordered_pair(f18(A,f16(A)),f19(A,f16(A))) = f16(A) | f17(A) != ordered_pair(B,C). [resolve(275,b,127,a)]. given #965 (F,wt=3): 16844 -empty(range_of(c4)). [back_unit_del(863),unit_del(a,15798)]. given #966 (F,wt=4): 16680 -empty(cross_product(c2,c3)). [back_unit_del(1875),unit_del(a,15798)]. given #967 (T,wt=5): 16626 member(f25(f24(c3)),c2). [back_unit_del(3617),unit_del(a,15798)]. given #968 (T,wt=5): 16733 member(f24(domain_of(c4)),c2). [back_unit_del(1797),unit_del(a,15798)]. given #969 (T,wt=5): 16773 member(f24(range_of(c4)),c3). [back_unit_del(1725),unit_del(a,15798)]. given #970 (T,wt=5): 16838 member(f25(f23(c3)),c2). [back_unit_del(1222),unit_del(a,15798)]. given #971 (A,wt=18): 496 empty(A) | ordered_pair(f18(A,f16(A)),f19(A,f16(A))) = f16(A) | member(f17(A),A). [resolve(275,b,125,a)]. given #972 (T,wt=5): 16895 member(f23(c3),range_of(c4)). [back_unit_del(677),unit_del(a,15798)]. given #973 (T,wt=4): 17136 member(f23(c3),c3). [resolve(16895,a,580,a)]. given #974 (T,wt=5): 16989 member(f23(domain_of(c4)),c2). [back_unit_del(774),unit_del(b,16822)]. given #975 (T,wt=5): 16990 member(f16(domain_of(c4)),c2). [back_unit_del(767),unit_del(b,16822)]. given #976 (A,wt=17): 497 empty(A) | ordered_pair(f18(A,f16(A)),f19(A,f16(A))) = f16(A) | -ilf_type(A,binary_relation_type). [resolve(275,b,123,a)]. given #977 (T,wt=5): 17058 member(f23(range_of(c4)),c3). [back_unit_del(765),unit_del(b,16844)]. given #978 (T,wt=5): 17059 member(f16(range_of(c4)),c3). [back_unit_del(758),unit_del(b,16844)]. given #979 (T,wt=5): 17101 ilf_type(f24(c2),member_type(c2)). [resolve(16800,a,212,c),unit_del(a,16801)]. given #980 (T,wt=5): 17102 ilf_type(f24(c4),member_type(c4)). [resolve(16878,a,212,c),unit_del(a,16879)]. given #981 (A,wt=18): 500 ilf_type(range_of(A),binary_relation_type) | -ilf_type(A,binary_relation_type) | member(ordered_pair(f1(A,f24(range_of(A))),f24(range_of(A))),A). [resolve(264,a,254,c)]. given #982 (T,wt=5): 17118 ilf_type(f16(c3),member_type(c3)). [resolve(17104,a,212,c),unit_del(a,15798)]. given #983 (T,wt=5): 17150 ilf_type(f23(c3),member_type(c3)). [resolve(17136,a,212,c),unit_del(a,15798)]. given #984 (T,wt=6): 15775 member(f24(c3),c3) | -empty(A). [resolve(15739,b,206,a)]. given #985 (T,wt=6): 15845 member(f1(c4,f16(c3)),c2). [back_unit_del(15540),unit_del(a,15798)]. given #986 (A,wt=17): 502 ilf_type(A,binary_relation_type) | member(f24(A),B) | member(f9(B,A),B) | -member(f10(B,A),B). [resolve(264,a,230,b)]. given #987 (T,wt=6): 15893 member(f2(c4,f16(c3)),c2). [back_unit_del(15489),unit_del(a,15798)]. given #988 (T,wt=6): 15949 member(f1(c4,f24(c3)),c2). [back_unit_del(15370),unit_del(a,15798)]. given #989 (T,wt=6): 15997 member(f2(c4,f24(c3)),c2). [back_unit_del(15319),unit_del(a,15798)]. given #990 (T,wt=6): 16329 member(f1(c4,f23(c3)),c2). [back_unit_del(11068),unit_del(a,15798)]. given #991 (A,wt=17): 503 ilf_type(A,binary_relation_type) | member(f24(A),B) | member(f9(B,A),B) | member(f10(B,A),A). [resolve(264,a,229,b)]. given #992 (T,wt=6): 16458 member(f2(c4,f23(c3)),c2). [back_unit_del(10786),unit_del(a,15798)]. given #993 (T,wt=6): 16581 member(f25(f16(c3)),domain_of(c4)). [back_unit_del(3699),unit_del(a,15798)]. given #994 (T,wt=6): 16661 member(f25(f24(c3)),domain_of(c4)). [back_unit_del(3576),unit_del(a,15798)]. given #995 (T,wt=6): 16741 ilf_type(f24(range_of(c4)),member_type(c3)). [back_unit_del(1757),unit_del(a,15798)]. given #996 (A,wt=17): 504 ilf_type(A,binary_relation_type) | member(f24(A),B) | -member(f9(B,A),A) | -member(f10(B,A),B). [resolve(264,a,228,b)]. given #997 (T,wt=6): 16777 member(f24(c4),cross_product(c2,c3)). [back_unit_del(1333),unit_del(b,15798)]. given #998 (T,wt=6): 16804 ilf_type(f25(f23(c3)),member_type(c2)). [back_unit_del(1305),unit_del(a,15798),unit_del(b,16801)]. given #999 (T,wt=6): 16821 member(f24(domain_of(c4)),domain_of(c4)). [back_unit_del(1239),unit_del(a,15798)]. given #1000 (T,wt=6): 16843 member(f24(range_of(c4)),range_of(c4)). [back_unit_del(864),unit_del(a,15798)]. given #1001 (A,wt=17): 505 ilf_type(A,binary_relation_type) | member(f24(A),B) | -member(f9(B,A),A) | member(f10(B,A),A). [resolve(264,a,227,b)]. given #1002 (T,wt=6): 16847 ilf_type(f23(c3),member_type(range_of(c4))). [back_unit_del(860),unit_del(a,15798),unit_del(b,16844)]. given #1003 (T,wt=6): 16893 member(f25(f23(c3)),domain_of(c4)). [back_unit_del(679),unit_del(a,15798)]. given #1004 (T,wt=6): 16909 ilf_type(f24(domain_of(c4)),member_type(c2)). [back_unit_del(16702),unit_del(a,16801)]. given #1005 (T,wt=6): 16910 ilf_type(f25(f24(c3)),member_type(c2)). [back_unit_del(16592),unit_del(a,16801)]. given #1006 (A,wt=17): 507 ilf_type(A,binary_relation_type) | member(f24(A),B) | member(f11(A,B),A) | -member(f12(A,B),A). [resolve(264,a,225,b)]. given #1007 (T,wt=6): 16911 ilf_type(f25(f16(c3)),member_type(c2)). [back_unit_del(16511),unit_del(a,16801)]. given #1008 (T,wt=6): 16933 ilf_type(f23(domain_of(c4)),member_type(c2)). [back_unit_del(1592),unit_del(a,16822),unit_del(b,16801)]. given #1009 (T,wt=6): 16934 ilf_type(f16(domain_of(c4)),member_type(c2)). [back_unit_del(1523),unit_del(a,16822),unit_del(b,16801)]. given #1010 (T,wt=6): 16991 ilf_type(f16(range_of(c4)),member_type(c3)). [back_unit_del(16775),unit_del(a,16844)]. given #1011 (A,wt=17): 508 ilf_type(A,binary_relation_type) | member(f24(A),B) | member(f11(A,B),A) | member(f12(A,B),B). [resolve(264,a,224,b)]. given #1012 (T,wt=6): 16992 ilf_type(f23(range_of(c4)),member_type(c3)). [back_unit_del(16774),unit_del(a,16844)]. given #1013 (T,wt=6): 16993 ilf_type(f16(c3),member_type(range_of(c4))). [back_unit_del(16552),unit_del(a,16844)]. given #1014 (T,wt=6): 17023 ilf_type(f24(c3),member_type(range_of(c4))). [back_unit_del(5770),unit_del(a,16844)]. given #1015 (T,wt=6): 17097 member(f16(c4),cross_product(c2,c3)). [back_unit_del(1339),unit_del(b,16879)]. given #1016 (A,wt=17): 509 ilf_type(A,binary_relation_type) | member(f24(A),B) | -member(f11(A,B),B) | -member(f12(A,B),A). [resolve(264,a,223,b)]. given #1017 (T,wt=6): 17098 member(f23(c4),cross_product(c2,c3)). [back_unit_del(956),unit_del(b,16879)]. given #1018 (T,wt=6): 17168 member(f23(range_of(c4)),range_of(c4)). [resolve(17058,a,5583,a)]. given #1019 (T,wt=6): 17174 member(f16(range_of(c4)),range_of(c4)). [resolve(17059,a,5583,a)]. given #1020 (T,wt=7): 15784 member(f24(c3),A) | c3 != A. [resolve(15779,a,231,b)]. given #1021 (A,wt=17): 510 ilf_type(A,binary_relation_type) | member(f24(A),B) | -member(f11(A,B),B) | member(f12(A,B),B). [resolve(264,a,222,b)]. given #1022 (T,wt=7): 15859 member(f1(c4,f16(c3)),domain_of(c4)). [back_unit_del(15526),unit_del(a,15798)]. given #1023 (T,wt=7): 15907 member(f2(c4,f16(c3)),domain_of(c4)). [back_unit_del(15475),unit_del(a,15798)]. given #1024 (T,wt=7): 15963 member(f1(c4,f24(c3)),domain_of(c4)). [back_unit_del(15356),unit_del(a,15798)]. given #1025 (T,wt=7): 16011 member(f2(c4,f24(c3)),domain_of(c4)). [back_unit_del(15305),unit_del(a,15798)]. given #1026 (A,wt=12): 511 ilf_type(A,binary_relation_type) | member(f24(A),B) | member(f14(A,B),A). [resolve(264,a,218,a)]. given #1027 (T,wt=7): 16045 member(f13(c4,A),c4) | -empty(A). [back_unit_del(14137),unit_del(b,15798)]. given #1028 (T,wt=7): 16120 member(f13(c2,A),c2) | -empty(A). [back_unit_del(14058),unit_del(b,15798)]. given #1029 (T,wt=7): 16233 member(f14(c2,A),c2) | -empty(A). [back_unit_del(12779),unit_del(a,15798)]. given #1030 (T,wt=7): 16343 member(f1(c4,f23(c3)),domain_of(c4)). [back_unit_del(11048),unit_del(a,15798)]. given #1031 (A,wt=12): 512 ilf_type(A,binary_relation_type) | member(f24(A),B) | -member(f14(A,B),B). [resolve(264,a,217,a)]. given #1032 (T,wt=7): 16374 member(f14(c4,A),c4) | -empty(A). [back_unit_del(10875),unit_del(a,15798)]. given #1033 (T,wt=7): 16472 member(f2(c4,f23(c3)),domain_of(c4)). [back_unit_del(10762),unit_del(a,15798)]. given #1034 (T,wt=7): 16683 ilf_type(f24(c4),member_type(cross_product(c2,c3))). [back_unit_del(1872),unit_del(a,15798),unit_del(b,16680)]. given #1035 (T,wt=7): 16795 member(f24(c2),A) | c2 != A. [back_unit_del(1314),unit_del(a,15798)]. given #1036 (A,wt=19): 514 ilf_type(A,binary_relation_type) | ordered_pair(f20(A,f24(A)),f21(A,f24(A))) = f24(A) | member(f22(A),A). [resolve(264,a,209,a)]. given #1037 (T,wt=7): 16825 ilf_type(f25(f23(c3)),member_type(domain_of(c4))). [back_unit_del(1235),unit_del(a,15798),unit_del(b,16822)]. given #1038 (T,wt=7): 16876 member(f24(c4),A) | c4 != A. [back_unit_del(701),unit_del(a,15798)]. given #1039 (T,wt=7): 16907 ilf_type(f16(c4),member_type(cross_product(c2,c3))). [back_unit_del(1893),unit_del(a,16879),unit_del(b,16680)]. given #1040 (T,wt=7): 16908 ilf_type(f23(c4),member_type(cross_product(c2,c3))). [back_unit_del(1788),unit_del(a,16879),unit_del(b,16680)]. given #1041 (A,wt=21): 515 ilf_type(A,binary_relation_type) | ordered_pair(f20(A,f24(A)),f21(A,f24(A))) = f24(A) | f22(A) != ordered_pair(B,C). [resolve(264,a,208,a)]. given #1042 (T,wt=7): 16912 ilf_type(f2(c4,f23(c3)),member_type(c2)). [back_unit_del(16429),unit_del(a,16801)]. given #1043 (T,wt=7): 16913 ilf_type(f1(c4,f23(c3)),member_type(c2)). [back_unit_del(16300),unit_del(a,16801)]. given #1044 (T,wt=7): 16916 ilf_type(f2(c4,f24(c3)),member_type(c2)). [back_unit_del(15969),unit_del(a,16801)]. given #1045 (T,wt=7): 16917 ilf_type(f1(c4,f24(c3)),member_type(c2)). [back_unit_del(15921),unit_del(a,16801)]. given #1046 (A,wt=16): 518 member(f6(A),B) | member(f9(B,power_set(A)),B) | -member(f10(B,power_set(A)),B). [resolve(499,a,230,b)]. given #1047 (T,wt=7): 16919 ilf_type(f2(c4,f16(c3)),member_type(c2)). [back_unit_del(15865),unit_del(a,16801)]. given #1048 (T,wt=7): 16920 ilf_type(f1(c4,f16(c3)),member_type(c2)). [back_unit_del(15817),unit_del(a,16801)]. given #1049 (T,wt=7): 16935 ilf_type(f25(f24(c3)),member_type(domain_of(c4))). [back_unit_del(16612),unit_del(a,16822)]. given #1050 (T,wt=7): 16936 ilf_type(f25(f16(c3)),member_type(domain_of(c4))). [back_unit_del(16531),unit_del(a,16822)]. given #1051 (A,wt=17): 519 member(f6(A),B) | member(f9(B,power_set(A)),B) | member(f10(B,power_set(A)),power_set(A)). [resolve(499,a,229,b)]. given #1052 (T,wt=7): 17106 member(f16(c3),A) | c3 != A. [resolve(17104,a,231,b)]. given #1053 (T,wt=7): 17138 member(f23(c3),A) | c3 != A. [resolve(17136,a,231,b)]. given #1054 (T,wt=7): 17226 ilf_type(f24(domain_of(c4)),member_type(domain_of(c4))). [resolve(16821,a,212,c),unit_del(a,16822)]. given #1055 (T,wt=7): 17227 ilf_type(f24(range_of(c4)),member_type(range_of(c4))). [resolve(16843,a,212,c),unit_del(a,16844)]. given #1056 (A,wt=17): 520 member(f6(A),B) | -member(f9(B,power_set(A)),power_set(A)) | -member(f10(B,power_set(A)),B). [resolve(499,a,228,b)]. given #1057 (T,wt=7): 17304 ilf_type(f23(range_of(c4)),member_type(range_of(c4))). [resolve(17168,a,212,c),unit_del(a,16844)]. given #1058 (T,wt=7): 17324 ilf_type(f16(range_of(c4)),member_type(range_of(c4))). [resolve(17174,a,212,c),unit_del(a,16844)]. given #1059 (T,wt=8): 15759 member(f3(range_of(c4),c3),A) | -empty(c3). [resolve(15739,a,206,a)]. given #1060 (T,wt=8): 15776 member(f24(c3),c3) | member(f24(A),A). [resolve(15739,b,205,a)]. given #1061 (A,wt=18): 521 member(f6(A),B) | -member(f9(B,power_set(A)),power_set(A)) | member(f10(B,power_set(A)),power_set(A)). [resolve(499,a,227,b)]. given #1062 (T,wt=8): 15780 member(f24(c2),c2) | member(f24(c3),A). [resolve(15779,a,13193,b)]. given #1063 (T,wt=8): 15782 member(f24(c4),c4) | member(f24(c3),A). [resolve(15779,a,1930,b)]. given #1064 (T,wt=8): 15795 member(f24(c3),A) | -member(c3,power_set(A)). [resolve(15779,a,214,a)]. given #1065 (T,wt=8): 15803 member(ordered_pair(f25(f24(c3)),f24(c3)),c4). [resolve(15779,a,116,a)]. given #1066 (A,wt=18): 522 member(f6(A),B) | member(f11(power_set(A),B),power_set(A)) | -member(f12(power_set(A),B),power_set(A)). [resolve(499,a,225,b)]. given #1067 (T,wt=8): 16523 member(f25(f16(c3)),A) | c2 != A. [back_unit_del(3766),unit_del(a,15798)]. given #1068 (T,wt=8): 16564 member(f16(c3),A) | range_of(c4) != A. [back_unit_del(3721),unit_del(a,15798)]. given #1069 (T,wt=8): 16604 member(f25(f24(c3)),A) | c2 != A. [back_unit_del(3643),unit_del(a,15798)]. given #1070 (T,wt=8): 16644 member(f24(c3),A) | range_of(c4) != A. [back_unit_del(3598),unit_del(a,15798)]. given #1071 (A,wt=17): 523 member(f6(A),B) | member(f11(power_set(A),B),power_set(A)) | member(f12(power_set(A),B),B). [resolve(499,a,224,b)]. given #1072 (T,wt=8): 16679 member(f24(cross_product(c2,c3)),cross_product(c2,c3)). [back_unit_del(1876),unit_del(a,15798)]. given #1073 (T,wt=8): 16714 member(f24(domain_of(c4)),A) | c2 != A. [back_unit_del(1816),unit_del(a,15798)]. given #1074 (T,wt=8): 16753 member(f24(range_of(c4)),A) | c3 != A. [back_unit_del(1745),unit_del(a,15798)]. given #1075 (T,wt=8): 16784 member(f24(c2),A) | -member(c2,power_set(A)). [back_unit_del(1325),unit_del(a,15798)]. given #1076 (A,wt=17): 524 member(f6(A),B) | -member(f11(power_set(A),B),B) | -member(f12(power_set(A),B),power_set(A)). [resolve(499,a,223,b)]. given #1077 (T,wt=8): 16816 member(f25(f23(c3)),A) | c2 != A. [back_unit_del(1293),unit_del(a,15798)]. given #1078 (T,wt=8): 16859 member(f23(c3),A) | range_of(c4) != A. [back_unit_del(848),unit_del(a,15798)]. given #1079 (T,wt=8): 16865 member(f24(c4),A) | -member(c4,power_set(A)). [back_unit_del(712),unit_del(a,15798)]. given #1080 (T,wt=8): 16897 member(ordered_pair(f25(f16(c3)),f16(c3)),c4). [back_unit_del(498),unit_del(a,15798)]. given #1081 (A,wt=16): 525 member(f6(A),B) | -member(f11(power_set(A),B),B) | member(f12(power_set(A),B),B). [resolve(499,a,222,b)]. given #1082 (T,wt=8): 16898 member(ordered_pair(f25(f23(c3)),f23(c3)),c4). [back_unit_del(270),unit_del(a,15798)]. given #1083 (T,wt=8): 16937 ilf_type(f2(c4,f23(c3)),member_type(domain_of(c4))). [back_unit_del(16444),unit_del(a,16822)]. given #1084 (T,wt=8): 16938 ilf_type(f1(c4,f23(c3)),member_type(domain_of(c4))). [back_unit_del(16315),unit_del(a,16822)]. given #1085 (T,wt=8): 16939 ilf_type(f2(c4,f24(c3)),member_type(domain_of(c4))). [back_unit_del(15983),unit_del(a,16822)]. given #1086 (A,wt=20): 530 ordered_pair(f20(power_set(A),f6(A)),f21(power_set(A),f6(A))) = f6(A) | member(f22(power_set(A)),power_set(A)). [resolve(499,a,209,a)]. given #1087 (T,wt=8): 16940 ilf_type(f1(c4,f24(c3)),member_type(domain_of(c4))). [back_unit_del(15935),unit_del(a,16822)]. given #1088 (T,wt=8): 16941 ilf_type(f2(c4,f16(c3)),member_type(domain_of(c4))). [back_unit_del(15879),unit_del(a,16822)]. given #1089 (T,wt=8): 16942 ilf_type(f1(c4,f16(c3)),member_type(domain_of(c4))). [back_unit_del(15831),unit_del(a,16822)]. given #1090 (T,wt=8): 16975 member(f23(domain_of(c4)),A) | c2 != A. [back_unit_del(1580),unit_del(a,16822)]. given #1091 (A,wt=21): 531 ordered_pair(f20(power_set(A),f6(A)),f21(power_set(A),f6(A))) = f6(A) | f22(power_set(A)) != ordered_pair(B,C). [resolve(499,a,208,a)]. given #1092 (T,wt=8): 16988 member(f16(domain_of(c4)),A) | c2 != A. [back_unit_del(1511),unit_del(a,16822)]. given #1093 (T,wt=8): 17042 member(f23(range_of(c4)),A) | c3 != A. [back_unit_del(1491),unit_del(a,16844)]. given #1094 (T,wt=8): 17056 member(f16(range_of(c4)),A) | c3 != A. [back_unit_del(1430),unit_del(a,16844)]. given #1095 (T,wt=8): 17117 member(f16(c3),A) | -member(c3,power_set(A)). [resolve(17104,a,214,a)]. given #1096 (A,wt=21): 532 -ilf_type(power_set(A),subset_type(cross_product(B,C))) | ordered_pair(f18(power_set(A),f6(A)),f19(power_set(A),f6(A))) = f6(A). [resolve(499,a,131,b)]. given #1097 (T,wt=8): 17149 member(f23(c3),A) | -member(c3,power_set(A)). [resolve(17136,a,214,a)]. given #1098 (T,wt=9): 15783 member(f13(c3,A),c3) | member(f24(c3),A). [resolve(15779,a,302,b)]. given #1099 (T,wt=7): 17596 member(f13(c3,A),c3) | -empty(A). [resolve(15783,b,206,a)]. given #1100 (T,wt=9): 15793 member(f24(c3),A) | member(f14(c3,A),c3). [resolve(15779,a,218,a)]. given #1101 (A,wt=21): 533 ordered_pair(f18(power_set(A),f6(A)),f19(power_set(A),f6(A))) = f6(A) | f17(power_set(A)) != ordered_pair(B,C). [resolve(499,a,127,a)]. given #1102 (T,wt=7): 17651 member(f14(c3,A),c3) | -empty(A). [resolve(15793,a,206,a)]. given #1103 (T,wt=9): 15794 member(f24(c3),A) | -member(f14(c3,A),A). [resolve(15779,a,217,a)]. given #1104 (T,wt=9): 15829 member(f1(c4,f16(c3)),A) | c2 != A. [back_unit_del(15556),unit_del(a,15798)]. given #1105 (T,wt=9): 15877 member(f2(c4,f16(c3)),A) | c2 != A. [back_unit_del(15508),unit_del(a,15798)]. given #1106 (A,wt=20): 534 ordered_pair(f18(power_set(A),f6(A)),f19(power_set(A),f6(A))) = f6(A) | member(f17(power_set(A)),power_set(A)). [resolve(499,a,125,a)]. given #1107 (T,wt=9): 15933 member(f1(c4,f24(c3)),A) | c2 != A. [back_unit_del(15386),unit_del(a,15798)]. given #1108 (T,wt=9): 15981 member(f2(c4,f24(c3)),A) | c2 != A. [back_unit_del(15335),unit_del(a,15798)]. given #1109 (T,wt=9): 16044 member(f13(c4,A),c4) | member(f24(A),A). [back_unit_del(14138),unit_del(b,15798)]. given #1110 (T,wt=9): 16119 member(f13(c2,A),c2) | member(f24(A),A). [back_unit_del(14059),unit_del(b,15798)]. given #1111 (A,wt=18): 535 ordered_pair(f18(power_set(A),f6(A)),f19(power_set(A),f6(A))) = f6(A) | -ilf_type(power_set(A),binary_relation_type). [resolve(499,a,123,a)]. given #1112 (T,wt=9): 16232 member(f14(c2,A),c2) | member(f24(A),A). [back_unit_del(12780),unit_del(a,15798)]. given #1113 (T,wt=9): 16312 member(f1(c4,f23(c3)),A) | c2 != A. [back_unit_del(11090),unit_del(a,15798)]. given #1114 (T,wt=9): 16373 member(f14(c4,A),c4) | member(f24(A),A). [back_unit_del(10876),unit_del(a,15798)]. given #1115 (T,wt=9): 16441 member(f2(c4,f23(c3)),A) | c2 != A. [back_unit_del(10808),unit_del(a,15798)]. given #1116 (A,wt=27): 541 ilf_type(c3,binary_relation_type) | ordered_pair(f18(c4,ordered_pair(f25(f17(c3)),f17(c3))),f19(c4,ordered_pair(f25(f17(c3)),f17(c3)))) = ordered_pair(f25(f17(c3)),f17(c3)). [back_unit_del(425),unit_del(c,540)]. given #1117 (T,wt=9): 16512 member(f25(f16(c3)),A) | -member(c2,power_set(A)). [back_unit_del(3777),unit_del(a,15798)]. given #1118 (T,wt=9): 16543 member(f25(f16(c3)),A) | domain_of(c4) != A. [back_unit_del(3746),unit_del(a,15798)]. given #1119 (T,wt=9): 16553 member(f16(c3),A) | -member(range_of(c4),power_set(A)). [back_unit_del(3732),unit_del(a,15798)]. given #1120 (T,wt=9): 16565 member(ordered_pair(f1(c4,f16(c3)),f16(c3)),c4). [back_unit_del(3720),unit_del(a,15798)]. given #1121 (A,wt=12): 543 ilf_type(c3,binary_relation_type) | member(ordered_pair(f2(c4,f17(c3)),f17(c3)),c4). [back_unit_del(403),unit_del(b,540)]. given #1122 (T,wt=9): 16582 member(ordered_pair(f2(c4,f16(c3)),f16(c3)),c4). [back_unit_del(3698),unit_del(a,15798)]. given #1123 (T,wt=9): 16593 member(f25(f24(c3)),A) | -member(c2,power_set(A)). [back_unit_del(3654),unit_del(a,15798)]. given #1124 (T,wt=9): 16624 member(f25(f24(c3)),A) | domain_of(c4) != A. [back_unit_del(3619),unit_del(a,15798)]. given #1125 (T,wt=9): 16633 member(f24(c3),A) | -member(range_of(c4),power_set(A)). [back_unit_del(3609),unit_del(a,15798)]. given #1126 (A,wt=26): 545 empty(cross_product(A,B)) | ordered_pair(f18(cross_product(A,B),f23(cross_product(A,B))),f19(cross_product(A,B),f23(cross_product(A,B)))) = f23(cross_product(A,B)). [resolve(266,b,451,a)]. given #1127 (T,wt=9): 16645 member(ordered_pair(f1(c4,f24(c3)),f24(c3)),c4). [back_unit_del(3597),unit_del(a,15798)]. given #1128 (T,wt=9): 16662 member(ordered_pair(f2(c4,f24(c3)),f24(c3)),c4). [back_unit_del(3575),unit_del(a,15798)]. given #1129 (T,wt=9): 16669 member(f13(c4,A),c4) | member(f24(c4),A). [back_unit_del(2426),unit_del(c,15798)]. given #1130 (T,wt=9): 16673 member(f13(c2,A),c2) | member(f24(c2),A). [back_unit_del(2409),unit_del(c,15798)]. given #1131 (A,wt=38): 547 empty(f16(power_set(cross_product(A,B)))) | ordered_pair(f18(f16(power_set(cross_product(A,B))),f23(f16(power_set(cross_product(A,B))))),f19(f16(power_set(cross_product(A,B))),f23(f16(power_set(cross_product(A,B)))))) = f23(f16(power_set(cross_product(A,B)))). [resolve(266,b,360,a)]. given #1132 (T,wt=9): 16695 member(f24(c4),A) | cross_product(c2,c3) != A. [back_unit_del(1860),unit_del(a,15798)]. given #1133 (T,wt=9): 16703 member(f24(domain_of(c4)),A) | -member(c2,power_set(A)). [back_unit_del(1827),unit_del(a,15798)]. given #1134 (T,wt=9): 16732 member(f24(domain_of(c4)),A) | domain_of(c4) != A. [back_unit_del(1798),unit_del(a,15798)]. given #1135 (T,wt=9): 16742 member(f24(range_of(c4)),A) | -member(c3,power_set(A)). [back_unit_del(1756),unit_del(a,15798)]. given #1136 (A,wt=32): 548 empty(f6(cross_product(A,B))) | ordered_pair(f18(f6(cross_product(A,B)),f23(f6(cross_product(A,B)))),f19(f6(cross_product(A,B)),f23(f6(cross_product(A,B))))) = f23(f6(cross_product(A,B))). [resolve(266,b,236,a)]. given #1137 (T,wt=9): 16771 member(f24(range_of(c4)),A) | range_of(c4) != A. [back_unit_del(1727),unit_del(a,15798)]. given #1138 (T,wt=9): 16785 member(f24(c2),A) | -member(f14(c2,A),A). [back_unit_del(1324),unit_del(a,15798)]. given #1139 (T,wt=9): 16786 member(f24(c2),A) | member(f14(c2,A),c2). [back_unit_del(1323),unit_del(a,15798)]. given #1140 (T,wt=9): 16805 member(f25(f23(c3)),A) | -member(c2,power_set(A)). [back_unit_del(1304),unit_del(a,15798)]. given #1141 (A,wt=17): 550 member(f24(power_set(A)),B) | member(f9(B,power_set(A)),B) | -member(f10(B,power_set(A)),B). [resolve(444,a,230,b)]. given #1142 (T,wt=9): 16837 member(f25(f23(c3)),A) | domain_of(c4) != A. [back_unit_del(1223),unit_del(a,15798)]. given #1143 (T,wt=9): 16848 member(f23(c3),A) | -member(range_of(c4),power_set(A)). [back_unit_del(859),unit_del(a,15798)]. given #1144 (T,wt=9): 16860 member(ordered_pair(f1(c4,f23(c3)),f23(c3)),c4). [back_unit_del(847),unit_del(a,15798)]. given #1145 (T,wt=9): 16866 member(f24(c4),A) | -member(f14(c4,A),A). [back_unit_del(711),unit_del(a,15798)]. given #1146 (A,wt=18): 551 member(f24(power_set(A)),B) | member(f9(B,power_set(A)),B) | member(f10(B,power_set(A)),power_set(A)). [resolve(444,a,229,b)]. given #1147 (T,wt=9): 16867 member(f24(c4),A) | member(f14(c4,A),c4). [back_unit_del(710),unit_del(a,15798)]. given #1148 (T,wt=9): 16880 ilf_type(ordered_pair(f25(f23(c3)),f23(c3)),member_type(c4)). [back_unit_del(692),unit_del(a,15798),unit_del(b,16879)]. given #1149 (T,wt=9): 16894 member(ordered_pair(f2(c4,f23(c3)),f23(c3)),c4). [back_unit_del(678),unit_del(a,15798)]. given #1150 (T,wt=9): 16932 ilf_type(c3,binary_relation_type) | ilf_type(f25(f17(c3)),member_type(c2)). [back_unit_del(2019),unit_del(b,16801)]. given #1151 (A,wt=18): 552 member(f24(power_set(A)),B) | -member(f9(B,power_set(A)),power_set(A)) | -member(f10(B,power_set(A)),B). [resolve(444,a,228,b)]. given #1152 (T,wt=9): 16964 member(f23(domain_of(c4)),A) | -member(c2,power_set(A)). [back_unit_del(1591),unit_del(a,16822)]. given #1153 (T,wt=9): 16977 member(f16(domain_of(c4)),A) | -member(c2,power_set(A)). [back_unit_del(1522),unit_del(a,16822)]. given #1154 (T,wt=9): 17008 ilf_type(ordered_pair(f25(f24(c3)),f24(c3)),member_type(c4)). [back_unit_del(12892),unit_del(a,16844),unit_del(b,16879)]. given #1155 (T,wt=9): 17031 member(f23(range_of(c4)),A) | -member(c3,power_set(A)). [back_unit_del(1502),unit_del(a,16844)]. given #1156 (A,wt=19): 553 member(f24(power_set(A)),B) | -member(f9(B,power_set(A)),power_set(A)) | member(f10(B,power_set(A)),power_set(A)). [resolve(444,a,227,b)]. given #1157 (T,wt=9): 17045 member(f16(range_of(c4)),A) | -member(c3,power_set(A)). [back_unit_del(1441),unit_del(a,16844)]. given #1158 (T,wt=9): 17057 ilf_type(c3,binary_relation_type) | ilf_type(f17(c3),member_type(range_of(c4))). [back_unit_del(1001),unit_del(b,16844)]. given #1159 (T,wt=9): 17060 ilf_type(ordered_pair(f25(f16(c3)),f16(c3)),member_type(c4)). [back_unit_del(16568),unit_del(a,16879)]. given #1160 (T,wt=9): 17087 member(f16(c4),A) | cross_product(c2,c3) != A. [back_unit_del(1881),unit_del(a,16879)]. given #1161 (A,wt=19): 554 member(f24(power_set(A)),B) | member(f11(power_set(A),B),power_set(A)) | -member(f12(power_set(A),B),power_set(A)). [resolve(444,a,225,b)]. given #1162 (T,wt=9): 17095 member(f23(c4),A) | cross_product(c2,c3) != A. [back_unit_del(1776),unit_del(a,16879)]. given #1163 (T,wt=9): 17105 member(f13(c3,A),c3) | member(f16(c3),A). [resolve(17104,a,302,b)]. given #1164 (T,wt=9): 17115 member(f16(c3),A) | member(f14(c3,A),c3). [resolve(17104,a,218,a)]. given #1165 (T,wt=9): 17116 member(f16(c3),A) | -member(f14(c3,A),A). [resolve(17104,a,217,a)]. given #1166 (A,wt=18): 555 member(f24(power_set(A)),B) | member(f11(power_set(A),B),power_set(A)) | member(f12(power_set(A),B),B). [resolve(444,a,224,b)]. given #1167 (T,wt=9): 17137 member(f13(c3,A),c3) | member(f23(c3),A). [resolve(17136,a,302,b)]. given #1168 (T,wt=9): 17147 member(f23(c3),A) | member(f14(c3,A),c3). [resolve(17136,a,218,a)]. given #1169 (T,wt=9): 17148 member(f23(c3),A) | -member(f14(c3,A),A). [resolve(17136,a,217,a)]. given #1170 (T,wt=9): 17292 member(f23(range_of(c4)),A) | range_of(c4) != A. [resolve(17168,a,231,b)]. given #1171 (A,wt=18): 556 member(f24(power_set(A)),B) | -member(f11(power_set(A),B),B) | -member(f12(power_set(A),B),power_set(A)). [resolve(444,a,223,b)]. given #1172 (T,wt=9): 17312 member(f16(range_of(c4)),A) | range_of(c4) != A. [resolve(17174,a,231,b)]. given #1173 (T,wt=9): 17461 member(f24(A),A) | ilf_type(f24(c3),member_type(c3)). [resolve(15776,a,212,c),unit_del(b,15798)]. given #1174 (T,wt=7): 18224 ilf_type(f24(c3),member_type(c3)) | -empty(A). [resolve(17461,a,206,a)]. given #1175 (T,wt=9): 17508 ilf_type(f24(cross_product(c2,c3)),member_type(cross_product(c2,c3))). [resolve(16679,a,212,c),unit_del(a,16680)]. given #1176 (A,wt=17): 557 member(f24(power_set(A)),B) | -member(f11(power_set(A),B),B) | member(f12(power_set(A),B),B). [resolve(444,a,222,b)]. given #1177 (T,wt=9): 17597 member(f13(c3,A),c3) | member(f24(A),A). [resolve(15783,b,205,a)]. given #1178 (T,wt=9): 17652 member(f14(c3,A),c3) | member(f24(A),A). [resolve(15793,a,205,a)]. given #1179 (T,wt=10): 15740 member(f24(c3),c3) | member(f7(range_of(c4),c3),A). [factor(15727,a,d),unit_del(c,260)]. given #1180 (T,wt=10): 15772 member(f24(c3),c3) | member(f4(range_of(c4),c3),c3). [resolve(15739,b,248,a),flip(c),unit_del(c,260)]. given #1181 (A,wt=12): 558 member(f24(power_set(A)),B) | member(f14(power_set(A),B),power_set(A)). [resolve(444,a,218,a)]. given #1182 (T,wt=10): 15818 member(f1(c4,f16(c3)),A) | -member(c2,power_set(A)). [back_unit_del(15567),unit_del(a,15798)]. given #1183 (T,wt=10): 15843 member(f1(c4,f16(c3)),A) | domain_of(c4) != A. [back_unit_del(15542),unit_del(a,15798)]. given #1184 (T,wt=10): 15866 member(f2(c4,f16(c3)),A) | -member(c2,power_set(A)). [back_unit_del(15519),unit_del(a,15798)]. given #1185 (T,wt=10): 15891 member(f2(c4,f16(c3)),A) | domain_of(c4) != A. [back_unit_del(15491),unit_del(a,15798)]. given #1186 (A,wt=23): 562 ordered_pair(f20(power_set(A),f24(power_set(A))),f21(power_set(A),f24(power_set(A)))) = f24(power_set(A)) | member(f22(power_set(A)),power_set(A)). [resolve(444,a,209,a)]. given #1187 (T,wt=10): 15922 member(f1(c4,f24(c3)),A) | -member(c2,power_set(A)). [back_unit_del(15397),unit_del(a,15798)]. given #1188 (T,wt=10): 15947 member(f1(c4,f24(c3)),A) | domain_of(c4) != A. [back_unit_del(15372),unit_del(a,15798)]. given #1189 (T,wt=10): 15970 member(f2(c4,f24(c3)),A) | -member(c2,power_set(A)). [back_unit_del(15346),unit_del(a,15798)]. given #1190 (T,wt=10): 15995 member(f2(c4,f24(c3)),A) | domain_of(c4) != A. [back_unit_del(15321),unit_del(a,15798)]. given #1191 (A,wt=24): 563 ordered_pair(f20(power_set(A),f24(power_set(A))),f21(power_set(A),f24(power_set(A)))) = f24(power_set(A)) | f22(power_set(A)) != ordered_pair(B,C). [resolve(444,a,208,a)]. given #1192 (T,wt=10): 16029 member(f23(c3),A) | member(f13(c3,A),range_of(c4)). [back_unit_del(14639),unit_del(b,15798)]. given #1193 (T,wt=8): 18414 member(f13(c3,A),range_of(c4)) | -empty(A). [resolve(16029,a,206,a)]. given #1194 (T,wt=10): 16031 member(f24(c3),A) | member(f13(c3,A),range_of(c4)). [back_unit_del(14534),unit_del(b,15798)]. given #1195 (T,wt=10): 16033 member(f16(c3),A) | member(f13(c3,A),range_of(c4)). [back_unit_del(14419),unit_del(b,15798)]. given #1196 (A,wt=24): 564 -ilf_type(power_set(A),subset_type(cross_product(B,C))) | ordered_pair(f18(power_set(A),f24(power_set(A))),f19(power_set(A),f24(power_set(A)))) = f24(power_set(A)). [resolve(444,a,131,b)]. given #1197 (T,wt=10): 16037 member(f13(c4,c3),c4) | ilf_type(f24(c4),member_type(c3)). [back_unit_del(14145),unit_del(b,15798)]. given #1198 (T,wt=10): 16080 member(f13(c4,f6(A)),c4) | member(f24(c4),A). [back_unit_del(14102),unit_del(b,15798)]. given #1199 (T,wt=8): 18634 member(f13(c4,f6(A)),c4) | -empty(A). [resolve(16080,b,206,a)]. given #1200 (T,wt=10): 16081 member(f13(c4,range_of(c4)),c4) | member(f24(c4),c3). [back_unit_del(14101),unit_del(b,15798)]. given #1201 (A,wt=24): 565 ordered_pair(f18(power_set(A),f24(power_set(A))),f19(power_set(A),f24(power_set(A)))) = f24(power_set(A)) | f17(power_set(A)) != ordered_pair(B,C). [resolve(444,a,127,a)]. given #1202 (T,wt=10): 16082 member(f13(c4,domain_of(c4)),c4) | member(f24(c4),c2). [back_unit_del(14100),unit_del(b,15798)]. given #1203 (T,wt=10): 16093 member(f13(c4,c3),c4) | member(f24(c4),range_of(c4)). [back_unit_del(14089),unit_del(b,15798)]. given #1204 (T,wt=10): 16112 member(f13(c2,c3),c2) | ilf_type(f24(c2),member_type(c3)). [back_unit_del(14066),unit_del(b,15798)]. given #1205 (T,wt=10): 16155 member(f13(c2,f6(A)),c2) | member(f24(c2),A). [back_unit_del(14023),unit_del(b,15798)]. given #1206 (A,wt=23): 566 ordered_pair(f18(power_set(A),f24(power_set(A))),f19(power_set(A),f24(power_set(A)))) = f24(power_set(A)) | member(f17(power_set(A)),power_set(A)). [resolve(444,a,125,a)]. given #1207 (T,wt=8): 18760 member(f13(c2,f6(A)),c2) | -empty(A). [resolve(16155,b,206,a)]. given #1208 (T,wt=10): 16156 member(f13(c2,range_of(c4)),c2) | member(f24(c2),c3). [back_unit_del(14022),unit_del(b,15798)]. given #1209 (T,wt=10): 16168 member(f13(c2,c3),c2) | member(f24(c2),range_of(c4)). [back_unit_del(14010),unit_del(b,15798)]. given #1210 (T,wt=10): 16192 member(f24(A),A) | member(f14(c3,A),range_of(c4)). [back_unit_del(13577),unit_del(a,15798)]. given #1211 (A,wt=21): 567 ordered_pair(f18(power_set(A),f24(power_set(A))),f19(power_set(A),f24(power_set(A)))) = f24(power_set(A)) | -ilf_type(power_set(A),binary_relation_type). [resolve(444,a,123,a)]. given #1212 (T,wt=8): 18827 member(f14(c3,A),range_of(c4)) | -empty(A). [resolve(16192,a,206,a)]. given #1213 (T,wt=10): 16206 member(f14(c2,c3),c2) | ilf_type(f24(c2),member_type(c3)). [back_unit_del(12806),unit_del(a,15798)]. given #1214 (T,wt=10): 16268 member(f14(c2,f6(A)),c2) | member(f24(c2),A). [back_unit_del(12744),unit_del(a,15798)]. given #1215 (T,wt=8): 18902 member(f14(c2,f6(A)),c2) | -empty(A). [resolve(16268,b,206,a)]. given #1216 (A,wt=16): 570 member(range_of(c4),A) | member(f9(A,power_set(c3)),A) | -member(f10(A,power_set(c3)),A). [resolve(568,a,230,b)]. given #1217 (T,wt=10): 16269 member(f14(c2,range_of(c4)),c2) | member(f24(c2),c3). [back_unit_del(12743),unit_del(a,15798)]. given #1218 (T,wt=10): 16281 member(f14(c2,c3),c2) | member(f24(c2),range_of(c4)). [back_unit_del(12731),unit_del(a,15798)]. given #1219 (T,wt=10): 16301 member(f1(c4,f23(c3)),A) | -member(c2,power_set(A)). [back_unit_del(11101),unit_del(a,15798)]. given #1220 (T,wt=10): 16327 member(f1(c4,f23(c3)),A) | domain_of(c4) != A. [back_unit_del(11070),unit_del(a,15798)]. given #1221 (A,wt=17): 571 member(range_of(c4),A) | member(f9(A,power_set(c3)),A) | member(f10(A,power_set(c3)),power_set(c3)). [resolve(568,a,229,b)]. given #1222 (T,wt=10): 16349 member(f14(c4,c3),c4) | ilf_type(f24(c4),member_type(c3)). [back_unit_del(10903),unit_del(a,15798)]. given #1223 (T,wt=10): 16409 member(f14(c4,f6(A)),c4) | member(f24(c4),A). [back_unit_del(10840),unit_del(a,15798)]. given #1224 (T,wt=8): 19047 member(f14(c4,f6(A)),c4) | -empty(A). [resolve(16409,b,206,a)]. given #1225 (T,wt=10): 16410 member(f14(c4,range_of(c4)),c4) | member(f24(c4),c3). [back_unit_del(10839),unit_del(a,15798)]. given #1226 (A,wt=17): 572 member(range_of(c4),A) | -member(f9(A,power_set(c3)),power_set(c3)) | -member(f10(A,power_set(c3)),A). [resolve(568,a,228,b)]. given #1227 (T,wt=10): 16411 member(f14(c4,domain_of(c4)),c4) | member(f24(c4),c2). [back_unit_del(10838),unit_del(a,15798)]. given #1228 (T,wt=10): 16421 member(f14(c4,c3),c4) | member(f24(c4),range_of(c4)). [back_unit_del(10828),unit_del(a,15798)]. given #1229 (T,wt=10): 16430 member(f2(c4,f23(c3)),A) | -member(c2,power_set(A)). [back_unit_del(10819),unit_del(a,15798)]. given #1230 (T,wt=10): 16456 member(f2(c4,f23(c3)),A) | domain_of(c4) != A. [back_unit_del(10788),unit_del(a,15798)]. given #1231 (A,wt=18): 573 member(range_of(c4),A) | -member(f9(A,power_set(c3)),power_set(c3)) | member(f10(A,power_set(c3)),power_set(c3)). [resolve(568,a,227,b)]. given #1232 (T,wt=10): 16476 member(f16(c3),A) | member(f14(c3,A),range_of(c4)). [back_unit_del(10194),unit_del(a,15798)]. given #1233 (T,wt=10): 16478 member(f24(c3),A) | member(f14(c3,A),range_of(c4)). [back_unit_del(10063),unit_del(a,15798)]. given #1234 (T,wt=10): 16495 member(f14(c3,A),range_of(c4)) | member(f23(c3),A). [back_unit_del(5647),unit_del(c,15798)]. given #1235 (T,wt=10): 16513 member(f25(f16(c3)),A) | -member(f14(c2,A),A). [back_unit_del(3776),unit_del(a,15798)]. given #1236 (A,wt=18): 574 member(range_of(c4),A) | member(f11(power_set(c3),A),power_set(c3)) | -member(f12(power_set(c3),A),power_set(c3)). [resolve(568,a,225,b)]. given #1237 (T,wt=10): 16514 member(f25(f16(c3)),A) | member(f14(c2,A),c2). [back_unit_del(3775),unit_del(a,15798)]. given #1238 (T,wt=10): 16524 member(f13(c2,A),c2) | member(f25(f16(c3)),A). [back_unit_del(3765),unit_del(a,15798)]. given #1239 (T,wt=10): 16532 member(f25(f16(c3)),A) | -member(domain_of(c4),power_set(A)). [back_unit_del(3757),unit_del(a,15798)]. given #1240 (T,wt=10): 16554 member(f16(c3),A) | -member(f14(range_of(c4),A),A). [back_unit_del(3731),unit_del(a,15798)]. given #1241 (A,wt=17): 575 member(range_of(c4),A) | member(f11(power_set(c3),A),power_set(c3)) | member(f12(power_set(c3),A),A). [resolve(568,a,224,b)]. given #1242 (T,wt=10): 16585 member(ordered_pair(f25(f16(c3)),f16(c3)),cross_product(c2,c3)). [back_unit_del(3695),unit_del(a,15798)]. given #1243 (T,wt=7): 19440 member(f16(c3),range_of(cross_product(c2,c3))). [resolve(16585,a,255,c),unit_del(a,453)]. given #1244 (T,wt=8): 19442 member(f25(f16(c3)),domain_of(cross_product(c2,c3))). [resolve(16585,a,252,b),unit_del(a,453)]. given #1245 (T,wt=8): 19459 ilf_type(f16(c3),member_type(range_of(cross_product(c2,c3)))). [back_unit_del(19456),unit_del(a,19457)]. given #1246 (A,wt=17): 576 member(range_of(c4),A) | -member(f11(power_set(c3),A),A) | -member(f12(power_set(c3),A),power_set(c3)). [resolve(568,a,223,b)]. given #1247 (F,wt=5): 19457 -empty(range_of(cross_product(c2,c3))). [resolve(19440,a,206,a)]. given #1248 (F,wt=5): 19466 -empty(domain_of(cross_product(c2,c3))). [resolve(19442,a,206,a)]. given #1249 (T,wt=9): 19468 ilf_type(f25(f16(c3)),member_type(domain_of(cross_product(c2,c3)))). [back_unit_del(19465),unit_del(a,19466)]. given #1250 (T,wt=10): 16594 member(f25(f24(c3)),A) | -member(f14(c2,A),A). [back_unit_del(3653),unit_del(a,15798)]. given #1251 (T,wt=10): 16595 member(f25(f24(c3)),A) | member(f14(c2,A),c2). [back_unit_del(3652),unit_del(a,15798)]. given #1252 (T,wt=10): 16605 member(f13(c2,A),c2) | member(f25(f24(c3)),A). [back_unit_del(3642),unit_del(a,15798)]. given #1253 (A,wt=16): 577 member(range_of(c4),A) | -member(f11(power_set(c3),A),A) | member(f12(power_set(c3),A),A). [resolve(568,a,222,b)]. given #1254 (T,wt=10): 16613 member(f25(f24(c3)),A) | -member(domain_of(c4),power_set(A)). [back_unit_del(3630),unit_del(a,15798)]. given #1255 (T,wt=10): 16634 member(f24(c3),A) | -member(f14(range_of(c4),A),A). [back_unit_del(3608),unit_del(a,15798)]. given #1256 (T,wt=10): 16664 member(ordered_pair(f25(f24(c3)),f24(c3)),cross_product(c2,c3)). [back_unit_del(3572),unit_del(a,15798)]. given #1257 (T,wt=7): 19599 member(f24(c3),range_of(cross_product(c2,c3))). [resolve(16664,a,255,c),unit_del(a,453)]. given #1258 (A,wt=20): 582 ordered_pair(f20(power_set(c3),range_of(c4)),f21(power_set(c3),range_of(c4))) = range_of(c4) | member(f22(power_set(c3)),power_set(c3)). [resolve(568,a,209,a)]. given #1259 (T,wt=8): 19601 member(f25(f24(c3)),domain_of(cross_product(c2,c3))). [resolve(16664,a,252,b),unit_del(a,453)]. given #1260 (T,wt=8): 19615 ilf_type(f24(c3),member_type(range_of(cross_product(c2,c3)))). [resolve(19599,a,212,c),unit_del(a,19457)]. given #1261 (T,wt=9): 19624 ilf_type(f25(f24(c3)),member_type(domain_of(cross_product(c2,c3)))). [resolve(19601,a,212,c),unit_del(a,19466)]. given #1262 (T,wt=10): 16665 ilf_type(range_of(c4),binary_relation_type) | ilf_type(f17(range_of(c4)),member_type(c3)). [back_unit_del(2529),unit_del(b,15798)]. given #1263 (A,wt=21): 583 ordered_pair(f20(power_set(c3),range_of(c4)),f21(power_set(c3),range_of(c4))) = range_of(c4) | f22(power_set(c3)) != ordered_pair(A,B). [resolve(568,a,208,a)]. given #1264 (T,wt=10): 16671 member(f13(c2,A),c2) | member(f25(f23(c3)),A). [back_unit_del(2411),unit_del(c,15798)]. given #1265 (T,wt=10): 16675 member(f13(c3,A),c3) | member(f24(range_of(c4)),A). [back_unit_del(2401),unit_del(c,15798)]. given #1266 (T,wt=10): 16676 member(f13(c2,A),c2) | member(f24(domain_of(c4)),A). [back_unit_del(2400),unit_del(c,15798)]. given #1267 (T,wt=10): 16684 member(f24(c4),A) | -member(cross_product(c2,c3),power_set(A)). [back_unit_del(1871),unit_del(a,15798)]. given #1268 (A,wt=21): 584 -ilf_type(power_set(c3),subset_type(cross_product(A,B))) | ordered_pair(f18(power_set(c3),range_of(c4)),f19(power_set(c3),range_of(c4))) = range_of(c4). [resolve(568,a,131,b)]. given #1269 (T,wt=10): 16704 member(f24(domain_of(c4)),A) | -member(f14(c2,A),A). [back_unit_del(1826),unit_del(a,15798)]. given #1270 (T,wt=10): 16705 member(f24(domain_of(c4)),A) | member(f14(c2,A),c2). [back_unit_del(1825),unit_del(a,15798)]. given #1271 (T,wt=10): 16721 member(f24(domain_of(c4)),A) | -member(domain_of(c4),power_set(A)). [back_unit_del(1809),unit_del(a,15798)]. given #1272 (T,wt=10): 16734 member(ordered_pair(f25(f24(range_of(c4))),f24(range_of(c4))),c4). [back_unit_del(1764),unit_del(a,15798)]. given #1273 (A,wt=21): 585 ordered_pair(f18(power_set(c3),range_of(c4)),f19(power_set(c3),range_of(c4))) = range_of(c4) | f17(power_set(c3)) != ordered_pair(A,B). [resolve(568,a,127,a)]. given #1274 (T,wt=7): 19873 member(f25(f24(range_of(c4))),domain_of(c4)). [resolve(16734,a,252,b),unit_del(a,540)]. given #1275 (T,wt=6): 19887 member(f25(f24(range_of(c4))),c2). [resolve(19873,a,600,a)]. given #1276 (T,wt=7): 19915 ilf_type(f25(f24(range_of(c4))),member_type(c2)). [resolve(19887,a,212,c),unit_del(a,16801)]. given #1277 (T,wt=8): 19901 ilf_type(f25(f24(range_of(c4))),member_type(domain_of(c4))). [resolve(19873,a,212,c),unit_del(a,16822)]. given #1278 (A,wt=20): 586 ordered_pair(f18(power_set(c3),range_of(c4)),f19(power_set(c3),range_of(c4))) = range_of(c4) | member(f17(power_set(c3)),power_set(c3)). [resolve(568,a,125,a)]. given #1279 (T,wt=9): 19903 member(f25(f24(range_of(c4))),A) | c2 != A. [resolve(19887,a,231,b)]. given #1280 (T,wt=10): 16743 member(f24(range_of(c4)),A) | -member(f14(c3,A),A). [back_unit_del(1755),unit_del(a,15798)]. given #1281 (T,wt=10): 16744 member(f24(range_of(c4)),A) | member(f14(c3,A),c3). [back_unit_del(1754),unit_del(a,15798)]. given #1282 (T,wt=10): 16760 member(f24(range_of(c4)),A) | -member(range_of(c4),power_set(A)). [back_unit_del(1738),unit_del(a,15798)]. given #1283 (A,wt=18): 587 ordered_pair(f18(power_set(c3),range_of(c4)),f19(power_set(c3),range_of(c4))) = range_of(c4) | -ilf_type(power_set(c3),binary_relation_type). [resolve(568,a,123,a)]. given #1284 (T,wt=10): 16776 member(ordered_pair(f25(f23(c3)),f23(c3)),cross_product(c2,c3)). [back_unit_del(1341),unit_del(b,15798)]. given #1285 (T,wt=7): 19984 member(f23(c3),range_of(cross_product(c2,c3))). [resolve(16776,a,255,c),unit_del(a,453)]. given #1286 (T,wt=8): 19986 member(f25(f23(c3)),domain_of(cross_product(c2,c3))). [resolve(16776,a,252,b),unit_del(a,453)]. given #1287 (T,wt=8): 20000 ilf_type(f23(c3),member_type(range_of(cross_product(c2,c3)))). [resolve(19984,a,212,c),unit_del(a,19457)]. given #1288 (A,wt=16): 590 member(domain_of(c4),A) | member(f9(A,power_set(c2)),A) | -member(f10(A,power_set(c2)),A). [resolve(588,a,230,b)]. given #1289 (T,wt=9): 20008 ilf_type(f25(f23(c3)),member_type(domain_of(cross_product(c2,c3)))). [resolve(19986,a,212,c),unit_del(a,19466)]. given #1290 (T,wt=10): 16806 member(f25(f23(c3)),A) | -member(f14(c2,A),A). [back_unit_del(1303),unit_del(a,15798)]. given #1291 (T,wt=10): 16807 member(f25(f23(c3)),A) | member(f14(c2,A),c2). [back_unit_del(1302),unit_del(a,15798)]. given #1292 (T,wt=10): 16826 member(f25(f23(c3)),A) | -member(domain_of(c4),power_set(A)). [back_unit_del(1234),unit_del(a,15798)]. given #1293 (A,wt=17): 591 member(domain_of(c4),A) | member(f9(A,power_set(c2)),A) | member(f10(A,power_set(c2)),power_set(c2)). [resolve(588,a,229,b)]. given #1294 (T,wt=10): 16849 member(f23(c3),A) | -member(f14(range_of(c4),A),A). [back_unit_del(858),unit_del(a,15798)]. given #1295 (T,wt=10): 16931 ilf_type(domain_of(c4),binary_relation_type) | ilf_type(f17(domain_of(c4)),member_type(c2)). [back_unit_del(2595),unit_del(b,16801)]. given #1296 (T,wt=10): 16950 member(f24(A),A) | member(f14(domain_of(c4),A),c2). [back_unit_del(13588),unit_del(a,16822)]. given #1297 (T,wt=8): 20130 member(f14(domain_of(c4),A),c2) | -empty(A). [resolve(16950,a,206,a)]. given #1298 (A,wt=17): 592 member(domain_of(c4),A) | -member(f9(A,power_set(c2)),power_set(c2)) | -member(f10(A,power_set(c2)),A). [resolve(588,a,228,b)]. given #1299 (T,wt=10): 16959 member(f13(c2,A),c2) | member(f16(domain_of(c4)),A). [back_unit_del(2420),unit_del(c,16822)]. given #1300 (T,wt=10): 16960 member(f13(c2,A),c2) | member(f23(domain_of(c4)),A). [back_unit_del(2418),unit_del(c,16822)]. given #1301 (T,wt=10): 16962 ilf_type(c3,binary_relation_type) | ilf_type(f25(f17(c3)),member_type(domain_of(c4))). [back_unit_del(1998),unit_del(b,16822)]. given #1302 (T,wt=10): 16965 member(f23(domain_of(c4)),A) | -member(f14(c2,A),A). [back_unit_del(1590),unit_del(a,16822)]. given #1303 (A,wt=18): 593 member(domain_of(c4),A) | -member(f9(A,power_set(c2)),power_set(c2)) | member(f10(A,power_set(c2)),power_set(c2)). [resolve(588,a,227,b)]. given #1304 (T,wt=10): 16966 member(f23(domain_of(c4)),A) | member(f14(c2,A),c2). [back_unit_del(1589),unit_del(a,16822)]. given #1305 (T,wt=10): 16978 member(f16(domain_of(c4)),A) | -member(f14(c2,A),A). [back_unit_del(1521),unit_del(a,16822)]. given #1306 (T,wt=10): 16979 member(f16(domain_of(c4)),A) | member(f14(c2,A),c2). [back_unit_del(1520),unit_del(a,16822)]. given #1307 (T,wt=10): 17006 member(f24(A),A) | member(f14(range_of(c4),A),c3). [back_unit_del(13589),unit_del(a,16844)]. given #1308 (A,wt=18): 594 member(domain_of(c4),A) | member(f11(power_set(c2),A),power_set(c2)) | -member(f12(power_set(c2),A),power_set(c2)). [resolve(588,a,225,b)]. given #1309 (T,wt=8): 20402 member(f14(range_of(c4),A),c3) | -empty(A). [resolve(17006,a,206,a)]. given #1310 (T,wt=10): 17020 empty(f6(c3)) | ilf_type(f16(f6(c3)),member_type(range_of(c4))). [back_unit_del(6210),unit_del(b,16844)]. given #1311 (T,wt=10): 17021 empty(f6(c3)) | ilf_type(f24(f6(c3)),member_type(range_of(c4))). [back_unit_del(6189),unit_del(b,16844)]. given #1312 (T,wt=10): 17022 empty(f6(c3)) | ilf_type(f23(f6(c3)),member_type(range_of(c4))). [back_unit_del(6168),unit_del(b,16844)]. given #1313 (A,wt=17): 595 member(domain_of(c4),A) | member(f11(power_set(c2),A),power_set(c2)) | member(f12(power_set(c2),A),A). [resolve(588,a,224,b)]. given #1314 (T,wt=10): 17026 member(f13(c3,A),c3) | member(f16(range_of(c4)),A). [back_unit_del(2423),unit_del(c,16844)]. given #1315 (T,wt=10): 17027 member(f13(c3,A),c3) | member(f23(range_of(c4)),A). [back_unit_del(2421),unit_del(c,16844)]. given #1316 (T,wt=10): 17029 member(ordered_pair(f25(f23(range_of(c4))),f23(range_of(c4))),c4). [back_unit_del(1510),unit_del(a,16844)]. given #1317 (T,wt=7): 20542 member(f25(f23(range_of(c4))),domain_of(c4)). [resolve(17029,a,252,b),unit_del(a,540)]. given #1318 (A,wt=17): 596 member(domain_of(c4),A) | -member(f11(power_set(c2),A),A) | -member(f12(power_set(c2),A),power_set(c2)). [resolve(588,a,223,b)]. given #1319 (T,wt=6): 20556 member(f25(f23(range_of(c4))),c2). [resolve(20542,a,600,a)]. given #1320 (T,wt=7): 20585 ilf_type(f25(f23(range_of(c4))),member_type(c2)). [resolve(20556,a,212,c),unit_del(a,16801)]. given #1321 (T,wt=8): 20570 ilf_type(f25(f23(range_of(c4))),member_type(domain_of(c4))). [resolve(20542,a,212,c),unit_del(a,16822)]. given #1322 (T,wt=9): 20573 member(f25(f23(range_of(c4))),A) | c2 != A. [resolve(20556,a,231,b)]. given #1323 (A,wt=16): 597 member(domain_of(c4),A) | -member(f11(power_set(c2),A),A) | member(f12(power_set(c2),A),A). [resolve(588,a,222,b)]. given #1324 (T,wt=10): 17032 member(f23(range_of(c4)),A) | -member(f14(c3,A),A). [back_unit_del(1501),unit_del(a,16844)]. given #1325 (T,wt=10): 17033 member(f23(range_of(c4)),A) | member(f14(c3,A),c3). [back_unit_del(1500),unit_del(a,16844)]. given #1326 (T,wt=10): 17043 member(ordered_pair(f25(f16(range_of(c4))),f16(range_of(c4))),c4). [back_unit_del(1451),unit_del(a,16844)]. given #1327 (T,wt=7): 20651 member(f25(f16(range_of(c4))),domain_of(c4)). [resolve(17043,a,252,b),unit_del(a,540)]. given #1328 (A,wt=20): 602 ordered_pair(f20(power_set(c2),domain_of(c4)),f21(power_set(c2),domain_of(c4))) = domain_of(c4) | member(f22(power_set(c2)),power_set(c2)). [resolve(588,a,209,a)]. given #1329 (T,wt=6): 20665 member(f25(f16(range_of(c4))),c2). [resolve(20651,a,600,a)]. given #1330 (T,wt=7): 20693 ilf_type(f25(f16(range_of(c4))),member_type(c2)). [resolve(20665,a,212,c),unit_del(a,16801)]. given #1331 (T,wt=8): 20679 ilf_type(f25(f16(range_of(c4))),member_type(domain_of(c4))). [resolve(20651,a,212,c),unit_del(a,16822)]. given #1332 (T,wt=9): 20681 member(f25(f16(range_of(c4))),A) | c2 != A. [resolve(20665,a,231,b)]. given #1333 (A,wt=21): 603 ordered_pair(f20(power_set(c2),domain_of(c4)),f21(power_set(c2),domain_of(c4))) = domain_of(c4) | f22(power_set(c2)) != ordered_pair(A,B). [resolve(588,a,208,a)]. given #1334 (T,wt=10): 17046 member(f16(range_of(c4)),A) | -member(f14(c3,A),A). [back_unit_del(1440),unit_del(a,16844)]. given #1335 (T,wt=10): 17047 member(f16(range_of(c4)),A) | member(f14(c3,A),c3). [back_unit_del(1439),unit_del(a,16844)]. given #1336 (T,wt=10): 17061 ilf_type(ordered_pair(f2(c4,f23(c3)),f23(c3)),member_type(c4)). [back_unit_del(16459),unit_del(a,16879)]. given #1337 (T,wt=10): 17062 ilf_type(ordered_pair(f1(c4,f23(c3)),f23(c3)),member_type(c4)). [back_unit_del(16330),unit_del(a,16879)]. given #1338 (A,wt=21): 604 -ilf_type(power_set(c2),subset_type(cross_product(A,B))) | ordered_pair(f18(power_set(c2),domain_of(c4)),f19(power_set(c2),domain_of(c4))) = domain_of(c4). [resolve(588,a,131,b)]. given #1339 (T,wt=10): 17063 ilf_type(ordered_pair(f2(c4,f24(c3)),f24(c3)),member_type(c4)). [back_unit_del(15998),unit_del(a,16879)]. given #1340 (T,wt=10): 17064 ilf_type(ordered_pair(f1(c4,f24(c3)),f24(c3)),member_type(c4)). [back_unit_del(15950),unit_del(a,16879)]. given #1341 (T,wt=10): 17065 ilf_type(ordered_pair(f2(c4,f16(c3)),f16(c3)),member_type(c4)). [back_unit_del(15894),unit_del(a,16879)]. given #1342 (T,wt=10): 17066 ilf_type(ordered_pair(f1(c4,f16(c3)),f16(c3)),member_type(c4)). [back_unit_del(15846),unit_del(a,16879)]. given #1343 (A,wt=21): 605 ordered_pair(f18(power_set(c2),domain_of(c4)),f19(power_set(c2),domain_of(c4))) = domain_of(c4) | f17(power_set(c2)) != ordered_pair(A,B). [resolve(588,a,127,a)]. given #1344 (T,wt=10): 17082 member(f16(c4),A) | -member(cross_product(c2,c3),power_set(A)). [back_unit_del(1892),unit_del(a,16879)]. given #1345 (T,wt=10): 17090 member(f23(c4),A) | -member(cross_product(c2,c3),power_set(A)). [back_unit_del(1787),unit_del(a,16879)]. given #1346 (T,wt=10): 17303 member(f23(range_of(c4)),A) | -member(range_of(c4),power_set(A)). [resolve(17168,a,214,a)]. given #1347 (T,wt=10): 17323 member(f16(range_of(c4)),A) | -member(range_of(c4),power_set(A)). [resolve(17174,a,214,a)]. given #1348 (A,wt=20): 606 ordered_pair(f18(power_set(c2),domain_of(c4)),f19(power_set(c2),domain_of(c4))) = domain_of(c4) | member(f17(power_set(c2)),power_set(c2)). [resolve(588,a,125,a)]. given #1349 (T,wt=10): 17465 member(f24(c3),A) | ilf_type(f15(c3,A),member_type(c3)). [resolve(15795,b,285,a),unit_del(b,15798)]. given #1350 (T,wt=8): 20810 ilf_type(f15(c3,A),member_type(c3)) | -empty(A). [resolve(17465,a,206,a)]. given #1351 (T,wt=10): 17509 member(f24(c2),A) | ilf_type(f15(c2,A),member_type(c2)). [resolve(16784,b,285,a),unit_del(b,16801)]. given #1352 (T,wt=8): 20855 ilf_type(f15(c2,A),member_type(c2)) | -empty(A). [resolve(17509,a,206,a)]. given #1353 (A,wt=18): 607 ordered_pair(f18(power_set(c2),domain_of(c4)),f19(power_set(c2),domain_of(c4))) = domain_of(c4) | -ilf_type(power_set(c2),binary_relation_type). [resolve(588,a,123,a)]. given #1354 (T,wt=10): 17511 member(f24(c4),A) | ilf_type(f15(c4,A),member_type(c4)). [resolve(16865,b,285,a),unit_del(b,16879)]. given #1355 (T,wt=8): 20901 ilf_type(f15(c4,A),member_type(c4)) | -empty(A). [resolve(17511,a,206,a)]. given #1356 (T,wt=10): 17525 member(f16(c3),A) | ilf_type(f15(c3,A),member_type(c3)). [resolve(17117,b,285,a),unit_del(b,15798)]. given #1357 (T,wt=10): 17530 member(f23(c3),A) | ilf_type(f15(c3,A),member_type(c3)). [resolve(17149,b,285,a),unit_del(b,15798)]. given #1358 (A,wt=38): 609 empty(f23(power_set(cross_product(A,B)))) | ordered_pair(f18(f23(power_set(cross_product(A,B))),f23(f23(power_set(cross_product(A,B))))),f19(f23(power_set(cross_product(A,B))),f23(f23(power_set(cross_product(A,B)))))) = f23(f23(power_set(cross_product(A,B)))). [resolve(608,a,266,b)]. given #1359 (T,wt=10): 17544 member(f24(c3),A) | ilf_type(f13(c3,A),member_type(c3)). [resolve(15783,a,212,c),unit_del(b,15798)]. given #1360 (T,wt=8): 21030 ilf_type(f13(c3,A),member_type(c3)) | -empty(A). [resolve(17544,a,206,a)]. given #1361 (T,wt=10): 17560 member(f13(c3,domain_of(c4)),c3) | member(f24(c3),c2). [resolve(15783,b,600,a)]. given #1362 (T,wt=10): 17561 member(f13(c3,f6(A)),c3) | member(f24(c3),A). [resolve(15783,b,528,a)]. given #1363 (A,wt=34): 614 empty(range_of(A)) | ordered_pair(f18(range_of(A),f23(range_of(A))),f19(range_of(A),f23(range_of(A)))) = f23(range_of(A)) | -ilf_type(A,binary_relation_type) | member(ordered_pair(f1(A,f17(range_of(A))),f17(range_of(A))),A). [resolve(268,c,254,c)]. given #1364 (T,wt=8): 21102 member(f13(c3,f6(A)),c3) | -empty(A). [resolve(17561,b,206,a)]. given #1365 (T,wt=10): 17615 member(f14(c3,domain_of(c4)),c3) | member(f24(c3),c2). [resolve(15793,a,600,a)]. given #1366 (T,wt=10): 17616 member(f14(c3,f6(A)),c3) | member(f24(c3),A). [resolve(15793,a,528,a)]. given #1367 (T,wt=8): 21176 member(f14(c3,f6(A)),c3) | -empty(A). [resolve(17616,b,206,a)]. given #1368 (A,wt=21): 615 empty(A) | ordered_pair(f18(A,f23(A)),f19(A,f23(A))) = f23(A) | member(f17(A),B) | A != B. [resolve(268,c,231,b)]. given #1369 (T,wt=10): 17670 member(f24(c3),A) | ilf_type(f14(c3,A),member_type(c3)). [resolve(15793,b,212,c),unit_del(b,15798)]. given #1370 (T,wt=8): 21220 ilf_type(f14(c3,A),member_type(c3)) | -empty(A). [resolve(17670,a,206,a)]. given #1371 (T,wt=10): 17828 ilf_type(c3,binary_relation_type) | member(f2(c4,f17(c3)),domain_of(c4)). [resolve(543,b,252,b),unit_del(b,540)]. given #1372 (T,wt=9): 21222 ilf_type(c3,binary_relation_type) | member(f2(c4,f17(c3)),c2). [resolve(17828,b,600,a)]. given #1373 (A,wt=28): 616 empty(A) | ordered_pair(f18(A,f23(A)),f19(A,f23(A))) = f23(A) | member(f17(A),B) | member(f9(B,A),B) | -member(f10(B,A),B). [resolve(268,c,230,b)]. given #1374 (T,wt=10): 17843 member(f24(c4),A) | ilf_type(f13(c4,A),member_type(c4)). [resolve(16669,a,212,c),unit_del(b,16879)]. given #1375 (T,wt=8): 21285 ilf_type(f13(c4,A),member_type(c4)) | -empty(A). [resolve(17843,a,206,a)]. given #1376 (T,wt=10): 17844 member(f24(c2),A) | ilf_type(f13(c2,A),member_type(c2)). [resolve(16673,a,212,c),unit_del(b,16801)]. given #1377 (T,wt=8): 21330 ilf_type(f13(c2,A),member_type(c2)) | -empty(A). [resolve(17844,a,206,a)]. given #1378 (A,wt=28): 617 empty(A) | ordered_pair(f18(A,f23(A)),f19(A,f23(A))) = f23(A) | member(f17(A),B) | member(f9(B,A),B) | member(f10(B,A),A). [resolve(268,c,229,b)]. given #1379 (T,wt=10): 17845 member(f24(c2),A) | ilf_type(f14(c2,A),member_type(c2)). [resolve(16786,b,212,c),unit_del(b,16801)]. given #1380 (T,wt=8): 21375 ilf_type(f14(c2,A),member_type(c2)) | -empty(A). [resolve(17845,a,206,a)]. given #1381 (T,wt=10): 17863 member(f24(c4),A) | ilf_type(f14(c4,A),member_type(c4)). [resolve(16867,b,212,c),unit_del(b,16879)]. given #1382 (T,wt=8): 21420 ilf_type(f14(c4,A),member_type(c4)) | -empty(A). [resolve(17863,a,206,a)]. given #1383 (A,wt=28): 618 empty(A) | ordered_pair(f18(A,f23(A)),f19(A,f23(A))) = f23(A) | member(f17(A),B) | -member(f9(B,A),A) | -member(f10(B,A),B). [resolve(268,c,228,b)]. given #1384 (T,wt=10): 17889 member(f16(c3),A) | ilf_type(f13(c3,A),member_type(c3)). [resolve(17105,a,212,c),unit_del(b,15798)]. given #1385 (T,wt=10): 17905 member(f13(c3,domain_of(c4)),c3) | member(f16(c3),c2). [resolve(17105,b,600,a)]. given #1386 (T,wt=10): 17906 member(f13(c3,f6(A)),c3) | member(f16(c3),A). [resolve(17105,b,528,a)]. given #1387 (T,wt=10): 17958 member(f14(c3,domain_of(c4)),c3) | member(f16(c3),c2). [resolve(17115,a,600,a)]. given #1388 (A,wt=28): 619 empty(A) | ordered_pair(f18(A,f23(A)),f19(A,f23(A))) = f23(A) | member(f17(A),B) | -member(f9(B,A),A) | member(f10(B,A),A). [resolve(268,c,227,b)]. given #1389 (T,wt=10): 17959 member(f14(c3,f6(A)),c3) | member(f16(c3),A). [resolve(17115,a,528,a)]. given #1390 (T,wt=10): 18011 member(f16(c3),A) | ilf_type(f14(c3,A),member_type(c3)). [resolve(17115,b,212,c),unit_del(b,15798)]. given #1391 (T,wt=10): 18060 member(f23(c3),A) | ilf_type(f13(c3,A),member_type(c3)). [resolve(17137,a,212,c),unit_del(b,15798)]. given #1392 (T,wt=10): 18076 member(f13(c3,domain_of(c4)),c3) | member(f23(c3),c2). [resolve(17137,b,600,a)]. given #1393 (A,wt=21): 620 empty(A) | ordered_pair(f18(A,f23(A)),f19(A,f23(A))) = f23(A) | member(f17(A),B) | B != A. [resolve(268,c,226,b)]. given #1394 (T,wt=10): 18077 member(f13(c3,f6(A)),c3) | member(f23(c3),A). [resolve(17137,b,528,a)]. given #1395 (T,wt=10): 18129 member(f14(c3,domain_of(c4)),c3) | member(f23(c3),c2). [resolve(17147,a,600,a)]. given #1396 (T,wt=10): 18130 member(f14(c3,f6(A)),c3) | member(f23(c3),A). [resolve(17147,a,528,a)]. given #1397 (T,wt=10): 18182 member(f23(c3),A) | ilf_type(f14(c3,A),member_type(c3)). [resolve(17147,b,212,c),unit_del(b,15798)]. given #1398 (A,wt=28): 621 empty(A) | ordered_pair(f18(A,f23(A)),f19(A,f23(A))) = f23(A) | member(f17(A),B) | member(f11(A,B),A) | -member(f12(A,B),A). [resolve(268,c,225,b)]. given #1399 (T,wt=10): 18199 ilf_type(f24(c3),member_type(c3)) | member(f24(f6(A)),A). [resolve(17461,a,528,a)]. given #1400 (T,wt=10): 18415 member(f13(c3,A),range_of(c4)) | member(f24(A),A). [resolve(16029,a,205,a)]. given #1401 (T,wt=10): 18635 member(f13(c4,f6(A)),c4) | member(f24(A),A). [resolve(16080,b,205,a)]. given #1402 (T,wt=10): 18761 member(f13(c2,f6(A)),c2) | member(f24(A),A). [resolve(16155,b,205,a)]. given #1403 (A,wt=28): 622 empty(A) | ordered_pair(f18(A,f23(A)),f19(A,f23(A))) = f23(A) | member(f17(A),B) | member(f11(A,B),A) | member(f12(A,B),B). [resolve(268,c,224,b)]. given #1404 (T,wt=10): 18903 member(f14(c2,f6(A)),c2) | member(f24(A),A). [resolve(16268,b,205,a)]. given #1405 (T,wt=10): 19048 member(f14(c4,f6(A)),c4) | member(f24(A),A). [resolve(16409,b,205,a)]. given #1406 (T,wt=10): 19450 member(f16(c3),A) | range_of(cross_product(c2,c3)) != A. [resolve(19440,a,231,b)]. given #1407 (T,wt=10): 19458 member(f24(range_of(cross_product(c2,c3))),range_of(cross_product(c2,c3))). [resolve(19440,a,205,a)]. given #1408 (A,wt=28): 623 empty(A) | ordered_pair(f18(A,f23(A)),f19(A,f23(A))) = f23(A) | member(f17(A),B) | -member(f11(A,B),B) | -member(f12(A,B),A). [resolve(268,c,223,b)]. given #1409 (T,wt=7): 21915 member(f24(range_of(cross_product(c2,c3))),c3). [resolve(19458,a,1637,a)]. given #1410 (T,wt=8): 21923 member(f24(range_of(cross_product(c2,c3))),range_of(c4)). [resolve(21915,a,5583,a)]. given #1411 (T,wt=8): 21937 ilf_type(f24(range_of(cross_product(c2,c3))),member_type(c3)). [resolve(21915,a,212,c),unit_del(a,15798)]. given #1412 (T,wt=9): 21947 ilf_type(f24(range_of(cross_product(c2,c3))),member_type(range_of(c4))). [resolve(21923,a,212,c),unit_del(a,16844)]. given #1413 (A,wt=28): 624 empty(A) | ordered_pair(f18(A,f23(A)),f19(A,f23(A))) = f23(A) | member(f17(A),B) | -member(f11(A,B),B) | member(f12(A,B),B). [resolve(268,c,222,b)]. given #1414 (T,wt=10): 19467 member(f24(domain_of(cross_product(c2,c3))),domain_of(cross_product(c2,c3))). [resolve(19442,a,205,a)]. given #1415 (T,wt=7): 21948 member(f24(domain_of(cross_product(c2,c3))),c2). [resolve(19467,a,1614,a)]. given #1416 (T,wt=8): 21968 ilf_type(f24(domain_of(cross_product(c2,c3))),member_type(c2)). [resolve(21948,a,212,c),unit_del(a,16801)]. given #1417 (T,wt=10): 19609 member(f24(c3),A) | range_of(cross_product(c2,c3)) != A. [resolve(19599,a,231,b)]. given #1418 (A,wt=23): 625 empty(A) | ordered_pair(f18(A,f23(A)),f19(A,f23(A))) = f23(A) | member(f17(A),B) | member(f14(A,B),A). [resolve(268,c,218,a)]. given #1419 (T,wt=10): 19889 member(f25(f24(range_of(c4))),A) | domain_of(c4) != A. [resolve(19873,a,231,b)]. given #1420 (T,wt=10): 19914 member(f25(f24(range_of(c4))),A) | -member(c2,power_set(A)). [resolve(19887,a,214,a)]. given #1421 (T,wt=10): 19994 member(f23(c3),A) | range_of(cross_product(c2,c3)) != A. [resolve(19984,a,231,b)]. given #1422 (T,wt=10): 20558 member(f25(f23(range_of(c4))),A) | domain_of(c4) != A. [resolve(20542,a,231,b)]. given #1423 (A,wt=23): 626 empty(A) | ordered_pair(f18(A,f23(A)),f19(A,f23(A))) = f23(A) | member(f17(A),B) | -member(f14(A,B),B). [resolve(268,c,217,a)]. given #1424 (T,wt=10): 20584 member(f25(f23(range_of(c4))),A) | -member(c2,power_set(A)). [resolve(20556,a,214,a)]. given #1425 (T,wt=10): 20667 member(f25(f16(range_of(c4))),A) | domain_of(c4) != A. [resolve(20651,a,231,b)]. given #1426 (T,wt=10): 20692 member(f25(f16(range_of(c4))),A) | -member(c2,power_set(A)). [resolve(20665,a,214,a)]. given #1427 (T,wt=10): 20811 ilf_type(f15(c3,A),member_type(c3)) | member(f24(A),A). [resolve(17465,a,205,a)]. given #1428 (A,wt=25): 627 ordered_pair(f18(power_set(A),f23(power_set(A))),f19(power_set(A),f23(power_set(A)))) = f23(power_set(A)) | -member(B,f17(power_set(A))) | member(B,A). [resolve(268,c,214,c),unit_del(a,213)]. given #1429 (T,wt=10): 20856 ilf_type(f15(c2,A),member_type(c2)) | member(f24(A),A). [resolve(17509,a,205,a)]. given #1430 (T,wt=10): 20902 ilf_type(f15(c4,A),member_type(c4)) | member(f24(A),A). [resolve(17511,a,205,a)]. given #1431 (T,wt=10): 21031 ilf_type(f13(c3,A),member_type(c3)) | member(f24(A),A). [resolve(17544,a,205,a)]. given #1432 (T,wt=10): 21103 member(f13(c3,f6(A)),c3) | member(f24(A),A). [resolve(17561,b,205,a)]. given #1433 (A,wt=22): 628 empty(A) | ordered_pair(f18(A,f23(A)),f19(A,f23(A))) = f23(A) | member(f17(A),B) | -member(A,power_set(B)). [resolve(268,c,214,a)]. given #1434 (T,wt=10): 21177 member(f14(c3,f6(A)),c3) | member(f24(A),A). [resolve(17616,b,205,a)]. given #1435 (T,wt=10): 21221 ilf_type(f14(c3,A),member_type(c3)) | member(f24(A),A). [resolve(17670,a,205,a)]. given #1436 (T,wt=10): 21242 ilf_type(c3,binary_relation_type) | ilf_type(f2(c4,f17(c3)),member_type(c2)). [resolve(21222,b,212,c),unit_del(b,16801)]. given #1437 (T,wt=10): 21286 ilf_type(f13(c4,A),member_type(c4)) | member(f24(A),A). [resolve(17843,a,205,a)]. given #1438 (A,wt=19): 629 empty(A) | ordered_pair(f18(A,f23(A)),f19(A,f23(A))) = f23(A) | ilf_type(f17(A),member_type(A)). [resolve(268,c,212,c),merge(c)]. given #1439 (T,wt=10): 21331 ilf_type(f13(c2,A),member_type(c2)) | member(f24(A),A). [resolve(17844,a,205,a)]. given #1440 (T,wt=10): 21376 ilf_type(f14(c2,A),member_type(c2)) | member(f24(A),A). [resolve(17845,a,205,a)]. given #1441 (T,wt=10): 21421 ilf_type(f14(c4,A),member_type(c4)) | member(f24(A),A). [resolve(17863,a,205,a)]. given #1442 (T,wt=10): 21925 member(f24(range_of(cross_product(c2,c3))),A) | c3 != A. [resolve(21915,a,231,b)]. given #1443 (A,wt=30): 630 empty(A) | ordered_pair(f18(A,f23(A)),f19(A,f23(A))) = f23(A) | ordered_pair(f20(A,f17(A)),f21(A,f17(A))) = f17(A) | member(f22(A),A). [resolve(268,c,209,a)]. given #1444 (T,wt=10): 21956 member(f24(domain_of(cross_product(c2,c3))),A) | c2 != A. [resolve(21948,a,231,b)]. given #1445 (T,wt=11): 4577 member(f24(A),A) | -member(B,f6(A)) | member(B,C). [resolve(4554,a,214,c)]. given #1446 (T,wt=11): 4590 member(f6(c4),power_set(A)) | member(f24(c4),cross_product(c2,c3)). [resolve(4554,b,750,a)]. given #1447 (T,wt=11): 4592 member(f6(domain_of(c4)),power_set(A)) | member(f24(domain_of(c4)),c2). [resolve(4554,b,600,a)]. given #1448 (A,wt=32): 631 empty(A) | ordered_pair(f18(A,f23(A)),f19(A,f23(A))) = f23(A) | ordered_pair(f20(A,f17(A)),f21(A,f17(A))) = f17(A) | f22(A) != ordered_pair(B,C). [resolve(268,c,208,a)]. given #1449 (T,wt=11): 4593 member(f6(range_of(c4)),power_set(A)) | member(f24(range_of(c4)),c3). [resolve(4554,b,580,a)]. given #1450 (T,wt=11): 4594 member(f6(f6(A)),power_set(B)) | member(f24(f6(A)),A). [resolve(4554,b,528,a)]. given #1451 (T,wt=8): 22331 member(f6(f6(A)),power_set(B)) | -empty(A). [resolve(4594,b,206,a)]. given #1452 (T,wt=10): 22332 member(f6(f6(A)),power_set(B)) | member(f24(A),A). [resolve(4594,b,205,a)]. given #1453 (A,wt=44): 633 empty(domain_of(f5(A,cross_product(B,C)))) | ordered_pair(f18(domain_of(f5(A,cross_product(B,C))),f23(domain_of(f5(A,cross_product(B,C))))),f19(domain_of(f5(A,cross_product(B,C))),f23(domain_of(f5(A,cross_product(B,C)))))) = f23(domain_of(f5(A,cross_product(B,C)))). [resolve(365,a,266,b)]. given #1454 (T,wt=10): 22363 member(f24(A),A) | -member(f24(A),f6(f6(A))). [factor(22340,a,c)]. given #1455 (T,wt=11): 4625 ilf_type(power_set(A),binary_relation_type) | ilf_type(f17(power_set(A)),member_type(power_set(A))). [resolve(948,b,237,b)]. given #1456 (T,wt=11): 4688 empty(f16(power_set(A))) | member(f24(A),B) | A != B. [resolve(4666,b,231,b)]. given #1457 (T,wt=11): 4693 empty(f16(power_set(A))) | member(f24(A),B) | B != A. [resolve(4666,b,226,b)]. given #1458 (A,wt=44): 637 empty(range_of(f5(cross_product(A,B),C))) | ordered_pair(f18(range_of(f5(cross_product(A,B),C)),f23(range_of(f5(cross_product(A,B),C)))),f19(range_of(f5(cross_product(A,B),C)),f23(range_of(f5(cross_product(A,B),C))))) = f23(range_of(f5(cross_product(A,B),C))). [resolve(367,a,266,b)]. given #1459 (T,wt=11): 4769 empty(f24(power_set(A))) | member(f24(A),B) | A != B. [resolve(4747,b,231,b)]. given #1460 (T,wt=11): 4774 empty(f24(power_set(A))) | member(f24(A),B) | B != A. [resolve(4747,b,226,b)]. given #1461 (T,wt=11): 5608 member(f23(f6(f6(c3))),range_of(c4)) | empty(f6(f6(c3))). [resolve(5583,a,1190,b)]. given #1462 (T,wt=11): 5609 member(f24(f6(f6(c3))),range_of(c4)) | empty(f6(f6(c3))). [resolve(5583,a,1156,b)]. given #1463 (A,wt=17): 642 ilf_type(c3,binary_relation_type) | member(f24(c4),A) | member(f9(A,c4),A) | -member(f10(A,c4),A). [resolve(421,b,230,b)]. given #1464 (T,wt=11): 5612 member(f16(f6(f6(c3))),range_of(c4)) | empty(f6(f6(c3))). [resolve(5583,a,1083,b)]. given #1465 (T,wt=11): 5613 member(f24(f16(power_set(c3))),range_of(c4)) | empty(f16(power_set(c3))). [resolve(5583,a,982,a)]. given #1466 (T,wt=11): 5614 member(f16(f16(power_set(c3))),range_of(c4)) | empty(f16(power_set(c3))). [resolve(5583,a,978,a)]. given #1467 (T,wt=11): 5615 member(f24(f24(power_set(c3))),range_of(c4)) | empty(f24(power_set(c3))). [resolve(5583,a,971,a)]. given #1468 (A,wt=17): 643 ilf_type(c3,binary_relation_type) | member(f24(c4),A) | member(f9(A,c4),A) | member(f10(A,c4),c4). [resolve(421,b,229,b)]. given #1469 (T,wt=11): 5616 member(f16(f24(power_set(c3))),range_of(c4)) | empty(f24(power_set(c3))). [resolve(5583,a,967,a)]. given #1470 (T,wt=11): 5617 member(f23(f24(power_set(c3))),range_of(c4)) | empty(f24(power_set(c3))). [resolve(5583,a,958,a)]. given #1471 (T,wt=11): 5618 member(f23(f16(power_set(c3))),range_of(c4)) | empty(f16(power_set(c3))). [resolve(5583,a,957,a)]. given #1472 (T,wt=11): 5619 member(f24(f6(c3)),range_of(c4)) | member(f6(c3),power_set(A)). [resolve(5583,a,923,b)]. given #1473 (A,wt=17): 644 ilf_type(c3,binary_relation_type) | member(f24(c4),A) | -member(f9(A,c4),c4) | -member(f10(A,c4),A). [resolve(421,b,228,b)]. given #1474 (T,wt=11): 5621 member(f23(f23(power_set(c3))),range_of(c4)) | empty(f23(power_set(c3))). [resolve(5583,a,878,a)]. given #1475 (T,wt=11): 5622 member(f24(f23(power_set(c3))),range_of(c4)) | empty(f23(power_set(c3))). [resolve(5583,a,873,a)]. given #1476 (T,wt=11): 5623 member(f16(f23(power_set(c3))),range_of(c4)) | empty(f23(power_set(c3))). [resolve(5583,a,869,a)]. given #1477 (T,wt=11): 5779 empty(f6(c3)) | member(f24(c3),A) | range_of(c4) != A. [resolve(5611,a,231,b)]. given #1478 (A,wt=17): 645 ilf_type(c3,binary_relation_type) | member(f24(c4),A) | -member(f9(A,c4),c4) | member(f10(A,c4),c4). [resolve(421,b,227,b)]. given #1479 (T,wt=11): 5801 ilf_type(c3,binary_relation_type) | member(f24(c3),A) | range_of(c4) != A. [resolve(5657,a,231,b)]. given #1480 (T,wt=11): 6344 member(f24(c3),range_of(c4)) | -member(A,c3) | member(A,B). [resolve(5652,b,214,c)]. given #1481 (T,wt=11): 6374 empty(f6(c3)) | member(f24(range_of(c4)),A) | c3 != A. [resolve(6352,b,231,b)]. given #1482 (T,wt=11): 6429 member(f24(c4),c4) | member(f24(c3),A) | empty(f6(c3)). [resolve(1930,b,1110,b)]. given #1483 (A,wt=17): 646 ilf_type(c3,binary_relation_type) | member(f24(c4),A) | member(f11(c4,A),c4) | -member(f12(c4,A),c4). [resolve(421,b,225,b)]. given #1484 (T,wt=11): 6560 A = B | member(f24(A),A) | member(f24(B),B). [resolve(351,b,205,a)]. given #1485 (T,wt=9): 22486 A = B | member(f24(B),B) | -empty(A). [resolve(6560,b,206,a)]. given #1486 (T,wt=11): 6735 ilf_type(f6(f6(c3)),binary_relation_type) | member(f24(f6(c3)),range_of(c4)). [resolve(2333,b,5583,a)]. given #1487 (T,wt=11): 6883 ilf_type(f6(f6(c4)),binary_relation_type) | member(f24(c4),cross_product(c2,c3)). [resolve(6778,b,750,a)]. given #1488 (A,wt=17): 647 ilf_type(c3,binary_relation_type) | member(f24(c4),A) | member(f11(c4,A),c4) | member(f12(c4,A),A). [resolve(421,b,224,b)]. given #1489 (T,wt=11): 6885 ilf_type(f6(f6(domain_of(c4))),binary_relation_type) | member(f24(domain_of(c4)),c2). [resolve(6778,b,600,a)]. given #1490 (T,wt=11): 6886 ilf_type(f6(f6(range_of(c4))),binary_relation_type) | member(f24(range_of(c4)),c3). [resolve(6778,b,580,a)]. given #1491 (T,wt=11): 6887 ilf_type(f6(f6(f6(A))),binary_relation_type) | member(f24(f6(A)),A). [resolve(6778,b,528,a)]. given #1492 (T,wt=8): 22534 ilf_type(f6(f6(f6(A))),binary_relation_type) | -empty(A). [resolve(6887,b,206,a)]. given #1493 (A,wt=17): 648 ilf_type(c3,binary_relation_type) | member(f24(c4),A) | -member(f11(c4,A),A) | -member(f12(c4,A),c4). [resolve(421,b,223,b)]. given #1494 (T,wt=10): 22535 ilf_type(f6(f6(f6(A))),binary_relation_type) | member(f24(A),A). [resolve(6887,b,205,a)]. given #1495 (T,wt=11): 6936 member(A,B) | ilf_type(f13(power_set(A),B),member_type(power_set(A))). [resolve(2455,a,212,c),unit_del(b,213)]. given #1496 (T,wt=10): 22679 ilf_type(f13(power_set(A),B),member_type(power_set(A))) | -empty(B). [resolve(6936,a,206,a)]. given #1497 (T,wt=11): 7152 empty(f6(f6(f6(c3)))) | member(f24(f6(c3)),range_of(c4)). [resolve(2888,b,5583,a)]. given #1498 (A,wt=17): 649 ilf_type(c3,binary_relation_type) | member(f24(c4),A) | -member(f11(c4,A),A) | member(f12(c4,A),A). [resolve(421,b,222,b)]. given #1499 (T,wt=11): 7209 empty(f6(f6(f6(c4)))) | member(f24(c4),cross_product(c2,c3)). [resolve(7196,b,750,a)]. given #1500 (T,wt=11): 7211 empty(f6(f6(f6(domain_of(c4))))) | member(f24(domain_of(c4)),c2). [resolve(7196,b,600,a)]. given #1501 (T,wt=11): 7212 empty(f6(f6(f6(range_of(c4))))) | member(f24(range_of(c4)),c3). [resolve(7196,b,580,a)]. given #1502 (T,wt=11): 7213 empty(f6(f6(f6(f6(A))))) | member(f24(f6(A)),A). [resolve(7196,b,528,a)]. given #1503 (A,wt=12): 650 ilf_type(c3,binary_relation_type) | member(f24(c4),A) | member(f14(c4,A),c4). [resolve(421,b,218,a)]. given #1504 (T,wt=8): 22719 empty(f6(f6(f6(f6(A))))) | -empty(A). [resolve(7213,b,206,a)]. given #1505 (T,wt=10): 22720 empty(f6(f6(f6(f6(A))))) | member(f24(A),A). [resolve(7213,b,205,a)]. given #1506 (T,wt=11): 7404 -member(A,domain_of(f16(power_set(cross_product(B,C))))) | member(A,B). [resolve(7385,a,214,c)]. given #1507 (T,wt=11): 7431 -member(A,range_of(f16(power_set(cross_product(B,C))))) | member(A,C). [resolve(7412,a,214,c)]. given #1508 (A,wt=12): 651 ilf_type(c3,binary_relation_type) | member(f24(c4),A) | -member(f14(c4,A),A). [resolve(421,b,217,a)]. given #1509 (T,wt=11): 7458 -member(A,domain_of(f23(power_set(cross_product(B,C))))) | member(A,B). [resolve(7439,a,214,c)]. given #1510 (T,wt=11): 7485 -member(A,range_of(f23(power_set(cross_product(B,C))))) | member(A,C). [resolve(7466,a,214,c)]. given #1511 (T,wt=11): 7512 -member(A,domain_of(f24(power_set(cross_product(B,C))))) | member(A,B). [resolve(7493,a,214,c)]. given #1512 (T,wt=11): 7539 -member(A,range_of(f24(power_set(cross_product(B,C))))) | member(A,C). [resolve(7520,a,214,c)]. given #1513 (A,wt=19): 653 ilf_type(c3,binary_relation_type) | ordered_pair(f20(c4,f24(c4)),f21(c4,f24(c4))) = f24(c4) | member(f22(c4),c4). [resolve(421,b,209,a)]. given #1514 (T,wt=11): 7673 ilf_type(domain_of(domain_of(f5(A,cross_product(B,C)))),member_type(power_set(B))). [resolve(3841,a,237,b)]. given #1515 (T,wt=10): 23414 member(domain_of(domain_of(f5(A,cross_product(B,C)))),power_set(B)). [resolve(7673,a,211,c),unit_del(a,213)]. given #1516 (T,wt=11): 7674 ilf_type(domain_of(domain_of(f5(A,cross_product(cross_product(B,C),D)))),binary_relation_type). [resolve(3841,a,129,a)]. given #1517 (T,wt=11): 7679 ilf_type(range_of(domain_of(f5(A,cross_product(B,C)))),member_type(power_set(C))). [resolve(3843,a,237,b)]. given #1518 (A,wt=21): 654 ilf_type(c3,binary_relation_type) | ordered_pair(f20(c4,f24(c4)),f21(c4,f24(c4))) = f24(c4) | f22(c4) != ordered_pair(A,B). [resolve(421,b,208,a)]. given #1519 (T,wt=10): 23424 member(range_of(domain_of(f5(A,cross_product(B,C)))),power_set(C)). [resolve(7679,a,211,c),unit_del(a,213)]. given #1520 (T,wt=11): 7680 ilf_type(range_of(domain_of(f5(A,cross_product(B,cross_product(C,D))))),binary_relation_type). [resolve(3843,a,129,a)]. given #1521 (T,wt=11): 7685 ilf_type(domain_of(range_of(f5(cross_product(A,B),C))),member_type(power_set(A))). [resolve(3845,a,237,b)]. given #1522 (T,wt=10): 23434 member(domain_of(range_of(f5(cross_product(A,B),C))),power_set(A)). [resolve(7685,a,211,c),unit_del(a,213)]. given #1523 (A,wt=14): 659 empty(c1) | ordered_pair(f18(c1,f23(c1)),f19(c1,f23(c1))) = f23(c1). [resolve(269,c,41,a)]. Low Water (displace): id=9401, wt=79.000 Low Water (displace): id=9407, wt=72.000 Low Water (displace): id=7716, wt=67.000 Low Water (displace): id=11235, wt=65.000 given #1524 (T,wt=11): 7686 ilf_type(domain_of(range_of(f5(cross_product(cross_product(A,B),C),D))),binary_relation_type). [resolve(3845,a,129,a)]. given #1525 (T,wt=11): 7691 ilf_type(range_of(range_of(f5(cross_product(A,B),C))),member_type(power_set(B))). [resolve(3847,a,237,b)]. given #1526 (T,wt=10): 23494 member(range_of(range_of(f5(cross_product(A,B),C))),power_set(B)). [resolve(7691,a,211,c),unit_del(a,213)]. given #1527 (T,wt=11): 7692 ilf_type(range_of(range_of(f5(cross_product(A,cross_product(B,C)),D))),binary_relation_type). [resolve(3847,a,129,a)]. given #1528 (A,wt=38): 665 empty(f24(power_set(cross_product(A,B)))) | ordered_pair(f18(f24(power_set(cross_product(A,B))),f23(f24(power_set(cross_product(A,B))))),f19(f24(power_set(cross_product(A,B))),f23(f24(power_set(cross_product(A,B)))))) = f23(f24(power_set(cross_product(A,B)))). [resolve(664,a,266,b)]. given #1529 (T,wt=11): 7701 ilf_type(domain_of(domain_of(cross_product(cross_product(A,B),C))),member_type(power_set(A))). [resolve(4060,a,237,b)]. given #1530 (T,wt=10): 23504 member(domain_of(domain_of(cross_product(cross_product(A,B),C))),power_set(A)). [resolve(7701,a,211,c),unit_del(a,213)]. given #1531 (T,wt=11): 7702 ilf_type(domain_of(domain_of(cross_product(cross_product(cross_product(A,B),C),D))),binary_relation_type). [resolve(4060,a,129,a)]. given #1532 (T,wt=11): 7707 ilf_type(range_of(domain_of(cross_product(cross_product(A,B),C))),member_type(power_set(B))). [resolve(4062,a,237,b)]. given #1533 (A,wt=25): 669 member(f17(f6(A)),A) | empty(f6(A)) | ordered_pair(f18(f6(A),f23(f6(A))),f19(f6(A),f23(f6(A)))) = f23(f6(A)). [resolve(528,a,268,c)]. given #1534 (T,wt=10): 23514 member(range_of(domain_of(cross_product(cross_product(A,B),C))),power_set(B)). [resolve(7707,a,211,c),unit_del(a,213)]. Low Water (displace): id=7767, wt=63.000 given #1535 (T,wt=11): 7708 ilf_type(range_of(domain_of(cross_product(cross_product(A,cross_product(B,C)),D))),binary_relation_type). [resolve(4062,a,129,a)]. given #1536 (T,wt=11): 7713 ilf_type(domain_of(range_of(cross_product(A,cross_product(B,C)))),member_type(power_set(B))). [resolve(4064,a,237,b)]. given #1537 (T,wt=10): 23524 member(domain_of(range_of(cross_product(A,cross_product(B,C)))),power_set(B)). [resolve(7713,a,211,c),unit_del(a,213)]. Low Water (displace): id=8062, wt=62.000 given #1538 (A,wt=16): 672 member(f4(A,f6(B)),B) | member(f3(A,f6(B)),A) | f6(B) = A. [resolve(528,a,250,b)]. given #1539 (T,wt=10): 23536 member(f3(A,f6(A)),A) | f6(A) = A. [resolve(672,a,251,b),merge(c),merge(d)]. Low Water (displace): id=9663, wt=61.000 given #1540 (T,wt=6): 23556 f6(A) = A | -empty(A). [resolve(23536,a,206,a)]. given #1541 (T,wt=8): 23557 f6(A) = A | member(f24(A),A). [resolve(23536,a,205,a)]. Low Water (displace): id=23562, wt=17.000 given #1542 (T,wt=11): 7714 ilf_type(domain_of(range_of(cross_product(A,cross_product(cross_product(B,C),D)))),binary_relation_type). [resolve(4064,a,129,a)]. given #1543 (A,wt=16): 673 member(f8(A,f6(B)),B) | f6(B) = A | member(f7(A,f6(B)),A). [resolve(528,a,234,c)]. given #1544 (T,wt=10): 23588 f6(A) = A | member(f7(A,f6(A)),A). [resolve(673,a,235,c),merge(c),merge(d)]. given #1545 (T,wt=11): 7719 ilf_type(range_of(range_of(cross_product(A,cross_product(B,C)))),member_type(power_set(C))). [resolve(4066,a,237,b)]. given #1546 (T,wt=10): 23609 member(range_of(range_of(cross_product(A,cross_product(B,C)))),power_set(C)). [resolve(7719,a,211,c),unit_del(a,213)]. given #1547 (T,wt=11): 7720 ilf_type(range_of(range_of(cross_product(A,cross_product(B,cross_product(C,D))))),binary_relation_type). [resolve(4066,a,129,a)]. given #1548 (A,wt=17): 721 member(f16(power_set(A)),B) | member(f9(B,power_set(A)),B) | -member(f10(B,power_set(A)),B). [resolve(719,a,230,b)]. given #1549 (T,wt=11): 7946 empty(f23(power_set(f6(c3)))) | member(f24(f6(c3)),range_of(c4)). [resolve(4208,b,5583,a)]. Low Water (displace): id=23624, wt=15.000 given #1550 (T,wt=11): 8007 empty(f23(power_set(f6(c4)))) | member(f24(c4),cross_product(c2,c3)). [resolve(7992,b,750,a)]. given #1551 (T,wt=11): 8009 empty(f23(power_set(f6(domain_of(c4))))) | member(f24(domain_of(c4)),c2). [resolve(7992,b,600,a)]. given #1552 (T,wt=11): 8010 empty(f23(power_set(f6(range_of(c4))))) | member(f24(range_of(c4)),c3). [resolve(7992,b,580,a)]. given #1553 (A,wt=18): 722 member(f16(power_set(A)),B) | member(f9(B,power_set(A)),B) | member(f10(B,power_set(A)),power_set(A)). [resolve(719,a,229,b)]. given #1554 (T,wt=11): 8011 empty(f23(power_set(f6(f6(A))))) | member(f24(f6(A)),A). [resolve(7992,b,528,a)]. given #1555 (T,wt=8): 23649 empty(f23(power_set(f6(f6(A))))) | -empty(A). [resolve(8011,b,206,a)]. given #1556 (T,wt=10): 23650 empty(f23(power_set(f6(f6(A))))) | member(f24(A),A). [resolve(8011,b,205,a)]. given #1557 (T,wt=11): 8064 ilf_type(range_of(c4),member_type(power_set(A))) | member(f24(c3),range_of(c4)). [resolve(4468,a,5583,a)]. given #1558 (A,wt=18): 723 member(f16(power_set(A)),B) | -member(f9(B,power_set(A)),power_set(A)) | -member(f10(B,power_set(A)),B). [resolve(719,a,228,b)]. given #1559 (T,wt=11): 8087 ilf_type(f6(c3),member_type(power_set(A))) | member(f24(c3),range_of(c4)). [resolve(4579,a,5583,a)]. given #1560 (T,wt=11): 8355 empty(f16(power_set(f6(c3)))) | member(f24(f6(c3)),range_of(c4)). [resolve(4680,b,5583,a)]. given #1561 (T,wt=11): 8416 empty(f16(power_set(f6(c4)))) | member(f24(c4),cross_product(c2,c3)). [resolve(8401,b,750,a)]. given #1562 (T,wt=11): 8418 empty(f16(power_set(f6(domain_of(c4))))) | member(f24(domain_of(c4)),c2). [resolve(8401,b,600,a)]. given #1563 (A,wt=19): 724 member(f16(power_set(A)),B) | -member(f9(B,power_set(A)),power_set(A)) | member(f10(B,power_set(A)),power_set(A)). [resolve(719,a,227,b)]. given #1564 (T,wt=11): 8419 empty(f16(power_set(f6(range_of(c4))))) | member(f24(range_of(c4)),c3). [resolve(8401,b,580,a)]. given #1565 (T,wt=11): 8420 empty(f16(power_set(f6(f6(A))))) | member(f24(f6(A)),A). [resolve(8401,b,528,a)]. Low Water (displace): id=23689, wt=13.000 given #1566 (T,wt=8): 23703 empty(f16(power_set(f6(f6(A))))) | -empty(A). [resolve(8420,b,206,a)]. given #1567 (T,wt=10): 23704 empty(f16(power_set(f6(f6(A))))) | member(f24(A),A). [resolve(8420,b,205,a)]. given #1568 (A,wt=19): 725 member(f16(power_set(A)),B) | member(f11(power_set(A),B),power_set(A)) | -member(f12(power_set(A),B),power_set(A)). [resolve(719,a,225,b)]. given #1569 (T,wt=11): 8790 empty(f24(power_set(f6(c3)))) | member(f24(f6(c3)),range_of(c4)). [resolve(4761,b,5583,a)]. given #1570 (T,wt=11): 8853 empty(f24(power_set(f6(c4)))) | member(f24(c4),cross_product(c2,c3)). [resolve(8838,b,750,a)]. given #1571 (T,wt=11): 8855 empty(f24(power_set(f6(domain_of(c4))))) | member(f24(domain_of(c4)),c2). [resolve(8838,b,600,a)]. given #1572 (T,wt=11): 8856 empty(f24(power_set(f6(range_of(c4))))) | member(f24(range_of(c4)),c3). [resolve(8838,b,580,a)]. given #1573 (A,wt=18): 726 member(f16(power_set(A)),B) | member(f11(power_set(A),B),power_set(A)) | member(f12(power_set(A),B),B). [resolve(719,a,224,b)]. given #1574 (T,wt=11): 8857 empty(f24(power_set(f6(f6(A))))) | member(f24(f6(A)),A). [resolve(8838,b,528,a)]. given #1575 (T,wt=8): 23759 empty(f24(power_set(f6(f6(A))))) | -empty(A). [resolve(8857,b,206,a)]. given #1576 (T,wt=10): 23760 empty(f24(power_set(f6(f6(A))))) | member(f24(A),A). [resolve(8857,b,205,a)]. given #1577 (T,wt=11): 8903 member(f24(range_of(c4)),range_of(c4)) | ilf_type(c3,member_type(power_set(A))). [resolve(5566,a,212,c),unit_del(b,213)]. given #1578 (A,wt=18): 727 member(f16(power_set(A)),B) | -member(f11(power_set(A),B),B) | -member(f12(power_set(A),B),power_set(A)). [resolve(719,a,223,b)]. given #1579 (T,wt=11): 9051 member(f24(range_of(c4)),c3) | -member(A,c3) | member(A,B). [resolve(8910,a,214,c)]. given #1580 (T,wt=11): 9101 member(f6(c3),power_set(A)) | member(f24(range_of(c4)),range_of(c4)). [resolve(5599,a,205,a)]. given #1581 (T,wt=11): 9750 ilf_type(f6(f6(c3)),binary_relation_type) | member(f24(range_of(c4)),range_of(c4)). [resolve(6877,b,205,a)]. given #1582 (T,wt=11): 9793 empty(f6(f6(f6(c3)))) | member(f24(range_of(c4)),range_of(c4)). [resolve(7202,b,205,a)]. given #1583 (A,wt=17): 728 member(f16(power_set(A)),B) | -member(f11(power_set(A),B),B) | member(f12(power_set(A),B),B). [resolve(719,a,222,b)]. given #1584 (T,wt=11): 9860 empty(f23(power_set(f6(c3)))) | member(f24(range_of(c4)),range_of(c4)). [resolve(7998,b,205,a)]. given #1585 (T,wt=11): 9902 empty(f16(power_set(f6(c3)))) | member(f24(range_of(c4)),range_of(c4)). [resolve(8407,b,205,a)]. given #1586 (T,wt=11): 9964 empty(f24(power_set(f6(c3)))) | member(f24(range_of(c4)),range_of(c4)). [resolve(8844,b,205,a)]. given #1587 (T,wt=11): 10401 ilf_type(c3,binary_relation_type) | member(f25(f24(c3)),A) | c2 != A. [resolve(10379,b,231,b)]. given #1588 (A,wt=12): 729 member(f16(power_set(A)),B) | member(f14(power_set(A),B),power_set(A)). [resolve(719,a,218,a)]. given #1589 (T,wt=11): 10471 member(f14(power_set(A),B),power_set(A)) | member(f24(B),B). [resolve(526,a,205,a)]. given #1590 (T,wt=11): 10507 member(f6(A),A) | -member(f6(A),f14(power_set(A),A)). [factor(10497,a,c)]. given #1591 (T,wt=11): 10617 member(range_of(c4),c3) | -member(range_of(c4),f14(power_set(c3),c3)). [factor(10607,a,c)]. given #1592 (T,wt=11): 10703 member(domain_of(c4),c2) | -member(domain_of(c4),f14(power_set(c2),c2)). [factor(10693,a,c)]. given #1593 (A,wt=23): 732 ordered_pair(f20(power_set(A),f16(power_set(A))),f21(power_set(A),f16(power_set(A)))) = f16(power_set(A)) | member(f22(power_set(A)),power_set(A)). [resolve(719,a,209,a)]. given #1594 (T,wt=11): 11177 ilf_type(f23(power_set(c4)),binary_relation_type) | member(f24(c4),cross_product(c2,c3)). [resolve(11162,b,750,a)]. given #1595 (T,wt=11): 11179 ilf_type(f23(power_set(domain_of(c4))),binary_relation_type) | member(f24(domain_of(c4)),c2). [resolve(11162,b,600,a)]. given #1596 (T,wt=11): 11180 ilf_type(f23(power_set(range_of(c4))),binary_relation_type) | member(f24(range_of(c4)),c3). [resolve(11162,b,580,a)]. given #1597 (T,wt=11): 11181 ilf_type(f23(power_set(f6(A))),binary_relation_type) | member(f24(f6(A)),A). [resolve(11162,b,528,a)]. given #1598 (A,wt=24): 733 ordered_pair(f20(power_set(A),f16(power_set(A))),f21(power_set(A),f16(power_set(A)))) = f16(power_set(A)) | f22(power_set(A)) != ordered_pair(B,C). [resolve(719,a,208,a)]. given #1599 (T,wt=8): 23885 ilf_type(f23(power_set(f6(A))),binary_relation_type) | -empty(A). [resolve(11181,b,206,a)]. given #1600 (T,wt=10): 23886 ilf_type(f23(power_set(f6(A))),binary_relation_type) | member(f24(A),A). [resolve(11181,b,205,a)]. given #1601 (T,wt=11): 11228 ilf_type(f23(power_set(c3)),binary_relation_type) | member(f24(range_of(c4)),range_of(c4)). [resolve(11168,b,205,a)]. given #1602 (T,wt=11): 11463 ilf_type(f24(power_set(c4)),binary_relation_type) | member(f24(c4),cross_product(c2,c3)). [resolve(11448,b,750,a)]. given #1603 (A,wt=24): 734 -ilf_type(power_set(A),subset_type(cross_product(B,C))) | ordered_pair(f18(power_set(A),f16(power_set(A))),f19(power_set(A),f16(power_set(A)))) = f16(power_set(A)). [resolve(719,a,131,b)]. given #1604 (T,wt=11): 11465 ilf_type(f24(power_set(domain_of(c4))),binary_relation_type) | member(f24(domain_of(c4)),c2). [resolve(11448,b,600,a)]. given #1605 (T,wt=11): 11466 ilf_type(f24(power_set(range_of(c4))),binary_relation_type) | member(f24(range_of(c4)),c3). [resolve(11448,b,580,a)]. given #1606 (T,wt=11): 11467 ilf_type(f24(power_set(f6(A))),binary_relation_type) | member(f24(f6(A)),A). [resolve(11448,b,528,a)]. given #1607 (T,wt=8): 23932 ilf_type(f24(power_set(f6(A))),binary_relation_type) | -empty(A). [resolve(11467,b,206,a)]. given #1608 (A,wt=24): 735 ordered_pair(f18(power_set(A),f16(power_set(A))),f19(power_set(A),f16(power_set(A)))) = f16(power_set(A)) | f17(power_set(A)) != ordered_pair(B,C). [resolve(719,a,127,a)]. given #1609 (T,wt=10): 23933 ilf_type(f24(power_set(f6(A))),binary_relation_type) | member(f24(A),A). [resolve(11467,b,205,a)]. given #1610 (T,wt=11): 11514 ilf_type(f24(power_set(c3)),binary_relation_type) | member(f24(range_of(c4)),range_of(c4)). [resolve(11454,b,205,a)]. given #1611 (T,wt=11): 11720 ilf_type(f16(power_set(c4)),binary_relation_type) | member(f24(c4),cross_product(c2,c3)). [resolve(11625,b,750,a)]. given #1612 (T,wt=11): 11722 ilf_type(f16(power_set(domain_of(c4))),binary_relation_type) | member(f24(domain_of(c4)),c2). [resolve(11625,b,600,a)]. given #1613 (A,wt=23): 736 ordered_pair(f18(power_set(A),f16(power_set(A))),f19(power_set(A),f16(power_set(A)))) = f16(power_set(A)) | member(f17(power_set(A)),power_set(A)). [resolve(719,a,125,a)]. given #1614 (T,wt=11): 11723 ilf_type(f16(power_set(range_of(c4))),binary_relation_type) | member(f24(range_of(c4)),c3). [resolve(11625,b,580,a)]. given #1615 (T,wt=11): 11724 ilf_type(f16(power_set(f6(A))),binary_relation_type) | member(f24(f6(A)),A). [resolve(11625,b,528,a)]. given #1616 (T,wt=8): 23979 ilf_type(f16(power_set(f6(A))),binary_relation_type) | -empty(A). [resolve(11724,b,206,a)]. given #1617 (T,wt=10): 23980 ilf_type(f16(power_set(f6(A))),binary_relation_type) | member(f24(A),A). [resolve(11724,b,205,a)]. given #1618 (A,wt=21): 737 ordered_pair(f18(power_set(A),f16(power_set(A))),f19(power_set(A),f16(power_set(A)))) = f16(power_set(A)) | -ilf_type(power_set(A),binary_relation_type). [resolve(719,a,123,a)]. given #1619 (T,wt=11): 11771 ilf_type(f16(power_set(c3)),binary_relation_type) | member(f24(range_of(c4)),range_of(c4)). [resolve(11711,b,205,a)]. given #1620 (T,wt=11): 11842 empty(f6(power_set(A))) | ilf_type(f16(f6(power_set(A))),subset_type(A)). [resolve(1106,c,238,b),unit_del(b,213)]. given #1621 (T,wt=11): 11907 empty(f6(f16(power_set(c4)))) | member(f24(c4),cross_product(c2,c3)). [resolve(11892,b,750,a)]. given #1622 (T,wt=11): 11909 empty(f6(f16(power_set(domain_of(c4))))) | member(f24(domain_of(c4)),c2). [resolve(11892,b,600,a)]. given #1623 (A,wt=19): 740 member(c4,A) | member(f9(A,power_set(cross_product(c2,c3))),A) | -member(f10(A,power_set(cross_product(c2,c3))),A). [resolve(738,a,230,b)]. given #1624 (T,wt=11): 11910 empty(f6(f16(power_set(range_of(c4))))) | member(f24(range_of(c4)),c3). [resolve(11892,b,580,a)]. given #1625 (T,wt=11): 11911 empty(f6(f16(power_set(f6(A))))) | member(f24(f6(A)),A). [resolve(11892,b,528,a)]. given #1626 (T,wt=8): 24029 empty(f6(f16(power_set(f6(A))))) | -empty(A). [resolve(11911,b,206,a)]. given #1627 (T,wt=10): 24030 empty(f6(f16(power_set(f6(A))))) | member(f24(A),A). [resolve(11911,b,205,a)]. given #1628 (A,wt=22): 741 member(c4,A) | member(f9(A,power_set(cross_product(c2,c3))),A) | member(f10(A,power_set(cross_product(c2,c3))),power_set(cross_product(c2,c3))). [resolve(738,a,229,b)]. given #1629 (T,wt=11): 11958 empty(f6(f16(power_set(c3)))) | member(f24(range_of(c4)),range_of(c4)). [resolve(11898,b,205,a)]. given #1630 (T,wt=11): 12046 empty(f6(f24(power_set(c4)))) | member(f24(c4),cross_product(c2,c3)). [resolve(12031,b,750,a)]. given #1631 (T,wt=11): 12048 empty(f6(f24(power_set(domain_of(c4))))) | member(f24(domain_of(c4)),c2). [resolve(12031,b,600,a)]. given #1632 (T,wt=11): 12049 empty(f6(f24(power_set(range_of(c4))))) | member(f24(range_of(c4)),c3). [resolve(12031,b,580,a)]. given #1633 (A,wt=22): 742 member(c4,A) | -member(f9(A,power_set(cross_product(c2,c3))),power_set(cross_product(c2,c3))) | -member(f10(A,power_set(cross_product(c2,c3))),A). [resolve(738,a,228,b)]. given #1634 (T,wt=11): 12050 empty(f6(f24(power_set(f6(A))))) | member(f24(f6(A)),A). [resolve(12031,b,528,a)]. given #1635 (T,wt=8): 24076 empty(f6(f24(power_set(f6(A))))) | -empty(A). [resolve(12050,b,206,a)]. given #1636 (T,wt=10): 24077 empty(f6(f24(power_set(f6(A))))) | member(f24(A),A). [resolve(12050,b,205,a)]. given #1637 (T,wt=11): 12097 empty(f6(f24(power_set(c3)))) | member(f24(range_of(c4)),range_of(c4)). [resolve(12037,b,205,a)]. given #1638 (A,wt=25): 743 member(c4,A) | -member(f9(A,power_set(cross_product(c2,c3))),power_set(cross_product(c2,c3))) | member(f10(A,power_set(cross_product(c2,c3))),power_set(cross_product(c2,c3))). [resolve(738,a,227,b)]. given #1639 (T,wt=11): 12166 empty(f6(f23(power_set(c4)))) | member(f24(c4),cross_product(c2,c3)). [resolve(12151,b,750,a)]. given #1640 (T,wt=11): 12168 empty(f6(f23(power_set(domain_of(c4))))) | member(f24(domain_of(c4)),c2). [resolve(12151,b,600,a)]. given #1641 (T,wt=11): 12169 empty(f6(f23(power_set(range_of(c4))))) | member(f24(range_of(c4)),c3). [resolve(12151,b,580,a)]. given #1642 (T,wt=11): 12170 empty(f6(f23(power_set(f6(A))))) | member(f24(f6(A)),A). [resolve(12151,b,528,a)]. given #1643 (A,wt=25): 744 member(c4,A) | member(f11(power_set(cross_product(c2,c3)),A),power_set(cross_product(c2,c3))) | -member(f12(power_set(cross_product(c2,c3)),A),power_set(cross_product(c2,c3))). [resolve(738,a,225,b)]. given #1644 (T,wt=8): 24123 empty(f6(f23(power_set(f6(A))))) | -empty(A). [resolve(12170,b,206,a)]. given #1645 (T,wt=10): 24124 empty(f6(f23(power_set(f6(A))))) | member(f24(A),A). [resolve(12170,b,205,a)]. given #1646 (T,wt=11): 12217 empty(f6(f23(power_set(c3)))) | member(f24(range_of(c4)),range_of(c4)). [resolve(12157,b,205,a)]. given #1647 (T,wt=11): 12368 empty(f6(c3)) | member(f24(c4),A) | -member(c4,power_set(A)). [resolve(12350,b,214,a)]. given #1648 (A,wt=22): 745 member(c4,A) | member(f11(power_set(cross_product(c2,c3)),A),power_set(cross_product(c2,c3))) | member(f12(power_set(cross_product(c2,c3)),A),A). [resolve(738,a,224,b)]. given #1649 (T,wt=11): 12399 empty(f6(c3)) | member(f25(f24(c3)),A) | c2 != A. [resolve(12375,b,231,b)]. given #1650 (T,wt=11): 12432 empty(f6(c3)) | member(f24(c2),A) | -member(c2,power_set(A)). [resolve(12415,b,214,a)]. given #1651 (T,wt=11): 12456 empty(f6(c3)) | member(f24(cross_product(c2,c3)),cross_product(c2,c3)). [resolve(12355,b,205,a)]. given #1652 (T,wt=11): 12484 empty(f6(c3)) | member(f24(domain_of(c4)),A) | c2 != A. [resolve(12463,b,231,b)]. given #1653 (A,wt=22): 746 member(c4,A) | -member(f11(power_set(cross_product(c2,c3)),A),A) | -member(f12(power_set(cross_product(c2,c3)),A),power_set(cross_product(c2,c3))). [resolve(738,a,223,b)]. given #1654 (T,wt=11): 12557 empty(f6(power_set(A))) | ilf_type(f24(f6(power_set(A))),subset_type(A)). [resolve(1180,c,238,b),unit_del(b,213)]. given #1655 (T,wt=11): 12558 empty(f6(power_set(A))) | ilf_type(f23(f6(power_set(A))),subset_type(A)). [resolve(1214,c,238,b),unit_del(b,213)]. given #1656 (T,wt=11): 13118 ilf_type(domain_of(domain_of(f6(cross_product(cross_product(A,B),C)))),subset_type(A)). [resolve(1767,a,203,a),rewrite([13117(5)])]. given #1657 (T,wt=11): 13120 ilf_type(range_of(domain_of(f6(cross_product(cross_product(A,B),C)))),subset_type(B)). [resolve(1767,a,201,a),rewrite([13119(5)])]. given #1658 (A,wt=19): 747 member(c4,A) | -member(f11(power_set(cross_product(c2,c3)),A),A) | member(f12(power_set(cross_product(c2,c3)),A),A). [resolve(738,a,222,b)]. given #1659 (T,wt=11): 13122 ilf_type(domain_of(range_of(f6(cross_product(A,cross_product(B,C))))),subset_type(B)). [resolve(1772,a,203,a),rewrite([13121(5)])]. given #1660 (T,wt=11): 13124 ilf_type(range_of(range_of(f6(cross_product(A,cross_product(B,C))))),subset_type(C)). [resolve(1772,a,201,a),rewrite([13123(5)])]. given #1661 (T,wt=11): 13182 member(f24(c2),c2) | member(c3,A) | power_set(B) != A. [resolve(13174,a,231,b)]. given #1662 (T,wt=11): 13203 member(c3,power_set(A)) | member(f24(c2),B) | c2 != B. [resolve(13174,b,231,b)]. given #1663 (A,wt=14): 748 member(c4,A) | member(f14(power_set(cross_product(c2,c3)),A),power_set(cross_product(c2,c3))). [resolve(738,a,218,a)]. given #1664 (T,wt=11): 13262 member(f24(domain_of(c4)),domain_of(c4)) | ilf_type(c3,member_type(power_set(A))). [resolve(13147,a,212,c),unit_del(b,213)]. given #1665 (T,wt=11): 13289 member(f24(domain_of(c4)),domain_of(c4)) | -member(f24(domain_of(c4)),c3). [factor(13260,a,c)]. given #1666 (T,wt=11): 13402 member(f24(domain_of(c4)),c2) | -member(A,c3) | member(A,B). [resolve(13269,a,214,c)]. given #1667 (T,wt=11): 13674 member(f24(A),A) | -member(f24(A),f14(power_set(A),A)). [factor(13620,a,c)]. given #1668 (A,wt=25): 752 ordered_pair(f20(power_set(cross_product(c2,c3)),c4),f21(power_set(cross_product(c2,c3)),c4)) = c4 | member(f22(power_set(cross_product(c2,c3))),power_set(cross_product(c2,c3))). [resolve(738,a,209,a)]. given #1669 (T,wt=11): 14240 member(f13(power_set(c2),A),power_set(c2)) | member(f24(A),A). [resolve(2434,b,205,a)]. given #1670 (T,wt=11): 14246 member(domain_of(c4),c2) | -member(domain_of(c4),f13(power_set(c2),c2)). [factor(14184,a,c)]. given #1671 (T,wt=11): 14326 member(f13(power_set(c3),A),power_set(c3)) | member(f24(A),A). [resolve(2435,b,205,a)]. given #1672 (T,wt=11): 14332 member(range_of(c4),c3) | -member(range_of(c4),f13(power_set(c3),c3)). [factor(14269,a,c)]. given #1673 (A,wt=24): 753 ordered_pair(f20(power_set(cross_product(c2,c3)),c4),f21(power_set(cross_product(c2,c3)),c4)) = c4 | f22(power_set(cross_product(c2,c3))) != ordered_pair(A,B). [resolve(738,a,208,a)]. given #1674 (T,wt=11): 14411 member(f13(power_set(A),B),power_set(A)) | member(f24(B),B). [resolve(2438,b,205,a)]. given #1675 (T,wt=11): 14417 member(f6(A),A) | -member(f6(A),f13(power_set(A),A)). [factor(14355,a,c)]. given #1676 (T,wt=11): 14523 member(f13(A,B),A) | empty(A) | member(f24(B),B). [resolve(2456,b,205,a)]. given #1677 (T,wt=10): 24261 member(f24(A),A) | member(f13(domain_of(c4),A),c2). [resolve(14523,a,600,a),unit_del(a,16822)]. given #1678 (A,wt=24): 754 -ilf_type(power_set(cross_product(c2,c3)),subset_type(cross_product(A,B))) | ordered_pair(f18(power_set(cross_product(c2,c3)),c4),f19(power_set(cross_product(c2,c3)),c4)) = c4. [resolve(738,a,131,b)]. given #1679 (T,wt=8): 24318 member(f13(domain_of(c4),A),c2) | -empty(A). [resolve(24261,a,206,a)]. given #1680 (T,wt=10): 24262 member(f24(A),A) | member(f13(range_of(c4),A),c3). [resolve(14523,a,580,a),unit_del(a,16844)]. given #1681 (T,wt=8): 24340 member(f13(range_of(c4),A),c3) | -empty(A). [resolve(24262,a,206,a)]. given #1682 (T,wt=11): 15742 member(f3(range_of(c4),c3),A) | member(f24(c3),range_of(c4)). [resolve(15739,a,5583,a)]. given #1683 (A,wt=24): 755 ordered_pair(f18(power_set(cross_product(c2,c3)),c4),f19(power_set(cross_product(c2,c3)),c4)) = c4 | f17(power_set(cross_product(c2,c3))) != ordered_pair(A,B). [resolve(738,a,127,a)]. given #1684 (T,wt=11): 15778 member(f24(c3),c3) | -member(f24(c3),f3(range_of(c4),c3)). [factor(15773,a,c)]. given #1685 (T,wt=11): 15819 member(f1(c4,f16(c3)),A) | -member(f14(c2,A),A). [back_unit_del(15566),unit_del(a,15798)]. given #1686 (T,wt=11): 15820 member(f1(c4,f16(c3)),A) | member(f14(c2,A),c2). [back_unit_del(15565),unit_del(a,15798)]. given #1687 (T,wt=11): 15830 member(f13(c2,A),c2) | member(f1(c4,f16(c3)),A). [back_unit_del(15555),unit_del(a,15798)]. given #1688 (A,wt=25): 756 ordered_pair(f18(power_set(cross_product(c2,c3)),c4),f19(power_set(cross_product(c2,c3)),c4)) = c4 | member(f17(power_set(cross_product(c2,c3))),power_set(cross_product(c2,c3))). [resolve(738,a,125,a)]. given #1689 (T,wt=11): 15832 member(f1(c4,f16(c3)),A) | -member(domain_of(c4),power_set(A)). [back_unit_del(15553),unit_del(a,15798)]. given #1690 (T,wt=11): 15861 member(ordered_pair(f1(c4,f16(c3)),f16(c3)),cross_product(c2,c3)). [back_unit_del(15524),unit_del(a,15798)]. given #1691 (T,wt=9): 24435 member(f1(c4,f16(c3)),domain_of(cross_product(c2,c3))). [resolve(15861,a,252,b),unit_del(a,453)]. given #1692 (T,wt=10): 24446 ilf_type(f1(c4,f16(c3)),member_type(domain_of(cross_product(c2,c3)))). [resolve(24435,a,212,c),unit_del(a,19466)]. given #1693 (A,wt=21): 757 ordered_pair(f18(power_set(cross_product(c2,c3)),c4),f19(power_set(cross_product(c2,c3)),c4)) = c4 | -ilf_type(power_set(cross_product(c2,c3)),binary_relation_type). [resolve(738,a,123,a)]. given #1694 (T,wt=11): 15867 member(f2(c4,f16(c3)),A) | -member(f14(c2,A),A). [back_unit_del(15518),unit_del(a,15798)]. given #1695 (T,wt=11): 15868 member(f2(c4,f16(c3)),A) | member(f14(c2,A),c2). [back_unit_del(15517),unit_del(a,15798)]. given #1696 (T,wt=11): 15878 member(f13(c2,A),c2) | member(f2(c4,f16(c3)),A). [back_unit_del(15507),unit_del(a,15798)]. given #1697 (T,wt=11): 15880 member(f2(c4,f16(c3)),A) | -member(domain_of(c4),power_set(A)). [back_unit_del(15502),unit_del(a,15798)]. given #1698 (A,wt=16): 762 member(f4(A,range_of(c4)),c3) | member(f3(A,range_of(c4)),A) | range_of(c4) = A. [resolve(580,a,250,b)]. given #1699 (T,wt=6): 24539 member(f3(c3,range_of(c4)),c3). [resolve(762,a,251,b),merge(c),merge(d),unit_del(b,260)]. given #1700 (T,wt=7): 24541 member(f3(c3,range_of(c4)),range_of(c4)). [resolve(24539,a,5583,a)]. given #1701 (T,wt=7): 24555 ilf_type(f3(c3,range_of(c4)),member_type(c3)). [resolve(24539,a,212,c),unit_del(a,15798)]. given #1702 (T,wt=7): 24559 member(f4(c3,range_of(c4)),range_of(c4)). [resolve(24541,a,248,a),unit_del(b,260)]. given #1703 (A,wt=16): 763 member(f8(A,range_of(c4)),c3) | range_of(c4) = A | member(f7(A,range_of(c4)),A). [resolve(580,a,234,c)]. given #1704 (T,wt=6): 24567 member(f4(c3,range_of(c4)),c3). [resolve(24559,a,580,a)]. ============================== PROOF ================================= % Proof 1 at 3.45 (+ 0.18) seconds. % Length of proof is 56. % Level of proof is 12. % Maximum clause weight is 19.000. % Given clauses 1704. 2 -ilf_type(A,set_type) | ilf_type(A,binary_relation_type) | -relation_like(A). [assumption]. 9 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,subset_type(cross_product(A,B))) | relation_like(C). [assumption]. 11 -ilf_type(A,binary_relation_type) | -ilf_type(B,set_type) | member(B,range_of(A)) | -ilf_type(C,set_type) | -member(ordered_pair(C,B),A). [assumption]. 22 -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(f3(A,B),A) | -member(f4(A,B),A) | B = A. [assumption]. 23 -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(f3(A,B),A) | member(f4(A,B),B) | B = A. [assumption]. 25 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(f3(A,B),B) | -member(f4(A,B),A) | B = A. [assumption]. 26 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(f3(A,B),B) | member(f4(A,B),B) | B = A. [assumption]. 31 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,relation_type(A,B)) | ilf_type(C,subset_type(cross_product(A,B))). [assumption]. 43 -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(B,member_type(power_set(A))) | -ilf_type(B,subset_type(A)). [assumption]. 83 -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(A,power_set(B)) | member(f15(A,B),A). [assumption]. 84 -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(A,power_set(B)) | -member(f15(A,B),B). [assumption]. 85 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | -member(C,A) | member(C,B) | -member(A,power_set(B)). [assumption]. 86 -ilf_type(A,set_type) | -empty(power_set(A)). [assumption]. 89 -ilf_type(A,set_type) | empty(B) | -ilf_type(B,set_type) | member(A,B) | -ilf_type(A,member_type(B)). [assumption]. 110 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,relation_type(A,B)) | range(A,B,C) = range_of(C). [assumption]. 111 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,relation_type(A,B)) | ilf_type(range(A,B,C),subset_type(B)). [assumption]. 112 ilf_type(A,set_type). [assumption]. 113 ilf_type(c4,relation_type(c2,c3)). [assumption]. 115 -ilf_type(A,set_type) | -member(A,c3) | member(ordered_pair(f25(A),A),c4). [assumption]. 116 -member(A,c3) | member(ordered_pair(f25(A),A),c4). [copy(115),unit_del(a,112)]. 117 range(c2,c3,c4) != c3. [assumption]. 128 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,subset_type(cross_product(A,B))) | -ilf_type(C,set_type) | ilf_type(C,binary_relation_type). [resolve(9,d,2,c)]. 129 -ilf_type(A,subset_type(cross_product(B,C))) | ilf_type(A,binary_relation_type). [copy(128),unit_del(a,112),unit_del(b,112),unit_del(d,112)]. 201 -ilf_type(A,relation_type(B,C)) | ilf_type(range(B,C,A),subset_type(C)). [back_unit_del(111),unit_del(a,112),unit_del(b,112)]. 202 -ilf_type(A,relation_type(B,C)) | range(B,C,A) = range_of(A). [back_unit_del(110),unit_del(a,112),unit_del(b,112)]. 211 empty(A) | member(B,A) | -ilf_type(B,member_type(A)). [back_unit_del(89),unit_del(a,112),unit_del(c,112)]. 213 -empty(power_set(A)). [back_unit_del(86),unit_del(a,112)]. 214 -member(A,B) | member(A,C) | -member(B,power_set(C)). [back_unit_del(85),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. 215 member(A,power_set(B)) | -member(f15(A,B),B). [back_unit_del(84),unit_del(a,112),unit_del(b,112)]. 216 member(A,power_set(B)) | member(f15(A,B),A). [back_unit_del(83),unit_del(a,112),unit_del(b,112)]. 237 ilf_type(A,member_type(power_set(B))) | -ilf_type(A,subset_type(B)). [back_unit_del(43),unit_del(a,112),unit_del(b,112)]. 244 -ilf_type(A,relation_type(B,C)) | ilf_type(A,subset_type(cross_product(B,C))). [back_unit_del(31),unit_del(a,112),unit_del(b,112)]. 248 -member(f3(A,B),B) | member(f4(A,B),B) | B = A. [back_unit_del(26),unit_del(a,112),unit_del(b,112)]. 249 -member(f3(A,B),B) | -member(f4(A,B),A) | B = A. [back_unit_del(25),unit_del(a,112),unit_del(b,112)]. 250 member(f3(A,B),A) | member(f4(A,B),B) | B = A. [back_unit_del(23),unit_del(a,112),unit_del(b,112)]. 251 member(f3(A,B),A) | -member(f4(A,B),A) | B = A. [back_unit_del(22),unit_del(a,112),unit_del(b,112)]. 255 -ilf_type(A,binary_relation_type) | member(B,range_of(A)) | -member(ordered_pair(C,B),A). [back_unit_del(11),unit_del(b,112),unit_del(d,112)]. 257 ilf_type(range(c2,c3,c4),subset_type(c3)). [resolve(201,a,113,a)]. 258 range(c2,c3,c4) = range_of(c4). [resolve(202,a,113,a)]. 259 ilf_type(range_of(c4),subset_type(c3)). [back_rewrite(257),rewrite([258(4)])]. 260 range_of(c4) != c3. [back_rewrite(117),rewrite([258(4)])]. 294 member(c3,power_set(A)) | member(ordered_pair(f25(f15(c3,A)),f15(c3,A)),c4). [resolve(216,b,116,a)]. 369 ilf_type(c4,subset_type(cross_product(c2,c3))). [resolve(244,a,113,a)]. 449 ilf_type(range_of(c4),member_type(power_set(c3))). [resolve(259,a,237,b)]. 540 ilf_type(c4,binary_relation_type). [resolve(369,a,129,a)]. 568 member(range_of(c4),power_set(c3)). [resolve(449,a,211,c),unit_del(a,213)]. 580 -member(A,range_of(c4)) | member(A,c3). [resolve(568,a,214,c)]. 762 member(f4(A,range_of(c4)),c3) | member(f3(A,range_of(c4)),A) | range_of(c4) = A. [resolve(580,a,250,b)]. 1836 member(c3,power_set(A)) | member(f15(c3,A),range_of(c4)). [resolve(294,b,255,c),unit_del(b,540)]. 5560 member(c3,power_set(range_of(c4))). [resolve(1836,b,215,b),merge(b)]. 5583 -member(A,c3) | member(A,range_of(c4)). [resolve(5560,a,214,c)]. 24539 member(f3(c3,range_of(c4)),c3). [resolve(762,a,251,b),merge(c),merge(d),unit_del(b,260)]. 24541 member(f3(c3,range_of(c4)),range_of(c4)). [resolve(24539,a,5583,a)]. 24559 member(f4(c3,range_of(c4)),range_of(c4)). [resolve(24541,a,248,a),unit_del(b,260)]. 24567 member(f4(c3,range_of(c4)),c3). [resolve(24559,a,580,a)]. 24580 $F. [resolve(24567,a,249,b),unit_del(a,24541),unit_del(b,260)]. ============================== end of proof ========================== ============================== STATISTICS ============================ Given=1704. Generated=49005. Kept=24555. proofs=1. Usable=1564. Sos=19999. Demods=46. Limbo=1, Disabled=3116. Hints=0. Kept_by_rule=0, Deleted_by_rule=14. Forward_subsumed=12832. Back_subsumed=187. Sos_limit_deleted=11603. Sos_displaced=948. Sos_removed=0. New_demodulators=46 (1 lex), Back_demodulated=57. Back_unit_deleted=1799. Demod_attempts=743485. Demod_rewrites=1614. Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. Nonunit_fsub_feature_tests=181887. Nonunit_bsub_feature_tests=13500. Megabytes=35.75. User_CPU=3.45, System_CPU=0.18, Wall_clock=3. ============================== end of statistics ===================== ============================== end of search ========================= Exiting with 1 proof. Process 23975 exit (max_proofs) Tue Nov 3 16:59:20 2009 ============================== continuing FOF reduction multisearch == Subproblem 2 of 6 (negated): ((all B (- ilf_type(B,binary_relation_type) | (all C (- ilf_type(C,set_type) | member(C,range_of(B)) | (all D (- ilf_type(D,set_type) | - member(ordered_pair(D,C),B))))))) & (all B (- ilf_type(B,binary_relation_type) | (all C (- ilf_type(C,set_type) | (exists D (ilf_type(D,set_type) & member(ordered_pair(D,C),B))) | - member(C,range_of(B)))))) & (all B (- ilf_type(B,binary_relation_type) | (all C (- ilf_type(C,set_type) | (exists D (ilf_type(D,set_type) & member(ordered_pair(D,C),B))) | (all D (- ilf_type(D,set_type) | - member(ordered_pair(D,C),B))))))) & (all B (- ilf_type(B,binary_relation_type) | ilf_type(range_of(B),set_type))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,binary_relation_type) | - member(ordered_pair(B,C),D) | member(B,domain_of(D)))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,binary_relation_type) | - member(ordered_pair(B,C),D) | member(C,range_of(D)))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (exists D (ilf_type(D,set_type) & member(D,B) & - member(D,C))) | (exists D (ilf_type(D,set_type) & - member(D,B) & member(D,C))) | =(C,B))))) & (all D (- ilf_type(D,set_type) | (all E (- ilf_type(E,set_type) | (all F (- ilf_type(F,set_type) | =(ordered_pair(D,E),F) | - =(unordered_pair(unordered_pair(D,E),singleton(D)),F))))))) & (all D (- ilf_type(D,set_type) | (all E (- ilf_type(E,set_type) | (all F (- ilf_type(F,set_type) | =(unordered_pair(unordered_pair(D,E),singleton(D)),F) | - =(ordered_pair(D,E),F))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | ilf_type(ordered_pair(B,C),set_type))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,subset_type(cross_product(B,C))) | ilf_type(D,relation_type(B,C)))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all E (- ilf_type(E,relation_type(B,C)) | ilf_type(E,subset_type(cross_product(B,C))))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (exists D ilf_type(D,relation_type(C,B))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | =(C,B) | - subset(B,C) | - subset(C,B))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | subset(B,C) | - =(C,B))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | subset(C,B) | - =(C,B))))) & (all B (- ilf_type(B,binary_relation_type) | ilf_type(domain_of(B),set_type))) & (all B (- ilf_type(B,set_type) | ilf_type(singleton(B),set_type))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | ilf_type(cross_product(B,C),set_type))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | ilf_type(unordered_pair(B,C),set_type))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | =(unordered_pair(C,B),unordered_pair(B,C)))))) & (all B (- ilf_type(B,set_type) | ilf_type(B,binary_relation_type) | - relation_like(B))) & (all B (- ilf_type(B,set_type) | relation_like(B) | - ilf_type(B,binary_relation_type))) & (exists B ilf_type(B,binary_relation_type)) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | ilf_type(C,subset_type(B)) | - ilf_type(C,member_type(power_set(B))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | ilf_type(C,member_type(power_set(B))) | - ilf_type(C,subset_type(B)))))) & (all B (- ilf_type(B,set_type) | (exists C ilf_type(C,subset_type(B))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | =(C,B) | (exists D (ilf_type(D,set_type) & member(D,B) & - member(D,C))) | (exists D (ilf_type(D,set_type) & - member(D,B) & member(D,C))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,set_type) | member(D,B) | - member(D,C))) | - =(C,B))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,set_type) | member(D,B) | - member(D,C))) | (exists D (ilf_type(D,set_type) & member(D,B) & - member(D,C))) | (exists D (ilf_type(D,set_type) & - member(D,B) & member(D,C))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,set_type) | member(D,C) | - member(D,B))) | - =(C,B))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,set_type) | member(D,C) | - member(D,B))) | (exists D (ilf_type(D,set_type) & member(D,B) & - member(D,C))) | (exists D (ilf_type(D,set_type) & - member(D,B) & member(D,C))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | subset(B,C) | (exists D (ilf_type(D,set_type) & member(D,B) & - member(D,C))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,set_type) | - member(D,B) | member(D,C))) | - subset(B,C))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,set_type) | - member(D,B) | member(D,C))) | (exists D (ilf_type(D,set_type) & member(D,B) & - member(D,C))))))) & (all B (- ilf_type(B,set_type) | subset(B,B))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | member(B,power_set(C)) | (exists D (ilf_type(D,set_type) & member(D,B) & - member(D,C))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,set_type) | - member(D,B) | member(D,C))) | - member(B,power_set(C)))))) & (all B (- ilf_type(B,set_type) | - empty(power_set(B)))) & (all B (- ilf_type(B,set_type) | ilf_type(power_set(B),set_type))) & (all B (- ilf_type(B,set_type) | (all C (empty(C) | - ilf_type(C,set_type) | ilf_type(B,member_type(C)) | - member(B,C))))) & (all B (- ilf_type(B,set_type) | (all C (empty(C) | - ilf_type(C,set_type) | member(B,C) | - ilf_type(B,member_type(C)))))) & (all B (empty(B) | - ilf_type(B,set_type) | (exists C ilf_type(C,member_type(B))))) & (all B (- ilf_type(B,set_type) | relation_like(B) | (exists C (ilf_type(C,set_type) & member(C,B) & (all D (- ilf_type(D,set_type) | (all E (- ilf_type(E,set_type) | - =(ordered_pair(D,E),C))))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | - member(C,B) | (exists D (ilf_type(D,set_type) & (exists E (ilf_type(E,set_type) & =(ordered_pair(D,E),C))))))) | - relation_like(B))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | - member(C,B) | (exists D (ilf_type(D,set_type) & (exists E (ilf_type(E,set_type) & =(ordered_pair(D,E),C))))))) | (exists C (ilf_type(C,set_type) & member(C,B) & (all D (- ilf_type(D,set_type) | (all E (- ilf_type(E,set_type) | - =(ordered_pair(D,E),C))))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,subset_type(cross_product(B,C))) | relation_like(D))))))) & (all B (- ilf_type(B,set_type) | empty(B) | (exists C (ilf_type(C,set_type) & member(C,B))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | - member(C,B))) | - empty(B))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | - member(C,B))) | (exists C (ilf_type(C,set_type) & member(C,B))))) & (all B (- empty(B) | - ilf_type(B,set_type) | relation_like(B))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,relation_type(B,C)) | =(domain(B,C,D),domain_of(D)))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,relation_type(B,C)) | ilf_type(domain(B,C,D),subset_type(B)))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,relation_type(B,C)) | =(range(B,C,D),range_of(D)))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,relation_type(B,C)) | ilf_type(range(B,C,D),subset_type(C)))))))) & (all B ilf_type(B,set_type)) & (exists B (ilf_type(B,set_type) & (exists C (ilf_type(C,set_type) & (exists D (ilf_type(D,relation_type(B,C)) & (exists E (ilf_type(E,set_type) & member(E,C) & (all F (- ilf_type(F,set_type) | - member(ordered_pair(F,E),D))))) & =(range(B,C,D),C)))))))). Max_seconds is 117 for this subproblem. Child search process 23976 started. ============================== PROCESS INITIAL CLAUSES =============== % Clauses before input processing: formulas(usable). end_of_list. formulas(sos). -ilf_type(A,binary_relation_type) | -ilf_type(B,set_type) | member(B,range_of(A)) | -ilf_type(C,set_type) | -member(ordered_pair(C,B),A). [assumption]. -ilf_type(A,binary_relation_type) | -ilf_type(B,set_type) | ilf_type(f1(A,B),set_type) | -member(B,range_of(A)). [assumption]. -ilf_type(A,binary_relation_type) | -ilf_type(B,set_type) | member(ordered_pair(f1(A,B),B),A) | -member(B,range_of(A)). [assumption]. -ilf_type(A,binary_relation_type) | -ilf_type(B,set_type) | ilf_type(f2(A,B),set_type) | -ilf_type(C,set_type) | -member(ordered_pair(C,B),A). [assumption]. -ilf_type(A,binary_relation_type) | -ilf_type(B,set_type) | member(ordered_pair(f2(A,B),B),A) | -ilf_type(C,set_type) | -member(ordered_pair(C,B),A). [assumption]. -ilf_type(A,binary_relation_type) | ilf_type(range_of(A),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,binary_relation_type) | -member(ordered_pair(A,B),C) | member(A,domain_of(C)). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,binary_relation_type) | -member(ordered_pair(A,B),C) | member(B,range_of(C)). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(f3(A,B),set_type) | ilf_type(f4(A,B),set_type) | B = A. [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(f3(A,B),set_type) | -member(f4(A,B),A) | B = A. [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(f3(A,B),set_type) | member(f4(A,B),B) | B = A. [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(f3(A,B),A) | ilf_type(f4(A,B),set_type) | B = A. [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(f3(A,B),A) | -member(f4(A,B),A) | B = A. [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(f3(A,B),A) | member(f4(A,B),B) | B = A. [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(f3(A,B),B) | ilf_type(f4(A,B),set_type) | B = A. [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(f3(A,B),B) | -member(f4(A,B),A) | B = A. [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(f3(A,B),B) | member(f4(A,B),B) | B = A. [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | ordered_pair(A,B) = C | unordered_pair(unordered_pair(A,B),singleton(A)) != C. [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | unordered_pair(unordered_pair(A,B),singleton(A)) = C | ordered_pair(A,B) != C. [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(ordered_pair(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,subset_type(cross_product(A,B))) | ilf_type(C,relation_type(A,B)). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,relation_type(A,B)) | ilf_type(C,subset_type(cross_product(A,B))). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(f5(A,B),relation_type(B,A)). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | -subset(A,B) | -subset(B,A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(A,B) | B != A. [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(B,A) | B != A. [assumption]. -ilf_type(A,binary_relation_type) | ilf_type(domain_of(A),set_type). [assumption]. -ilf_type(A,set_type) | ilf_type(singleton(A),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(cross_product(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(unordered_pair(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | unordered_pair(B,A) = unordered_pair(A,B). [assumption]. -ilf_type(A,set_type) | ilf_type(A,binary_relation_type) | -relation_like(A). [assumption]. -ilf_type(A,set_type) | relation_like(A) | -ilf_type(A,binary_relation_type). [assumption]. ilf_type(c1,binary_relation_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(B,subset_type(A)) | -ilf_type(B,member_type(power_set(A))). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(B,member_type(power_set(A))) | -ilf_type(B,subset_type(A)). [assumption]. -ilf_type(A,set_type) | ilf_type(f6(A),subset_type(A)). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | ilf_type(f7(A,B),set_type) | ilf_type(f8(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | ilf_type(f7(A,B),set_type) | -member(f8(A,B),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | ilf_type(f7(A,B),set_type) | member(f8(A,B),B). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | member(f7(A,B),A) | ilf_type(f8(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | member(f7(A,B),A) | -member(f8(A,B),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | member(f7(A,B),A) | member(f8(A,B),B). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | -member(f7(A,B),B) | ilf_type(f8(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | -member(f7(A,B),B) | -member(f8(A,B),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | -member(f7(A,B),B) | member(f8(A,B),B). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,A) | -member(C,B) | B != A. [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,A) | -member(C,B) | ilf_type(f9(A,B),set_type) | ilf_type(f10(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,A) | -member(C,B) | ilf_type(f9(A,B),set_type) | -member(f10(A,B),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,A) | -member(C,B) | ilf_type(f9(A,B),set_type) | member(f10(A,B),B). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,A) | -member(C,B) | member(f9(A,B),A) | ilf_type(f10(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,A) | -member(C,B) | member(f9(A,B),A) | -member(f10(A,B),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,A) | -member(C,B) | member(f9(A,B),A) | member(f10(A,B),B). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,A) | -member(C,B) | -member(f9(A,B),B) | ilf_type(f10(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,A) | -member(C,B) | -member(f9(A,B),B) | -member(f10(A,B),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,A) | -member(C,B) | -member(f9(A,B),B) | member(f10(A,B),B). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,B) | -member(C,A) | B != A. [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,B) | -member(C,A) | ilf_type(f11(A,B),set_type) | ilf_type(f12(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,B) | -member(C,A) | ilf_type(f11(A,B),set_type) | -member(f12(A,B),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,B) | -member(C,A) | ilf_type(f11(A,B),set_type) | member(f12(A,B),B). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,B) | -member(C,A) | member(f11(A,B),A) | ilf_type(f12(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,B) | -member(C,A) | member(f11(A,B),A) | -member(f12(A,B),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,B) | -member(C,A) | member(f11(A,B),A) | member(f12(A,B),B). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,B) | -member(C,A) | -member(f11(A,B),B) | ilf_type(f12(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,B) | -member(C,A) | -member(f11(A,B),B) | -member(f12(A,B),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,B) | -member(C,A) | -member(f11(A,B),B) | member(f12(A,B),B). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(A,B) | ilf_type(f13(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(A,B) | member(f13(A,B),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(A,B) | -member(f13(A,B),B). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | -member(C,A) | member(C,B) | -subset(A,B). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | -member(C,A) | member(C,B) | ilf_type(f14(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | -member(C,A) | member(C,B) | member(f14(A,B),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | -member(C,A) | member(C,B) | -member(f14(A,B),B). [assumption]. -ilf_type(A,set_type) | subset(A,A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(A,power_set(B)) | ilf_type(f15(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(A,power_set(B)) | member(f15(A,B),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(A,power_set(B)) | -member(f15(A,B),B). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | -member(C,A) | member(C,B) | -member(A,power_set(B)). [assumption]. -ilf_type(A,set_type) | -empty(power_set(A)). [assumption]. -ilf_type(A,set_type) | ilf_type(power_set(A),set_type). [assumption]. -ilf_type(A,set_type) | empty(B) | -ilf_type(B,set_type) | ilf_type(A,member_type(B)) | -member(A,B). [assumption]. -ilf_type(A,set_type) | empty(B) | -ilf_type(B,set_type) | member(A,B) | -ilf_type(A,member_type(B)). [assumption]. empty(A) | -ilf_type(A,set_type) | ilf_type(f16(A),member_type(A)). [assumption]. -ilf_type(A,set_type) | relation_like(A) | ilf_type(f17(A),set_type). [assumption]. -ilf_type(A,set_type) | relation_like(A) | member(f17(A),A). [assumption]. -ilf_type(A,set_type) | relation_like(A) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | ordered_pair(B,C) != f17(A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f18(A,B),set_type) | -relation_like(A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f19(A,B),set_type) | -relation_like(A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f18(A,B),f19(A,B)) = B | -relation_like(A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f20(A,B),set_type) | ilf_type(f22(A),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f20(A,B),set_type) | member(f22(A),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f20(A,B),set_type) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | ordered_pair(C,D) != f22(A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f21(A,B),set_type) | ilf_type(f22(A),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f21(A,B),set_type) | member(f22(A),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f21(A,B),set_type) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | ordered_pair(C,D) != f22(A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f20(A,B),f21(A,B)) = B | ilf_type(f22(A),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f20(A,B),f21(A,B)) = B | member(f22(A),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f20(A,B),f21(A,B)) = B | -ilf_type(C,set_type) | -ilf_type(D,set_type) | ordered_pair(C,D) != f22(A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,subset_type(cross_product(A,B))) | relation_like(C). [assumption]. -ilf_type(A,set_type) | empty(A) | ilf_type(f23(A),set_type). [assumption]. -ilf_type(A,set_type) | empty(A) | member(f23(A),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | -empty(A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f24(A),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | member(f24(A),A). [assumption]. -empty(A) | -ilf_type(A,set_type) | relation_like(A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,relation_type(A,B)) | domain(A,B,C) = domain_of(C). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,relation_type(A,B)) | ilf_type(domain(A,B,C),subset_type(A)). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,relation_type(A,B)) | range(A,B,C) = range_of(C). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,relation_type(A,B)) | ilf_type(range(A,B,C),subset_type(B)). [assumption]. ilf_type(A,set_type). [assumption]. ilf_type(c2,set_type). [assumption]. ilf_type(c3,set_type). [assumption]. ilf_type(c4,relation_type(c2,c3)). [assumption]. ilf_type(c5,set_type). [assumption]. member(c5,c3). [assumption]. -ilf_type(A,set_type) | -member(ordered_pair(A,c5),c4). [assumption]. range(c2,c3,c4) = c3. [assumption]. end_of_list. formulas(demodulators). end_of_list. ============================== PREDICATE ELIMINATION ================= Eliminating relation_like/1 1 -ilf_type(A,set_type) | relation_like(A) | -ilf_type(A,binary_relation_type). [assumption]. 2 -ilf_type(A,set_type) | ilf_type(A,binary_relation_type) | -relation_like(A). [assumption]. 3 -ilf_type(A,set_type) | relation_like(A) | ilf_type(f17(A),set_type). [assumption]. 4 -ilf_type(A,set_type) | relation_like(A) | member(f17(A),A). [assumption]. Derived: -ilf_type(A,set_type) | member(f17(A),A) | -ilf_type(A,set_type) | ilf_type(A,binary_relation_type). [resolve(4,b,2,c)]. 5 -ilf_type(A,set_type) | relation_like(A) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | ordered_pair(B,C) != f17(A). [assumption]. Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | ordered_pair(B,C) != f17(A) | -ilf_type(A,set_type) | ilf_type(A,binary_relation_type). [resolve(5,b,2,c)]. 6 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f18(A,B),set_type) | -relation_like(A). [assumption]. 7 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f19(A,B),set_type) | -relation_like(A). [assumption]. 8 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f18(A,B),f19(A,B)) = B | -relation_like(A). [assumption]. Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f18(A,B),f19(A,B)) = B | -ilf_type(A,set_type) | -ilf_type(A,binary_relation_type). [resolve(8,e,1,b)]. Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f18(A,B),f19(A,B)) = B | -ilf_type(A,set_type) | member(f17(A),A). [resolve(8,e,4,b)]. Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f18(A,B),f19(A,B)) = B | -ilf_type(A,set_type) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | ordered_pair(C,D) != f17(A). [resolve(8,e,5,b)]. 9 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,subset_type(cross_product(A,B))) | relation_like(C). [assumption]. Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,subset_type(cross_product(A,B))) | -ilf_type(C,set_type) | ilf_type(C,binary_relation_type). [resolve(9,d,2,c)]. Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,subset_type(cross_product(A,B))) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | -member(D,C) | ordered_pair(f18(C,D),f19(C,D)) = D. [resolve(9,d,8,e)]. 10 -empty(A) | -ilf_type(A,set_type) | relation_like(A). [assumption]. Derived: -empty(A) | -ilf_type(A,set_type) | -ilf_type(A,set_type) | ilf_type(A,binary_relation_type). [resolve(10,c,2,c)]. Derived: -empty(A) | -ilf_type(A,set_type) | -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f18(A,B),f19(A,B)) = B. [resolve(10,c,8,e)]. ============================== end predicate elimination ============= Term ordering decisions: Predicate symbol precedence: predicate_order([ =, empty, ilf_type, member, subset ]). Function symbol precedence: function_order([ set_type, binary_relation_type, c1, c2, c3, c4, c5, ordered_pair, relation_type, unordered_pair, cross_product, f1, f2, f3, f4, f5, f7, f8, f9, f10, f11, f12, f13, f14, f15, f18, f19, f20, f21, subset_type, power_set, range_of, member_type, domain_of, singleton, f6, f16, f17, f22, f23, f24, range, domain ]). After inverse_order: (no changes). Unfolding symbols: (none). Auto_inference settings: % set(paramodulation). % (positive equality literals) % set(binary_resolution). % (non-Horn) Auto_process settings: % set(factor). % (non-Horn) % set(unit_deletion). % (non-Horn) kept: 11 -ilf_type(A,binary_relation_type) | -ilf_type(B,set_type) | member(B,range_of(A)) | -ilf_type(C,set_type) | -member(ordered_pair(C,B),A). [assumption]. kept: 12 -ilf_type(A,binary_relation_type) | -ilf_type(B,set_type) | ilf_type(f1(A,B),set_type) | -member(B,range_of(A)). [assumption]. kept: 13 -ilf_type(A,binary_relation_type) | -ilf_type(B,set_type) | member(ordered_pair(f1(A,B),B),A) | -member(B,range_of(A)). [assumption]. kept: 14 -ilf_type(A,binary_relation_type) | -ilf_type(B,set_type) | ilf_type(f2(A,B),set_type) | -ilf_type(C,set_type) | -member(ordered_pair(C,B),A). [assumption]. kept: 15 -ilf_type(A,binary_relation_type) | -ilf_type(B,set_type) | member(ordered_pair(f2(A,B),B),A) | -ilf_type(C,set_type) | -member(ordered_pair(C,B),A). [assumption]. kept: 16 -ilf_type(A,binary_relation_type) | ilf_type(range_of(A),set_type). [assumption]. kept: 17 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,binary_relation_type) | -member(ordered_pair(A,B),C) | member(A,domain_of(C)). [assumption]. kept: 18 -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(f3(A,B),set_type) | ilf_type(f4(A,B),set_type) | B = A. [assumption]. kept: 19 -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(f3(A,B),set_type) | -member(f4(A,B),A) | B = A. [assumption]. kept: 20 -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(f3(A,B),set_type) | member(f4(A,B),B) | B = A. [assumption]. kept: 21 -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(f3(A,B),A) | ilf_type(f4(A,B),set_type) | B = A. [assumption]. kept: 22 -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(f3(A,B),A) | -member(f4(A,B),A) | B = A. [assumption]. kept: 23 -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(f3(A,B),A) | member(f4(A,B),B) | B = A. [assumption]. kept: 24 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(f3(A,B),B) | ilf_type(f4(A,B),set_type) | B = A. [assumption]. kept: 25 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(f3(A,B),B) | -member(f4(A,B),A) | B = A. [assumption]. kept: 26 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(f3(A,B),B) | member(f4(A,B),B) | B = A. [assumption]. kept: 27 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | ordered_pair(A,B) = C | unordered_pair(unordered_pair(A,B),singleton(A)) != C. [assumption]. kept: 28 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | unordered_pair(unordered_pair(A,B),singleton(A)) = C | ordered_pair(A,B) != C. [assumption]. kept: 29 -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(ordered_pair(A,B),set_type). [assumption]. kept: 30 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,subset_type(cross_product(A,B))) | ilf_type(C,relation_type(A,B)). [assumption]. kept: 31 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,relation_type(A,B)) | ilf_type(C,subset_type(cross_product(A,B))). [assumption]. kept: 32 -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(f5(A,B),relation_type(B,A)). [assumption]. kept: 33 -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | -subset(A,B) | -subset(B,A). [assumption]. kept: 34 -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(A,B) | B != A. [assumption]. kept: 35 -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(B,A) | B != A. [assumption]. kept: 36 -ilf_type(A,binary_relation_type) | ilf_type(domain_of(A),set_type). [assumption]. kept: 37 -ilf_type(A,set_type) | ilf_type(singleton(A),set_type). [assumption]. kept: 38 -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(cross_product(A,B),set_type). [assumption]. kept: 39 -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(unordered_pair(A,B),set_type). [assumption]. kept: 40 -ilf_type(A,set_type) | -ilf_type(B,set_type) | unordered_pair(B,A) = unordered_pair(A,B). [assumption]. kept: 41 ilf_type(c1,binary_relation_type). [assumption]. kept: 42 -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(B,subset_type(A)) | -ilf_type(B,member_type(power_set(A))). [assumption]. kept: 43 -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(B,member_type(power_set(A))) | -ilf_type(B,subset_type(A)). [assumption]. kept: 44 -ilf_type(A,set_type) | ilf_type(f6(A),subset_type(A)). [assumption]. kept: 45 -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | ilf_type(f7(A,B),set_type) | ilf_type(f8(A,B),set_type). [assumption]. kept: 46 -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | ilf_type(f7(A,B),set_type) | -member(f8(A,B),A). [assumption]. kept: 47 -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | ilf_type(f7(A,B),set_type) | member(f8(A,B),B). [assumption]. kept: 48 -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | member(f7(A,B),A) | ilf_type(f8(A,B),set_type). [assumption]. kept: 49 -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | member(f7(A,B),A) | -member(f8(A,B),A). [assumption]. kept: 50 -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | member(f7(A,B),A) | member(f8(A,B),B). [assumption]. kept: 51 -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | -member(f7(A,B),B) | ilf_type(f8(A,B),set_type). [assumption]. kept: 52 -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | -member(f7(A,B),B) | -member(f8(A,B),A). [assumption]. kept: 53 -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | -member(f7(A,B),B) | member(f8(A,B),B). [assumption]. kept: 54 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,A) | -member(C,B) | B != A. [assumption]. kept: 55 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,A) | -member(C,B) | ilf_type(f9(A,B),set_type) | ilf_type(f10(A,B),set_type). [assumption]. kept: 56 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,A) | -member(C,B) | ilf_type(f9(A,B),set_type) | -member(f10(A,B),A). [assumption]. kept: 57 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,A) | -member(C,B) | ilf_type(f9(A,B),set_type) | member(f10(A,B),B). [assumption]. kept: 58 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,A) | -member(C,B) | member(f9(A,B),A) | ilf_type(f10(A,B),set_type). [assumption]. kept: 59 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,A) | -member(C,B) | member(f9(A,B),A) | -member(f10(A,B),A). [assumption]. kept: 60 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,A) | -member(C,B) | member(f9(A,B),A) | member(f10(A,B),B). [assumption]. kept: 61 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,A) | -member(C,B) | -member(f9(A,B),B) | ilf_type(f10(A,B),set_type). [assumption]. kept: 62 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,A) | -member(C,B) | -member(f9(A,B),B) | -member(f10(A,B),A). [assumption]. kept: 63 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,A) | -member(C,B) | -member(f9(A,B),B) | member(f10(A,B),B). [assumption]. kept: 64 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,B) | -member(C,A) | B != A. [assumption]. kept: 65 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,B) | -member(C,A) | ilf_type(f11(A,B),set_type) | ilf_type(f12(A,B),set_type). [assumption]. kept: 66 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,B) | -member(C,A) | ilf_type(f11(A,B),set_type) | -member(f12(A,B),A). [assumption]. kept: 67 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,B) | -member(C,A) | ilf_type(f11(A,B),set_type) | member(f12(A,B),B). [assumption]. kept: 68 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,B) | -member(C,A) | member(f11(A,B),A) | ilf_type(f12(A,B),set_type). [assumption]. kept: 69 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,B) | -member(C,A) | member(f11(A,B),A) | -member(f12(A,B),A). [assumption]. kept: 70 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,B) | -member(C,A) | member(f11(A,B),A) | member(f12(A,B),B). [assumption]. kept: 71 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,B) | -member(C,A) | -member(f11(A,B),B) | ilf_type(f12(A,B),set_type). [assumption]. kept: 72 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,B) | -member(C,A) | -member(f11(A,B),B) | -member(f12(A,B),A). [assumption]. kept: 73 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,B) | -member(C,A) | -member(f11(A,B),B) | member(f12(A,B),B). [assumption]. kept: 74 -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(A,B) | ilf_type(f13(A,B),set_type). [assumption]. kept: 75 -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(A,B) | member(f13(A,B),A). [assumption]. kept: 76 -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(A,B) | -member(f13(A,B),B). [assumption]. kept: 77 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | -member(C,A) | member(C,B) | -subset(A,B). [assumption]. kept: 78 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | -member(C,A) | member(C,B) | ilf_type(f14(A,B),set_type). [assumption]. kept: 79 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | -member(C,A) | member(C,B) | member(f14(A,B),A). [assumption]. kept: 80 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | -member(C,A) | member(C,B) | -member(f14(A,B),B). [assumption]. kept: 81 -ilf_type(A,set_type) | subset(A,A). [assumption]. kept: 82 -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(A,power_set(B)) | ilf_type(f15(A,B),set_type). [assumption]. kept: 83 -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(A,power_set(B)) | member(f15(A,B),A). [assumption]. kept: 84 -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(A,power_set(B)) | -member(f15(A,B),B). [assumption]. kept: 85 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | -member(C,A) | member(C,B) | -member(A,power_set(B)). [assumption]. kept: 86 -ilf_type(A,set_type) | -empty(power_set(A)). [assumption]. kept: 87 -ilf_type(A,set_type) | ilf_type(power_set(A),set_type). [assumption]. kept: 88 -ilf_type(A,set_type) | empty(B) | -ilf_type(B,set_type) | ilf_type(A,member_type(B)) | -member(A,B). [assumption]. kept: 89 -ilf_type(A,set_type) | empty(B) | -ilf_type(B,set_type) | member(A,B) | -ilf_type(A,member_type(B)). [assumption]. kept: 90 empty(A) | -ilf_type(A,set_type) | ilf_type(f16(A),member_type(A)). [assumption]. kept: 91 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f20(A,B),set_type) | ilf_type(f22(A),set_type). [assumption]. kept: 92 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f20(A,B),set_type) | member(f22(A),A). [assumption]. 93 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f20(A,B),set_type) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | ordered_pair(C,D) != f22(A). [assumption]. kept: 94 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f20(A,B),set_type) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | f22(A) != ordered_pair(C,D). [copy(93),flip(g)]. kept: 95 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f21(A,B),set_type) | ilf_type(f22(A),set_type). [assumption]. kept: 96 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f21(A,B),set_type) | member(f22(A),A). [assumption]. 97 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f21(A,B),set_type) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | ordered_pair(C,D) != f22(A). [assumption]. kept: 98 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f21(A,B),set_type) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | f22(A) != ordered_pair(C,D). [copy(97),flip(g)]. kept: 99 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f20(A,B),f21(A,B)) = B | ilf_type(f22(A),set_type). [assumption]. kept: 100 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f20(A,B),f21(A,B)) = B | member(f22(A),A). [assumption]. 101 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f20(A,B),f21(A,B)) = B | -ilf_type(C,set_type) | -ilf_type(D,set_type) | ordered_pair(C,D) != f22(A). [assumption]. kept: 102 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f20(A,B),f21(A,B)) = B | -ilf_type(C,set_type) | -ilf_type(D,set_type) | f22(A) != ordered_pair(C,D). [copy(101),flip(g)]. kept: 103 -ilf_type(A,set_type) | empty(A) | ilf_type(f23(A),set_type). [assumption]. kept: 104 -ilf_type(A,set_type) | empty(A) | member(f23(A),A). [assumption]. kept: 105 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | -empty(A). [assumption]. kept: 106 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f24(A),set_type). [assumption]. kept: 107 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | member(f24(A),A). [assumption]. kept: 108 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,relation_type(A,B)) | domain(A,B,C) = domain_of(C). [assumption]. kept: 109 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,relation_type(A,B)) | ilf_type(domain(A,B,C),subset_type(A)). [assumption]. kept: 110 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,relation_type(A,B)) | range(A,B,C) = range_of(C). [assumption]. kept: 111 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,relation_type(A,B)) | ilf_type(range(A,B,C),subset_type(B)). [assumption]. kept: 112 ilf_type(A,set_type). [assumption]. kept: 113 ilf_type(c4,relation_type(c2,c3)). [assumption]. kept: 114 member(c5,c3). [assumption]. 115 -ilf_type(A,set_type) | -member(ordered_pair(A,c5),c4). [assumption]. kept: 116 -member(ordered_pair(A,c5),c4). [copy(115),unit_del(a,112)]. kept: 117 range(c2,c3,c4) = c3. [assumption]. 118 -ilf_type(A,set_type) | member(f17(A),A) | -ilf_type(A,set_type) | ilf_type(A,binary_relation_type). [resolve(4,b,2,c)]. kept: 119 member(f17(A),A) | ilf_type(A,binary_relation_type). [copy(118),merge(c),unit_del(a,112)]. 120 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | ordered_pair(B,C) != f17(A) | -ilf_type(A,set_type) | ilf_type(A,binary_relation_type). [resolve(5,b,2,c)]. kept: 121 f17(A) != ordered_pair(B,C) | ilf_type(A,binary_relation_type). [copy(120),flip(d),merge(e),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. 122 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f18(A,B),f19(A,B)) = B | -ilf_type(A,set_type) | -ilf_type(A,binary_relation_type). [resolve(8,e,1,b)]. kept: 123 -member(A,B) | ordered_pair(f18(B,A),f19(B,A)) = A | -ilf_type(B,binary_relation_type). [copy(122),merge(e),unit_del(a,112),unit_del(b,112)]. 124 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f18(A,B),f19(A,B)) = B | -ilf_type(A,set_type) | member(f17(A),A). [resolve(8,e,4,b)]. kept: 125 -member(A,B) | ordered_pair(f18(B,A),f19(B,A)) = A | member(f17(B),B). [copy(124),merge(e),unit_del(a,112),unit_del(b,112)]. 126 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f18(A,B),f19(A,B)) = B | -ilf_type(A,set_type) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | ordered_pair(C,D) != f17(A). [resolve(8,e,5,b)]. kept: 127 -member(A,B) | ordered_pair(f18(B,A),f19(B,A)) = A | f17(B) != ordered_pair(C,D). [copy(126),flip(h),merge(e),unit_del(a,112),unit_del(b,112),unit_del(e,112),unit_del(f,112)]. 128 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,subset_type(cross_product(A,B))) | -ilf_type(C,set_type) | ilf_type(C,binary_relation_type). [resolve(9,d,2,c)]. kept: 129 -ilf_type(A,subset_type(cross_product(B,C))) | ilf_type(A,binary_relation_type). [copy(128),unit_del(a,112),unit_del(b,112),unit_del(d,112)]. 130 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,subset_type(cross_product(A,B))) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | -member(D,C) | ordered_pair(f18(C,D),f19(C,D)) = D. [resolve(9,d,8,e)]. kept: 131 -ilf_type(A,subset_type(cross_product(B,C))) | -member(D,A) | ordered_pair(f18(A,D),f19(A,D)) = D. [copy(130),unit_del(a,112),unit_del(b,112),unit_del(d,112),unit_del(e,112)]. 132 -empty(A) | -ilf_type(A,set_type) | -ilf_type(A,set_type) | ilf_type(A,binary_relation_type). [resolve(10,c,2,c)]. kept: 133 -empty(A) | ilf_type(A,binary_relation_type). [copy(132),merge(c),unit_del(b,112)]. 134 -empty(A) | -ilf_type(A,set_type) | -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f18(A,B),f19(A,B)) = B. [resolve(10,c,8,e)]. kept: 135 -empty(A) | -member(B,A) | ordered_pair(f18(A,B),f19(A,B)) = B. [copy(134),merge(c),unit_del(b,112),unit_del(c,112)]. kept: 136 -ilf_type(A,binary_relation_type) | member(B,range_of(A)) | -member(ordered_pair(B,B),A). [factor(11,b,d),unit_del(b,112)]. kept: 137 -ilf_type(A,binary_relation_type) | member(ordered_pair(f2(A,B),B),A) | -member(ordered_pair(B,B),A). [factor(15,b,d),unit_del(b,112)]. kept: 138 -ilf_type(A,binary_relation_type) | -member(ordered_pair(B,B),A) | member(B,domain_of(A)). [factor(17,a,b),unit_del(a,112)]. kept: 139 ordered_pair(A,A) = B | unordered_pair(unordered_pair(A,A),singleton(A)) != B. [factor(27,a,b),unit_del(a,112),unit_del(b,112)]. kept: 140 ordered_pair(A,B) = A | unordered_pair(unordered_pair(A,B),singleton(A)) != A. [factor(27,a,c),unit_del(a,112),unit_del(b,112)]. kept: 141 ordered_pair(A,B) = B | unordered_pair(unordered_pair(A,B),singleton(A)) != B. [factor(27,b,c),unit_del(a,112),unit_del(b,112)]. kept: 142 unordered_pair(unordered_pair(A,A),singleton(A)) = B | ordered_pair(A,A) != B. [factor(28,a,b),unit_del(a,112),unit_del(b,112)]. kept: 143 unordered_pair(unordered_pair(A,B),singleton(A)) = A | ordered_pair(A,B) != A. [factor(28,a,c),unit_del(a,112),unit_del(b,112)]. kept: 144 unordered_pair(unordered_pair(A,B),singleton(A)) = B | ordered_pair(A,B) != B. [factor(28,b,c),unit_del(a,112),unit_del(b,112)]. kept: 145 -ilf_type(A,subset_type(cross_product(B,B))) | ilf_type(A,relation_type(B,B)). [factor(30,a,b),unit_del(a,112)]. kept: 146 -ilf_type(A,relation_type(B,B)) | ilf_type(A,subset_type(cross_product(B,B))). [factor(31,a,b),unit_del(a,112)]. kept: 147 ilf_type(f5(A,A),relation_type(A,A)). [factor(32,a,b),unit_del(a,112)]. kept: 148 subset(A,A). [factor(34,a,b),xx(c),unit_del(a,112)]. kept: 149 ilf_type(A,subset_type(A)) | -ilf_type(A,member_type(power_set(A))). [factor(42,a,b),unit_del(a,112)]. kept: 150 ilf_type(A,member_type(power_set(A))) | -ilf_type(A,subset_type(A)). [factor(43,a,b),unit_del(a,112)]. kept: 151 member(A,A) | -member(A,B) | B != A. [factor(54,a,c),unit_del(a,112),unit_del(b,112)]. kept: 152 member(A,B) | -member(A,A) | A != B. [factor(54,b,c),unit_del(a,112),unit_del(b,112)]. kept: 153 member(A,A) | -member(A,B) | member(f9(A,B),A) | -member(f10(A,B),A). [factor(59,a,c),unit_del(a,112),unit_del(b,112)]. kept: 154 member(A,B) | -member(A,A) | member(f9(B,A),B) | -member(f10(B,A),B). [factor(59,b,c),unit_del(a,112),unit_del(b,112)]. kept: 155 member(f9(A,B),A) | -member(f9(A,B),B) | -member(f10(A,B),A). [factor(59,d,f),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. kept: 156 member(A,A) | -member(A,B) | member(f9(A,B),A) | member(f10(A,B),B). [factor(60,a,c),unit_del(a,112),unit_del(b,112)]. kept: 157 member(A,B) | -member(A,A) | member(f9(B,A),B) | member(f10(B,A),A). [factor(60,b,c),unit_del(a,112),unit_del(b,112)]. kept: 158 member(f9(A,B),A) | -member(f9(A,B),B) | member(f10(A,B),B). [factor(60,d,f),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. kept: 159 member(A,A) | -member(A,B) | -member(f9(A,B),B) | -member(f10(A,B),A). [factor(62,a,c),unit_del(a,112),unit_del(b,112)]. kept: 160 member(A,B) | -member(A,A) | -member(f9(B,A),A) | -member(f10(B,A),B). [factor(62,b,c),unit_del(a,112),unit_del(b,112)]. kept: 161 member(A,A) | -member(A,B) | -member(f9(A,B),B) | member(f10(A,B),B). [factor(63,a,c),unit_del(a,112),unit_del(b,112)]. kept: 162 member(A,B) | -member(A,A) | -member(f9(B,A),A) | member(f10(B,A),A). [factor(63,b,c),unit_del(a,112),unit_del(b,112)]. kept: 163 member(A,B) | -member(A,A) | B != A. [factor(64,a,c),unit_del(a,112),unit_del(b,112)]. kept: 164 member(A,A) | -member(A,B) | A != B. [factor(64,b,c),unit_del(a,112),unit_del(b,112)]. kept: 165 member(A,B) | -member(A,A) | member(f11(A,B),A) | -member(f12(A,B),A). [factor(69,a,c),unit_del(a,112),unit_del(b,112)]. kept: 166 member(A,A) | -member(A,B) | member(f11(B,A),B) | -member(f12(B,A),B). [factor(69,b,c),unit_del(a,112),unit_del(b,112)]. kept: 167 member(f12(A,B),B) | -member(f12(A,B),A) | member(f11(A,B),A). [factor(69,e,g),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. kept: 168 member(A,B) | -member(A,A) | member(f11(A,B),A) | member(f12(A,B),B). [factor(70,a,c),unit_del(a,112),unit_del(b,112)]. kept: 169 member(A,A) | -member(A,B) | member(f11(B,A),B) | member(f12(B,A),A). [factor(70,b,c),unit_del(a,112),unit_del(b,112)]. kept: 170 member(A,B) | -member(A,A) | -member(f11(A,B),B) | -member(f12(A,B),A). [factor(72,a,c),unit_del(a,112),unit_del(b,112)]. kept: 171 member(A,A) | -member(A,B) | -member(f11(B,A),A) | -member(f12(B,A),B). [factor(72,b,c),unit_del(a,112),unit_del(b,112)]. kept: 172 member(f12(A,B),B) | -member(f12(A,B),A) | -member(f11(A,B),B). [factor(72,e,g),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. kept: 173 member(A,B) | -member(A,A) | -member(f11(A,B),B) | member(f12(A,B),B). [factor(73,a,c),unit_del(a,112),unit_del(b,112)]. kept: 174 member(A,A) | -member(A,B) | -member(f11(B,A),A) | member(f12(B,A),A). [factor(73,b,c),unit_del(a,112),unit_del(b,112)]. kept: 175 -member(A,A) | member(A,B) | -subset(A,B). [factor(77,a,c),unit_del(a,112),unit_del(b,112)]. kept: 176 -member(A,B) | member(A,A) | -subset(B,A). [factor(77,b,c),unit_del(a,112),unit_del(b,112)]. kept: 177 -member(A,A) | member(A,B) | member(f14(A,B),A). [factor(79,a,c),unit_del(a,112),unit_del(b,112)]. kept: 178 -member(A,B) | member(A,A) | member(f14(B,A),B). [factor(79,b,c),unit_del(a,112),unit_del(b,112)]. kept: 179 -member(A,A) | member(A,B) | -member(f14(A,B),B). [factor(80,a,c),unit_del(a,112),unit_del(b,112)]. kept: 180 -member(A,B) | member(A,A) | -member(f14(B,A),A). [factor(80,b,c),unit_del(a,112),unit_del(b,112)]. kept: 181 member(A,power_set(A)) | member(f15(A,A),A). [factor(83,a,b),unit_del(a,112)]. kept: 182 member(A,power_set(A)) | -member(f15(A,A),A). [factor(84,a,b),unit_del(a,112)]. kept: 183 -member(A,A) | member(A,B) | -member(A,power_set(B)). [factor(85,a,c),unit_del(a,112),unit_del(b,112)]. kept: 184 -member(A,B) | member(A,A) | -member(B,power_set(A)). [factor(85,b,c),unit_del(a,112),unit_del(b,112)]. kept: 185 -member(power_set(A),power_set(A)) | member(power_set(A),A). [factor(85,d,f),merge(c),unit_del(a,112),unit_del(b,112)]. kept: 186 empty(A) | ilf_type(A,member_type(A)) | -member(A,A). [factor(88,a,c),unit_del(a,112)]. kept: 187 empty(A) | member(A,A) | -ilf_type(A,member_type(A)). [factor(89,a,c),unit_del(a,112)]. kept: 188 -member(A,A) | ordered_pair(f20(A,A),f21(A,A)) = A | member(f22(A),A). [factor(100,a,b),unit_del(a,112)]. kept: 189 -member(A,A) | ordered_pair(f20(A,A),f21(A,A)) = A | f22(A) != ordered_pair(B,C). [factor(102,a,b),unit_del(a,112),unit_del(d,112),unit_del(e,112)]. kept: 190 -member(A,B) | ordered_pair(f20(B,A),f21(B,A)) = A | f22(B) != ordered_pair(B,C). [factor(102,a,e),unit_del(a,112),unit_del(b,112),unit_del(e,112)]. kept: 191 -member(A,B) | ordered_pair(f20(B,A),f21(B,A)) = A | f22(B) != ordered_pair(C,B). [factor(102,a,f),unit_del(a,112),unit_del(b,112),unit_del(e,112)]. kept: 192 -member(A,B) | ordered_pair(f20(B,A),f21(B,A)) = A | f22(B) != ordered_pair(A,C). [factor(102,b,e),unit_del(a,112),unit_del(b,112),unit_del(e,112)]. kept: 193 -member(A,B) | ordered_pair(f20(B,A),f21(B,A)) = A | f22(B) != ordered_pair(C,A). [factor(102,b,f),unit_del(a,112),unit_del(b,112),unit_del(e,112)]. kept: 194 -member(A,B) | ordered_pair(f20(B,A),f21(B,A)) = A | f22(B) != ordered_pair(C,C). [factor(102,e,f),unit_del(a,112),unit_del(b,112),unit_del(e,112)]. kept: 195 -member(A,A) | -empty(A). [factor(105,a,b),unit_del(a,112)]. kept: 196 -member(A,A) | member(f24(A),A). [factor(107,a,b),unit_del(a,112)]. kept: 197 -ilf_type(A,relation_type(B,B)) | domain(B,B,A) = domain_of(A). [factor(108,a,b),unit_del(a,112)]. kept: 198 -ilf_type(A,relation_type(B,B)) | ilf_type(domain(B,B,A),subset_type(B)). [factor(109,a,b),unit_del(a,112)]. kept: 199 -ilf_type(A,relation_type(B,B)) | range(B,B,A) = range_of(A). [factor(110,a,b),unit_del(a,112)]. kept: 200 -ilf_type(A,relation_type(B,B)) | ilf_type(range(B,B,A),subset_type(B)). [factor(111,a,b),unit_del(a,112)]. kept: 201 -ilf_type(A,relation_type(B,C)) | ilf_type(range(B,C,A),subset_type(C)). [back_unit_del(111),unit_del(a,112),unit_del(b,112)]. kept: 202 -ilf_type(A,relation_type(B,C)) | range(B,C,A) = range_of(A). [back_unit_del(110),unit_del(a,112),unit_del(b,112)]. kept: 203 -ilf_type(A,relation_type(B,C)) | ilf_type(domain(B,C,A),subset_type(B)). [back_unit_del(109),unit_del(a,112),unit_del(b,112)]. kept: 204 -ilf_type(A,relation_type(B,C)) | domain(B,C,A) = domain_of(A). [back_unit_del(108),unit_del(a,112),unit_del(b,112)]. kept: 205 -member(A,B) | member(f24(B),B). [back_unit_del(107),unit_del(a,112),unit_del(b,112)]. kept: 206 -member(A,B) | -empty(B). [back_unit_del(105),unit_del(a,112),unit_del(b,112)]. kept: 207 empty(A) | member(f23(A),A). [back_unit_del(104),unit_del(a,112)]. kept: 208 -member(A,B) | ordered_pair(f20(B,A),f21(B,A)) = A | f22(B) != ordered_pair(C,D). [back_unit_del(102),unit_del(a,112),unit_del(b,112),unit_del(e,112),unit_del(f,112)]. kept: 209 -member(A,B) | ordered_pair(f20(B,A),f21(B,A)) = A | member(f22(B),B). [back_unit_del(100),unit_del(a,112),unit_del(b,112)]. kept: 210 empty(A) | ilf_type(f16(A),member_type(A)). [back_unit_del(90),unit_del(b,112)]. kept: 211 empty(A) | member(B,A) | -ilf_type(B,member_type(A)). [back_unit_del(89),unit_del(a,112),unit_del(c,112)]. kept: 212 empty(A) | ilf_type(B,member_type(A)) | -member(B,A). [back_unit_del(88),unit_del(a,112),unit_del(c,112)]. kept: 213 -empty(power_set(A)). [back_unit_del(86),unit_del(a,112)]. kept: 214 -member(A,B) | member(A,C) | -member(B,power_set(C)). [back_unit_del(85),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. kept: 215 member(A,power_set(B)) | -member(f15(A,B),B). [back_unit_del(84),unit_del(a,112),unit_del(b,112)]. kept: 216 member(A,power_set(B)) | member(f15(A,B),A). [back_unit_del(83),unit_del(a,112),unit_del(b,112)]. kept: 217 -member(A,B) | member(A,C) | -member(f14(B,C),C). [back_unit_del(80),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. kept: 218 -member(A,B) | member(A,C) | member(f14(B,C),B). [back_unit_del(79),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. kept: 219 -member(A,B) | member(A,C) | -subset(B,C). [back_unit_del(77),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. kept: 220 subset(A,B) | -member(f13(A,B),B). [back_unit_del(76),unit_del(a,112),unit_del(b,112)]. kept: 221 subset(A,B) | member(f13(A,B),A). [back_unit_del(75),unit_del(a,112),unit_del(b,112)]. kept: 222 member(A,B) | -member(A,C) | -member(f11(C,B),B) | member(f12(C,B),B). [back_unit_del(73),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. kept: 223 member(A,B) | -member(A,C) | -member(f11(C,B),B) | -member(f12(C,B),C). [back_unit_del(72),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. kept: 224 member(A,B) | -member(A,C) | member(f11(C,B),C) | member(f12(C,B),B). [back_unit_del(70),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. kept: 225 member(A,B) | -member(A,C) | member(f11(C,B),C) | -member(f12(C,B),C). [back_unit_del(69),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. kept: 226 member(A,B) | -member(A,C) | B != C. [back_unit_del(64),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. kept: 227 member(A,B) | -member(A,C) | -member(f9(B,C),C) | member(f10(B,C),C). [back_unit_del(63),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. kept: 228 member(A,B) | -member(A,C) | -member(f9(B,C),C) | -member(f10(B,C),B). [back_unit_del(62),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. kept: 229 member(A,B) | -member(A,C) | member(f9(B,C),B) | member(f10(B,C),C). [back_unit_del(60),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. kept: 230 member(A,B) | -member(A,C) | member(f9(B,C),B) | -member(f10(B,C),B). [back_unit_del(59),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. kept: 231 member(A,B) | -member(A,C) | C != B. [back_unit_del(54),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. kept: 232 A = B | -member(f7(B,A),A) | member(f8(B,A),A). [back_unit_del(53),unit_del(a,112),unit_del(b,112)]. kept: 233 A = B | -member(f7(B,A),A) | -member(f8(B,A),B). [back_unit_del(52),unit_del(a,112),unit_del(b,112)]. kept: 234 A = B | member(f7(B,A),B) | member(f8(B,A),A). [back_unit_del(50),unit_del(a,112),unit_del(b,112)]. kept: 235 A = B | member(f7(B,A),B) | -member(f8(B,A),B). [back_unit_del(49),unit_del(a,112),unit_del(b,112)]. kept: 236 ilf_type(f6(A),subset_type(A)). [back_unit_del(44),unit_del(a,112)]. kept: 237 ilf_type(A,member_type(power_set(B))) | -ilf_type(A,subset_type(B)). [back_unit_del(43),unit_del(a,112),unit_del(b,112)]. kept: 238 ilf_type(A,subset_type(B)) | -ilf_type(A,member_type(power_set(B))). [back_unit_del(42),unit_del(a,112),unit_del(b,112)]. % Operation unordered_pair is commutative; C redundancy checks enabled. kept: 239 unordered_pair(A,B) = unordered_pair(B,A). [back_unit_del(40),unit_del(a,112),unit_del(b,112)]. kept: 240 subset(A,B) | A != B. [back_unit_del(35),unit_del(a,112),unit_del(b,112)]. kept: 241 subset(A,B) | B != A. [back_unit_del(34),unit_del(a,112),unit_del(b,112)]. kept: 242 A = B | -subset(B,A) | -subset(A,B). [back_unit_del(33),unit_del(a,112),unit_del(b,112)]. kept: 243 ilf_type(f5(A,B),relation_type(B,A)). [back_unit_del(32),unit_del(a,112),unit_del(b,112)]. kept: 244 -ilf_type(A,relation_type(B,C)) | ilf_type(A,subset_type(cross_product(B,C))). [back_unit_del(31),unit_del(a,112),unit_del(b,112)]. kept: 245 -ilf_type(A,subset_type(cross_product(B,C))) | ilf_type(A,relation_type(B,C)). [back_unit_del(30),unit_del(a,112),unit_del(b,112)]. kept: 246 unordered_pair(unordered_pair(A,B),singleton(A)) = C | ordered_pair(A,B) != C. [back_unit_del(28),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. kept: 247 ordered_pair(A,B) = C | unordered_pair(unordered_pair(A,B),singleton(A)) != C. [back_unit_del(27),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. kept: 248 -member(f3(A,B),B) | member(f4(A,B),B) | B = A. [back_unit_del(26),unit_del(a,112),unit_del(b,112)]. kept: 249 -member(f3(A,B),B) | -member(f4(A,B),A) | B = A. [back_unit_del(25),unit_del(a,112),unit_del(b,112)]. kept: 250 member(f3(A,B),A) | member(f4(A,B),B) | B = A. [back_unit_del(23),unit_del(a,112),unit_del(b,112)]. kept: 251 member(f3(A,B),A) | -member(f4(A,B),A) | B = A. [back_unit_del(22),unit_del(a,112),unit_del(b,112)]. kept: 252 -ilf_type(A,binary_relation_type) | -member(ordered_pair(B,C),A) | member(B,domain_of(A)). [back_unit_del(17),unit_del(a,112),unit_del(b,112)]. kept: 253 -ilf_type(A,binary_relation_type) | member(ordered_pair(f2(A,B),B),A) | -member(ordered_pair(C,B),A). [back_unit_del(15),unit_del(b,112),unit_del(d,112)]. kept: 254 -ilf_type(A,binary_relation_type) | member(ordered_pair(f1(A,B),B),A) | -member(B,range_of(A)). [back_unit_del(13),unit_del(b,112)]. kept: 255 -ilf_type(A,binary_relation_type) | member(B,range_of(A)) | -member(ordered_pair(C,B),A). [back_unit_del(11),unit_del(b,112),unit_del(d,112)]. ============================== end of process initial clauses ======== ============================== CLAUSES FOR SEARCH ==================== % Clauses after input processing: formulas(usable). end_of_list. formulas(sos). 41 ilf_type(c1,binary_relation_type). [assumption]. 112 ilf_type(A,set_type). [assumption]. 113 ilf_type(c4,relation_type(c2,c3)). [assumption]. 114 member(c5,c3). [assumption]. 116 -member(ordered_pair(A,c5),c4). [copy(115),unit_del(a,112)]. 117 range(c2,c3,c4) = c3. [assumption]. 119 member(f17(A),A) | ilf_type(A,binary_relation_type). [copy(118),merge(c),unit_del(a,112)]. 121 f17(A) != ordered_pair(B,C) | ilf_type(A,binary_relation_type). [copy(120),flip(d),merge(e),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. 123 -member(A,B) | ordered_pair(f18(B,A),f19(B,A)) = A | -ilf_type(B,binary_relation_type). [copy(122),merge(e),unit_del(a,112),unit_del(b,112)]. 125 -member(A,B) | ordered_pair(f18(B,A),f19(B,A)) = A | member(f17(B),B). [copy(124),merge(e),unit_del(a,112),unit_del(b,112)]. 127 -member(A,B) | ordered_pair(f18(B,A),f19(B,A)) = A | f17(B) != ordered_pair(C,D). [copy(126),flip(h),merge(e),unit_del(a,112),unit_del(b,112),unit_del(e,112),unit_del(f,112)]. 129 -ilf_type(A,subset_type(cross_product(B,C))) | ilf_type(A,binary_relation_type). [copy(128),unit_del(a,112),unit_del(b,112),unit_del(d,112)]. 131 -ilf_type(A,subset_type(cross_product(B,C))) | -member(D,A) | ordered_pair(f18(A,D),f19(A,D)) = D. [copy(130),unit_del(a,112),unit_del(b,112),unit_del(d,112),unit_del(e,112)]. 133 -empty(A) | ilf_type(A,binary_relation_type). [copy(132),merge(c),unit_del(b,112)]. 148 subset(A,A). [factor(34,a,b),xx(c),unit_del(a,112)]. 155 member(f9(A,B),A) | -member(f9(A,B),B) | -member(f10(A,B),A). [factor(59,d,f),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. 158 member(f9(A,B),A) | -member(f9(A,B),B) | member(f10(A,B),B). [factor(60,d,f),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. 167 member(f12(A,B),B) | -member(f12(A,B),A) | member(f11(A,B),A). [factor(69,e,g),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. 172 member(f12(A,B),B) | -member(f12(A,B),A) | -member(f11(A,B),B). [factor(72,e,g),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. 185 -member(power_set(A),power_set(A)) | member(power_set(A),A). [factor(85,d,f),merge(c),unit_del(a,112),unit_del(b,112)]. 201 -ilf_type(A,relation_type(B,C)) | ilf_type(range(B,C,A),subset_type(C)). [back_unit_del(111),unit_del(a,112),unit_del(b,112)]. 202 -ilf_type(A,relation_type(B,C)) | range(B,C,A) = range_of(A). [back_unit_del(110),unit_del(a,112),unit_del(b,112)]. 203 -ilf_type(A,relation_type(B,C)) | ilf_type(domain(B,C,A),subset_type(B)). [back_unit_del(109),unit_del(a,112),unit_del(b,112)]. 204 -ilf_type(A,relation_type(B,C)) | domain(B,C,A) = domain_of(A). [back_unit_del(108),unit_del(a,112),unit_del(b,112)]. 205 -member(A,B) | member(f24(B),B). [back_unit_del(107),unit_del(a,112),unit_del(b,112)]. 206 -member(A,B) | -empty(B). [back_unit_del(105),unit_del(a,112),unit_del(b,112)]. 207 empty(A) | member(f23(A),A). [back_unit_del(104),unit_del(a,112)]. 208 -member(A,B) | ordered_pair(f20(B,A),f21(B,A)) = A | f22(B) != ordered_pair(C,D). [back_unit_del(102),unit_del(a,112),unit_del(b,112),unit_del(e,112),unit_del(f,112)]. 209 -member(A,B) | ordered_pair(f20(B,A),f21(B,A)) = A | member(f22(B),B). [back_unit_del(100),unit_del(a,112),unit_del(b,112)]. 210 empty(A) | ilf_type(f16(A),member_type(A)). [back_unit_del(90),unit_del(b,112)]. 211 empty(A) | member(B,A) | -ilf_type(B,member_type(A)). [back_unit_del(89),unit_del(a,112),unit_del(c,112)]. 212 empty(A) | ilf_type(B,member_type(A)) | -member(B,A). [back_unit_del(88),unit_del(a,112),unit_del(c,112)]. 213 -empty(power_set(A)). [back_unit_del(86),unit_del(a,112)]. 214 -member(A,B) | member(A,C) | -member(B,power_set(C)). [back_unit_del(85),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. 215 member(A,power_set(B)) | -member(f15(A,B),B). [back_unit_del(84),unit_del(a,112),unit_del(b,112)]. 216 member(A,power_set(B)) | member(f15(A,B),A). [back_unit_del(83),unit_del(a,112),unit_del(b,112)]. 217 -member(A,B) | member(A,C) | -member(f14(B,C),C). [back_unit_del(80),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. 218 -member(A,B) | member(A,C) | member(f14(B,C),B). [back_unit_del(79),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. 219 -member(A,B) | member(A,C) | -subset(B,C). [back_unit_del(77),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. 220 subset(A,B) | -member(f13(A,B),B). [back_unit_del(76),unit_del(a,112),unit_del(b,112)]. 221 subset(A,B) | member(f13(A,B),A). [back_unit_del(75),unit_del(a,112),unit_del(b,112)]. 222 member(A,B) | -member(A,C) | -member(f11(C,B),B) | member(f12(C,B),B). [back_unit_del(73),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. 223 member(A,B) | -member(A,C) | -member(f11(C,B),B) | -member(f12(C,B),C). [back_unit_del(72),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. 224 member(A,B) | -member(A,C) | member(f11(C,B),C) | member(f12(C,B),B). [back_unit_del(70),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. 225 member(A,B) | -member(A,C) | member(f11(C,B),C) | -member(f12(C,B),C). [back_unit_del(69),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. 226 member(A,B) | -member(A,C) | B != C. [back_unit_del(64),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. 227 member(A,B) | -member(A,C) | -member(f9(B,C),C) | member(f10(B,C),C). [back_unit_del(63),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. 228 member(A,B) | -member(A,C) | -member(f9(B,C),C) | -member(f10(B,C),B). [back_unit_del(62),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. 229 member(A,B) | -member(A,C) | member(f9(B,C),B) | member(f10(B,C),C). [back_unit_del(60),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. 230 member(A,B) | -member(A,C) | member(f9(B,C),B) | -member(f10(B,C),B). [back_unit_del(59),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. 231 member(A,B) | -member(A,C) | C != B. [back_unit_del(54),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. 232 A = B | -member(f7(B,A),A) | member(f8(B,A),A). [back_unit_del(53),unit_del(a,112),unit_del(b,112)]. 233 A = B | -member(f7(B,A),A) | -member(f8(B,A),B). [back_unit_del(52),unit_del(a,112),unit_del(b,112)]. 234 A = B | member(f7(B,A),B) | member(f8(B,A),A). [back_unit_del(50),unit_del(a,112),unit_del(b,112)]. 235 A = B | member(f7(B,A),B) | -member(f8(B,A),B). [back_unit_del(49),unit_del(a,112),unit_del(b,112)]. 236 ilf_type(f6(A),subset_type(A)). [back_unit_del(44),unit_del(a,112)]. 237 ilf_type(A,member_type(power_set(B))) | -ilf_type(A,subset_type(B)). [back_unit_del(43),unit_del(a,112),unit_del(b,112)]. 238 ilf_type(A,subset_type(B)) | -ilf_type(A,member_type(power_set(B))). [back_unit_del(42),unit_del(a,112),unit_del(b,112)]. 239 unordered_pair(A,B) = unordered_pair(B,A). [back_unit_del(40),unit_del(a,112),unit_del(b,112)]. 240 subset(A,B) | A != B. [back_unit_del(35),unit_del(a,112),unit_del(b,112)]. 241 subset(A,B) | B != A. [back_unit_del(34),unit_del(a,112),unit_del(b,112)]. 242 A = B | -subset(B,A) | -subset(A,B). [back_unit_del(33),unit_del(a,112),unit_del(b,112)]. 243 ilf_type(f5(A,B),relation_type(B,A)). [back_unit_del(32),unit_del(a,112),unit_del(b,112)]. 244 -ilf_type(A,relation_type(B,C)) | ilf_type(A,subset_type(cross_product(B,C))). [back_unit_del(31),unit_del(a,112),unit_del(b,112)]. 245 -ilf_type(A,subset_type(cross_product(B,C))) | ilf_type(A,relation_type(B,C)). [back_unit_del(30),unit_del(a,112),unit_del(b,112)]. 246 unordered_pair(unordered_pair(A,B),singleton(A)) = C | ordered_pair(A,B) != C. [back_unit_del(28),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. 247 ordered_pair(A,B) = C | unordered_pair(unordered_pair(A,B),singleton(A)) != C. [back_unit_del(27),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. 248 -member(f3(A,B),B) | member(f4(A,B),B) | B = A. [back_unit_del(26),unit_del(a,112),unit_del(b,112)]. 249 -member(f3(A,B),B) | -member(f4(A,B),A) | B = A. [back_unit_del(25),unit_del(a,112),unit_del(b,112)]. 250 member(f3(A,B),A) | member(f4(A,B),B) | B = A. [back_unit_del(23),unit_del(a,112),unit_del(b,112)]. 251 member(f3(A,B),A) | -member(f4(A,B),A) | B = A. [back_unit_del(22),unit_del(a,112),unit_del(b,112)]. 252 -ilf_type(A,binary_relation_type) | -member(ordered_pair(B,C),A) | member(B,domain_of(A)). [back_unit_del(17),unit_del(a,112),unit_del(b,112)]. 253 -ilf_type(A,binary_relation_type) | member(ordered_pair(f2(A,B),B),A) | -member(ordered_pair(C,B),A). [back_unit_del(15),unit_del(b,112),unit_del(d,112)]. 254 -ilf_type(A,binary_relation_type) | member(ordered_pair(f1(A,B),B),A) | -member(B,range_of(A)). [back_unit_del(13),unit_del(b,112)]. 255 -ilf_type(A,binary_relation_type) | member(B,range_of(A)) | -member(ordered_pair(C,B),A). [back_unit_del(11),unit_del(b,112),unit_del(d,112)]. end_of_list. formulas(demodulators). 117 range(c2,c3,c4) = c3. [assumption]. 239 unordered_pair(A,B) = unordered_pair(B,A). [back_unit_del(40),unit_del(a,112),unit_del(b,112)]. % (lex-dep) end_of_list. ============================== end of clauses for search ============= ============================== SEARCH ================================ % Starting search at 0.02 seconds. given #1 (I,wt=3): 41 ilf_type(c1,binary_relation_type). [assumption]. given #2 (I,wt=3): 112 ilf_type(A,set_type). [assumption]. given #3 (I,wt=5): 113 ilf_type(c4,relation_type(c2,c3)). [assumption]. given #4 (I,wt=3): 114 member(c5,c3). [assumption]. given #5 (I,wt=5): 116 -member(ordered_pair(A,c5),c4). [copy(115),unit_del(a,112)]. given #6 (I,wt=6): 117 range(c2,c3,c4) = c3. [assumption]. given #7 (I,wt=7): 119 member(f17(A),A) | ilf_type(A,binary_relation_type). [copy(118),merge(c),unit_del(a,112)]. given #8 (I,wt=9): 121 f17(A) != ordered_pair(B,C) | ilf_type(A,binary_relation_type). [copy(120),flip(d),merge(e),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. given #9 (I,wt=15): 123 -member(A,B) | ordered_pair(f18(B,A),f19(B,A)) = A | -ilf_type(B,binary_relation_type). [copy(122),merge(e),unit_del(a,112),unit_del(b,112)]. given #10 (I,wt=16): 125 -member(A,B) | ordered_pair(f18(B,A),f19(B,A)) = A | member(f17(B),B). [copy(124),merge(e),unit_del(a,112),unit_del(b,112)]. given #11 (I,wt=18): 127 -member(A,B) | ordered_pair(f18(B,A),f19(B,A)) = A | f17(B) != ordered_pair(C,D). [copy(126),flip(h),merge(e),unit_del(a,112),unit_del(b,112),unit_del(e,112),unit_del(f,112)]. given #12 (I,wt=9): 129 -ilf_type(A,subset_type(cross_product(B,C))) | ilf_type(A,binary_relation_type). [copy(128),unit_del(a,112),unit_del(b,112),unit_del(d,112)]. given #13 (I,wt=18): 131 -ilf_type(A,subset_type(cross_product(B,C))) | -member(D,A) | ordered_pair(f18(A,D),f19(A,D)) = D. [copy(130),unit_del(a,112),unit_del(b,112),unit_del(d,112),unit_del(e,112)]. given #14 (I,wt=5): 133 -empty(A) | ilf_type(A,binary_relation_type). [copy(132),merge(c),unit_del(b,112)]. given #15 (I,wt=3): 148 subset(A,A). [factor(34,a,b),xx(c),unit_del(a,112)]. given #16 (I,wt=15): 155 member(f9(A,B),A) | -member(f9(A,B),B) | -member(f10(A,B),A). [factor(59,d,f),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. given #17 (I,wt=15): 158 member(f9(A,B),A) | -member(f9(A,B),B) | member(f10(A,B),B). [factor(60,d,f),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. given #18 (I,wt=15): 167 member(f12(A,B),B) | -member(f12(A,B),A) | member(f11(A,B),A). [factor(69,e,g),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. given #19 (I,wt=15): 172 member(f12(A,B),B) | -member(f12(A,B),A) | -member(f11(A,B),B). [factor(72,e,g),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. given #20 (I,wt=9): 185 -member(power_set(A),power_set(A)) | member(power_set(A),A). [factor(85,d,f),merge(c),unit_del(a,112),unit_del(b,112)]. given #21 (I,wt=12): 201 -ilf_type(A,relation_type(B,C)) | ilf_type(range(B,C,A),subset_type(C)). [back_unit_del(111),unit_del(a,112),unit_del(b,112)]. given #22 (I,wt=12): 202 -ilf_type(A,relation_type(B,C)) | range(B,C,A) = range_of(A). [back_unit_del(110),unit_del(a,112),unit_del(b,112)]. given #23 (I,wt=12): 203 -ilf_type(A,relation_type(B,C)) | ilf_type(domain(B,C,A),subset_type(B)). [back_unit_del(109),unit_del(a,112),unit_del(b,112)]. given #24 (I,wt=12): 204 -ilf_type(A,relation_type(B,C)) | domain(B,C,A) = domain_of(A). [back_unit_del(108),unit_del(a,112),unit_del(b,112)]. given #25 (I,wt=7): 205 -member(A,B) | member(f24(B),B). [back_unit_del(107),unit_del(a,112),unit_del(b,112)]. given #26 (I,wt=5): 206 -member(A,B) | -empty(B). [back_unit_del(105),unit_del(a,112),unit_del(b,112)]. given #27 (I,wt=6): 207 empty(A) | member(f23(A),A). [back_unit_del(104),unit_del(a,112)]. given #28 (I,wt=18): 208 -member(A,B) | ordered_pair(f20(B,A),f21(B,A)) = A | f22(B) != ordered_pair(C,D). [back_unit_del(102),unit_del(a,112),unit_del(b,112),unit_del(e,112),unit_del(f,112)]. given #29 (I,wt=16): 209 -member(A,B) | ordered_pair(f20(B,A),f21(B,A)) = A | member(f22(B),B). [back_unit_del(100),unit_del(a,112),unit_del(b,112)]. given #30 (I,wt=7): 210 empty(A) | ilf_type(f16(A),member_type(A)). [back_unit_del(90),unit_del(b,112)]. given #31 (I,wt=9): 211 empty(A) | member(B,A) | -ilf_type(B,member_type(A)). [back_unit_del(89),unit_del(a,112),unit_del(c,112)]. given #32 (I,wt=9): 212 empty(A) | ilf_type(B,member_type(A)) | -member(B,A). [back_unit_del(88),unit_del(a,112),unit_del(c,112)]. given #33 (I,wt=3): 213 -empty(power_set(A)). [back_unit_del(86),unit_del(a,112)]. given #34 (I,wt=10): 214 -member(A,B) | member(A,C) | -member(B,power_set(C)). [back_unit_del(85),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. given #35 (I,wt=9): 215 member(A,power_set(B)) | -member(f15(A,B),B). [back_unit_del(84),unit_del(a,112),unit_del(b,112)]. given #36 (I,wt=9): 216 member(A,power_set(B)) | member(f15(A,B),A). [back_unit_del(83),unit_del(a,112),unit_del(b,112)]. given #37 (I,wt=11): 217 -member(A,B) | member(A,C) | -member(f14(B,C),C). [back_unit_del(80),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. given #38 (I,wt=11): 218 -member(A,B) | member(A,C) | member(f14(B,C),B). [back_unit_del(79),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. given #39 (I,wt=9): 219 -member(A,B) | member(A,C) | -subset(B,C). [back_unit_del(77),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. given #40 (I,wt=8): 220 subset(A,B) | -member(f13(A,B),B). [back_unit_del(76),unit_del(a,112),unit_del(b,112)]. given #41 (I,wt=8): 221 subset(A,B) | member(f13(A,B),A). [back_unit_del(75),unit_del(a,112),unit_del(b,112)]. given #42 (I,wt=16): 222 member(A,B) | -member(A,C) | -member(f11(C,B),B) | member(f12(C,B),B). [back_unit_del(73),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. given #43 (I,wt=16): 223 member(A,B) | -member(A,C) | -member(f11(C,B),B) | -member(f12(C,B),C). [back_unit_del(72),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. given #44 (I,wt=16): 224 member(A,B) | -member(A,C) | member(f11(C,B),C) | member(f12(C,B),B). [back_unit_del(70),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. given #45 (I,wt=16): 225 member(A,B) | -member(A,C) | member(f11(C,B),C) | -member(f12(C,B),C). [back_unit_del(69),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. given #46 (I,wt=9): 226 member(A,B) | -member(A,C) | B != C. [back_unit_del(64),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. given #47 (I,wt=16): 227 member(A,B) | -member(A,C) | -member(f9(B,C),C) | member(f10(B,C),C). [back_unit_del(63),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. given #48 (I,wt=16): 228 member(A,B) | -member(A,C) | -member(f9(B,C),C) | -member(f10(B,C),B). [back_unit_del(62),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. given #49 (I,wt=16): 229 member(A,B) | -member(A,C) | member(f9(B,C),B) | member(f10(B,C),C). [back_unit_del(60),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. given #50 (I,wt=16): 230 member(A,B) | -member(A,C) | member(f9(B,C),B) | -member(f10(B,C),B). [back_unit_del(59),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. given #51 (I,wt=9): 231 member(A,B) | -member(A,C) | C != B. [back_unit_del(54),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. given #52 (I,wt=13): 232 A = B | -member(f7(B,A),A) | member(f8(B,A),A). [back_unit_del(53),unit_del(a,112),unit_del(b,112)]. given #53 (I,wt=13): 233 A = B | -member(f7(B,A),A) | -member(f8(B,A),B). [back_unit_del(52),unit_del(a,112),unit_del(b,112)]. given #54 (I,wt=13): 234 A = B | member(f7(B,A),B) | member(f8(B,A),A). [back_unit_del(50),unit_del(a,112),unit_del(b,112)]. given #55 (I,wt=13): 235 A = B | member(f7(B,A),B) | -member(f8(B,A),B). [back_unit_del(49),unit_del(a,112),unit_del(b,112)]. given #56 (I,wt=5): 236 ilf_type(f6(A),subset_type(A)). [back_unit_del(44),unit_del(a,112)]. given #57 (I,wt=9): 237 ilf_type(A,member_type(power_set(B))) | -ilf_type(A,subset_type(B)). [back_unit_del(43),unit_del(a,112),unit_del(b,112)]. given #58 (I,wt=9): 238 ilf_type(A,subset_type(B)) | -ilf_type(A,member_type(power_set(B))). [back_unit_del(42),unit_del(a,112),unit_del(b,112)]. given #59 (I,wt=7): 239 unordered_pair(A,B) = unordered_pair(B,A). [back_unit_del(40),unit_del(a,112),unit_del(b,112)]. given #60 (I,wt=6): 240 subset(A,B) | A != B. [back_unit_del(35),unit_del(a,112),unit_del(b,112)]. given #61 (I,wt=6): 241 subset(A,B) | B != A. [back_unit_del(34),unit_del(a,112),unit_del(b,112)]. given #62 (I,wt=9): 242 A = B | -subset(B,A) | -subset(A,B). [back_unit_del(33),unit_del(a,112),unit_del(b,112)]. given #63 (I,wt=7): 243 ilf_type(f5(A,B),relation_type(B,A)). [back_unit_del(32),unit_del(a,112),unit_del(b,112)]. given #64 (I,wt=11): 244 -ilf_type(A,relation_type(B,C)) | ilf_type(A,subset_type(cross_product(B,C))). [back_unit_del(31),unit_del(a,112),unit_del(b,112)]. given #65 (I,wt=11): 245 -ilf_type(A,subset_type(cross_product(B,C))) | ilf_type(A,relation_type(B,C)). [back_unit_del(30),unit_del(a,112),unit_del(b,112)]. given #66 (I,wt=13): 246 unordered_pair(unordered_pair(A,B),singleton(A)) = C | ordered_pair(A,B) != C. [back_unit_del(28),unit_del(a,112),unit_del(b,112),unit_del(c,112)]. given #67 (I,wt=13): 248 -member(f3(A,B),B) | member(f4(A,B),B) | B = A. [back_unit_del(26),unit_del(a,112),unit_del(b,112)]. given #68 (I,wt=13): 249 -member(f3(A,B),B) | -member(f4(A,B),A) | B = A. [back_unit_del(25),unit_del(a,112),unit_del(b,112)]. given #69 (I,wt=13): 250 member(f3(A,B),A) | member(f4(A,B),B) | B = A. [back_unit_del(23),unit_del(a,112),unit_del(b,112)]. given #70 (I,wt=13): 251 member(f3(A,B),A) | -member(f4(A,B),A) | B = A. [back_unit_del(22),unit_del(a,112),unit_del(b,112)]. given #71 (I,wt=12): 252 -ilf_type(A,binary_relation_type) | -member(ordered_pair(B,C),A) | member(B,domain_of(A)). [back_unit_del(17),unit_del(a,112),unit_del(b,112)]. given #72 (I,wt=15): 253 -ilf_type(A,binary_relation_type) | member(ordered_pair(f2(A,B),B),A) | -member(ordered_pair(C,B),A). [back_unit_del(15),unit_del(b,112),unit_del(d,112)]. given #73 (I,wt=14): 254 -ilf_type(A,binary_relation_type) | member(ordered_pair(f1(A,B),B),A) | -member(B,range_of(A)). [back_unit_del(13),unit_del(b,112)]. given #74 (I,wt=12): 255 -ilf_type(A,binary_relation_type) | member(B,range_of(A)) | -member(ordered_pair(C,B),A). [back_unit_del(11),unit_del(b,112),unit_del(d,112)]. given #75 (A,wt=12): 256 ordered_pair(f18(c3,c5),f19(c3,c5)) = c5 | -ilf_type(c3,binary_relation_type). [resolve(123,a,114,a)]. given #76 (F,wt=2): 267 -empty(c3). [resolve(206,a,114,a)]. given #77 (T,wt=4): 260 ilf_type(c3,subset_type(c3)). [resolve(201,a,113,a),rewrite([117(4)])]. given #78 (T,wt=4): 261 range_of(c4) = c3. [resolve(202,a,113,a),rewrite([117(4)]),flip(a)]. given #79 (T,wt=4): 266 member(f24(c3),c3). [resolve(205,a,114,a)]. given #80 (T,wt=4): 282 ilf_type(c5,member_type(c3)). [resolve(212,c,114,a),unit_del(a,267)]. given #81 (A,wt=13): 257 ordered_pair(f18(c3,c5),f19(c3,c5)) = c5 | member(f17(c3),c3). [resolve(125,a,114,a)]. given #82 (T,wt=4): 288 member(A,power_set(A)). [resolve(216,b,215,b),merge(b)]. given #83 (T,wt=5): 264 ilf_type(domain_of(c4),subset_type(c2)). [back_rewrite(262),rewrite([263(4)])]. given #84 (T,wt=5): 430 ilf_type(f24(c3),member_type(c3)). [resolve(266,a,212,c),unit_del(a,267)]. given #85 (T,wt=5): 467 ilf_type(A,member_type(power_set(A))). [resolve(288,a,212,c),unit_del(a,213)]. given #86 (A,wt=15): 258 ordered_pair(f18(c3,c5),f19(c3,c5)) = c5 | f17(c3) != ordered_pair(A,B). [resolve(127,a,114,a)]. given #87 (T,wt=4): 476 ilf_type(A,subset_type(A)). [resolve(467,a,238,b)]. given #88 (T,wt=5): 478 ilf_type(cross_product(A,B),binary_relation_type). [resolve(476,a,129,a)]. given #89 (T,wt=6): 268 empty(A) | member(f24(A),A). [resolve(207,b,205,a)]. given #90 (T,wt=6): 279 empty(A) | member(f16(A),A). [resolve(211,c,210,b),merge(c)]. given #91 (A,wt=15): 259 -ilf_type(c3,subset_type(cross_product(A,B))) | ordered_pair(f18(c3,c5),f19(c3,c5)) = c5. [resolve(131,b,114,a)]. given #92 (T,wt=6): 294 member(A,power_set(B)) | -empty(A). [resolve(216,b,206,a)]. given #93 (T,wt=6): 329 member(c5,A) | c3 != A. [resolve(226,b,114,a),flip(b)]. given #94 (T,wt=6): 373 ilf_type(f6(cross_product(A,B)),binary_relation_type). [resolve(236,a,129,a)]. given #95 (T,wt=6): 374 ilf_type(f6(A),member_type(power_set(A))). [resolve(237,b,236,a)]. given #96 (A,wt=7): 263 domain(c2,c3,c4) = domain_of(c4). [resolve(204,a,113,a)]. given #97 (T,wt=5): 522 member(f6(A),power_set(A)). [resolve(374,a,211,c),unit_del(a,213)]. given #98 (T,wt=6): 375 ilf_type(f16(power_set(A)),subset_type(A)). [resolve(238,b,210,b),unit_del(b,213)]. given #99 (T,wt=6): 384 ilf_type(c4,subset_type(cross_product(c2,c3))). [resolve(244,a,113,a)]. given #100 (T,wt=3): 546 ilf_type(c4,binary_relation_type). [resolve(384,a,129,a)]. given #101 (A,wt=7): 265 member(f24(A),A) | ilf_type(A,binary_relation_type). [resolve(205,a,119,a)]. given #102 (T,wt=6): 470 member(f24(power_set(A)),power_set(A)). [resolve(288,a,205,a)]. given #103 (T,wt=6): 475 ilf_type(domain_of(c4),member_type(power_set(c2))). [resolve(264,a,237,b)]. given #104 (T,wt=5): 583 member(domain_of(c4),power_set(c2)). [resolve(475,a,211,c),unit_del(a,213)]. given #105 (T,wt=7): 280 empty(A) | ilf_type(f23(A),member_type(A)). [resolve(212,c,207,b),merge(c)]. given #106 (A,wt=20): 269 empty(A) | -ilf_type(A,subset_type(cross_product(B,C))) | ordered_pair(f18(A,f23(A)),f19(A,f23(A))) = f23(A). [resolve(207,b,131,b)]. given #107 (T,wt=6): 603 ilf_type(f23(power_set(A)),subset_type(A)). [resolve(280,b,238,b),unit_del(a,213)]. given #108 (T,wt=7): 285 member(c5,A) | -member(c3,power_set(A)). [resolve(214,a,114,a)]. given #109 (T,wt=7): 376 subset(unordered_pair(A,B),unordered_pair(B,A)). [resolve(240,b,239,a)]. given #110 (T,wt=7): 380 ilf_type(domain_of(f5(A,B)),subset_type(B)). [resolve(243,a,203,a),rewrite([379(2)])]. given #111 (A,wt=20): 270 empty(A) | ordered_pair(f18(A,f23(A)),f19(A,f23(A))) = f23(A) | f17(A) != ordered_pair(B,C). [resolve(207,b,127,a)]. given #112 (T,wt=7): 382 ilf_type(range_of(f5(A,B)),subset_type(A)). [resolve(243,a,201,a),rewrite([381(2)])]. given #113 (T,wt=7): 418 member(f24(c3),A) | c3 != A. [resolve(266,a,231,b)]. given #114 (T,wt=7): 455 member(A,B) | power_set(A) != B. [resolve(288,a,231,b)]. given #115 (T,wt=7): 477 ilf_type(cross_product(A,B),relation_type(A,B)). [resolve(476,a,245,a)]. given #116 (A,wt=18): 271 empty(A) | ordered_pair(f18(A,f23(A)),f19(A,f23(A))) = f23(A) | member(f17(A),A). [resolve(207,b,125,a)]. given #117 (T,wt=7): 494 empty(A) | ilf_type(f24(A),member_type(A)). [resolve(268,b,212,c),merge(b)]. given #118 (T,wt=6): 643 ilf_type(f24(power_set(A)),subset_type(A)). [resolve(494,b,238,b),unit_del(a,213)]. given #119 (T,wt=7): 534 -member(A,f6(B)) | member(A,B). [resolve(522,a,214,c)]. given #120 (T,wt=7): 543 ilf_type(f16(power_set(A)),member_type(power_set(A))). [resolve(375,a,237,b)]. given #121 (A,wt=17): 272 empty(A) | ordered_pair(f18(A,f23(A)),f19(A,f23(A))) = f23(A) | -ilf_type(A,binary_relation_type). [resolve(207,b,123,a)]. given #122 (T,wt=6): 656 member(f16(power_set(A)),power_set(A)). [resolve(543,a,211,c),unit_del(a,213)]. given #123 (T,wt=7): 544 ilf_type(f16(power_set(cross_product(A,B))),binary_relation_type). [resolve(375,a,129,a)]. given #124 (T,wt=7): 545 ilf_type(c4,member_type(power_set(cross_product(c2,c3)))). [resolve(384,a,237,b)]. given #125 (T,wt=6): 676 member(c4,power_set(cross_product(c2,c3))). [resolve(545,a,211,c),unit_del(a,213)]. given #126 (A,wt=20): 273 ordered_pair(f20(A,f23(A)),f21(A,f23(A))) = f23(A) | f22(A) != ordered_pair(B,C) | empty(A). [resolve(208,a,207,b)]. given #127 (T,wt=7): 576 ilf_type(f24(power_set(A)),member_type(power_set(A))). [resolve(470,a,212,c),unit_del(a,213)]. given #128 (T,wt=7): 595 -member(A,domain_of(c4)) | member(A,c2). [resolve(583,a,214,c)]. given #129 (T,wt=7): 610 ilf_type(f23(power_set(A)),member_type(power_set(A))). [resolve(603,a,237,b)]. given #130 (T,wt=6): 705 member(f23(power_set(A)),power_set(A)). [resolve(610,a,211,c),unit_del(a,213)]. given #131 (A,wt=21): 274 ordered_pair(f20(A,f17(A)),f21(A,f17(A))) = f17(A) | f22(A) != ordered_pair(B,C) | ilf_type(A,binary_relation_type). [resolve(208,a,119,a)]. given #132 (T,wt=7): 611 ilf_type(f23(power_set(cross_product(A,B))),binary_relation_type). [resolve(603,a,129,a)]. given #133 (T,wt=7): 622 ilf_type(domain_of(cross_product(A,B)),subset_type(A)). [resolve(477,a,203,a),rewrite([621(2)])]. given #134 (T,wt=7): 624 ilf_type(range_of(cross_product(A,B)),subset_type(B)). [resolve(477,a,201,a),rewrite([623(2)])]. given #135 (T,wt=7): 646 ilf_type(f24(power_set(cross_product(A,B))),binary_relation_type). [resolve(643,a,129,a)]. given #136 (A,wt=15): 275 ordered_pair(f20(c3,c5),f21(c3,c5)) = c5 | f22(c3) != ordered_pair(A,B). [resolve(208,a,114,a)]. given #137 (T,wt=8): 286 -member(A,f23(power_set(B))) | member(A,B). [resolve(214,c,207,b),unit_del(c,213)]. given #138 (T,wt=8): 295 member(A,power_set(B)) | member(f24(A),A). [resolve(216,b,205,a)]. given #139 (T,wt=8): 304 member(c5,A) | -member(f14(c3,A),A). [resolve(217,a,114,a)]. given #140 (T,wt=8): 308 member(c5,A) | member(f14(c3,A),c3). [resolve(218,a,114,a)]. given #141 (A,wt=18): 276 ordered_pair(f20(A,f23(A)),f21(A,f23(A))) = f23(A) | member(f22(A),A) | empty(A). [resolve(209,a,207,b)]. given #142 (T,wt=8): 383 ilf_type(f5(A,B),subset_type(cross_product(B,A))). [resolve(244,a,243,a)]. given #143 (T,wt=5): 852 ilf_type(f5(A,B),binary_relation_type). [resolve(383,a,129,a)]. given #144 (T,wt=8): 385 ilf_type(f6(cross_product(A,B)),relation_type(A,B)). [resolve(245,a,236,a)]. given #145 (T,wt=8): 429 member(f24(c3),A) | -member(c3,power_set(A)). [resolve(266,a,214,a)]. given #146 (A,wt=19): 277 ordered_pair(f20(A,f17(A)),f21(A,f17(A))) = f17(A) | member(f22(A),A) | ilf_type(A,binary_relation_type). [resolve(209,a,119,a)]. given #147 (T,wt=8): 466 member(A,B) | -member(power_set(A),power_set(B)). [resolve(288,a,214,a)]. given #148 (T,wt=8): 492 -member(A,f24(power_set(B))) | member(A,B). [resolve(268,b,214,c),unit_del(a,213)]. given #149 (T,wt=8): 514 -member(A,f16(power_set(B))) | member(A,B). [resolve(279,b,214,c),unit_del(a,213)]. given #150 (T,wt=8): 523 member(f6(A),B) | power_set(A) != B. [resolve(522,a,231,b)]. given #151 (A,wt=13): 278 ordered_pair(f20(c3,c5),f21(c3,c5)) = c5 | member(f22(c3),c3). [resolve(209,a,114,a)]. given #152 (T,wt=8): 584 member(domain_of(c4),A) | power_set(c2) != A. [resolve(583,a,231,b)]. given #153 (T,wt=8): 615 ilf_type(domain_of(f5(A,B)),member_type(power_set(B))). [resolve(380,a,237,b)]. given #154 (T,wt=7): 917 member(domain_of(f5(A,B)),power_set(B)). [resolve(615,a,211,c),unit_del(a,213)]. given #155 (T,wt=8): 616 ilf_type(domain_of(f5(A,cross_product(B,C))),binary_relation_type). [resolve(380,a,129,a)]. given #156 (A,wt=10): 281 empty(A) | ilf_type(f17(A),member_type(A)) | ilf_type(A,binary_relation_type). [resolve(212,c,119,a)]. given #157 (T,wt=8): 619 ilf_type(range_of(f5(A,B)),member_type(power_set(A))). [resolve(382,a,237,b)]. given #158 (T,wt=7): 938 member(range_of(f5(A,B)),power_set(A)). [resolve(619,a,211,c),unit_del(a,213)]. given #159 (T,wt=8): 620 ilf_type(range_of(f5(cross_product(A,B),C)),binary_relation_type). [resolve(382,a,129,a)]. given #160 (T,wt=8): 647 member(f16(f6(A)),A) | empty(f6(A)). [resolve(534,a,279,b)]. given #161 (A,wt=10): 283 member(f23(A),B) | -member(A,power_set(B)) | empty(A). [resolve(214,a,207,b)]. given #162 (T,wt=5): 981 empty(f6(A)) | -empty(A). [resolve(647,a,206,a)]. given #163 (T,wt=7): 982 empty(f6(A)) | member(f24(A),A). [resolve(647,a,205,a)]. given #164 (T,wt=8): 649 member(f24(f6(A)),A) | empty(f6(A)). [resolve(534,a,268,b)]. given #165 (T,wt=8): 654 member(f23(f6(A)),A) | empty(f6(A)). [resolve(534,a,207,b)]. given #166 (A,wt=11): 284 member(f17(A),B) | -member(A,power_set(B)) | ilf_type(A,binary_relation_type). [resolve(214,a,119,a)]. given #167 (T,wt=8): 688 -member(A,c4) | member(A,cross_product(c2,c3)). [resolve(676,a,214,c)]. given #168 (T,wt=8): 696 member(f16(domain_of(c4)),c2) | empty(domain_of(c4)). [resolve(595,a,279,b)]. given #169 (T,wt=5): 1117 empty(domain_of(c4)) | -empty(c2). [resolve(696,a,206,a)]. given #170 (T,wt=7): 1118 empty(domain_of(c4)) | member(f24(c2),c2). [resolve(696,a,205,a)]. given #171 (A,wt=12): 287 -member(A,f17(power_set(B))) | member(A,B) | ilf_type(power_set(B),binary_relation_type). [resolve(214,c,119,a)]. given #172 (T,wt=8): 698 member(f24(domain_of(c4)),c2) | empty(domain_of(c4)). [resolve(595,a,268,b)]. given #173 (T,wt=8): 703 member(f23(domain_of(c4)),c2) | empty(domain_of(c4)). [resolve(595,a,207,b)]. given #174 (T,wt=8): 726 ilf_type(domain_of(cross_product(A,B)),member_type(power_set(A))). [resolve(622,a,237,b)]. given #175 (T,wt=7): 1193 member(domain_of(cross_product(A,B)),power_set(A)). [resolve(726,a,211,c),unit_del(a,213)]. given #176 (A,wt=14): 289 member(power_set(A),power_set(B)) | -member(C,f15(power_set(A),B)) | member(C,A). [resolve(216,b,214,c)]. given #177 (T,wt=8): 727 ilf_type(domain_of(cross_product(cross_product(A,B),C)),binary_relation_type). [resolve(622,a,129,a)]. given #178 (T,wt=8): 730 ilf_type(range_of(cross_product(A,B)),member_type(power_set(B))). [resolve(624,a,237,b)]. given #179 (T,wt=7): 1229 member(range_of(cross_product(A,B)),power_set(B)). [resolve(730,a,211,c),unit_del(a,213)]. given #180 (T,wt=8): 731 ilf_type(range_of(cross_product(A,cross_product(B,C))),binary_relation_type). [resolve(624,a,129,a)]. given #181 (A,wt=13): 290 member(A,power_set(B)) | member(f15(A,B),C) | -member(A,power_set(C)). [resolve(216,b,214,a)]. given #182 (T,wt=8): 854 ilf_type(domain_of(f6(cross_product(A,B))),subset_type(A)). [resolve(385,a,203,a),rewrite([853(3)])]. given #183 (T,wt=8): 856 ilf_type(range_of(f6(cross_product(A,B))),subset_type(B)). [resolve(385,a,201,a),rewrite([855(3)])]. given #184 (T,wt=8): 989 member(f23(c4),cross_product(c2,c3)) | empty(c4). [resolve(283,b,676,a)]. given #185 (T,wt=6): 1286 empty(c4) | -empty(cross_product(c2,c3)). [resolve(989,a,206,a)]. given #186 (A,wt=12): 291 member(A,power_set(B)) | empty(A) | ilf_type(f15(A,B),member_type(A)). [resolve(216,b,212,c)]. given #187 (T,wt=8): 1096 member(f16(c4),cross_product(c2,c3)) | empty(c4). [resolve(688,a,279,b)]. given #188 (T,wt=8): 1098 member(f24(c4),cross_product(c2,c3)) | empty(c4). [resolve(688,a,268,b)]. given #189 (T,wt=9): 327 member(f23(A),B) | B != A | empty(A). [resolve(226,b,207,b)]. given #190 (T,wt=4): 1382 member(f23(c3),c3). [resolve(327,b,261,a),rewrite([261(4)]),unit_del(b,267)]. given #191 (A,wt=23): 292 member(A,power_set(B)) | ordered_pair(f20(A,f15(A,B)),f21(A,f15(A,B))) = f15(A,B) | member(f22(A),A). [resolve(216,b,209,a)]. given #192 (T,wt=5): 1396 ilf_type(f23(c3),member_type(c3)). [resolve(1382,a,212,c),unit_del(a,267)]. given #193 (T,wt=7): 1384 member(f23(c3),A) | c3 != A. [resolve(1382,a,231,b)]. given #194 (T,wt=8): 1395 member(f23(c3),A) | -member(c3,power_set(A)). [resolve(1382,a,214,a)]. given #195 (T,wt=9): 347 member(f23(A),B) | A != B | empty(A). [resolve(231,b,207,b)]. given #196 (A,wt=25): 293 member(A,power_set(B)) | ordered_pair(f20(A,f15(A,B)),f21(A,f15(A,B))) = f15(A,B) | f22(A) != ordered_pair(C,D). [resolve(216,b,208,a)]. given #197 (T,wt=9): 427 member(f24(c3),A) | member(f14(c3,A),c3). [resolve(266,a,218,a)]. given #198 (T,wt=7): 1519 member(f14(c3,A),c3) | -empty(A). [resolve(427,a,206,a)]. given #199 (T,wt=9): 428 member(f24(c3),A) | -member(f14(c3,A),A). [resolve(266,a,217,a)]. given #200 (T,wt=9): 465 member(A,B) | -member(f14(power_set(A),B),B). [resolve(288,a,217,a)]. given #201 (A,wt=25): 296 member(A,power_set(B)) | -ilf_type(A,subset_type(cross_product(C,D))) | ordered_pair(f18(A,f15(A,B)),f19(A,f15(A,B))) = f15(A,B). [resolve(216,b,131,b)]. given #202 (T,wt=9): 480 empty(A) | member(f24(A),B) | A != B. [resolve(268,b,231,b)]. given #203 (T,wt=9): 485 empty(A) | member(f24(A),B) | B != A. [resolve(268,b,226,b)]. given #204 (T,wt=9): 502 empty(A) | member(f16(A),B) | A != B. [resolve(279,b,231,b)]. given #205 (T,wt=4): 1565 member(f16(c3),c3). [resolve(502,c,261,a),rewrite([261(2),261(4)]),unit_del(a,267)]. given #206 (A,wt=25): 297 member(A,power_set(B)) | ordered_pair(f18(A,f15(A,B)),f19(A,f15(A,B))) = f15(A,B) | f17(A) != ordered_pair(C,D). [resolve(216,b,127,a)]. given #207 (T,wt=5): 1579 ilf_type(f16(c3),member_type(c3)). [resolve(1565,a,212,c),unit_del(a,267)]. given #208 (T,wt=7): 1567 member(f16(c3),A) | c3 != A. [resolve(1565,a,231,b)]. given #209 (T,wt=8): 1578 member(f16(c3),A) | -member(c3,power_set(A)). [resolve(1565,a,214,a)]. given #210 (T,wt=9): 507 empty(A) | member(f16(A),B) | B != A. [resolve(279,b,226,b)]. given #211 (A,wt=23): 298 member(A,power_set(B)) | ordered_pair(f18(A,f15(A,B)),f19(A,f15(A,B))) = f15(A,B) | member(f17(A),A). [resolve(216,b,125,a)]. given #212 (T,wt=9): 535 member(f6(A),B) | -member(power_set(A),power_set(B)). [resolve(522,a,214,a)]. given #213 (T,wt=9): 542 ilf_type(f16(power_set(cross_product(A,B))),relation_type(A,B)). [resolve(375,a,245,a)]. given #214 (T,wt=9): 564 member(f24(power_set(A)),B) | power_set(A) != B. [resolve(470,a,231,b)]. given #215 (T,wt=9): 596 member(domain_of(c4),A) | -member(power_set(c2),power_set(A)). [resolve(583,a,214,a)]. given #216 (A,wt=22): 299 member(A,power_set(B)) | ordered_pair(f18(A,f15(A,B)),f19(A,f15(A,B))) = f15(A,B) | -ilf_type(A,binary_relation_type). [resolve(216,b,123,a)]. given #217 (T,wt=9): 609 ilf_type(f23(power_set(cross_product(A,B))),relation_type(A,B)). [resolve(603,a,245,a)]. given #218 (T,wt=9): 645 ilf_type(f24(power_set(cross_product(A,B))),relation_type(A,B)). [resolve(643,a,245,a)]. given #219 (T,wt=9): 650 member(f24(f6(A)),A) | ilf_type(f6(A),binary_relation_type). [resolve(534,a,265,a)]. given #220 (T,wt=6): 1721 ilf_type(f6(A),binary_relation_type) | -empty(A). [resolve(650,a,206,a)]. given #221 (A,wt=15): 300 member(power_set(power_set(A)),power_set(A)) | -member(power_set(power_set(A)),f15(power_set(power_set(A)),A)). [factor(289,a,c)]. given #222 (T,wt=8): 1722 ilf_type(f6(A),binary_relation_type) | member(f24(A),A). [resolve(650,a,205,a)]. given #223 (T,wt=9): 655 member(f17(f6(A)),A) | ilf_type(f6(A),binary_relation_type). [resolve(534,a,119,a)]. given #224 (T,wt=9): 658 member(f16(power_set(A)),B) | power_set(A) != B. [resolve(656,a,231,b)]. given #225 (T,wt=9): 677 member(c4,A) | power_set(cross_product(c2,c3)) != A. [resolve(676,a,231,b)]. given #226 (A,wt=14): 301 member(f15(A,B),C) | -member(f14(A,C),C) | member(A,power_set(B)). [resolve(217,a,216,b)]. given #227 (T,wt=9): 699 member(f24(domain_of(c4)),c2) | ilf_type(domain_of(c4),binary_relation_type). [resolve(595,a,265,a)]. given #228 (T,wt=6): 1807 ilf_type(domain_of(c4),binary_relation_type) | -empty(c2). [resolve(699,a,206,a)]. given #229 (T,wt=8): 1808 ilf_type(domain_of(c4),binary_relation_type) | member(f24(c2),c2). [resolve(699,a,205,a)]. given #230 (T,wt=9): 704 member(f17(domain_of(c4)),c2) | ilf_type(domain_of(c4),binary_relation_type). [resolve(595,a,119,a)]. given #231 (A,wt=11): 302 member(f23(A),B) | -member(f14(A,B),B) | empty(A). [resolve(217,a,207,b)]. given #232 (T,wt=9): 706 member(f23(power_set(A)),B) | power_set(A) != B. [resolve(705,a,231,b)]. given #233 (T,wt=9): 771 member(f24(A),A) | ilf_type(A,member_type(power_set(B))). [resolve(295,a,212,c),unit_del(b,213)]. given #234 (T,wt=7): 1878 ilf_type(A,member_type(power_set(B))) | -empty(A). [resolve(771,a,206,a)]. given #235 (T,wt=9): 820 member(c5,A) | ilf_type(f14(c3,A),member_type(c3)). [resolve(308,b,212,c),unit_del(b,267)]. given #236 (A,wt=12): 303 member(f17(A),B) | -member(f14(A,B),B) | ilf_type(A,binary_relation_type). [resolve(217,a,119,a)]. given #237 (T,wt=8): 1912 ilf_type(f14(c3,A),member_type(c3)) | -empty(A). [resolve(820,a,206,a)]. given #238 (T,wt=9): 851 ilf_type(f5(A,B),member_type(power_set(cross_product(B,A)))). [resolve(383,a,237,b)]. given #239 (T,wt=8): 1922 member(f5(A,B),power_set(cross_product(B,A))). [resolve(851,a,211,c),unit_del(a,213)]. given #240 (T,wt=9): 929 -member(A,domain_of(f5(B,C))) | member(A,C). [resolve(917,a,214,c)]. given #241 (A,wt=14): 305 member(f15(A,B),C) | member(f14(A,C),A) | member(A,power_set(B)). [resolve(218,a,216,b)]. given #242 (T,wt=9): 950 -member(A,range_of(f5(B,C))) | member(A,B). [resolve(938,a,214,c)]. given #243 (T,wt=9): 998 empty(f6(domain_of(c4))) | member(f24(domain_of(c4)),c2). [resolve(982,b,595,a)]. given #244 (T,wt=6): 2090 empty(f6(domain_of(c4))) | -empty(c2). [resolve(998,b,206,a)]. given #245 (T,wt=8): 2091 empty(f6(domain_of(c4))) | member(f24(c2),c2). [resolve(998,b,205,a)]. given #246 (A,wt=11): 306 member(f23(A),B) | member(f14(A,B),A) | empty(A). [resolve(218,a,207,b)]. given #247 (T,wt=9): 999 empty(f6(f6(A))) | member(f24(f6(A)),A). [resolve(982,b,534,a)]. given #248 (T,wt=6): 2219 empty(f6(f6(A))) | -empty(A). [resolve(999,b,206,a)]. given #249 (T,wt=8): 2220 empty(f6(f6(A))) | member(f24(A),A). [resolve(999,b,205,a)]. given #250 (T,wt=9): 1091 member(f24(c4),cross_product(c2,c3)) | empty(f6(c4)). [resolve(688,a,982,b)]. given #251 (A,wt=12): 307 member(f17(A),B) | member(f14(A,B),A) | ilf_type(A,binary_relation_type). [resolve(218,a,119,a)]. given #252 (T,wt=7): 2270 empty(f6(c4)) | -empty(cross_product(c2,c3)). [resolve(1091,a,206,a)]. given #253 (T,wt=9): 1207 -member(A,domain_of(cross_product(B,C))) | member(A,B). [resolve(1193,a,214,c)]. given #254 (T,wt=9): 1243 -member(A,range_of(cross_product(B,C))) | member(A,C). [resolve(1229,a,214,c)]. given #255 (T,wt=9): 1265 ilf_type(domain_of(f6(cross_product(A,B))),member_type(power_set(A))). [resolve(854,a,237,b)]. given #256 (A,wt=11): 309 member(f13(A,B),A) | -member(C,A) | member(C,B). [resolve(221,a,219,c)]. given #257 (T,wt=8): 2404 member(domain_of(f6(cross_product(A,B))),power_set(A)). [resolve(1265,a,211,c),unit_del(a,213)]. given #258 (T,wt=8): 2473 member(f13(c3,A),c3) | member(c5,A). [resolve(309,b,114,a)]. given #259 (T,wt=9): 1266 ilf_type(domain_of(f6(cross_product(cross_product(A,B),C))),binary_relation_type). [resolve(854,a,129,a)]. given #260 (T,wt=9): 1269 ilf_type(range_of(f6(cross_product(A,B))),member_type(power_set(B))). [resolve(856,a,237,b)]. given #261 (A,wt=19): 310 member(f15(A,B),C) | -member(f11(A,C),C) | member(f12(A,C),C) | member(A,power_set(B)). [resolve(222,b,216,b)]. given #262 (T,wt=8): 2518 member(range_of(f6(cross_product(A,B))),power_set(B)). [resolve(1269,a,211,c),unit_del(a,213)]. given #263 (T,wt=9): 1270 ilf_type(range_of(f6(cross_product(A,cross_product(B,C)))),binary_relation_type). [resolve(856,a,129,a)]. given #264 (T,wt=9): 1296 ilf_type(f15(c3,A),member_type(c3)) | member(c5,A). [resolve(291,a,285,b),unit_del(a,267)]. given #265 (T,wt=8): 2580 ilf_type(f15(c3,A),member_type(c3)) | -empty(A). [resolve(1296,b,206,a)]. given #266 (A,wt=16): 311 member(f23(A),B) | -member(f11(A,B),B) | member(f12(A,B),B) | empty(A). [resolve(222,b,207,b)]. given #267 (T,wt=9): 1393 member(f23(c3),A) | member(f14(c3,A),c3). [resolve(1382,a,218,a)]. given #268 (T,wt=9): 1394 member(f23(c3),A) | -member(f14(c3,A),A). [resolve(1382,a,217,a)]. given #269 (T,wt=9): 1520 member(f14(c3,A),c3) | member(f24(A),A). [resolve(427,a,205,a)]. given #270 (T,wt=9): 1576 member(f16(c3),A) | member(f14(c3,A),c3). [resolve(1565,a,218,a)]. given #271 (A,wt=17): 312 member(f17(A),B) | -member(f11(A,B),B) | member(f12(A,B),B) | ilf_type(A,binary_relation_type). [resolve(222,b,119,a)]. given #272 (T,wt=9): 1577 member(f16(c3),A) | -member(f14(c3,A),A). [resolve(1565,a,217,a)]. given #273 (T,wt=9): 1677 ilf_type(domain_of(f16(power_set(cross_product(A,B)))),subset_type(A)). [resolve(542,a,203,a),rewrite([1676(4)])]. given #274 (T,wt=9): 1679 ilf_type(range_of(f16(power_set(cross_product(A,B)))),subset_type(B)). [resolve(542,a,201,a),rewrite([1678(4)])]. given #275 (T,wt=9): 1685 ilf_type(domain_of(f23(power_set(cross_product(A,B)))),subset_type(A)). [resolve(609,a,203,a),rewrite([1684(4)])]. given #276 (A,wt=13): 313 member(c5,A) | -member(f11(c3,A),A) | member(f12(c3,A),A). [resolve(222,b,114,a)]. given #277 (T,wt=9): 1687 ilf_type(range_of(f23(power_set(cross_product(A,B)))),subset_type(B)). [resolve(609,a,201,a),rewrite([1686(4)])]. given #278 (T,wt=9): 1689 ilf_type(domain_of(f24(power_set(cross_product(A,B)))),subset_type(A)). [resolve(645,a,203,a),rewrite([1688(4)])]. given #279 (T,wt=9): 1691 ilf_type(range_of(f24(power_set(cross_product(A,B)))),subset_type(B)). [resolve(645,a,201,a),rewrite([1690(4)])]. given #280 (T,wt=9): 1990 member(f14(A,B),A) | member(A,power_set(B)). [resolve(305,a,215,b),merge(c)]. given #281 (A,wt=19): 314 member(f15(A,B),C) | -member(f11(A,C),C) | -member(f12(A,C),A) | member(A,power_set(B)). [resolve(223,b,216,b)]. given #282 (T,wt=9): 2145 member(f14(A,B),A) | empty(A) | -empty(B). [resolve(306,a,206,a)]. given #283 (T,wt=9): 2410 member(f13(c3,A),c3) | member(f16(c3),A). [resolve(309,b,1565,a)]. given #284 (T,wt=7): 2884 member(f13(c3,A),c3) | -empty(A). [resolve(2410,b,206,a)]. given #285 (T,wt=9): 2411 member(f13(c3,A),c3) | member(f23(c3),A). [resolve(309,b,1382,a)]. given #286 (A,wt=16): 315 member(f23(A),B) | -member(f11(A,B),B) | -member(f12(A,B),A) | empty(A). [resolve(223,b,207,b)]. given #287 (T,wt=9): 2465 member(f13(c3,A),c3) | member(f24(c3),A). [resolve(309,b,266,a)]. given #288 (T,wt=9): 2511 member(c5,A) | ilf_type(f13(c3,A),member_type(c3)). [resolve(2473,a,212,c),unit_del(b,267)]. given #289 (T,wt=8): 3047 ilf_type(f13(c3,A),member_type(c3)) | -empty(A). [resolve(2511,a,206,a)]. given #290 (T,wt=9): 2885 member(f13(c3,A),c3) | member(f24(A),A). [resolve(2410,b,205,a)]. given #291 (A,wt=17): 316 member(f17(A),B) | -member(f11(A,B),B) | -member(f12(A,B),A) | ilf_type(A,binary_relation_type). [resolve(223,b,119,a)]. given #292 (T,wt=10): 328 member(f17(A),B) | B != A | ilf_type(A,binary_relation_type). [resolve(226,b,119,a)]. given #293 (T,wt=10): 348 member(f17(A),B) | A != B | ilf_type(A,binary_relation_type). [resolve(231,b,119,a)]. given #294 (T,wt=10): 366 A = B | member(f7(B,A),B) | -empty(A). [resolve(234,c,206,a)]. given #295 (T,wt=10): 386 unordered_pair(unordered_pair(A,B),singleton(A)) = ordered_pair(A,B). [xx_res(246,b)]. given #296 (A,wt=13): 317 member(c5,A) | -member(f11(c3,A),A) | -member(f12(c3,A),c3). [resolve(223,b,114,a)]. given #297 (T,wt=10): 404 member(f3(A,B),A) | B = A | -empty(B). [resolve(250,b,206,a)]. given #298 (T,wt=10): 464 member(A,B) | member(f14(power_set(A),B),power_set(A)). [resolve(288,a,218,a)]. given #299 (T,wt=9): 3118 member(A,A) | -member(A,f14(power_set(A),A)). [factor(3109,a,c)]. given #300 (T,wt=10): 493 empty(A) | member(f24(A),B) | -member(A,power_set(B)). [resolve(268,b,214,a)]. given #301 (A,wt=19): 318 member(f15(A,B),C) | member(f11(A,C),A) | member(f12(A,C),C) | member(A,power_set(B)). [resolve(224,b,216,b)]. given #302 (T,wt=10): 515 empty(A) | member(f16(A),B) | -member(A,power_set(B)). [resolve(279,b,214,a)]. given #303 (T,wt=10): 533 member(f6(A),B) | -member(f14(power_set(A),B),B). [resolve(522,a,217,a)]. given #304 (T,wt=10): 547 member(ordered_pair(f1(c4,A),A),c4) | -member(A,c3). [back_unit_del(417),unit_del(a,546)]. ============================== PROOF ================================= % Proof 1 at 0.29 (+ 0.11) seconds. % Length of proof is 22. % Level of proof is 5. % Maximum clause weight is 18.000. % Given clauses 304. 2 -ilf_type(A,set_type) | ilf_type(A,binary_relation_type) | -relation_like(A). [assumption]. 9 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,subset_type(cross_product(A,B))) | relation_like(C). [assumption]. 13 -ilf_type(A,binary_relation_type) | -ilf_type(B,set_type) | member(ordered_pair(f1(A,B),B),A) | -member(B,range_of(A)). [assumption]. 31 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,relation_type(A,B)) | ilf_type(C,subset_type(cross_product(A,B))). [assumption]. 110 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,relation_type(A,B)) | range(A,B,C) = range_of(C). [assumption]. 112 ilf_type(A,set_type). [assumption]. 113 ilf_type(c4,relation_type(c2,c3)). [assumption]. 114 member(c5,c3). [assumption]. 115 -ilf_type(A,set_type) | -member(ordered_pair(A,c5),c4). [assumption]. 116 -member(ordered_pair(A,c5),c4). [copy(115),unit_del(a,112)]. 117 range(c2,c3,c4) = c3. [assumption]. 128 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,subset_type(cross_product(A,B))) | -ilf_type(C,set_type) | ilf_type(C,binary_relation_type). [resolve(9,d,2,c)]. 129 -ilf_type(A,subset_type(cross_product(B,C))) | ilf_type(A,binary_relation_type). [copy(128),unit_del(a,112),unit_del(b,112),unit_del(d,112)]. 202 -ilf_type(A,relation_type(B,C)) | range(B,C,A) = range_of(A). [back_unit_del(110),unit_del(a,112),unit_del(b,112)]. 244 -ilf_type(A,relation_type(B,C)) | ilf_type(A,subset_type(cross_product(B,C))). [back_unit_del(31),unit_del(a,112),unit_del(b,112)]. 254 -ilf_type(A,binary_relation_type) | member(ordered_pair(f1(A,B),B),A) | -member(B,range_of(A)). [back_unit_del(13),unit_del(b,112)]. 261 range_of(c4) = c3. [resolve(202,a,113,a),rewrite([117(4)]),flip(a)]. 384 ilf_type(c4,subset_type(cross_product(c2,c3))). [resolve(244,a,113,a)]. 417 -ilf_type(c4,binary_relation_type) | member(ordered_pair(f1(c4,A),A),c4) | -member(A,c3). [para(261(a,1),254(c,2))]. 546 ilf_type(c4,binary_relation_type). [resolve(384,a,129,a)]. 547 member(ordered_pair(f1(c4,A),A),c4) | -member(A,c3). [back_unit_del(417),unit_del(a,546)]. 3373 $F. [resolve(547,b,114,a),unit_del(a,116)]. ============================== end of proof ========================== ============================== STATISTICS ============================ Given=304. Generated=4287. Kept=3349. proofs=1. Usable=302. Sos=2822. Demods=20. Limbo=50, Disabled=301. Hints=0. Kept_by_rule=0, Deleted_by_rule=0. Forward_subsumed=937. Back_subsumed=115. Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. New_demodulators=20 (1 lex), Back_demodulated=3. Back_unit_deleted=57. Demod_attempts=49490. Demod_rewrites=141. Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. Nonunit_fsub_feature_tests=10305. Nonunit_bsub_feature_tests=5535. Megabytes=6.15. User_CPU=0.29, System_CPU=0.11, Wall_clock=4. ============================== end of statistics ===================== ============================== end of search ========================= Exiting with 1 proof. Process 23976 exit (max_proofs) Tue Nov 3 16:59:21 2009 ============================== continuing FOF reduction multisearch == Subproblem 3 of 6 (negated): ((all B (- ilf_type(B,binary_relation_type) | (all C (- ilf_type(C,set_type) | member(C,range_of(B)) | (all D (- ilf_type(D,set_type) | - member(ordered_pair(D,C),B))))))) & (all B (- ilf_type(B,binary_relation_type) | (all C (- ilf_type(C,set_type) | (exists D (ilf_type(D,set_type) & member(ordered_pair(D,C),B))) | - member(C,range_of(B)))))) & (all B (- ilf_type(B,binary_relation_type) | (all C (- ilf_type(C,set_type) | (exists D (ilf_type(D,set_type) & member(ordered_pair(D,C),B))) | (all D (- ilf_type(D,set_type) | - member(ordered_pair(D,C),B))))))) & (all B (- ilf_type(B,binary_relation_type) | ilf_type(range_of(B),set_type))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,binary_relation_type) | - member(ordered_pair(B,C),D) | member(B,domain_of(D)))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,binary_relation_type) | - member(ordered_pair(B,C),D) | member(C,range_of(D)))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (exists D (ilf_type(D,set_type) & member(D,B) & - member(D,C))) | (exists D (ilf_type(D,set_type) & - member(D,B) & member(D,C))) | =(C,B))))) & (all C (- ilf_type(C,set_type))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | ilf_type(ordered_pair(B,C),set_type))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,subset_type(cross_product(B,C))) | ilf_type(D,relation_type(B,C)))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all E (- ilf_type(E,relation_type(B,C)) | ilf_type(E,subset_type(cross_product(B,C))))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (exists D ilf_type(D,relation_type(C,B))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | =(C,B) | - subset(B,C) | - subset(C,B))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | subset(B,C) | - =(C,B))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | subset(C,B) | - =(C,B))))) & (all B (- ilf_type(B,binary_relation_type) | ilf_type(domain_of(B),set_type))) & (all B (- ilf_type(B,set_type) | ilf_type(singleton(B),set_type))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | ilf_type(cross_product(B,C),set_type))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | ilf_type(unordered_pair(B,C),set_type))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | =(unordered_pair(C,B),unordered_pair(B,C)))))) & (all B (- ilf_type(B,set_type) | ilf_type(B,binary_relation_type) | - relation_like(B))) & (all B (- ilf_type(B,set_type) | relation_like(B) | - ilf_type(B,binary_relation_type))) & (exists B ilf_type(B,binary_relation_type)) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | ilf_type(C,subset_type(B)) | - ilf_type(C,member_type(power_set(B))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | ilf_type(C,member_type(power_set(B))) | - ilf_type(C,subset_type(B)))))) & (all B (- ilf_type(B,set_type) | (exists C ilf_type(C,subset_type(B))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | =(C,B) | (exists D (ilf_type(D,set_type) & member(D,B) & - member(D,C))) | (exists D (ilf_type(D,set_type) & - member(D,B) & member(D,C))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,set_type) | member(D,B) | - member(D,C))) | - =(C,B))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,set_type) | member(D,B) | - member(D,C))) | (exists D (ilf_type(D,set_type) & member(D,B) & - member(D,C))) | (exists D (ilf_type(D,set_type) & - member(D,B) & member(D,C))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,set_type) | member(D,C) | - member(D,B))) | - =(C,B))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,set_type) | member(D,C) | - member(D,B))) | (exists D (ilf_type(D,set_type) & member(D,B) & - member(D,C))) | (exists D (ilf_type(D,set_type) & - member(D,B) & member(D,C))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | subset(B,C) | (exists D (ilf_type(D,set_type) & member(D,B) & - member(D,C))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,set_type) | - member(D,B) | member(D,C))) | - subset(B,C))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,set_type) | - member(D,B) | member(D,C))) | (exists D (ilf_type(D,set_type) & member(D,B) & - member(D,C))))))) & (all B (- ilf_type(B,set_type) | subset(B,B))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | member(B,power_set(C)) | (exists D (ilf_type(D,set_type) & member(D,B) & - member(D,C))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,set_type) | - member(D,B) | member(D,C))) | - member(B,power_set(C)))))) & (all B (- ilf_type(B,set_type) | - empty(power_set(B)))) & (all B (- ilf_type(B,set_type) | ilf_type(power_set(B),set_type))) & (all B (- ilf_type(B,set_type) | (all C (empty(C) | - ilf_type(C,set_type) | ilf_type(B,member_type(C)) | - member(B,C))))) & (all B (- ilf_type(B,set_type) | (all C (empty(C) | - ilf_type(C,set_type) | member(B,C) | - ilf_type(B,member_type(C)))))) & (all B (empty(B) | - ilf_type(B,set_type) | (exists C ilf_type(C,member_type(B))))) & (all B (- ilf_type(B,set_type) | relation_like(B) | (exists C (ilf_type(C,set_type) & member(C,B) & (all D (- ilf_type(D,set_type) | (all E (- ilf_type(E,set_type) | - =(ordered_pair(D,E),C))))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | - member(C,B) | (exists D (ilf_type(D,set_type) & (exists E (ilf_type(E,set_type) & =(ordered_pair(D,E),C))))))) | - relation_like(B))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | - member(C,B) | (exists D (ilf_type(D,set_type) & (exists E (ilf_type(E,set_type) & =(ordered_pair(D,E),C))))))) | (exists C (ilf_type(C,set_type) & member(C,B) & (all D (- ilf_type(D,set_type) | (all E (- ilf_type(E,set_type) | - =(ordered_pair(D,E),C))))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,subset_type(cross_product(B,C))) | relation_like(D))))))) & (all B (- ilf_type(B,set_type) | empty(B) | (exists C (ilf_type(C,set_type) & member(C,B))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | - member(C,B))) | - empty(B))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | - member(C,B))) | (exists C (ilf_type(C,set_type) & member(C,B))))) & (all B (- empty(B) | - ilf_type(B,set_type) | relation_like(B))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,relation_type(B,C)) | =(domain(B,C,D),domain_of(D)))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,relation_type(B,C)) | ilf_type(domain(B,C,D),subset_type(B)))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,relation_type(B,C)) | =(range(B,C,D),range_of(D)))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,relation_type(B,C)) | ilf_type(range(B,C,D),subset_type(C)))))))) & (all B ilf_type(B,set_type)) & (exists B (ilf_type(B,set_type) & (exists C (ilf_type(C,set_type) & (exists D (ilf_type(D,relation_type(B,C)) & (all E (- ilf_type(E,set_type) | - member(E,C) | (exists F (ilf_type(F,set_type) & member(ordered_pair(F,E),D))))) & - =(range(B,C,D),C)))))))). Max_seconds is 117 for this subproblem. Child search process 23977 started. ============================== PROCESS INITIAL CLAUSES =============== % Clauses before input processing: formulas(usable). end_of_list. formulas(sos). -ilf_type(A,binary_relation_type) | -ilf_type(B,set_type) | member(B,range_of(A)) | -ilf_type(C,set_type) | -member(ordered_pair(C,B),A). [assumption]. -ilf_type(A,binary_relation_type) | -ilf_type(B,set_type) | ilf_type(f1(A,B),set_type) | -member(B,range_of(A)). [assumption]. -ilf_type(A,binary_relation_type) | -ilf_type(B,set_type) | member(ordered_pair(f1(A,B),B),A) | -member(B,range_of(A)). [assumption]. -ilf_type(A,binary_relation_type) | -ilf_type(B,set_type) | ilf_type(f2(A,B),set_type) | -ilf_type(C,set_type) | -member(ordered_pair(C,B),A). [assumption]. -ilf_type(A,binary_relation_type) | -ilf_type(B,set_type) | member(ordered_pair(f2(A,B),B),A) | -ilf_type(C,set_type) | -member(ordered_pair(C,B),A). [assumption]. -ilf_type(A,binary_relation_type) | ilf_type(range_of(A),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,binary_relation_type) | -member(ordered_pair(A,B),C) | member(A,domain_of(C)). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,binary_relation_type) | -member(ordered_pair(A,B),C) | member(B,range_of(C)). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(f3(A,B),set_type) | ilf_type(f4(A,B),set_type) | B = A. [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(f3(A,B),set_type) | -member(f4(A,B),A) | B = A. [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(f3(A,B),set_type) | member(f4(A,B),B) | B = A. [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(f3(A,B),A) | ilf_type(f4(A,B),set_type) | B = A. [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(f3(A,B),A) | -member(f4(A,B),A) | B = A. [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(f3(A,B),A) | member(f4(A,B),B) | B = A. [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(f3(A,B),B) | ilf_type(f4(A,B),set_type) | B = A. [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(f3(A,B),B) | -member(f4(A,B),A) | B = A. [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(f3(A,B),B) | member(f4(A,B),B) | B = A. [assumption]. -ilf_type(A,set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(ordered_pair(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,subset_type(cross_product(A,B))) | ilf_type(C,relation_type(A,B)). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,relation_type(A,B)) | ilf_type(C,subset_type(cross_product(A,B))). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(f5(A,B),relation_type(B,A)). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | -subset(A,B) | -subset(B,A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(A,B) | B != A. [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(B,A) | B != A. [assumption]. -ilf_type(A,binary_relation_type) | ilf_type(domain_of(A),set_type). [assumption]. -ilf_type(A,set_type) | ilf_type(singleton(A),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(cross_product(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(unordered_pair(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | unordered_pair(B,A) = unordered_pair(A,B). [assumption]. -ilf_type(A,set_type) | ilf_type(A,binary_relation_type) | -relation_like(A). [assumption]. -ilf_type(A,set_type) | relation_like(A) | -ilf_type(A,binary_relation_type). [assumption]. ilf_type(c1,binary_relation_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(B,subset_type(A)) | -ilf_type(B,member_type(power_set(A))). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(B,member_type(power_set(A))) | -ilf_type(B,subset_type(A)). [assumption]. -ilf_type(A,set_type) | ilf_type(f6(A),subset_type(A)). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | ilf_type(f7(A,B),set_type) | ilf_type(f8(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | ilf_type(f7(A,B),set_type) | -member(f8(A,B),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | ilf_type(f7(A,B),set_type) | member(f8(A,B),B). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | member(f7(A,B),A) | ilf_type(f8(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | member(f7(A,B),A) | -member(f8(A,B),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | member(f7(A,B),A) | member(f8(A,B),B). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | -member(f7(A,B),B) | ilf_type(f8(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | -member(f7(A,B),B) | -member(f8(A,B),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | -member(f7(A,B),B) | member(f8(A,B),B). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,A) | -member(C,B) | B != A. [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,A) | -member(C,B) | ilf_type(f9(A,B),set_type) | ilf_type(f10(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,A) | -member(C,B) | ilf_type(f9(A,B),set_type) | -member(f10(A,B),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,A) | -member(C,B) | ilf_type(f9(A,B),set_type) | member(f10(A,B),B). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,A) | -member(C,B) | member(f9(A,B),A) | ilf_type(f10(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,A) | -member(C,B) | member(f9(A,B),A) | -member(f10(A,B),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,A) | -member(C,B) | member(f9(A,B),A) | member(f10(A,B),B). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,A) | -member(C,B) | -member(f9(A,B),B) | ilf_type(f10(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,A) | -member(C,B) | -member(f9(A,B),B) | -member(f10(A,B),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,A) | -member(C,B) | -member(f9(A,B),B) | member(f10(A,B),B). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,B) | -member(C,A) | B != A. [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,B) | -member(C,A) | ilf_type(f11(A,B),set_type) | ilf_type(f12(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,B) | -member(C,A) | ilf_type(f11(A,B),set_type) | -member(f12(A,B),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,B) | -member(C,A) | ilf_type(f11(A,B),set_type) | member(f12(A,B),B). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,B) | -member(C,A) | member(f11(A,B),A) | ilf_type(f12(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,B) | -member(C,A) | member(f11(A,B),A) | -member(f12(A,B),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,B) | -member(C,A) | member(f11(A,B),A) | member(f12(A,B),B). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,B) | -member(C,A) | -member(f11(A,B),B) | ilf_type(f12(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,B) | -member(C,A) | -member(f11(A,B),B) | -member(f12(A,B),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,B) | -member(C,A) | -member(f11(A,B),B) | member(f12(A,B),B). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(A,B) | ilf_type(f13(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(A,B) | member(f13(A,B),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(A,B) | -member(f13(A,B),B). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | -member(C,A) | member(C,B) | -subset(A,B). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | -member(C,A) | member(C,B) | ilf_type(f14(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | -member(C,A) | member(C,B) | member(f14(A,B),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | -member(C,A) | member(C,B) | -member(f14(A,B),B). [assumption]. -ilf_type(A,set_type) | subset(A,A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(A,power_set(B)) | ilf_type(f15(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(A,power_set(B)) | member(f15(A,B),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(A,power_set(B)) | -member(f15(A,B),B). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | -member(C,A) | member(C,B) | -member(A,power_set(B)). [assumption]. -ilf_type(A,set_type) | -empty(power_set(A)). [assumption]. -ilf_type(A,set_type) | ilf_type(power_set(A),set_type). [assumption]. -ilf_type(A,set_type) | empty(B) | -ilf_type(B,set_type) | ilf_type(A,member_type(B)) | -member(A,B). [assumption]. -ilf_type(A,set_type) | empty(B) | -ilf_type(B,set_type) | member(A,B) | -ilf_type(A,member_type(B)). [assumption]. empty(A) | -ilf_type(A,set_type) | ilf_type(f16(A),member_type(A)). [assumption]. -ilf_type(A,set_type) | relation_like(A) | ilf_type(f17(A),set_type). [assumption]. -ilf_type(A,set_type) | relation_like(A) | member(f17(A),A). [assumption]. -ilf_type(A,set_type) | relation_like(A) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | ordered_pair(B,C) != f17(A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f18(A,B),set_type) | -relation_like(A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f19(A,B),set_type) | -relation_like(A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f18(A,B),f19(A,B)) = B | -relation_like(A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f20(A,B),set_type) | ilf_type(f22(A),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f20(A,B),set_type) | member(f22(A),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f20(A,B),set_type) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | ordered_pair(C,D) != f22(A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f21(A,B),set_type) | ilf_type(f22(A),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f21(A,B),set_type) | member(f22(A),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f21(A,B),set_type) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | ordered_pair(C,D) != f22(A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f20(A,B),f21(A,B)) = B | ilf_type(f22(A),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f20(A,B),f21(A,B)) = B | member(f22(A),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f20(A,B),f21(A,B)) = B | -ilf_type(C,set_type) | -ilf_type(D,set_type) | ordered_pair(C,D) != f22(A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,subset_type(cross_product(A,B))) | relation_like(C). [assumption]. -ilf_type(A,set_type) | empty(A) | ilf_type(f23(A),set_type). [assumption]. -ilf_type(A,set_type) | empty(A) | member(f23(A),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | -empty(A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f24(A),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | member(f24(A),A). [assumption]. -empty(A) | -ilf_type(A,set_type) | relation_like(A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,relation_type(A,B)) | domain(A,B,C) = domain_of(C). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,relation_type(A,B)) | ilf_type(domain(A,B,C),subset_type(A)). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,relation_type(A,B)) | range(A,B,C) = range_of(C). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,relation_type(A,B)) | ilf_type(range(A,B,C),subset_type(B)). [assumption]. ilf_type(A,set_type). [assumption]. ilf_type(c2,set_type). [assumption]. ilf_type(c3,set_type). [assumption]. ilf_type(c4,relation_type(c2,c3)). [assumption]. -ilf_type(A,set_type) | -member(A,c3) | ilf_type(f25(A),set_type). [assumption]. -ilf_type(A,set_type) | -member(A,c3) | member(ordered_pair(f25(A),A),c4). [assumption]. range(c2,c3,c4) != c3. [assumption]. end_of_list. formulas(demodulators). end_of_list. ============================== PREDICATE ELIMINATION ================= Eliminating relation_like/1 1 -ilf_type(A,set_type) | relation_like(A) | -ilf_type(A,binary_relation_type). [assumption]. 2 -ilf_type(A,set_type) | ilf_type(A,binary_relation_type) | -relation_like(A). [assumption]. 3 -ilf_type(A,set_type) | relation_like(A) | ilf_type(f17(A),set_type). [assumption]. 4 -ilf_type(A,set_type) | relation_like(A) | member(f17(A),A). [assumption]. Derived: -ilf_type(A,set_type) | member(f17(A),A) | -ilf_type(A,set_type) | ilf_type(A,binary_relation_type). [resolve(4,b,2,c)]. 5 -ilf_type(A,set_type) | relation_like(A) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | ordered_pair(B,C) != f17(A). [assumption]. Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | ordered_pair(B,C) != f17(A) | -ilf_type(A,set_type) | ilf_type(A,binary_relation_type). [resolve(5,b,2,c)]. 6 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f18(A,B),set_type) | -relation_like(A). [assumption]. 7 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f19(A,B),set_type) | -relation_like(A). [assumption]. 8 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f18(A,B),f19(A,B)) = B | -relation_like(A). [assumption]. Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f18(A,B),f19(A,B)) = B | -ilf_type(A,set_type) | -ilf_type(A,binary_relation_type). [resolve(8,e,1,b)]. Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f18(A,B),f19(A,B)) = B | -ilf_type(A,set_type) | member(f17(A),A). [resolve(8,e,4,b)]. Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f18(A,B),f19(A,B)) = B | -ilf_type(A,set_type) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | ordered_pair(C,D) != f17(A). [resolve(8,e,5,b)]. 9 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,subset_type(cross_product(A,B))) | relation_like(C). [assumption]. Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,subset_type(cross_product(A,B))) | -ilf_type(C,set_type) | ilf_type(C,binary_relation_type). [resolve(9,d,2,c)]. Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,subset_type(cross_product(A,B))) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | -member(D,C) | ordered_pair(f18(C,D),f19(C,D)) = D. [resolve(9,d,8,e)]. 10 -empty(A) | -ilf_type(A,set_type) | relation_like(A). [assumption]. Derived: -empty(A) | -ilf_type(A,set_type) | -ilf_type(A,set_type) | ilf_type(A,binary_relation_type). [resolve(10,c,2,c)]. Derived: -empty(A) | -ilf_type(A,set_type) | -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f18(A,B),f19(A,B)) = B. [resolve(10,c,8,e)]. ============================== end predicate elimination ============= Term ordering decisions: Predicate symbol precedence: predicate_order([ =, empty, ilf_type, member, subset ]). Function symbol precedence: function_order([ set_type, binary_relation_type, c1, c2, c3, c4, ordered_pair, relation_type, cross_product, unordered_pair, f1, f2, f3, f4, f5, f7, f8, f9, f10, f11, f12, f13, f14, f15, f18, f19, f20, f21, subset_type, power_set, range_of, member_type, domain_of, singleton, f6, f16, f17, f22, f23, f24, f25, domain, range ]). After inverse_order: (no changes). Unfolding symbols: (none). Auto_inference settings: % set(paramodulation). % (positive equality literals) % set(binary_resolution). % (non-Horn) Auto_process settings: % set(factor). % (non-Horn) % set(unit_deletion). % (non-Horn) kept: 11 -ilf_type(A,binary_relation_type) | -ilf_type(B,set_type) | member(B,range_of(A)) | -ilf_type(C,set_type) | -member(ordered_pair(C,B),A). [assumption]. kept: 12 -ilf_type(A,binary_relation_type) | -ilf_type(B,set_type) | ilf_type(f1(A,B),set_type) | -member(B,range_of(A)). [assumption]. kept: 13 -ilf_type(A,binary_relation_type) | -ilf_type(B,set_type) | member(ordered_pair(f1(A,B),B),A) | -member(B,range_of(A)). [assumption]. kept: 14 -ilf_type(A,binary_relation_type) | -ilf_type(B,set_type) | ilf_type(f2(A,B),set_type) | -ilf_type(C,set_type) | -member(ordered_pair(C,B),A). [assumption]. kept: 15 -ilf_type(A,binary_relation_type) | -ilf_type(B,set_type) | member(ordered_pair(f2(A,B),B),A) | -ilf_type(C,set_type) | -member(ordered_pair(C,B),A). [assumption]. kept: 16 -ilf_type(A,binary_relation_type) | ilf_type(range_of(A),set_type). [assumption]. kept: 17 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,binary_relation_type) | -member(ordered_pair(A,B),C) | member(A,domain_of(C)). [assumption]. kept: 18 -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(f3(A,B),set_type) | ilf_type(f4(A,B),set_type) | B = A. [assumption]. kept: 19 -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(f3(A,B),set_type) | -member(f4(A,B),A) | B = A. [assumption]. kept: 20 -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(f3(A,B),set_type) | member(f4(A,B),B) | B = A. [assumption]. kept: 21 -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(f3(A,B),A) | ilf_type(f4(A,B),set_type) | B = A. [assumption]. kept: 22 -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(f3(A,B),A) | -member(f4(A,B),A) | B = A. [assumption]. kept: 23 -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(f3(A,B),A) | member(f4(A,B),B) | B = A. [assumption]. kept: 24 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(f3(A,B),B) | ilf_type(f4(A,B),set_type) | B = A. [assumption]. kept: 25 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(f3(A,B),B) | -member(f4(A,B),A) | B = A. [assumption]. kept: 26 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(f3(A,B),B) | member(f4(A,B),B) | B = A. [assumption]. kept: 27 -ilf_type(A,set_type). [assumption]. 28 -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(ordered_pair(A,B),set_type). [assumption]. 29 -ilf_type(A,binary_relation_type) | ilf_type(domain_of(A),set_type). [assumption]. kept: 30 -ilf_type(A,binary_relation_type). [copy(29),unit_del(b,27)]. 31 -ilf_type(A,set_type) | ilf_type(singleton(A),set_type). [assumption]. 32 -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(cross_product(A,B),set_type). [assumption]. 33 -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(unordered_pair(A,B),set_type). [assumption]. 34 ilf_type(c1,binary_relation_type). [assumption]. ============================== PROOF ================================= % Proof 1 at 0.01 (+ 0.00) seconds. % Length of proof is 5. % Level of proof is 2. % Maximum clause weight is 3.000. % Given clauses 0. 27 -ilf_type(A,set_type). [assumption]. 29 -ilf_type(A,binary_relation_type) | ilf_type(domain_of(A),set_type). [assumption]. 30 -ilf_type(A,binary_relation_type). [copy(29),unit_del(b,27)]. 34 ilf_type(c1,binary_relation_type). [assumption]. 35 $F. [copy(34),unit_del(a,30)]. ============================== end of proof ========================== ============================== STATISTICS ============================ Given=0. Generated=31. Kept=18. proofs=1. Usable=0. Sos=0. Demods=0. Limbo=18, Disabled=41. Hints=0. Kept_by_rule=0, Deleted_by_rule=0. Forward_subsumed=12. Back_subsumed=0. Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. New_demodulators=0 (0 lex), Back_demodulated=0. Back_unit_deleted=0. Demod_attempts=0. Demod_rewrites=0. Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. Nonunit_fsub_feature_tests=2. Nonunit_bsub_feature_tests=0. Megabytes=0.46. User_CPU=0.01, System_CPU=0.00, Wall_clock=4. ============================== end of statistics ===================== ============================== end of search ========================= Exiting with 1 proof. Process 23977 exit (max_proofs) Tue Nov 3 16:59:21 2009 ============================== continuing FOF reduction multisearch == Subproblem 4 of 6 (negated): ((all B (- ilf_type(B,binary_relation_type) | (all C (- ilf_type(C,set_type) | member(C,range_of(B)) | (all D (- ilf_type(D,set_type) | - member(ordered_pair(D,C),B))))))) & (all B (- ilf_type(B,binary_relation_type) | (all C (- ilf_type(C,set_type) | (exists D (ilf_type(D,set_type) & member(ordered_pair(D,C),B))) | - member(C,range_of(B)))))) & (all B (- ilf_type(B,binary_relation_type) | (all C (- ilf_type(C,set_type) | (exists D (ilf_type(D,set_type) & member(ordered_pair(D,C),B))) | (all D (- ilf_type(D,set_type) | - member(ordered_pair(D,C),B))))))) & (all B (- ilf_type(B,binary_relation_type) | ilf_type(range_of(B),set_type))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,binary_relation_type) | - member(ordered_pair(B,C),D) | member(B,domain_of(D)))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,binary_relation_type) | - member(ordered_pair(B,C),D) | member(C,range_of(D)))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (exists D (ilf_type(D,set_type) & member(D,B) & - member(D,C))) | (exists D (ilf_type(D,set_type) & - member(D,B) & member(D,C))) | =(C,B))))) & (all C (- ilf_type(C,set_type))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | ilf_type(ordered_pair(B,C),set_type))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,subset_type(cross_product(B,C))) | ilf_type(D,relation_type(B,C)))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all E (- ilf_type(E,relation_type(B,C)) | ilf_type(E,subset_type(cross_product(B,C))))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (exists D ilf_type(D,relation_type(C,B))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | =(C,B) | - subset(B,C) | - subset(C,B))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | subset(B,C) | - =(C,B))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | subset(C,B) | - =(C,B))))) & (all B (- ilf_type(B,binary_relation_type) | ilf_type(domain_of(B),set_type))) & (all B (- ilf_type(B,set_type) | ilf_type(singleton(B),set_type))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | ilf_type(cross_product(B,C),set_type))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | ilf_type(unordered_pair(B,C),set_type))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | =(unordered_pair(C,B),unordered_pair(B,C)))))) & (all B (- ilf_type(B,set_type) | ilf_type(B,binary_relation_type) | - relation_like(B))) & (all B (- ilf_type(B,set_type) | relation_like(B) | - ilf_type(B,binary_relation_type))) & (exists B ilf_type(B,binary_relation_type)) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | ilf_type(C,subset_type(B)) | - ilf_type(C,member_type(power_set(B))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | ilf_type(C,member_type(power_set(B))) | - ilf_type(C,subset_type(B)))))) & (all B (- ilf_type(B,set_type) | (exists C ilf_type(C,subset_type(B))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | =(C,B) | (exists D (ilf_type(D,set_type) & member(D,B) & - member(D,C))) | (exists D (ilf_type(D,set_type) & - member(D,B) & member(D,C))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,set_type) | member(D,B) | - member(D,C))) | - =(C,B))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,set_type) | member(D,B) | - member(D,C))) | (exists D (ilf_type(D,set_type) & member(D,B) & - member(D,C))) | (exists D (ilf_type(D,set_type) & - member(D,B) & member(D,C))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,set_type) | member(D,C) | - member(D,B))) | - =(C,B))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,set_type) | member(D,C) | - member(D,B))) | (exists D (ilf_type(D,set_type) & member(D,B) & - member(D,C))) | (exists D (ilf_type(D,set_type) & - member(D,B) & member(D,C))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | subset(B,C) | (exists D (ilf_type(D,set_type) & member(D,B) & - member(D,C))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,set_type) | - member(D,B) | member(D,C))) | - subset(B,C))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,set_type) | - member(D,B) | member(D,C))) | (exists D (ilf_type(D,set_type) & member(D,B) & - member(D,C))))))) & (all B (- ilf_type(B,set_type) | subset(B,B))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | member(B,power_set(C)) | (exists D (ilf_type(D,set_type) & member(D,B) & - member(D,C))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,set_type) | - member(D,B) | member(D,C))) | - member(B,power_set(C)))))) & (all B (- ilf_type(B,set_type) | - empty(power_set(B)))) & (all B (- ilf_type(B,set_type) | ilf_type(power_set(B),set_type))) & (all B (- ilf_type(B,set_type) | (all C (empty(C) | - ilf_type(C,set_type) | ilf_type(B,member_type(C)) | - member(B,C))))) & (all B (- ilf_type(B,set_type) | (all C (empty(C) | - ilf_type(C,set_type) | member(B,C) | - ilf_type(B,member_type(C)))))) & (all B (empty(B) | - ilf_type(B,set_type) | (exists C ilf_type(C,member_type(B))))) & (all B (- ilf_type(B,set_type) | relation_like(B) | (exists C (ilf_type(C,set_type) & member(C,B) & (all D (- ilf_type(D,set_type) | (all E (- ilf_type(E,set_type) | - =(ordered_pair(D,E),C))))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | - member(C,B) | (exists D (ilf_type(D,set_type) & (exists E (ilf_type(E,set_type) & =(ordered_pair(D,E),C))))))) | - relation_like(B))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | - member(C,B) | (exists D (ilf_type(D,set_type) & (exists E (ilf_type(E,set_type) & =(ordered_pair(D,E),C))))))) | (exists C (ilf_type(C,set_type) & member(C,B) & (all D (- ilf_type(D,set_type) | (all E (- ilf_type(E,set_type) | - =(ordered_pair(D,E),C))))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,subset_type(cross_product(B,C))) | relation_like(D))))))) & (all B (- ilf_type(B,set_type) | empty(B) | (exists C (ilf_type(C,set_type) & member(C,B))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | - member(C,B))) | - empty(B))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | - member(C,B))) | (exists C (ilf_type(C,set_type) & member(C,B))))) & (all B (- empty(B) | - ilf_type(B,set_type) | relation_like(B))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,relation_type(B,C)) | =(domain(B,C,D),domain_of(D)))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,relation_type(B,C)) | ilf_type(domain(B,C,D),subset_type(B)))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,relation_type(B,C)) | =(range(B,C,D),range_of(D)))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,relation_type(B,C)) | ilf_type(range(B,C,D),subset_type(C)))))))) & (all B ilf_type(B,set_type)) & (exists B (ilf_type(B,set_type) & (exists C (ilf_type(C,set_type) & (exists D (ilf_type(D,relation_type(B,C)) & (exists E (ilf_type(E,set_type) & member(E,C) & (all F (- ilf_type(F,set_type) | - member(ordered_pair(F,E),D))))) & =(range(B,C,D),C)))))))). Max_seconds is 117 for this subproblem. Child search process 23978 started. ============================== PROCESS INITIAL CLAUSES =============== % Clauses before input processing: formulas(usable). end_of_list. formulas(sos). -ilf_type(A,binary_relation_type) | -ilf_type(B,set_type) | member(B,range_of(A)) | -ilf_type(C,set_type) | -member(ordered_pair(C,B),A). [assumption]. -ilf_type(A,binary_relation_type) | -ilf_type(B,set_type) | ilf_type(f1(A,B),set_type) | -member(B,range_of(A)). [assumption]. -ilf_type(A,binary_relation_type) | -ilf_type(B,set_type) | member(ordered_pair(f1(A,B),B),A) | -member(B,range_of(A)). [assumption]. -ilf_type(A,binary_relation_type) | -ilf_type(B,set_type) | ilf_type(f2(A,B),set_type) | -ilf_type(C,set_type) | -member(ordered_pair(C,B),A). [assumption]. -ilf_type(A,binary_relation_type) | -ilf_type(B,set_type) | member(ordered_pair(f2(A,B),B),A) | -ilf_type(C,set_type) | -member(ordered_pair(C,B),A). [assumption]. -ilf_type(A,binary_relation_type) | ilf_type(range_of(A),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,binary_relation_type) | -member(ordered_pair(A,B),C) | member(A,domain_of(C)). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,binary_relation_type) | -member(ordered_pair(A,B),C) | member(B,range_of(C)). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(f3(A,B),set_type) | ilf_type(f4(A,B),set_type) | B = A. [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(f3(A,B),set_type) | -member(f4(A,B),A) | B = A. [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(f3(A,B),set_type) | member(f4(A,B),B) | B = A. [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(f3(A,B),A) | ilf_type(f4(A,B),set_type) | B = A. [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(f3(A,B),A) | -member(f4(A,B),A) | B = A. [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(f3(A,B),A) | member(f4(A,B),B) | B = A. [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(f3(A,B),B) | ilf_type(f4(A,B),set_type) | B = A. [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(f3(A,B),B) | -member(f4(A,B),A) | B = A. [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(f3(A,B),B) | member(f4(A,B),B) | B = A. [assumption]. -ilf_type(A,set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(ordered_pair(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,subset_type(cross_product(A,B))) | ilf_type(C,relation_type(A,B)). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,relation_type(A,B)) | ilf_type(C,subset_type(cross_product(A,B))). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(f5(A,B),relation_type(B,A)). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | -subset(A,B) | -subset(B,A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(A,B) | B != A. [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(B,A) | B != A. [assumption]. -ilf_type(A,binary_relation_type) | ilf_type(domain_of(A),set_type). [assumption]. -ilf_type(A,set_type) | ilf_type(singleton(A),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(cross_product(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(unordered_pair(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | unordered_pair(B,A) = unordered_pair(A,B). [assumption]. -ilf_type(A,set_type) | ilf_type(A,binary_relation_type) | -relation_like(A). [assumption]. -ilf_type(A,set_type) | relation_like(A) | -ilf_type(A,binary_relation_type). [assumption]. ilf_type(c1,binary_relation_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(B,subset_type(A)) | -ilf_type(B,member_type(power_set(A))). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(B,member_type(power_set(A))) | -ilf_type(B,subset_type(A)). [assumption]. -ilf_type(A,set_type) | ilf_type(f6(A),subset_type(A)). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | ilf_type(f7(A,B),set_type) | ilf_type(f8(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | ilf_type(f7(A,B),set_type) | -member(f8(A,B),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | ilf_type(f7(A,B),set_type) | member(f8(A,B),B). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | member(f7(A,B),A) | ilf_type(f8(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | member(f7(A,B),A) | -member(f8(A,B),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | member(f7(A,B),A) | member(f8(A,B),B). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | -member(f7(A,B),B) | ilf_type(f8(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | -member(f7(A,B),B) | -member(f8(A,B),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | -member(f7(A,B),B) | member(f8(A,B),B). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,A) | -member(C,B) | B != A. [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,A) | -member(C,B) | ilf_type(f9(A,B),set_type) | ilf_type(f10(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,A) | -member(C,B) | ilf_type(f9(A,B),set_type) | -member(f10(A,B),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,A) | -member(C,B) | ilf_type(f9(A,B),set_type) | member(f10(A,B),B). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,A) | -member(C,B) | member(f9(A,B),A) | ilf_type(f10(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,A) | -member(C,B) | member(f9(A,B),A) | -member(f10(A,B),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,A) | -member(C,B) | member(f9(A,B),A) | member(f10(A,B),B). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,A) | -member(C,B) | -member(f9(A,B),B) | ilf_type(f10(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,A) | -member(C,B) | -member(f9(A,B),B) | -member(f10(A,B),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,A) | -member(C,B) | -member(f9(A,B),B) | member(f10(A,B),B). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,B) | -member(C,A) | B != A. [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,B) | -member(C,A) | ilf_type(f11(A,B),set_type) | ilf_type(f12(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,B) | -member(C,A) | ilf_type(f11(A,B),set_type) | -member(f12(A,B),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,B) | -member(C,A) | ilf_type(f11(A,B),set_type) | member(f12(A,B),B). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,B) | -member(C,A) | member(f11(A,B),A) | ilf_type(f12(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,B) | -member(C,A) | member(f11(A,B),A) | -member(f12(A,B),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,B) | -member(C,A) | member(f11(A,B),A) | member(f12(A,B),B). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,B) | -member(C,A) | -member(f11(A,B),B) | ilf_type(f12(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,B) | -member(C,A) | -member(f11(A,B),B) | -member(f12(A,B),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,B) | -member(C,A) | -member(f11(A,B),B) | member(f12(A,B),B). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(A,B) | ilf_type(f13(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(A,B) | member(f13(A,B),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(A,B) | -member(f13(A,B),B). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | -member(C,A) | member(C,B) | -subset(A,B). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | -member(C,A) | member(C,B) | ilf_type(f14(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | -member(C,A) | member(C,B) | member(f14(A,B),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | -member(C,A) | member(C,B) | -member(f14(A,B),B). [assumption]. -ilf_type(A,set_type) | subset(A,A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(A,power_set(B)) | ilf_type(f15(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(A,power_set(B)) | member(f15(A,B),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(A,power_set(B)) | -member(f15(A,B),B). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | -member(C,A) | member(C,B) | -member(A,power_set(B)). [assumption]. -ilf_type(A,set_type) | -empty(power_set(A)). [assumption]. -ilf_type(A,set_type) | ilf_type(power_set(A),set_type). [assumption]. -ilf_type(A,set_type) | empty(B) | -ilf_type(B,set_type) | ilf_type(A,member_type(B)) | -member(A,B). [assumption]. -ilf_type(A,set_type) | empty(B) | -ilf_type(B,set_type) | member(A,B) | -ilf_type(A,member_type(B)). [assumption]. empty(A) | -ilf_type(A,set_type) | ilf_type(f16(A),member_type(A)). [assumption]. -ilf_type(A,set_type) | relation_like(A) | ilf_type(f17(A),set_type). [assumption]. -ilf_type(A,set_type) | relation_like(A) | member(f17(A),A). [assumption]. -ilf_type(A,set_type) | relation_like(A) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | ordered_pair(B,C) != f17(A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f18(A,B),set_type) | -relation_like(A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f19(A,B),set_type) | -relation_like(A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f18(A,B),f19(A,B)) = B | -relation_like(A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f20(A,B),set_type) | ilf_type(f22(A),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f20(A,B),set_type) | member(f22(A),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f20(A,B),set_type) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | ordered_pair(C,D) != f22(A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f21(A,B),set_type) | ilf_type(f22(A),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f21(A,B),set_type) | member(f22(A),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f21(A,B),set_type) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | ordered_pair(C,D) != f22(A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f20(A,B),f21(A,B)) = B | ilf_type(f22(A),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f20(A,B),f21(A,B)) = B | member(f22(A),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f20(A,B),f21(A,B)) = B | -ilf_type(C,set_type) | -ilf_type(D,set_type) | ordered_pair(C,D) != f22(A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,subset_type(cross_product(A,B))) | relation_like(C). [assumption]. -ilf_type(A,set_type) | empty(A) | ilf_type(f23(A),set_type). [assumption]. -ilf_type(A,set_type) | empty(A) | member(f23(A),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | -empty(A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f24(A),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | member(f24(A),A). [assumption]. -empty(A) | -ilf_type(A,set_type) | relation_like(A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,relation_type(A,B)) | domain(A,B,C) = domain_of(C). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,relation_type(A,B)) | ilf_type(domain(A,B,C),subset_type(A)). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,relation_type(A,B)) | range(A,B,C) = range_of(C). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,relation_type(A,B)) | ilf_type(range(A,B,C),subset_type(B)). [assumption]. ilf_type(A,set_type). [assumption]. ilf_type(c2,set_type). [assumption]. ilf_type(c3,set_type). [assumption]. ilf_type(c4,relation_type(c2,c3)). [assumption]. ilf_type(c5,set_type). [assumption]. member(c5,c3). [assumption]. -ilf_type(A,set_type) | -member(ordered_pair(A,c5),c4). [assumption]. range(c2,c3,c4) = c3. [assumption]. end_of_list. formulas(demodulators). end_of_list. ============================== PREDICATE ELIMINATION ================= Eliminating relation_like/1 1 -ilf_type(A,set_type) | relation_like(A) | -ilf_type(A,binary_relation_type). [assumption]. 2 -ilf_type(A,set_type) | ilf_type(A,binary_relation_type) | -relation_like(A). [assumption]. 3 -ilf_type(A,set_type) | relation_like(A) | ilf_type(f17(A),set_type). [assumption]. 4 -ilf_type(A,set_type) | relation_like(A) | member(f17(A),A). [assumption]. Derived: -ilf_type(A,set_type) | member(f17(A),A) | -ilf_type(A,set_type) | ilf_type(A,binary_relation_type). [resolve(4,b,2,c)]. 5 -ilf_type(A,set_type) | relation_like(A) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | ordered_pair(B,C) != f17(A). [assumption]. Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | ordered_pair(B,C) != f17(A) | -ilf_type(A,set_type) | ilf_type(A,binary_relation_type). [resolve(5,b,2,c)]. 6 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f18(A,B),set_type) | -relation_like(A). [assumption]. 7 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f19(A,B),set_type) | -relation_like(A). [assumption]. 8 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f18(A,B),f19(A,B)) = B | -relation_like(A). [assumption]. Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f18(A,B),f19(A,B)) = B | -ilf_type(A,set_type) | -ilf_type(A,binary_relation_type). [resolve(8,e,1,b)]. Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f18(A,B),f19(A,B)) = B | -ilf_type(A,set_type) | member(f17(A),A). [resolve(8,e,4,b)]. Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f18(A,B),f19(A,B)) = B | -ilf_type(A,set_type) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | ordered_pair(C,D) != f17(A). [resolve(8,e,5,b)]. 9 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,subset_type(cross_product(A,B))) | relation_like(C). [assumption]. Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,subset_type(cross_product(A,B))) | -ilf_type(C,set_type) | ilf_type(C,binary_relation_type). [resolve(9,d,2,c)]. Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,subset_type(cross_product(A,B))) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | -member(D,C) | ordered_pair(f18(C,D),f19(C,D)) = D. [resolve(9,d,8,e)]. 10 -empty(A) | -ilf_type(A,set_type) | relation_like(A). [assumption]. Derived: -empty(A) | -ilf_type(A,set_type) | -ilf_type(A,set_type) | ilf_type(A,binary_relation_type). [resolve(10,c,2,c)]. Derived: -empty(A) | -ilf_type(A,set_type) | -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f18(A,B),f19(A,B)) = B. [resolve(10,c,8,e)]. ============================== end predicate elimination ============= Term ordering decisions: Predicate symbol precedence: predicate_order([ =, empty, ilf_type, member, subset ]). Function symbol precedence: function_order([ set_type, binary_relation_type, c1, c2, c3, c4, c5, ordered_pair, relation_type, cross_product, unordered_pair, f1, f2, f3, f4, f5, f7, f8, f9, f10, f11, f12, f13, f14, f15, f18, f19, f20, f21, subset_type, power_set, range_of, member_type, domain_of, singleton, f6, f16, f17, f22, f23, f24, range, domain ]). After inverse_order: (no changes). Unfolding symbols: (none). Auto_inference settings: % set(paramodulation). % (positive equality literals) % set(binary_resolution). % (non-Horn) Auto_process settings: % set(factor). % (non-Horn) % set(unit_deletion). % (non-Horn) kept: 11 -ilf_type(A,binary_relation_type) | -ilf_type(B,set_type) | member(B,range_of(A)) | -ilf_type(C,set_type) | -member(ordered_pair(C,B),A). [assumption]. kept: 12 -ilf_type(A,binary_relation_type) | -ilf_type(B,set_type) | ilf_type(f1(A,B),set_type) | -member(B,range_of(A)). [assumption]. kept: 13 -ilf_type(A,binary_relation_type) | -ilf_type(B,set_type) | member(ordered_pair(f1(A,B),B),A) | -member(B,range_of(A)). [assumption]. kept: 14 -ilf_type(A,binary_relation_type) | -ilf_type(B,set_type) | ilf_type(f2(A,B),set_type) | -ilf_type(C,set_type) | -member(ordered_pair(C,B),A). [assumption]. kept: 15 -ilf_type(A,binary_relation_type) | -ilf_type(B,set_type) | member(ordered_pair(f2(A,B),B),A) | -ilf_type(C,set_type) | -member(ordered_pair(C,B),A). [assumption]. kept: 16 -ilf_type(A,binary_relation_type) | ilf_type(range_of(A),set_type). [assumption]. kept: 17 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,binary_relation_type) | -member(ordered_pair(A,B),C) | member(A,domain_of(C)). [assumption]. kept: 18 -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(f3(A,B),set_type) | ilf_type(f4(A,B),set_type) | B = A. [assumption]. kept: 19 -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(f3(A,B),set_type) | -member(f4(A,B),A) | B = A. [assumption]. kept: 20 -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(f3(A,B),set_type) | member(f4(A,B),B) | B = A. [assumption]. kept: 21 -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(f3(A,B),A) | ilf_type(f4(A,B),set_type) | B = A. [assumption]. kept: 22 -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(f3(A,B),A) | -member(f4(A,B),A) | B = A. [assumption]. kept: 23 -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(f3(A,B),A) | member(f4(A,B),B) | B = A. [assumption]. kept: 24 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(f3(A,B),B) | ilf_type(f4(A,B),set_type) | B = A. [assumption]. kept: 25 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(f3(A,B),B) | -member(f4(A,B),A) | B = A. [assumption]. kept: 26 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(f3(A,B),B) | member(f4(A,B),B) | B = A. [assumption]. kept: 27 -ilf_type(A,set_type). [assumption]. 28 -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(ordered_pair(A,B),set_type). [assumption]. 29 -ilf_type(A,binary_relation_type) | ilf_type(domain_of(A),set_type). [assumption]. kept: 30 -ilf_type(A,binary_relation_type). [copy(29),unit_del(b,27)]. 31 -ilf_type(A,set_type) | ilf_type(singleton(A),set_type). [assumption]. 32 -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(cross_product(A,B),set_type). [assumption]. 33 -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(unordered_pair(A,B),set_type). [assumption]. 34 ilf_type(c1,binary_relation_type). [assumption]. ============================== PROOF ================================= % Proof 1 at 0.01 (+ 0.00) seconds. % Length of proof is 5. % Level of proof is 2. % Maximum clause weight is 3.000. % Given clauses 0. 27 -ilf_type(A,set_type). [assumption]. 29 -ilf_type(A,binary_relation_type) | ilf_type(domain_of(A),set_type). [assumption]. 30 -ilf_type(A,binary_relation_type). [copy(29),unit_del(b,27)]. 34 ilf_type(c1,binary_relation_type). [assumption]. 35 $F. [copy(34),unit_del(a,30)]. ============================== end of proof ========================== ============================== STATISTICS ============================ Given=0. Generated=31. Kept=18. proofs=1. Usable=0. Sos=0. Demods=0. Limbo=18, Disabled=41. Hints=0. Kept_by_rule=0, Deleted_by_rule=0. Forward_subsumed=12. Back_subsumed=0. Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. New_demodulators=0 (0 lex), Back_demodulated=0. Back_unit_deleted=0. Demod_attempts=0. Demod_rewrites=0. Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. Nonunit_fsub_feature_tests=2. Nonunit_bsub_feature_tests=0. Megabytes=0.47. User_CPU=0.01, System_CPU=0.00, Wall_clock=4. ============================== end of statistics ===================== ============================== end of search ========================= Exiting with 1 proof. Process 23978 exit (max_proofs) Tue Nov 3 16:59:21 2009 ============================== continuing FOF reduction multisearch == Subproblem 5 of 6 (negated): ((all B (- ilf_type(B,binary_relation_type) | (all C (- ilf_type(C,set_type) | member(C,range_of(B)) | (all D (- ilf_type(D,set_type) | - member(ordered_pair(D,C),B))))))) & (all B (- ilf_type(B,binary_relation_type) | (all C (- ilf_type(C,set_type) | (exists D (ilf_type(D,set_type) & member(ordered_pair(D,C),B))) | - member(C,range_of(B)))))) & (all B (- ilf_type(B,binary_relation_type) | (all C (- ilf_type(C,set_type) | (exists D (ilf_type(D,set_type) & member(ordered_pair(D,C),B))) | (all D (- ilf_type(D,set_type) | - member(ordered_pair(D,C),B))))))) & (all B (- ilf_type(B,binary_relation_type) | ilf_type(range_of(B),set_type))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,binary_relation_type) | - member(ordered_pair(B,C),D) | member(B,domain_of(D)))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,binary_relation_type) | - member(ordered_pair(B,C),D) | member(C,range_of(D)))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (exists D (ilf_type(D,set_type) & member(D,B) & - member(D,C))) | (exists D (ilf_type(D,set_type) & - member(D,B) & member(D,C))) | =(C,B))))) & (all B (- ilf_type(B,set_type))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | ilf_type(ordered_pair(B,C),set_type))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,subset_type(cross_product(B,C))) | ilf_type(D,relation_type(B,C)))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all E (- ilf_type(E,relation_type(B,C)) | ilf_type(E,subset_type(cross_product(B,C))))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (exists D ilf_type(D,relation_type(C,B))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | =(C,B) | - subset(B,C) | - subset(C,B))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | subset(B,C) | - =(C,B))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | subset(C,B) | - =(C,B))))) & (all B (- ilf_type(B,binary_relation_type) | ilf_type(domain_of(B),set_type))) & (all B (- ilf_type(B,set_type) | ilf_type(singleton(B),set_type))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | ilf_type(cross_product(B,C),set_type))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | ilf_type(unordered_pair(B,C),set_type))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | =(unordered_pair(C,B),unordered_pair(B,C)))))) & (all B (- ilf_type(B,set_type) | ilf_type(B,binary_relation_type) | - relation_like(B))) & (all B (- ilf_type(B,set_type) | relation_like(B) | - ilf_type(B,binary_relation_type))) & (exists B ilf_type(B,binary_relation_type)) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | ilf_type(C,subset_type(B)) | - ilf_type(C,member_type(power_set(B))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | ilf_type(C,member_type(power_set(B))) | - ilf_type(C,subset_type(B)))))) & (all B (- ilf_type(B,set_type) | (exists C ilf_type(C,subset_type(B))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | =(C,B) | (exists D (ilf_type(D,set_type) & member(D,B) & - member(D,C))) | (exists D (ilf_type(D,set_type) & - member(D,B) & member(D,C))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,set_type) | member(D,B) | - member(D,C))) | - =(C,B))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,set_type) | member(D,B) | - member(D,C))) | (exists D (ilf_type(D,set_type) & member(D,B) & - member(D,C))) | (exists D (ilf_type(D,set_type) & - member(D,B) & member(D,C))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,set_type) | member(D,C) | - member(D,B))) | - =(C,B))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,set_type) | member(D,C) | - member(D,B))) | (exists D (ilf_type(D,set_type) & member(D,B) & - member(D,C))) | (exists D (ilf_type(D,set_type) & - member(D,B) & member(D,C))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | subset(B,C) | (exists D (ilf_type(D,set_type) & member(D,B) & - member(D,C))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,set_type) | - member(D,B) | member(D,C))) | - subset(B,C))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,set_type) | - member(D,B) | member(D,C))) | (exists D (ilf_type(D,set_type) & member(D,B) & - member(D,C))))))) & (all B (- ilf_type(B,set_type) | subset(B,B))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | member(B,power_set(C)) | (exists D (ilf_type(D,set_type) & member(D,B) & - member(D,C))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,set_type) | - member(D,B) | member(D,C))) | - member(B,power_set(C)))))) & (all B (- ilf_type(B,set_type) | - empty(power_set(B)))) & (all B (- ilf_type(B,set_type) | ilf_type(power_set(B),set_type))) & (all B (- ilf_type(B,set_type) | (all C (empty(C) | - ilf_type(C,set_type) | ilf_type(B,member_type(C)) | - member(B,C))))) & (all B (- ilf_type(B,set_type) | (all C (empty(C) | - ilf_type(C,set_type) | member(B,C) | - ilf_type(B,member_type(C)))))) & (all B (empty(B) | - ilf_type(B,set_type) | (exists C ilf_type(C,member_type(B))))) & (all B (- ilf_type(B,set_type) | relation_like(B) | (exists C (ilf_type(C,set_type) & member(C,B) & (all D (- ilf_type(D,set_type) | (all E (- ilf_type(E,set_type) | - =(ordered_pair(D,E),C))))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | - member(C,B) | (exists D (ilf_type(D,set_type) & (exists E (ilf_type(E,set_type) & =(ordered_pair(D,E),C))))))) | - relation_like(B))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | - member(C,B) | (exists D (ilf_type(D,set_type) & (exists E (ilf_type(E,set_type) & =(ordered_pair(D,E),C))))))) | (exists C (ilf_type(C,set_type) & member(C,B) & (all D (- ilf_type(D,set_type) | (all E (- ilf_type(E,set_type) | - =(ordered_pair(D,E),C))))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,subset_type(cross_product(B,C))) | relation_like(D))))))) & (all B (- ilf_type(B,set_type) | empty(B) | (exists C (ilf_type(C,set_type) & member(C,B))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | - member(C,B))) | - empty(B))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | - member(C,B))) | (exists C (ilf_type(C,set_type) & member(C,B))))) & (all B (- empty(B) | - ilf_type(B,set_type) | relation_like(B))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,relation_type(B,C)) | =(domain(B,C,D),domain_of(D)))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,relation_type(B,C)) | ilf_type(domain(B,C,D),subset_type(B)))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,relation_type(B,C)) | =(range(B,C,D),range_of(D)))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,relation_type(B,C)) | ilf_type(range(B,C,D),subset_type(C)))))))) & (all B ilf_type(B,set_type)) & (exists B (ilf_type(B,set_type) & (exists C (ilf_type(C,set_type) & (exists D (ilf_type(D,relation_type(B,C)) & (all E (- ilf_type(E,set_type) | - member(E,C) | (exists F (ilf_type(F,set_type) & member(ordered_pair(F,E),D))))) & - =(range(B,C,D),C)))))))). Max_seconds is 117 for this subproblem. Child search process 23979 started. ============================== PROCESS INITIAL CLAUSES =============== % Clauses before input processing: formulas(usable). end_of_list. formulas(sos). -ilf_type(A,binary_relation_type) | -ilf_type(B,set_type) | member(B,range_of(A)) | -ilf_type(C,set_type) | -member(ordered_pair(C,B),A). [assumption]. -ilf_type(A,binary_relation_type) | -ilf_type(B,set_type) | ilf_type(f1(A,B),set_type) | -member(B,range_of(A)). [assumption]. -ilf_type(A,binary_relation_type) | -ilf_type(B,set_type) | member(ordered_pair(f1(A,B),B),A) | -member(B,range_of(A)). [assumption]. -ilf_type(A,binary_relation_type) | -ilf_type(B,set_type) | ilf_type(f2(A,B),set_type) | -ilf_type(C,set_type) | -member(ordered_pair(C,B),A). [assumption]. -ilf_type(A,binary_relation_type) | -ilf_type(B,set_type) | member(ordered_pair(f2(A,B),B),A) | -ilf_type(C,set_type) | -member(ordered_pair(C,B),A). [assumption]. -ilf_type(A,binary_relation_type) | ilf_type(range_of(A),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,binary_relation_type) | -member(ordered_pair(A,B),C) | member(A,domain_of(C)). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,binary_relation_type) | -member(ordered_pair(A,B),C) | member(B,range_of(C)). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(f3(A,B),set_type) | ilf_type(f4(A,B),set_type) | B = A. [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(f3(A,B),set_type) | -member(f4(A,B),A) | B = A. [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(f3(A,B),set_type) | member(f4(A,B),B) | B = A. [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(f3(A,B),A) | ilf_type(f4(A,B),set_type) | B = A. [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(f3(A,B),A) | -member(f4(A,B),A) | B = A. [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(f3(A,B),A) | member(f4(A,B),B) | B = A. [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(f3(A,B),B) | ilf_type(f4(A,B),set_type) | B = A. [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(f3(A,B),B) | -member(f4(A,B),A) | B = A. [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(f3(A,B),B) | member(f4(A,B),B) | B = A. [assumption]. -ilf_type(A,set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(ordered_pair(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,subset_type(cross_product(A,B))) | ilf_type(C,relation_type(A,B)). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,relation_type(A,B)) | ilf_type(C,subset_type(cross_product(A,B))). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(f5(A,B),relation_type(B,A)). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | -subset(A,B) | -subset(B,A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(A,B) | B != A. [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(B,A) | B != A. [assumption]. -ilf_type(A,binary_relation_type) | ilf_type(domain_of(A),set_type). [assumption]. -ilf_type(A,set_type) | ilf_type(singleton(A),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(cross_product(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(unordered_pair(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | unordered_pair(B,A) = unordered_pair(A,B). [assumption]. -ilf_type(A,set_type) | ilf_type(A,binary_relation_type) | -relation_like(A). [assumption]. -ilf_type(A,set_type) | relation_like(A) | -ilf_type(A,binary_relation_type). [assumption]. ilf_type(c1,binary_relation_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(B,subset_type(A)) | -ilf_type(B,member_type(power_set(A))). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(B,member_type(power_set(A))) | -ilf_type(B,subset_type(A)). [assumption]. -ilf_type(A,set_type) | ilf_type(f6(A),subset_type(A)). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | ilf_type(f7(A,B),set_type) | ilf_type(f8(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | ilf_type(f7(A,B),set_type) | -member(f8(A,B),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | ilf_type(f7(A,B),set_type) | member(f8(A,B),B). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | member(f7(A,B),A) | ilf_type(f8(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | member(f7(A,B),A) | -member(f8(A,B),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | member(f7(A,B),A) | member(f8(A,B),B). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | -member(f7(A,B),B) | ilf_type(f8(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | -member(f7(A,B),B) | -member(f8(A,B),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | -member(f7(A,B),B) | member(f8(A,B),B). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,A) | -member(C,B) | B != A. [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,A) | -member(C,B) | ilf_type(f9(A,B),set_type) | ilf_type(f10(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,A) | -member(C,B) | ilf_type(f9(A,B),set_type) | -member(f10(A,B),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,A) | -member(C,B) | ilf_type(f9(A,B),set_type) | member(f10(A,B),B). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,A) | -member(C,B) | member(f9(A,B),A) | ilf_type(f10(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,A) | -member(C,B) | member(f9(A,B),A) | -member(f10(A,B),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,A) | -member(C,B) | member(f9(A,B),A) | member(f10(A,B),B). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,A) | -member(C,B) | -member(f9(A,B),B) | ilf_type(f10(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,A) | -member(C,B) | -member(f9(A,B),B) | -member(f10(A,B),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,A) | -member(C,B) | -member(f9(A,B),B) | member(f10(A,B),B). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,B) | -member(C,A) | B != A. [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,B) | -member(C,A) | ilf_type(f11(A,B),set_type) | ilf_type(f12(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,B) | -member(C,A) | ilf_type(f11(A,B),set_type) | -member(f12(A,B),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,B) | -member(C,A) | ilf_type(f11(A,B),set_type) | member(f12(A,B),B). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,B) | -member(C,A) | member(f11(A,B),A) | ilf_type(f12(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,B) | -member(C,A) | member(f11(A,B),A) | -member(f12(A,B),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,B) | -member(C,A) | member(f11(A,B),A) | member(f12(A,B),B). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,B) | -member(C,A) | -member(f11(A,B),B) | ilf_type(f12(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,B) | -member(C,A) | -member(f11(A,B),B) | -member(f12(A,B),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,B) | -member(C,A) | -member(f11(A,B),B) | member(f12(A,B),B). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(A,B) | ilf_type(f13(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(A,B) | member(f13(A,B),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(A,B) | -member(f13(A,B),B). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | -member(C,A) | member(C,B) | -subset(A,B). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | -member(C,A) | member(C,B) | ilf_type(f14(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | -member(C,A) | member(C,B) | member(f14(A,B),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | -member(C,A) | member(C,B) | -member(f14(A,B),B). [assumption]. -ilf_type(A,set_type) | subset(A,A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(A,power_set(B)) | ilf_type(f15(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(A,power_set(B)) | member(f15(A,B),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(A,power_set(B)) | -member(f15(A,B),B). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | -member(C,A) | member(C,B) | -member(A,power_set(B)). [assumption]. -ilf_type(A,set_type) | -empty(power_set(A)). [assumption]. -ilf_type(A,set_type) | ilf_type(power_set(A),set_type). [assumption]. -ilf_type(A,set_type) | empty(B) | -ilf_type(B,set_type) | ilf_type(A,member_type(B)) | -member(A,B). [assumption]. -ilf_type(A,set_type) | empty(B) | -ilf_type(B,set_type) | member(A,B) | -ilf_type(A,member_type(B)). [assumption]. empty(A) | -ilf_type(A,set_type) | ilf_type(f16(A),member_type(A)). [assumption]. -ilf_type(A,set_type) | relation_like(A) | ilf_type(f17(A),set_type). [assumption]. -ilf_type(A,set_type) | relation_like(A) | member(f17(A),A). [assumption]. -ilf_type(A,set_type) | relation_like(A) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | ordered_pair(B,C) != f17(A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f18(A,B),set_type) | -relation_like(A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f19(A,B),set_type) | -relation_like(A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f18(A,B),f19(A,B)) = B | -relation_like(A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f20(A,B),set_type) | ilf_type(f22(A),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f20(A,B),set_type) | member(f22(A),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f20(A,B),set_type) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | ordered_pair(C,D) != f22(A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f21(A,B),set_type) | ilf_type(f22(A),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f21(A,B),set_type) | member(f22(A),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f21(A,B),set_type) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | ordered_pair(C,D) != f22(A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f20(A,B),f21(A,B)) = B | ilf_type(f22(A),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f20(A,B),f21(A,B)) = B | member(f22(A),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f20(A,B),f21(A,B)) = B | -ilf_type(C,set_type) | -ilf_type(D,set_type) | ordered_pair(C,D) != f22(A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,subset_type(cross_product(A,B))) | relation_like(C). [assumption]. -ilf_type(A,set_type) | empty(A) | ilf_type(f23(A),set_type). [assumption]. -ilf_type(A,set_type) | empty(A) | member(f23(A),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | -empty(A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f24(A),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | member(f24(A),A). [assumption]. -empty(A) | -ilf_type(A,set_type) | relation_like(A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,relation_type(A,B)) | domain(A,B,C) = domain_of(C). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,relation_type(A,B)) | ilf_type(domain(A,B,C),subset_type(A)). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,relation_type(A,B)) | range(A,B,C) = range_of(C). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,relation_type(A,B)) | ilf_type(range(A,B,C),subset_type(B)). [assumption]. ilf_type(A,set_type). [assumption]. ilf_type(c2,set_type). [assumption]. ilf_type(c3,set_type). [assumption]. ilf_type(c4,relation_type(c2,c3)). [assumption]. -ilf_type(A,set_type) | -member(A,c3) | ilf_type(f25(A),set_type). [assumption]. -ilf_type(A,set_type) | -member(A,c3) | member(ordered_pair(f25(A),A),c4). [assumption]. range(c2,c3,c4) != c3. [assumption]. end_of_list. formulas(demodulators). end_of_list. ============================== PREDICATE ELIMINATION ================= Eliminating relation_like/1 1 -ilf_type(A,set_type) | relation_like(A) | -ilf_type(A,binary_relation_type). [assumption]. 2 -ilf_type(A,set_type) | ilf_type(A,binary_relation_type) | -relation_like(A). [assumption]. 3 -ilf_type(A,set_type) | relation_like(A) | ilf_type(f17(A),set_type). [assumption]. 4 -ilf_type(A,set_type) | relation_like(A) | member(f17(A),A). [assumption]. Derived: -ilf_type(A,set_type) | member(f17(A),A) | -ilf_type(A,set_type) | ilf_type(A,binary_relation_type). [resolve(4,b,2,c)]. 5 -ilf_type(A,set_type) | relation_like(A) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | ordered_pair(B,C) != f17(A). [assumption]. Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | ordered_pair(B,C) != f17(A) | -ilf_type(A,set_type) | ilf_type(A,binary_relation_type). [resolve(5,b,2,c)]. 6 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f18(A,B),set_type) | -relation_like(A). [assumption]. 7 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f19(A,B),set_type) | -relation_like(A). [assumption]. 8 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f18(A,B),f19(A,B)) = B | -relation_like(A). [assumption]. Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f18(A,B),f19(A,B)) = B | -ilf_type(A,set_type) | -ilf_type(A,binary_relation_type). [resolve(8,e,1,b)]. Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f18(A,B),f19(A,B)) = B | -ilf_type(A,set_type) | member(f17(A),A). [resolve(8,e,4,b)]. Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f18(A,B),f19(A,B)) = B | -ilf_type(A,set_type) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | ordered_pair(C,D) != f17(A). [resolve(8,e,5,b)]. 9 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,subset_type(cross_product(A,B))) | relation_like(C). [assumption]. Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,subset_type(cross_product(A,B))) | -ilf_type(C,set_type) | ilf_type(C,binary_relation_type). [resolve(9,d,2,c)]. Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,subset_type(cross_product(A,B))) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | -member(D,C) | ordered_pair(f18(C,D),f19(C,D)) = D. [resolve(9,d,8,e)]. 10 -empty(A) | -ilf_type(A,set_type) | relation_like(A). [assumption]. Derived: -empty(A) | -ilf_type(A,set_type) | -ilf_type(A,set_type) | ilf_type(A,binary_relation_type). [resolve(10,c,2,c)]. Derived: -empty(A) | -ilf_type(A,set_type) | -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f18(A,B),f19(A,B)) = B. [resolve(10,c,8,e)]. ============================== end predicate elimination ============= Term ordering decisions: Predicate symbol precedence: predicate_order([ =, empty, ilf_type, member, subset ]). Function symbol precedence: function_order([ set_type, binary_relation_type, c1, c2, c3, c4, ordered_pair, relation_type, cross_product, unordered_pair, f1, f2, f3, f4, f5, f7, f8, f9, f10, f11, f12, f13, f14, f15, f18, f19, f20, f21, subset_type, power_set, range_of, member_type, domain_of, singleton, f6, f16, f17, f22, f23, f24, f25, domain, range ]). After inverse_order: (no changes). Unfolding symbols: (none). Auto_inference settings: % set(paramodulation). % (positive equality literals) % set(binary_resolution). % (non-Horn) Auto_process settings: % set(factor). % (non-Horn) % set(unit_deletion). % (non-Horn) kept: 11 -ilf_type(A,binary_relation_type) | -ilf_type(B,set_type) | member(B,range_of(A)) | -ilf_type(C,set_type) | -member(ordered_pair(C,B),A). [assumption]. kept: 12 -ilf_type(A,binary_relation_type) | -ilf_type(B,set_type) | ilf_type(f1(A,B),set_type) | -member(B,range_of(A)). [assumption]. kept: 13 -ilf_type(A,binary_relation_type) | -ilf_type(B,set_type) | member(ordered_pair(f1(A,B),B),A) | -member(B,range_of(A)). [assumption]. kept: 14 -ilf_type(A,binary_relation_type) | -ilf_type(B,set_type) | ilf_type(f2(A,B),set_type) | -ilf_type(C,set_type) | -member(ordered_pair(C,B),A). [assumption]. kept: 15 -ilf_type(A,binary_relation_type) | -ilf_type(B,set_type) | member(ordered_pair(f2(A,B),B),A) | -ilf_type(C,set_type) | -member(ordered_pair(C,B),A). [assumption]. kept: 16 -ilf_type(A,binary_relation_type) | ilf_type(range_of(A),set_type). [assumption]. kept: 17 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,binary_relation_type) | -member(ordered_pair(A,B),C) | member(A,domain_of(C)). [assumption]. kept: 18 -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(f3(A,B),set_type) | ilf_type(f4(A,B),set_type) | B = A. [assumption]. kept: 19 -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(f3(A,B),set_type) | -member(f4(A,B),A) | B = A. [assumption]. kept: 20 -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(f3(A,B),set_type) | member(f4(A,B),B) | B = A. [assumption]. kept: 21 -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(f3(A,B),A) | ilf_type(f4(A,B),set_type) | B = A. [assumption]. kept: 22 -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(f3(A,B),A) | -member(f4(A,B),A) | B = A. [assumption]. kept: 23 -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(f3(A,B),A) | member(f4(A,B),B) | B = A. [assumption]. kept: 24 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(f3(A,B),B) | ilf_type(f4(A,B),set_type) | B = A. [assumption]. kept: 25 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(f3(A,B),B) | -member(f4(A,B),A) | B = A. [assumption]. kept: 26 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(f3(A,B),B) | member(f4(A,B),B) | B = A. [assumption]. kept: 27 -ilf_type(A,set_type). [assumption]. 28 -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(ordered_pair(A,B),set_type). [assumption]. 29 -ilf_type(A,binary_relation_type) | ilf_type(domain_of(A),set_type). [assumption]. kept: 30 -ilf_type(A,binary_relation_type). [copy(29),unit_del(b,27)]. 31 -ilf_type(A,set_type) | ilf_type(singleton(A),set_type). [assumption]. 32 -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(cross_product(A,B),set_type). [assumption]. 33 -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(unordered_pair(A,B),set_type). [assumption]. 34 ilf_type(c1,binary_relation_type). [assumption]. ============================== PROOF ================================= % Proof 1 at 0.00 (+ 0.00) seconds. % Length of proof is 5. % Level of proof is 2. % Maximum clause weight is 3.000. % Given clauses 0. 27 -ilf_type(A,set_type). [assumption]. 29 -ilf_type(A,binary_relation_type) | ilf_type(domain_of(A),set_type). [assumption]. 30 -ilf_type(A,binary_relation_type). [copy(29),unit_del(b,27)]. 34 ilf_type(c1,binary_relation_type). [assumption]. 35 $F. [copy(34),unit_del(a,30)]. ============================== end of proof ========================== ============================== STATISTICS ============================ Given=0. Generated=31. Kept=18. proofs=1. Usable=0. Sos=0. Demods=0. Limbo=18, Disabled=41. Hints=0. Kept_by_rule=0, Deleted_by_rule=0. Forward_subsumed=12. Back_subsumed=0. Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. New_demodulators=0 (0 lex), Back_demodulated=0. Back_unit_deleted=0. Demod_attempts=0. Demod_rewrites=0. Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. Nonunit_fsub_feature_tests=2. Nonunit_bsub_feature_tests=0. Megabytes=0.47. User_CPU=0.00, System_CPU=0.00, Wall_clock=4. ============================== end of statistics ===================== ============================== end of search ========================= Exiting with 1 proof. Process 23979 exit (max_proofs) Tue Nov 3 16:59:21 2009 ============================== continuing FOF reduction multisearch == Subproblem 6 of 6 (negated): ((all B (- ilf_type(B,binary_relation_type) | (all C (- ilf_type(C,set_type) | member(C,range_of(B)) | (all D (- ilf_type(D,set_type) | - member(ordered_pair(D,C),B))))))) & (all B (- ilf_type(B,binary_relation_type) | (all C (- ilf_type(C,set_type) | (exists D (ilf_type(D,set_type) & member(ordered_pair(D,C),B))) | - member(C,range_of(B)))))) & (all B (- ilf_type(B,binary_relation_type) | (all C (- ilf_type(C,set_type) | (exists D (ilf_type(D,set_type) & member(ordered_pair(D,C),B))) | (all D (- ilf_type(D,set_type) | - member(ordered_pair(D,C),B))))))) & (all B (- ilf_type(B,binary_relation_type) | ilf_type(range_of(B),set_type))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,binary_relation_type) | - member(ordered_pair(B,C),D) | member(B,domain_of(D)))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,binary_relation_type) | - member(ordered_pair(B,C),D) | member(C,range_of(D)))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (exists D (ilf_type(D,set_type) & member(D,B) & - member(D,C))) | (exists D (ilf_type(D,set_type) & - member(D,B) & member(D,C))) | =(C,B))))) & (all B (- ilf_type(B,set_type))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | ilf_type(ordered_pair(B,C),set_type))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,subset_type(cross_product(B,C))) | ilf_type(D,relation_type(B,C)))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all E (- ilf_type(E,relation_type(B,C)) | ilf_type(E,subset_type(cross_product(B,C))))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (exists D ilf_type(D,relation_type(C,B))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | =(C,B) | - subset(B,C) | - subset(C,B))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | subset(B,C) | - =(C,B))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | subset(C,B) | - =(C,B))))) & (all B (- ilf_type(B,binary_relation_type) | ilf_type(domain_of(B),set_type))) & (all B (- ilf_type(B,set_type) | ilf_type(singleton(B),set_type))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | ilf_type(cross_product(B,C),set_type))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | ilf_type(unordered_pair(B,C),set_type))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | =(unordered_pair(C,B),unordered_pair(B,C)))))) & (all B (- ilf_type(B,set_type) | ilf_type(B,binary_relation_type) | - relation_like(B))) & (all B (- ilf_type(B,set_type) | relation_like(B) | - ilf_type(B,binary_relation_type))) & (exists B ilf_type(B,binary_relation_type)) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | ilf_type(C,subset_type(B)) | - ilf_type(C,member_type(power_set(B))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | ilf_type(C,member_type(power_set(B))) | - ilf_type(C,subset_type(B)))))) & (all B (- ilf_type(B,set_type) | (exists C ilf_type(C,subset_type(B))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | =(C,B) | (exists D (ilf_type(D,set_type) & member(D,B) & - member(D,C))) | (exists D (ilf_type(D,set_type) & - member(D,B) & member(D,C))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,set_type) | member(D,B) | - member(D,C))) | - =(C,B))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,set_type) | member(D,B) | - member(D,C))) | (exists D (ilf_type(D,set_type) & member(D,B) & - member(D,C))) | (exists D (ilf_type(D,set_type) & - member(D,B) & member(D,C))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,set_type) | member(D,C) | - member(D,B))) | - =(C,B))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,set_type) | member(D,C) | - member(D,B))) | (exists D (ilf_type(D,set_type) & member(D,B) & - member(D,C))) | (exists D (ilf_type(D,set_type) & - member(D,B) & member(D,C))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | subset(B,C) | (exists D (ilf_type(D,set_type) & member(D,B) & - member(D,C))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,set_type) | - member(D,B) | member(D,C))) | - subset(B,C))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,set_type) | - member(D,B) | member(D,C))) | (exists D (ilf_type(D,set_type) & member(D,B) & - member(D,C))))))) & (all B (- ilf_type(B,set_type) | subset(B,B))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | member(B,power_set(C)) | (exists D (ilf_type(D,set_type) & member(D,B) & - member(D,C))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,set_type) | - member(D,B) | member(D,C))) | - member(B,power_set(C)))))) & (all B (- ilf_type(B,set_type) | - empty(power_set(B)))) & (all B (- ilf_type(B,set_type) | ilf_type(power_set(B),set_type))) & (all B (- ilf_type(B,set_type) | (all C (empty(C) | - ilf_type(C,set_type) | ilf_type(B,member_type(C)) | - member(B,C))))) & (all B (- ilf_type(B,set_type) | (all C (empty(C) | - ilf_type(C,set_type) | member(B,C) | - ilf_type(B,member_type(C)))))) & (all B (empty(B) | - ilf_type(B,set_type) | (exists C ilf_type(C,member_type(B))))) & (all B (- ilf_type(B,set_type) | relation_like(B) | (exists C (ilf_type(C,set_type) & member(C,B) & (all D (- ilf_type(D,set_type) | (all E (- ilf_type(E,set_type) | - =(ordered_pair(D,E),C))))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | - member(C,B) | (exists D (ilf_type(D,set_type) & (exists E (ilf_type(E,set_type) & =(ordered_pair(D,E),C))))))) | - relation_like(B))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | - member(C,B) | (exists D (ilf_type(D,set_type) & (exists E (ilf_type(E,set_type) & =(ordered_pair(D,E),C))))))) | (exists C (ilf_type(C,set_type) & member(C,B) & (all D (- ilf_type(D,set_type) | (all E (- ilf_type(E,set_type) | - =(ordered_pair(D,E),C))))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,subset_type(cross_product(B,C))) | relation_like(D))))))) & (all B (- ilf_type(B,set_type) | empty(B) | (exists C (ilf_type(C,set_type) & member(C,B))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | - member(C,B))) | - empty(B))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | - member(C,B))) | (exists C (ilf_type(C,set_type) & member(C,B))))) & (all B (- empty(B) | - ilf_type(B,set_type) | relation_like(B))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,relation_type(B,C)) | =(domain(B,C,D),domain_of(D)))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,relation_type(B,C)) | ilf_type(domain(B,C,D),subset_type(B)))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,relation_type(B,C)) | =(range(B,C,D),range_of(D)))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,relation_type(B,C)) | ilf_type(range(B,C,D),subset_type(C)))))))) & (all B ilf_type(B,set_type)) & (exists B (ilf_type(B,set_type) & (exists C (ilf_type(C,set_type) & (exists D (ilf_type(D,relation_type(B,C)) & (exists E (ilf_type(E,set_type) & member(E,C) & (all F (- ilf_type(F,set_type) | - member(ordered_pair(F,E),D))))) & =(range(B,C,D),C)))))))). Max_seconds is 117 for this subproblem. Child search process 23980 started. ============================== PROCESS INITIAL CLAUSES =============== % Clauses before input processing: formulas(usable). end_of_list. formulas(sos). -ilf_type(A,binary_relation_type) | -ilf_type(B,set_type) | member(B,range_of(A)) | -ilf_type(C,set_type) | -member(ordered_pair(C,B),A). [assumption]. -ilf_type(A,binary_relation_type) | -ilf_type(B,set_type) | ilf_type(f1(A,B),set_type) | -member(B,range_of(A)). [assumption]. -ilf_type(A,binary_relation_type) | -ilf_type(B,set_type) | member(ordered_pair(f1(A,B),B),A) | -member(B,range_of(A)). [assumption]. -ilf_type(A,binary_relation_type) | -ilf_type(B,set_type) | ilf_type(f2(A,B),set_type) | -ilf_type(C,set_type) | -member(ordered_pair(C,B),A). [assumption]. -ilf_type(A,binary_relation_type) | -ilf_type(B,set_type) | member(ordered_pair(f2(A,B),B),A) | -ilf_type(C,set_type) | -member(ordered_pair(C,B),A). [assumption]. -ilf_type(A,binary_relation_type) | ilf_type(range_of(A),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,binary_relation_type) | -member(ordered_pair(A,B),C) | member(A,domain_of(C)). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,binary_relation_type) | -member(ordered_pair(A,B),C) | member(B,range_of(C)). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(f3(A,B),set_type) | ilf_type(f4(A,B),set_type) | B = A. [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(f3(A,B),set_type) | -member(f4(A,B),A) | B = A. [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(f3(A,B),set_type) | member(f4(A,B),B) | B = A. [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(f3(A,B),A) | ilf_type(f4(A,B),set_type) | B = A. [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(f3(A,B),A) | -member(f4(A,B),A) | B = A. [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(f3(A,B),A) | member(f4(A,B),B) | B = A. [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(f3(A,B),B) | ilf_type(f4(A,B),set_type) | B = A. [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(f3(A,B),B) | -member(f4(A,B),A) | B = A. [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(f3(A,B),B) | member(f4(A,B),B) | B = A. [assumption]. -ilf_type(A,set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(ordered_pair(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,subset_type(cross_product(A,B))) | ilf_type(C,relation_type(A,B)). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,relation_type(A,B)) | ilf_type(C,subset_type(cross_product(A,B))). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(f5(A,B),relation_type(B,A)). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | -subset(A,B) | -subset(B,A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(A,B) | B != A. [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(B,A) | B != A. [assumption]. -ilf_type(A,binary_relation_type) | ilf_type(domain_of(A),set_type). [assumption]. -ilf_type(A,set_type) | ilf_type(singleton(A),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(cross_product(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(unordered_pair(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | unordered_pair(B,A) = unordered_pair(A,B). [assumption]. -ilf_type(A,set_type) | ilf_type(A,binary_relation_type) | -relation_like(A). [assumption]. -ilf_type(A,set_type) | relation_like(A) | -ilf_type(A,binary_relation_type). [assumption]. ilf_type(c1,binary_relation_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(B,subset_type(A)) | -ilf_type(B,member_type(power_set(A))). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(B,member_type(power_set(A))) | -ilf_type(B,subset_type(A)). [assumption]. -ilf_type(A,set_type) | ilf_type(f6(A),subset_type(A)). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | ilf_type(f7(A,B),set_type) | ilf_type(f8(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | ilf_type(f7(A,B),set_type) | -member(f8(A,B),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | ilf_type(f7(A,B),set_type) | member(f8(A,B),B). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | member(f7(A,B),A) | ilf_type(f8(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | member(f7(A,B),A) | -member(f8(A,B),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | member(f7(A,B),A) | member(f8(A,B),B). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | -member(f7(A,B),B) | ilf_type(f8(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | -member(f7(A,B),B) | -member(f8(A,B),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | -member(f7(A,B),B) | member(f8(A,B),B). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,A) | -member(C,B) | B != A. [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,A) | -member(C,B) | ilf_type(f9(A,B),set_type) | ilf_type(f10(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,A) | -member(C,B) | ilf_type(f9(A,B),set_type) | -member(f10(A,B),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,A) | -member(C,B) | ilf_type(f9(A,B),set_type) | member(f10(A,B),B). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,A) | -member(C,B) | member(f9(A,B),A) | ilf_type(f10(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,A) | -member(C,B) | member(f9(A,B),A) | -member(f10(A,B),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,A) | -member(C,B) | member(f9(A,B),A) | member(f10(A,B),B). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,A) | -member(C,B) | -member(f9(A,B),B) | ilf_type(f10(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,A) | -member(C,B) | -member(f9(A,B),B) | -member(f10(A,B),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,A) | -member(C,B) | -member(f9(A,B),B) | member(f10(A,B),B). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,B) | -member(C,A) | B != A. [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,B) | -member(C,A) | ilf_type(f11(A,B),set_type) | ilf_type(f12(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,B) | -member(C,A) | ilf_type(f11(A,B),set_type) | -member(f12(A,B),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,B) | -member(C,A) | ilf_type(f11(A,B),set_type) | member(f12(A,B),B). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,B) | -member(C,A) | member(f11(A,B),A) | ilf_type(f12(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,B) | -member(C,A) | member(f11(A,B),A) | -member(f12(A,B),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,B) | -member(C,A) | member(f11(A,B),A) | member(f12(A,B),B). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,B) | -member(C,A) | -member(f11(A,B),B) | ilf_type(f12(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,B) | -member(C,A) | -member(f11(A,B),B) | -member(f12(A,B),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | member(C,B) | -member(C,A) | -member(f11(A,B),B) | member(f12(A,B),B). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(A,B) | ilf_type(f13(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(A,B) | member(f13(A,B),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(A,B) | -member(f13(A,B),B). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | -member(C,A) | member(C,B) | -subset(A,B). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | -member(C,A) | member(C,B) | ilf_type(f14(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | -member(C,A) | member(C,B) | member(f14(A,B),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | -member(C,A) | member(C,B) | -member(f14(A,B),B). [assumption]. -ilf_type(A,set_type) | subset(A,A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(A,power_set(B)) | ilf_type(f15(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(A,power_set(B)) | member(f15(A,B),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(A,power_set(B)) | -member(f15(A,B),B). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | -member(C,A) | member(C,B) | -member(A,power_set(B)). [assumption]. -ilf_type(A,set_type) | -empty(power_set(A)). [assumption]. -ilf_type(A,set_type) | ilf_type(power_set(A),set_type). [assumption]. -ilf_type(A,set_type) | empty(B) | -ilf_type(B,set_type) | ilf_type(A,member_type(B)) | -member(A,B). [assumption]. -ilf_type(A,set_type) | empty(B) | -ilf_type(B,set_type) | member(A,B) | -ilf_type(A,member_type(B)). [assumption]. empty(A) | -ilf_type(A,set_type) | ilf_type(f16(A),member_type(A)). [assumption]. -ilf_type(A,set_type) | relation_like(A) | ilf_type(f17(A),set_type). [assumption]. -ilf_type(A,set_type) | relation_like(A) | member(f17(A),A). [assumption]. -ilf_type(A,set_type) | relation_like(A) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | ordered_pair(B,C) != f17(A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f18(A,B),set_type) | -relation_like(A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f19(A,B),set_type) | -relation_like(A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f18(A,B),f19(A,B)) = B | -relation_like(A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f20(A,B),set_type) | ilf_type(f22(A),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f20(A,B),set_type) | member(f22(A),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f20(A,B),set_type) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | ordered_pair(C,D) != f22(A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f21(A,B),set_type) | ilf_type(f22(A),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f21(A,B),set_type) | member(f22(A),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f21(A,B),set_type) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | ordered_pair(C,D) != f22(A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f20(A,B),f21(A,B)) = B | ilf_type(f22(A),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f20(A,B),f21(A,B)) = B | member(f22(A),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f20(A,B),f21(A,B)) = B | -ilf_type(C,set_type) | -ilf_type(D,set_type) | ordered_pair(C,D) != f22(A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,subset_type(cross_product(A,B))) | relation_like(C). [assumption]. -ilf_type(A,set_type) | empty(A) | ilf_type(f23(A),set_type). [assumption]. -ilf_type(A,set_type) | empty(A) | member(f23(A),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | -empty(A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f24(A),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | member(f24(A),A). [assumption]. -empty(A) | -ilf_type(A,set_type) | relation_like(A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,relation_type(A,B)) | domain(A,B,C) = domain_of(C). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,relation_type(A,B)) | ilf_type(domain(A,B,C),subset_type(A)). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,relation_type(A,B)) | range(A,B,C) = range_of(C). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,relation_type(A,B)) | ilf_type(range(A,B,C),subset_type(B)). [assumption]. ilf_type(A,set_type). [assumption]. ilf_type(c2,set_type). [assumption]. ilf_type(c3,set_type). [assumption]. ilf_type(c4,relation_type(c2,c3)). [assumption]. ilf_type(c5,set_type). [assumption]. member(c5,c3). [assumption]. -ilf_type(A,set_type) | -member(ordered_pair(A,c5),c4). [assumption]. range(c2,c3,c4) = c3. [assumption]. end_of_list. formulas(demodulators). end_of_list. ============================== PREDICATE ELIMINATION ================= Eliminating relation_like/1 1 -ilf_type(A,set_type) | relation_like(A) | -ilf_type(A,binary_relation_type). [assumption]. 2 -ilf_type(A,set_type) | ilf_type(A,binary_relation_type) | -relation_like(A). [assumption]. 3 -ilf_type(A,set_type) | relation_like(A) | ilf_type(f17(A),set_type). [assumption]. 4 -ilf_type(A,set_type) | relation_like(A) | member(f17(A),A). [assumption]. Derived: -ilf_type(A,set_type) | member(f17(A),A) | -ilf_type(A,set_type) | ilf_type(A,binary_relation_type). [resolve(4,b,2,c)]. 5 -ilf_type(A,set_type) | relation_like(A) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | ordered_pair(B,C) != f17(A). [assumption]. Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | ordered_pair(B,C) != f17(A) | -ilf_type(A,set_type) | ilf_type(A,binary_relation_type). [resolve(5,b,2,c)]. 6 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f18(A,B),set_type) | -relation_like(A). [assumption]. 7 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f19(A,B),set_type) | -relation_like(A). [assumption]. 8 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f18(A,B),f19(A,B)) = B | -relation_like(A). [assumption]. Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f18(A,B),f19(A,B)) = B | -ilf_type(A,set_type) | -ilf_type(A,binary_relation_type). [resolve(8,e,1,b)]. Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f18(A,B),f19(A,B)) = B | -ilf_type(A,set_type) | member(f17(A),A). [resolve(8,e,4,b)]. Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f18(A,B),f19(A,B)) = B | -ilf_type(A,set_type) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | ordered_pair(C,D) != f17(A). [resolve(8,e,5,b)]. 9 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,subset_type(cross_product(A,B))) | relation_like(C). [assumption]. Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,subset_type(cross_product(A,B))) | -ilf_type(C,set_type) | ilf_type(C,binary_relation_type). [resolve(9,d,2,c)]. Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,subset_type(cross_product(A,B))) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | -member(D,C) | ordered_pair(f18(C,D),f19(C,D)) = D. [resolve(9,d,8,e)]. 10 -empty(A) | -ilf_type(A,set_type) | relation_like(A). [assumption]. Derived: -empty(A) | -ilf_type(A,set_type) | -ilf_type(A,set_type) | ilf_type(A,binary_relation_type). [resolve(10,c,2,c)]. Derived: -empty(A) | -ilf_type(A,set_type) | -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f18(A,B),f19(A,B)) = B. [resolve(10,c,8,e)]. ============================== end predicate elimination ============= Term ordering decisions: Predicate symbol precedence: predicate_order([ =, empty, ilf_type, member, subset ]). Function symbol precedence: function_order([ set_type, binary_relation_type, c1, c2, c3, c4, c5, ordered_pair, relation_type, cross_product, unordered_pair, f1, f2, f3, f4, f5, f7, f8, f9, f10, f11, f12, f13, f14, f15, f18, f19, f20, f21, subset_type, power_set, range_of, member_type, domain_of, singleton, f6, f16, f17, f22, f23, f24, range, domain ]). After inverse_order: (no changes). Unfolding symbols: (none). Auto_inference settings: % set(paramodulation). % (positive equality literals) % set(binary_resolution). % (non-Horn) Auto_process settings: % set(factor). % (non-Horn) % set(unit_deletion). % (non-Horn) kept: 11 -ilf_type(A,binary_relation_type) | -ilf_type(B,set_type) | member(B,range_of(A)) | -ilf_type(C,set_type) | -member(ordered_pair(C,B),A). [assumption]. kept: 12 -ilf_type(A,binary_relation_type) | -ilf_type(B,set_type) | ilf_type(f1(A,B),set_type) | -member(B,range_of(A)). [assumption]. kept: 13 -ilf_type(A,binary_relation_type) | -ilf_type(B,set_type) | member(ordered_pair(f1(A,B),B),A) | -member(B,range_of(A)). [assumption]. kept: 14 -ilf_type(A,binary_relation_type) | -ilf_type(B,set_type) | ilf_type(f2(A,B),set_type) | -ilf_type(C,set_type) | -member(ordered_pair(C,B),A). [assumption]. kept: 15 -ilf_type(A,binary_relation_type) | -ilf_type(B,set_type) | member(ordered_pair(f2(A,B),B),A) | -ilf_type(C,set_type) | -member(ordered_pair(C,B),A). [assumption]. kept: 16 -ilf_type(A,binary_relation_type) | ilf_type(range_of(A),set_type). [assumption]. kept: 17 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,binary_relation_type) | -member(ordered_pair(A,B),C) | member(A,domain_of(C)). [assumption]. kept: 18 -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(f3(A,B),set_type) | ilf_type(f4(A,B),set_type) | B = A. [assumption]. kept: 19 -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(f3(A,B),set_type) | -member(f4(A,B),A) | B = A. [assumption]. kept: 20 -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(f3(A,B),set_type) | member(f4(A,B),B) | B = A. [assumption]. kept: 21 -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(f3(A,B),A) | ilf_type(f4(A,B),set_type) | B = A. [assumption]. kept: 22 -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(f3(A,B),A) | -member(f4(A,B),A) | B = A. [assumption]. kept: 23 -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(f3(A,B),A) | member(f4(A,B),B) | B = A. [assumption]. kept: 24 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(f3(A,B),B) | ilf_type(f4(A,B),set_type) | B = A. [assumption]. kept: 25 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(f3(A,B),B) | -member(f4(A,B),A) | B = A. [assumption]. kept: 26 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(f3(A,B),B) | member(f4(A,B),B) | B = A. [assumption]. kept: 27 -ilf_type(A,set_type). [assumption]. 28 -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(ordered_pair(A,B),set_type). [assumption]. 29 -ilf_type(A,binary_relation_type) | ilf_type(domain_of(A),set_type). [assumption]. kept: 30 -ilf_type(A,binary_relation_type). [copy(29),unit_del(b,27)]. 31 -ilf_type(A,set_type) | ilf_type(singleton(A),set_type). [assumption]. 32 -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(cross_product(A,B),set_type). [assumption]. 33 -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(unordered_pair(A,B),set_type). [assumption]. 34 ilf_type(c1,binary_relation_type). [assumption]. ============================== PROOF ================================= % Proof 1 at 0.01 (+ 0.00) seconds. % Length of proof is 5. % Level of proof is 2. % Maximum clause weight is 3.000. % Given clauses 0. 27 -ilf_type(A,set_type). [assumption]. 29 -ilf_type(A,binary_relation_type) | ilf_type(domain_of(A),set_type). [assumption]. 30 -ilf_type(A,binary_relation_type). [copy(29),unit_del(b,27)]. 34 ilf_type(c1,binary_relation_type). [assumption]. 35 $F. [copy(34),unit_del(a,30)]. ============================== end of proof ========================== ============================== STATISTICS ============================ Given=0. Generated=31. Kept=18. proofs=1. Usable=0. Sos=0. Demods=0. Limbo=18, Disabled=41. Hints=0. Kept_by_rule=0, Deleted_by_rule=0. Forward_subsumed=12. Back_subsumed=0. Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. New_demodulators=0 (0 lex), Back_demodulated=0. Back_unit_deleted=0. Demod_attempts=0. Demod_rewrites=0. Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. Nonunit_fsub_feature_tests=2. Nonunit_bsub_feature_tests=0. Megabytes=0.47. User_CPU=0.01, System_CPU=0.00, Wall_clock=4. ============================== end of statistics ===================== ============================== end of search ========================= Exiting with 1 proof. Process 23980 exit (max_proofs) Tue Nov 3 16:59:21 2009 ============================== end of multisearch ==================== All 6 subproblems have been proved, so we are done. Total user_CPU=3.84, system_CPU=0.32, wall_clock=4. THEOREM PROVED Exiting. Process 23974 exit (max_proofs) Tue Nov 3 16:59:21 2009