============================== FOF-Prover9 =========================== FOF-Prover9 (32) version March-2007, March 2007. Process 20966 was started by mccune on cleo, Mon Mar 19 17:01:34 2007 The command was "/home/mccune/bin/fof-prover9 -f SET668+3.in". ============================== end of head =========================== ============================== INPUT ================================= % Reading from file SET668+3.in set(prolog_style_variables). formulas(assumptions). (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (subset(B,C) & subset(C,B) -> 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,relation_type(B,C)) -> (subset(identity_relation_of(D),E) -> subset(D,domain(B,C,E)) & subset(D,range(B,C,E))))))))))). (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,set_type) -> (member(ordered_pair(C,D),identity_relation_of(B)) <-> member(C,B) & C = D))))))). (all B (ilf_type(B,set_type) -> ilf_type(identity_relation_of(B),binary_relation_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) -> (subset(B,C) <-> (all D (ilf_type(D,set_type) -> (member(D,B) -> member(D,C))))))))). (all B (ilf_type(B,binary_relation_type) -> (all C (ilf_type(C,binary_relation_type) -> (subset(B,C) <-> (all D (ilf_type(D,set_type) -> (all E (ilf_type(E,set_type) -> (member(ordered_pair(D,E),B) -> member(ordered_pair(D,E),C))))))))))). (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) -> (all C (ilf_type(C,set_type) -> ilf_type(cross_product(B,C),set_type))))). (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) -> ilf_type(ordered_pair(B,C),set_type))))). (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) -> subset(B,B))). (all B (ilf_type(B,binary_relation_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(C,B)) -> (subset(identity_relation_of(C),D) -> C = domain(C,B,D) & subset(C,range(C,B,D))))))))). end_of_list. ============================== end of input ========================== % clear(auto_denials), because it is incompatiable with FOF reduction. Attempting problem reduction; original problem has = <482,104>. Problem reduction (0.00 sec) gives 2 independent subproblems: ( <641,82> <641,82> ). Max nnf_size of subproblems is 641; max cnf_max is 82. ============================== FOF REDUCTION MULTISEARCH ============= Subproblem 1 of 2 (negated): ((all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | - subset(B,C) | - subset(C,B) | =(C,B))))) & (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,relation_type(B,C)) | - subset(identity_relation_of(D),E) | subset(D,domain(B,C,E)))))))))) & (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,relation_type(B,C)) | - subset(identity_relation_of(D),E) | subset(D,range(B,C,E)))))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | - member(C,B) | (all D (- ilf_type(D,set_type) | member(ordered_pair(C,D),identity_relation_of(B)) | - =(D,C))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | member(C,B) | (all D (- ilf_type(D,set_type) | - member(ordered_pair(C,D),identity_relation_of(B)))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,set_type) | =(D,C) | - member(ordered_pair(C,D),identity_relation_of(B)))))))) & (all B (- ilf_type(B,set_type) | ilf_type(identity_relation_of(B),binary_relation_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) | 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,binary_relation_type) | (all C (- ilf_type(C,binary_relation_type) | subset(B,C) | (exists D (ilf_type(D,set_type) & (exists E (ilf_type(E,set_type) & member(ordered_pair(D,E),B) & - member(ordered_pair(D,E),C))))))))) & (all B (- ilf_type(B,binary_relation_type) | (all C (- ilf_type(C,binary_relation_type) | (all D (- ilf_type(D,set_type) | (all E (- ilf_type(E,set_type) | - member(ordered_pair(D,E),B) | member(ordered_pair(D,E),C))))) | - subset(B,C))))) & (all B (- ilf_type(B,binary_relation_type) | (all C (- ilf_type(C,binary_relation_type) | (all D (- ilf_type(D,set_type) | (all E (- ilf_type(E,set_type) | - member(ordered_pair(D,E),B) | member(ordered_pair(D,E),C))))) | (exists D (ilf_type(D,set_type) & (exists E (ilf_type(E,set_type) & member(ordered_pair(D,E),B) & - member(ordered_pair(D,E),C))))))))) & (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) | (all C (- ilf_type(C,set_type) | ilf_type(cross_product(B,C),set_type))))) & (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) | ilf_type(ordered_pair(B,C),set_type))))) & (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) | subset(B,B))) & (all B (- ilf_type(B,binary_relation_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_of(D),domain(B,C,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_of(D),range(B,C,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(C,B)) & subset(identity_relation_of(C),D) & - =(domain(C,B,D),C)))))))). Child search process 20967 started. ============================== PROCESS INITIAL CLAUSES =============== % Clauses before input processing: formulas(usable). end_of_list. formulas(sos). -ilf_type(A,set_type) | -ilf_type(B,set_type) | -subset(A,B) | -subset(B,A) | B = A. [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | -ilf_type(D,relation_type(A,B)) | -subset(identity_relation_of(C),D) | subset(C,domain(A,B,D)). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | -ilf_type(D,relation_type(A,B)) | -subset(identity_relation_of(C),D) | subset(C,range(A,B,D)). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | -ilf_type(C,set_type) | member(ordered_pair(B,C),identity_relation_of(A)) | C != B. [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(B,A) | -ilf_type(C,set_type) | -member(ordered_pair(B,C),identity_relation_of(A)). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | C = B | -member(ordered_pair(B,C),identity_relation_of(A)). [assumption]. -ilf_type(A,set_type) | ilf_type(identity_relation_of(A),binary_relation_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(f1(A,B),relation_type(B,A)). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(A,B) | ilf_type(f2(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(A,B) | member(f2(A,B),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(A,B) | -member(f2(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(f3(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(f3(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(f3(A,B),B). [assumption]. -ilf_type(A,binary_relation_type) | -ilf_type(B,binary_relation_type) | subset(A,B) | ilf_type(f4(A,B),set_type). [assumption]. -ilf_type(A,binary_relation_type) | -ilf_type(B,binary_relation_type) | subset(A,B) | ilf_type(f5(A,B),set_type). [assumption]. -ilf_type(A,binary_relation_type) | -ilf_type(B,binary_relation_type) | subset(A,B) | member(ordered_pair(f4(A,B),f5(A,B)),A). [assumption]. -ilf_type(A,binary_relation_type) | -ilf_type(B,binary_relation_type) | subset(A,B) | -member(ordered_pair(f4(A,B),f5(A,B)),B). [assumption]. -ilf_type(A,binary_relation_type) | -ilf_type(B,binary_relation_type) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | -member(ordered_pair(C,D),A) | member(ordered_pair(C,D),B) | -subset(A,B). [assumption]. -ilf_type(A,binary_relation_type) | -ilf_type(B,binary_relation_type) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | -member(ordered_pair(C,D),A) | member(ordered_pair(C,D),B) | ilf_type(f6(A,B),set_type). [assumption]. -ilf_type(A,binary_relation_type) | -ilf_type(B,binary_relation_type) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | -member(ordered_pair(C,D),A) | member(ordered_pair(C,D),B) | ilf_type(f7(A,B),set_type). [assumption]. -ilf_type(A,binary_relation_type) | -ilf_type(B,binary_relation_type) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | -member(ordered_pair(C,D),A) | member(ordered_pair(C,D),B) | member(ordered_pair(f6(A,B),f7(A,B)),A). [assumption]. -ilf_type(A,binary_relation_type) | -ilf_type(B,binary_relation_type) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | -member(ordered_pair(C,D),A) | member(ordered_pair(C,D),B) | -member(ordered_pair(f6(A,B),f7(A,B)),B). [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(B,set_type) | ilf_type(cross_product(A,B),set_type). [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(ordered_pair(A,B),set_type). [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(f8(A),subset_type(A)). [assumption]. -ilf_type(A,set_type) | subset(A,A). [assumption]. -ilf_type(A,binary_relation_type) | subset(A,A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(A,power_set(B)) | ilf_type(f9(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(A,power_set(B)) | member(f9(A,B),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(A,power_set(B)) | -member(f9(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(f10(A),member_type(A)). [assumption]. -ilf_type(A,set_type) | relation_like(A) | ilf_type(f11(A),set_type). [assumption]. -ilf_type(A,set_type) | relation_like(A) | member(f11(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) != f11(A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f12(A,B),set_type) | -relation_like(A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f13(A,B),set_type) | -relation_like(A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f12(A,B),f13(A,B)) = B | -relation_like(A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f14(A,B),set_type) | ilf_type(f16(A),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f14(A,B),set_type) | member(f16(A),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f14(A,B),set_type) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | ordered_pair(C,D) != f16(A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f15(A,B),set_type) | ilf_type(f16(A),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f15(A,B),set_type) | member(f16(A),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f15(A,B),set_type) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | ordered_pair(C,D) != f16(A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f14(A,B),f15(A,B)) = B | ilf_type(f16(A),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f14(A,B),f15(A,B)) = B | member(f16(A),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f14(A,B),f15(A,B)) = B | -ilf_type(C,set_type) | -ilf_type(D,set_type) | ordered_pair(C,D) != f16(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(f17(A),set_type). [assumption]. -ilf_type(A,set_type) | empty(A) | member(f17(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(f18(A),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | member(f18(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_of(C) = domain(A,B,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_of(C) = range(A,B,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(c3,c2)). [assumption]. subset(identity_relation_of(c3),c4). [assumption]. domain(c3,c2,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(f11(A),set_type). [assumption]. 4 -ilf_type(A,set_type) | relation_like(A) | member(f11(A),A). [assumption]. Derived: -ilf_type(A,set_type) | member(f11(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) != f11(A). [assumption]. Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | ordered_pair(B,C) != f11(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(f12(A,B),set_type) | -relation_like(A). [assumption]. 7 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f13(A,B),set_type) | -relation_like(A). [assumption]. 8 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f12(A,B),f13(A,B)) = B | -relation_like(A). [assumption]. Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f12(A,B),f13(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(f12(A,B),f13(A,B)) = B | -ilf_type(A,set_type) | member(f11(A),A). [resolve(8,e,4,b)]. Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f12(A,B),f13(A,B)) = B | -ilf_type(A,set_type) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | ordered_pair(C,D) != f11(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(f12(C,D),f13(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(f12(A,B),f13(A,B)) = B. [resolve(10,c,8,e)]. ============================== end predicate elimination ============= Term ordering decisions: Relation symbol precedence: lex([ empty, ilf_type, member, subset, =, relation_like ]). Function symbol precedence: lex([ set_type, binary_relation_type, c1, c2, c3, c4, ordered_pair, relation_type, cross_product, f1, f2, f3, f4, f5, f6, f7, f9, f12, f13, f14, f15, subset_type, identity_relation_of, power_set, member_type, domain_of, range_of, f8, f10, f11, f16, f17, f18, domain, range ]). After inverse_order: (no changes). Unfolding symbols: (none). Auto_inference settings: % set(paramodulation). % (positive equality literals) % set(paramodulation) -> set(back_demod). % set(binary_resolution). % (non-Horn) % set(neg_ur_resolution). % (non-Horn, less than 100 clauses) Auto_process settings: % set(factor). % (non-Horn) % set(back_unit_deletion). % (non-Horn) % set(back_unit_deletion) -> set(unit_deletion). ============================== end of process initial clauses ======== ============================== CLAUSES FOR SEARCH ==================== % Clauses after input processing: formulas(usable). end_of_list. formulas(sos). 30 -ilf_type(A,binary_relation_type) | -ilf_type(B,binary_relation_type) | subset(A,B) | member(ordered_pair(f4(A,B),f5(A,B)),A). [assumption]. 31 -ilf_type(A,binary_relation_type) | -ilf_type(B,binary_relation_type) | subset(A,B) | -member(ordered_pair(f4(A,B),f5(A,B)),B). [assumption]. 43 ilf_type(c1,binary_relation_type). [assumption]. 81 ilf_type(A,set_type). [assumption]. 82 ilf_type(c4,relation_type(c3,c2)). [assumption]. 83 subset(identity_relation_of(c3),c4). [assumption]. 84 domain(c3,c2,c4) != c3. [assumption]. 86 member(f11(A),A) | ilf_type(A,binary_relation_type). [copy(85),merge(c),unit_del(a,81)]. 88 f11(A) != ordered_pair(B,C) | ilf_type(A,binary_relation_type). [copy(87),flip(d),merge(e),unit_del(a,81),unit_del(b,81),unit_del(c,81)]. 90 -member(A,B) | ordered_pair(f12(B,A),f13(B,A)) = A | -ilf_type(B,binary_relation_type). [copy(89),merge(e),unit_del(a,81),unit_del(b,81)]. 92 -member(A,B) | ordered_pair(f12(B,A),f13(B,A)) = A | member(f11(B),B). [copy(91),merge(e),unit_del(a,81),unit_del(b,81)]. 94 -member(A,B) | ordered_pair(f12(B,A),f13(B,A)) = A | f11(B) != ordered_pair(C,D). [copy(93),flip(h),merge(e),unit_del(a,81),unit_del(b,81),unit_del(e,81),unit_del(f,81)]. 96 -ilf_type(A,subset_type(cross_product(B,C))) | ilf_type(A,binary_relation_type). [copy(95),unit_del(a,81),unit_del(b,81),unit_del(d,81)]. 98 -ilf_type(A,subset_type(cross_product(B,C))) | -member(D,A) | ordered_pair(f12(A,D),f13(A,D)) = D. [copy(97),unit_del(a,81),unit_del(b,81),unit_del(d,81),unit_del(e,81)]. 100 -empty(A) | ilf_type(A,binary_relation_type). [copy(99),merge(c),unit_del(b,81)]. 111 -member(A,B) | member(ordered_pair(A,A),identity_relation_of(B)). [factor(14,b,d),xx(e),unit_del(a,81),unit_del(b,81)]. 131 subset(A,A). [factor(37,a,b),xx(c),unit_del(a,81)]. 138 -member(power_set(A),power_set(A)) | member(power_set(A),A). [factor(52,d,f),merge(c),unit_del(a,81),unit_del(b,81)]. 154 -ilf_type(A,relation_type(B,C)) | ilf_type(range(B,C,A),subset_type(C)). [back_unit_del(80),unit_del(a,81),unit_del(b,81)]. 155 -ilf_type(A,relation_type(B,C)) | range(B,C,A) = range_of(A). [back_unit_del(79),unit_del(a,81),unit_del(b,81)]. 156 -ilf_type(A,relation_type(B,C)) | ilf_type(domain(B,C,A),subset_type(B)). [back_unit_del(77),unit_del(a,81),unit_del(b,81)]. 157 -ilf_type(A,relation_type(B,C)) | domain(B,C,A) = domain_of(A). [back_unit_del(76),unit_del(a,81),unit_del(b,81)]. 158 -member(A,B) | member(f18(B),B). [back_unit_del(74),unit_del(a,81),unit_del(b,81)]. 159 -member(A,B) | -empty(B). [back_unit_del(72),unit_del(a,81),unit_del(b,81)]. 160 empty(A) | member(f17(A),A). [back_unit_del(71),unit_del(a,81)]. 161 -member(A,B) | ordered_pair(f14(B,A),f15(B,A)) = A | f16(B) != ordered_pair(C,D). [back_unit_del(69),unit_del(a,81),unit_del(b,81),unit_del(e,81),unit_del(f,81)]. 162 -member(A,B) | ordered_pair(f14(B,A),f15(B,A)) = A | member(f16(B),B). [back_unit_del(67),unit_del(a,81),unit_del(b,81)]. 163 empty(A) | ilf_type(f10(A),member_type(A)). [back_unit_del(57),unit_del(b,81)]. 164 empty(A) | member(B,A) | -ilf_type(B,member_type(A)). [back_unit_del(56),unit_del(a,81),unit_del(c,81)]. 165 empty(A) | ilf_type(B,member_type(A)) | -member(B,A). [back_unit_del(55),unit_del(a,81),unit_del(c,81)]. 166 -empty(power_set(A)). [back_unit_del(53),unit_del(a,81)]. 167 -member(A,B) | member(A,C) | -member(B,power_set(C)). [back_unit_del(52),unit_del(a,81),unit_del(b,81),unit_del(c,81)]. 168 member(A,power_set(B)) | -member(f9(A,B),B). [back_unit_del(51),unit_del(a,81),unit_del(b,81)]. 169 member(A,power_set(B)) | member(f9(A,B),A). [back_unit_del(50),unit_del(a,81),unit_del(b,81)]. 170 ilf_type(f8(A),subset_type(A)). [back_unit_del(46),unit_del(a,81)]. 171 ilf_type(A,member_type(power_set(B))) | -ilf_type(A,subset_type(B)). [back_unit_del(45),unit_del(a,81),unit_del(b,81)]. 172 ilf_type(A,subset_type(B)) | -ilf_type(A,member_type(power_set(B))). [back_unit_del(44),unit_del(a,81),unit_del(b,81)]. 173 subset(A,B) | A != B. [back_unit_del(38),unit_del(a,81),unit_del(b,81)]. 174 subset(A,B) | B != A. [back_unit_del(37),unit_del(a,81),unit_del(b,81)]. 175 -ilf_type(A,binary_relation_type) | -ilf_type(B,binary_relation_type) | -member(ordered_pair(C,D),A) | member(ordered_pair(C,D),B) | -member(ordered_pair(f6(A,B),f7(A,B)),B). [back_unit_del(36),unit_del(c,81),unit_del(d,81)]. 176 -ilf_type(A,binary_relation_type) | -ilf_type(B,binary_relation_type) | -member(ordered_pair(C,D),A) | member(ordered_pair(C,D),B) | member(ordered_pair(f6(A,B),f7(A,B)),A). [back_unit_del(35),unit_del(c,81),unit_del(d,81)]. 178 -member(A,B) | member(A,C) | -member(f3(B,C),C). [back_unit_del(27),unit_del(a,81),unit_del(b,81),unit_del(c,81)]. 179 -member(A,B) | member(A,C) | member(f3(B,C),B). [back_unit_del(26),unit_del(a,81),unit_del(b,81),unit_del(c,81)]. 180 -member(A,B) | member(A,C) | -subset(B,C). [back_unit_del(24),unit_del(a,81),unit_del(b,81),unit_del(c,81)]. 181 subset(A,B) | -member(f2(A,B),B). [back_unit_del(23),unit_del(a,81),unit_del(b,81)]. 182 subset(A,B) | member(f2(A,B),A). [back_unit_del(22),unit_del(a,81),unit_del(b,81)]. 183 ilf_type(f1(A,B),relation_type(B,A)). [back_unit_del(20),unit_del(a,81),unit_del(b,81)]. 184 -ilf_type(A,relation_type(B,C)) | ilf_type(A,subset_type(cross_product(B,C))). [back_unit_del(19),unit_del(a,81),unit_del(b,81)]. 185 -ilf_type(A,subset_type(cross_product(B,C))) | ilf_type(A,relation_type(B,C)). [back_unit_del(18),unit_del(a,81),unit_del(b,81)]. 186 ilf_type(identity_relation_of(A),binary_relation_type). [back_unit_del(17),unit_del(a,81)]. 187 A = B | -member(ordered_pair(B,A),identity_relation_of(C)). [back_unit_del(16),unit_del(a,81),unit_del(b,81),unit_del(c,81)]. 188 member(A,B) | -member(ordered_pair(A,C),identity_relation_of(B)). [back_unit_del(15),unit_del(a,81),unit_del(b,81),unit_del(d,81)]. 189 -member(A,B) | member(ordered_pair(A,C),identity_relation_of(B)) | C != A. [back_unit_del(14),unit_del(a,81),unit_del(b,81),unit_del(d,81)]. 190 -ilf_type(A,relation_type(B,C)) | -subset(identity_relation_of(D),A) | subset(D,range(B,C,A)). [back_unit_del(13),unit_del(a,81),unit_del(b,81),unit_del(c,81)]. 191 -ilf_type(A,relation_type(B,C)) | -subset(identity_relation_of(D),A) | subset(D,domain(B,C,A)). [back_unit_del(12),unit_del(a,81),unit_del(b,81),unit_del(c,81)]. 192 -subset(A,B) | -subset(B,A) | B = A. [back_unit_del(11),unit_del(a,81),unit_del(b,81)]. end_of_list. formulas(demodulators). end_of_list. ============================== end of clauses for search ============= ============================== SEARCH ================================ % Starting search at 0.02 seconds. given #1 (I,wt=18): 30 -ilf_type(A,binary_relation_type) | -ilf_type(B,binary_relation_type) | subset(A,B) | member(ordered_pair(f4(A,B),f5(A,B)),A). [assumption]. given #2 (I,wt=18): 31 -ilf_type(A,binary_relation_type) | -ilf_type(B,binary_relation_type) | subset(A,B) | -member(ordered_pair(f4(A,B),f5(A,B)),B). [assumption]. given #3 (I,wt=3): 43 ilf_type(c1,binary_relation_type). [assumption]. given #4 (I,wt=3): 81 ilf_type(A,set_type). [assumption]. given #5 (I,wt=5): 82 ilf_type(c4,relation_type(c3,c2)). [assumption]. given #6 (I,wt=4): 83 subset(identity_relation_of(c3),c4). [assumption]. given #7 (I,wt=6): 84 domain(c3,c2,c4) != c3. [assumption]. given #8 (I,wt=7): 86 member(f11(A),A) | ilf_type(A,binary_relation_type). [copy(85),merge(c),unit_del(a,81)]. given #9 (I,wt=9): 88 f11(A) != ordered_pair(B,C) | ilf_type(A,binary_relation_type). [copy(87),flip(d),merge(e),unit_del(a,81),unit_del(b,81),unit_del(c,81)]. given #10 (I,wt=15): 90 -member(A,B) | ordered_pair(f12(B,A),f13(B,A)) = A | -ilf_type(B,binary_relation_type). [copy(89),merge(e),unit_del(a,81),unit_del(b,81)]. given #11 (I,wt=16): 92 -member(A,B) | ordered_pair(f12(B,A),f13(B,A)) = A | member(f11(B),B). [copy(91),merge(e),unit_del(a,81),unit_del(b,81)]. given #12 (I,wt=18): 94 -member(A,B) | ordered_pair(f12(B,A),f13(B,A)) = A | f11(B) != ordered_pair(C,D). [copy(93),flip(h),merge(e),unit_del(a,81),unit_del(b,81),unit_del(e,81),unit_del(f,81)]. given #13 (I,wt=9): 96 -ilf_type(A,subset_type(cross_product(B,C))) | ilf_type(A,binary_relation_type). [copy(95),unit_del(a,81),unit_del(b,81),unit_del(d,81)]. given #14 (I,wt=18): 98 -ilf_type(A,subset_type(cross_product(B,C))) | -member(D,A) | ordered_pair(f12(A,D),f13(A,D)) = D. [copy(97),unit_del(a,81),unit_del(b,81),unit_del(d,81),unit_del(e,81)]. given #15 (I,wt=5): 100 -empty(A) | ilf_type(A,binary_relation_type). [copy(99),merge(c),unit_del(b,81)]. given #16 (I,wt=9): 111 -member(A,B) | member(ordered_pair(A,A),identity_relation_of(B)). [factor(14,b,d),xx(e),unit_del(a,81),unit_del(b,81)]. given #17 (I,wt=3): 131 subset(A,A). [factor(37,a,b),xx(c),unit_del(a,81)]. given #18 (I,wt=9): 138 -member(power_set(A),power_set(A)) | member(power_set(A),A). [factor(52,d,f),merge(c),unit_del(a,81),unit_del(b,81)]. given #19 (I,wt=12): 154 -ilf_type(A,relation_type(B,C)) | ilf_type(range(B,C,A),subset_type(C)). [back_unit_del(80),unit_del(a,81),unit_del(b,81)]. given #20 (I,wt=12): 155 -ilf_type(A,relation_type(B,C)) | range(B,C,A) = range_of(A). [back_unit_del(79),unit_del(a,81),unit_del(b,81)]. given #21 (I,wt=12): 156 -ilf_type(A,relation_type(B,C)) | ilf_type(domain(B,C,A),subset_type(B)). [back_unit_del(77),unit_del(a,81),unit_del(b,81)]. given #22 (I,wt=12): 157 -ilf_type(A,relation_type(B,C)) | domain(B,C,A) = domain_of(A). [back_unit_del(76),unit_del(a,81),unit_del(b,81)]. given #23 (I,wt=7): 158 -member(A,B) | member(f18(B),B). [back_unit_del(74),unit_del(a,81),unit_del(b,81)]. given #24 (I,wt=5): 159 -member(A,B) | -empty(B). [back_unit_del(72),unit_del(a,81),unit_del(b,81)]. given #25 (I,wt=6): 160 empty(A) | member(f17(A),A). [back_unit_del(71),unit_del(a,81)]. given #26 (I,wt=18): 161 -member(A,B) | ordered_pair(f14(B,A),f15(B,A)) = A | f16(B) != ordered_pair(C,D). [back_unit_del(69),unit_del(a,81),unit_del(b,81),unit_del(e,81),unit_del(f,81)]. given #27 (I,wt=16): 162 -member(A,B) | ordered_pair(f14(B,A),f15(B,A)) = A | member(f16(B),B). [back_unit_del(67),unit_del(a,81),unit_del(b,81)]. given #28 (I,wt=7): 163 empty(A) | ilf_type(f10(A),member_type(A)). [back_unit_del(57),unit_del(b,81)]. given #29 (I,wt=9): 164 empty(A) | member(B,A) | -ilf_type(B,member_type(A)). [back_unit_del(56),unit_del(a,81),unit_del(c,81)]. given #30 (I,wt=9): 165 empty(A) | ilf_type(B,member_type(A)) | -member(B,A). [back_unit_del(55),unit_del(a,81),unit_del(c,81)]. given #31 (I,wt=3): 166 -empty(power_set(A)). [back_unit_del(53),unit_del(a,81)]. given #32 (I,wt=10): 167 -member(A,B) | member(A,C) | -member(B,power_set(C)). [back_unit_del(52),unit_del(a,81),unit_del(b,81),unit_del(c,81)]. given #33 (I,wt=9): 168 member(A,power_set(B)) | -member(f9(A,B),B). [back_unit_del(51),unit_del(a,81),unit_del(b,81)]. given #34 (I,wt=9): 169 member(A,power_set(B)) | member(f9(A,B),A). [back_unit_del(50),unit_del(a,81),unit_del(b,81)]. given #35 (I,wt=5): 170 ilf_type(f8(A),subset_type(A)). [back_unit_del(46),unit_del(a,81)]. given #36 (I,wt=9): 171 ilf_type(A,member_type(power_set(B))) | -ilf_type(A,subset_type(B)). [back_unit_del(45),unit_del(a,81),unit_del(b,81)]. given #37 (I,wt=9): 172 ilf_type(A,subset_type(B)) | -ilf_type(A,member_type(power_set(B))). [back_unit_del(44),unit_del(a,81),unit_del(b,81)]. given #38 (I,wt=6): 173 subset(A,B) | A != B. [back_unit_del(38),unit_del(a,81),unit_del(b,81)]. given #39 (I,wt=6): 174 subset(A,B) | B != A. [back_unit_del(37),unit_del(a,81),unit_del(b,81)]. given #40 (I,wt=25): 175 -ilf_type(A,binary_relation_type) | -ilf_type(B,binary_relation_type) | -member(ordered_pair(C,D),A) | member(ordered_pair(C,D),B) | -member(ordered_pair(f6(A,B),f7(A,B)),B). [back_unit_del(36),unit_del(c,81),unit_del(d,81)]. given #41 (I,wt=25): 176 -ilf_type(A,binary_relation_type) | -ilf_type(B,binary_relation_type) | -member(ordered_pair(C,D),A) | member(ordered_pair(C,D),B) | member(ordered_pair(f6(A,B),f7(A,B)),A). [back_unit_del(35),unit_del(c,81),unit_del(d,81)]. given #42 (I,wt=11): 178 -member(A,B) | member(A,C) | -member(f3(B,C),C). [back_unit_del(27),unit_del(a,81),unit_del(b,81),unit_del(c,81)]. given #43 (I,wt=11): 179 -member(A,B) | member(A,C) | member(f3(B,C),B). [back_unit_del(26),unit_del(a,81),unit_del(b,81),unit_del(c,81)]. given #44 (I,wt=9): 180 -member(A,B) | member(A,C) | -subset(B,C). [back_unit_del(24),unit_del(a,81),unit_del(b,81),unit_del(c,81)]. given #45 (I,wt=8): 181 subset(A,B) | -member(f2(A,B),B). [back_unit_del(23),unit_del(a,81),unit_del(b,81)]. given #46 (I,wt=8): 182 subset(A,B) | member(f2(A,B),A). [back_unit_del(22),unit_del(a,81),unit_del(b,81)]. given #47 (I,wt=7): 183 ilf_type(f1(A,B),relation_type(B,A)). [back_unit_del(20),unit_del(a,81),unit_del(b,81)]. given #48 (I,wt=11): 184 -ilf_type(A,relation_type(B,C)) | ilf_type(A,subset_type(cross_product(B,C))). [back_unit_del(19),unit_del(a,81),unit_del(b,81)]. given #49 (I,wt=11): 185 -ilf_type(A,subset_type(cross_product(B,C))) | ilf_type(A,relation_type(B,C)). [back_unit_del(18),unit_del(a,81),unit_del(b,81)]. given #50 (I,wt=4): 186 ilf_type(identity_relation_of(A),binary_relation_type). [back_unit_del(17),unit_del(a,81)]. given #51 (I,wt=9): 187 A = B | -member(ordered_pair(B,A),identity_relation_of(C)). [back_unit_del(16),unit_del(a,81),unit_del(b,81),unit_del(c,81)]. given #52 (I,wt=9): 188 member(A,B) | -member(ordered_pair(A,C),identity_relation_of(B)). [back_unit_del(15),unit_del(a,81),unit_del(b,81),unit_del(d,81)]. given #53 (I,wt=12): 189 -member(A,B) | member(ordered_pair(A,C),identity_relation_of(B)) | C != A. [back_unit_del(14),unit_del(a,81),unit_del(b,81),unit_del(d,81)]. given #54 (I,wt=15): 190 -ilf_type(A,relation_type(B,C)) | -subset(identity_relation_of(D),A) | subset(D,range(B,C,A)). [back_unit_del(13),unit_del(a,81),unit_del(b,81),unit_del(c,81)]. given #55 (I,wt=15): 191 -ilf_type(A,relation_type(B,C)) | -subset(identity_relation_of(D),A) | subset(D,domain(B,C,A)). [back_unit_del(12),unit_del(a,81),unit_del(b,81),unit_del(c,81)]. given #56 (I,wt=9): 192 -subset(A,B) | -subset(B,A) | B = A. [back_unit_del(11),unit_del(a,81),unit_del(b,81)]. given #57 (A,wt=15): 193 -ilf_type(A,binary_relation_type) | subset(A,c1) | member(ordered_pair(f4(A,c1),f5(A,c1)),A). [resolve(43,a,30,b)]. given #58 (F,wt=4): 202 domain_of(c4) != c3. [back_rewrite(84),rewrite(200(4))]. given #59 (F,wt=7): 260 -member(ordered_pair(c3,domain_of(c4)),identity_relation_of(A)). [ur(187,a,202,a)]. given #60 (F,wt=7): 261 -member(ordered_pair(domain_of(c4),c3),identity_relation_of(A)). [ur(187,a,202,a(flip))]. given #61 (F,wt=10): 262 -member(ordered_pair(ordered_pair(c3,domain_of(c4)),A),identity_relation_of(identity_relation_of(B))). [ur(188,a,260,a)]. given #62 (T,wt=4): 218 member(A,power_set(A)). [resolve(169,b,168,b),merge(b)]. given #63 (T,wt=5): 198 ilf_type(range_of(c4),subset_type(c2)). [back_rewrite(196),rewrite(197(4))]. given #64 (T,wt=5): 201 ilf_type(domain_of(c4),subset_type(c3)). [back_rewrite(199),rewrite(200(4))]. given #65 (T,wt=5): 270 ilf_type(A,member_type(power_set(A))). [resolve(218,a,165,c),unit_del(a,166)]. given #66 (A,wt=15): 194 -ilf_type(A,binary_relation_type) | subset(c1,A) | member(ordered_pair(f4(c1,A),f5(c1,A)),c1). [resolve(43,a,30,a)]. given #67 (F,wt=8): 278 -subset(power_set(ordered_pair(domain_of(c4),c3)),identity_relation_of(A)). [ur(180,a,218,a,b,261,a)]. given #68 (F,wt=8): 279 -subset(power_set(ordered_pair(c3,domain_of(c4))),identity_relation_of(A)). [ur(180,a,218,a,b,260,a)]. given #69 (F,wt=8): 292 power_set(ordered_pair(domain_of(c4),c3)) != identity_relation_of(A). [ur(174,a,278,a),flip(a)]. given #70 (F,wt=8): 295 power_set(ordered_pair(c3,domain_of(c4))) != identity_relation_of(A). [ur(174,a,279,a),flip(a)]. given #71 (T,wt=4): 288 ilf_type(A,subset_type(A)). [resolve(270,a,172,b)]. given #72 (T,wt=5): 301 ilf_type(cross_product(A,B),binary_relation_type). [resolve(288,a,96,a)]. given #73 (T,wt=6): 204 empty(A) | member(f18(A),A). [resolve(160,b,158,a)]. given #74 (T,wt=6): 211 empty(A) | member(f10(A),A). [resolve(164,c,163,b),merge(c)]. given #75 (A,wt=11): 195 member(ordered_pair(f11(A),f11(A)),identity_relation_of(A)) | ilf_type(A,binary_relation_type). [resolve(111,a,86,a)]. given #76 (F,wt=9): 284 -member(power_set(ordered_pair(domain_of(c4),c3)),power_set(identity_relation_of(A))). [ur(167,a,218,a,b,261,a)]. given #77 (F,wt=9): 285 -member(power_set(ordered_pair(c3,domain_of(c4))),power_set(identity_relation_of(A))). [ur(167,a,218,a,b,260,a)]. given #78 (F,wt=10): 263 -member(ordered_pair(ordered_pair(domain_of(c4),c3),A),identity_relation_of(identity_relation_of(B))). [ur(188,a,261,a)]. given #79 (F,wt=10): 339 -subset(power_set(power_set(ordered_pair(domain_of(c4),c3))),power_set(identity_relation_of(A))). [ur(180,a,218,a,b,284,a)]. given #80 (T,wt=6): 223 member(A,power_set(B)) | -empty(A). [resolve(169,b,159,a)]. given #81 (T,wt=6): 230 ilf_type(f8(cross_product(A,B)),binary_relation_type). [resolve(170,a,96,a)]. given #82 (T,wt=6): 231 ilf_type(f8(A),member_type(power_set(A))). [resolve(171,b,170,a)]. given #83 (T,wt=5): 361 member(f8(A),power_set(A)). [resolve(231,a,164,c),unit_del(a,166)]. given #84 (A,wt=7): 197 range(c3,c2,c4) = range_of(c4). [resolve(155,a,82,a)]. given #85 (F,wt=8): 375 -member(ordered_pair(domain_of(c4),c3),f8(identity_relation_of(A))). [ur(167,b,261,a,c,361,a)]. given #86 (F,wt=8): 376 -member(ordered_pair(c3,domain_of(c4)),f8(identity_relation_of(A))). [ur(167,b,260,a,c,361,a)]. given #87 (F,wt=9): 378 -subset(power_set(ordered_pair(domain_of(c4),c3)),f8(identity_relation_of(A))). [ur(180,a,218,a,b,375,a)]. given #88 (F,wt=9): 380 -member(ordered_pair(domain_of(c4),c3),f8(f8(identity_relation_of(A)))). [ur(167,b,375,a,c,361,a)]. given #89 (T,wt=6): 232 ilf_type(f10(power_set(A)),subset_type(A)). [resolve(172,b,163,b),unit_del(b,166)]. given #90 (T,wt=6): 246 ilf_type(c4,subset_type(cross_product(c3,c2))). [resolve(184,a,82,a)]. given #91 (T,wt=3): 399 ilf_type(c4,binary_relation_type). [resolve(246,a,96,a)]. given #92 (T,wt=6): 272 member(f18(power_set(A)),power_set(A)). [resolve(218,a,158,a)]. given #93 (A,wt=7): 200 domain(c3,c2,c4) = domain_of(c4). [resolve(157,a,82,a)]. given #94 (F,wt=9): 383 -subset(power_set(ordered_pair(c3,domain_of(c4))),f8(identity_relation_of(A))). [ur(180,a,218,a,b,376,a)]. given #95 (F,wt=9): 385 -member(ordered_pair(c3,domain_of(c4)),f8(f8(identity_relation_of(A)))). [ur(167,b,376,a,c,361,a)]. given #96 (F,wt=9): 389 f8(identity_relation_of(A)) != power_set(ordered_pair(domain_of(c4),c3)). [ur(174,a,378,a)]. given #97 (F,wt=9): 420 -member(ordered_pair(domain_of(c4),c3),f18(power_set(identity_relation_of(A)))). [ur(167,b,261,a,c,272,a)]. given #98 (T,wt=6): 286 ilf_type(range_of(c4),member_type(power_set(c2))). [resolve(198,a,171,b)]. given #99 (T,wt=5): 439 member(range_of(c4),power_set(c2)). [resolve(286,a,164,c),unit_del(a,166)]. given #100 (T,wt=6): 287 ilf_type(domain_of(c4),member_type(power_set(c3))). [resolve(201,a,171,b)]. given #101 (T,wt=5): 449 member(domain_of(c4),power_set(c3)). [resolve(287,a,164,c),unit_del(a,166)]. given #102 (A,wt=7): 203 member(f18(A),A) | ilf_type(A,binary_relation_type). [resolve(158,a,86,a)]. given #103 (F,wt=9): 421 -member(ordered_pair(c3,domain_of(c4)),f18(power_set(identity_relation_of(A)))). [ur(167,b,260,a,c,272,a)]. given #104 (F,wt=9): 424 f8(identity_relation_of(A)) != power_set(ordered_pair(c3,domain_of(c4))). [ur(174,a,383,a)]. given #105 (F,wt=10): 343 -ilf_type(power_set(ordered_pair(domain_of(c4),c3)),member_type(power_set(identity_relation_of(A)))). [ur(164,a,166,a,b,284,a)]. given #106 (F,wt=9): 472 -ilf_type(power_set(ordered_pair(domain_of(c4),c3)),subset_type(identity_relation_of(A))). [ur(171,a,343,a)]. given #107 (T,wt=6): 332 ilf_type(A,binary_relation_type) | -empty(identity_relation_of(A)). [resolve(195,a,159,a)]. given #108 (T,wt=7): 212 empty(A) | ilf_type(f17(A),member_type(A)). [resolve(165,c,160,b),merge(c)]. given #109 (T,wt=6): 473 ilf_type(f17(power_set(A)),subset_type(A)). [resolve(212,b,172,b),unit_del(a,166)]. given #110 (T,wt=7): 239 -member(A,identity_relation_of(c3)) | member(A,c4). [resolve(180,c,83,a)]. given #111 (A,wt=10): 205 empty(A) | member(ordered_pair(f17(A),f17(A)),identity_relation_of(A)). [resolve(160,b,111,a)]. given #112 (F,wt=10): 345 -subset(power_set(power_set(ordered_pair(c3,domain_of(c4)))),power_set(identity_relation_of(A))). [ur(180,a,218,a,b,285,a)]. given #113 (F,wt=10): 349 -ilf_type(power_set(ordered_pair(c3,domain_of(c4))),member_type(power_set(identity_relation_of(A)))). [ur(164,a,166,a,b,285,a)]. given #114 (F,wt=9): 499 -ilf_type(power_set(ordered_pair(c3,domain_of(c4))),subset_type(identity_relation_of(A))). [ur(171,a,349,a)]. given #115 (F,wt=10): 356 power_set(power_set(ordered_pair(domain_of(c4),c3))) != power_set(identity_relation_of(A)). [ur(174,a,339,a),flip(a)]. given #116 (T,wt=5): 490 empty(A) | -empty(identity_relation_of(A)). [resolve(205,b,159,a)]. given #117 (T,wt=7): 242 ilf_type(domain_of(f1(A,B)),subset_type(B)). [resolve(183,a,156,a),rewrite(241(2))]. given #118 (T,wt=7): 244 ilf_type(range_of(f1(A,B)),subset_type(A)). [resolve(183,a,154,a),rewrite(243(2))]. given #119 (T,wt=7): 273 member(ordered_pair(A,A),identity_relation_of(power_set(A))). [resolve(218,a,111,a)]. given #120 (A,wt=20): 206 empty(A) | -ilf_type(A,subset_type(cross_product(B,C))) | ordered_pair(f12(A,f17(A)),f13(A,f17(A))) = f17(A). [resolve(160,b,98,b)]. given #121 (F,wt=4): 502 -empty(identity_relation_of(power_set(A))). [ur(490,a,166,a)]. given #122 (F,wt=5): 536 -empty(identity_relation_of(identity_relation_of(power_set(A)))). [ur(490,a,502,a)]. given #123 (F,wt=6): 539 -empty(identity_relation_of(identity_relation_of(identity_relation_of(power_set(A))))). [ur(490,a,536,a)]. given #124 (F,wt=7): 544 -empty(identity_relation_of(identity_relation_of(identity_relation_of(identity_relation_of(power_set(A)))))). [ur(490,a,539,a)]. given #125 (T,wt=7): 300 ilf_type(cross_product(A,B),relation_type(A,B)). [resolve(288,a,185,a)]. given #126 (T,wt=7): 310 empty(A) | ilf_type(f18(A),member_type(A)). [resolve(204,b,165,c),merge(b)]. given #127 (T,wt=6): 558 ilf_type(f18(power_set(A)),subset_type(A)). [resolve(310,b,172,b),unit_del(a,166)]. given #128 (T,wt=7): 364 -member(A,f8(B)) | member(A,B). [resolve(361,a,167,c)]. given #129 (A,wt=18): 207 empty(A) | ordered_pair(f12(A,f17(A)),f13(A,f17(A))) = f17(A) | member(f11(A),A). [resolve(160,b,92,a)]. given #130 (F,wt=8): 549 -empty(identity_relation_of(identity_relation_of(identity_relation_of(identity_relation_of(identity_relation_of(power_set(A))))))). [ur(490,a,544,a)]. given #131 (F,wt=9): 537 -ilf_type(ordered_pair(domain_of(c4),c3),member_type(identity_relation_of(power_set(A)))). [ur(164,a,502,a,b,261,a)]. given #132 (F,wt=9): 538 -ilf_type(ordered_pair(c3,domain_of(c4)),member_type(identity_relation_of(power_set(A)))). [ur(164,a,502,a,b,260,a)]. given #133 (F,wt=9): 581 -empty(identity_relation_of(identity_relation_of(identity_relation_of(identity_relation_of(identity_relation_of(identity_relation_of(power_set(A)))))))). [ur(490,a,549,a)]. given #134 (T,wt=7): 396 ilf_type(f10(power_set(A)),member_type(power_set(A))). [resolve(232,a,171,b)]. given #135 (T,wt=6): 591 member(f10(power_set(A)),power_set(A)). [resolve(396,a,164,c),unit_del(a,166)]. given #136 (T,wt=7): 397 ilf_type(f10(power_set(cross_product(A,B))),binary_relation_type). [resolve(232,a,96,a)]. given #137 (T,wt=7): 398 ilf_type(c4,member_type(power_set(cross_product(c3,c2)))). [resolve(246,a,171,b)]. given #138 (A,wt=17): 208 empty(A) | ordered_pair(f12(A,f17(A)),f13(A,f17(A))) = f17(A) | -ilf_type(A,binary_relation_type). [resolve(160,b,90,a)]. given #139 (F,wt=9): 610 -member(ordered_pair(domain_of(c4),c3),f10(power_set(identity_relation_of(A)))). [ur(167,b,261,a,c,591,a)]. given #140 (F,wt=9): 611 -member(ordered_pair(c3,domain_of(c4)),f10(power_set(identity_relation_of(A)))). [ur(167,b,260,a,c,591,a)]. given #141 (F,wt=10): 371 -member(power_set(ordered_pair(c3,domain_of(c4))),f8(power_set(identity_relation_of(A)))). [ur(167,b,285,a,c,361,a)]. given #142 (F,wt=10): 372 -member(power_set(ordered_pair(domain_of(c4),c3)),f8(power_set(identity_relation_of(A)))). [ur(167,b,284,a,c,361,a)]. given #143 (T,wt=6): 616 member(c4,power_set(cross_product(c3,c2))). [resolve(398,a,164,c),unit_del(a,166)]. given #144 (T,wt=7): 407 ilf_type(f18(power_set(A)),member_type(power_set(A))). [resolve(272,a,165,c),unit_del(a,166)]. given #145 (T,wt=7): 442 -member(A,range_of(c4)) | member(A,c2). [resolve(439,a,167,c)]. given #146 (T,wt=7): 452 -member(A,domain_of(c4)) | member(A,c3). [resolve(449,a,167,c)]. given #147 (A,wt=18): 209 ordered_pair(f14(A,f17(A)),f15(A,f17(A))) = f17(A) | member(f16(A),A) | empty(A). [resolve(162,a,160,b)]. given #148 (F,wt=10): 381 -member(power_set(ordered_pair(domain_of(c4),c3)),power_set(f8(identity_relation_of(A)))). [ur(167,a,218,a,b,375,a)]. given #149 (F,wt=10): 386 -member(power_set(ordered_pair(c3,domain_of(c4))),power_set(f8(identity_relation_of(A)))). [ur(167,a,218,a,b,376,a)]. given #150 (F,wt=10): 391 -subset(power_set(ordered_pair(domain_of(c4),c3)),f8(f8(identity_relation_of(A)))). [ur(180,a,218,a,b,380,a)]. given #151 (F,wt=10): 393 -member(ordered_pair(domain_of(c4),c3),f8(f8(f8(identity_relation_of(A))))). [ur(167,b,380,a,c,361,a)]. given #152 (T,wt=7): 475 ilf_type(f17(power_set(A)),member_type(power_set(A))). [resolve(473,a,171,b)]. given #153 (T,wt=6): 709 member(f17(power_set(A)),power_set(A)). [resolve(475,a,164,c),unit_del(a,166)]. given #154 (T,wt=7): 476 ilf_type(f17(power_set(cross_product(A,B))),binary_relation_type). [resolve(473,a,96,a)]. given #155 (T,wt=7): 555 ilf_type(domain_of(cross_product(A,B)),subset_type(A)). [resolve(300,a,156,a),rewrite(554(2))]. given #156 (A,wt=19): 210 ordered_pair(f14(A,f11(A)),f15(A,f11(A))) = f11(A) | member(f16(A),A) | ilf_type(A,binary_relation_type). [resolve(162,a,86,a)]. given #157 (F,wt=9): 735 -member(ordered_pair(domain_of(c4),c3),f17(power_set(identity_relation_of(A)))). [ur(167,b,261,a,c,709,a)]. given #158 (F,wt=9): 736 -member(ordered_pair(c3,domain_of(c4)),f17(power_set(identity_relation_of(A)))). [ur(167,b,260,a,c,709,a)]. given #159 (F,wt=10): 414 -member(ordered_pair(c3,domain_of(c4)),f18(power_set(f8(identity_relation_of(A))))). [ur(167,b,376,a,c,272,a)]. given #160 (F,wt=10): 415 -member(ordered_pair(domain_of(c4),c3),f18(power_set(f8(identity_relation_of(A))))). [ur(167,b,375,a,c,272,a)]. given #161 (T,wt=7): 557 ilf_type(range_of(cross_product(A,B)),subset_type(B)). [resolve(300,a,154,a),rewrite(556(2))]. given #162 (T,wt=7): 561 ilf_type(f18(power_set(cross_product(A,B))),binary_relation_type). [resolve(558,a,96,a)]. given #163 (T,wt=7): 750 member(f16(A),A) | ilf_type(A,binary_relation_type). [resolve(210,a,88,a(flip)),merge(c)]. given #164 (T,wt=8): 216 -member(A,f17(power_set(B))) | member(A,B). [resolve(167,c,160,b),unit_del(c,166)]. given #165 (A,wt=10): 213 empty(A) | ilf_type(f11(A),member_type(A)) | ilf_type(A,binary_relation_type). [resolve(165,c,86,a)]. given #166 (F,wt=10): 426 -subset(power_set(ordered_pair(c3,domain_of(c4))),f8(f8(identity_relation_of(A)))). [ur(180,a,218,a,b,385,a)]. given #167 (F,wt=10): 428 -member(ordered_pair(c3,domain_of(c4)),f8(f8(f8(identity_relation_of(A))))). [ur(167,b,385,a,c,361,a)]. given #168 (F,wt=10): 434 -subset(power_set(ordered_pair(domain_of(c4),c3)),f18(power_set(identity_relation_of(A)))). [ur(180,a,218,a,b,420,a)]. given #169 (F,wt=10): 436 -member(ordered_pair(domain_of(c4),c3),f8(f18(power_set(identity_relation_of(A))))). [ur(167,b,420,a,c,361,a)]. given #170 (T,wt=8): 224 member(A,power_set(B)) | member(f18(A),A). [resolve(169,b,158,a)]. given #171 (T,wt=8): 245 ilf_type(f1(A,B),subset_type(cross_product(B,A))). [resolve(184,a,183,a)]. given #172 (T,wt=5): 861 ilf_type(f1(A,B),binary_relation_type). [resolve(245,a,96,a)]. given #173 (T,wt=8): 247 ilf_type(f8(cross_product(A,B)),relation_type(A,B)). [resolve(185,a,170,a)]. given #174 (A,wt=10): 214 member(f17(A),B) | -member(A,power_set(B)) | empty(A). [resolve(167,a,160,b)]. given #175 (F,wt=10): 465 -subset(power_set(ordered_pair(c3,domain_of(c4))),f18(power_set(identity_relation_of(A)))). [ur(180,a,218,a,b,421,a)]. given #176 (F,wt=10): 467 -member(ordered_pair(c3,domain_of(c4)),f8(f18(power_set(identity_relation_of(A))))). [ur(167,b,421,a,c,361,a)]. given #177 (F,wt=10): 498 power_set(power_set(ordered_pair(c3,domain_of(c4)))) != power_set(identity_relation_of(A)). [ur(174,a,345,a),flip(a)]. given #178 (F,wt=10): 521 -subset(identity_relation_of(power_set(ordered_pair(domain_of(c4),c3))),identity_relation_of(identity_relation_of(A))). [ur(180,a,273,a,b,263,a)]. given #179 (T,wt=8): 257 -subset(c4,identity_relation_of(c3)) | identity_relation_of(c3) = c4. [resolve(192,a,83,a),flip(b)]. given #180 (T,wt=8): 269 member(A,B) | -member(power_set(A),power_set(B)). [resolve(218,a,167,a)]. given #181 (T,wt=8): 308 -member(A,f18(power_set(B))) | member(A,B). [resolve(204,b,167,c),unit_del(a,166)]. given #182 (T,wt=8): 318 -member(A,f10(power_set(B))) | member(A,B). [resolve(211,b,167,c),unit_del(a,166)]. given #183 (A,wt=11): 215 member(f11(A),B) | -member(A,power_set(B)) | ilf_type(A,binary_relation_type). [resolve(167,a,86,a)]. given #184 (F,wt=10): 522 -subset(identity_relation_of(power_set(ordered_pair(c3,domain_of(c4)))),identity_relation_of(identity_relation_of(A))). [ur(180,a,273,a,b,262,a)]. given #185 (F,wt=10): 542 -ilf_type(ordered_pair(domain_of(c4),c3),member_type(identity_relation_of(identity_relation_of(power_set(A))))). [ur(164,a,536,a,b,261,a)]. given #186 (F,wt=10): 543 -ilf_type(ordered_pair(c3,domain_of(c4)),member_type(identity_relation_of(identity_relation_of(power_set(A))))). [ur(164,a,536,a,b,260,a)]. given #187 (F,wt=10): 586 -empty(identity_relation_of(identity_relation_of(identity_relation_of(identity_relation_of(identity_relation_of(identity_relation_of(identity_relation_of(power_set(A))))))))). [ur(490,a,581,a)]. given #188 (T,wt=8): 477 member(f10(identity_relation_of(c3)),c4) | empty(identity_relation_of(c3)). [resolve(239,a,211,b)]. given #189 (T,wt=5): 925 empty(identity_relation_of(c3)) | -empty(c4). [resolve(477,a,159,a)]. given #190 (T,wt=7): 926 empty(identity_relation_of(c3)) | member(f18(c4),c4). [resolve(477,a,158,a)]. given #191 (T,wt=8): 478 member(f18(identity_relation_of(c3)),c4) | empty(identity_relation_of(c3)). [resolve(239,a,204,b)]. given #192 (A,wt=12): 217 -member(A,f11(power_set(B))) | member(A,B) | ilf_type(power_set(B),binary_relation_type). [resolve(167,c,86,a)]. given #193 (F,wt=10): 604 -member(ordered_pair(c3,domain_of(c4)),f10(power_set(f8(identity_relation_of(A))))). [ur(167,b,376,a,c,591,a)]. given #194 (F,wt=10): 605 -member(ordered_pair(domain_of(c4),c3),f10(power_set(f8(identity_relation_of(A))))). [ur(167,b,375,a,c,591,a)]. given #195 (F,wt=10): 619 -member(ordered_pair(domain_of(c4),c3),f8(f10(power_set(identity_relation_of(A))))). [ur(364,b,610,a)]. given #196 (F,wt=10): 621 -subset(power_set(ordered_pair(domain_of(c4),c3)),f10(power_set(identity_relation_of(A)))). [ur(180,a,218,a,b,610,a)]. given #197 (T,wt=8): 481 member(f17(identity_relation_of(c3)),c4) | empty(identity_relation_of(c3)). [resolve(239,a,160,b)]. given #198 (T,wt=8): 491 empty(A) | member(f18(identity_relation_of(A)),identity_relation_of(A)). [resolve(205,b,158,a)]. given #199 (T,wt=7): 990 empty(c3) | member(f18(identity_relation_of(c3)),c4). [resolve(491,b,239,a)]. given #200 (T,wt=4): 1004 empty(c3) | -empty(c4). [resolve(990,b,159,a)]. given #201 (A,wt=14): 219 member(power_set(A),power_set(B)) | -member(C,f9(power_set(A),B)) | member(C,A). [resolve(169,b,167,c)]. given #202 (F,wt=10): 626 -member(ordered_pair(c3,domain_of(c4)),f8(f10(power_set(identity_relation_of(A))))). [ur(364,b,611,a)]. given #203 (F,wt=10): 628 -subset(power_set(ordered_pair(c3,domain_of(c4))),f10(power_set(identity_relation_of(A)))). [ur(180,a,218,a,b,611,a)]. given #204 (F,wt=10): 701 f8(f8(identity_relation_of(A))) != power_set(ordered_pair(domain_of(c4),c3)). [ur(174,a,391,a)]. given #205 (F,wt=10): 727 -member(ordered_pair(c3,domain_of(c4)),f17(power_set(f8(identity_relation_of(A))))). [ur(167,b,376,a,c,709,a)]. given #206 (T,wt=6): 1005 empty(c3) | member(f18(c4),c4). [resolve(990,b,158,a)]. given #207 (T,wt=8): 504 ilf_type(domain_of(f1(A,B)),member_type(power_set(B))). [resolve(242,a,171,b)]. given #208 (T,wt=7): 1045 member(domain_of(f1(A,B)),power_set(B)). [resolve(504,a,164,c),unit_del(a,166)]. given #209 (T,wt=8): 505 ilf_type(domain_of(f1(A,cross_product(B,C))),binary_relation_type). [resolve(242,a,96,a)]. given #210 (A,wt=13): 220 member(A,power_set(B)) | member(f9(A,B),C) | -member(A,power_set(C)). [resolve(169,b,167,a)]. given #211 (F,wt=10): 728 -member(ordered_pair(domain_of(c4),c3),f17(power_set(f8(identity_relation_of(A))))). [ur(167,b,375,a,c,709,a)]. given #212 (F,wt=10): 751 -member(ordered_pair(domain_of(c4),c3),f8(f17(power_set(identity_relation_of(A))))). [ur(364,b,735,a)]. given #213 (F,wt=10): 753 -subset(power_set(ordered_pair(domain_of(c4),c3)),f17(power_set(identity_relation_of(A)))). [ur(180,a,218,a,b,735,a)]. given #214 (F,wt=10): 759 -member(ordered_pair(c3,domain_of(c4)),f8(f17(power_set(identity_relation_of(A))))). [ur(364,b,736,a)]. given #215 (T,wt=8): 507 ilf_type(range_of(f1(A,B)),member_type(power_set(A))). [resolve(244,a,171,b)]. given #216 (T,wt=7): 1125 member(range_of(f1(A,B)),power_set(A)). [resolve(507,a,164,c),unit_del(a,166)]. given #217 (T,wt=8): 508 ilf_type(range_of(f1(cross_product(A,B),C)),binary_relation_type). [resolve(244,a,96,a)]. given #218 (T,wt=8): 514 ilf_type(ordered_pair(A,A),member_type(identity_relation_of(power_set(A)))). [resolve(273,a,165,c),unit_del(a,502)]. given #219 (A,wt=12): 221 member(A,power_set(B)) | empty(A) | ilf_type(f9(A,B),member_type(A)). [resolve(169,b,165,c)]. given #220 (F,wt=10): 761 -subset(power_set(ordered_pair(c3,domain_of(c4))),f17(power_set(identity_relation_of(A)))). [ur(180,a,218,a,b,736,a)]. given #221 (F,wt=10): 810 f8(f8(identity_relation_of(A))) != power_set(ordered_pair(c3,domain_of(c4))). [ur(174,a,426,a)]. given #222 (F,wt=10): 821 f18(power_set(identity_relation_of(A))) != power_set(ordered_pair(domain_of(c4),c3)). [ur(174,a,434,a)]. given #223 (F,wt=10): 878 f18(power_set(identity_relation_of(A))) != power_set(ordered_pair(c3,domain_of(c4))). [ur(174,a,465,a)]. given #224 (T,wt=8): 516 member(f18(identity_relation_of(power_set(A))),identity_relation_of(power_set(A))). [resolve(273,a,158,a)]. given #225 (T,wt=8): 562 member(f10(f8(A)),A) | empty(f8(A)). [resolve(364,a,211,b)]. given #226 (T,wt=5): 1238 empty(f8(A)) | -empty(A). [resolve(562,a,159,a)]. given #227 (T,wt=7): 1239 empty(f8(A)) | member(f18(A),A). [resolve(562,a,158,a)]. given #228 (A,wt=23): 222 member(A,power_set(B)) | ordered_pair(f14(A,f9(A,B)),f15(A,f9(A,B))) = f9(A,B) | member(f16(A),A). [resolve(169,b,162,a)]. given #229 (F,wt=10): 891 identity_relation_of(power_set(ordered_pair(domain_of(c4),c3))) != identity_relation_of(identity_relation_of(A)). [ur(174,a,521,a),flip(a)]. given #230 (F,wt=10): 913 identity_relation_of(power_set(ordered_pair(c3,domain_of(c4)))) != identity_relation_of(identity_relation_of(A)). [ur(174,a,522,a),flip(a)]. given #231 (F,wt=10): 980 f10(power_set(identity_relation_of(A))) != power_set(ordered_pair(domain_of(c4),c3)). [ur(174,a,621,a)]. given #232 (F,wt=10): 1026 f10(power_set(identity_relation_of(A))) != power_set(ordered_pair(c3,domain_of(c4))). [ur(174,a,628,a)]. given #233 (T,wt=8): 563 member(f18(f8(A)),A) | empty(f8(A)). [resolve(364,a,204,b)]. given #234 (T,wt=8): 566 member(f17(f8(A)),A) | empty(f8(A)). [resolve(364,a,160,b)]. given #235 (T,wt=8): 649 -member(A,c4) | member(A,cross_product(c3,c2)). [resolve(616,a,167,c)]. given #236 (T,wt=8): 656 member(f10(range_of(c4)),c2) | empty(range_of(c4)). [resolve(442,a,211,b)]. given #237 (A,wt=14): 225 member(A,power_set(B)) | member(ordered_pair(f9(A,B),f9(A,B)),identity_relation_of(A)). [resolve(169,b,111,a)]. given #238 (F,wt=10): 1086 -member(ordered_pair(domain_of(c4),c3),domain_of(f1(A,identity_relation_of(B)))). [ur(167,b,261,a,c,1045,a)]. given #239 (F,wt=10): 1087 -member(ordered_pair(c3,domain_of(c4)),domain_of(f1(A,identity_relation_of(B)))). [ur(167,b,260,a,c,1045,a)]. given #240 (F,wt=10): 1115 f17(power_set(identity_relation_of(A))) != power_set(ordered_pair(domain_of(c4),c3)). [ur(174,a,753,a)]. given #241 (F,wt=10): 1170 -member(ordered_pair(domain_of(c4),c3),range_of(f1(identity_relation_of(A),B))). [ur(167,b,261,a,c,1125,a)]. given #242 (T,wt=5): 1345 empty(range_of(c4)) | -empty(c2). [resolve(656,a,159,a)]. given #243 (T,wt=7): 1346 empty(range_of(c4)) | member(f18(c2),c2). [resolve(656,a,158,a)]. given #244 (T,wt=7): 1359 member(A,power_set(B)) | -empty(identity_relation_of(A)). [resolve(225,b,159,a)]. given #245 (T,wt=8): 657 member(f18(range_of(c4)),c2) | empty(range_of(c4)). [resolve(442,a,204,b)]. given #246 (A,wt=25): 226 member(A,power_set(B)) | -ilf_type(A,subset_type(cross_product(C,D))) | ordered_pair(f12(A,f9(A,B)),f13(A,f9(A,B))) = f9(A,B). [resolve(169,b,98,b)]. given #247 (F,wt=10): 1171 -member(ordered_pair(c3,domain_of(c4)),range_of(f1(identity_relation_of(A),B))). [ur(167,b,260,a,c,1125,a)]. given #248 (F,wt=10): 1204 f17(power_set(identity_relation_of(A))) != power_set(ordered_pair(c3,domain_of(c4))). [ur(174,a,761,a)]. given #249 (F,wt=11): 277 -subset(power_set(ordered_pair(ordered_pair(c3,domain_of(c4)),A)),identity_relation_of(identity_relation_of(B))). [ur(180,a,218,a,b,262,a)]. given #250 (F,wt=11): 281 -member(f3(power_set(ordered_pair(domain_of(c4),c3)),identity_relation_of(A)),identity_relation_of(A)). [ur(178,a,218,a,b,261,a)]. given #251 (T,wt=8): 660 member(f17(range_of(c4)),c2) | empty(range_of(c4)). [resolve(442,a,160,b)]. given #252 (T,wt=8): 662 member(f10(domain_of(c4)),c3) | empty(domain_of(c4)). [resolve(452,a,211,b)]. given #253 (T,wt=5): 1471 empty(domain_of(c4)) | -empty(c3). [resolve(662,a,159,a)]. given #254 (T,wt=7): 1472 empty(domain_of(c4)) | member(f18(c3),c3). [resolve(662,a,158,a)]. given #255 (A,wt=23): 227 member(A,power_set(B)) | ordered_pair(f12(A,f9(A,B)),f13(A,f9(A,B))) = f9(A,B) | member(f11(A),A). [resolve(169,b,92,a)]. given #256 (F,wt=11): 282 -member(f3(power_set(ordered_pair(c3,domain_of(c4))),identity_relation_of(A)),identity_relation_of(A)). [ur(178,a,218,a,b,260,a)]. given #257 (F,wt=11): 291 -member(f2(power_set(ordered_pair(domain_of(c4),c3)),identity_relation_of(A)),identity_relation_of(A)). [ur(181,a,278,a)]. given #258 (F,wt=11): 294 -member(f2(power_set(ordered_pair(c3,domain_of(c4))),identity_relation_of(A)),identity_relation_of(A)). [ur(181,a,279,a)]. given #259 (F,wt=11): 296 -member(ordered_pair(identity_relation_of(A),power_set(ordered_pair(domain_of(c4),c3))),identity_relation_of(B)). [ur(187,a,292,a)]. given #260 (T,wt=8): 663 member(f18(domain_of(c4)),c3) | empty(domain_of(c4)). [resolve(452,a,204,b)]. given #261 (T,wt=8): 666 member(f17(domain_of(c4)),c3) | empty(domain_of(c4)). [resolve(452,a,160,b)]. given #262 (T,wt=8): 743 ilf_type(domain_of(cross_product(A,B)),member_type(power_set(A))). [resolve(555,a,171,b)]. given #263 (T,wt=7): 1585 member(domain_of(cross_product(A,B)),power_set(A)). [resolve(743,a,164,c),unit_del(a,166)]. given #264 (A,wt=22): 228 member(A,power_set(B)) | ordered_pair(f12(A,f9(A,B)),f13(A,f9(A,B))) = f9(A,B) | -ilf_type(A,binary_relation_type). [resolve(169,b,90,a)]. given #265 (F,wt=10): 1639 -member(ordered_pair(domain_of(c4),c3),domain_of(cross_product(identity_relation_of(A),B))). [ur(167,b,261,a,c,1585,a)]. given #266 (F,wt=10): 1640 -member(ordered_pair(c3,domain_of(c4)),domain_of(cross_product(identity_relation_of(A),B))). [ur(167,b,260,a,c,1585,a)]. given #267 (F,wt=11): 297 -member(ordered_pair(power_set(ordered_pair(domain_of(c4),c3)),identity_relation_of(A)),identity_relation_of(B)). [ur(187,a,292,a(flip))]. given #268 (F,wt=11): 298 -member(ordered_pair(identity_relation_of(A),power_set(ordered_pair(c3,domain_of(c4)))),identity_relation_of(B)). [ur(187,a,295,a)]. given #269 (T,wt=8): 744 ilf_type(domain_of(cross_product(cross_product(A,B),C)),binary_relation_type). [resolve(555,a,96,a)]. given #270 (T,wt=8): 785 ilf_type(range_of(cross_product(A,B)),member_type(power_set(B))). [resolve(557,a,171,b)]. given #271 (T,wt=7): 1705 member(range_of(cross_product(A,B)),power_set(B)). [resolve(785,a,164,c),unit_del(a,166)]. given #272 (T,wt=8): 786 ilf_type(range_of(cross_product(A,cross_product(B,C))),binary_relation_type). [resolve(557,a,96,a)]. given #273 (A,wt=15): 229 member(power_set(power_set(A)),power_set(A)) | -member(power_set(power_set(A)),f9(power_set(power_set(A)),A)). [factor(219,a,c)]. given #274 (F,wt=10): 1763 -member(ordered_pair(domain_of(c4),c3),range_of(cross_product(A,identity_relation_of(B)))). [ur(167,b,261,a,c,1705,a)]. given #275 (F,wt=10): 1764 -member(ordered_pair(c3,domain_of(c4)),range_of(cross_product(A,identity_relation_of(B)))). [ur(167,b,260,a,c,1705,a)]. given #276 (F,wt=11): 299 -member(ordered_pair(power_set(ordered_pair(c3,domain_of(c4))),identity_relation_of(A)),identity_relation_of(B)). [ur(187,a,295,a(flip))]. given #277 (F,wt=11): 341 -member(f9(power_set(ordered_pair(domain_of(c4),c3)),identity_relation_of(A)),identity_relation_of(A)). [ur(168,a,284,a)]. given #278 (T,wt=8): 867 ilf_type(domain_of(f8(cross_product(A,B))),subset_type(A)). [resolve(247,a,156,a),rewrite(866(3))]. given #279 (T,wt=8): 869 ilf_type(range_of(f8(cross_product(A,B))),subset_type(B)). [resolve(247,a,154,a),rewrite(868(3))]. given #280 (T,wt=8): 871 member(f17(c4),cross_product(c3,c2)) | empty(c4). [resolve(214,b,616,a)]. given #281 (T,wt=6): 1846 empty(c4) | -empty(cross_product(c3,c2)). [resolve(871,a,159,a)]. given #282 (A,wt=14): 233 member(f9(A,B),C) | -member(f3(A,C),C) | member(A,power_set(B)). [resolve(178,a,169,b)]. given #283 (F,wt=11): 342 -member(power_set(power_set(ordered_pair(domain_of(c4),c3))),power_set(power_set(identity_relation_of(A)))). [ur(167,a,218,a,b,284,a)]. given #284 (F,wt=11): 347 -member(f9(power_set(ordered_pair(c3,domain_of(c4))),identity_relation_of(A)),identity_relation_of(A)). [ur(168,a,285,a)]. given #285 (F,wt=11): 348 -member(power_set(power_set(ordered_pair(c3,domain_of(c4)))),power_set(power_set(identity_relation_of(A)))). [ur(167,a,218,a,b,285,a)]. given #286 (F,wt=11): 351 -subset(power_set(ordered_pair(ordered_pair(domain_of(c4),c3),A)),identity_relation_of(identity_relation_of(B))). [ur(180,a,218,a,b,263,a)]. given #287 (T,wt=8): 1328 member(f18(c4),cross_product(c3,c2)) | empty(c3). [resolve(649,a,1005,b)]. given #288 (T,wt=6): 1911 empty(c3) | -empty(cross_product(c3,c2)). [resolve(1328,a,159,a)]. given #289 (T,wt=8): 1338 member(f10(c4),cross_product(c3,c2)) | empty(c4). [resolve(649,a,211,b)]. given #290 (T,wt=8): 1339 member(f18(c4),cross_product(c3,c2)) | empty(c4). [resolve(649,a,204,b)]. given #291 (A,wt=11): 234 member(f17(A),B) | -member(f3(A,B),B) | empty(A). [resolve(178,a,160,b)]. given #292 (F,wt=11): 373 -member(ordered_pair(ordered_pair(domain_of(c4),c3),A),f8(identity_relation_of(identity_relation_of(B)))). [ur(167,b,263,a,c,361,a)]. given #293 (F,wt=11): 374 -member(ordered_pair(ordered_pair(c3,domain_of(c4)),A),f8(identity_relation_of(identity_relation_of(B)))). [ur(167,b,262,a,c,361,a)]. given #294 (F,wt=11): 377 -member(ordered_pair(ordered_pair(domain_of(c4),c3),A),identity_relation_of(f8(identity_relation_of(B)))). [ur(188,a,375,a)]. given #295 (F,wt=11): 382 -member(ordered_pair(ordered_pair(c3,domain_of(c4)),A),identity_relation_of(f8(identity_relation_of(B)))). [ur(188,a,376,a)]. given #296 (T,wt=9): 266 member(A,B) | -member(f3(power_set(A),B),B). [resolve(218,a,178,a)]. given #297 (T,wt=9): 333 ilf_type(A,binary_relation_type) | member(f18(identity_relation_of(A)),identity_relation_of(A)). [resolve(195,a,158,a)]. given #298 (T,wt=8): 2001 ilf_type(c3,binary_relation_type) | member(f18(identity_relation_of(c3)),c4). [resolve(333,b,239,a)]. given #299 (T,wt=5): 2016 ilf_type(c3,binary_relation_type) | -empty(c4). [resolve(2001,b,159,a)]. given #300 (A,wt=12): 235 member(f11(A),B) | -member(f3(A,B),B) | ilf_type(A,binary_relation_type). [resolve(178,a,86,a)]. given #301 (F,wt=11): 394 -member(power_set(ordered_pair(domain_of(c4),c3)),power_set(f8(f8(identity_relation_of(A))))). [ur(167,a,218,a,b,380,a)]. given #302 (F,wt=11): 413 -member(ordered_pair(domain_of(c4),c3),f18(power_set(f8(f8(identity_relation_of(A)))))). [ur(167,b,380,a,c,272,a)]. given #303 (F,wt=11): 416 -member(power_set(ordered_pair(c3,domain_of(c4))),f18(power_set(power_set(identity_relation_of(A))))). [ur(167,b,285,a,c,272,a)]. given #304 (F,wt=11): 417 -member(power_set(ordered_pair(domain_of(c4),c3)),f18(power_set(power_set(identity_relation_of(A))))). [ur(167,b,284,a,c,272,a)]. given #305 (T,wt=7): 2017 ilf_type(c3,binary_relation_type) | member(f18(c4),c4). [resolve(2001,b,158,a)]. given #306 (T,wt=9): 365 member(f8(A),B) | -member(power_set(A),power_set(B)). [resolve(361,a,167,a)]. given #307 (T,wt=9): 367 member(ordered_pair(f8(A),f8(A)),identity_relation_of(power_set(A))). [resolve(361,a,111,a)]. given #308 (T,wt=9): 395 ilf_type(f10(power_set(cross_product(A,B))),relation_type(A,B)). [resolve(232,a,185,a)]. given #309 (A,wt=14): 236 member(f9(A,B),C) | member(f3(A,C),A) | member(A,power_set(B)). [resolve(179,a,169,b)]. given #310 (F,wt=11): 429 -member(ordered_pair(c3,domain_of(c4)),f18(power_set(f8(f8(identity_relation_of(A)))))). [ur(167,b,385,a,c,272,a)]. given #311 (F,wt=11): 430 -member(power_set(ordered_pair(c3,domain_of(c4))),power_set(f8(f8(identity_relation_of(A))))). [ur(167,a,218,a,b,385,a)]. given #312 (F,wt=11): 437 -member(ordered_pair(domain_of(c4),c3),f18(power_set(f18(power_set(identity_relation_of(A)))))). [ur(167,b,420,a,c,272,a)]. given #313 (F,wt=11): 438 -member(power_set(ordered_pair(domain_of(c4),c3)),power_set(f18(power_set(identity_relation_of(A))))). [ur(167,a,218,a,b,420,a)]. given #314 (T,wt=9): 443 member(range_of(c4),A) | -member(power_set(c2),power_set(A)). [resolve(439,a,167,a)]. given #315 (T,wt=9): 445 member(ordered_pair(range_of(c4),range_of(c4)),identity_relation_of(power_set(c2))). [resolve(439,a,111,a)]. given #316 (T,wt=9): 453 member(domain_of(c4),A) | -member(power_set(c3),power_set(A)). [resolve(449,a,167,a)]. given #317 (T,wt=9): 455 member(ordered_pair(domain_of(c4),domain_of(c4)),identity_relation_of(power_set(c3))). [resolve(449,a,111,a)]. given #318 (A,wt=11): 237 member(f17(A),B) | member(f3(A,B),A) | empty(A). [resolve(179,a,160,b)]. given #319 (F,wt=11): 468 -member(ordered_pair(c3,domain_of(c4)),f18(power_set(f18(power_set(identity_relation_of(A)))))). [ur(167,b,421,a,c,272,a)]. given #320 (F,wt=11): 469 -member(power_set(ordered_pair(c3,domain_of(c4))),power_set(f18(power_set(identity_relation_of(A))))). [ur(167,a,218,a,b,421,a)]. given #321 (F,wt=11): 527 -member(identity_relation_of(power_set(ordered_pair(domain_of(c4),c3))),power_set(identity_relation_of(identity_relation_of(A)))). [ur(167,a,273,a,b,263,a)]. given #322 (F,wt=11): 528 -member(identity_relation_of(power_set(ordered_pair(c3,domain_of(c4)))),power_set(identity_relation_of(identity_relation_of(A)))). [ur(167,a,273,a,b,262,a)]. given #323 (T,wt=9): 474 ilf_type(f17(power_set(cross_product(A,B))),relation_type(A,B)). [resolve(473,a,185,a)]. given #324 (T,wt=9): 482 empty(c3) | member(ordered_pair(f17(c3),f17(c3)),c4). [resolve(205,b,239,a)]. given #325 (T,wt=9): 560 ilf_type(f18(power_set(cross_product(A,B))),relation_type(A,B)). [resolve(558,a,185,a)]. given #326 (T,wt=9): 564 member(f18(f8(A)),A) | ilf_type(f8(A),binary_relation_type). [resolve(364,a,203,a)]. given #327 (A,wt=12): 238 member(f11(A),B) | member(f3(A,B),A) | ilf_type(A,binary_relation_type). [resolve(179,a,86,a)]. given #328 (F,wt=11): 547 -ilf_type(ordered_pair(domain_of(c4),c3),member_type(identity_relation_of(identity_relation_of(identity_relation_of(power_set(A)))))). [ur(164,a,539,a,b,261,a)]. given #329 (F,wt=11): 548 -ilf_type(ordered_pair(c3,domain_of(c4)),member_type(identity_relation_of(identity_relation_of(identity_relation_of(power_set(A)))))). [ur(164,a,539,a,b,260,a)]. given #330 (F,wt=11): 600 -member(ordered_pair(c3,domain_of(c4)),f10(power_set(f18(power_set(identity_relation_of(A)))))). [ur(167,b,421,a,c,591,a)]. given #331 (F,wt=11): 601 -member(ordered_pair(domain_of(c4),c3),f10(power_set(f18(power_set(identity_relation_of(A)))))). [ur(167,b,420,a,c,591,a)]. given #332 (T,wt=6): 2383 ilf_type(f8(A),binary_relation_type) | -empty(A). [resolve(564,a,159,a)]. given #333 (T,wt=8): 2384 ilf_type(f8(A),binary_relation_type) | member(f18(A),A). [resolve(564,a,158,a)]. given #334 (T,wt=9): 567 member(f11(f8(A)),A) | ilf_type(f8(A),binary_relation_type). [resolve(364,a,86,a)]. given #335 (T,wt=9): 652 member(ordered_pair(c4,c4),identity_relation_of(power_set(cross_product(c3,c2)))). [resolve(616,a,111,a)]. given #336 (A,wt=11): 240 member(f2(A,B),A) | -member(C,A) | member(C,B). [resolve(182,a,180,c)]. given #337 (F,wt=11): 602 -member(ordered_pair(c3,domain_of(c4)),f10(power_set(f8(f8(identity_relation_of(A)))))). [ur(167,b,385,a,c,591,a)]. given #338 (F,wt=11): 603 -member(ordered_pair(domain_of(c4),c3),f10(power_set(f8(f8(identity_relation_of(A)))))). [ur(167,b,380,a,c,591,a)]. given #339 (F,wt=11): 606 -member(power_set(ordered_pair(c3,domain_of(c4))),f10(power_set(power_set(identity_relation_of(A))))). [ur(167,b,285,a,c,591,a)]. given #340 (F,wt=11): 607 -member(power_set(ordered_pair(domain_of(c4),c3)),f10(power_set(power_set(identity_relation_of(A))))). [ur(167,b,284,a,c,591,a)]. given #341 (T,wt=9): 658 member(f18(range_of(c4)),c2) | ilf_type(range_of(c4),binary_relation_type). [resolve(442,a,203,a)]. given #342 (T,wt=6): 2632 ilf_type(range_of(c4),binary_relation_type) | -empty(c2). [resolve(658,a,159,a)]. given #343 (T,wt=8): 2633 ilf_type(range_of(c4),binary_relation_type) | member(f18(c2),c2). [resolve(658,a,158,a)]. given #344 (T,wt=9): 661 member(f11(range_of(c4)),c2) | ilf_type(range_of(c4),binary_relation_type). [resolve(442,a,86,a)]. given #345 (A,wt=11): 241 domain(A,B,f1(B,A)) = domain_of(f1(B,A)). [resolve(183,a,157,a)]. given #346 (F,wt=11): 623 -member(ordered_pair(domain_of(c4),c3),f10(power_set(f10(power_set(identity_relation_of(A)))))). [ur(167,b,610,a,c,591,a)]. given #347 (F,wt=11): 624 -member(ordered_pair(domain_of(c4),c3),f18(power_set(f10(power_set(identity_relation_of(A)))))). [ur(167,b,610,a,c,272,a)]. given #348 (F,wt=11): 625 -member(power_set(ordered_pair(domain_of(c4),c3)),power_set(f10(power_set(identity_relation_of(A))))). [ur(167,a,218,a,b,610,a)]. given #349 (F,wt=11): 630 -member(ordered_pair(c3,domain_of(c4)),f10(power_set(f10(power_set(identity_relation_of(A)))))). [ur(167,b,611,a,c,591,a)]. given #350 (T,wt=9): 664 member(f18(domain_of(c4)),c3) | ilf_type(domain_of(c4),binary_relation_type). [resolve(452,a,203,a)]. given #351 (T,wt=6): 2714 ilf_type(domain_of(c4),binary_relation_type) | -empty(c3). [resolve(664,a,159,a)]. given #352 (T,wt=8): 2715 ilf_type(domain_of(c4),binary_relation_type) | member(f18(c3),c3). [resolve(664,a,158,a)]. given #353 (T,wt=9): 667 member(f11(domain_of(c4)),c3) | ilf_type(domain_of(c4),binary_relation_type). [resolve(452,a,86,a)]. given #354 (A,wt=11): 243 range(A,B,f1(B,A)) = range_of(f1(B,A)). [resolve(183,a,155,a)]. given #355 (F,wt=11): 631 -member(ordered_pair(c3,domain_of(c4)),f18(power_set(f10(power_set(identity_relation_of(A)))))). [ur(167,b,611,a,c,272,a)]. given #356 (F,wt=11): 632 -member(power_set(ordered_pair(c3,domain_of(c4))),power_set(f10(power_set(identity_relation_of(A))))). [ur(167,a,218,a,b,611,a)]. given #357 (F,wt=11): 633 -member(power_set(ordered_pair(c3,domain_of(c4))),f8(f8(power_set(identity_relation_of(A))))). [ur(364,b,371,a)]. given #358 (F,wt=11): 635 -subset(power_set(power_set(ordered_pair(c3,domain_of(c4)))),f8(power_set(identity_relation_of(A)))). [ur(180,a,218,a,b,371,a)]. given #359 (T,wt=9): 791 ilf_type(domain_of(c4),binary_relation_type) | member(f16(domain_of(c4)),c3). [resolve(750,a,452,a)]. given #360 (T,wt=9): 792 ilf_type(range_of(c4),binary_relation_type) | member(f16(range_of(c4)),c2). [resolve(750,a,442,a)]. given #361 (T,wt=9): 793 ilf_type(f8(A),binary_relation_type) | member(f16(f8(A)),A). [resolve(750,a,364,a)]. given #362 (T,wt=9): 839 member(f18(A),A) | ilf_type(A,member_type(power_set(B))). [resolve(224,a,165,c),unit_del(b,166)]. given #363 (A,wt=18): 248 -ilf_type(A,binary_relation_type) | subset(A,identity_relation_of(B)) | member(ordered_pair(f4(A,identity_relation_of(B)),f5(A,identity_relation_of(B))),A). [resolve(186,a,30,b)]. given #364 (F,wt=11): 640 -member(power_set(ordered_pair(domain_of(c4),c3)),f8(f8(power_set(identity_relation_of(A))))). [ur(364,b,372,a)]. given #365 (F,wt=11): 642 -subset(power_set(power_set(ordered_pair(domain_of(c4),c3))),f8(power_set(identity_relation_of(A)))). [ur(180,a,218,a,b,372,a)]. given #366 (F,wt=11): 681 -member(power_set(ordered_pair(domain_of(c4),c3)),f8(power_set(f8(identity_relation_of(A))))). [ur(364,b,381,a)]. given #367 (F,wt=11): 683 -subset(power_set(power_set(ordered_pair(domain_of(c4),c3))),power_set(f8(identity_relation_of(A)))). [ur(180,a,218,a,b,381,a)]. given #368 (T,wt=7): 2840 ilf_type(A,member_type(power_set(B))) | -empty(A). [resolve(839,a,159,a)]. given #369 (T,wt=9): 860 ilf_type(f1(A,B),member_type(power_set(cross_product(B,A)))). [resolve(245,a,171,b)]. given #370 (T,wt=8): 2887 member(f1(A,B),power_set(cross_product(B,A))). [resolve(860,a,164,c),unit_del(a,166)]. given #371 (T,wt=9): 1050 -member(A,domain_of(f1(B,C))) | member(A,C). [resolve(1045,a,167,c)]. given #372 (A,wt=19): 249 -ilf_type(A,binary_relation_type) | subset(identity_relation_of(B),A) | member(ordered_pair(f4(identity_relation_of(B),A),f5(identity_relation_of(B),A)),identity_relation_of(B)). [resolve(186,a,30,a)]. given #373 (F,wt=11): 689 -ilf_type(power_set(ordered_pair(domain_of(c4),c3)),member_type(power_set(f8(identity_relation_of(A))))). [ur(164,a,166,a,b,381,a)]. given #374 (F,wt=10): 2931 -ilf_type(power_set(ordered_pair(domain_of(c4),c3)),subset_type(f8(identity_relation_of(A)))). [ur(171,a,689,a)]. given #375 (F,wt=11): 690 -member(power_set(ordered_pair(c3,domain_of(c4))),f8(power_set(f8(identity_relation_of(A))))). [ur(364,b,386,a)]. given #376 (F,wt=11): 692 -subset(power_set(power_set(ordered_pair(c3,domain_of(c4)))),power_set(f8(identity_relation_of(A)))). [ur(180,a,218,a,b,386,a)]. given #377 (T,wt=9): 1131 -member(A,range_of(f1(B,C))) | member(A,B). [resolve(1125,a,167,c)]. given #378 (T,wt=9): 1214 ilf_type(f18(identity_relation_of(power_set(A))),member_type(identity_relation_of(power_set(A)))). [resolve(516,a,165,c),unit_del(a,502)]. given #379 (T,wt=9): 1244 empty(f8(domain_of(c4))) | member(f18(domain_of(c4)),c3). [resolve(1239,b,452,a)]. given #380 (T,wt=6): 2973 empty(f8(domain_of(c4))) | -empty(c3). [resolve(1244,b,159,a)]. given #381 (A,wt=18): 250 -ilf_type(A,relation_type(B,C)) | subset(D,range(B,C,A)) | member(f2(identity_relation_of(D),A),identity_relation_of(D)). [resolve(190,b,182,a)]. given #382 (F,wt=11): 698 -ilf_type(power_set(ordered_pair(c3,domain_of(c4))),member_type(power_set(f8(identity_relation_of(A))))). [ur(164,a,166,a,b,386,a)]. given #383 (F,wt=10): 2986 -ilf_type(power_set(ordered_pair(c3,domain_of(c4))),subset_type(f8(identity_relation_of(A)))). [ur(171,a,698,a)]. given #384 (F,wt=11): 702 -member(ordered_pair(domain_of(c4),c3),f8(f8(f8(f8(identity_relation_of(A)))))). [ur(364,b,393,a)]. given #385 (F,wt=11): 704 -subset(power_set(ordered_pair(domain_of(c4),c3)),f8(f8(f8(identity_relation_of(A))))). [ur(180,a,218,a,b,393,a)]. given #386 (T,wt=8): 2974 empty(f8(domain_of(c4))) | member(f18(c3),c3). [resolve(1244,b,158,a)]. given #387 (T,wt=9): 1245 empty(f8(range_of(c4))) | member(f18(range_of(c4)),c2). [resolve(1239,b,442,a)]. given #388 (T,wt=6): 3017 empty(f8(range_of(c4))) | -empty(c2). [resolve(1245,b,159,a)]. given #389 (T,wt=8): 3018 empty(f8(range_of(c4))) | member(f18(c2),c2). [resolve(1245,b,158,a)]. given #390 (A,wt=13): 251 -ilf_type(identity_relation_of(A),relation_type(B,C)) | subset(A,range(B,C,identity_relation_of(A))). [resolve(190,b,131,a)]. given #391 (F,wt=11): 718 -member(ordered_pair(c3,domain_of(c4)),f17(power_set(f10(power_set(identity_relation_of(A)))))). [ur(167,b,611,a,c,709,a)]. given #392 (F,wt=11): 719 -member(ordered_pair(domain_of(c4),c3),f17(power_set(f10(power_set(identity_relation_of(A)))))). [ur(167,b,610,a,c,709,a)]. given #393 (F,wt=11): 720 -member(ordered_pair(c3,domain_of(c4)),f17(power_set(f18(power_set(identity_relation_of(A)))))). [ur(167,b,421,a,c,709,a)]. given #394 (F,wt=11): 721 -member(ordered_pair(domain_of(c4),c3),f17(power_set(f18(power_set(identity_relation_of(A)))))). [ur(167,b,420,a,c,709,a)]. given #395 (T,wt=9): 1246 empty(f8(f8(A))) | member(f18(f8(A)),A). [resolve(1239,b,364,a)]. given #396 (T,wt=6): 3102 empty(f8(f8(A))) | -empty(A). [resolve(1246,b,159,a)]. given #397 (T,wt=8): 3103 empty(f8(f8(A))) | member(f18(A),A). [resolve(1246,b,158,a)]. given #398 (T,wt=9): 1249 empty(f8(identity_relation_of(c3))) | member(f18(identity_relation_of(c3)),c4). [resolve(1239,b,239,a)]. given #399 (A,wt=11): 252 -ilf_type(c4,relation_type(A,B)) | subset(c3,range(A,B,c4)). [resolve(190,b,83,a)]. given #400 (F,wt=11): 724 -member(ordered_pair(c3,domain_of(c4)),f17(power_set(f8(f8(identity_relation_of(A)))))). [ur(167,b,385,a,c,709,a)]. given #401 (F,wt=11): 726 -member(ordered_pair(domain_of(c4),c3),f17(power_set(f8(f8(identity_relation_of(A)))))). [ur(167,b,380,a,c,709,a)]. given #402 (F,wt=11): 731 -member(power_set(ordered_pair(c3,domain_of(c4))),f17(power_set(power_set(identity_relation_of(A))))). [ur(167,b,285,a,c,709,a)]. given #403 (F,wt=11): 732 -member(power_set(ordered_pair(domain_of(c4),c3)),f17(power_set(power_set(identity_relation_of(A))))). [ur(167,b,284,a,c,709,a)]. given #404 (T,wt=4): 3142 subset(c3,range_of(c4)). [resolve(252,a,82,a),rewrite(197(5))]. given #405 (T,wt=6): 3136 empty(f8(identity_relation_of(c3))) | -empty(c4). [resolve(1249,b,159,a)]. given #406 (T,wt=7): 3192 -member(A,c3) | member(A,range_of(c4)). [resolve(3142,a,180,c)]. given #407 (T,wt=7): 3222 member(f10(c3),range_of(c4)) | empty(c3). [resolve(3192,a,211,b)]. given #408 (A,wt=18): 253 -ilf_type(A,relation_type(B,C)) | subset(D,domain(B,C,A)) | member(f2(identity_relation_of(D),A),identity_relation_of(D)). [resolve(191,b,182,a)]. given #409 (F,wt=11): 755 -member(ordered_pair(domain_of(c4),c3),f17(power_set(f17(power_set(identity_relation_of(A)))))). [ur(167,b,735,a,c,709,a)]. given #410 (F,wt=11): 756 -member(ordered_pair(domain_of(c4),c3),f10(power_set(f17(power_set(identity_relation_of(A)))))). [ur(167,b,735,a,c,591,a)]. given #411 (F,wt=11): 757 -member(ordered_pair(domain_of(c4),c3),f18(power_set(f17(power_set(identity_relation_of(A)))))). [ur(167,b,735,a,c,272,a)]. given #412 (F,wt=11): 758 -member(power_set(ordered_pair(domain_of(c4),c3)),power_set(f17(power_set(identity_relation_of(A))))). [ur(167,a,218,a,b,735,a)]. given #413 (T,wt=5): 3235 empty(c3) | -empty(range_of(c4)). [resolve(3222,a,159,a)]. given #414 (T,wt=6): 3228 empty(c3) | member(f10(c3),c2). [resolve(3222,a,442,a)]. given #415 (T,wt=4): 3305 empty(c3) | -empty(c2). [resolve(3228,b,159,a)]. given #416 (T,wt=6): 3306 empty(c3) | member(f18(c2),c2). [resolve(3228,b,158,a)]. given #417 (A,wt=13): 254 -ilf_type(identity_relation_of(A),relation_type(B,C)) | subset(A,domain(B,C,identity_relation_of(A))). [resolve(191,b,131,a)]. given #418 (F,wt=11): 763 -member(ordered_pair(c3,domain_of(c4)),f17(power_set(f17(power_set(identity_relation_of(A)))))). [ur(167,b,736,a,c,709,a)]. given #419 (F,wt=11): 764 -member(ordered_pair(c3,domain_of(c4)),f10(power_set(f17(power_set(identity_relation_of(A)))))). [ur(167,b,736,a,c,591,a)]. given #420 (F,wt=11): 765 -member(ordered_pair(c3,domain_of(c4)),f18(power_set(f17(power_set(identity_relation_of(A)))))). [ur(167,b,736,a,c,272,a)]. given #421 (F,wt=11): 766 -member(power_set(ordered_pair(c3,domain_of(c4))),power_set(f17(power_set(identity_relation_of(A))))). [ur(167,a,218,a,b,736,a)]. given #422 (T,wt=7): 3223 member(f18(c3),range_of(c4)) | empty(c3). [resolve(3192,a,204,b)]. given #423 (T,wt=6): 3371 empty(c3) | member(f18(c3),c2). [resolve(3223,a,442,a)]. given #424 (T,wt=7): 3226 member(f17(c3),range_of(c4)) | empty(c3). [resolve(3192,a,160,b)]. given #425 (T,wt=6): 3392 empty(c3) | member(f17(c3),c2). [resolve(3226,a,442,a)]. given #426 (A,wt=11): 255 -ilf_type(c4,relation_type(A,B)) | subset(c3,domain(A,B,c4)). [resolve(191,b,83,a)]. given #427 (F,wt=11): 767 -member(ordered_pair(c3,domain_of(c4)),f8(f18(power_set(f8(identity_relation_of(A)))))). [ur(364,b,414,a)]. given #428 (F,wt=11): 769 -subset(power_set(ordered_pair(c3,domain_of(c4))),f18(power_set(f8(identity_relation_of(A))))). [ur(180,a,218,a,b,414,a)]. given #429 (F,wt=11): 775 -member(ordered_pair(domain_of(c4),c3),f8(f18(power_set(f8(identity_relation_of(A)))))). [ur(364,b,415,a)]. given #430 (F,wt=11): 777 -subset(power_set(ordered_pair(domain_of(c4),c3)),f18(power_set(f8(identity_relation_of(A))))). [ur(180,a,218,a,b,415,a)]. given #431 (T,wt=4): 3413 subset(c3,domain_of(c4)). [resolve(255,a,82,a),rewrite(200(5))]. given #432 (T,wt=7): 3445 -member(A,c3) | member(A,domain_of(c4)). [resolve(3413,a,180,c)]. given #433 (T,wt=7): 3468 member(f10(c3),domain_of(c4)) | empty(c3). [resolve(3445,a,211,b)]. given #434 (T,wt=5): 3480 empty(c3) | -empty(domain_of(c4)). [resolve(3468,a,159,a)]. given #435 (A,wt=11): 256 -subset(A,B) | A = B | member(f2(B,A),B). [resolve(192,a,182,a)]. given #436 (F,wt=4): 3444 -subset(domain_of(c4),c3). [resolve(3413,a,192,b),flip(b),unit_del(b,202)]. given #437 (F,wt=6): 3489 -member(f2(domain_of(c4),c3),c3). [ur(181,a,3444,a)]. ============================== PROOF ================================= % Proof 1 at 0.32 (+ 0.01) seconds. % Length of proof is 39. % Level of proof is 8. % Maximum clause weight is 24. % Given clauses 437. 11 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -subset(A,B) | -subset(B,A) | B = A. [assumption]. 12 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | -ilf_type(D,relation_type(A,B)) | -subset(identity_relation_of(C),D) | subset(C,domain(A,B,D)). [assumption]. 22 -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(A,B) | member(f2(A,B),A). [assumption]. 23 -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(A,B) | -member(f2(A,B),B). [assumption]. 45 -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]. 52 -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]. 53 -ilf_type(A,set_type) | -empty(power_set(A)). [assumption]. 56 -ilf_type(A,set_type) | empty(B) | -ilf_type(B,set_type) | member(A,B) | -ilf_type(A,member_type(B)). [assumption]. 75 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,relation_type(A,B)) | domain_of(C) = domain(A,B,C). [assumption]. 76 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,relation_type(A,B)) | domain(A,B,C) = domain_of(C). [copy(75),flip(d)]. 77 -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]. 81 ilf_type(A,set_type). [assumption]. 82 ilf_type(c4,relation_type(c3,c2)). [assumption]. 83 subset(identity_relation_of(c3),c4). [assumption]. 84 domain(c3,c2,c4) != c3. [assumption]. 156 -ilf_type(A,relation_type(B,C)) | ilf_type(domain(B,C,A),subset_type(B)). [back_unit_del(77),unit_del(a,81),unit_del(b,81)]. 157 -ilf_type(A,relation_type(B,C)) | domain(B,C,A) = domain_of(A). [back_unit_del(76),unit_del(a,81),unit_del(b,81)]. 164 empty(A) | member(B,A) | -ilf_type(B,member_type(A)). [back_unit_del(56),unit_del(a,81),unit_del(c,81)]. 166 -empty(power_set(A)). [back_unit_del(53),unit_del(a,81)]. 167 -member(A,B) | member(A,C) | -member(B,power_set(C)). [back_unit_del(52),unit_del(a,81),unit_del(b,81),unit_del(c,81)]. 171 ilf_type(A,member_type(power_set(B))) | -ilf_type(A,subset_type(B)). [back_unit_del(45),unit_del(a,81),unit_del(b,81)]. 181 subset(A,B) | -member(f2(A,B),B). [back_unit_del(23),unit_del(a,81),unit_del(b,81)]. 182 subset(A,B) | member(f2(A,B),A). [back_unit_del(22),unit_del(a,81),unit_del(b,81)]. 191 -ilf_type(A,relation_type(B,C)) | -subset(identity_relation_of(D),A) | subset(D,domain(B,C,A)). [back_unit_del(12),unit_del(a,81),unit_del(b,81),unit_del(c,81)]. 192 -subset(A,B) | -subset(B,A) | B = A. [back_unit_del(11),unit_del(a,81),unit_del(b,81)]. 199 ilf_type(domain(c3,c2,c4),subset_type(c3)). [resolve(156,a,82,a)]. 200 domain(c3,c2,c4) = domain_of(c4). [resolve(157,a,82,a)]. 201 ilf_type(domain_of(c4),subset_type(c3)). [back_rewrite(199),rewrite(200(4))]. 202 domain_of(c4) != c3. [back_rewrite(84),rewrite(200(4))]. 255 -ilf_type(c4,relation_type(A,B)) | subset(c3,domain(A,B,c4)). [resolve(191,b,83,a)]. 256 -subset(A,B) | A = B | member(f2(B,A),B). [resolve(192,a,182,a)]. 287 ilf_type(domain_of(c4),member_type(power_set(c3))). [resolve(201,a,171,b)]. 449 member(domain_of(c4),power_set(c3)). [resolve(287,a,164,c),unit_del(a,166)]. 452 -member(A,domain_of(c4)) | member(A,c3). [resolve(449,a,167,c)]. 3413 subset(c3,domain_of(c4)). [resolve(255,a,82,a),rewrite(200(5))]. 3444 -subset(domain_of(c4),c3). [resolve(3413,a,192,b),flip(b),unit_del(b,202)]. 3486 member(f2(domain_of(c4),c3),domain_of(c4)). [resolve(256,a,3413,a),flip(a),unit_del(a,202)]. 3489 -member(f2(domain_of(c4),c3),c3). [ur(181,a,3444,a)]. 3492 $F. [ur(452,b,3489,a),unit_del(a,3486)]. ============================== end of proof ========================== ============================== STATISTICS ============================ Given=437. Generated=5172. Kept=3467. proofs=1. Usable=435. Sos=2858. Demods=20. Limbo=2, Disabled=263. Hints=0. Weight_deleted=4. Literals_deleted=0. Forward_subsumed=1700. Back_subsumed=129. Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. New_demodulators=20 (0 lex), Back_demodulated=3. Back_unit_deleted=40. Demod_attempts=55515. Demod_rewrites=59. Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. Nonunit_fsub_feature_tests=4811. Nonunit_bsub_feature_tests=2993. Megabytes=4.43. User_CPU=0.32, System_CPU=0.01, Wall_clock=0. ============================== end of statistics ===================== ============================== end of search ========================= Exiting with 1 proof. Process 20967 exit (max_proofs) Mon Mar 19 17:01:34 2007 ============================== continuing FOF reduction multisearch == Subproblem 2 of 2 (negated): ((all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | - subset(B,C) | - subset(C,B) | =(C,B))))) & (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,relation_type(B,C)) | - subset(identity_relation_of(D),E) | subset(D,domain(B,C,E)))))))))) & (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,relation_type(B,C)) | - subset(identity_relation_of(D),E) | subset(D,range(B,C,E)))))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | - member(C,B) | (all D (- ilf_type(D,set_type) | member(ordered_pair(C,D),identity_relation_of(B)) | - =(D,C))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | member(C,B) | (all D (- ilf_type(D,set_type) | - member(ordered_pair(C,D),identity_relation_of(B)))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,set_type) | =(D,C) | - member(ordered_pair(C,D),identity_relation_of(B)))))))) & (all B (- ilf_type(B,set_type) | ilf_type(identity_relation_of(B),binary_relation_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) | 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,binary_relation_type) | (all C (- ilf_type(C,binary_relation_type) | subset(B,C) | (exists D (ilf_type(D,set_type) & (exists E (ilf_type(E,set_type) & member(ordered_pair(D,E),B) & - member(ordered_pair(D,E),C))))))))) & (all B (- ilf_type(B,binary_relation_type) | (all C (- ilf_type(C,binary_relation_type) | (all D (- ilf_type(D,set_type) | (all E (- ilf_type(E,set_type) | - member(ordered_pair(D,E),B) | member(ordered_pair(D,E),C))))) | - subset(B,C))))) & (all B (- ilf_type(B,binary_relation_type) | (all C (- ilf_type(C,binary_relation_type) | (all D (- ilf_type(D,set_type) | (all E (- ilf_type(E,set_type) | - member(ordered_pair(D,E),B) | member(ordered_pair(D,E),C))))) | (exists D (ilf_type(D,set_type) & (exists E (ilf_type(E,set_type) & member(ordered_pair(D,E),B) & - member(ordered_pair(D,E),C))))))))) & (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) | (all C (- ilf_type(C,set_type) | ilf_type(cross_product(B,C),set_type))))) & (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) | ilf_type(ordered_pair(B,C),set_type))))) & (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) | subset(B,B))) & (all B (- ilf_type(B,binary_relation_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_of(D),domain(B,C,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_of(D),range(B,C,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(C,B)) & subset(identity_relation_of(C),D) & - subset(C,range(C,B,D))))))))). Child search process 20968 started. ============================== PROCESS INITIAL CLAUSES =============== % Clauses before input processing: formulas(usable). end_of_list. formulas(sos). -ilf_type(A,set_type) | -ilf_type(B,set_type) | -subset(A,B) | -subset(B,A) | B = A. [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | -ilf_type(D,relation_type(A,B)) | -subset(identity_relation_of(C),D) | subset(C,domain(A,B,D)). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | -ilf_type(D,relation_type(A,B)) | -subset(identity_relation_of(C),D) | subset(C,range(A,B,D)). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | -ilf_type(C,set_type) | member(ordered_pair(B,C),identity_relation_of(A)) | C != B. [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(B,A) | -ilf_type(C,set_type) | -member(ordered_pair(B,C),identity_relation_of(A)). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | C = B | -member(ordered_pair(B,C),identity_relation_of(A)). [assumption]. -ilf_type(A,set_type) | ilf_type(identity_relation_of(A),binary_relation_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(f1(A,B),relation_type(B,A)). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(A,B) | ilf_type(f2(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(A,B) | member(f2(A,B),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(A,B) | -member(f2(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(f3(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(f3(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(f3(A,B),B). [assumption]. -ilf_type(A,binary_relation_type) | -ilf_type(B,binary_relation_type) | subset(A,B) | ilf_type(f4(A,B),set_type). [assumption]. -ilf_type(A,binary_relation_type) | -ilf_type(B,binary_relation_type) | subset(A,B) | ilf_type(f5(A,B),set_type). [assumption]. -ilf_type(A,binary_relation_type) | -ilf_type(B,binary_relation_type) | subset(A,B) | member(ordered_pair(f4(A,B),f5(A,B)),A). [assumption]. -ilf_type(A,binary_relation_type) | -ilf_type(B,binary_relation_type) | subset(A,B) | -member(ordered_pair(f4(A,B),f5(A,B)),B). [assumption]. -ilf_type(A,binary_relation_type) | -ilf_type(B,binary_relation_type) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | -member(ordered_pair(C,D),A) | member(ordered_pair(C,D),B) | -subset(A,B). [assumption]. -ilf_type(A,binary_relation_type) | -ilf_type(B,binary_relation_type) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | -member(ordered_pair(C,D),A) | member(ordered_pair(C,D),B) | ilf_type(f6(A,B),set_type). [assumption]. -ilf_type(A,binary_relation_type) | -ilf_type(B,binary_relation_type) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | -member(ordered_pair(C,D),A) | member(ordered_pair(C,D),B) | ilf_type(f7(A,B),set_type). [assumption]. -ilf_type(A,binary_relation_type) | -ilf_type(B,binary_relation_type) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | -member(ordered_pair(C,D),A) | member(ordered_pair(C,D),B) | member(ordered_pair(f6(A,B),f7(A,B)),A). [assumption]. -ilf_type(A,binary_relation_type) | -ilf_type(B,binary_relation_type) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | -member(ordered_pair(C,D),A) | member(ordered_pair(C,D),B) | -member(ordered_pair(f6(A,B),f7(A,B)),B). [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(B,set_type) | ilf_type(cross_product(A,B),set_type). [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(ordered_pair(A,B),set_type). [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(f8(A),subset_type(A)). [assumption]. -ilf_type(A,set_type) | subset(A,A). [assumption]. -ilf_type(A,binary_relation_type) | subset(A,A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(A,power_set(B)) | ilf_type(f9(A,B),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(A,power_set(B)) | member(f9(A,B),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(A,power_set(B)) | -member(f9(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(f10(A),member_type(A)). [assumption]. -ilf_type(A,set_type) | relation_like(A) | ilf_type(f11(A),set_type). [assumption]. -ilf_type(A,set_type) | relation_like(A) | member(f11(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) != f11(A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f12(A,B),set_type) | -relation_like(A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f13(A,B),set_type) | -relation_like(A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f12(A,B),f13(A,B)) = B | -relation_like(A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f14(A,B),set_type) | ilf_type(f16(A),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f14(A,B),set_type) | member(f16(A),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f14(A,B),set_type) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | ordered_pair(C,D) != f16(A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f15(A,B),set_type) | ilf_type(f16(A),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f15(A,B),set_type) | member(f16(A),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f15(A,B),set_type) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | ordered_pair(C,D) != f16(A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f14(A,B),f15(A,B)) = B | ilf_type(f16(A),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f14(A,B),f15(A,B)) = B | member(f16(A),A). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f14(A,B),f15(A,B)) = B | -ilf_type(C,set_type) | -ilf_type(D,set_type) | ordered_pair(C,D) != f16(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(f17(A),set_type). [assumption]. -ilf_type(A,set_type) | empty(A) | member(f17(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(f18(A),set_type). [assumption]. -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | member(f18(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_of(C) = domain(A,B,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_of(C) = range(A,B,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(c3,c2)). [assumption]. subset(identity_relation_of(c3),c4). [assumption]. -subset(c3,range(c3,c2,c4)). [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(f11(A),set_type). [assumption]. 4 -ilf_type(A,set_type) | relation_like(A) | member(f11(A),A). [assumption]. Derived: -ilf_type(A,set_type) | member(f11(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) != f11(A). [assumption]. Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | ordered_pair(B,C) != f11(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(f12(A,B),set_type) | -relation_like(A). [assumption]. 7 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f13(A,B),set_type) | -relation_like(A). [assumption]. 8 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f12(A,B),f13(A,B)) = B | -relation_like(A). [assumption]. Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f12(A,B),f13(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(f12(A,B),f13(A,B)) = B | -ilf_type(A,set_type) | member(f11(A),A). [resolve(8,e,4,b)]. Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f12(A,B),f13(A,B)) = B | -ilf_type(A,set_type) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | ordered_pair(C,D) != f11(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(f12(C,D),f13(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(f12(A,B),f13(A,B)) = B. [resolve(10,c,8,e)]. ============================== end predicate elimination ============= Term ordering decisions: Relation symbol precedence: lex([ empty, ilf_type, member, subset, =, relation_like ]). Function symbol precedence: lex([ set_type, binary_relation_type, c1, c2, c3, c4, ordered_pair, relation_type, cross_product, f1, f2, f3, f4, f5, f6, f7, f9, f12, f13, f14, f15, subset_type, identity_relation_of, power_set, member_type, domain_of, range_of, f8, f10, f11, f16, f17, f18, domain, range ]). After inverse_order: (no changes). Unfolding symbols: (none). Auto_inference settings: % set(paramodulation). % (positive equality literals) % set(paramodulation) -> set(back_demod). % set(binary_resolution). % (non-Horn) % set(neg_ur_resolution). % (non-Horn, less than 100 clauses) Auto_process settings: % set(factor). % (non-Horn) % set(back_unit_deletion). % (non-Horn) % set(back_unit_deletion) -> set(unit_deletion). ============================== end of process initial clauses ======== ============================== CLAUSES FOR SEARCH ==================== % Clauses after input processing: formulas(usable). end_of_list. formulas(sos). 30 -ilf_type(A,binary_relation_type) | -ilf_type(B,binary_relation_type) | subset(A,B) | member(ordered_pair(f4(A,B),f5(A,B)),A). [assumption]. 31 -ilf_type(A,binary_relation_type) | -ilf_type(B,binary_relation_type) | subset(A,B) | -member(ordered_pair(f4(A,B),f5(A,B)),B). [assumption]. 43 ilf_type(c1,binary_relation_type). [assumption]. 81 ilf_type(A,set_type). [assumption]. 82 ilf_type(c4,relation_type(c3,c2)). [assumption]. 83 subset(identity_relation_of(c3),c4). [assumption]. 84 -subset(c3,range(c3,c2,c4)). [assumption]. 86 member(f11(A),A) | ilf_type(A,binary_relation_type). [copy(85),merge(c),unit_del(a,81)]. 88 f11(A) != ordered_pair(B,C) | ilf_type(A,binary_relation_type). [copy(87),flip(d),merge(e),unit_del(a,81),unit_del(b,81),unit_del(c,81)]. 90 -member(A,B) | ordered_pair(f12(B,A),f13(B,A)) = A | -ilf_type(B,binary_relation_type). [copy(89),merge(e),unit_del(a,81),unit_del(b,81)]. 92 -member(A,B) | ordered_pair(f12(B,A),f13(B,A)) = A | member(f11(B),B). [copy(91),merge(e),unit_del(a,81),unit_del(b,81)]. 94 -member(A,B) | ordered_pair(f12(B,A),f13(B,A)) = A | f11(B) != ordered_pair(C,D). [copy(93),flip(h),merge(e),unit_del(a,81),unit_del(b,81),unit_del(e,81),unit_del(f,81)]. 96 -ilf_type(A,subset_type(cross_product(B,C))) | ilf_type(A,binary_relation_type). [copy(95),unit_del(a,81),unit_del(b,81),unit_del(d,81)]. 98 -ilf_type(A,subset_type(cross_product(B,C))) | -member(D,A) | ordered_pair(f12(A,D),f13(A,D)) = D. [copy(97),unit_del(a,81),unit_del(b,81),unit_del(d,81),unit_del(e,81)]. 100 -empty(A) | ilf_type(A,binary_relation_type). [copy(99),merge(c),unit_del(b,81)]. 111 -member(A,B) | member(ordered_pair(A,A),identity_relation_of(B)). [factor(14,b,d),xx(e),unit_del(a,81),unit_del(b,81)]. 131 subset(A,A). [factor(37,a,b),xx(c),unit_del(a,81)]. 138 -member(power_set(A),power_set(A)) | member(power_set(A),A). [factor(52,d,f),merge(c),unit_del(a,81),unit_del(b,81)]. 154 -ilf_type(A,relation_type(B,C)) | ilf_type(range(B,C,A),subset_type(C)). [back_unit_del(80),unit_del(a,81),unit_del(b,81)]. 155 -ilf_type(A,relation_type(B,C)) | range(B,C,A) = range_of(A). [back_unit_del(79),unit_del(a,81),unit_del(b,81)]. 156 -ilf_type(A,relation_type(B,C)) | ilf_type(domain(B,C,A),subset_type(B)). [back_unit_del(77),unit_del(a,81),unit_del(b,81)]. 157 -ilf_type(A,relation_type(B,C)) | domain(B,C,A) = domain_of(A). [back_unit_del(76),unit_del(a,81),unit_del(b,81)]. 158 -member(A,B) | member(f18(B),B). [back_unit_del(74),unit_del(a,81),unit_del(b,81)]. 159 -member(A,B) | -empty(B). [back_unit_del(72),unit_del(a,81),unit_del(b,81)]. 160 empty(A) | member(f17(A),A). [back_unit_del(71),unit_del(a,81)]. 161 -member(A,B) | ordered_pair(f14(B,A),f15(B,A)) = A | f16(B) != ordered_pair(C,D). [back_unit_del(69),unit_del(a,81),unit_del(b,81),unit_del(e,81),unit_del(f,81)]. 162 -member(A,B) | ordered_pair(f14(B,A),f15(B,A)) = A | member(f16(B),B). [back_unit_del(67),unit_del(a,81),unit_del(b,81)]. 163 empty(A) | ilf_type(f10(A),member_type(A)). [back_unit_del(57),unit_del(b,81)]. 164 empty(A) | member(B,A) | -ilf_type(B,member_type(A)). [back_unit_del(56),unit_del(a,81),unit_del(c,81)]. 165 empty(A) | ilf_type(B,member_type(A)) | -member(B,A). [back_unit_del(55),unit_del(a,81),unit_del(c,81)]. 166 -empty(power_set(A)). [back_unit_del(53),unit_del(a,81)]. 167 -member(A,B) | member(A,C) | -member(B,power_set(C)). [back_unit_del(52),unit_del(a,81),unit_del(b,81),unit_del(c,81)]. 168 member(A,power_set(B)) | -member(f9(A,B),B). [back_unit_del(51),unit_del(a,81),unit_del(b,81)]. 169 member(A,power_set(B)) | member(f9(A,B),A). [back_unit_del(50),unit_del(a,81),unit_del(b,81)]. 170 ilf_type(f8(A),subset_type(A)). [back_unit_del(46),unit_del(a,81)]. 171 ilf_type(A,member_type(power_set(B))) | -ilf_type(A,subset_type(B)). [back_unit_del(45),unit_del(a,81),unit_del(b,81)]. 172 ilf_type(A,subset_type(B)) | -ilf_type(A,member_type(power_set(B))). [back_unit_del(44),unit_del(a,81),unit_del(b,81)]. 173 subset(A,B) | A != B. [back_unit_del(38),unit_del(a,81),unit_del(b,81)]. 174 subset(A,B) | B != A. [back_unit_del(37),unit_del(a,81),unit_del(b,81)]. 175 -ilf_type(A,binary_relation_type) | -ilf_type(B,binary_relation_type) | -member(ordered_pair(C,D),A) | member(ordered_pair(C,D),B) | -member(ordered_pair(f6(A,B),f7(A,B)),B). [back_unit_del(36),unit_del(c,81),unit_del(d,81)]. 176 -ilf_type(A,binary_relation_type) | -ilf_type(B,binary_relation_type) | -member(ordered_pair(C,D),A) | member(ordered_pair(C,D),B) | member(ordered_pair(f6(A,B),f7(A,B)),A). [back_unit_del(35),unit_del(c,81),unit_del(d,81)]. 178 -member(A,B) | member(A,C) | -member(f3(B,C),C). [back_unit_del(27),unit_del(a,81),unit_del(b,81),unit_del(c,81)]. 179 -member(A,B) | member(A,C) | member(f3(B,C),B). [back_unit_del(26),unit_del(a,81),unit_del(b,81),unit_del(c,81)]. 180 -member(A,B) | member(A,C) | -subset(B,C). [back_unit_del(24),unit_del(a,81),unit_del(b,81),unit_del(c,81)]. 181 subset(A,B) | -member(f2(A,B),B). [back_unit_del(23),unit_del(a,81),unit_del(b,81)]. 182 subset(A,B) | member(f2(A,B),A). [back_unit_del(22),unit_del(a,81),unit_del(b,81)]. 183 ilf_type(f1(A,B),relation_type(B,A)). [back_unit_del(20),unit_del(a,81),unit_del(b,81)]. 184 -ilf_type(A,relation_type(B,C)) | ilf_type(A,subset_type(cross_product(B,C))). [back_unit_del(19),unit_del(a,81),unit_del(b,81)]. 185 -ilf_type(A,subset_type(cross_product(B,C))) | ilf_type(A,relation_type(B,C)). [back_unit_del(18),unit_del(a,81),unit_del(b,81)]. 186 ilf_type(identity_relation_of(A),binary_relation_type). [back_unit_del(17),unit_del(a,81)]. 187 A = B | -member(ordered_pair(B,A),identity_relation_of(C)). [back_unit_del(16),unit_del(a,81),unit_del(b,81),unit_del(c,81)]. 188 member(A,B) | -member(ordered_pair(A,C),identity_relation_of(B)). [back_unit_del(15),unit_del(a,81),unit_del(b,81),unit_del(d,81)]. 189 -member(A,B) | member(ordered_pair(A,C),identity_relation_of(B)) | C != A. [back_unit_del(14),unit_del(a,81),unit_del(b,81),unit_del(d,81)]. 190 -ilf_type(A,relation_type(B,C)) | -subset(identity_relation_of(D),A) | subset(D,range(B,C,A)). [back_unit_del(13),unit_del(a,81),unit_del(b,81),unit_del(c,81)]. 191 -ilf_type(A,relation_type(B,C)) | -subset(identity_relation_of(D),A) | subset(D,domain(B,C,A)). [back_unit_del(12),unit_del(a,81),unit_del(b,81),unit_del(c,81)]. 192 -subset(A,B) | -subset(B,A) | B = A. [back_unit_del(11),unit_del(a,81),unit_del(b,81)]. end_of_list. formulas(demodulators). end_of_list. ============================== end of clauses for search ============= ============================== SEARCH ================================ % Starting search at 0.02 seconds. given #1 (I,wt=18): 30 -ilf_type(A,binary_relation_type) | -ilf_type(B,binary_relation_type) | subset(A,B) | member(ordered_pair(f4(A,B),f5(A,B)),A). [assumption]. given #2 (I,wt=18): 31 -ilf_type(A,binary_relation_type) | -ilf_type(B,binary_relation_type) | subset(A,B) | -member(ordered_pair(f4(A,B),f5(A,B)),B). [assumption]. given #3 (I,wt=3): 43 ilf_type(c1,binary_relation_type). [assumption]. given #4 (I,wt=3): 81 ilf_type(A,set_type). [assumption]. given #5 (I,wt=5): 82 ilf_type(c4,relation_type(c3,c2)). [assumption]. given #6 (I,wt=4): 83 subset(identity_relation_of(c3),c4). [assumption]. given #7 (I,wt=6): 84 -subset(c3,range(c3,c2,c4)). [assumption]. given #8 (I,wt=7): 86 member(f11(A),A) | ilf_type(A,binary_relation_type). [copy(85),merge(c),unit_del(a,81)]. given #9 (I,wt=9): 88 f11(A) != ordered_pair(B,C) | ilf_type(A,binary_relation_type). [copy(87),flip(d),merge(e),unit_del(a,81),unit_del(b,81),unit_del(c,81)]. given #10 (I,wt=15): 90 -member(A,B) | ordered_pair(f12(B,A),f13(B,A)) = A | -ilf_type(B,binary_relation_type). [copy(89),merge(e),unit_del(a,81),unit_del(b,81)]. given #11 (I,wt=16): 92 -member(A,B) | ordered_pair(f12(B,A),f13(B,A)) = A | member(f11(B),B). [copy(91),merge(e),unit_del(a,81),unit_del(b,81)]. given #12 (I,wt=18): 94 -member(A,B) | ordered_pair(f12(B,A),f13(B,A)) = A | f11(B) != ordered_pair(C,D). [copy(93),flip(h),merge(e),unit_del(a,81),unit_del(b,81),unit_del(e,81),unit_del(f,81)]. given #13 (I,wt=9): 96 -ilf_type(A,subset_type(cross_product(B,C))) | ilf_type(A,binary_relation_type). [copy(95),unit_del(a,81),unit_del(b,81),unit_del(d,81)]. given #14 (I,wt=18): 98 -ilf_type(A,subset_type(cross_product(B,C))) | -member(D,A) | ordered_pair(f12(A,D),f13(A,D)) = D. [copy(97),unit_del(a,81),unit_del(b,81),unit_del(d,81),unit_del(e,81)]. given #15 (I,wt=5): 100 -empty(A) | ilf_type(A,binary_relation_type). [copy(99),merge(c),unit_del(b,81)]. given #16 (I,wt=9): 111 -member(A,B) | member(ordered_pair(A,A),identity_relation_of(B)). [factor(14,b,d),xx(e),unit_del(a,81),unit_del(b,81)]. given #17 (I,wt=3): 131 subset(A,A). [factor(37,a,b),xx(c),unit_del(a,81)]. given #18 (I,wt=9): 138 -member(power_set(A),power_set(A)) | member(power_set(A),A). [factor(52,d,f),merge(c),unit_del(a,81),unit_del(b,81)]. given #19 (I,wt=12): 154 -ilf_type(A,relation_type(B,C)) | ilf_type(range(B,C,A),subset_type(C)). [back_unit_del(80),unit_del(a,81),unit_del(b,81)]. given #20 (I,wt=12): 155 -ilf_type(A,relation_type(B,C)) | range(B,C,A) = range_of(A). [back_unit_del(79),unit_del(a,81),unit_del(b,81)]. given #21 (I,wt=12): 156 -ilf_type(A,relation_type(B,C)) | ilf_type(domain(B,C,A),subset_type(B)). [back_unit_del(77),unit_del(a,81),unit_del(b,81)]. given #22 (I,wt=12): 157 -ilf_type(A,relation_type(B,C)) | domain(B,C,A) = domain_of(A). [back_unit_del(76),unit_del(a,81),unit_del(b,81)]. given #23 (I,wt=7): 158 -member(A,B) | member(f18(B),B). [back_unit_del(74),unit_del(a,81),unit_del(b,81)]. given #24 (I,wt=5): 159 -member(A,B) | -empty(B). [back_unit_del(72),unit_del(a,81),unit_del(b,81)]. given #25 (I,wt=6): 160 empty(A) | member(f17(A),A). [back_unit_del(71),unit_del(a,81)]. given #26 (I,wt=18): 161 -member(A,B) | ordered_pair(f14(B,A),f15(B,A)) = A | f16(B) != ordered_pair(C,D). [back_unit_del(69),unit_del(a,81),unit_del(b,81),unit_del(e,81),unit_del(f,81)]. given #27 (I,wt=16): 162 -member(A,B) | ordered_pair(f14(B,A),f15(B,A)) = A | member(f16(B),B). [back_unit_del(67),unit_del(a,81),unit_del(b,81)]. given #28 (I,wt=7): 163 empty(A) | ilf_type(f10(A),member_type(A)). [back_unit_del(57),unit_del(b,81)]. given #29 (I,wt=9): 164 empty(A) | member(B,A) | -ilf_type(B,member_type(A)). [back_unit_del(56),unit_del(a,81),unit_del(c,81)]. given #30 (I,wt=9): 165 empty(A) | ilf_type(B,member_type(A)) | -member(B,A). [back_unit_del(55),unit_del(a,81),unit_del(c,81)]. given #31 (I,wt=3): 166 -empty(power_set(A)). [back_unit_del(53),unit_del(a,81)]. given #32 (I,wt=10): 167 -member(A,B) | member(A,C) | -member(B,power_set(C)). [back_unit_del(52),unit_del(a,81),unit_del(b,81),unit_del(c,81)]. given #33 (I,wt=9): 168 member(A,power_set(B)) | -member(f9(A,B),B). [back_unit_del(51),unit_del(a,81),unit_del(b,81)]. given #34 (I,wt=9): 169 member(A,power_set(B)) | member(f9(A,B),A). [back_unit_del(50),unit_del(a,81),unit_del(b,81)]. given #35 (I,wt=5): 170 ilf_type(f8(A),subset_type(A)). [back_unit_del(46),unit_del(a,81)]. given #36 (I,wt=9): 171 ilf_type(A,member_type(power_set(B))) | -ilf_type(A,subset_type(B)). [back_unit_del(45),unit_del(a,81),unit_del(b,81)]. given #37 (I,wt=9): 172 ilf_type(A,subset_type(B)) | -ilf_type(A,member_type(power_set(B))). [back_unit_del(44),unit_del(a,81),unit_del(b,81)]. given #38 (I,wt=6): 173 subset(A,B) | A != B. [back_unit_del(38),unit_del(a,81),unit_del(b,81)]. given #39 (I,wt=6): 174 subset(A,B) | B != A. [back_unit_del(37),unit_del(a,81),unit_del(b,81)]. given #40 (I,wt=25): 175 -ilf_type(A,binary_relation_type) | -ilf_type(B,binary_relation_type) | -member(ordered_pair(C,D),A) | member(ordered_pair(C,D),B) | -member(ordered_pair(f6(A,B),f7(A,B)),B). [back_unit_del(36),unit_del(c,81),unit_del(d,81)]. given #41 (I,wt=25): 176 -ilf_type(A,binary_relation_type) | -ilf_type(B,binary_relation_type) | -member(ordered_pair(C,D),A) | member(ordered_pair(C,D),B) | member(ordered_pair(f6(A,B),f7(A,B)),A). [back_unit_del(35),unit_del(c,81),unit_del(d,81)]. given #42 (I,wt=11): 178 -member(A,B) | member(A,C) | -member(f3(B,C),C). [back_unit_del(27),unit_del(a,81),unit_del(b,81),unit_del(c,81)]. given #43 (I,wt=11): 179 -member(A,B) | member(A,C) | member(f3(B,C),B). [back_unit_del(26),unit_del(a,81),unit_del(b,81),unit_del(c,81)]. given #44 (I,wt=9): 180 -member(A,B) | member(A,C) | -subset(B,C). [back_unit_del(24),unit_del(a,81),unit_del(b,81),unit_del(c,81)]. given #45 (I,wt=8): 181 subset(A,B) | -member(f2(A,B),B). [back_unit_del(23),unit_del(a,81),unit_del(b,81)]. given #46 (I,wt=8): 182 subset(A,B) | member(f2(A,B),A). [back_unit_del(22),unit_del(a,81),unit_del(b,81)]. given #47 (I,wt=7): 183 ilf_type(f1(A,B),relation_type(B,A)). [back_unit_del(20),unit_del(a,81),unit_del(b,81)]. given #48 (I,wt=11): 184 -ilf_type(A,relation_type(B,C)) | ilf_type(A,subset_type(cross_product(B,C))). [back_unit_del(19),unit_del(a,81),unit_del(b,81)]. given #49 (I,wt=11): 185 -ilf_type(A,subset_type(cross_product(B,C))) | ilf_type(A,relation_type(B,C)). [back_unit_del(18),unit_del(a,81),unit_del(b,81)]. given #50 (I,wt=4): 186 ilf_type(identity_relation_of(A),binary_relation_type). [back_unit_del(17),unit_del(a,81)]. given #51 (I,wt=9): 187 A = B | -member(ordered_pair(B,A),identity_relation_of(C)). [back_unit_del(16),unit_del(a,81),unit_del(b,81),unit_del(c,81)]. given #52 (I,wt=9): 188 member(A,B) | -member(ordered_pair(A,C),identity_relation_of(B)). [back_unit_del(15),unit_del(a,81),unit_del(b,81),unit_del(d,81)]. given #53 (I,wt=12): 189 -member(A,B) | member(ordered_pair(A,C),identity_relation_of(B)) | C != A. [back_unit_del(14),unit_del(a,81),unit_del(b,81),unit_del(d,81)]. given #54 (I,wt=15): 190 -ilf_type(A,relation_type(B,C)) | -subset(identity_relation_of(D),A) | subset(D,range(B,C,A)). [back_unit_del(13),unit_del(a,81),unit_del(b,81),unit_del(c,81)]. given #55 (I,wt=15): 191 -ilf_type(A,relation_type(B,C)) | -subset(identity_relation_of(D),A) | subset(D,domain(B,C,A)). [back_unit_del(12),unit_del(a,81),unit_del(b,81),unit_del(c,81)]. given #56 (I,wt=9): 192 -subset(A,B) | -subset(B,A) | B = A. [back_unit_del(11),unit_del(a,81),unit_del(b,81)]. given #57 (A,wt=15): 193 -ilf_type(A,binary_relation_type) | subset(A,c1) | member(ordered_pair(f4(A,c1),f5(A,c1)),A). [resolve(43,a,30,b)]. given #58 (F,wt=4): 199 -subset(c3,range_of(c4)). [back_rewrite(84),rewrite(197(5))]. given #59 (F,wt=4): 262 range_of(c4) != c3. [ur(174,a,199,a)]. given #60 (F,wt=7): 261 -member(f2(c3,range_of(c4)),range_of(c4)). [ur(181,a,199,a)]. given #61 (F,wt=7): 263 -member(ordered_pair(c3,range_of(c4)),identity_relation_of(A)). [ur(187,a,262,a)]. given #62 (T,wt=4): 218 member(A,power_set(A)). [resolve(169,b,168,b),merge(b)]. given #63 (T,wt=5): 198 ilf_type(range_of(c4),subset_type(c2)). [back_rewrite(196),rewrite(197(4))]. given #64 (T,wt=5): 202 ilf_type(domain_of(c4),subset_type(c3)). [back_rewrite(200),rewrite(201(4))]. given #65 (T,wt=5): 272 ilf_type(A,member_type(power_set(A))). [resolve(218,a,165,c),unit_del(a,166)]. given #66 (A,wt=15): 194 -ilf_type(A,binary_relation_type) | subset(c1,A) | member(ordered_pair(f4(c1,A),f5(c1,A)),c1). [resolve(43,a,30,a)]. given #67 (F,wt=7): 264 -member(ordered_pair(range_of(c4),c3),identity_relation_of(A)). [ur(187,a,262,a(flip))]. given #68 (F,wt=8): 279 -subset(power_set(ordered_pair(c3,range_of(c4))),identity_relation_of(A)). [ur(180,a,218,a,b,263,a)]. given #69 (F,wt=8): 280 -subset(power_set(f2(c3,range_of(c4))),range_of(c4)). [ur(180,a,218,a,b,261,a)]. given #70 (F,wt=8): 290 -subset(power_set(ordered_pair(range_of(c4),c3)),identity_relation_of(A)). [ur(180,a,218,a,b,264,a)]. given #71 (T,wt=4): 287 ilf_type(A,subset_type(A)). [resolve(272,a,172,b