============================== FOF-Prover9 =========================== FOF-Prover9 (32) version 2009-11A, November 2009. Process 23984 was started by mccune on cleo, Tue Nov 3 16:59:21 2009 The command was "/home/mccune/LADR/bin/fof-prover9 -f SET668+3.in". ============================== end of head =========================== ============================== INPUT ================================= % Reading from file SET668+3.in assign(max_seconds,30). 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 (0.01 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)))))))). Max_seconds is 30 for this subproblem. Child search process 23985 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: Predicate symbol precedence: predicate_order([ =, empty, ilf_type, member, subset ]). Function symbol precedence: function_order([ set_type, binary_relation_type, c1, c2, c3, c4, ordered_pair, relation_type, cross_product, 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(binary_resolution). % (non-Horn) % set(neg_ur_resolution). % (non-Horn, less than 100 clauses) Auto_process settings: % set(factor). % (non-Horn) % set(unit_deletion). % (non-Horn) kept: 11 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -subset(A,B) | -subset(B,A) | B = A. [assumption]. kept: 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]. kept: 13 -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]. kept: 14 -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]. kept: 15 -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]. kept: 16 -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]. kept: 17 -ilf_type(A,set_type) | ilf_type(identity_relation_of(A),binary_relation_type). [assumption]. kept: 18 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,subset_type(cross_product(A,B))) | ilf_type(C,relation_type(A,B)). [assumption]. kept: 19 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,relation_type(A,B)) | ilf_type(C,subset_type(cross_product(A,B))). [assumption]. kept: 20 -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(f1(A,B),relation_type(B,A)). [assumption]. kept: 21 -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(A,B) | ilf_type(f2(A,B),set_type). [assumption]. kept: 22 -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(A,B) | member(f2(A,B),A). [assumption]. kept: 23 -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(A,B) | -member(f2(A,B),B). [assumption]. kept: 24 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | -member(C,A) | member(C,B) | -subset(A,B). [assumption]. kept: 25 -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]. kept: 26 -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]. kept: 27 -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]. kept: 28 -ilf_type(A,binary_relation_type) | -ilf_type(B,binary_relation_type) | subset(A,B) | ilf_type(f4(A,B),set_type). [assumption]. kept: 29 -ilf_type(A,binary_relation_type) | -ilf_type(B,binary_relation_type) | subset(A,B) | ilf_type(f5(A,B),set_type). [assumption]. kept: 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]. kept: 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]. kept: 32 -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]. kept: 33 -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]. kept: 34 -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]. kept: 35 -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]. kept: 36 -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]. kept: 37 -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(A,B) | B != A. [assumption]. kept: 38 -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(B,A) | B != A. [assumption]. kept: 39 -ilf_type(A,binary_relation_type) | ilf_type(domain_of(A),set_type). [assumption]. kept: 40 -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(cross_product(A,B),set_type). [assumption]. kept: 41 -ilf_type(A,binary_relation_type) | ilf_type(range_of(A),set_type). [assumption]. kept: 42 -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(ordered_pair(A,B),set_type). [assumption]. kept: 43 ilf_type(c1,binary_relation_type). [assumption]. kept: 44 -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(B,subset_type(A)) | -ilf_type(B,member_type(power_set(A))). [assumption]. kept: 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]. kept: 46 -ilf_type(A,set_type) | ilf_type(f8(A),subset_type(A)). [assumption]. kept: 47 -ilf_type(A,set_type) | subset(A,A). [assumption]. kept: 48 -ilf_type(A,binary_relation_type) | subset(A,A). [assumption]. kept: 49 -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(A,power_set(B)) | ilf_type(f9(A,B),set_type). [assumption]. kept: 50 -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(A,power_set(B)) | member(f9(A,B),A). [assumption]. kept: 51 -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(A,power_set(B)) | -member(f9(A,B),B). [assumption]. kept: 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]. kept: 53 -ilf_type(A,set_type) | -empty(power_set(A)). [assumption]. kept: 54 -ilf_type(A,set_type) | ilf_type(power_set(A),set_type). [assumption]. kept: 55 -ilf_type(A,set_type) | empty(B) | -ilf_type(B,set_type) | ilf_type(A,member_type(B)) | -member(A,B). [assumption]. kept: 56 -ilf_type(A,set_type) | empty(B) | -ilf_type(B,set_type) | member(A,B) | -ilf_type(A,member_type(B)). [assumption]. kept: 57 empty(A) | -ilf_type(A,set_type) | ilf_type(f10(A),member_type(A)). [assumption]. kept: 58 -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]. kept: 59 -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]. 60 -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]. kept: 61 -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) | f16(A) != ordered_pair(C,D). [copy(60),flip(g)]. kept: 62 -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]. kept: 63 -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]. 64 -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]. kept: 65 -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) | f16(A) != ordered_pair(C,D). [copy(64),flip(g)]. kept: 66 -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]. kept: 67 -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]. 68 -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]. kept: 69 -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) | f16(A) != ordered_pair(C,D). [copy(68),flip(g)]. kept: 70 -ilf_type(A,set_type) | empty(A) | ilf_type(f17(A),set_type). [assumption]. kept: 71 -ilf_type(A,set_type) | empty(A) | member(f17(A),A). [assumption]. kept: 72 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | -empty(A). [assumption]. kept: 73 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f18(A),set_type). [assumption]. kept: 74 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | member(f18(A),A). [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]. kept: 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)]. kept: 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]. 78 -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]. kept: 79 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,relation_type(A,B)) | range(A,B,C) = range_of(C). [copy(78),flip(d)]. kept: 80 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,relation_type(A,B)) | ilf_type(range(A,B,C),subset_type(B)). [assumption]. kept: 81 ilf_type(A,set_type). [assumption]. kept: 82 ilf_type(c4,relation_type(c3,c2)). [assumption]. kept: 83 subset(identity_relation_of(c3),c4). [assumption]. kept: 84 domain(c3,c2,c4) != c3. [assumption]. 85 -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)]. kept: 86 member(f11(A),A) | ilf_type(A,binary_relation_type). [copy(85),merge(c),unit_del(a,81)]. 87 -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)]. kept: 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)]. 89 -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)]. kept: 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)]. 91 -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)]. kept: 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)]. 93 -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)]. kept: 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)]. 95 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,subset_type(cross_product(A,B))) | -ilf_type(C,set_type) | ilf_type(C,binary_relation_type). [resolve(9,d,2,c)]. kept: 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)]. 97 -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)]. kept: 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)]. 99 -empty(A) | -ilf_type(A,set_type) | -ilf_type(A,set_type) | ilf_type(A,binary_relation_type). [resolve(10,c,2,c)]. kept: 100 -empty(A) | ilf_type(A,binary_relation_type). [copy(99),merge(c),unit_del(b,81)]. 101 -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)]. kept: 102 -empty(A) | -member(B,A) | ordered_pair(f12(A,B),f13(A,B)) = B. [copy(101),merge(c),unit_del(b,81),unit_del(c,81)]. kept: 103 -ilf_type(A,relation_type(B,B)) | -subset(identity_relation_of(C),A) | subset(C,domain(B,B,A)). [factor(12,a,b),unit_del(a,81),unit_del(b,81)]. kept: 104 -ilf_type(A,relation_type(B,C)) | -subset(identity_relation_of(B),A) | subset(B,domain(B,C,A)). [factor(12,a,c),unit_del(a,81),unit_del(b,81)]. kept: 105 -ilf_type(A,relation_type(B,C)) | -subset(identity_relation_of(C),A) | subset(C,domain(B,C,A)). [factor(12,b,c),unit_del(a,81),unit_del(b,81)]. kept: 106 -ilf_type(A,relation_type(B,B)) | -subset(identity_relation_of(C),A) | subset(C,range(B,B,A)). [factor(13,a,b),unit_del(a,81),unit_del(b,81)]. kept: 107 -ilf_type(A,relation_type(B,C)) | -subset(identity_relation_of(B),A) | subset(B,range(B,C,A)). [factor(13,a,c),unit_del(a,81),unit_del(b,81)]. kept: 108 -ilf_type(A,relation_type(B,C)) | -subset(identity_relation_of(C),A) | subset(C,range(B,C,A)). [factor(13,b,c),unit_del(a,81),unit_del(b,81)]. kept: 109 -member(A,A) | member(ordered_pair(A,B),identity_relation_of(A)) | B != A. [factor(14,a,b),unit_del(a,81),unit_del(c,81)]. kept: 110 -member(A,B) | member(ordered_pair(A,B),identity_relation_of(B)) | B != A. [factor(14,a,d),unit_del(a,81),unit_del(b,81)]. kept: 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)]. kept: 112 member(A,A) | -member(ordered_pair(A,B),identity_relation_of(A)). [factor(15,a,b),unit_del(a,81),unit_del(c,81)]. kept: 113 member(A,B) | -member(ordered_pair(A,B),identity_relation_of(B)). [factor(15,a,d),unit_del(a,81),unit_del(b,81)]. kept: 114 member(A,B) | -member(ordered_pair(A,A),identity_relation_of(B)). [factor(15,b,d),unit_del(a,81),unit_del(b,81)]. kept: 115 A = B | -member(ordered_pair(B,A),identity_relation_of(B)). [factor(16,a,b),unit_del(a,81),unit_del(b,81)]. kept: 116 A = B | -member(ordered_pair(B,A),identity_relation_of(A)). [factor(16,a,c),unit_del(a,81),unit_del(b,81)]. kept: 117 -ilf_type(A,subset_type(cross_product(B,B))) | ilf_type(A,relation_type(B,B)). [factor(18,a,b),unit_del(a,81)]. kept: 118 -ilf_type(A,relation_type(B,B)) | ilf_type(A,subset_type(cross_product(B,B))). [factor(19,a,b),unit_del(a,81)]. kept: 119 ilf_type(f1(A,A),relation_type(A,A)). [factor(20,a,b),unit_del(a,81)]. kept: 120 subset(A,A) | member(f2(A,A),A). [factor(22,a,b),unit_del(a,81)]. kept: 121 subset(A,A) | -member(f2(A,A),A). [factor(23,a,b),unit_del(a,81)]. kept: 122 -member(A,A) | member(A,B) | -subset(A,B). [factor(24,a,c),unit_del(a,81),unit_del(b,81)]. kept: 123 -member(A,B) | member(A,A) | -subset(B,A). [factor(24,b,c),unit_del(a,81),unit_del(b,81)]. kept: 124 -member(A,A) | member(A,B) | member(f3(A,B),A). [factor(26,a,c),unit_del(a,81),unit_del(b,81)]. kept: 125 -member(A,B) | member(A,A) | member(f3(B,A),B). [factor(26,b,c),unit_del(a,81),unit_del(b,81)]. kept: 126 -member(A,A) | member(A,B) | -member(f3(A,B),B). [factor(27,a,c),unit_del(a,81),unit_del(b,81)]. kept: 127 -member(A,B) | member(A,A) | -member(f3(B,A),A). [factor(27,b,c),unit_del(a,81),unit_del(b,81)]. kept: 128 -ilf_type(A,binary_relation_type) | -ilf_type(B,binary_relation_type) | -member(ordered_pair(C,C),A) | member(ordered_pair(C,C),B) | -subset(A,B). [factor(32,c,d),unit_del(c,81)]. kept: 129 -ilf_type(A,binary_relation_type) | -ilf_type(B,binary_relation_type) | -member(ordered_pair(C,C),A) | member(ordered_pair(C,C),B) | member(ordered_pair(f6(A,B),f7(A,B)),A). [factor(35,c,d),unit_del(c,81)]. kept: 130 -ilf_type(A,binary_relation_type) | -ilf_type(B,binary_relation_type) | -member(ordered_pair(C,C),A) | member(ordered_pair(C,C),B) | -member(ordered_pair(f6(A,B),f7(A,B)),B). [factor(36,c,d),unit_del(c,81)]. kept: 131 subset(A,A). [factor(37,a,b),xx(c),unit_del(a,81)]. kept: 132 ilf_type(A,subset_type(A)) | -ilf_type(A,member_type(power_set(A))). [factor(44,a,b),unit_del(a,81)]. kept: 133 ilf_type(A,member_type(power_set(A))) | -ilf_type(A,subset_type(A)). [factor(45,a,b),unit_del(a,81)]. kept: 134 member(A,power_set(A)) | member(f9(A,A),A). [factor(50,a,b),unit_del(a,81)]. kept: 135 member(A,power_set(A)) | -member(f9(A,A),A). [factor(51,a,b),unit_del(a,81)]. kept: 136 -member(A,A) | member(A,B) | -member(A,power_set(B)). [factor(52,a,c),unit_del(a,81),unit_del(b,81)]. kept: 137 -member(A,B) | member(A,A) | -member(B,power_set(A)). [factor(52,b,c),unit_del(a,81),unit_del(b,81)]. kept: 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)]. kept: 139 empty(A) | ilf_type(A,member_type(A)) | -member(A,A). [factor(55,a,c),unit_del(a,81)]. kept: 140 empty(A) | member(A,A) | -ilf_type(A,member_type(A)). [factor(56,a,c),unit_del(a,81)]. kept: 141 -member(A,A) | ordered_pair(f14(A,A),f15(A,A)) = A | member(f16(A),A). [factor(67,a,b),unit_del(a,81)]. kept: 142 -member(A,A) | ordered_pair(f14(A,A),f15(A,A)) = A | f16(A) != ordered_pair(B,C). [factor(69,a,b),unit_del(a,81),unit_del(d,81),unit_del(e,81)]. kept: 143 -member(A,B) | ordered_pair(f14(B,A),f15(B,A)) = A | f16(B) != ordered_pair(B,C). [factor(69,a,e),unit_del(a,81),unit_del(b,81),unit_del(e,81)]. kept: 144 -member(A,B) | ordered_pair(f14(B,A),f15(B,A)) = A | f16(B) != ordered_pair(C,B). [factor(69,a,f),unit_del(a,81),unit_del(b,81),unit_del(e,81)]. kept: 145 -member(A,B) | ordered_pair(f14(B,A),f15(B,A)) = A | f16(B) != ordered_pair(A,C). [factor(69,b,e),unit_del(a,81),unit_del(b,81),unit_del(e,81)]. kept: 146 -member(A,B) | ordered_pair(f14(B,A),f15(B,A)) = A | f16(B) != ordered_pair(C,A). [factor(69,b,f),unit_del(a,81),unit_del(b,81),unit_del(e,81)]. kept: 147 -member(A,B) | ordered_pair(f14(B,A),f15(B,A)) = A | f16(B) != ordered_pair(C,C). [factor(69,e,f),unit_del(a,81),unit_del(b,81),unit_del(e,81)]. kept: 148 -member(A,A) | -empty(A). [factor(72,a,b),unit_del(a,81)]. kept: 149 -member(A,A) | member(f18(A),A). [factor(74,a,b),unit_del(a,81)]. kept: 150 -ilf_type(A,relation_type(B,B)) | domain(B,B,A) = domain_of(A). [factor(76,a,b),unit_del(a,81)]. kept: 151 -ilf_type(A,relation_type(B,B)) | ilf_type(domain(B,B,A),subset_type(B)). [factor(77,a,b),unit_del(a,81)]. kept: 152 -ilf_type(A,relation_type(B,B)) | range(B,B,A) = range_of(A). [factor(79,a,b),unit_del(a,81)]. kept: 153 -ilf_type(A,relation_type(B,B)) | ilf_type(range(B,B,A),subset_type(B)). [factor(80,a,b),unit_del(a,81)]. kept: 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)]. kept: 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)]. kept: 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)]. kept: 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)]. kept: 158 -member(A,B) | member(f18(B),B). [back_unit_del(74),unit_del(a,81),unit_del(b,81)]. kept: 159 -member(A,B) | -empty(B). [back_unit_del(72),unit_del(a,81),unit_del(b,81)]. kept: 160 empty(A) | member(f17(A),A). [back_unit_del(71),unit_del(a,81)]. kept: 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)]. kept: 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)]. kept: 163 empty(A) | ilf_type(f10(A),member_type(A)). [back_unit_del(57),unit_del(b,81)]. kept: 164 empty(A) | member(B,A) | -ilf_type(B,member_type(A)). [back_unit_del(56),unit_del(a,81),unit_del(c,81)]. kept: 165 empty(A) | ilf_type(B,member_type(A)) | -member(B,A). [back_unit_del(55),unit_del(a,81),unit_del(c,81)]. kept: 166 -empty(power_set(A)). [back_unit_del(53),unit_del(a,81)]. kept: 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)]. kept: 168 member(A,power_set(B)) | -member(f9(A,B),B). [back_unit_del(51),unit_del(a,81),unit_del(b,81)]. kept: 169 member(A,power_set(B)) | member(f9(A,B),A). [back_unit_del(50),unit_del(a,81),unit_del(b,81)]. kept: 170 ilf_type(f8(A),subset_type(A)). [back_unit_del(46),unit_del(a,81)]. kept: 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)]. kept: 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)]. kept: 173 subset(A,B) | A != B. [back_unit_del(38),unit_del(a,81),unit_del(b,81)]. kept: 174 subset(A,B) | B != A. [back_unit_del(37),unit_del(a,81),unit_del(b,81)]. kept: 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)]. kept: 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)]. kept: 177 -ilf_type(A,binary_relation_type) | -ilf_type(B,binary_relation_type) | -member(ordered_pair(C,D),A) | member(ordered_pair(C,D),B) | -subset(A,B). [back_unit_del(32),unit_del(c,81),unit_del(d,81)]. kept: 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)]. kept: 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)]. kept: 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)]. kept: 181 subset(A,B) | -member(f2(A,B),B). [back_unit_del(23),unit_del(a,81),unit_del(b,81)]. kept: 182 subset(A,B) | member(f2(A,B),A). [back_unit_del(22),unit_del(a,81),unit_del(b,81)]. kept: 183 ilf_type(f1(A,B),relation_type(B,A)). [back_unit_del(20),unit_del(a,81),unit_del(b,81)]. kept: 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)]. kept: 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)]. kept: 186 ilf_type(identity_relation_of(A),binary_relation_type). [back_unit_del(17),unit_del(a,81)]. kept: 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)]. kept: 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)]. kept: 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)]. kept: 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)]. kept: 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)]. kept: 192 -subset(A,B) | -subset(B,A) | B = A. [back_unit_del(11),unit_del(a,81),unit_del(b,81)]. ============================== 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): 268 -member(ordered_pair(c3,domain_of(c4)),identity_relation_of(A)). [ur(187,a,202,a)]. given #60 (F,wt=7): 269 -member(ordered_pair(domain_of(c4),c3),identity_relation_of(A)). [ur(187,a,202,a(flip))]. given #61 (F,wt=10): 270 -member(ordered_pair(ordered_pair(c3,domain_of(c4)),A),identity_relation_of(identity_relation_of(B))). [ur(188,a,268,a)]. given #62 (T,wt=4): 221 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): 279 ilf_type(A,member_type(power_set(A))). [resolve(221,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): 289 -subset(power_set(ordered_pair(domain_of(c4),c3)),identity_relation_of(A)). [ur(180,a,221,a,b,269,a)]. given #68 (F,wt=8): 290 -subset(power_set(ordered_pair(c3,domain_of(c4))),identity_relation_of(A)). [ur(180,a,221,a,b,268,a)]. given #69 (F,wt=8): 303 power_set(ordered_pair(domain_of(c4),c3)) != identity_relation_of(A). [ur(174,a,289,a),flip(a)]. given #70 (F,wt=8): 306 power_set(ordered_pair(c3,domain_of(c4))) != identity_relation_of(A). [ur(174,a,290,a),flip(a)]. given #71 (T,wt=4): 299 ilf_type(A,subset_type(A)). [resolve(279,a,172,b)]. given #72 (T,wt=5): 312 ilf_type(cross_product(A,B),binary_relation_type). [resolve(299,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): 214 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): 295 -member(power_set(ordered_pair(domain_of(c4),c3)),power_set(identity_relation_of(A))). [ur(167,a,221,a,b,269,a)]. given #77 (F,wt=9): 296 -member(power_set(ordered_pair(c3,domain_of(c4))),power_set(identity_relation_of(A))). [ur(167,a,221,a,b,268,a)]. given #78 (F,wt=10): 271 -member(ordered_pair(ordered_pair(domain_of(c4),c3),A),identity_relation_of(identity_relation_of(B))). [ur(188,a,269,a)]. given #79 (F,wt=10): 359 -subset(power_set(power_set(ordered_pair(domain_of(c4),c3))),power_set(identity_relation_of(A))). [ur(180,a,221,a,b,295,a)]. given #80 (T,wt=6): 227 member(A,power_set(B)) | -empty(A). [resolve(169,b,159,a)]. given #81 (T,wt=6): 235 ilf_type(f8(cross_product(A,B)),binary_relation_type). [resolve(170,a,96,a)]. given #82 (T,wt=6): 236 ilf_type(f8(A),member_type(power_set(A))). [resolve(171,b,170,a)]. given #83 (T,wt=5): 381 member(f8(A),power_set(A)). [resolve(236,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): 398 -member(ordered_pair(domain_of(c4),c3),f8(identity_relation_of(A))). [ur(167,b,269,a,c,381,a)]. given #86 (F,wt=8): 399 -member(ordered_pair(c3,domain_of(c4)),f8(identity_relation_of(A))). [ur(167,b,268,a,c,381,a)]. given #87 (F,wt=9): 401 -subset(power_set(ordered_pair(domain_of(c4),c3)),f8(identity_relation_of(A))). [ur(180,a,221,a,b,398,a)]. given #88 (F,wt=9): 403 -member(ordered_pair(domain_of(c4),c3),f8(f8(identity_relation_of(A)))). [ur(167,b,398,a,c,381,a)]. given #89 (T,wt=6): 237 ilf_type(f10(power_set(A)),subset_type(A)). [resolve(172,b,163,b),unit_del(b,166)]. given #90 (T,wt=6): 251 ilf_type(c4,subset_type(cross_product(c3,c2))). [resolve(184,a,82,a)]. given #91 (T,wt=3): 422 ilf_type(c4,binary_relation_type). [resolve(251,a,96,a)]. given #92 (T,wt=6): 282 member(f18(power_set(A)),power_set(A)). [resolve(221,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): 406 -subset(power_set(ordered_pair(c3,domain_of(c4))),f8(identity_relation_of(A))). [ur(180,a,221,a,b,399,a)]. given #95 (F,wt=9): 408 -member(ordered_pair(c3,domain_of(c4)),f8(f8(identity_relation_of(A)))). [ur(167,b,399,a,c,381,a)]. given #96 (F,wt=9): 412 f8(identity_relation_of(A)) != power_set(ordered_pair(domain_of(c4),c3)). [ur(174,a,401,a)]. given #97 (F,wt=9): 446 -member(ordered_pair(domain_of(c4),c3),f18(power_set(identity_relation_of(A)))). [ur(167,b,269,a,c,282,a)]. given #98 (T,wt=6): 297 ilf_type(range_of(c4),member_type(power_set(c2))). [resolve(198,a,171,b)]. given #99 (T,wt=5): 465 member(range_of(c4),power_set(c2)). [resolve(297,a,164,c),unit_del(a,166)]. given #100 (T,wt=6): 298 ilf_type(domain_of(c4),member_type(power_set(c3))). [resolve(201,a,171,b)]. given #101 (T,wt=5): 478 member(domain_of(c4),power_set(c3)). [resolve(298,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): 447 -member(ordered_pair(c3,domain_of(c4)),f18(power_set(identity_relation_of(A)))). [ur(167,b,268,a,c,282,a)]. given #104 (F,wt=9): 450 f8(identity_relation_of(A)) != power_set(ordered_pair(c3,domain_of(c4))). [ur(174,a,406,a)]. given #105 (F,wt=10): 363 -ilf_type(power_set(ordered_pair(domain_of(c4),c3)),member_type(power_set(identity_relation_of(A)))). [ur(164,a,166,a,b,295,a)]. given #106 (F,wt=9): 506 -ilf_type(power_set(ordered_pair(domain_of(c4),c3)),subset_type(identity_relation_of(A))). [ur(171,a,363,a)]. given #107 (T,wt=6): 351 ilf_type(A,binary_relation_type) | -empty(identity_relation_of(A)). [resolve(195,a,159,a)]. given #108 (T,wt=7): 215 empty(A) | ilf_type(f17(A),member_type(A)). [resolve(165,c,160,b),merge(c)]. given #109 (T,wt=6): 507 ilf_type(f17(power_set(A)),subset_type(A)). [resolve(215,b,172,b),unit_del(a,166)]. given #110 (T,wt=7): 244 -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): 365 -subset(power_set(power_set(ordered_pair(c3,domain_of(c4)))),power_set(identity_relation_of(A))). [ur(180,a,221,a,b,296,a)]. given #113 (F,wt=10): 369 -ilf_type(power_set(ordered_pair(c3,domain_of(c4))),member_type(power_set(identity_relation_of(A)))). [ur(164,a,166,a,b,296,a)]. given #114 (F,wt=9): 536 -ilf_type(power_set(ordered_pair(c3,domain_of(c4))),subset_type(identity_relation_of(A))). [ur(171,a,369,a)]. given #115 (F,wt=10): 376 power_set(power_set(ordered_pair(domain_of(c4),c3))) != power_set(identity_relation_of(A)). [ur(174,a,359,a),flip(a)]. given #116 (T,wt=5): 526 empty(A) | -empty(identity_relation_of(A)). [resolve(205,b,159,a)]. given #117 (T,wt=7): 247 ilf_type(domain_of(f1(A,B)),subset_type(B)). [resolve(183,a,156,a),rewrite([246(2)])]. given #118 (T,wt=7): 249 ilf_type(range_of(f1(A,B)),subset_type(A)). [resolve(183,a,154,a),rewrite([248(2)])]. given #119 (T,wt=7): 283 member(ordered_pair(A,A),identity_relation_of(power_set(A))). [resolve(221,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): 539 -empty(identity_relation_of(power_set(A))). [ur(526,a,166,a)]. given #122 (F,wt=5): 576 -empty(identity_relation_of(identity_relation_of(power_set(A)))). [ur(526,a,539,a)]. given #123 (F,wt=6): 579 -empty(identity_relation_of(identity_relation_of(identity_relation_of(power_set(A))))). [ur(526,a,576,a)]. given #124 (F,wt=7): 584 -empty(identity_relation_of(identity_relation_of(identity_relation_of(identity_relation_of(power_set(A)))))). [ur(526,a,579,a)]. given #125 (T,wt=7): 311 ilf_type(cross_product(A,B),relation_type(A,B)). [resolve(299,a,185,a)]. given #126 (T,wt=7): 322 empty(A) | ilf_type(f18(A),member_type(A)). [resolve(204,b,165,c),merge(b)]. given #127 (T,wt=6): 598 ilf_type(f18(power_set(A)),subset_type(A)). [resolve(322,b,172,b),unit_del(a,166)]. given #128 (T,wt=7): 385 -member(A,f8(B)) | member(A,B). [resolve(381,a,167,c)]. given #129 (A,wt=20): 207 empty(A) | ordered_pair(f12(A,f17(A)),f13(A,f17(A))) = f17(A) | f11(A) != ordered_pair(B,C). [resolve(160,b,94,a)]. given #130 (F,wt=8): 589 -empty(identity_relation_of(identity_relation_of(identity_relation_of(identity_relation_of(identity_relation_of(power_set(A))))))). [ur(526,a,584,a)]. given #131 (F,wt=9): 577 -ilf_type(ordered_pair(domain_of(c4),c3),member_type(identity_relation_of(power_set(A)))). [ur(164,a,539,a,b,269,a)]. given #132 (F,wt=9): 578 -ilf_type(ordered_pair(c3,domain_of(c4)),member_type(identity_relation_of(power_set(A)))). [ur(164,a,539,a,b,268,a)]. given #133 (F,wt=9): 608 -empty(identity_relation_of(identity_relation_of(identity_relation_of(identity_relation_of(identity_relation_of(identity_relation_of(power_set(A)))))))). [ur(526,a,589,a)]. given #134 (T,wt=7): 419 ilf_type(f10(power_set(A)),member_type(power_set(A))). [resolve(237,a,171,b)]. given #135 (T,wt=6): 618 member(f10(power_set(A)),power_set(A)). [resolve(419,a,164,c),unit_del(a,166)]. given #136 (T,wt=7): 420 ilf_type(f10(power_set(cross_product(A,B))),binary_relation_type). [resolve(237,a,96,a)]. given #137 (T,wt=7): 421 ilf_type(c4,member_type(power_set(cross_product(c3,c2)))). [resolve(251,a,171,b)]. given #138 (A,wt=18): 208 empty(A) | ordered_pair(f12(A,f17(A)),f13(A,f17(A))) = f17(A) | member(f11(A),A). [resolve(160,b,92,a)]. given #139 (F,wt=9): 640 -member(ordered_pair(domain_of(c4),c3),f10(power_set(identity_relation_of(A)))). [ur(167,b,269,a,c,618,a)]. given #140 (F,wt=9): 641 -member(ordered_pair(c3,domain_of(c4)),f10(power_set(identity_relation_of(A)))). [ur(167,b,268,a,c,618,a)]. given #141 (F,wt=10): 394 -member(power_set(ordered_pair(c3,domain_of(c4))),f8(power_set(identity_relation_of(A)))). [ur(167,b,296,a,c,381,a)]. given #142 (F,wt=10): 395 -member(power_set(ordered_pair(domain_of(c4),c3)),f8(power_set(identity_relation_of(A)))). [ur(167,b,295,a,c,381,a)]. given #143 (T,wt=6): 646 member(c4,power_set(cross_product(c3,c2))). [resolve(421,a,164,c),unit_del(a,166)]. given #144 (T,wt=7): 431 ilf_type(f18(power_set(A)),member_type(power_set(A))). [resolve(282,a,165,c),unit_del(a,166)]. given #145 (T,wt=7): 469 -member(A,range_of(c4)) | member(A,c2). [resolve(465,a,167,c)]. given #146 (T,wt=7): 482 -member(A,domain_of(c4)) | member(A,c3). [resolve(478,a,167,c)]. given #147 (A,wt=17): 209 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 #148 (F,wt=10): 404 -member(power_set(ordered_pair(domain_of(c4),c3)),power_set(f8(identity_relation_of(A)))). [ur(167,a,221,a,b,398,a)]. given #149 (F,wt=10): 409 -member(power_set(ordered_pair(c3,domain_of(c4))),power_set(f8(identity_relation_of(A)))). [ur(167,a,221,a,b,399,a)]. given #150 (F,wt=10): 414 -subset(power_set(ordered_pair(domain_of(c4),c3)),f8(f8(identity_relation_of(A)))). [ur(180,a,221,a,b,403,a)]. given #151 (F,wt=10): 416 -member(ordered_pair(domain_of(c4),c3),f8(f8(f8(identity_relation_of(A))))). [ur(167,b,403,a,c,381,a)]. given #152 (T,wt=7): 509 ilf_type(f17(power_set(A)),member_type(power_set(A))). [resolve(507,a,171,b)]. given #153 (T,wt=6): 742 member(f17(power_set(A)),power_set(A)). [resolve(509,a,164,c),unit_del(a,166)]. given #154 (T,wt=7): 510 ilf_type(f17(power_set(cross_product(A,B))),binary_relation_type). [resolve(507,a,96,a)]. given #155 (T,wt=7): 595 ilf_type(domain_of(cross_product(A,B)),subset_type(A)). [resolve(311,a,156,a),rewrite([594(2)])]. given #156 (A,wt=20): 210 ordered_pair(f14(A,f17(A)),f15(A,f17(A))) = f17(A) | f16(A) != ordered_pair(B,C) | empty(A). [resolve(161,a,160,b)]. given #157 (F,wt=9): 771 -member(ordered_pair(domain_of(c4),c3),f17(power_set(identity_relation_of(A)))). [ur(167,b,269,a,c,742,a)]. given #158 (F,wt=9): 772 -member(ordered_pair(c3,domain_of(c4)),f17(power_set(identity_relation_of(A)))). [ur(167,b,268,a,c,742,a)]. given #159 (F,wt=10): 440 -member(ordered_pair(c3,domain_of(c4)),f18(power_set(f8(identity_relation_of(A))))). [ur(167,b,399,a,c,282,a)]. given #160 (F,wt=10): 441 -member(ordered_pair(domain_of(c4),c3),f18(power_set(f8(identity_relation_of(A))))). [ur(167,b,398,a,c,282,a)]. given #161 (T,wt=7): 597 ilf_type(range_of(cross_product(A,B)),subset_type(B)). [resolve(311,a,154,a),rewrite([596(2)])]. given #162 (T,wt=7): 601 ilf_type(f18(power_set(cross_product(A,B))),binary_relation_type). [resolve(598,a,96,a)]. given #163 (T,wt=8): 219 -member(A,f17(power_set(B))) | member(A,B). [resolve(167,c,160,b),unit_del(c,166)]. given #164 (T,wt=8): 228 member(A,power_set(B)) | member(f18(A),A). [resolve(169,b,158,a)]. given #165 (A,wt=21): 211 ordered_pair(f14(A,f11(A)),f15(A,f11(A))) = f11(A) | f16(A) != ordered_pair(B,C) | ilf_type(A,binary_relation_type). [resolve(161,a,86,a)]. given #166 (F,wt=10): 452 -subset(power_set(ordered_pair(c3,domain_of(c4))),f8(f8(identity_relation_of(A)))). [ur(180,a,221,a,b,408,a)]. given #167 (F,wt=10): 454 -member(ordered_pair(c3,domain_of(c4)),f8(f8(f8(identity_relation_of(A))))). [ur(167,b,408,a,c,381,a)]. given #168 (F,wt=10): 460 -subset(power_set(ordered_pair(domain_of(c4),c3)),f18(power_set(identity_relation_of(A)))). [ur(180,a,221,a,b,446,a)]. given #169 (F,wt=10): 462 -member(ordered_pair(domain_of(c4),c3),f8(f18(power_set(identity_relation_of(A))))). [ur(167,b,446,a,c,381,a)]. given #170 (T,wt=8): 250 ilf_type(f1(A,B),subset_type(cross_product(B,A))). [resolve(184,a,183,a)]. given #171 (T,wt=5): 887 ilf_type(f1(A,B),binary_relation_type). [resolve(250,a,96,a)]. given #172 (T,wt=8): 252 ilf_type(f8(cross_product(A,B)),relation_type(A,B)). [resolve(185,a,170,a)]. given #173 (T,wt=8): 265 -subset(c4,identity_relation_of(c3)) | identity_relation_of(c3) = c4. [resolve(192,a,83,a),flip(b)]. given #174 (A,wt=18): 212 ordered_pair(f14(A,f17(A)),f15(A,f17(A))) = f17(A) | member(f16(A),A) | empty(A). [resolve(162,a,160,b)]. given #175 (F,wt=10): 499 -subset(power_set(ordered_pair(c3,domain_of(c4))),f18(power_set(identity_relation_of(A)))). [ur(180,a,221,a,b,447,a)]. given #176 (F,wt=10): 501 -member(ordered_pair(c3,domain_of(c4)),f8(f18(power_set(identity_relation_of(A))))). [ur(167,b,447,a,c,381,a)]. given #177 (F,wt=10): 535 power_set(power_set(ordered_pair(c3,domain_of(c4)))) != power_set(identity_relation_of(A)). [ur(174,a,365,a),flip(a)]. given #178 (F,wt=10): 561 -subset(identity_relation_of(power_set(ordered_pair(domain_of(c4),c3))),identity_relation_of(identity_relation_of(A))). [ur(180,a,283,a,b,271,a)]. given #179 (T,wt=8): 278 member(A,B) | -member(power_set(A),power_set(B)). [resolve(221,a,167,a)]. given #180 (T,wt=8): 320 -member(A,f18(power_set(B))) | member(A,B). [resolve(204,b,167,c),unit_del(a,166)]. given #181 (T,wt=8): 333 -member(A,f10(power_set(B))) | member(A,B). [resolve(214,b,167,c),unit_del(a,166)]. given #182 (T,wt=8): 511 member(f10(identity_relation_of(c3)),c4) | empty(identity_relation_of(c3)). [resolve(244,a,214,b)]. given #183 (A,wt=19): 213 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 #184 (F,wt=10): 562 -subset(identity_relation_of(power_set(ordered_pair(c3,domain_of(c4)))),identity_relation_of(identity_relation_of(A))). [ur(180,a,283,a,b,270,a)]. given #185 (F,wt=10): 582 -ilf_type(ordered_pair(domain_of(c4),c3),member_type(identity_relation_of(identity_relation_of(power_set(A))))). [ur(164,a,576,a,b,269,a)]. given #186 (F,wt=10): 583 -ilf_type(ordered_pair(c3,domain_of(c4)),member_type(identity_relation_of(identity_relation_of(power_set(A))))). [ur(164,a,576,a,b,268,a)]. given #187 (F,wt=10): 613 -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(526,a,608,a)]. given #188 (T,wt=5): 955 empty(identity_relation_of(c3)) | -empty(c4). [resolve(511,a,159,a)]. given #189 (T,wt=7): 956 empty(identity_relation_of(c3)) | member(f18(c4),c4). [resolve(511,a,158,a)]. given #190 (T,wt=8): 512 member(f18(identity_relation_of(c3)),c4) | empty(identity_relation_of(c3)). [resolve(244,a,204,b)]. given #191 (T,wt=8): 515 member(f17(identity_relation_of(c3)),c4) | empty(identity_relation_of(c3)). [resolve(244,a,160,b)]. given #192 (A,wt=10): 216 empty(A) | ilf_type(f11(A),member_type(A)) | ilf_type(A,binary_relation_type). [resolve(165,c,86,a)]. given #193 (F,wt=10): 634 -member(ordered_pair(c3,domain_of(c4)),f10(power_set(f8(identity_relation_of(A))))). [ur(167,b,399,a,c,618,a)]. given #194 (F,wt=10): 635 -member(ordered_pair(domain_of(c4),c3),f10(power_set(f8(identity_relation_of(A))))). [ur(167,b,398,a,c,618,a)]. given #195 (F,wt=10): 658 -member(ordered_pair(domain_of(c4),c3),f8(f10(power_set(identity_relation_of(A))))). [ur(385,b,640,a)]. given #196 (F,wt=10): 660 -subset(power_set(ordered_pair(domain_of(c4),c3)),f10(power_set(identity_relation_of(A)))). [ur(180,a,221,a,b,640,a)]. given #197 (T,wt=8): 527 empty(A) | member(f18(identity_relation_of(A)),identity_relation_of(A)). [resolve(205,b,158,a)]. given #198 (T,wt=7): 1047 empty(c3) | member(f18(identity_relation_of(c3)),c4). [resolve(527,b,244,a)]. given #199 (T,wt=4): 1066 empty(c3) | -empty(c4). [resolve(1047,b,159,a)]. given #200 (T,wt=6): 1067 empty(c3) | member(f18(c4),c4). [resolve(1047,b,158,a)]. given #201 (A,wt=10): 217 member(f17(A),B) | -member(A,power_set(B)) | empty(A). [resolve(167,a,160,b)]. given #202 (F,wt=10): 665 -member(ordered_pair(c3,domain_of(c4)),f8(f10(power_set(identity_relation_of(A))))). [ur(385,b,641,a)]. given #203 (F,wt=10): 667 -subset(power_set(ordered_pair(c3,domain_of(c4))),f10(power_set(identity_relation_of(A)))). [ur(180,a,221,a,b,641,a)]. given #204 (F,wt=10): 734 f8(f8(identity_relation_of(A))) != power_set(ordered_pair(domain_of(c4),c3)). [ur(174,a,414,a)]. given #205 (F,wt=10): 763 -member(ordered_pair(c3,domain_of(c4)),f17(power_set(f8(identity_relation_of(A))))). [ur(167,b,399,a,c,742,a)]. given #206 (T,wt=8): 541 ilf_type(domain_of(f1(A,B)),member_type(power_set(B))). [resolve(247,a,171,b)]. given #207 (T,wt=7): 1111 member(domain_of(f1(A,B)),power_set(B)). [resolve(541,a,164,c),unit_del(a,166)]. given #208 (T,wt=8): 542 ilf_type(domain_of(f1(A,cross_product(B,C))),binary_relation_type). [resolve(247,a,96,a)]. given #209 (T,wt=8): 544 ilf_type(range_of(f1(A,B)),member_type(power_set(A))). [resolve(249,a,171,b)]. given #210 (A,wt=11): 218 member(f11(A),B) | -member(A,power_set(B)) | ilf_type(A,binary_relation_type). [resolve(167,a,86,a)]. given #211 (F,wt=10): 764 -member(ordered_pair(domain_of(c4),c3),f17(power_set(f8(identity_relation_of(A))))). [ur(167,b,398,a,c,742,a)]. given #212 (F,wt=10): 781 -member(ordered_pair(domain_of(c4),c3),f8(f17(power_set(identity_relation_of(A))))). [ur(385,b,771,a)]. given #213 (F,wt=10): 783 -subset(power_set(ordered_pair(domain_of(c4),c3)),f17(power_set(identity_relation_of(A)))). [ur(180,a,221,a,b,771,a)]. given #214 (F,wt=10): 789 -member(ordered_pair(c3,domain_of(c4)),f8(f17(power_set(identity_relation_of(A))))). [ur(385,b,772,a)]. given #215 (T,wt=7): 1160 member(range_of(f1(A,B)),power_set(A)). [resolve(544,a,164,c),unit_del(a,166)]. given #216 (T,wt=8): 545 ilf_type(range_of(f1(cross_product(A,B),C)),binary_relation_type). [resolve(249,a,96,a)]. given #217 (T,wt=8): 552 ilf_type(ordered_pair(A,A),member_type(identity_relation_of(power_set(A)))). [resolve(283,a,165,c),unit_del(a,539)]. given #218 (T,wt=8): 555 member(f18(identity_relation_of(power_set(A))),identity_relation_of(power_set(A))). [resolve(283,a,158,a)]. given #219 (A,wt=12): 220 -member(A,f11(power_set(B))) | member(A,B) | ilf_type(power_set(B),binary_relation_type). [resolve(167,c,86,a)]. given #220 (F,wt=10): 791 -subset(power_set(ordered_pair(c3,domain_of(c4))),f17(power_set(identity_relation_of(A)))). [ur(180,a,221,a,b,772,a)]. given #221 (F,wt=10): 865 f8(f8(identity_relation_of(A))) != power_set(ordered_pair(c3,domain_of(c4))). [ur(174,a,452,a)]. given #222 (F,wt=10): 876 f18(power_set(identity_relation_of(A))) != power_set(ordered_pair(domain_of(c4),c3)). [ur(174,a,460,a)]. given #223 (F,wt=10): 915 f18(power_set(identity_relation_of(A))) != power_set(ordered_pair(c3,domain_of(c4))). [ur(174,a,499,a)]. given #224 (T,wt=8): 602 member(f10(f8(A)),A) | empty(f8(A)). [resolve(385,a,214,b)]. given #225 (T,wt=5): 1296 empty(f8(A)) | -empty(A). [resolve(602,a,159,a)]. given #226 (T,wt=7): 1297 empty(f8(A)) | member(f18(A),A). [resolve(602,a,158,a)]. given #227 (T,wt=8): 603 member(f18(f8(A)),A) | empty(f8(A)). [resolve(385,a,204,b)]. given #228 (A,wt=14): 222 member(power_set(A),power_set(B)) | -member(C,f9(power_set(A),B)) | member(C,A). [resolve(169,b,167,c)]. given #229 (F,wt=10): 928 identity_relation_of(power_set(ordered_pair(domain_of(c4),c3))) != identity_relation_of(identity_relation_of(A)). [ur(174,a,561,a),flip(a)]. given #230 (F,wt=10): 977 identity_relation_of(power_set(ordered_pair(c3,domain_of(c4)))) != identity_relation_of(identity_relation_of(A)). [ur(174,a,562,a),flip(a)]. given #231 (F,wt=10): 1046 f10(power_set(identity_relation_of(A))) != power_set(ordered_pair(domain_of(c4),c3)). [ur(174,a,660,a)]. given #232 (F,wt=10): 1100 f10(power_set(identity_relation_of(A))) != power_set(ordered_pair(c3,domain_of(c4))). [ur(174,a,667,a)]. given #233 (T,wt=8): 606 member(f17(f8(A)),A) | empty(f8(A)). [resolve(385,a,160,b)]. given #234 (T,wt=8): 689 -member(A,c4) | member(A,cross_product(c3,c2)). [resolve(646,a,167,c)]. given #235 (T,wt=8): 698 member(f10(range_of(c4)),c2) | empty(range_of(c4)). [resolve(469,a,214,b)]. given #236 (T,wt=5): 1410 empty(range_of(c4)) | -empty(c2). [resolve(698,a,159,a)]. given #237 (A,wt=13): 223 member(A,power_set(B)) | member(f9(A,B),C) | -member(A,power_set(C)). [resolve(169,b,167,a)]. given #238 (F,wt=10): 1154 -member(ordered_pair(domain_of(c4),c3),domain_of(f1(A,identity_relation_of(B)))). [ur(167,b,269,a,c,1111,a)]. given #239 (F,wt=10): 1155 -member(ordered_pair(c3,domain_of(c4)),domain_of(f1(A,identity_relation_of(B)))). [ur(167,b,268,a,c,1111,a)]. given #240 (F,wt=10): 1187 f17(power_set(identity_relation_of(A))) != power_set(ordered_pair(domain_of(c4),c3)). [ur(174,a,783,a)]. given #241 (F,wt=10): 1243 -member(ordered_pair(domain_of(c4),c3),range_of(f1(identity_relation_of(A),B))). [ur(167,b,269,a,c,1160,a)]. given #242 (T,wt=7): 1411 empty(range_of(c4)) | member(f18(c2),c2). [resolve(698,a,158,a)]. given #243 (T,wt=8): 700 member(f18(range_of(c4)),c2) | empty(range_of(c4)). [resolve(469,a,204,b)]. given #244 (T,wt=8): 703 member(f17(range_of(c4)),c2) | empty(range_of(c4)). [resolve(469,a,160,b)]. given #245 (T,wt=8): 705 member(f10(domain_of(c4)),c3) | empty(domain_of(c4)). [resolve(482,a,214,b)]. given #246 (A,wt=12): 224 member(A,power_set(B)) | empty(A) | ilf_type(f9(A,B),member_type(A)). [resolve(169,b,165,c)]. given #247 (F,wt=10): 1244 -member(ordered_pair(c3,domain_of(c4)),range_of(f1(identity_relation_of(A),B))). [ur(167,b,268,a,c,1160,a)]. given #248 (F,wt=10): 1271 f17(power_set(identity_relation_of(A))) != power_set(ordered_pair(c3,domain_of(c4))). [ur(174,a,791,a)]. given #249 (F,wt=11): 288 -subset(power_set(ordered_pair(ordered_pair(c3,domain_of(c4)),A)),identity_relation_of(identity_relation_of(B))). [ur(180,a,221,a,b,270,a)]. given #250 (F,wt=11): 292 -member(f3(power_set(ordered_pair(domain_of(c4),c3)),identity_relation_of(A)),identity_relation_of(A)). [ur(178,a,221,a,b,269,a)]. given #251 (T,wt=5): 1499 empty(domain_of(c4)) | -empty(c3). [resolve(705,a,159,a)]. given #252 (T,wt=7): 1500 empty(domain_of(c4)) | member(f18(c3),c3). [resolve(705,a,158,a)]. given #253 (T,wt=8): 707 member(f18(domain_of(c4)),c3) | empty(domain_of(c4)). [resolve(482,a,204,b)]. given #254 (T,wt=8): 710 member(f17(domain_of(c4)),c3) | empty(domain_of(c4)). [resolve(482,a,160,b)]. given #255 (A,wt=23): 225 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 #256 (F,wt=11): 293 -member(f3(power_set(ordered_pair(c3,domain_of(c4))),identity_relation_of(A)),identity_relation_of(A)). [ur(178,a,221,a,b,268,a)]. given #257 (F,wt=11): 302 -member(f2(power_set(ordered_pair(domain_of(c4),c3)),identity_relation_of(A)),identity_relation_of(A)). [ur(181,a,289,a)]. given #258 (F,wt=11): 305 -member(f2(power_set(ordered_pair(c3,domain_of(c4))),identity_relation_of(A)),identity_relation_of(A)). [ur(181,a,290,a)]. given #259 (F,wt=11): 307 -member(ordered_pair(identity_relation_of(A),power_set(ordered_pair(domain_of(c4),c3))),identity_relation_of(B)). [ur(187,a,303,a)]. given #260 (T,wt=8): 779 ilf_type(domain_of(cross_product(A,B)),member_type(power_set(A))). [resolve(595,a,171,b)]. given #261 (T,wt=7): 1725 member(domain_of(cross_product(A,B)),power_set(A)). [resolve(779,a,164,c),unit_del(a,166)]. given #262 (T,wt=8): 780 ilf_type(domain_of(cross_product(cross_product(A,B),C)),binary_relation_type). [resolve(595,a,96,a)]. given #263 (T,wt=8): 815 ilf_type(range_of(cross_product(A,B)),member_type(power_set(B))). [resolve(597,a,171,b)]. given #264 (A,wt=25): 226 member(A,power_set(B)) | ordered_pair(f14(A,f9(A,B)),f15(A,f9(A,B))) = f9(A,B) | f16(A) != ordered_pair(C,D). [resolve(169,b,161,a)]. given #265 (F,wt=10): 1782 -member(ordered_pair(domain_of(c4),c3),domain_of(cross_product(identity_relation_of(A),B))). [ur(167,b,269,a,c,1725,a)]. given #266 (F,wt=10): 1783 -member(ordered_pair(c3,domain_of(c4)),domain_of(cross_product(identity_relation_of(A),B))). [ur(167,b,268,a,c,1725,a)]. given #267 (F,wt=11): 308 -member(ordered_pair(power_set(ordered_pair(domain_of(c4),c3)),identity_relation_of(A)),identity_relation_of(B)). [ur(187,a,303,a(flip))]. given #268 (F,wt=11): 309 -member(ordered_pair(identity_relation_of(A),power_set(ordered_pair(c3,domain_of(c4)))),identity_relation_of(B)). [ur(187,a,306,a)]. given #269 (T,wt=7): 1788 member(range_of(cross_product(A,B)),power_set(B)). [resolve(815,a,164,c),unit_del(a,166)]. given #270 (T,wt=8): 816 ilf_type(range_of(cross_product(A,cross_product(B,C))),binary_relation_type). [resolve(597,a,96,a)]. given #271 (T,wt=8): 893 ilf_type(domain_of(f8(cross_product(A,B))),subset_type(A)). [resolve(252,a,156,a),rewrite([892(3)])]. given #272 (T,wt=8): 895 ilf_type(range_of(f8(cross_product(A,B))),subset_type(B)). [resolve(252,a,154,a),rewrite([894(3)])]. given #273 (A,wt=14): 229 member(A,power_set(B)) | member(ordered_pair(f9(A,B),f9(A,B)),identity_relation_of(A)). [resolve(169,b,111,a)]. given #274 (F,wt=10): 1907 -member(ordered_pair(domain_of(c4),c3),range_of(cross_product(A,identity_relation_of(B)))). [ur(167,b,269,a,c,1788,a)]. given #275 (F,wt=10): 1908 -member(ordered_pair(c3,domain_of(c4)),range_of(cross_product(A,identity_relation_of(B)))). [ur(167,b,268,a,c,1788,a)]. given #276 (F,wt=11): 310 -member(ordered_pair(power_set(ordered_pair(c3,domain_of(c4))),identity_relation_of(A)),identity_relation_of(B)). [ur(187,a,306,a(flip))]. given #277 (F,wt=11): 361 -member(f9(power_set(ordered_pair(domain_of(c4),c3)),identity_relation_of(A)),identity_relation_of(A)). [ur(168,a,295,a)]. given #278 (T,wt=7): 1931 member(A,power_set(B)) | -empty(identity_relation_of(A)). [resolve(229,b,159,a)]. given #279 (T,wt=8): 1084 member(f17(c4),cross_product(c3,c2)) | empty(c4). [resolve(217,b,646,a)]. given #280 (T,wt=6): 2007 empty(c4) | -empty(cross_product(c3,c2)). [resolve(1084,a,159,a)]. given #281 (T,wt=8): 1389 member(f18(c4),cross_product(c3,c2)) | empty(c3). [resolve(689,a,1067,b)]. given #282 (A,wt=25): 230 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 #283 (F,wt=11): 362 -member(power_set(power_set(ordered_pair(domain_of(c4),c3))),power_set(power_set(identity_relation_of(A)))). [ur(167,a,221,a,b,295,a)]. given #284 (F,wt=11): 367 -member(f9(power_set(ordered_pair(c3,domain_of(c4))),identity_relation_of(A)),identity_relation_of(A)). [ur(168,a,296,a)]. given #285 (F,wt=11): 368 -member(power_set(power_set(ordered_pair(c3,domain_of(c4)))),power_set(power_set(identity_relation_of(A)))). [ur(167,a,221,a,b,296,a)]. given #286 (F,wt=11): 371 -subset(power_set(ordered_pair(ordered_pair(domain_of(c4),c3),A)),identity_relation_of(identity_relation_of(B))). [ur(180,a,221,a,b,271,a)]. given #287 (T,wt=6): 2021 empty(c3) | -empty(cross_product(c3,c2)). [resolve(1389,a,159,a)]. given #288 (T,wt=8): 1399 member(f10(c4),cross_product(c3,c2)) | empty(c4). [resolve(689,a,214,b)]. given #289 (T,wt=8): 1401 member(f18(c4),cross_product(c3,c2)) | empty(c4). [resolve(689,a,204,b)]. given #290 (T,wt=9): 275 member(A,B) | -member(f3(power_set(A),B),B). [resolve(221,a,178,a)]. given #291 (A,wt=25): 231 member(A,power_set(B)) | ordered_pair(f12(A,f9(A,B)),f13(A,f9(A,B))) = f9(A,B) | f11(A) != ordered_pair(C,D). [resolve(169,b,94,a)]. given #292 (F,wt=11): 396 -member(ordered_pair(ordered_pair(domain_of(c4),c3),A),f8(identity_relation_of(identity_relation_of(B)))). [ur(167,b,271,a,c,381,a)]. given #293 (F,wt=11): 397 -member(ordered_pair(ordered_pair(c3,domain_of(c4)),A),f8(identity_relation_of(identity_relation_of(B)))). [ur(167,b,270,a,c,381,a)]. given #294 (F,wt=11): 400 -member(ordered_pair(ordered_pair(domain_of(c4),c3),A),identity_relation_of(f8(identity_relation_of(B)))). [ur(188,a,398,a)]. given #295 (F,wt=11): 405 -member(ordered_pair(ordered_pair(c3,domain_of(c4)),A),identity_relation_of(f8(identity_relation_of(B)))). [ur(188,a,399,a)]. given #296 (T,wt=9): 352 ilf_type(A,binary_relation_type) | member(f18(identity_relation_of(A)),identity_relation_of(A)). [resolve(195,a,158,a)]. given #297 (T,wt=8): 2184 ilf_type(c3,binary_relation_type) | member(f18(identity_relation_of(c3)),c4). [resolve(352,b,244,a)]. given #298 (T,wt=5): 2204 ilf_type(c3,binary_relation_type) | -empty(c4). [resolve(2184,b,159,a)]. given #299 (T,wt=7): 2205 ilf_type(c3,binary_relation_type) | member(f18(c4),c4). [resolve(2184,b,158,a)]. given #300 (A,wt=23): 232 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 #301 (F,wt=11): 417 -member(power_set(ordered_pair(domain_of(c4),c3)),power_set(f8(f8(identity_relation_of(A))))). [ur(167,a,221,a,b,403,a)]. given #302 (F,wt=11): 439 -member(ordered_pair(domain_of(c4),c3),f18(power_set(f8(f8(identity_relation_of(A)))))). [ur(167,b,403,a,c,282,a)]. given #303 (F,wt=11): 442 -member(power_set(ordered_pair(c3,domain_of(c4))),f18(power_set(power_set(identity_relation_of(A))))). [ur(167,b,296,a,c,282,a)]. given #304 (F,wt=11): 443 -member(power_set(ordered_pair(domain_of(c4),c3)),f18(power_set(power_set(identity_relation_of(A))))). [ur(167,b,295,a,c,282,a)]. given #305 (T,wt=9): 386 member(f8(A),B) | -member(power_set(A),power_set(B)). [resolve(381,a,167,a)]. given #306 (T,wt=9): 389 member(ordered_pair(f8(A),f8(A)),identity_relation_of(power_set(A))). [resolve(381,a,111,a)]. given #307 (T,wt=9): 418 ilf_type(f10(power_set(cross_product(A,B))),relation_type(A,B)). [resolve(237,a,185,a)]. given #308 (T,wt=9): 470 member(range_of(c4),A) | -member(power_set(c2),power_set(A)). [resolve(465,a,167,a)]. given #309 (A,wt=22): 233 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 #310 (F,wt=11): 455 -member(ordered_pair(c3,domain_of(c4)),f18(power_set(f8(f8(identity_relation_of(A)))))). [ur(167,b,408,a,c,282,a)]. given #311 (F,wt=11): 456 -member(power_set(ordered_pair(c3,domain_of(c4))),power_set(f8(f8(identity_relation_of(A))))). [ur(167,a,221,a,b,408,a)]. given #312 (F,wt=11): 463 -member(ordered_pair(domain_of(c4),c3),f18(power_set(f18(power_set(identity_relation_of(A)))))). [ur(167,b,446,a,c,282,a)]. given #313 (F,wt=11): 464 -member(power_set(ordered_pair(domain_of(c4),c3)),power_set(f18(power_set(identity_relation_of(A))))). [ur(167,a,221,a,b,446,a)]. given #314 (T,wt=9): 473 member(ordered_pair(range_of(c4),range_of(c4)),identity_relation_of(power_set(c2))). [resolve(465,a,111,a)]. given #315 (T,wt=9): 483 member(domain_of(c4),A) | -member(power_set(c3),power_set(A)). [resolve(478,a,167,a)]. given #316 (T,wt=9): 486 member(ordered_pair(domain_of(c4),domain_of(c4)),identity_relation_of(power_set(c3))). [resolve(478,a,111,a)]. given #317 (T,wt=9): 508 ilf_type(f17(power_set(cross_product(A,B))),relation_type(A,B)). [resolve(507,a,185,a)]. given #318 (A,wt=15): 234 member(power_set(power_set(A)),power_set(A)) | -member(power_set(power_set(A)),f9(power_set(power_set(A)),A)). [factor(222,a,c)]. given #319 (F,wt=11): 502 -member(ordered_pair(c3,domain_of(c4)),f18(power_set(f18(power_set(identity_relation_of(A)))))). [ur(167,b,447,a,c,282,a)]. given #320 (F,wt=11): 503 -member(power_set(ordered_pair(c3,domain_of(c4))),power_set(f18(power_set(identity_relation_of(A))))). [ur(167,a,221,a,b,447,a)]. given #321 (F,wt=11): 567 -member(identity_relation_of(power_set(ordered_pair(domain_of(c4),c3))),power_set(identity_relation_of(identity_relation_of(A)))). [ur(167,a,283,a,b,271,a)]. given #322 (F,wt=11): 568 -member(identity_relation_of(power_set(ordered_pair(c3,domain_of(c4)))),power_set(identity_relation_of(identity_relation_of(A)))). [ur(167,a,283,a,b,270,a)]. given #323 (T,wt=9): 516 empty(c3) | member(ordered_pair(f17(c3),f17(c3)),c4). [resolve(205,b,244,a)]. given #324 (T,wt=9): 600 ilf_type(f18(power_set(cross_product(A,B))),relation_type(A,B)). [resolve(598,a,185,a)]. given #325 (T,wt=9): 604 member(f18(f8(A)),A) | ilf_type(f8(A),binary_relation_type). [resolve(385,a,203,a)]. given #326 (T,wt=6): 2552 ilf_type(f8(A),binary_relation_type) | -empty(A). [resolve(604,a,159,a)]. given #327 (A,wt=14): 238 member(f9(A,B),C) | -member(f3(A,C),C) | member(A,power_set(B)). [resolve(178,a,169,b)]. given #328 (F,wt=11): 587 -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,579,a,b,269,a)]. given #329 (F,wt=11): 588 -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,579,a,b,268,a)]. given #330 (F,wt=11): 630 -member(ordered_pair(c3,domain_of(c4)),f10(power_set(f18(power_set(identity_relation_of(A)))))). [ur(167,b,447,a,c,618,a)]. given #331 (F,wt=11): 631 -member(ordered_pair(domain_of(c4),c3),f10(power_set(f18(power_set(identity_relation_of(A)))))). [ur(167,b,446,a,c,618,a)]. given #332 (T,wt=8): 2553 ilf_type(f8(A),binary_relation_type) | member(f18(A),A). [resolve(604,a,158,a)]. given #333 (T,wt=9): 607 member(f11(f8(A)),A) | ilf_type(f8(A),binary_relation_type). [resolve(385,a,86,a)]. given #334 (T,wt=9): 693 member(ordered_pair(c4,c4),identity_relation_of(power_set(cross_product(c3,c2)))). [resolve(646,a,111,a)]. given #335 (T,wt=9): 701 member(f18(range_of(c4)),c2) | ilf_type(range_of(c4),binary_relation_type). [resolve(469,a,203,a)]. given #336 (A,wt=11): 239 member(f17(A),B) | -member(f3(A,B),B) | empty(A). [resolve(178,a,160,b)]. given #337 (F,wt=11): 632 -member(ordered_pair(c3,domain_of(c4)),f10(power_set(f8(f8(identity_relation_of(A)))))). [ur(167,b,408,a,c,618,a)]. given #338 (F,wt=11): 633 -member(ordered_pair(domain_of(c4),c3),f10(power_set(f8(f8(identity_relation_of(A)))))). [ur(167,b,403,a,c,618,a)]. given #339 (F,wt=11): 636 -member(power_set(ordered_pair(c3,domain_of(c4))),f10(power_set(power_set(identity_relation_of(A))))). [ur(167,b,296,a,c,618,a)]. given #340 (F,wt=11): 637 -member(power_set(ordered_pair(domain_of(c4),c3)),f10(power_set(power_set(identity_relation_of(A))))). [ur(167,b,295,a,c,618,a)]. given #341 (T,wt=6): 2655 ilf_type(range_of(c4),binary_relation_type) | -empty(c2). [resolve(701,a,159,a)]. given #342 (T,wt=8): 2656 ilf_type(range_of(c4),binary_relation_type) | member(f18(c2),c2). [resolve(701,a,158,a)]. given #343 (T,wt=9): 704 member(f11(range_of(c4)),c2) | ilf_type(range_of(c4),binary_relation_type). [resolve(469,a,86,a)]. given #344 (T,wt=9): 708 member(f18(domain_of(c4)),c3) | ilf_type(domain_of(c4),binary_relation_type). [resolve(482,a,203,a)]. given #345 (A,wt=12): 240 member(f11(A),B) | -member(f3(A,B),B) | ilf_type(A,binary_relation_type). [resolve(178,a,86,a)]. given #346 (F,wt=11): 662 -member(ordered_pair(domain_of(c4),c3),f10(power_set(f10(power_set(identity_relation_of(A)))))). [ur(167,b,640,a,c,618,a)]. given #347 (F,wt=11): 663 -member(ordered_pair(domain_of(c4),c3),f18(power_set(f10(power_set(identity_relation_of(A)))))). [ur(167,b,640,a,c,282,a)]. given #348 (F,wt=11): 664 -member(power_set(ordered_pair(domain_of(c4),c3)),power_set(f10(power_set(identity_relation_of(A))))). [ur(167,a,221,a,b,640,a)]. given #349 (F,wt=11): 669 -member(ordered_pair(c3,domain_of(c4)),f10(power_set(f10(power_set(identity_relation_of(A)))))). [ur(167,b,641,a,c,618,a)]. given #350 (T,wt=6): 2744 ilf_type(domain_of(c4),binary_relation_type) | -empty(c3). [resolve(708,a,159,a)]. given #351 (T,wt=8): 2745 ilf_type(domain_of(c4),binary_relation_type) | member(f18(c3),c3). [resolve(708,a,158,a)]. given #352 (T,wt=9): 711 member(f11(domain_of(c4)),c3) | ilf_type(domain_of(c4),binary_relation_type). [resolve(482,a,86,a)]. given #353 (T,wt=9): 838 member(f18(A),A) | ilf_type(A,member_type(power_set(B))). [resolve(228,a,165,c),unit_del(b,166)]. given #354 (A,wt=14): 241 member(f9(A,B),C) | member(f3(A,C),A) | member(A,power_set(B)). [resolve(179,a,169,b)]. given #355 (F,wt=11): 670 -member(ordered_pair(c3,domain_of(c4)),f18(power_set(f10(power_set(identity_relation_of(A)))))). [ur(167,b,641,a,c,282,a)]. given #356 (F,wt=11): 671 -member(power_set(ordered_pair(c3,domain_of(c4))),power_set(f10(power_set(identity_relation_of(A))))). [ur(167,a,221,a,b,641,a)]. given #357 (F,wt=11): 672 -member(power_set(ordered_pair(c3,domain_of(c4))),f8(f8(power_set(identity_relation_of(A))))). [ur(385,b,394,a)]. given #358 (F,wt=11): 674 -subset(power_set(power_set(ordered_pair(c3,domain_of(c4)))),f8(power_set(identity_relation_of(A)))). [ur(180,a,221,a,b,394,a)]. given #359 (T,wt=7): 2847 ilf_type(A,member_type(power_set(B))) | -empty(A). [resolve(838,a,159,a)]. given #360 (T,wt=9): 886 ilf_type(f1(A,B),member_type(power_set(cross_product(B,A)))). [resolve(250,a,171,b)]. given #361 (T,wt=8): 2962 member(f1(A,B),power_set(cross_product(B,A))). [resolve(886,a,164,c),unit_del(a,166)]. given #362 (T,wt=9): 1116 -member(A,domain_of(f1(B,C))) | member(A,C). [resolve(1111,a,167,c)]. given #363 (A,wt=11): 242 member(f17(A),B) | member(f3(A,B),A) | empty(A). [resolve(179,a,160,b)]. given #364 (F,wt=11): 679 -member(power_set(ordered_pair(domain_of(c4),c3)),f8(f8(power_set(identity_relation_of(A))))). [ur(385,b,395,a)]. given #365 (F,wt=11): 681 -subset(power_set(power_set(ordered_pair(domain_of(c4),c3))),f8(power_set(identity_relation_of(A)))). [ur(180,a,221,a,b,395,a)]. given #366 (F,wt=11): 714 -member(power_set(ordered_pair(domain_of(c4),c3)),f8(power_set(f8(identity_relation_of(A))))). [ur(385,b,404,a)]. given #367 (F,wt=11): 716 -subset(power_set(power_set(ordered_pair(domain_of(c4),c3))),power_set(f8(identity_relation_of(A)))). [ur(180,a,221,a,b,404,a)]. given #368 (T,wt=9): 1202 -member(A,range_of(f1(B,C))) | member(A,B). [resolve(1160,a,167,c)]. given #369 (T,wt=9): 1253 ilf_type(f18(identity_relation_of(power_set(A))),member_type(identity_relation_of(power_set(A)))). [resolve(555,a,165,c),unit_del(a,539)]. given #370 (T,wt=9): 1303 empty(f8(domain_of(c4))) | member(f18(domain_of(c4)),c3). [resolve(1297,b,482,a)]. given #371 (T,wt=6): 3112 empty(f8(domain_of(c4))) | -empty(c3). [resolve(1303,b,159,a)]. given #372 (A,wt=12): 243 member(f11(A),B) | member(f3(A,B),A) | ilf_type(A,binary_relation_type). [resolve(179,a,86,a)]. given #373 (F,wt=11): 722 -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,404,a)]. given #374 (F,wt=10): 3174 -ilf_type(power_set(ordered_pair(domain_of(c4),c3)),subset_type(f8(identity_relation_of(A)))). [ur(171,a,722,a)]. given #375 (F,wt=11): 723 -member(power_set(ordered_pair(c3,domain_of(c4))),f8(power_set(f8(identity_relation_of(A))))). [ur(385,b,409,a)]. given #376 (F,wt=11): 725 -subset(power_set(power_set(ordered_pair(c3,domain_of(c4)))),power_set(f8(identity_relation_of(A)))). [ur(180,a,221,a,b,409,a)]. given #377 (T,wt=8): 3113 empty(f8(domain_of(c4))) | member(f18(c3),c3). [resolve(1303,b,158,a)]. given #378 (T,wt=9): 1304 empty(f8(range_of(c4))) | member(f18(range_of(c4)),c2). [resolve(1297,b,469,a)]. given #379 (T,wt=6): 3208 empty(f8(range_of(c4))) | -empty(c2). [resolve(1304,b,159,a)]. given #380 (T,wt=8): 3209 empty(f8(range_of(c4))) | member(f18(c2),c2). [resolve(1304,b,158,a)]. given #381 (A,wt=11): 245 member(f2(A,B),A) | -member(C,A) | member(C,B). [resolve(182,a,180,c)]. given #382 (F,wt=11): 731 -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,409,a)]. given #383 (F,wt=10): 3312 -ilf_type(power_set(ordered_pair(c3,domain_of(c4))),subset_type(f8(identity_relation_of(A)))). [ur(171,a,731,a)]. given #384 (F,wt=11): 735 -member(ordered_pair(domain_of(c4),c3),f8(f8(f8(f8(identity_relation_of(A)))))). [ur(385,b,416,a)]. given #385 (F,wt=11): 737 -subset(power_set(ordered_pair(domain_of(c4),c3)),f8(f8(f8(identity_relation_of(A))))). [ur(180,a,221,a,b,416,a)]. given #386 (T,wt=9): 1305 empty(f8(f8(A))) | member(f18(f8(A)),A). [resolve(1297,b,385,a)]. given #387 (T,wt=6): 3352 empty(f8(f8(A))) | -empty(A). [resolve(1305,b,159,a)]. given #388 (T,wt=8): 3353 empty(f8(f8(A))) | member(f18(A),A). [resolve(1305,b,158,a)]. given #389 (T,wt=9): 1308 empty(f8(identity_relation_of(c3))) | member(f18(identity_relation_of(c3)),c4). [resolve(1297,b,244,a)]. given #390 (A,wt=11): 246 domain(A,B,f1(B,A)) = domain_of(f1(B,A)). [resolve(183,a,157,a)]. given #391 (F,wt=11): 754 -member(ordered_pair(c3,domain_of(c4)),f17(power_set(f10(power_set(identity_relation_of(A)))))). [ur(167,b,641,a,c,742,a)]. given #392 (F,wt=11): 755 -member(ordered_pair(domain_of(c4),c3),f17(power_set(f10(power_set(identity_relation_of(A)))))). [ur(167,b,640,a,c,742,a)]. given #393 (F,wt=11): 756 -member(ordered_pair(c3,domain_of(c4)),f17(power_set(f18(power_set(identity_relation_of(A)))))). [ur(167,b,447,a,c,742,a)]. given #394 (F,wt=11): 757 -member(ordered_pair(domain_of(c4),c3),f17(power_set(f18(power_set(identity_relation_of(A)))))). [ur(167,b,446,a,c,742,a)]. given #395 (T,wt=6): 3392 empty(f8(identity_relation_of(c3))) | -empty(c4). [resolve(1308,b,159,a)]. given #396 (T,wt=8): 3393 empty(f8(identity_relation_of(c3))) | member(f18(c4),c4). [resolve(1308,b,158,a)]. given #397 (T,wt=9): 1388 member(f18(c4),cross_product(c3,c2)) | empty(f8(c4)). [resolve(689,a,1297,b)]. given #398 (T,wt=7): 3468 empty(f8(c4)) | -empty(cross_product(c3,c2)). [resolve(1388,a,159,a)]. given #399 (A,wt=11): 248 range(A,B,f1(B,A)) = range_of(f1(B,A)). [resolve(183,a,155,a)]. given #400 (F,wt=11): 760 -member(ordered_pair(c3,domain_of(c4)),f17(power_set(f8(f8(identity_relation_of(A)))))). [ur(167,b,408,a,c,742,a)]. given #401 (F,wt=11): 762 -member(ordered_pair(domain_of(c4),c3),f17(power_set(f8(f8(identity_relation_of(A)))))). [ur(167,b,403,a,c,742,a)]. given #402 (F,wt=11): 767 -member(power_set(ordered_pair(c3,domain_of(c4))),f17(power_set(power_set(identity_relation_of(A))))). [ur(167,b,296,a,c,742,a)]. given #403 (F,wt=11): 768 -member(power_set(ordered_pair(domain_of(c4),c3)),f17(power_set(power_set(identity_relation_of(A))))). [ur(167,b,295,a,c,742,a)]. given #404 (T,wt=9): 1390 member(f18(identity_relation_of(c3)),cross_product(c3,c2)) | empty(c3). [resolve(689,a,1047,b)]. given #405 (T,wt=9): 1391 member(f18(c4),cross_product(c3,c2)) | empty(identity_relation_of(c3)). [resolve(689,a,956,b)]. given #406 (T,wt=7): 3544 empty(identity_relation_of(c3)) | -empty(cross_product(c3,c2)). [resolve(1391,a,159,a)]. given #407 (T,wt=9): 1732 -member(A,domain_of(cross_product(B,C))) | member(A,B). [resolve(1725,a,167,c)]. given #408 (A,wt=18): 253 -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 #409 (F,wt=11): 785 -member(ordered_pair(domain_of(c4),c3),f17(power_set(f17(power_set(identity_relation_of(A)))))). [ur(167,b,771,a,c,742,a)]. given #410 (F,wt=11): 786 -member(ordered_pair(domain_of(c4),c3),f10(power_set(f17(power_set(identity_relation_of(A)))))). [ur(167,b,771,a,c,618,a)]. given #411 (F,wt=11): 787 -member(ordered_pair(domain_of(c4),c3),f18(power_set(f17(power_set(identity_relation_of(A)))))). [ur(167,b,771,a,c,282,a)]. given #412 (F,wt=11): 788 -member(power_set(ordered_pair(domain_of(c4),c3)),power_set(f17(power_set(identity_relation_of(A))))). [ur(167,a,221,a,b,771,a)]. given #413 (T,wt=9): 1853 -member(A,range_of(cross_product(B,C))) | member(A,C). [resolve(1788,a,167,c)]. given #414 (T,wt=9): 1915 ilf_type(domain_of(f8(cross_product(A,B))),member_type(power_set(A))). [resolve(893,a,171,b)]. given #415 (T,wt=8): 3666 member(domain_of(f8(cross_product(A,B))),power_set(A)). [resolve(1915,a,164,c),unit_del(a,166)]. given #416 (T,wt=9): 1916 ilf_type(domain_of(f8(cross_product(cross_product(A,B),C))),binary_relation_type). [resolve(893,a,96,a)]. given #417 (A,wt=19): 254 -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 #418 (F,wt=11): 793 -member(ordered_pair(c3,domain_of(c4)),f17(power_set(f17(power_set(identity_relation_of(A)))))). [ur(167,b,772,a,c,742,a)]. given #419 (F,wt=11): 794 -member(ordered_pair(c3,domain_of(c4)),f10(power_set(f17(power_set(identity_relation_of(A)))))). [ur(167,b,772,a,c,618,a)]. given #420 (F,wt=11): 795 -member(ordered_pair(c3,domain_of(c4)),f18(power_set(f17(power_set(identity_relation_of(A)))))). [ur(167,b,772,a,c,282,a)]. given #421 (F,wt=11): 796 -member(power_set(ordered_pair(c3,domain_of(c4))),power_set(f17(power_set(identity_relation_of(A))))). [ur(167,a,221,a,b,772,a)]. given #422 (T,wt=9): 1919 ilf_type(range_of(f8(cross_product(A,B))),member_type(power_set(B))). [resolve(895,a,171,b)]. given #423 (T,wt=8): 3856 member(range_of(f8(cross_product(A,B))),power_set(B)). [resolve(1919,a,164,c),unit_del(a,166)]. given #424 (T,wt=9): 1920 ilf_type(range_of(f8(cross_product(A,cross_product(B,C)))),binary_relation_type). [resolve(895,a,96,a)]. given #425 (T,wt=9): 2211 ilf_type(c3,binary_relation_type) | member(f18(c4),cross_product(c3,c2)). [resolve(2205,b,689,a)]. given #426 (A,wt=17): 255 member(ordered_pair(f9(A,B),C),identity_relation_of(A)) | f9(A,B) != C | member(A,power_set(B)). [resolve(189,a,169,b),flip(b)]. given #427 (F,wt=11): 797 -member(ordered_pair(c3,domain_of(c4)),f8(f18(power_set(f8(identity_relation_of(A)))))). [ur(385,b,440,a)]. given #428 (F,wt=11): 799 -subset(power_set(ordered_pair(c3,domain_of(c4))),f18(power_set(f8(identity_relation_of(A))))). [ur(180,a,221,a,b,440,a)]. given #429 (F,wt=11): 805 -member(ordered_pair(domain_of(c4),c3),f8(f18(power_set(f8(identity_relation_of(A)))))). [ur(385,b,441,a)]. given #430 (F,wt=11): 807 -subset(power_set(ordered_pair(domain_of(c4),c3)),f18(power_set(f8(identity_relation_of(A))))). [ur(180,a,221,a,b,441,a)]. given #431 (T,wt=7): 3990 ilf_type(c3,binary_relation_type) | -empty(cross_product(c3,c2)). [resolve(2211,b,159,a)]. given #432 (T,wt=9): 2348 ilf_type(domain_of(f10(power_set(cross_product(A,B)))),subset_type(A)). [resolve(418,a,156,a),rewrite([2347(4)])]. given #433 (T,wt=9): 2350 ilf_type(range_of(f10(power_set(cross_product(A,B)))),subset_type(B)). [resolve(418,a,154,a),rewrite([2349(4)])]. given #434 (T,wt=9): 2446 ilf_type(domain_of(f17(power_set(cross_product(A,B)))),subset_type(A)). [resolve(508,a,156,a),rewrite([2445(4)])]. given #435 (A,wt=13): 256 member(ordered_pair(f17(A),B),identity_relation_of(A)) | f17(A) != B | empty(A). [resolve(189,a,160,b),flip(b)]. given #436 (F,wt=11): 866 -member(ordered_pair(c3,domain_of(c4)),f8(f8(f8(f8(identity_relation_of(A)))))). [ur(385,b,454,a)]. given #437 (F,wt=11): 869 -subset(power_set(ordered_pair(c3,domain_of(c4))),f8(f8(f8(identity_relation_of(A))))). [ur(180,a,221,a,b,454,a)]. given #438 (F,wt=11): 877 -member(ordered_pair(domain_of(c4),c3),f8(f8(f18(power_set(identity_relation_of(A)))))). [ur(385,b,462,a)]. given #439 (F,wt=11): 880 -subset(power_set(ordered_pair(domain_of(c4),c3)),f8(f18(power_set(identity_relation_of(A))))). [ur(180,a,221,a,b,462,a)]. given #440 (T,wt=9): 2448 ilf_type(range_of(f17(power_set(cross_product(A,B)))),subset_type(B)). [resolve(508,a,154,a),rewrite([2447(4)])]. given #441 (T,wt=9): 2528 ilf_type(domain_of(f18(power_set(cross_product(A,B)))),subset_type(A)). [resolve(600,a,156,a),rewrite([2527(4)])]. given #442 (T,wt=9): 2530 ilf_type(range_of(f18(power_set(cross_product(A,B)))),subset_type(B)). [resolve(600,a,154,a),rewrite([2529(4)])]. given #443 (T,wt=9): 2871 member(f3(A,B),A) | member(A,power_set(B)). [resolve(241,a,168,b),merge(c)]. given #444 (A,wt=14): 257 member(ordered_pair(f11(A),B),identity_relation_of(A)) | f11(A) != B | ilf_type(A,binary_relation_type). [resolve(189,a,86,a),flip(b)]. given #445 (F,wt=11): 916 -member(ordered_pair(c3,domain_of(c4)),f8(f8(f18(power_set(identity_relation_of(A)))))). [ur(385,b,501,a)]. given #446 (F,wt=11): 919 -subset(power_set(ordered_pair(c3,domain_of(c4))),f8(f18(power_set(identity_relation_of(A))))). [ur(180,a,221,a,b,501,a)]. given #447 (F,wt=11): 979 -empty(identity_relation_of(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(526,a,613,a)]. given #448 (F,wt=11): 1020 -member(ordered_pair(c3,domain_of(c4)),f8(f10(power_set(f8(identity_relation_of(A)))))). [ur(385,b,634,a)]. given #449 (T,wt=9): 3018 member(f3(A,B),A) | empty(A) | -empty(B). [resolve(242,a,159,a)]. given #450 (T,wt=10): 273 member(ordered_pair(A,B),identity_relation_of(power_set(A))) | B != A. [resolve(221,a,189,a)]. given #451 (T,wt=10): 274 member(A,B) | member(f3(power_set(A),B),power_set(A)). [resolve(221,a,179,a)]. given #452 (T,wt=9): 4190 member(A,A) | -member(A,f3(power_set(A),A)). [factor(4180,a,c)]. given #453 (A,wt=18): 258 -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 #454 (F,wt=11): 1026 -subset(power_set(ordered_pair(c3,domain_of(c4))),f10(power_set(f8(identity_relation_of(A))))). [ur(180,a,221,a,b,634,a)]. given #455 (F,wt=11): 1028 -member(ordered_pair(domain_of(c4),c3),f8(f10(power_set(f8(identity_relation_of(A)))))). [ur(385,b,635,a)]. given #456 (F,wt=11): 1034 -subset(power_set(ordered_pair(domain_of(c4),c3)),f10(power_set(f8(identity_relation_of(A))))). [ur(180,a,221,a,b,635,a)]. given #457 (F,wt=11): 1036 -member(ordered_pair(domain_of(c4),c3),f8(f8(f10(power_set(identity_relation_of(A)))))). [ur(385,b,658,a)]. given #458 (T,wt=10): 321 empty(A) | member(f18(A),B) | -member(A,power_set(B)). [resolve(204,b,167,a)]. given #459 (T,wt=10): 325 empty(A) | member(ordered_pair(f18(A),f18(A)),identity_relation_of(A)). [resolve(204,b,111,a)]. given #460 (T,wt=9): 4261 empty(c3) | member(ordered_pair(f18(c3),f18(c3)),c4). [resolve(325,b,244,a)]. given #461 (T,wt=10): 334 empty(A) | member(f10(A),B) | -member(A,power_set(B)). [resolve(214,b,167,a)]. given #462 (A,wt=13): 259 -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 #463 (F,wt=11): 1042 -subset(power_set(ordered_pair(domain_of(c4),c3)),f8(f10(power_set(identity_relation_of(A))))). [ur(180,a,221,a,b,658,a)]. given #464 (F,wt=11): 1090 -member(ordered_pair(c3,domain_of(c4)),f8(f8(f10(power_set(identity_relation_of(A)))))). [ur(385,b,665,a)]. given #465 (F,wt=11): 1096 -subset(power_set(ordered_pair(c3,domain_of(c4))),f8(f10(power_set(identity_relation_of(A))))). [ur(180,a,221,a,b,665,a)]. given #466 (F,wt=11): 1103 -member(ordered_pair(c3,domain_of(c4)),f8(f17(power_set(f8(identity_relation_of(A)))))). [ur(385,b,763,a)]. given #467 (T,wt=10): 337 empty(A) | member(ordered_pair(f10(A),f10(A)),identity_relation_of(A)). [resolve(214,b,111,a)]. given #468 (T,wt=9): 4352 empty(c3) | member(ordered_pair(f10(c3),f10(c3)),c4). [resolve(337,b,244,a)]. given #469 (T,wt=10): 384 member(f8(A),B) | -member(f3(power_set(A),B),B). [resolve(381,a,178,a)]. given #470 (T,wt=10): 430 member(f18(power_set(A)),B) | -member(power_set(A),power_set(B)). [resolve(282,a,167,a)]. given #471 (A,wt=11): 260 -ilf_type(c4,relation_type(A,B)) | subset(c3,range(A,B,c4)). [resolve(190,b,83,a)]. given #472 (F,wt=11): 1109 -subset(power_set(ordered_pair(c3,domain_of(c4))),f17(power_set(f8(identity_relation_of(A))))). [ur(180,a,221,a,b,763,a)]. given #473 (F,wt=11): 1146 -member(ordered_pair(c3,domain_of(c4)),domain_of(f1(A,f8(identity_relation_of(B))))). [ur(167,b,399,a,c,1111,a)]. given #474 (F,wt=11): 1147 -member(ordered_pair(domain_of(c4),c3),domain_of(f1(A,f8(identity_relation_of(B))))). [ur(167,b,398,a,c,1111,a)]. given #475 (F,wt=11): 1167 -member(ordered_pair(domain_of(c4),c3),f8(f17(power_set(f8(identity_relation_of(A)))))). [ur(385,b,764,a)]. given #476 (T,wt=4): 4390 subset(c3,range_of(c4)). [resolve(260,a,82,a),rewrite([197(5)])]. given #477 (T,wt=7): 4437 -member(A,c3) | member(A,range_of(c4)). [resolve(4390,a,180,c)]. given #478 (T,wt=7): 4467 member(f10(c3),range_of(c4)) | empty(c3). [resolve(4437,a,214,b)]. given #479 (T,wt=5): 4485 empty(c3) | -empty(range_of(c4)). [resolve(4467,a,159,a)]. given #480 (A,wt=18): 261 -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 #481 (F,wt=11): 1173 -subset(power_set(ordered_pair(domain_of(c4),c3)),f17(power_set(f8(identity_relation_of(A))))). [ur(180,a,221,a,b,764,a)]. given #482 (F,wt=11): 1176 -member(ordered_pair(domain_of(c4),c3),f8(f8(f17(power_set(identity_relation_of(A)))))). [ur(385,b,781,a)]. given #483 (F,wt=11): 1182 -subset(power_set(ordered_pair(domain_of(c4),c3)),f8(f17(power_set(identity_relation_of(A))))). [ur(180,a,221,a,b,781,a)]. given #484 (F,wt=11): 1188 -member(ordered_pair(c3,domain_of(c4)),f8(f8(f17(power_set(identity_relation_of(A)))))). [ur(385,b,789,a)]. given #485 (T,wt=6): 4476 empty(c3) | member(f10(c3),c2). [resolve(4467,a,469,a)]. given #486 (T,wt=4): 4541 empty(c3) | -empty(c2). [resolve(4476,b,159,a)]. given #487 (T,wt=6): 4542 empty(c3) | member(f18(c2),c2). [resolve(4476,b,158,a)]. given #488 (T,wt=7): 4471 member(f18(c3),range_of(c4)) | empty(c3). [resolve(4437,a,204,b)]. given #489 (A,wt=13): 262 -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 #490 (F,wt=11): 1194 -subset(power_set(ordered_pair(c3,domain_of(c4))),f8(f17(power_set(identity_relation_of(A))))). [ur(180,a,221,a,b,789,a)]. given #491 (F,wt=11): 1235 -member(ordered_pair(c3,domain_of(c4)),range_of(f1(f8(identity_relation_of(A)),B))). [ur(167,b,399,a,c,1160,a)]. given #492 (F,wt=11): 1236 -member(ordered_pair(domain_of(c4),c3),range_of(f1(f8(identity_relation_of(A)),B))). [ur(167,b,398,a,c,1160,a)]. given #493 (F,wt=11): 1425 -member(ordered_pair(domain_of(c4),c3),f8(domain_of(f1(A,identity_relation_of(B))))). [ur(385,b,1154,a)]. given #494 (T,wt=6): 4560 empty(c3) | member(f18(c3),c2). [resolve(4471,a,469,a)]. given #495 (T,wt=7): 4474 member(f17(c3),range_of(c4)) | empty(c3). [resolve(4437,a,160,b)]. given #496 (T,wt=6): 4632 empty(c3) | member(f17(c3),c2). [resolve(4474,a,469,a)]. given #497 (T,wt=8): 4436 -subset(range_of(c4),c3) | range_of(c4) = c3. [resolve(4390,a,192,b),flip(b)]. given #498 (A,wt=11): 263 -ilf_type(c4,relation_type(A,B)) | subset(c3,domain(A,B,c4)). [resolve(191,b,83,a)]. given #499 (F,wt=11): 1431 -subset(power_set(ordered_pair(domain_of(c4),c3)),domain_of(f1(A,identity_relation_of(B)))). [ur(180,a,221,a,b,1154,a)]. NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 26 (0.00 of 0.48 sec). given #500 (F,wt=11): 1435 -member(ordered_pair(c3,domain_of(c4)),f8(domain_of(f1(A,identity_relation_of(B))))). [ur(385,b,1155,a)]. given #501 (F,wt=11): 1441 -subset(power_set(ordered_pair(c3,domain_of(c4))),domain_of(f1(A,identity_relation_of(B)))). [ur(180,a,221,a,b,1155,a)]. given #502 (F,wt=11): 1447 -member(ordered_pair(domain_of(c4),c3),f8(range_of(f1(identity_relation_of(A),B)))). [ur(385,b,1243,a)]. given #503 (T,wt=4): 4660 subset(c3,domain_of(c4)). [resolve(263,a,82,a),rewrite([200(5)])]. given #504 (T,wt=7): 4696 -member(A,c3) | member(A,domain_of(c4)). [resolve(4660,a,180,c)]. given #505 (T,wt=7): 4720 member(f10(c3),domain_of(c4)) | empty(c3). [resolve(4696,a,214,b)]. given #506 (T,wt=5): 4737 empty(c3) | -empty(domain_of(c4)). [resolve(4720,a,159,a)]. given #507 (A,wt=11): 264 -subset(A,B) | A = B | member(f2(B,A),B). [resolve(192,a,182,a)]. given #508 (F,wt=4): 4695 -subset(domain_of(c4),c3). [resolve(4660,a,192,b),flip(b),unit_del(b,202)]. given #509 (F,wt=6): 4746 -member(f2(domain_of(c4),c3),c3). [ur(181,a,4695,a)]. ============================== PROOF ================================= % Proof 1 at 0.49 (+ 0.02) seconds. % Length of proof is 39. % Level of proof is 8. % Maximum clause weight is 24.000. % Given clauses 509. 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)])]. 263 -ilf_type(c4,relation_type(A,B)) | subset(c3,domain(A,B,c4)). [resolve(191,b,83,a)]. 264 -subset(A,B) | A = B | member(f2(B,A),B). [resolve(192,a,182,a)]. 298 ilf_type(domain_of(c4),member_type(power_set(c3))). [resolve(201,a,171,b)]. 478 member(domain_of(c4),power_set(c3)). [resolve(298,a,164,c),unit_del(a,166)]. 482 -member(A,domain_of(c4)) | member(A,c3). [resolve(478,a,167,c)]. 4660 subset(c3,domain_of(c4)). [resolve(263,a,82,a),rewrite([200(5)])]. 4695 -subset(domain_of(c4),c3). [resolve(4660,a,192,b),flip(b),unit_del(b,202)]. 4744 member(f2(domain_of(c4),c3),domain_of(c4)). [resolve(264,a,4660,a),flip(a),unit_del(a,202)]. 4746 -member(f2(domain_of(c4),c3),c3). [ur(181,a,4695,a)]. 4751 $F. [ur(482,b,4746,a),unit_del(a,4744)]. ============================== end of proof ========================== ============================== STATISTICS ============================ Given=509. Generated=7002. Kept=4726. proofs=1. Usable=508. Sos=3995. Demods=20. Limbo=4, Disabled=310. Hints=0. Kept_by_rule=0, Deleted_by_rule=2. Forward_subsumed=2273. Back_subsumed=176. Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. New_demodulators=20 (0 lex), Back_demodulated=3. Back_unit_deleted=40. Demod_attempts=82351. Demod_rewrites=59. Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. Nonunit_fsub_feature_tests=7531. Nonunit_bsub_feature_tests=4188. Megabytes=6.37. User_CPU=0.49, System_CPU=0.02, Wall_clock=1. ============================== end of statistics ===================== ============================== end of search ========================= Exiting with 1 proof. Process 23985 exit (max_proofs) Tue Nov 3 16:59:22 2009 ============================== 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))))))))). Max_seconds is 30 for this subproblem. Child search process 23986 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: Predicate symbol precedence: predicate_order([ =, empty, ilf_type, member, subset ]). Function symbol precedence: function_order([ set_type, binary_relation_type, c1, c2, c3, c4, ordered_pair, relation_type, cross_product, 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(binary_resolution). % (non-Horn) % set(neg_ur_resolution). % (non-Horn, less than 100 clauses) Auto_process settings: % set(factor). % (non-Horn) % set(unit_deletion). % (non-Horn) kept: 11 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -subset(A,B) | -subset(B,A) | B = A. [assumption]. kept: 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]. kept: 13 -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]. kept: 14 -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]. kept: 15 -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]. kept: 16 -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]. kept: 17 -ilf_type(A,set_type) | ilf_type(identity_relation_of(A),binary_relation_type). [assumption]. kept: 18 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,subset_type(cross_product(A,B))) | ilf_type(C,relation_type(A,B)). [assumption]. kept: 19 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,relation_type(A,B)) | ilf_type(C,subset_type(cross_product(A,B))). [assumption]. kept: 20 -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(f1(A,B),relation_type(B,A)). [assumption]. kept: 21 -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(A,B) | ilf_type(f2(A,B),set_type). [assumption]. kept: 22 -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(A,B) | member(f2(A,B),A). [assumption]. kept: 23 -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(A,B) | -member(f2(A,B),B). [assumption]. kept: 24 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | -member(C,A) | member(C,B) | -subset(A,B). [assumption]. kept: 25 -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]. kept: 26 -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]. kept: 27 -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]. kept: 28 -ilf_type(A,binary_relation_type) | -ilf_type(B,binary_relation_type) | subset(A,B) | ilf_type(f4(A,B),set_type). [assumption]. kept: 29 -ilf_type(A,binary_relation_type) | -ilf_type(B,binary_relation_type) | subset(A,B) | ilf_type(f5(A,B),set_type). [assumption]. kept: 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]. kept: 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]. kept: 32 -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]. kept: 33 -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]. kept: 34 -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]. kept: 35 -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]. kept: 36 -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]. kept: 37 -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(A,B) | B != A. [assumption]. kept: 38 -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(B,A) | B != A. [assumption]. kept: 39 -ilf_type(A,binary_relation_type) | ilf_type(domain_of(A),set_type). [assumption]. kept: 40 -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(cross_product(A,B),set_type). [assumption]. kept: 41 -ilf_type(A,binary_relation_type) | ilf_type(range_of(A),set_type). [assumption]. kept: 42 -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(ordered_pair(A,B),set_type). [assumption]. kept: 43 ilf_type(c1,binary_relation_type). [assumption]. kept: 44 -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(B,subset_type(A)) | -ilf_type(B,member_type(power_set(A))). [assumption]. kept: 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]. kept: 46 -ilf_type(A,set_type) | ilf_type(f8(A),subset_type(A)). [assumption]. kept: 47 -ilf_type(A,set_type) | subset(A,A). [assumption]. kept: 48 -ilf_type(A,binary_relation_type) | subset(A,A). [assumption]. kept: 49 -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(A,power_set(B)) | ilf_type(f9(A,B),set_type). [assumption]. kept: 50 -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(A,power_set(B)) | member(f9(A,B),A). [assumption]. kept: 51 -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(A,power_set(B)) | -member(f9(A,B),B). [assumption]. kept: 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]. kept: 53 -ilf_type(A,set_type) | -empty(power_set(A)). [assumption]. kept: 54 -ilf_type(A,set_type) | ilf_type(power_set(A),set_type). [assumption]. kept: 55 -ilf_type(A,set_type) | empty(B) | -ilf_type(B,set_type) | ilf_type(A,member_type(B)) | -member(A,B). [assumption]. kept: 56 -ilf_type(A,set_type) | empty(B) | -ilf_type(B,set_type) | member(A,B) | -ilf_type(A,member_type(B)). [assumption]. kept: 57 empty(A) | -ilf_type(A,set_type) | ilf_type(f10(A),member_type(A)). [assumption]. kept: 58 -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]. kept: 59 -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]. 60 -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]. kept: 61 -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) | f16(A) != ordered_pair(C,D). [copy(60),flip(g)]. kept: 62 -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]. kept: 63 -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]. 64 -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]. kept: 65 -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) | f16(A) != ordered_pair(C,D). [copy(64),flip(g)]. kept: 66 -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]. kept: 67 -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]. 68 -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]. kept: 69 -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) | f16(A) != ordered_pair(C,D). [copy(68),flip(g)]. kept: 70 -ilf_type(A,set_type) | empty(A) | ilf_type(f17(A),set_type). [assumption]. kept: 71 -ilf_type(A,set_type) | empty(A) | member(f17(A),A). [assumption]. kept: 72 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | -empty(A). [assumption]. kept: 73 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f18(A),set_type). [assumption]. kept: 74 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | member(f18(A),A). [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]. kept: 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)]. kept: 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]. 78 -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]. kept: 79 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,relation_type(A,B)) | range(A,B,C) = range_of(C). [copy(78),flip(d)]. kept: 80 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,relation_type(A,B)) | ilf_type(range(A,B,C),subset_type(B)). [assumption]. kept: 81 ilf_type(A,set_type). [assumption]. kept: 82 ilf_type(c4,relation_type(c3,c2)). [assumption]. kept: 83 subset(identity_relation_of(c3),c4). [assumption]. kept: 84 -subset(c3,range(c3,c2,c4)). [assumption]. 85 -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)]. kept: 86 member(f11(A),A) | ilf_type(A,binary_relation_type). [copy(85),merge(c),unit_del(a,81)]. 87 -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)]. kept: 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)]. 89 -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)]. kept: 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)]. 91 -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)]. kept: 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)]. 93 -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)]. kept: 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)]. 95 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,subset_type(cross_product(A,B))) | -ilf_type(C,set_type) | ilf_type(C,binary_relation_type). [resolve(9,d,2,c)]. kept: 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)]. 97 -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)]. kept: 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)]. 99 -empty(A) | -ilf_type(A,set_type) | -ilf_type(A,set_type) | ilf_type(A,binary_relation_type). [resolve(10,c,2,c)]. kept: 100 -empty(A) | ilf_type(A,binary_relation_type). [copy(99),merge(c),unit_del(b,81)]. 101 -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)]. kept: 102 -empty(A) | -member(B,A) | ordered_pair(f12(A,B),f13(A,B)) = B. [copy(101),merge(c),unit_del(b,81),unit_del(c,81)]. kept: 103 -ilf_type(A,relation_type(B,B)) | -subset(identity_relation_of(C),A) | subset(C,domain(B,B,A)). [factor(12,a,b),unit_del(a,81),unit_del(b,81)]. kept: 104 -ilf_type(A,relation_type(B,C)) | -subset(identity_relation_of(B),A) | subset(B,domain(B,C,A)). [factor(12,a,c),unit_del(a,81),unit_del(b,81)]. kept: 105 -ilf_type(A,relation_type(B,C)) | -subset(identity_relation_of(C),A) | subset(C,domain(B,C,A)). [factor(12,b,c),unit_del(a,81),unit_del(b,81)]. kept: 106 -ilf_type(A,relation_type(B,B)) | -subset(identity_relation_of(C),A) | subset(C,range(B,B,A)). [factor(13,a,b),unit_del(a,81),unit_del(b,81)]. kept: 107 -ilf_type(A,relation_type(B,C)) | -subset(identity_relation_of(B),A) | subset(B,range(B,C,A)). [factor(13,a,c),unit_del(a,81),unit_del(b,81)]. kept: 108 -ilf_type(A,relation_type(B,C)) | -subset(identity_relation_of(C),A) | subset(C,range(B,C,A)). [factor(13,b,c),unit_del(a,81),unit_del(b,81)]. kept: 109 -member(A,A) | member(ordered_pair(A,B),identity_relation_of(A)) | B != A. [factor(14,a,b),unit_del(a,81),unit_del(c,81)]. kept: 110 -member(A,B) | member(ordered_pair(A,B),identity_relation_of(B)) | B != A. [factor(14,a,d),unit_del(a,81),unit_del(b,81)]. kept: 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)]. kept: 112 member(A,A) | -member(ordered_pair(A,B),identity_relation_of(A)). [factor(15,a,b),unit_del(a,81),unit_del(c,81)]. kept: 113 member(A,B) | -member(ordered_pair(A,B),identity_relation_of(B)). [factor(15,a,d),unit_del(a,81),unit_del(b,81)]. kept: 114 member(A,B) | -member(ordered_pair(A,A),identity_relation_of(B)). [factor(15,b,d),unit_del(a,81),unit_del(b,81)]. kept: 115 A = B | -member(ordered_pair(B,A),identity_relation_of(B)). [factor(16,a,b),unit_del(a,81),unit_del(b,81)]. kept: 116 A = B | -member(ordered_pair(B,A),identity_relation_of(A)). [factor(16,a,c),unit_del(a,81),unit_del(b,81)]. kept: 117 -ilf_type(A,subset_type(cross_product(B,B))) | ilf_type(A,relation_type(B,B)). [factor(18,a,b),unit_del(a,81)]. kept: 118 -ilf_type(A,relation_type(B,B)) | ilf_type(A,subset_type(cross_product(B,B))). [factor(19,a,b),unit_del(a,81)]. kept: 119 ilf_type(f1(A,A),relation_type(A,A)). [factor(20,a,b),unit_del(a,81)]. kept: 120 subset(A,A) | member(f2(A,A),A). [factor(22,a,b),unit_del(a,81)]. kept: 121 subset(A,A) | -member(f2(A,A),A). [factor(23,a,b),unit_del(a,81)]. kept: 122 -member(A,A) | member(A,B) | -subset(A,B). [factor(24,a,c),unit_del(a,81),unit_del(b,81)]. kept: 123 -member(A,B) | member(A,A) | -subset(B,A). [factor(24,b,c),unit_del(a,81),unit_del(b,81)]. kept: 124 -member(A,A) | member(A,B) | member(f3(A,B),A). [factor(26,a,c),unit_del(a,81),unit_del(b,81)]. kept: 125 -member(A,B) | member(A,A) | member(f3(B,A),B). [factor(26,b,c),unit_del(a,81),unit_del(b,81)]. kept: 126 -member(A,A) | member(A,B) | -member(f3(A,B),B). [factor(27,a,c),unit_del(a,81),unit_del(b,81)]. kept: 127 -member(A,B) | member(A,A) | -member(f3(B,A),A). [factor(27,b,c),unit_del(a,81),unit_del(b,81)]. kept: 128 -ilf_type(A,binary_relation_type) | -ilf_type(B,binary_relation_type) | -member(ordered_pair(C,C),A) | member(ordered_pair(C,C),B) | -subset(A,B). [factor(32,c,d),unit_del(c,81)]. kept: 129 -ilf_type(A,binary_relation_type) | -ilf_type(B,binary_relation_type) | -member(ordered_pair(C,C),A) | member(ordered_pair(C,C),B) | member(ordered_pair(f6(A,B),f7(A,B)),A). [factor(35,c,d),unit_del(c,81)]. kept: 130 -ilf_type(A,binary_relation_type) | -ilf_type(B,binary_relation_type) | -member(ordered_pair(C,C),A) | member(ordered_pair(C,C),B) | -member(ordered_pair(f6(A,B),f7(A,B)),B). [factor(36,c,d),unit_del(c,81)]. kept: 131 subset(A,A). [factor(37,a,b),xx(c),unit_del(a,81)]. kept: 132 ilf_type(A,subset_type(A)) | -ilf_type(A,member_type(power_set(A))). [factor(44,a,b),unit_del(a,81)]. kept: 133 ilf_type(A,member_type(power_set(A))) | -ilf_type(A,subset_type(A)). [factor(45,a,b),unit_del(a,81)]. kept: 134 member(A,power_set(A)) | member(f9(A,A),A). [factor(50,a,b),unit_del(a,81)]. kept: 135 member(A,power_set(A)) | -member(f9(A,A),A). [factor(51,a,b),unit_del(a,81)]. kept: 136 -member(A,A) | member(A,B) | -member(A,power_set(B)). [factor(52,a,c),unit_del(a,81),unit_del(b,81)]. kept: 137 -member(A,B) | member(A,A) | -member(B,power_set(A)). [factor(52,b,c),unit_del(a,81),unit_del(b,81)]. kept: 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)]. kept: 139 empty(A) | ilf_type(A,member_type(A)) | -member(A,A). [factor(55,a,c),unit_del(a,81)]. kept: 140 empty(A) | member(A,A) | -ilf_type(A,member_type(A)). [factor(56,a,c),unit_del(a,81)]. kept: 141 -member(A,A) | ordered_pair(f14(A,A),f15(A,A)) = A | member(f16(A),A). [factor(67,a,b),unit_del(a,81)]. kept: 142 -member(A,A) | ordered_pair(f14(A,A),f15(A,A)) = A | f16(A) != ordered_pair(B,C). [factor(69,a,b),unit_del(a,81),unit_del(d,81),unit_del(e,81)]. kept: 143 -member(A,B) | ordered_pair(f14(B,A),f15(B,A)) = A | f16(B) != ordered_pair(B,C). [factor(69,a,e),unit_del(a,81),unit_del(b,81),unit_del(e,81)]. kept: 144 -member(A,B) | ordered_pair(f14(B,A),f15(B,A)) = A | f16(B) != ordered_pair(C,B). [factor(69,a,f),unit_del(a,81),unit_del(b,81),unit_del(e,81)]. kept: 145 -member(A,B) | ordered_pair(f14(B,A),f15(B,A)) = A | f16(B) != ordered_pair(A,C). [factor(69,b,e),unit_del(a,81),unit_del(b,81),unit_del(e,81)]. kept: 146 -member(A,B) | ordered_pair(f14(B,A),f15(B,A)) = A | f16(B) != ordered_pair(C,A). [factor(69,b,f),unit_del(a,81),unit_del(b,81),unit_del(e,81)]. kept: 147 -member(A,B) | ordered_pair(f14(B,A),f15(B,A)) = A | f16(B) != ordered_pair(C,C). [factor(69,e,f),unit_del(a,81),unit_del(b,81),unit_del(e,81)]. kept: 148 -member(A,A) | -empty(A). [factor(72,a,b),unit_del(a,81)]. kept: 149 -member(A,A) | member(f18(A),A). [factor(74,a,b),unit_del(a,81)]. kept: 150 -ilf_type(A,relation_type(B,B)) | domain(B,B,A) = domain_of(A). [factor(76,a,b),unit_del(a,81)]. kept: 151 -ilf_type(A,relation_type(B,B)) | ilf_type(domain(B,B,A),subset_type(B)). [factor(77,a,b),unit_del(a,81)]. kept: 152 -ilf_type(A,relation_type(B,B)) | range(B,B,A) = range_of(A). [factor(79,a,b),unit_del(a,81)]. kept: 153 -ilf_type(A,relation_type(B,B)) | ilf_type(range(B,B,A),subset_type(B)). [factor(80,a,b),unit_del(a,81)]. kept: 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)]. kept: 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)]. kept: 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)]. kept: 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)]. kept: 158 -member(A,B) | member(f18(B),B). [back_unit_del(74),unit_del(a,81),unit_del(b,81)]. kept: 159 -member(A,B) | -empty(B). [back_unit_del(72),unit_del(a,81),unit_del(b,81)]. kept: 160 empty(A) | member(f17(A),A). [back_unit_del(71),unit_del(a,81)]. kept: 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)]. kept: 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)]. kept: 163 empty(A) | ilf_type(f10(A),member_type(A)). [back_unit_del(57),unit_del(b,81)]. kept: 164 empty(A) | member(B,A) | -ilf_type(B,member_type(A)). [back_unit_del(56),unit_del(a,81),unit_del(c,81)]. kept: 165 empty(A) | ilf_type(B,member_type(A)) | -member(B,A). [back_unit_del(55),unit_del(a,81),unit_del(c,81)]. kept: 166 -empty(power_set(A)). [back_unit_del(53),unit_del(a,81)]. kept: 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)]. kept: 168 member(A,power_set(B)) | -member(f9(A,B),B). [back_unit_del(51),unit_del(a,81),unit_del(b,81)]. kept: 169 member(A,power_set(B)) | member(f9(A,B),A). [back_unit_del(50),unit_del(a,81),unit_del(b,81)]. kept: 170 ilf_type(f8(A),subset_type(A)). [back_unit_del(46),unit_del(a,81)]. kept: 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)]. kept: 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)]. kept: 173 subset(A,B) | A != B. [back_unit_del(38),unit_del(a,81),unit_del(b,81)]. kept: 174 subset(A,B) | B != A. [back_unit_del(37),unit_del(a,81),unit_del(b,81)]. kept: 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)]. kept: 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)]. kept: 177 -ilf_type(A,binary_relation_type) | -ilf_type(B,binary_relation_type) | -member(ordered_pair(C,D),A) | member(ordered_pair(C,D),B) | -subset(A,B). [back_unit_del(32),unit_del(c,81),unit_del(d,81)]. kept: 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)]. kept: 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)]. kept: 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)]. kept: 181 subset(A,B) | -member(f2(A,B),B). [back_unit_del(23),unit_del(a,81),unit_del(b,81)]. kept: 182 subset(A,B) | member(f2(A,B),A). [back_unit_del(22),unit_del(a,81),unit_del(b,81)]. kept: 183 ilf_type(f1(A,B),relation_type(B,A)). [back_unit_del(20),unit_del(a,81),unit_del(b,81)]. kept: 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)]. kept: 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)]. kept: 186 ilf_type(identity_relation_of(A),binary_relation_type). [back_unit_del(17),unit_del(a,81)]. kept: 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)]. kept: 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)]. kept: 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)]. kept: 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)]. kept: 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)]. kept: 192 -subset(A,B) | -subset(B,A) | B = A. [back_unit_del(11),unit_del(a,81),unit_del(b,81)]. ============================== 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): 270 range_of(c4) != c3. [ur(174,a,199,a)]. given #60 (F,wt=7): 269 -member(f2(c3,range_of(c4)),range_of(c4)). [ur(181,a,199,a)]. given #61 (F,wt=7): 271 -member(ordered_pair(c3,range_of(c4)),identity_relation_of(A)). [ur(187,a,270,a)]. given #62 (T,wt=4): 221 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): 281 ilf_type(A,member_type(power_set(A))). [resolve(221,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): 272 -member(ordered_pair(range_of(c4),c3),identity_relation_of(A)). [ur(187,a,270,a(flip))]. given #68 (F,wt=8): 290 -subset(power_set(ordered_pair(c3,range_of(c4))),identity_relation_of(A)). [ur(180,a,221,a,b,271,a)]. given #69 (F,wt=8): 291 -subset(power_set(f2(c3,range_of(c4))),range_of(c4)). [ur(180,a,221,a,b,269,a)]. given #70 (F,wt=8): 301 -subset(power_set(ordered_pair(range_of(c4),c3)),identity_relation_of(A)). [ur(180,a,221,a,b,272,a)]. given #71 (T,wt=4): 298 ilf_type(A,subset_type(A)). [resolve(281,a,172,b)]. given #72 (T,wt=5): 314 ilf_type(cross_product(A,B),binary_relation_type). [resolve(298,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): 214 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=8): 306 power_set(ordered_pair(c3,range_of(c4))) != identity_relation_of(A). [ur(174,a,290,a),flip(a)]. given #77 (F,wt=8): 309 power_set(f2(c3,range_of(c4))) != range_of(c4). [ur(174,a,291,a),flip(a)]. given #78 (F,wt=8): 312 power_set(ordered_pair(range_of(c4),c3)) != identity_relation_of(A). [ur(174,a,301,a),flip(a)]. given #79 (F,wt=9): 294 -member(power_set(ordered_pair(c3,range_of(c4))),power_set(identity_relation_of(A))). [ur(167,a,221,a,b,271,a)]. given #80 (T,wt=6): 227 member(A,power_set(B)) | -empty(A). [resolve(169,b,159,a)]. given #81 (T,wt=6): 235 ilf_type(f8(cross_product(A,B)),binary_relation_type). [resolve(170,a,96,a)]. given #82 (T,wt=6): 236 ilf_type(f8(A),member_type(power_set(A))). [resolve(171,b,170,a)]. given #83 (T,wt=5): 376 member(f8(A),power_set(A)). [resolve(236,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): 390 -member(ordered_pair(range_of(c4),c3),f8(identity_relation_of(A))). [ur(167,b,272,a,c,376,a)]. given #86 (F,wt=8): 391 -member(ordered_pair(c3,range_of(c4)),f8(identity_relation_of(A))). [ur(167,b,271,a,c,376,a)]. given #87 (F,wt=8): 392 -member(f2(c3,range_of(c4)),f8(range_of(c4))). [ur(167,b,269,a,c,376,a)]. given #88 (F,wt=9): 295 -member(power_set(f2(c3,range_of(c4))),power_set(range_of(c4))). [ur(167,a,221,a,b,269,a)]. given #89 (T,wt=6): 237 ilf_type(f10(power_set(A)),subset_type(A)). [resolve(172,b,163,b),unit_del(b,166)]. given #90 (T,wt=6): 251 ilf_type(c4,subset_type(cross_product(c3,c2))). [resolve(184,a,82,a)]. given #91 (T,wt=3): 419 ilf_type(c4,binary_relation_type). [resolve(251,a,96,a)]. given #92 (T,wt=6): 268 member(f2(c3,range_of(c4)),c3). [resolve(199,a,182,a)]. given #93 (A,wt=7): 201 domain(c3,c2,c4) = domain_of(c4). [resolve(157,a,82,a)]. given #94 (F,wt=2): 431 -empty(c3). [resolve(268,a,159,a)]. given #95 (F,wt=5): 438 -subset(c3,f8(range_of(c4))). [ur(180,a,268,a,b,392,a)]. given #96 (F,wt=5): 442 -member(c3,power_set(range_of(c4))). [ur(167,a,268,a,b,269,a)]. given #97 (F,wt=5): 446 f8(range_of(c4)) != c3. [ur(174,a,438,a)]. given #98 (T,wt=4): 432 member(f18(c3),c3). [resolve(268,a,158,a)]. given #99 (T,wt=5): 460 ilf_type(f18(c3),member_type(c3)). [resolve(432,a,165,c),unit_del(a,431)]. given #100 (T,wt=6): 284 member(f18(power_set(A)),power_set(A)). [resolve(221,a,158,a)]. given #101 (T,wt=6): 296 ilf_type(range_of(c4),member_type(power_set(c2))). [resolve(198,a,171,b)]. 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=6): 441 -member(c3,power_set(f8(range_of(c4)))). [ur(167,a,268,a,b,392,a)]. given #104 (F,wt=6): 448 -subset(power_set(c3),power_set(range_of(c4))). [ur(180,a,221,a,b,442,a)]. given #105 (F,wt=6): 451 -member(c3,f8(power_set(range_of(c4)))). [ur(167,b,442,a,c,376,a)]. given #106 (F,wt=6): 453 -ilf_type(c3,member_type(power_set(range_of(c4)))). [ur(164,a,166,a,b,442,a)]. given #107 (T,wt=5): 489 member(range_of(c4),power_set(c2)). [resolve(296,a,164,c),unit_del(a,166)]. given #108 (T,wt=6): 297 ilf_type(domain_of(c4),member_type(power_set(c3))). [resolve(202,a,171,b)]. given #109 (T,wt=5): 527 member(domain_of(c4),power_set(c3)). [resolve(297,a,164,c),unit_del(a,166)]. given #110 (T,wt=6): 353 ilf_type(A,binary_relation_type) | -empty(identity_relation_of(A)). [resolve(195,a,159,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=5): 514 -ilf_type(c3,subset_type(range_of(c4))). [ur(171,a,453,a)]. given #113 (F,wt=6): 507 power_set(range_of(c4)) != power_set(c3). [ur(174,a,448,a)]. given #114 (F,wt=7): 440 -member(f3(c3,range_of(c4)),range_of(c4)). [ur(178,a,268,a,b,269,a)]. given #115 (F,wt=7): 450 -member(f9(c3,range_of(c4)),range_of(c4)). [ur(168,a,442,a)]. given #116 (T,wt=5): 549 empty(A) | -empty(identity_relation_of(A)). [resolve(205,b,159,a)]. given #117 (T,wt=7): 215 empty(A) | ilf_type(f17(A),member_type(A)). [resolve(165,c,160,b),merge(c)]. given #118 (T,wt=6): 572 ilf_type(f17(power_set(A)),subset_type(A)). [resolve(215,b,172,b),unit_del(a,166)]. given #119 (T,wt=7): 244 -member(A,identity_relation_of(c3)) | member(A,c4). [resolve(180,c,83,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=3): 570 -empty(identity_relation_of(c3)). [ur(549,a,431,a)]. given #122 (F,wt=4): 571 -empty(identity_relation_of(power_set(A))). [ur(549,a,166,a)]. given #123 (F,wt=4): 587 -empty(identity_relation_of(identity_relation_of(c3))). [ur(549,a,570,a)]. given #124 (F,wt=5): 590 -empty(identity_relation_of(identity_relation_of(power_set(A)))). [ur(549,a,571,a)]. given #125 (T,wt=5): 576 member(f10(identity_relation_of(c3)),c4). [resolve(244,a,214,b),unit_del(b,570)]. given #126 (T,wt=4): 607 member(f18(c4),c4). [resolve(576,a,158,a)]. given #127 (T,wt=5): 578 member(f18(identity_relation_of(c3)),c4). [resolve(244,a,204,b),unit_del(b,570)]. given #128 (T,wt=5): 581 member(f17(identity_relation_of(c3)),c4). [resolve(244,a,160,b),unit_del(b,570)]. given #129 (A,wt=20): 207 empty(A) | ordered_pair(f12(A,f17(A)),f13(A,f17(A))) = f17(A) | f11(A) != ordered_pair(B,C). [resolve(160,b,94,a)]. given #130 (F,wt=2): 606 -empty(c4). [resolve(576,a,159,a)]. given #131 (F,wt=3): 651 -empty(identity_relation_of(c4)). [ur(549,a,606,a)]. given #132 (F,wt=4): 652 -empty(identity_relation_of(identity_relation_of(c4))). [ur(549,a,651,a)]. given #133 (F,wt=5): 593 -empty(identity_relation_of(identity_relation_of(identity_relation_of(c3)))). [ur(549,a,587,a)]. given #134 (T,wt=5): 619 ilf_type(f18(c4),member_type(c4)). [resolve(607,a,165,c),unit_del(a,606)]. given #135 (T,wt=6): 613 ilf_type(f10(identity_relation_of(c3)),member_type(c4)). [back_unit_del(603),unit_del(a,606)]. given #136 (T,wt=6): 631 ilf_type(f18(identity_relation_of(c3)),member_type(c4)). [resolve(578,a,165,c),unit_del(a,606)]. given #137 (T,wt=6): 643 ilf_type(f17(identity_relation_of(c3)),member_type(c4)). [resolve(581,a,165,c),unit_del(a,606)]. given #138 (A,wt=18): 208 empty(A) | ordered_pair(f12(A,f17(A)),f13(A,f17(A))) = f17(A) | member(f11(A),A). [resolve(160,b,92,a)]. given #139 (F,wt=5): 655 -empty(identity_relation_of(identity_relation_of(identity_relation_of(c4)))). [ur(549,a,652,a)]. given #140 (F,wt=6): 596 -empty(identity_relation_of(identity_relation_of(identity_relation_of(power_set(A))))). [ur(549,a,590,a)]. given #141 (F,wt=6): 658 -empty(identity_relation_of(identity_relation_of(identity_relation_of(identity_relation_of(c3))))). [ur(549,a,593,a)]. given #142 (F,wt=6): 671 -empty(identity_relation_of(identity_relation_of(identity_relation_of(identity_relation_of(c4))))). [ur(549,a,655,a)]. given #143 (T,wt=7): 247 ilf_type(domain_of(f1(A,B)),subset_type(B)). [resolve(183,a,156,a),rewrite([246(2)])]. given #144 (T,wt=7): 249 ilf_type(range_of(f1(A,B)),subset_type(A)). [resolve(183,a,154,a),rewrite([248(2)])]. given #145 (T,wt=7): 285 member(ordered_pair(A,A),identity_relation_of(power_set(A))). [resolve(221,a,111,a)]. given #146 (T,wt=7): 313 ilf_type(cross_product(A,B),relation_type(A,B)). [resolve(298,a,185,a)]. given #147 (A,wt=17): 209 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 #148 (F,wt=7): 452 -member(power_set(c3),power_set(power_set(range_of(c4)))). [ur(167,a,221,a,b,442,a)]. given #149 (F,wt=7): 480 -member(c3,f18(power_set(power_set(range_of(c4))))). [ur(167,b,442,a,c,284,a)]. given #150 (F,wt=7): 498 -subset(power_set(c3),power_set(f8(range_of(c4)))). [ur(180,a,221,a,b,441,a)]. given #151 (F,wt=7): 501 -member(c3,f8(power_set(f8(range_of(c4))))). [ur(167,b,441,a,c,376,a)]. given #152 (T,wt=7): 324 empty(A) | ilf_type(f18(A),member_type(A)). [resolve(204,b,165,c),merge(b)]. given #153 (T,wt=6): 735 ilf_type(f18(power_set(A)),subset_type(A)). [resolve(324,b,172,b),unit_del(a,166)]. given #154 (T,wt=7): 380 -member(A,f8(B)) | member(A,B). [resolve(376,a,167,c)]. given #155 (T,wt=7): 416 ilf_type(f10(power_set(A)),member_type(power_set(A))). [resolve(237,a,171,b)]. given #156 (A,wt=20): 210 ordered_pair(f14(A,f17(A)),f15(A,f17(A))) = f17(A) | f16(A) != ordered_pair(B,C) | empty(A). [resolve(161,a,160,b)]. given #157 (F,wt=7): 504 -ilf_type(c3,member_type(power_set(f8(range_of(c4))))). [ur(164,a,166,a,b,441,a)]. given #158 (F,wt=6): 747 -ilf_type(c3,subset_type(f8(range_of(c4)))). [ur(171,a,504,a)]. given #159 (F,wt=7): 509 -subset(power_set(c3),f8(power_set(range_of(c4)))). [ur(180,a,221,a,b,451,a)]. given #160 (F,wt=7): 511 -member(c3,f8(f8(power_set(range_of(c4))))). [ur(167,b,451,a,c,376,a)]. given #161 (T,wt=6): 746 member(f10(power_set(A)),power_set(A)). [resolve(416,a,164,c),unit_del(a,166)]. given #162 (T,wt=7): 417 ilf_type(f10(power_set(cross_product(A,B))),binary_relation_type). [resolve(237,a,96,a)]. given #163 (T,wt=7): 418 ilf_type(c4,member_type(power_set(cross_product(c3,c2)))). [resolve(251,a,171,b)]. given #164 (T,wt=6): 789 member(c4,power_set(cross_product(c3,c2))). [resolve(418,a,164,c),unit_del(a,166)]. given #165 (A,wt=21): 211 ordered_pair(f14(A,f11(A)),f15(A,f11(A))) = f11(A) | f16(A) != ordered_pair(B,C) | ilf_type(A,binary_relation_type). [resolve(161,a,86,a)]. given #166 (F,wt=7): 674 -empty(identity_relation_of(identity_relation_of(identity_relation_of(identity_relation_of(power_set(A)))))). [ur(549,a,596,a)]. given #167 (F,wt=7): 677 -empty(identity_relation_of(identity_relation_of(identity_relation_of(identity_relation_of(identity_relation_of(c3)))))). [ur(549,a,658,a)]. given #168 (F,wt=7): 680 -empty(identity_relation_of(identity_relation_of(identity_relation_of(identity_relation_of(identity_relation_of(c4)))))). [ur(549,a,671,a)]. given #169 (F,wt=7): 728 power_set(f8(range_of(c4))) != power_set(c3). [ur(174,a,498,a)]. given #170 (T,wt=7): 443 ilf_type(f2(c3,range_of(c4)),member_type(c3)). [back_unit_del(428),unit_del(a,431)]. given #171 (T,wt=7): 444 member(f2(c3,f8(range_of(c4))),c3). [resolve(438,a,182,a)]. given #172 (T,wt=7): 472 ilf_type(f18(power_set(A)),member_type(power_set(A))). [resolve(284,a,165,c),unit_del(a,166)]. given #173 (T,wt=7): 518 -member(A,range_of(c4)) | member(A,c2). [resolve(489,a,167,c)]. given #174 (A,wt=18): 212 ordered_pair(f14(A,f17(A)),f15(A,f17(A))) = f17(A) | member(f16(A),A) | empty(A). [resolve(162,a,160,b)]. given #175 (F,wt=7): 750 f8(power_set(range_of(c4))) != power_set(c3). [ur(174,a,509,a)]. given #176 (F,wt=7): 774 -member(c3,f10(power_set(power_set(range_of(c4))))). [ur(167,b,442,a,c,746,a)]. given #177 (F,wt=8): 447 -member(ordered_pair(c3,A),identity_relation_of(power_set(range_of(c4)))). [ur(188,a,442,a)]. given #178 (F,wt=8): 454 -member(ordered_pair(c3,f8(range_of(c4))),identity_relation_of(A)). [ur(187,a,446,a)]. given #179 (T,wt=7): 531 -member(A,domain_of(c4)) | member(A,c3). [resolve(527,a,167,c)]. given #180 (T,wt=7): 574 ilf_type(f17(power_set(A)),member_type(power_set(A))). [resolve(572,a,171,b)]. given #181 (T,wt=6): 896 member(f17(power_set(A)),power_set(A)). [resolve(574,a,164,c),unit_del(a,166)]. given #182 (T,wt=7): 575 ilf_type(f17(power_set(cross_product(A,B))),binary_relation_type). [resolve(572,a,96,a)]. given #183 (A,wt=19): 213 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 #184 (F,wt=7): 917 -member(c3,f17(power_set(power_set(range_of(c4))))). [ur(167,b,442,a,c,896,a)]. given #185 (F,wt=8): 455 -member(ordered_pair(f8(range_of(c4)),c3),identity_relation_of(A)). [ur(187,a,446,a(flip))]. given #186 (F,wt=8): 502 -member(c3,f18(power_set(power_set(f8(range_of(c4)))))). [ur(167,b,441,a,c,284,a)]. given #187 (F,wt=8): 503 -member(power_set(c3),power_set(power_set(f8(range_of(c4))))). [ur(167,a,221,a,b,441,a)]. given #188 (T,wt=7): 577 member(ordered_pair(f17(c3),f17(c3)),c4). [resolve(244,a,205,b),unit_del(b,431)]. given #189 (T,wt=7): 707 ilf_type(domain_of(cross_product(A,B)),subset_type(A)). [resolve(313,a,156,a),rewrite([706(2)])]. given #190 (T,wt=7): 709 ilf_type(range_of(cross_product(A,B)),subset_type(B)). [resolve(313,a,154,a),rewrite([708(2)])]. given #191 (T,wt=7): 738 ilf_type(f18(power_set(cross_product(A,B))),binary_relation_type). [resolve(735,a,96,a)]. given #192 (A,wt=10): 216 empty(A) | ilf_type(f11(A),member_type(A)) | ilf_type(A,binary_relation_type). [resolve(165,c,86,a)]. given #193 (F,wt=8): 512 -member(c3,f18(power_set(f8(power_set(range_of(c4)))))). [ur(167,b,451,a,c,284,a)]. given #194 (F,wt=8): 513 -member(power_set(c3),power_set(f8(power_set(range_of(c4))))). [ur(167,a,221,a,b,451,a)]. given #195 (F,wt=8): 559 -subset(power_set(f3(c3,range_of(c4))),range_of(c4)). [ur(180,a,221,a,b,440,a)]. given #196 (F,wt=8): 561 -member(f3(c3,range_of(c4)),f8(range_of(c4))). [ur(167,b,440,a,c,376,a)]. given #197 (T,wt=8): 219 -member(A,f17(power_set(B))) | member(A,B). [resolve(167,c,160,b),unit_del(c,166)]. given #198 (T,wt=8): 228 member(A,power_set(B)) | member(f18(A),A). [resolve(169,b,158,a)]. given #199 (T,wt=8): 250 ilf_type(f1(A,B),subset_type(cross_product(B,A))). [resolve(184,a,183,a)]. given #200 (T,wt=5): 1091 ilf_type(f1(A,B),binary_relation_type). [resolve(250,a,96,a)]. given #201 (A,wt=10): 217 member(f17(A),B) | -member(A,power_set(B)) | empty(A). [resolve(167,a,160,b)]. given #202 (F,wt=8): 565 -subset(power_set(f9(c3,range_of(c4))),range_of(c4)). [ur(180,a,221,a,b,450,a)]. given #203 (F,wt=8): 567 -member(f9(c3,range_of(c4)),f8(range_of(c4))). [ur(167,b,450,a,c,376,a)]. given #204 (F,wt=8): 588 -ilf_type(ordered_pair(range_of(c4),c3),member_type(identity_relation_of(c3))). [ur(164,a,570,a,b,272,a)]. given #205 (F,wt=8): 589 -ilf_type(ordered_pair(c3,range_of(c4)),member_type(identity_relation_of(c3))). [ur(164,a,570,a,b,271,a)]. given #206 (T,wt=6): 1096 member(f17(c4),cross_product(c3,c2)). [resolve(217,b,789,a),unit_del(b,606)]. given #207 (T,wt=7): 1129 ilf_type(f17(c4),member_type(cross_product(c3,c2))). [back_unit_del(1119),unit_del(a,1122)]. given #208 (T,wt=8): 252 ilf_type(f8(cross_product(A,B)),relation_type(A,B)). [resolve(185,a,170,a)]. given #209 (T,wt=8): 265 -subset(c4,identity_relation_of(c3)) | identity_relation_of(c3) = c4. [resolve(192,a,83,a),flip(b)]. given #210 (A,wt=11): 218 member(f11(A),B) | -member(A,power_set(B)) | ilf_type(A,binary_relation_type). [resolve(167,a,86,a)]. given #211 (F,wt=4): 1122 -empty(cross_product(c3,c2)). [resolve(1096,a,159,a)]. given #212 (F,wt=5): 1142 -empty(identity_relation_of(cross_product(c3,c2))). [ur(549,a,1122,a)]. given #213 (F,wt=6): 1143 -empty(identity_relation_of(identity_relation_of(cross_product(c3,c2)))). [ur(549,a,1142,a)]. given #214 (F,wt=7): 1148 -empty(identity_relation_of(identity_relation_of(identity_relation_of(cross_product(c3,c2))))). [ur(549,a,1143,a)]. given #215 (T,wt=8): 280 member(A,B) | -member(power_set(A),power_set(B)). [resolve(221,a,167,a)]. given #216 (T,wt=8): 322 -member(A,f18(power_set(B))) | member(A,B). [resolve(204,b,167,c),unit_del(a,166)]. given #217 (T,wt=8): 335 -member(A,f10(power_set(B))) | member(A,B). [resolve(214,b,167,c),unit_del(a,166)]. given #218 (T,wt=8): 459 member(f18(c3),A) | -member(c3,power_set(A)). [resolve(432,a,167,a)]. given #219 (A,wt=12): 220 -member(A,f11(power_set(B))) | member(A,B) | ilf_type(power_set(B),binary_relation_type). [resolve(167,c,86,a)]. given #220 (F,wt=8): 653 -ilf_type(ordered_pair(range_of(c4),c3),member_type(identity_relation_of(c4))). [ur(164,a,651,a,b,272,a)]. given #221 (F,wt=8): 654 -ilf_type(ordered_pair(c3,range_of(c4)),member_type(identity_relation_of(c4))). [ur(164,a,651,a,b,271,a)]. given #222 (F,wt=8): 713 -subset(power_set(power_set(c3)),power_set(power_set(range_of(c4)))). [ur(180,a,221,a,b,452,a)]. given #223 (F,wt=8): 716 -member(power_set(c3),f8(power_set(power_set(range_of(c4))))). [ur(167,b,452,a,c,376,a)]. given #224 (T,wt=8): 463 member(ordered_pair(f18(c3),f18(c3)),identity_relation_of(c3)). [resolve(432,a,111,a)]. given #225 (T,wt=6): 1203 member(f18(identity_relation_of(c3)),identity_relation_of(c3)). [resolve(463,a,158,a)]. given #226 (T,wt=7): 1193 member(ordered_pair(f18(c3),f18(c3)),c4). [resolve(463,a,244,a)]. given #227 (T,wt=7): 1213 ilf_type(f18(identity_relation_of(c3)),member_type(identity_relation_of(c3))). [resolve(1203,a,165,c),unit_del(a,570)]. given #228 (A,wt=14): 222 member(power_set(A),power_set(B)) | -member(C,f9(power_set(A),B)) | member(C,A). [resolve(169,b,167,c)]. given #229 (F,wt=8): 719 -ilf_type(power_set(c3),member_type(power_set(power_set(range_of(c4))))). [ur(164,a,166,a,b,452,a)]. given #230 (F,wt=7): 1243 -ilf_type(power_set(c3),subset_type(power_set(range_of(c4)))). [ur(171,a,719,a)]. given #231 (F,wt=8): 721 -subset(power_set(c3),f18(power_set(power_set(range_of(c4))))). [ur(180,a,221,a,b,480,a)]. given #232 (F,wt=8): 723 -member(c3,f8(f18(power_set(power_set(range_of(c4)))))). [ur(167,b,480,a,c,376,a)]. given #233 (T,wt=8): 550 empty(A) | member(f18(identity_relation_of(A)),identity_relation_of(A)). [resolve(205,b,158,a)]. given #234 (T,wt=8): 618 member(f18(c4),A) | -member(c4,power_set(A)). [resolve(607,a,167,a)]. given #235 (T,wt=6): 1266 member(f18(c4),cross_product(c3,c2)). [resolve(618,b,789,a)]. given #236 (T,wt=7): 1271 ilf_type(f18(c4),member_type(cross_product(c3,c2))). [resolve(1266,a,165,c),unit_del(a,1122)]. given #237 (A,wt=13): 223 member(A,power_set(B)) | member(f9(A,B),C) | -member(A,power_set(C)). [resolve(169,b,167,a)]. given #238 (F,wt=8): 730 -subset(power_set(c3),f8(power_set(f8(range_of(c4))))). [ur(180,a,221,a,b,501,a)]. given #239 (F,wt=8): 732 -member(c3,f8(f8(power_set(f8(range_of(c4)))))). [ur(167,b,501,a,c,376,a)]. given #240 (F,wt=8): 751 -member(c3,f8(f8(f8(power_set(range_of(c4)))))). [ur(380,b,511,a)]. given #241 (F,wt=8): 753 -subset(power_set(c3),f8(f8(power_set(range_of(c4))))). [ur(180,a,221,a,b,511,a)]. given #242 (T,wt=8): 622 member(ordered_pair(f18(c4),f18(c4)),identity_relation_of(c4)). [resolve(607,a,111,a)]. given #243 (T,wt=6): 1314 member(f18(identity_relation_of(c4)),identity_relation_of(c4)). [resolve(622,a,158,a)]. given #244 (T,wt=7): 1324 ilf_type(f18(identity_relation_of(c4)),member_type(identity_relation_of(c4))). [resolve(1314,a,165,c),unit_del(a,651)]. given #245 (T,wt=8): 685 ilf_type(domain_of(f1(A,B)),member_type(power_set(B))). [resolve(247,a,171,b)]. given #246 (A,wt=12): 224 member(A,power_set(B)) | empty(A) | ilf_type(f9(A,B),member_type(A)). [resolve(169,b,165,c)]. given #247 (F,wt=8): 772 -member(c3,f10(power_set(f8(power_set(range_of(c4)))))). [ur(167,b,451,a,c,746,a)]. given #248 (F,wt=8): 775 -member(c3,f10(power_set(power_set(f8(range_of(c4)))))). [ur(167,b,441,a,c,746,a)]. given #249 (F,wt=8): 802 -empty(identity_relation_of(identity_relation_of(identity_relation_of(identity_relation_of(identity_relation_of(power_set(A))))))). [ur(549,a,674,a)]. given #250 (F,wt=8): 805 -empty(identity_relation_of(identity_relation_of(identity_relation_of(identity_relation_of(identity_relation_of(identity_relation_of(c3))))))). [ur(549,a,677,a)]. given #251 (T,wt=7): 1332 member(domain_of(f1(A,B)),power_set(B)). [resolve(685,a,164,c),unit_del(a,166)]. given #252 (T,wt=7): 1338 ilf_type(f9(c3,range_of(c4)),member_type(c3)). [resolve(224,a,442,a),unit_del(a,431)]. given #253 (T,wt=6): 1442 member(f9(c3,range_of(c4)),c3). [resolve(1338,a,164,c),unit_del(a,431)]. given #254 (T,wt=8): 686 ilf_type(domain_of(f1(A,cross_product(B,C))),binary_relation_type). [resolve(247,a,96,a)]. given #255 (A,wt=23): 225 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 #256 (F,wt=8): 808 -empty(identity_relation_of(identity_relation_of(identity_relation_of(identity_relation_of(identity_relation_of(identity_relation_of(c4))))))). [ur(549,a,680,a)]. given #257 (F,wt=8): 848 -member(c3,f8(f10(power_set(power_set(range_of(c4)))))). [ur(380,b,774,a)]. given #258 (F,wt=8): 850 -subset(power_set(c3),f10(power_set(power_set(range_of(c4))))). [ur(180,a,221,a,b,774,a)]. given #259 (F,wt=8): 857 -subset(identity_relation_of(power_set(c3)),identity_relation_of(power_set(range_of(c4)))). [ur(180,a,285,a,b,447,a)]. given #260 (T,wt=8): 689 ilf_type(range_of(f1(A,B)),member_type(power_set(A))). [resolve(249,a,171,b)]. given #261 (T,wt=7): 1537 member(range_of(f1(A,B)),power_set(A)). [resolve(689,a,164,c),unit_del(a,166)]. given #262 (T,wt=8): 690 ilf_type(range_of(f1(cross_product(A,B),C)),binary_relation_type). [resolve(249,a,96,a)]. given #263 (T,wt=8): 697 ilf_type(ordered_pair(A,A),member_type(identity_relation_of(power_set(A)))). [resolve(285,a,165,c),unit_del(a,571)]. given #264 (A,wt=25): 226 member(A,power_set(B)) | ordered_pair(f14(A,f9(A,B)),f15(A,f9(A,B))) = f9(A,B) | f16(A) != ordered_pair(C,D). [resolve(169,b,161,a)]. given #265 (F,wt=8): 914 -member(c3,f17(power_set(f8(power_set(range_of(c4)))))). [ur(167,b,451,a,c,896,a)]. given #266 (F,wt=8): 918 -member(c3,f17(power_set(power_set(f8(range_of(c4)))))). [ur(167,b,441,a,c,896,a)]. given #267 (F,wt=8): 942 -member(c3,f8(f17(power_set(power_set(range_of(c4)))))). [ur(380,b,917,a)]. given #268 (F,wt=8): 944 -subset(power_set(c3),f17(power_set(power_set(range_of(c4))))). [ur(180,a,221,a,b,917,a)]. given #269 (T,wt=8): 700 member(f18(identity_relation_of(power_set(A))),identity_relation_of(power_set(A))). [resolve(285,a,158,a)]. given #270 (T,wt=8): 739 member(f10(f8(A)),A) | empty(f8(A)). [resolve(380,a,214,b)]. given #271 (T,wt=5): 1657 empty(f8(A)) | -empty(A). [resolve(739,a,159,a)]. given #272 (T,wt=7): 1658 empty(f8(A)) | member(f18(A),A). [resolve(739,a,158,a)]. given #273 (A,wt=14): 229 member(A,power_set(B)) | member(ordered_pair(f9(A,B),f9(A,B)),identity_relation_of(A)). [resolve(169,b,111,a)]. given #274 (F,wt=8): 1037 power_set(f3(c3,range_of(c4))) != range_of(c4). [ur(174,a,559,a),flip(a)]. given #275 (F,wt=8): 1106 power_set(f9(c3,range_of(c4))) != range_of(c4). [ur(174,a,565,a),flip(a)]. given #276 (F,wt=8): 1153 -empty(identity_relation_of(identity_relation_of(identity_relation_of(identity_relation_of(cross_product(c3,c2)))))). [ur(549,a,1148,a)]. given #277 (F,wt=8): 1184 power_set(power_set(range_of(c4))) != power_set(power_set(c3)). [ur(174,a,713,a)]. given #278 (T,wt=7): 1693 member(A,power_set(B)) | -empty(identity_relation_of(A)). [resolve(229,b,159,a)]. given #279 (T,wt=8): 741 member(f18(f8(A)),A) | empty(f8(A)). [resolve(380,a,204,b)]. given #280 (T,wt=8): 744 member(f17(f8(A)),A) | empty(f8(A)). [resolve(380,a,160,b)]. given #281 (T,wt=8): 793 -member(A,c4) | member(A,cross_product(c3,c2)). [resolve(789,a,167,c)]. given #282 (A,wt=25): 230 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 #283 (F,wt=8): 1246 f18(power_set(power_set(range_of(c4)))) != power_set(c3). [ur(174,a,721,a)]. given #284 (F,wt=8): 1285 f8(power_set(f8(range_of(c4)))) != power_set(c3). [ur(174,a,730,a)]. given #285 (F,wt=8): 1304 f8(f8(power_set(range_of(c4)))) != power_set(c3). [ur(174,a,753,a)]. given #286 (F,wt=8): 1431 -member(c3,domain_of(f1(A,power_set(range_of(c4))))). [ur(167,b,442,a,c,1332,a)]. given #287 (T,wt=6): 1770 member(f10(c4),cross_product(c3,c2)). [resolve(793,a,214,b),unit_del(b,606)]. given #288 (T,wt=7): 1765 member(f17(identity_relation_of(c3)),cross_product(c3,c2)). [resolve(793,a,581,a)]. given #289 (T,wt=7): 1766 member(f18(identity_relation_of(c3)),cross_product(c3,c2)). [resolve(793,a,578,a)]. given #290 (T,wt=7): 1768 member(f10(identity_relation_of(c3)),cross_product(c3,c2)). [resolve(793,a,576,a)]. given #291 (A,wt=25): 231 member(A,power_set(B)) | ordered_pair(f12(A,f9(A,B)),f13(A,f9(A,B))) = f9(A,B) | f11(A) != ordered_pair(C,D). [resolve(169,b,94,a)]. given #292 (F,wt=8): 1532 f10(power_set(power_set(range_of(c4)))) != power_set(c3). [ur(174,a,850,a)]. given #293 (F,wt=8): 1535 identity_relation_of(power_set(range_of(c4))) != identity_relation_of(power_set(c3)). [ur(174,a,857,a)]. given #294 (F,wt=8): 1577 -member(c3,range_of(f1(power_set(range_of(c4)),A))). [ur(167,b,442,a,c,1537,a)]. given #295 (F,wt=8): 1624 f17(power_set(power_set(range_of(c4)))) != power_set(c3). [ur(174,a,944,a)]. given #296 (T,wt=7): 1803 ilf_type(f10(c4),member_type(cross_product(c3,c2))). [resolve(1770,a,165,c),unit_del(a,1122)]. given #297 (T,wt=8): 817 ilf_type(f2(c3,f8(range_of(c4))),member_type(c3)). [resolve(444,a,165,c),unit_del(a,431)]. given #298 (T,wt=8): 825 member(f10(range_of(c4)),c2) | empty(range_of(c4)). [resolve(518,a,214,b)]. given #299 (T,wt=5): 1870 empty(range_of(c4)) | -empty(c2). [resolve(825,a,159,a)]. given #300 (A,wt=23): 232 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 #301 (F,wt=9): 303 -member(power_set(ordered_pair(range_of(c4),c3)),power_set(identity_relation_of(A))). [ur(167,a,221,a,b,272,a)]. given #302 (F,wt=9): 394 -subset(power_set(ordered_pair(range_of(c4),c3)),f8(identity_relation_of(A))). [ur(180,a,221,a,b,390,a)]. given #303 (F,wt=9): 396 -member(ordered_pair(range_of(c4),c3),f8(f8(identity_relation_of(A)))). [ur(167,b,390,a,c,376,a)]. given #304 (F,wt=9): 399 -subset(power_set(ordered_pair(c3,range_of(c4))),f8(identity_relation_of(A))). [ur(180,a,221,a,b,391,a)]. given #305 (T,wt=7): 1871 empty(range_of(c4)) | member(f18(c2),c2). [resolve(825,a,158,a)]. given #306 (T,wt=8): 827 member(f18(range_of(c4)),c2) | empty(range_of(c4)). [resolve(518,a,204,b)]. given #307 (T,wt=8): 830 member(f17(range_of(c4)),c2) | empty(range_of(c4)). [resolve(518,a,160,b)]. given #308 (T,wt=8): 888 member(f10(domain_of(c4)),c3) | empty(domain_of(c4)). [resolve(531,a,214,b)]. given #309 (A,wt=22): 233 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 #310 (F,wt=9): 401 -member(ordered_pair(c3,range_of(c4)),f8(f8(identity_relation_of(A)))). [ur(167,b,391,a,c,376,a)]. given #311 (F,wt=9): 404 -subset(power_set(f2(c3,range_of(c4))),f8(range_of(c4))). [ur(180,a,221,a,b,392,a)]. given #312 (F,wt=9): 406 -member(f2(c3,range_of(c4)),f8(f8(range_of(c4)))). [ur(167,b,392,a,c,376,a)]. given #313 (F,wt=6): 2031 -subset(c3,f8(f8(range_of(c4)))). [ur(180,a,268,a,b,406,a)]. given #314 (T,wt=8): 891 member(f18(domain_of(c4)),c3) | empty(domain_of(c4)). [resolve(531,a,204,b)]. given #315 (T,wt=8): 894 member(f17(domain_of(c4)),c3) | empty(domain_of(c4)). [resolve(531,a,160,b)]. given #316 (T,wt=8): 996 ilf_type(ordered_pair(f17(c3),f17(c3)),member_type(c4)). [resolve(577,a,165,c),unit_del(a,606)]. given #317 (T,wt=8): 1006 ilf_type(domain_of(cross_product(A,B)),member_type(power_set(A))). [resolve(707,a,171,b)]. given #318 (A,wt=15): 234 member(power_set(power_set(A)),power_set(A)) | -member(power_set(power_set(A)),f9(power_set(power_set(A)),A)). [factor(222,a,c)]. given #319 (F,wt=6): 2040 f8(f8(range_of(c4))) != c3. [ur(174,a,2031,a)]. given #320 (F,wt=7): 2037 -member(c3,power_set(f8(f8(range_of(c4))))). [ur(167,a,268,a,b,406,a)]. given #321 (F,wt=8): 2071 -member(c3,f8(power_set(f8(f8(range_of(c4)))))). [ur(380,b,2037,a)]. given #322 (F,wt=8): 2077 -subset(power_set(c3),power_set(f8(f8(range_of(c4))))). [ur(180,a,221,a,b,2037,a)]. given #323 (T,wt=7): 2065 member(domain_of(cross_product(A,B)),power_set(A)). [resolve(1006,a,164,c),unit_del(a,166)]. given #324 (T,wt=8): 1007 ilf_type(domain_of(cross_product(cross_product(A,B),C)),binary_relation_type). [resolve(707,a,96,a)]. given #325 (T,wt=8): 1010 ilf_type(range_of(cross_product(A,B)),member_type(power_set(B))). [resolve(709,a,171,b)]. given #326 (T,wt=7): 2161 member(range_of(cross_product(A,B)),power_set(B)). [resolve(1010,a,164,c),unit_del(a,166)]. given #327 (A,wt=14): 238 member(f9(A,B),C) | -member(f3(A,C),C) | member(A,power_set(B)). [resolve(178,a,169,b)]. given #328 (F,wt=8): 2082 -ilf_type(c3,member_type(power_set(f8(f8(range_of(c4)))))). [ur(164,a,166,a,b,2037,a)]. given #329 (F,wt=7): 2227 -ilf_type(c3,subset_type(f8(f8(range_of(c4))))). [ur(171,a,2082,a)]. given #330 (F,wt=8): 2095 power_set(f8(f8(range_of(c4)))) != power_set(c3). [ur(174,a,2077,a)]. given #331 (F,wt=8): 2142 -member(c3,domain_of(cross_product(power_set(range_of(c4)),A))). [ur(167,b,442,a,c,2065,a)]. given #332 (T,wt=8): 1011 ilf_type(range_of(cross_product(A,cross_product(B,C))),binary_relation_type). [resolve(709,a,96,a)]. given #333 (T,wt=8): 1123 member(f18(cross_product(c3,c2)),cross_product(c3,c2)). [resolve(1096,a,158,a)]. given #334 (T,wt=8): 1131 ilf_type(domain_of(f8(cross_product(A,B))),subset_type(A)). [resolve(252,a,156,a),rewrite([1130(3)])]. given #335 (T,wt=8): 1133 ilf_type(range_of(f8(cross_product(A,B))),subset_type(B)). [resolve(252,a,154,a),rewrite([1132(3)])]. given #336 (A,wt=11): 239 member(f17(A),B) | -member(f3(A,B),B) | empty(A). [resolve(178,a,160,b)]. given #337 (F,wt=8): 2208 -member(c3,range_of(cross_product(A,power_set(range_of(c4))))). [ur(167,b,442,a,c,2161,a)]. given #338 (F,wt=9): 439 -member(f3(c3,f8(range_of(c4))),f8(range_of(c4))). [ur(178,a,268,a,b,392,a)]. given #339 (F,wt=9): 445 -member(f2(c3,f8(range_of(c4))),f8(range_of(c4))). [ur(181,a,438,a)]. given #340 (F,wt=9): 486 -member(ordered_pair(range_of(c4),c3),f18(power_set(identity_relation_of(A)))). [ur(167,b,272,a,c,284,a)]. given #341 (T,wt=8): 1227 ilf_type(ordered_pair(f18(c3),f18(c3)),member_type(c4)). [resolve(1193,a,165,c),unit_del(a,606)]. given #342 (T,wt=8): 1339 ilf_type(f9(c3,f8(range_of(c4))),member_type(c3)). [resolve(224,a,441,a),unit_del(a,431)]. given #343 (T,wt=7): 2320 member(f9(c3,f8(range_of(c4))),c3). [resolve(1339,a,164,c),unit_del(a,431)]. given #344 (T,wt=8): 1815 ilf_type(f17(identity_relation_of(c3)),member_type(cross_product(c3,c2))). [resolve(1765,a,165,c),unit_del(a,1122)]. given #345 (A,wt=12): 240 member(f11(A),B) | -member(f3(A,B),B) | ilf_type(A,binary_relation_type). [resolve(178,a,86,a)]. given #346 (F,wt=9): 487 -member(ordered_pair(c3,range_of(c4)),f18(power_set(identity_relation_of(A)))). [ur(167,b,271,a,c,284,a)]. given #347 (F,wt=9): 488 -member(f2(c3,range_of(c4)),f18(power_set(range_of(c4)))). [ur(167,b,269,a,c,284,a)]. given #348 (F,wt=6): 2352 -subset(c3,f18(power_set(range_of(c4)))). [ur(180,a,268,a,b,488,a)]. given #349 (F,wt=6): 2363 f18(power_set(range_of(c4))) != c3. [ur(174,a,2352,a)]. given #350 (T,wt=8): 1827 ilf_type(f18(identity_relation_of(c3)),member_type(cross_product(c3,c2))). [resolve(1766,a,165,c),unit_del(a,1122)]. given #351 (T,wt=8): 1839 ilf_type(f10(identity_relation_of(c3)),member_type(cross_product(c3,c2))). [resolve(1768,a,165,c),unit_del(a,1122)]. given #352 (T,wt=8): 2038 member(f2(c3,f8(f8(range_of(c4)))),c3). [resolve(2031,a,182,a)]. given #353 (T,wt=8): 2361 member(f2(c3,f18(power_set(range_of(c4)))),c3). [resolve(2352,a,182,a)]. given #354 (A,wt=14): 241 member(f9(A,B),C) | member(f3(A,C),A) | member(A,power_set(B)). [resolve(179,a,169,b)]. given #355 (F,wt=7): 2360 -member(c3,power_set(f18(power_set(range_of(c4))))). [ur(167,a,268,a,b,488,a)]. given #356 (F,wt=8): 2458 -member(c3,f8(power_set(f18(power_set(range_of(c4)))))). [ur(380,b,2360,a)]. given #357 (F,wt=8): 2464 -subset(power_set(c3),power_set(f18(power_set(range_of(c4))))). [ur(180,a,221,a,b,2360,a)]. given #358 (F,wt=8): 2471 -ilf_type(c3,member_type(power_set(f18(power_set(range_of(c4)))))). [ur(164,a,166,a,b,2360,a)]. given #359 (T,wt=6): 2394 member(f3(c3,range_of(c4)),c3). [resolve(241,a,450,a),unit_del(b,442)]. given #360 (T,wt=7): 2391 member(f3(c3,f8(range_of(c4))),c3). [resolve(241,a,567,a),unit_del(b,442)]. given #361 (T,wt=7): 2492 ilf_type(f3(c3,range_of(c4)),member_type(c3)). [resolve(2394,a,165,c),unit_del(a,431)]. given #362 (T,wt=8): 2504 ilf_type(f3(c3,f8(range_of(c4))),member_type(c3)). [resolve(2391,a,165,c),unit_del(a,431)]. given #363 (A,wt=11): 242 member(f17(A),B) | member(f3(A,B),A) | empty(A). [resolve(179,a,160,b)]. given #364 (F,wt=7): 2487 -ilf_type(c3,subset_type(f18(power_set(range_of(c4))))). [ur(171,a,2471,a)]. given #365 (F,wt=8): 2486 power_set(f18(power_set(range_of(c4)))) != power_set(c3). [ur(174,a,2464,a)]. given #366 (F,wt=9): 497 -member(ordered_pair(c3,A),identity_relation_of(power_set(f8(range_of(c4))))). [ur(188,a,441,a)]. given #367 (F,wt=9): 500 -member(f9(c3,f8(range_of(c4))),f8(range_of(c4))). [ur(168,a,441,a)]. given #368 (T,wt=9): 277 member(A,B) | -member(f3(power_set(A),B),B). [resolve(221,a,178,a)]. given #369 (T,wt=9): 354 ilf_type(A,binary_relation_type) | member(f18(identity_relation_of(A)),identity_relation_of(A)). [resolve(195,a,158,a)]. given #370 (T,wt=9): 381 member(f8(A),B) | -member(power_set(A),power_set(B)). [resolve(376,a,167,a)]. given #371 (T,wt=9): 384 member(ordered_pair(f8(A),f8(A)),identity_relation_of(power_set(A))). [resolve(376,a,111,a)]. given #372 (A,wt=12): 243 member(f11(A),B) | member(f3(A,B),A) | ilf_type(A,binary_relation_type). [resolve(179,a,86,a)]. given #373 (F,wt=9): 508 -member(ordered_pair(c3,A),identity_relation_of(f8(power_set(range_of(c4))))). [ur(188,a,451,a)]. given #374 (F,wt=9): 556 -member(ordered_pair(power_set(c3),power_set(range_of(c4))),identity_relation_of(A)). [ur(187,a,507,a)]. given #375 (F,wt=9): 557 -member(ordered_pair(power_set(range_of(c4)),power_set(c3)),identity_relation_of(A)). [ur(187,a,507,a(flip))]. given #376 (F,wt=9): 562 -member(f3(c3,range_of(c4)),f18(power_set(range_of(c4)))). [ur(167,b,440,a,c,284,a)]. given #377 (T,wt=9): 415 ilf_type(f10(power_set(cross_product(A,B))),relation_type(A,B)). [resolve(237,a,185,a)]. given #378 (T,wt=9): 457 member(f18(c3),A) | member(f3(c3,A),c3). [resolve(432,a,179,a)]. given #379 (T,wt=7): 2799 member(f3(c3,A),c3) | -empty(A). [resolve(457,a,159,a)]. given #380 (T,wt=9): 458 member(f18(c3),A) | -member(f3(c3,A),A). [resolve(432,a,178,a)]. given #381 (A,wt=11): 245 member(f2(A,B),A) | -member(C,A) | member(C,B). [resolve(182,a,180,c)]. given #382 (F,wt=9): 563 -member(power_set(f3(c3,range_of(c4))),power_set(range_of(c4))). [ur(167,a,221,a,b,440,a)]. given #383 (F,wt=9): 568 -member(f9(c3,range_of(c4)),f18(power_set(range_of(c4)))). [ur(167,b,450,a,c,284,a)]. given #384 (F,wt=9): 569 -member(power_set(f9(c3,range_of(c4))),power_set(range_of(c4))). [ur(167,a,221,a,b,450,a)]. given #385 (F,wt=9): 591 -ilf_type(ordered_pair(range_of(c4),c3),member_type(identity_relation_of(power_set(A)))). [ur(164,a,571,a,b,272,a)]. given #386 (T,wt=8): 2922 member(f3(c3,f18(power_set(range_of(c4)))),c3). [resolve(568,a,241,a),unit_del(b,442)]. given #387 (T,wt=9): 505 member(f2(power_set(c3),power_set(range_of(c4))),power_set(c3)). [resolve(448,a,182,a)]. given #388 (T,wt=9): 519 member(range_of(c4),A) | -member(power_set(c2),power_set(A)). [resolve(489,a,167,a)]. given #389 (T,wt=9): 522 member(ordered_pair(range_of(c4),range_of(c4)),identity_relation_of(power_set(c2))). [resolve(489,a,111,a)]. given #390 (A,wt=11): 246 domain(A,B,f1(B,A)) = domain_of(f1(B,A)). [resolve(183,a,157,a)]. given #391 (F,wt=9): 592 -ilf_type(ordered_pair(c3,range_of(c4)),member_type(identity_relation_of(power_set(A)))). [ur(164,a,571,a,b,271,a)]. given #392 (F,wt=9): 594 -ilf_type(ordered_pair(range_of(c4),c3),member_type(identity_relation_of(identity_relation_of(c3)))). [ur(164,a,587,a,b,272,a)]. given #393 (F,wt=9): 595 -ilf_type(ordered_pair(c3,range_of(c4)),member_type(identity_relation_of(identity_relation_of(c3)))). [ur(164,a,587,a,b,271,a)]. given #394 (F,wt=9): 656 -ilf_type(ordered_pair(range_of(c4),c3),member_type(identity_relation_of(identity_relation_of(c4)))). [ur(164,a,652,a,b,272,a)]. given #395 (T,wt=9): 532 member(domain_of(c4),A) | -member(power_set(c3),power_set(A)). [resolve(527,a,167,a)]. given #396 (T,wt=9): 535 member(ordered_pair(domain_of(c4),domain_of(c4)),identity_relation_of(power_set(c3))). [resolve(527,a,111,a)]. given #397 (T,wt=9): 573 ilf_type(f17(power_set(cross_product(A,B))),relation_type(A,B)). [resolve(572,a,185,a)]. given #398 (T,wt=9): 602 member(f10(identity_relation_of(c3)),A) | -member(c4,power_set(A)). [resolve(576,a,167,a)]. given #399 (A,wt=11): 248 range(A,B,f1(B,A)) = range_of(f1(B,A)). [resolve(183,a,155,a)]. given #400 (F,wt=9): 657 -ilf_type(ordered_pair(c3,range_of(c4)),member_type(identity_relation_of(identity_relation_of(c4)))). [ur(164,a,652,a,b,271,a)]. given #401 (F,wt=9): 717 -member(power_set(c3),f18(power_set(power_set(power_set(range_of(c4)))))). [ur(167,b,452,a,c,284,a)]. given #402 (F,wt=9): 718 -member(power_set(power_set(c3)),power_set(power_set(power_set(range_of(c4))))). [ur(167,a,221,a,b,452,a)]. given #403 (F,wt=9): 724 -member(c3,f18(power_set(f18(power_set(power_set(range_of(c4))))))). [ur(167,b,480,a,c,284,a)]. given #404 (T,wt=9): 616 member(f18(c4),A) | member(f3(c4,A),c4). [resolve(607,a,179,a)]. given #405 (T,wt=7): 3086 member(f3(c4,A),c4) | -empty(A). [resolve(616,a,159,a)]. given #406 (T,wt=9): 617 member(f18(c4),A) | -member(f3(c4,A),A). [resolve(607,a,178,a)]. given #407 (T,wt=9): 630 member(f18(identity_relation_of(c3)),A) | -member(c4,power_set(A)). [resolve(578,a,167,a)]. given #408 (A,wt=18): 253 -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 #409 (F,wt=9): 725 -member(power_set(c3),power_set(f18(power_set(power_set(range_of(c4)))))). [ur(167,a,221,a,b,480,a)]. given #410 (F,wt=9): 733 -member(c3,f18(power_set(f8(power_set(f8(range_of(c4))))))). [ur(167,b,501,a,c,284,a)]. given #411 (F,wt=9): 734 -member(power_set(c3),power_set(f8(power_set(f8(range_of(c4)))))). [ur(167,a,221,a,b,501,a)]. given #412 (F,wt=9): 755 -member(c3,f18(power_set(f8(f8(power_set(range_of(c4))))))). [ur(167,b,511,a,c,284,a)]. given #413 (T,wt=9): 642 member(f17(identity_relation_of(c3)),A) | -member(c4,power_set(A)). [resolve(581,a,167,a)]. given #414 (T,wt=9): 737 ilf_type(f18(power_set(cross_product(A,B))),relation_type(A,B)). [resolve(735,a,185,a)]. given #415 (T,wt=9): 742 member(f18(f8(A)),A) | ilf_type(f8(A),binary_relation_type). [resolve(380,a,203,a)]. given #416 (T,wt=6): 3214 ilf_type(f8(A),binary_relation_type) | -empty(A). [resolve(742,a,159,a)]. given #417 (A,wt=19): 254 -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 #418 (F,wt=9): 756 -member(power_set(c3),power_set(f8(f8(power_set(range_of(c4)))))). [ur(167,a,221,a,b,511,a)]. given #419 (F,wt=9): 768 -member(c3,f10(power_set(f8(f8(power_set(range_of(c4))))))). [ur(167,b,511,a,c,746,a)]. given #420 (F,wt=9): 769 -member(c3,f10(power_set(f8(power_set(f8(range_of(c4))))))). [ur(167,b,501,a,c,746,a)]. given #421 (F,wt=9): 770 -member(c3,f10(power_set(f18(power_set(power_set(range_of(c4))))))). [ur(167,b,480,a,c,746,a)]. given #422 (T,wt=8): 3215 ilf_type(f8(A),binary_relation_type) | member(f18(A),A). [resolve(742,a,158,a)]. given #423 (T,wt=9): 745 member(f11(f8(A)),A) | ilf_type(f8(A),binary_relation_type). [resolve(380,a,86,a)]. given #424 (T,wt=9): 797 member(ordered_pair(c4,c4),identity_relation_of(power_set(cross_product(c3,c2)))). [resolve(789,a,111,a)]. given #425 (T,wt=9): 828 member(f18(range_of(c4)),c2) | ilf_type(range_of(c4),binary_relation_type). [resolve(518,a,203,a)]. given #426 (A,wt=17): 255 member(ordered_pair(f9(A,B),C),identity_relation_of(A)) | f9(A,B) != C | member(A,power_set(B)). [resolve(189,a,169,b),flip(b)]. given #427 (F,wt=9): 771 -member(power_set(c3),f10(power_set(power_set(power_set(range_of(c4)))))). [ur(167,b,452,a,c,746,a)]. given #428 (F,wt=9): 773 -member(f9(c3,range_of(c4)),f10(power_set(range_of(c4)))). [ur(167,b,450,a,c,746,a)]. given #429 (F,wt=6): 3384 -subset(c3,f10(power_set(range_of(c4)))). [ur(180,a,1442,a,b,773,a)]. given #430 (F,wt=6): 3392 f10(power_set(range_of(c4))) != c3. [ur(174,a,3384,a)]. given #431 (T,wt=6): 3355 ilf_type(range_of(c4),binary_relation_type) | -empty(c2). [resolve(828,a,159,a)]. given #432 (T,wt=8): 3356 ilf_type(range_of(c4),binary_relation_type) | member(f18(c2),c2). [resolve(828,a,158,a)]. given #433 (T,wt=8): 3374 member(f3(c3,f10(power_set(range_of(c4)))),c3). [resolve(773,a,241,a),unit_del(b,442)]. given #434 (T,wt=8): 3390 member(f2(c3,f10(power_set(range_of(c4)))),c3). [resolve(3384,a,182,a)]. given #435 (A,wt=13): 256 member(ordered_pair(f17(A),B),identity_relation_of(A)) | f17(A) != B | empty(A). [resolve(189,a,160,b),flip(b)]. given #436 (F,wt=7): 3381 -member(c3,power_set(f10(power_set(range_of(c4))))). [ur(223,a,442,a,b,773,a)]. given #437 (F,wt=8): 3436 -member(c3,f8(power_set(f10(power_set(range_of(c4)))))). [ur(380,b,3381,a)]. given #438 (F,wt=8): 3443 -subset(power_set(c3),power_set(f10(power_set(range_of(c4))))). [ur(180,a,221,a,b,3381,a)]. given #439 (F,wt=8): 3449 -ilf_type(c3,member_type(power_set(f10(power_set(range_of(c4)))))). [ur(164,a,166,a,b,3381,a)]. given #440 (T,wt=9): 831 member(f11(range_of(c4)),c2) | ilf_type(range_of(c4),binary_relation_type). [resolve(518,a,86,a)]. given #441 (T,wt=9): 892 member(f18(domain_of(c4)),c3) | ilf_type(domain_of(c4),binary_relation_type). [resolve(531,a,203,a)]. given #442 (T,wt=9): 895 member(f11(domain_of(c4)),c3) | ilf_type(domain_of(c4),binary_relation_type). [resolve(531,a,86,a)]. given #443 (T,wt=9): 1065 member(f18(A),A) | ilf_type(A,member_type(power_set(B))). [resolve(228,a,165,c),unit_del(b,166)]. given #444 (A,wt=14): 257 member(ordered_pair(f11(A),B),identity_relation_of(A)) | f11(A) != B | ilf_type(A,binary_relation_type). [resolve(189,a,86,a),flip(b)]. given #445 (F,wt=7): 3465 -ilf_type(c3,subset_type(f10(power_set(range_of(c4))))). [ur(171,a,3449,a)]. given #446 (F,wt=8): 3464 power_set(f10(power_set(range_of(c4)))) != power_set(c3). [ur(174,a,3443,a)]. given #447 (F,wt=9): 776 -member(f3(c3,range_of(c4)),f10(power_set(range_of(c4)))). [ur(167,b,440,a,c,746,a)]. given #448 (F,wt=9): 782 -member(ordered_pair(range_of(c4),c3),f10(power_set(identity_relation_of(A)))). [ur(167,b,272,a,c,746,a)]. given #449 (T,wt=7): 3520 ilf_type(A,member_type(power_set(B))) | -empty(A). [resolve(1065,a,159,a)]. given #450 (T,wt=9): 1090 ilf_type(f1(A,B),member_type(power_set(cross_product(B,A)))). [resolve(250,a,171,b)]. given #451 (T,wt=8): 3552 member(f1(A,B),power_set(cross_product(B,A))). [resolve(1090,a,164,c),unit_del(a,166)]. given #452 (T,wt=9): 1200 ilf_type(ordered_pair(f18(c3),f18(c3)),member_type(identity_relation_of(c3))). [resolve(463,a,165,c),unit_del(a,570)]. given #453 (A,wt=18): 258 -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 #454 (F,wt=9): 783 -member(ordered_pair(c3,range_of(c4)),f10(power_set(identity_relation_of(A)))). [ur(167,b,271,a,c,746,a)]. given #455 (F,wt=9): 784 -member(f2(c3,range_of(c4)),f10(power_set(range_of(c4)))). [ur(167,b,269,a,c,746,a)]. given #456 (F,wt=9): 852 -member(c3,f10(power_set(f10(power_set(power_set(range_of(c4))))))). [ur(167,b,774,a,c,746,a)]. given #457 (F,wt=9): 853 -member(c3,f18(power_set(f10(power_set(power_set(range_of(c4))))))). [ur(167,b,774,a,c,284,a)]. given #458 (T,wt=9): 1311 ilf_type(ordered_pair(f18(c4),f18(c4)),member_type(identity_relation_of(c4))). [resolve(622,a,165,c),unit_del(a,651)]. given #459 (T,wt=9): 1399 -member(A,domain_of(f1(B,C))) | member(A,C). [resolve(1332,a,167,c)]. given #460 (T,wt=9): 1544 -member(A,range_of(f1(B,C))) | member(A,B). [resolve(1537,a,167,c)]. given #461 (T,wt=9): 1629 ilf_type(f18(identity_relation_of(power_set(A))),member_type(identity_relation_of(power_set(A)))). [resolve(700,a,165,c),unit_del(a,571)]. given #462 (A,wt=13): 259 -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 #463 (F,wt=9): 854 -member(power_set(c3),power_set(f10(power_set(power_set(range_of(c4)))))). [ur(167,a,221,a,b,774,a)]. given #464 (F,wt=9): 855 -member(ordered_pair(c3,A),f8(identity_relation_of(power_set(range_of(c4))))). [ur(380,b,447,a)]. given #465 (F,wt=9): 858 -subset(power_set(ordered_pair(c3,A)),identity_relation_of(power_set(range_of(c4)))). [ur(180,a,221,a,b,447,a)]. given #466 (F,wt=9): 864 -member(identity_relation_of(power_set(c3)),power_set(identity_relation_of(power_set(range_of(c4))))). [ur(167,a,285,a,b,447,a)]. given #467 (T,wt=9): 1664 empty(f8(domain_of(c4))) | member(f18(domain_of(c4)),c3). [resolve(1658,b,531,a)]. given #468 (T,wt=9): 1665 empty(f8(range_of(c4))) | member(f18(range_of(c4)),c2). [resolve(1658,b,518,a)]. given #469 (T,wt=6): 3746 empty(f8(range_of(c4))) | -empty(c2). [resolve(1665,b,159,a)]. given #470 (T,wt=8): 3747 empty(f8(range_of(c4))) | member(f18(c2),c2). [resolve(1665,b,158,a)]. given #471 (A,wt=11): 260 -ilf_type(c4,relation_type(A,B)) | subset(c3,range(A,B,c4)). [resolve(190,b,83,a)]. ============================== PROOF ================================= % Proof 1 at 0.37 (+ 0.01) seconds. % Length of proof is 13. % Level of proof is 5. % Maximum clause weight is 24.000. % Given clauses 471. 13 -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]. 78 -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]. 79 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,relation_type(A,B)) | range(A,B,C) = range_of(C). [copy(78),flip(d)]. 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]. 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)]. 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)]. 197 range(c3,c2,c4) = range_of(c4). [resolve(155,a,82,a)]. 199 -subset(c3,range_of(c4)). [back_rewrite(84),rewrite([197(5)])]. 260 -ilf_type(c4,relation_type(A,B)) | subset(c3,range(A,B,c4)). [resolve(190,b,83,a)]. 3765 $F. [resolve(260,a,82,a),rewrite([197(5)]),unit_del(a,199)]. ============================== end of proof ========================== ============================== STATISTICS ============================ Given=471. Generated=5454. Kept=3740. proofs=1. Usable=470. Sos=3063. Demods=38. Limbo=0, Disabled=298. Hints=0. Kept_by_rule=0, Deleted_by_rule=2. Forward_subsumed=1711. Back_subsumed=160. Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. New_demodulators=38 (0 lex), Back_demodulated=3. Back_unit_deleted=44. Demod_attempts=60127. Demod_rewrites=41. Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. Nonunit_fsub_feature_tests=4793. Nonunit_bsub_feature_tests=3169. Megabytes=5.27. User_CPU=0.37, System_CPU=0.01, Wall_clock=1. ============================== end of statistics ===================== ============================== end of search ========================= Exiting with 1 proof. Process 23986 exit (max_proofs) Tue Nov 3 16:59:22 2009 ============================== end of multisearch ==================== All 2 subproblems have been proved, so we are done. Total user_CPU=0.89, system_CPU=0.04, wall_clock=1. THEOREM PROVED Exiting. Process 23984 exit (max_proofs) Tue Nov 3 16:59:22 2009