============================== FOF-Prover9 =========================== FOF-Prover9 (32) version 22-May-2007, May 2007. Process 27399 was started by mccune on cleo, Tue May 22 14:45:19 2007 The command was "/home/mccune/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 (0.00 sec) gives 2 independent subproblems: ( <641,82> <641,82> ). Max nnf_size of subproblems is 641; max cnf_max is 82. ============================== FOF REDUCTION MULTISEARCH ============= Subproblem 1 of 2 (negated): ((all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | - subset(B,C) | - subset(C,B) | =(C,B))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,set_type) | (all E (- ilf_type(E,relation_type(B,C)) | - subset(identity_relation_of(D),E) | subset(D,domain(B,C,E)))))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,set_type) | (all E (- ilf_type(E,relation_type(B,C)) | - subset(identity_relation_of(D),E) | subset(D,range(B,C,E)))))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | - member(C,B) | (all D (- ilf_type(D,set_type) | member(ordered_pair(C,D),identity_relation_of(B)) | - =(D,C))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | member(C,B) | (all D (- ilf_type(D,set_type) | - member(ordered_pair(C,D),identity_relation_of(B)))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,set_type) | =(D,C) | - member(ordered_pair(C,D),identity_relation_of(B)))))))) & (all B (- ilf_type(B,set_type) | ilf_type(identity_relation_of(B),binary_relation_type))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,subset_type(cross_product(B,C))) | ilf_type(D,relation_type(B,C)))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all E (- ilf_type(E,relation_type(B,C)) | ilf_type(E,subset_type(cross_product(B,C))))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (exists D ilf_type(D,relation_type(C,B))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | subset(B,C) | (exists D (ilf_type(D,set_type) & member(D,B) & - member(D,C))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,set_type) | - member(D,B) | member(D,C))) | - subset(B,C))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,set_type) | - member(D,B) | member(D,C))) | (exists D (ilf_type(D,set_type) & member(D,B) & - member(D,C))))))) & (all B (- ilf_type(B,binary_relation_type) | (all C (- ilf_type(C,binary_relation_type) | subset(B,C) | (exists D (ilf_type(D,set_type) & (exists E (ilf_type(E,set_type) & member(ordered_pair(D,E),B) & - member(ordered_pair(D,E),C))))))))) & (all B (- ilf_type(B,binary_relation_type) | (all C (- ilf_type(C,binary_relation_type) | (all D (- ilf_type(D,set_type) | (all E (- ilf_type(E,set_type) | - member(ordered_pair(D,E),B) | member(ordered_pair(D,E),C))))) | - subset(B,C))))) & (all B (- ilf_type(B,binary_relation_type) | (all C (- ilf_type(C,binary_relation_type) | (all D (- ilf_type(D,set_type) | (all E (- ilf_type(E,set_type) | - member(ordered_pair(D,E),B) | member(ordered_pair(D,E),C))))) | (exists D (ilf_type(D,set_type) & (exists E (ilf_type(E,set_type) & member(ordered_pair(D,E),B) & - member(ordered_pair(D,E),C))))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | =(C,B) | - subset(B,C) | - subset(C,B))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | subset(B,C) | - =(C,B))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | subset(C,B) | - =(C,B))))) & (all B (- ilf_type(B,binary_relation_type) | ilf_type(domain_of(B),set_type))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | ilf_type(cross_product(B,C),set_type))))) & (all B (- ilf_type(B,binary_relation_type) | ilf_type(range_of(B),set_type))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | ilf_type(ordered_pair(B,C),set_type))))) & (all B (- ilf_type(B,set_type) | ilf_type(B,binary_relation_type) | - relation_like(B))) & (all B (- ilf_type(B,set_type) | relation_like(B) | - ilf_type(B,binary_relation_type))) & (exists B ilf_type(B,binary_relation_type)) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | ilf_type(C,subset_type(B)) | - ilf_type(C,member_type(power_set(B))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | ilf_type(C,member_type(power_set(B))) | - ilf_type(C,subset_type(B)))))) & (all B (- ilf_type(B,set_type) | (exists C ilf_type(C,subset_type(B))))) & (all B (- ilf_type(B,set_type) | subset(B,B))) & (all B (- ilf_type(B,binary_relation_type) | subset(B,B))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | member(B,power_set(C)) | (exists D (ilf_type(D,set_type) & member(D,B) & - member(D,C))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,set_type) | - member(D,B) | member(D,C))) | - member(B,power_set(C)))))) & (all B (- ilf_type(B,set_type) | - empty(power_set(B)))) & (all B (- ilf_type(B,set_type) | ilf_type(power_set(B),set_type))) & (all B (- ilf_type(B,set_type) | (all C (empty(C) | - ilf_type(C,set_type) | ilf_type(B,member_type(C)) | - member(B,C))))) & (all B (- ilf_type(B,set_type) | (all C (empty(C) | - ilf_type(C,set_type) | member(B,C) | - ilf_type(B,member_type(C)))))) & (all B (empty(B) | - ilf_type(B,set_type) | (exists C ilf_type(C,member_type(B))))) & (all B (- ilf_type(B,set_type) | relation_like(B) | (exists C (ilf_type(C,set_type) & member(C,B) & (all D (- ilf_type(D,set_type) | (all E (- ilf_type(E,set_type) | - =(ordered_pair(D,E),C))))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | - member(C,B) | (exists D (ilf_type(D,set_type) & (exists E (ilf_type(E,set_type) & =(ordered_pair(D,E),C))))))) | - relation_like(B))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | - member(C,B) | (exists D (ilf_type(D,set_type) & (exists E (ilf_type(E,set_type) & =(ordered_pair(D,E),C))))))) | (exists C (ilf_type(C,set_type) & member(C,B) & (all D (- ilf_type(D,set_type) | (all E (- ilf_type(E,set_type) | - =(ordered_pair(D,E),C))))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,subset_type(cross_product(B,C))) | relation_like(D))))))) & (all B (- ilf_type(B,set_type) | empty(B) | (exists C (ilf_type(C,set_type) & member(C,B))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | - member(C,B))) | - empty(B))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | - member(C,B))) | (exists C (ilf_type(C,set_type) & member(C,B))))) & (all B (- empty(B) | - ilf_type(B,set_type) | relation_like(B))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,relation_type(B,C)) | =(domain_of(D),domain(B,C,D)))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,relation_type(B,C)) | ilf_type(domain(B,C,D),subset_type(B)))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,relation_type(B,C)) | =(range_of(D),range(B,C,D)))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,relation_type(B,C)) | ilf_type(range(B,C,D),subset_type(C)))))))) & (all B ilf_type(B,set_type)) & (exists B (ilf_type(B,set_type) & (exists C (ilf_type(C,set_type) & (exists D (ilf_type(D,relation_type(C,B)) & subset(identity_relation_of(C),D) & - =(domain(C,B,D),C)))))))). Max_seconds is 30 for this subproblem. Child search process 27400 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(paramodulation) -> set(back_demod). % set(binary_resolution). % (non-Horn) % set(neg_ur_resolution). % (non-Horn, less than 100 clauses) Auto_process settings: % set(factor). % (non-Horn) % set(back_unit_deletion). % (non-Horn) % set(back_unit_deletion) -> set(unit_deletion). ============================== end of process initial clauses ======== ============================== CLAUSES FOR SEARCH ==================== % Clauses after input processing: formulas(usable). end_of_list. formulas(sos). 30 -ilf_type(A,binary_relation_type) | -ilf_type(B,binary_relation_type) | subset(A,B) | member(ordered_pair(f4(A,B),f5(A,B)),A). [assumption]. 31 -ilf_type(A,binary_relation_type) | -ilf_type(B,binary_relation_type) | subset(A,B) | -member(ordered_pair(f4(A,B),f5(A,B)),B). [assumption]. 43 ilf_type(c1,binary_relation_type). [assumption]. 81 ilf_type(A,set_type). [assumption]. 82 ilf_type(c4,relation_type(c3,c2)). [assumption]. 83 subset(identity_relation_of(c3),c4). [assumption]. 84 domain(c3,c2,c4) != c3. [assumption]. 86 member(f11(A),A) | ilf_type(A,binary_relation_type). [copy(85),merge(c),unit_del(a,81)]. 88 f11(A) != ordered_pair(B,C) | ilf_type(A,binary_relation_type). [copy(87),flip(d),merge(e),unit_del(a,81),unit_del(b,81),unit_del(c,81)]. 90 -member(A,B) | ordered_pair(f12(B,A),f13(B,A)) = A | -ilf_type(B,binary_relation_type). [copy(89),merge(e),unit_del(a,81),unit_del(b,81)]. 92 -member(A,B) | ordered_pair(f12(B,A),f13(B,A)) = A | member(f11(B),B). [copy(91),merge(e),unit_del(a,81),unit_del(b,81)]. 94 -member(A,B) | ordered_pair(f12(B,A),f13(B,A)) = A | f11(B) != ordered_pair(C,D). [copy(93),flip(h),merge(e),unit_del(a,81),unit_del(b,81),unit_del(e,81),unit_del(f,81)]. 96 -ilf_type(A,subset_type(cross_product(B,C))) | ilf_type(A,binary_relation_type). [copy(95),unit_del(a,81),unit_del(b,81),unit_del(d,81)]. 98 -ilf_type(A,subset_type(cross_product(B,C))) | -member(D,A) | ordered_pair(f12(A,D),f13(A,D)) = D. [copy(97),unit_del(a,81),unit_del(b,81),unit_del(d,81),unit_del(e,81)]. 100 -empty(A) | ilf_type(A,binary_relation_type). [copy(99),merge(c),unit_del(b,81)]. 111 -member(A,B) | member(ordered_pair(A,A),identity_relation_of(B)). [factor(14,b,d),xx(e),unit_del(a,81),unit_del(b,81)]. 131 subset(A,A). [factor(37,a,b),xx(c),unit_del(a,81)]. 138 -member(power_set(A),power_set(A)) | member(power_set(A),A). [factor(52,d,f),merge(c),unit_del(a,81),unit_del(b,81)]. 154 -ilf_type(A,relation_type(B,C)) | ilf_type(range(B,C,A),subset_type(C)). [back_unit_del(80),unit_del(a,81),unit_del(b,81)]. 155 -ilf_type(A,relation_type(B,C)) | range(B,C,A) = range_of(A). [back_unit_del(79),unit_del(a,81),unit_del(b,81)]. 156 -ilf_type(A,relation_type(B,C)) | ilf_type(domain(B,C,A),subset_type(B)). [back_unit_del(77),unit_del(a,81),unit_del(b,81)]. 157 -ilf_type(A,relation_type(B,C)) | domain(B,C,A) = domain_of(A). [back_unit_del(76),unit_del(a,81),unit_del(b,81)]. 158 -member(A,B) | member(f18(B),B). [back_unit_del(74),unit_del(a,81),unit_del(b,81)]. 159 -member(A,B) | -empty(B). [back_unit_del(72),unit_del(a,81),unit_del(b,81)]. 160 empty(A) | member(f17(A),A). [back_unit_del(71),unit_del(a,81)]. 161 -member(A,B) | ordered_pair(f14(B,A),f15(B,A)) = A | f16(B) != ordered_pair(C,D). [back_unit_del(69),unit_del(a,81),unit_del(b,81),unit_del(e,81),unit_del(f,81)]. 162 -member(A,B) | ordered_pair(f14(B,A),f15(B,A)) = A | member(f16(B),B). [back_unit_del(67),unit_del(a,81),unit_del(b,81)]. 163 empty(A) | ilf_type(f10(A),member_type(A)). [back_unit_del(57),unit_del(b,81)]. 164 empty(A) | member(B,A) | -ilf_type(B,member_type(A)). [back_unit_del(56),unit_del(a,81),unit_del(c,81)]. 165 empty(A) | ilf_type(B,member_type(A)) | -member(B,A). [back_unit_del(55),unit_del(a,81),unit_del(c,81)]. 166 -empty(power_set(A)). [back_unit_del(53),unit_del(a,81)]. 167 -member(A,B) | member(A,C) | -member(B,power_set(C)). [back_unit_del(52),unit_del(a,81),unit_del(b,81),unit_del(c,81)]. 168 member(A,power_set(B)) | -member(f9(A,B),B). [back_unit_del(51),unit_del(a,81),unit_del(b,81)]. 169 member(A,power_set(B)) | member(f9(A,B),A). [back_unit_del(50),unit_del(a,81),unit_del(b,81)]. 170 ilf_type(f8(A),subset_type(A)). [back_unit_del(46),unit_del(a,81)]. 171 ilf_type(A,member_type(power_set(B))) | -ilf_type(A,subset_type(B)). [back_unit_del(45),unit_del(a,81),unit_del(b,81)]. 172 ilf_type(A,subset_type(B)) | -ilf_type(A,member_type(power_set(B))). [back_unit_del(44),unit_del(a,81),unit_del(b,81)]. 173 subset(A,B) | A != B. [back_unit_del(38),unit_del(a,81),unit_del(b,81)]. 174 subset(A,B) | B != A. [back_unit_del(37),unit_del(a,81),unit_del(b,81)]. 175 -ilf_type(A,binary_relation_type) | -ilf_type(B,binary_relation_type) | -member(ordered_pair(C,D),A) | member(ordered_pair(C,D),B) | -member(ordered_pair(f6(A,B),f7(A,B)),B). [back_unit_del(36),unit_del(c,81),unit_del(d,81)]. 176 -ilf_type(A,binary_relation_type) | -ilf_type(B,binary_relation_type) | -member(ordered_pair(C,D),A) | member(ordered_pair(C,D),B) | member(ordered_pair(f6(A,B),f7(A,B)),A). [back_unit_del(35),unit_del(c,81),unit_del(d,81)]. 178 -member(A,B) | member(A,C) | -member(f3(B,C),C). [back_unit_del(27),unit_del(a,81),unit_del(b,81),unit_del(c,81)]. 179 -member(A,B) | member(A,C) | member(f3(B,C),B). [back_unit_del(26),unit_del(a,81),unit_del(b,81),unit_del(c,81)]. 180 -member(A,B) | member(A,C) | -subset(B,C). [back_unit_del(24),unit_del(a,81),unit_del(b,81),unit_del(c,81)]. 181 subset(A,B) | -member(f2(A,B),B). [back_unit_del(23),unit_del(a,81),unit_del(b,81)]. 182 subset(A,B) | member(f2(A,B),A). [back_unit_del(22),unit_del(a,81),unit_del(b,81)]. 183 ilf_type(f1(A,B),relation_type(B,A)). [back_unit_del(20),unit_del(a,81),unit_del(b,81)]. 184 -ilf_type(A,relation_type(B,C)) | ilf_type(A,subset_type(cross_product(B,C))). [back_unit_del(19),unit_del(a,81),unit_del(b,81)]. 185 -ilf_type(A,subset_type(cross_product(B,C))) | ilf_type(A,relation_type(B,C)). [back_unit_del(18),unit_del(a,81),unit_del(b,81)]. 186 ilf_type(identity_relation_of(A),binary_relation_type). [back_unit_del(17),unit_del(a,81)]. 187 A = B | -member(ordered_pair(B,A),identity_relation_of(C)). [back_unit_del(16),unit_del(a,81),unit_del(b,81),unit_del(c,81)]. 188 member(A,B) | -member(ordered_pair(A,C),identity_relation_of(B)). [back_unit_del(15),unit_del(a,81),unit_del(b,81),unit_del(d,81)]. 189 -member(A,B) | member(ordered_pair(A,C),identity_relation_of(B)) | C != A. [back_unit_del(14),unit_del(a,81),unit_del(b,81),unit_del(d,81)]. 190 -ilf_type(A,relation_type(B,C)) | -subset(identity_relation_of(D),A) | subset(D,range(B,C,A)). [back_unit_del(13),unit_del(a,81),unit_del(b,81),unit_del(c,81)]. 191 -ilf_type(A,relation_type(B,C)) | -subset(identity_relation_of(D),A) | subset(D,domain(B,C,A)). [back_unit_del(12),unit_del(a,81),unit_del(b,81),unit_del(c,81)]. 192 -subset(A,B) | -subset(B,A) | B = A. [back_unit_del(11),unit_del(a,81),unit_del(b,81)]. end_of_list. formulas(demodulators). end_of_list. ============================== end of clauses for search ============= ============================== SEARCH ================================ % Starting search at 0.02 seconds. given #1 (I,wt=18): 30 -ilf_type(A,binary_relation_type) | -ilf_type(B,binary_relation_type) | subset(A,B) | member(ordered_pair(f4(A,B),f5(A,B)),A). [assumption]. given #2 (I,wt=18): 31 -ilf_type(A,binary_relation_type) | -ilf_type(B,binary_relation_type) | subset(A,B) | -member(ordered_pair(f4(A,B),f5(A,B)),B). [assumption]. given #3 (I,wt=3): 43 ilf_type(c1,binary_relation_type). [assumption]. given #4 (I,wt=3): 81 ilf_type(A,set_type). [assumption]. given #5 (I,wt=5): 82 ilf_type(c4,relation_type(c3,c2)). [assumption]. given #6 (I,wt=4): 83 subset(identity_relation_of(c3),c4). [assumption]. given #7 (I,wt=6): 84 domain(c3,c2,c4) != c3. [assumption]. given #8 (I,wt=7): 86 member(f11(A),A) | ilf_type(A,binary_relation_type). [copy(85),merge(c),unit_del(a,81)]. given #9 (I,wt=9): 88 f11(A) != ordered_pair(B,C) | ilf_type(A,binary_relation_type). [copy(87),flip(d),merge(e),unit_del(a,81),unit_del(b,81),unit_del(c,81)]. given #10 (I,wt=15): 90 -member(A,B) | ordered_pair(f12(B,A),f13(B,A)) = A | -ilf_type(B,binary_relation_type). [copy(89),merge(e),unit_del(a,81),unit_del(b,81)]. given #11 (I,wt=16): 92 -member(A,B) | ordered_pair(f12(B,A),f13(B,A)) = A | member(f11(B),B). [copy(91),merge(e),unit_del(a,81),unit_del(b,81)]. given #12 (I,wt=18): 94 -member(A,B) | ordered_pair(f12(B,A),f13(B,A)) = A | f11(B) != ordered_pair(C,D). [copy(93),flip(h),merge(e),unit_del(a,81),unit_del(b,81),unit_del(e,81),unit_del(f,81)]. given #13 (I,wt=9): 96 -ilf_type(A,subset_type(cross_product(B,C))) | ilf_type(A,binary_relation_type). [copy(95),unit_del(a,81),unit_del(b,81),unit_del(d,81)]. given #14 (I,wt=18): 98 -ilf_type(A,subset_type(cross_product(B,C))) | -member(D,A) | ordered_pair(f12(A,D),f13(A,D)) = D. [copy(97),unit_del(a,81),unit_del(b,81),unit_del(d,81),unit_del(e,81)]. given #15 (I,wt=5): 100 -empty(A) | ilf_type(A,binary_relation_type). [copy(99),merge(c),unit_del(b,81)]. given #16 (I,wt=9): 111 -member(A,B) | member(ordered_pair(A,A),identity_relation_of(B)). [factor(14,b,d),xx(e),unit_del(a,81),unit_del(b,81)]. given #17 (I,wt=3): 131 subset(A,A). [factor(37,a,b),xx(c),unit_del(a,81)]. given #18 (I,wt=9): 138 -member(power_set(A),power_set(A)) | member(power_set(A),A). [factor(52,d,f),merge(c),unit_del(a,81),unit_del(b,81)]. given #19 (I,wt=12): 154 -ilf_type(A,relation_type(B,C)) | ilf_type(range(B,C,A),subset_type(C)). [back_unit_del(80),unit_del(a,81),unit_del(b,81)]. given #20 (I,wt=12): 155 -ilf_type(A,relation_type(B,C)) | range(B,C,A) = range_of(A). [back_unit_del(79),unit_del(a,81),unit_del(b,81)]. given #21 (I,wt=12): 156 -ilf_type(A,relation_type(B,C)) | ilf_type(domain(B,C,A),subset_type(B)). [back_unit_del(77),unit_del(a,81),unit_del(b,81)]. given #22 (I,wt=12): 157 -ilf_type(A,relation_type(B,C)) | domain(B,C,A) = domain_of(A). [back_unit_del(76),unit_del(a,81),unit_del(b,81)]. given #23 (I,wt=7): 158 -member(A,B) | member(f18(B),B). [back_unit_del(74),unit_del(a,81),unit_del(b,81)]. given #24 (I,wt=5): 159 -member(A,B) | -empty(B). [back_unit_del(72),unit_del(a,81),unit_del(b,81)]. given #25 (I,wt=6): 160 empty(A) | member(f17(A),A). [back_unit_del(71),unit_del(a,81)]. given #26 (I,wt=18): 161 -member(A,B) | ordered_pair(f14(B,A),f15(B,A)) = A | f16(B) != ordered_pair(C,D). [back_unit_del(69),unit_del(a,81),unit_del(b,81),unit_del(e,81),unit_del(f,81)]. given #27 (I,wt=16): 162 -member(A,B) | ordered_pair(f14(B,A),f15(B,A)) = A | member(f16(B),B). [back_unit_del(67),unit_del(a,81),unit_del(b,81)]. given #28 (I,wt=7): 163 empty(A) | ilf_type(f10(A),member_type(A)). [back_unit_del(57),unit_del(b,81)]. given #29 (I,wt=9): 164 empty(A) | member(B,A) | -ilf_type(B,member_type(A)). [back_unit_del(56),unit_del(a,81),unit_del(c,81)]. given #30 (I,wt=9): 165 empty(A) | ilf_type(B,member_type(A)) | -member(B,A). [back_unit_del(55),unit_del(a,81),unit_del(c,81)]. given #31 (I,wt=3): 166 -empty(power_set(A)). [back_unit_del(53),unit_del(a,81)]. given #32 (I,wt=10): 167 -member(A,B) | member(A,C) | -member(B,power_set(C)). [back_unit_del(52),unit_del(a,81),unit_del(b,81),unit_del(c,81)]. given #33 (I,wt=9): 168 member(A,power_set(B)) | -member(f9(A,B),B). [back_unit_del(51),unit_del(a,81),unit_del(b,81)]. given #34 (I,wt=9): 169 member(A,power_set(B)) | member(f9(A,B),A). [back_unit_del(50),unit_del(a,81),unit_del(b,81)]. given #35 (I,wt=5): 170 ilf_type(f8(A),subset_type(A)). [back_unit_del(46),unit_del(a,81)]. given #36 (I,wt=9): 171 ilf_type(A,member_type(power_set(B))) | -ilf_type(A,subset_type(B)). [back_unit_del(45),unit_del(a,81),unit_del(b,81)]. given #37 (I,wt=9): 172 ilf_type(A,subset_type(B)) | -ilf_type(A,member_type(power_set(B))). [back_unit_del(44),unit_del(a,81),unit_del(b,81)]. given #38 (I,wt=6): 173 subset(A,B) | A != B. [back_unit_del(38),unit_del(a,81),unit_del(b,81)]. given #39 (I,wt=6): 174 subset(A,B) | B != A. [back_unit_del(37),unit_del(a,81),unit_del(b,81)]. given #40 (I,wt=25): 175 -ilf_type(A,binary_relation_type) | -ilf_type(B,binary_relation_type) | -member(ordered_pair(C,D),A) | member(ordered_pair(C,D),B) | -member(ordered_pair(f6(A,B),f7(A,B)),B). [back_unit_del(36),unit_del(c,81),unit_del(d,81)]. given #41 (I,wt=25): 176 -ilf_type(A,binary_relation_type) | -ilf_type(B,binary_relation_type) | -member(ordered_pair(C,D),A) | member(ordered_pair(C,D),B) | member(ordered_pair(f6(A,B),f7(A,B)),A). [back_unit_del(35),unit_del(c,81),unit_del(d,81)]. given #42 (I,wt=11): 178 -member(A,B) | member(A,C) | -member(f3(B,C),C). [back_unit_del(27),unit_del(a,81),unit_del(b,81),unit_del(c,81)]. given #43 (I,wt=11): 179 -member(A,B) | member(A,C) | member(f3(B,C),B). [back_unit_del(26),unit_del(a,81),unit_del(b,81),unit_del(c,81)]. given #44 (I,wt=9): 180 -member(A,B) | member(A,C) | -subset(B,C). [back_unit_del(24),unit_del(a,81),unit_del(b,81),unit_del(c,81)]. given #45 (I,wt=8): 181 subset(A,B) | -member(f2(A,B),B). [back_unit_del(23),unit_del(a,81),unit_del(b,81)]. given #46 (I,wt=8): 182 subset(A,B) | member(f2(A,B),A). [back_unit_del(22),unit_del(a,81),unit_del(b,81)]. given #47 (I,wt=7): 183 ilf_type(f1(A,B),relation_type(B,A)). [back_unit_del(20),unit_del(a,81),unit_del(b,81)]. given #48 (I,wt=11): 184 -ilf_type(A,relation_type(B,C)) | ilf_type(A,subset_type(cross_product(B,C))). [back_unit_del(19),unit_del(a,81),unit_del(b,81)]. given #49 (I,wt=11): 185 -ilf_type(A,subset_type(cross_product(B,C))) | ilf_type(A,relation_type(B,C)). [back_unit_del(18),unit_del(a,81),unit_del(b,81)]. given #50 (I,wt=4): 186 ilf_type(identity_relation_of(A),binary_relation_type). [back_unit_del(17),unit_del(a,81)]. given #51 (I,wt=9): 187 A = B | -member(ordered_pair(B,A),identity_relation_of(C)). [back_unit_del(16),unit_del(a,81),unit_del(b,81),unit_del(c,81)]. given #52 (I,wt=9): 188 member(A,B) | -member(ordered_pair(A,C),identity_relation_of(B)). [back_unit_del(15),unit_del(a,81),unit_del(b,81),unit_del(d,81)]. given #53 (I,wt=12): 189 -member(A,B) | member(ordered_pair(A,C),identity_relation_of(B)) | C != A. [back_unit_del(14),unit_del(a,81),unit_del(b,81),unit_del(d,81)]. given #54 (I,wt=15): 190 -ilf_type(A,relation_type(B,C)) | -subset(identity_relation_of(D),A) | subset(D,range(B,C,A)). [back_unit_del(13),unit_del(a,81),unit_del(b,81),unit_del(c,81)]. given #55 (I,wt=15): 191 -ilf_type(A,relation_type(B,C)) | -subset(identity_relation_of(D),A) | subset(D,domain(B,C,A)). [back_unit_del(12),unit_del(a,81),unit_del(b,81),unit_del(c,81)]. given #56 (I,wt=9): 192 -subset(A,B) | -subset(B,A) | B = A. [back_unit_del(11),unit_del(a,81),unit_del(b,81)]. given #57 (A,wt=15): 193 -ilf_type(A,binary_relation_type) | subset(A,c1) | member(ordered_pair(f4(A,c1),f5(A,c1)),A). [resolve(43,a,30,b)]. given #58 (F,wt=4): 202 domain_of(c4) != c3. [back_rewrite(84),rewrite([200(4)])]. given #59 (F,wt=7): 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 0.46 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 0.46 (+ 0.00) seconds. % Length of proof is 39. % Level of proof is 8. % Maximum clause weight is 24. % 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. Weight_deleted=2. Literals_deleted=0. 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=6.30. User_CPU=0.46, System_CPU=0.00, Wall_clock=0. ============================== end of statistics ===================== ============================== end of search ========================= Exiting with 1 proof. Process 27400 exit (max_proofs) Tue May 22 14:45:19 2007 ============================== continuing FOF reduction multisearch == Subproblem 2 of 2 (negated): ((all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | - subset(B,C) | - subset(C,B) | =(C,B))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,set_type) | (all E (- ilf_type(E,relation_type(B,C)) | - subset(identity_relation_of(D),E) | subset(D,domain(B,C,E)))))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,set_type) | (all E (- ilf_type(E,relation_type(B,C)) | - subset(identity_relation_of(D),E) | subset(D,range(B,C,E)))))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | - member(C,B) | (all D (- ilf_type(D,set_type) | member(ordered_pair(C,D),identity_relation_of(B)) | - =(D,C))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | member(C,B) | (all D (- ilf_type(D,set_type) | - member(ordered_pair(C,D),identity_relation_of(B)))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,set_type) | =(D,C) | - member(ordered_pair(C,D),identity_relation_of(B)))))))) & (all B (- ilf_type(B,set_type) | ilf_type(identity_relation_of(B),binary_relation_type))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,subset_type(cross_product(B,C))) | ilf_type(D,relation_type(B,C)))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all E (- ilf_type(E,relation_type(B,C)) | ilf_type(E,subset_type(cross_product(B,C))))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (exists D ilf_type(D,relation_type(C,B))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | subset(B,C) | (exists D (ilf_type(D,set_type) & member(D,B) & - member(D,C))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,set_type) | - member(D,B) | member(D,C))) | - subset(B,C))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,set_type) | - member(D,B) | member(D,C))) | (exists D (ilf_type(D,set_type) & member(D,B) & - member(D,C))))))) & (all B (- ilf_type(B,binary_relation_type) | (all C (- ilf_type(C,binary_relation_type) | subset(B,C) | (exists D (ilf_type(D,set_type) & (exists E (ilf_type(E,set_type) & member(ordered_pair(D,E),B) & - member(ordered_pair(D,E),C))))))))) & (all B (- ilf_type(B,binary_relation_type) | (all C (- ilf_type(C,binary_relation_type) | (all D (- ilf_type(D,set_type) | (all E (- ilf_type(E,set_type) | - member(ordered_pair(D,E),B) | member(ordered_pair(D,E),C))))) | - subset(B,C))))) & (all B (- ilf_type(B,binary_relation_type) | (all C (- ilf_type(C,binary_relation_type) | (all D (- ilf_type(D,set_type) | (all E (- ilf_type(E,set_type) | - member(ordered_pair(D,E),B) | member(ordered_pair(D,E),C))))) | (exists D (ilf_type(D,set_type) & (exists E (ilf_type(E,set_type) & member(ordered_pair(D,E),B) & - member(ordered_pair(D,E),C))))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | =(C,B) | - subset(B,C) | - subset(C,B))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | subset(B,C) | - =(C,B))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | subset(C,B) | - =(C,B))))) & (all B (- ilf_type(B,binary_relation_type) | ilf_type(domain_of(B),set_type))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | ilf_type(cross_product(B,C),set_type))))) & (all B (- ilf_type(B,binary_relation_type) | ilf_type(range_of(B),set_type))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | ilf_type(ordered_pair(B,C),set_type))))) & (all B (- ilf_type(B,set_type) | ilf_type(B,binary_relation_type) | - relation_like(B))) & (all B (- ilf_type(B,set_type) | relation_like(B) | - ilf_type(B,binary_relation_type))) & (exists B ilf_type(B,binary_relation_type)) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | ilf_type(C,subset_type(B)) | - ilf_type(C,member_type(power_set(B))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | ilf_type(C,member_type(power_set(B))) | - ilf_type(C,subset_type(B)))))) & (all B (- ilf_type(B,set_type) | (exists C ilf_type(C,subset_type(B))))) & (all B (- ilf_type(B,set_type) | subset(B,B))) & (all B (- ilf_type(B,binary_relation_type) | subset(B,B))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | member(B,power_set(C)) | (exists D (ilf_type(D,set_type) & member(D,B) & - member(D,C))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,set_type) | - member(D,B) | member(D,C))) | - member(B,power_set(C)))))) & (all B (- ilf_type(B,set_type) | - empty(power_set(B)))) & (all B (- ilf_type(B,set_type) | ilf_type(power_set(B),set_type))) & (all B (- ilf_type(B,set_type) | (all C (empty(C) | - ilf_type(C,set_type) | ilf_type(B,member_type(C)) | - member(B,C))))) & (all B (- ilf_type(B,set_type) | (all C (empty(C) | - ilf_type(C,set_type) | member(B,C) | - ilf_type(B,member_type(C)))))) & (all B (empty(B) | - ilf_type(B,set_type) | (exists C ilf_type(C,member_type(B))))) & (all B (- ilf_type(B,set_type) | relation_like(B) | (exists C (ilf_type(C,set_type) & member(C,B) & (all D (- ilf_type(D,set_type) | (all E (- ilf_type(E,set_type) | - =(ordered_pair(D,E),C))))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | - member(C,B) | (exists D (ilf_type(D,set_type) & (exists E (ilf_type(E,set_type) & =(ordered_pair(D,E),C))))))) | - relation_like(B))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | - member(C,B) | (exists D (ilf_type(D,set_type) & (exists E (ilf_type(E,set_type) & =(ordered_pair(D,E),C))))))) | (exists C (ilf_type(C,set_type) & member(C,B) & (all D (- ilf_type(D,set_type) | (all E (- ilf_type(E,set_type) | - =(ordered_pair(D,E),C))))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,subset_type(cross_product(B,C))) | relation_like(D))))))) & (all B (- ilf_type(B,set_type) | empty(B) | (exists C (ilf_type(C,set_type) & member(C,B))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | - member(C,B))) | - empty(B))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | - member(C,B))) | (exists C (ilf_type(C,set_type) & member(C,B))))) & (all B (- empty(B) | - ilf_type(B,set_type) | relation_like(B))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,relation_type(B,C)) | =(domain_of(D),domain(B,C,D)))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,relation_type(B,C)) | ilf_type(domain(B,C,D),subset_type(B)))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,relation_type(B,C)) | =(range_of(D),range(B,C,D)))))))) & (all B (- ilf_type(B,set_type) | (all C (- ilf_type(C,set_type) | (all D (- ilf_type(D,relation_type(B,C)) | ilf_type(range(B,C,D),subset_type(C)))))))) & (all B ilf_type(B,set_type)) & (exists B (ilf_type(B,set_type) & (exists C (ilf_type(C,set_type) & (exists D (ilf_type(D,relation_type(C,B)) & subset(identity_relation_of(C),D) & - subset(C,range(C,B,D))))))))). Max_seconds is 30 for this subproblem. Child search process 27401 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(paramodulation) -> set(back_demod). % set(binary_resolution). % (non-Horn) % set(neg_ur_resolution). % (non-Horn, less than 100 clauses) Auto_process settings: % set(factor). % (non-Horn) % set(back_unit_deletion). % (non-Horn) % set(back_unit_deletion) -> set(unit_deletion). ============================== end of process initial clauses ======== ============================== CLAUSES FOR SEARCH ==================== % Clauses after input processing: formulas(usable). end_of_list. formulas(sos). 30 -ilf_type(A,binary_relation_type) | -ilf_type(B,binary_relation_type) | subset(A,B) | member(ordered_pair(f4(A,B),f5(A,B)),A). [assumption]. 31 -ilf_type(A,binary_relation_type) | -ilf_type(B,binary_relation_type) | subset(A,B) | -member(ordered_pair(f4(A,B),f5(A,B)),B). [assumption]. 43 ilf_type(c1,binary_relation_type). [assumption]. 81 ilf_type(A,set_type). [assumption]. 82 ilf_type(c4,relation_type(c3,c2)). [assumption]. 83 subset(identity_relation_of(c3),c4). [assumption]. 84 -subset(c3,range(c3,c2,c4)). [assumption]. 86 member(f11(A),A) | ilf_type(A,binary_relation_type). [copy(85),merge(c),unit_del(a,81)]. 88 f11(A) != ordered_pair(B,C) | ilf_type(A,binary_relation_type). [copy(87),flip(d),merge(e),unit_del(a,81),unit_del(b,81),unit_del(c,81)]. 90 -member(A,B) | ordered_pair(f12(B,A),f13(B,A)) = A | -ilf_type(B,binary_relation_type). [copy(89),merge(e),unit_del(a,81),unit_del(b,81)]. 92 -member(A,B) | ordered_pair(f12(B,A),f13(B,A)) = A | member(f11(B),B). [copy(91),merge(e),unit_del(a,81),unit_del(b,81)]. 94 -member(A,B) | ordered_pair(f12(B,A),f13(B,A)) = A | f11(B) != ordered_pair(C,D). [copy(93),flip(h),merge(e),unit_del(a,81),unit_del(b,81),unit_del(e,81),unit_del(f,81)]. 96 -ilf_type(A,subset_type(cross_product(B,C))) | ilf_type(A,binary_relation_type). [copy(95),unit_del(a,81),unit_del(b,81),unit_del(d,81)]. 98 -ilf_type(A,subset_type(cross_product(B,C))) | -member(D,A) | ordered_pair(f12(A,D),f13(A,D)) = D. [copy(97),unit_del(a,81),unit_del(b,81),unit_del(d,81),unit_del(e,81)]. 100 -empty(A) | ilf_type(A,binary_relation_type). [copy(99),merge(c),unit_del(b,81)]. 111 -member(A,B) | member(ordered_pair(A,A),identity_relation_of(B)). [factor(14,b,d),xx(e),unit_del(a,81),unit_del(b,81)]. 131 subset(A,A). [factor(37,a,b),xx(c),unit_del(a,81)]. 138 -member(power_set(A),power_set(A)) | member(power_set(A),A). [factor(52,d,f),merge(c),unit_del(a,81),unit_del(b,81)]. 154 -ilf_type(A,relation_type(B,C)) | ilf_type(range(B,C,A),subset_type(C)). [back_unit_del(80),unit_del(a,81),unit_del(b,81)]. 155 -ilf_type(A,relation_type(B,C)) | range(B,C,A) = range_of(A). [back_unit_del(79),unit_del(a,81),unit_del(b,81)]. 156 -ilf_type(A,relation_type(B,C)) | ilf_type(domain(B,C,A),subset_type(B)). [back_unit_del(77),unit_del(a,81),unit_del(b,81)]. 157 -ilf_type(A,relation_type(B,C)) | domain(B,C,A) = domain_of(A). [back_unit_del(76),unit_del(a,81),unit_del(b,81)]. 158 -member(A,B) | member(f18(B),B). [back_unit_del(74),unit_del(a,81),unit_del(b,81)]. 159 -member(A,B) | -empty(B). [back_unit_del(72),unit_del(a,81),unit_del(b,81)]. 160 empty(A) | member(f17(A),A). [back_unit_del(71),unit_del(a,81)]. 161 -member(A,B) | ordered_pair(f14(B,A),f15(B,A)) = A | f16(B) != ordered_pair(C,D). [back_unit_del(69),unit_del(a,81),unit_del(b,81),unit_del(e,81),unit_del(f,81)]. 162 -member(A,B) | ordered_pair(f14(B,A),f15(B,A)) = A | member(f16(B),B). [back_unit_del(67),unit_del(a,81),unit_del(b,81)]. 163 empty(A) | ilf_type(f10(A),member_type(A)). [back_unit_del(57),unit_del(b,81)]. 164 empty(A) | member(B,A) | -ilf_type(B,member_type(A)). [back_unit_del(56),unit_del(a,81),unit_del(c,81)]. 165 empty(A) | ilf_type(B,member_type(A)) | -member(B,A). [back_unit_del(55),unit_del(a,81),unit_del(c,81)]. 166 -empty(power_set(A)). [back_unit_del(53),unit_del(a,81)]. 167 -member(A,B) | member(A,C) | -member(B,power_set(C)). [back_unit_del(52),unit_del(a,81),unit_del(b,81),unit_del(c,81)]. 168 member(A,power_set(B)) | -member(f9(A,B),B). [back_unit_del(51),unit_del(a,81),unit_del(b,81)]. 169 member(A,power_set(B)) | member(f9(A,B),A). [back_unit_del(50),unit_del(a,81),unit_del(b,81)]. 170 ilf_type(f8(A),subset_type(A)). [back_unit_del(46),unit_del(a,81)]. 171 ilf_type(A,member_type(power_set(B))) | -ilf_type(A,subset_type(B)). [back_unit_del(45),unit_del(a,81),unit_del(b,81)]. 172 ilf_type(A,subset_type(B)) | -ilf_type(A,member_type(power_set(B))). [back_unit_del(44),unit_del(a,81),unit_del(b,81)]. 173 subset(A,B) | A != B. [back_unit_del(38),unit_del(a,81),unit_del(b,81)]. 174 subset(A,B) | B != A. [back_unit_del(37),unit_del(a,81),unit_del(b,81)]. 175 -ilf_type(A,binary_relation_type) | -ilf_type(B,binary_relation_type) | -member(ordered_pair(C,D),A) | member(ordered_pair(C,D),B) | -member(ordered_pair(f6(A,B),f7(A,B)),B). [back_unit_del(36),unit_del(c,81),unit_del(d,81)]. 176 -ilf_type(A,binary_relation_type) | -ilf_type(B,binary_relation_type) | -member(ordered_pair(C,D),A) | member(ordered_pair(C,D),B) | member(ordered_pair(f6(A,B),f7(A,B)),A). [back_unit_del(35),unit_del(c,81),unit_del(d,81)]. 178 -member(A,B) | member(A,C) | -member(f3(B,C),C). [back_unit_del(27),unit_del(a,81),unit_del(b,81),unit_del(c,81)]. 179 -member(A,B) | member(A,C) | member(f3(B,C),B). [back_unit_del(26),unit_del(a,81),unit_del(b,81),unit_del(c,81)]. 180 -member(A,B) | member(A,C) | -subset(B,C). [back_unit_del(24),unit_del(a,81),unit_del(b,81),unit_del(c,81)]. 181 subset(A,B) | -member(f2(A,B),B). [back_unit_del(23),unit_del(a,81),unit_del(b,81)]. 182 subset(A,B) | member(f2(A,B),A). [back_unit_del(22),unit_del(a,81),unit_del(b,81)]. 183 ilf_type(f1(A,B),relation_type(B,A)). [back_unit_del(20),unit_del(a,81),unit_del(b,81)]. 184 -ilf_type(A,relation_type(B,C)) | ilf_type(A,subset_type(cross_product(B,C))). [back_unit_del(19),unit_del(a,81),unit_del(b,81)]. 185 -ilf_type(A,subset_type(cross_product(B,C))) | ilf_type(A,relation_type(B,C)). [back_unit_del(18),unit_del(a,81),unit_del(b,81)]. 186 ilf_type(identity_relation_of(A),binary_relation_type). [back_unit_del(17),unit_del(a,81)]. 187 A = B | -member(ordered_pair(B,A),identity_relation_of(C)). [back_unit_del(16),unit_del(a,81),unit_del(b,81),unit_del(c,81)]. 188 member(A,B) | -member(ordered_pair(A,C),identity_relation_of(B)). [back_unit_del(15),unit_del(a,81),unit_del(b,81),unit_del(d,81)]. 189 -member(A,B) | member(ordered_pair(A,C