%---------------- SGGS v1.0 (IJCAR 2020 submission) ----------------% ------ Parsing...successful ------ Proving... use I- not ground preserving Gamma_0: (extend-no-conflict) 0: intersection(X0,X1,X2), [member(h(X0,X1,X2), X2)], member(h(X0,X1,X2),X1) Gamma_1: (extend-no-conflict) 0: intersection(X0,X1,X2), [member(h(X0,X1,X2), X2)], member(h(X0,X1,X2),X1) 1: [intersection(X0,X0,X0)], ~(member(h(X0,X0,X0),X0)) Gamma_2: (extend-no-conflict) 0: intersection(X0,X1,X2), [member(h(X0,X1,X2), X2)], member(h(X0,X1,X2),X1) 1: [intersection(X0,X0,X0)], ~(member(h(X0,X0,X0),X0)) 2: [member(member_of_1_not_of_2(X0,X1),X0)], subset(X0,X1) Gamma_3: (extend-no-conflict) 0: intersection(X0,X1,X2), [member(h(X0,X1,X2), X2)], member(h(X0,X1,X2),X1) 1: [intersection(X0,X0,X0)], ~(member(h(X0,X0,X0),X0)) 2: [member(member_of_1_not_of_2(X0,X1),X0)], subset(X0,X1) 3: ~(member(member_of_1_not_of_2(X0,X0),X0)), [subset(X0,X0)] Gamma_4: (extend-no-conflict) 0: intersection(X0,X1,X2), [member(h(X0,X1,X2), X2)], member(h(X0,X1,X2),X1) 1: [intersection(X0,X0,X0)], ~(member(h(X0,X0,X0),X0)) 2: [member(member_of_1_not_of_2(X0,X1),X0)], subset(X0,X1) 3: ~(member(member_of_1_not_of_2(X0,X0),X0)), [subset(X0,X0)] 4: [equal_sets(X0,X0)], ~(subset(X0,X0)) Gamma_5: (extend-no-conflict) 0: intersection(X0,X1,X2), [member(h(X0,X1,X2), X2)], member(h(X0,X1,X2),X1) 1: [intersection(X0,X0,X0)], ~(member(h(X0,X0,X0),X0)) 2: [member(member_of_1_not_of_2(X0,X1),X0)], subset(X0,X1) 3: ~(member(member_of_1_not_of_2(X0,X0),X0)), [subset(X0,X0)] 4: [equal_sets(X0,X0)], ~(subset(X0,X0)) 5: [intersection(d,a,d)] Gamma_6: (extend-no-conflict) 0: intersection(X0,X1,X2), [member(h(X0,X1,X2), X2)], member(h(X0,X1,X2),X1) 1: [intersection(X0,X0,X0)], ~(member(h(X0,X0,X0),X0)) 2: [member(member_of_1_not_of_2(X0,X1),X0)], subset(X0,X1) 3: ~(member(member_of_1_not_of_2(X0,X0),X0)), [subset(X0,X0)] 4: [equal_sets(X0,X0)], ~(subset(X0,X0)) 5: [intersection(d,a,d)] 6: ~(intersection(d,a,d)), [member(member_of_1_not_of_2(d,X0),a)], ~( member(member_of_1_not_of_2(d,X0),d)) Gamma_7: (extend-no-conflict) 0: intersection(X0,X1,X2), [member(h(X0,X1,X2), X2)], member(h(X0,X1,X2),X1) 1: [intersection(X0,X0,X0)], ~(member(h(X0,X0,X0),X0)) 2: [member(member_of_1_not_of_2(X0,X1),X0)], subset(X0,X1) 3: ~(member(member_of_1_not_of_2(X0,X0),X0)), [subset(X0,X0)] 4: [equal_sets(X0,X0)], ~(subset(X0,X0)) 5: [intersection(d,a,d)] 6: ~(intersection(d,a,d)), [member(member_of_1_not_of_2(d,X0),a)], ~( member(member_of_1_not_of_2(d,X0),d)) 7: ~(intersection(d,a,d)), [member(h(X0,X1,d),a)], ~(member(h(X0,X1,d),d)) Gamma_8: (extend-no-conflict) 0: intersection(X0,X1,X2), [member(h(X0,X1,X2), X2)], member(h(X0,X1,X2),X1) 1: [intersection(X0,X0,X0)], ~(member(h(X0,X0,X0),X0)) 2: [member(member_of_1_not_of_2(X0,X1),X0)], subset(X0,X1) 3: ~(member(member_of_1_not_of_2(X0,X0),X0)), [subset(X0,X0)] 4: [equal_sets(X0,X0)], ~(subset(X0,X0)) 5: [intersection(d,a,d)] 6: ~(intersection(d,a,d)), [member(member_of_1_not_of_2(d,X0),a)], ~( member(member_of_1_not_of_2(d,X0),d)) 7: ~(intersection(d,a,d)), [member(h(X0,X1,d),a)], ~(member(h(X0,X1,d),d)) 8: [intersection(a,a,d)], ~(member(h(a,a,d),a)), ~(member(h(a,a,d),d)) Gamma_9: (extend-no-conflict) 0: intersection(X0,X1,X2), [member(h(X0,X1,X2), X2)], member(h(X0,X1,X2),X1) 1: [intersection(X0,X0,X0)], ~(member(h(X0,X0,X0),X0)) 2: [member(member_of_1_not_of_2(X0,X1),X0)], subset(X0,X1) 3: ~(member(member_of_1_not_of_2(X0,X0),X0)), [subset(X0,X0)] 4: [equal_sets(X0,X0)], ~(subset(X0,X0)) 5: [intersection(d,a,d)] 6: ~(intersection(d,a,d)), [member(member_of_1_not_of_2(d,X0),a)], ~( member(member_of_1_not_of_2(d,X0),d)) 7: ~(intersection(d,a,d)), [member(h(X0,X1,d),a)], ~(member(h(X0,X1,d),d)) 8: [intersection(a,a,d)], ~(member(h(a,a,d),a)), ~(member(h(a,a,d),d)) 9: [intersection(a,d,d)], ~(member(h(a,d,d),a)), ~(member(h(a,d,d),d)) Gamma_10: (extend-no-conflict) 0: intersection(X0,X1,X2), [member( h(X0,X1,X2),X2)], member(h(X0,X1,X2),X1) 1: [intersection(X0,X0,X0)], ~(member(h(X0,X0,X0),X0)) 2: [member(member_of_1_not_of_2(X0,X1),X0)], subset(X0,X1) 3: ~(member(member_of_1_not_of_2(X0,X0),X0)), [subset(X0,X0)] 4: [equal_sets(X0,X0)], ~(subset(X0,X0)) 5: [intersection(d,a,d)] 6: ~(intersection(d,a,d)), [member(member_of_1_not_of_2(d,X0),a)], ~( member(member_of_1_not_of_2(d,X0),d)) 7: ~(intersection(d,a,d)), [member(h(X0,X1,d),a)], ~(member(h(X0,X1,d),d)) 8: [intersection(a,a,d)], ~(member(h(a,a,d),a)), ~(member(h(a,a,d),d)) 9: [intersection(a,d,d)], ~(member(h(a,d,d),a)), ~(member(h(a,d,d),d)) 10: ~(intersection(a,a,d)), ~(member(member_of_1_not_of_2(a,X0),a)), [member( member_of_1_not_of_2(a,X0),d)] Gamma_11: (extend-no-conflict) 0: intersection(X0,X1,X2), [member( h(X0,X1,X2),X2)], member(h(X0,X1,X2),X1) 1: [intersection(X0,X0,X0)], ~(member(h(X0,X0,X0),X0)) 2: [member(member_of_1_not_of_2(X0,X1),X0)], subset(X0,X1) 3: ~(member(member_of_1_not_of_2(X0,X0),X0)), [subset(X0,X0)] 4: [equal_sets(X0,X0)], ~(subset(X0,X0)) 5: [intersection(d,a,d)] 6: ~(intersection(d,a,d)), [member(member_of_1_not_of_2(d,X0),a)], ~( member(member_of_1_not_of_2(d,X0),d)) 7: ~(intersection(d,a,d)), [member(h(X0,X1,d),a)], ~(member(h(X0,X1,d),d)) 8: [intersection(a,a,d)], ~(member(h(a,a,d),a)), ~(member(h(a,a,d),d)) 9: [intersection(a,d,d)], ~(member(h(a,d,d),a)), ~(member(h(a,d,d),d)) 10: ~(intersection(a,a,d)), ~(member(member_of_1_not_of_2(a,X0),a)), [member( member_of_1_not_of_2(a,X0),d)] 11: ~(intersection(a,a,d)), ~(member(h(X0,X1,a),a)), [member(h(X0,X1,a), d)] Gamma_12: (extend-no-conflict) 0: intersection(X0,X1,X2), [member( h(X0,X1,X2),X2)], member(h(X0,X1,X2),X1) 1: [intersection(X0,X0,X0)], ~(member(h(X0,X0,X0),X0)) 2: [member(member_of_1_not_of_2(X0,X1),X0)], subset(X0,X1) 3: ~(member(member_of_1_not_of_2(X0,X0),X0)), [subset(X0,X0)] 4: [equal_sets(X0,X0)], ~(subset(X0,X0)) 5: [intersection(d,a,d)] 6: ~(intersection(d,a,d)), [member(member_of_1_not_of_2(d,X0),a)], ~( member(member_of_1_not_of_2(d,X0),d)) 7: ~(intersection(d,a,d)), [member(h(X0,X1,d),a)], ~(member(h(X0,X1,d),d)) 8: [intersection(a,a,d)], ~(member(h(a,a,d),a)), ~(member(h(a,a,d),d)) 9: [intersection(a,d,d)], ~(member(h(a,d,d),a)), ~(member(h(a,d,d),d)) 10: ~(intersection(a,a,d)), ~(member(member_of_1_not_of_2(a,X0),a)), [member( member_of_1_not_of_2(a,X0),d)] 11: ~(intersection(a,a,d)), ~(member(h(X0,X1,a),a)), [member(h(X0,X1,a), d)] 12: [intersection(d,d,a)], ~(member(h(d,d,a),a)), ~(member(h(d,d,a),d)) Gamma_13: (extend-no-conflict) 0: intersection(X0,X1,X2), [member( h(X0,X1,X2),X2)], member(h(X0,X1,X2),X1) 1: [intersection(X0,X0,X0)], ~(member(h(X0,X0,X0),X0)) 2: [member(member_of_1_not_of_2(X0,X1),X0)], subset(X0,X1) 3: ~(member(member_of_1_not_of_2(X0,X0),X0)), [subset(X0,X0)] 4: [equal_sets(X0,X0)], ~(subset(X0,X0)) 5: [intersection(d,a,d)] 6: ~(intersection(d,a,d)), [member(member_of_1_not_of_2(d,X0),a)], ~( member(member_of_1_not_of_2(d,X0),d)) 7: ~(intersection(d,a,d)), [member(h(X0,X1,d),a)], ~(member(h(X0,X1,d),d)) 8: [intersection(a,a,d)], ~(member(h(a,a,d),a)), ~(member(h(a,a,d),d)) 9: [intersection(a,d,d)], ~(member(h(a,d,d),a)), ~(member(h(a,d,d),d)) 10: ~(intersection(a,a,d)), ~(member(member_of_1_not_of_2(a,X0),a)), [member( member_of_1_not_of_2(a,X0),d)] 11: ~(intersection(a,a,d)), ~(member(h(X0,X1,a),a)), [member(h(X0,X1,a), d)] 12: [intersection(d,d,a)], ~(member(h(d,d,a),a)), ~(member(h(d,d,a),d)) 13: [intersection(a,d,a)], ~(member(h(a,d,a),a)), ~(member(h(a,d,a),d)) Gamma_14: (extend-no-conflict) 0: intersection(X0,X1,X2), [member( h(X0,X1,X2),X2)], member(h(X0,X1,X2),X1) 1: [intersection(X0,X0,X0)], ~(member(h(X0,X0,X0),X0)) 2: [member(member_of_1_not_of_2(X0,X1),X0)], subset(X0,X1) 3: ~(member(member_of_1_not_of_2(X0,X0),X0)), [subset(X0,X0)] 4: [equal_sets(X0,X0)], ~(subset(X0,X0)) 5: [intersection(d,a,d)] 6: ~(intersection(d,a,d)), [member(member_of_1_not_of_2(d,X0),a)], ~( member(member_of_1_not_of_2(d,X0),d)) 7: ~(intersection(d,a,d)), [member(h(X0,X1,d),a)], ~(member(h(X0,X1,d),d)) 8: [intersection(a,a,d)], ~(member(h(a,a,d),a)), ~(member(h(a,a,d),d)) 9: [intersection(a,d,d)], ~(member(h(a,d,d),a)), ~(member(h(a,d,d),d)) 10: ~(intersection(a,a,d)), ~(member(member_of_1_not_of_2(a,X0),a)), [member( member_of_1_not_of_2(a,X0),d)] 11: ~(intersection(a,a,d)), ~(member(h(X0,X1,a),a)), [member(h(X0,X1,a), d)] 12: [intersection(d,d,a)], ~(member(h(d,d,a),a)), ~(member(h(d,d,a),d)) 13: [intersection(a,d,a)], ~(member(h(a,d,a),a)), ~(member(h(a,d,a),d)) 14: [intersection(d,a,a)], ~(member(h(d,a,a),a)), ~(member(h(d,a,a),d)) Gamma_15: (extend-no-conflict) 0: intersection(X0,X1,X2), [member( h(X0,X1,X2),X2)], member(h(X0,X1,X2),X1) 1: [intersection(X0,X0,X0)], ~(member(h(X0,X0,X0),X0)) 2: [member(member_of_1_not_of_2(X0,X1),X0)], subset(X0,X1) 3: ~(member(member_of_1_not_of_2(X0,X0),X0)), [subset(X0,X0)] 4: [equal_sets(X0,X0)], ~(subset(X0,X0)) 5: [intersection(d,a,d)] 6: ~(intersection(d,a,d)), [member(member_of_1_not_of_2(d,X0),a)], ~( member(member_of_1_not_of_2(d,X0),d)) 7: ~(intersection(d,a,d)), [member(h(X0,X1,d),a)], ~(member(h(X0,X1,d),d)) 8: [intersection(a,a,d)], ~(member(h(a,a,d),a)), ~(member(h(a,a,d),d)) 9: [intersection(a,d,d)], ~(member(h(a,d,d),a)), ~(member(h(a,d,d),d)) 10: ~(intersection(a,a,d)), ~(member(member_of_1_not_of_2(a,X0),a)), [member( member_of_1_not_of_2(a,X0),d)] 11: ~(intersection(a,a,d)), ~(member(h(X0,X1,a),a)), [member(h(X0,X1,a), d)] 12: [intersection(d,d,a)], ~(member(h(d,d,a),a)), ~(member(h(d,d,a),d)) 13: [intersection(a,d,a)], ~(member(h(a,d,a),a)), ~(member(h(a,d,a),d)) 14: [intersection(d,a,a)], ~(member(h(d,a,a),a)), ~(member(h(d,a,a),d)) 15: ~(member(member_of_1_not_of_2(a,d),d)), [subset(a,d)] Gamma_16: (extend-no-conflict) 0: intersection(X0,X1,X2), [member( h(X0,X1,X2),X2)], member(h(X0,X1,X2),X1) 1: [intersection(X0,X0,X0)], ~(member(h(X0,X0,X0),X0)) 2: [member(member_of_1_not_of_2(X0,X1),X0)], subset(X0,X1) 3: ~(member(member_of_1_not_of_2(X0,X0),X0)), [subset(X0,X0)] 4: [equal_sets(X0,X0)], ~(subset(X0,X0)) 5: [intersection(d,a,d)] 6: ~(intersection(d,a,d)), [member(member_of_1_not_of_2(d,X0),a)], ~( member(member_of_1_not_of_2(d,X0),d)) 7: ~(intersection(d,a,d)), [member(h(X0,X1,d),a)], ~(member(h(X0,X1,d),d)) 8: [intersection(a,a,d)], ~(member(h(a,a,d),a)), ~(member(h(a,a,d),d)) 9: [intersection(a,d,d)], ~(member(h(a,d,d),a)), ~(member(h(a,d,d),d)) 10: ~(intersection(a,a,d)), ~(member(member_of_1_not_of_2(a,X0),a)), [member( member_of_1_not_of_2(a,X0),d)] 11: ~(intersection(a,a,d)), ~(member(h(X0,X1,a),a)), [member(h(X0,X1,a), d)] 12: [intersection(d,d,a)], ~(member(h(d,d,a),a)), ~(member(h(d,d,a),d)) 13: [intersection(a,d,a)], ~(member(h(a,d,a),a)), ~(member(h(a,d,a),d)) 14: [intersection(d,a,a)], ~(member(h(d,a,a),a)), ~(member(h(d,a,a),d)) 15: ~(member(member_of_1_not_of_2(a,d),d)), [subset(a,d)] 16: ~(member(member_of_1_not_of_2(d,a),a)), [subset(d,a)] Gamma_17: (extend-conflict) 0: intersection(X0,X1,X2), [member(h(X0,X1,X2), X2)], member(h(X0,X1,X2),X1) 1: [intersection(X0,X0,X0)], ~(member(h(X0,X0,X0),X0)) 2: [member(member_of_1_not_of_2(X0,X1),X0)], subset(X0,X1) 3: ~(member(member_of_1_not_of_2(X0,X0),X0)), [subset(X0,X0)] 4: [equal_sets(X0,X0)], ~(subset(X0,X0)) 5: [intersection(d,a,d)] 6: ~(intersection(d,a,d)), [member(member_of_1_not_of_2(d,X0),a)], ~( member(member_of_1_not_of_2(d,X0),d)) 7: ~(intersection(d,a,d)), [member(h(X0,X1,d),a)], ~(member(h(X0,X1,d),d)) 8: [intersection(a,a,d)], ~(member(h(a,a,d),a)), ~(member(h(a,a,d),d)) 9: [intersection(a,d,d)], ~(member(h(a,d,d),a)), ~(member(h(a,d,d),d)) 10: ~(intersection(a,a,d)), ~(member(member_of_1_not_of_2(a,X0),a)), [member( member_of_1_not_of_2(a,X0),d)] 11: ~(intersection(a,a,d)), ~(member(h(X0,X1,a),a)), [member(h(X0,X1,a), d)] 12: [intersection(d,d,a)], ~(member(h(d,d,a),a)), ~(member(h(d,d,a),d)) 13: [intersection(a,d,a)], ~(member(h(a,d,a),a)), ~(member(h(a,d,a),d)) 14: [intersection(d,a,a)], ~(member(h(d,a,a),a)), ~(member(h(d,a,a),d)) 15: ~(member(member_of_1_not_of_2(a,d),d)), [subset(a,d)] 16: ~(member(member_of_1_not_of_2(d,a),a)), [subset(d,a)] 17: [~(subset(d,a))] Gamma_18: (move) 0: intersection(X0,X1,X2), [member(h(X0,X1,X2),X2)], member( h(X0,X1,X2),X1) 1: [intersection(X0,X0,X0)], ~(member(h(X0,X0,X0),X0)) 2: [member(member_of_1_not_of_2(X0,X1),X0)], subset(X0,X1) 3: ~(member(member_of_1_not_of_2(X0,X0),X0)), [subset(X0,X0)] 4: [equal_sets(X0,X0)], ~(subset(X0,X0)) 5: [intersection(d,a,d)] 6: ~(intersection(d,a,d)), [member(member_of_1_not_of_2(d,X0),a)], ~( member(member_of_1_not_of_2(d,X0),d)) 7: ~(intersection(d,a,d)), [member(h(X0,X1,d),a)], ~(member(h(X0,X1,d),d)) 8: [intersection(a,a,d)], ~(member(h(a,a,d),a)), ~(member(h(a,a,d),d)) 9: [intersection(a,d,d)], ~(member(h(a,d,d),a)), ~(member(h(a,d,d),d)) 10: ~(intersection(a,a,d)), ~(member(member_of_1_not_of_2(a,X0),a)), [member( member_of_1_not_of_2(a,X0),d)] 11: ~(intersection(a,a,d)), ~(member(h(X0,X1,a),a)), [member(h(X0,X1,a), d)] 12: [intersection(d,d,a)], ~(member(h(d,d,a),a)), ~(member(h(d,d,a),d)) 13: [intersection(a,d,a)], ~(member(h(a,d,a),a)), ~(member(h(a,d,a),d)) 14: [intersection(d,a,a)], ~(member(h(d,a,a),a)), ~(member(h(d,a,a),d)) 15: ~(member(member_of_1_not_of_2(a,d),d)), [subset(a,d)] 16: [~(subset(d,a))] 17: ~(member(member_of_1_not_of_2(d,a),a)), [subset(d,a)] Gamma_19: (resolve) 0: intersection(X0,X1,X2), [member(h(X0,X1,X2), X2)], member(h(X0,X1,X2),X1) 1: [intersection(X0,X0,X0)], ~(member(h(X0,X0,X0),X0)) 2: [member(member_of_1_not_of_2(X0,X1),X0)], subset(X0,X1) 3: ~(member(member_of_1_not_of_2(X0,X0),X0)), [subset(X0,X0)] 4: [equal_sets(X0,X0)], ~(subset(X0,X0)) 5: [intersection(d,a,d)] 6: ~(intersection(d,a,d)), [member(member_of_1_not_of_2(d,X0),a)], ~( member(member_of_1_not_of_2(d,X0),d)) 7: ~(intersection(d,a,d)), [member(h(X0,X1,d),a)], ~(member(h(X0,X1,d),d)) 8: [intersection(a,a,d)], ~(member(h(a,a,d),a)), ~(member(h(a,a,d),d)) 9: [intersection(a,d,d)], ~(member(h(a,d,d),a)), ~(member(h(a,d,d),d)) 10: ~(intersection(a,a,d)), ~(member(member_of_1_not_of_2(a,X0),a)), [member( member_of_1_not_of_2(a,X0),d)] 11: ~(intersection(a,a,d)), ~(member(h(X0,X1,a),a)), [member(h(X0,X1,a), d)] 12: [intersection(d,d,a)], ~(member(h(d,d,a),a)), ~(member(h(d,d,a),d)) 13: [intersection(a,d,a)], ~(member(h(a,d,a),a)), ~(member(h(a,d,a),d)) 14: [intersection(d,a,a)], ~(member(h(d,a,a),a)), ~(member(h(d,a,a),d)) 15: ~(member(member_of_1_not_of_2(a,d),d)), [subset(a,d)] 16: [~(subset(d,a))] 17: [~(member(member_of_1_not_of_2(d,a),a))] Gamma_20: (extend-conflict) 0: intersection(X0,X1,X2), [member(h(X0,X1,X2), X2)], member(h(X0,X1,X2),X1) 1: [intersection(X0,X0,X0)], ~(member(h(X0,X0,X0),X0)) 2: [member(member_of_1_not_of_2(X0,X1),X0)], subset(X0,X1) 3: ~(member(member_of_1_not_of_2(X0,X0),X0)), [subset(X0,X0)] 4: [equal_sets(X0,X0)], ~(subset(X0,X0)) 5: [intersection(d,a,d)] 6: ~(intersection(d,a,d)), [member(member_of_1_not_of_2(d,X0),a)], ~( member(member_of_1_not_of_2(d,X0),d)) 7: ~(intersection(d,a,d)), [member(h(X0,X1,d),a)], ~(member(h(X0,X1,d),d)) 8: [intersection(a,a,d)], ~(member(h(a,a,d),a)), ~(member(h(a,a,d),d)) 9: [intersection(a,d,d)], ~(member(h(a,d,d),a)), ~(member(h(a,d,d),d)) 10: ~(intersection(a,a,d)), ~(member(member_of_1_not_of_2(a,X0),a)), [member( member_of_1_not_of_2(a,X0),d)] 11: ~(intersection(a,a,d)), ~(member(h(X0,X1,a),a)), [member(h(X0,X1,a), d)] 12: [intersection(d,d,a)], ~(member(h(d,d,a),a)), ~(member(h(d,d,a),d)) 13: [intersection(a,d,a)], ~(member(h(a,d,a),a)), ~(member(h(a,d,a),d)) 14: [intersection(d,a,a)], ~(member(h(d,a,a),a)), ~(member(h(d,a,a),d)) 15: ~(member(member_of_1_not_of_2(a,d),d)), [subset(a,d)] 16: [~(subset(d,a))] 17: [~(member(member_of_1_not_of_2(d,a),a))] Gamma_21: (move) 0: intersection(X0,X1,X2), [member(h(X0,X1,X2),X2)], member( h(X0,X1,X2),X1) 1: [intersection(X0,X0,X0)], ~(member(h(X0,X0,X0),X0)) 2: [member(member_of_1_not_of_2(X0,X1),X0)], subset(X0,X1) 3: ~(member(member_of_1_not_of_2(X0,X0),X0)), [subset(X0,X0)] 4: [equal_sets(X0,X0)], ~(subset(X0,X0)) 5: [intersection(d,a,d)] 6: [~(member(member_of_1_not_of_2(d,a),a))] 7: ~(intersection(d,a,d)), [member(member_of_1_not_of_2(d,X0),a)], ~( member(member_of_1_not_of_2(d,X0),d)) 8: ~(intersection(d,a,d)), [member(h(X0,X1,d),a)], ~(member(h(X0,X1,d),d)) 9: [intersection(a,a,d)], ~(member(h(a,a,d),a)), ~(member(h(a,a,d),d)) 10: [intersection(a,d,d)], ~(member(h(a,d,d),a)), ~(member(h(a,d,d),d)) 11: ~(intersection(a,a,d)), ~(member(member_of_1_not_of_2(a,X0),a)), [member( member_of_1_not_of_2(a,X0),d)] 12: ~(intersection(a,a,d)), ~(member(h(X0,X1,a),a)), [member(h(X0,X1,a), d)] 13: [intersection(d,d,a)], ~(member(h(d,d,a),a)), ~(member(h(d,d,a),d)) 14: [intersection(a,d,a)], ~(member(h(a,d,a),a)), ~(member(h(a,d,a),d)) 15: [intersection(d,a,a)], ~(member(h(d,a,a),a)), ~(member(h(d,a,a),d)) 16: ~(member(member_of_1_not_of_2(a,d),d)), [subset(a,d)] 17: [~(subset(d,a))] Gamma_22: (right-split) 0: intersection(X0,X1,X2), [member(h(X0,X1,X2), X2)], member(h(X0,X1,X2),X1) 1: [intersection(X0,X0,X0)], ~(member(h(X0,X0,X0),X0)) 2: [member(member_of_1_not_of_2(X0,X1),X0)], subset(X0,X1) 3: ~(member(member_of_1_not_of_2(X0,X0),X0)), [subset(X0,X0)] 4: [equal_sets(X0,X0)], ~(subset(X0,X0)) 5: [intersection(d,a,d)] 6: [~(member(member_of_1_not_of_2(d,a),a))] 7: ~(intersection(d,a,d)), [member(member_of_1_not_of_2(d,a),a)], ~( member(member_of_1_not_of_2(d,a),d)) 8: top(X0) != a | ~(intersection(d,a,d)), [member(member_of_1_not_of_2(d,X0), a)], ~(member(member_of_1_not_of_2(d,X0),d)) 9: ~(intersection(d,a,d)), [member(h(X0,X1,d),a)], ~(member(h(X0,X1,d),d)) 10: [intersection(a,a,d)], ~(member(h(a,a,d),a)), ~(member(h(a,a,d),d)) 11: [intersection(a,d,d)], ~(member(h(a,d,d),a)), ~(member(h(a,d,d),d)) 12: ~(intersection(a,a,d)), ~(member(member_of_1_not_of_2(a,X0),a)), [member( member_of_1_not_of_2(a,X0),d)] 13: ~(intersection(a,a,d)), ~(member(h(X0,X1,a),a)), [member(h(X0,X1,a), d)] 14: [intersection(d,d,a)], ~(member(h(d,d,a),a)), ~(member(h(d,d,a),d)) 15: [intersection(a,d,a)], ~(member(h(a,d,a),a)), ~(member(h(a,d,a),d)) 16: [intersection(d,a,a)], ~(member(h(d,a,a),a)), ~(member(h(d,a,a),d)) 17: ~(member(member_of_1_not_of_2(a,d),d)), [subset(a,d)] 18: [~(subset(d,a))] Gamma_23: (resolve) 0: intersection(X0,X1,X2), [member(h(X0,X1,X2), X2)], member(h(X0,X1,X2),X1) 1: [intersection(X0,X0,X0)], ~(member(h(X0,X0,X0),X0)) 2: [member(member_of_1_not_of_2(X0,X1),X0)], subset(X0,X1) 3: ~(member(member_of_1_not_of_2(X0,X0),X0)), [subset(X0,X0)] 4: [equal_sets(X0,X0)], ~(subset(X0,X0)) 5: [intersection(d,a,d)] 6: [~(member(member_of_1_not_of_2(d,a),a))] 7: [~(intersection(d,a,d))], ~(member(member_of_1_not_of_2(d,a),d)) 8: top(X0) != a | ~(intersection(d,a,d)), [member(member_of_1_not_of_2(d,X0), a)], ~(member(member_of_1_not_of_2(d,X0),d)) 9: ~(intersection(d,a,d)), [member(h(X0,X1,d),a)], ~(member(h(X0,X1,d),d)) 10: [intersection(a,a,d)], ~(member(h(a,a,d),a)), ~(member(h(a,a,d),d)) 11: [intersection(a,d,d)], ~(member(h(a,d,d),a)), ~(member(h(a,d,d),d)) 12: ~(intersection(a,a,d)), ~(member(member_of_1_not_of_2(a,X0),a)), [member( member_of_1_not_of_2(a,X0),d)] 13: ~(intersection(a,a,d)), ~(member(h(X0,X1,a),a)), [member(h(X0,X1,a), d)] 14: [intersection(d,d,a)], ~(member(h(d,d,a),a)), ~(member(h(d,d,a),d)) 15: [intersection(a,d,a)], ~(member(h(a,d,a),a)), ~(member(h(a,d,a),d)) 16: [intersection(d,a,a)], ~(member(h(d,a,a),a)), ~(member(h(d,a,a),d)) 17: ~(member(member_of_1_not_of_2(a,d),d)), [subset(a,d)] 18: [~(subset(d,a))] Gamma_24: (extend-conflict) 0: intersection(X0,X1,X2), [member(h(X0,X1,X2), X2)], member(h(X0,X1,X2),X1) 1: [intersection(X0,X0,X0)], ~(member(h(X0,X0,X0),X0)) 2: [member(member_of_1_not_of_2(X0,X1),X0)], subset(X0,X1) 3: ~(member(member_of_1_not_of_2(X0,X0),X0)), [subset(X0,X0)] 4: [equal_sets(X0,X0)], ~(subset(X0,X0)) 5: [intersection(d,a,d)] 6: [~(member(member_of_1_not_of_2(d,a),a))] 7: [~(intersection(d,a,d))], ~(member(member_of_1_not_of_2(d,a),d)) 8: top(X0) != a | ~(intersection(d,a,d)), [member(member_of_1_not_of_2(d,X0), a)], ~(member(member_of_1_not_of_2(d,X0),d)) 9: ~(intersection(d,a,d)), [member(h(X0,X1,d),a)], ~(member(h(X0,X1,d),d)) 10: [intersection(a,a,d)], ~(member(h(a,a,d),a)), ~(member(h(a,a,d),d)) 11: [intersection(a,d,d)], ~(member(h(a,d,d),a)), ~(member(h(a,d,d),d)) 12: ~(intersection(a,a,d)), ~(member(member_of_1_not_of_2(a,X0),a)), [member( member_of_1_not_of_2(a,X0),d)] 13: ~(intersection(a,a,d)), ~(member(h(X0,X1,a),a)), [member(h(X0,X1,a), d)] 14: [intersection(d,d,a)], ~(member(h(d,d,a),a)), ~(member(h(d,d,a),d)) 15: [intersection(a,d,a)], ~(member(h(a,d,a),a)), ~(member(h(a,d,a),d)) 16: [intersection(d,a,a)], ~(member(h(d,a,a),a)), ~(member(h(d,a,a),d)) 17: ~(member(member_of_1_not_of_2(a,d),d)), [subset(a,d)] 18: [~(subset(d,a))] Gamma_25: (move) 0: intersection(X0,X1,X2), [member(h(X0,X1,X2),X2)], member( h(X0,X1,X2),X1) 1: [intersection(X0,X0,X0)], ~(member(h(X0,X0,X0),X0)) 2: [member(member_of_1_not_of_2(X0,X1),X0)], subset(X0,X1) 3: ~(member(member_of_1_not_of_2(X0,X0),X0)), [subset(X0,X0)] 4: [equal_sets(X0,X0)], ~(subset(X0,X0)) 5: [~(intersection(d,a,d))], ~(member(member_of_1_not_of_2(d,a),d)) 6: [intersection(d,a,d)] 7: [~(member(member_of_1_not_of_2(d,a),a))] 8: top(X0) != a | ~(intersection(d,a,d)), [member(member_of_1_not_of_2(d,X0), a)], ~(member(member_of_1_not_of_2(d,X0),d)) 9: ~(intersection(d,a,d)), [member(h(X0,X1,d),a)], ~(member(h(X0,X1,d),d)) 10: [intersection(a,a,d)], ~(member(h(a,a,d),a)), ~(member(h(a,a,d),d)) 11: [intersection(a,d,d)], ~(member(h(a,d,d),a)), ~(member(h(a,d,d),d)) 12: ~(intersection(a,a,d)), ~(member(member_of_1_not_of_2(a,X0),a)), [member( member_of_1_not_of_2(a,X0),d)] 13: ~(intersection(a,a,d)), ~(member(h(X0,X1,a),a)), [member(h(X0,X1,a), d)] 14: [intersection(d,d,a)], ~(member(h(d,d,a),a)), ~(member(h(d,d,a),d)) 15: [intersection(a,d,a)], ~(member(h(a,d,a),a)), ~(member(h(a,d,a),d)) 16: [intersection(d,a,a)], ~(member(h(d,a,a),a)), ~(member(h(d,a,a),d)) 17: ~(member(member_of_1_not_of_2(a,d),d)), [subset(a,d)] 18: [~(subset(d,a))] Gamma_26: (resolve) 0: intersection(X0,X1,X2), [member(h(X0,X1,X2), X2)], member(h(X0,X1,X2),X1) 1: [intersection(X0,X0,X0)], ~(member(h(X0,X0,X0),X0)) 2: [member(member_of_1_not_of_2(X0,X1),X0)], subset(X0,X1) 3: ~(member(member_of_1_not_of_2(X0,X0),X0)), [subset(X0,X0)] 4: [equal_sets(X0,X0)], ~(subset(X0,X0)) 5: [~(intersection(d,a,d))], ~(member(member_of_1_not_of_2(d,a),d)) 6: [~(member(member_of_1_not_of_2(d,a),d))] 7: [~(member(member_of_1_not_of_2(d,a),a))] 8: [intersection(a,a,d)], ~(member(h(a,a,d),a)), ~(member(h(a,a,d),d)) 9: [intersection(a,d,d)], ~(member(h(a,d,d),a)), ~(member(h(a,d,d),d)) 10: ~(intersection(a,a,d)), ~(member(member_of_1_not_of_2(a,X0),a)), [member( member_of_1_not_of_2(a,X0),d)] 11: ~(intersection(a,a,d)), ~(member(h(X0,X1,a),a)), [member(h(X0,X1,a), d)] 12: [intersection(d,d,a)], ~(member(h(d,d,a),a)), ~(member(h(d,d,a),d)) 13: [intersection(a,d,a)], ~(member(h(a,d,a),a)), ~(member(h(a,d,a),d)) 14: [intersection(d,a,a)], ~(member(h(d,a,a),a)), ~(member(h(d,a,a),d)) 15: ~(member(member_of_1_not_of_2(a,d),d)), [subset(a,d)] 16: [~(subset(d,a))] Gamma_27: (extend-conflict) 0: intersection(X0,X1,X2), [member(h(X0,X1,X2), X2)], member(h(X0,X1,X2),X1) 1: [intersection(X0,X0,X0)], ~(member(h(X0,X0,X0),X0)) 2: [member(member_of_1_not_of_2(X0,X1),X0)], subset(X0,X1) 3: ~(member(member_of_1_not_of_2(X0,X0),X0)), [subset(X0,X0)] 4: [equal_sets(X0,X0)], ~(subset(X0,X0)) 5: [~(intersection(d,a,d))], ~(member(member_of_1_not_of_2(d,a),d)) 6: [~(member(member_of_1_not_of_2(d,a),d))] 7: [~(member(member_of_1_not_of_2(d,a),a))] 8: [intersection(a,a,d)], ~(member(h(a,a,d),a)), ~(member(h(a,a,d),d)) 9: [intersection(a,d,d)], ~(member(h(a,d,d),a)), ~(member(h(a,d,d),d)) 10: ~(intersection(a,a,d)), ~(member(member_of_1_not_of_2(a,X0),a)), [member( member_of_1_not_of_2(a,X0),d)] 11: ~(intersection(a,a,d)), ~(member(h(X0,X1,a),a)), [member(h(X0,X1,a), d)] 12: [intersection(d,d,a)], ~(member(h(d,d,a),a)), ~(member(h(d,d,a),d)) 13: [intersection(a,d,a)], ~(member(h(a,d,a),a)), ~(member(h(a,d,a),d)) 14: [intersection(d,a,a)], ~(member(h(d,a,a),a)), ~(member(h(d,a,a),d)) 15: ~(member(member_of_1_not_of_2(a,d),d)), [subset(a,d)] 16: [~(subset(d,a))] Gamma_28: (move) 0: intersection(X0,X1,X2), [member(h(X0,X1,X2),X2)], member( h(X0,X1,X2),X1) 1: [intersection(X0,X0,X0)], ~(member(h(X0,X0,X0),X0)) 2: [~(member(member_of_1_not_of_2(d,a),d))] 3: [member(member_of_1_not_of_2(X0,X1),X0)], subset(X0,X1) 4: ~(member(member_of_1_not_of_2(X0,X0),X0)), [subset(X0,X0)] 5: [equal_sets(X0,X0)], ~(subset(X0,X0)) 6: [~(intersection(d,a,d))], ~(member(member_of_1_not_of_2(d,a),d)) 7: [~(member(member_of_1_not_of_2(d,a),a))] 8: [intersection(a,a,d)], ~(member(h(a,a,d),a)), ~(member(h(a,a,d),d)) 9: [intersection(a,d,d)], ~(member(h(a,d,d),a)), ~(member(h(a,d,d),d)) 10: ~(intersection(a,a,d)), ~(member(member_of_1_not_of_2(a,X0),a)), [member( member_of_1_not_of_2(a,X0),d)] 11: ~(intersection(a,a,d)), ~(member(h(X0,X1,a),a)), [member(h(X0,X1,a), d)] 12: [intersection(d,d,a)], ~(member(h(d,d,a),a)), ~(member(h(d,d,a),d)) 13: [intersection(a,d,a)], ~(member(h(a,d,a),a)), ~(member(h(a,d,a),d)) 14: [intersection(d,a,a)], ~(member(h(d,a,a),a)), ~(member(h(d,a,a),d)) 15: ~(member(member_of_1_not_of_2(a,d),d)), [subset(a,d)] 16: [~(subset(d,a))] Gamma_29: (right-split) 0: intersection(X0,X1,X2), [member(h(X0,X1,X2), X2)], member(h(X0,X1,X2),X1) 1: [intersection(X0,X0,X0)], ~(member(h(X0,X0,X0),X0)) 2: [~(member(member_of_1_not_of_2(d,a),d))] 3: top(X0) != d | [member(member_of_1_not_of_2(d,a),d)], subset(d,a) 4: top(X0) != d & top(X0) != d | [member(member_of_1_not_of_2(X0,a), X0)], subset(X0,a) 5: top(X0) != d & top(X1) != a | [member(member_of_1_not_of_2(d,X0), d)], subset(d,X0) 6: top(X0) != d & top(X1) != a & top(X0) != d | [member(member_of_1_not_of_2(X0,X1), X0)], subset(X0,X1) 7: ~(member(member_of_1_not_of_2(X0,X0),X0)), [subset(X0,X0)] 8: [equal_sets(X0,X0)], ~(subset(X0,X0)) 9: [~(intersection(d,a,d))], ~(member(member_of_1_not_of_2(d,a),d)) 10: [~(member(member_of_1_not_of_2(d,a),a))] 11: [intersection(a,a,d)], ~(member(h(a,a,d),a)), ~(member(h(a,a,d),d)) 12: [intersection(a,d,d)], ~(member(h(a,d,d),a)), ~(member(h(a,d,d),d)) 13: ~(intersection(a,a,d)), ~(member(member_of_1_not_of_2(a,X0),a)), [member( member_of_1_not_of_2(a,X0),d)] 14: ~(intersection(a,a,d)), ~(member(h(X0,X1,a),a)), [member(h(X0,X1,a), d)] 15: [intersection(d,d,a)], ~(member(h(d,d,a),a)), ~(member(h(d,d,a),d)) 16: [intersection(a,d,a)], ~(member(h(a,d,a),a)), ~(member(h(a,d,a),d)) 17: [intersection(d,a,a)], ~(member(h(d,a,a),a)), ~(member(h(d,a,a),d)) 18: ~(member(member_of_1_not_of_2(a,d),d)), [subset(a,d)] 19: [~(subset(d,a))] Gamma_30: (resolve) 0: intersection(X0,X1,X2), [member(h(X0,X1,X2), X2)], member(h(X0,X1,X2),X1) 1: [intersection(X0,X0,X0)], ~(member(h(X0,X0,X0),X0)) 2: [~(member(member_of_1_not_of_2(d,a),d))] 3: top(X0) != d | [subset(d,a)] 4: top(X0) != d & top(X0) != d | [member(member_of_1_not_of_2(X0,a), X0)], subset(X0,a) 5: top(X0) != d & top(X1) != a | [member(member_of_1_not_of_2(d,X0), d)], subset(d,X0) 6: top(X0) != d & top(X1) != a & top(X0) != d | [member(member_of_1_not_of_2(X0,X1), X0)], subset(X0,X1) 7: ~(member(member_of_1_not_of_2(X0,X0),X0)), [subset(X0,X0)] 8: [equal_sets(X0,X0)], ~(subset(X0,X0)) 9: [~(member(member_of_1_not_of_2(d,a),a))] 10: [intersection(a,a,d)], ~(member(h(a,a,d),a)), ~(member(h(a,a,d),d)) 11: [intersection(a,d,d)], ~(member(h(a,d,d),a)), ~(member(h(a,d,d),d)) 12: ~(intersection(a,a,d)), ~(member(member_of_1_not_of_2(a,X0),a)), [member( member_of_1_not_of_2(a,X0),d)] 13: ~(intersection(a,a,d)), ~(member(h(X0,X1,a),a)), [member(h(X0,X1,a), d)] 14: [intersection(d,d,a)], ~(member(h(d,d,a),a)), ~(member(h(d,d,a),d)) 15: [intersection(a,d,a)], ~(member(h(a,d,a),a)), ~(member(h(a,d,a),d)) 16: [intersection(d,a,a)], ~(member(h(d,a,a),a)), ~(member(h(d,a,a),d)) 17: ~(member(member_of_1_not_of_2(a,d),d)), [subset(a,d)] 18: [~(subset(d,a))] Gamma_31: (extend-conflict) 0: intersection(X0,X1,X2), [member(h(X0,X1,X2), X2)], member(h(X0,X1,X2),X1) 1: [intersection(X0,X0,X0)], ~(member(h(X0,X0,X0),X0)) 2: [~(member(member_of_1_not_of_2(d,a),d))] 3: [subset(d,a)] 4: top(X0) != d & top(X0) != d | [member(member_of_1_not_of_2(X0,a), X0)], subset(X0,a) 5: top(X0) != d & top(X1) != a | [member(member_of_1_not_of_2(d,X0), d)], subset(d,X0) 6: top(X0) != d & top(X1) != a & top(X0) != d | [member(member_of_1_not_of_2(X0,X1), X0)], subset(X0,X1) 7: ~(member(member_of_1_not_of_2(X0,X0),X0)), [subset(X0,X0)] 8: [equal_sets(X0,X0)], ~(subset(X0,X0)) 9: [~(member(member_of_1_not_of_2(d,a),a))] 10: [intersection(a,a,d)], ~(member(h(a,a,d),a)), ~(member(h(a,a,d),d)) 11: [intersection(a,d,d)], ~(member(h(a,d,d),a)), ~(member(h(a,d,d),d)) 12: ~(intersection(a,a,d)), ~(member(member_of_1_not_of_2(a,X0),a)), [member( member_of_1_not_of_2(a,X0),d)] 13: ~(intersection(a,a,d)), ~(member(h(X0,X1,a),a)), [member(h(X0,X1,a), d)] 14: [intersection(d,d,a)], ~(member(h(d,d,a),a)), ~(member(h(d,d,a),d)) 15: [intersection(a,d,a)], ~(member(h(a,d,a),a)), ~(member(h(a,d,a),d)) 16: [intersection(d,a,a)], ~(member(h(d,a,a),a)), ~(member(h(d,a,a),d)) 17: ~(member(member_of_1_not_of_2(a,d),d)), [subset(a,d)] 18: [~(subset(d,a))] Gamma_32: (move) 0: intersection(X0,X1,X2), [member(h(X0,X1,X2),X2)], member( h(X0,X1,X2),X1) 1: [intersection(X0,X0,X0)], ~(member(h(X0,X0,X0),X0)) 2: [~(member(member_of_1_not_of_2(d,a),d))] 3: [~(subset(d,a))] 4: [subset(d,a)] 5: top(X0) != d & top(X0) != d | [member(member_of_1_not_of_2(X0,a), X0)], subset(X0,a) 6: top(X0) != d & top(X1) != a | [member(member_of_1_not_of_2(d,X0), d)], subset(d,X0) 7: top(X0) != d & top(X1) != a & top(X0) != d | [member(member_of_1_not_of_2(X0,X1), X0)], subset(X0,X1) 8: ~(member(member_of_1_not_of_2(X0,X0),X0)), [subset(X0,X0)] 9: [equal_sets(X0,X0)], ~(subset(X0,X0)) 10: [~(member(member_of_1_not_of_2(d,a),a))] 11: [intersection(a,a,d)], ~(member(h(a,a,d),a)), ~(member(h(a,a,d),d)) 12: [intersection(a,d,d)], ~(member(h(a,d,d),a)), ~(member(h(a,d,d),d)) 13: ~(intersection(a,a,d)), ~(member(member_of_1_not_of_2(a,X0),a)), [member( member_of_1_not_of_2(a,X0),d)] 14: ~(intersection(a,a,d)), ~(member(h(X0,X1,a),a)), [member(h(X0,X1,a), d)] 15: [intersection(d,d,a)], ~(member(h(d,d,a),a)), ~(member(h(d,d,a),d)) 16: [intersection(a,d,a)], ~(member(h(a,d,a),a)), ~(member(h(a,d,a),d)) 17: [intersection(d,a,a)], ~(member(h(d,a,a),a)), ~(member(h(d,a,a),d)) 18: ~(member(member_of_1_not_of_2(a,d),d)), [subset(a,d)] Gamma_33: (resolve) 0: intersection(X0,X1,X2), [member(h(X0,X1,X2), X2)], member(h(X0,X1,X2),X1) 1: [intersection(X0,X0,X0)], ~(member(h(X0,X0,X0),X0)) 2: [~(member(member_of_1_not_of_2(d,a),d))] 3: [~(subset(d,a))] 4: [] 5: top(X0) != d & top(X0) != d | [member(member_of_1_not_of_2(X0,a), X0)], subset(X0,a) 6: top(X0) != d & top(X1) != a | [member(member_of_1_not_of_2(d,X0), d)], subset(d,X0) 7: top(X0) != d & top(X1) != a & top(X0) != d | [member(member_of_1_not_of_2(X0,X1), X0)], subset(X0,X1) 8: ~(member(member_of_1_not_of_2(X0,X0),X0)), [subset(X0,X0)] 9: [equal_sets(X0,X0)], ~(subset(X0,X0)) 10: [~(member(member_of_1_not_of_2(d,a),a))] 11: [intersection(a,a,d)], ~(member(h(a,a,d),a)), ~(member(h(a,a,d),d)) 12: [intersection(a,d,d)], ~(member(h(a,d,d),a)), ~(member(h(a,d,d),d)) 13: ~(intersection(a,a,d)), ~(member(member_of_1_not_of_2(a,X0),a)), [member( member_of_1_not_of_2(a,X0),d)] 14: ~(intersection(a,a,d)), ~(member(h(X0,X1,a),a)), [member(h(X0,X1,a), d)] 15: [intersection(d,d,a)], ~(member(h(d,d,a),a)), ~(member(h(d,d,a),d)) 16: [intersection(a,d,a)], ~(member(h(a,d,a),a)), ~(member(h(a,d,a),d)) 17: [intersection(d,a,a)], ~(member(h(d,a,a),a)), ~(member(h(d,a,a),d)) 18: ~(member(member_of_1_not_of_2(a,d),d)), [subset(a,d)] SZS status Unsatisfiable