0.00/0.03 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.04 % Command : java -Xss128m -Xmx4g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar %s -t %d -p --atp cvc4=/export/starexec/sandbox2/solver/bin/externals/cvc4 --atp e=/export/starexec/sandbox2/solver/bin/externals/eprover --atp iprover=/export/starexec/sandbox2/solver/bin/externals/iprover 0.03/0.24 % Computer : n140.star.cs.uiowa.edu 0.03/0.24 % Model : x86_64 x86_64 0.03/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz 0.03/0.24 % Memory : 32218.625MB 0.03/0.24 % OS : Linux 3.10.0-693.2.2.el7.x86_64 0.03/0.24 % CPULimit : 300 0.03/0.24 % DateTime : Sat Jul 14 05:41:24 CDT 2018 0.03/0.24 % CPUTime : 2.38/1.45 % [INFO] Running in sequential loop mode. 3.12/1.68 % [CONFIG] Using configuration: timeout(300) with strategy 3.35/1.76 % [INFO] iprover registered as external prover. 3.35/1.76 % [INFO] e registered as external prover. 3.35/1.77 % [INFO] cvc4 registered as external prover. 3.35/1.77 % [INFO] Parsing finished. Scanning for conjecture ... 3.78/1.83 % [INFO] Found a conjecture and 28 axioms. Running axiom selection ... 3.78/1.91 % [INFO] Axiom selection finished. Selected 28 axioms (removed 0 axioms). 4.47/2.01 % [INFO] Type checking passed. Searching for refutation ... 89.99/24.45 % [INFO] Killing All external provers ... 89.99/24.47 % Time passed: 24124ms 89.99/24.47 % Effective reasoning time: 22994ms 89.99/24.47 % Solved by strategy 89.99/24.47 % Axioms used in derivation (28): power_set, unordered_pair, inverse_image3, union, intersection, inverse_predicate, isomorphism, empty_set, one_to_one, surjective, injective, increasing_function, decreasing_function, image3, subset, equal_maps, inverse_function, equal_set, compose_function, inverse_image2, singleton, image2, identity, difference, maps, compose_predicate, sum, product 89.99/24.47 % No. of inferences in proof: 511 89.99/24.47 % No. of processed clauses: 207 89.99/24.47 % No. of generated clauses: 1911 89.99/24.47 % No. of forward subsumed clauses: 43 89.99/24.47 % No. of backward subsumed clauses: 0 89.99/24.47 % No. of ground rewrite rules in store: 5 89.99/24.47 % No. of non-ground rewrite rules in store: 48 89.99/24.47 % No. of positive (non-rewrite) units in store: 0 89.99/24.47 % No. of negative (non-rewrite) units in store: 69 89.99/24.47 % No. of choice functions detected: 0 89.99/24.47 % No. of choice instantiations: 0 89.99/24.47 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 24124 ms resp. 22994 ms w/o parsing 90.45/24.81 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p 90.45/24.81 thf(maps_type, type, maps: ($i > ($i > ($i > $o)))). 90.45/24.81 thf(subset_type, type, subset: ($i > ($i > $o))). 90.45/24.81 thf(image2_type, type, image2: ($i > ($i > $i))). 90.45/24.81 thf(apply_type, type, apply: ($i > ($i > ($i > $o)))). 90.45/24.81 thf(member_type, type, member: ($i > ($i > $o))). 90.45/24.81 thf(injective_type, type, injective: ($i > ($i > ($i > $o)))). 90.45/24.81 thf(surjective_type, type, surjective: ($i > ($i > ($i > $o)))). 90.45/24.81 thf(one_to_one_type, type, one_to_one: ($i > ($i > ($i > $o)))). 90.45/24.81 thf(inverse_image3_type, type, inverse_image3: ($i > ($i > ($i > $i)))). 90.45/24.81 thf(decreasing_type, type, decreasing: ($i > ($i > ($i > ($i > ($i > $o)))))). 90.45/24.81 thf(power_set_type, type, power_set: ($i > $i)). 90.45/24.81 thf(intersection_type, type, intersection: ($i > ($i > $i))). 90.45/24.81 thf(image3_type, type, image3: ($i > ($i > ($i > $i)))). 90.45/24.81 thf(union_type, type, union: ($i > ($i > $i))). 90.45/24.81 thf(singleton_type, type, singleton: ($i > $i)). 90.45/24.81 thf(equal_set_type, type, equal_set: ($i > ($i > $o))). 90.45/24.81 thf(inverse_image2_type, type, inverse_image2: ($i > ($i > $i))). 90.45/24.81 thf(product_type, type, product: ($i > $i)). 90.45/24.81 thf(empty_set_type, type, empty_set: $i). 90.45/24.81 thf(compose_predicate_type, type, compose_predicate: ($i > ($i > ($i > ($i > ($i > ($i > $o))))))). 90.45/24.81 thf(difference_type, type, difference: ($i > ($i > $i))). 90.45/24.81 thf(inverse_function_type, type, inverse_function: ($i > ($i > ($i > $i)))). 90.45/24.81 thf(inverse_predicate_type, type, inverse_predicate: ($i > ($i > ($i > ($i > $o))))). 90.45/24.81 thf(equal_maps_type, type, equal_maps: ($i > ($i > ($i > ($i > $o))))). 90.45/24.81 thf(compose_function_type, type, compose_function: ($i > ($i > ($i > ($i > ($i > $i)))))). 90.45/24.81 thf(identity_type, type, identity: ($i > ($i > $o))). 90.45/24.81 thf(isomorphism_type, type, isomorphism: ($i > ($i > ($i > ($i > ($i > $o)))))). 90.45/24.81 thf(sum_type, type, sum: ($i > $i)). 90.45/24.81 thf(unordered_pair_type, type, unordered_pair: ($i > ($i > $i))). 90.45/24.81 thf(increasing_type, type, increasing: ($i > ($i > ($i > ($i > ($i > $o)))))). 90.45/24.81 thf(sk1_type, type, sk1: $i). 90.45/24.81 thf(sk2_type, type, sk2: $i). 90.45/24.81 thf(sk3_type, type, sk3: $i). 90.45/24.81 thf(sk4_type, type, sk4: $i). 90.45/24.81 thf(sk5_type, type, sk5: $i). 90.45/24.81 thf(sk6_type, type, sk6: ($i > ($i > ($i > $i)))). 90.45/24.81 thf(sk7_type, type, sk7: ($i > ($i > ($i > ($i > $i))))). 90.45/24.81 thf(sk8_type, type, sk8: ($i > ($i > ($i > ($i > ($i > $i)))))). 90.45/24.81 thf(sk9_type, type, sk9: ($i > ($i > ($i > ($i > ($i > $i)))))). 90.45/24.81 thf(sk10_type, type, sk10: ($i > ($i > ($i > ($i > ($i > $i)))))). 90.45/24.81 thf(sk11_type, type, sk11: ($i > ($i > ($i > ($i > ($i > $i)))))). 90.45/24.81 thf(sk14_type, type, sk14: ($i > ($i > $i))). 90.45/24.81 thf(sk34_type, type, sk34: ($i > ($i > $i))). 90.45/24.81 thf(sk38_type, type, sk38: ($i > ($i > $i))). 90.45/24.81 thf(15,axiom,((! [A:$i]: ~ (member @ A @ empty_set))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set)). 90.45/24.81 thf(136,plain,((! [A:$i]: ~ (member @ A @ empty_set))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[15])). 90.45/24.81 thf(137,plain,((~ (? [A:$i]: (member @ A @ empty_set)))),inference(miniscope,[status(thm)],[136])). 90.45/24.81 thf(138,plain,(! [A:$i] : ((~ (member @ A @ empty_set)))),inference(cnf,[status(esa)],[137])). 90.45/24.81 thf(14,axiom,((! [A:$i,B:$i]: ((member @ A @ (product @ B)) <=> (! [C:$i]: ((member @ C @ B) => (member @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product)). 90.45/24.81 thf(129,plain,((! [A:$i,B:$i]: (((member @ A @ (product @ B)) => (! [C:$i]: ((member @ C @ B) => (member @ A @ C)))) & ((! [C:$i]: ((member @ C @ B) => (member @ A @ C))) => (member @ A @ (product @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[14])). 90.45/24.81 thf(130,plain,((! [A:$i,B:$i]: ((member @ A @ (product @ B)) => (! [C:$i]: ((member @ C @ B) => (member @ A @ C)))) & ! [A:$i,B:$i]: ((! [C:$i]: ((member @ C @ B) => (member @ A @ C))) => (member @ A @ (product @ B))))),inference(miniscope,[status(thm)],[129])). 90.45/24.81 thf(131,plain,(! [B:$i,A:$i] : ((member @ (sk14 @ B @ A) @ B) | (member @ A @ (product @ B)))),inference(cnf,[status(esa)],[130])). 90.45/24.81 thf(134,plain,(! [B:$i,A:$i] : ((member @ (sk14 @ B @ A) @ B) | (member @ A @ (product @ B)))),inference(simp,[status(thm)],[131])). 90.45/24.81 thf(4,axiom,((! [A:$i,B:$i,C:$i]: ((member @ C @ (image2 @ A @ B)) <=> (? [D:$i]: ((apply @ A @ D @ C) & (member @ D @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',image2)). 90.45/24.81 thf(46,plain,((! [A:$i,B:$i,C:$i]: (((member @ C @ (image2 @ A @ B)) => (? [D:$i]: ((apply @ A @ D @ C) & (member @ D @ B)))) & ((? [D:$i]: ((apply @ A @ D @ C) & (member @ D @ B))) => (member @ C @ (image2 @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])). 90.45/24.81 thf(47,plain,((! [A:$i,B:$i,C:$i]: ((member @ C @ (image2 @ A @ B)) => (? [D:$i]: ((apply @ A @ D @ C) & (member @ D @ B)))) & ! [A:$i,B:$i,C:$i]: ((? [D:$i]: ((apply @ A @ D @ C) & (member @ D @ B))) => (member @ C @ (image2 @ A @ B))))),inference(miniscope,[status(thm)],[46])). 90.45/24.81 thf(50,plain,(! [C:$i,B:$i,A:$i] : ((~ (member @ C @ (image2 @ A @ B))) | (member @ (sk6 @ C @ B @ A) @ B))),inference(cnf,[status(esa)],[47])). 90.45/24.81 thf(855,plain,(! [D:$i,C:$i,B:$i,A:$i] : ((~ (member @ C @ (image2 @ A @ B))) | ((member @ (sk6 @ C @ B @ A) @ B) != (member @ D @ empty_set)))),inference(paramod_ordered,[status(thm)],[50,138])). 90.45/24.81 thf(856,plain,(! [B:$i,A:$i] : ((~ (member @ A @ (image2 @ B @ empty_set))))),inference(pattern_uni,[status(thm)],[855:[bind(A, $thf(G)),bind(B, $thf(empty_set)),bind(C, $thf(E)),bind(D, $thf(sk6 @ E @ empty_set @ G))]])). 90.45/24.81 thf(925,plain,(! [B:$i,A:$i] : ((~ (member @ A @ (image2 @ B @ empty_set))))),inference(simp,[status(thm)],[856])). 90.45/24.81 thf(941,plain,(! [D:$i,C:$i,B:$i,A:$i] : ((member @ A @ (product @ B)) | ((member @ (sk14 @ B @ A) @ B) != (member @ C @ (image2 @ D @ empty_set))))),inference(paramod_ordered,[status(thm)],[134,925])). 90.45/24.81 thf(942,plain,(! [B:$i,A:$i] : ((member @ A @ (product @ (image2 @ B @ empty_set))))),inference(pattern_uni,[status(thm)],[941:[bind(A, $thf(F)),bind(B, $thf(image2 @ G @ empty_set)),bind(C, $thf(sk14 @ (image2 @ G @ empty_set) @ F)),bind(D, $thf(G))]])). 90.45/24.81 thf(958,plain,(! [B:$i,A:$i] : ((member @ A @ (product @ (image2 @ B @ empty_set))))),inference(simp,[status(thm)],[942])). 90.45/24.81 thf(619,plain,(! [C:$i,B:$i,A:$i] : ((member @ A @ (product @ B)) | ((member @ (sk14 @ B @ A) @ B) != (member @ C @ empty_set)))),inference(paramod_ordered,[status(thm)],[134,138])). 90.45/24.81 thf(620,plain,(! [A:$i] : ((member @ A @ (product @ empty_set)))),inference(pattern_uni,[status(thm)],[619:[bind(A, $thf(E)),bind(B, $thf(empty_set)),bind(C, $thf(sk14 @ empty_set @ E))]])). 90.45/24.81 thf(668,plain,(! [A:$i] : ((member @ A @ (product @ empty_set)))),inference(simp,[status(thm)],[620])). 90.45/24.81 thf(17,axiom,((! [A:$i,B:$i,C:$i]: (((member @ A @ C) & ~ (member @ A @ B)) <=> (member @ A @ (difference @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference)). 90.45/24.81 thf(161,plain,((! [A:$i,B:$i,C:$i]: ((((member @ A @ C) & ~ (member @ A @ B)) => (member @ A @ (difference @ C @ B))) & ((member @ A @ (difference @ C @ B)) => ((member @ A @ C) & ~ (member @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[17])). 90.45/24.81 thf(162,plain,((! [A:$i,B:$i,C:$i]: (((member @ A @ C) & ~ (member @ A @ B)) => (member @ A @ (difference @ C @ B))) & ! [A:$i,B:$i,C:$i]: ((member @ A @ (difference @ C @ B)) => ((member @ A @ C) & ~ (member @ A @ B))))),inference(miniscope,[status(thm)],[161])). 90.45/24.81 thf(164,plain,(! [C:$i,B:$i,A:$i] : ((~ (member @ A @ (difference @ C @ B))) | (~ (member @ A @ B)))),inference(cnf,[status(esa)],[162])). 90.45/24.81 thf(167,plain,(! [C:$i,B:$i,A:$i] : ((~ (member @ A @ (difference @ C @ B))) | (~ (member @ A @ B)))),inference(simp,[status(thm)],[164])). 90.45/24.81 thf(726,plain,(! [D:$i,C:$i,B:$i,A:$i] : ((~ (member @ B @ (difference @ D @ C))) | ((member @ A @ (product @ empty_set)) != (member @ B @ C)))),inference(paramod_ordered,[status(thm)],[668,167])). 90.45/24.81 thf(727,plain,(! [B:$i,A:$i] : ((~ (member @ A @ (difference @ B @ (product @ empty_set)))))),inference(pattern_uni,[status(thm)],[726:[bind(A, $thf(A)),bind(B, $thf(A)),bind(C, $thf(product @ empty_set)),bind(D, $thf(D))]])). 90.45/24.81 thf(765,plain,(! [B:$i,A:$i] : ((~ (member @ A @ (difference @ B @ (product @ empty_set)))))),inference(simp,[status(thm)],[727])). 90.45/24.81 thf(1118,plain,(! [D:$i,C:$i,B:$i,A:$i] : (((member @ A @ (product @ (image2 @ B @ empty_set))) != (member @ C @ (difference @ D @ (product @ empty_set)))))),inference(paramod_ordered,[status(thm)],[958,765])). 90.45/24.81 thf(1146,plain,(! [D:$i,C:$i,B:$i,A:$i] : ((A != C) | ((product @ (image2 @ B @ empty_set)) != (difference @ D @ (product @ empty_set))))),inference(simp,[status(thm)],[1118])). 90.45/24.81 thf(1168,plain,(! [B:$i,A:$i] : (((product @ (image2 @ A @ empty_set)) != (difference @ B @ (product @ empty_set))))),inference(simp,[status(thm)],[1146])). 90.45/24.81 thf(770,plain,(! [D:$i,C:$i,B:$i,A:$i] : ((member @ A @ (product @ B)) | ((member @ (sk14 @ B @ A) @ B) != (member @ C @ (difference @ D @ (product @ empty_set)))))),inference(paramod_ordered,[status(thm)],[134,765])). 90.45/24.81 thf(771,plain,(! [B:$i,A:$i] : ((member @ A @ (product @ (difference @ B @ (product @ empty_set)))))),inference(pattern_uni,[status(thm)],[770:[bind(A, $thf(F)),bind(B, $thf(difference @ G @ (product @ empty_set))),bind(C, $thf(sk14 @ (difference @ G @ (product @ empty_set)) @ F)),bind(D, $thf(G))]])). 90.45/24.81 thf(787,plain,(! [B:$i,A:$i] : ((member @ A @ (product @ (difference @ B @ (product @ empty_set)))))),inference(simp,[status(thm)],[771])). 90.45/24.81 thf(1197,plain,(! [E:$i,D:$i,C:$i,B:$i,A:$i] : ((~ (member @ C @ (difference @ E @ D))) | ((member @ A @ (product @ (difference @ B @ (product @ empty_set)))) != (member @ C @ D)))),inference(paramod_ordered,[status(thm)],[787,167])). 90.45/24.81 thf(1198,plain,(! [C:$i,B:$i,A:$i] : ((~ (member @ A @ (difference @ B @ (product @ (difference @ C @ (product @ empty_set)))))))),inference(pattern_uni,[status(thm)],[1197:[bind(A, $thf(A)),bind(B, $thf(G)),bind(C, $thf(A)),bind(D, $thf(product @ (difference @ G @ (product @ empty_set)))),bind(E, $thf(E))]])). 90.45/24.81 thf(1244,plain,(! [C:$i,B:$i,A:$i] : ((~ (member @ A @ (difference @ B @ (product @ (difference @ C @ (product @ empty_set)))))))),inference(simp,[status(thm)],[1198])). 90.45/24.81 thf(3305,plain,(! [E:$i,D:$i,C:$i,B:$i,A:$i] : ((member @ A @ (product @ B)) | ((member @ (sk14 @ B @ A) @ B) != (member @ C @ (difference @ D @ (product @ (difference @ E @ (product @ empty_set)))))))),inference(paramod_ordered,[status(thm)],[134,1244])). 90.45/24.81 thf(3306,plain,(! [C:$i,B:$i,A:$i] : ((member @ A @ (product @ (difference @ B @ (product @ (difference @ C @ (product @ empty_set)))))))),inference(pattern_uni,[status(thm)],[3305:[bind(A, $thf(G)),bind(B, $thf(difference @ H @ (product @ (difference @ K @ (product @ empty_set))))),bind(C, $thf(sk14 @ (difference @ H @ (product @ (difference @ K @ (product @ empty_set)))) @ G)),bind(D, $thf(H)),bind(E, $thf(K))]])). 90.45/24.81 thf(3345,plain,(! [C:$i,B:$i,A:$i] : ((member @ A @ (product @ (difference @ B @ (product @ (difference @ C @ (product @ empty_set)))))))),inference(simp,[status(thm)],[3306])). 90.45/24.81 thf(1188,plain,(! [D:$i,C:$i,B:$i,A:$i] : (((member @ A @ (product @ (difference @ B @ (product @ empty_set)))) != (member @ C @ (image2 @ D @ empty_set))))),inference(paramod_ordered,[status(thm)],[787,925])). 90.45/24.81 thf(1227,plain,(! [D:$i,C:$i,B:$i,A:$i] : ((A != C) | ((product @ (difference @ B @ (product @ empty_set))) != (image2 @ D @ empty_set)))),inference(simp,[status(thm)],[1188])). 90.45/24.81 thf(1237,plain,(! [B:$i,A:$i] : (((product @ (difference @ A @ (product @ empty_set))) != (image2 @ B @ empty_set)))),inference(simp,[status(thm)],[1227])). 90.45/24.81 thf(29,axiom,((! [A:$i,B:$i,C:$i]: ((member @ A @ (unordered_pair @ B @ C)) <=> ((A = C) | (B = A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair)). 90.45/24.81 thf(287,plain,((! [A:$i,B:$i,C:$i]: (((member @ A @ (unordered_pair @ B @ C)) => ((A = C) | (B = A))) & (((A = C) | (B = A)) => (member @ A @ (unordered_pair @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[29])). 90.45/24.81 thf(288,plain,((! [A:$i,B:$i,C:$i]: ((member @ A @ (unordered_pair @ B @ C)) => ((A = C) | (B = A))) & ! [A:$i,B:$i,C:$i]: (((A = C) | (B = A)) => (member @ A @ (unordered_pair @ B @ C))))),inference(miniscope,[status(thm)],[287])). 90.45/24.81 thf(289,plain,(! [C:$i,B:$i,A:$i] : ((~ (A = C)) | (member @ A @ (unordered_pair @ B @ C)))),inference(cnf,[status(esa)],[288])). 90.45/24.81 thf(292,plain,(! [C:$i,B:$i,A:$i] : ((A != C) | (member @ A @ (unordered_pair @ B @ C)))),inference(lifteq,[status(thm)],[289])). 90.45/24.81 thf(293,plain,(! [B:$i,A:$i] : ((member @ B @ (unordered_pair @ A @ B)))),inference(simp,[status(thm)],[292])). 90.45/24.81 thf(939,plain,(! [D:$i,C:$i,B:$i,A:$i] : (((member @ B @ (unordered_pair @ A @ B)) != (member @ C @ (image2 @ D @ empty_set))))),inference(paramod_ordered,[status(thm)],[293,925])). 90.45/24.81 thf(954,plain,(! [D:$i,C:$i,B:$i,A:$i] : ((B != C) | ((unordered_pair @ A @ B) != (image2 @ D @ empty_set)))),inference(simp,[status(thm)],[939])). 90.45/24.81 thf(962,plain,(! [C:$i,B:$i,A:$i] : (((unordered_pair @ A @ B) != (image2 @ C @ empty_set)))),inference(simp,[status(thm)],[954])). 90.45/24.81 thf(1,conjecture,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((maps @ A @ C @ D) & (subset @ E @ D) & (E = (image2 @ A @ C)) & ! [F:$i,G:$i]: (((apply @ B @ F @ G) <=> (apply @ A @ F @ G)) <= ((member @ G @ E) & (member @ F @ C)))) => (maps @ B @ C @ E)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thII21)). 90.45/24.81 thf(2,negated_conjecture,((~ (! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((maps @ A @ C @ D) & (subset @ E @ D) & (E = (image2 @ A @ C)) & ! [F:$i,G:$i]: (((apply @ B @ F @ G) <=> (apply @ A @ F @ G)) <= ((member @ G @ E) & (member @ F @ C)))) => (maps @ B @ C @ E))))),inference(neg_conjecture,[status(cth)],[1])). 90.45/24.81 thf(31,plain,((~ (! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((maps @ A @ C @ D) & (subset @ E @ D) & (E = (image2 @ A @ C)) & ! [F:$i,G:$i]: ((((apply @ B @ F @ G) => (apply @ A @ F @ G)) & ((apply @ A @ F @ G) => (apply @ B @ F @ G))) | ~ ((member @ G @ E) & (member @ F @ C)))) => (maps @ B @ C @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])). 90.45/24.81 thf(32,plain,((sk5 = (image2 @ sk1 @ sk3))),inference(cnf,[status(esa)],[31])). 90.45/24.81 thf(38,plain,(((image2 @ sk1 @ sk3) = sk5)),inference(lifteq,[status(thm)],[32])). 90.45/24.81 thf(11,axiom,((! [A:$i,B:$i]: ((A = B) <=> (member @ A @ (singleton @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton)). 90.45/24.81 thf(107,plain,((! [A:$i,B:$i]: (((A = B) => (member @ A @ (singleton @ B))) & ((member @ A @ (singleton @ B)) => (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[11])). 90.45/24.81 thf(108,plain,((! [A:$i,B:$i]: ((A = B) => (member @ A @ (singleton @ B))) & ! [A:$i,B:$i]: ((member @ A @ (singleton @ B)) => (A = B)))),inference(miniscope,[status(thm)],[107])). 90.45/24.81 thf(110,plain,(! [B:$i,A:$i] : ((~ (A = B)) | (member @ A @ (singleton @ B)))),inference(cnf,[status(esa)],[108])). 90.45/24.81 thf(113,plain,(! [B:$i,A:$i] : ((A != B) | (member @ A @ (singleton @ B)))),inference(lifteq,[status(thm)],[110])). 90.45/24.81 thf(114,plain,(! [A:$i] : ((member @ A @ (singleton @ A)))),inference(simp,[status(thm)],[113])). 90.45/24.81 thf(949,plain,(! [E:$i,D:$i,C:$i,B:$i,A:$i] : ((~ (member @ C @ (image2 @ A @ B))) | ((member @ (sk6 @ C @ B @ A) @ B) != (member @ D @ (image2 @ E @ empty_set))))),inference(paramod_ordered,[status(thm)],[50,925])). 90.45/24.81 thf(950,plain,(! [C:$i,B:$i,A:$i] : ((~ (member @ A @ (image2 @ B @ (image2 @ C @ empty_set)))))),inference(pattern_uni,[status(thm)],[949:[bind(A, $thf(H)),bind(B, $thf(image2 @ I @ empty_set)),bind(C, $thf(F)),bind(D, $thf(sk6 @ F @ (image2 @ I @ empty_set) @ H)),bind(E, $thf(I))]])). 90.45/24.81 thf(964,plain,(! [C:$i,B:$i,A:$i] : ((~ (member @ A @ (image2 @ B @ (image2 @ C @ empty_set)))))),inference(simp,[status(thm)],[950])). 90.45/24.81 thf(1689,plain,(! [D:$i,C:$i,B:$i,A:$i] : (((member @ A @ (singleton @ A)) != (member @ B @ (image2 @ C @ (image2 @ D @ empty_set)))))),inference(paramod_ordered,[status(thm)],[114,964])). 90.45/24.81 thf(1698,plain,(! [D:$i,C:$i,B:$i,A:$i] : ((A != B) | ((singleton @ A) != (image2 @ C @ (image2 @ D @ empty_set))))),inference(simp,[status(thm)],[1689])). 90.45/24.81 thf(1713,plain,(! [C:$i,B:$i,A:$i] : (((singleton @ A) != (image2 @ B @ (image2 @ C @ empty_set))))),inference(simp,[status(thm)],[1698])). 90.45/24.81 thf(2246,plain,(! [C:$i,B:$i,A:$i] : (((image2 @ B @ sk5) != (singleton @ A)) | ((image2 @ sk1 @ sk3) != (image2 @ C @ empty_set)))),inference(paramod_ordered,[status(thm)],[38,1713])). 90.45/24.81 thf(2248,plain,(! [C:$i,B:$i,A:$i] : (((image2 @ B @ sk5) != (singleton @ A)) | (sk1 != C) | (sk3 != empty_set))),inference(simp,[status(thm)],[2246])). 90.45/24.81 thf(2250,plain,(! [B:$i,A:$i] : (((image2 @ B @ sk5) != (singleton @ A)) | (sk3 != empty_set))),inference(simp,[status(thm)],[2248])). 90.45/24.81 thf(24,axiom,((! [A:$i,B:$i]: ((subset @ A @ B) <=> (! [C:$i]: ((member @ C @ B) <= (member @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset)). 90.45/24.81 thf(230,plain,((! [A:$i,B:$i]: (((subset @ A @ B) => (! [C:$i]: ((member @ C @ B) | ~ (member @ C @ A)))) & ((! [C:$i]: ((member @ C @ B) | ~ (member @ C @ A))) => (subset @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[24])). 90.45/24.81 thf(231,plain,((! [A:$i,B:$i]: ((subset @ A @ B) => (! [C:$i]: ((member @ C @ B) | ~ (member @ C @ A)))) & ! [A:$i,B:$i]: ((! [C:$i]: ((member @ C @ B) | ~ (member @ C @ A))) => (subset @ A @ B)))),inference(miniscope,[status(thm)],[230])). 90.45/24.81 thf(233,plain,(! [B:$i,A:$i] : ((member @ (sk34 @ B @ A) @ A) | (subset @ A @ B))),inference(cnf,[status(esa)],[231])). 90.45/24.81 thf(236,plain,(! [B:$i,A:$i] : ((member @ (sk34 @ B @ A) @ A) | (subset @ A @ B))),inference(simp,[status(thm)],[233])). 90.45/24.81 thf(392,plain,(! [C:$i,B:$i,A:$i] : ((subset @ A @ B) | ((member @ (sk34 @ B @ A) @ A) != (member @ C @ empty_set)))),inference(paramod_ordered,[status(thm)],[236,138])). 90.45/24.81 thf(393,plain,(! [A:$i] : ((subset @ empty_set @ A))),inference(pattern_uni,[status(thm)],[392:[bind(A, $thf(empty_set)),bind(B, $thf(D)),bind(C, $thf(sk34 @ D @ empty_set))]])). 90.45/24.81 thf(408,plain,(! [A:$i] : ((subset @ empty_set @ A))),inference(simp,[status(thm)],[393])). 90.45/24.81 thf(12,axiom,((! [A:$i,B:$i]: (((subset @ A @ B) & (subset @ B @ A)) <=> (equal_set @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_set)). 90.45/24.81 thf(115,plain,((! [A:$i,B:$i]: ((((subset @ A @ B) & (subset @ B @ A)) => (equal_set @ A @ B)) & ((equal_set @ A @ B) => ((subset @ A @ B) & (subset @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[12])). 90.45/24.81 thf(22,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i]: (((member @ F @ C) & (member @ G @ E)) => ((? [H:$i]: ((member @ H @ D) & (apply @ A @ H @ G) & (apply @ B @ F @ H))) <=> (apply @ (compose_function @ A @ B @ C @ D @ E) @ F @ G))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_function)). 90.45/24.81 thf(217,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i]: (((member @ F @ C) & (member @ G @ E)) => (((? [H:$i]: ((member @ H @ D) & (apply @ A @ H @ G) & (apply @ B @ F @ H))) => (apply @ (compose_function @ A @ B @ C @ D @ E) @ F @ G)) & ((apply @ (compose_function @ A @ B @ C @ D @ E) @ F @ G) => (? [H:$i]: ((member @ H @ D) & (apply @ A @ H @ G) & (apply @ B @ F @ H)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[22])). 90.45/24.81 thf(940,plain,(! [B:$i,A:$i] : ((~ (member @ A @ sk5)) | ((image2 @ sk1 @ sk3) != (image2 @ B @ empty_set)))),inference(paramod_ordered,[status(thm)],[38,925])). 90.45/24.81 thf(956,plain,(! [B:$i,A:$i] : ((~ (member @ A @ sk5)) | (sk1 != B) | (sk3 != empty_set))),inference(simp,[status(thm)],[940])). 90.45/24.81 thf(957,plain,(! [A:$i] : ((~ (member @ A @ sk5)) | (sk3 != empty_set))),inference(simp,[status(thm)],[956])). 90.45/24.81 thf(986,plain,(! [B:$i,A:$i] : ((sk3 != empty_set) | ((member @ A @ (singleton @ A)) != (member @ B @ sk5)))),inference(paramod_ordered,[status(thm)],[114,957])). 90.45/24.81 thf(989,plain,(! [B:$i,A:$i] : ((sk3 != empty_set) | (A != B) | ((singleton @ A) != sk5))),inference(simp,[status(thm)],[986])). 90.45/24.81 thf(994,plain,(! [A:$i] : ((sk3 != empty_set) | ((singleton @ A) != sk5))),inference(simp,[status(thm)],[989])). 90.45/24.81 thf(1110,plain,(! [C:$i,B:$i,A:$i] : (((member @ A @ (product @ (image2 @ B @ empty_set))) != (member @ C @ empty_set)))),inference(paramod_ordered,[status(thm)],[958,138])). 90.45/24.81 thf(1138,plain,(! [C:$i,B:$i,A:$i] : ((A != C) | ((product @ (image2 @ B @ empty_set)) != empty_set))),inference(simp,[status(thm)],[1110])). 90.45/24.81 thf(1164,plain,(! [A:$i] : (((product @ (image2 @ A @ empty_set)) != empty_set))),inference(simp,[status(thm)],[1138])). 90.45/24.81 thf(377,plain,(! [D:$i,C:$i,B:$i,A:$i] : ((~ (member @ B @ (difference @ D @ C))) | ((member @ A @ (singleton @ A)) != (member @ B @ C)))),inference(paramod_ordered,[status(thm)],[114,167])). 90.45/24.81 thf(378,plain,(! [B:$i,A:$i] : ((~ (member @ B @ (difference @ A @ (singleton @ B)))))),inference(pattern_uni,[status(thm)],[377:[bind(A, $thf(E)),bind(B, $thf(E)),bind(C, $thf(singleton @ E))]])). 90.45/24.81 thf(390,plain,(! [B:$i,A:$i] : ((~ (member @ B @ (difference @ A @ (singleton @ B)))))),inference(simp,[status(thm)],[378])). 90.45/24.81 thf(1205,plain,(! [D:$i,C:$i,B:$i,A:$i] : (((member @ A @ (product @ (difference @ B @ (product @ empty_set)))) != (member @ D @ (difference @ C @ (singleton @ D)))))),inference(paramod_ordered,[status(thm)],[787,390])). 90.45/24.81 thf(1215,plain,(! [D:$i,C:$i,B:$i,A:$i] : ((A != D) | ((product @ (difference @ B @ (product @ empty_set))) != (difference @ C @ (singleton @ D))))),inference(simp,[status(thm)],[1205])). 90.45/24.81 thf(1233,plain,(! [C:$i,B:$i,A:$i] : (((product @ (difference @ A @ (product @ empty_set))) != (difference @ B @ (singleton @ C))))),inference(simp,[status(thm)],[1215])). 90.45/24.81 thf(26,axiom,((! [A:$i,B:$i]: ((identity @ A @ B) <=> (! [C:$i]: ((member @ C @ B) => (apply @ A @ C @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity)). 90.45/24.81 thf(254,plain,((! [A:$i,B:$i]: (((identity @ A @ B) => (! [C:$i]: ((member @ C @ B) => (apply @ A @ C @ C)))) & ((! [C:$i]: ((member @ C @ B) => (apply @ A @ C @ C))) => (identity @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[26])). 90.45/24.81 thf(255,plain,((! [A:$i,B:$i]: ((identity @ A @ B) => (! [C:$i]: ((member @ C @ B) => (apply @ A @ C @ C)))) & ! [A:$i,B:$i]: ((! [C:$i]: ((member @ C @ B) => (apply @ A @ C @ C))) => (identity @ A @ B)))),inference(miniscope,[status(thm)],[254])). 90.45/24.81 thf(256,plain,(! [B:$i,A:$i] : ((member @ (sk38 @ B @ A) @ B) | (identity @ A @ B))),inference(cnf,[status(esa)],[255])). 90.45/24.81 thf(259,plain,(! [B:$i,A:$i] : ((member @ (sk38 @ B @ A) @ B) | (identity @ A @ B))),inference(simp,[status(thm)],[256])). 90.45/24.81 thf(49,plain,(! [C:$i,B:$i,A:$i] : ((~ (member @ C @ (image2 @ A @ B))) | (apply @ A @ (sk6 @ C @ B @ A) @ C))),inference(cnf,[status(esa)],[47])). 90.45/24.81 thf(677,plain,(! [C:$i,B:$i,A:$i] : ((~ (member @ C @ sk5)) | (apply @ A @ (sk6 @ C @ B @ A) @ C) | ((image2 @ sk1 @ sk3) != (image2 @ A @ B)))),inference(paramod_ordered,[status(thm)],[38,49])). 90.45/24.81 thf(678,plain,(! [A:$i] : ((~ (member @ A @ sk5)) | (apply @ sk1 @ (sk6 @ A @ sk3 @ sk1) @ A))),inference(pattern_uni,[status(thm)],[677:[bind(A, $thf(sk1)),bind(B, $thf(sk3))]])). 90.45/24.81 thf(706,plain,(! [A:$i] : ((~ (member @ A @ sk5)) | (apply @ sk1 @ (sk6 @ A @ sk3 @ sk1) @ A))),inference(simp,[status(thm)],[678])). 90.45/24.81 thf(794,plain,(! [C:$i,B:$i,A:$i] : ((identity @ A @ B) | (apply @ sk1 @ (sk6 @ C @ sk3 @ sk1) @ C) | ((member @ (sk38 @ B @ A) @ B) != (member @ C @ sk5)))),inference(paramod_ordered,[status(thm)],[259,706])). 90.45/24.81 thf(795,plain,(! [A:$i] : ((identity @ A @ sk5) | (apply @ sk1 @ (sk6 @ (sk38 @ sk5 @ A) @ sk3 @ sk1) @ (sk38 @ sk5 @ A)))),inference(pattern_uni,[status(thm)],[794:[bind(A, $thf(E)),bind(B, $thf(sk5)),bind(C, $thf(sk38 @ sk5 @ E))]])). 90.45/24.81 thf(829,plain,(! [A:$i] : ((identity @ A @ sk5) | (apply @ sk1 @ (sk6 @ (sk38 @ sk5 @ A) @ sk3 @ sk1) @ (sk38 @ sk5 @ A)))),inference(simp,[status(thm)],[795])). 90.45/24.81 thf(37,plain,((subset @ sk5 @ sk4)),inference(cnf,[status(esa)],[31])). 90.45/24.81 thf(1676,plain,(! [E:$i,D:$i,C:$i,B:$i,A:$i] : ((member @ A @ (product @ B)) | ((member @ (sk14 @ B @ A) @ B) != (member @ C @ (image2 @ D @ (image2 @ E @ empty_set)))))),inference(paramod_ordered,[status(thm)],[134,964])). 90.45/24.81 thf(1677,plain,(! [C:$i,B:$i,A:$i] : ((member @ A @ (product @ (image2 @ B @ (image2 @ C @ empty_set)))))),inference(pattern_uni,[status(thm)],[1676:[bind(A, $thf(G)),bind(B, $thf(image2 @ H @ (image2 @ J @ empty_set))),bind(C, $thf(sk14 @ (image2 @ H @ (image2 @ J @ empty_set)) @ G)),bind(D, $thf(H)),bind(E, $thf(J))]])). 90.45/24.81 thf(1703,plain,(! [C:$i,B:$i,A:$i] : ((member @ A @ (product @ (image2 @ B @ (image2 @ C @ empty_set)))))),inference(simp,[status(thm)],[1677])). 90.45/24.81 thf(376,plain,(! [D:$i,C:$i,B:$i,A:$i] : ((~ (member @ B @ C)) | ((member @ A @ (singleton @ A)) != (member @ B @ (difference @ D @ C))))),inference(paramod_ordered,[status(thm)],[114,167])). 90.45/24.81 thf(382,plain,(! [D:$i,C:$i,B:$i,A:$i] : ((~ (member @ B @ C)) | (A != B) | ((singleton @ A) != (difference @ D @ C)))),inference(simp,[status(thm)],[376])). 90.45/24.81 thf(389,plain,(! [C:$i,B:$i,A:$i] : ((~ (member @ A @ B)) | ((singleton @ A) != (difference @ C @ B)))),inference(simp,[status(thm)],[382])). 90.45/24.81 thf(5,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((member @ D @ C) & ? [E:$i]: ((apply @ A @ D @ E) & (member @ E @ B))) <=> (member @ D @ (inverse_image3 @ A @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_image3)). 90.45/24.81 thf(52,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((((member @ D @ C) & ? [E:$i]: ((apply @ A @ D @ E) & (member @ E @ B))) => (member @ D @ (inverse_image3 @ A @ B @ C))) & ((member @ D @ (inverse_image3 @ A @ B @ C)) => ((member @ D @ C) & ? [E:$i]: ((apply @ A @ D @ E) & (member @ E @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])). 90.45/24.81 thf(1682,plain,(! [E:$i,D:$i,C:$i,B:$i,A:$i] : ((subset @ A @ B) | ((member @ (sk34 @ B @ A) @ A) != (member @ C @ (image2 @ D @ (image2 @ E @ empty_set)))))),inference(paramod_ordered,[status(thm)],[236,964])). 90.45/24.81 thf(1683,plain,(! [C:$i,B:$i,A:$i] : ((subset @ (image2 @ B @ (image2 @ C @ empty_set)) @ A))),inference(pattern_uni,[status(thm)],[1682:[bind(A, $thf(image2 @ H @ (image2 @ J @ empty_set))),bind(B, $thf(F)),bind(C, $thf(sk34 @ F @ (image2 @ H @ (image2 @ J @ empty_set)))),bind(D, $thf(H)),bind(E, $thf(J))]])). 90.45/24.81 thf(1709,plain,(! [C:$i,B:$i,A:$i] : ((subset @ (image2 @ B @ (image2 @ C @ empty_set)) @ A))),inference(simp,[status(thm)],[1683])). 90.45/24.81 thf(1114,plain,(! [C:$i,B:$i,A:$i] : ((sk3 != empty_set) | ((member @ A @ (product @ (image2 @ B @ empty_set))) != (member @ C @ sk5)))),inference(paramod_ordered,[status(thm)],[958,957])). 90.45/24.81 thf(1147,plain,(! [C:$i,B:$i,A:$i] : ((sk3 != empty_set) | (A != C) | ((product @ (image2 @ B @ empty_set)) != sk5))),inference(simp,[status(thm)],[1114])). 90.45/24.81 thf(1159,plain,(! [A:$i] : ((sk3 != empty_set) | ((product @ (image2 @ A @ empty_set)) != sk5))),inference(simp,[status(thm)],[1147])). 90.45/24.81 thf(1428,plain,(! [A:$i] : ((sk3 != empty_set) | ((product @ sk5) != sk5) | ((image2 @ sk1 @ sk3) != (image2 @ A @ empty_set)))),inference(paramod_ordered,[status(thm)],[38,1159])). 90.45/24.81 thf(1429,plain,(! [A:$i] : ((sk3 != empty_set) | ((product @ sk5) != sk5) | (sk1 != A) | (sk3 != empty_set))),inference(simp,[status(thm)],[1428])). 90.45/24.81 thf(1430,plain,((sk3 != empty_set) | ((product @ sk5) != sk5)),inference(simp,[status(thm)],[1429])). 90.45/24.81 thf(867,plain,(! [E:$i,D:$i,C:$i,B:$i,A:$i] : ((~ (member @ C @ (image2 @ A @ B))) | ((member @ (sk6 @ C @ B @ A) @ B) != (member @ D @ (difference @ E @ (product @ empty_set)))))),inference(paramod_ordered,[status(thm)],[50,765])). 90.45/24.81 thf(868,plain,(! [C:$i,B:$i,A:$i] : ((~ (member @ A @ (image2 @ B @ (difference @ C @ (product @ empty_set))))))),inference(pattern_uni,[status(thm)],[867:[bind(A, $thf(H)),bind(B, $thf(difference @ I @ (product @ empty_set))),bind(C, $thf(F)),bind(D, $thf(sk6 @ F @ (difference @ I @ (product @ empty_set)) @ H)),bind(E, $thf(I))]])). 90.45/24.81 thf(929,plain,(! [C:$i,B:$i,A:$i] : ((~ (member @ A @ (image2 @ B @ (difference @ C @ (product @ empty_set))))))),inference(simp,[status(thm)],[868])). 90.45/24.81 thf(2572,plain,(! [E:$i,D:$i,C:$i,B:$i,A:$i] : ((member @ A @ (product @ B)) | ((member @ (sk14 @ B @ A) @ B) != (member @ C @ (image2 @ D @ (difference @ E @ (product @ empty_set))))))),inference(paramod_ordered,[status(thm)],[134,929])). 90.45/24.81 thf(2573,plain,(! [C:$i,B:$i,A:$i] : ((member @ A @ (product @ (image2 @ B @ (difference @ C @ (product @ empty_set))))))),inference(pattern_uni,[status(thm)],[2572:[bind(A, $thf(G)),bind(B, $thf(image2 @ H @ (difference @ J @ (product @ empty_set)))),bind(C, $thf(sk14 @ (image2 @ H @ (difference @ J @ (product @ empty_set))) @ G)),bind(D, $thf(H)),bind(E, $thf(J))]])). 90.45/24.81 thf(2606,plain,(! [C:$i,B:$i,A:$i] : ((member @ A @ (product @ (image2 @ B @ (difference @ C @ (product @ empty_set))))))),inference(simp,[status(thm)],[2573])). 90.45/24.81 thf(3048,plain,(! [D:$i,C:$i,B:$i,A:$i] : (((member @ A @ (product @ (image2 @ B @ (difference @ C @ (product @ empty_set))))) != (member @ D @ empty_set)))),inference(paramod_ordered,[status(thm)],[2606,138])). 90.45/24.81 thf(3116,plain,(! [D:$i,C:$i,B:$i,A:$i] : ((A != D) | ((product @ (image2 @ B @ (difference @ C @ (product @ empty_set)))) != empty_set))),inference(simp,[status(thm)],[3048])). 90.45/24.81 thf(3131,plain,(! [B:$i,A:$i] : (((product @ (image2 @ A @ (difference @ B @ (product @ empty_set)))) != empty_set))),inference(simp,[status(thm)],[3116])). 90.45/24.81 thf(772,plain,(! [D:$i,C:$i,B:$i,A:$i] : ((identity @ A @ B) | ((member @ (sk38 @ B @ A) @ B) != (member @ C @ (difference @ D @ (product @ empty_set)))))),inference(paramod_ordered,[status(thm)],[259,765])). 90.45/24.81 thf(773,plain,(! [B:$i,A:$i] : ((identity @ A @ (difference @ B @ (product @ empty_set))))),inference(pattern_uni,[status(thm)],[772:[bind(A, $thf(F)),bind(B, $thf(difference @ G @ (product @ empty_set))),bind(C, $thf(sk38 @ (difference @ G @ (product @ empty_set)) @ F)),bind(D, $thf(G))]])). 90.45/24.81 thf(785,plain,(! [B:$i,A:$i] : ((identity @ A @ (difference @ B @ (product @ empty_set))))),inference(simp,[status(thm)],[773])). 90.45/24.81 thf(1123,plain,(! [E:$i,D:$i,C:$i,B:$i,A:$i] : ((~ (member @ C @ (difference @ E @ D))) | ((member @ A @ (product @ (image2 @ B @ empty_set))) != (member @ C @ D)))),inference(paramod_ordered,[status(thm)],[958,167])). 90.45/24.81 thf(1124,plain,(! [C:$i,B:$i,A:$i] : ((~ (member @ A @ (difference @ B @ (product @ (image2 @ C @ empty_set))))))),inference(pattern_uni,[status(thm)],[1123:[bind(A, $thf(A)),bind(B, $thf(G)),bind(C, $thf(A)),bind(D, $thf(product @ (image2 @ G @ empty_set))),bind(E, $thf(E))]])). 90.45/24.81 thf(1170,plain,(! [C:$i,B:$i,A:$i] : ((~ (member @ A @ (difference @ B @ (product @ (image2 @ C @ empty_set))))))),inference(simp,[status(thm)],[1124])). 90.45/24.81 thf(2681,plain,(! [E:$i,D:$i,C:$i,B:$i,A:$i] : ((identity @ A @ B) | ((member @ (sk38 @ B @ A) @ B) != (member @ C @ (difference @ D @ (product @ (image2 @ E @ empty_set))))))),inference(paramod_ordered,[status(thm)],[259,1170])). 90.45/24.81 thf(2682,plain,(! [C:$i,B:$i,A:$i] : ((identity @ A @ (difference @ B @ (product @ (image2 @ C @ empty_set)))))),inference(pattern_uni,[status(thm)],[2681:[bind(A, $thf(G)),bind(B, $thf(difference @ H @ (product @ (image2 @ K @ empty_set)))),bind(C, $thf(sk38 @ (difference @ H @ (product @ (image2 @ K @ empty_set))) @ G)),bind(D, $thf(H)),bind(E, $thf(K))]])). 90.45/24.81 thf(2708,plain,(! [C:$i,B:$i,A:$i] : ((identity @ A @ (difference @ B @ (product @ (image2 @ C @ empty_set)))))),inference(simp,[status(thm)],[2682])). 90.45/24.81 thf(53,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((member @ D @ C) & ? [E:$i]: ((apply @ A @ D @ E) & (member @ E @ B))) => (member @ D @ (inverse_image3 @ A @ B @ C))) & ! [A:$i,B:$i,C:$i,D:$i]: ((member @ D @ (inverse_image3 @ A @ B @ C)) => ((member @ D @ C) & ? [E:$i]: ((apply @ A @ D @ E) & (member @ E @ B)))))),inference(miniscope,[status(thm)],[52])). 90.45/24.81 thf(57,plain,(! [E:$i,D:$i,C:$i,B:$i,A:$i] : ((~ (member @ D @ C)) | (~ (apply @ A @ D @ E)) | (~ (member @ E @ B)) | (member @ D @ (inverse_image3 @ A @ B @ C)))),inference(cnf,[status(esa)],[53])). 90.45/24.81 thf(6,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((decreasing @ A @ B @ C @ D @ E) <=> (! [F:$i,G:$i,H:$i,I:$i]: (((member @ F @ B) & (member @ G @ D) & (member @ H @ B) & (member @ I @ D) & (apply @ A @ H @ I) & (apply @ A @ F @ G) & (apply @ C @ F @ H)) => (apply @ E @ I @ G)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',decreasing_function)). 90.45/24.81 thf(61,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((decreasing @ A @ B @ C @ D @ E) => (! [F:$i,G:$i,H:$i,I:$i]: (((member @ F @ B) & (member @ G @ D) & (member @ H @ B) & (member @ I @ D) & (apply @ A @ H @ I) & (apply @ A @ F @ G) & (apply @ C @ F @ H)) => (apply @ E @ I @ G)))) & ((! [F:$i,G:$i,H:$i,I:$i]: (((member @ F @ B) & (member @ G @ D) & (member @ H @ B) & (member @ I @ D) & (apply @ A @ H @ I) & (apply @ A @ F @ G) & (apply @ C @ F @ H)) => (apply @ E @ I @ G))) => (decreasing @ A @ B @ C @ D @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])). 90.45/24.81 thf(62,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((decreasing @ A @ B @ C @ D @ E) => (! [F:$i,G:$i,H:$i,I:$i]: (((member @ F @ B) & (member @ G @ D) & (member @ H @ B) & (member @ I @ D) & (apply @ A @ H @ I) & (apply @ A @ F @ G) & (apply @ C @ F @ H)) => (apply @ E @ I @ G)))) & ! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((! [F:$i,G:$i,H:$i,I:$i]: (((member @ F @ B) & (member @ G @ D) & (member @ H @ B) & (member @ I @ D) & (apply @ A @ H @ I) & (apply @ A @ F @ G) & (apply @ C @ F @ H)) => (apply @ E @ I @ G))) => (decreasing @ A @ B @ C @ D @ E)))),inference(miniscope,[status(thm)],[61])). 90.45/24.81 thf(63,plain,(! [E:$i,D:$i,C:$i,B:$i,A:$i] : ((apply @ A @ (sk8 @ E @ D @ C @ B @ A) @ (sk9 @ E @ D @ C @ B @ A)) | (decreasing @ A @ B @ C @ D @ E))),inference(cnf,[status(esa)],[62])). 90.45/24.81 thf(78,plain,(! [E:$i,D:$i,C:$i,B:$i,A:$i] : ((apply @ A @ (sk8 @ E @ D @ C @ B @ A) @ (sk9 @ E @ D @ C @ B @ A)) | (decreasing @ A @ B @ C @ D @ E))),inference(simp,[status(thm)],[63])). 90.45/24.81 thf(27,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((! [F:$i,G:$i,H:$i,I:$i]: (((member @ F @ B) & (member @ G @ D) & (member @ H @ B) & (member @ I @ D) & (apply @ A @ H @ I) & (apply @ A @ F @ G)) => ((apply @ E @ G @ I) <=> (apply @ C @ F @ H))) & (one_to_one @ A @ B @ D) & (maps @ A @ B @ D)) <=> (isomorphism @ A @ B @ C @ D @ E)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isomorphism)). 90.45/24.81 thf(261,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((! [F:$i,G:$i,H:$i,I:$i]: (((member @ F @ B) & (member @ G @ D) & (member @ H @ B) & (member @ I @ D) & (apply @ A @ H @ I) & (apply @ A @ F @ G)) => (((apply @ E @ G @ I) => (apply @ C @ F @ H)) & ((apply @ C @ F @ H) => (apply @ E @ G @ I)))) & (one_to_one @ A @ B @ D) & (maps @ A @ B @ D)) => (isomorphism @ A @ B @ C @ D @ E)) & ((isomorphism @ A @ B @ C @ D @ E) => (! [F:$i,G:$i,H:$i,I:$i]: (((member @ F @ B) & (member @ G @ D) & (member @ H @ B) & (member @ I @ D) & (apply @ A @ H @ I) & (apply @ A @ F @ G)) => (((apply @ E @ G @ I) => (apply @ C @ F @ H)) & ((apply @ C @ F @ H) => (apply @ E @ G @ I)))) & (one_to_one @ A @ B @ D) & (maps @ A @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[27])). 90.45/24.81 thf(1189,plain,(! [C:$i,B:$i,A:$i] : ((sk3 != empty_set) | ((member @ A @ (product @ (difference @ B @ (product @ empty_set)))) != (member @ C @ sk5)))),inference(paramod_ordered,[status(thm)],[787,957])). 90.45/24.81 thf(1228,plain,(! [C:$i,B:$i,A:$i] : ((sk3 != empty_set) | (A != C) | ((product @ (difference @ B @ (product @ empty_set))) != sk5))),inference(simp,[status(thm)],[1189])). 90.45/24.81 thf(1232,plain,(! [A:$i] : ((sk3 != empty_set) | ((product @ (difference @ A @ (product @ empty_set))) != sk5))),inference(simp,[status(thm)],[1228])). 90.45/24.81 thf(2581,plain,(! [D:$i,C:$i,B:$i,A:$i] : (((member @ A @ (product @ empty_set)) != (member @ B @ (image2 @ C @ (difference @ D @ (product @ empty_set))))))),inference(paramod_ordered,[status(thm)],[668,929])). 90.45/24.81 thf(2594,plain,(! [D:$i,C:$i,B:$i,A:$i] : ((A != B) | ((image2 @ C @ (difference @ D @ (product @ empty_set))) != (product @ empty_set)))),inference(simp,[status(thm)],[2581])). 90.45/24.81 thf(2616,plain,(! [B:$i,A:$i] : (((image2 @ A @ (difference @ B @ (product @ empty_set))) != (product @ empty_set)))),inference(simp,[status(thm)],[2594])). 90.45/24.81 thf(774,plain,(! [D:$i,C:$i,B:$i,A:$i] : ((subset @ A @ B) | ((member @ (sk34 @ B @ A) @ A) != (member @ C @ (difference @ D @ (product @ empty_set)))))),inference(paramod_ordered,[status(thm)],[236,765])). 90.45/24.81 thf(775,plain,(! [B:$i,A:$i] : ((subset @ (difference @ B @ (product @ empty_set)) @ A))),inference(pattern_uni,[status(thm)],[774:[bind(A, $thf(difference @ G @ (product @ empty_set))),bind(B, $thf(E)),bind(C, $thf(sk34 @ E @ (difference @ G @ (product @ empty_set)))),bind(D, $thf(G))]])). 90.45/24.81 thf(789,plain,(! [B:$i,A:$i] : ((subset @ (difference @ B @ (product @ empty_set)) @ A))),inference(simp,[status(thm)],[775])). 90.45/24.81 thf(319,plain,(! [B:$i,A:$i] : (((member @ A @ (singleton @ A)) != (member @ B @ empty_set)))),inference(paramod_ordered,[status(thm)],[114,138])). 90.45/24.81 thf(320,plain,(! [B:$i,A:$i] : ((A != B) | ((singleton @ A) != empty_set))),inference(simp,[status(thm)],[319])). 90.45/24.81 thf(321,plain,(! [A:$i] : (((singleton @ A) != empty_set))),inference(simp,[status(thm)],[320])). 90.45/24.81 thf(2370,plain,(! [E:$i,D:$i,C:$i,B:$i,A:$i] : (((member @ A @ (product @ (image2 @ B @ (image2 @ C @ empty_set)))) != (member @ D @ (image2 @ E @ empty_set))))),inference(paramod_ordered,[status(thm)],[1703,925])). 90.45/24.81 thf(2416,plain,(! [E:$i,D:$i,C:$i,B:$i,A:$i] : ((A != D) | ((product @ (image2 @ B @ (image2 @ C @ empty_set))) != (image2 @ E @ empty_set)))),inference(simp,[status(thm)],[2370])). 90.45/24.81 thf(2469,plain,(! [C:$i,B:$i,A:$i] : (((product @ (image2 @ A @ (image2 @ B @ empty_set))) != (image2 @ C @ empty_set)))),inference(simp,[status(thm)],[2416])). 90.45/24.81 thf(340,plain,(! [C:$i,B:$i,A:$i] : (((member @ B @ (unordered_pair @ A @ B)) != (member @ C @ empty_set)))),inference(paramod_ordered,[status(thm)],[293,138])). 90.45/24.81 thf(345,plain,(! [C:$i,B:$i,A:$i] : ((B != C) | ((unordered_pair @ A @ B) != empty_set))),inference(simp,[status(thm)],[340])). 90.45/24.81 thf(353,plain,(! [B:$i,A:$i] : (((unordered_pair @ A @ B) != empty_set))),inference(simp,[status(thm)],[345])). 90.45/24.81 thf(290,plain,(! [C:$i,B:$i,A:$i] : ((~ (B = A)) | (member @ A @ (unordered_pair @ B @ C)))),inference(cnf,[status(esa)],[288])). 90.45/24.81 thf(294,plain,(! [C:$i,B:$i,A:$i] : ((B != A) | (member @ A @ (unordered_pair @ B @ C)))),inference(lifteq,[status(thm)],[290])). 90.45/24.81 thf(295,plain,(! [B:$i,A:$i] : ((member @ A @ (unordered_pair @ A @ B)))),inference(simp,[status(thm)],[294])). 90.45/24.81 thf(445,plain,(! [D:$i,C:$i,B:$i,A:$i] : (((member @ A @ (unordered_pair @ A @ B)) != (member @ D @ (difference @ C @ (singleton @ D)))))),inference(paramod_ordered,[status(thm)],[295,390])). 90.45/24.81 thf(449,plain,(! [D:$i,C:$i,B:$i,A:$i] : ((A != D) | ((unordered_pair @ A @ B) != (difference @ C @ (singleton @ D))))),inference(simp,[status(thm)],[445])). 90.45/24.81 thf(453,plain,(! [C:$i,B:$i,A:$i] : (((unordered_pair @ C @ A) != (difference @ B @ (singleton @ C))))),inference(simp,[status(thm)],[449])). 90.45/24.81 thf(975,plain,(! [C:$i,B:$i,A:$i] : ((sk3 != empty_set) | ((member @ B @ (unordered_pair @ A @ B)) != (member @ C @ sk5)))),inference(paramod_ordered,[status(thm)],[293,957])). 90.45/24.81 thf(987,plain,(! [C:$i,B:$i,A:$i] : ((sk3 != empty_set) | (B != C) | ((unordered_pair @ A @ B) != sk5))),inference(simp,[status(thm)],[975])). 90.45/24.81 thf(998,plain,(! [B:$i,A:$i] : ((sk3 != empty_set) | ((unordered_pair @ A @ B) != sk5))),inference(simp,[status(thm)],[987])). 90.45/24.81 thf(65,plain,(! [E:$i,D:$i,C:$i,B:$i,A:$i] : ((member @ (sk10 @ E @ D @ C @ B @ A) @ B) | (decreasing @ A @ B @ C @ D @ E))),inference(cnf,[status(esa)],[62])). 90.45/24.81 thf(74,plain,(! [E:$i,D:$i,C:$i,B:$i,A:$i] : ((member @ (sk10 @ E @ D @ C @ B @ A) @ B) | (decreasing @ A @ B @ C @ D @ E))),inference(simp,[status(thm)],[65])). 90.45/24.81 thf(56,plain,(! [D:$i,C:$i,B:$i,A:$i] : ((~ (member @ D @ (inverse_image3 @ A @ B @ C))) | (member @ (sk7 @ D @ C @ B @ A) @ B))),inference(cnf,[status(esa)],[53])). 90.45/24.81 thf(60,plain,(! [D:$i,C:$i,B:$i,A:$i] : ((~ (member @ D @ (inverse_image3 @ A @ B @ C))) | (member @ (sk7 @ D @ C @ B @ A) @ B))),inference(simp,[status(thm)],[56])). 90.45/24.81 thf(8,axiom,((! [A:$i,B:$i,C:$i]: ((member @ A @ (intersection @ B @ C)) <=> ((member @ A @ B) & (member @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection)). 90.45/24.81 thf(85,plain,((! [A:$i,B:$i,C:$i]: (((member @ A @ (intersection @ B @ C)) => ((member @ A @ B) & (member @ A @ C))) & (((member @ A @ B) & (member @ A @ C)) => (member @ A @ (intersection @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8])). 90.45/24.81 thf(718,plain,(! [B:$i,A:$i] : (((member @ A @ (product @ empty_set)) != (member @ B @ empty_set)))),inference(paramod_ordered,[status(thm)],[668,138])). 90.45/24.81 thf(743,plain,(! [B:$i,A:$i] : ((A != B) | ((product @ empty_set) != empty_set))),inference(simp,[status(thm)],[718])). 90.45/24.81 thf(761,plain,(((product @ empty_set) != empty_set)),inference(simp,[status(thm)],[743])). 90.45/24.81 thf(1719,plain,(! [C:$i,B:$i,A:$i] : ((subset @ sk5 @ A) | ((image2 @ sk1 @ sk3) != (image2 @ B @ (image2 @ C @ empty_set))))),inference(paramod_ordered,[status(thm)],[38,1709])). 90.45/24.81 thf(1721,plain,(! [C:$i,B:$i,A:$i] : ((subset @ sk5 @ A) | (sk1 != B) | ((image2 @ C @ empty_set) != sk3))),inference(simp,[status(thm)],[1719])). 90.45/24.81 thf(1723,plain,(! [B:$i,A:$i] : ((subset @ sk5 @ A) | ((image2 @ B @ empty_set) != sk3))),inference(simp,[status(thm)],[1721])). 90.45/24.81 thf(1111,plain,(! [E:$i,D:$i,C:$i,B:$i,A:$i] : (((singleton @ C) != (difference @ E @ D)) | ((member @ A @ (product @ (image2 @ B @ empty_set))) != (member @ C @ D)))),inference(paramod_ordered,[status(thm)],[958,389])). 90.45/24.81 thf(1112,plain,(! [C:$i,B:$i,A:$i] : (((singleton @ A) != (difference @ B @ (product @ (image2 @ C @ empty_set)))))),inference(pattern_uni,[status(thm)],[1111:[bind(A, $thf(A)),bind(B, $thf(G)),bind(C, $thf(A)),bind(D, $thf(product @ (image2 @ G @ empty_set))),bind(E, $thf(E))]])). 90.45/24.81 thf(1174,plain,(! [C:$i,B:$i,A:$i] : (((singleton @ A) != (difference @ B @ (product @ (image2 @ C @ empty_set)))))),inference(simp,[status(thm)],[1112])). 90.45/24.81 thf(30,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((increasing @ A @ B @ C @ D @ E) <=> (! [F:$i,G:$i,H:$i,I:$i]: (((member @ H @ B) & (apply @ C @ F @ H) & (apply @ A @ H @ I) & (apply @ A @ F @ G) & (member @ I @ D) & (member @ G @ D) & (member @ F @ B)) => (apply @ E @ G @ I)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',increasing_function)). 90.45/24.81 thf(297,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((increasing @ A @ B @ C @ D @ E) => (! [F:$i,G:$i,H:$i,I:$i]: (((member @ H @ B) & (apply @ C @ F @ H) & (apply @ A @ H @ I) & (apply @ A @ F @ G) & (member @ I @ D) & (member @ G @ D) & (member @ F @ B)) => (apply @ E @ G @ I)))) & ((! [F:$i,G:$i,H:$i,I:$i]: (((member @ H @ B) & (apply @ C @ F @ H) & (apply @ A @ H @ I) & (apply @ A @ F @ G) & (member @ I @ D) & (member @ G @ D) & (member @ F @ B)) => (apply @ E @ G @ I))) => (increasing @ A @ B @ C @ D @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[30])). 90.45/24.81 thf(769,plain,(! [D:$i,C:$i,B:$i,A:$i] : (((member @ B @ (unordered_pair @ A @ B)) != (member @ C @ (difference @ D @ (product @ empty_set)))))),inference(paramod_ordered,[status(thm)],[293,765])). 90.45/24.81 thf(781,plain,(! [D:$i,C:$i,B:$i,A:$i] : ((B != C) | ((unordered_pair @ A @ B) != (difference @ D @ (product @ empty_set))))),inference(simp,[status(thm)],[769])). 90.45/24.81 thf(788,plain,(! [C:$i,B:$i,A:$i] : (((unordered_pair @ A @ B) != (difference @ C @ (product @ empty_set))))),inference(simp,[status(thm)],[781])). 90.45/24.81 thf(33,plain,((maps @ sk1 @ sk3 @ sk4)),inference(cnf,[status(esa)],[31])). 90.45/24.81 thf(3311,plain,(! [E:$i,D:$i,C:$i,B:$i,A:$i] : ((subset @ A @ B) | ((member @ (sk34 @ B @ A) @ A) != (member @ C @ (difference @ D @ (product @ (difference @ E @ (product @ empty_set)))))))),inference(paramod_ordered,[status(thm)],[236,1244])). 90.45/24.81 thf(3312,plain,(! [C:$i,B:$i,A:$i] : ((subset @ (difference @ B @ (product @ (difference @ C @ (product @ empty_set)))) @ A))),inference(pattern_uni,[status(thm)],[3311:[bind(A, $thf(difference @ H @ (product @ (difference @ K @ (product @ empty_set))))),bind(B, $thf(F)),bind(C, $thf(sk34 @ F @ (difference @ H @ (product @ (difference @ K @ (product @ empty_set)))))),bind(D, $thf(H)),bind(E, $thf(K))]])). 90.45/24.81 thf(3339,plain,(! [C:$i,B:$i,A:$i] : ((subset @ (difference @ B @ (product @ (difference @ C @ (product @ empty_set)))) @ A))),inference(simp,[status(thm)],[3312])). 90.45/24.81 thf(1724,plain,(! [E:$i,D:$i,C:$i,B:$i,A:$i] : ((~ (member @ D @ (inverse_image3 @ A @ B @ C))) | ((member @ (sk7 @ D @ C @ B @ A) @ B) != (member @ E @ empty_set)))),inference(paramod_ordered,[status(thm)],[60,138])). 90.45/24.81 thf(1725,plain,(! [C:$i,B:$i,A:$i] : ((~ (member @ A @ (inverse_image3 @ C @ empty_set @ B))))),inference(pattern_uni,[status(thm)],[1724:[bind(A, $thf(I)),bind(B, $thf(empty_set)),bind(C, $thf(G)),bind(D, $thf(F)),bind(E, $thf(sk7 @ F @ G @ empty_set @ I))]])). 90.45/24.81 thf(1846,plain,(! [C:$i,B:$i,A:$i] : ((~ (member @ A @ (inverse_image3 @ C @ empty_set @ B))))),inference(simp,[status(thm)],[1725])). 90.45/24.81 thf(1865,plain,(! [E:$i,D:$i,C:$i,B:$i,A:$i] : (((member @ A @ (product @ (difference @ B @ (product @ empty_set)))) != (member @ C @ (inverse_image3 @ E @ empty_set @ D))))),inference(paramod_ordered,[status(thm)],[787,1846])). 90.45/24.81 thf(1879,plain,(! [E:$i,D:$i,C:$i,B:$i,A:$i] : ((A != C) | ((product @ (difference @ B @ (product @ empty_set))) != (inverse_image3 @ E @ empty_set @ D)))),inference(simp,[status(thm)],[1865])). 90.45/24.81 thf(1883,plain,(! [C:$i,B:$i,A:$i] : (((product @ (difference @ A @ (product @ empty_set))) != (inverse_image3 @ C @ empty_set @ B)))),inference(simp,[status(thm)],[1879])). 90.45/24.81 thf(2362,plain,(! [D:$i,C:$i,B:$i,A:$i] : (((member @ A @ (product @ (image2 @ B @ (image2 @ C @ empty_set)))) != (member @ D @ empty_set)))),inference(paramod_ordered,[status(thm)],[1703,138])). 90.45/24.81 thf(2431,plain,(! [D:$i,C:$i,B:$i,A:$i] : ((A != D) | ((product @ (image2 @ B @ (image2 @ C @ empty_set))) != empty_set))),inference(simp,[status(thm)],[2362])). 90.45/24.81 thf(2468,plain,(! [B:$i,A:$i] : (((product @ (image2 @ A @ (image2 @ B @ empty_set))) != empty_set))),inference(simp,[status(thm)],[2431])). 90.45/24.81 thf(2561,plain,(! [B:$i,A:$i] : (((product @ (image2 @ A @ sk5)) != empty_set) | ((image2 @ sk1 @ sk3) != (image2 @ B @ empty_set)))),inference(paramod_ordered,[status(thm)],[38,2468])). 90.45/24.81 thf(2563,plain,(! [B:$i,A:$i] : (((product @ (image2 @ A @ sk5)) != empty_set) | (sk1 != B) | (sk3 != empty_set))),inference(simp,[status(thm)],[2561])). 90.45/24.81 thf(2565,plain,(! [A:$i] : (((product @ (image2 @ A @ sk5)) != empty_set) | (sk3 != empty_set))),inference(simp,[status(thm)],[2563])). 90.45/24.81 thf(1863,plain,(! [E:$i,D:$i,C:$i,B:$i,A:$i] : ((identity @ A @ B) | ((member @ (sk38 @ B @ A) @ B) != (member @ C @ (inverse_image3 @ E @ empty_set @ D))))),inference(paramod_ordered,[status(thm)],[259,1846])). 90.45/24.81 thf(1864,plain,(! [C:$i,B:$i,A:$i] : ((identity @ A @ (inverse_image3 @ B @ empty_set @ C)))),inference(pattern_uni,[status(thm)],[1863:[bind(A, $thf(G)),bind(B, $thf(inverse_image3 @ H @ empty_set @ J)),bind(C, $thf(sk38 @ (inverse_image3 @ H @ empty_set @ J) @ G)),bind(D, $thf(J)),bind(E, $thf(H))]])). 90.45/24.81 thf(1888,plain,(! [C:$i,B:$i,A:$i] : ((identity @ A @ (inverse_image3 @ B @ empty_set @ C)))),inference(simp,[status(thm)],[1864])). 90.45/24.81 thf(1860,plain,(! [E:$i,D:$i,C:$i,B:$i,A:$i] : ((member @ A @ (product @ B)) | ((member @ (sk14 @ B @ A) @ B) != (member @ C @ (inverse_image3 @ E @ empty_set @ D))))),inference(paramod_ordered,[status(thm)],[134,1846])). 90.45/24.81 thf(1861,plain,(! [C:$i,B:$i,A:$i] : ((member @ A @ (product @ (inverse_image3 @ B @ empty_set @ C))))),inference(pattern_uni,[status(thm)],[1860:[bind(A, $thf(G)),bind(B, $thf(inverse_image3 @ H @ empty_set @ J)),bind(C, $thf(sk14 @ (inverse_image3 @ H @ empty_set @ J) @ G)),bind(D, $thf(J)),bind(E, $thf(H))]])). 90.45/24.81 thf(1894,plain,(! [C:$i,B:$i,A:$i] : ((member @ A @ (product @ (inverse_image3 @ B @ empty_set @ C))))),inference(simp,[status(thm)],[1861])). 90.45/24.81 thf(2260,plain,(! [E:$i,D:$i,C:$i,B:$i,A:$i] : (((member @ A @ (product @ (inverse_image3 @ B @ empty_set @ C))) != (member @ D @ (image2 @ E @ empty_set))))),inference(paramod_ordered,[status(thm)],[1894,925])). 90.45/24.81 thf(2307,plain,(! [E:$i,D:$i,C:$i,B:$i,A:$i] : ((A != D) | ((product @ (inverse_image3 @ B @ empty_set @ C)) != (image2 @ E @ empty_set)))),inference(simp,[status(thm)],[2260])). 90.45/24.81 thf(2327,plain,(! [C:$i,B:$i,A:$i] : (((product @ (inverse_image3 @ A @ empty_set @ B)) != (image2 @ C @ empty_set)))),inference(simp,[status(thm)],[2307])). 90.45/24.81 thf(374,plain,(! [E:$i,D:$i,C:$i,B:$i,A:$i] : ((~ (member @ C @ (difference @ E @ D))) | ((member @ A @ (unordered_pair @ A @ B)) != (member @ C @ D)))),inference(paramod_ordered,[status(thm)],[295,167])). 90.45/24.81 thf(375,plain,(! [C:$i,B:$i,A:$i] : ((~ (member @ B @ (difference @ A @ (unordered_pair @ B @ C)))))),inference(pattern_uni,[status(thm)],[374:[bind(A, $thf(F)),bind(B, $thf(G)),bind(C, $thf(F)),bind(D, $thf(unordered_pair @ F @ G))]])). 90.45/24.81 thf(388,plain,(! [C:$i,B:$i,A:$i] : ((~ (member @ B @ (difference @ A @ (unordered_pair @ B @ C)))))),inference(simp,[status(thm)],[375])). 90.45/24.81 thf(721,plain,(! [D:$i,C:$i,B:$i,A:$i] : (((member @ A @ (product @ empty_set)) != (member @ C @ (difference @ B @ (unordered_pair @ C @ D)))))),inference(paramod_ordered,[status(thm)],[668,388])). 90.45/24.81 thf(742,plain,(! [D:$i,C:$i,B:$i,A:$i] : ((A != C) | ((difference @ B @ (unordered_pair @ C @ D)) != (product @ empty_set)))),inference(simp,[status(thm)],[721])). 90.45/24.81 thf(757,plain,(! [C:$i,B:$i,A:$i] : (((difference @ A @ (unordered_pair @ B @ C)) != (product @ empty_set)))),inference(simp,[status(thm)],[742])). 90.45/24.81 thf(945,plain,(! [D:$i,C:$i,B:$i,A:$i] : ((subset @ A @ B) | ((member @ (sk34 @ B @ A) @ A) != (member @ C @ (image2 @ D @ empty_set))))),inference(paramod_ordered,[status(thm)],[236,925])). 90.45/24.81 thf(946,plain,(! [B:$i,A:$i] : ((subset @ (image2 @ B @ empty_set) @ A))),inference(pattern_uni,[status(thm)],[945:[bind(A, $thf(image2 @ G @ empty_set)),bind(B, $thf(E)),bind(C, $thf(sk34 @ E @ (image2 @ G @ empty_set))),bind(D, $thf(G))]])). 90.45/24.81 thf(963,plain,(! [B:$i,A:$i] : ((subset @ (image2 @ B @ empty_set) @ A))),inference(simp,[status(thm)],[946])). 90.45/24.81 thf(972,plain,(! [B:$i,A:$i] : ((subset @ sk5 @ A) | ((image2 @ sk1 @ sk3) != (image2 @ B @ empty_set)))),inference(paramod_ordered,[status(thm)],[38,963])). 90.45/24.81 thf(973,plain,(! [B:$i,A:$i] : ((subset @ sk5 @ A) | (sk1 != B) | (sk3 != empty_set))),inference(simp,[status(thm)],[972])). 90.45/24.81 thf(974,plain,(! [A:$i] : ((subset @ sk5 @ A) | (sk3 != empty_set))),inference(simp,[status(thm)],[973])). 90.45/24.81 thf(1192,plain,(! [D:$i,C:$i,B:$i,A:$i] : (((member @ A @ (product @ (difference @ B @ (product @ empty_set)))) != (member @ C @ (difference @ D @ (product @ empty_set)))))),inference(paramod_ordered,[status(thm)],[787,765])). 90.45/24.81 thf(1223,plain,(! [D:$i,C:$i,B:$i,A:$i] : ((A != C) | ((product @ (difference @ B @ (product @ empty_set))) != (difference @ D @ (product @ empty_set))))),inference(simp,[status(thm)],[1192])). 90.45/24.81 thf(1234,plain,(! [B:$i,A:$i] : (((product @ (difference @ A @ (product @ empty_set))) != (difference @ B @ (product @ empty_set))))),inference(simp,[status(thm)],[1223])). 90.45/24.81 thf(66,plain,(! [E:$i,D:$i,C:$i,B:$i,A:$i] : ((apply @ A @ (sk10 @ E @ D @ C @ B @ A) @ (sk11 @ E @ D @ C @ B @ A)) | (decreasing @ A @ B @ C @ D @ E))),inference(cnf,[status(esa)],[62])). 90.45/24.81 thf(77,plain,(! [E:$i,D:$i,C:$i,B:$i,A:$i] : ((apply @ A @ (sk10 @ E @ D @ C @ B @ A) @ (sk11 @ E @ D @ C @ B @ A)) | (decreasing @ A @ B @ C @ D @ E))),inference(simp,[status(thm)],[66])). 90.45/24.81 thf(1422,plain,(! [B:$i,A:$i] : (((difference @ B @ (product @ empty_set)) != (product @ sk5)) | ((image2 @ sk1 @ sk3) != (image2 @ A @ empty_set)))),inference(paramod_ordered,[status(thm)],[38,1168])). 90.45/24.81 thf(1423,plain,(! [B:$i,A:$i] : (((difference @ B @ (product @ empty_set)) != (product @ sk5)) | (sk1 != A) | (sk3 != empty_set))),inference(simp,[status(thm)],[1422])). 90.45/24.81 thf(1424,plain,(! [A:$i] : (((difference @ A @ (product @ empty_set)) != (product @ sk5)) | (sk3 != empty_set))),inference(simp,[status(thm)],[1423])). 90.45/24.81 thf(2578,plain,(! [E:$i,D:$i,C:$i,B:$i,A:$i] : ((subset @ A @ B) | ((member @ (sk34 @ B @ A) @ A) != (member @ C @ (image2 @ D @ (difference @ E @ (product @ empty_set))))))),inference(paramod_ordered,[status(thm)],[236,929])). 90.45/24.81 thf(2579,plain,(! [C:$i,B:$i,A:$i] : ((subset @ (image2 @ B @ (difference @ C @ (product @ empty_set))) @ A))),inference(pattern_uni,[status(thm)],[2578:[bind(A, $thf(image2 @ H @ (difference @ J @ (product @ empty_set)))),bind(B, $thf(F)),bind(C, $thf(sk34 @ F @ (image2 @ H @ (difference @ J @ (product @ empty_set))))),bind(D, $thf(H)),bind(E, $thf(J))]])). 90.45/24.81 thf(2613,plain,(! [C:$i,B:$i,A:$i] : ((subset @ (image2 @ B @ (difference @ C @ (product @ empty_set))) @ A))),inference(simp,[status(thm)],[2579])). 90.45/24.81 thf(2252,plain,(! [D:$i,C:$i,B:$i,A:$i] : (((member @ A @ (product @ (inverse_image3 @ B @ empty_set @ C))) != (member @ D @ empty_set)))),inference(paramod_ordered,[status(thm)],[1894,138])). 90.45/24.81 thf(2310,plain,(! [D:$i,C:$i,B:$i,A:$i] : ((A != D) | ((product @ (inverse_image3 @ B @ empty_set @ C)) != empty_set))),inference(simp,[status(thm)],[2252])). 90.45/24.81 thf(2349,plain,(! [B:$i,A:$i] : (((product @ (inverse_image3 @ A @ empty_set @ B)) != empty_set))),inference(simp,[status(thm)],[2310])). 90.45/24.81 thf(3308,plain,(! [E:$i,D:$i,C:$i,B:$i,A:$i] : ((identity @ A @ B) | ((member @ (sk38 @ B @ A) @ B) != (member @ C @ (difference @ D @ (product @ (difference @ E @ (product @ empty_set)))))))),inference(paramod_ordered,[status(thm)],[259,1244])). 90.45/24.81 thf(3309,plain,(! [C:$i,B:$i,A:$i] : ((identity @ A @ (difference @ B @ (product @ (difference @ C @ (product @ empty_set))))))),inference(pattern_uni,[status(thm)],[3308:[bind(A, $thf(G)),bind(B, $thf(difference @ H @ (product @ (difference @ K @ (product @ empty_set))))),bind(C, $thf(sk38 @ (difference @ H @ (product @ (difference @ K @ (product @ empty_set)))) @ G)),bind(D, $thf(H)),bind(E, $thf(K))]])). 90.45/24.81 thf(3354,plain,(! [C:$i,B:$i,A:$i] : ((identity @ A @ (difference @ B @ (product @ (difference @ C @ (product @ empty_set))))))),inference(simp,[status(thm)],[3309])). 90.45/24.81 thf(1185,plain,(! [C:$i,B:$i,A:$i] : (((member @ A @ (product @ (difference @ B @ (product @ empty_set)))) != (member @ C @ empty_set)))),inference(paramod_ordered,[status(thm)],[787,138])). 90.45/24.81 thf(1225,plain,(! [C:$i,B:$i,A:$i] : ((A != C) | ((product @ (difference @ B @ (product @ empty_set))) != empty_set))),inference(simp,[status(thm)],[1185])). 90.45/24.81 thf(1246,plain,(! [A:$i] : (((product @ (difference @ A @ (product @ empty_set))) != empty_set))),inference(simp,[status(thm)],[1225])). 90.45/24.81 thf(1678,plain,(! [E:$i,D:$i,C:$i,B:$i,A:$i] : (((member @ A @ (product @ (image2 @ B @ empty_set))) != (member @ C @ (image2 @ D @ (image2 @ E @ empty_set)))))),inference(paramod_ordered,[status(thm)],[958,964])). 90.45/24.81 thf(1699,plain,(! [E:$i,D:$i,C:$i,B:$i,A:$i] : ((A != C) | ((product @ (image2 @ B @ empty_set)) != (image2 @ D @ (image2 @ E @ empty_set))))),inference(simp,[status(thm)],[1678])). 90.45/24.81 thf(1715,plain,(! [C:$i,B:$i,A:$i] : (((product @ (image2 @ A @ empty_set)) != (image2 @ B @ (image2 @ C @ empty_set))))),inference(simp,[status(thm)],[1699])). 90.45/24.81 thf(70,plain,(! [E:$i,D:$i,C:$i,B:$i,A:$i] : ((apply @ C @ (sk8 @ E @ D @ C @ B @ A) @ (sk10 @ E @ D @ C @ B @ A)) | (decreasing @ A @ B @ C @ D @ E))),inference(cnf,[status(esa)],[62])). 90.45/24.81 thf(73,plain,(! [E:$i,D:$i,C:$i,B:$i,A:$i] : ((apply @ C @ (sk8 @ E @ D @ C @ B @ A) @ (sk10 @ E @ D @ C @ B @ A)) | (decreasing @ A @ B @ C @ D @ E))),inference(simp,[status(thm)],[70])). 90.45/24.81 thf(25,axiom,((! [A:$i,B:$i,C:$i]: ((injective @ A @ B @ C) <=> (! [D:$i,E:$i,F:$i]: (((E = D) <= ((apply @ A @ E @ F) & (apply @ A @ D @ F))) <= ((member @ D @ B) & (member @ E @ B) & (member @ F @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',injective)). 90.45/24.81 thf(237,plain,((! [A:$i,B:$i,C:$i]: (((injective @ A @ B @ C) => (! [D:$i,E:$i,F:$i]: ((E = D) | ~ ((apply @ A @ E @ F) & (apply @ A @ D @ F)) | ~ ((member @ D @ B) & (member @ E @ B) & (member @ F @ C))))) & ((! [D:$i,E:$i,F:$i]: ((E = D) | ~ ((apply @ A @ E @ F) & (apply @ A @ D @ F)) | ~ ((member @ D @ B) & (member @ E @ B) & (member @ F @ C)))) => (injective @ A @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[25])). 90.45/24.81 thf(21,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((! [E:$i,F:$i,G:$i]: (((member @ E @ C) & (member @ G @ D) & (member @ F @ D)) => ((F = G) <= ((apply @ B @ E @ G) & (apply @ A @ E @ F))))) <=> (equal_maps @ A @ B @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_maps)). 90.45/24.81 thf(205,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((! [E:$i,F:$i,G:$i]: (((member @ E @ C) & (member @ G @ D) & (member @ F @ D)) => ((F = G) | ~ ((apply @ B @ E @ G) & (apply @ A @ E @ F))))) => (equal_maps @ A @ B @ C @ D)) & ((equal_maps @ A @ B @ C @ D) => (! [E:$i,F:$i,G:$i]: (((member @ E @ C) & (member @ G @ D) & (member @ F @ D)) => ((F = G) | ~ ((apply @ B @ E @ G) & (apply @ A @ E @ F))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[21])). 90.45/24.81 thf(1679,plain,(! [E:$i,D:$i,C:$i,B:$i,A:$i] : ((identity @ A @ B) | ((member @ (sk38 @ B @ A) @ B) != (member @ C @ (image2 @ D @ (image2 @ E @ empty_set)))))),inference(paramod_ordered,[status(thm)],[259,964])). 90.45/24.81 thf(1680,plain,(! [C:$i,B:$i,A:$i] : ((identity @ A @ (image2 @ B @ (image2 @ C @ empty_set))))),inference(pattern_uni,[status(thm)],[1679:[bind(A, $thf(G)),bind(B, $thf(image2 @ H @ (image2 @ J @ empty_set))),bind(C, $thf(sk38 @ (image2 @ H @ (image2 @ J @ empty_set)) @ G)),bind(D, $thf(H)),bind(E, $thf(J))]])). 90.45/24.81 thf(1712,plain,(! [C:$i,B:$i,A:$i] : ((identity @ A @ (image2 @ B @ (image2 @ C @ empty_set))))),inference(simp,[status(thm)],[1680])). 90.45/24.81 thf(1868,plain,(! [D:$i,C:$i,B:$i,A:$i] : (((member @ A @ (product @ empty_set)) != (member @ B @ (inverse_image3 @ D @ empty_set @ C))))),inference(paramod_ordered,[status(thm)],[668,1846])). 90.45/24.81 thf(1876,plain,(! [D:$i,C:$i,B:$i,A:$i] : ((A != B) | ((inverse_image3 @ D @ empty_set @ C) != (product @ empty_set)))),inference(simp,[status(thm)],[1868])). 90.45/24.81 thf(1895,plain,(! [B:$i,A:$i] : (((inverse_image3 @ B @ empty_set @ A) != (product @ empty_set)))),inference(simp,[status(thm)],[1876])). 90.45/24.81 thf(2575,plain,(! [E:$i,D:$i,C:$i,B:$i,A:$i] : ((identity @ A @ B) | ((member @ (sk38 @ B @ A) @ B) != (member @ C @ (image2 @ D @ (difference @ E @ (product @ empty_set))))))),inference(paramod_ordered,[status(thm)],[259,929])). 90.45/24.81 thf(2576,plain,(! [C:$i,B:$i,A:$i] : ((identity @ A @ (image2 @ B @ (difference @ C @ (product @ empty_set)))))),inference(pattern_uni,[status(thm)],[2575:[bind(A, $thf(G)),bind(B, $thf(image2 @ H @ (difference @ J @ (product @ empty_set)))),bind(C, $thf(sk38 @ (image2 @ H @ (difference @ J @ (product @ empty_set))) @ G)),bind(D, $thf(H)),bind(E, $thf(J))]])). 90.45/24.81 thf(2617,plain,(! [C:$i,B:$i,A:$i] : ((identity @ A @ (image2 @ B @ (difference @ C @ (product @ empty_set)))))),inference(simp,[status(thm)],[2576])). 90.45/24.81 thf(951,plain,(! [C:$i,B:$i,A:$i] : (((member @ A @ (singleton @ A)) != (member @ B @ (image2 @ C @ empty_set))))),inference(paramod_ordered,[status(thm)],[114,925])). 90.45/24.81 thf(955,plain,(! [C:$i,B:$i,A:$i] : ((A != B) | ((singleton @ A) != (image2 @ C @ empty_set)))),inference(simp,[status(thm)],[951])). 90.45/24.81 thf(965,plain,(! [B:$i,A:$i] : (((singleton @ A) != (image2 @ B @ empty_set)))),inference(simp,[status(thm)],[955])). 90.45/24.81 thf(34,plain,((~ (maps @ sk2 @ sk3 @ sk5))),inference(cnf,[status(esa)],[31])). 90.45/24.81 thf(3,axiom,((! [A:$i,B:$i,C:$i]: (((injective @ A @ B @ C) & (surjective @ A @ B @ C)) <=> (one_to_one @ A @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',one_to_one)). 90.45/24.81 thf(39,plain,((! [A:$i,B:$i,C:$i]: ((((injective @ A @ B @ C) & (surjective @ A @ B @ C)) => (one_to_one @ A @ B @ C)) & ((one_to_one @ A @ B @ C) => ((injective @ A @ B @ C) & (surjective @ A @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])). 90.45/24.81 thf(40,plain,((! [A:$i,B:$i,C:$i]: (((injective @ A @ B @ C) & (surjective @ A @ B @ C)) => (one_to_one @ A @ B @ C)) & ! [A:$i,B:$i,C:$i]: ((one_to_one @ A @ B @ C) => ((injective @ A @ B @ C) & (surjective @ A @ B @ C))))),inference(miniscope,[status(thm)],[39])). 90.45/24.81 thf(42,plain,(! [C:$i,B:$i,A:$i] : ((~ (one_to_one @ A @ B @ C)) | (surjective @ A @ B @ C))),inference(cnf,[status(esa)],[40])). 90.45/24.81 thf(45,plain,(! [C:$i,B:$i,A:$i] : ((~ (one_to_one @ A @ B @ C)) | (surjective @ A @ B @ C))),inference(simp,[status(thm)],[42])). 90.45/24.81 thf(796,plain,(! [C:$i,B:$i,A:$i] : ((subset @ A @ B) | (apply @ sk1 @ (sk6 @ C @ sk3 @ sk1) @ C) | ((member @ (sk34 @ B @ A) @ A) != (member @ C @ sk5)))),inference(paramod_ordered,[status(thm)],[236,706])). 90.45/24.81 thf(797,plain,(! [A:$i] : ((subset @ sk5 @ A) | (apply @ sk1 @ (sk6 @ (sk34 @ A @ sk5) @ sk3 @ sk1) @ (sk34 @ A @ sk5)))),inference(pattern_uni,[status(thm)],[796:[bind(A, $thf(sk5)),bind(B, $thf(D)),bind(C, $thf(sk34 @ D @ sk5))]])). 90.45/24.81 thf(819,plain,(! [A:$i] : ((subset @ sk5 @ A) | (apply @ sk1 @ (sk6 @ (sk34 @ A @ sk5) @ sk3 @ sk1) @ (sk34 @ A @ sk5)))),inference(simp,[status(thm)],[797])). 90.45/24.81 thf(35,plain,(! [B:$i,A:$i] : ((~ (apply @ sk2 @ A @ B)) | (apply @ sk1 @ A @ B) | (~ (member @ B @ sk5)) | (~ (member @ A @ sk3)))),inference(cnf,[status(esa)],[31])). 90.45/24.81 thf(322,plain,(! [C:$i,B:$i,A:$i] : ((~ (apply @ sk2 @ B @ C)) | (apply @ sk1 @ B @ C) | (~ (member @ B @ sk3)) | ((member @ A @ (singleton @ A)) != (member @ C @ sk5)))),inference(paramod_ordered,[status(thm)],[114,35])). 90.45/24.81 thf(324,plain,(! [C:$i,B:$i,A:$i] : ((apply @ sk1 @ B @ C) | (~ (apply @ sk2 @ B @ C)) | (~ (member @ B @ sk3)) | (A != C) | ((singleton @ A) != sk5))),inference(simp,[status(thm)],[322])). 90.45/24.81 thf(326,plain,(! [B:$i,A:$i] : ((apply @ sk1 @ A @ B) | (~ (apply @ sk2 @ A @ B)) | (~ (member @ A @ sk3)) | ((singleton @ B) != sk5))),inference(simp,[status(thm)],[324])). 90.45/24.81 thf(417,plain,(! [C:$i,B:$i,A:$i] : ((apply @ sk1 @ B @ C) | (~ (apply @ sk2 @ B @ C)) | ((singleton @ C) != sk5) | ((member @ A @ (singleton @ A)) != (member @ B @ sk3)))),inference(paramod_ordered,[status(thm)],[114,326])). 90.45/24.81 thf(420,plain,(! [C:$i,B:$i,A:$i] : ((apply @ sk1 @ B @ C) | (~ (apply @ sk2 @ B @ C)) | ((singleton @ C) != sk5) | (A != B) | ((singleton @ A) != sk3))),inference(simp,[status(thm)],[417])). 90.45/24.81 thf(423,plain,(! [B:$i,A:$i] : ((apply @ sk1 @ A @ B) | (~ (apply @ sk2 @ A @ B)) | ((singleton @ B) != sk5) | ((singleton @ A) != sk3))),inference(simp,[status(thm)],[420])). 90.45/24.81 thf(1869,plain,(! [E:$i,D:$i,C:$i,B:$i,A:$i] : (((member @ A @ (unordered_pair @ A @ B)) != (member @ C @ (inverse_image3 @ E @ empty_set @ D))))),inference(paramod_ordered,[status(thm)],[295,1846])). 90.45/24.81 thf(1882,plain,(! [E:$i,D:$i,C:$i,B:$i,A:$i] : ((A != C) | ((unordered_pair @ A @ B) != (inverse_image3 @ E @ empty_set @ D)))),inference(simp,[status(thm)],[1869])). 90.45/24.81 thf(1884,plain,(! [D:$i,C:$i,B:$i,A:$i] : (((unordered_pair @ B @ A) != (inverse_image3 @ D @ empty_set @ C)))),inference(simp,[status(thm)],[1882])). 90.45/24.81 thf(41,plain,(! [C:$i,B:$i,A:$i] : ((~ (one_to_one @ A @ B @ C)) | (injective @ A @ B @ C))),inference(cnf,[status(esa)],[40])). 90.45/24.81 thf(44,plain,(! [C:$i,B:$i,A:$i] : ((~ (one_to_one @ A @ B @ C)) | (injective @ A @ B @ C))),inference(simp,[status(thm)],[41])). 90.45/24.81 thf(798,plain,(! [B:$i,A:$i] : ((apply @ sk1 @ (sk6 @ B @ sk3 @ sk1) @ B) | ((member @ A @ (product @ empty_set)) != (member @ B @ sk5)))),inference(paramod_ordered,[status(thm)],[668,706])). 90.45/24.81 thf(811,plain,(! [B:$i,A:$i] : ((apply @ sk1 @ (sk6 @ B @ sk3 @ sk1) @ B) | (A != B) | ((product @ empty_set) != sk5))),inference(simp,[status(thm)],[798])). 90.45/24.81 thf(826,plain,(! [A:$i] : ((apply @ sk1 @ (sk6 @ A @ sk3 @ sk1) @ A) | ((product @ empty_set) != sk5))),inference(simp,[status(thm)],[811])). 90.45/24.81 thf(55,plain,(! [D:$i,C:$i,B:$i,A:$i] : ((~ (member @ D @ (inverse_image3 @ A @ B @ C))) | (apply @ A @ D @ (sk7 @ D @ C @ B @ A)))),inference(cnf,[status(esa)],[53])). 90.45/24.81 thf(59,plain,(! [D:$i,C:$i,B:$i,A:$i] : ((~ (member @ D @ (inverse_image3 @ A @ B @ C))) | (apply @ A @ D @ (sk7 @ D @ C @ B @ A)))),inference(simp,[status(thm)],[55])). 90.45/24.81 thf(2678,plain,(! [E:$i,D:$i,C:$i,B:$i,A:$i] : ((member @ A @ (product @ B)) | ((member @ (sk14 @ B @ A) @ B) != (member @ C @ (difference @ D @ (product @ (image2 @ E @ empty_set))))))),inference(paramod_ordered,[status(thm)],[134,1170])). 90.45/24.81 thf(2679,plain,(! [C:$i,B:$i,A:$i] : ((member @ A @ (product @ (difference @ B @ (product @ (image2 @ C @ empty_set))))))),inference(pattern_uni,[status(thm)],[2678:[bind(A, $thf(G)),bind(B, $thf(difference @ H @ (product @ (image2 @ K @ empty_set)))),bind(C, $thf(sk14 @ (difference @ H @ (product @ (image2 @ K @ empty_set))) @ G)),bind(D, $thf(H)),bind(E, $thf(K))]])). 90.45/24.81 thf(2716,plain,(! [C:$i,B:$i,A:$i] : ((member @ A @ (product @ (difference @ B @ (product @ (image2 @ C @ empty_set))))))),inference(simp,[status(thm)],[2679])). 90.45/24.81 thf(28,axiom,((! [A:$i,B:$i]: ((member @ A @ (sum @ B)) <=> (? [C:$i]: ((member @ C @ B) & (member @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum)). 90.45/24.81 thf(281,plain,((! [A:$i,B:$i]: (((member @ A @ (sum @ B)) => (? [C:$i]: ((member @ C @ B) & (member @ A @ C)))) & ((? [C:$i]: ((member @ C @ B) & (member @ A @ C))) => (member @ A @ (sum @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[28])). 90.45/24.81 thf(1186,plain,(! [E:$i,D:$i,C:$i,B:$i,A:$i] : (((singleton @ C) != (difference @ E @ D)) | ((member @ A @ (product @ (difference @ B @ (product @ empty_set)))) != (member @ C @ D)))),inference(paramod_ordered,[status(thm)],[787,389])). 90.45/24.81 thf(1187,plain,(! [C:$i,B:$i,A:$i] : (((singleton @ A) != (difference @ B @ (product @ (difference @ C @ (product @ empty_set))))))),inference(pattern_uni,[status(thm)],[1186:[bind(A, $thf(A)),bind(B, $thf(G)),bind(C, $thf(A)),bind(D, $thf(product @ (difference @ G @ (product @ empty_set)))),bind(E, $thf(E))]])). 90.45/24.81 thf(1239,plain,(! [C:$i,B:$i,A:$i] : (((singleton @ A) != (difference @ B @ (product @ (difference @ C @ (product @ empty_set))))))),inference(simp,[status(thm)],[1187])). 90.45/24.81 thf(371,plain,(! [E:$i,D:$i,C:$i,B:$i,A:$i] : ((~ (member @ C @ (difference @ E @ D))) | ((member @ B @ (unordered_pair @ A @ B)) != (member @ C @ D)))),inference(paramod_ordered,[status(thm)],[293,167])). 90.45/24.83 thf(372,plain,(! [C:$i,B:$i,A:$i] : ((~ (member @ C @ (difference @ A @ (unordered_pair @ B @ C)))))),inference(pattern_uni,[status(thm)],[371:[bind(A, $thf(F)),bind(B, $thf(G)),bind(C, $thf(G)),bind(D, $thf(unordered_pair @ F @ G))]])). 90.45/24.83 thf(386,plain,(! [C:$i,B:$i,A:$i] : ((~ (member @ C @ (difference @ A @ (unordered_pair @ B @ C)))))),inference(simp,[status(thm)],[372])). 90.45/24.83 thf(458,plain,(! [D:$i,C:$i,B:$i,A:$i] : (((member @ A @ (singleton @ A)) != (member @ D @ (difference @ B @ (unordered_pair @ C @ D)))))),inference(paramod_ordered,[status(thm)],[114,386])). 90.45/24.83 thf(462,plain,(! [D:$i,C:$i,B:$i,A:$i] : ((A != D) | ((singleton @ A) != (difference @ B @ (unordered_pair @ C @ D))))),inference(simp,[status(thm)],[458])). 90.45/24.83 thf(466,plain,(! [C:$i,B:$i,A:$i] : (((difference @ A @ (unordered_pair @ B @ C)) != (singleton @ C)))),inference(simp,[status(thm)],[462])). 90.45/24.83 thf(1862,plain,(! [E:$i,D:$i,C:$i,B:$i,A:$i] : (((member @ A @ (product @ (image2 @ B @ empty_set))) != (member @ C @ (inverse_image3 @ E @ empty_set @ D))))),inference(paramod_ordered,[status(thm)],[958,1846])). 90.45/24.83 thf(1880,plain,(! [E:$i,D:$i,C:$i,B:$i,A:$i] : ((A != C) | ((product @ (image2 @ B @ empty_set)) != (inverse_image3 @ E @ empty_set @ D)))),inference(simp,[status(thm)],[1862])). 90.45/24.83 thf(1897,plain,(! [C:$i,B:$i,A:$i] : (((product @ (image2 @ A @ empty_set)) != (inverse_image3 @ C @ empty_set @ B)))),inference(simp,[status(thm)],[1880])). 90.45/24.83 thf(3357,plain,(! [D:$i,C:$i,B:$i,A:$i] : (((member @ A @ (product @ (difference @ B @ (product @ (image2 @ C @ empty_set))))) != (member @ D @ empty_set)))),inference(paramod_ordered,[status(thm)],[2716,138])). 90.45/24.83 thf(3416,plain,(! [D:$i,C:$i,B:$i,A:$i] : ((A != D) | ((product @ (difference @ B @ (product @ (image2 @ C @ empty_set)))) != empty_set))),inference(simp,[status(thm)],[3357])). 90.45/24.83 thf(3462,plain,(! [B:$i,A:$i] : (((product @ (difference @ A @ (product @ (image2 @ B @ empty_set)))) != empty_set))),inference(simp,[status(thm)],[3416])). 90.45/24.83 thf(3530,plain,(! [B:$i,A:$i] : (((product @ (difference @ A @ (product @ sk5))) != empty_set) | ((image2 @ sk1 @ sk3) != (image2 @ B @ empty_set)))),inference(paramod_ordered,[status(thm)],[38,3462])). 90.45/24.83 thf(3531,plain,(! [B:$i,A:$i] : (((product @ (difference @ A @ (product @ sk5))) != empty_set) | (sk1 != B) | (sk3 != empty_set))),inference(simp,[status(thm)],[3530])). 90.45/24.83 thf(3532,plain,(! [A:$i] : (((product @ (difference @ A @ (product @ sk5))) != empty_set) | (sk3 != empty_set))),inference(simp,[status(thm)],[3531])). 90.45/24.83 thf(733,plain,(! [C:$i,B:$i,A:$i] : (((member @ A @ (product @ empty_set)) != (member @ C @ (difference @ B @ (singleton @ C)))))),inference(paramod_ordered,[status(thm)],[668,390])). 90.45/24.83 thf(744,plain,(! [C:$i,B:$i,A:$i] : ((A != C) | ((difference @ B @ (singleton @ C)) != (product @ empty_set)))),inference(simp,[status(thm)],[733])). 90.45/24.83 thf(764,plain,(! [B:$i,A:$i] : (((difference @ A @ (singleton @ B)) != (product @ empty_set)))),inference(simp,[status(thm)],[744])). 90.45/24.83 thf(20,axiom,((! [A:$i,B:$i,C:$i]: ((! [D:$i]: ((member @ D @ B) => (? [E:$i]: ((member @ E @ C) & (apply @ A @ D @ E)))) & ! [D:$i,E:$i,F:$i]: (((member @ F @ C) & (member @ E @ C) & (member @ D @ B)) => (((apply @ A @ D @ E) & (apply @ A @ D @ F)) => (F = E)))) <=> (maps @ A @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maps)). 90.45/24.83 thf(187,plain,((! [A:$i,B:$i,C:$i]: (((! [D:$i]: ((member @ D @ B) => (? [E:$i]: ((member @ E @ C) & (apply @ A @ D @ E)))) & ! [D:$i,E:$i,F:$i]: (((member @ F @ C) & (member @ E @ C) & (member @ D @ B)) => (((apply @ A @ D @ E) & (apply @ A @ D @ F)) => (F = E)))) => (maps @ A @ B @ C)) & ((maps @ A @ B @ C) => (! [D:$i]: ((member @ D @ B) => (? [E:$i]: ((member @ E @ C) & (apply @ A @ D @ E)))) & ! [D:$i,E:$i,F:$i]: (((member @ F @ C) & (member @ E @ C) & (member @ D @ B)) => (((apply @ A @ D @ E) & (apply @ A @ D @ F)) => (F = E)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[20])). 90.45/24.83 thf(3316,plain,(! [D:$i,C:$i,B:$i,A:$i] : (((member @ A @ (product @ empty_set)) != (member @ B @ (difference @ C @ (product @ (difference @ D @ (product @ empty_set)))))))),inference(paramod_ordered,[status(thm)],[668,1244])). 90.45/24.83 thf(3336,plain,(! [D:$i,C:$i,B:$i,A:$i] : ((A != B) | ((difference @ C @ (product @ (difference @ D @ (product @ empty_set)))) != (product @ empty_set)))),inference(simp,[status(thm)],[3316])). 90.45/24.83 thf(3352,plain,(! [B:$i,A:$i] : (((difference @ A @ (product @ (difference @ B @ (product @ empty_set)))) != (product @ empty_set)))),inference(simp,[status(thm)],[3336])). 90.45/24.83 thf(1684,plain,(! [D:$i,C:$i,B:$i,A:$i] : (((member @ A @ (product @ empty_set)) != (member @ B @ (image2 @ C @ (image2 @ D @ empty_set)))))),inference(paramod_ordered,[status(thm)],[668,964])). 90.45/24.83 thf(1695,plain,(! [D:$i,C:$i,B:$i,A:$i] : ((A != B) | ((image2 @ C @ (image2 @ D @ empty_set)) != (product @ empty_set)))),inference(simp,[status(thm)],[1684])). 90.45/24.83 thf(1711,plain,(! [B:$i,A:$i] : (((image2 @ A @ (image2 @ B @ empty_set)) != (product @ empty_set)))),inference(simp,[status(thm)],[1695])). 90.45/24.83 thf(1849,plain,(! [B:$i,A:$i] : (((product @ empty_set) != sk5) | ((image2 @ sk1 @ sk3) != (image2 @ A @ (image2 @ B @ empty_set))))),inference(paramod_ordered,[status(thm)],[38,1711])). 90.45/24.83 thf(1851,plain,(! [B:$i,A:$i] : (((product @ empty_set) != sk5) | (sk1 != A) | ((image2 @ B @ empty_set) != sk3))),inference(simp,[status(thm)],[1849])). 90.45/24.83 thf(1853,plain,(! [A:$i] : (((product @ empty_set) != sk5) | ((image2 @ A @ empty_set) != sk3))),inference(simp,[status(thm)],[1851])). 90.45/24.83 thf(777,plain,(! [D:$i,C:$i,B:$i,A:$i] : (((member @ A @ (unordered_pair @ A @ B)) != (member @ C @ (difference @ D @ (product @ empty_set)))))),inference(paramod_ordered,[status(thm)],[295,765])). 90.45/24.83 thf(779,plain,(! [D:$i,C:$i,B:$i,A:$i] : ((A != C) | ((unordered_pair @ A @ B) != (difference @ D @ (product @ empty_set))))),inference(simp,[status(thm)],[777])). 90.45/24.83 thf(784,plain,(! [C:$i,B:$i,A:$i] : (((unordered_pair @ B @ A) != (difference @ C @ (product @ empty_set))))),inference(simp,[status(thm)],[779])). 90.45/24.83 thf(976,plain,(! [C:$i,B:$i,A:$i] : ((member @ A @ (product @ B)) | (sk3 != empty_set) | ((member @ (sk14 @ B @ A) @ B) != (member @ C @ sk5)))),inference(paramod_ordered,[status(thm)],[134,957])). 90.45/24.83 thf(977,plain,(! [A:$i] : ((member @ A @ (product @ sk5)) | (sk3 != empty_set))),inference(pattern_uni,[status(thm)],[976:[bind(A, $thf(E)),bind(B, $thf(sk5)),bind(C, $thf(sk14 @ sk5 @ E))]])). 90.45/24.83 thf(991,plain,(! [A:$i] : ((member @ A @ (product @ sk5)) | (sk3 != empty_set))),inference(simp,[status(thm)],[977])). 90.45/24.83 thf(379,plain,(! [C:$i,B:$i,A:$i] : ((~ (member @ A @ B)) | ((member @ A @ (difference @ C @ B)) != (member @ A @ B)) | ~ ($true))),inference(eqfactor_ordered,[status(thm)],[167])). 90.45/24.83 thf(381,plain,(! [C:$i,B:$i,A:$i] : ((~ (member @ A @ B)) | (A != A) | ((difference @ C @ B) != B))),inference(simp,[status(thm)],[379])). 90.45/24.83 thf(387,plain,(! [C:$i,B:$i,A:$i] : ((~ (member @ A @ B)) | ((difference @ C @ B) != B))),inference(simp,[status(thm)],[381])). 90.45/24.83 thf(1471,plain,(! [D:$i,C:$i,B:$i,A:$i] : ((sk3 != empty_set) | ((difference @ D @ C) != C) | ((member @ A @ (product @ sk5)) != (member @ B @ C)))),inference(paramod_ordered,[status(thm)],[991,387])). 90.45/24.83 thf(1472,plain,(! [A:$i] : ((sk3 != empty_set) | ((difference @ A @ (product @ sk5)) != (product @ sk5)))),inference(pattern_uni,[status(thm)],[1471:[bind(A, $thf(A)),bind(B, $thf(A)),bind(C, $thf(product @ sk5)),bind(D, $thf(D))]])). 90.45/24.83 thf(1524,plain,(! [A:$i] : ((sk3 != empty_set) | ((difference @ A @ (product @ sk5)) != (product @ sk5)))),inference(simp,[status(thm)],[1472])). 90.45/24.83 thf(443,plain,(! [D:$i,C:$i,B:$i,A:$i] : (((member @ B @ (unordered_pair @ A @ B)) != (member @ D @ (difference @ C @ (singleton @ D)))))),inference(paramod_ordered,[status(thm)],[293,390])). 90.45/24.83 thf(447,plain,(! [D:$i,C:$i,B:$i,A:$i] : ((B != D) | ((unordered_pair @ A @ B) != (difference @ C @ (singleton @ D))))),inference(simp,[status(thm)],[443])). 90.45/24.83 thf(451,plain,(! [C:$i,B:$i,A:$i] : (((unordered_pair @ A @ C) != (difference @ B @ (singleton @ C))))),inference(simp,[status(thm)],[447])). 90.45/24.83 thf(71,plain,(! [E:$i,D:$i,C:$i,B:$i,A:$i] : ((member @ (sk11 @ E @ D @ C @ B @ A) @ D) | (decreasing @ A @ B @ C @ D @ E))),inference(cnf,[status(esa)],[62])). 90.45/24.83 thf(76,plain,(! [E:$i,D:$i,C:$i,B:$i,A:$i] : ((member @ (sk11 @ E @ D @ C @ B @ A) @ D) | (decreasing @ A @ B @ C @ D @ E))),inference(simp,[status(thm)],[71])). 90.45/24.83 thf(1718,plain,(! [C:$i,B:$i,A:$i] : ((subset @ (image2 @ B @ sk5) @ A) | ((image2 @ sk1 @ sk3) != (image2 @ C @ empty_set)))),inference(paramod_ordered,[status(thm)],[38,1709])). 90.45/24.83 thf(1720,plain,(! [C:$i,B:$i,A:$i] : ((subset @ (image2 @ B @ sk5) @ A) | (sk1 != C) | (sk3 != empty_set))),inference(simp,[status(thm)],[1718])). 90.45/24.83 thf(1722,plain,(! [B:$i,A:$i] : ((subset @ (image2 @ B @ sk5) @ A) | (sk3 != empty_set))),inference(simp,[status(thm)],[1720])). 90.45/24.83 thf(316,plain,(((maps @ sk2 @ sk3 @ sk5) != (maps @ sk1 @ sk3 @ sk4))),inference(paramod_ordered,[status(thm)],[33,34])). 90.45/24.83 thf(317,plain,((sk2 != sk1) | (sk3 != sk3) | (sk5 != sk4)),inference(simp,[status(thm)],[316])). 90.45/24.83 thf(318,plain,((sk2 != sk1) | (sk5 != sk4)),inference(simp,[status(thm)],[317])). 90.45/24.83 thf(355,plain,(! [C:$i,B:$i,A:$i] : (((member @ A @ (unordered_pair @ A @ B)) != (member @ C @ empty_set)))),inference(paramod_ordered,[status(thm)],[295,138])). 90.45/24.83 thf(362,plain,(! [C:$i,B:$i,A:$i] : ((A != C) | ((unordered_pair @ A @ B) != empty_set))),inference(simp,[status(thm)],[355])). 90.45/24.83 thf(367,plain,(! [B:$i,A:$i] : (((unordered_pair @ B @ A) != empty_set))),inference(simp,[status(thm)],[362])). 90.45/24.83 thf(9,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((? [E:$i]: ((member @ E @ B) & (apply @ A @ E @ D)) & (member @ D @ C)) <=> (member @ D @ (image3 @ A @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',image3)). 90.45/24.83 thf(91,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((? [E:$i]: ((member @ E @ B) & (apply @ A @ E @ D)) & (member @ D @ C)) => (member @ D @ (image3 @ A @ B @ C))) & ((member @ D @ (image3 @ A @ B @ C)) => (? [E:$i]: ((member @ E @ B) & (apply @ A @ E @ D)) & (member @ D @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[9])). 90.45/24.83 thf(2687,plain,(! [D:$i,C:$i,B:$i,A:$i] : (((member @ A @ (product @ empty_set)) != (member @ B @ (difference @ C @ (product @ (image2 @ D @ empty_set))))))),inference(paramod_ordered,[status(thm)],[668,1170])). 90.45/24.83 thf(2704,plain,(! [D:$i,C:$i,B:$i,A:$i] : ((A != B) | ((difference @ C @ (product @ (image2 @ D @ empty_set))) != (product @ empty_set)))),inference(simp,[status(thm)],[2687])). 90.45/24.83 thf(2720,plain,(! [B:$i,A:$i] : (((difference @ A @ (product @ (image2 @ B @ empty_set))) != (product @ empty_set)))),inference(simp,[status(thm)],[2704])). 90.45/24.83 thf(2723,plain,(! [B:$i,A:$i] : (((difference @ A @ (product @ sk5)) != (product @ empty_set)) | ((image2 @ sk1 @ sk3) != (image2 @ B @ empty_set)))),inference(paramod_ordered,[status(thm)],[38,2720])). 90.45/24.83 thf(2724,plain,(! [B:$i,A:$i] : (((difference @ A @ (product @ sk5)) != (product @ empty_set)) | (sk1 != B) | (sk3 != empty_set))),inference(simp,[status(thm)],[2723])). 90.45/24.83 thf(2725,plain,(! [A:$i] : (((difference @ A @ (product @ sk5)) != (product @ empty_set)) | (sk3 != empty_set))),inference(simp,[status(thm)],[2724])). 90.45/24.83 thf(948,plain,(! [D:$i,C:$i,B:$i,A:$i] : (((member @ A @ (unordered_pair @ A @ B)) != (member @ C @ (image2 @ D @ empty_set))))),inference(paramod_ordered,[status(thm)],[295,925])). 90.45/24.83 thf(952,plain,(! [D:$i,C:$i,B:$i,A:$i] : ((A != C) | ((unordered_pair @ A @ B) != (image2 @ D @ empty_set)))),inference(simp,[status(thm)],[948])). 90.45/24.83 thf(959,plain,(! [C:$i,B:$i,A:$i] : (((unordered_pair @ B @ A) != (image2 @ C @ empty_set)))),inference(simp,[status(thm)],[952])). 90.45/24.83 thf(2618,plain,(! [B:$i,A:$i] : (((product @ empty_set) != sk5) | ((image2 @ sk1 @ sk3) != (image2 @ A @ (difference @ B @ (product @ empty_set)))))),inference(paramod_ordered,[status(thm)],[38,2616])). 90.45/24.83 thf(2619,plain,(! [B:$i,A:$i] : (((product @ empty_set) != sk5) | (sk1 != A) | ((difference @ B @ (product @ empty_set)) != sk3))),inference(simp,[status(thm)],[2618])). 90.45/24.83 thf(2620,plain,(! [A:$i] : (((product @ empty_set) != sk5) | ((difference @ A @ (product @ empty_set)) != sk3))),inference(simp,[status(thm)],[2619])). 90.45/24.83 thf(2240,plain,(! [C:$i,B:$i,A:$i] : ((identity @ A @ (image2 @ B @ sk5)) | ((image2 @ sk1 @ sk3) != (image2 @ C @ empty_set)))),inference(paramod_ordered,[status(thm)],[38,1712])). 90.45/24.83 thf(2242,plain,(! [C:$i,B:$i,A:$i] : ((identity @ A @ (image2 @ B @ sk5)) | (sk1 != C) | (sk3 != empty_set))),inference(simp,[status(thm)],[2240])). 90.45/24.83 thf(2244,plain,(! [B:$i,A:$i] : ((identity @ A @ (image2 @ B @ sk5)) | (sk3 != empty_set))),inference(simp,[status(thm)],[2242])). 90.45/24.83 thf(479,plain,(! [C:$i,B:$i,A:$i] : ((identity @ A @ B) | ((member @ (sk38 @ B @ A) @ B) != (member @ C @ empty_set)))),inference(paramod_ordered,[status(thm)],[259,138])). 90.45/24.83 thf(480,plain,(! [A:$i] : ((identity @ A @ empty_set))),inference(pattern_uni,[status(thm)],[479:[bind(A, $thf(E)),bind(B, $thf(empty_set)),bind(C, $thf(sk38 @ empty_set @ E))]])). 90.45/24.83 thf(505,plain,(! [A:$i] : ((identity @ A @ empty_set))),inference(simp,[status(thm)],[480])). 90.45/24.83 thf(7,axiom,((! [A:$i,B:$i]: ((member @ A @ (power_set @ B)) <=> (subset @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',power_set)). 90.45/24.83 thf(80,plain,((! [A:$i,B:$i]: (((member @ A @ (power_set @ B)) => (subset @ A @ B)) & ((subset @ A @ B) => (member @ A @ (power_set @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])). 90.45/24.83 thf(1113,plain,(! [D:$i,C:$i,B:$i,A:$i] : (((member @ A @ (product @ (image2 @ B @ empty_set))) != (member @ C @ (image2 @ D @ empty_set))))),inference(paramod_ordered,[status(thm)],[958,925])). 90.45/24.83 thf(1152,plain,(! [D:$i,C:$i,B:$i,A:$i] : ((A != C) | ((product @ (image2 @ B @ empty_set)) != (image2 @ D @ empty_set)))),inference(simp,[status(thm)],[1113])). 90.45/24.83 thf(1181,plain,(! [B:$i,A:$i] : (((product @ (image2 @ A @ empty_set)) != (image2 @ B @ empty_set)))),inference(simp,[status(thm)],[1152])). 90.45/24.83 thf(1416,plain,(! [B:$i,A:$i] : (((image2 @ B @ empty_set) != (product @ sk5)) | ((image2 @ sk1 @ sk3) != (image2 @ A @ empty_set)))),inference(paramod_ordered,[status(thm)],[38,1181])). 90.45/24.83 thf(1418,plain,(! [B:$i,A:$i] : (((image2 @ B @ empty_set) != (product @ sk5)) | (sk1 != A) | (sk3 != empty_set))),inference(simp,[status(thm)],[1416])). 90.45/24.83 thf(1420,plain,(! [A:$i] : (((image2 @ A @ empty_set) != (product @ sk5)) | (sk3 != empty_set))),inference(simp,[status(thm)],[1418])). 90.45/24.83 thf(2264,plain,(! [E:$i,D:$i,C:$i,B:$i,A:$i] : (((member @ A @ (product @ (inverse_image3 @ B @ empty_set @ C))) != (member @ D @ (difference @ E @ (product @ empty_set)))))),inference(paramod_ordered,[status(thm)],[1894,765])). 90.45/24.83 thf(2304,plain,(! [E:$i,D:$i,C:$i,B:$i,A:$i] : ((A != D) | ((product @ (inverse_image3 @ B @ empty_set @ C)) != (difference @ E @ (product @ empty_set))))),inference(simp,[status(thm)],[2264])). 90.45/24.83 thf(2333,plain,(! [C:$i,B:$i,A:$i] : (((product @ (inverse_image3 @ A @ empty_set @ B)) != (difference @ C @ (product @ empty_set))))),inference(simp,[status(thm)],[2304])). 90.45/24.83 thf(2738,plain,(! [F:$i,E:$i,D:$i,C:$i,B:$i,A:$i] : ((decreasing @ A @ B @ C @ D @ E) | ((member @ (sk10 @ E @ D @ C @ B @ A) @ B) != (member @ F @ empty_set)))),inference(paramod_ordered,[status(thm)],[74,138])). 90.45/24.83 thf(2739,plain,(! [D:$i,C:$i,B:$i,A:$i] : ((decreasing @ D @ empty_set @ C @ B @ A))),inference(pattern_uni,[status(thm)],[2738:[bind(A, $thf(K)),bind(B, $thf(empty_set)),bind(C, $thf(I)),bind(D, $thf(H)),bind(E, $thf(G)),bind(F, $thf(sk10 @ G @ H @ I @ empty_set @ K))]])). 90.45/24.83 thf(2846,plain,(! [D:$i,C:$i,B:$i,A:$i] : ((decreasing @ D @ empty_set @ C @ B @ A))),inference(simp,[status(thm)],[2739])). 90.45/24.83 thf(2560,plain,(! [B:$i,A:$i] : (((product @ sk5) != empty_set) | ((image2 @ sk1 @ sk3) != (image2 @ A @ (image2 @ B @ empty_set))))),inference(paramod_ordered,[status(thm)],[38,2468])). 90.45/24.83 thf(2562,plain,(! [B:$i,A:$i] : (((product @ sk5) != empty_set) | (sk1 != A) | ((image2 @ B @ empty_set) != sk3))),inference(simp,[status(thm)],[2560])). 90.45/24.83 thf(2564,plain,(! [A:$i] : (((product @ sk5) != empty_set) | ((image2 @ A @ empty_set) != sk3))),inference(simp,[status(thm)],[2562])). 90.45/24.83 thf(723,plain,(! [D:$i,C:$i,B:$i,A:$i] : (((difference @ D @ C) != C) | ((member @ A @ (product @ empty_set)) != (member @ B @ C)))),inference(paramod_ordered,[status(thm)],[668,387])). 90.45/24.83 thf(724,plain,(! [A:$i] : (((difference @ A @ (product @ empty_set)) != (product @ empty_set)))),inference(pattern_uni,[status(thm)],[723:[bind(A, $thf(A)),bind(B, $thf(A)),bind(C, $thf(product @ empty_set)),bind(D, $thf(D))]])). 90.45/24.83 thf(754,plain,(! [A:$i] : (((difference @ A @ (product @ empty_set)) != (product @ empty_set)))),inference(simp,[status(thm)],[724])). 90.45/24.83 thf(947,plain,(! [C:$i,B:$i,A:$i] : (((member @ A @ (product @ empty_set)) != (member @ B @ (image2 @ C @ empty_set))))),inference(paramod_ordered,[status(thm)],[668,925])). 90.45/24.83 thf(953,plain,(! [C:$i,B:$i,A:$i] : ((A != B) | ((image2 @ C @ empty_set) != (product @ empty_set)))),inference(simp,[status(thm)],[947])). 90.45/24.83 thf(960,plain,(! [A:$i] : (((image2 @ A @ empty_set) != (product @ empty_set)))),inference(simp,[status(thm)],[953])). 90.45/24.83 thf(966,plain,(! [A:$i] : (((product @ empty_set) != sk5) | ((image2 @ sk1 @ sk3) != (image2 @ A @ empty_set)))),inference(paramod_ordered,[status(thm)],[38,960])). 90.45/24.83 thf(967,plain,(! [A:$i] : (((product @ empty_set) != sk5) | (sk1 != A) | (sk3 != empty_set))),inference(simp,[status(thm)],[966])). 90.45/24.83 thf(968,plain,(((product @ empty_set) != sk5) | (sk3 != empty_set)),inference(simp,[status(thm)],[967])). 90.45/24.83 thf(943,plain,(! [D:$i,C:$i,B:$i,A:$i] : ((identity @ A @ B) | ((member @ (sk38 @ B @ A) @ B) != (member @ C @ (image2 @ D @ empty_set))))),inference(paramod_ordered,[status(thm)],[259,925])). 90.45/24.83 thf(944,plain,(! [B:$i,A:$i] : ((identity @ A @ (image2 @ B @ empty_set)))),inference(pattern_uni,[status(thm)],[943:[bind(A, $thf(F)),bind(B, $thf(image2 @ G @ empty_set)),bind(C, $thf(sk38 @ (image2 @ G @ empty_set) @ F)),bind(D, $thf(G))]])). 90.45/24.83 thf(961,plain,(! [B:$i,A:$i] : ((identity @ A @ (image2 @ B @ empty_set)))),inference(simp,[status(thm)],[944])). 90.45/24.83 thf(969,plain,(! [B:$i,A:$i] : ((identity @ A @ sk5) | ((image2 @ sk1 @ sk3) != (image2 @ B @ empty_set)))),inference(paramod_ordered,[status(thm)],[38,961])). 90.45/24.83 thf(970,plain,(! [B:$i,A:$i] : ((identity @ A @ sk5) | (sk1 != B) | (sk3 != empty_set))),inference(simp,[status(thm)],[969])). 90.45/24.83 thf(971,plain,(! [A:$i] : ((identity @ A @ sk5) | (sk3 != empty_set))),inference(simp,[status(thm)],[970])). 90.45/24.83 thf(323,plain,(! [C:$i,B:$i,A:$i] : ((~ (apply @ sk2 @ B @ C)) | (apply @ sk1 @ B @ C) | (~ (member @ C @ sk5)) | ((member @ A @ (singleton @ A)) != (member @ B @ sk3)))),inference(paramod_ordered,[status(thm)],[114,35])). 90.45/24.83 thf(325,plain,(! [C:$i,B:$i,A:$i] : ((apply @ sk1 @ B @ C) | (~ (apply @ sk2 @ B @ C)) | (~ (member @ C @ sk5)) | (A != B) | ((singleton @ A) != sk3))),inference(simp,[status(thm)],[323])). 90.45/24.83 thf(327,plain,(! [B:$i,A:$i] : ((apply @ sk1 @ A @ B) | (~ (apply @ sk2 @ A @ B)) | (~ (member @ B @ sk5)) | ((singleton @ A) != sk3))),inference(simp,[status(thm)],[325])). 90.45/24.83 thf(983,plain,(! [C:$i,B:$i,A:$i] : ((sk3 != empty_set) | ((member @ A @ (unordered_pair @ A @ B)) != (member @ C @ sk5)))),inference(paramod_ordered,[status(thm)],[295,957])). 90.45/24.83 thf(988,plain,(! [C:$i,B:$i,A:$i] : ((sk3 != empty_set) | (A != C) | ((unordered_pair @ A @ B) != sk5))),inference(simp,[status(thm)],[983])). 90.45/24.83 thf(993,plain,(! [B:$i,A:$i] : ((sk3 != empty_set) | ((unordered_pair @ B @ A) != sk5))),inference(simp,[status(thm)],[988])). 90.45/24.83 thf(36,plain,(! [B:$i,A:$i] : ((~ (apply @ sk1 @ A @ B)) | (apply @ sk2 @ A @ B) | (~ (member @ B @ sk5)) | (~ (member @ A @ sk3)))),inference(cnf,[status(esa)],[31])). 90.45/24.83 thf(330,plain,(! [C:$i,B:$i,A:$i] : ((~ (apply @ sk1 @ B @ C)) | (apply @ sk2 @ B @ C) | (~ (member @ B @ sk3)) | ((member @ A @ (singleton @ A)) != (member @ C @ sk5)))),inference(paramod_ordered,[status(thm)],[114,36])). 90.45/24.83 thf(333,plain,(! [C:$i,B:$i,A:$i] : ((apply @ sk2 @ B @ C) | (~ (apply @ sk1 @ B @ C)) | (~ (member @ B @ sk3)) | (A != C) | ((singleton @ A) != sk5))),inference(simp,[status(thm)],[330])). 90.45/24.83 thf(336,plain,(! [B:$i,A:$i] : ((apply @ sk2 @ A @ B) | (~ (apply @ sk1 @ A @ B)) | (~ (member @ A @ sk3)) | ((singleton @ B) != sk5))),inference(simp,[status(thm)],[333])). 90.45/24.83 thf(2684,plain,(! [E:$i,D:$i,C:$i,B:$i,A:$i] : ((subset @ A @ B) | ((member @ (sk34 @ B @ A) @ A) != (member @ C @ (difference @ D @ (product @ (image2 @ E @ empty_set))))))),inference(paramod_ordered,[status(thm)],[236,1170])). 90.45/24.83 thf(2685,plain,(! [C:$i,B:$i,A:$i] : ((subset @ (difference @ B @ (product @ (image2 @ C @ empty_set))) @ A))),inference(pattern_uni,[status(thm)],[2684:[bind(A, $thf(difference @ H @ (product @ (image2 @ K @ empty_set)))),bind(B, $thf(F)),bind(C, $thf(sk34 @ F @ (difference @ H @ (product @ (image2 @ K @ empty_set))))),bind(D, $thf(H)),bind(E, $thf(K))]])). 90.45/24.83 thf(2711,plain,(! [C:$i,B:$i,A:$i] : ((subset @ (difference @ B @ (product @ (image2 @ C @ empty_set))) @ A))),inference(simp,[status(thm)],[2685])). 90.45/24.83 thf(69,plain,(! [E:$i,D:$i,C:$i,B:$i,A:$i] : ((~ (apply @ E @ (sk11 @ E @ D @ C @ B @ A) @ (sk9 @ E @ D @ C @ B @ A))) | (decreasing @ A @ B @ C @ D @ E))),inference(cnf,[status(esa)],[62])). 90.45/24.83 thf(72,plain,(! [E:$i,D:$i,C:$i,B:$i,A:$i] : ((~ (apply @ E @ (sk11 @ E @ D @ C @ B @ A) @ (sk9 @ E @ D @ C @ B @ A))) | (decreasing @ A @ B @ C @ D @ E))),inference(simp,[status(thm)],[69])). 90.45/24.83 thf(1675,plain,(! [C:$i,B:$i,A:$i] : ((~ (member @ A @ sk5)) | ((image2 @ sk1 @ sk3) != (image2 @ B @ (image2 @ C @ empty_set))))),inference(paramod_ordered,[status(thm)],[38,964])). 90.45/24.83 thf(1693,plain,(! [C:$i,B:$i,A:$i] : ((~ (member @ A @ sk5)) | (sk1 != B) | ((image2 @ C @ empty_set) != sk3))),inference(simp,[status(thm)],[1675])). 90.45/24.83 thf(1717,plain,(! [B:$i,A:$i] : ((~ (member @ A @ sk5)) | ((image2 @ B @ empty_set) != sk3))),inference(simp,[status(thm)],[1693])). 90.45/24.83 thf(64,plain,(! [E:$i,D:$i,C:$i,B:$i,A:$i] : ((member @ (sk9 @ E @ D @ C @ B @ A) @ D) | (decreasing @ A @ B @ C @ D @ E))),inference(cnf,[status(esa)],[62])). 90.45/24.83 thf(75,plain,(! [E:$i,D:$i,C:$i,B:$i,A:$i] : ((member @ (sk9 @ E @ D @ C @ B @ A) @ D) | (decreasing @ A @ B @ C @ D @ E))),inference(simp,[status(thm)],[64])). 90.45/24.83 thf(2921,plain,(! [F:$i,E:$i,D:$i,C:$i,B:$i,A:$i] : ((decreasing @ A @ B @ C @ D @ E) | ((member @ (sk9 @ E @ D @ C @ B @ A) @ D) != (member @ F @ empty_set)))),inference(paramod_ordered,[status(thm)],[75,138])). 90.45/24.83 thf(2922,plain,(! [D:$i,C:$i,B:$i,A:$i] : ((decreasing @ D @ C @ B @ empty_set @ A))),inference(pattern_uni,[status(thm)],[2921:[bind(A, $thf(K)),bind(B, $thf(J)),bind(C, $thf(I)),bind(D, $thf(empty_set)),bind(E, $thf(G)),bind(F, $thf(sk9 @ G @ empty_set @ I @ J @ K))]])). 90.45/24.83 thf(3007,plain,(! [D:$i,C:$i,B:$i,A:$i] : ((decreasing @ D @ C @ B @ empty_set @ A))),inference(simp,[status(thm)],[2922])). 90.45/24.83 thf(43,plain,(! [C:$i,B:$i,A:$i] : ((~ (injective @ A @ B @ C)) | (~ (surjective @ A @ B @ C)) | (one_to_one @ A @ B @ C))),inference(cnf,[status(esa)],[40])). 90.45/24.83 thf(1131,plain,(! [D:$i,C:$i,B:$i,A:$i] : (((member @ A @ (product @ (image2 @ B @ empty_set))) != (member @ D @ (difference @ C @ (singleton @ D)))))),inference(paramod_ordered,[status(thm)],[958,390])). 90.45/24.83 thf(1148,plain,(! [D:$i,C:$i,B:$i,A:$i] : ((A != D) | ((product @ (image2 @ B @ empty_set)) != (difference @ C @ (singleton @ D))))),inference(simp,[status(thm)],[1131])). 90.45/24.83 thf(1180,plain,(! [C:$i,B:$i,A:$i] : (((product @ (image2 @ A @ empty_set)) != (difference @ B @ (singleton @ C))))),inference(simp,[status(thm)],[1148])). 90.45/24.83 thf(2247,plain,(! [C:$i,B:$i,A:$i] : (((singleton @ A) != sk5) | ((image2 @ sk1 @ sk3) != (image2 @ B @ (image2 @ C @ empty_set))))),inference(paramod_ordered,[status(thm)],[38,1713])). 90.45/24.83 thf(2249,plain,(! [C:$i,B:$i,A:$i] : (((singleton @ A) != sk5) | (sk1 != B) | ((image2 @ C @ empty_set) != sk3))),inference(simp,[status(thm)],[2247])). 90.45/24.83 thf(2251,plain,(! [B:$i,A:$i] : (((singleton @ A) != sk5) | ((image2 @ B @ empty_set) != sk3))),inference(simp,[status(thm)],[2249])). 90.45/24.83 thf(1850,plain,(! [B:$i,A:$i] : (((image2 @ A @ sk5) != (product @ empty_set)) | ((image2 @ sk1 @ sk3) != (image2 @ B @ empty_set)))),inference(paramod_ordered,[status(thm)],[38,1711])). 90.45/24.83 thf(1852,plain,(! [B:$i,A:$i] : (((image2 @ A @ sk5) != (product @ empty_set)) | (sk1 != B) | (sk3 != empty_set))),inference(simp,[status(thm)],[1850])). 90.45/24.83 thf(1854,plain,(! [A:$i] : (((image2 @ A @ sk5) != (product @ empty_set)) | (sk3 != empty_set))),inference(simp,[status(thm)],[1852])). 90.45/24.83 thf(19,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((inverse_predicate @ A @ B @ C @ D) <=> (! [E:$i,F:$i]: (((apply @ A @ F @ E) <=> (apply @ B @ E @ F)) <= ((member @ E @ C) & (member @ F @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_predicate)). 90.45/24.83 thf(171,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((inverse_predicate @ A @ B @ C @ D) => (! [E:$i,F:$i]: ((((apply @ A @ F @ E) => (apply @ B @ E @ F)) & ((apply @ B @ E @ F) => (apply @ A @ F @ E))) | ~ ((member @ E @ C) & (member @ F @ D))))) & ((! [E:$i,F:$i]: ((((apply @ A @ F @ E) => (apply @ B @ E @ F)) & ((apply @ B @ E @ F) => (apply @ A @ F @ E))) | ~ ((member @ E @ C) & (member @ F @ D)))) => (inverse_predicate @ A @ B @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[19])). 90.45/24.83 thf(16,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: ((compose_predicate @ A @ B @ C @ D @ E @ F) <=> (! [G:$i,H:$i]: (((member @ G @ D) & (member @ H @ F)) => ((? [I:$i]: ((member @ I @ E) & (apply @ C @ G @ I) & (apply @ B @ I @ H))) <=> (apply @ A @ G @ H))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_predicate)). 90.45/24.83 thf(139,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: (((compose_predicate @ A @ B @ C @ D @ E @ F) => (! [G:$i,H:$i]: (((member @ G @ D) & (member @ H @ F)) => (((? [I:$i]: ((member @ I @ E) & (apply @ C @ G @ I) & (apply @ B @ I @ H))) => (apply @ A @ G @ H)) & ((apply @ A @ G @ H) => (? [I:$i]: ((member @ I @ E) & (apply @ C @ G @ I) & (apply @ B @ I @ H)))))))) & ((! [G:$i,H:$i]: (((member @ G @ D) & (member @ H @ F)) => (((? [I:$i]: ((member @ I @ E) & (apply @ C @ G @ I) & (apply @ B @ I @ H))) => (apply @ A @ G @ H)) & ((apply @ A @ G @ H) => (? [I:$i]: ((member @ I @ E) & (apply @ C @ G @ I) & (apply @ B @ I @ H))))))) => (compose_predicate @ A @ B @ C @ D @ E @ F))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[16])). 90.45/24.83 thf(984,plain,(! [D:$i,C:$i,B:$i,A:$i] : ((~ (member @ C @ (image2 @ A @ B))) | (sk3 != empty_set) | ((member @ (sk6 @ C @ B @ A) @ B) != (member @ D @ sk5)))),inference(paramod_ordered,[status(thm)],[50,957])). 90.45/24.83 thf(985,plain,(! [B:$i,A:$i] : ((~ (member @ A @ (image2 @ B @ sk5))) | (sk3 != empty_set))),inference(pattern_uni,[status(thm)],[984:[bind(A, $thf(G)),bind(B, $thf(sk5)),bind(C, $thf(E)),bind(D, $thf(sk6 @ E @ sk5 @ G))]])). 90.45/24.83 thf(995,plain,(! [B:$i,A:$i] : ((~ (member @ A @ (image2 @ B @ sk5))) | (sk3 != empty_set))),inference(simp,[status(thm)],[985])). 90.45/24.83 thf(54,plain,(! [D:$i,C:$i,B:$i,A:$i] : ((~ (member @ D @ (inverse_image3 @ A @ B @ C))) | (member @ D @ C))),inference(cnf,[status(esa)],[53])). 90.45/24.83 thf(58,plain,(! [D:$i,C:$i,B:$i,A:$i] : ((~ (member @ D @ (inverse_image3 @ A @ B @ C))) | (member @ D @ C))),inference(simp,[status(thm)],[54])). 90.45/24.83 thf(470,plain,(! [D:$i,C:$i,B:$i,A:$i] : (((member @ A @ (singleton @ A)) != (member @ C @ (difference @ B @ (unordered_pair @ C @ D)))))),inference(paramod_ordered,[status(thm)],[114,388])). 90.45/24.83 thf(474,plain,(! [D:$i,C:$i,B:$i,A:$i] : ((A != C) | ((singleton @ A) != (difference @ B @ (unordered_pair @ C @ D))))),inference(simp,[status(thm)],[470])). 90.45/24.83 thf(478,plain,(! [C:$i,B:$i,A:$i] : (((difference @ A @ (unordered_pair @ B @ C)) != (singleton @ B)))),inference(simp,[status(thm)],[474])). 90.45/24.83 thf(1873,plain,(! [D:$i,C:$i,B:$i,A:$i] : (((member @ A @ (singleton @ A)) != (member @ B @ (inverse_image3 @ D @ empty_set @ C))))),inference(paramod_ordered,[status(thm)],[114,1846])). 90.45/24.83 thf(1881,plain,(! [D:$i,C:$i,B:$i,A:$i] : ((A != B) | ((singleton @ A) != (inverse_image3 @ D @ empty_set @ C)))),inference(simp,[status(thm)],[1873])). 90.45/24.83 thf(1893,plain,(! [C:$i,B:$i,A:$i] : (((singleton @ A) != (inverse_image3 @ C @ empty_set @ B)))),inference(simp,[status(thm)],[1881])). 90.45/24.83 thf(2497,plain,(! [C:$i,B:$i,A:$i] : ((sk3 != empty_set) | ((member @ A @ (product @ sk5)) != (member @ B @ (image2 @ C @ sk5))))),inference(paramod_ordered,[status(thm)],[991,995])). 90.45/24.83 thf(2504,plain,(! [C:$i,B:$i,A:$i] : ((sk3 != empty_set) | (A != B) | ((image2 @ C @ sk5) != (product @ sk5)))),inference(simp,[status(thm)],[2497])). 90.45/24.83 thf(2517,plain,(! [A:$i] : ((sk3 != empty_set) | ((image2 @ A @ sk5) != (product @ sk5)))),inference(simp,[status(thm)],[2504])). 90.45/24.83 thf(18,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((apply @ A @ D @ E) <=> (apply @ (inverse_function @ A @ B @ C) @ E @ D)) <= ((member @ D @ B) & (member @ E @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_function)). 90.45/24.83 thf(168,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((((apply @ A @ D @ E) => (apply @ (inverse_function @ A @ B @ C) @ E @ D)) & ((apply @ (inverse_function @ A @ B @ C) @ E @ D) => (apply @ A @ D @ E))) | ~ ((member @ D @ B) & (member @ E @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[18])). 90.45/24.83 thf(48,plain,(! [D:$i,C:$i,B:$i,A:$i] : ((~ (apply @ A @ D @ C)) | (~ (member @ D @ B)) | (member @ C @ (image2 @ A @ B)))),inference(cnf,[status(esa)],[47])). 90.45/24.83 thf(51,plain,(! [D:$i,C:$i,B:$i,A:$i] : ((~ (apply @ A @ D @ C)) | (~ (member @ D @ B)) | (member @ C @ (image2 @ A @ B)))),inference(simp,[status(thm)],[48])). 90.45/24.83 thf(719,plain,(! [D:$i,C:$i,B:$i,A:$i] : (((singleton @ B) != (difference @ D @ C)) | ((member @ A @ (product @ empty_set)) != (member @ B @ C)))),inference(paramod_ordered,[status(thm)],[668,389])). 90.45/24.83 thf(720,plain,(! [B:$i,A:$i] : (((singleton @ A) != (difference @ B @ (product @ empty_set))))),inference(pattern_uni,[status(thm)],[719:[bind(A, $thf(A)),bind(B, $thf(A)),bind(C, $thf(product @ empty_set)),bind(D, $thf(D))]])). 90.45/24.83 thf(767,plain,(! [B:$i,A:$i] : (((singleton @ A) != (difference @ B @ (product @ empty_set))))),inference(simp,[status(thm)],[720])). 90.45/24.83 thf(1857,plain,(! [E:$i,D:$i,C:$i,B:$i,A:$i] : (((member @ B @ (unordered_pair @ A @ B)) != (member @ C @ (inverse_image3 @ E @ empty_set @ D))))),inference(paramod_ordered,[status(thm)],[293,1846])). 90.45/24.83 thf(1878,plain,(! [E:$i,D:$i,C:$i,B:$i,A:$i] : ((B != C) | ((unordered_pair @ A @ B) != (inverse_image3 @ E @ empty_set @ D)))),inference(simp,[status(thm)],[1857])). 90.45/24.83 thf(1891,plain,(! [D:$i,C:$i,B:$i,A:$i] : (((unordered_pair @ A @ B) != (inverse_image3 @ D @ empty_set @ C)))),inference(simp,[status(thm)],[1878])). 90.45/24.83 thf(68,plain,(! [I:$i,H:$i,G:$i,F:$i,E:$i,D:$i,C:$i,B:$i,A:$i] : ((~ (decreasing @ A @ B @ C @ D @ E)) | (~ (member @ F @ B)) | (~ (member @ G @ D)) | (~ (member @ H @ B)) | (~ (member @ I @ D)) | (~ (apply @ A @ H @ I)) | (~ (apply @ A @ F @ G)) | (~ (apply @ C @ F @ H)) | (apply @ E @ I @ G))),inference(cnf,[status(esa)],[62])). 90.45/24.83 thf(1866,plain,(! [E:$i,D:$i,C:$i,B:$i,A:$i] : ((subset @ A @ B) | ((member @ (sk34 @ B @ A) @ A) != (member @ C @ (inverse_image3 @ E @ empty_set @ D))))),inference(paramod_ordered,[status(thm)],[236,1846])). 90.45/24.83 thf(1867,plain,(! [C:$i,B:$i,A:$i] : ((subset @ (inverse_image3 @ B @ empty_set @ C) @ A))),inference(pattern_uni,[status(thm)],[1866:[bind(A, $thf(inverse_image3 @ H @ empty_set @ J)),bind(B, $thf(F)),bind(C, $thf(sk34 @ F @ (inverse_image3 @ H @ empty_set @ J))),bind(D, $thf(J)),bind(E, $thf(H))]])). 90.45/24.83 thf(1885,plain,(! [C:$i,B:$i,A:$i] : ((subset @ (inverse_image3 @ B @ empty_set @ C) @ A))),inference(simp,[status(thm)],[1867])). 90.45/24.83 thf(331,plain,(! [C:$i,B:$i,A:$i] : ((~ (apply @ sk1 @ B @ C)) | (apply @ sk2 @ B @ C) | (~ (member @ C @ sk5)) | ((member @ A @ (singleton @ A)) != (member @ B @ sk3)))),inference(paramod_ordered,[status(thm)],[114,36])). 90.45/24.83 thf(334,plain,(! [C:$i,B:$i,A:$i] : ((apply @ sk2 @ B @ C) | (~ (apply @ sk1 @ B @ C)) | (~ (member @ C @ sk5)) | (A != B) | ((singleton @ A) != sk3))),inference(simp,[status(thm)],[331])). 90.45/24.83 thf(337,plain,(! [B:$i,A:$i] : ((apply @ sk2 @ A @ B) | (~ (apply @ sk1 @ A @ B)) | (~ (member @ B @ sk5)) | ((singleton @ A) != sk3))),inference(simp,[status(thm)],[334])). 90.45/24.83 thf(13,axiom,((! [A:$i,B:$i,C:$i]: ((? [D:$i]: ((member @ D @ B) & (apply @ A @ C @ D))) <=> (member @ C @ (inverse_image2 @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_image2)). 90.45/24.83 thf(122,plain,((! [A:$i,B:$i,C:$i]: (((? [D:$i]: ((member @ D @ B) & (apply @ A @ C @ D))) => (member @ C @ (inverse_image2 @ A @ B))) & ((member @ C @ (inverse_image2 @ A @ B)) => (? [D:$i]: ((member @ D @ B) & (apply @ A @ C @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[13])). 90.45/24.83 thf(1182,plain,(! [A:$i] : (((product @ sk5) != empty_set) | ((image2 @ sk1 @ sk3) != (image2 @ A @ empty_set)))),inference(paramod_ordered,[status(thm)],[38,1164])). 90.45/24.83 thf(1183,plain,(! [A:$i] : (((product @ sk5) != empty_set) | (sk1 != A) | (sk3 != empty_set))),inference(simp,[status(thm)],[1182])). 90.45/24.83 thf(1184,plain,(((product @ sk5) != empty_set) | (sk3 != empty_set)),inference(simp,[status(thm)],[1183])). 90.45/24.83 thf(2586,plain,(! [D:$i,C:$i,B:$i,A:$i] : (((member @ A @ (singleton @ A)) != (member @ B @ (image2 @ C @ (difference @ D @ (product @ empty_set))))))),inference(paramod_ordered,[status(thm)],[114,929])). 90.45/24.83 thf(2591,plain,(! [D:$i,C:$i,B:$i,A:$i] : ((A != B) | ((singleton @ A) != (image2 @ C @ (difference @ D @ (product @ empty_set)))))),inference(simp,[status(thm)],[2586])). 90.45/24.83 thf(2615,plain,(! [C:$i,B:$i,A:$i] : (((singleton @ A) != (image2 @ B @ (difference @ C @ (product @ empty_set)))))),inference(simp,[status(thm)],[2591])). 90.45/24.83 thf(23,axiom,((! [A:$i,B:$i,C:$i]: ((! [D:$i]: ((? [E:$i]: ((member @ E @ B) & (apply @ A @ E @ D))) <= (member @ D @ C))) <=> (surjective @ A @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',surjective)). 90.45/24.83 thf(222,plain,((! [A:$i,B:$i,C:$i]: (((! [D:$i]: (? [E:$i]: ((member @ E @ B) & (apply @ A @ E @ D)) | ~ (member @ D @ C))) => (surjective @ A @ B @ C)) & ((surjective @ A @ B @ C) => (! [D:$i]: (? [E:$i]: ((member @ E @ B) & (apply @ A @ E @ D)) | ~ (member @ D @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[23])). 90.45/24.83 thf(446,plain,(! [C:$i,B:$i,A:$i] : (((member @ A @ (singleton @ A)) != (member @ C @ (difference @ B @ (singleton @ C)))))),inference(paramod_ordered,[status(thm)],[114,390])). 90.45/24.83 thf(450,plain,(! [C:$i,B:$i,A:$i] : ((A != C) | ((singleton @ A) != (difference @ B @ (singleton @ C))))),inference(simp,[status(thm)],[446])). 90.45/24.83 thf(454,plain,(! [B:$i,A:$i] : (((difference @ A @ (singleton @ B)) != (singleton @ B)))),inference(simp,[status(thm)],[450])). 90.45/24.83 thf(3294,plain,(! [B:$i,A:$i] : (((product @ sk5) != empty_set) | ((image2 @ sk1 @ sk3) != (image2 @ A @ (difference @ B @ (product @ empty_set)))))),inference(paramod_ordered,[status(thm)],[38,3131])). 90.45/24.83 thf(3295,plain,(! [B:$i,A:$i] : (((product @ sk5) != empty_set) | (sk1 != A) | ((difference @ B @ (product @ empty_set)) != sk3))),inference(simp,[status(thm)],[3294])). 90.45/24.83 thf(3296,plain,(! [A:$i] : (((product @ sk5) != empty_set) | ((difference @ A @ (product @ empty_set)) != sk3))),inference(simp,[status(thm)],[3295])). 90.45/24.83 thf(10,axiom,((! [A:$i,B:$i,C:$i]: ((member @ A @ (union @ B @ C)) <=> ((member @ A @ C) | (member @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union)). 90.45/24.83 thf(100,plain,((! [A:$i,B:$i,C:$i]: (((member @ A @ (union @ B @ C)) => ((member @ A @ C) | (member @ A @ B))) & (((member @ A @ C) | (member @ A @ B)) => (member @ A @ (union @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[10])). 90.45/24.83 thf(6194,plain,($false),inference(cvc4,[status(thm)],[138,1168,3345,1237,962,2250,408,115,217,994,1164,1233,829,37,1703,389,52,1709,1430,3131,785,2708,46,57,78,261,1232,2616,789,321,2469,353,61,293,453,998,74,60,925,85,761,1723,957,1174,38,297,2606,788,33,3339,1883,2565,1888,1159,2327,757,974,1234,388,77,1424,2613,2349,706,3354,129,1246,1715,134,73,237,205,765,1712,1846,1170,1895,2617,965,34,45,161,819,423,1884,44,826,958,59,2716,281,259,787,1239,49,466,236,1897,3532,764,187,3352,1853,1894,784,1524,230,451,76,1722,318,39,387,367,91,964,668,2725,959,2620,2244,505,80,167,35,1420,2333,2846,2564,754,968,1181,295,971,327,3462,2720,993,1711,50,2468,31,336,2711,72,386,1717,3007,43,991,1180,961,963,2251,390,114,1854,171,139,1244,995,75,58,929,478,1893,287,2517,36,168,51,326,107,136,767,1891,960,1713,68,1885,254,337,122,1184,2615,222,454,3296,100])). 90.45/24.83 % SZS output end CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p 90.45/24.83 % [INFO] Killing All external provers ... 90.63/24.87 EOF