0.01/0.03 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.01/0.04 % 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 0.02/0.24 % Computer : n005.star.cs.uiowa.edu 0.02/0.24 % Model : x86_64 x86_64 0.02/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz 0.02/0.24 % Memory : 32218.625MB 0.02/0.24 % OS : Linux 3.10.0-693.2.2.el7.x86_64 0.02/0.24 % CPULimit : 300 0.02/0.24 % DateTime : Sat Jul 14 05:34:40 CDT 2018 0.02/0.24 % CPUTime : 2.34/1.44 % [INFO] Running in sequential loop mode. 3.09/1.68 % [CONFIG] Using configuration: timeout(300) with strategy 3.32/1.76 % [INFO] iprover registered as external prover. 3.32/1.76 % [INFO] e registered as external prover. 3.32/1.76 % [INFO] cvc4 registered as external prover. 3.32/1.77 % [INFO] Parsing finished. Scanning for conjecture ... 3.77/1.83 % [INFO] Found a conjecture and 28 axioms. Running axiom selection ... 3.77/1.90 % [INFO] Axiom selection finished. Selected 28 axioms (removed 0 axioms). 4.36/2.01 % [INFO] Type checking passed. Searching for refutation ... 122.36/32.71 % [INFO] Killing All external provers ... 122.36/32.71 % Time passed: 32372ms 122.36/32.71 % Effective reasoning time: 31256ms 122.36/32.71 % Solved by strategy 122.36/32.71 % 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 122.36/32.71 % No. of inferences in proof: 499 122.36/32.71 % No. of processed clauses: 221 122.36/32.71 % No. of generated clauses: 4108 122.36/32.71 % No. of forward subsumed clauses: 39 122.36/32.71 % No. of backward subsumed clauses: 0 122.36/32.71 % No. of ground rewrite rules in store: 27 122.36/32.71 % No. of non-ground rewrite rules in store: 35 122.36/32.71 % No. of positive (non-rewrite) units in store: 0 122.36/32.71 % No. of negative (non-rewrite) units in store: 62 122.36/32.71 % No. of choice functions detected: 0 122.36/32.71 % No. of choice instantiations: 0 122.36/32.71 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 32372 ms resp. 31256 ms w/o parsing 122.84/33.11 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p 122.84/33.11 thf(increasing_type, type, increasing: ($i > ($i > ($i > ($i > ($i > $o)))))). 122.84/33.11 thf(inverse_function_type, type, inverse_function: ($i > ($i > ($i > $i)))). 122.84/33.11 thf(isomorphism_type, type, isomorphism: ($i > ($i > ($i > ($i > ($i > $o)))))). 122.84/33.11 thf(one_to_one_type, type, one_to_one: ($i > ($i > ($i > $o)))). 122.84/33.11 thf(maps_type, type, maps: ($i > ($i > ($i > $o)))). 122.84/33.11 thf(subset_type, type, subset: ($i > ($i > $o))). 122.84/33.11 thf(equal_set_type, type, equal_set: ($i > ($i > $o))). 122.84/33.11 thf(image2_type, type, image2: ($i > ($i > $i))). 122.84/33.11 thf(member_type, type, member: ($i > ($i > $o))). 122.84/33.11 thf(apply_type, type, apply: ($i > ($i > ($i > $o)))). 122.84/33.11 thf(inverse_image3_type, type, inverse_image3: ($i > ($i > ($i > $i)))). 122.84/33.11 thf(decreasing_type, type, decreasing: ($i > ($i > ($i > ($i > ($i > $o)))))). 122.84/33.11 thf(power_set_type, type, power_set: ($i > $i)). 122.84/33.11 thf(intersection_type, type, intersection: ($i > ($i > $i))). 122.84/33.11 thf(image3_type, type, image3: ($i > ($i > ($i > $i)))). 122.84/33.11 thf(union_type, type, union: ($i > ($i > $i))). 122.84/33.11 thf(singleton_type, type, singleton: ($i > $i)). 122.84/33.11 thf(inverse_image2_type, type, inverse_image2: ($i > ($i > $i))). 122.84/33.11 thf(product_type, type, product: ($i > $i)). 122.84/33.11 thf(empty_set_type, type, empty_set: $i). 122.84/33.11 thf(compose_predicate_type, type, compose_predicate: ($i > ($i > ($i > ($i > ($i > ($i > $o))))))). 122.84/33.11 thf(difference_type, type, difference: ($i > ($i > $i))). 122.84/33.11 thf(inverse_predicate_type, type, inverse_predicate: ($i > ($i > ($i > ($i > $o))))). 122.84/33.11 thf(equal_maps_type, type, equal_maps: ($i > ($i > ($i > ($i > $o))))). 122.84/33.11 thf(compose_function_type, type, compose_function: ($i > ($i > ($i > ($i > ($i > $i)))))). 122.84/33.11 thf(surjective_type, type, surjective: ($i > ($i > ($i > $o)))). 122.84/33.11 thf(injective_type, type, injective: ($i > ($i > ($i > $o)))). 122.84/33.11 thf(identity_type, type, identity: ($i > ($i > $o))). 122.84/33.11 thf(sum_type, type, sum: ($i > $i)). 122.84/33.11 thf(unordered_pair_type, type, unordered_pair: ($i > ($i > $i))). 122.84/33.11 thf(sk1_type, type, sk1: $i). 122.84/33.11 thf(sk2_type, type, sk2: $i). 122.84/33.11 thf(sk3_type, type, sk3: $i). 122.84/33.11 thf(sk4_type, type, sk4: $o). 122.84/33.11 thf(sk5_type, type, sk5: $i). 122.84/33.11 thf(sk6_type, type, sk6: $i). 122.84/33.11 thf(sk7_type, type, sk7: $i). 122.84/33.11 thf(sk8_type, type, sk8: $i). 122.84/33.11 thf(sk9_type, type, sk9: ($i > ($i > ($i > $i)))). 122.84/33.11 thf(sk10_type, type, sk10: ($i > ($i > ($i > ($i > $i))))). 122.84/33.11 thf(sk11_type, type, sk11: ($i > ($i > ($i > ($i > ($i > $i)))))). 122.84/33.11 thf(sk12_type, type, sk12: ($i > ($i > ($i > ($i > ($i > $i)))))). 122.84/33.11 thf(sk13_type, type, sk13: ($i > ($i > ($i > ($i > ($i > $i)))))). 122.84/33.11 thf(sk14_type, type, sk14: ($i > ($i > ($i > ($i > ($i > $i)))))). 122.84/33.11 thf(sk17_type, type, sk17: ($i > ($i > $i))). 122.84/33.11 thf(sk29_type, type, sk29: ($i > ($i > ($i > $i)))). 122.84/33.11 thf(sk31_type, type, sk31: ($i > ($i > $i))). 122.84/33.11 thf(sk35_type, type, sk35: ($i > ($i > $i))). 122.84/33.11 thf(11,axiom,((! [A:$i,B:$i]: ((A = B) <=> (member @ A @ (singleton @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton)). 122.84/33.11 thf(108,plain,((! [A:$i,B:$i]: (((A = B) => (member @ A @ (singleton @ B))) & ((member @ A @ (singleton @ B)) => (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[11])). 122.84/33.11 thf(109,plain,((! [A:$i,B:$i]: ((A = B) => (member @ A @ (singleton @ B))) & ! [A:$i,B:$i]: ((member @ A @ (singleton @ B)) => (A = B)))),inference(miniscope,[status(thm)],[108])). 122.84/33.11 thf(110,plain,(! [B:$i,A:$i] : ((~ (member @ A @ (singleton @ B))) | (A = B))),inference(cnf,[status(esa)],[109])). 122.84/33.11 thf(112,plain,(! [B:$i,A:$i] : ((A = B) | (~ (member @ A @ (singleton @ B))))),inference(lifteq,[status(thm)],[110])). 122.84/33.11 thf(113,plain,(! [B:$i,A:$i] : ((A = B) | (~ (member @ A @ (singleton @ B))))),inference(simp,[status(thm)],[112])). 122.84/33.11 thf(111,plain,(! [B:$i,A:$i] : ((~ (A = B)) | (member @ A @ (singleton @ B)))),inference(cnf,[status(esa)],[109])). 122.84/33.11 thf(114,plain,(! [B:$i,A:$i] : ((A != B) | (member @ A @ (singleton @ B)))),inference(lifteq,[status(thm)],[111])). 122.84/33.11 thf(115,plain,(! [A:$i] : ((member @ A @ (singleton @ A)))),inference(simp,[status(thm)],[114])). 122.84/33.11 thf(13,axiom,((! [A:$i,B:$i]: ((member @ A @ (product @ B)) <=> (! [C:$i]: ((member @ C @ B) => (member @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product)). 122.84/33.11 thf(123,plain,((! [A:$i,B:$i]: (((member @ A @ (product @ B)) => (! [C:$i]: ((member @ C @ B) => (member @ A @ C)))) & ((! [C:$i]: ((member @ C @ B) => (member @ A @ C))) => (member @ A @ (product @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[13])). 122.84/33.11 thf(124,plain,((! [A:$i,B:$i]: ((member @ A @ (product @ B)) => (! [C:$i]: ((member @ C @ B) => (member @ A @ C)))) & ! [A:$i,B:$i]: ((! [C:$i]: ((member @ C @ B) => (member @ A @ C))) => (member @ A @ (product @ B))))),inference(miniscope,[status(thm)],[123])). 122.84/33.11 thf(125,plain,(! [B:$i,A:$i] : ((member @ (sk17 @ B @ A) @ B) | (member @ A @ (product @ B)))),inference(cnf,[status(esa)],[124])). 122.84/33.11 thf(128,plain,(! [B:$i,A:$i] : ((member @ (sk17 @ B @ A) @ B) | (member @ A @ (product @ B)))),inference(simp,[status(thm)],[125])). 122.84/33.11 thf(14,axiom,((! [A:$i]: ~ (member @ A @ empty_set))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set)). 122.84/33.11 thf(130,plain,((! [A:$i]: ~ (member @ A @ empty_set))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[14])). 122.84/33.11 thf(131,plain,((~ (? [A:$i]: (member @ A @ empty_set)))),inference(miniscope,[status(thm)],[130])). 122.84/33.11 thf(132,plain,(! [A:$i] : ((~ (member @ A @ empty_set)))),inference(cnf,[status(esa)],[131])). 122.84/33.11 thf(475,plain,(! [C:$i,B:$i,A:$i] : ((member @ A @ (product @ B)) | ((member @ (sk17 @ B @ A) @ B) != (member @ C @ empty_set)))),inference(paramod_ordered,[status(thm)],[128,132])). 122.84/33.11 thf(476,plain,(! [A:$i] : ((member @ A @ (product @ empty_set)))),inference(pattern_uni,[status(thm)],[475:[bind(A, $thf(E)),bind(B, $thf(empty_set)),bind(C, $thf(sk17 @ empty_set @ E))]])). 122.84/33.11 thf(499,plain,(! [A:$i] : ((member @ A @ (product @ empty_set)))),inference(simp,[status(thm)],[476])). 122.84/33.11 thf(502,plain,(! [B:$i,A:$i] : (((member @ A @ (product @ empty_set)) != (member @ B @ empty_set)))),inference(paramod_ordered,[status(thm)],[499,132])). 122.84/33.11 thf(517,plain,(! [B:$i,A:$i] : ((A != B) | ((product @ empty_set) != empty_set))),inference(simp,[status(thm)],[502])). 122.84/33.11 thf(523,plain,(((product @ empty_set) != empty_set)),inference(simp,[status(thm)],[517])). 122.84/33.11 thf(683,plain,(! [B:$i,A:$i] : ((~ (member @ A @ (singleton @ B))) | (B != empty_set) | (A != (product @ empty_set)))),inference(paramod_ordered,[status(thm)],[113,523])). 122.84/33.11 thf(684,plain,(! [A:$i] : ((~ (member @ (product @ empty_set) @ (singleton @ A))) | (A != empty_set))),inference(pattern_uni,[status(thm)],[683:[bind(A, $thf(product @ empty_set)),bind(B, $thf(B))]])). 122.84/33.11 thf(1582,plain,((~ (member @ (product @ empty_set) @ (singleton @ empty_set)))),inference(simp,[status(thm)],[684])). 122.84/33.11 thf(1748,plain,(! [A:$i] : (((member @ A @ (product @ empty_set)) != (member @ (product @ empty_set) @ (singleton @ empty_set))))),inference(paramod_ordered,[status(thm)],[499,1582])). 122.84/33.11 thf(1777,plain,(! [A:$i] : ((A != (product @ empty_set)) | ((product @ empty_set) != (singleton @ empty_set)))),inference(simp,[status(thm)],[1748])). 122.84/33.11 thf(1793,plain,(((product @ empty_set) != (singleton @ empty_set))),inference(simp,[status(thm)],[1777])). 122.84/33.11 thf(1796,plain,(! [B:$i,A:$i] : ((~ (member @ A @ (singleton @ B))) | (B != (singleton @ empty_set)) | (A != (product @ empty_set)))),inference(paramod_ordered,[status(thm)],[113,1793])). 122.84/33.11 thf(1797,plain,(! [A:$i] : ((~ (member @ (product @ empty_set) @ (singleton @ A))) | (A != (singleton @ empty_set)))),inference(pattern_uni,[status(thm)],[1796:[bind(A, $thf(product @ empty_set)),bind(B, $thf(B))]])). 122.84/33.11 thf(1804,plain,((~ (member @ (product @ empty_set) @ (singleton @ (singleton @ empty_set))))),inference(simp,[status(thm)],[1797])). 122.84/33.11 thf(2021,plain,(! [A:$i] : (((member @ A @ (singleton @ A)) != (member @ (product @ empty_set) @ (singleton @ (singleton @ empty_set)))))),inference(paramod_ordered,[status(thm)],[115,1804])). 122.84/33.11 thf(2062,plain,(! [A:$i] : ((A != (product @ empty_set)) | ((singleton @ A) != (singleton @ (singleton @ empty_set))))),inference(simp,[status(thm)],[2021])). 122.84/33.11 thf(2064,plain,(((singleton @ (product @ empty_set)) != (singleton @ (singleton @ empty_set)))),inference(simp,[status(thm)],[2062])). 122.84/33.11 thf(2155,plain,(! [B:$i,A:$i] : ((~ (member @ A @ (singleton @ B))) | (A != (singleton @ (singleton @ empty_set))) | (B != (singleton @ (product @ empty_set))))),inference(paramod_ordered,[status(thm)],[113,2064])). 122.84/33.11 thf(2156,plain,(! [A:$i] : ((~ (member @ A @ (singleton @ (singleton @ (product @ empty_set))))) | (A != (singleton @ (singleton @ empty_set))))),inference(pattern_uni,[status(thm)],[2155:[bind(A, $thf(A)),bind(B, $thf(singleton @ (product @ empty_set)))]])). 122.84/33.11 thf(2163,plain,((~ (member @ (singleton @ (singleton @ empty_set)) @ (singleton @ (singleton @ (product @ empty_set)))))),inference(simp,[status(thm)],[2156])). 122.84/33.11 thf(6,axiom,((! [A:$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)). 122.84/33.11 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:$i]: (((member @ F @ B) & (member @ G @ D) & (member @ H @ B) & (member @ I @ D) & (apply @ A @ H @ I) & (apply @ A @ F @ G) & (apply @ C @ F @ H)) => (apply @ E @ I @ G)))) & ((! [F:$i,G:$i,H:$i,I:$i]: (((member @ F @ B) & (member @ G @ D) & (member @ H @ B) & (member @ I @ D) & (apply @ A @ H @ I) & (apply @ A @ F @ G) & (apply @ C @ F @ H)) => (apply @ E @ I @ G))) => (decreasing @ A @ B @ C @ D @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])). 122.84/33.11 thf(63,plain,((! [A:$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:$i]: (((member @ F @ B) & (member @ G @ D) & (member @ H @ B) & (member @ I @ D) & (apply @ A @ H @ I) & (apply @ A @ F @ G) & (apply @ C @ F @ H)) => (apply @ E @ I @ G))) => (decreasing @ A @ B @ C @ D @ E)))),inference(miniscope,[status(thm)],[62])). 122.84/33.11 thf(69,plain,(! [I:$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)],[63])). 122.84/33.11 thf(25,axiom,((! [A:$i,B:$i,C:$i]: ((member @ A @ (unordered_pair @ B @ C)) <=> ((A = C) | (B = A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair)). 122.84/33.11 thf(240,plain,((! [A:$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)],[25])). 122.84/33.11 thf(241,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)],[240])). 122.84/33.11 thf(242,plain,(! [C:$i,B:$i,A:$i] : ((~ (A = C)) | (member @ A @ (unordered_pair @ B @ C)))),inference(cnf,[status(esa)],[241])). 122.84/33.11 thf(245,plain,(! [C:$i,B:$i,A:$i] : ((A != C) | (member @ A @ (unordered_pair @ B @ C)))),inference(lifteq,[status(thm)],[242])). 122.84/33.11 thf(246,plain,(! [B:$i,A:$i] : ((member @ B @ (unordered_pair @ A @ B)))),inference(simp,[status(thm)],[245])). 122.84/33.11 thf(16,axiom,((! [A:$i,B:$i,C:$i]: (((member @ A @ C) & ~ (member @ A @ B)) <=> (member @ A @ (difference @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference)). 122.84/33.11 thf(155,plain,((! [A:$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)],[16])). 122.84/33.11 thf(156,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)],[155])). 122.84/33.11 thf(158,plain,(! [C:$i,B:$i,A:$i] : ((~ (member @ A @ (difference @ C @ B))) | (~ (member @ A @ B)))),inference(cnf,[status(esa)],[156])). 122.84/33.11 thf(161,plain,(! [C:$i,B:$i,A:$i] : ((~ (member @ A @ (difference @ C @ B))) | (~ (member @ A @ B)))),inference(simp,[status(thm)],[158])). 122.84/33.11 thf(336,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)],[115,161])). 122.84/33.11 thf(337,plain,(! [B:$i,A:$i] : ((~ (member @ B @ (difference @ A @ (singleton @ B)))))),inference(pattern_uni,[status(thm)],[336:[bind(A, $thf(E)),bind(B, $thf(E)),bind(C, $thf(singleton @ E))]])). 122.84/33.11 thf(356,plain,(! [B:$i,A:$i] : ((~ (member @ B @ (difference @ A @ (singleton @ B)))))),inference(simp,[status(thm)],[337])). 122.84/33.11 thf(359,plain,(! [D:$i,C:$i,B:$i,A:$i] : (((member @ B @ (unordered_pair @ A @ B)) != (member @ D @ (difference @ C @ (singleton @ D)))))),inference(paramod_ordered,[status(thm)],[246,356])). 122.84/33.11 thf(362,plain,(! [D:$i,C:$i,B:$i,A:$i] : ((B != D) | ((unordered_pair @ A @ B) != (difference @ C @ (singleton @ D))))),inference(simp,[status(thm)],[359])). 122.84/33.11 thf(365,plain,(! [C:$i,B:$i,A:$i] : (((unordered_pair @ A @ C) != (difference @ B @ (singleton @ C))))),inference(simp,[status(thm)],[362])). 122.84/33.11 thf(10,axiom,((! [A:$i,B:$i,C:$i]: ((member @ A @ (union @ B @ C)) <=> ((member @ A @ C) | (member @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union)). 122.84/33.11 thf(101,plain,((! [A:$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])). 122.84/33.11 thf(2024,plain,(! [A:$i] : (((member @ A @ (product @ empty_set)) != (member @ (product @ empty_set) @ (singleton @ (singleton @ empty_set)))))),inference(paramod_ordered,[status(thm)],[499,1804])). 122.84/33.11 thf(2054,plain,(! [A:$i] : ((A != (product @ empty_set)) | ((product @ empty_set) != (singleton @ (singleton @ empty_set))))),inference(simp,[status(thm)],[2024])). 122.84/33.11 thf(2075,plain,(((product @ empty_set) != (singleton @ (singleton @ empty_set)))),inference(simp,[status(thm)],[2054])). 122.84/33.11 thf(2079,plain,(! [B:$i,A:$i] : ((~ (member @ A @ (singleton @ B))) | (B != (singleton @ (singleton @ empty_set))) | (A != (product @ empty_set)))),inference(paramod_ordered,[status(thm)],[113,2075])). 122.84/33.11 thf(2080,plain,(! [A:$i] : ((~ (member @ (product @ empty_set) @ (singleton @ A))) | (A != (singleton @ (singleton @ empty_set))))),inference(pattern_uni,[status(thm)],[2079:[bind(A, $thf(product @ empty_set)),bind(B, $thf(B))]])). 122.84/33.11 thf(2087,plain,((~ (member @ (product @ empty_set) @ (singleton @ (singleton @ (singleton @ empty_set)))))),inference(simp,[status(thm)],[2080])). 122.84/33.11 thf(2705,plain,(! [A:$i] : (((member @ A @ (product @ empty_set)) != (member @ (product @ empty_set) @ (singleton @ (singleton @ (singleton @ empty_set))))))),inference(paramod_ordered,[status(thm)],[499,2087])). 122.84/33.11 thf(2741,plain,(! [A:$i] : ((A != (product @ empty_set)) | ((product @ empty_set) != (singleton @ (singleton @ (singleton @ empty_set)))))),inference(simp,[status(thm)],[2705])). 122.84/33.11 thf(2756,plain,(((product @ empty_set) != (singleton @ (singleton @ (singleton @ empty_set))))),inference(simp,[status(thm)],[2741])). 122.84/33.11 thf(2772,plain,(! [B:$i,A:$i] : ((~ (member @ A @ (singleton @ B))) | (A != (singleton @ (singleton @ (singleton @ empty_set)))) | (B != (product @ empty_set)))),inference(paramod_ordered,[status(thm)],[113,2756])). 122.84/33.11 thf(2773,plain,(! [A:$i] : ((~ (member @ A @ (singleton @ (product @ empty_set)))) | (A != (singleton @ (singleton @ (singleton @ empty_set)))))),inference(pattern_uni,[status(thm)],[2772:[bind(A, $thf(A)),bind(B, $thf(product @ empty_set))]])). 122.84/33.11 thf(2778,plain,((~ (member @ (singleton @ (singleton @ (singleton @ empty_set))) @ (singleton @ (product @ empty_set))))),inference(simp,[status(thm)],[2773])). 122.84/33.11 thf(2768,plain,(! [B:$i,A:$i] : ((~ (member @ A @ (singleton @ B))) | (B != (singleton @ (singleton @ (singleton @ empty_set)))) | (A != (product @ empty_set)))),inference(paramod_ordered,[status(thm)],[113,2756])). 122.84/33.11 thf(2769,plain,(! [A:$i] : ((~ (member @ (product @ empty_set) @ (singleton @ A))) | (A != (singleton @ (singleton @ (singleton @ empty_set)))))),inference(pattern_uni,[status(thm)],[2768:[bind(A, $thf(product @ empty_set)),bind(B, $thf(B))]])). 122.84/33.11 thf(2776,plain,((~ (member @ (product @ empty_set) @ (singleton @ (singleton @ (singleton @ (singleton @ empty_set))))))),inference(simp,[status(thm)],[2769])). 122.84/33.11 thf(3961,plain,(! [A:$i] : (((member @ A @ (singleton @ A)) != (member @ (product @ empty_set) @ (singleton @ (singleton @ (singleton @ (singleton @ empty_set)))))))),inference(paramod_ordered,[status(thm)],[115,2776])). 122.84/33.11 thf(4012,plain,(! [A:$i] : ((A != (product @ empty_set)) | ((singleton @ A) != (singleton @ (singleton @ (singleton @ (singleton @ empty_set))))))),inference(simp,[status(thm)],[3961])). 122.84/33.11 thf(4022,plain,(((singleton @ (product @ empty_set)) != (singleton @ (singleton @ (singleton @ (singleton @ empty_set)))))),inference(simp,[status(thm)],[4012])). 122.84/33.11 thf(24,axiom,((! [A:$i,B:$i]: ((member @ A @ (sum @ B)) <=> (? [C:$i]: ((member @ C @ B) & (member @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum)). 122.84/33.11 thf(234,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)],[24])). 122.84/33.11 thf(1,conjecture,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((((increasing @ A @ B @ D @ C @ E) & (increasing @ (inverse_function @ A @ B @ C) @ C @ E @ B @ D)) <=> (isomorphism @ A @ B @ D @ C @ E)) <= ((one_to_one @ A @ B @ C) & (maps @ A @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thII41)). 122.84/33.11 thf(2,negated_conjecture,((~ (! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((((increasing @ A @ B @ D @ C @ E) & (increasing @ (inverse_function @ A @ B @ C) @ C @ E @ B @ D)) <=> (isomorphism @ A @ B @ D @ C @ E)) <= ((one_to_one @ A @ B @ C) & (maps @ A @ B @ C)))))),inference(neg_conjecture,[status(cth)],[1])). 122.84/33.11 thf(31,plain,((~ (! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((((increasing @ A @ B @ D @ C @ E) & (increasing @ (inverse_function @ A @ B @ C) @ C @ E @ B @ D)) => (isomorphism @ A @ B @ D @ C @ E)) & ((isomorphism @ A @ B @ D @ C @ E) => ((increasing @ A @ B @ D @ C @ E) & (increasing @ (inverse_function @ A @ B @ C) @ C @ E @ B @ D)))) | ~ ((one_to_one @ A @ B @ C) & (maps @ A @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])). 122.84/33.11 thf(32,plain,((~ (! [A:$i,B:$i,C:$i]: ((! [D:$i,E:$i]: (((increasing @ A @ B @ D @ C @ E) & (increasing @ (inverse_function @ A @ B @ C) @ C @ E @ B @ D)) => (isomorphism @ A @ B @ D @ C @ E)) & ! [D:$i,E:$i]: ((isomorphism @ A @ B @ D @ C @ E) => ((increasing @ A @ B @ D @ C @ E) & (increasing @ (inverse_function @ A @ B @ C) @ C @ E @ B @ D)))) | ~ ((one_to_one @ A @ B @ C) & (maps @ A @ B @ C)))))),inference(miniscope,[status(thm)],[31])). 122.84/33.11 thf(35,plain,((maps @ sk1 @ sk2 @ sk3)),inference(cnf,[status(esa)],[32])). 122.84/33.11 thf(1105,plain,(! [B:$i,A:$i] : ((~ (member @ A @ (singleton @ B))) | (maps @ B @ sk2 @ sk3) | (A != sk1))),inference(paramod_ordered,[status(thm)],[113,35])). 122.84/33.11 thf(1106,plain,(! [A:$i] : ((~ (member @ sk1 @ (singleton @ A))) | (maps @ A @ sk2 @ sk3))),inference(pattern_uni,[status(thm)],[1105:[bind(A, $thf(sk1))]])). 122.84/33.11 thf(1433,plain,(! [A:$i] : ((~ (member @ sk1 @ (singleton @ A))) | (maps @ A @ sk2 @ sk3))),inference(simp,[status(thm)],[1106])). 122.84/33.11 thf(4938,plain,(! [B:$i,A:$i] : ((maps @ B @ sk2 @ sk3) | ((member @ A @ (product @ empty_set)) != (member @ sk1 @ (singleton @ B))))),inference(paramod_ordered,[status(thm)],[499,1433])). 122.84/33.11 thf(4968,plain,(! [B:$i,A:$i] : ((maps @ B @ sk2 @ sk3) | (A != sk1) | ((product @ empty_set) != (singleton @ B)))),inference(simp,[status(thm)],[4938])). 122.84/33.11 thf(4992,plain,(! [A:$i] : ((maps @ A @ sk2 @ sk3) | ((product @ empty_set) != (singleton @ A)))),inference(simp,[status(thm)],[4968])). 122.84/33.11 thf(317,plain,(! [B:$i,A:$i] : (((member @ A @ (singleton @ A)) != (member @ B @ empty_set)))),inference(paramod_ordered,[status(thm)],[115,132])). 122.84/33.11 thf(318,plain,(! [B:$i,A:$i] : ((A != B) | ((singleton @ A) != empty_set))),inference(simp,[status(thm)],[317])). 122.84/33.11 thf(319,plain,(! [A:$i] : (((singleton @ A) != empty_set))),inference(simp,[status(thm)],[318])). 122.84/33.11 thf(1175,plain,(! [C:$i,B:$i,A:$i] : ((~ (member @ A @ (singleton @ B))) | (B != empty_set) | (A != (singleton @ C)))),inference(paramod_ordered,[status(thm)],[113,319])). 122.84/33.11 thf(1176,plain,(! [B:$i,A:$i] : ((~ (member @ (singleton @ B) @ (singleton @ A))) | (A != empty_set))),inference(pattern_uni,[status(thm)],[1175:[bind(A, $thf(singleton @ D)),bind(B, $thf(B)),bind(C, $thf(D))]])). 122.84/33.11 thf(1522,plain,(! [A:$i] : ((~ (member @ (singleton @ A) @ (singleton @ empty_set))))),inference(simp,[status(thm)],[1176])). 122.84/33.11 thf(687,plain,(! [B:$i,A:$i] : ((~ (member @ A @ (singleton @ B))) | (A != empty_set) | (B != (product @ empty_set)))),inference(paramod_ordered,[status(thm)],[113,523])). 122.84/33.11 thf(688,plain,(! [A:$i] : ((~ (member @ A @ (singleton @ (product @ empty_set)))) | (A != empty_set))),inference(pattern_uni,[status(thm)],[687:[bind(A, $thf(A)),bind(B, $thf(product @ empty_set))]])). 122.84/33.11 thf(1569,plain,((~ (member @ empty_set @ (singleton @ (product @ empty_set))))),inference(simp,[status(thm)],[688])). 122.84/33.11 thf(1698,plain,(! [A:$i] : (((member @ A @ (product @ empty_set)) != (member @ empty_set @ (singleton @ (product @ empty_set)))))),inference(paramod_ordered,[status(thm)],[499,1569])). 122.84/33.11 thf(1727,plain,(! [A:$i] : ((A != empty_set) | ((singleton @ (product @ empty_set)) != (product @ empty_set)))),inference(simp,[status(thm)],[1698])). 122.84/33.11 thf(1739,plain,(((singleton @ (product @ empty_set)) != (product @ empty_set))),inference(simp,[status(thm)],[1727])). 122.84/33.11 thf(1824,plain,(! [B:$i,A:$i] : ((~ (member @ A @ (singleton @ B))) | (B != (product @ empty_set)) | (A != (singleton @ (product @ empty_set))))),inference(paramod_ordered,[status(thm)],[113,1739])). 122.84/33.11 thf(1825,plain,(! [A:$i] : ((~ (member @ (singleton @ (product @ empty_set)) @ (singleton @ A))) | (A != (product @ empty_set)))),inference(pattern_uni,[status(thm)],[1824:[bind(A, $thf(singleton @ (product @ empty_set))),bind(B, $thf(B))]])). 122.84/33.11 thf(1836,plain,((~ (member @ (singleton @ (product @ empty_set)) @ (singleton @ (product @ empty_set))))),inference(simp,[status(thm)],[1825])). 122.84/33.11 thf(2570,plain,(! [A:$i] : (((member @ A @ (singleton @ A)) != (member @ (singleton @ (product @ empty_set)) @ (singleton @ (product @ empty_set)))))),inference(paramod_ordered,[status(thm)],[115,1836])). 122.84/33.11 thf(2610,plain,(! [A:$i] : ((A != (singleton @ (product @ empty_set))) | ((singleton @ A) != (singleton @ (product @ empty_set))))),inference(simp,[status(thm)],[2570])). 122.84/33.11 thf(2627,plain,(((singleton @ (singleton @ (product @ empty_set))) != (singleton @ (product @ empty_set)))),inference(simp,[status(thm)],[2610])). 122.84/33.11 thf(3031,plain,(! [B:$i,A:$i] : ((~ (member @ A @ (singleton @ B))) | (A != (singleton @ (product @ empty_set))) | (B != (singleton @ (singleton @ (product @ empty_set)))))),inference(paramod_ordered,[status(thm)],[113,2627])). 122.84/33.11 thf(3032,plain,(! [A:$i] : ((~ (member @ A @ (singleton @ (singleton @ (singleton @ (product @ empty_set)))))) | (A != (singleton @ (product @ empty_set))))),inference(pattern_uni,[status(thm)],[3031:[bind(A, $thf(A)),bind(B, $thf(singleton @ (singleton @ (product @ empty_set))))]])). 122.84/33.11 thf(3040,plain,((~ (member @ (singleton @ (product @ empty_set)) @ (singleton @ (singleton @ (singleton @ (product @ empty_set))))))),inference(simp,[status(thm)],[3032])). 122.84/33.11 thf(1696,plain,(! [A:$i] : (((member @ A @ (singleton @ A)) != (member @ empty_set @ (singleton @ (product @ empty_set)))))),inference(paramod_ordered,[status(thm)],[115,1569])). 122.84/33.11 thf(1724,plain,(! [A:$i] : ((A != empty_set) | ((singleton @ A) != (singleton @ (product @ empty_set))))),inference(simp,[status(thm)],[1696])). 122.84/33.11 thf(1735,plain,(((singleton @ (product @ empty_set)) != (singleton @ empty_set))),inference(simp,[status(thm)],[1724])). 122.84/33.11 thf(1814,plain,(! [B:$i,A:$i] : ((~ (member @ A @ (singleton @ B))) | (A != (singleton @ empty_set)) | (B != (singleton @ (product @ empty_set))))),inference(paramod_ordered,[status(thm)],[113,1735])). 122.84/33.11 thf(1815,plain,(! [A:$i] : ((~ (member @ A @ (singleton @ (singleton @ (product @ empty_set))))) | (A != (singleton @ empty_set)))),inference(pattern_uni,[status(thm)],[1814:[bind(A, $thf(A)),bind(B, $thf(singleton @ (product @ empty_set)))]])). 122.84/33.11 thf(1820,plain,((~ (member @ (singleton @ empty_set) @ (singleton @ (singleton @ (product @ empty_set)))))),inference(simp,[status(thm)],[1815])). 122.84/33.11 thf(2168,plain,(! [A:$i] : (((member @ A @ (product @ empty_set)) != (member @ (singleton @ empty_set) @ (singleton @ (singleton @ (product @ empty_set))))))),inference(paramod_ordered,[status(thm)],[499,1820])). 122.84/33.11 thf(2202,plain,(! [A:$i] : ((A != (singleton @ empty_set)) | ((singleton @ (singleton @ (product @ empty_set))) != (product @ empty_set)))),inference(simp,[status(thm)],[2168])). 122.84/33.11 thf(2222,plain,(((singleton @ (singleton @ (product @ empty_set))) != (product @ empty_set))),inference(simp,[status(thm)],[2202])). 122.84/33.11 thf(2491,plain,(! [B:$i,A:$i] : ((~ (member @ A @ (singleton @ B))) | (A != (product @ empty_set)) | (B != (singleton @ (singleton @ (product @ empty_set)))))),inference(paramod_ordered,[status(thm)],[113,2222])). 122.84/33.11 thf(2492,plain,(! [A:$i] : ((~ (member @ A @ (singleton @ (singleton @ (singleton @ (product @ empty_set)))))) | (A != (product @ empty_set)))),inference(pattern_uni,[status(thm)],[2491:[bind(A, $thf(A)),bind(B, $thf(singleton @ (singleton @ (product @ empty_set))))]])). 122.84/33.11 thf(2500,plain,((~ (member @ (product @ empty_set) @ (singleton @ (singleton @ (singleton @ (product @ empty_set))))))),inference(simp,[status(thm)],[2492])). 122.84/33.11 thf(3791,plain,(! [A:$i] : (((member @ A @ (product @ empty_set)) != (member @ (product @ empty_set) @ (singleton @ (singleton @ (singleton @ (product @ empty_set)))))))),inference(paramod_ordered,[status(thm)],[499,2500])). 122.84/33.11 thf(3835,plain,(! [A:$i] : ((A != (product @ empty_set)) | ((singleton @ (singleton @ (singleton @ (product @ empty_set)))) != (product @ empty_set)))),inference(simp,[status(thm)],[3791])). 122.84/33.11 thf(3846,plain,(((singleton @ (singleton @ (singleton @ (product @ empty_set)))) != (product @ empty_set))),inference(simp,[status(thm)],[3835])). 122.84/33.11 thf(3873,plain,(! [B:$i,A:$i] : ((~ (member @ A @ (singleton @ B))) | (A != (product @ empty_set)) | (B != (singleton @ (singleton @ (singleton @ (product @ empty_set))))))),inference(paramod_ordered,[status(thm)],[113,3846])). 122.84/33.11 thf(3874,plain,(! [A:$i] : ((~ (member @ A @ (singleton @ (singleton @ (singleton @ (singleton @ (product @ empty_set))))))) | (A != (product @ empty_set)))),inference(pattern_uni,[status(thm)],[3873:[bind(A, $thf(A)),bind(B, $thf(singleton @ (singleton @ (singleton @ (product @ empty_set)))))]])). 122.84/33.11 thf(3885,plain,((~ (member @ (product @ empty_set) @ (singleton @ (singleton @ (singleton @ (singleton @ (product @ empty_set)))))))),inference(simp,[status(thm)],[3874])). 122.84/33.11 thf(5631,plain,(! [A:$i] : (((member @ A @ (product @ empty_set)) != (member @ (product @ empty_set) @ (singleton @ (singleton @ (singleton @ (singleton @ (product @ empty_set))))))))),inference(paramod_ordered,[status(thm)],[499,3885])). 122.84/33.11 thf(5680,plain,(! [A:$i] : ((A != (product @ empty_set)) | ((singleton @ (singleton @ (singleton @ (singleton @ (product @ empty_set))))) != (product @ empty_set)))),inference(simp,[status(thm)],[5631])). 122.84/33.11 thf(5691,plain,(((singleton @ (singleton @ (singleton @ (singleton @ (product @ empty_set))))) != (product @ empty_set))),inference(simp,[status(thm)],[5680])). 122.84/33.11 thf(505,plain,(! [D:$i,C:$i,B:$i,A:$i] : ((~ (member @ B @ (difference @ D @ C))) | ((member @ A @ (product @ empty_set)) != (member @ B @ C)))),inference(paramod_ordered,[status(thm)],[499,161])). 122.84/33.11 thf(506,plain,(! [B:$i,A:$i] : ((~ (member @ A @ (difference @ B @ (product @ empty_set)))))),inference(pattern_uni,[status(thm)],[505:[bind(A, $thf(A)),bind(B, $thf(A)),bind(C, $thf(product @ empty_set)),bind(D, $thf(D))]])). 122.84/33.11 thf(525,plain,(! [B:$i,A:$i] : ((~ (member @ A @ (difference @ B @ (product @ empty_set)))))),inference(simp,[status(thm)],[506])). 122.84/33.11 thf(540,plain,(! [D:$i,C:$i,B:$i,A:$i] : (((member @ B @ (unordered_pair @ A @ B)) != (member @ C @ (difference @ D @ (product @ empty_set)))))),inference(paramod_ordered,[status(thm)],[246,525])). 122.84/33.11 thf(545,plain,(! [D:$i,C:$i,B:$i,A:$i] : ((B != C) | ((unordered_pair @ A @ B) != (difference @ D @ (product @ empty_set))))),inference(simp,[status(thm)],[540])). 122.84/33.11 thf(550,plain,(! [C:$i,B:$i,A:$i] : (((unordered_pair @ A @ B) != (difference @ C @ (product @ empty_set))))),inference(simp,[status(thm)],[545])). 122.84/33.11 thf(2149,plain,(! [B:$i,A:$i] : ((~ (member @ A @ (singleton @ B))) | (B != (singleton @ (singleton @ empty_set))) | (A != (singleton @ (product @ empty_set))))),inference(paramod_ordered,[status(thm)],[113,2064])). 122.84/33.11 thf(2150,plain,(! [A:$i] : ((~ (member @ (singleton @ (product @ empty_set)) @ (singleton @ A))) | (A != (singleton @ (singleton @ empty_set))))),inference(pattern_uni,[status(thm)],[2149:[bind(A, $thf(singleton @ (product @ empty_set))),bind(B, $thf(B))]])). 122.84/33.11 thf(2162,plain,((~ (member @ (singleton @ (product @ empty_set)) @ (singleton @ (singleton @ (singleton @ empty_set)))))),inference(simp,[status(thm)],[2150])). 122.84/33.11 thf(3360,plain,(! [A:$i] : (((member @ A @ (singleton @ A)) != (member @ (singleton @ (product @ empty_set)) @ (singleton @ (singleton @ (singleton @ empty_set))))))),inference(paramod_ordered,[status(thm)],[115,2162])). 122.84/33.11 thf(3410,plain,(! [A:$i] : ((A != (singleton @ (product @ empty_set))) | ((singleton @ A) != (singleton @ (singleton @ (singleton @ empty_set)))))),inference(simp,[status(thm)],[3360])). 122.84/33.11 thf(3414,plain,(((singleton @ (singleton @ (product @ empty_set))) != (singleton @ (singleton @ (singleton @ empty_set))))),inference(simp,[status(thm)],[3410])). 122.84/33.11 thf(21,axiom,((! [A:$i,B:$i]: ((subset @ A @ B) <=> (! [C:$i]: ((member @ C @ B) <= (member @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset)). 122.84/33.11 thf(203,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)],[21])). 122.84/33.11 thf(204,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)],[203])). 122.84/33.11 thf(206,plain,(! [B:$i,A:$i] : ((member @ (sk31 @ B @ A) @ A) | (subset @ A @ B))),inference(cnf,[status(esa)],[204])). 122.84/33.11 thf(209,plain,(! [B:$i,A:$i] : ((member @ (sk31 @ B @ A) @ A) | (subset @ A @ B))),inference(simp,[status(thm)],[206])). 122.84/33.11 thf(1113,plain,(! [B:$i,A:$i] : ((~ (member @ A @ (singleton @ B))) | (maps @ sk1 @ A @ sk3) | (B != sk2))),inference(paramod_ordered,[status(thm)],[113,35])). 122.84/33.11 thf(1114,plain,(! [A:$i] : ((~ (member @ A @ (singleton @ sk2))) | (maps @ sk1 @ A @ sk3))),inference(pattern_uni,[status(thm)],[1113:[bind(A, $thf(A)),bind(B, $thf(sk2))]])). 122.84/33.11 thf(3555,plain,(! [C:$i,B:$i,A:$i] : ((subset @ A @ B) | (maps @ sk1 @ C @ sk3) | ((member @ (sk31 @ B @ A) @ A) != (member @ C @ (singleton @ sk2))))),inference(paramod_ordered,[status(thm)],[209,1114])). 122.84/33.11 thf(3556,plain,(! [A:$i] : ((subset @ (singleton @ sk2) @ A) | (maps @ sk1 @ (sk31 @ A @ (singleton @ sk2)) @ sk3))),inference(pattern_uni,[status(thm)],[3555:[bind(A, $thf(singleton @ sk2)),bind(B, $thf(D)),bind(C, $thf(sk31 @ D @ (singleton @ sk2)))]])). 122.84/33.11 thf(3577,plain,(! [A:$i] : ((subset @ (singleton @ sk2) @ A) | (maps @ sk1 @ (sk31 @ A @ (singleton @ sk2)) @ sk3))),inference(simp,[status(thm)],[3556])). 122.84/33.11 thf(366,plain,(! [C:$i,B:$i,A:$i] : ((subset @ A @ B) | ((member @ (sk31 @ B @ A) @ A) != (member @ C @ empty_set)))),inference(paramod_ordered,[status(thm)],[209,132])). 122.84/33.11 thf(367,plain,(! [A:$i] : ((subset @ empty_set @ A))),inference(pattern_uni,[status(thm)],[366:[bind(A, $thf(empty_set)),bind(B, $thf(D)),bind(C, $thf(sk31 @ D @ empty_set))]])). 122.84/33.11 thf(374,plain,(! [A:$i] : ((subset @ empty_set @ A))),inference(simp,[status(thm)],[367])). 122.84/33.11 thf(3,axiom,((! [A:$i,B:$i]: (((subset @ A @ B) & (subset @ B @ A)) <=> (equal_set @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_set)). 122.84/33.11 thf(40,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)],[3])). 122.84/33.11 thf(41,plain,((! [A:$i,B:$i]: (((subset @ A @ B) & (subset @ B @ A)) => (equal_set @ A @ B)) & ! [A:$i,B:$i]: ((equal_set @ A @ B) => ((subset @ A @ B) & (subset @ B @ A))))),inference(miniscope,[status(thm)],[40])). 122.84/33.11 thf(44,plain,(! [B:$i,A:$i] : ((~ (subset @ A @ B)) | (~ (subset @ B @ A)) | (equal_set @ A @ B))),inference(cnf,[status(esa)],[41])). 122.84/33.11 thf(389,plain,(! [C:$i,B:$i,A:$i] : ((~ (subset @ C @ B)) | (equal_set @ B @ C) | ((subset @ empty_set @ A) != (subset @ B @ C)))),inference(paramod_ordered,[status(thm)],[374,44])). 122.84/33.11 thf(390,plain,(! [A:$i] : ((~ (subset @ A @ empty_set)) | (equal_set @ empty_set @ A))),inference(pattern_uni,[status(thm)],[389:[bind(A, $thf(A)),bind(B, $thf(empty_set)),bind(C, $thf(A))]])). 122.84/33.11 thf(435,plain,(! [B:$i,A:$i] : ((equal_set @ empty_set @ B) | ((subset @ empty_set @ A) != (subset @ B @ empty_set)))),inference(paramod_ordered,[status(thm)],[374,390])). 122.84/33.11 thf(436,plain,((equal_set @ empty_set @ empty_set)),inference(pattern_uni,[status(thm)],[435:[bind(A, $thf(empty_set)),bind(B, $thf(empty_set))]])). 122.84/33.11 thf(37,plain,((increasing @ sk1 @ sk2 @ sk5 @ sk3 @ sk6) | ~ (sk4)),inference(cnf,[status(esa)],[32])). 122.84/33.11 thf(33,plain,((one_to_one @ sk1 @ sk2 @ sk3)),inference(cnf,[status(esa)],[32])). 122.84/33.11 thf(826,plain,(! [B:$i,A:$i] : ((~ (member @ A @ (singleton @ B))) | (one_to_one @ B @ sk2 @ sk3) | (A != sk1))),inference(paramod_ordered,[status(thm)],[113,33])). 122.84/33.11 thf(827,plain,(! [A:$i] : ((~ (member @ sk1 @ (singleton @ A))) | (one_to_one @ A @ sk2 @ sk3))),inference(pattern_uni,[status(thm)],[826:[bind(A, $thf(sk1))]])). 122.84/33.11 thf(1518,plain,(! [A:$i] : ((~ (member @ sk1 @ (singleton @ A))) | (one_to_one @ A @ sk2 @ sk3))),inference(simp,[status(thm)],[827])). 122.84/33.11 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)). 122.84/33.11 thf(47,plain,((! [A:$i,B:$i,C:$i]: (((member @ C @ (image2 @ A @ B)) => (? [D:$i]: ((apply @ A @ D @ C) & (member @ D @ B)))) & ((? [D:$i]: ((apply @ A @ D @ C) & (member @ D @ B))) => (member @ C @ (image2 @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])). 122.84/33.11 thf(48,plain,((! [A:$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:$i]: ((apply @ A @ D @ C) & (member @ D @ B))) => (member @ C @ (image2 @ A @ B))))),inference(miniscope,[status(thm)],[47])). 122.84/33.11 thf(49,plain,(! [D:$i,C:$i,B:$i,A:$i] : ((~ (apply @ A @ D @ C)) | (~ (member @ D @ B)) | (member @ C @ (image2 @ A @ B)))),inference(cnf,[status(esa)],[48])). 122.84/33.11 thf(52,plain,(! [D:$i,C:$i,B:$i,A:$i] : ((~ (apply @ A @ D @ C)) | (~ (member @ D @ B)) | (member @ C @ (image2 @ A @ B)))),inference(simp,[status(thm)],[49])). 122.84/33.11 thf(538,plain,(! [D:$i,C:$i,B:$i,A:$i] : ((subset @ A @ B) | ((member @ (sk31 @ B @ A) @ A) != (member @ C @ (difference @ D @ (product @ empty_set)))))),inference(paramod_ordered,[status(thm)],[209,525])). 122.84/33.11 thf(539,plain,(! [B:$i,A:$i] : ((subset @ (difference @ B @ (product @ empty_set)) @ A))),inference(pattern_uni,[status(thm)],[538:[bind(A, $thf(difference @ G @ (product @ empty_set))),bind(B, $thf(E)),bind(C, $thf(sk31 @ E @ (difference @ G @ (product @ empty_set)))),bind(D, $thf(G))]])). 122.84/33.11 thf(552,plain,(! [B:$i,A:$i] : ((subset @ (difference @ B @ (product @ empty_set)) @ A))),inference(simp,[status(thm)],[539])). 122.84/33.11 thf(391,plain,(! [C:$i,B:$i,A:$i] : ((~ (subset @ B @ C)) | (equal_set @ B @ C) | ((subset @ empty_set @ A) != (subset @ C @ B)))),inference(paramod_ordered,[status(thm)],[374,44])). 122.84/33.11 thf(392,plain,(! [A:$i] : ((~ (subset @ A @ empty_set)) | (equal_set @ A @ empty_set))),inference(pattern_uni,[status(thm)],[391:[bind(A, $thf(A)),bind(B, $thf(A)),bind(C, $thf(empty_set))]])). 122.84/33.11 thf(562,plain,(! [C:$i,B:$i,A:$i] : ((equal_set @ C @ empty_set) | ((subset @ (difference @ B @ (product @ empty_set)) @ A) != (subset @ C @ empty_set)))),inference(paramod_ordered,[status(thm)],[552,392])). 122.84/33.11 thf(563,plain,(! [A:$i] : ((equal_set @ (difference @ A @ (product @ empty_set)) @ empty_set))),inference(pattern_uni,[status(thm)],[562:[bind(A, $thf(empty_set)),bind(B, $thf(D)),bind(C, $thf(difference @ D @ (product @ empty_set)))]])). 122.84/33.11 thf(570,plain,(! [A:$i] : ((equal_set @ (difference @ A @ (product @ empty_set)) @ empty_set))),inference(simp,[status(thm)],[563])). 122.84/33.11 thf(832,plain,(! [B:$i,A:$i] : ((~ (member @ A @ (singleton @ B))) | (one_to_one @ A @ sk2 @ sk3) | (B != sk1))),inference(paramod_ordered,[status(thm)],[113,33])). 122.84/33.11 thf(833,plain,(! [A:$i] : ((~ (member @ A @ (singleton @ sk1))) | (one_to_one @ A @ sk2 @ sk3))),inference(pattern_uni,[status(thm)],[832:[bind(A, $thf(A)),bind(B, $thf(sk1))]])). 122.84/33.11 thf(1880,plain,(! [C:$i,B:$i,A:$i] : ((subset @ A @ B) | (one_to_one @ C @ sk2 @ sk3) | ((member @ (sk31 @ B @ A) @ A) != (member @ C @ (singleton @ sk1))))),inference(paramod_ordered,[status(thm)],[209,833])). 122.84/33.11 thf(1881,plain,(! [A:$i] : ((subset @ (singleton @ sk1) @ A) | (one_to_one @ (sk31 @ A @ (singleton @ sk1)) @ sk2 @ sk3))),inference(pattern_uni,[status(thm)],[1880:[bind(A, $thf(singleton @ sk1)),bind(B, $thf(D)),bind(C, $thf(sk31 @ D @ (singleton @ sk1)))]])). 122.84/33.11 thf(1907,plain,(! [A:$i] : ((subset @ (singleton @ sk1) @ A) | (one_to_one @ (sk31 @ A @ (singleton @ sk1)) @ sk2 @ sk3))),inference(simp,[status(thm)],[1881])). 122.84/33.11 thf(43,plain,(! [B:$i,A:$i] : ((~ (equal_set @ A @ B)) | (subset @ B @ A))),inference(cnf,[status(esa)],[41])). 122.84/33.11 thf(46,plain,(! [B:$i,A:$i] : ((~ (equal_set @ A @ B)) | (subset @ B @ A))),inference(simp,[status(thm)],[43])). 122.84/33.11 thf(1107,plain,(! [B:$i,A:$i] : ((~ (member @ A @ (singleton @ B))) | (maps @ sk1 @ B @ sk3) | (A != sk2))),inference(paramod_ordered,[status(thm)],[113,35])). 122.84/33.11 thf(1108,plain,(! [A:$i] : ((~ (member @ sk2 @ (singleton @ A))) | (maps @ sk1 @ A @ sk3))),inference(pattern_uni,[status(thm)],[1107:[bind(A, $thf(sk2))]])). 122.84/33.11 thf(1572,plain,(! [A:$i] : ((~ (member @ sk2 @ (singleton @ A))) | (maps @ sk1 @ A @ sk3))),inference(simp,[status(thm)],[1108])). 122.84/33.11 thf(828,plain,(! [B:$i,A:$i] : ((~ (member @ A @ (singleton @ B))) | (one_to_one @ sk1 @ B @ sk3) | (A != sk2))),inference(paramod_ordered,[status(thm)],[113,33])). 122.84/33.11 thf(829,plain,(! [A:$i] : ((~ (member @ sk2 @ (singleton @ A))) | (one_to_one @ sk1 @ A @ sk3))),inference(pattern_uni,[status(thm)],[828:[bind(A, $thf(sk2))]])). 122.84/33.11 thf(1373,plain,(! [A:$i] : ((~ (member @ sk2 @ (singleton @ A))) | (one_to_one @ sk1 @ A @ sk3))),inference(simp,[status(thm)],[829])). 122.84/33.11 thf(27,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)). 122.84/33.11 thf(253,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:$i]: (((member @ F @ C) & (member @ E @ C) & (member @ D @ B)) => (((apply @ A @ D @ E) & (apply @ A @ D @ F)) => (F = E)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[27])). 122.84/33.11 thf(5,axiom,((! [A:$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)). 122.84/33.11 thf(53,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((((member @ D @ C) & ? [E:$i]: ((apply @ A @ D @ E) & (member @ E @ B))) => (member @ D @ (inverse_image3 @ A @ B @ C))) & ((member @ D @ (inverse_image3 @ A @ B @ C)) => ((member @ D @ C) & ? [E:$i]: ((apply @ A @ D @ E) & (member @ E @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])). 122.84/33.11 thf(54,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)],[53])). 122.84/33.11 thf(57,plain,(! [D:$i,C:$i,B:$i,A:$i] : ((~ (member @ D @ (inverse_image3 @ A @ B @ C))) | (member @ (sk10 @ D @ C @ B @ A) @ B))),inference(cnf,[status(esa)],[54])). 122.84/33.11 thf(61,plain,(! [D:$i,C:$i,B:$i,A:$i] : ((~ (member @ D @ (inverse_image3 @ A @ B @ C))) | (member @ (sk10 @ D @ C @ B @ A) @ B))),inference(simp,[status(thm)],[57])). 122.84/33.11 thf(536,plain,(! [D:$i,C:$i,B:$i,A:$i] : ((member @ A @ (product @ B)) | ((member @ (sk17 @ B @ A) @ B) != (member @ C @ (difference @ D @ (product @ empty_set)))))),inference(paramod_ordered,[status(thm)],[128,525])). 122.84/33.11 thf(537,plain,(! [B:$i,A:$i] : ((member @ A @ (product @ (difference @ B @ (product @ empty_set)))))),inference(pattern_uni,[status(thm)],[536:[bind(A, $thf(F)),bind(B, $thf(difference @ G @ (product @ empty_set))),bind(C, $thf(sk17 @ (difference @ G @ (product @ empty_set)) @ F)),bind(D, $thf(G))]])). 122.84/33.11 thf(549,plain,(! [B:$i,A:$i] : ((member @ A @ (product @ (difference @ B @ (product @ empty_set)))))),inference(simp,[status(thm)],[537])). 122.84/33.11 thf(620,plain,(! [D:$i,C:$i,B:$i,A:$i] : (((member @ A @ (product @ (difference @ B @ (product @ empty_set)))) != (member @ C @ (difference @ D @ (product @ empty_set)))))),inference(paramod_ordered,[status(thm)],[549,525])). 122.84/33.11 thf(630,plain,(! [D:$i,C:$i,B:$i,A:$i] : ((A != C) | ((product @ (difference @ B @ (product @ empty_set))) != (difference @ D @ (product @ empty_set))))),inference(simp,[status(thm)],[620])). 122.84/33.11 thf(634,plain,(! [B:$i,A:$i] : (((product @ (difference @ A @ (product @ empty_set))) != (difference @ B @ (product @ empty_set))))),inference(simp,[status(thm)],[630])). 122.84/33.11 thf(15,axiom,((! [A:$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)). 122.84/33.11 thf(133,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)],[15])). 122.84/33.11 thf(12,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)). 122.84/33.11 thf(116,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:$i]: ((member @ D @ B) & (apply @ A @ C @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[12])). 122.84/33.11 thf(65,plain,(! [E:$i,D:$i,C:$i,B:$i,A:$i] : ((~ (apply @ E @ (sk14 @ E @ D @ C @ B @ A) @ (sk12 @ E @ D @ C @ B @ A))) | (decreasing @ A @ B @ C @ D @ E))),inference(cnf,[status(esa)],[63])). 122.84/33.11 thf(74,plain,(! [E:$i,D:$i,C:$i,B:$i,A:$i] : ((~ (apply @ E @ (sk14 @ E @ D @ C @ B @ A) @ (sk12 @ E @ D @ C @ B @ A))) | (decreasing @ A @ B @ C @ D @ E))),inference(simp,[status(thm)],[65])). 122.84/33.11 thf(243,plain,(! [C:$i,B:$i,A:$i] : ((~ (B = A)) | (member @ A @ (unordered_pair @ B @ C)))),inference(cnf,[status(esa)],[241])). 122.84/33.11 thf(247,plain,(! [C:$i,B:$i,A:$i] : ((B != A) | (member @ A @ (unordered_pair @ B @ C)))),inference(lifteq,[status(thm)],[243])). 122.84/33.11 thf(248,plain,(! [B:$i,A:$i] : ((member @ A @ (unordered_pair @ A @ B)))),inference(simp,[status(thm)],[247])). 122.84/33.11 thf(56,plain,(! [D:$i,C:$i,B:$i,A:$i] : ((~ (member @ D @ (inverse_image3 @ A @ B @ C))) | (apply @ A @ D @ (sk10 @ D @ C @ B @ A)))),inference(cnf,[status(esa)],[54])). 122.84/33.11 thf(60,plain,(! [D:$i,C:$i,B:$i,A:$i] : ((~ (member @ D @ (inverse_image3 @ A @ B @ C))) | (apply @ A @ D @ (sk10 @ D @ C @ B @ A)))),inference(simp,[status(thm)],[56])). 122.84/33.11 thf(3787,plain,(! [A:$i] : (((member @ A @ (singleton @ A)) != (member @ (product @ empty_set) @ (singleton @ (singleton @ (singleton @ (product @ empty_set)))))))),inference(paramod_ordered,[status(thm)],[115,2500])). 122.84/33.11 thf(3832,plain,(! [A:$i] : ((A != (product @ empty_set)) | ((singleton @ A) != (singleton @ (singleton @ (singleton @ (product @ empty_set))))))),inference(simp,[status(thm)],[3787])). 122.84/33.11 thf(3852,plain,(((singleton @ (singleton @ (singleton @ (product @ empty_set)))) != (singleton @ (product @ empty_set)))),inference(simp,[status(thm)],[3832])). 122.84/33.11 thf(834,plain,(! [B:$i,A:$i] : ((~ (member @ A @ (singleton @ B))) | (one_to_one @ sk1 @ A @ sk3) | (B != sk2))),inference(paramod_ordered,[status(thm)],[113,33])). 122.84/33.11 thf(835,plain,(! [A:$i] : ((~ (member @ A @ (singleton @ sk2))) | (one_to_one @ sk1 @ A @ sk3))),inference(pattern_uni,[status(thm)],[834:[bind(A, $thf(A)),bind(B, $thf(sk2))]])). 122.84/33.11 thf(2262,plain,(! [B:$i,A:$i] : ((one_to_one @ sk1 @ B @ sk3) | ((member @ A @ (product @ empty_set)) != (member @ B @ (singleton @ sk2))))),inference(paramod_ordered,[status(thm)],[499,835])). 122.84/33.11 thf(2295,plain,(! [B:$i,A:$i] : ((one_to_one @ sk1 @ B @ sk3) | (A != B) | ((product @ empty_set) != (singleton @ sk2)))),inference(simp,[status(thm)],[2262])). 122.84/33.11 thf(2296,plain,(! [A:$i] : ((one_to_one @ sk1 @ A @ sk3) | ((product @ empty_set) != (singleton @ sk2)))),inference(simp,[status(thm)],[2295])). 122.84/33.11 thf(3965,plain,(! [A:$i] : (((member @ A @ (product @ empty_set)) != (member @ (product @ empty_set) @ (singleton @ (singleton @ (singleton @ (singleton @ empty_set)))))))),inference(paramod_ordered,[status(thm)],[499,2776])). 122.84/33.11 thf(4014,plain,(! [A:$i] : ((A != (product @ empty_set)) | ((product @ empty_set) != (singleton @ (singleton @ (singleton @ (singleton @ empty_set))))))),inference(simp,[status(thm)],[3965])). 122.84/33.11 thf(4031,plain,(((product @ empty_set) != (singleton @ (singleton @ (singleton @ (singleton @ empty_set)))))),inference(simp,[status(thm)],[4014])). 122.84/33.11 thf(830,plain,(! [B:$i,A:$i] : ((~ (member @ A @ (singleton @ B))) | (one_to_one @ sk1 @ sk2 @ B) | (A != sk3))),inference(paramod_ordered,[status(thm)],[113,33])). 122.84/33.11 thf(831,plain,(! [A:$i] : ((~ (member @ sk3 @ (singleton @ A))) | (one_to_one @ sk1 @ sk2 @ A))),inference(pattern_uni,[status(thm)],[830:[bind(A, $thf(sk3))]])). 122.84/33.11 thf(1496,plain,(! [A:$i] : ((~ (member @ sk3 @ (singleton @ A))) | (one_to_one @ sk1 @ sk2 @ A))),inference(simp,[status(thm)],[831])). 122.84/33.11 thf(5001,plain,(! [B:$i,A:$i] : ((one_to_one @ sk1 @ sk2 @ B) | ((member @ A @ (product @ empty_set)) != (member @ sk3 @ (singleton @ B))))),inference(paramod_ordered,[status(thm)],[499,1496])). 122.84/33.11 thf(5035,plain,(! [B:$i,A:$i] : ((one_to_one @ sk1 @ sk2 @ B) | (A != sk3) | ((product @ empty_set) != (singleton @ B)))),inference(simp,[status(thm)],[5001])). 122.84/33.11 thf(5049,plain,(! [A:$i] : ((one_to_one @ sk1 @ sk2 @ A) | ((product @ empty_set) != (singleton @ A)))),inference(simp,[status(thm)],[5035])). 122.84/33.11 thf(332,plain,(! [C:$i,B:$i,A:$i] : (((member @ A @ (unordered_pair @ A @ B)) != (member @ C @ empty_set)))),inference(paramod_ordered,[status(thm)],[248,132])). 122.84/33.11 thf(333,plain,(! [C:$i,B:$i,A:$i] : ((A != C) | ((unordered_pair @ A @ B) != empty_set))),inference(simp,[status(thm)],[332])). 122.84/33.11 thf(334,plain,(! [B:$i,A:$i] : (((unordered_pair @ B @ A) != empty_set))),inference(simp,[status(thm)],[333])). 122.84/33.11 thf(38,plain,(sk4 | (isomorphism @ sk1 @ sk2 @ sk7 @ sk3 @ sk8)),inference(cnf,[status(esa)],[32])). 122.84/33.11 thf(9,axiom,((! [A:$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)). 122.84/33.11 thf(92,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])). 122.84/33.11 thf(4384,plain,(! [B:$i,A:$i] : ((~ (member @ A @ (singleton @ B))) | (B != (singleton @ (singleton @ (singleton @ (singleton @ empty_set))))) | (A != (product @ empty_set)))),inference(paramod_ordered,[status(thm)],[113,4031])). 122.84/33.11 thf(4385,plain,(! [A:$i] : ((~ (member @ (product @ empty_set) @ (singleton @ A))) | (A != (singleton @ (singleton @ (singleton @ (singleton @ empty_set))))))),inference(pattern_uni,[status(thm)],[4384:[bind(A, $thf(product @ empty_set)),bind(B, $thf(B))]])). 122.84/33.11 thf(4392,plain,((~ (member @ (product @ empty_set) @ (singleton @ (singleton @ (singleton @ (singleton @ (singleton @ empty_set)))))))),inference(simp,[status(thm)],[4385])). 122.84/33.11 thf(5820,plain,(! [A:$i] : (((member @ A @ (product @ empty_set)) != (member @ (product @ empty_set) @ (singleton @ (singleton @ (singleton @ (singleton @ (singleton @ empty_set))))))))),inference(paramod_ordered,[status(thm)],[499,4392])). 122.84/33.11 thf(5862,plain,(! [A:$i] : ((A != (product @ empty_set)) | ((product @ empty_set) != (singleton @ (singleton @ (singleton @ (singleton @ (singleton @ empty_set)))))))),inference(simp,[status(thm)],[5820])). 122.84/33.11 thf(5879,plain,(((product @ empty_set) != (singleton @ (singleton @ (singleton @ (singleton @ (singleton @ empty_set))))))),inference(simp,[status(thm)],[5862])). 122.84/33.11 thf(1830,plain,(! [B:$i,A:$i] : ((~ (member @ A @ (singleton @ B))) | (A != (product @ empty_set)) | (B != (singleton @ (product @ empty_set))))),inference(paramod_ordered,[status(thm)],[113,1739])). 122.84/33.11 thf(1831,plain,(! [A:$i] : ((~ (member @ A @ (singleton @ (singleton @ (product @ empty_set))))) | (A != (product @ empty_set)))),inference(pattern_uni,[status(thm)],[1830:[bind(A, $thf(A)),bind(B, $thf(singleton @ (product @ empty_set)))]])). 122.84/33.11 thf(1837,plain,((~ (member @ (product @ empty_set) @ (singleton @ (singleton @ (product @ empty_set)))))),inference(simp,[status(thm)],[1831])). 122.84/33.11 thf(20,axiom,((! [A:$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)). 122.84/33.11 thf(195,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:$i]: ((member @ E @ B) & (apply @ A @ E @ D)) | ~ (member @ D @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[20])). 122.84/33.11 thf(196,plain,((! [A:$i,B:$i,C:$i]: ((! [D:$i]: (? [E:$i]: ((member @ E @ B) & (apply @ A @ E @ D)) | ~ (member @ D @ C))) => (surjective @ A @ B @ C)) & ! [A:$i,B:$i,C:$i]: ((surjective @ A @ B @ C) => (! [D:$i]: (? [E:$i]: ((member @ E @ B) & (apply @ A @ E @ D)) | ~ (member @ D @ C)))))),inference(miniscope,[status(thm)],[195])). 122.84/33.11 thf(200,plain,(! [C:$i,B:$i,A:$i] : ((member @ (sk29 @ C @ B @ A) @ C) | (surjective @ A @ B @ C))),inference(cnf,[status(esa)],[196])). 122.84/33.11 thf(641,plain,(! [D:$i,C:$i,B:$i,A:$i] : ((surjective @ A @ B @ C) | ((member @ (sk29 @ C @ B @ A) @ C) != (member @ D @ empty_set)))),inference(paramod_ordered,[status(thm)],[200,132])). 122.84/33.11 thf(642,plain,(! [B:$i,A:$i] : ((surjective @ B @ A @ empty_set))),inference(pattern_uni,[status(thm)],[641:[bind(A, $thf(G)),bind(B, $thf(F)),bind(C, $thf(empty_set)),bind(D, $thf(sk29 @ empty_set @ F @ G))]])). 122.84/33.11 thf(665,plain,(! [B:$i,A:$i] : ((surjective @ B @ A @ empty_set))),inference(simp,[status(thm)],[642])). 122.84/33.11 thf(503,plain,(! [C:$i,B:$i,A:$i] : (((member @ A @ (product @ empty_set)) != (member @ C @ (difference @ B @ (singleton @ C)))))),inference(paramod_ordered,[status(thm)],[499,356])). 122.84/33.11 thf(516,plain,(! [C:$i,B:$i,A:$i] : ((A != C) | ((difference @ B @ (singleton @ C)) != (product @ empty_set)))),inference(simp,[status(thm)],[503])). 122.84/33.11 thf(522,plain,(! [B:$i,A:$i] : (((difference @ A @ (singleton @ B)) != (product @ empty_set)))),inference(simp,[status(thm)],[516])). 122.84/33.11 thf(1111,plain,(! [B:$i,A:$i] : ((~ (member @ A @ (singleton @ B))) | (maps @ A @ sk2 @ sk3) | (B != sk1))),inference(paramod_ordered,[status(thm)],[113,35])). 122.84/33.11 thf(1112,plain,(! [A:$i] : ((~ (member @ A @ (singleton @ sk1))) | (maps @ A @ sk2 @ sk3))),inference(pattern_uni,[status(thm)],[1111:[bind(A, $thf(A)),bind(B, $thf(sk1))]])). 122.84/33.11 thf(3095,plain,(! [B:$i,A:$i] : ((maps @ B @ sk2 @ sk3) | ((member @ A @ (product @ empty_set)) != (member @ B @ (singleton @ sk1))))),inference(paramod_ordered,[status(thm)],[499,1112])). 122.84/33.11 thf(3129,plain,(! [B:$i,A:$i] : ((maps @ B @ sk2 @ sk3) | (A != B) | ((product @ empty_set) != (singleton @ sk1)))),inference(simp,[status(thm)],[3095])). 122.84/33.11 thf(3144,plain,(! [A:$i] : ((maps @ A @ sk2 @ sk3) | ((product @ empty_set) != (singleton @ sk1)))),inference(simp,[status(thm)],[3129])). 122.84/33.11 thf(342,plain,(! [E:$i,D:$i,C:$i,B:$i,A:$i] : ((~ (member @ C @ (difference @ E @ D))) | ((member @ B @ (unordered_pair @ A @ B)) != (member @ C @ D)))),inference(paramod_ordered,[status(thm)],[246,161])). 122.84/33.11 thf(343,plain,(! [C:$i,B:$i,A:$i] : ((~ (member @ C @ (difference @ A @ (unordered_pair @ B @ C)))))),inference(pattern_uni,[status(thm)],[342:[bind(A, $thf(F)),bind(B, $thf(G)),bind(C, $thf(G)),bind(D, $thf(unordered_pair @ F @ G))]])). 122.84/33.11 thf(354,plain,(! [C:$i,B:$i,A:$i] : ((~ (member @ C @ (difference @ A @ (unordered_pair @ B @ C)))))),inference(simp,[status(thm)],[343])). 122.84/33.11 thf(512,plain,(! [D:$i,C:$i,B:$i,A:$i] : (((member @ A @ (product @ empty_set)) != (member @ D @ (difference @ B @ (unordered_pair @ C @ D)))))),inference(paramod_ordered,[status(thm)],[499,354])). 122.84/33.11 thf(515,plain,(! [D:$i,C:$i,B:$i,A:$i] : ((A != D) | ((difference @ B @ (unordered_pair @ C @ D)) != (product @ empty_set)))),inference(simp,[status(thm)],[512])). 122.84/33.11 thf(519,plain,(! [C:$i,B:$i,A:$i] : (((difference @ A @ (unordered_pair @ B @ C)) != (product @ empty_set)))),inference(simp,[status(thm)],[515])). 122.84/33.11 thf(4478,plain,(! [B:$i,A:$i] : ((~ (member @ A @ (singleton @ B))) | (A != (singleton @ (singleton @ (singleton @ empty_set)))) | (B != (singleton @ (singleton @ (product @ empty_set)))))),inference(paramod_ordered,[status(thm)],[113,3414])). 122.84/33.11 thf(4479,plain,(! [A:$i] : ((~ (member @ A @ (singleton @ (singleton @ (singleton @ (product @ empty_set)))))) | (A != (singleton @ (singleton @ (singleton @ empty_set)))))),inference(pattern_uni,[status(thm)],[4478:[bind(A, $thf(A)),bind(B, $thf(singleton @ (singleton @ (product @ empty_set))))]])). 122.84/33.11 thf(4486,plain,((~ (member @ (singleton @ (singleton @ (singleton @ empty_set))) @ (singleton @ (singleton @ (singleton @ (product @ empty_set))))))),inference(simp,[status(thm)],[4479])). 122.84/33.11 thf(23,axiom,((! [A:$i,B:$i]: ((identity @ A @ B) <=> (! [C:$i]: ((member @ C @ B) => (apply @ A @ C @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity)). 122.84/33.11 thf(227,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)],[23])). 122.84/33.11 thf(228,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)],[227])). 122.84/33.11 thf(229,plain,(! [B:$i,A:$i] : ((member @ (sk35 @ B @ A) @ B) | (identity @ A @ B))),inference(cnf,[status(esa)],[228])). 122.84/33.11 thf(232,plain,(! [B:$i,A:$i] : ((member @ (sk35 @ B @ A) @ B) | (identity @ A @ B))),inference(simp,[status(thm)],[229])). 122.84/33.11 thf(836,plain,(! [B:$i,A:$i] : ((~ (member @ A @ (singleton @ B))) | (one_to_one @ sk1 @ sk2 @ A) | (B != sk3))),inference(paramod_ordered,[status(thm)],[113,33])). 122.84/33.11 thf(837,plain,(! [A:$i] : ((~ (member @ A @ (singleton @ sk3))) | (one_to_one @ sk1 @ sk2 @ A))),inference(pattern_uni,[status(thm)],[836:[bind(A, $thf(A)),bind(B, $thf(sk3))]])). 122.84/33.11 thf(2841,plain,(! [C:$i,B:$i,A:$i] : ((identity @ A @ B) | (one_to_one @ sk1 @ sk2 @ C) | ((member @ (sk35 @ B @ A) @ B) != (member @ C @ (singleton @ sk3))))),inference(paramod_ordered,[status(thm)],[232,837])). 122.84/33.11 thf(2842,plain,(! [A:$i] : ((identity @ A @ (singleton @ sk3)) | (one_to_one @ sk1 @ sk2 @ (sk35 @ (singleton @ sk3) @ A)))),inference(pattern_uni,[status(thm)],[2841:[bind(A, $thf(E)),bind(B, $thf(singleton @ sk3)),bind(C, $thf(sk35 @ (singleton @ sk3) @ E))]])). 122.84/33.11 thf(2858,plain,(! [A:$i] : ((identity @ A @ (singleton @ sk3)) | (one_to_one @ sk1 @ sk2 @ (sk35 @ (singleton @ sk3) @ A)))),inference(simp,[status(thm)],[2842])). 122.84/33.11 thf(2702,plain,(! [A:$i] : (((member @ A @ (singleton @ A)) != (member @ (product @ empty_set) @ (singleton @ (singleton @ (singleton @ empty_set))))))),inference(paramod_ordered,[status(thm)],[115,2087])). 122.84/33.11 thf(2743,plain,(! [A:$i] : ((A != (product @ empty_set)) | ((singleton @ A) != (singleton @ (singleton @ (singleton @ empty_set)))))),inference(simp,[status(thm)],[2702])). 122.84/33.11 thf(2764,plain,(((singleton @ (product @ empty_set)) != (singleton @ (singleton @ (singleton @ empty_set))))),inference(simp,[status(thm)],[2743])). 122.84/33.11 thf(3051,plain,(! [B:$i,A:$i] : ((~ (member @ A @ (singleton @ B))) | (A != (singleton @ (singleton @ (singleton @ empty_set)))) | (B != (singleton @ (product @ empty_set))))),inference(paramod_ordered,[status(thm)],[113,2764])). 122.84/33.11 thf(3052,plain,(! [A:$i] : ((~ (member @ A @ (singleton @ (singleton @ (product @ empty_set))))) | (A != (singleton @ (singleton @ (singleton @ empty_set)))))),inference(pattern_uni,[status(thm)],[3051:[bind(A, $thf(A)),bind(B, $thf(singleton @ (product @ empty_set)))]])). 122.84/33.11 thf(3060,plain,((~ (member @ (singleton @ (singleton @ (singleton @ empty_set))) @ (singleton @ (singleton @ (product @ empty_set)))))),inference(simp,[status(thm)],[3052])). 122.84/33.11 thf(2165,plain,(! [A:$i] : (((member @ A @ (singleton @ A)) != (member @ (singleton @ empty_set) @ (singleton @ (singleton @ (product @ empty_set))))))),inference(paramod_ordered,[status(thm)],[115,1820])). 122.84/33.11 thf(2207,plain,(! [A:$i] : ((A != (singleton @ empty_set)) | ((singleton @ A) != (singleton @ (singleton @ (product @ empty_set)))))),inference(simp,[status(thm)],[2165])). 122.84/33.11 thf(2221,plain,(((singleton @ (singleton @ (product @ empty_set))) != (singleton @ (singleton @ empty_set)))),inference(simp,[status(thm)],[2207])). 122.84/33.11 thf(3009,plain,(! [B:$i,A:$i] : ((~ (member @ A @ (singleton @ B))) | (A != (singleton @ (singleton @ empty_set))) | (B != (singleton @ (singleton @ (product @ empty_set)))))),inference(paramod_ordered,[status(thm)],[113,2221])). 122.84/33.11 thf(3010,plain,(! [A:$i] : ((~ (member @ A @ (singleton @ (singleton @ (singleton @ (product @ empty_set)))))) | (A != (singleton @ (singleton @ empty_set))))),inference(pattern_uni,[status(thm)],[3009:[bind(A, $thf(A)),bind(B, $thf(singleton @ (singleton @ (product @ empty_set))))]])). 122.84/33.11 thf(3019,plain,((~ (member @ (singleton @ (singleton @ empty_set)) @ (singleton @ (singleton @ (singleton @ (product @ empty_set))))))),inference(simp,[status(thm)],[3010])). 122.84/33.11 thf(4745,plain,(! [A:$i] : (((member @ A @ (singleton @ A)) != (member @ (singleton @ (singleton @ empty_set)) @ (singleton @ (singleton @ (singleton @ (product @ empty_set)))))))),inference(paramod_ordered,[status(thm)],[115,3019])). 122.84/33.11 thf(4800,plain,(! [A:$i] : ((A != (singleton @ (singleton @ empty_set))) | ((singleton @ A) != (singleton @ (singleton @ (singleton @ (product @ empty_set))))))),inference(simp,[status(thm)],[4745])). 122.84/33.11 thf(4817,plain,(((singleton @ (singleton @ (singleton @ (product @ empty_set)))) != (singleton @ (singleton @ (singleton @ empty_set))))),inference(simp,[status(thm)],[4800])). 122.84/33.11 thf(34,plain,(sk4 | (~ (increasing @ sk1 @ sk2 @ sk7 @ sk3 @ sk8)) | (~ (increasing @ (inverse_function @ sk1 @ sk2 @ sk3) @ sk3 @ sk8 @ sk2 @ sk7))),inference(cnf,[status(esa)],[32])). 122.84/33.11 thf(325,plain,(sk4 | (~ (increasing @ sk1 @ sk2 @ sk7 @ sk3 @ sk8)) | ((increasing @ (inverse_function @ sk1 @ sk2 @ sk3) @ sk3 @ sk8 @ sk2 @ sk7) != (increasing @ sk1 @ sk2 @ sk7 @ sk3 @ sk8)) | ~ ($true)),inference(eqfactor_ordered,[status(thm)],[34])). 122.84/33.11 thf(327,plain,(sk4 | (~ (increasing @ sk1 @ sk2 @ sk7 @ sk3 @ sk8)) | ((inverse_function @ sk1 @ sk2 @ sk3) != sk1) | (sk3 != sk2) | (sk8 != sk7) | (sk3 != sk2) | (sk8 != sk7)),inference(simp,[status(thm)],[325])). 122.84/33.11 thf(328,plain,(sk4 | (~ (increasing @ sk1 @ sk2 @ sk7 @ sk3 @ sk8)) | ((inverse_function @ sk1 @ sk2 @ sk3) != sk1) | (sk3 != sk2) | (sk8 != sk7)),inference(simp,[status(thm)],[327])). 122.84/33.11 thf(66,plain,(! [E:$i,D:$i,C:$i,B:$i,A:$i] : ((member @ (sk12 @ E @ D @ C @ B @ A) @ D) | (decreasing @ A @ B @ C @ D @ E))),inference(cnf,[status(esa)],[63])). 122.84/33.11 thf(77,plain,(! [E:$i,D:$i,C:$i,B:$i,A:$i] : ((member @ (sk12 @ E @ D @ C @ B @ A) @ D) | (decreasing @ A @ B @ C @ D @ E))),inference(simp,[status(thm)],[66])). 122.84/33.11 thf(2289,plain,(! [C:$i,B:$i,A:$i] : ((identity @ A @ B) | (one_to_one @ sk1 @ C @ sk3) | ((member @ (sk35 @ B @ A) @ B) != (member @ C @ (singleton @ sk2))))),inference(paramod_ordered,[status(thm)],[232,835])). 122.84/33.11 thf(2290,plain,(! [A:$i] : ((identity @ A @ (singleton @ sk2)) | (one_to_one @ sk1 @ (sk35 @ (singleton @ sk2) @ A) @ sk3))),inference(pattern_uni,[status(thm)],[2289:[bind(A, $thf(E)),bind(B, $thf(singleton @ sk2)),bind(C, $thf(sk35 @ (singleton @ sk2) @ E))]])). 122.84/33.11 thf(2312,plain,(! [A:$i] : ((identity @ A @ (singleton @ sk2)) | (one_to_one @ sk1 @ (sk35 @ (singleton @ sk2) @ A) @ sk3))),inference(simp,[status(thm)],[2290])). 122.84/33.11 thf(611,plain,(! [C:$i,B:$i,A:$i] : (((member @ A @ (product @ (difference @ B @ (product @ empty_set)))) != (member @ C @ empty_set)))),inference(paramod_ordered,[status(thm)],[549,132])). 122.84/33.11 thf(626,plain,(! [C:$i,B:$i,A:$i] : ((A != C) | ((product @ (difference @ B @ (product @ empty_set))) != empty_set))),inference(simp,[status(thm)],[611])). 122.84/33.11 thf(637,plain,(! [A:$i] : (((product @ (difference @ A @ (product @ empty_set))) != empty_set))),inference(simp,[status(thm)],[626])). 122.84/33.11 thf(541,plain,(! [D:$i,C:$i,B:$i,A:$i] : ((identity @ A @ B) | ((member @ (sk35 @ B @ A) @ B) != (member @ C @ (difference @ D @ (product @ empty_set)))))),inference(paramod_ordered,[status(thm)],[232,525])). 122.84/33.11 thf(542,plain,(! [B:$i,A:$i] : ((identity @ A @ (difference @ B @ (product @ empty_set))))),inference(pattern_uni,[status(thm)],[541:[bind(A, $thf(F)),bind(B, $thf(difference @ G @ (product @ empty_set))),bind(C, $thf(sk35 @ (difference @ G @ (product @ empty_set)) @ F)),bind(D, $thf(G))]])). 122.84/33.11 thf(547,plain,(! [B:$i,A:$i] : ((identity @ A @ (difference @ B @ (product @ empty_set))))),inference(simp,[status(thm)],[542])). 122.84/33.11 thf(3123,plain,(! [C:$i,B:$i,A:$i] : ((identity @ A @ B) | (maps @ C @ sk2 @ sk3) | ((member @ (sk35 @ B @ A) @ B) != (member @ C @ (singleton @ sk1))))),inference(paramod_ordered,[status(thm)],[232,1112])). 122.84/33.11 thf(3124,plain,(! [A:$i] : ((identity @ A @ (singleton @ sk1)) | (maps @ (sk35 @ (singleton @ sk1) @ A) @ sk2 @ sk3))),inference(pattern_uni,[status(thm)],[3123:[bind(A, $thf(E)),bind(B, $thf(singleton @ sk1)),bind(C, $thf(sk35 @ (singleton @ sk1) @ E))]])). 122.84/33.11 thf(3147,plain,(! [A:$i] : ((identity @ A @ (singleton @ sk1)) | (maps @ (sk35 @ (singleton @ sk1) @ A) @ sk2 @ sk3))),inference(simp,[status(thm)],[3124])). 122.84/33.11 thf(70,plain,(! [E:$i,D:$i,C:$i,B:$i,A:$i] : ((apply @ A @ (sk11 @ E @ D @ C @ B @ A) @ (sk12 @ E @ D @ C @ B @ A)) | (decreasing @ A @ B @ C @ D @ E))),inference(cnf,[status(esa)],[63])). 122.84/33.11 thf(73,plain,(! [E:$i,D:$i,C:$i,B:$i,A:$i] : ((apply @ A @ (sk11 @ E @ D @ C @ B @ A) @ (sk12 @ E @ D @ C @ B @ A)) | (decreasing @ A @ B @ C @ D @ E))),inference(simp,[status(thm)],[70])). 122.84/33.11 thf(2083,plain,(! [B:$i,A:$i] : ((~ (member @ A @ (singleton @ B))) | (A != (singleton @ (singleton @ empty_set))) | (B != (product @ empty_set)))),inference(paramod_ordered,[status(thm)],[113,2075])). 122.84/33.11 thf(2084,plain,(! [A:$i] : ((~ (member @ A @ (singleton @ (product @ empty_set)))) | (A != (singleton @ (singleton @ empty_set))))),inference(pattern_uni,[status(thm)],[2083:[bind(A, $thf(A)),bind(B, $thf(product @ empty_set))]])). 122.84/33.11 thf(2089,plain,((~ (member @ (singleton @ (singleton @ empty_set)) @ (singleton @ (product @ empty_set))))),inference(simp,[status(thm)],[2084])). 122.84/33.11 thf(30,axiom,((! [A:$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)). 122.84/33.11 thf(298,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:$i]: (((member @ H @ B) & (apply @ C @ F @ H) & (apply @ A @ H @ I) & (apply @ A @ F @ G) & (member @ I @ D) & (member @ G @ D) & (member @ F @ B)) => (apply @ E @ G @ I))) => (increasing @ A @ B @ C @ D @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[30])). 122.84/33.11 thf(3023,plain,(! [B:$i,A:$i] : ((~ (member @ A @ (singleton @ B))) | (B != (singleton @ (product @ empty_set))) | (A != (singleton @ (singleton @ (product @ empty_set)))))),inference(paramod_ordered,[status(thm)],[113,2627])). 122.84/33.11 thf(3024,plain,(! [A:$i] : ((~ (member @ (singleton @ (singleton @ (product @ empty_set))) @ (singleton @ A))) | (A != (singleton @ (product @ empty_set))))),inference(pattern_uni,[status(thm)],[3023:[bind(A, $thf(singleton @ (singleton @ (product @ empty_set)))),bind(B, $thf(B))]])). 122.84/33.11 thf(3042,plain,((~ (member @ (singleton @ (singleton @ (product @ empty_set))) @ (singleton @ (singleton @ (product @ empty_set)))))),inference(simp,[status(thm)],[3024])). 122.84/33.11 thf(42,plain,(! [B:$i,A:$i] : ((~ (equal_set @ A @ B)) | (subset @ A @ B))),inference(cnf,[status(esa)],[41])). 122.84/33.11 thf(45,plain,(! [B:$i,A:$i] : ((~ (equal_set @ A @ B)) | (subset @ A @ B))),inference(simp,[status(thm)],[42])). 122.84/33.11 thf(568,plain,(! [C:$i,B:$i,A:$i] : ((equal_set @ empty_set @ C) | ((subset @ (difference @ B @ (product @ empty_set)) @ A) != (subset @ C @ empty_set)))),inference(paramod_ordered,[status(thm)],[552,390])). 122.84/33.11 thf(569,plain,(! [A:$i] : ((equal_set @ empty_set @ (difference @ A @ (product @ empty_set))))),inference(pattern_uni,[status(thm)],[568:[bind(A, $thf(empty_set)),bind(B, $thf(D)),bind(C, $thf(difference @ D @ (product @ empty_set)))]])). 122.84/33.11 thf(573,plain,(! [A:$i] : ((equal_set @ empty_set @ (difference @ A @ (product @ empty_set))))),inference(simp,[status(thm)],[569])). 122.84/33.11 thf(1177,plain,(! [C:$i,B:$i,A:$i] : ((~ (member @ A @ (singleton @ B))) | (A != empty_set) | (B != (singleton @ C)))),inference(paramod_ordered,[status(thm)],[113,319])). 122.84/33.11 thf(1178,plain,(! [B:$i,A:$i] : ((~ (member @ A @ (singleton @ (singleton @ B)))) | (A != empty_set))),inference(pattern_uni,[status(thm)],[1177:[bind(A, $thf(A)),bind(B, $thf(singleton @ D)),bind(C, $thf(D))]])). 122.84/33.11 thf(1427,plain,(! [A:$i] : ((~ (member @ empty_set @ (singleton @ (singleton @ A)))))),inference(simp,[status(thm)],[1178])). 122.84/33.11 thf(3231,plain,(! [B:$i,A:$i] : (((member @ A @ (product @ empty_set)) != (member @ empty_set @ (singleton @ (singleton @ B)))))),inference(paramod_ordered,[status(thm)],[499,1427])). 122.84/33.11 thf(3255,plain,(! [B:$i,A:$i] : ((A != empty_set) | ((product @ empty_set) != (singleton @ (singleton @ B))))),inference(simp,[status(thm)],[3231])). 122.84/33.11 thf(3274,plain,(! [A:$i] : (((product @ empty_set) != (singleton @ (singleton @ A))))),inference(simp,[status(thm)],[3255])). 122.84/33.11 thf(1109,plain,(! [B:$i,A:$i] : ((~ (member @ A @ (singleton @ B))) | (maps @ sk1 @ sk2 @ B) | (A != sk3))),inference(paramod_ordered,[status(thm)],[113,35])). 122.84/33.11 thf(1110,plain,(! [A:$i] : ((~ (member @ sk3 @ (singleton @ A))) | (maps @ sk1 @ sk2 @ A))),inference(pattern_uni,[status(thm)],[1109:[bind(A, $thf(sk3))]])). 122.84/33.11 thf(1357,plain,(! [A:$i] : ((~ (member @ sk3 @ (singleton @ A))) | (maps @ sk1 @ sk2 @ A))),inference(simp,[status(thm)],[1110])). 122.84/33.11 thf(4553,plain,(! [B:$i,A:$i] : ((maps @ sk1 @ sk2 @ B) | ((member @ A @ (product @ empty_set)) != (member @ sk3 @ (singleton @ B))))),inference(paramod_ordered,[status(thm)],[499,1357])). 122.84/33.11 thf(4582,plain,(! [B:$i,A:$i] : ((maps @ sk1 @ sk2 @ B) | (A != sk3) | ((product @ empty_set) != (singleton @ B)))),inference(simp,[status(thm)],[4553])). 122.84/33.11 thf(4599,plain,(! [A:$i] : ((maps @ sk1 @ sk2 @ A) | ((product @ empty_set) != (singleton @ A)))),inference(simp,[status(thm)],[4582])). 122.84/33.11 thf(5627,plain,(! [A:$i] : (((member @ A @ (singleton @ A)) != (member @ (product @ empty_set) @ (singleton @ (singleton @ (singleton @ (singleton @ (product @ empty_set))))))))),inference(paramod_ordered,[status(thm)],[115,3885])). 122.84/33.11 thf(5678,plain,(! [A:$i] : ((A != (product @ empty_set)) | ((singleton @ A) != (singleton @ (singleton @ (singleton @ (singleton @ (product @ empty_set)))))))),inference(simp,[status(thm)],[5627])). 122.84/33.11 thf(5698,plain,(((singleton @ (singleton @ (singleton @ (singleton @ (product @ empty_set))))) != (singleton @ (product @ empty_set)))),inference(simp,[status(thm)],[5678])). 122.84/33.11 thf(339,plain,(! [E:$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)],[248,161])). 122.84/33.11 thf(340,plain,(! [C:$i,B:$i,A:$i] : ((~ (member @ B @ (difference @ A @ (unordered_pair @ B @ C)))))),inference(pattern_uni,[status(thm)],[339:[bind(A, $thf(F)),bind(B, $thf(G)),bind(C, $thf(F)),bind(D, $thf(unordered_pair @ F @ G))]])). 122.84/33.11 thf(351,plain,(! [C:$i,B:$i,A:$i] : ((~ (member @ B @ (difference @ A @ (unordered_pair @ B @ C)))))),inference(simp,[status(thm)],[340])). 122.84/33.11 thf(394,plain,(! [E:$i,D:$i,C:$i,B:$i,A:$i] : (((member @ A @ (unordered_pair @ A @ B)) != (member @ D @ (difference @ C @ (unordered_pair @ D @ E)))))),inference(paramod_ordered,[status(thm)],[248,351])). 122.84/33.11 thf(398,plain,(! [E:$i,D:$i,C:$i,B:$i,A:$i] : ((A != D) | ((unordered_pair @ A @ B) != (difference @ C @ (unordered_pair @ D @ E))))),inference(simp,[status(thm)],[394])). 122.84/33.11 thf(402,plain,(! [D:$i,C:$i,B:$i,A:$i] : (((unordered_pair @ C @ A) != (difference @ B @ (unordered_pair @ C @ D))))),inference(simp,[status(thm)],[398])). 122.84/33.11 thf(2813,plain,(! [B:$i,A:$i] : ((one_to_one @ sk1 @ sk2 @ B) | ((member @ A @ (product @ empty_set)) != (member @ B @ (singleton @ sk3))))),inference(paramod_ordered,[status(thm)],[499,837])). 122.84/33.11 thf(2844,plain,(! [B:$i,A:$i] : ((one_to_one @ sk1 @ sk2 @ B) | (A != B) | ((product @ empty_set) != (singleton @ sk3)))),inference(simp,[status(thm)],[2813])). 122.84/33.11 thf(2849,plain,(! [A:$i] : ((one_to_one @ sk1 @ sk2 @ A) | ((product @ empty_set) != (singleton @ sk3)))),inference(simp,[status(thm)],[2844])). 122.84/33.11 thf(1115,plain,(! [B:$i,A:$i] : ((~ (member @ A @ (singleton @ B))) | (maps @ sk1 @ sk2 @ A) | (B != sk3))),inference(paramod_ordered,[status(thm)],[113,35])). 122.84/33.11 thf(1116,plain,(! [A:$i] : ((~ (member @ A @ (singleton @ sk3))) | (maps @ sk1 @ sk2 @ A))),inference(pattern_uni,[status(thm)],[1115:[bind(A, $thf(A)),bind(B, $thf(sk3))]])). 122.84/33.11 thf(4071,plain,(! [B:$i,A:$i] : ((maps @ sk1 @ sk2 @ B) | ((member @ A @ (product @ empty_set)) != (member @ B @ (singleton @ sk3))))),inference(paramod_ordered,[status(thm)],[499,1116])). 122.84/33.11 thf(4106,plain,(! [B:$i,A:$i] : ((maps @ sk1 @ sk2 @ B) | (A != B) | ((product @ empty_set) != (singleton @ sk3)))),inference(simp,[status(thm)],[4071])). 122.84/33.11 thf(4122,plain,(! [A:$i] : ((maps @ sk1 @ sk2 @ A) | ((product @ empty_set) != (singleton @ sk3)))),inference(simp,[status(thm)],[4106])). 122.84/33.11 thf(29,axiom,((! [A:$i,B:$i,C:$i]: (((injective @ A @ B @ C) & (surjective @ A @ B @ C)) <=> (one_to_one @ A @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',one_to_one)). 122.84/33.11 thf(291,plain,((! [A:$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)],[29])). 122.84/33.11 thf(55,plain,(! [D:$i,C:$i,B:$i,A:$i] : ((~ (member @ D @ (inverse_image3 @ A @ B @ C))) | (member @ D @ C))),inference(cnf,[status(esa)],[54])). 122.84/33.11 thf(59,plain,(! [D:$i,C:$i,B:$i,A:$i] : ((~ (member @ D @ (inverse_image3 @ A @ B @ C))) | (member @ D @ C))),inference(simp,[status(thm)],[55])). 122.84/33.11 thf(3536,plain,(! [B:$i,A:$i] : ((maps @ sk1 @ B @ sk3) | ((member @ A @ (product @ empty_set)) != (member @ B @ (singleton @ sk2))))),inference(paramod_ordered,[status(thm)],[499,1114])). 122.84/33.11 thf(3570,plain,(! [B:$i,A:$i] : ((maps @ sk1 @ B @ sk3) | (A != B) | ((product @ empty_set) != (singleton @ sk2)))),inference(simp,[status(thm)],[3536])). 122.84/33.11 thf(3590,plain,(! [A:$i] : ((maps @ sk1 @ A @ sk3) | ((product @ empty_set) != (singleton @ sk2)))),inference(simp,[status(thm)],[3570])). 122.84/33.11 thf(405,plain,(! [D:$i,C:$i,B:$i,A:$i] : (((member @ A @ (singleton @ A)) != (member @ D @ (difference @ B @ (unordered_pair @ C @ D)))))),inference(paramod_ordered,[status(thm)],[115,354])). 122.84/33.11 thf(409,plain,(! [D:$i,C:$i,B:$i,A:$i] : ((A != D) | ((singleton @ A) != (difference @ B @ (unordered_pair @ C @ D))))),inference(simp,[status(thm)],[405])). 122.84/33.11 thf(413,plain,(! [C:$i,B:$i,A:$i] : (((difference @ A @ (unordered_pair @ B @ C)) != (singleton @ C)))),inference(simp,[status(thm)],[409])). 122.84/33.11 thf(335,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)],[115,161])). 122.84/33.11 thf(347,plain,(! [D:$i,C:$i,B:$i,A:$i] : ((~ (member @ B @ C)) | (A != B) | ((singleton @ A) != (difference @ D @ C)))),inference(simp,[status(thm)],[335])). 122.84/33.11 thf(350,plain,(! [C:$i,B:$i,A:$i] : ((~ (member @ A @ B)) | ((singleton @ A) != (difference @ C @ B)))),inference(simp,[status(thm)],[347])). 122.84/33.11 thf(8,axiom,((! [A:$i,B:$i,C:$i]: ((member @ A @ (intersection @ B @ C)) <=> ((member @ A @ B) & (member @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection)). 122.84/33.11 thf(86,plain,((! [A:$i,B:$i,C:$i]: (((member @ A @ (intersection @ B @ C)) => ((member @ A @ B) & (member @ A @ C))) & (((member @ A @ B) & (member @ A @ C)) => (member @ A @ (intersection @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8])). 122.84/33.11 thf(1800,plain,(! [B:$i,A:$i] : ((~ (member @ A @ (singleton @ B))) | (A != (singleton @ empty_set)) | (B != (product @ empty_set)))),inference(paramod_ordered,[status(thm)],[113,1793])). 122.84/33.11 thf(1801,plain,(! [A:$i] : ((~ (member @ A @ (singleton @ (product @ empty_set)))) | (A != (singleton @ empty_set)))),inference(pattern_uni,[status(thm)],[1800:[bind(A, $thf(A)),bind(B, $thf(product @ empty_set))]])). 122.84/33.11 thf(1806,plain,((~ (member @ (singleton @ empty_set) @ (singleton @ (product @ empty_set))))),inference(simp,[status(thm)],[1801])). 122.84/33.11 thf(7,axiom,((! [A:$i,B:$i]: ((member @ A @ (power_set @ B)) <=> (subset @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',power_set)). 122.84/33.11 thf(81,plain,((! [A:$i,B:$i]: (((member @ A @ (power_set @ B)) => (subset @ A @ B)) & ((subset @ A @ B) => (member @ A @ (power_set @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])). 122.84/33.11 thf(71,plain,(! [E:$i,D:$i,C:$i,B:$i,A:$i] : ((member @ (sk13 @ E @ D @ C @ B @ A) @ B) | (decreasing @ A @ B @ C @ D @ E))),inference(cnf,[status(esa)],[63])). 122.84/33.11 thf(76,plain,(! [E:$i,D:$i,C:$i,B:$i,A:$i] : ((member @ (sk13 @ E @ D @ C @ B @ A) @ B) | (decreasing @ A @ B @ C @ D @ E))),inference(simp,[status(thm)],[71])). 122.84/33.11 thf(39,plain,((~ (isomorphism @ sk1 @ sk2 @ sk5 @ sk3 @ sk6)) | ~ (sk4)),inference(cnf,[status(esa)],[32])). 122.84/33.11 thf(28,axiom,((! [A:$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)). 122.84/33.11 thf(271,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:$i]: (((member @ F @ B) & (member @ G @ D) & (member @ H @ B) & (member @ I @ D) & (apply @ A @ H @ I) & (apply @ A @ F @ G)) => (((apply @ E @ G @ I) => (apply @ C @ F @ H)) & ((apply @ C @ F @ H) => (apply @ E @ G @ I)))) & (one_to_one @ A @ B @ D) & (maps @ A @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[28])). 122.84/33.11 thf(507,plain,(! [D:$i,C:$i,B:$i,A:$i] : (((singleton @ B) != (difference @ D @ C)) | ((member @ A @ (product @ empty_set)) != (member @ B @ C)))),inference(paramod_ordered,[status(thm)],[499,350])). 122.84/33.11 thf(508,plain,(! [B:$i,A:$i] : (((singleton @ A) != (difference @ B @ (product @ empty_set))))),inference(pattern_uni,[status(thm)],[507:[bind(A, $thf(A)),bind(B, $thf(A)),bind(C, $thf(product @ empty_set)),bind(D, $thf(D))]])). 122.84/33.11 thf(520,plain,(! [B:$i,A:$i] : (((singleton @ A) != (difference @ B @ (product @ empty_set))))),inference(simp,[status(thm)],[508])). 122.84/33.11 thf(5816,plain,(! [A:$i] : (((member @ A @ (singleton @ A)) != (member @ (product @ empty_set) @ (singleton @ (singleton @ (singleton @ (singleton @ (singleton @ empty_set))))))))),inference(paramod_ordered,[status(thm)],[115,4392])). 122.84/33.11 thf(5870,plain,(! [A:$i] : ((A != (product @ empty_set)) | ((singleton @ A) != (singleton @ (singleton @ (singleton @ (singleton @ (singleton @ empty_set)))))))),inference(simp,[status(thm)],[5816])). 122.84/33.11 thf(5885,plain,(((singleton @ (product @ empty_set)) != (singleton @ (singleton @ (singleton @ (singleton @ (singleton @ empty_set))))))),inference(simp,[status(thm)],[5870])). 122.84/33.11 thf(652,plain,(! [E:$i,D:$i,C:$i,B:$i,A:$i] : ((surjective @ A @ B @ C) | ((member @ (sk29 @ C @ B @ A) @ C) != (member @ D @ (difference @ E @ (product @ empty_set)))))),inference(paramod_ordered,[status(thm)],[200,525])). 122.84/33.11 thf(653,plain,(! [C:$i,B:$i,A:$i] : ((surjective @ B @ A @ (difference @ C @ (product @ empty_set))))),inference(pattern_uni,[status(thm)],[652:[bind(A, $thf(H)),bind(B, $thf(G)),bind(C, $thf(difference @ I @ (product @ empty_set))),bind(D, $thf(sk29 @ (difference @ I @ (product @ empty_set)) @ G @ H)),bind(E, $thf(I))]])). 122.84/33.11 thf(668,plain,(! [C:$i,B:$i,A:$i] : ((surjective @ B @ A @ (difference @ C @ (product @ empty_set))))),inference(simp,[status(thm)],[653])). 122.84/33.11 thf(4388,plain,(! [B:$i,A:$i] : ((~ (member @ A @ (singleton @ B))) | (A != (singleton @ (singleton @ (singleton @ (singleton @ empty_set))))) | (B != (product @ empty_set)))),inference(paramod_ordered,[status(thm)],[113,4031])). 122.84/33.11 thf(4389,plain,(! [A:$i] : ((~ (member @ A @ (singleton @ (product @ empty_set)))) | (A != (singleton @ (singleton @ (singleton @ (singleton @ empty_set))))))),inference(pattern_uni,[status(thm)],[4388:[bind(A, $thf(A)),bind(B, $thf(product @ empty_set))]])). 122.84/33.11 thf(4394,plain,((~ (member @ (singleton @ (singleton @ (singleton @ (singleton @ empty_set)))) @ (singleton @ (product @ empty_set))))),inference(simp,[status(thm)],[4389])). 122.84/33.11 thf(17,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((inverse_predicate @ A @ B @ C @ D) <=> (! [E:$i,F:$i]: (((apply @ A @ F @ E) <=> (apply @ B @ E @ F)) <= ((member @ E @ C) & (member @ F @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_predicate)). 122.84/33.11 thf(162,plain,((! [A:$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:$i]: ((((apply @ A @ F @ E) => (apply @ B @ E @ F)) & ((apply @ B @ E @ F) => (apply @ A @ F @ E))) | ~ ((member @ E @ C) & (member @ F @ D)))) => (inverse_predicate @ A @ B @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[17])). 122.84/33.11 thf(2483,plain,(! [B:$i,A:$i] : ((~ (member @ A @ (singleton @ B))) | (B != (product @ empty_set)) | (A != (singleton @ (singleton @ (product @ empty_set)))))),inference(paramod_ordered,[status(thm)],[113,2222])). 122.84/33.11 thf(2484,plain,(! [A:$i] : ((~ (member @ (singleton @ (singleton @ (product @ empty_set))) @ (singleton @ A))) | (A != (product @ empty_set)))),inference(pattern_uni,[status(thm)],[2483:[bind(A, $thf(singleton @ (singleton @ (product @ empty_set)))),bind(B, $thf(B))]])). 122.84/33.11 thf(2503,plain,((~ (member @ (singleton @ (singleton @ (product @ empty_set))) @ (singleton @ (product @ empty_set))))),inference(simp,[status(thm)],[2484])). 122.84/33.11 thf(344,plain,(! [C:$i,B:$i,A:$i] : ((~ (member @ A @ B)) | ((member @ A @ (difference @ C @ B)) != (member @ A @ B)) | ~ ($true))),inference(eqfactor_ordered,[status(thm)],[161])). 122.84/33.11 thf(346,plain,(! [C:$i,B:$i,A:$i] : ((~ (member @ A @ B)) | (A != A) | ((difference @ C @ B) != B))),inference(simp,[status(thm)],[344])). 122.84/33.11 thf(355,plain,(! [C:$i,B:$i,A:$i] : ((~ (member @ A @ B)) | ((difference @ C @ B) != B))),inference(simp,[status(thm)],[346])). 122.84/33.11 thf(2281,plain,(! [C:$i,B:$i,A:$i] : ((subset @ A @ B) | (one_to_one @ sk1 @ C @ sk3) | ((member @ (sk31 @ B @ A) @ A) != (member @ C @ (singleton @ sk2))))),inference(paramod_ordered,[status(thm)],[209,835])). 122.84/33.11 thf(2282,plain,(! [A:$i] : ((subset @ (singleton @ sk2) @ A) | (one_to_one @ sk1 @ (sk31 @ A @ (singleton @ sk2)) @ sk3))),inference(pattern_uni,[status(thm)],[2281:[bind(A, $thf(singleton @ sk2)),bind(B, $thf(D)),bind(C, $thf(sk31 @ D @ (singleton @ sk2)))]])). 122.84/33.11 thf(2298,plain,(! [A:$i] : ((subset @ (singleton @ sk2) @ A) | (one_to_one @ sk1 @ (sk31 @ A @ (singleton @ sk2)) @ sk3))),inference(simp,[status(thm)],[2282])). 122.84/33.11 thf(50,plain,(! [C:$i,B:$i,A:$i] : ((~ (member @ C @ (image2 @ A @ B))) | (apply @ A @ (sk9 @ C @ B @ A) @ C))),inference(cnf,[status(esa)],[48])). 122.84/33.11 thf(329,plain,(! [C:$i,B:$i,A:$i] : (((member @ B @ (unordered_pair @ A @ B)) != (member @ C @ empty_set)))),inference(paramod_ordered,[status(thm)],[246,132])). 122.84/33.11 thf(330,plain,(! [C:$i,B:$i,A:$i] : ((B != C) | ((unordered_pair @ A @ B) != empty_set))),inference(simp,[status(thm)],[329])). 122.84/33.11 thf(331,plain,(! [B:$i,A:$i] : (((unordered_pair @ A @ B) != empty_set))),inference(simp,[status(thm)],[330])). 122.84/33.11 thf(1767,plain,(! [B:$i,A:$i] : (((member @ B @ (unordered_pair @ A @ B)) != (member @ (product @ empty_set) @ (singleton @ empty_set))))),inference(paramod_ordered,[status(thm)],[246,1582])). 122.84/33.11 thf(1772,plain,(! [B:$i,A:$i] : ((B != (product @ empty_set)) | ((unordered_pair @ A @ B) != (singleton @ empty_set)))),inference(simp,[status(thm)],[1767])). 122.84/33.11 thf(1785,plain,(! [A:$i] : (((unordered_pair @ A @ (product @ empty_set)) != (singleton @ empty_set)))),inference(simp,[status(thm)],[1772])). 122.84/33.11 thf(1697,plain,(! [B:$i,A:$i] : (((member @ A @ (unordered_pair @ A @ B)) != (member @ empty_set @ (singleton @ (product @ empty_set)))))),inference(paramod_ordered,[status(thm)],[248,1569])). 122.84/33.11 thf(1723,plain,(! [B:$i,A:$i] : ((A != empty_set) | ((unordered_pair @ A @ B) != (singleton @ (product @ empty_set))))),inference(simp,[status(thm)],[1697])). 122.84/33.11 thf(1738,plain,(! [A:$i] : (((unordered_pair @ empty_set @ A) != (singleton @ (product @ empty_set))))),inference(simp,[status(thm)],[1723])). 122.84/33.11 thf(3045,plain,(! [B:$i,A:$i] : ((~ (member @ A @ (singleton @ B))) | (B != (singleton @ (singleton @ (singleton @ empty_set)))) | (A != (singleton @ (product @ empty_set))))),inference(paramod_ordered,[status(thm)],[113,2764])). 122.84/33.11 thf(3046,plain,(! [A:$i] : ((~ (member @ (singleton @ (product @ empty_set)) @ (singleton @ A))) | (A != (singleton @ (singleton @ (singleton @ empty_set)))))),inference(pattern_uni,[status(thm)],[3045:[bind(A, $thf(singleton @ (product @ empty_set))),bind(B, $thf(B))]])). 122.84/33.11 thf(3057,plain,((~ (member @ (singleton @ (product @ empty_set)) @ (singleton @ (singleton @ (singleton @ (singleton @ empty_set))))))),inference(simp,[status(thm)],[3046])). 122.84/33.11 thf(5280,plain,(! [A:$i] : (((member @ A @ (singleton @ A)) != (member @ (singleton @ (product @ empty_set)) @ (singleton @ (singleton @ (singleton @ (singleton @ empty_set)))))))),inference(paramod_ordered,[status(thm)],[115,3057])). 122.84/33.11 thf(5337,plain,(! [A:$i] : ((A != (singleton @ (product @ empty_set))) | ((singleton @ A) != (singleton @ (singleton @ (singleton @ (singleton @ empty_set))))))),inference(simp,[status(thm)],[5280])). 122.84/33.11 thf(5347,plain,(((singleton @ (singleton @ (product @ empty_set))) != (singleton @ (singleton @ (singleton @ (singleton @ empty_set)))))),inference(simp,[status(thm)],[5337])). 122.84/33.11 thf(26,axiom,((! [A:$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)). 122.84/33.11 thf(250,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((((apply @ A @ D @ E) => (apply @ (inverse_function @ A @ B @ C) @ E @ D)) & ((apply @ (inverse_function @ A @ B @ C) @ E @ D) => (apply @ A @ D @ E))) | ~ ((member @ D @ B) & (member @ E @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[26])). 122.84/33.11 thf(3114,plain,(! [C:$i,B:$i,A:$i] : ((subset @ A @ B) | (maps @ C @ sk2 @ sk3) | ((member @ (sk31 @ B @ A) @ A) != (member @ C @ (singleton @ sk1))))),inference(paramod_ordered,[status(thm)],[209,1112])). 122.84/33.11 thf(3115,plain,(! [A:$i] : ((subset @ (singleton @ sk1) @ A) | (maps @ (sk31 @ A @ (singleton @ sk1)) @ sk2 @ sk3))),inference(pattern_uni,[status(thm)],[3114:[bind(A, $thf(singleton @ sk1)),bind(B, $thf(D)),bind(C, $thf(sk31 @ D @ (singleton @ sk1)))]])). 122.84/33.11 thf(3139,plain,(! [A:$i] : ((subset @ (singleton @ sk1) @ A) | (maps @ (sk31 @ A @ (singleton @ sk1)) @ sk2 @ sk3))),inference(simp,[status(thm)],[3115])). 122.84/33.11 thf(357,plain,(! [C:$i,B:$i,A:$i] : (((member @ A @ (singleton @ A)) != (member @ C @ (difference @ B @ (singleton @ C)))))),inference(paramod_ordered,[status(thm)],[115,356])). 122.84/33.11 thf(360,plain,(! [C:$i,B:$i,A:$i] : ((A != C) | ((singleton @ A) != (difference @ B @ (singleton @ C))))),inference(simp,[status(thm)],[357])). 122.84/33.11 thf(363,plain,(! [B:$i,A:$i] : (((difference @ A @ (singleton @ B)) != (singleton @ B)))),inference(simp,[status(thm)],[360])). 122.84/33.11 thf(509,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)],[499,355])). 122.84/33.11 thf(510,plain,(! [A:$i] : (((difference @ A @ (product @ empty_set)) != (product @ empty_set)))),inference(pattern_uni,[status(thm)],[509:[bind(A, $thf(A)),bind(B, $thf(A)),bind(C, $thf(product @ empty_set)),bind(D, $thf(D))]])). 122.84/33.11 thf(524,plain,(! [A:$i] : (((difference @ A @ (product @ empty_set)) != (product @ empty_set)))),inference(simp,[status(thm)],[510])). 122.84/33.11 thf(2832,plain,(! [C:$i,B:$i,A:$i] : ((subset @ A @ B) | (one_to_one @ sk1 @ sk2 @ C) | ((member @ (sk31 @ B @ A) @ A) != (member @ C @ (singleton @ sk3))))),inference(paramod_ordered,[status(thm)],[209,837])). 122.84/33.11 thf(2833,plain,(! [A:$i] : ((subset @ (singleton @ sk3) @ A) | (one_to_one @ sk1 @ sk2 @ (sk31 @ A @ (singleton @ sk3))))),inference(pattern_uni,[status(thm)],[2832:[bind(A, $thf(singleton @ sk3)),bind(B, $thf(D)),bind(C, $thf(sk31 @ D @ (singleton @ sk3)))]])). 122.84/33.11 thf(2853,plain,(! [A:$i] : ((subset @ (singleton @ sk3) @ A) | (one_to_one @ sk1 @ sk2 @ (sk31 @ A @ (singleton @ sk3))))),inference(simp,[status(thm)],[2833])). 122.84/33.11 thf(393,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)],[115,351])). 122.84/33.11 thf(397,plain,(! [D:$i,C:$i,B:$i,A:$i] : ((A != C) | ((singleton @ A) != (difference @ B @ (unordered_pair @ C @ D))))),inference(simp,[status(thm)],[393])). 122.84/33.11 thf(401,plain,(! [C:$i,B:$i,A:$i] : (((difference @ A @ (unordered_pair @ B @ C)) != (singleton @ B)))),inference(simp,[status(thm)],[397])). 122.84/33.11 thf(1808,plain,(! [B:$i,A:$i] : ((~ (member @ A @ (singleton @ B))) | (B != (singleton @ empty_set)) | (A != (singleton @ (product @ empty_set))))),inference(paramod_ordered,[status(thm)],[113,1735])). 122.84/33.11 thf(1809,plain,(! [A:$i] : ((~ (member @ (singleton @ (product @ empty_set)) @ (singleton @ A))) | (A != (singleton @ empty_set)))),inference(pattern_uni,[status(thm)],[1808:[bind(A, $thf(singleton @ (product @ empty_set))),bind(B, $thf(B))]])). 122.84/33.11 thf(1822,plain,((~ (member @ (singleton @ (product @ empty_set)) @ (singleton @ (singleton @ empty_set))))),inference(simp,[status(thm)],[1809])). 122.84/33.11 thf(64,plain,(! [E:$i,D:$i,C:$i,B:$i,A:$i] : ((apply @ C @ (sk11 @ E @ D @ C @ B @ A) @ (sk13 @ E @ D @ C @ B @ A)) | (decreasing @ A @ B @ C @ D @ E))),inference(cnf,[status(esa)],[63])). 122.84/33.11 thf(75,plain,(! [E:$i,D:$i,C:$i,B:$i,A:$i] : ((apply @ C @ (sk11 @ E @ D @ C @ B @ A) @ (sk13 @ E @ D @ C @ B @ A)) | (decreasing @ A @ B @ C @ D @ E))),inference(simp,[status(thm)],[64])). 122.84/33.11 thf(58,plain,(! [E:$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)],[54])). 122.84/33.11 thf(417,plain,(! [C:$i,B:$i,A:$i] : ((identity @ A @ B) | ((member @ (sk35 @ B @ A) @ B) != (member @ C @ empty_set)))),inference(paramod_ordered,[status(thm)],[232,132])). 122.84/33.11 thf(418,plain,(! [A:$i] : ((identity @ A @ empty_set))),inference(pattern_uni,[status(thm)],[417:[bind(A, $thf(E)),bind(B, $thf(empty_set)),bind(C, $thf(sk35 @ empty_set @ E))]])). 122.84/33.11 thf(433,plain,(! [A:$i] : ((identity @ A @ empty_set))),inference(simp,[status(thm)],[418])). 122.84/33.11 thf(3564,plain,(! [C:$i,B:$i,A:$i] : ((identity @ A @ B) | (maps @ sk1 @ C @ sk3) | ((member @ (sk35 @ B @ A) @ B) != (member @ C @ (singleton @ sk2))))),inference(paramod_ordered,[status(thm)],[232,1114])). 122.84/33.11 thf(3565,plain,(! [A:$i] : ((identity @ A @ (singleton @ sk2)) | (maps @ sk1 @ (sk35 @ (singleton @ sk2) @ A) @ sk3))),inference(pattern_uni,[status(thm)],[3564:[bind(A, $thf(E)),bind(B, $thf(singleton @ sk2)),bind(C, $thf(sk35 @ (singleton @ sk2) @ E))]])). 122.84/33.11 thf(3585,plain,(! [A:$i] : ((identity @ A @ (singleton @ sk2)) | (maps @ sk1 @ (sk35 @ (singleton @ sk2) @ A) @ sk3))),inference(simp,[status(thm)],[3565])). 122.84/33.11 thf(1861,plain,(! [B:$i,A:$i] : ((one_to_one @ B @ sk2 @ sk3) | ((member @ A @ (product @ empty_set)) != (member @ B @ (singleton @ sk1))))),inference(paramod_ordered,[status(thm)],[499,833])). 122.84/33.11 thf(1893,plain,(! [B:$i,A:$i] : ((one_to_one @ B @ sk2 @ sk3) | (A != B) | ((product @ empty_set) != (singleton @ sk1)))),inference(simp,[status(thm)],[1861])). 122.84/33.11 thf(1908,plain,(! [A:$i] : ((one_to_one @ A @ sk2 @ sk3) | ((product @ empty_set) != (singleton @ sk1)))),inference(simp,[status(thm)],[1893])). 122.84/33.11 thf(36,plain,((increasing @ (inverse_function @ sk1 @ sk2 @ sk3) @ sk3 @ sk6 @ sk2 @ sk5) | ~ (sk4)),inference(cnf,[status(esa)],[32])). 122.84/33.11 thf(51,plain,(! [C:$i,B:$i,A:$i] : ((~ (member @ C @ (image2 @ A @ B))) | (member @ (sk9 @ C @ B @ A) @ B))),inference(cnf,[status(esa)],[48])). 122.84/33.11 thf(19,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)). 122.84/33.11 thf(190,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:$i]: ((member @ H @ D) & (apply @ A @ H @ G) & (apply @ B @ F @ H)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[19])). 122.84/33.11 thf(22,axiom,((! [A:$i,B:$i,C:$i]: ((injective @ A @ B @ C) <=> (! [D:$i,E:$i,F:$i]: (((E = D) <= ((apply @ A @ E @ F) & (apply @ A @ D @ F))) <= ((member @ D @ B) & (member @ E @ B) & (member @ F @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',injective)). 122.84/33.11 thf(210,plain,((! [A:$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)],[22])). 122.84/33.11 thf(326,plain,(sk4 | (~ (increasing @ sk1 @ sk2 @ sk7 @ sk3 @ sk8)) | ((increasing @ (inverse_function @ sk1 @ sk2 @ sk3) @ sk3 @ sk8 @ sk2 @ sk7) != (increasing @ sk1 @ sk2 @ sk7 @ sk3 @ sk8))),inference(simp,[status(thm)],[325])). 122.84/33.11 thf(3228,plain,(! [B:$i,A:$i] : (((member @ A @ (singleton @ A)) != (member @ empty_set @ (singleton @ (singleton @ B)))))),inference(paramod_ordered,[status(thm)],[115,1427])). 122.84/33.11 thf(3260,plain,(! [B:$i,A:$i] : ((A != empty_set) | ((singleton @ A) != (singleton @ (singleton @ B))))),inference(simp,[status(thm)],[3228])). 122.84/33.11 thf(3277,plain,(! [A:$i] : (((singleton @ (singleton @ A)) != (singleton @ empty_set)))),inference(simp,[status(thm)],[3260])). 122.84/33.11 thf(1747,plain,(! [B:$i,A:$i] : (((member @ A @ (unordered_pair @ A @ B)) != (member @ (product @ empty_set) @ (singleton @ empty_set))))),inference(paramod_ordered,[status(thm)],[248,1582])). 122.84/33.11 thf(1775,plain,(! [B:$i,A:$i] : ((A != (product @ empty_set)) | ((unordered_pair @ A @ B) != (singleton @ empty_set)))),inference(simp,[status(thm)],[1747])). 122.84/33.11 thf(1789,plain,(! [A:$i] : (((unordered_pair @ (product @ empty_set) @ A) != (singleton @ empty_set)))),inference(simp,[status(thm)],[1775])). 122.84/33.11 thf(5122,plain,(! [A:$i] : (((member @ A @ (singleton @ A)) != (member @ (singleton @ (product @ empty_set)) @ (singleton @ (singleton @ (singleton @ (product @ empty_set)))))))),inference(paramod_ordered,[status(thm)],[115,3040])). 122.84/33.11 thf(5172,plain,(! [A:$i] : ((A != (singleton @ (product @ empty_set))) | ((singleton @ A) != (singleton @ (singleton @ (singleton @ (product @ empty_set))))))),inference(simp,[status(thm)],[5122])). 122.84/33.11 thf(5200,plain,(((singleton @ (singleton @ (singleton @ (product @ empty_set)))) != (singleton @ (singleton @ (product @ empty_set))))),inference(simp,[status(thm)],[5172])). 122.84/33.11 thf(3001,plain,(! [B:$i,A:$i] : ((~ (member @ A @ (singleton @ B))) | (B != (singleton @ (singleton @ empty_set))) | (A != (singleton @ (singleton @ (product @ empty_set)))))),inference(paramod_ordered,[status(thm)],[113,2221])). 122.84/33.11 thf(3002,plain,(! [A:$i] : ((~ (member @ (singleton @ (singleton @ (product @ empty_set))) @ (singleton @ A))) | (A != (singleton @ (singleton @ empty_set))))),inference(pattern_uni,[status(thm)],[3001:[bind(A, $thf(singleton @ (singleton @ (product @ empty_set)))),bind(B, $thf(B))]])). 122.84/33.11 thf(3020,plain,((~ (member @ (singleton @ (singleton @ (product @ empty_set))) @ (singleton @ (singleton @ (singleton @ empty_set)))))),inference(simp,[status(thm)],[3002])). 122.84/33.11 thf(4616,plain,(! [B:$i,A:$i] : ((one_to_one @ sk1 @ B @ sk3) | ((member @ A @ (product @ empty_set)) != (member @ sk2 @ (singleton @ B))))),inference(paramod_ordered,[status(thm)],[499,1373])). 122.84/33.11 thf(4648,plain,(! [B:$i,A:$i] : ((one_to_one @ sk1 @ B @ sk3) | (A != sk2) | ((product @ empty_set) != (singleton @ B)))),inference(simp,[status(thm)],[4616])). 122.84/33.11 thf(4659,plain,(! [A:$i] : ((one_to_one @ sk1 @ A @ sk3) | ((product @ empty_set) != (singleton @ A)))),inference(simp,[status(thm)],[4648])). 122.84/33.11 thf(3863,plain,(! [B:$i,A:$i] : ((~ (member @ A @ (singleton @ B))) | (B != (product @ empty_set)) | (A != (singleton @ (singleton @ (singleton @ (product @ empty_set))))))),inference(paramod_ordered,[status(thm)],[113,3846])). 122.84/33.11 thf(3864,plain,(! [A:$i] : ((~ (member @ (singleton @ (singleton @ (singleton @ (product @ empty_set)))) @ (singleton @ A))) | (A != (product @ empty_set)))),inference(pattern_uni,[status(thm)],[3863:[bind(A, $thf(singleton @ (singleton @ (singleton @ (product @ empty_set))))),bind(B, $thf(B))]])). 122.84/33.11 thf(3886,plain,((~ (member @ (singleton @ (singleton @ (singleton @ (product @ empty_set)))) @ (singleton @ (product @ empty_set))))),inference(simp,[status(thm)],[3864])). 122.84/33.11 thf(18,axiom,((! [A:$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)). 122.84/33.11 thf(178,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)],[18])). 122.84/33.11 thf(1888,plain,(! [C:$i,B:$i,A:$i] : ((identity @ A @ B) | (one_to_one @ C @ sk2 @ sk3) | ((member @ (sk35 @ B @ A) @ B) != (member @ C @ (singleton @ sk1))))),inference(paramod_ordered,[status(thm)],[232,833])). 122.84/33.11 thf(1889,plain,(! [A:$i] : ((identity @ A @ (singleton @ sk1)) | (one_to_one @ (sk35 @ (singleton @ sk1) @ A) @ sk2 @ sk3))),inference(pattern_uni,[status(thm)],[1888:[bind(A, $thf(E)),bind(B, $thf(singleton @ sk1)),bind(C, $thf(sk35 @ (singleton @ sk1) @ E))]])). 122.84/33.11 thf(1902,plain,(! [A:$i] : ((identity @ A @ (singleton @ sk1)) | (one_to_one @ (sk35 @ (singleton @ sk1) @ A) @ sk2 @ sk3))),inference(simp,[status(thm)],[1889])). 122.84/33.11 thf(1717,plain,(! [B:$i,A:$i] : (((member @ B @ (unordered_pair @ A @ B)) != (member @ empty_set @ (singleton @ (product @ empty_set)))))),inference(paramod_ordered,[status(thm)],[246,1569])). 122.84/33.11 thf(1730,plain,(! [B:$i,A:$i] : ((B != empty_set) | ((unordered_pair @ A @ B) != (singleton @ (product @ empty_set))))),inference(simp,[status(thm)],[1717])). 122.84/33.11 thf(1737,plain,(! [A:$i] : (((unordered_pair @ A @ empty_set) != (singleton @ (product @ empty_set))))),inference(simp,[status(thm)],[1730])). 122.84/33.11 thf(358,plain,(! [D:$i,C:$i,B:$i,A:$i] : (((member @ A @ (unordered_pair @ A @ B)) != (member @ D @ (difference @ C @ (singleton @ D)))))),inference(paramod_ordered,[status(thm)],[248,356])). 122.84/33.11 thf(361,plain,(! [D:$i,C:$i,B:$i,A:$i] : ((A != D) | ((unordered_pair @ A @ B) != (difference @ C @ (singleton @ D))))),inference(simp,[status(thm)],[358])). 122.84/33.11 thf(364,plain,(! [C:$i,B:$i,A:$i] : (((unordered_pair @ C @ A) != (difference @ B @ (singleton @ C))))),inference(simp,[status(thm)],[361])). 122.84/33.11 thf(12281,plain,($false),inference(cvc4,[status(thm)],[2163,69,365,101,2778,4022,234,4992,523,115,1522,2776,3040,1569,5691,1793,550,1735,2627,3414,3577,436,37,1518,52,570,1907,46,1572,2222,1373,253,61,634,132,133,1433,116,74,248,60,3852,2296,4031,5049,334,38,392,33,92,5879,1837,665,522,3144,1836,519,1804,4486,53,356,2858,499,3060,4817,328,3846,77,1739,2312,637,547,837,1114,2756,3147,73,128,2089,2221,298,3042,34,45,161,573,3274,4599,5698,402,44,2849,4122,291,59,3590,413,350,86,113,1806,81,76,39,271,552,520,240,5885,668,155,108,1820,1112,2075,130,2064,1496,35,4394,162,374,2503,209,123,355,2298,525,3019,50,3885,331,1785,1738,31,2500,5347,1427,4392,250,3139,363,203,524,319,2853,40,351,390,401,2764,1822,75,58,246,433,3585,2162,549,1116,1908,833,36,835,51,190,210,326,3277,195,1789,5200,3057,1582,1357,3020,47,4659,3886,200,62,178,1902,227,354,1737,2087,364,232])). 122.84/33.11 % SZS output end CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p 122.84/33.11 % [INFO] Killing All external provers ... 122.99/33.17 EOF