TSTP Solution File: GRP184-4 by Matita---1.0
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%------------------------------------------------------------------------------
% File : Matita---1.0
% Problem : GRP184-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : matitaprover --timeout %d --tptppath /export/starexec/sandbox2/benchmark %s
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 10:29:29 EDT 2022
% Result : Unsatisfiable 1.85s 0.83s
% Output : CNFRefutation 1.85s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GRP184-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.12/0.13 % Command : matitaprover --timeout %d --tptppath /export/starexec/sandbox2/benchmark %s
% 0.12/0.34 % Computer : n028.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jun 13 10:51:07 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 30800: Facts:
% 0.12/0.34 30800: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
% 0.12/0.34 30800: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
% 0.12/0.34 30800: Id : 4, {_}:
% 0.12/0.34 multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
% 0.12/0.34 [8, 7, 6] by associativity ?6 ?7 ?8
% 0.12/0.34 30800: Id : 5, {_}:
% 0.12/0.34 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
% 0.12/0.34 [11, 10] by symmetry_of_glb ?10 ?11
% 0.12/0.34 30800: Id : 6, {_}:
% 0.12/0.34 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
% 0.12/0.34 [14, 13] by symmetry_of_lub ?13 ?14
% 0.12/0.34 30800: Id : 7, {_}:
% 0.12/0.34 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
% 0.12/0.34 =?=
% 0.12/0.34 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
% 0.12/0.34 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
% 0.12/0.34 30800: Id : 8, {_}:
% 0.12/0.34 least_upper_bound ?20 (least_upper_bound ?21 ?22)
% 0.12/0.34 =?=
% 0.12/0.34 least_upper_bound (least_upper_bound ?20 ?21) ?22
% 0.12/0.34 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
% 0.12/0.34 30800: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
% 0.12/0.34 30800: Id : 10, {_}:
% 0.12/0.34 greatest_lower_bound ?26 ?26 =>= ?26
% 0.12/0.34 [26] by idempotence_of_gld ?26
% 0.12/0.34 30800: Id : 11, {_}:
% 0.12/0.34 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
% 0.12/0.34 [29, 28] by lub_absorbtion ?28 ?29
% 0.12/0.34 30800: Id : 12, {_}:
% 0.12/0.34 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
% 0.12/0.34 [32, 31] by glb_absorbtion ?31 ?32
% 0.12/0.34 30800: Id : 13, {_}:
% 0.12/0.34 multiply ?34 (least_upper_bound ?35 ?36)
% 0.12/0.34 =<=
% 0.12/0.34 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
% 0.12/0.34 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
% 0.12/0.34 30800: Id : 14, {_}:
% 0.12/0.34 multiply ?38 (greatest_lower_bound ?39 ?40)
% 0.12/0.34 =<=
% 0.12/0.34 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
% 0.12/0.34 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
% 0.12/0.34 30800: Id : 15, {_}:
% 0.12/0.34 multiply (least_upper_bound ?42 ?43) ?44
% 0.12/0.34 =<=
% 0.12/0.34 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
% 0.12/0.34 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
% 0.12/0.34 30800: Id : 16, {_}:
% 0.12/0.34 multiply (greatest_lower_bound ?46 ?47) ?48
% 0.12/0.34 =<=
% 0.12/0.34 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
% 0.12/0.34 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
% 0.12/0.34 30800: Id : 17, {_}: inverse identity =>= identity [] by p21x_1
% 0.12/0.34 30800: Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p21x_2 ?51
% 0.12/0.34 30800: Id : 19, {_}:
% 0.12/0.34 inverse (multiply ?53 ?54) =<= multiply (inverse ?54) (inverse ?53)
% 0.12/0.34 [54, 53] by p21x_3 ?53 ?54
% 0.12/0.34 30800: Id : 20, {_}:
% 0.12/0.34 inverse (greatest_lower_bound ?56 ?57)
% 0.12/0.34 =<=
% 0.12/0.34 least_upper_bound (inverse ?56) (inverse ?57)
% 0.12/0.34 [57, 56] by p21x_4 ?56 ?57
% 0.12/0.34 30800: Id : 21, {_}:
% 0.12/0.34 inverse (least_upper_bound ?59 ?60)
% 0.12/0.34 =<=
% 0.12/0.34 greatest_lower_bound (inverse ?59) (inverse ?60)
% 0.12/0.34 [60, 59] by p21x_5 ?59 ?60
% 0.12/0.34 30800: Goal:
% 0.12/0.34 30800: Id : 1, {_}:
% 0.12/0.34 multiply (least_upper_bound a identity)
% 0.12/0.34 (inverse (greatest_lower_bound a identity))
% 0.12/0.34 =>=
% 0.12/0.34 multiply (inverse (greatest_lower_bound a identity))
% 0.12/0.34 (least_upper_bound a identity)
% 0.12/0.34 [] by prove_p21x
% 1.85/0.83 Statistics :
% 1.85/0.83 Max weight : 17
% 1.85/0.83 Found proof, 0.486607s
% 1.85/0.83 % SZS status Unsatisfiable for theBenchmark.p
% 1.85/0.83 % SZS output start CNFRefutation for theBenchmark.p
% 1.85/0.83 Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
% 1.85/0.83 Id : 8, {_}: least_upper_bound ?20 (least_upper_bound ?21 ?22) =<= least_upper_bound (least_upper_bound ?20 ?21) ?22 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
% 1.85/0.83 Id : 6, {_}: least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 [14, 13] by symmetry_of_lub ?13 ?14
% 1.85/0.83 Id : 17, {_}: inverse identity =>= identity [] by p21x_1
% 1.85/0.83 Id : 302, {_}: inverse (multiply ?526 ?527) =?= multiply (inverse ?527) (inverse ?526) [527, 526] by p21x_3 ?526 ?527
% 1.85/0.83 Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
% 1.85/0.83 Id : 20, {_}: inverse (greatest_lower_bound ?56 ?57) =>= least_upper_bound (inverse ?56) (inverse ?57) [57, 56] by p21x_4 ?56 ?57
% 1.85/0.83 Id : 18, {_}: inverse (inverse ?51) =>= ?51 [51] by p21x_2 ?51
% 1.85/0.83 Id : 13, {_}: multiply ?34 (least_upper_bound ?35 ?36) =>= least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
% 1.85/0.83 Id : 15, {_}: multiply (least_upper_bound ?42 ?43) ?44 =>= least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
% 1.85/0.83 Id : 329, {_}: inverse (least_upper_bound (inverse ?571) (inverse ?572)) =<= greatest_lower_bound ?571 ?572 [572, 571] by Super 18 with 20 at 1,2
% 1.85/0.83 Id : 303, {_}: inverse (multiply identity ?529) =<= multiply (inverse ?529) identity [529] by Super 302 with 17 at 2,3
% 1.85/0.83 Id : 442, {_}: inverse ?684 =<= multiply (inverse ?684) identity [684] by Demod 303 with 2 at 1,2
% 1.85/0.83 Id : 444, {_}: inverse (inverse ?687) =<= multiply ?687 identity [687] by Super 442 with 18 at 1,3
% 1.85/0.83 Id : 453, {_}: ?687 =<= multiply ?687 identity [687] by Demod 444 with 18 at 2
% 1.85/0.83 Id : 288, {_}: multiply ?505 (inverse ?505) =>= identity [505] by Super 3 with 18 at 1,2
% 1.85/0.83 Id : 986, {_}: least_upper_bound (inverse a) (least_upper_bound identity (least_upper_bound a identity)) === least_upper_bound (inverse a) (least_upper_bound identity (least_upper_bound a identity)) [] by Demod 985 with 6 at 2,2,3
% 1.85/0.83 Id : 985, {_}: least_upper_bound (inverse a) (least_upper_bound identity (least_upper_bound a identity)) =<= least_upper_bound (inverse a) (least_upper_bound identity (least_upper_bound identity a)) [] by Demod 984 with 6 at 2,2,2
% 1.85/0.83 Id : 984, {_}: least_upper_bound (inverse a) (least_upper_bound identity (least_upper_bound identity a)) === least_upper_bound (inverse a) (least_upper_bound identity (least_upper_bound identity a)) [] by Demod 983 with 2 at 2,2,2,3
% 1.85/0.83 Id : 983, {_}: least_upper_bound (inverse a) (least_upper_bound identity (least_upper_bound identity a)) =<= least_upper_bound (inverse a) (least_upper_bound identity (least_upper_bound identity (multiply identity a))) [] by Demod 982 with 453 at 2,2,2,2
% 1.85/0.83 Id : 982, {_}: least_upper_bound (inverse a) (least_upper_bound identity (least_upper_bound identity (multiply a identity))) =<= least_upper_bound (inverse a) (least_upper_bound identity (least_upper_bound identity (multiply identity a))) [] by Demod 981 with 17 at 1,2,2,2,3
% 1.85/0.83 Id : 981, {_}: least_upper_bound (inverse a) (least_upper_bound identity (least_upper_bound identity (multiply a identity))) =<= least_upper_bound (inverse a) (least_upper_bound identity (least_upper_bound identity (multiply (inverse identity) a))) [] by Demod 980 with 3 at 1,2,2,3
% 1.85/0.83 Id : 980, {_}: least_upper_bound (inverse a) (least_upper_bound identity (least_upper_bound identity (multiply a identity))) =<= least_upper_bound (inverse a) (least_upper_bound identity (least_upper_bound (multiply (inverse a) a) (multiply (inverse identity) a))) [] by Demod 979 with 17 at 1,2,3
% 1.85/0.83 Id : 979, {_}: least_upper_bound (inverse a) (least_upper_bound identity (least_upper_bound identity (multiply a identity))) =<= least_upper_bound (inverse a) (least_upper_bound (inverse identity) (least_upper_bound (multiply (inverse a) a) (multiply (inverse identity) a))) [] by Demod 978 with 17 at 2,2,2,2,2
% 1.85/0.83 Id : 978, {_}: least_upper_bound (inverse a) (least_upper_bound identity (least_upper_bound identity (multiply a (inverse identity)))) =<= least_upper_bound (inverse a) (least_upper_bound (inverse identity) (least_upper_bound (multiply (inverse a) a) (multiply (inverse identity) a))) [] by Demod 977 with 288 at 1,2,2,2
% 1.85/0.83 Id : 977, {_}: least_upper_bound (inverse a) (least_upper_bound identity (least_upper_bound (multiply a (inverse a)) (multiply a (inverse identity)))) =<= least_upper_bound (inverse a) (least_upper_bound (inverse identity) (least_upper_bound (multiply (inverse a) a) (multiply (inverse identity) a))) [] by Demod 976 with 17 at 1,2,2
% 1.85/0.83 Id : 976, {_}: least_upper_bound (inverse a) (least_upper_bound (inverse identity) (least_upper_bound (multiply a (inverse a)) (multiply a (inverse identity)))) =<= least_upper_bound (inverse a) (least_upper_bound (inverse identity) (least_upper_bound (multiply (inverse a) a) (multiply (inverse identity) a))) [] by Demod 975 with 8 at 3
% 1.85/0.83 Id : 975, {_}: least_upper_bound (inverse a) (least_upper_bound (inverse identity) (least_upper_bound (multiply a (inverse a)) (multiply a (inverse identity)))) =<= least_upper_bound (least_upper_bound (inverse a) (inverse identity)) (least_upper_bound (multiply (inverse a) a) (multiply (inverse identity) a)) [] by Demod 974 with 8 at 2
% 1.85/0.83 Id : 974, {_}: least_upper_bound (least_upper_bound (inverse a) (inverse identity)) (least_upper_bound (multiply a (inverse a)) (multiply a (inverse identity))) =<= least_upper_bound (least_upper_bound (inverse a) (inverse identity)) (least_upper_bound (multiply (inverse a) a) (multiply (inverse identity) a)) [] by Demod 973 with 15 at 2,3
% 1.85/0.83 Id : 973, {_}: least_upper_bound (least_upper_bound (inverse a) (inverse identity)) (least_upper_bound (multiply a (inverse a)) (multiply a (inverse identity))) =<= least_upper_bound (least_upper_bound (inverse a) (inverse identity)) (multiply (least_upper_bound (inverse a) (inverse identity)) a) [] by Demod 972 with 18 at 1,3
% 1.85/0.83 Id : 972, {_}: least_upper_bound (least_upper_bound (inverse a) (inverse identity)) (least_upper_bound (multiply a (inverse a)) (multiply a (inverse identity))) =<= least_upper_bound (inverse (inverse (least_upper_bound (inverse a) (inverse identity)))) (multiply (least_upper_bound (inverse a) (inverse identity)) a) [] by Demod 971 with 13 at 2,2
% 1.85/0.83 Id : 971, {_}: least_upper_bound (least_upper_bound (inverse a) (inverse identity)) (multiply a (least_upper_bound (inverse a) (inverse identity))) =<= least_upper_bound (inverse (inverse (least_upper_bound (inverse a) (inverse identity)))) (multiply (least_upper_bound (inverse a) (inverse identity)) a) [] by Demod 970 with 18 at 1,2
% 1.85/0.83 Id : 970, {_}: least_upper_bound (inverse (inverse (least_upper_bound (inverse a) (inverse identity)))) (multiply a (least_upper_bound (inverse a) (inverse identity))) =<= least_upper_bound (inverse (inverse (least_upper_bound (inverse a) (inverse identity)))) (multiply (least_upper_bound (inverse a) (inverse identity)) a) [] by Demod 969 with 18 at 1,2,3
% 1.85/0.83 Id : 969, {_}: least_upper_bound (inverse (inverse (least_upper_bound (inverse a) (inverse identity)))) (multiply a (least_upper_bound (inverse a) (inverse identity))) =<= least_upper_bound (inverse (inverse (least_upper_bound (inverse a) (inverse identity)))) (multiply (inverse (inverse (least_upper_bound (inverse a) (inverse identity)))) a) [] by Demod 968 with 329 at 1,1,3
% 1.85/0.83 Id : 968, {_}: least_upper_bound (inverse (inverse (least_upper_bound (inverse a) (inverse identity)))) (multiply a (least_upper_bound (inverse a) (inverse identity))) =<= least_upper_bound (inverse (greatest_lower_bound a identity)) (multiply (inverse (inverse (least_upper_bound (inverse a) (inverse identity)))) a) [] by Demod 967 with 18 at 2,2,2
% 1.85/0.83 Id : 967, {_}: least_upper_bound (inverse (inverse (least_upper_bound (inverse a) (inverse identity)))) (multiply a (inverse (inverse (least_upper_bound (inverse a) (inverse identity))))) =<= least_upper_bound (inverse (greatest_lower_bound a identity)) (multiply (inverse (inverse (least_upper_bound (inverse a) (inverse identity)))) a) [] by Demod 966 with 329 at 1,1,2
% 1.85/0.83 Id : 966, {_}: least_upper_bound (inverse (greatest_lower_bound a identity)) (multiply a (inverse (inverse (least_upper_bound (inverse a) (inverse identity))))) =<= least_upper_bound (inverse (greatest_lower_bound a identity)) (multiply (inverse (inverse (least_upper_bound (inverse a) (inverse identity)))) a) [] by Demod 965 with 6 at 3
% 1.85/0.83 Id : 965, {_}: least_upper_bound (inverse (greatest_lower_bound a identity)) (multiply a (inverse (inverse (least_upper_bound (inverse a) (inverse identity))))) =<= least_upper_bound (multiply (inverse (inverse (least_upper_bound (inverse a) (inverse identity)))) a) (inverse (greatest_lower_bound a identity)) [] by Demod 964 with 6 at 2
% 1.85/0.83 Id : 964, {_}: least_upper_bound (multiply a (inverse (inverse (least_upper_bound (inverse a) (inverse identity))))) (inverse (greatest_lower_bound a identity)) =<= least_upper_bound (multiply (inverse (inverse (least_upper_bound (inverse a) (inverse identity)))) a) (inverse (greatest_lower_bound a identity)) [] by Demod 963 with 453 at 2,3
% 1.85/0.83 Id : 963, {_}: least_upper_bound (multiply a (inverse (inverse (least_upper_bound (inverse a) (inverse identity))))) (inverse (greatest_lower_bound a identity)) =<= least_upper_bound (multiply (inverse (inverse (least_upper_bound (inverse a) (inverse identity)))) a) (multiply (inverse (greatest_lower_bound a identity)) identity) [] by Demod 962 with 329 at 1,1,1,3
% 1.85/0.83 Id : 962, {_}: least_upper_bound (multiply a (inverse (inverse (least_upper_bound (inverse a) (inverse identity))))) (inverse (greatest_lower_bound a identity)) =<= least_upper_bound (multiply (inverse (greatest_lower_bound a identity)) a) (multiply (inverse (greatest_lower_bound a identity)) identity) [] by Demod 961 with 2 at 2,2
% 1.85/0.83 Id : 961, {_}: least_upper_bound (multiply a (inverse (inverse (least_upper_bound (inverse a) (inverse identity))))) (multiply identity (inverse (greatest_lower_bound a identity))) =<= least_upper_bound (multiply (inverse (greatest_lower_bound a identity)) a) (multiply (inverse (greatest_lower_bound a identity)) identity) [] by Demod 960 with 329 at 1,2,1,2
% 1.85/0.83 Id : 960, {_}: least_upper_bound (multiply a (inverse (greatest_lower_bound a identity))) (multiply identity (inverse (greatest_lower_bound a identity))) =<= least_upper_bound (multiply (inverse (greatest_lower_bound a identity)) a) (multiply (inverse (greatest_lower_bound a identity)) identity) [] by Demod 959 with 13 at 3
% 1.85/0.83 Id : 959, {_}: least_upper_bound (multiply a (inverse (greatest_lower_bound a identity))) (multiply identity (inverse (greatest_lower_bound a identity))) =<= multiply (inverse (greatest_lower_bound a identity)) (least_upper_bound a identity) [] by Demod 1 with 15 at 2
% 1.85/0.83 Id : 1, {_}: multiply (least_upper_bound a identity) (inverse (greatest_lower_bound a identity)) =<= multiply (inverse (greatest_lower_bound a identity)) (least_upper_bound a identity) [] by prove_p21x
% 1.85/0.83 % SZS output end CNFRefutation for theBenchmark.p
% 1.85/0.83 30802: solved /export/starexec/sandbox2/benchmark/theBenchmark.p in 0.490358 using lpo
%------------------------------------------------------------------------------