TSTP Solution File: LAT005-10 by Matita---1.0
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%------------------------------------------------------------------------------
% File : Matita---1.0
% Problem : LAT005-10 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : matitaprover --timeout %d --tptppath /export/starexec/sandbox/benchmark %s
% Computer : n018.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 : Sun Jul 17 05:55:31 EDT 2022
% Result : Unsatisfiable 15.33s 4.16s
% Output : CNFRefutation 15.33s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LAT005-10 : TPTP v8.1.0. Released v7.5.0.
% 0.03/0.13 % Command : matitaprover --timeout %d --tptppath /export/starexec/sandbox/benchmark %s
% 0.13/0.34 % Computer : n018.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Wed Jun 29 03:38:15 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 322: Facts:
% 0.13/0.34 322: Id : 2, {_}: ifeq3 ?2 ?2 ?3 ?4 =>= ?3 [4, 3, 2] by ifeq_axiom ?2 ?3 ?4
% 0.13/0.34 322: Id : 3, {_}: ifeq2 ?6 ?6 ?7 ?8 =>= ?7 [8, 7, 6] by ifeq_axiom_001 ?6 ?7 ?8
% 0.13/0.34 322: Id : 4, {_}:
% 0.13/0.34 ifeq ?10 ?10 ?11 ?12 =>= ?11
% 0.13/0.34 [12, 11, 10] by ifeq_axiom_002 ?10 ?11 ?12
% 0.13/0.34 322: Id : 5, {_}: meet ?14 ?14 =>= ?14 [14] by idempotence_of_meet ?14
% 0.13/0.34 322: Id : 6, {_}: join ?16 ?16 =>= ?16 [16] by idempotence_of_join ?16
% 0.13/0.34 322: Id : 7, {_}: meet ?18 (join ?18 ?19) =>= ?18 [19, 18] by absorption1 ?18 ?19
% 0.13/0.34 322: Id : 8, {_}: join ?21 (meet ?21 ?22) =>= ?21 [22, 21] by absorption2 ?21 ?22
% 0.13/0.34 322: Id : 9, {_}:
% 0.13/0.34 meet ?24 ?25 =?= meet ?25 ?24
% 0.13/0.34 [25, 24] by commutativity_of_meet ?24 ?25
% 0.13/0.34 322: Id : 10, {_}:
% 0.13/0.34 join ?27 ?28 =?= join ?28 ?27
% 0.13/0.34 [28, 27] by commutativity_of_join ?27 ?28
% 0.13/0.34 322: Id : 11, {_}:
% 0.13/0.34 meet (meet ?30 ?31) ?32 =?= meet ?30 (meet ?31 ?32)
% 0.13/0.34 [32, 31, 30] by associativity_of_meet ?30 ?31 ?32
% 0.13/0.34 322: Id : 12, {_}:
% 0.13/0.34 join (join ?34 ?35) ?36 =?= join ?34 (join ?35 ?36)
% 0.13/0.34 [36, 35, 34] by associativity_of_join ?34 ?35 ?36
% 0.13/0.34 322: Id : 13, {_}: meet ?38 n0 =>= n0 [38] by x_meet_0 ?38
% 0.13/0.34 322: Id : 14, {_}: join ?40 n0 =>= ?40 [40] by x_join_0 ?40
% 0.13/0.34 322: Id : 15, {_}: meet ?42 n1 =>= ?42 [42] by x_meet_1 ?42
% 0.13/0.34 322: Id : 16, {_}: join ?44 n1 =>= n1 [44] by x_join_1 ?44
% 0.13/0.34 322: Id : 17, {_}:
% 0.13/0.34 ifeq3 (meet ?46 ?47) ?46 (meet ?47 (join ?46 ?48))
% 0.13/0.34 (join ?46 (meet ?48 ?47))
% 0.13/0.34 =>=
% 0.13/0.34 join ?46 (meet ?48 ?47)
% 0.13/0.34 [48, 47, 46] by modular ?46 ?47 ?48
% 0.13/0.34 322: Id : 18, {_}:
% 0.13/0.34 ifeq (complement ?50 ?51) true (meet ?50 ?51) n0 =>= n0
% 0.13/0.34 [51, 50] by complement_meet ?50 ?51
% 0.13/0.34 322: Id : 19, {_}:
% 0.13/0.34 ifeq (complement ?53 ?54) true (join ?53 ?54) n1 =>= n1
% 0.13/0.34 [54, 53] by complement_join ?53 ?54
% 0.13/0.34 322: Id : 20, {_}:
% 0.13/0.34 ifeq2 (join ?56 ?57) n1
% 0.13/0.34 (ifeq2 (meet ?56 ?57) n0 (complement ?56 ?57) true) true
% 0.13/0.34 =>=
% 0.13/0.34 true
% 0.13/0.34 [57, 56] by meet_join_complement ?56 ?57
% 0.13/0.34 322: Id : 21, {_}: complement r1 (join a b) =>= true [] by complement_of_a_join_b
% 0.13/0.34 322: Id : 22, {_}: complement r2 (meet a b) =>= true [] by complement_of_a_meet_b
% 0.13/0.34 322: Goal:
% 0.13/0.34 322: Id : 1, {_}:
% 0.13/0.34 r1 =<= meet (join r1 (meet r2 b)) (join r1 (meet r2 a))
% 0.13/0.34 [] by prove_lemma
% 15.33/4.16 Statistics :
% 15.33/4.16 Max weight : 27
% 15.33/4.16 Found proof, 3.818043s
% 15.33/4.16 % SZS status Unsatisfiable for theBenchmark.p
% 15.33/4.16 % SZS output start CNFRefutation for theBenchmark.p
% 15.33/4.16 Id : 13, {_}: meet ?38 n0 =>= n0 [38] by x_meet_0 ?38
% 15.33/4.16 Id : 8, {_}: join ?21 (meet ?21 ?22) =>= ?21 [22, 21] by absorption2 ?21 ?22
% 15.33/4.16 Id : 97, {_}: join (join ?234 ?235) ?236 =>= join ?234 (join ?235 ?236) [236, 235, 234] by associativity_of_join ?234 ?235 ?236
% 15.33/4.16 Id : 15, {_}: meet ?42 n1 =>= ?42 [42] by x_meet_1 ?42
% 15.33/4.16 Id : 22, {_}: complement r2 (meet a b) =>= true [] by complement_of_a_meet_b
% 15.33/4.16 Id : 19, {_}: ifeq (complement ?53 ?54) true (join ?53 ?54) n1 =>= n1 [54, 53] by complement_join ?53 ?54
% 15.33/4.16 Id : 14, {_}: join ?40 n0 =>= ?40 [40] by x_join_0 ?40
% 15.33/4.16 Id : 4, {_}: ifeq ?10 ?10 ?11 ?12 =>= ?11 [12, 11, 10] by ifeq_axiom_002 ?10 ?11 ?12
% 15.33/4.16 Id : 21, {_}: complement r1 (join a b) =>= true [] by complement_of_a_join_b
% 15.33/4.16 Id : 18, {_}: ifeq (complement ?50 ?51) true (meet ?50 ?51) n0 =>= n0 [51, 50] by complement_meet ?50 ?51
% 15.33/4.16 Id : 17, {_}: ifeq3 (meet ?46 ?47) ?46 (meet ?47 (join ?46 ?48)) (join ?46 (meet ?48 ?47)) =>= join ?46 (meet ?48 ?47) [48, 47, 46] by modular ?46 ?47 ?48
% 15.33/4.16 Id : 10, {_}: join ?27 ?28 =?= join ?28 ?27 [28, 27] by commutativity_of_join ?27 ?28
% 15.33/4.16 Id : 74, {_}: meet (meet ?172 ?173) ?174 =>= meet ?172 (meet ?173 ?174) [174, 173, 172] by associativity_of_meet ?172 ?173 ?174
% 15.33/4.16 Id : 9, {_}: meet ?24 ?25 =?= meet ?25 ?24 [25, 24] by commutativity_of_meet ?24 ?25
% 15.33/4.16 Id : 11, {_}: meet (meet ?30 ?31) ?32 =>= meet ?30 (meet ?31 ?32) [32, 31, 30] by associativity_of_meet ?30 ?31 ?32
% 15.33/4.16 Id : 2, {_}: ifeq3 ?2 ?2 ?3 ?4 =>= ?3 [4, 3, 2] by ifeq_axiom ?2 ?3 ?4
% 15.33/4.16 Id : 7, {_}: meet ?18 (join ?18 ?19) =>= ?18 [19, 18] by absorption1 ?18 ?19
% 15.33/4.16 Id : 186, {_}: ifeq3 (meet ?375 ?376) ?375 (meet ?376 (join ?375 ?377)) (join ?375 (meet ?377 ?376)) =>= join ?375 (meet ?377 ?376) [377, 376, 375] by modular ?375 ?376 ?377
% 15.33/4.16 Id : 212, {_}: ifeq3 ?472 ?472 (meet (join ?472 ?473) (join ?472 ?474)) (join ?472 (meet ?474 (join ?472 ?473))) =>= join ?472 (meet ?474 (join ?472 ?473)) [474, 473, 472] by Super 186 with 7 at 1,2
% 15.33/4.16 Id : 252, {_}: meet (join ?472 ?473) (join ?472 ?474) =>= join ?472 (meet ?474 (join ?472 ?473)) [474, 473, 472] by Demod 212 with 2 at 2
% 15.33/4.16 Id : 69, {_}: meet ?153 (meet ?154 ?155) =?= meet ?154 (meet ?155 ?153) [155, 154, 153] by Super 9 with 11 at 3
% 15.33/4.16 Id : 77, {_}: meet (meet ?183 ?184) ?185 =>= meet ?184 (meet ?183 ?185) [185, 184, 183] by Super 74 with 9 at 1,2
% 15.33/4.16 Id : 85, {_}: meet ?183 (meet ?184 ?185) =?= meet ?184 (meet ?183 ?185) [185, 184, 183] by Demod 77 with 11 at 2
% 15.33/4.16 Id : 57, {_}: meet ?129 (join ?130 ?129) =>= ?129 [130, 129] by Super 7 with 10 at 2,2
% 15.33/4.16 Id : 669, {_}: ifeq3 ?947 ?947 (meet (join ?948 ?947) (join ?947 ?949)) (join ?947 (meet ?949 (join ?948 ?947))) =>= join ?947 (meet ?949 (join ?948 ?947)) [949, 948, 947] by Super 17 with 57 at 1,2
% 15.33/4.16 Id : 694, {_}: meet (join ?948 ?947) (join ?947 ?949) =>= join ?947 (meet ?949 (join ?948 ?947)) [949, 947, 948] by Demod 669 with 2 at 2
% 15.33/4.16 Id : 18764, {_}: meet (join ?18156 ?18157) (join ?18158 ?18156) =>= join ?18156 (meet ?18157 (join ?18158 ?18156)) [18158, 18157, 18156] by Super 9 with 694 at 3
% 15.33/4.16 Id : 13961, {_}: meet (join ?13640 ?13641) (join ?13640 ?13642) =>= join ?13640 (meet ?13642 (join ?13640 ?13641)) [13642, 13641, 13640] by Demod 212 with 2 at 2
% 15.33/4.16 Id : 13964, {_}: meet (join ?13651 ?13652) (join ?13653 ?13651) =>= join ?13651 (meet ?13653 (join ?13651 ?13652)) [13653, 13652, 13651] by Super 13961 with 10 at 2,2
% 15.33/4.16 Id : 53935, {_}: join ?51603 (meet ?51604 (join ?51603 ?51605)) =?= join ?51603 (meet ?51605 (join ?51604 ?51603)) [51605, 51604, 51603] by Demod 18764 with 13964 at 2
% 15.33/4.16 Id : 312, {_}: ifeq true true (meet r1 (join a b)) n0 =>= n0 [] by Super 18 with 21 at 1,2
% 15.33/4.16 Id : 316, {_}: meet r1 (join a b) =>= n0 [] by Demod 312 with 4 at 2
% 15.33/4.16 Id : 54058, {_}: join b (meet a (join b r1)) =>= join b n0 [] by Super 53935 with 316 at 2,3
% 15.33/4.16 Id : 54951, {_}: join b (meet a (join b r1)) =>= join n0 b [] by Demod 54058 with 10 at 3
% 15.33/4.16 Id : 135, {_}: join n0 ?307 =>= ?307 [307] by Super 10 with 14 at 3
% 15.33/4.16 Id : 54952, {_}: join b (meet a (join b r1)) =>= b [] by Demod 54951 with 135 at 3
% 15.33/4.16 Id : 55479, {_}: meet (meet a (join b r1)) b =>= meet a (join b r1) [] by Super 57 with 54952 at 2,2
% 15.33/4.16 Id : 55560, {_}: meet b (meet a (join b r1)) =>= meet a (join b r1) [] by Demod 55479 with 9 at 2
% 15.33/4.16 Id : 55561, {_}: meet a (meet (join b r1) b) =>= meet a (join b r1) [] by Demod 55560 with 69 at 2
% 15.33/4.16 Id : 55562, {_}: meet a (meet b (join b r1)) =>= meet a (join b r1) [] by Demod 55561 with 9 at 2,2
% 15.33/4.16 Id : 55563, {_}: meet a b =<= meet a (join b r1) [] by Demod 55562 with 7 at 2,2
% 15.33/4.16 Id : 57805, {_}: meet a (meet ?54842 (join b r1)) =>= meet ?54842 (meet a b) [54842] by Super 85 with 55563 at 2,3
% 15.33/4.16 Id : 57827, {_}: meet a (join r1 (meet b (join r1 ?54878))) =>= meet (join r1 ?54878) (meet a b) [54878] by Super 57805 with 13964 at 2,2
% 15.33/4.16 Id : 67163, {_}: meet a (join r1 (meet b (join r1 ?60891))) =>= meet a (meet b (join r1 ?60891)) [60891] by Demod 57827 with 69 at 3
% 15.33/4.16 Id : 55464, {_}: meet b (join (meet a (join b r1)) ?52784) =<= join (meet a (join b r1)) (meet ?52784 (join b (meet a (join b r1)))) [52784] by Super 694 with 54952 at 1,2
% 15.33/4.16 Id : 55598, {_}: meet b (join (meet a (join b r1)) ?52784) =>= join (meet a (join b r1)) (meet ?52784 b) [52784] by Demod 55464 with 54952 at 2,2,3
% 15.33/4.16 Id : 59968, {_}: meet b (join (meet a b) ?52784) =<= join (meet a (join b r1)) (meet ?52784 b) [52784] by Demod 55598 with 55563 at 1,2,2
% 15.33/4.16 Id : 60017, {_}: meet b (join (meet a b) ?56296) =>= join (meet a b) (meet ?56296 b) [56296] by Demod 59968 with 55563 at 1,3
% 15.33/4.16 Id : 60384, {_}: meet b (join ?56526 (meet a b)) =>= join (meet a b) (meet ?56526 b) [56526] by Super 60017 with 10 at 2,2
% 15.33/4.16 Id : 322, {_}: ifeq true true (join r2 (meet a b)) n1 =>= n1 [] by Super 19 with 22 at 1,2
% 15.33/4.16 Id : 325, {_}: join r2 (meet a b) =>= n1 [] by Demod 322 with 4 at 2
% 15.33/4.16 Id : 60400, {_}: meet b n1 =<= join (meet a b) (meet r2 b) [] by Super 60384 with 325 at 2,2
% 15.33/4.16 Id : 60547, {_}: meet n1 b =<= join (meet a b) (meet r2 b) [] by Demod 60400 with 9 at 2
% 15.33/4.16 Id : 60548, {_}: meet n1 b =<= join (meet a b) (meet b r2) [] by Demod 60547 with 9 at 2,3
% 15.33/4.16 Id : 152, {_}: meet n1 ?332 =>= ?332 [332] by Super 9 with 15 at 3
% 15.33/4.16 Id : 60549, {_}: b =<= join (meet a b) (meet b r2) [] by Demod 60548 with 152 at 2
% 15.33/4.16 Id : 60619, {_}: meet b (join (meet b r2) ?56598) =<= join (meet b r2) (meet ?56598 (join (meet a b) (meet b r2))) [56598] by Super 694 with 60549 at 1,2
% 15.33/4.16 Id : 61429, {_}: meet b (join (meet b r2) ?57223) =>= join (meet b r2) (meet ?57223 b) [57223] by Demod 60619 with 60549 at 2,2,3
% 15.33/4.16 Id : 61440, {_}: meet b (join ?57244 (meet b r2)) =>= join (meet b r2) (meet ?57244 b) [57244] by Super 61429 with 10 at 2,2
% 15.33/4.16 Id : 67213, {_}: meet a (join r1 (join (meet b r2) (meet r1 b))) =>= meet a (meet b (join r1 (meet b r2))) [] by Super 67163 with 61440 at 2,2,2
% 15.33/4.16 Id : 11595, {_}: join ?11281 ?11282 =<= join ?11281 (join (meet ?11281 ?11283) ?11282) [11283, 11282, 11281] by Super 97 with 8 at 1,2
% 15.33/4.16 Id : 11653, {_}: join ?11451 ?11452 =<= join ?11451 (join ?11452 (meet ?11451 ?11453)) [11453, 11452, 11451] by Super 11595 with 10 at 2,3
% 15.33/4.16 Id : 67427, {_}: meet a (join r1 (meet b r2)) =<= meet a (meet b (join r1 (meet b r2))) [] by Demod 67213 with 11653 at 2,2
% 15.33/4.16 Id : 67428, {_}: meet a (join r1 (meet b r2)) =<= meet a (join (meet b r2) (meet r1 b)) [] by Demod 67427 with 61440 at 2,3
% 15.33/4.16 Id : 67429, {_}: meet a (join r1 (meet b r2)) =<= meet a (join (meet b r2) (meet b r1)) [] by Demod 67428 with 9 at 2,2,3
% 15.33/4.16 Id : 636, {_}: meet n0 ?911 =<= meet r1 (meet (join a b) ?911) [911] by Super 11 with 316 at 1,2
% 15.33/4.16 Id : 117, {_}: meet n0 ?283 =>= n0 [283] by Super 9 with 13 at 3
% 15.33/4.16 Id : 1598, {_}: n0 =<= meet r1 (meet (join a b) ?1963) [1963] by Demod 636 with 117 at 2
% 15.33/4.16 Id : 2222, {_}: n0 =<= meet r1 (meet ?2502 (join a b)) [2502] by Super 1598 with 9 at 2,3
% 15.33/4.16 Id : 2233, {_}: n0 =<= meet r1 b [] by Super 2222 with 57 at 2,3
% 15.33/4.16 Id : 2289, {_}: n0 =<= meet b r1 [] by Demod 2233 with 9 at 3
% 15.33/4.16 Id : 67430, {_}: meet a (join r1 (meet b r2)) =?= meet a (join (meet b r2) n0) [] by Demod 67429 with 2289 at 2,2,3
% 15.33/4.16 Id : 67431, {_}: meet a (join r1 (meet b r2)) =?= meet a (join n0 (meet b r2)) [] by Demod 67430 with 10 at 2,3
% 15.33/4.16 Id : 67432, {_}: meet a (join r1 (meet b r2)) =>= meet a (meet b r2) [] by Demod 67431 with 135 at 2,3
% 15.33/4.16 Id : 321, {_}: ifeq true true (meet r2 (meet a b)) n0 =>= n0 [] by Super 18 with 22 at 1,2
% 15.33/4.16 Id : 326, {_}: meet r2 (meet a b) =>= n0 [] by Demod 321 with 4 at 2
% 15.33/4.16 Id : 917, {_}: meet a (meet b r2) =>= n0 [] by Demod 326 with 69 at 2
% 15.33/4.16 Id : 67433, {_}: meet a (join r1 (meet b r2)) =>= n0 [] by Demod 67432 with 917 at 3
% 15.33/4.16 Id : 67487, {_}: meet a (meet ?61062 (join r1 (meet b r2))) =>= meet ?61062 n0 [61062] by Super 85 with 67433 at 2,3
% 15.33/4.16 Id : 67553, {_}: meet a (meet ?61062 (join r1 (meet b r2))) =>= n0 [61062] by Demod 67487 with 13 at 3
% 15.33/4.16 Id : 79823, {_}: r1 =?= r1 [] by Demod 79822 with 135 at 3
% 15.33/4.16 Id : 79822, {_}: r1 =<= join n0 r1 [] by Demod 79821 with 10 at 3
% 15.33/4.16 Id : 79821, {_}: r1 =<= join r1 n0 [] by Demod 79820 with 67553 at 2,3
% 15.33/4.16 Id : 79820, {_}: r1 =<= join r1 (meet a (meet r2 (join r1 (meet b r2)))) [] by Demod 79819 with 9 at 2,2,2,2,3
% 15.33/4.16 Id : 79819, {_}: r1 =<= join r1 (meet a (meet r2 (join r1 (meet r2 b)))) [] by Demod 79818 with 9 at 2,2,3
% 15.33/4.16 Id : 79818, {_}: r1 =<= join r1 (meet a (meet (join r1 (meet r2 b)) r2)) [] by Demod 79817 with 69 at 2,3
% 15.33/4.16 Id : 79817, {_}: r1 =<= join r1 (meet r2 (meet a (join r1 (meet r2 b)))) [] by Demod 79816 with 11 at 2,3
% 15.33/4.16 Id : 79816, {_}: r1 =<= join r1 (meet (meet r2 a) (join r1 (meet r2 b))) [] by Demod 1 with 252 at 3
% 15.33/4.16 Id : 1, {_}: r1 =<= meet (join r1 (meet r2 b)) (join r1 (meet r2 a)) [] by prove_lemma
% 15.33/4.16 % SZS output end CNFRefutation for theBenchmark.p
% 15.33/4.16 323: solved /export/starexec/sandbox/benchmark/theBenchmark.p in 3.818031 using kbo
%------------------------------------------------------------------------------