TSTP Solution File: RNG008-3 by Matita---1.0
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%------------------------------------------------------------------------------
% File : Matita---1.0
% Problem : RNG008-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : matitaprover --timeout %d --tptppath /export/starexec/sandbox2/benchmark %s
% Computer : n026.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 : Mon Jul 18 20:35:27 EDT 2022
% Result : Unsatisfiable 9.19s 2.61s
% Output : CNFRefutation 9.19s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : RNG008-3 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.12 % Command : matitaprover --timeout %d --tptppath /export/starexec/sandbox2/benchmark %s
% 0.12/0.33 % Computer : n026.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon May 30 18:55:55 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 29843: Facts:
% 0.12/0.33 29843: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_identity ?2
% 0.12/0.33 29843: Id : 3, {_}:
% 0.12/0.33 add (additive_inverse ?4) ?4 =>= additive_identity
% 0.12/0.33 [4] by left_additive_inverse ?4
% 0.12/0.33 29843: Id : 4, {_}:
% 0.12/0.33 multiply ?6 (add ?7 ?8) =<= add (multiply ?6 ?7) (multiply ?6 ?8)
% 0.12/0.33 [8, 7, 6] by distribute1 ?6 ?7 ?8
% 0.12/0.33 29843: Id : 5, {_}:
% 0.12/0.33 multiply (add ?10 ?11) ?12
% 0.12/0.33 =<=
% 0.12/0.33 add (multiply ?10 ?12) (multiply ?11 ?12)
% 0.12/0.33 [12, 11, 10] by distribute2 ?10 ?11 ?12
% 0.12/0.33 29843: Id : 6, {_}:
% 0.12/0.33 additive_inverse additive_identity =>= additive_identity
% 0.12/0.33 [] by additive_inverse_identity
% 0.12/0.33 29843: Id : 7, {_}:
% 0.12/0.33 additive_inverse (additive_inverse ?15) =>= ?15
% 0.12/0.33 [15] by additive_inverse_additive_inverse ?15
% 0.12/0.33 29843: Id : 8, {_}:
% 0.12/0.33 multiply ?17 additive_identity =>= additive_identity
% 0.12/0.33 [17] by multiply_additive_id1 ?17
% 0.12/0.33 29843: Id : 9, {_}:
% 0.12/0.33 multiply additive_identity ?19 =>= additive_identity
% 0.12/0.33 [19] by multiply_additive_id2 ?19
% 0.12/0.33 29843: Id : 10, {_}:
% 0.12/0.33 additive_inverse (add ?21 ?22)
% 0.12/0.33 =<=
% 0.12/0.33 add (additive_inverse ?21) (additive_inverse ?22)
% 0.12/0.33 [22, 21] by distribute_additive_inverse ?21 ?22
% 0.12/0.33 29843: Id : 11, {_}:
% 0.12/0.33 multiply ?24 (additive_inverse ?25)
% 0.12/0.33 =>=
% 0.12/0.33 additive_inverse (multiply ?24 ?25)
% 0.12/0.33 [25, 24] by multiply_additive_inverse1 ?24 ?25
% 0.12/0.33 29843: Id : 12, {_}:
% 0.12/0.33 multiply (additive_inverse ?27) ?28
% 0.12/0.33 =>=
% 0.12/0.33 additive_inverse (multiply ?27 ?28)
% 0.12/0.33 [28, 27] by multiply_additive_inverse2 ?27 ?28
% 0.12/0.33 29843: Id : 13, {_}:
% 0.12/0.33 add (add ?30 ?31) ?32 =?= add ?30 (add ?31 ?32)
% 0.12/0.33 [32, 31, 30] by associative_addition ?30 ?31 ?32
% 0.18/0.33 29843: Id : 14, {_}:
% 0.18/0.33 add ?34 ?35 =?= add ?35 ?34
% 0.18/0.33 [35, 34] by commutative_addition ?34 ?35
% 0.18/0.33 29843: Id : 15, {_}:
% 0.18/0.33 multiply (multiply ?37 ?38) ?39 =?= multiply ?37 (multiply ?38 ?39)
% 0.18/0.33 [39, 38, 37] by associative_multiplication ?37 ?38 ?39
% 0.18/0.33 29843: Id : 16, {_}: add ?41 additive_identity =>= ?41 [41] by right_identity ?41
% 0.18/0.33 29843: Id : 17, {_}:
% 0.18/0.33 add ?43 (additive_inverse ?43) =>= additive_identity
% 0.18/0.33 [43] by right_inverse ?43
% 0.18/0.33 29843: Id : 18, {_}: multiply ?45 ?45 =>= ?45 [45] by boolean_ring ?45
% 0.18/0.33 29843: Id : 19, {_}: multiply a b =>= c [] by a_times_b_is_c
% 0.18/0.33 29843: Goal:
% 0.18/0.33 29843: Id : 1, {_}: multiply b a =>= c [] by prove_commutativity
% 9.19/2.61 Statistics :
% 9.19/2.61 Max weight : 18
% 9.19/2.61 Found proof, 2.273670s
% 9.19/2.61 % SZS status Unsatisfiable for theBenchmark.p
% 9.19/2.61 % SZS output start CNFRefutation for theBenchmark.p
% 9.19/2.61 Id : 8, {_}: multiply ?17 additive_identity =>= additive_identity [17] by multiply_additive_id1 ?17
% 9.19/2.61 Id : 16, {_}: add ?41 additive_identity =>= ?41 [41] by right_identity ?41
% 9.19/2.61 Id : 13, {_}: add (add ?30 ?31) ?32 =>= add ?30 (add ?31 ?32) [32, 31, 30] by associative_addition ?30 ?31 ?32
% 9.19/2.61 Id : 5, {_}: multiply (add ?10 ?11) ?12 =<= add (multiply ?10 ?12) (multiply ?11 ?12) [12, 11, 10] by distribute2 ?10 ?11 ?12
% 9.19/2.61 Id : 9, {_}: multiply additive_identity ?19 =>= additive_identity [19] by multiply_additive_id2 ?19
% 9.19/2.61 Id : 19, {_}: multiply a b =>= c [] by a_times_b_is_c
% 9.19/2.61 Id : 4, {_}: multiply ?6 (add ?7 ?8) =<= add (multiply ?6 ?7) (multiply ?6 ?8) [8, 7, 6] by distribute1 ?6 ?7 ?8
% 9.19/2.61 Id : 15, {_}: multiply (multiply ?37 ?38) ?39 =>= multiply ?37 (multiply ?38 ?39) [39, 38, 37] by associative_multiplication ?37 ?38 ?39
% 9.19/2.61 Id : 14, {_}: add ?34 ?35 =?= add ?35 ?34 [35, 34] by commutative_addition ?34 ?35
% 9.19/2.61 Id : 7, {_}: additive_inverse (additive_inverse ?15) =>= ?15 [15] by additive_inverse_additive_inverse ?15
% 9.19/2.61 Id : 12, {_}: multiply (additive_inverse ?27) ?28 =>= additive_inverse (multiply ?27 ?28) [28, 27] by multiply_additive_inverse2 ?27 ?28
% 9.19/2.61 Id : 18, {_}: multiply ?45 ?45 =>= ?45 [45] by boolean_ring ?45
% 9.19/2.61 Id : 11, {_}: multiply ?24 (additive_inverse ?25) =>= additive_inverse (multiply ?24 ?25) [25, 24] by multiply_additive_inverse1 ?24 ?25
% 9.19/2.61 Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_identity ?2
% 9.19/2.61 Id : 3, {_}: add (additive_inverse ?4) ?4 =>= additive_identity [4] by left_additive_inverse ?4
% 9.19/2.61 Id : 148, {_}: add (add ?209 ?210) ?211 =>= add ?209 (add ?210 ?211) [211, 210, 209] by associative_addition ?209 ?210 ?211
% 9.19/2.61 Id : 150, {_}: add additive_identity ?216 =<= add (additive_inverse ?217) (add ?217 ?216) [217, 216] by Super 148 with 3 at 1,2
% 9.19/2.61 Id : 157, {_}: ?216 =<= add (additive_inverse ?217) (add ?217 ?216) [217, 216] by Demod 150 with 2 at 2
% 9.19/2.61 Id : 307, {_}: additive_inverse ?464 =<= additive_inverse (multiply (additive_inverse ?464) ?464) [464] by Super 11 with 18 at 2
% 9.19/2.61 Id : 315, {_}: additive_inverse ?464 =<= additive_inverse (additive_inverse (multiply ?464 ?464)) [464] by Demod 307 with 12 at 1,3
% 9.19/2.61 Id : 316, {_}: additive_inverse ?464 =<= multiply ?464 ?464 [464] by Demod 315 with 7 at 3
% 9.19/2.61 Id : 317, {_}: additive_inverse ?464 =>= ?464 [464] by Demod 316 with 18 at 3
% 9.19/2.61 Id : 1350, {_}: ?1481 =<= add ?1482 (add ?1482 ?1481) [1482, 1481] by Demod 157 with 317 at 1,3
% 9.19/2.61 Id : 1353, {_}: ?1490 =<= add ?1491 (add ?1490 ?1491) [1491, 1490] by Super 1350 with 14 at 2,3
% 9.19/2.61 Id : 33972, {_}: multiply ?29440 ?29441 =<= multiply ?29440 (multiply ?29441 (multiply ?29440 ?29441)) [29441, 29440] by Super 15 with 18 at 2
% 9.19/2.61 Id : 332, {_}: multiply a (add b ?485) =>= add c (multiply a ?485) [485] by Super 4 with 19 at 1,3
% 9.19/2.61 Id : 5431, {_}: multiply (add c (multiply a ?5365)) ?5366 =>= multiply a (multiply (add b ?5365) ?5366) [5366, 5365] by Super 15 with 332 at 1,2
% 9.19/2.61 Id : 1452, {_}: multiply ?1611 ?1612 =<= multiply ?1611 (multiply ?1611 ?1612) [1612, 1611] by Super 15 with 18 at 1,2
% 9.19/2.61 Id : 1457, {_}: multiply a b =?= multiply a c [] by Super 1452 with 19 at 2,3
% 9.19/2.61 Id : 1498, {_}: c =<= multiply a c [] by Demod 1457 with 19 at 2
% 9.19/2.61 Id : 5452, {_}: multiply (add c c) ?5424 =<= multiply a (multiply (add b c) ?5424) [5424] by Super 5431 with 1498 at 2,1,2
% 9.19/2.61 Id : 161, {_}: add ?4 (additive_inverse ?4) =>= additive_identity [4] by Demod 3 with 14 at 2
% 9.19/2.61 Id : 353, {_}: add ?4 ?4 =>= additive_identity [4] by Demod 161 with 317 at 2,2
% 9.19/2.61 Id : 5609, {_}: multiply additive_identity ?5424 =<= multiply a (multiply (add b c) ?5424) [5424] by Demod 5452 with 353 at 1,2
% 9.19/2.61 Id : 5610, {_}: additive_identity =<= multiply a (multiply (add b c) ?5424) [5424] by Demod 5609 with 9 at 2
% 9.19/2.61 Id : 34134, {_}: multiply (add b c) a =?= multiply (add b c) additive_identity [] by Super 33972 with 5610 at 2,3
% 9.19/2.61 Id : 152, {_}: add (multiply ?224 (add ?225 ?226)) ?227 =<= add (multiply ?224 ?225) (add (multiply ?224 ?226) ?227) [227, 226, 225, 224] by Super 148 with 4 at 1,2
% 9.19/2.61 Id : 418, {_}: multiply c ?565 =<= multiply a (multiply b ?565) [565] by Super 15 with 19 at 1,2
% 9.19/2.61 Id : 420, {_}: multiply c b =>= multiply a b [] by Super 418 with 18 at 2,3
% 9.19/2.61 Id : 428, {_}: multiply c b =>= c [] by Demod 420 with 19 at 3
% 9.19/2.61 Id : 530, {_}: add (multiply c (add ?717 b)) ?718 =>= add (multiply c ?717) (add c ?718) [718, 717] by Super 152 with 428 at 1,2,3
% 9.19/2.61 Id : 527, {_}: multiply c (add ?711 b) =>= add (multiply c ?711) c [711] by Super 4 with 428 at 2,3
% 9.19/2.61 Id : 536, {_}: multiply c (add ?711 b) =>= add c (multiply c ?711) [711] by Demod 527 with 14 at 3
% 9.19/2.61 Id : 7740, {_}: add (add c (multiply c ?717)) ?718 =>= add (multiply c ?717) (add c ?718) [718, 717] by Demod 530 with 536 at 1,2
% 9.19/2.61 Id : 164, {_}: add ?250 (add ?251 ?252) =?= add ?251 (add ?252 ?250) [252, 251, 250] by Super 13 with 14 at 2
% 9.19/2.61 Id : 7741, {_}: add (add c (multiply c ?717)) ?718 =>= add c (add ?718 (multiply c ?717)) [718, 717] by Demod 7740 with 164 at 3
% 9.19/2.61 Id : 7742, {_}: add c (add (multiply c ?717) ?718) =?= add c (add ?718 (multiply c ?717)) [718, 717] by Demod 7741 with 13 at 2
% 9.19/2.61 Id : 5435, {_}: multiply (add c a) ?5376 =<= multiply a (multiply (add b a) ?5376) [5376] by Super 5431 with 18 at 2,1,2
% 9.19/2.61 Id : 5806, {_}: multiply (add a c) ?5628 =<= multiply a (multiply (add b a) ?5628) [5628] by Demod 5435 with 14 at 1,2
% 9.19/2.61 Id : 303, {_}: multiply ?454 (add ?454 ?455) =>= add ?454 (multiply ?454 ?455) [455, 454] by Super 4 with 18 at 1,3
% 9.19/2.61 Id : 5814, {_}: multiply (add a c) (add (add b a) ?5643) =<= multiply a (add (add b a) (multiply (add b a) ?5643)) [5643] by Super 5806 with 303 at 2,3
% 9.19/2.61 Id : 5859, {_}: multiply (add a c) (add b (add a ?5643)) =<= multiply a (add (add b a) (multiply (add b a) ?5643)) [5643] by Demod 5814 with 13 at 2,2
% 9.19/2.61 Id : 5860, {_}: multiply (add a c) (add b (add a ?5643)) =<= multiply a (add b (add a (multiply (add b a) ?5643))) [5643] by Demod 5859 with 13 at 2,3
% 9.19/2.61 Id : 5861, {_}: multiply (add a c) (add b (add a ?5643)) =<= add c (multiply a (add a (multiply (add b a) ?5643))) [5643] by Demod 5860 with 332 at 3
% 9.19/2.61 Id : 5862, {_}: multiply (add a c) (add b (add a ?5643)) =<= add c (add a (multiply a (multiply (add b a) ?5643))) [5643] by Demod 5861 with 303 at 2,3
% 9.19/2.61 Id : 5863, {_}: multiply (add a c) (add b (add a ?5643)) =<= add a (add (multiply a (multiply (add b a) ?5643)) c) [5643] by Demod 5862 with 164 at 3
% 9.19/2.61 Id : 5864, {_}: multiply (add a c) (add b (add a ?5643)) =<= add a (add c (multiply a (multiply (add b a) ?5643))) [5643] by Demod 5863 with 14 at 2,3
% 9.19/2.61 Id : 5571, {_}: multiply (add a c) ?5376 =<= multiply a (multiply (add b a) ?5376) [5376] by Demod 5435 with 14 at 1,2
% 9.19/2.61 Id : 25739, {_}: multiply (add a c) (add b (add a ?24054)) =>= add a (add c (multiply (add a c) ?24054)) [24054] by Demod 5864 with 5571 at 2,2,3
% 9.19/2.61 Id : 25746, {_}: multiply (add a c) (add b additive_identity) =<= add a (add c (multiply (add a c) a)) [] by Super 25739 with 353 at 2,2,2
% 9.19/2.61 Id : 25846, {_}: multiply (add a c) b =<= add a (add c (multiply (add a c) a)) [] by Demod 25746 with 16 at 2,2
% 9.19/2.61 Id : 305, {_}: multiply (add ?460 ?461) ?460 =>= add ?460 (multiply ?461 ?460) [461, 460] by Super 5 with 18 at 1,3
% 9.19/2.61 Id : 25847, {_}: multiply (add a c) b =<= add a (add c (add a (multiply c a))) [] by Demod 25846 with 305 at 2,2,3
% 9.19/2.61 Id : 330, {_}: multiply (add a ?481) b =>= add c (multiply ?481 b) [481] by Super 5 with 19 at 1,3
% 9.19/2.61 Id : 25848, {_}: add c (multiply c b) =<= add a (add c (add a (multiply c a))) [] by Demod 25847 with 330 at 2
% 9.19/2.61 Id : 25849, {_}: add c (multiply c b) =<= add a (add a (add (multiply c a) c)) [] by Demod 25848 with 164 at 2,3
% 9.19/2.61 Id : 25850, {_}: add c c =<= add a (add a (add (multiply c a) c)) [] by Demod 25849 with 428 at 2,2
% 9.19/2.61 Id : 1337, {_}: ?216 =<= add ?217 (add ?217 ?216) [217, 216] by Demod 157 with 317 at 1,3
% 9.19/2.61 Id : 25851, {_}: add c c =<= add (multiply c a) c [] by Demod 25850 with 1337 at 3
% 9.19/2.61 Id : 25852, {_}: additive_identity =<= add (multiply c a) c [] by Demod 25851 with 353 at 2
% 9.19/2.61 Id : 25853, {_}: additive_identity =<= add c (multiply c a) [] by Demod 25852 with 14 at 3
% 9.19/2.61 Id : 25933, {_}: add c (add (multiply c a) c) =>= add c additive_identity [] by Super 7742 with 25853 at 2,3
% 9.19/2.61 Id : 25974, {_}: multiply c a =>= add c additive_identity [] by Demod 25933 with 1353 at 2
% 9.19/2.61 Id : 25975, {_}: multiply c a =>= c [] by Demod 25974 with 16 at 3
% 9.19/2.61 Id : 26110, {_}: multiply (add ?24203 c) a =>= add (multiply ?24203 a) c [24203] by Super 5 with 25975 at 2,3
% 9.19/2.61 Id : 26151, {_}: multiply (add ?24203 c) a =>= add c (multiply ?24203 a) [24203] by Demod 26110 with 14 at 3
% 9.19/2.61 Id : 34629, {_}: add c (multiply b a) =<= multiply (add b c) additive_identity [] by Demod 34134 with 26151 at 2
% 9.19/2.61 Id : 34630, {_}: add c (multiply b a) =>= additive_identity [] by Demod 34629 with 8 at 3
% 9.19/2.61 Id : 35128, {_}: c =<= add (multiply b a) additive_identity [] by Super 1353 with 34630 at 2,3
% 9.19/2.61 Id : 35224, {_}: c =<= add additive_identity (multiply b a) [] by Demod 35128 with 14 at 3
% 9.19/2.61 Id : 35225, {_}: c =<= multiply b a [] by Demod 35224 with 2 at 3
% 9.19/2.61 Id : 35436, {_}: c =?= c [] by Demod 1 with 35225 at 2
% 9.19/2.61 Id : 1, {_}: multiply b a =>= c [] by prove_commutativity
% 9.19/2.61 % SZS output end CNFRefutation for theBenchmark.p
% 9.19/2.61 29844: solved /export/starexec/sandbox2/benchmark/theBenchmark.p in 2.277896 using kbo
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