TSTP Solution File: BOO010-2 by Matita---1.0
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%------------------------------------------------------------------------------
% File : Matita---1.0
% Problem : BOO010-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : matitaprover --timeout %d --tptppath /export/starexec/sandbox2/benchmark %s
% Computer : n022.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 : Thu Jul 14 23:44:12 EDT 2022
% Result : Unsatisfiable 1.32s 0.64s
% Output : CNFRefutation 1.32s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : BOO010-2 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.13 % Command : matitaprover --timeout %d --tptppath /export/starexec/sandbox2/benchmark %s
% 0.12/0.34 % Computer : n022.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 : Wed Jun 1 18:18:22 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 25877: Facts:
% 0.12/0.34 25877: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
% 0.12/0.34 25877: Id : 3, {_}:
% 0.12/0.34 multiply ?5 ?6 =?= multiply ?6 ?5
% 0.12/0.34 [6, 5] by commutativity_of_multiply ?5 ?6
% 0.12/0.35 25877: Id : 4, {_}:
% 0.12/0.35 add (multiply ?8 ?9) ?10 =<= multiply (add ?8 ?10) (add ?9 ?10)
% 0.12/0.35 [10, 9, 8] by distributivity1 ?8 ?9 ?10
% 0.12/0.35 25877: Id : 5, {_}:
% 0.12/0.35 add ?12 (multiply ?13 ?14) =<= multiply (add ?12 ?13) (add ?12 ?14)
% 0.12/0.35 [14, 13, 12] by distributivity2 ?12 ?13 ?14
% 0.12/0.35 25877: Id : 6, {_}:
% 0.12/0.35 multiply (add ?16 ?17) ?18
% 0.12/0.35 =<=
% 0.12/0.35 add (multiply ?16 ?18) (multiply ?17 ?18)
% 0.12/0.35 [18, 17, 16] by distributivity3 ?16 ?17 ?18
% 0.12/0.35 25877: Id : 7, {_}:
% 0.12/0.35 multiply ?20 (add ?21 ?22)
% 0.12/0.35 =<=
% 0.12/0.35 add (multiply ?20 ?21) (multiply ?20 ?22)
% 0.12/0.35 [22, 21, 20] by distributivity4 ?20 ?21 ?22
% 0.12/0.35 25877: Id : 8, {_}:
% 0.12/0.35 add ?24 (inverse ?24) =>= multiplicative_identity
% 0.12/0.35 [24] by additive_inverse1 ?24
% 0.12/0.35 25877: Id : 9, {_}:
% 0.12/0.35 add (inverse ?26) ?26 =>= multiplicative_identity
% 0.12/0.35 [26] by additive_inverse2 ?26
% 0.12/0.35 25877: Id : 10, {_}:
% 0.12/0.35 multiply ?28 (inverse ?28) =>= additive_identity
% 0.12/0.35 [28] by multiplicative_inverse1 ?28
% 0.12/0.35 25877: Id : 11, {_}:
% 0.12/0.35 multiply (inverse ?30) ?30 =>= additive_identity
% 0.12/0.35 [30] by multiplicative_inverse2 ?30
% 0.12/0.35 25877: Id : 12, {_}:
% 0.12/0.35 multiply ?32 multiplicative_identity =>= ?32
% 0.12/0.35 [32] by multiplicative_id1 ?32
% 0.12/0.35 25877: Id : 13, {_}:
% 0.12/0.35 multiply multiplicative_identity ?34 =>= ?34
% 0.12/0.35 [34] by multiplicative_id2 ?34
% 0.12/0.35 25877: Id : 14, {_}: add ?36 additive_identity =>= ?36 [36] by additive_id1 ?36
% 0.12/0.35 25877: Id : 15, {_}: add additive_identity ?38 =>= ?38 [38] by additive_id2 ?38
% 0.12/0.35 25877: Goal:
% 0.12/0.35 25877: Id : 1, {_}: add a (multiply a b) =>= a [] by prove_a_plus_ab_is_a
% 1.32/0.64 Statistics :
% 1.32/0.64 Max weight : 14
% 1.32/0.64 Found proof, 0.299719s
% 1.32/0.64 % SZS status Unsatisfiable for theBenchmark.p
% 1.32/0.64 % SZS output start CNFRefutation for theBenchmark.p
% 1.32/0.64 Id : 11, {_}: multiply (inverse ?30) ?30 =>= additive_identity [30] by multiplicative_inverse2 ?30
% 1.32/0.64 Id : 12, {_}: multiply ?32 multiplicative_identity =>= ?32 [32] by multiplicative_id1 ?32
% 1.32/0.64 Id : 15, {_}: add additive_identity ?38 =>= ?38 [38] by additive_id2 ?38
% 1.32/0.64 Id : 7, {_}: multiply ?20 (add ?21 ?22) =<= add (multiply ?20 ?21) (multiply ?20 ?22) [22, 21, 20] by distributivity4 ?20 ?21 ?22
% 1.32/0.64 Id : 3, {_}: multiply ?5 ?6 =?= multiply ?6 ?5 [6, 5] by commutativity_of_multiply ?5 ?6
% 1.32/0.64 Id : 9, {_}: add (inverse ?26) ?26 =>= multiplicative_identity [26] by additive_inverse2 ?26
% 1.32/0.64 Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
% 1.32/0.64 Id : 14, {_}: add ?36 additive_identity =>= ?36 [36] by additive_id1 ?36
% 1.32/0.64 Id : 10, {_}: multiply ?28 (inverse ?28) =>= additive_identity [28] by multiplicative_inverse1 ?28
% 1.32/0.64 Id : 13, {_}: multiply multiplicative_identity ?34 =>= ?34 [34] by multiplicative_id2 ?34
% 1.32/0.64 Id : 8, {_}: add ?24 (inverse ?24) =>= multiplicative_identity [24] by additive_inverse1 ?24
% 1.32/0.64 Id : 5, {_}: add ?12 (multiply ?13 ?14) =<= multiply (add ?12 ?13) (add ?12 ?14) [14, 13, 12] by distributivity2 ?12 ?13 ?14
% 1.32/0.64 Id : 4, {_}: add (multiply ?8 ?9) ?10 =<= multiply (add ?8 ?10) (add ?9 ?10) [10, 9, 8] by distributivity1 ?8 ?9 ?10
% 1.32/0.64 Id : 115, {_}: add ?335 (multiply (inverse ?335) ?336) =>= multiply multiplicative_identity (add ?335 ?336) [336, 335] by Super 5 with 8 at 1,3
% 1.32/0.64 Id : 1330, {_}: add ?1604 (multiply (inverse ?1604) ?1605) =>= add ?1604 ?1605 [1605, 1604] by Demod 115 with 13 at 3
% 1.32/0.64 Id : 1334, {_}: add ?1614 additive_identity =<= add ?1614 (inverse (inverse ?1614)) [1614] by Super 1330 with 10 at 2,2
% 1.32/0.64 Id : 1369, {_}: ?1614 =<= add ?1614 (inverse (inverse ?1614)) [1614] by Demod 1334 with 14 at 2
% 1.32/0.64 Id : 1556, {_}: add (multiply ?1832 ?1833) (inverse (inverse ?1833)) =<= multiply (add ?1832 (inverse (inverse ?1833))) ?1833 [1833, 1832] by Super 4 with 1369 at 2,3
% 1.32/0.64 Id : 1573, {_}: add (inverse (inverse ?1833)) (multiply ?1832 ?1833) =<= multiply (add ?1832 (inverse (inverse ?1833))) ?1833 [1832, 1833] by Demod 1556 with 2 at 2
% 1.32/0.64 Id : 128, {_}: add (multiply ?355 (inverse ?356)) ?356 =>= multiply (add ?355 ?356) multiplicative_identity [356, 355] by Super 4 with 9 at 2,3
% 1.32/0.64 Id : 134, {_}: add (multiply ?355 (inverse ?356)) ?356 =>= multiply multiplicative_identity (add ?355 ?356) [356, 355] by Demod 128 with 3 at 3
% 1.32/0.64 Id : 2544, {_}: add (multiply ?355 (inverse ?356)) ?356 =>= add ?355 ?356 [356, 355] by Demod 134 with 13 at 3
% 1.32/0.65 Id : 145, {_}: multiply ?381 (add (inverse ?381) ?382) =>= add additive_identity (multiply ?381 ?382) [382, 381] by Super 7 with 10 at 1,3
% 1.32/0.65 Id : 2643, {_}: multiply ?2768 (add (inverse ?2768) ?2769) =>= multiply ?2768 ?2769 [2769, 2768] by Demod 145 with 15 at 3
% 1.32/0.65 Id : 2658, {_}: multiply ?2805 (inverse ?2805) =<= multiply ?2805 (inverse (inverse (inverse ?2805))) [2805] by Super 2643 with 1369 at 2,2
% 1.32/0.65 Id : 2728, {_}: additive_identity =<= multiply ?2805 (inverse (inverse (inverse ?2805))) [2805] by Demod 2658 with 10 at 2
% 1.32/0.65 Id : 2911, {_}: add additive_identity (inverse (inverse ?2973)) =?= add ?2973 (inverse (inverse ?2973)) [2973] by Super 2544 with 2728 at 1,2
% 1.32/0.65 Id : 2921, {_}: inverse (inverse ?2973) =<= add ?2973 (inverse (inverse ?2973)) [2973] by Demod 2911 with 15 at 2
% 1.32/0.65 Id : 2922, {_}: inverse (inverse ?2973) =>= ?2973 [2973] by Demod 2921 with 1369 at 3
% 1.32/0.65 Id : 6514, {_}: add ?1833 (multiply ?1832 ?1833) =<= multiply (add ?1832 (inverse (inverse ?1833))) ?1833 [1832, 1833] by Demod 1573 with 2922 at 1,2
% 1.32/0.65 Id : 6515, {_}: add ?1833 (multiply ?1832 ?1833) =<= multiply (add ?1832 ?1833) ?1833 [1832, 1833] by Demod 6514 with 2922 at 2,1,3
% 1.32/0.65 Id : 228, {_}: add (multiply ?504 additive_identity) ?505 =<= multiply (add ?504 ?505) ?505 [505, 504] by Super 4 with 15 at 2,3
% 1.32/0.65 Id : 471, {_}: multiply ?753 (add ?754 ?753) =>= add (multiply ?754 additive_identity) ?753 [754, 753] by Super 3 with 228 at 3
% 1.32/0.65 Id : 229, {_}: add (multiply additive_identity ?507) ?508 =<= multiply ?508 (add ?507 ?508) [508, 507] by Super 4 with 15 at 1,3
% 1.32/0.65 Id : 874, {_}: add (multiply additive_identity ?754) ?753 =?= add (multiply ?754 additive_identity) ?753 [753, 754] by Demod 471 with 229 at 2
% 1.32/0.65 Id : 423, {_}: add ?696 (multiply additive_identity ?697) =<= multiply ?696 (add ?696 ?697) [697, 696] by Super 5 with 14 at 1,3
% 1.32/0.65 Id : 426, {_}: add (inverse ?704) (multiply additive_identity ?704) =>= multiply (inverse ?704) multiplicative_identity [704] by Super 423 with 9 at 2,3
% 1.32/0.65 Id : 451, {_}: add (inverse ?704) (multiply additive_identity ?704) =>= multiply multiplicative_identity (inverse ?704) [704] by Demod 426 with 3 at 3
% 1.32/0.65 Id : 452, {_}: add (inverse ?704) (multiply additive_identity ?704) =>= inverse ?704 [704] by Demod 451 with 13 at 3
% 1.32/0.65 Id : 2625, {_}: multiply ?381 (add (inverse ?381) ?382) =>= multiply ?381 ?382 [382, 381] by Demod 145 with 15 at 3
% 1.32/0.65 Id : 2631, {_}: add (inverse (add (inverse additive_identity) ?2733)) (multiply additive_identity ?2733) =>= inverse (add (inverse additive_identity) ?2733) [2733] by Super 452 with 2625 at 2,2
% 1.32/0.65 Id : 214, {_}: inverse additive_identity =>= multiplicative_identity [] by Super 9 with 14 at 2
% 1.32/0.65 Id : 2687, {_}: add (inverse (add multiplicative_identity ?2733)) (multiply additive_identity ?2733) =>= inverse (add (inverse additive_identity) ?2733) [2733] by Demod 2631 with 214 at 1,1,1,2
% 1.32/0.65 Id : 2688, {_}: add (inverse (add multiplicative_identity ?2733)) (multiply additive_identity ?2733) =>= inverse (add multiplicative_identity ?2733) [2733] by Demod 2687 with 214 at 1,1,3
% 1.32/0.65 Id : 1336, {_}: add ?1618 (inverse ?1618) =>= add ?1618 multiplicative_identity [1618] by Super 1330 with 12 at 2,2
% 1.32/0.65 Id : 1371, {_}: multiplicative_identity =<= add ?1618 multiplicative_identity [1618] by Demod 1336 with 8 at 2
% 1.32/0.65 Id : 1390, {_}: add multiplicative_identity ?1671 =>= multiplicative_identity [1671] by Super 2 with 1371 at 3
% 1.32/0.65 Id : 2689, {_}: add (inverse multiplicative_identity) (multiply additive_identity ?2733) =>= inverse (add multiplicative_identity ?2733) [2733] by Demod 2688 with 1390 at 1,1,2
% 1.32/0.65 Id : 2690, {_}: add (inverse multiplicative_identity) (multiply additive_identity ?2733) =>= inverse multiplicative_identity [2733] by Demod 2689 with 1390 at 1,3
% 1.32/0.65 Id : 176, {_}: inverse multiplicative_identity =>= additive_identity [] by Super 11 with 12 at 2
% 1.32/0.65 Id : 2691, {_}: add additive_identity (multiply additive_identity ?2733) =>= inverse multiplicative_identity [2733] by Demod 2690 with 176 at 1,2
% 1.32/0.65 Id : 2692, {_}: add additive_identity (multiply additive_identity ?2733) =>= additive_identity [2733] by Demod 2691 with 176 at 3
% 1.32/0.65 Id : 2693, {_}: multiply additive_identity ?2733 =>= additive_identity [2733] by Demod 2692 with 15 at 2
% 1.32/0.65 Id : 2750, {_}: add additive_identity ?753 =<= add (multiply ?754 additive_identity) ?753 [754, 753] by Demod 874 with 2693 at 1,2
% 1.32/0.65 Id : 2770, {_}: ?753 =<= add (multiply ?754 additive_identity) ?753 [754, 753] by Demod 2750 with 15 at 2
% 1.32/0.65 Id : 2772, {_}: ?505 =<= multiply (add ?504 ?505) ?505 [504, 505] by Demod 228 with 2770 at 2
% 1.32/0.65 Id : 6548, {_}: add ?6854 (multiply ?6855 ?6854) =>= ?6854 [6855, 6854] by Demod 6515 with 2772 at 3
% 1.32/0.65 Id : 6549, {_}: add ?6857 (multiply ?6857 ?6858) =>= ?6857 [6858, 6857] by Super 6548 with 3 at 2,2
% 1.32/0.65 Id : 6888, {_}: a === a [] by Demod 1 with 6549 at 2
% 1.32/0.65 Id : 1, {_}: add a (multiply a b) =>= a [] by prove_a_plus_ab_is_a
% 1.32/0.65 % SZS output end CNFRefutation for theBenchmark.p
% 1.32/0.65 25880: solved /export/starexec/sandbox2/benchmark/theBenchmark.p in 0.302639 using nrkbo
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