TSTP Solution File: BOO007-2 by Matita---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Matita---1.0
% Problem : BOO007-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : matitaprover --timeout %d --tptppath /export/starexec/sandbox2/benchmark %s
% Computer : 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 : Thu Jul 14 23:44:11 EDT 2022
% Result : Unsatisfiable 9.16s 2.67s
% Output : CNFRefutation 9.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : BOO007-2 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.12 % Command : matitaprover --timeout %d --tptppath /export/starexec/sandbox2/benchmark %s
% 0.12/0.33 % Computer : n018.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 : Wed Jun 1 17:45:14 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 2587: Facts:
% 0.12/0.34 2587: Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
% 0.12/0.34 2587: Id : 3, {_}:
% 0.12/0.34 multiply ?5 ?6 =?= multiply ?6 ?5
% 0.12/0.34 [6, 5] by commutativity_of_multiply ?5 ?6
% 0.12/0.34 2587: Id : 4, {_}:
% 0.12/0.34 add (multiply ?8 ?9) ?10 =<= multiply (add ?8 ?10) (add ?9 ?10)
% 0.12/0.34 [10, 9, 8] by distributivity1 ?8 ?9 ?10
% 0.12/0.34 2587: Id : 5, {_}:
% 0.12/0.34 add ?12 (multiply ?13 ?14) =<= multiply (add ?12 ?13) (add ?12 ?14)
% 0.12/0.34 [14, 13, 12] by distributivity2 ?12 ?13 ?14
% 0.12/0.34 2587: Id : 6, {_}:
% 0.12/0.34 multiply (add ?16 ?17) ?18
% 0.12/0.34 =<=
% 0.12/0.34 add (multiply ?16 ?18) (multiply ?17 ?18)
% 0.12/0.34 [18, 17, 16] by distributivity3 ?16 ?17 ?18
% 0.12/0.34 2587: Id : 7, {_}:
% 0.12/0.34 multiply ?20 (add ?21 ?22)
% 0.12/0.34 =<=
% 0.12/0.34 add (multiply ?20 ?21) (multiply ?20 ?22)
% 0.12/0.34 [22, 21, 20] by distributivity4 ?20 ?21 ?22
% 0.12/0.34 2587: Id : 8, {_}:
% 0.12/0.34 add ?24 (inverse ?24) =>= multiplicative_identity
% 0.12/0.34 [24] by additive_inverse1 ?24
% 0.12/0.34 2587: Id : 9, {_}:
% 0.12/0.34 add (inverse ?26) ?26 =>= multiplicative_identity
% 0.12/0.34 [26] by additive_inverse2 ?26
% 0.12/0.34 2587: Id : 10, {_}:
% 0.12/0.34 multiply ?28 (inverse ?28) =>= additive_identity
% 0.12/0.34 [28] by multiplicative_inverse1 ?28
% 0.12/0.34 2587: Id : 11, {_}:
% 0.12/0.34 multiply (inverse ?30) ?30 =>= additive_identity
% 0.12/0.34 [30] by multiplicative_inverse2 ?30
% 0.12/0.34 2587: Id : 12, {_}:
% 0.12/0.34 multiply ?32 multiplicative_identity =>= ?32
% 0.12/0.34 [32] by multiplicative_id1 ?32
% 0.12/0.34 2587: Id : 13, {_}:
% 0.12/0.34 multiply multiplicative_identity ?34 =>= ?34
% 0.12/0.34 [34] by multiplicative_id2 ?34
% 0.12/0.34 2587: Id : 14, {_}: add ?36 additive_identity =>= ?36 [36] by additive_id1 ?36
% 0.12/0.34 2587: Id : 15, {_}: add additive_identity ?38 =>= ?38 [38] by additive_id2 ?38
% 0.12/0.34 2587: Goal:
% 0.12/0.34 2587: Id : 1, {_}:
% 0.12/0.34 multiply a (multiply b c) =<= multiply (multiply a b) c
% 0.12/0.34 [] by prove_associativity
% 9.16/2.67 Statistics :
% 9.16/2.67 Max weight : 22
% 9.16/2.67 Found proof, 2.335740s
% 9.16/2.67 % SZS status Unsatisfiable for theBenchmark.p
% 9.16/2.67 % SZS output start CNFRefutation for theBenchmark.p
% 9.16/2.67 Id : 12, {_}: multiply ?32 multiplicative_identity =>= ?32 [32] by multiplicative_id1 ?32
% 9.16/2.67 Id : 15, {_}: add additive_identity ?38 =>= ?38 [38] by additive_id2 ?38
% 9.16/2.67 Id : 7, {_}: multiply ?20 (add ?21 ?22) =<= add (multiply ?20 ?21) (multiply ?20 ?22) [22, 21, 20] by distributivity4 ?20 ?21 ?22
% 9.16/2.67 Id : 14, {_}: add ?36 additive_identity =>= ?36 [36] by additive_id1 ?36
% 9.16/2.67 Id : 10, {_}: multiply ?28 (inverse ?28) =>= additive_identity [28] by multiplicative_inverse1 ?28
% 9.16/2.67 Id : 13, {_}: multiply multiplicative_identity ?34 =>= ?34 [34] by multiplicative_id2 ?34
% 9.16/2.67 Id : 8, {_}: add ?24 (inverse ?24) =>= multiplicative_identity [24] by additive_inverse1 ?24
% 9.16/2.67 Id : 2, {_}: add ?2 ?3 =?= add ?3 ?2 [3, 2] by commutativity_of_add ?2 ?3
% 9.16/2.67 Id : 29, {_}: add (multiply ?78 ?79) ?80 =<= multiply (add ?78 ?80) (add ?79 ?80) [80, 79, 78] by distributivity1 ?78 ?79 ?80
% 9.16/2.67 Id : 5, {_}: add ?12 (multiply ?13 ?14) =<= multiply (add ?12 ?13) (add ?12 ?14) [14, 13, 12] by distributivity2 ?12 ?13 ?14
% 9.16/2.67 Id : 6, {_}: multiply (add ?16 ?17) ?18 =<= add (multiply ?16 ?18) (multiply ?17 ?18) [18, 17, 16] by distributivity3 ?16 ?17 ?18
% 9.16/2.67 Id : 4, {_}: add (multiply ?8 ?9) ?10 =<= multiply (add ?8 ?10) (add ?9 ?10) [10, 9, 8] by distributivity1 ?8 ?9 ?10
% 9.16/2.67 Id : 3, {_}: multiply ?5 ?6 =?= multiply ?6 ?5 [6, 5] by commutativity_of_multiply ?5 ?6
% 9.16/2.67 Id : 59, {_}: add (multiply ?156 (multiply ?157 ?158)) (multiply ?159 ?158) =<= multiply (add ?156 (multiply ?159 ?158)) (multiply (add ?157 ?159) ?158) [159, 158, 157, 156] by Super 4 with 6 at 2,3
% 9.16/2.67 Id : 42, {_}: multiply (add ?110 ?111) (add ?110 ?112) =>= add ?110 (multiply ?112 ?111) [112, 111, 110] by Super 3 with 5 at 3
% 9.16/2.67 Id : 54, {_}: add ?110 (multiply ?111 ?112) =?= add ?110 (multiply ?112 ?111) [112, 111, 110] by Demod 42 with 5 at 2
% 9.16/2.67 Id : 32, {_}: add (multiply ?90 ?91) ?92 =<= multiply (add ?92 ?90) (add ?91 ?92) [92, 91, 90] by Super 29 with 2 at 1,3
% 9.16/2.67 Id : 111, {_}: add ?333 (multiply (inverse ?333) ?334) =>= multiply multiplicative_identity (add ?333 ?334) [334, 333] by Super 5 with 8 at 1,3
% 9.16/2.67 Id : 2044, {_}: add ?2663 (multiply (inverse ?2663) ?2664) =>= add ?2663 ?2664 [2664, 2663] by Demod 111 with 13 at 3
% 9.16/2.67 Id : 2048, {_}: add ?2673 additive_identity =<= add ?2673 (inverse (inverse ?2673)) [2673] by Super 2044 with 10 at 2,2
% 9.16/2.67 Id : 2094, {_}: ?2673 =<= add ?2673 (inverse (inverse ?2673)) [2673] by Demod 2048 with 14 at 2
% 9.16/2.67 Id : 2566, {_}: add (multiply ?3198 ?3199) (inverse (inverse ?3199)) =<= multiply (add (inverse (inverse ?3199)) ?3198) ?3199 [3199, 3198] by Super 32 with 2094 at 2,3
% 9.16/2.67 Id : 2578, {_}: add (inverse (inverse ?3199)) (multiply ?3198 ?3199) =<= multiply (add (inverse (inverse ?3199)) ?3198) ?3199 [3198, 3199] by Demod 2566 with 2 at 2
% 9.16/2.67 Id : 2579, {_}: add (inverse (inverse ?3199)) (multiply ?3198 ?3199) =<= multiply ?3199 (add (inverse (inverse ?3199)) ?3198) [3198, 3199] by Demod 2578 with 3 at 3
% 9.16/2.67 Id : 110, {_}: add ?330 (multiply ?331 (inverse ?330)) =>= multiply (add ?330 ?331) multiplicative_identity [331, 330] by Super 5 with 8 at 2,3
% 9.16/2.67 Id : 114, {_}: add ?330 (multiply ?331 (inverse ?330)) =>= multiply multiplicative_identity (add ?330 ?331) [331, 330] by Demod 110 with 3 at 3
% 9.16/2.67 Id : 3057, {_}: add ?330 (multiply ?331 (inverse ?330)) =>= add ?330 ?331 [331, 330] by Demod 114 with 13 at 3
% 9.16/2.67 Id : 130, {_}: multiply ?347 (add (inverse ?347) ?348) =>= add additive_identity (multiply ?347 ?348) [348, 347] by Super 7 with 10 at 1,3
% 9.16/2.67 Id : 3445, {_}: multiply ?4207 (add (inverse ?4207) ?4208) =>= multiply ?4207 ?4208 [4208, 4207] by Demod 130 with 15 at 3
% 9.16/2.67 Id : 3458, {_}: multiply ?4242 (inverse ?4242) =<= multiply ?4242 (inverse (inverse (inverse ?4242))) [4242] by Super 3445 with 2094 at 2,2
% 9.16/2.67 Id : 3540, {_}: additive_identity =<= multiply ?4242 (inverse (inverse (inverse ?4242))) [4242] by Demod 3458 with 10 at 2
% 9.16/2.67 Id : 3704, {_}: add (inverse (inverse ?4364)) additive_identity =?= add (inverse (inverse ?4364)) ?4364 [4364] by Super 3057 with 3540 at 2,2
% 9.16/2.67 Id : 3735, {_}: add additive_identity (inverse (inverse ?4364)) =<= add (inverse (inverse ?4364)) ?4364 [4364] by Demod 3704 with 2 at 2
% 9.16/2.67 Id : 3736, {_}: add additive_identity (inverse (inverse ?4364)) =?= add ?4364 (inverse (inverse ?4364)) [4364] by Demod 3735 with 2 at 3
% 9.16/2.67 Id : 3737, {_}: inverse (inverse ?4364) =<= add ?4364 (inverse (inverse ?4364)) [4364] by Demod 3736 with 15 at 2
% 9.16/2.67 Id : 3738, {_}: inverse (inverse ?4364) =>= ?4364 [4364] by Demod 3737 with 2094 at 3
% 9.16/2.67 Id : 6025, {_}: add ?3199 (multiply ?3198 ?3199) =<= multiply ?3199 (add (inverse (inverse ?3199)) ?3198) [3198, 3199] by Demod 2579 with 3738 at 1,2
% 9.16/2.67 Id : 6026, {_}: add ?3199 (multiply ?3198 ?3199) =<= multiply ?3199 (add ?3199 ?3198) [3198, 3199] by Demod 6025 with 3738 at 1,2,3
% 9.16/2.67 Id : 204, {_}: add ?439 (multiply additive_identity ?440) =<= multiply ?439 (add ?439 ?440) [440, 439] by Super 5 with 14 at 1,3
% 9.16/2.67 Id : 850, {_}: add (multiply additive_identity ?1253) ?1254 =<= multiply ?1254 (add ?1253 ?1254) [1254, 1253] by Super 4 with 15 at 1,3
% 9.16/2.67 Id : 852, {_}: add (multiply additive_identity ?1259) (inverse ?1259) =>= multiply (inverse ?1259) multiplicative_identity [1259] by Super 850 with 8 at 2,3
% 9.16/2.67 Id : 892, {_}: add (inverse ?1259) (multiply additive_identity ?1259) =>= multiply (inverse ?1259) multiplicative_identity [1259] by Demod 852 with 2 at 2
% 9.16/2.67 Id : 893, {_}: add (inverse ?1259) (multiply additive_identity ?1259) =>= multiply multiplicative_identity (inverse ?1259) [1259] by Demod 892 with 3 at 3
% 9.16/2.67 Id : 894, {_}: add (inverse ?1259) (multiply additive_identity ?1259) =>= inverse ?1259 [1259] by Demod 893 with 13 at 3
% 9.16/2.67 Id : 3424, {_}: multiply ?347 (add (inverse ?347) ?348) =>= multiply ?347 ?348 [348, 347] by Demod 130 with 15 at 3
% 9.16/2.67 Id : 3441, {_}: add (inverse (add (inverse additive_identity) ?4198)) (multiply additive_identity ?4198) =>= inverse (add (inverse additive_identity) ?4198) [4198] by Super 894 with 3424 at 2,2
% 9.16/2.67 Id : 3484, {_}: add (multiply additive_identity ?4198) (inverse (add (inverse additive_identity) ?4198)) =>= inverse (add (inverse additive_identity) ?4198) [4198] by Demod 3441 with 2 at 2
% 9.16/2.67 Id : 225, {_}: inverse additive_identity =>= multiplicative_identity [] by Super 8 with 15 at 2
% 9.16/2.67 Id : 3485, {_}: add (multiply additive_identity ?4198) (inverse (add (inverse additive_identity) ?4198)) =>= inverse (add multiplicative_identity ?4198) [4198] by Demod 3484 with 225 at 1,1,3
% 9.16/2.67 Id : 3486, {_}: add (multiply additive_identity ?4198) (inverse (add multiplicative_identity ?4198)) =>= inverse (add multiplicative_identity ?4198) [4198] by Demod 3485 with 225 at 1,1,2,2
% 9.16/2.67 Id : 2049, {_}: add ?2675 (inverse ?2675) =>= add ?2675 multiplicative_identity [2675] by Super 2044 with 12 at 2,2
% 9.16/2.67 Id : 2095, {_}: multiplicative_identity =<= add ?2675 multiplicative_identity [2675] by Demod 2049 with 8 at 2
% 9.16/2.67 Id : 2122, {_}: add multiplicative_identity ?2741 =>= multiplicative_identity [2741] by Super 2 with 2095 at 3
% 9.16/2.67 Id : 3487, {_}: add (multiply additive_identity ?4198) (inverse (add multiplicative_identity ?4198)) =>= inverse multiplicative_identity [4198] by Demod 3486 with 2122 at 1,3
% 9.16/2.67 Id : 3488, {_}: add (multiply additive_identity ?4198) (inverse multiplicative_identity) =>= inverse multiplicative_identity [4198] by Demod 3487 with 2122 at 1,2,2
% 9.16/2.67 Id : 171, {_}: inverse multiplicative_identity =>= additive_identity [] by Super 10 with 13 at 2
% 9.16/2.67 Id : 3489, {_}: add (multiply additive_identity ?4198) (inverse multiplicative_identity) =>= additive_identity [4198] by Demod 3488 with 171 at 3
% 9.16/2.67 Id : 3490, {_}: add (inverse multiplicative_identity) (multiply additive_identity ?4198) =>= additive_identity [4198] by Demod 3489 with 2 at 2
% 9.16/2.67 Id : 3491, {_}: add additive_identity (multiply additive_identity ?4198) =>= additive_identity [4198] by Demod 3490 with 171 at 1,2
% 9.16/2.67 Id : 3492, {_}: multiply additive_identity ?4198 =>= additive_identity [4198] by Demod 3491 with 15 at 2
% 9.16/2.67 Id : 3571, {_}: add ?439 additive_identity =<= multiply ?439 (add ?439 ?440) [440, 439] by Demod 204 with 3492 at 2,2
% 9.16/2.67 Id : 3588, {_}: ?439 =<= multiply ?439 (add ?439 ?440) [440, 439] by Demod 3571 with 14 at 2
% 9.16/2.67 Id : 6027, {_}: add ?3199 (multiply ?3198 ?3199) =>= ?3199 [3198, 3199] by Demod 6026 with 3588 at 3
% 9.16/2.67 Id : 6034, {_}: add ?7121 (multiply ?7121 ?7122) =>= ?7121 [7122, 7121] by Super 54 with 6027 at 3
% 9.16/2.67 Id : 6161, {_}: add (multiply ?7316 (multiply ?7317 ?7318)) (multiply ?7316 ?7318) =>= multiply ?7316 (multiply (add ?7317 ?7316) ?7318) [7318, 7317, 7316] by Super 59 with 6034 at 1,3
% 9.16/2.68 Id : 6260, {_}: add (multiply ?7316 ?7318) (multiply ?7316 (multiply ?7317 ?7318)) =>= multiply ?7316 (multiply (add ?7317 ?7316) ?7318) [7317, 7318, 7316] by Demod 6161 with 2 at 2
% 9.16/2.68 Id : 6261, {_}: multiply ?7316 (add ?7318 (multiply ?7317 ?7318)) =?= multiply ?7316 (multiply (add ?7317 ?7316) ?7318) [7317, 7318, 7316] by Demod 6260 with 7 at 2
% 9.16/2.68 Id : 18904, {_}: multiply ?26922 ?26923 =<= multiply ?26922 (multiply (add ?26924 ?26922) ?26923) [26924, 26923, 26922] by Demod 6261 with 6027 at 2,2
% 9.16/2.68 Id : 18923, {_}: multiply (multiply ?27001 ?27002) ?27003 =<= multiply (multiply ?27001 ?27002) (multiply ?27002 ?27003) [27003, 27002, 27001] by Super 18904 with 6027 at 1,2,3
% 9.16/2.68 Id : 133, {_}: multiply (add ?355 ?356) (inverse ?355) =>= add additive_identity (multiply ?356 (inverse ?355)) [356, 355] by Super 6 with 10 at 1,3
% 9.16/2.68 Id : 138, {_}: multiply (inverse ?355) (add ?355 ?356) =>= add additive_identity (multiply ?356 (inverse ?355)) [356, 355] by Demod 133 with 3 at 2
% 9.16/2.68 Id : 4053, {_}: multiply (inverse ?355) (add ?355 ?356) =>= multiply ?356 (inverse ?355) [356, 355] by Demod 138 with 15 at 3
% 9.16/2.68 Id : 322, {_}: add (multiply ?587 ?588) ?589 =<= multiply (add ?587 ?589) (add ?589 ?588) [589, 588, 587] by Super 29 with 2 at 2,3
% 9.16/2.68 Id : 331, {_}: add (multiply ?622 ?623) (inverse ?622) =?= multiply multiplicative_identity (add (inverse ?622) ?623) [623, 622] by Super 322 with 8 at 1,3
% 9.16/2.68 Id : 353, {_}: add (inverse ?622) (multiply ?622 ?623) =?= multiply multiplicative_identity (add (inverse ?622) ?623) [623, 622] by Demod 331 with 2 at 2
% 9.16/2.68 Id : 354, {_}: add (inverse ?622) (multiply ?622 ?623) =>= add (inverse ?622) ?623 [623, 622] by Demod 353 with 13 at 3
% 9.16/2.68 Id : 4256, {_}: multiply (inverse (inverse ?5042)) (add (inverse ?5042) ?5043) =>= multiply (multiply ?5042 ?5043) (inverse (inverse ?5042)) [5043, 5042] by Super 4053 with 354 at 2,2
% 9.16/2.68 Id : 4283, {_}: multiply ?5043 (inverse (inverse ?5042)) =<= multiply (multiply ?5042 ?5043) (inverse (inverse ?5042)) [5042, 5043] by Demod 4256 with 4053 at 2
% 9.16/2.68 Id : 4284, {_}: multiply ?5043 (inverse (inverse ?5042)) =<= multiply (inverse (inverse ?5042)) (multiply ?5042 ?5043) [5042, 5043] by Demod 4283 with 3 at 3
% 9.16/2.68 Id : 4285, {_}: multiply ?5043 ?5042 =<= multiply (inverse (inverse ?5042)) (multiply ?5042 ?5043) [5042, 5043] by Demod 4284 with 3738 at 2,2
% 9.16/2.68 Id : 4286, {_}: multiply ?5043 ?5042 =<= multiply ?5042 (multiply ?5042 ?5043) [5042, 5043] by Demod 4285 with 3738 at 1,3
% 9.16/2.68 Id : 18924, {_}: multiply (multiply ?27005 ?27006) ?27007 =<= multiply (multiply ?27005 ?27006) (multiply ?27005 ?27007) [27007, 27006, 27005] by Super 18904 with 6034 at 1,2,3
% 9.16/2.68 Id : 32879, {_}: multiply (multiply ?53542 ?53543) (multiply ?53542 ?53544) =<= multiply (multiply ?53542 ?53544) (multiply (multiply ?53542 ?53544) ?53543) [53544, 53543, 53542] by Super 4286 with 18924 at 2,3
% 9.16/2.68 Id : 33095, {_}: multiply (multiply ?53542 ?53543) ?53544 =<= multiply (multiply ?53542 ?53544) (multiply (multiply ?53542 ?53544) ?53543) [53544, 53543, 53542] by Demod 32879 with 18924 at 2
% 9.16/2.68 Id : 33096, {_}: multiply (multiply ?53542 ?53543) ?53544 =>= multiply ?53543 (multiply ?53542 ?53544) [53544, 53543, 53542] by Demod 33095 with 4286 at 3
% 9.16/2.68 Id : 33340, {_}: multiply ?27002 (multiply ?27001 ?27003) =<= multiply (multiply ?27001 ?27002) (multiply ?27002 ?27003) [27003, 27001, 27002] by Demod 18923 with 33096 at 2
% 9.16/2.68 Id : 33341, {_}: multiply ?27002 (multiply ?27001 ?27003) =<= multiply ?27002 (multiply ?27001 (multiply ?27002 ?27003)) [27003, 27001, 27002] by Demod 33340 with 33096 at 3
% 9.16/2.68 Id : 224, {_}: add (multiply additive_identity ?467) ?468 =<= multiply ?468 (add ?467 ?468) [468, 467] by Super 4 with 15 at 1,3
% 9.16/2.68 Id : 3570, {_}: add additive_identity ?468 =<= multiply ?468 (add ?467 ?468) [467, 468] by Demod 224 with 3492 at 1,2
% 9.16/2.68 Id : 3589, {_}: ?468 =<= multiply ?468 (add ?467 ?468) [467, 468] by Demod 3570 with 15 at 2
% 9.16/2.68 Id : 6171, {_}: add ?7349 (multiply ?7350 (multiply ?7349 ?7351)) =>= multiply (add ?7349 ?7350) ?7349 [7351, 7350, 7349] by Super 5 with 6034 at 2,3
% 9.16/2.68 Id : 6241, {_}: add ?7349 (multiply ?7350 (multiply ?7349 ?7351)) =>= multiply ?7349 (add ?7349 ?7350) [7351, 7350, 7349] by Demod 6171 with 3 at 3
% 9.16/2.68 Id : 6242, {_}: add ?7349 (multiply ?7350 (multiply ?7349 ?7351)) =>= ?7349 [7351, 7350, 7349] by Demod 6241 with 3588 at 3
% 9.16/2.68 Id : 17682, {_}: multiply ?24311 (multiply ?24312 ?24313) =<= multiply (multiply ?24311 (multiply ?24312 ?24313)) ?24312 [24313, 24312, 24311] by Super 3589 with 6242 at 2,3
% 9.16/2.68 Id : 17854, {_}: multiply ?24311 (multiply ?24312 ?24313) =<= multiply ?24312 (multiply ?24311 (multiply ?24312 ?24313)) [24313, 24312, 24311] by Demod 17682 with 3 at 3
% 9.16/2.68 Id : 33342, {_}: multiply ?27002 (multiply ?27001 ?27003) =?= multiply ?27001 (multiply ?27002 ?27003) [27003, 27001, 27002] by Demod 33341 with 17854 at 3
% 9.16/2.68 Id : 33793, {_}: multiply a (multiply b c) =?= multiply a (multiply b c) [] by Demod 33792 with 3 at 2,3
% 9.16/2.68 Id : 33792, {_}: multiply a (multiply b c) =?= multiply a (multiply c b) [] by Demod 33791 with 33342 at 3
% 9.16/2.68 Id : 33791, {_}: multiply a (multiply b c) =<= multiply c (multiply a b) [] by Demod 1 with 3 at 3
% 9.16/2.68 Id : 1, {_}: multiply a (multiply b c) =<= multiply (multiply a b) c [] by prove_associativity
% 9.16/2.68 % SZS output end CNFRefutation for theBenchmark.p
% 9.16/2.68 2588: solved /export/starexec/sandbox2/benchmark/theBenchmark.p in 2.336914 using kbo
%------------------------------------------------------------------------------