TSTP Solution File: NUN134-1 by Matita---1.0
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% File : Matita---1.0
% Problem : NUN134-1 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : matitaprover --timeout %d --tptppath /export/starexec/sandbox2/benchmark %s
% Computer : n023.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 16:34:48 EDT 2022
% Result : Unsatisfiable 0.95s 0.61s
% Output : CNFRefutation 0.95s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUN134-1 : TPTP v8.1.0. Released v8.1.0.
% 0.06/0.12 % Command : matitaprover --timeout %d --tptppath /export/starexec/sandbox2/benchmark %s
% 0.12/0.33 % Computer : n023.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 : Thu Jun 2 04:48:56 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 21569: Facts:
% 0.12/0.34 21569: Id : 2, {_}: + ?2 ?3 =?= + ?3 ?2 [3, 2] by plus_comm ?2 ?3
% 0.12/0.34 21569: Id : 3, {_}:
% 0.12/0.34 + ?5 (+ ?6 ?7) =?= + (+ ?5 ?6) ?7
% 0.12/0.34 [7, 6, 5] by plus_assoc ?5 ?6 ?7
% 0.12/0.34 21569: Id : 4, {_}: times ?9 ?10 =?= times ?10 ?9 [10, 9] by times_comm ?9 ?10
% 0.12/0.34 21569: Id : 5, {_}:
% 0.12/0.34 times ?12 (times ?13 ?14) =?= times (times ?12 ?13) ?14
% 0.12/0.34 [14, 13, 12] by times_assoc ?12 ?13 ?14
% 0.12/0.34 21569: Id : 6, {_}: + ?16 zero =>= ?16 [16] by plus_zero ?16
% 0.12/0.34 21569: Id : 7, {_}: times ?18 zero =>= zero [18] by times_zero ?18
% 0.12/0.34 21569: Id : 8, {_}: times ?20 one =>= ?20 [20] by times_one ?20
% 0.12/0.34 21569: Id : 9, {_}:
% 0.12/0.34 times ?22 (+ ?23 ?24) =<= + (times ?22 ?23) (times ?22 ?24)
% 0.12/0.34 [24, 23, 22] by distr ?22 ?23 ?24
% 0.12/0.34 21569: Id : 10, {_}:
% 0.12/0.34 times (+ ?26 ?27) ?28 =<= + (times ?26 ?28) (times ?27 ?28)
% 0.12/0.34 [28, 27, 26] by distr_001 ?26 ?27 ?28
% 0.12/0.34 21569: Id : 11, {_}: + (s ?30) ?31 =>= s (+ ?30 ?31) [31, 30] by plus_s ?30 ?31
% 0.12/0.34 21569: Id : 12, {_}:
% 0.12/0.34 times (s ?33) ?34 =<= + ?34 (times ?33 ?34)
% 0.12/0.34 [34, 33] by times_s ?33 ?34
% 0.12/0.34 21569: Id : 13, {_}: sum zero =>= zero [] by sum_zero
% 0.12/0.34 21569: Id : 14, {_}: sum (s ?37) =<= + (s ?37) (sum ?37) [37] by sum_s ?37
% 0.12/0.34 21569: Id : 15, {_}: + (sum a) (sum a) =>= times a (s a) [] by induction_hypothesis
% 0.12/0.34 21569: Goal:
% 0.12/0.34 21569: Id : 1, {_}: + (sum (s a)) (sum (s a)) =>= times (s a) (s (s a)) [] by goal
% 0.95/0.61 Statistics :
% 0.95/0.61 Max weight : 16
% 0.95/0.61 Found proof, 0.273921s
% 0.95/0.61 % SZS status Unsatisfiable for theBenchmark.p
% 0.95/0.61 % SZS output start CNFRefutation for theBenchmark.p
% 0.95/0.61 Id : 12, {_}: times (s ?33) ?34 =<= + ?34 (times ?33 ?34) [34, 33] by times_s ?33 ?34
% 0.95/0.61 Id : 15, {_}: + (sum a) (sum a) =>= times a (s a) [] by induction_hypothesis
% 0.95/0.61 Id : 4, {_}: times ?9 ?10 =?= times ?10 ?9 [10, 9] by times_comm ?9 ?10
% 0.95/0.61 Id : 8, {_}: times ?20 one =>= ?20 [20] by times_one ?20
% 0.95/0.61 Id : 199, {_}: times (s ?544) ?545 =<= + ?545 (times ?544 ?545) [545, 544] by times_s ?544 ?545
% 0.95/0.61 Id : 11, {_}: + (s ?30) ?31 =>= s (+ ?30 ?31) [31, 30] by plus_s ?30 ?31
% 0.95/0.61 Id : 2, {_}: + ?2 ?3 =?= + ?3 ?2 [3, 2] by plus_comm ?2 ?3
% 0.95/0.61 Id : 14, {_}: sum (s ?37) =<= + (s ?37) (sum ?37) [37] by sum_s ?37
% 0.95/0.61 Id : 3, {_}: + ?5 (+ ?6 ?7) =?= + (+ ?5 ?6) ?7 [7, 6, 5] by plus_assoc ?5 ?6 ?7
% 0.95/0.61 Id : 222, {_}: sum (s ?37) =<= + (sum ?37) (s ?37) [37] by Demod 14 with 2 at 3
% 0.95/0.61 Id : 223, {_}: + (sum ?586) (+ (s ?586) ?587) =>= + (sum (s ?586)) ?587 [587, 586] by Super 3 with 222 at 1,3
% 0.95/0.61 Id : 230, {_}: + (sum ?586) (s (+ ?586 ?587)) =>= + (sum (s ?586)) ?587 [587, 586] by Demod 223 with 11 at 2,2
% 0.95/0.61 Id : 179, {_}: + ?494 (s ?495) =>= s (+ ?495 ?494) [495, 494] by Super 2 with 11 at 3
% 0.95/0.61 Id : 3418, {_}: s (+ (+ ?586 ?587) (sum ?586)) =>= + (sum (s ?586)) ?587 [587, 586] by Demod 230 with 179 at 2
% 0.95/0.61 Id : 203, {_}: times (s ?556) one =>= + one ?556 [556] by Super 199 with 8 at 2,3
% 0.95/0.61 Id : 218, {_}: times one (s ?556) =>= + one ?556 [556] by Demod 203 with 4 at 2
% 0.95/0.61 Id : 99, {_}: times one ?303 =>= ?303 [303] by Super 4 with 8 at 3
% 0.95/0.61 Id : 339, {_}: s ?556 =<= + one ?556 [556] by Demod 218 with 99 at 2
% 0.95/0.61 Id : 342, {_}: + ?697 one =>= s ?697 [697] by Super 2 with 339 at 3
% 0.95/0.61 Id : 379, {_}: + ?725 (+ one ?726) =>= + (s ?725) ?726 [726, 725] by Super 3 with 342 at 1,3
% 0.95/0.61 Id : 395, {_}: + ?725 (s ?726) =?= + (s ?725) ?726 [726, 725] by Demod 379 with 339 at 2,2
% 0.95/0.61 Id : 396, {_}: + ?725 (s ?726) =>= s (+ ?725 ?726) [726, 725] by Demod 395 with 11 at 3
% 0.95/0.61 Id : 467, {_}: s (+ ?726 ?725) =?= s (+ ?725 ?726) [725, 726] by Demod 396 with 179 at 2
% 0.95/0.61 Id : 3419, {_}: s (+ (sum ?586) (+ ?586 ?587)) =>= + (sum (s ?586)) ?587 [587, 586] by Demod 3418 with 467 at 2
% 0.95/0.61 Id : 3430, {_}: s (+ (sum ?2691) (+ ?2691 ?2692)) =>= + (sum (s ?2691)) ?2692 [2692, 2691] by Demod 3418 with 467 at 2
% 0.95/0.61 Id : 831, {_}: + (sum a) (+ (sum a) ?1220) =>= + (times a (s a)) ?1220 [1220] by Super 3 with 15 at 1,3
% 0.95/0.61 Id : 832, {_}: + (sum a) (+ ?1222 (sum a)) =>= + (times a (s a)) ?1222 [1222] by Super 831 with 2 at 2,2
% 0.95/0.61 Id : 3456, {_}: s (+ (times a (s a)) a) =>= + (sum (s a)) (sum a) [] by Super 3430 with 832 at 1,2
% 0.95/0.61 Id : 3527, {_}: s (+ a (times a (s a))) =>= + (sum (s a)) (sum a) [] by Demod 3456 with 467 at 2
% 0.95/0.61 Id : 3528, {_}: s (+ a (times a (s a))) =>= + (sum a) (sum (s a)) [] by Demod 3527 with 2 at 3
% 0.95/0.61 Id : 198, {_}: times (s ?541) (s ?542) =<= s (+ ?542 (times ?541 (s ?542))) [542, 541] by Super 11 with 12 at 2
% 0.95/0.61 Id : 3529, {_}: times (s a) (s a) =<= + (sum a) (sum (s a)) [] by Demod 3528 with 198 at 2
% 0.95/0.61 Id : 3600, {_}: + (sum a) (+ (sum (s a)) ?2808) =>= + (times (s a) (s a)) ?2808 [2808] by Super 3 with 3529 at 1,3
% 0.95/0.61 Id : 3601, {_}: + (sum a) (+ ?2810 (sum (s a))) =>= + (times (s a) (s a)) ?2810 [2810] by Super 3600 with 2 at 2,2
% 0.95/0.61 Id : 3668, {_}: s (+ (times (s a) (s a)) a) =>= + (sum (s a)) (sum (s a)) [] by Super 3419 with 3601 at 1,2
% 0.95/0.61 Id : 3684, {_}: s (+ a (times (s a) (s a))) =>= + (sum (s a)) (sum (s a)) [] by Demod 3668 with 467 at 2
% 0.95/0.61 Id : 3685, {_}: times (s (s a)) (s a) =<= + (sum (s a)) (sum (s a)) [] by Demod 3684 with 198 at 2
% 0.95/0.61 Id : 3686, {_}: times (s a) (s (s a)) =<= + (sum (s a)) (sum (s a)) [] by Demod 3685 with 4 at 2
% 0.95/0.61 Id : 3738, {_}: times (s a) (s (s a)) === times (s a) (s (s a)) [] by Demod 1 with 3686 at 2
% 0.95/0.61 Id : 1, {_}: + (sum (s a)) (sum (s a)) =>= times (s a) (s (s a)) [] by goal
% 0.95/0.61 % SZS output end CNFRefutation for theBenchmark.p
% 0.95/0.61 21572: solved /export/starexec/sandbox2/benchmark/theBenchmark.p in 0.27629 using nrkbo
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