TSTP Solution File: LCL153-1 by Matita---1.0
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% File : Matita---1.0
% Problem : LCL153-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : matitaprover --timeout %d --tptppath /export/starexec/sandbox/benchmark %s
% Computer : n012.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 12:42:43 EDT 2022
% Result : Unsatisfiable 0.19s 0.57s
% Output : CNFRefutation 1.06s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : LCL153-1 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.12 % Command : matitaprover --timeout %d --tptppath /export/starexec/sandbox/benchmark %s
% 0.12/0.33 % Computer : n012.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 : Sun Jul 3 21:15:16 EDT 2022
% 0.19/0.33 % CPUTime :
% 0.19/0.34 13393: Facts:
% 0.19/0.34 13393: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
% 0.19/0.34 13393: Id : 3, {_}:
% 0.19/0.34 implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
% 0.19/0.34 =>=
% 0.19/0.34 truth
% 0.19/0.34 [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
% 0.19/0.34 13393: Id : 4, {_}:
% 0.19/0.34 implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
% 0.19/0.34 [9, 8] by wajsberg_3 ?8 ?9
% 0.19/0.34 13393: Id : 5, {_}:
% 0.19/0.34 implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
% 0.19/0.34 [12, 11] by wajsberg_4 ?11 ?12
% 0.19/0.34 13393: Id : 6, {_}:
% 0.19/0.34 or ?14 ?15 =<= implies (not ?14) ?15
% 0.19/0.34 [15, 14] by or_definition ?14 ?15
% 0.19/0.34 13393: Id : 7, {_}:
% 0.19/0.34 or (or ?17 ?18) ?19 =?= or ?17 (or ?18 ?19)
% 0.19/0.34 [19, 18, 17] by or_associativity ?17 ?18 ?19
% 0.19/0.34 13393: Id : 8, {_}: or ?21 ?22 =?= or ?22 ?21 [22, 21] by or_commutativity ?21 ?22
% 0.19/0.34 13393: Id : 9, {_}:
% 0.19/0.34 and ?24 ?25 =<= not (or (not ?24) (not ?25))
% 0.19/0.34 [25, 24] by and_definition ?24 ?25
% 0.19/0.34 13393: Id : 10, {_}:
% 0.19/0.34 and (and ?27 ?28) ?29 =?= and ?27 (and ?28 ?29)
% 0.19/0.34 [29, 28, 27] by and_associativity ?27 ?28 ?29
% 0.19/0.34 13393: Id : 11, {_}:
% 0.19/0.34 and ?31 ?32 =?= and ?32 ?31
% 0.19/0.34 [32, 31] by and_commutativity ?31 ?32
% 0.19/0.34 13393: Id : 12, {_}:
% 0.19/0.34 xor ?34 ?35 =<= or (and ?34 (not ?35)) (and (not ?34) ?35)
% 0.19/0.34 [35, 34] by xor_definition ?34 ?35
% 0.19/0.34 13393: Id : 13, {_}:
% 0.19/0.34 xor ?37 ?38 =?= xor ?38 ?37
% 0.19/0.34 [38, 37] by xor_commutativity ?37 ?38
% 0.19/0.34 13393: Id : 14, {_}:
% 0.19/0.34 and_star ?40 ?41 =<= not (or (not ?40) (not ?41))
% 0.19/0.34 [41, 40] by and_star_definition ?40 ?41
% 0.19/0.34 13393: Id : 15, {_}:
% 0.19/0.34 and_star (and_star ?43 ?44) ?45 =?= and_star ?43 (and_star ?44 ?45)
% 0.19/0.34 [45, 44, 43] by and_star_associativity ?43 ?44 ?45
% 0.19/0.34 13393: Id : 16, {_}:
% 0.19/0.34 and_star ?47 ?48 =?= and_star ?48 ?47
% 0.19/0.34 [48, 47] by and_star_commutativity ?47 ?48
% 0.19/0.34 13393: Id : 17, {_}: not truth =>= falsehood [] by false_definition
% 0.19/0.34 13393: Goal:
% 0.19/0.34 13393: Id : 1, {_}: not x =<= xor x truth [] by prove_alternative_wajsberg_axiom
% 0.19/0.57 Statistics :
% 0.19/0.57 Max weight : 25
% 0.19/0.57 Found proof, 0.226841s
% 0.19/0.57 % SZS status Unsatisfiable for theBenchmark.p
% 0.19/0.57 % SZS output start CNFRefutation for theBenchmark.p
% 0.19/0.57 Id : 11, {_}: and ?31 ?32 =?= and ?32 ?31 [32, 31] by and_commutativity ?31 ?32
% 0.19/0.57 Id : 17, {_}: not truth =>= falsehood [] by false_definition
% 0.19/0.57 Id : 3, {_}: implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6)) =>= truth [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
% 0.19/0.57 Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
% 0.19/0.57 Id : 20, {_}: implies (implies ?55 ?56) (implies (implies ?56 ?57) (implies ?55 ?57)) =>= truth [57, 56, 55] by wajsberg_2 ?55 ?56 ?57
% 0.19/0.57 Id : 8, {_}: or ?21 ?22 =?= or ?22 ?21 [22, 21] by or_commutativity ?21 ?22
% 0.19/0.57 Id : 6, {_}: or ?14 ?15 =<= implies (not ?14) ?15 [15, 14] by or_definition ?14 ?15
% 0.19/0.57 Id : 5, {_}: implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth [12, 11] by wajsberg_4 ?11 ?12
% 0.19/0.57 Id : 4, {_}: implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8 [9, 8] by wajsberg_3 ?8 ?9
% 0.19/0.57 Id : 9, {_}: and ?24 ?25 =<= not (or (not ?24) (not ?25)) [25, 24] by and_definition ?24 ?25
% 0.19/0.57 Id : 14, {_}: and_star ?40 ?41 =<= not (or (not ?40) (not ?41)) [41, 40] by and_star_definition ?40 ?41
% 0.19/0.57 Id : 12, {_}: xor ?34 ?35 =<= or (and ?34 (not ?35)) (and (not ?34) ?35) [35, 34] by xor_definition ?34 ?35
% 0.19/0.57 Id : 173, {_}: and_star ?40 ?41 =<= and ?40 ?41 [41, 40] by Demod 14 with 9 at 3
% 0.19/0.57 Id : 181, {_}: xor ?34 ?35 =<= or (and_star ?34 (not ?35)) (and (not ?34) ?35) [35, 34] by Demod 12 with 173 at 1,3
% 0.19/0.57 Id : 182, {_}: xor ?34 ?35 =<= or (and_star ?34 (not ?35)) (and_star (not ?34) ?35) [35, 34] by Demod 181 with 173 at 2,3
% 0.19/0.57 Id : 176, {_}: and_star ?24 ?25 =<= not (or (not ?24) (not ?25)) [25, 24] by Demod 9 with 173 at 2
% 0.19/0.57 Id : 70, {_}: implies (or ?11 (not ?12)) (implies ?12 ?11) =>= truth [12, 11] by Demod 5 with 6 at 1,2
% 0.19/0.57 Id : 409, {_}: implies (implies ?1001 truth) (implies ?1002 (implies ?1001 ?1002)) =>= truth [1002, 1001] by Super 20 with 2 at 1,2,2
% 0.19/0.57 Id : 410, {_}: implies (implies truth truth) (implies ?1004 ?1004) =>= truth [1004] by Super 409 with 2 at 2,2,2
% 0.19/0.57 Id : 445, {_}: implies truth (implies ?1004 ?1004) =>= truth [1004] by Demod 410 with 2 at 1,2
% 0.19/0.57 Id : 446, {_}: implies ?1004 ?1004 =>= truth [1004] by Demod 445 with 2 at 2
% 0.19/0.57 Id : 471, {_}: or ?1085 (not ?1085) =>= truth [1085] by Super 6 with 446 at 3
% 0.19/0.57 Id : 525, {_}: or (not ?1140) ?1140 =>= truth [1140] by Super 8 with 471 at 3
% 0.19/0.57 Id : 730, {_}: implies truth (implies ?1343 (not (not ?1343))) =>= truth [1343] by Super 70 with 525 at 1,2
% 0.19/0.57 Id : 746, {_}: implies ?1343 (not (not ?1343)) =>= truth [1343] by Demod 730 with 2 at 2
% 0.19/0.57 Id : 1240, {_}: implies (implies (not (not ?1854)) ?1854) ?1854 =>= implies truth (not (not ?1854)) [1854] by Super 4 with 746 at 1,3
% 0.19/0.57 Id : 1290, {_}: implies (or (not ?1854) ?1854) ?1854 =>= implies truth (not (not ?1854)) [1854] by Demod 1240 with 6 at 1,2
% 0.19/0.57 Id : 1291, {_}: implies (or (not ?1854) ?1854) ?1854 =>= not (not ?1854) [1854] by Demod 1290 with 2 at 3
% 0.19/0.57 Id : 1292, {_}: implies truth ?1854 =>= not (not ?1854) [1854] by Demod 1291 with 525 at 1,2
% 0.19/0.57 Id : 1293, {_}: ?1854 =<= not (not ?1854) [1854] by Demod 1292 with 2 at 2
% 0.19/0.57 Id : 1467, {_}: and_star ?2348 (not ?2349) =<= not (or (not ?2348) ?2349) [2349, 2348] by Super 176 with 1293 at 2,1,3
% 0.19/0.57 Id : 1471, {_}: or (not ?2360) ?2361 =>= implies ?2360 ?2361 [2361, 2360] by Super 6 with 1293 at 1,3
% 0.19/0.57 Id : 2595, {_}: and_star ?2348 (not ?2349) =>= not (implies ?2348 ?2349) [2349, 2348] by Demod 1467 with 1471 at 1,3
% 0.19/0.57 Id : 2597, {_}: xor ?34 ?35 =<= or (not (implies ?34 ?35)) (and_star (not ?34) ?35) [35, 34] by Demod 182 with 2595 at 1,3
% 1.06/0.57 Id : 2600, {_}: xor ?34 ?35 =<= implies (implies ?34 ?35) (and_star (not ?34) ?35) [35, 34] by Demod 2597 with 1471 at 3
% 1.06/0.57 Id : 2759, {_}: implies (implies (implies ?3953 ?3954) ?3955) (implies (implies ?3955 ?3954) (implies (implies ?3954 ?3953) ?3953)) =>= truth [3955, 3954, 3953] by Super 3 with 4 at 2,2,2
% 1.06/0.57 Id : 25, {_}: implies (implies (implies (implies ?75 ?76) ?76) ?75) truth =>= truth [76, 75] by Super 20 with 3 at 2,2
% 1.06/0.57 Id : 2780, {_}: implies (implies (implies truth (implies (implies truth ?4038) ?4038)) ?4039) (implies (implies ?4039 (implies (implies truth ?4038) ?4038)) truth) =>= truth [4039, 4038] by Super 2759 with 25 at 2,2,2
% 1.06/0.57 Id : 2893, {_}: implies (implies (implies (implies truth ?4038) ?4038) ?4039) (implies (implies ?4039 (implies (implies truth ?4038) ?4038)) truth) =>= truth [4039, 4038] by Demod 2780 with 2 at 1,1,2
% 1.06/0.57 Id : 2894, {_}: implies (implies (implies (implies truth ?4038) ?4038) ?4039) (implies (implies ?4039 (implies ?4038 ?4038)) truth) =>= truth [4039, 4038] by Demod 2893 with 2 at 1,2,1,2,2
% 1.06/0.57 Id : 2895, {_}: implies (implies (implies ?4038 ?4038) ?4039) (implies (implies ?4039 (implies ?4038 ?4038)) truth) =>= truth [4039, 4038] by Demod 2894 with 2 at 1,1,1,2
% 1.06/0.57 Id : 2896, {_}: implies (implies (implies ?4038 ?4038) ?4039) (implies (implies ?4039 truth) truth) =>= truth [4039, 4038] by Demod 2895 with 446 at 2,1,2,2
% 1.06/0.57 Id : 2897, {_}: implies (implies truth ?4039) (implies (implies ?4039 truth) truth) =>= truth [4039] by Demod 2896 with 446 at 1,1,2
% 1.06/0.57 Id : 190, {_}: implies (or ?532 falsehood) (implies truth ?532) =>= truth [532] by Super 70 with 17 at 2,1,2
% 1.06/0.57 Id : 344, {_}: implies (or ?896 falsehood) ?896 =>= truth [896] by Demod 190 with 2 at 2,2
% 1.06/0.57 Id : 346, {_}: implies (or falsehood ?901) ?901 =>= truth [901] by Super 344 with 8 at 1,2
% 1.06/0.57 Id : 521, {_}: implies truth (not falsehood) =>= truth [] by Super 346 with 471 at 1,2
% 1.06/0.57 Id : 546, {_}: not falsehood =>= truth [] by Demod 521 with 2 at 2
% 1.06/0.57 Id : 811, {_}: and_star falsehood ?1423 =<= not (or truth (not ?1423)) [1423] by Super 176 with 546 at 1,1,3
% 1.06/0.57 Id : 555, {_}: and_star falsehood ?1170 =<= not (or truth (not ?1170)) [1170] by Super 176 with 546 at 1,1,3
% 1.06/0.57 Id : 815, {_}: and_star falsehood (or truth (not ?1430)) =>= not (or truth (and_star falsehood ?1430)) [1430] by Super 811 with 555 at 2,1,3
% 1.06/0.57 Id : 1593, {_}: or ?2480 (not ?2481) =>= implies ?2481 ?2480 [2481, 2480] by Super 8 with 1471 at 3
% 1.06/0.57 Id : 2120, {_}: and_star falsehood (implies ?1430 truth) =<= not (or truth (and_star falsehood ?1430)) [1430] by Demod 815 with 1593 at 2,2
% 1.06/0.57 Id : 2130, {_}: or truth (and_star falsehood ?3298) =<= not (and_star falsehood (implies ?3298 truth)) [3298] by Super 1293 with 2120 at 1,3
% 1.06/0.57 Id : 1476, {_}: ?2372 =<= not (not ?2372) [2372] by Demod 1292 with 2 at 2
% 1.06/0.57 Id : 1480, {_}: or truth (not ?2379) =>= not (and_star falsehood ?2379) [2379] by Super 1476 with 555 at 1,3
% 1.06/0.57 Id : 1869, {_}: implies ?2379 truth =<= not (and_star falsehood ?2379) [2379] by Demod 1480 with 1593 at 2
% 1.06/0.57 Id : 2140, {_}: or truth (and_star falsehood ?3298) =<= implies (implies ?3298 truth) truth [3298] by Demod 2130 with 1869 at 3
% 1.06/0.57 Id : 2177, {_}: implies (implies truth ?3370) ?3370 =>= or truth (and_star falsehood ?3370) [3370] by Super 4 with 2140 at 3
% 1.06/0.57 Id : 2201, {_}: implies ?3370 ?3370 =?= or truth (and_star falsehood ?3370) [3370] by Demod 2177 with 2 at 1,2
% 1.06/0.57 Id : 2202, {_}: truth =<= or truth (and_star falsehood ?3370) [3370] by Demod 2201 with 446 at 2
% 1.06/0.57 Id : 2254, {_}: truth =<= implies (implies ?3298 truth) truth [3298] by Demod 2140 with 2202 at 2
% 1.06/0.57 Id : 2898, {_}: implies (implies truth ?4039) truth =>= truth [4039] by Demod 2897 with 2254 at 2,2
% 1.06/0.57 Id : 2899, {_}: implies ?4039 truth =>= truth [4039] by Demod 2898 with 2 at 1,2
% 1.06/0.57 Id : 3054, {_}: xor ?4339 truth =<= implies truth (and_star (not ?4339) truth) [4339] by Super 2600 with 2899 at 1,3
% 1.06/0.57 Id : 3063, {_}: xor ?4339 truth =<= and_star (not ?4339) truth [4339] by Demod 3054 with 2 at 3
% 1.06/0.57 Id : 174, {_}: and_star ?31 ?32 =<= and ?32 ?31 [32, 31] by Demod 11 with 173 at 2
% 1.06/0.57 Id : 175, {_}: and_star ?31 ?32 =?= and_star ?32 ?31 [32, 31] by Demod 174 with 173 at 3
% 1.06/0.57 Id : 3064, {_}: xor ?4339 truth =<= and_star truth (not ?4339) [4339] by Demod 3063 with 175 at 3
% 1.06/0.57 Id : 186, {_}: and_star truth ?524 =<= not (or falsehood (not ?524)) [524] by Super 176 with 17 at 1,1,3
% 1.06/0.57 Id : 558, {_}: or falsehood ?1176 =<= implies truth ?1176 [1176] by Super 6 with 546 at 1,3
% 1.06/0.57 Id : 566, {_}: or falsehood ?1176 =>= ?1176 [1176] by Demod 558 with 2 at 3
% 1.06/0.57 Id : 589, {_}: and_star truth ?524 =>= not (not ?524) [524] by Demod 186 with 566 at 1,3
% 1.06/0.57 Id : 1461, {_}: and_star truth ?524 =>= ?524 [524] by Demod 589 with 1293 at 3
% 1.06/0.57 Id : 3065, {_}: xor ?4339 truth =>= not ?4339 [4339] by Demod 3064 with 1461 at 3
% 1.06/0.57 Id : 3179, {_}: not x === not x [] by Demod 1 with 3065 at 3
% 1.06/0.57 Id : 1, {_}: not x =<= xor x truth [] by prove_alternative_wajsberg_axiom
% 1.06/0.57 % SZS output end CNFRefutation for theBenchmark.p
% 1.06/0.57 13393: solved /export/starexec/sandbox/benchmark/theBenchmark.p in 0.231143 using nrkbo
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