TSTP Solution File: LCL159-1 by Matita---1.0
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%------------------------------------------------------------------------------
% File : Matita---1.0
% Problem : LCL159-1 : 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 : Sun Jul 17 12:42:45 EDT 2022
% Result : Unsatisfiable 4.95s 1.62s
% Output : CNFRefutation 4.95s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : LCL159-1 : TPTP v8.1.0. Released v1.0.0.
% 0.08/0.13 % Command : matitaprover --timeout %d --tptppath /export/starexec/sandbox2/benchmark %s
% 0.13/0.34 % Computer : n026.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sat Jul 2 10:29:05 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 30871: Facts:
% 0.13/0.34 30871: Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
% 0.13/0.34 30871: Id : 3, {_}:
% 0.13/0.34 implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6))
% 0.13/0.34 =>=
% 0.13/0.34 truth
% 0.13/0.34 [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
% 0.13/0.34 30871: Id : 4, {_}:
% 0.13/0.34 implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8
% 0.13/0.34 [9, 8] by wajsberg_3 ?8 ?9
% 0.13/0.34 30871: Id : 5, {_}:
% 0.13/0.34 implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth
% 0.13/0.34 [12, 11] by wajsberg_4 ?11 ?12
% 0.13/0.34 30871: Id : 6, {_}:
% 0.13/0.34 or ?14 ?15 =<= implies (not ?14) ?15
% 0.13/0.34 [15, 14] by or_definition ?14 ?15
% 0.13/0.34 30871: Id : 7, {_}:
% 0.13/0.34 or (or ?17 ?18) ?19 =?= or ?17 (or ?18 ?19)
% 0.13/0.34 [19, 18, 17] by or_associativity ?17 ?18 ?19
% 0.13/0.34 30871: Id : 8, {_}: or ?21 ?22 =?= or ?22 ?21 [22, 21] by or_commutativity ?21 ?22
% 0.13/0.34 30871: Id : 9, {_}:
% 0.13/0.34 and ?24 ?25 =<= not (or (not ?24) (not ?25))
% 0.13/0.34 [25, 24] by and_definition ?24 ?25
% 0.13/0.34 30871: Id : 10, {_}:
% 0.13/0.34 and (and ?27 ?28) ?29 =?= and ?27 (and ?28 ?29)
% 0.13/0.34 [29, 28, 27] by and_associativity ?27 ?28 ?29
% 0.13/0.34 30871: Id : 11, {_}:
% 0.13/0.34 and ?31 ?32 =?= and ?32 ?31
% 0.13/0.34 [32, 31] by and_commutativity ?31 ?32
% 0.13/0.34 30871: Id : 12, {_}:
% 0.13/0.34 xor ?34 ?35 =<= or (and ?34 (not ?35)) (and (not ?34) ?35)
% 0.13/0.34 [35, 34] by xor_definition ?34 ?35
% 0.13/0.34 30871: Id : 13, {_}:
% 0.13/0.34 xor ?37 ?38 =?= xor ?38 ?37
% 0.13/0.34 [38, 37] by xor_commutativity ?37 ?38
% 0.13/0.34 30871: Id : 14, {_}:
% 0.13/0.34 and_star ?40 ?41 =<= not (or (not ?40) (not ?41))
% 0.13/0.34 [41, 40] by and_star_definition ?40 ?41
% 0.13/0.34 30871: Id : 15, {_}:
% 0.13/0.34 and_star (and_star ?43 ?44) ?45 =?= and_star ?43 (and_star ?44 ?45)
% 0.13/0.34 [45, 44, 43] by and_star_associativity ?43 ?44 ?45
% 0.13/0.34 30871: Id : 16, {_}:
% 0.13/0.34 and_star ?47 ?48 =?= and_star ?48 ?47
% 0.13/0.34 [48, 47] by and_star_commutativity ?47 ?48
% 0.13/0.34 30871: Id : 17, {_}: not truth =>= falsehood [] by false_definition
% 0.13/0.34 30871: Goal:
% 0.13/0.34 30871: Id : 1, {_}:
% 0.13/0.34 xor x (xor truth y) =<= xor (xor x truth) y
% 0.13/0.34 [] by prove_alternative_wajsberg_axiom
% 4.95/1.62 Statistics :
% 4.95/1.62 Max weight : 25
% 4.95/1.62 Found proof, 1.276186s
% 4.95/1.62 % SZS status Unsatisfiable for theBenchmark.p
% 4.95/1.62 % SZS output start CNFRefutation for theBenchmark.p
% 4.95/1.62 Id : 11, {_}: and ?31 ?32 =?= and ?32 ?31 [32, 31] by and_commutativity ?31 ?32
% 4.95/1.62 Id : 13, {_}: xor ?37 ?38 =?= xor ?38 ?37 [38, 37] by xor_commutativity ?37 ?38
% 4.95/1.62 Id : 4, {_}: implies (implies ?8 ?9) ?9 =?= implies (implies ?9 ?8) ?8 [9, 8] by wajsberg_3 ?8 ?9
% 4.95/1.62 Id : 3, {_}: implies (implies ?4 ?5) (implies (implies ?5 ?6) (implies ?4 ?6)) =>= truth [6, 5, 4] by wajsberg_2 ?4 ?5 ?6
% 4.95/1.62 Id : 7, {_}: or (or ?17 ?18) ?19 =>= or ?17 (or ?18 ?19) [19, 18, 17] by or_associativity ?17 ?18 ?19
% 4.95/1.62 Id : 12, {_}: xor ?34 ?35 =<= or (and ?34 (not ?35)) (and (not ?34) ?35) [35, 34] by xor_definition ?34 ?35
% 4.95/1.62 Id : 10, {_}: and (and ?27 ?28) ?29 =>= and ?27 (and ?28 ?29) [29, 28, 27] by and_associativity ?27 ?28 ?29
% 4.95/1.62 Id : 14, {_}: and_star ?40 ?41 =<= not (or (not ?40) (not ?41)) [41, 40] by and_star_definition ?40 ?41
% 4.95/1.62 Id : 9, {_}: and ?24 ?25 =<= not (or (not ?24) (not ?25)) [25, 24] by and_definition ?24 ?25
% 4.95/1.62 Id : 20, {_}: implies (implies ?55 ?56) (implies (implies ?56 ?57) (implies ?55 ?57)) =>= truth [57, 56, 55] by wajsberg_2 ?55 ?56 ?57
% 4.95/1.62 Id : 2, {_}: implies truth ?2 =>= ?2 [2] by wajsberg_1 ?2
% 4.95/1.62 Id : 17, {_}: not truth =>= falsehood [] by false_definition
% 4.95/1.62 Id : 5, {_}: implies (implies (not ?11) (not ?12)) (implies ?12 ?11) =>= truth [12, 11] by wajsberg_4 ?11 ?12
% 4.95/1.62 Id : 6, {_}: or ?14 ?15 =<= implies (not ?14) ?15 [15, 14] by or_definition ?14 ?15
% 4.95/1.62 Id : 8, {_}: or ?21 ?22 =?= or ?22 ?21 [22, 21] by or_commutativity ?21 ?22
% 4.95/1.62 Id : 70, {_}: implies (or ?11 (not ?12)) (implies ?12 ?11) =>= truth [12, 11] by Demod 5 with 6 at 1,2
% 4.95/1.62 Id : 173, {_}: implies (or ?413 falsehood) (implies truth ?413) =>= truth [413] by Super 70 with 17 at 2,1,2
% 4.95/1.62 Id : 400, {_}: implies (or ?837 falsehood) ?837 =>= truth [837] by Demod 173 with 2 at 2,2
% 4.95/1.62 Id : 1130, {_}: implies (or falsehood ?1679) ?1679 =>= truth [1679] by Super 400 with 8 at 1,2
% 4.95/1.62 Id : 429, {_}: implies (implies ?888 truth) (implies ?889 (implies ?888 ?889)) =>= truth [889, 888] by Super 20 with 2 at 1,2,2
% 4.95/1.62 Id : 430, {_}: implies (implies truth truth) (implies ?891 ?891) =>= truth [891] by Super 429 with 2 at 2,2,2
% 4.95/1.62 Id : 465, {_}: implies truth (implies ?891 ?891) =>= truth [891] by Demod 430 with 2 at 1,2
% 4.95/1.62 Id : 466, {_}: implies ?891 ?891 =>= truth [891] by Demod 465 with 2 at 2
% 4.95/1.62 Id : 492, {_}: or ?974 (not ?974) =>= truth [974] by Super 6 with 466 at 3
% 4.95/1.62 Id : 1134, {_}: implies truth (not falsehood) =>= truth [] by Super 1130 with 492 at 1,2
% 4.95/1.62 Id : 1160, {_}: not falsehood =>= truth [] by Demod 1134 with 2 at 2
% 4.95/1.62 Id : 1169, {_}: or falsehood ?1701 =<= implies truth ?1701 [1701] by Super 6 with 1160 at 1,3
% 4.95/1.62 Id : 1184, {_}: or falsehood ?1701 =>= ?1701 [1701] by Demod 1169 with 2 at 3
% 4.95/1.62 Id : 1236, {_}: or ?1723 falsehood =>= ?1723 [1723] by Super 8 with 1184 at 3
% 4.95/1.62 Id : 154, {_}: and_star ?40 ?41 =<= and ?40 ?41 [41, 40] by Demod 14 with 9 at 3
% 4.95/1.62 Id : 157, {_}: and_star ?24 ?25 =<= not (or (not ?24) (not ?25)) [25, 24] by Demod 9 with 154 at 2
% 4.95/1.62 Id : 169, {_}: and_star truth ?405 =<= not (or falsehood (not ?405)) [405] by Super 157 with 17 at 1,1,3
% 4.95/1.62 Id : 294, {_}: and_star truth ?703 =<= not (or falsehood (not ?703)) [703] by Super 157 with 17 at 1,1,3
% 4.95/1.62 Id : 295, {_}: and_star truth truth =<= not (or falsehood falsehood) [] by Super 294 with 17 at 2,1,3
% 4.95/1.62 Id : 313, {_}: and_star truth (or falsehood falsehood) =<= not (or falsehood (and_star truth truth)) [] by Super 169 with 295 at 2,1,3
% 4.95/1.62 Id : 339, {_}: and_star (or falsehood (and_star truth truth)) ?749 =<= not (or (and_star truth (or falsehood falsehood)) (not ?749)) [749] by Super 157 with 313 at 1,1,3
% 4.95/1.62 Id : 10750, {_}: and_star (and_star truth truth) ?749 =<= not (or (and_star truth (or falsehood falsehood)) (not ?749)) [749] by Demod 339 with 1184 at 1,2
% 4.95/1.62 Id : 1205, {_}: and_star truth ?405 =>= not (not ?405) [405] by Demod 169 with 1184 at 1,3
% 4.95/1.62 Id : 10751, {_}: and_star (and_star truth truth) ?749 =<= not (or (not (not (or falsehood falsehood))) (not ?749)) [749] by Demod 10750 with 1205 at 1,1,3
% 4.95/1.62 Id : 158, {_}: and_star (and ?27 ?28) ?29 =<= and ?27 (and ?28 ?29) [29, 28, 27] by Demod 10 with 154 at 2
% 4.95/1.62 Id : 159, {_}: and_star (and ?27 ?28) ?29 =>= and_star ?27 (and ?28 ?29) [29, 28, 27] by Demod 158 with 154 at 3
% 4.95/1.62 Id : 160, {_}: and_star (and_star ?27 ?28) ?29 =>= and_star ?27 (and ?28 ?29) [29, 28, 27] by Demod 159 with 154 at 1,2
% 4.95/1.62 Id : 161, {_}: and_star (and_star ?27 ?28) ?29 =>= and_star ?27 (and_star ?28 ?29) [29, 28, 27] by Demod 160 with 154 at 2,3
% 4.95/1.62 Id : 10752, {_}: and_star truth (and_star truth ?749) =<= not (or (not (not (or falsehood falsehood))) (not ?749)) [749] by Demod 10751 with 161 at 2
% 4.95/1.62 Id : 10753, {_}: and_star truth (and_star truth ?749) =<= and_star (not (or falsehood falsehood)) ?749 [749] by Demod 10752 with 157 at 3
% 4.95/1.62 Id : 10754, {_}: not (not (and_star truth ?749)) =<= and_star (not (or falsehood falsehood)) ?749 [749] by Demod 10753 with 1205 at 2
% 4.95/1.62 Id : 10755, {_}: not (not (and_star truth ?749)) =>= and_star (not falsehood) ?749 [749] by Demod 10754 with 1184 at 1,1,3
% 4.95/1.62 Id : 10756, {_}: not (not (not (not ?749))) =>= and_star (not falsehood) ?749 [749] by Demod 10755 with 1205 at 1,1,2
% 4.95/1.62 Id : 10757, {_}: not (not (not (not ?749))) =>= and_star truth ?749 [749] by Demod 10756 with 1160 at 1,3
% 4.95/1.62 Id : 162, {_}: xor ?34 ?35 =<= or (and_star ?34 (not ?35)) (and (not ?34) ?35) [35, 34] by Demod 12 with 154 at 1,3
% 4.95/1.62 Id : 163, {_}: xor ?34 ?35 =<= or (and_star ?34 (not ?35)) (and_star (not ?34) ?35) [35, 34] by Demod 162 with 154 at 2,3
% 4.95/1.62 Id : 170, {_}: xor truth ?407 =<= or (and_star truth (not ?407)) (and_star falsehood ?407) [407] by Super 163 with 17 at 1,2,3
% 4.95/1.62 Id : 177, {_}: xor truth ?407 =<= or (and_star falsehood ?407) (and_star truth (not ?407)) [407] by Demod 170 with 8 at 3
% 4.95/1.62 Id : 1173, {_}: and_star falsehood ?1709 =<= not (or truth (not ?1709)) [1709] by Super 157 with 1160 at 1,1,3
% 4.95/1.62 Id : 1296, {_}: or (or truth (not ?1777)) ?1778 =>= implies (and_star falsehood ?1777) ?1778 [1778, 1777] by Super 6 with 1173 at 1,3
% 4.95/1.62 Id : 2480, {_}: or truth (or (not ?3327) ?3328) =>= implies (and_star falsehood ?3327) ?3328 [3328, 3327] by Demod 1296 with 7 at 2
% 4.95/1.62 Id : 2493, {_}: or truth (not ?3362) =<= implies (and_star falsehood ?3362) falsehood [3362] by Super 2480 with 1236 at 2,2
% 4.95/1.62 Id : 1319, {_}: or truth (or (not ?1777) ?1778) =>= implies (and_star falsehood ?1777) ?1778 [1778, 1777] by Demod 1296 with 7 at 2
% 4.95/1.62 Id : 2477, {_}: or (or (not ?3318) ?3319) truth =>= implies (and_star falsehood ?3318) ?3319 [3319, 3318] by Super 8 with 1319 at 2
% 4.95/1.62 Id : 2503, {_}: or (not ?3318) (or ?3319 truth) =>= implies (and_star falsehood ?3318) ?3319 [3319, 3318] by Demod 2477 with 7 at 2
% 4.95/1.62 Id : 21, {_}: implies (implies truth ?59) (implies (implies ?59 ?60) ?60) =>= truth [60, 59] by Super 20 with 2 at 2,2,2
% 4.95/1.62 Id : 29, {_}: implies ?59 (implies (implies ?59 ?60) ?60) =>= truth [60, 59] by Demod 21 with 2 at 1,2
% 4.95/1.62 Id : 5293, {_}: implies (implies ?6304 (implies ?6305 ?6306)) (implies (implies (implies ?6306 ?6305) ?6305) (implies ?6304 ?6306)) =>= truth [6306, 6305, 6304] by Super 3 with 4 at 1,2,2
% 4.95/1.62 Id : 22, {_}: implies (implies (implies ?62 ?63) ?64) (implies (implies ?64 (implies (implies ?63 ?65) (implies ?62 ?65))) truth) =>= truth [65, 64, 63, 62] by Super 20 with 3 at 2,2,2
% 4.95/1.62 Id : 5347, {_}: implies (implies (implies ?6517 (implies (implies ?6517 ?6518) (implies truth ?6518))) (implies ?6517 truth)) truth =>= truth [6518, 6517] by Super 5293 with 22 at 2,2
% 4.95/1.62 Id : 5472, {_}: implies (implies (implies ?6517 (implies (implies ?6517 ?6518) ?6518)) (implies ?6517 truth)) truth =>= truth [6518, 6517] by Demod 5347 with 2 at 2,2,1,1,2
% 4.95/1.62 Id : 5473, {_}: implies (implies truth (implies ?6517 truth)) truth =>= truth [6517] by Demod 5472 with 29 at 1,1,2
% 4.95/1.62 Id : 5474, {_}: implies (implies ?6517 truth) truth =>= truth [6517] by Demod 5473 with 2 at 1,2
% 4.95/1.62 Id : 5536, {_}: implies ?6728 truth =>= truth [6728] by Super 29 with 5474 at 2,2
% 4.95/1.62 Id : 5711, {_}: or ?6896 truth =>= truth [6896] by Super 6 with 5536 at 3
% 4.95/1.62 Id : 5983, {_}: or (not ?3318) truth =<= implies (and_star falsehood ?3318) ?3319 [3319, 3318] by Demod 2503 with 5711 at 2,2
% 4.95/1.62 Id : 5984, {_}: truth =<= implies (and_star falsehood ?3318) ?3319 [3319, 3318] by Demod 5983 with 5711 at 2
% 4.95/1.62 Id : 5992, {_}: or truth (not ?3362) =>= truth [3362] by Demod 2493 with 5984 at 3
% 4.95/1.62 Id : 5999, {_}: and_star falsehood ?1709 =>= not truth [1709] by Demod 1173 with 5992 at 1,3
% 4.95/1.62 Id : 6000, {_}: and_star falsehood ?1709 =>= falsehood [1709] by Demod 5999 with 17 at 3
% 4.95/1.62 Id : 7710, {_}: xor truth ?407 =<= or falsehood (and_star truth (not ?407)) [407] by Demod 177 with 6000 at 1,3
% 4.95/1.62 Id : 7711, {_}: xor truth ?407 =<= or falsehood (not (not (not ?407))) [407] by Demod 7710 with 1205 at 2,3
% 4.95/1.62 Id : 7712, {_}: xor truth ?407 =<= not (not (not ?407)) [407] by Demod 7711 with 1184 at 3
% 4.95/1.62 Id : 10758, {_}: xor truth (not ?749) =>= and_star truth ?749 [749] by Demod 10757 with 7712 at 2
% 4.95/1.62 Id : 10759, {_}: xor truth (not ?749) =>= not (not ?749) [749] by Demod 10758 with 1205 at 3
% 4.95/1.62 Id : 7736, {_}: xor truth ?8667 =<= not (not (not ?8667)) [8667] by Demod 7711 with 1184 at 3
% 4.95/1.62 Id : 7741, {_}: xor truth (not ?8676) =>= not (xor truth ?8676) [8676] by Super 7736 with 7712 at 1,3
% 4.95/1.62 Id : 10760, {_}: not (xor truth ?749) =>= not (not ?749) [749] by Demod 10759 with 7741 at 2
% 4.95/1.62 Id : 10799, {_}: or (xor truth ?11366) ?11367 =<= implies (not (not ?11366)) ?11367 [11367, 11366] by Super 6 with 10760 at 1,3
% 4.95/1.62 Id : 10843, {_}: or (xor truth ?11366) ?11367 =>= or (not ?11366) ?11367 [11367, 11366] by Demod 10799 with 6 at 3
% 4.95/1.62 Id : 11219, {_}: or (not ?11677) falsehood =>= xor truth ?11677 [11677] by Super 1236 with 10843 at 2
% 4.95/1.62 Id : 11260, {_}: or falsehood (not ?11677) =>= xor truth ?11677 [11677] by Demod 11219 with 8 at 2
% 4.95/1.62 Id : 11261, {_}: not ?11677 =<= xor truth ?11677 [11677] by Demod 11260 with 1184 at 2
% 4.95/1.62 Id : 11342, {_}: xor ?11764 truth =>= not ?11764 [11764] by Super 13 with 11261 at 3
% 4.95/1.62 Id : 4670, {_}: or truth ?5748 =<= or ?5749 (or (not ?5749) ?5748) [5749, 5748] by Super 7 with 492 at 1,2
% 4.95/1.62 Id : 4687, {_}: or truth (not (not ?5793)) =>= or ?5793 truth [5793] by Super 4670 with 492 at 2,3
% 4.95/1.62 Id : 4776, {_}: and_star falsehood (not ?5840) =>= not (or ?5840 truth) [5840] by Super 1173 with 4687 at 1,3
% 4.95/1.62 Id : 4871, {_}: xor falsehood ?5907 =<= or (not (or ?5907 truth)) (and_star (not falsehood) ?5907) [5907] by Super 163 with 4776 at 1,3
% 4.95/1.62 Id : 4936, {_}: xor falsehood ?5907 =<= or (not (or ?5907 truth)) (and_star truth ?5907) [5907] by Demod 4871 with 1160 at 1,2,3
% 4.95/1.62 Id : 4937, {_}: xor falsehood ?5907 =<= or (and_star truth ?5907) (not (or ?5907 truth)) [5907] by Demod 4936 with 8 at 3
% 4.95/1.62 Id : 4938, {_}: xor falsehood ?5907 =<= or (not (not ?5907)) (not (or ?5907 truth)) [5907] by Demod 4937 with 1205 at 1,3
% 4.95/1.62 Id : 554, {_}: and_star ?1033 (not ?1033) =>= not truth [1033] by Super 157 with 492 at 1,3
% 4.95/1.62 Id : 563, {_}: and_star ?1033 (not ?1033) =>= falsehood [1033] by Demod 554 with 17 at 3
% 4.95/1.62 Id : 704, {_}: and_star falsehood ?1200 =<= and_star ?1201 (and_star (not ?1201) ?1200) [1201, 1200] by Super 161 with 563 at 1,2
% 4.95/1.62 Id : 6170, {_}: falsehood =<= and_star ?7035 (and_star (not ?7035) ?7036) [7036, 7035] by Demod 704 with 6000 at 2
% 4.95/1.62 Id : 6176, {_}: falsehood =<= and_star ?7052 falsehood [7052] by Super 6170 with 563 at 2,3
% 4.95/1.62 Id : 6222, {_}: xor ?7073 falsehood =<= or (and_star ?7073 (not falsehood)) falsehood [7073] by Super 163 with 6176 at 2,3
% 4.95/1.62 Id : 6249, {_}: xor ?7073 falsehood =<= or falsehood (and_star ?7073 (not falsehood)) [7073] by Demod 6222 with 8 at 3
% 4.95/1.62 Id : 6250, {_}: xor ?7073 falsehood =<= and_star ?7073 (not falsehood) [7073] by Demod 6249 with 1184 at 3
% 4.95/1.62 Id : 6251, {_}: xor ?7073 falsehood =<= and_star ?7073 truth [7073] by Demod 6250 with 1160 at 2,3
% 4.95/1.62 Id : 1302, {_}: and_star falsehood ?1794 =<= not (or truth (not ?1794)) [1794] by Super 157 with 1160 at 1,1,3
% 4.95/1.62 Id : 1304, {_}: and_star falsehood falsehood =<= not (or truth truth) [] by Super 1302 with 1160 at 2,1,3
% 4.95/1.62 Id : 1338, {_}: and_star ?1819 (or truth truth) =<= not (or (not ?1819) (and_star falsehood falsehood)) [1819] by Super 157 with 1304 at 2,1,3
% 4.95/1.62 Id : 1235, {_}: implies (not ?1721) (implies ?1721 falsehood) =>= truth [1721] by Super 70 with 1184 at 1,2
% 4.95/1.62 Id : 1248, {_}: or ?1721 (implies ?1721 falsehood) =>= truth [1721] by Demod 1235 with 6 at 2
% 4.95/1.62 Id : 2494, {_}: or truth truth =<= implies (and_star falsehood ?3364) (implies (not ?3364) falsehood) [3364] by Super 2480 with 1248 at 2,2
% 4.95/1.62 Id : 2523, {_}: or truth truth =<= implies (and_star falsehood ?3364) (or ?3364 falsehood) [3364] by Demod 2494 with 6 at 2,3
% 4.95/1.62 Id : 2710, {_}: or truth truth =<= implies (and_star falsehood ?3633) ?3633 [3633] by Demod 2523 with 1236 at 2,3
% 4.95/1.62 Id : 155, {_}: and_star ?31 ?32 =<= and ?32 ?31 [32, 31] by Demod 11 with 154 at 2
% 4.95/1.62 Id : 156, {_}: and_star ?31 ?32 =?= and_star ?32 ?31 [32, 31] by Demod 155 with 154 at 3
% 4.95/1.62 Id : 2713, {_}: or truth truth =<= implies (and_star ?3639 falsehood) ?3639 [3639] by Super 2710 with 156 at 1,3
% 4.95/1.62 Id : 5691, {_}: or truth truth =>= truth [] by Super 2713 with 5536 at 3
% 4.95/1.62 Id : 5846, {_}: and_star ?1819 truth =<= not (or (not ?1819) (and_star falsehood falsehood)) [1819] by Demod 1338 with 5691 at 2,2
% 4.95/1.62 Id : 5850, {_}: and_star falsehood falsehood =>= not truth [] by Demod 1304 with 5691 at 1,3
% 4.95/1.62 Id : 5870, {_}: and_star falsehood falsehood =>= falsehood [] by Demod 5850 with 17 at 3
% 4.95/1.62 Id : 5913, {_}: and_star ?1819 truth =<= not (or (not ?1819) falsehood) [1819] by Demod 5846 with 5870 at 2,1,3
% 4.95/1.62 Id : 5914, {_}: and_star ?1819 truth =<= not (or falsehood (not ?1819)) [1819] by Demod 5913 with 8 at 1,3
% 4.95/1.62 Id : 5915, {_}: and_star ?1819 truth =>= not (not ?1819) [1819] by Demod 5914 with 1184 at 1,3
% 4.95/1.62 Id : 6252, {_}: xor ?7073 falsehood =>= not (not ?7073) [7073] by Demod 6251 with 5915 at 3
% 4.95/1.62 Id : 6265, {_}: xor falsehood ?7105 =>= not (not ?7105) [7105] by Super 13 with 6252 at 3
% 4.95/1.62 Id : 11861, {_}: not (not ?5907) =<= or (not (not ?5907)) (not (or ?5907 truth)) [5907] by Demod 4938 with 6265 at 2
% 4.95/1.62 Id : 7719, {_}: or (not (not ?8613)) ?8614 =<= implies (xor truth ?8613) ?8614 [8614, 8613] by Super 6 with 7712 at 1,3
% 4.95/1.62 Id : 11314, {_}: or (not (not ?8613)) ?8614 =>= implies (not ?8613) ?8614 [8614, 8613] by Demod 7719 with 11261 at 1,3
% 4.95/1.62 Id : 11329, {_}: or (not (not ?8613)) ?8614 =>= or ?8613 ?8614 [8614, 8613] by Demod 11314 with 6 at 3
% 4.95/1.62 Id : 11862, {_}: not (not ?5907) =<= or ?5907 (not (or ?5907 truth)) [5907] by Demod 11861 with 11329 at 3
% 4.95/1.62 Id : 11863, {_}: not (not ?5907) =<= or ?5907 (not truth) [5907] by Demod 11862 with 5711 at 1,2,3
% 4.95/1.62 Id : 11864, {_}: not (not ?5907) =<= or ?5907 falsehood [5907] by Demod 11863 with 17 at 2,3
% 4.95/1.62 Id : 11865, {_}: not (not ?5907) =>= ?5907 [5907] by Demod 11864 with 1236 at 3
% 4.95/1.62 Id : 11887, {_}: and_star ?11942 (not ?11943) =<= not (or (not ?11942) ?11943) [11943, 11942] by Super 157 with 11865 at 2,1,3
% 4.95/1.62 Id : 11891, {_}: or (not ?11954) ?11955 =>= implies ?11954 ?11955 [11955, 11954] by Super 6 with 11865 at 1,3
% 4.95/1.62 Id : 12573, {_}: and_star ?11942 (not ?11943) =>= not (implies ?11942 ?11943) [11943, 11942] by Demod 11887 with 11891 at 1,3
% 4.95/1.62 Id : 12575, {_}: xor ?34 ?35 =<= or (not (implies ?34 ?35)) (and_star (not ?34) ?35) [35, 34] by Demod 163 with 12573 at 1,3
% 4.95/1.62 Id : 12581, {_}: xor ?34 ?35 =<= implies (implies ?34 ?35) (and_star (not ?34) ?35) [35, 34] by Demod 12575 with 11891 at 3
% 4.95/1.62 Id : 12584, {_}: xor ?12457 (not ?12458) =<= implies (implies ?12457 (not ?12458)) (not (implies (not ?12457) ?12458)) [12458, 12457] by Super 12581 with 12573 at 2,3
% 4.95/1.62 Id : 104, {_}: or (or (not ?269) (not ?270)) ?271 =>= implies (and ?269 ?270) ?271 [271, 270, 269] by Super 6 with 9 at 1,3
% 4.95/1.62 Id : 111, {_}: or (not ?269) (or (not ?270) ?271) =>= implies (and ?269 ?270) ?271 [271, 270, 269] by Demod 104 with 7 at 2
% 4.95/1.62 Id : 7011, {_}: or (not ?269) (or (not ?270) ?271) =>= implies (and_star ?269 ?270) ?271 [271, 270, 269] by Demod 111 with 154 at 1,3
% 4.95/1.62 Id : 11918, {_}: implies ?269 (or (not ?270) ?271) =>= implies (and_star ?269 ?270) ?271 [271, 270, 269] by Demod 7011 with 11891 at 2
% 4.95/1.62 Id : 11919, {_}: implies ?269 (implies ?270 ?271) =<= implies (and_star ?269 ?270) ?271 [271, 270, 269] by Demod 11918 with 11891 at 2,2
% 4.95/1.62 Id : 11939, {_}: implies ?11994 falsehood =>= not ?11994 [11994] by Super 1236 with 11891 at 2
% 4.95/1.62 Id : 11999, {_}: implies ?12062 (implies ?12063 falsehood) =>= not (and_star ?12062 ?12063) [12063, 12062] by Super 11919 with 11939 at 3
% 4.95/1.62 Id : 12204, {_}: implies ?12062 (not ?12063) =>= not (and_star ?12062 ?12063) [12063, 12062] by Demod 11999 with 11939 at 2,2
% 4.95/1.62 Id : 12624, {_}: xor ?12457 (not ?12458) =<= not (and_star (implies ?12457 (not ?12458)) (implies (not ?12457) ?12458)) [12458, 12457] by Demod 12584 with 12204 at 3
% 4.95/1.62 Id : 12625, {_}: xor ?12457 (not ?12458) =<= not (and_star (not (and_star ?12457 ?12458)) (implies (not ?12457) ?12458)) [12458, 12457] by Demod 12624 with 12204 at 1,1,3
% 4.95/1.62 Id : 12626, {_}: xor ?12457 (not ?12458) =<= not (and_star (not (and_star ?12457 ?12458)) (or ?12457 ?12458)) [12458, 12457] by Demod 12625 with 6 at 2,1,3
% 4.95/1.62 Id : 12627, {_}: xor ?12457 (not ?12458) =<= not (and_star (or ?12457 ?12458) (not (and_star ?12457 ?12458))) [12458, 12457] by Demod 12626 with 156 at 1,3
% 4.95/1.62 Id : 12628, {_}: xor ?12457 (not ?12458) =<= not (not (implies (or ?12457 ?12458) (and_star ?12457 ?12458))) [12458, 12457] by Demod 12627 with 12573 at 1,3
% 4.95/1.62 Id : 16475, {_}: xor ?16301 (not ?16302) =<= implies (or ?16301 ?16302) (and_star ?16301 ?16302) [16302, 16301] by Demod 12628 with 11865 at 3
% 4.95/1.62 Id : 16486, {_}: xor ?16332 (not ?16333) =<= implies (or ?16333 ?16332) (and_star ?16332 ?16333) [16333, 16332] by Super 16475 with 8 at 1,3
% 4.95/1.62 Id : 16476, {_}: xor ?16304 (not ?16305) =<= implies (or ?16304 ?16305) (and_star ?16305 ?16304) [16305, 16304] by Super 16475 with 156 at 2,3
% 4.95/1.62 Id : 21406, {_}: xor ?16332 (not ?16333) =?= xor ?16333 (not ?16332) [16333, 16332] by Demod 16486 with 16476 at 3
% 4.95/1.62 Id : 21515, {_}: xor x (not y) =?= xor x (not y) [] by Demod 21514 with 21406 at 3
% 4.95/1.62 Id : 21514, {_}: xor x (not y) =<= xor y (not x) [] by Demod 21513 with 11342 at 2,3
% 4.95/1.62 Id : 21513, {_}: xor x (not y) =<= xor y (xor x truth) [] by Demod 21512 with 13 at 3
% 4.95/1.62 Id : 21512, {_}: xor x (not y) =<= xor (xor x truth) y [] by Demod 1 with 11261 at 2,2
% 4.95/1.62 Id : 1, {_}: xor x (xor truth y) =<= xor (xor x truth) y [] by prove_alternative_wajsberg_axiom
% 4.95/1.62 % SZS output end CNFRefutation for theBenchmark.p
% 4.95/1.62 30872: solved /export/starexec/sandbox2/benchmark/theBenchmark.p in 1.281367 using kbo
%------------------------------------------------------------------------------