TSTP Solution File: GRP167-3 by Matita---1.0
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%------------------------------------------------------------------------------
% File : Matita---1.0
% Problem : GRP167-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : matitaprover --timeout %d --tptppath /export/starexec/sandbox/benchmark %s
% Computer : n014.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 : Sat Jul 16 10:29:18 EDT 2022
% Result : Unsatisfiable 267.62s 67.28s
% Output : CNFRefutation 268.02s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GRP167-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.12/0.12 % Command : matitaprover --timeout %d --tptppath /export/starexec/sandbox/benchmark %s
% 0.13/0.33 % Computer : n014.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon Jun 13 13:01:22 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 18371: Facts:
% 0.13/0.34 18371: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
% 0.13/0.34 18371: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
% 0.13/0.34 18371: Id : 4, {_}:
% 0.13/0.34 multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
% 0.13/0.34 [8, 7, 6] by associativity ?6 ?7 ?8
% 0.13/0.34 18371: Id : 5, {_}:
% 0.13/0.34 greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10
% 0.13/0.34 [11, 10] by symmetry_of_glb ?10 ?11
% 0.13/0.34 18371: Id : 6, {_}:
% 0.13/0.34 least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13
% 0.13/0.34 [14, 13] by symmetry_of_lub ?13 ?14
% 0.13/0.34 18371: Id : 7, {_}:
% 0.13/0.34 greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18)
% 0.13/0.34 =?=
% 0.13/0.34 greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18
% 0.13/0.34 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
% 0.13/0.34 18371: Id : 8, {_}:
% 0.13/0.34 least_upper_bound ?20 (least_upper_bound ?21 ?22)
% 0.13/0.34 =?=
% 0.13/0.34 least_upper_bound (least_upper_bound ?20 ?21) ?22
% 0.13/0.34 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
% 0.13/0.34 18371: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
% 0.13/0.34 18371: Id : 10, {_}:
% 0.13/0.34 greatest_lower_bound ?26 ?26 =>= ?26
% 0.13/0.34 [26] by idempotence_of_gld ?26
% 0.13/0.34 18371: Id : 11, {_}:
% 0.13/0.34 least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28
% 0.13/0.34 [29, 28] by lub_absorbtion ?28 ?29
% 0.13/0.34 18371: Id : 12, {_}:
% 0.13/0.34 greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31
% 0.13/0.34 [32, 31] by glb_absorbtion ?31 ?32
% 0.13/0.34 18371: Id : 13, {_}:
% 0.13/0.34 multiply ?34 (least_upper_bound ?35 ?36)
% 0.13/0.34 =<=
% 0.13/0.34 least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36)
% 0.13/0.34 [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
% 0.13/0.34 18371: Id : 14, {_}:
% 0.13/0.34 multiply ?38 (greatest_lower_bound ?39 ?40)
% 0.13/0.34 =<=
% 0.13/0.34 greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40)
% 0.13/0.34 [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
% 0.13/0.34 18371: Id : 15, {_}:
% 0.13/0.34 multiply (least_upper_bound ?42 ?43) ?44
% 0.13/0.34 =<=
% 0.13/0.34 least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44)
% 0.13/0.34 [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
% 0.13/0.34 18371: Id : 16, {_}:
% 0.13/0.34 multiply (greatest_lower_bound ?46 ?47) ?48
% 0.13/0.34 =<=
% 0.13/0.34 greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48)
% 0.13/0.34 [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
% 0.13/0.34 18371: Goal:
% 0.13/0.34 18371: Id : 1, {_}:
% 0.13/0.34 a
% 0.13/0.34 =<=
% 0.13/0.34 multiply (least_upper_bound a identity)
% 0.13/0.34 (greatest_lower_bound a identity)
% 0.13/0.34 [] by prove_p19
% 267.62/67.28 Statistics :
% 267.62/67.28 Max weight : 19
% 267.62/67.28 Found proof, 66.936589s
% 267.62/67.28 % SZS status Unsatisfiable for theBenchmark.p
% 267.62/67.28 % SZS output start CNFRefutation for theBenchmark.p
% 267.62/67.28 Id : 11, {_}: least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 [29, 28] by lub_absorbtion ?28 ?29
% 267.62/67.28 Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
% 267.62/67.28 Id : 8, {_}: least_upper_bound ?20 (least_upper_bound ?21 ?22) =<= least_upper_bound (least_upper_bound ?20 ?21) ?22 [22, 21, 20] by associativity_of_lub ?20 ?21 ?22
% 267.62/67.28 Id : 114, {_}: multiply ?294 (least_upper_bound ?295 ?296) =<= least_upper_bound (multiply ?294 ?295) (multiply ?294 ?296) [296, 295, 294] by monotony_lub1 ?294 ?295 ?296
% 267.62/67.28 Id : 187, {_}: multiply (least_upper_bound ?419 ?420) ?421 =<= least_upper_bound (multiply ?419 ?421) (multiply ?420 ?421) [421, 420, 419] by monotony_lub2 ?419 ?420 ?421
% 267.62/67.28 Id : 13, {_}: multiply ?34 (least_upper_bound ?35 ?36) =<= least_upper_bound (multiply ?34 ?35) (multiply ?34 ?36) [36, 35, 34] by monotony_lub1 ?34 ?35 ?36
% 267.62/67.28 Id : 96, {_}: greatest_lower_bound ?251 (least_upper_bound ?251 ?252) =>= ?251 [252, 251] by glb_absorbtion ?251 ?252
% 267.62/67.28 Id : 6, {_}: least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 [14, 13] by symmetry_of_lub ?13 ?14
% 267.62/67.28 Id : 12, {_}: greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 [32, 31] by glb_absorbtion ?31 ?32
% 267.62/67.28 Id : 149, {_}: multiply ?355 (greatest_lower_bound ?356 ?357) =<= greatest_lower_bound (multiply ?355 ?356) (multiply ?355 ?357) [357, 356, 355] by monotony_glb1 ?355 ?356 ?357
% 267.62/67.28 Id : 10, {_}: greatest_lower_bound ?26 ?26 =>= ?26 [26] by idempotence_of_gld ?26
% 267.62/67.28 Id : 7, {_}: greatest_lower_bound ?16 (greatest_lower_bound ?17 ?18) =<= greatest_lower_bound (greatest_lower_bound ?16 ?17) ?18 [18, 17, 16] by associativity_of_glb ?16 ?17 ?18
% 267.62/67.28 Id : 217, {_}: multiply (greatest_lower_bound ?486 ?487) ?488 =<= greatest_lower_bound (multiply ?486 ?488) (multiply ?487 ?488) [488, 487, 486] by monotony_glb2 ?486 ?487 ?488
% 267.62/67.28 Id : 14, {_}: multiply ?38 (greatest_lower_bound ?39 ?40) =<= greatest_lower_bound (multiply ?38 ?39) (multiply ?38 ?40) [40, 39, 38] by monotony_glb1 ?38 ?39 ?40
% 267.62/67.28 Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
% 267.62/67.28 Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
% 267.62/67.28 Id : 21, {_}: multiply (multiply ?57 ?58) ?59 =>= multiply ?57 (multiply ?58 ?59) [59, 58, 57] by associativity ?57 ?58 ?59
% 267.62/67.28 Id : 5, {_}: greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 [11, 10] by symmetry_of_glb ?10 ?11
% 267.62/67.28 Id : 82, {_}: least_upper_bound ?217 (greatest_lower_bound ?217 ?218) =>= ?217 [218, 217] by lub_absorbtion ?217 ?218
% 267.62/67.28 Id : 4, {_}: multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) [8, 7, 6] by associativity ?6 ?7 ?8
% 267.62/67.28 Id : 83, {_}: least_upper_bound ?220 (greatest_lower_bound ?221 ?220) =>= ?220 [221, 220] by Super 82 with 5 at 2,2
% 267.62/67.28 Id : 23, {_}: multiply identity ?64 =<= multiply (inverse ?65) (multiply ?65 ?64) [65, 64] by Super 21 with 3 at 1,2
% 267.62/67.28 Id : 27, {_}: ?64 =<= multiply (inverse ?65) (multiply ?65 ?64) [65, 64] by Demod 23 with 2 at 2
% 267.62/67.28 Id : 296, {_}: ?625 =<= multiply (inverse ?626) (multiply ?626 ?625) [626, 625] by Demod 23 with 2 at 2
% 267.62/67.28 Id : 426, {_}: multiply ?820 ?821 =<= multiply (inverse (inverse ?820)) ?821 [821, 820] by Super 296 with 27 at 2,3
% 267.62/67.28 Id : 428, {_}: multiply ?825 (inverse ?825) =>= identity [825] by Super 426 with 3 at 3
% 267.62/67.28 Id : 536, {_}: multiply ?1035 (greatest_lower_bound (inverse ?1035) ?1036) =>= greatest_lower_bound identity (multiply ?1035 ?1036) [1036, 1035] by Super 14 with 428 at 1,3
% 267.62/67.28 Id : 2074, {_}: greatest_lower_bound (inverse ?3473) ?3474 =<= multiply (inverse ?3473) (greatest_lower_bound identity (multiply ?3473 ?3474)) [3474, 3473] by Super 27 with 536 at 2,3
% 267.62/67.28 Id : 222, {_}: multiply (greatest_lower_bound (inverse ?504) ?505) ?504 =>= greatest_lower_bound identity (multiply ?505 ?504) [505, 504] by Super 217 with 3 at 1,3
% 268.02/67.31 Id : 45607, {_}: greatest_lower_bound (inverse ?55035) ?55036 =<= multiply (inverse ?55035) (greatest_lower_bound identity (multiply ?55035 ?55036)) [55036, 55035] by Super 27 with 536 at 2,3
% 268.02/67.31 Id : 429, {_}: multiply ?827 (multiply (inverse ?827) ?828) =>= ?828 [828, 827] by Super 426 with 27 at 3
% 268.02/67.31 Id : 45621, {_}: greatest_lower_bound (inverse ?55076) (multiply (inverse ?55076) ?55077) =>= multiply (inverse ?55076) (greatest_lower_bound identity ?55077) [55077, 55076] by Super 45607 with 429 at 2,2,3
% 268.02/67.31 Id : 45906, {_}: multiply (multiply (inverse ?55327) (greatest_lower_bound identity ?55328)) ?55327 =>= greatest_lower_bound identity (multiply (multiply (inverse ?55327) ?55328) ?55327) [55328, 55327] by Super 222 with 45621 at 1,2
% 268.02/67.31 Id : 46017, {_}: multiply (inverse ?55327) (multiply (greatest_lower_bound identity ?55328) ?55327) =>= greatest_lower_bound identity (multiply (multiply (inverse ?55327) ?55328) ?55327) [55328, 55327] by Demod 45906 with 4 at 2
% 268.02/67.31 Id : 46018, {_}: multiply (inverse ?55327) (multiply (greatest_lower_bound identity ?55328) ?55327) =>= greatest_lower_bound identity (multiply (inverse ?55327) (multiply ?55328 ?55327)) [55328, 55327] by Demod 46017 with 4 at 2,3
% 268.02/67.31 Id : 137121, {_}: greatest_lower_bound (inverse (inverse ?139426)) (multiply (greatest_lower_bound identity ?139427) ?139426) =<= multiply (inverse (inverse ?139426)) (greatest_lower_bound identity (greatest_lower_bound identity (multiply (inverse ?139426) (multiply ?139427 ?139426)))) [139427, 139426] by Super 2074 with 46018 at 2,2,3
% 268.02/67.31 Id : 298, {_}: ?630 =<= multiply (inverse (inverse ?630)) identity [630] by Super 296 with 3 at 2,3
% 268.02/67.31 Id : 300, {_}: multiply ?636 ?637 =<= multiply (inverse (inverse ?636)) ?637 [637, 636] by Super 296 with 27 at 2,3
% 268.02/67.31 Id : 412, {_}: ?630 =<= multiply ?630 identity [630] by Demod 298 with 300 at 3
% 268.02/67.31 Id : 413, {_}: inverse (inverse ?774) =<= multiply ?774 identity [774] by Super 412 with 300 at 3
% 268.02/67.31 Id : 452, {_}: inverse (inverse ?774) =>= ?774 [774] by Demod 413 with 412 at 3
% 268.02/67.31 Id : 137317, {_}: greatest_lower_bound ?139426 (multiply (greatest_lower_bound identity ?139427) ?139426) =<= multiply (inverse (inverse ?139426)) (greatest_lower_bound identity (greatest_lower_bound identity (multiply (inverse ?139426) (multiply ?139427 ?139426)))) [139427, 139426] by Demod 137121 with 452 at 1,2
% 268.02/67.31 Id : 137318, {_}: greatest_lower_bound ?139426 (multiply (greatest_lower_bound identity ?139427) ?139426) =<= multiply ?139426 (greatest_lower_bound identity (greatest_lower_bound identity (multiply (inverse ?139426) (multiply ?139427 ?139426)))) [139427, 139426] by Demod 137317 with 452 at 1,3
% 268.02/67.31 Id : 74, {_}: greatest_lower_bound ?193 (greatest_lower_bound ?193 ?194) =>= greatest_lower_bound ?193 ?194 [194, 193] by Super 7 with 10 at 1,3
% 268.02/67.31 Id : 137319, {_}: greatest_lower_bound ?139426 (multiply (greatest_lower_bound identity ?139427) ?139426) =<= multiply ?139426 (greatest_lower_bound identity (multiply (inverse ?139426) (multiply ?139427 ?139426))) [139427, 139426] by Demod 137318 with 74 at 2,3
% 268.02/67.31 Id : 154, {_}: multiply (inverse ?373) (greatest_lower_bound ?373 ?374) =>= greatest_lower_bound identity (multiply (inverse ?373) ?374) [374, 373] by Super 149 with 3 at 1,3
% 268.02/67.31 Id : 1213, {_}: greatest_lower_bound ?2106 ?2107 =<= multiply (inverse (inverse ?2106)) (greatest_lower_bound identity (multiply (inverse ?2106) ?2107)) [2107, 2106] by Super 27 with 154 at 2,3
% 268.02/67.31 Id : 1249, {_}: greatest_lower_bound ?2106 ?2107 =<= multiply ?2106 (greatest_lower_bound identity (multiply (inverse ?2106) ?2107)) [2107, 2106] by Demod 1213 with 452 at 1,3
% 268.02/67.31 Id : 138719, {_}: greatest_lower_bound ?141225 (multiply (greatest_lower_bound identity ?141226) ?141225) =>= greatest_lower_bound ?141225 (multiply ?141226 ?141225) [141226, 141225] by Demod 137319 with 1249 at 3
% 268.02/67.31 Id : 138724, {_}: greatest_lower_bound ?141239 (multiply identity ?141239) =<= greatest_lower_bound ?141239 (multiply (least_upper_bound identity ?141240) ?141239) [141240, 141239] by Super 138719 with 12 at 1,2,2
% 268.02/67.31 Id : 139245, {_}: greatest_lower_bound ?141239 ?141239 =<= greatest_lower_bound ?141239 (multiply (least_upper_bound identity ?141240) ?141239) [141240, 141239] by Demod 138724 with 2 at 2,2
% 268.02/67.31 Id : 139246, {_}: ?141239 =<= greatest_lower_bound ?141239 (multiply (least_upper_bound identity ?141240) ?141239) [141240, 141239] by Demod 139245 with 10 at 2
% 268.02/67.31 Id : 143996, {_}: least_upper_bound (multiply (least_upper_bound identity ?145700) ?145701) ?145701 =>= multiply (least_upper_bound identity ?145700) ?145701 [145701, 145700] by Super 83 with 139246 at 2,2
% 268.02/67.31 Id : 150074, {_}: least_upper_bound ?150090 (multiply (least_upper_bound identity ?150091) ?150090) =>= multiply (least_upper_bound identity ?150091) ?150090 [150091, 150090] by Demod 143996 with 6 at 2
% 268.02/67.31 Id : 150077, {_}: least_upper_bound ?150099 (multiply (least_upper_bound ?150100 identity) ?150099) =>= multiply (least_upper_bound identity ?150100) ?150099 [150100, 150099] by Super 150074 with 6 at 1,2,2
% 268.02/67.31 Id : 97, {_}: greatest_lower_bound ?254 (least_upper_bound ?255 ?254) =>= ?254 [255, 254] by Super 96 with 6 at 2,2
% 268.02/67.31 Id : 138730, {_}: greatest_lower_bound ?141261 (multiply identity ?141261) =<= greatest_lower_bound ?141261 (multiply (least_upper_bound ?141262 identity) ?141261) [141262, 141261] by Super 138719 with 97 at 1,2,2
% 268.02/67.31 Id : 139251, {_}: greatest_lower_bound ?141261 ?141261 =<= greatest_lower_bound ?141261 (multiply (least_upper_bound ?141262 identity) ?141261) [141262, 141261] by Demod 138730 with 2 at 2,2
% 268.02/67.31 Id : 139252, {_}: ?141261 =<= greatest_lower_bound ?141261 (multiply (least_upper_bound ?141262 identity) ?141261) [141262, 141261] by Demod 139251 with 10 at 2
% 268.02/67.31 Id : 144994, {_}: least_upper_bound (multiply (least_upper_bound ?146503 identity) ?146504) ?146504 =>= multiply (least_upper_bound ?146503 identity) ?146504 [146504, 146503] by Super 83 with 139252 at 2,2
% 268.02/67.31 Id : 145376, {_}: least_upper_bound ?146504 (multiply (least_upper_bound ?146503 identity) ?146504) =>= multiply (least_upper_bound ?146503 identity) ?146504 [146503, 146504] by Demod 144994 with 6 at 2
% 268.02/67.31 Id : 155117, {_}: multiply (least_upper_bound ?150100 identity) ?150099 =?= multiply (least_upper_bound identity ?150100) ?150099 [150099, 150100] by Demod 150077 with 145376 at 2
% 268.02/67.31 Id : 541, {_}: multiply ?1048 (least_upper_bound (inverse ?1048) ?1049) =>= least_upper_bound identity (multiply ?1048 ?1049) [1049, 1048] by Super 13 with 428 at 1,3
% 268.02/67.31 Id : 70737, {_}: least_upper_bound (inverse ?77742) ?77743 =<= multiply (inverse ?77742) (least_upper_bound identity (multiply ?77742 ?77743)) [77743, 77742] by Super 27 with 541 at 2,3
% 268.02/67.31 Id : 70751, {_}: least_upper_bound (inverse ?77783) (multiply (inverse ?77783) ?77784) =>= multiply (inverse ?77783) (least_upper_bound identity ?77784) [77784, 77783] by Super 70737 with 429 at 2,2,3
% 268.02/67.31 Id : 192, {_}: multiply (least_upper_bound (inverse ?437) ?438) ?437 =>= least_upper_bound identity (multiply ?438 ?437) [438, 437] by Super 187 with 3 at 1,3
% 268.02/67.31 Id : 71112, {_}: multiply (multiply (inverse ?78097) (least_upper_bound identity ?78098)) ?78097 =>= least_upper_bound identity (multiply (multiply (inverse ?78097) ?78098) ?78097) [78098, 78097] by Super 192 with 70751 at 1,2
% 268.02/67.31 Id : 71242, {_}: multiply (inverse ?78097) (multiply (least_upper_bound identity ?78098) ?78097) =>= least_upper_bound identity (multiply (multiply (inverse ?78097) ?78098) ?78097) [78098, 78097] by Demod 71112 with 4 at 2
% 268.02/67.31 Id : 172416, {_}: multiply (inverse ?166842) (multiply (least_upper_bound identity ?166843) ?166842) =>= least_upper_bound identity (multiply (inverse ?166842) (multiply ?166843 ?166842)) [166843, 166842] by Demod 71242 with 4 at 2,3
% 268.02/67.31 Id : 172551, {_}: multiply ?167279 (multiply (least_upper_bound identity ?167280) (inverse ?167279)) =<= least_upper_bound identity (multiply (inverse (inverse ?167279)) (multiply ?167280 (inverse ?167279))) [167280, 167279] by Super 172416 with 452 at 1,2
% 268.02/67.31 Id : 173075, {_}: multiply ?167279 (multiply (least_upper_bound identity ?167280) (inverse ?167279)) =>= least_upper_bound identity (multiply ?167279 (multiply ?167280 (inverse ?167279))) [167280, 167279] by Demod 172551 with 452 at 1,2,3
% 268.02/67.31 Id : 219507, {_}: multiply (least_upper_bound identity ?207418) (inverse ?207419) =<= multiply (inverse ?207419) (least_upper_bound identity (multiply ?207419 (multiply ?207418 (inverse ?207419)))) [207419, 207418] by Super 27 with 173075 at 2,3
% 268.02/67.31 Id : 2294, {_}: least_upper_bound (inverse ?3967) ?3968 =<= multiply (inverse ?3967) (least_upper_bound identity (multiply ?3967 ?3968)) [3968, 3967] by Super 27 with 541 at 2,3
% 268.02/67.31 Id : 219842, {_}: multiply (least_upper_bound identity ?207418) (inverse ?207419) =<= least_upper_bound (inverse ?207419) (multiply ?207418 (inverse ?207419)) [207419, 207418] by Demod 219507 with 2294 at 3
% 268.02/67.31 Id : 220861, {_}: multiply (least_upper_bound identity (inverse ?209066)) (inverse ?209066) =>= multiply (inverse ?209066) (least_upper_bound identity (inverse ?209066)) [209066] by Super 70751 with 219842 at 2
% 268.02/67.31 Id : 220863, {_}: multiply (least_upper_bound identity (inverse (inverse ?209069))) ?209069 =<= multiply (inverse (inverse ?209069)) (least_upper_bound identity (inverse (inverse ?209069))) [209069] by Super 220861 with 452 at 2,2
% 268.02/67.31 Id : 221092, {_}: multiply (least_upper_bound identity ?209069) ?209069 =<= multiply (inverse (inverse ?209069)) (least_upper_bound identity (inverse (inverse ?209069))) [209069] by Demod 220863 with 452 at 2,1,2
% 268.02/67.31 Id : 221093, {_}: multiply (least_upper_bound identity ?209069) ?209069 =<= multiply ?209069 (least_upper_bound identity (inverse (inverse ?209069))) [209069] by Demod 221092 with 452 at 1,3
% 268.02/67.31 Id : 221094, {_}: multiply (least_upper_bound identity ?209069) ?209069 =>= multiply ?209069 (least_upper_bound identity ?209069) [209069] by Demod 221093 with 452 at 2,2,3
% 268.02/67.31 Id : 221522, {_}: multiply (least_upper_bound ?209492 identity) ?209492 =>= multiply ?209492 (least_upper_bound identity ?209492) [209492] by Super 155117 with 221094 at 3
% 268.02/67.31 Id : 223682, {_}: multiply (multiply ?210883 (least_upper_bound identity ?210883)) ?210884 =>= multiply (least_upper_bound ?210883 identity) (multiply ?210883 ?210884) [210884, 210883] by Super 4 with 221522 at 1,2
% 268.02/67.31 Id : 223801, {_}: multiply ?210883 (multiply (least_upper_bound identity ?210883) ?210884) =<= multiply (least_upper_bound ?210883 identity) (multiply ?210883 ?210884) [210884, 210883] by Demod 223682 with 4 at 2
% 268.02/67.31 Id : 538, {_}: identity =<= multiply ?1041 (multiply ?1042 (inverse (multiply ?1041 ?1042))) [1042, 1041] by Super 4 with 428 at 2
% 268.02/67.31 Id : 315054, {_}: multiply ?281807 (inverse (multiply ?281808 ?281807)) =>= multiply (inverse ?281808) identity [281808, 281807] by Super 27 with 538 at 2,3
% 268.02/67.31 Id : 315910, {_}: multiply ?283103 (inverse (multiply ?283104 ?283103)) =>= inverse ?283104 [283104, 283103] by Demod 315054 with 412 at 3
% 268.02/67.31 Id : 190, {_}: multiply (least_upper_bound ?429 (multiply ?430 ?431)) ?432 =<= least_upper_bound (multiply ?429 ?432) (multiply ?430 (multiply ?431 ?432)) [432, 431, 430, 429] by Super 187 with 4 at 2,3
% 268.02/67.31 Id : 191, {_}: multiply (least_upper_bound identity ?434) ?435 =?= least_upper_bound ?435 (multiply ?434 ?435) [435, 434] by Super 187 with 2 at 1,3
% 268.02/67.31 Id : 269138, {_}: multiply (least_upper_bound ?244913 (multiply ?244914 ?244913)) ?244915 =>= multiply (least_upper_bound identity ?244914) (multiply ?244913 ?244915) [244915, 244914, 244913] by Super 190 with 191 at 3
% 268.02/67.31 Id : 269140, {_}: multiply (least_upper_bound ?244920 identity) ?244921 =<= multiply (least_upper_bound identity (inverse ?244920)) (multiply ?244920 ?244921) [244921, 244920] by Super 269138 with 3 at 2,1,2
% 268.02/67.31 Id : 316069, {_}: multiply (multiply ?283566 ?283567) (inverse (multiply (least_upper_bound ?283566 identity) ?283567)) =>= inverse (least_upper_bound identity (inverse ?283566)) [283567, 283566] by Super 315910 with 269140 at 1,2,2
% 268.02/67.31 Id : 316395, {_}: multiply ?283566 (multiply ?283567 (inverse (multiply (least_upper_bound ?283566 identity) ?283567))) =>= inverse (least_upper_bound identity (inverse ?283566)) [283567, 283566] by Demod 316069 with 4 at 2
% 268.02/67.31 Id : 315458, {_}: multiply ?281807 (inverse (multiply ?281808 ?281807)) =>= inverse ?281808 [281808, 281807] by Demod 315054 with 412 at 3
% 268.02/67.31 Id : 316396, {_}: multiply ?283566 (inverse (least_upper_bound ?283566 identity)) =>= inverse (least_upper_bound identity (inverse ?283566)) [283566] by Demod 316395 with 315458 at 2,2
% 268.02/67.31 Id : 319626, {_}: multiply ?286698 (multiply (least_upper_bound identity ?286698) (inverse (least_upper_bound ?286698 identity))) =>= multiply (least_upper_bound ?286698 identity) (inverse (least_upper_bound identity (inverse ?286698))) [286698] by Super 223801 with 316396 at 2,3
% 268.02/67.31 Id : 116, {_}: multiply (inverse ?301) (least_upper_bound ?302 ?301) =>= least_upper_bound (multiply (inverse ?301) ?302) identity [302, 301] by Super 114 with 3 at 2,3
% 268.02/67.31 Id : 1155, {_}: multiply (inverse ?2053) (least_upper_bound ?2054 ?2053) =>= least_upper_bound identity (multiply (inverse ?2053) ?2054) [2054, 2053] by Demod 116 with 6 at 3
% 268.02/67.31 Id : 69, {_}: least_upper_bound ?180 (least_upper_bound ?180 ?181) =>= least_upper_bound ?180 ?181 [181, 180] by Super 8 with 9 at 1,3
% 268.02/67.31 Id : 1159, {_}: multiply (inverse (least_upper_bound ?2064 ?2065)) (least_upper_bound ?2064 ?2065) =>= least_upper_bound identity (multiply (inverse (least_upper_bound ?2064 ?2065)) ?2064) [2065, 2064] by Super 1155 with 69 at 2,2
% 268.02/67.31 Id : 19629, {_}: identity =<= least_upper_bound identity (multiply (inverse (least_upper_bound ?26210 ?26211)) ?26210) [26211, 26210] by Demod 1159 with 3 at 2
% 268.02/67.31 Id : 19687, {_}: identity =<= least_upper_bound identity (inverse (least_upper_bound identity ?26374)) [26374] by Super 19629 with 412 at 2,3
% 268.02/67.31 Id : 19825, {_}: greatest_lower_bound (inverse (least_upper_bound identity ?26427)) identity =>= inverse (least_upper_bound identity ?26427) [26427] by Super 97 with 19687 at 2,2
% 268.02/67.31 Id : 20187, {_}: greatest_lower_bound identity (inverse (least_upper_bound identity ?26836)) =>= inverse (least_upper_bound identity ?26836) [26836] by Demod 19825 with 5 at 2
% 268.02/67.31 Id : 20190, {_}: greatest_lower_bound identity (inverse (least_upper_bound ?26842 identity)) =>= inverse (least_upper_bound identity ?26842) [26842] by Super 20187 with 6 at 1,2,2
% 268.02/67.31 Id : 19841, {_}: identity =<= least_upper_bound identity (inverse (least_upper_bound identity ?26461)) [26461] by Super 19629 with 412 at 2,3
% 268.02/67.31 Id : 19844, {_}: identity =<= least_upper_bound identity (inverse (least_upper_bound ?26467 identity)) [26467] by Super 19841 with 6 at 1,2,3
% 268.02/67.31 Id : 20002, {_}: greatest_lower_bound (inverse (least_upper_bound ?26589 identity)) identity =>= inverse (least_upper_bound ?26589 identity) [26589] by Super 97 with 19844 at 2,2
% 268.02/67.31 Id : 20069, {_}: greatest_lower_bound identity (inverse (least_upper_bound ?26589 identity)) =>= inverse (least_upper_bound ?26589 identity) [26589] by Demod 20002 with 5 at 2
% 268.02/67.31 Id : 20819, {_}: inverse (least_upper_bound ?26842 identity) =?= inverse (least_upper_bound identity ?26842) [26842] by Demod 20190 with 20069 at 2
% 268.02/67.31 Id : 20843, {_}: multiply (least_upper_bound identity ?27214) (inverse (least_upper_bound ?27214 identity)) =>= identity [27214] by Super 428 with 20819 at 2,2
% 268.02/67.31 Id : 319751, {_}: multiply ?286698 identity =<= multiply (least_upper_bound ?286698 identity) (inverse (least_upper_bound identity (inverse ?286698))) [286698] by Demod 319626 with 20843 at 2,2
% 268.02/67.31 Id : 319752, {_}: ?286698 =<= multiply (least_upper_bound ?286698 identity) (inverse (least_upper_bound identity (inverse ?286698))) [286698] by Demod 319751 with 412 at 2
% 268.02/67.31 Id : 315860, {_}: multiply ?282943 (inverse ?282944) =<= inverse (multiply ?282944 (inverse ?282943)) [282944, 282943] by Super 429 with 315458 at 2,2
% 268.02/67.31 Id : 315921, {_}: multiply ?283137 (inverse (least_upper_bound identity (multiply ?283138 ?283137))) =>= inverse (least_upper_bound (inverse ?283137) ?283138) [283138, 283137] by Super 315910 with 192 at 1,2,2
% 268.02/67.31 Id : 335216, {_}: multiply (least_upper_bound identity (multiply ?298654 ?298655)) (inverse ?298655) =>= inverse (inverse (least_upper_bound (inverse ?298655) ?298654)) [298655, 298654] by Super 315860 with 315921 at 1,3
% 268.02/67.31 Id : 467322, {_}: multiply (least_upper_bound identity (multiply ?382837 ?382838)) (inverse ?382838) =>= least_upper_bound (inverse ?382838) ?382837 [382838, 382837] by Demod 335216 with 452 at 3
% 268.02/67.31 Id : 119, {_}: multiply (inverse ?312) (least_upper_bound ?312 ?313) =>= least_upper_bound identity (multiply (inverse ?312) ?313) [313, 312] by Super 114 with 3 at 1,3
% 268.02/67.31 Id : 927, {_}: least_upper_bound ?1750 ?1751 =<= multiply (inverse (inverse ?1750)) (least_upper_bound identity (multiply (inverse ?1750) ?1751)) [1751, 1750] by Super 27 with 119 at 2,3
% 268.02/67.31 Id : 956, {_}: least_upper_bound ?1750 ?1751 =<= multiply ?1750 (least_upper_bound identity (multiply (inverse ?1750) ?1751)) [1751, 1750] by Demod 927 with 452 at 1,3
% 268.02/67.31 Id : 137124, {_}: least_upper_bound (inverse (inverse ?139439)) (multiply (greatest_lower_bound identity ?139440) ?139439) =<= multiply (inverse (inverse ?139439)) (least_upper_bound identity (greatest_lower_bound identity (multiply (inverse ?139439) (multiply ?139440 ?139439)))) [139440, 139439] by Super 2294 with 46018 at 2,2,3
% 268.02/67.31 Id : 137308, {_}: least_upper_bound ?139439 (multiply (greatest_lower_bound identity ?139440) ?139439) =<= multiply (inverse (inverse ?139439)) (least_upper_bound identity (greatest_lower_bound identity (multiply (inverse ?139439) (multiply ?139440 ?139439)))) [139440, 139439] by Demod 137124 with 452 at 1,2
% 268.02/67.31 Id : 137309, {_}: least_upper_bound ?139439 (multiply (greatest_lower_bound identity ?139440) ?139439) =<= multiply ?139439 (least_upper_bound identity (greatest_lower_bound identity (multiply (inverse ?139439) (multiply ?139440 ?139439)))) [139440, 139439] by Demod 137308 with 452 at 1,3
% 268.02/67.31 Id : 137310, {_}: least_upper_bound ?139439 (multiply (greatest_lower_bound identity ?139440) ?139439) =>= multiply ?139439 identity [139440, 139439] by Demod 137309 with 11 at 2,3
% 268.02/67.31 Id : 137311, {_}: least_upper_bound ?139439 (multiply (greatest_lower_bound identity ?139440) ?139439) =>= ?139439 [139440, 139439] by Demod 137310 with 412 at 3
% 268.02/67.31 Id : 137753, {_}: greatest_lower_bound (multiply (greatest_lower_bound identity ?140201) ?140202) ?140202 =>= multiply (greatest_lower_bound identity ?140201) ?140202 [140202, 140201] by Super 97 with 137311 at 2,2
% 268.02/67.31 Id : 138138, {_}: greatest_lower_bound ?140202 (multiply (greatest_lower_bound identity ?140201) ?140202) =>= multiply (greatest_lower_bound identity ?140201) ?140202 [140201, 140202] by Demod 137753 with 5 at 2
% 268.02/67.31 Id : 137320, {_}: greatest_lower_bound ?139426 (multiply (greatest_lower_bound identity ?139427) ?139426) =>= greatest_lower_bound ?139426 (multiply ?139427 ?139426) [139427, 139426] by Demod 137319 with 1249 at 3
% 268.02/67.31 Id : 140315, {_}: greatest_lower_bound ?140202 (multiply ?140201 ?140202) =?= multiply (greatest_lower_bound identity ?140201) ?140202 [140201, 140202] by Demod 138138 with 137320 at 2
% 268.02/67.31 Id : 200130, {_}: multiply (greatest_lower_bound ?189297 (multiply ?189298 ?189297)) ?189299 =>= multiply (greatest_lower_bound identity ?189298) (multiply ?189297 ?189299) [189299, 189298, 189297] by Super 4 with 140315 at 1,2
% 268.02/67.31 Id : 200132, {_}: multiply (greatest_lower_bound ?189304 identity) ?189305 =<= multiply (greatest_lower_bound identity (inverse ?189304)) (multiply ?189304 ?189305) [189305, 189304] by Super 200130 with 3 at 2,1,2
% 268.02/67.31 Id : 316054, {_}: multiply (multiply ?283521 ?283522) (inverse (multiply (greatest_lower_bound ?283521 identity) ?283522)) =>= inverse (greatest_lower_bound identity (inverse ?283521)) [283522, 283521] by Super 315910 with 200132 at 1,2,2
% 268.02/67.31 Id : 316366, {_}: multiply ?283521 (multiply ?283522 (inverse (multiply (greatest_lower_bound ?283521 identity) ?283522))) =>= inverse (greatest_lower_bound identity (inverse ?283521)) [283522, 283521] by Demod 316054 with 4 at 2
% 268.02/67.31 Id : 316367, {_}: multiply ?283521 (inverse (greatest_lower_bound ?283521 identity)) =>= inverse (greatest_lower_bound identity (inverse ?283521)) [283521] by Demod 316366 with 315458 at 2,2
% 268.02/67.31 Id : 318536, {_}: multiply (inverse (greatest_lower_bound ?286318 identity)) (inverse (inverse (greatest_lower_bound identity (inverse ?286318)))) =>= inverse ?286318 [286318] by Super 315458 with 316367 at 1,2,2
% 268.02/67.31 Id : 315848, {_}: inverse (multiply ?282898 ?282899) =<= multiply (inverse ?282899) (inverse ?282898) [282899, 282898] by Super 27 with 315458 at 2,3
% 268.02/67.31 Id : 318599, {_}: inverse (multiply (inverse (greatest_lower_bound identity (inverse ?286318))) (greatest_lower_bound ?286318 identity)) =>= inverse ?286318 [286318] by Demod 318536 with 315848 at 2
% 268.02/67.31 Id : 316544, {_}: inverse (multiply ?284052 ?284053) =<= multiply (inverse ?284053) (inverse ?284052) [284053, 284052] by Super 27 with 315458 at 2,3
% 268.02/67.31 Id : 316546, {_}: inverse (multiply (inverse ?284057) ?284058) =>= multiply (inverse ?284058) ?284057 [284058, 284057] by Super 316544 with 452 at 2,3
% 268.02/67.31 Id : 318600, {_}: multiply (inverse (greatest_lower_bound ?286318 identity)) (greatest_lower_bound identity (inverse ?286318)) =>= inverse ?286318 [286318] by Demod 318599 with 316546 at 2
% 268.02/67.31 Id : 382108, {_}: least_upper_bound (greatest_lower_bound ?327972 identity) (greatest_lower_bound identity (inverse ?327972)) =<= multiply (greatest_lower_bound ?327972 identity) (least_upper_bound identity (inverse ?327972)) [327972] by Super 956 with 318600 at 2,2,3
% 268.02/67.31 Id : 467587, {_}: multiply (least_upper_bound identity (least_upper_bound (greatest_lower_bound ?383632 identity) (greatest_lower_bound identity (inverse ?383632)))) (inverse (least_upper_bound identity (inverse ?383632))) =>= least_upper_bound (inverse (least_upper_bound identity (inverse ?383632))) (greatest_lower_bound ?383632 identity) [383632] by Super 467322 with 382108 at 2,1,2
% 268.02/67.31 Id : 617, {_}: least_upper_bound ?1152 (least_upper_bound (greatest_lower_bound ?1153 ?1152) ?1154) =>= least_upper_bound ?1152 ?1154 [1154, 1153, 1152] by Super 8 with 83 at 1,3
% 268.02/67.31 Id : 468616, {_}: multiply (least_upper_bound identity (greatest_lower_bound identity (inverse ?383632))) (inverse (least_upper_bound identity (inverse ?383632))) =>= least_upper_bound (inverse (least_upper_bound identity (inverse ?383632))) (greatest_lower_bound ?383632 identity) [383632] by Demod 467587 with 617 at 1,2
% 268.02/67.31 Id : 468617, {_}: multiply (least_upper_bound identity (greatest_lower_bound identity (inverse ?383632))) (inverse (least_upper_bound identity (inverse ?383632))) =>= least_upper_bound (greatest_lower_bound ?383632 identity) (inverse (least_upper_bound identity (inverse ?383632))) [383632] by Demod 468616 with 6 at 3
% 268.02/67.31 Id : 468618, {_}: multiply identity (inverse (least_upper_bound identity (inverse ?383632))) =<= least_upper_bound (greatest_lower_bound ?383632 identity) (inverse (least_upper_bound identity (inverse ?383632))) [383632] by Demod 468617 with 11 at 1,2
% 268.02/67.31 Id : 468619, {_}: inverse (least_upper_bound identity (inverse ?383632)) =<= least_upper_bound (greatest_lower_bound ?383632 identity) (inverse (least_upper_bound identity (inverse ?383632))) [383632] by Demod 468618 with 2 at 2
% 268.02/67.31 Id : 554562, {_}: greatest_lower_bound (greatest_lower_bound ?440612 identity) (inverse (least_upper_bound identity (inverse ?440612))) =>= greatest_lower_bound ?440612 identity [440612] by Super 12 with 468619 at 2,2
% 268.02/67.31 Id : 554829, {_}: greatest_lower_bound ?440612 (greatest_lower_bound identity (inverse (least_upper_bound identity (inverse ?440612)))) =>= greatest_lower_bound ?440612 identity [440612] by Demod 554562 with 7 at 2
% 268.02/67.31 Id : 19919, {_}: greatest_lower_bound identity (inverse (least_upper_bound identity ?26427)) =>= inverse (least_upper_bound identity ?26427) [26427] by Demod 19825 with 5 at 2
% 268.02/67.31 Id : 554830, {_}: greatest_lower_bound ?440612 (inverse (least_upper_bound identity (inverse ?440612))) =>= greatest_lower_bound ?440612 identity [440612] by Demod 554829 with 19919 at 2,2
% 268.02/67.31 Id : 189, {_}: multiply (least_upper_bound ?426 (inverse ?427)) ?427 =>= least_upper_bound (multiply ?426 ?427) identity [427, 426] by Super 187 with 3 at 2,3
% 268.02/67.31 Id : 205, {_}: multiply (least_upper_bound ?426 (inverse ?427)) ?427 =>= least_upper_bound identity (multiply ?426 ?427) [427, 426] by Demod 189 with 6 at 3
% 268.02/67.31 Id : 45617, {_}: greatest_lower_bound (inverse (least_upper_bound ?55065 (inverse ?55066))) ?55066 =<= multiply (inverse (least_upper_bound ?55065 (inverse ?55066))) (greatest_lower_bound identity (least_upper_bound identity (multiply ?55065 ?55066))) [55066, 55065] by Super 45607 with 205 at 2,2,3
% 268.02/67.31 Id : 45730, {_}: greatest_lower_bound ?55066 (inverse (least_upper_bound ?55065 (inverse ?55066))) =<= multiply (inverse (least_upper_bound ?55065 (inverse ?55066))) (greatest_lower_bound identity (least_upper_bound identity (multiply ?55065 ?55066))) [55065, 55066] by Demod 45617 with 5 at 2
% 268.02/67.31 Id : 45731, {_}: greatest_lower_bound ?55066 (inverse (least_upper_bound ?55065 (inverse ?55066))) =?= multiply (inverse (least_upper_bound ?55065 (inverse ?55066))) identity [55065, 55066] by Demod 45730 with 12 at 2,3
% 268.02/67.31 Id : 45732, {_}: greatest_lower_bound ?55066 (inverse (least_upper_bound ?55065 (inverse ?55066))) =>= inverse (least_upper_bound ?55065 (inverse ?55066)) [55065, 55066] by Demod 45731 with 412 at 3
% 268.02/67.31 Id : 554831, {_}: inverse (least_upper_bound identity (inverse ?440612)) =>= greatest_lower_bound ?440612 identity [440612] by Demod 554830 with 45732 at 2
% 268.02/67.31 Id : 555508, {_}: ?286698 =<= multiply (least_upper_bound ?286698 identity) (greatest_lower_bound ?286698 identity) [286698] by Demod 319752 with 554831 at 2,3
% 268.02/67.31 Id : 557068, {_}: a =?= a [] by Demod 1 with 555508 at 3
% 268.02/67.31 Id : 1, {_}: a =<= multiply (least_upper_bound a identity) (greatest_lower_bound a identity) [] by prove_p19
% 268.02/67.31 % SZS output end CNFRefutation for theBenchmark.p
% 268.02/67.31 18372: solved /export/starexec/sandbox/benchmark/theBenchmark.p in 66.963481 using kbo
%------------------------------------------------------------------------------