TSTP Solution File: GRP178-2 by Matita---1.0
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%------------------------------------------------------------------------------
% File : Matita---1.0
% Problem : GRP178-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : matitaprover --timeout %d --tptppath /export/starexec/sandbox/benchmark %s
% Computer : n006.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 10:29:24 EDT 2022
% Result : Unsatisfiable 265.61s 66.74s
% Output : CNFRefutation 265.61s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GRP178-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.04/0.13 % Command : matitaprover --timeout %d --tptppath /export/starexec/sandbox/benchmark %s
% 0.13/0.34 % Computer : n006.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 : Mon Jun 13 08:11:11 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 32042: Facts:
% 0.13/0.34 32042: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
% 0.13/0.34 32042: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
% 0.13/0.34 32042: 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 32042: 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 32042: 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 32042: 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 32042: 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 32042: Id : 9, {_}: least_upper_bound ?24 ?24 =>= ?24 [24] by idempotence_of_lub ?24
% 0.13/0.34 32042: 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 32042: 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 32042: 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 32042: 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 32042: 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 32042: 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 32042: 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 32042: Id : 17, {_}: greatest_lower_bound identity a =>= identity [] by p09b_1
% 0.13/0.34 32042: Id : 18, {_}: greatest_lower_bound identity b =>= identity [] by p09b_2
% 0.13/0.34 32042: Id : 19, {_}: greatest_lower_bound identity c =>= identity [] by p09b_3
% 0.13/0.34 32042: Id : 20, {_}: greatest_lower_bound a b =>= identity [] by p09b_4
% 0.13/0.34 32042: Goal:
% 0.13/0.34 32042: Id : 1, {_}:
% 0.13/0.34 greatest_lower_bound a (multiply b c) =>= greatest_lower_bound a c
% 0.13/0.34 [] by prove_p09b
% 265.61/66.74 Statistics :
% 265.61/66.74 Max weight : 16
% 265.61/66.74 Found proof, 66.393125s
% 265.61/66.74 % SZS status Unsatisfiable for theBenchmark.p
% 265.61/66.74 % SZS output start CNFRefutation for theBenchmark.p
% 265.61/66.74 Id : 16, {_}: multiply (greatest_lower_bound ?46 ?47) ?48 =>= greatest_lower_bound (multiply ?46 ?48) (multiply ?47 ?48) [48, 47, 46] by monotony_glb2 ?46 ?47 ?48
% 265.61/66.74 Id : 15, {_}: multiply (least_upper_bound ?42 ?43) ?44 =>= least_upper_bound (multiply ?42 ?44) (multiply ?43 ?44) [44, 43, 42] by monotony_lub2 ?42 ?43 ?44
% 265.61/66.74 Id : 61, {_}: least_upper_bound ?155 (least_upper_bound ?156 ?157) =<= least_upper_bound (least_upper_bound ?155 ?156) ?157 [157, 156, 155] by associativity_of_lub ?155 ?156 ?157
% 265.61/66.74 Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
% 265.61/66.74 Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
% 265.61/66.74 Id : 25, {_}: multiply (multiply ?61 ?62) ?63 =>= multiply ?61 (multiply ?62 ?63) [63, 62, 61] by associativity ?61 ?62 ?63
% 265.61/66.74 Id : 20, {_}: greatest_lower_bound a b =>= identity [] by p09b_4
% 265.61/66.74 Id : 19, {_}: greatest_lower_bound identity c =>= identity [] by p09b_3
% 265.61/66.74 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
% 265.61/66.74 Id : 86, {_}: least_upper_bound ?221 (greatest_lower_bound ?221 ?222) =>= ?221 [222, 221] by lub_absorbtion ?221 ?222
% 265.61/66.74 Id : 6, {_}: least_upper_bound ?13 ?14 =?= least_upper_bound ?14 ?13 [14, 13] by symmetry_of_lub ?13 ?14
% 265.61/66.74 Id : 5, {_}: greatest_lower_bound ?10 ?11 =?= greatest_lower_bound ?11 ?10 [11, 10] by symmetry_of_glb ?10 ?11
% 265.61/66.74 Id : 17, {_}: greatest_lower_bound identity a =>= identity [] by p09b_1
% 265.61/66.74 Id : 11, {_}: least_upper_bound ?28 (greatest_lower_bound ?28 ?29) =>= ?28 [29, 28] by lub_absorbtion ?28 ?29
% 265.61/66.74 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
% 265.61/66.74 Id : 12, {_}: greatest_lower_bound ?31 (least_upper_bound ?31 ?32) =>= ?31 [32, 31] by glb_absorbtion ?31 ?32
% 265.61/66.74 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
% 265.61/66.74 Id : 98, {_}: greatest_lower_bound ?249 (greatest_lower_bound ?250 (least_upper_bound (greatest_lower_bound ?249 ?250) ?251)) =>= greatest_lower_bound ?249 ?250 [251, 250, 249] by Super 7 with 12 at 3
% 265.61/66.74 Id : 84, {_}: least_upper_bound ?213 (least_upper_bound (greatest_lower_bound ?213 ?214) ?215) =>= least_upper_bound ?213 ?215 [215, 214, 213] by Super 8 with 11 at 1,3
% 265.61/66.74 Id : 269, {_}: greatest_lower_bound a identity =>= identity [] by Demod 17 with 5 at 2
% 265.61/66.74 Id : 274, {_}: least_upper_bound a identity =>= a [] by Super 11 with 269 at 2,2
% 265.61/66.74 Id : 633, {_}: least_upper_bound a (least_upper_bound identity ?783) =>= least_upper_bound a ?783 [783] by Super 8 with 274 at 1,3
% 265.61/66.74 Id : 634, {_}: least_upper_bound a (least_upper_bound ?785 identity) =>= least_upper_bound a ?785 [785] by Super 633 with 6 at 2,2
% 265.61/66.74 Id : 59, {_}: least_upper_bound ?147 (least_upper_bound ?148 ?149) =?= least_upper_bound ?148 (least_upper_bound ?149 ?147) [149, 148, 147] by Super 6 with 8 at 3
% 265.61/66.74 Id : 2003, {_}: least_upper_bound identity (least_upper_bound a ?2380) =>= least_upper_bound a ?2380 [2380] by Super 634 with 59 at 2
% 265.61/66.74 Id : 37429, {_}: least_upper_bound identity (least_upper_bound ?31165 (least_upper_bound ?31166 a)) =>= least_upper_bound a (least_upper_bound ?31165 ?31166) [31166, 31165] by Super 2003 with 59 at 2,2
% 265.61/66.74 Id : 166472, {_}: least_upper_bound identity (least_upper_bound ?108456 (least_upper_bound a ?108457)) =>= least_upper_bound a (least_upper_bound ?108456 ?108457) [108457, 108456] by Super 37429 with 6 at 2,2,2
% 265.61/66.74 Id : 87, {_}: least_upper_bound ?224 (greatest_lower_bound ?225 ?224) =>= ?224 [225, 224] by Super 86 with 5 at 2,2
% 265.61/66.74 Id : 295, {_}: greatest_lower_bound c identity =>= identity [] by Demod 19 with 5 at 2
% 265.61/66.74 Id : 297, {_}: multiply ?516 identity =<= greatest_lower_bound (multiply ?516 c) (multiply ?516 identity) [516] by Super 14 with 295 at 2,2
% 265.61/66.74 Id : 311, {_}: multiply ?528 identity =>= greatest_lower_bound (multiply ?528 a) (multiply ?528 b) [528] by Super 14 with 20 at 2,2
% 265.61/66.74 Id : 27, {_}: multiply identity ?68 =<= multiply (inverse ?69) (multiply ?69 ?68) [69, 68] by Super 25 with 3 at 1,2
% 265.61/66.74 Id : 382, {_}: ?597 =<= multiply (inverse ?598) (multiply ?598 ?597) [598, 597] by Demod 27 with 2 at 2
% 265.61/66.74 Id : 384, {_}: ?602 =<= multiply (inverse (inverse ?602)) identity [602] by Super 382 with 3 at 2,3
% 265.61/66.74 Id : 860, {_}: ?602 =<= greatest_lower_bound (multiply (inverse (inverse ?602)) a) (multiply (inverse (inverse ?602)) b) [602] by Demod 384 with 311 at 3
% 265.61/66.74 Id : 31, {_}: ?68 =<= multiply (inverse ?69) (multiply ?69 ?68) [69, 68] by Demod 27 with 2 at 2
% 265.61/66.74 Id : 390, {_}: multiply ?624 ?625 =<= multiply (inverse (inverse ?624)) ?625 [625, 624] by Super 382 with 31 at 2,3
% 265.61/66.74 Id : 2597, {_}: ?602 =<= greatest_lower_bound (multiply ?602 a) (multiply (inverse (inverse ?602)) b) [602] by Demod 860 with 390 at 1,3
% 265.61/66.74 Id : 2598, {_}: ?602 =<= greatest_lower_bound (multiply ?602 a) (multiply ?602 b) [602] by Demod 2597 with 390 at 2,3
% 265.61/66.74 Id : 2599, {_}: multiply ?528 identity =>= ?528 [528] by Demod 311 with 2598 at 3
% 265.61/66.74 Id : 30216, {_}: ?516 =<= greatest_lower_bound (multiply ?516 c) (multiply ?516 identity) [516] by Demod 297 with 2599 at 2
% 265.61/66.74 Id : 30217, {_}: ?516 =<= greatest_lower_bound (multiply ?516 c) ?516 [516] by Demod 30216 with 2599 at 2,3
% 265.61/66.74 Id : 30218, {_}: ?516 =<= greatest_lower_bound ?516 (multiply ?516 c) [516] by Demod 30217 with 5 at 3
% 265.61/66.74 Id : 30232, {_}: least_upper_bound (multiply ?24700 c) ?24700 =>= multiply ?24700 c [24700] by Super 87 with 30218 at 2,2
% 265.61/66.74 Id : 30330, {_}: least_upper_bound ?24700 (multiply ?24700 c) =>= multiply ?24700 c [24700] by Demod 30232 with 6 at 2
% 265.61/66.74 Id : 166505, {_}: least_upper_bound identity (least_upper_bound ?108560 (multiply a c)) =>= least_upper_bound a (least_upper_bound ?108560 (multiply a c)) [108560] by Super 166472 with 30330 at 2,2,2
% 265.61/66.74 Id : 62, {_}: least_upper_bound ?159 (least_upper_bound ?160 ?161) =<= least_upper_bound (least_upper_bound ?160 ?159) ?161 [161, 160, 159] by Super 61 with 6 at 1,3
% 265.61/66.74 Id : 2399, {_}: least_upper_bound ?2815 (least_upper_bound ?2816 ?2817) =?= least_upper_bound ?2816 (least_upper_bound ?2815 ?2817) [2817, 2816, 2815] by Demod 62 with 8 at 3
% 265.61/66.74 Id : 300, {_}: least_upper_bound c identity =>= c [] by Super 11 with 295 at 2,2
% 265.61/66.74 Id : 840, {_}: least_upper_bound c (least_upper_bound identity ?1092) =>= least_upper_bound c ?1092 [1092] by Super 8 with 300 at 1,3
% 265.61/66.74 Id : 841, {_}: least_upper_bound c (least_upper_bound ?1094 identity) =>= least_upper_bound c ?1094 [1094] by Super 840 with 6 at 2,2
% 265.61/66.74 Id : 1777, {_}: least_upper_bound identity (least_upper_bound c ?2107) =>= least_upper_bound c ?2107 [2107] by Super 841 with 59 at 2
% 265.61/66.74 Id : 322, {_}: multiply a ?540 =<= least_upper_bound (multiply a ?540) (multiply identity ?540) [540] by Super 15 with 274 at 1,2
% 265.61/66.74 Id : 325, {_}: multiply a ?540 =<= least_upper_bound (multiply a ?540) ?540 [540] by Demod 322 with 2 at 2,3
% 265.61/66.74 Id : 326, {_}: multiply a ?540 =<= least_upper_bound ?540 (multiply a ?540) [540] by Demod 325 with 6 at 3
% 265.61/66.74 Id : 2170, {_}: least_upper_bound identity (multiply a c) =>= least_upper_bound c (multiply a c) [] by Super 1777 with 326 at 2,2
% 265.61/66.74 Id : 2202, {_}: least_upper_bound identity (multiply a c) =>= multiply a c [] by Demod 2170 with 326 at 3
% 265.61/66.74 Id : 2417, {_}: least_upper_bound identity (least_upper_bound ?2871 (multiply a c)) =>= least_upper_bound ?2871 (multiply a c) [2871] by Super 2399 with 2202 at 2,3
% 265.61/66.74 Id : 166887, {_}: least_upper_bound ?108560 (multiply a c) =<= least_upper_bound a (least_upper_bound ?108560 (multiply a c)) [108560] by Demod 166505 with 2417 at 2
% 265.61/66.74 Id : 167861, {_}: least_upper_bound (greatest_lower_bound a ?109301) (multiply a c) =>= least_upper_bound a (multiply a c) [109301] by Super 84 with 166887 at 2
% 265.61/66.74 Id : 167933, {_}: least_upper_bound (greatest_lower_bound a ?109301) (multiply a c) =>= multiply a c [109301] by Demod 167861 with 30330 at 3
% 265.61/66.74 Id : 176280, {_}: greatest_lower_bound a (greatest_lower_bound ?115060 (multiply a c)) =>= greatest_lower_bound a ?115060 [115060] by Super 98 with 167933 at 2,2,2
% 265.61/66.74 Id : 184601, {_}: greatest_lower_bound a (greatest_lower_bound (multiply a c) ?120414) =>= greatest_lower_bound a ?120414 [120414] by Super 176280 with 5 at 2,2
% 265.61/66.74 Id : 312, {_}: multiply identity ?530 =>= greatest_lower_bound (multiply a ?530) (multiply b ?530) [530] by Super 16 with 20 at 1,2
% 265.61/66.74 Id : 315, {_}: ?530 =<= greatest_lower_bound (multiply a ?530) (multiply b ?530) [530] by Demod 312 with 2 at 2
% 265.61/66.74 Id : 184630, {_}: greatest_lower_bound a c =<= greatest_lower_bound a (multiply b c) [] by Super 184601 with 315 at 2,2
% 265.61/66.74 Id : 184973, {_}: greatest_lower_bound a c === greatest_lower_bound a c [] by Demod 1 with 184630 at 2
% 265.61/66.74 Id : 1, {_}: greatest_lower_bound a (multiply b c) =>= greatest_lower_bound a c [] by prove_p09b
% 265.61/66.74 % SZS output end CNFRefutation for theBenchmark.p
% 265.61/66.74 32044: solved /export/starexec/sandbox/benchmark/theBenchmark.p in 66.389313 using lpo
%------------------------------------------------------------------------------