TSTP Solution File: RNG008-4 by Matita---1.0
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%------------------------------------------------------------------------------
% File : Matita---1.0
% Problem : RNG008-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : matitaprover --timeout %d --tptppath /export/starexec/sandbox/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 : Mon Jul 18 20:35:28 EDT 2022
% Result : Unsatisfiable 9.71s 2.79s
% Output : CNFRefutation 9.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : RNG008-4 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.12 % Command : matitaprover --timeout %d --tptppath /export/starexec/sandbox/benchmark %s
% 0.12/0.33 % Computer : n026.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 : Mon May 30 12:35:55 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 30580: Facts:
% 0.12/0.33 30580: Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_identity ?2
% 0.12/0.33 30580: Id : 3, {_}:
% 0.12/0.33 add (additive_inverse ?4) ?4 =>= additive_identity
% 0.12/0.33 [4] by left_additive_inverse ?4
% 0.12/0.34 30580: Id : 4, {_}:
% 0.12/0.34 multiply ?6 (add ?7 ?8) =<= add (multiply ?6 ?7) (multiply ?6 ?8)
% 0.12/0.34 [8, 7, 6] by distribute1 ?6 ?7 ?8
% 0.12/0.34 30580: Id : 5, {_}:
% 0.12/0.34 multiply (add ?10 ?11) ?12
% 0.12/0.34 =<=
% 0.12/0.34 add (multiply ?10 ?12) (multiply ?11 ?12)
% 0.12/0.34 [12, 11, 10] by distribute2 ?10 ?11 ?12
% 0.12/0.34 30580: Id : 6, {_}:
% 0.12/0.34 additive_inverse additive_identity =>= additive_identity
% 0.12/0.34 [] by additive_inverse_identity
% 0.12/0.34 30580: Id : 7, {_}:
% 0.12/0.34 additive_inverse (additive_inverse ?15) =>= ?15
% 0.12/0.34 [15] by additive_inverse_additive_inverse ?15
% 0.12/0.34 30580: Id : 8, {_}:
% 0.12/0.34 multiply ?17 additive_identity =>= additive_identity
% 0.12/0.34 [17] by multiply_additive_id1 ?17
% 0.12/0.34 30580: Id : 9, {_}:
% 0.12/0.34 multiply additive_identity ?19 =>= additive_identity
% 0.12/0.34 [19] by multiply_additive_id2 ?19
% 0.12/0.34 30580: Id : 10, {_}:
% 0.12/0.34 additive_inverse (add ?21 ?22)
% 0.12/0.34 =<=
% 0.12/0.34 add (additive_inverse ?21) (additive_inverse ?22)
% 0.12/0.34 [22, 21] by distribute_additive_inverse ?21 ?22
% 0.12/0.34 30580: Id : 11, {_}:
% 0.12/0.34 multiply ?24 (additive_inverse ?25)
% 0.12/0.34 =>=
% 0.12/0.34 additive_inverse (multiply ?24 ?25)
% 0.12/0.34 [25, 24] by multiply_additive_inverse1 ?24 ?25
% 0.12/0.34 30580: Id : 12, {_}:
% 0.12/0.34 multiply (additive_inverse ?27) ?28
% 0.12/0.34 =>=
% 0.12/0.34 additive_inverse (multiply ?27 ?28)
% 0.12/0.34 [28, 27] by multiply_additive_inverse2 ?27 ?28
% 0.12/0.34 30580: Id : 13, {_}:
% 0.12/0.34 add (add ?30 ?31) ?32 =?= add ?30 (add ?31 ?32)
% 0.12/0.34 [32, 31, 30] by associative_addition ?30 ?31 ?32
% 0.12/0.34 30580: Id : 14, {_}:
% 0.12/0.34 add ?34 ?35 =?= add ?35 ?34
% 0.12/0.34 [35, 34] by commutative_addition ?34 ?35
% 0.12/0.34 30580: Id : 15, {_}:
% 0.12/0.34 multiply (multiply ?37 ?38) ?39 =?= multiply ?37 (multiply ?38 ?39)
% 0.12/0.34 [39, 38, 37] by associative_multiplication ?37 ?38 ?39
% 0.12/0.34 30580: Id : 16, {_}: multiply ?41 ?41 =>= ?41 [41] by boolean_ring ?41
% 0.12/0.34 30580: Id : 17, {_}: multiply a b =>= c [] by a_times_b_is_c
% 0.12/0.34 30580: Goal:
% 0.12/0.34 30580: Id : 1, {_}: multiply b a =>= c [] by prove_commutativity
% 9.71/2.79 Statistics :
% 9.71/2.79 Max weight : 18
% 9.71/2.79 Found proof, 2.455973s
% 9.71/2.79 % SZS status Unsatisfiable for theBenchmark.p
% 9.71/2.79 % SZS output start CNFRefutation for theBenchmark.p
% 9.71/2.79 Id : 9, {_}: multiply additive_identity ?19 =>= additive_identity [19] by multiply_additive_id2 ?19
% 9.71/2.79 Id : 8, {_}: multiply ?17 additive_identity =>= additive_identity [17] by multiply_additive_id1 ?17
% 9.71/2.79 Id : 146, {_}: add (add ?205 ?206) ?207 =>= add ?205 (add ?206 ?207) [207, 206, 205] by associative_addition ?205 ?206 ?207
% 9.71/2.79 Id : 2, {_}: add additive_identity ?2 =>= ?2 [2] by left_identity ?2
% 9.71/2.79 Id : 7, {_}: additive_inverse (additive_inverse ?15) =>= ?15 [15] by additive_inverse_additive_inverse ?15
% 9.71/2.79 Id : 11, {_}: multiply ?24 (additive_inverse ?25) =>= additive_inverse (multiply ?24 ?25) [25, 24] by multiply_additive_inverse1 ?24 ?25
% 9.71/2.79 Id : 12, {_}: multiply (additive_inverse ?27) ?28 =>= additive_inverse (multiply ?27 ?28) [28, 27] by multiply_additive_inverse2 ?27 ?28
% 9.71/2.79 Id : 3, {_}: add (additive_inverse ?4) ?4 =>= additive_identity [4] by left_additive_inverse ?4
% 9.71/2.79 Id : 16, {_}: multiply ?41 ?41 =>= ?41 [41] by boolean_ring ?41
% 9.71/2.79 Id : 15, {_}: multiply (multiply ?37 ?38) ?39 =>= multiply ?37 (multiply ?38 ?39) [39, 38, 37] by associative_multiplication ?37 ?38 ?39
% 9.71/2.79 Id : 14, {_}: add ?34 ?35 =?= add ?35 ?34 [35, 34] by commutative_addition ?34 ?35
% 9.71/2.79 Id : 13, {_}: add (add ?30 ?31) ?32 =>= add ?30 (add ?31 ?32) [32, 31, 30] by associative_addition ?30 ?31 ?32
% 9.71/2.79 Id : 17, {_}: multiply a b =>= c [] by a_times_b_is_c
% 9.71/2.79 Id : 4, {_}: multiply ?6 (add ?7 ?8) =<= add (multiply ?6 ?7) (multiply ?6 ?8) [8, 7, 6] by distribute1 ?6 ?7 ?8
% 9.71/2.79 Id : 5, {_}: multiply (add ?10 ?11) ?12 =<= add (multiply ?10 ?12) (multiply ?11 ?12) [12, 11, 10] by distribute2 ?10 ?11 ?12
% 9.71/2.79 Id : 285, {_}: multiply a (add b ?433) =>= add c (multiply a ?433) [433] by Super 4 with 17 at 1,3
% 9.71/2.79 Id : 162, {_}: add ?246 (add ?247 ?248) =?= add ?247 (add ?248 ?246) [248, 247, 246] by Super 13 with 14 at 2
% 9.71/2.79 Id : 2224, {_}: multiply a (add ?2475 (add b ?2476)) =>= add c (multiply a (add ?2476 ?2475)) [2476, 2475] by Super 285 with 162 at 2,2
% 9.71/2.79 Id : 284, {_}: multiply a (add ?431 b) =>= add (multiply a ?431) c [431] by Super 4 with 17 at 2,3
% 9.71/2.79 Id : 291, {_}: multiply a (add ?431 b) =>= add c (multiply a ?431) [431] by Demod 284 with 14 at 3
% 9.71/2.79 Id : 657, {_}: multiply a (add (add ?893 b) ?894) =<= add (add c (multiply a ?893)) (multiply a ?894) [894, 893] by Super 4 with 291 at 1,3
% 9.71/2.79 Id : 672, {_}: multiply a (add ?893 (add b ?894)) =<= add (add c (multiply a ?893)) (multiply a ?894) [894, 893] by Demod 657 with 13 at 2,2
% 9.71/2.79 Id : 673, {_}: multiply a (add ?893 (add b ?894)) =<= add c (add (multiply a ?893) (multiply a ?894)) [894, 893] by Demod 672 with 13 at 3
% 9.71/2.79 Id : 674, {_}: multiply a (add ?893 (add b ?894)) =>= add c (multiply a (add ?893 ?894)) [894, 893] by Demod 673 with 4 at 2,3
% 9.71/2.79 Id : 16014, {_}: add c (multiply a (add ?2475 ?2476)) =?= add c (multiply a (add ?2476 ?2475)) [2476, 2475] by Demod 2224 with 674 at 2
% 9.71/2.79 Id : 5543, {_}: multiply (add c (multiply a ?5922)) ?5923 =>= multiply a (multiply (add b ?5922) ?5923) [5923, 5922] by Super 15 with 285 at 1,2
% 9.71/2.79 Id : 5547, {_}: multiply (add c a) ?5933 =<= multiply a (multiply (add b a) ?5933) [5933] by Super 5543 with 16 at 2,1,2
% 9.71/2.79 Id : 5861, {_}: multiply (add a c) ?6183 =<= multiply a (multiply (add b a) ?6183) [6183] by Demod 5547 with 14 at 1,2
% 9.71/2.79 Id : 257, {_}: multiply ?404 (add ?404 ?405) =>= add ?404 (multiply ?404 ?405) [405, 404] by Super 4 with 16 at 1,3
% 9.71/2.79 Id : 5870, {_}: multiply (add a c) (add (add b a) ?6199) =<= multiply a (add (add b a) (multiply (add b a) ?6199)) [6199] by Super 5861 with 257 at 2,3
% 9.71/2.79 Id : 5919, {_}: multiply (add a c) (add b (add a ?6199)) =<= multiply a (add (add b a) (multiply (add b a) ?6199)) [6199] by Demod 5870 with 13 at 2,2
% 9.71/2.79 Id : 5920, {_}: multiply (add a c) (add b (add a ?6199)) =<= multiply a (add b (add a (multiply (add b a) ?6199))) [6199] by Demod 5919 with 13 at 2,3
% 9.71/2.79 Id : 5921, {_}: multiply (add a c) (add b (add a ?6199)) =<= add c (multiply a (add a (multiply (add b a) ?6199))) [6199] by Demod 5920 with 285 at 3
% 9.71/2.79 Id : 5922, {_}: multiply (add a c) (add b (add a ?6199)) =<= add c (add a (multiply a (multiply (add b a) ?6199))) [6199] by Demod 5921 with 257 at 2,3
% 9.71/2.79 Id : 5923, {_}: multiply (add a c) (add b (add a ?6199)) =<= add a (add (multiply a (multiply (add b a) ?6199)) c) [6199] by Demod 5922 with 162 at 3
% 9.71/2.79 Id : 5924, {_}: multiply (add a c) (add b (add a ?6199)) =<= add a (add c (multiply a (multiply (add b a) ?6199))) [6199] by Demod 5923 with 14 at 2,3
% 9.71/2.79 Id : 5645, {_}: multiply (add a c) ?5933 =<= multiply a (multiply (add b a) ?5933) [5933] by Demod 5547 with 14 at 1,2
% 9.71/2.79 Id : 22609, {_}: multiply (add a c) (add b (add a ?21452)) =>= add a (add c (multiply (add a c) ?21452)) [21452] by Demod 5924 with 5645 at 2,2,3
% 9.71/2.79 Id : 159, {_}: add ?4 (additive_inverse ?4) =>= additive_identity [4] by Demod 3 with 14 at 2
% 9.71/2.79 Id : 259, {_}: additive_inverse ?408 =<= additive_inverse (multiply ?408 (additive_inverse ?408)) [408] by Super 12 with 16 at 2
% 9.71/2.79 Id : 269, {_}: additive_inverse ?408 =<= additive_inverse (additive_inverse (multiply ?408 ?408)) [408] by Demod 259 with 11 at 1,3
% 9.71/2.79 Id : 270, {_}: additive_inverse ?408 =<= multiply ?408 ?408 [408] by Demod 269 with 7 at 3
% 9.71/2.79 Id : 271, {_}: additive_inverse ?408 =>= ?408 [408] by Demod 270 with 16 at 3
% 9.71/2.79 Id : 394, {_}: add ?4 ?4 =>= additive_identity [4] by Demod 159 with 271 at 2,2
% 9.71/2.79 Id : 22616, {_}: multiply (add a c) (add b additive_identity) =<= add a (add c (multiply (add a c) a)) [] by Super 22609 with 394 at 2,2,2
% 9.71/2.79 Id : 166, {_}: add ?262 additive_identity =>= ?262 [262] by Super 2 with 14 at 2
% 9.71/2.79 Id : 22711, {_}: multiply (add a c) b =<= add a (add c (multiply (add a c) a)) [] by Demod 22616 with 166 at 2,2
% 9.71/2.79 Id : 255, {_}: multiply (add ?398 ?399) ?398 =>= add ?398 (multiply ?399 ?398) [399, 398] by Super 5 with 16 at 1,3
% 9.71/2.79 Id : 22712, {_}: multiply (add a c) b =<= add a (add c (add a (multiply c a))) [] by Demod 22711 with 255 at 2,2,3
% 9.71/2.79 Id : 287, {_}: multiply (add a ?437) b =>= add c (multiply ?437 b) [437] by Super 5 with 17 at 1,3
% 9.71/2.79 Id : 22713, {_}: add c (multiply c b) =<= add a (add c (add a (multiply c a))) [] by Demod 22712 with 287 at 2
% 9.71/2.79 Id : 22714, {_}: add c (multiply c b) =<= add a (add a (add (multiply c a) c)) [] by Demod 22713 with 162 at 2,3
% 9.71/2.79 Id : 448, {_}: multiply c ?626 =<= multiply a (multiply b ?626) [626] by Super 15 with 17 at 1,2
% 9.71/2.79 Id : 450, {_}: multiply c b =>= multiply a b [] by Super 448 with 16 at 2,3
% 9.71/2.79 Id : 458, {_}: multiply c b =>= c [] by Demod 450 with 17 at 3
% 9.71/2.79 Id : 22715, {_}: add c c =<= add a (add a (add (multiply c a) c)) [] by Demod 22714 with 458 at 2,2
% 9.71/2.79 Id : 148, {_}: add additive_identity ?212 =<= add (additive_inverse ?213) (add ?213 ?212) [213, 212] by Super 146 with 3 at 1,2
% 9.71/2.79 Id : 155, {_}: ?212 =<= add (additive_inverse ?213) (add ?213 ?212) [213, 212] by Demod 148 with 2 at 2
% 9.71/2.79 Id : 1363, {_}: ?212 =<= add ?213 (add ?213 ?212) [213, 212] by Demod 155 with 271 at 1,3
% 9.71/2.79 Id : 22716, {_}: add c c =<= add (multiply c a) c [] by Demod 22715 with 1363 at 3
% 9.71/2.79 Id : 22717, {_}: additive_identity =<= add (multiply c a) c [] by Demod 22716 with 394 at 2
% 9.71/2.79 Id : 22718, {_}: additive_identity =<= add c (multiply c a) [] by Demod 22717 with 14 at 3
% 9.71/2.79 Id : 22802, {_}: add c (multiply a (add (multiply c a) c)) =>= add c (multiply a additive_identity) [] by Super 16014 with 22718 at 2,2,3
% 9.71/2.79 Id : 1765, {_}: multiply ?1960 ?1961 =<= multiply ?1960 (multiply ?1960 ?1961) [1961, 1960] by Super 15 with 16 at 1,2
% 9.71/2.79 Id : 1770, {_}: multiply a b =?= multiply a c [] by Super 1765 with 17 at 2,3
% 9.71/2.79 Id : 1813, {_}: c =<= multiply a c [] by Demod 1770 with 17 at 2
% 9.71/2.79 Id : 1844, {_}: multiply a (add ?2025 c) =>= add (multiply a ?2025) c [2025] by Super 4 with 1813 at 2,3
% 9.71/2.79 Id : 1856, {_}: multiply a (add ?2025 c) =>= add c (multiply a ?2025) [2025] by Demod 1844 with 14 at 3
% 9.71/2.79 Id : 22837, {_}: add c (add c (multiply a (multiply c a))) =>= add c (multiply a additive_identity) [] by Demod 22802 with 1856 at 2,2
% 9.71/2.79 Id : 22838, {_}: add c (add c (multiply a (multiply c a))) =>= add c additive_identity [] by Demod 22837 with 8 at 2,3
% 9.71/2.79 Id : 22839, {_}: multiply a (multiply c a) =>= add c additive_identity [] by Demod 22838 with 1363 at 2
% 9.71/2.79 Id : 22840, {_}: multiply a (multiply c a) =>= c [] by Demod 22839 with 166 at 3
% 9.71/2.79 Id : 283, {_}: multiply c ?429 =<= multiply a (multiply b ?429) [429] by Super 15 with 17 at 1,2
% 9.71/2.79 Id : 1783, {_}: multiply a (multiply b ?2000) =?= multiply a (multiply c ?2000) [2000] by Super 1765 with 283 at 2,3
% 9.71/2.79 Id : 1832, {_}: multiply c ?2000 =<= multiply a (multiply c ?2000) [2000] by Demod 1783 with 283 at 2
% 9.71/2.79 Id : 22841, {_}: multiply c a =>= c [] by Demod 22840 with 1832 at 2
% 9.71/2.79 Id : 23414, {_}: multiply (add c ?22010) a =>= add c (multiply ?22010 a) [22010] by Super 5 with 22841 at 1,3
% 9.71/2.79 Id : 23434, {_}: multiply (add ?22058 (add c ?22059)) a =>= add c (multiply (add ?22059 ?22058) a) [22059, 22058] by Super 23414 with 162 at 1,2
% 9.71/2.79 Id : 160, {_}: add (add ?238 ?239) ?240 =>= add ?239 (add ?238 ?240) [240, 239, 238] by Super 13 with 14 at 1,2
% 9.71/2.79 Id : 194, {_}: add ?238 (add ?239 ?240) =?= add ?239 (add ?238 ?240) [240, 239, 238] by Demod 160 with 13 at 2
% 9.71/2.79 Id : 23422, {_}: multiply (add ?22026 (add c ?22027)) a =>= add c (multiply (add ?22026 ?22027) a) [22027, 22026] by Super 23414 with 194 at 1,2
% 9.71/2.79 Id : 33476, {_}: add c (multiply (add ?22058 ?22059) a) =?= add c (multiply (add ?22059 ?22058) a) [22059, 22058] by Demod 23434 with 23422 at 2
% 9.71/2.79 Id : 35042, {_}: multiply ?31134 ?31135 =<= multiply ?31134 (multiply ?31135 (multiply ?31134 ?31135)) [31135, 31134] by Super 15 with 16 at 2
% 9.71/2.79 Id : 5566, {_}: multiply (add c c) ?5989 =<= multiply a (multiply (add b c) ?5989) [5989] by Super 5543 with 1813 at 2,1,2
% 9.71/2.79 Id : 5685, {_}: multiply additive_identity ?5989 =<= multiply a (multiply (add b c) ?5989) [5989] by Demod 5566 with 394 at 1,2
% 9.71/2.79 Id : 5686, {_}: additive_identity =<= multiply a (multiply (add b c) ?5989) [5989] by Demod 5685 with 9 at 2
% 9.71/2.79 Id : 35194, {_}: multiply (add b c) a =?= multiply (add b c) additive_identity [] by Super 35042 with 5686 at 2,3
% 9.71/2.79 Id : 22978, {_}: multiply (add ?21602 c) a =>= add (multiply ?21602 a) c [21602] by Super 5 with 22841 at 2,3
% 9.71/2.79 Id : 23013, {_}: multiply (add ?21602 c) a =>= add c (multiply ?21602 a) [21602] by Demod 22978 with 14 at 3
% 9.71/2.79 Id : 35668, {_}: add c (multiply b a) =<= multiply (add b c) additive_identity [] by Demod 35194 with 23013 at 2
% 9.71/2.79 Id : 35669, {_}: add c (multiply b a) =>= additive_identity [] by Demod 35668 with 8 at 3
% 9.71/2.79 Id : 35826, {_}: add c (multiply (add (multiply b a) c) a) =>= add c (multiply additive_identity a) [] by Super 33476 with 35669 at 1,2,3
% 9.71/2.79 Id : 164, {_}: multiply (add ?254 ?255) ?256 =<= add (multiply ?255 ?256) (multiply ?254 ?256) [256, 255, 254] by Super 5 with 14 at 3
% 9.71/2.79 Id : 192, {_}: multiply (add ?254 ?255) ?256 =?= multiply (add ?255 ?254) ?256 [256, 255, 254] by Demod 164 with 5 at 3
% 9.71/2.79 Id : 35840, {_}: add c (multiply (add c (multiply b a)) a) =>= add c (multiply additive_identity a) [] by Demod 35826 with 192 at 2,2
% 9.71/2.79 Id : 35841, {_}: add c (multiply (add c (multiply b a)) a) =>= add c additive_identity [] by Demod 35840 with 9 at 2,3
% 9.71/2.79 Id : 22979, {_}: multiply (add c ?21604) a =>= add c (multiply ?21604 a) [21604] by Super 5 with 22841 at 1,3
% 9.71/2.79 Id : 35842, {_}: add c (add c (multiply (multiply b a) a)) =>= add c additive_identity [] by Demod 35841 with 22979 at 2,2
% 9.71/2.79 Id : 35843, {_}: add c (add c (multiply (multiply b a) a)) =>= c [] by Demod 35842 with 166 at 3
% 9.71/2.79 Id : 35844, {_}: multiply (multiply b a) a =>= c [] by Demod 35843 with 1363 at 2
% 9.71/2.79 Id : 35845, {_}: multiply b (multiply a a) =>= c [] by Demod 35844 with 15 at 2
% 9.71/2.79 Id : 35846, {_}: multiply b a =>= c [] by Demod 35845 with 16 at 2,2
% 9.71/2.79 Id : 36113, {_}: c =?= c [] by Demod 1 with 35846 at 2
% 9.71/2.79 Id : 1, {_}: multiply b a =>= c [] by prove_commutativity
% 9.71/2.79 % SZS output end CNFRefutation for theBenchmark.p
% 9.71/2.79 30581: solved /export/starexec/sandbox/benchmark/theBenchmark.p in 2.46014 using kbo
%------------------------------------------------------------------------------