%------------------------------------------------------------------------------
% File     : Matita---1.0
% Problem  : RNG026-7 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : matitaprover --timeout %d --tptppath /export/starexec/sandbox/benchmark %s

% Computer : n017.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 20:35:30 EDT 2022

% Result   : Unsatisfiable 133.19s 33.66s
% Output   : CNFRefutation 133.42s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : RNG026-7 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.12  % Command  : matitaprover --timeout %d --tptppath /export/starexec/sandbox/benchmark %s
% 0.12/0.34  % Computer : n017.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Mon May 30 06:29:25 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.34  6465: Facts:
% 0.12/0.34  6465:  Id :   2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
% 0.12/0.34  6465:  Id :   3, {_}:
% 0.12/0.34            add ?4 additive_identity =>= ?4
% 0.12/0.34            [4] by right_additive_identity ?4
% 0.12/0.34  6465:  Id :   4, {_}:
% 0.12/0.34            multiply additive_identity ?6 =>= additive_identity
% 0.12/0.34            [6] by left_multiplicative_zero ?6
% 0.12/0.34  6465:  Id :   5, {_}:
% 0.12/0.34            multiply ?8 additive_identity =>= additive_identity
% 0.12/0.34            [8] by right_multiplicative_zero ?8
% 0.12/0.34  6465:  Id :   6, {_}:
% 0.12/0.34            add (additive_inverse ?10) ?10 =>= additive_identity
% 0.12/0.34            [10] by left_additive_inverse ?10
% 0.12/0.34  6465:  Id :   7, {_}:
% 0.12/0.34            add ?12 (additive_inverse ?12) =>= additive_identity
% 0.12/0.34            [12] by right_additive_inverse ?12
% 0.12/0.34  6465:  Id :   8, {_}:
% 0.12/0.34            additive_inverse (additive_inverse ?14) =>= ?14
% 0.12/0.34            [14] by additive_inverse_additive_inverse ?14
% 0.12/0.34  6465:  Id :   9, {_}:
% 0.12/0.34            multiply ?16 (add ?17 ?18)
% 0.12/0.34            =<=
% 0.12/0.34            add (multiply ?16 ?17) (multiply ?16 ?18)
% 0.12/0.34            [18, 17, 16] by distribute1 ?16 ?17 ?18
% 0.12/0.34  6465:  Id :  10, {_}:
% 0.12/0.34            multiply (add ?20 ?21) ?22
% 0.12/0.34            =<=
% 0.12/0.34            add (multiply ?20 ?22) (multiply ?21 ?22)
% 0.12/0.34            [22, 21, 20] by distribute2 ?20 ?21 ?22
% 0.12/0.34  6465:  Id :  11, {_}:
% 0.12/0.34            add ?24 ?25 =?= add ?25 ?24
% 0.12/0.34            [25, 24] by commutativity_for_addition ?24 ?25
% 0.12/0.34  6465:  Id :  12, {_}:
% 0.12/0.34            add ?27 (add ?28 ?29) =?= add (add ?27 ?28) ?29
% 0.12/0.34            [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
% 0.12/0.34  6465:  Id :  13, {_}:
% 0.12/0.34            multiply (multiply ?31 ?32) ?32 =?= multiply ?31 (multiply ?32 ?32)
% 0.12/0.34            [32, 31] by right_alternative ?31 ?32
% 0.12/0.34  6465:  Id :  14, {_}:
% 0.12/0.34            multiply (multiply ?34 ?34) ?35 =?= multiply ?34 (multiply ?34 ?35)
% 0.12/0.34            [35, 34] by left_alternative ?34 ?35
% 0.12/0.34  6465:  Id :  15, {_}:
% 0.12/0.34            associator ?37 ?38 ?39
% 0.12/0.34            =<=
% 0.12/0.34            add (multiply (multiply ?37 ?38) ?39)
% 0.12/0.34              (additive_inverse (multiply ?37 (multiply ?38 ?39)))
% 0.12/0.34            [39, 38, 37] by associator ?37 ?38 ?39
% 0.12/0.34  6465:  Id :  16, {_}:
% 0.12/0.34            commutator ?41 ?42
% 0.12/0.34            =<=
% 0.12/0.34            add (multiply ?42 ?41) (additive_inverse (multiply ?41 ?42))
% 0.12/0.34            [42, 41] by commutator ?41 ?42
% 0.12/0.34  6465:  Id :  17, {_}:
% 0.12/0.34            multiply (additive_inverse ?44) (additive_inverse ?45)
% 0.12/0.34            =>=
% 0.12/0.34            multiply ?44 ?45
% 0.12/0.34            [45, 44] by product_of_inverses ?44 ?45
% 0.12/0.34  6465:  Id :  18, {_}:
% 0.12/0.34            multiply (additive_inverse ?47) ?48
% 0.12/0.34            =>=
% 0.12/0.34            additive_inverse (multiply ?47 ?48)
% 0.12/0.34            [48, 47] by inverse_product1 ?47 ?48
% 0.12/0.34  6465:  Id :  19, {_}:
% 0.12/0.34            multiply ?50 (additive_inverse ?51)
% 0.12/0.34            =>=
% 0.12/0.34            additive_inverse (multiply ?50 ?51)
% 0.12/0.34            [51, 50] by inverse_product2 ?50 ?51
% 0.12/0.34  6465:  Id :  20, {_}:
% 0.12/0.34            multiply ?53 (add ?54 (additive_inverse ?55))
% 0.12/0.34            =<=
% 0.12/0.34            add (multiply ?53 ?54) (additive_inverse (multiply ?53 ?55))
% 0.12/0.34            [55, 54, 53] by distributivity_of_difference1 ?53 ?54 ?55
% 0.12/0.34  6465:  Id :  21, {_}:
% 0.12/0.34            multiply (add ?57 (additive_inverse ?58)) ?59
% 0.12/0.34            =<=
% 0.12/0.34            add (multiply ?57 ?59) (additive_inverse (multiply ?58 ?59))
% 0.12/0.34            [59, 58, 57] by distributivity_of_difference2 ?57 ?58 ?59
% 0.12/0.34  6465:  Id :  22, {_}:
% 0.12/0.34            multiply (additive_inverse ?61) (add ?62 ?63)
% 0.12/0.34            =<=
% 0.12/0.34            add (additive_inverse (multiply ?61 ?62))
% 0.12/0.34              (additive_inverse (multiply ?61 ?63))
% 0.12/0.34            [63, 62, 61] by distributivity_of_difference3 ?61 ?62 ?63
% 0.12/0.34  6465:  Id :  23, {_}:
% 0.12/0.34            multiply (add ?65 ?66) (additive_inverse ?67)
% 0.12/0.34            =<=
% 0.12/0.34            add (additive_inverse (multiply ?65 ?67))
% 0.12/0.34              (additive_inverse (multiply ?66 ?67))
% 0.12/0.34            [67, 66, 65] by distributivity_of_difference4 ?65 ?66 ?67
% 0.12/0.34  6465: Goal:
% 0.12/0.35  6465:  Id :   1, {_}:
% 0.12/0.35            add
% 0.12/0.35              (add (associator (multiply a b) c d)
% 0.12/0.35                (associator a b (multiply c d)))
% 0.12/0.35              (additive_inverse
% 0.12/0.35                (add
% 0.12/0.35                  (add (associator a (multiply b c) d)
% 0.12/0.35                    (multiply a (associator b c d)))
% 0.12/0.35                  (multiply (associator a b c) d)))
% 0.12/0.35            =>=
% 0.12/0.35            additive_identity
% 0.12/0.35            [] by prove_teichmuller_identity
% 133.19/33.66  Statistics :
% 133.19/33.66  Max weight : 86
% 133.19/33.66  Found proof, 33.317920s
% 133.19/33.66  % SZS status Unsatisfiable for theBenchmark.p
% 133.19/33.66  % SZS output start CNFRefutation for theBenchmark.p
% 133.19/33.66  Id :  18, {_}: multiply (additive_inverse ?47) ?48 =>= additive_inverse (multiply ?47 ?48) [48, 47] by inverse_product1 ?47 ?48
% 133.19/33.66  Id :  19, {_}: multiply ?50 (additive_inverse ?51) =>= additive_inverse (multiply ?50 ?51) [51, 50] by inverse_product2 ?50 ?51
% 133.19/33.66  Id :  10, {_}: multiply (add ?20 ?21) ?22 =>= add (multiply ?20 ?22) (multiply ?21 ?22) [22, 21, 20] by distribute2 ?20 ?21 ?22
% 133.19/33.66  Id :   9, {_}: multiply ?16 (add ?17 ?18) =>= add (multiply ?16 ?17) (multiply ?16 ?18) [18, 17, 16] by distribute1 ?16 ?17 ?18
% 133.19/33.66  Id :   8, {_}: additive_inverse (additive_inverse ?14) =>= ?14 [14] by additive_inverse_additive_inverse ?14
% 133.19/33.66  Id :   2, {_}: add additive_identity ?2 =>= ?2 [2] by left_additive_identity ?2
% 133.19/33.66  Id :   7, {_}: add ?12 (additive_inverse ?12) =>= additive_identity [12] by right_additive_inverse ?12
% 133.19/33.66  Id : 144, {_}: add ?242 (add ?243 ?244) =<= add (add ?242 ?243) ?244 [244, 243, 242] by associativity_for_addition ?242 ?243 ?244
% 133.19/33.66  Id :  15, {_}: associator ?37 ?38 ?39 =>= add (multiply (multiply ?37 ?38) ?39) (additive_inverse (multiply ?37 (multiply ?38 ?39))) [39, 38, 37] by associator ?37 ?38 ?39
% 133.19/33.66  Id :  12, {_}: add ?27 (add ?28 ?29) =<= add (add ?27 ?28) ?29 [29, 28, 27] by associativity_for_addition ?27 ?28 ?29
% 133.19/33.66  Id :  11, {_}: add ?24 ?25 =?= add ?25 ?24 [25, 24] by commutativity_for_addition ?24 ?25
% 133.19/33.66  Id : 142, {_}: add ?234 (add ?235 ?236) =?= add ?235 (add ?236 ?234) [236, 235, 234] by Super 11 with 12 at 3
% 133.19/33.66  Id : 311, {_}: associator ?37 ?38 ?39 =>= add (additive_inverse (multiply ?37 (multiply ?38 ?39))) (multiply (multiply ?37 ?38) ?39) [39, 38, 37] by Demod 15 with 11 at 3
% 133.19/33.66  Id : 147, {_}: add ?252 (add (additive_inverse ?252) ?253) =>= add additive_identity ?253 [253, 252] by Super 144 with 7 at 1,3
% 133.19/33.66  Id : 167, {_}: add ?252 (add (additive_inverse ?252) ?253) =>= ?253 [253, 252] by Demod 147 with 2 at 3
% 133.19/33.66  Id : 1264, {_}: add ?1086 (add (additive_inverse ?1086) ?1087) =>= ?1087 [1087, 1086] by Demod 147 with 2 at 3
% 133.19/33.66  Id : 1324, {_}: add (additive_inverse ?1133) (add ?1133 ?1134) =>= ?1134 [1134, 1133] by Super 1264 with 8 at 1,2,2
% 133.19/33.66  Id : 1459, {_}: add (additive_inverse ?1271) (add ?1272 ?1271) =>= ?1272 [1272, 1271] by Super 1324 with 11 at 2,2
% 133.19/33.66  Id : 1328, {_}: add (additive_inverse ?1142) (add ?1143 ?1142) =>= ?1143 [1143, 1142] by Super 1324 with 11 at 2,2
% 133.19/33.66  Id : 1468, {_}: add (additive_inverse (add ?1297 ?1298)) ?1297 =>= additive_inverse ?1298 [1298, 1297] by Super 1459 with 1328 at 2,2
% 133.19/33.66  Id : 1499, {_}: add ?1297 (additive_inverse (add ?1297 ?1298)) =>= additive_inverse ?1298 [1298, 1297] by Demod 1468 with 11 at 2
% 133.19/33.66  Id : 1836, {_}: add ?1781 (additive_inverse ?1782) =<= additive_inverse (add (additive_inverse ?1781) ?1782) [1782, 1781] by Super 167 with 1499 at 2,2
% 133.19/33.66  Id : 1929, {_}: additive_inverse (add ?1896 (additive_inverse ?1897)) =<= add (additive_inverse ?1896) ?1897 [1897, 1896] by Super 8 with 1836 at 1,2
% 133.42/33.66  Id : 148, {_}: add ?255 (add ?256 ?257) =<= add (add ?256 ?255) ?257 [257, 256, 255] by Super 144 with 11 at 1,3
% 133.42/33.66  Id : 168, {_}: add ?255 (add ?256 ?257) =?= add ?256 (add ?255 ?257) [257, 256, 255] by Demod 148 with 12 at 3
% 133.42/33.66  Id : 1265, {_}: add (additive_inverse ?1089) (add ?1089 ?1090) =>= ?1090 [1090, 1089] by Super 1264 with 8 at 1,2,2
% 133.42/33.66  Id : 1466, {_}: add (additive_inverse (add ?1291 ?1292)) ?1292 =>= additive_inverse ?1291 [1292, 1291] by Super 1459 with 1265 at 2,2
% 133.42/33.66  Id : 1497, {_}: add ?1292 (additive_inverse (add ?1291 ?1292)) =>= additive_inverse ?1291 [1291, 1292] by Demod 1466 with 11 at 2
% 133.42/33.66  Id : 3202, {_}: additive_identity === additive_identity [] by Demod 3201 with 7 at 2
% 133.42/33.66  Id : 3201, {_}: add (multiply a (multiply (multiply b c) d)) (additive_inverse (multiply a (multiply (multiply b c) d))) =>= additive_identity [] by Demod 3200 with 1497 at 2,2
% 133.42/33.66  Id : 3200, {_}: add (multiply a (multiply (multiply b c) d)) (add (multiply (multiply (multiply a b) c) d) (additive_inverse (add (multiply a (multiply (multiply b c) d)) (multiply (multiply (multiply a b) c) d)))) =>= additive_identity [] by Demod 3199 with 8 at 2,1,2,2,2
% 133.42/33.66  Id : 3199, {_}: add (multiply a (multiply (multiply b c) d)) (add (multiply (multiply (multiply a b) c) d) (additive_inverse (add (multiply a (multiply (multiply b c) d)) (additive_inverse (additive_inverse (multiply (multiply (multiply a b) c) d)))))) =>= additive_identity [] by Demod 3198 with 1499 at 2,1,2,2,2
% 133.42/33.66  Id : 3198, {_}: add (multiply a (multiply (multiply b c) d)) (add (multiply (multiply (multiply a b) c) d) (additive_inverse (add (multiply a (multiply (multiply b c) d)) (add (multiply (multiply a (multiply b c)) d) (additive_inverse (add (multiply (multiply a (multiply b c)) d) (additive_inverse (multiply (multiply (multiply a b) c) d)))))))) =>= additive_identity [] by Demod 3197 with 1929 at 2,2,1,2,2,2
% 133.42/33.66  Id : 3197, {_}: add (multiply a (multiply (multiply b c) d)) (add (multiply (multiply (multiply a b) c) d) (additive_inverse (add (multiply a (multiply (multiply b c) d)) (add (multiply (multiply a (multiply b c)) d) (add (additive_inverse (multiply (multiply a (multiply b c)) d)) (multiply (multiply (multiply a b) c) d)))))) =>= additive_identity [] by Demod 3196 with 168 at 1,2,2,2
% 133.42/33.66  Id : 3196, {_}: add (multiply a (multiply (multiply b c) d)) (add (multiply (multiply (multiply a b) c) d) (additive_inverse (add (multiply (multiply a (multiply b c)) d) (add (multiply a (multiply (multiply b c) d)) (add (additive_inverse (multiply (multiply a (multiply b c)) d)) (multiply (multiply (multiply a b) c) d)))))) =>= additive_identity [] by Demod 3195 with 8 at 2
% 133.42/33.66  Id : 3195, {_}: additive_inverse (additive_inverse (add (multiply a (multiply (multiply b c) d)) (add (multiply (multiply (multiply a b) c) d) (additive_inverse (add (multiply (multiply a (multiply b c)) d) (add (multiply a (multiply (multiply b c) d)) (add (additive_inverse (multiply (multiply a (multiply b c)) d)) (multiply (multiply (multiply a b) c) d)))))))) =>= additive_identity [] by Demod 3194 with 1499 at 1,2
% 133.42/33.66  Id : 3194, {_}: additive_inverse (add (multiply a (multiply b (multiply c d))) (additive_inverse (add (multiply a (multiply b (multiply c d))) (add (multiply a (multiply (multiply b c) d)) (add (multiply (multiply (multiply a b) c) d) (additive_inverse (add (multiply (multiply a (multiply b c)) d) (add (multiply a (multiply (multiply b c) d)) (add (additive_inverse (multiply (multiply a (multiply b c)) d)) (multiply (multiply (multiply a b) c) d)))))))))) =>= additive_identity [] by Demod 3193 with 168 at 1,2,1,2
% 133.42/33.66  Id : 3193, {_}: additive_inverse (add (multiply a (multiply b (multiply c d))) (additive_inverse (add (multiply a (multiply (multiply b c) d)) (add (multiply a (multiply b (multiply c d))) (add (multiply (multiply (multiply a b) c) d) (additive_inverse (add (multiply (multiply a (multiply b c)) d) (add (multiply a (multiply (multiply b c) d)) (add (additive_inverse (multiply (multiply a (multiply b c)) d)) (multiply (multiply (multiply a b) c) d)))))))))) =>= additive_identity [] by Demod 3192 with 168 at 2,1,2,1,2
% 133.42/33.66  Id : 3192, {_}: additive_inverse (add (multiply a (multiply b (multiply c d))) (additive_inverse (add (multiply a (multiply (multiply b c) d)) (add (multiply (multiply (multiply a b) c) d) (add (multiply a (multiply b (multiply c d))) (additive_inverse (add (multiply (multiply a (multiply b c)) d) (add (multiply a (multiply (multiply b c) d)) (add (additive_inverse (multiply (multiply a (multiply b c)) d)) (multiply (multiply (multiply a b) c) d)))))))))) =>= additive_identity [] by Demod 3191 with 8 at 2,2,1,2,1,2
% 133.42/33.66  Id : 3191, {_}: additive_inverse (add (multiply a (multiply b (multiply c d))) (additive_inverse (add (multiply a (multiply (multiply b c) d)) (add (multiply (multiply (multiply a b) c) d) (additive_inverse (additive_inverse (add (multiply a (multiply b (multiply c d))) (additive_inverse (add (multiply (multiply a (multiply b c)) d) (add (multiply a (multiply (multiply b c) d)) (add (additive_inverse (multiply (multiply a (multiply b c)) d)) (multiply (multiply (multiply a b) c) d)))))))))))) =>= additive_identity [] by Demod 3190 with 1929 at 1,2,2,1,2,1,2
% 133.42/33.67  Id : 3190, {_}: additive_inverse (add (multiply a (multiply b (multiply c d))) (additive_inverse (add (multiply a (multiply (multiply b c) d)) (add (multiply (multiply (multiply a b) c) d) (additive_inverse (add (additive_inverse (multiply a (multiply b (multiply c d)))) (add (multiply (multiply a (multiply b c)) d) (add (multiply a (multiply (multiply b c) d)) (add (additive_inverse (multiply (multiply a (multiply b c)) d)) (multiply (multiply (multiply a b) c) d)))))))))) =>= additive_identity [] by Demod 3189 with 168 at 1,2,2,1,2,1,2
% 133.42/33.67  Id : 3189, {_}: additive_inverse (add (multiply a (multiply b (multiply c d))) (additive_inverse (add (multiply a (multiply (multiply b c) d)) (add (multiply (multiply (multiply a b) c) d) (additive_inverse (add (multiply (multiply a (multiply b c)) d) (add (additive_inverse (multiply a (multiply b (multiply c d)))) (add (multiply a (multiply (multiply b c) d)) (add (additive_inverse (multiply (multiply a (multiply b c)) d)) (multiply (multiply (multiply a b) c) d)))))))))) =>= additive_identity [] by Demod 3188 with 168 at 1,2,1,2
% 133.42/33.67  Id : 3188, {_}: additive_inverse (add (multiply a (multiply b (multiply c d))) (additive_inverse (add (multiply (multiply (multiply a b) c) d) (add (multiply a (multiply (multiply b c) d)) (additive_inverse (add (multiply (multiply a (multiply b c)) d) (add (additive_inverse (multiply a (multiply b (multiply c d)))) (add (multiply a (multiply (multiply b c) d)) (add (additive_inverse (multiply (multiply a (multiply b c)) d)) (multiply (multiply (multiply a b) c) d)))))))))) =>= additive_identity [] by Demod 3187 with 1499 at 2,1,2
% 133.42/33.67  Id : 3187, {_}: additive_inverse (add (multiply a (multiply b (multiply c d))) (add (multiply (multiply a b) (multiply c d)) (additive_inverse (add (multiply (multiply a b) (multiply c d)) (add (multiply (multiply (multiply a b) c) d) (add (multiply a (multiply (multiply b c) d)) (additive_inverse (add (multiply (multiply a (multiply b c)) d) (add (additive_inverse (multiply a (multiply b (multiply c d)))) (add (multiply a (multiply (multiply b c) d)) (add (additive_inverse (multiply (multiply a (multiply b c)) d)) (multiply (multiply (multiply a b) c) d)))))))))))) =>= additive_identity [] by Demod 3186 with 168 at 1,2,2,1,2
% 133.42/33.67  Id : 3186, {_}: additive_inverse (add (multiply a (multiply b (multiply c d))) (add (multiply (multiply a b) (multiply c d)) (additive_inverse (add (multiply (multiply (multiply a b) c) d) (add (multiply (multiply a b) (multiply c d)) (add (multiply a (multiply (multiply b c) d)) (additive_inverse (add (multiply (multiply a (multiply b c)) d) (add (additive_inverse (multiply a (multiply b (multiply c d)))) (add (multiply a (multiply (multiply b c) d)) (add (additive_inverse (multiply (multiply a (multiply b c)) d)) (multiply (multiply (multiply a b) c) d)))))))))))) =>= additive_identity [] by Demod 3185 with 8 at 2,1,2
% 133.42/33.67  Id : 3185, {_}: additive_inverse (add (multiply a (multiply b (multiply c d))) (additive_inverse (additive_inverse (add (multiply (multiply a b) (multiply c d)) (additive_inverse (add (multiply (multiply (multiply a b) c) d) (add (multiply (multiply a b) (multiply c d)) (add (multiply a (multiply (multiply b c) d)) (additive_inverse (add (multiply (multiply a (multiply b c)) d) (add (additive_inverse (multiply a (multiply b (multiply c d)))) (add (multiply a (multiply (multiply b c) d)) (add (additive_inverse (multiply (multiply a (multiply b c)) d)) (multiply (multiply (multiply a b) c) d)))))))))))))) =>= additive_identity [] by Demod 3184 with 1929 at 1,2,1,2
% 133.42/33.67  Id : 3184, {_}: additive_inverse (add (multiply a (multiply b (multiply c d))) (additive_inverse (add (additive_inverse (multiply (multiply a b) (multiply c d))) (add (multiply (multiply (multiply a b) c) d) (add (multiply (multiply a b) (multiply c d)) (add (multiply a (multiply (multiply b c) d)) (additive_inverse (add (multiply (multiply a (multiply b c)) d) (add (additive_inverse (multiply a (multiply b (multiply c d)))) (add (multiply a (multiply (multiply b c) d)) (add (additive_inverse (multiply (multiply a (multiply b c)) d)) (multiply (multiply (multiply a b) c) d)))))))))))) =>= additive_identity [] by Demod 2014 with 1929 at 2
% 133.42/33.67  Id : 2014, {_}: add (additive_inverse (multiply a (multiply b (multiply c d)))) (add (additive_inverse (multiply (multiply a b) (multiply c d))) (add (multiply (multiply (multiply a b) c) d) (add (multiply (multiply a b) (multiply c d)) (add (multiply a (multiply (multiply b c) d)) (additive_inverse (add (multiply (multiply a (multiply b c)) d) (add (additive_inverse (multiply a (multiply b (multiply c d)))) (add (multiply a (multiply (multiply b c) d)) (add (additive_inverse (multiply (multiply a (multiply b c)) d)) (multiply (multiply (multiply a b) c) d)))))))))) =>= additive_identity [] by Demod 2013 with 18 at 1,2,2,2,1,2,2,2,2,2,2
% 133.42/33.67  Id : 2013, {_}: add (additive_inverse (multiply a (multiply b (multiply c d)))) (add (additive_inverse (multiply (multiply a b) (multiply c d))) (add (multiply (multiply (multiply a b) c) d) (add (multiply (multiply a b) (multiply c d)) (add (multiply a (multiply (multiply b c) d)) (additive_inverse (add (multiply (multiply a (multiply b c)) d) (add (additive_inverse (multiply a (multiply b (multiply c d)))) (add (multiply a (multiply (multiply b c) d)) (add (multiply (additive_inverse (multiply a (multiply b c))) d) (multiply (multiply (multiply a b) c) d)))))))))) =>= additive_identity [] by Demod 2012 with 19 at 1,2,1,2,2,2,2,2,2
% 133.42/33.67  Id : 2012, {_}: add (additive_inverse (multiply a (multiply b (multiply c d)))) (add (additive_inverse (multiply (multiply a b) (multiply c d))) (add (multiply (multiply (multiply a b) c) d) (add (multiply (multiply a b) (multiply c d)) (add (multiply a (multiply (multiply b c) d)) (additive_inverse (add (multiply (multiply a (multiply b c)) d) (add (multiply a (additive_inverse (multiply b (multiply c d)))) (add (multiply a (multiply (multiply b c) d)) (add (multiply (additive_inverse (multiply a (multiply b c))) d) (multiply (multiply (multiply a b) c) d)))))))))) =>= additive_identity [] by Demod 2011 with 12 at 2,1,2,2,2,2,2,2
% 133.42/33.67  Id : 2011, {_}: add (additive_inverse (multiply a (multiply b (multiply c d)))) (add (additive_inverse (multiply (multiply a b) (multiply c d))) (add (multiply (multiply (multiply a b) c) d) (add (multiply (multiply a b) (multiply c d)) (add (multiply a (multiply (multiply b c) d)) (additive_inverse (add (multiply (multiply a (multiply b c)) d) (add (add (multiply a (additive_inverse (multiply b (multiply c d)))) (multiply a (multiply (multiply b c) d))) (add (multiply (additive_inverse (multiply a (multiply b c))) d) (multiply (multiply (multiply a b) c) d))))))))) =>= additive_identity [] by Demod 2010 with 10 at 2,2,1,2,2,2,2,2,2
% 133.42/33.67  Id : 2010, {_}: add (additive_inverse (multiply a (multiply b (multiply c d)))) (add (additive_inverse (multiply (multiply a b) (multiply c d))) (add (multiply (multiply (multiply a b) c) d) (add (multiply (multiply a b) (multiply c d)) (add (multiply a (multiply (multiply b c) d)) (additive_inverse (add (multiply (multiply a (multiply b c)) d) (add (add (multiply a (additive_inverse (multiply b (multiply c d)))) (multiply a (multiply (multiply b c) d))) (multiply (add (additive_inverse (multiply a (multiply b c))) (multiply (multiply a b) c)) d)))))))) =>= additive_identity [] by Demod 2009 with 9 at 1,2,1,2,2,2,2,2,2
% 133.42/33.67  Id : 2009, {_}: add (additive_inverse (multiply a (multiply b (multiply c d)))) (add (additive_inverse (multiply (multiply a b) (multiply c d))) (add (multiply (multiply (multiply a b) c) d) (add (multiply (multiply a b) (multiply c d)) (add (multiply a (multiply (multiply b c) d)) (additive_inverse (add (multiply (multiply a (multiply b c)) d) (add (multiply a (add (additive_inverse (multiply b (multiply c d))) (multiply (multiply b c) d))) (multiply (add (additive_inverse (multiply a (multiply b c))) (multiply (multiply a b) c)) d)))))))) =>= additive_identity [] by Demod 2008 with 1836 at 2,2,2,2,2
% 133.42/33.67  Id : 2008, {_}: add (additive_inverse (multiply a (multiply b (multiply c d)))) (add (additive_inverse (multiply (multiply a b) (multiply c d))) (add (multiply (multiply (multiply a b) c) d) (add (multiply (multiply a b) (multiply c d)) (additive_inverse (add (additive_inverse (multiply a (multiply (multiply b c) d))) (add (multiply (multiply a (multiply b c)) d) (add (multiply a (add (additive_inverse (multiply b (multiply c d))) (multiply (multiply b c) d))) (multiply (add (additive_inverse (multiply a (multiply b c))) (multiply (multiply a b) c)) d)))))))) =>= additive_identity [] by Demod 2007 with 12 at 1,2,2,2,2,2
% 133.42/33.67  Id : 2007, {_}: add (additive_inverse (multiply a (multiply b (multiply c d)))) (add (additive_inverse (multiply (multiply a b) (multiply c d))) (add (multiply (multiply (multiply a b) c) d) (add (multiply (multiply a b) (multiply c d)) (additive_inverse (add (add (additive_inverse (multiply a (multiply (multiply b c) d))) (multiply (multiply a (multiply b c)) d)) (add (multiply a (add (additive_inverse (multiply b (multiply c d))) (multiply (multiply b c) d))) (multiply (add (additive_inverse (multiply a (multiply b c))) (multiply (multiply a b) c)) d))))))) =>= additive_identity [] by Demod 2006 with 12 at 1,2,2,2,2,2
% 133.42/33.67  Id : 2006, {_}: add (additive_inverse (multiply a (multiply b (multiply c d)))) (add (additive_inverse (multiply (multiply a b) (multiply c d))) (add (multiply (multiply (multiply a b) c) d) (add (multiply (multiply a b) (multiply c d)) (additive_inverse (add (add (add (additive_inverse (multiply a (multiply (multiply b c) d))) (multiply (multiply a (multiply b c)) d)) (multiply a (add (additive_inverse (multiply b (multiply c d))) (multiply (multiply b c) d)))) (multiply (add (additive_inverse (multiply a (multiply b c))) (multiply (multiply a b) c)) d)))))) =>= additive_identity [] by Demod 2005 with 11 at 1,2,2,2,2,2
% 133.42/33.67  Id : 2005, {_}: add (additive_inverse (multiply a (multiply b (multiply c d)))) (add (additive_inverse (multiply (multiply a b) (multiply c d))) (add (multiply (multiply (multiply a b) c) d) (add (multiply (multiply a b) (multiply c d)) (additive_inverse (add (multiply (add (additive_inverse (multiply a (multiply b c))) (multiply (multiply a b) c)) d) (add (add (additive_inverse (multiply a (multiply (multiply b c) d))) (multiply (multiply a (multiply b c)) d)) (multiply a (add (additive_inverse (multiply b (multiply c d))) (multiply (multiply b c) d))))))))) =>= additive_identity [] by Demod 2004 with 311 at 2,2,2,1,2,2,2,2,2
% 133.42/33.67  Id : 2004, {_}: add (additive_inverse (multiply a (multiply b (multiply c d)))) (add (additive_inverse (multiply (multiply a b) (multiply c d))) (add (multiply (multiply (multiply a b) c) d) (add (multiply (multiply a b) (multiply c d)) (additive_inverse (add (multiply (add (additive_inverse (multiply a (multiply b c))) (multiply (multiply a b) c)) d) (add (add (additive_inverse (multiply a (multiply (multiply b c) d))) (multiply (multiply a (multiply b c)) d)) (multiply a (associator b c d)))))))) =>= additive_identity [] by Demod 2003 with 311 at 1,2,1,2,2,2,2,2
% 133.42/33.67  Id : 2003, {_}: add (additive_inverse (multiply a (multiply b (multiply c d)))) (add (additive_inverse (multiply (multiply a b) (multiply c d))) (add (multiply (multiply (multiply a b) c) d) (add (multiply (multiply a b) (multiply c d)) (additive_inverse (add (multiply (add (additive_inverse (multiply a (multiply b c))) (multiply (multiply a b) c)) d) (add (associator a (multiply b c) d) (multiply a (associator b c d)))))))) =>= additive_identity [] by Demod 2002 with 311 at 1,1,1,2,2,2,2,2
% 133.42/33.67  Id : 2002, {_}: add (additive_inverse (multiply a (multiply b (multiply c d)))) (add (additive_inverse (multiply (multiply a b) (multiply c d))) (add (multiply (multiply (multiply a b) c) d) (add (multiply (multiply a b) (multiply c d)) (additive_inverse (add (multiply (associator a b c) d) (add (associator a (multiply b c) d) (multiply a (associator b c d)))))))) =>= additive_identity [] by Demod 2001 with 12 at 2,2
% 133.42/33.67  Id : 2001, {_}: add (additive_inverse (multiply a (multiply b (multiply c d)))) (add (add (additive_inverse (multiply (multiply a b) (multiply c d))) (multiply (multiply (multiply a b) c) d)) (add (multiply (multiply a b) (multiply c d)) (additive_inverse (add (multiply (associator a b c) d) (add (associator a (multiply b c) d) (multiply a (associator b c d))))))) =>= additive_identity [] by Demod 2000 with 142 at 2,2
% 133.42/33.67  Id : 2000, {_}: add (additive_inverse (multiply a (multiply b (multiply c d)))) (add (multiply (multiply a b) (multiply c d)) (add (additive_inverse (add (multiply (associator a b c) d) (add (associator a (multiply b c) d) (multiply a (associator b c d))))) (add (additive_inverse (multiply (multiply a b) (multiply c d))) (multiply (multiply (multiply a b) c) d)))) =>= additive_identity [] by Demod 1999 with 12 at 2
% 133.42/33.67  Id : 1999, {_}: add (add (additive_inverse (multiply a (multiply b (multiply c d)))) (multiply (multiply a b) (multiply c d))) (add (additive_inverse (add (multiply (associator a b c) d) (add (associator a (multiply b c) d) (multiply a (associator b c d))))) (add (additive_inverse (multiply (multiply a b) (multiply c d))) (multiply (multiply (multiply a b) c) d))) =>= additive_identity [] by Demod 1998 with 311 at 2,2,2
% 133.42/33.67  Id : 1998, {_}: add (add (additive_inverse (multiply a (multiply b (multiply c d)))) (multiply (multiply a b) (multiply c d))) (add (additive_inverse (add (multiply (associator a b c) d) (add (associator a (multiply b c) d) (multiply a (associator b c d))))) (associator (multiply a b) c d)) =>= additive_identity [] by Demod 1997 with 11 at 1,1,2,2
% 133.42/33.67  Id : 1997, {_}: add (add (additive_inverse (multiply a (multiply b (multiply c d)))) (multiply (multiply a b) (multiply c d))) (add (additive_inverse (add (add (associator a (multiply b c) d) (multiply a (associator b c d))) (multiply (associator a b c) d))) (associator (multiply a b) c d)) =>= additive_identity [] by Demod 1996 with 311 at 1,2
% 133.42/33.67  Id : 1996, {_}: add (associator a b (multiply c d)) (add (additive_inverse (add (add (associator a (multiply b c) d) (multiply a (associator b c d))) (multiply (associator a b c) d))) (associator (multiply a b) c d)) =>= additive_identity [] by Demod 1995 with 142 at 2
% 133.42/33.67  Id : 1995, {_}: add (additive_inverse (add (add (associator a (multiply b c) d) (multiply a (associator b c d))) (multiply (associator a b c) d))) (add (associator (multiply a b) c d) (associator a b (multiply c d))) =>= additive_identity [] by Demod 1 with 11 at 2
% 133.42/33.67  Id :   1, {_}: add (add (associator (multiply a b) c d) (associator a b (multiply c d))) (additive_inverse (add (add (associator a (multiply b c) d) (multiply a (associator b c d))) (multiply (associator a b c) d))) =>= additive_identity [] by prove_teichmuller_identity
% 133.42/33.67  % SZS output end CNFRefutation for theBenchmark.p
% 133.42/33.67  6467: solved /export/starexec/sandbox/benchmark/theBenchmark.p in 33.327457 using lpo
%------------------------------------------------------------------------------