TSTP Solution File: GRP002-4 by Matita---1.0
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%------------------------------------------------------------------------------
% File : Matita---1.0
% Problem : GRP002-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : matitaprover --timeout %d --tptppath /export/starexec/sandbox2/benchmark %s
% Computer : n009.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 10:28:21 EDT 2022
% Result : Unsatisfiable 6.02s 1.83s
% Output : CNFRefutation 6.02s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP002-4 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : matitaprover --timeout %d --tptppath /export/starexec/sandbox2/benchmark %s
% 0.14/0.34 % Computer : n009.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Mon Jun 13 16:22:53 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.34 2872: Facts:
% 0.14/0.34 2872: Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
% 0.14/0.34 2872: Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
% 0.14/0.34 2872: Id : 4, {_}:
% 0.14/0.34 multiply (multiply ?6 ?7) ?8 =?= multiply ?6 (multiply ?7 ?8)
% 0.14/0.34 [8, 7, 6] by associativity ?6 ?7 ?8
% 0.14/0.34 2872: Id : 5, {_}: multiply ?10 identity =>= ?10 [10] by right_identity ?10
% 0.14/0.34 2872: Id : 6, {_}:
% 0.14/0.34 multiply ?12 (inverse ?12) =>= identity
% 0.14/0.34 [12] by right_inverse ?12
% 0.14/0.34 2872: Id : 7, {_}:
% 0.14/0.34 commutator ?14 ?15
% 0.14/0.34 =<=
% 0.14/0.34 multiply ?14 (multiply ?15 (multiply (inverse ?14) (inverse ?15)))
% 0.14/0.34 [15, 14] by commutator ?14 ?15
% 0.14/0.34 2872: Id : 8, {_}:
% 0.14/0.34 multiply ?17 (multiply ?17 ?17) =>= identity
% 0.14/0.34 [17] by x_cubed_is_identity ?17
% 0.14/0.34 2872: Goal:
% 0.14/0.34 2872: Id : 1, {_}:
% 0.14/0.34 commutator (commutator a b) b =>= identity
% 0.14/0.34 [] by prove_commutator
% 6.02/1.83 Statistics :
% 6.02/1.83 Max weight : 26
% 6.02/1.83 Found proof, 1.487149s
% 6.02/1.83 % SZS status Unsatisfiable for theBenchmark.p
% 6.02/1.83 % SZS output start CNFRefutation for theBenchmark.p
% 6.02/1.83 Id : 8, {_}: multiply ?17 (multiply ?17 ?17) =>= identity [17] by x_cubed_is_identity ?17
% 6.02/1.83 Id : 5, {_}: multiply ?10 identity =>= ?10 [10] by right_identity ?10
% 6.02/1.83 Id : 6, {_}: multiply ?12 (inverse ?12) =>= identity [12] by right_inverse ?12
% 6.02/1.83 Id : 4, {_}: multiply (multiply ?6 ?7) ?8 =>= multiply ?6 (multiply ?7 ?8) [8, 7, 6] by associativity ?6 ?7 ?8
% 6.02/1.83 Id : 2, {_}: multiply identity ?2 =>= ?2 [2] by left_identity ?2
% 6.02/1.83 Id : 3, {_}: multiply (inverse ?4) ?4 =>= identity [4] by left_inverse ?4
% 6.02/1.83 Id : 13, {_}: multiply (multiply ?26 ?27) ?28 =>= multiply ?26 (multiply ?27 ?28) [28, 27, 26] by associativity ?26 ?27 ?28
% 6.02/1.83 Id : 7, {_}: commutator ?14 ?15 =<= multiply ?14 (multiply ?15 (multiply (inverse ?14) (inverse ?15))) [15, 14] by commutator ?14 ?15
% 6.02/1.83 Id : 15, {_}: multiply identity ?33 =<= multiply (inverse ?34) (multiply ?34 ?33) [34, 33] by Super 13 with 3 at 1,2
% 6.02/1.83 Id : 19, {_}: ?33 =<= multiply (inverse ?34) (multiply ?34 ?33) [34, 33] by Demod 15 with 2 at 2
% 6.02/1.83 Id : 36, {_}: identity =<= multiply ?65 (multiply ?66 (inverse (multiply ?65 ?66))) [66, 65] by Super 4 with 6 at 2
% 6.02/1.83 Id : 156, {_}: multiply ?214 (inverse (multiply ?215 ?214)) =>= multiply (inverse ?215) identity [215, 214] by Super 19 with 36 at 2,3
% 6.02/1.83 Id : 182, {_}: multiply ?214 (inverse (multiply ?215 ?214)) =>= inverse ?215 [215, 214] by Demod 156 with 5 at 3
% 6.02/1.83 Id : 429, {_}: inverse (multiply ?457 ?458) =<= multiply (inverse ?458) (inverse ?457) [458, 457] by Super 19 with 182 at 2,3
% 6.02/1.83 Id : 479, {_}: commutator ?14 ?15 =<= multiply ?14 (multiply ?15 (inverse (multiply ?15 ?14))) [15, 14] by Demod 7 with 429 at 2,2,3
% 6.02/1.83 Id : 487, {_}: multiply (inverse (multiply ?538 ?539)) ?540 =<= multiply (inverse ?539) (multiply (inverse ?538) ?540) [540, 539, 538] by Super 4 with 429 at 1,2
% 6.02/1.83 Id : 2599, {_}: commutator (inverse ?2949) (inverse ?2950) =<= multiply (inverse (multiply ?2950 ?2949)) (inverse (multiply (inverse ?2950) (inverse ?2949))) [2950, 2949] by Super 479 with 487 at 3
% 6.02/1.83 Id : 2663, {_}: commutator (inverse ?2949) (inverse ?2950) =<= inverse (multiply (multiply (inverse ?2950) (inverse ?2949)) (multiply ?2950 ?2949)) [2950, 2949] by Demod 2599 with 429 at 3
% 6.02/1.83 Id : 2664, {_}: commutator (inverse ?2949) (inverse ?2950) =<= inverse (multiply (inverse ?2950) (multiply (inverse ?2949) (multiply ?2950 ?2949))) [2950, 2949] by Demod 2663 with 4 at 1,3
% 6.02/1.83 Id : 491, {_}: inverse (multiply ?550 ?551) =<= multiply (inverse ?551) (inverse ?550) [551, 550] by Super 19 with 182 at 2,3
% 6.02/1.83 Id : 95, {_}: ?148 =<= multiply (inverse ?149) (multiply ?149 ?148) [149, 148] by Demod 15 with 2 at 2
% 6.02/1.83 Id : 97, {_}: ?153 =<= multiply (inverse (inverse ?153)) identity [153] by Super 95 with 3 at 2,3
% 6.02/1.83 Id : 109, {_}: ?153 =<= inverse (inverse ?153) [153] by Demod 97 with 5 at 3
% 6.02/1.83 Id : 493, {_}: inverse (multiply (inverse ?555) ?556) =>= multiply (inverse ?556) ?555 [556, 555] by Super 491 with 109 at 2,3
% 6.02/1.83 Id : 2665, {_}: commutator (inverse ?2949) (inverse ?2950) =<= multiply (inverse (multiply (inverse ?2949) (multiply ?2950 ?2949))) ?2950 [2950, 2949] by Demod 2664 with 493 at 3
% 6.02/1.83 Id : 2666, {_}: commutator (inverse ?2949) (inverse ?2950) =<= multiply (multiply (inverse (multiply ?2950 ?2949)) ?2949) ?2950 [2950, 2949] by Demod 2665 with 493 at 1,3
% 6.02/1.83 Id : 2667, {_}: commutator (inverse ?2949) (inverse ?2950) =<= multiply (inverse (multiply ?2950 ?2949)) (multiply ?2949 ?2950) [2950, 2949] by Demod 2666 with 4 at 3
% 6.02/1.83 Id : 436, {_}: multiply ?479 (inverse (multiply ?480 ?479)) =>= inverse ?480 [480, 479] by Demod 156 with 5 at 3
% 6.02/1.83 Id : 443, {_}: multiply (inverse (multiply ?496 ?497)) (inverse (inverse ?496)) =>= inverse ?497 [497, 496] by Super 436 with 182 at 1,2,2
% 6.02/1.83 Id : 464, {_}: multiply (inverse (multiply ?496 ?497)) ?496 =>= inverse ?497 [497, 496] by Demod 443 with 109 at 2,2
% 6.02/1.83 Id : 44, {_}: multiply (commutator ?78 ?79) ?80 =<= multiply ?78 (multiply (multiply ?79 (multiply (inverse ?78) (inverse ?79))) ?80) [80, 79, 78] by Super 4 with 7 at 1,2
% 6.02/1.83 Id : 54, {_}: multiply (commutator ?78 ?79) ?80 =<= multiply ?78 (multiply ?79 (multiply (multiply (inverse ?78) (inverse ?79)) ?80)) [80, 79, 78] by Demod 44 with 4 at 2,3
% 6.02/1.83 Id : 1724, {_}: multiply (commutator ?2010 ?2011) ?2012 =<= multiply ?2010 (multiply ?2011 (multiply (inverse ?2010) (multiply (inverse ?2011) ?2012))) [2012, 2011, 2010] by Demod 54 with 4 at 2,2,3
% 6.02/1.83 Id : 45, {_}: commutator (multiply ?82 ?83) ?84 =<= multiply ?82 (multiply ?83 (multiply ?84 (multiply (inverse (multiply ?82 ?83)) (inverse ?84)))) [84, 83, 82] by Super 4 with 7 at 2
% 6.02/1.83 Id : 604, {_}: commutator (multiply ?82 ?83) ?84 =<= multiply ?82 (multiply ?83 (multiply ?84 (inverse (multiply ?84 (multiply ?82 ?83))))) [84, 83, 82] by Demod 45 with 429 at 2,2,2,3
% 6.02/1.83 Id : 1762, {_}: multiply (commutator ?2155 ?2156) (inverse (multiply (inverse ?2156) (multiply ?2156 (inverse ?2155)))) =>= multiply ?2155 (commutator (multiply ?2156 (inverse ?2155)) (inverse ?2156)) [2156, 2155] by Super 1724 with 604 at 2,3
% 6.02/1.83 Id : 1900, {_}: multiply (commutator ?2155 ?2156) (multiply (inverse (multiply ?2156 (inverse ?2155))) ?2156) =>= multiply ?2155 (commutator (multiply ?2156 (inverse ?2155)) (inverse ?2156)) [2156, 2155] by Demod 1762 with 493 at 2,2
% 6.02/1.83 Id : 616, {_}: commutator (multiply ?687 ?688) ?689 =<= multiply ?687 (multiply ?688 (multiply ?689 (inverse (multiply ?689 (multiply ?687 ?688))))) [689, 688, 687] by Demod 45 with 429 at 2,2,2,3
% 6.02/1.83 Id : 634, {_}: commutator (multiply ?754 ?755) (inverse ?754) =<= multiply ?754 (multiply ?755 (multiply (inverse ?754) (inverse ?755))) [755, 754] by Super 616 with 19 at 1,2,2,2,3
% 6.02/1.83 Id : 735, {_}: commutator (multiply ?754 ?755) (inverse ?754) =<= multiply ?754 (multiply ?755 (inverse (multiply ?755 ?754))) [755, 754] by Demod 634 with 429 at 2,2,3
% 6.02/1.83 Id : 736, {_}: commutator (multiply ?754 ?755) (inverse ?754) =>= commutator ?754 ?755 [755, 754] by Demod 735 with 479 at 3
% 6.02/1.83 Id : 1901, {_}: multiply (commutator ?2155 ?2156) (multiply (inverse (multiply ?2156 (inverse ?2155))) ?2156) =>= multiply ?2155 (commutator ?2156 (inverse ?2155)) [2156, 2155] by Demod 1900 with 736 at 2,3
% 6.02/1.83 Id : 1902, {_}: multiply (commutator ?2155 ?2156) (inverse (inverse ?2155)) =>= multiply ?2155 (commutator ?2156 (inverse ?2155)) [2156, 2155] by Demod 1901 with 464 at 2,2
% 6.02/1.83 Id : 1903, {_}: multiply (commutator ?2155 ?2156) ?2155 =<= multiply ?2155 (commutator ?2156 (inverse ?2155)) [2156, 2155] by Demod 1902 with 109 at 2,2
% 6.02/1.83 Id : 2078, {_}: multiply (inverse (multiply (commutator ?2341 ?2342) ?2341)) ?2341 =>= inverse (commutator ?2342 (inverse ?2341)) [2342, 2341] by Super 464 with 1903 at 1,1,2
% 6.02/1.83 Id : 35, {_}: multiply identity ?62 =<= multiply ?63 (multiply (inverse ?63) ?62) [63, 62] by Super 4 with 6 at 1,2
% 6.02/1.83 Id : 42, {_}: ?62 =<= multiply ?63 (multiply (inverse ?63) ?62) [63, 62] by Demod 35 with 2 at 2
% 6.02/1.83 Id : 551, {_}: inverse (multiply ?612 (inverse ?613)) =>= multiply ?613 (inverse ?612) [613, 612] by Super 42 with 182 at 2,3
% 6.02/1.83 Id : 3221, {_}: inverse (multiply ?3523 (multiply ?3524 (inverse ?3525))) =>= multiply ?3525 (inverse (multiply ?3523 ?3524)) [3525, 3524, 3523] by Super 551 with 4 at 1,2
% 6.02/1.83 Id : 3243, {_}: inverse (commutator ?3606 ?3607) =<= multiply (multiply ?3607 ?3606) (inverse (multiply ?3606 ?3607)) [3607, 3606] by Super 3221 with 479 at 1,2
% 6.02/1.83 Id : 3369, {_}: inverse (commutator ?3606 ?3607) =<= multiply ?3607 (multiply ?3606 (inverse (multiply ?3606 ?3607))) [3607, 3606] by Demod 3243 with 4 at 3
% 6.02/1.83 Id : 3370, {_}: inverse (commutator ?3606 ?3607) =>= commutator ?3607 ?3606 [3607, 3606] by Demod 3369 with 479 at 3
% 6.02/1.83 Id : 21436, {_}: multiply (inverse (multiply (commutator ?2341 ?2342) ?2341)) ?2341 =>= commutator (inverse ?2341) ?2342 [2342, 2341] by Demod 2078 with 3370 at 3
% 6.02/1.83 Id : 3402, {_}: multiply (inverse (multiply (commutator ?3712 ?3713) ?3714)) ?3715 =>= multiply (inverse ?3714) (multiply (commutator ?3713 ?3712) ?3715) [3715, 3714, 3713, 3712] by Super 487 with 3370 at 1,2,3
% 6.02/1.83 Id : 29717, {_}: multiply (inverse ?2341) (multiply (commutator ?2342 ?2341) ?2341) =>= commutator (inverse ?2341) ?2342 [2342, 2341] by Demod 21436 with 3402 at 2
% 6.02/1.83 Id : 434, {_}: inverse (multiply ?473 (inverse ?474)) =>= multiply ?474 (inverse ?473) [474, 473] by Super 42 with 182 at 2,3
% 6.02/1.83 Id : 101, {_}: multiply ?163 ?163 =?= multiply (inverse ?163) identity [163] by Super 95 with 8 at 2,3
% 6.02/1.83 Id : 112, {_}: multiply ?163 ?163 =>= inverse ?163 [163] by Demod 101 with 5 at 3
% 6.02/1.83 Id : 229, {_}: multiply (inverse ?283) ?284 =<= multiply ?283 (multiply ?283 ?284) [284, 283] by Super 4 with 112 at 1,2
% 6.02/1.83 Id : 230, {_}: inverse (multiply ?286 ?287) =<= multiply ?286 (multiply ?287 (multiply ?286 ?287)) [287, 286] by Super 4 with 112 at 2
% 6.02/1.83 Id : 32914, {_}: multiply (inverse ?31323) (multiply ?31324 (multiply ?31323 ?31324)) =>= multiply ?31323 (inverse (multiply ?31323 ?31324)) [31324, 31323] by Super 229 with 230 at 2,3
% 6.02/1.83 Id : 430, {_}: multiply (inverse ?460) ?461 =<= multiply ?462 (multiply (inverse (multiply ?460 ?462)) ?461) [462, 461, 460] by Super 4 with 182 at 1,2
% 6.02/1.83 Id : 32974, {_}: multiply (inverse (inverse (multiply ?31514 ?31515))) (multiply (inverse ?31514) ?31515) =<= multiply (inverse (multiply ?31514 ?31515)) (inverse (multiply (inverse (multiply ?31514 ?31515)) ?31515)) [31515, 31514] by Super 32914 with 430 at 2,2
% 6.02/1.83 Id : 33774, {_}: multiply (inverse (multiply ?31514 (inverse (multiply ?31514 ?31515)))) ?31515 =<= multiply (inverse (multiply ?31514 ?31515)) (inverse (multiply (inverse (multiply ?31514 ?31515)) ?31515)) [31515, 31514] by Demod 32974 with 487 at 2
% 6.02/1.83 Id : 102, {_}: multiply ?165 (multiply (inverse ?166) (inverse ?165)) =?= multiply (inverse ?166) (commutator ?166 ?165) [166, 165] by Super 95 with 7 at 2,3
% 6.02/1.83 Id : 8354, {_}: multiply ?165 (inverse (multiply ?165 ?166)) =?= multiply (inverse ?166) (commutator ?166 ?165) [166, 165] by Demod 102 with 429 at 2,2
% 6.02/1.83 Id : 3384, {_}: inverse (multiply (commutator ?3645 ?3646) ?3647) =<= multiply (inverse ?3647) (commutator ?3646 ?3645) [3647, 3646, 3645] by Super 493 with 3370 at 1,1,2
% 6.02/1.83 Id : 8355, {_}: multiply ?165 (inverse (multiply ?165 ?166)) =?= inverse (multiply (commutator ?165 ?166) ?166) [166, 165] by Demod 8354 with 3384 at 3
% 6.02/1.83 Id : 33775, {_}: multiply (inverse (multiply ?31514 (inverse (multiply ?31514 ?31515)))) ?31515 =?= inverse (multiply (commutator (inverse (multiply ?31514 ?31515)) ?31515) ?31515) [31515, 31514] by Demod 33774 with 8355 at 3
% 6.02/1.83 Id : 33776, {_}: multiply (multiply (multiply ?31514 ?31515) (inverse ?31514)) ?31515 =?= inverse (multiply (commutator (inverse (multiply ?31514 ?31515)) ?31515) ?31515) [31515, 31514] by Demod 33775 with 434 at 1,2
% 6.02/1.83 Id : 997, {_}: commutator (multiply ?1060 ?1061) (inverse ?1060) =>= commutator ?1060 ?1061 [1061, 1060] by Demod 735 with 479 at 3
% 6.02/1.83 Id : 1013, {_}: commutator (inverse (multiply ?1105 ?1106)) (inverse (inverse ?1106)) =>= commutator (inverse ?1106) (inverse ?1105) [1106, 1105] by Super 997 with 429 at 1,2
% 6.02/1.83 Id : 1034, {_}: commutator (inverse (multiply ?1105 ?1106)) ?1106 =>= commutator (inverse ?1106) (inverse ?1105) [1106, 1105] by Demod 1013 with 109 at 2,2
% 6.02/1.83 Id : 33777, {_}: multiply (multiply (multiply ?31514 ?31515) (inverse ?31514)) ?31515 =>= inverse (multiply (commutator (inverse ?31515) (inverse ?31514)) ?31515) [31515, 31514] by Demod 33776 with 1034 at 1,1,3
% 6.02/1.83 Id : 33778, {_}: multiply (multiply ?31514 ?31515) (multiply (inverse ?31514) ?31515) =>= inverse (multiply (commutator (inverse ?31515) (inverse ?31514)) ?31515) [31515, 31514] by Demod 33777 with 4 at 2
% 6.02/1.83 Id : 33779, {_}: multiply ?31514 (multiply ?31515 (multiply (inverse ?31514) ?31515)) =>= inverse (multiply (commutator (inverse ?31515) (inverse ?31514)) ?31515) [31515, 31514] by Demod 33778 with 4 at 2
% 6.02/1.83 Id : 1732, {_}: multiply (commutator ?2040 ?2041) (inverse ?2041) =<= multiply ?2040 (multiply ?2041 (multiply (inverse ?2040) (inverse (inverse ?2041)))) [2041, 2040] by Super 1724 with 112 at 2,2,2,3
% 6.02/1.83 Id : 1832, {_}: multiply (commutator ?2040 ?2041) (inverse ?2041) =<= multiply ?2040 (multiply ?2041 (inverse (multiply (inverse ?2041) ?2040))) [2041, 2040] by Demod 1732 with 429 at 2,2,3
% 6.02/1.83 Id : 1833, {_}: multiply (commutator ?2040 ?2041) (inverse ?2041) =<= multiply ?2040 (multiply ?2041 (multiply (inverse ?2040) ?2041)) [2041, 2040] by Demod 1832 with 493 at 2,2,3
% 6.02/1.83 Id : 3386, {_}: inverse (multiply ?3653 (commutator ?3654 ?3655)) =<= multiply (commutator ?3655 ?3654) (inverse ?3653) [3655, 3654, 3653] by Super 429 with 3370 at 1,3
% 6.02/1.83 Id : 16724, {_}: inverse (multiply ?2041 (commutator ?2041 ?2040)) =<= multiply ?2040 (multiply ?2041 (multiply (inverse ?2040) ?2041)) [2040, 2041] by Demod 1833 with 3386 at 2
% 6.02/1.83 Id : 33780, {_}: inverse (multiply ?31515 (commutator ?31515 ?31514)) =<= inverse (multiply (commutator (inverse ?31515) (inverse ?31514)) ?31515) [31514, 31515] by Demod 33779 with 16724 at 2
% 6.02/1.83 Id : 34970, {_}: inverse (multiply (inverse ?32389) (commutator (inverse ?32389) ?32390)) =<= multiply ?32389 (inverse (commutator (inverse (inverse ?32389)) (inverse ?32390))) [32390, 32389] by Super 434 with 33780 at 2
% 6.02/1.83 Id : 35147, {_}: multiply (inverse (commutator (inverse ?32389) ?32390)) ?32389 =<= multiply ?32389 (inverse (commutator (inverse (inverse ?32389)) (inverse ?32390))) [32390, 32389] by Demod 34970 with 493 at 2
% 6.02/1.83 Id : 35148, {_}: multiply (inverse (commutator (inverse ?32389) ?32390)) ?32389 =<= multiply ?32389 (commutator (inverse ?32390) (inverse (inverse ?32389))) [32390, 32389] by Demod 35147 with 3370 at 2,3
% 6.02/1.83 Id : 35149, {_}: multiply (commutator ?32390 (inverse ?32389)) ?32389 =<= multiply ?32389 (commutator (inverse ?32390) (inverse (inverse ?32389))) [32389, 32390] by Demod 35148 with 3370 at 1,2
% 6.02/1.83 Id : 35724, {_}: multiply (commutator ?33281 (inverse ?33282)) ?33282 =>= multiply ?33282 (commutator (inverse ?33281) ?33282) [33282, 33281] by Demod 35149 with 109 at 2,2,3
% 6.02/1.83 Id : 433, {_}: commutator ?470 (multiply ?471 (inverse ?470)) =<= multiply ?470 (multiply (multiply ?471 (inverse ?470)) (inverse ?471)) [471, 470] by Super 7 with 182 at 2,2,3
% 6.02/1.83 Id : 451, {_}: commutator ?470 (multiply ?471 (inverse ?470)) =<= multiply ?470 (multiply ?471 (multiply (inverse ?470) (inverse ?471))) [471, 470] by Demod 433 with 4 at 2,3
% 6.02/1.83 Id : 869, {_}: commutator ?925 (multiply ?926 (inverse ?925)) =>= commutator ?925 ?926 [926, 925] by Demod 451 with 7 at 3
% 6.02/1.83 Id : 1036, {_}: commutator (inverse ?1118) (multiply ?1119 ?1118) =>= commutator (inverse ?1118) ?1119 [1119, 1118] by Super 869 with 109 at 2,2,2
% 6.02/1.83 Id : 1043, {_}: commutator (inverse (inverse (multiply ?1135 ?1136))) (inverse ?1135) =?= commutator (inverse (inverse (multiply ?1135 ?1136))) ?1136 [1136, 1135] by Super 1036 with 182 at 2,2
% 6.02/1.83 Id : 1069, {_}: commutator (multiply ?1135 ?1136) (inverse ?1135) =?= commutator (inverse (inverse (multiply ?1135 ?1136))) ?1136 [1136, 1135] by Demod 1043 with 109 at 1,2
% 6.02/1.83 Id : 1070, {_}: commutator (multiply ?1135 ?1136) (inverse ?1135) =?= commutator (multiply ?1135 ?1136) ?1136 [1136, 1135] by Demod 1069 with 109 at 1,3
% 6.02/1.83 Id : 1089, {_}: commutator ?1180 ?1181 =<= commutator (multiply ?1180 ?1181) ?1181 [1181, 1180] by Demod 1070 with 736 at 2
% 6.02/1.83 Id : 1097, {_}: commutator (inverse (multiply ?1200 ?1201)) ?1200 =>= commutator (inverse ?1201) ?1200 [1201, 1200] by Super 1089 with 464 at 1,3
% 6.02/1.83 Id : 35743, {_}: multiply (commutator (inverse ?33343) (inverse ?33344)) ?33344 =<= multiply ?33344 (commutator (inverse (inverse (multiply (inverse ?33344) ?33343))) ?33344) [33344, 33343] by Super 35724 with 1097 at 1,2
% 6.02/1.83 Id : 35150, {_}: multiply (commutator ?32390 (inverse ?32389)) ?32389 =>= multiply ?32389 (commutator (inverse ?32390) ?32389) [32389, 32390] by Demod 35149 with 109 at 2,2,3
% 6.02/1.83 Id : 36047, {_}: multiply ?33344 (commutator (inverse (inverse ?33343)) ?33344) =<= multiply ?33344 (commutator (inverse (inverse (multiply (inverse ?33344) ?33343))) ?33344) [33343, 33344] by Demod 35743 with 35150 at 2
% 6.02/1.83 Id : 36048, {_}: multiply ?33344 (commutator (inverse (inverse ?33343)) ?33344) =<= multiply ?33344 (commutator (multiply (inverse ?33344) ?33343) ?33344) [33343, 33344] by Demod 36047 with 109 at 1,2,3
% 6.02/1.83 Id : 36049, {_}: multiply ?33344 (commutator ?33343 ?33344) =<= multiply ?33344 (commutator (multiply (inverse ?33344) ?33343) ?33344) [33343, 33344] by Demod 36048 with 109 at 1,2,2
% 6.02/1.83 Id : 1001, {_}: commutator (multiply (inverse ?1073) ?1074) ?1073 =>= commutator (inverse ?1073) ?1074 [1074, 1073] by Super 997 with 109 at 2,2
% 6.02/1.83 Id : 36050, {_}: multiply ?33344 (commutator ?33343 ?33344) =<= multiply ?33344 (commutator (inverse ?33344) ?33343) [33343, 33344] by Demod 36049 with 1001 at 2,3
% 6.02/1.83 Id : 55, {_}: multiply (commutator ?78 ?79) ?80 =<= multiply ?78 (multiply ?79 (multiply (inverse ?78) (multiply (inverse ?79) ?80))) [80, 79, 78] by Demod 54 with 4 at 2,2,3
% 6.02/1.83 Id : 1760, {_}: multiply (commutator ?2148 ?2149) (multiply (inverse (inverse ?2148)) ?2150) =>= multiply ?2148 (multiply (commutator ?2149 (inverse ?2148)) ?2150) [2150, 2149, 2148] by Super 1724 with 55 at 2,3
% 6.02/1.83 Id : 18274, {_}: multiply (commutator ?17204 ?17205) (multiply ?17204 ?17206) =<= multiply ?17204 (multiply (commutator ?17205 (inverse ?17204)) ?17206) [17206, 17205, 17204] by Demod 1760 with 109 at 1,2,2
% 6.02/1.83 Id : 18316, {_}: multiply (commutator ?17374 ?17375) (multiply ?17374 (commutator ?17375 (inverse ?17374))) =>= multiply ?17374 (inverse (commutator ?17375 (inverse ?17374))) [17375, 17374] by Super 18274 with 112 at 2,3
% 6.02/1.83 Id : 18583, {_}: multiply (commutator ?17374 ?17375) (multiply (commutator ?17374 ?17375) ?17374) =>= multiply ?17374 (inverse (commutator ?17375 (inverse ?17374))) [17375, 17374] by Demod 18316 with 1903 at 2,2
% 6.02/1.83 Id : 18584, {_}: multiply (commutator ?17374 ?17375) (multiply (commutator ?17374 ?17375) ?17374) =>= multiply ?17374 (commutator (inverse ?17374) ?17375) [17375, 17374] by Demod 18583 with 3370 at 2,3
% 6.02/1.83 Id : 18585, {_}: multiply (inverse (commutator ?17374 ?17375)) ?17374 =>= multiply ?17374 (commutator (inverse ?17374) ?17375) [17375, 17374] by Demod 18584 with 229 at 2
% 6.02/1.83 Id : 18586, {_}: multiply (commutator ?17375 ?17374) ?17374 =<= multiply ?17374 (commutator (inverse ?17374) ?17375) [17374, 17375] by Demod 18585 with 3370 at 1,2
% 6.02/1.83 Id : 36051, {_}: multiply ?33344 (commutator ?33343 ?33344) =<= multiply (commutator ?33343 ?33344) ?33344 [33343, 33344] by Demod 36050 with 18586 at 3
% 6.02/1.83 Id : 36182, {_}: multiply (inverse ?2341) (multiply ?2341 (commutator ?2342 ?2341)) =>= commutator (inverse ?2341) ?2342 [2342, 2341] by Demod 29717 with 36051 at 2,2
% 6.02/1.83 Id : 36200, {_}: commutator ?2342 ?2341 =<= commutator (inverse ?2341) ?2342 [2341, 2342] by Demod 36182 with 19 at 2
% 6.02/1.83 Id : 36259, {_}: commutator (inverse ?2950) ?2949 =<= multiply (inverse (multiply ?2950 ?2949)) (multiply ?2949 ?2950) [2949, 2950] by Demod 2667 with 36200 at 2
% 6.02/1.83 Id : 36260, {_}: commutator ?2949 ?2950 =<= multiply (inverse (multiply ?2950 ?2949)) (multiply ?2949 ?2950) [2950, 2949] by Demod 36259 with 36200 at 2
% 6.02/1.83 Id : 36369, {_}: commutator (commutator ?33481 ?33482) ?33482 =<= multiply (inverse (multiply ?33482 (commutator ?33481 ?33482))) (multiply ?33482 (commutator ?33481 ?33482)) [33482, 33481] by Super 36260 with 36051 at 2,3
% 6.02/1.83 Id : 36627, {_}: commutator (commutator ?33481 ?33482) ?33482 =>= identity [33482, 33481] by Demod 36369 with 3 at 3
% 6.02/1.83 Id : 37200, {_}: identity =?= identity [] by Demod 1 with 36627 at 2
% 6.02/1.83 Id : 1, {_}: commutator (commutator a b) b =>= identity [] by prove_commutator
% 6.02/1.83 % SZS output end CNFRefutation for theBenchmark.p
% 6.02/1.83 2873: solved /export/starexec/sandbox2/benchmark/theBenchmark.p in 1.492613 using kbo
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