%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : GRP128-2.006 : TPTP v8.1.2. Released v1.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n029.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  : 300s
% DateTime : Fri May  3 02:21:21 EDT 2024

% Result   : Unsatisfiable 7.42s 1.63s
% Output   : CNFRefutation 8.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   46
% Syntax   : Number of clauses     :  925 (  89 unt;  77 nHn; 925 RR)
%            Number of literals    : 2428 (   0 equ;1640 neg)
%            Maximal clause size   :    8 (   2 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    6 (   5 usr;   1 prp; 0-3 aty)
%            Number of functors    :    6 (   6 usr;   6 con; 0-0 aty)
%            Number of variables   :  780 (   2 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(c_49,plain,
    next(e_1,e_2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_then_e_2) ).

cnf(c_50,plain,
    next(e_2,e_3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_then_e_3) ).

cnf(c_51,plain,
    next(e_3,e_4),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_then_e_4) ).

cnf(c_52,plain,
    next(e_4,e_5),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_then_e_5) ).

cnf(c_59,plain,
    greater(e_3,e_2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_greater_e_2) ).

cnf(c_60,plain,
    greater(e_4,e_2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_greater_e_2) ).

cnf(c_61,plain,
    greater(e_5,e_2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_5_greater_e_2) ).

cnf(c_62,plain,
    greater(e_6,e_2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_6_greater_e_2) ).

cnf(c_63,plain,
    greater(e_4,e_3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_greater_e_3) ).

cnf(c_64,plain,
    greater(e_5,e_3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_5_greater_e_3) ).

cnf(c_65,plain,
    greater(e_6,e_3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_6_greater_e_3) ).

cnf(c_66,plain,
    greater(e_5,e_4),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_5_greater_e_4) ).

cnf(c_67,plain,
    greater(e_6,e_4),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_6_greater_e_4) ).

cnf(c_68,plain,
    greater(e_6,e_5),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_6_greater_e_5) ).

cnf(c_69,plain,
    ( ~ product(X0,e_1,X1)
    | ~ next(X0,X2)
    | ~ greater(X1,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',no_redundancy) ).

cnf(c_70,plain,
    group_element(e_1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_1) ).

cnf(c_71,plain,
    group_element(e_2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_2) ).

cnf(c_72,plain,
    group_element(e_3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_3) ).

cnf(c_73,plain,
    group_element(e_4),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_4) ).

cnf(c_74,plain,
    group_element(e_5),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_5) ).

cnf(c_75,plain,
    group_element(e_6),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_6) ).

cnf(c_76,plain,
    ~ equalish(e_1,e_2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_2) ).

cnf(c_77,plain,
    ~ equalish(e_1,e_3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_3) ).

cnf(c_78,plain,
    ~ equalish(e_1,e_4),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_4) ).

cnf(c_79,plain,
    ~ equalish(e_1,e_5),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_5) ).

cnf(c_80,plain,
    ~ equalish(e_1,e_6),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_6) ).

cnf(c_81,plain,
    ~ equalish(e_2,e_1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_1) ).

cnf(c_82,plain,
    ~ equalish(e_2,e_3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_3) ).

cnf(c_83,plain,
    ~ equalish(e_2,e_4),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_4) ).

cnf(c_84,plain,
    ~ equalish(e_2,e_5),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_5) ).

cnf(c_85,plain,
    ~ equalish(e_2,e_6),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_6) ).

cnf(c_86,plain,
    ~ equalish(e_3,e_1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_1) ).

cnf(c_88,plain,
    ~ equalish(e_3,e_4),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_4) ).

cnf(c_89,plain,
    ~ equalish(e_3,e_5),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_5) ).

cnf(c_90,plain,
    ~ equalish(e_3,e_6),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_6) ).

cnf(c_91,plain,
    ~ equalish(e_4,e_1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_is_not_e_1) ).

cnf(c_93,plain,
    ~ equalish(e_4,e_3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_is_not_e_3) ).

cnf(c_94,plain,
    ~ equalish(e_4,e_5),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_is_not_e_5) ).

cnf(c_95,plain,
    ~ equalish(e_4,e_6),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_is_not_e_6) ).

cnf(c_98,plain,
    ~ equalish(e_5,e_3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_5_is_not_e_3) ).

cnf(c_100,plain,
    ~ equalish(e_5,e_6),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_5_is_not_e_6) ).

cnf(c_106,plain,
    ( ~ group_element(X0)
    | ~ group_element(X1)
    | product(X0,X1,e_1)
    | product(X0,X1,e_2)
    | product(X0,X1,e_3)
    | product(X0,X1,e_4)
    | product(X0,X1,e_5)
    | product(X0,X1,e_6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_total_function1) ).

cnf(c_107,plain,
    ( ~ product(X0,X1,X2)
    | ~ product(X0,X1,X3)
    | equalish(X2,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_total_function2) ).

cnf(c_108,plain,
    ( ~ product(X0,X1,X2)
    | ~ product(X0,X3,X2)
    | equalish(X1,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_right_cancellation) ).

cnf(c_109,plain,
    ( ~ product(X0,X1,X2)
    | ~ product(X3,X1,X2)
    | equalish(X0,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_left_cancellation) ).

cnf(c_110,negated_conjecture,
    ( ~ product(X0,X1,X2)
    | ~ product(X2,X1,X3)
    | product(X0,X2,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg3) ).

cnf(c_113,plain,
    ( ~ group_element(e_1)
    | product(e_1,e_1,e_1)
    | product(e_1,e_1,e_2)
    | product(e_1,e_1,e_3)
    | product(e_1,e_1,e_4)
    | product(e_1,e_1,e_5)
    | product(e_1,e_1,e_6) ),
    inference(instantiation,[status(thm)],[c_106]) ).

cnf(c_272,plain,
    ( ~ product(e_1,e_1,X0)
    | ~ greater(X0,e_2) ),
    inference(resolution,[status(thm)],[c_49,c_69]) ).

cnf(c_280,plain,
    ( ~ product(e_2,e_1,X0)
    | ~ greater(X0,e_3) ),
    inference(resolution,[status(thm)],[c_50,c_69]) ).

cnf(c_288,plain,
    ( ~ product(e_3,e_1,X0)
    | ~ greater(X0,e_4) ),
    inference(resolution,[status(thm)],[c_51,c_69]) ).

cnf(c_296,plain,
    ( ~ product(e_4,e_1,X0)
    | ~ greater(X0,e_5) ),
    inference(resolution,[status(thm)],[c_52,c_69]) ).

cnf(c_322,plain,
    ~ product(e_1,e_1,e_3),
    inference(resolution,[status(thm)],[c_59,c_272]) ).

cnf(c_326,plain,
    ~ product(e_1,e_1,e_4),
    inference(resolution,[status(thm)],[c_60,c_272]) ).

cnf(c_330,plain,
    ~ product(e_1,e_1,e_5),
    inference(resolution,[status(thm)],[c_61,c_272]) ).

cnf(c_334,plain,
    ~ product(e_1,e_1,e_6),
    inference(resolution,[status(thm)],[c_62,c_272]) ).

cnf(c_338,plain,
    ~ product(e_2,e_1,e_4),
    inference(resolution,[status(thm)],[c_63,c_280]) ).

cnf(c_342,plain,
    ~ product(e_2,e_1,e_5),
    inference(resolution,[status(thm)],[c_64,c_280]) ).

cnf(c_346,plain,
    ~ product(e_2,e_1,e_6),
    inference(resolution,[status(thm)],[c_65,c_280]) ).

cnf(c_350,plain,
    ~ product(e_3,e_1,e_5),
    inference(resolution,[status(thm)],[c_66,c_288]) ).

cnf(c_354,plain,
    ~ product(e_3,e_1,e_6),
    inference(resolution,[status(thm)],[c_67,c_288]) ).

cnf(c_358,plain,
    ~ product(e_4,e_1,e_6),
    inference(resolution,[status(thm)],[c_68,c_296]) ).

cnf(c_372,plain,
    ( ~ product(X0,X1,e_1)
    | ~ product(X0,X1,e_2) ),
    inference(resolution,[status(thm)],[c_76,c_107]) ).

cnf(c_380,plain,
    ( ~ product(X0,e_1,X1)
    | ~ product(X0,e_2,X1) ),
    inference(resolution,[status(thm)],[c_76,c_108]) ).

cnf(c_381,plain,
    ( ~ product(e_1,e_1,e_1)
    | ~ product(e_1,e_2,e_1) ),
    inference(instantiation,[status(thm)],[c_380]) ).

cnf(c_388,plain,
    ( ~ product(e_1,X0,X1)
    | ~ product(e_2,X0,X1) ),
    inference(resolution,[status(thm)],[c_76,c_109]) ).

cnf(c_389,plain,
    ( ~ product(e_1,e_1,e_1)
    | ~ product(e_2,e_1,e_1) ),
    inference(instantiation,[status(thm)],[c_388]) ).

cnf(c_396,plain,
    ( ~ product(X0,X1,e_1)
    | ~ product(X0,X1,e_3) ),
    inference(resolution,[status(thm)],[c_77,c_107]) ).

cnf(c_403,plain,
    ( ~ product(X0,e_1,X1)
    | ~ product(X0,e_3,X1) ),
    inference(resolution,[status(thm)],[c_77,c_108]) ).

cnf(c_404,plain,
    ( ~ product(e_1,e_1,e_1)
    | ~ product(e_1,e_3,e_1) ),
    inference(instantiation,[status(thm)],[c_403]) ).

cnf(c_411,plain,
    ( ~ product(e_1,X0,X1)
    | ~ product(e_3,X0,X1) ),
    inference(resolution,[status(thm)],[c_77,c_109]) ).

cnf(c_412,plain,
    ( ~ product(e_1,e_1,e_1)
    | ~ product(e_3,e_1,e_1) ),
    inference(instantiation,[status(thm)],[c_411]) ).

cnf(c_419,plain,
    ( ~ product(X0,X1,e_1)
    | ~ product(X0,X1,e_4) ),
    inference(resolution,[status(thm)],[c_78,c_107]) ).

cnf(c_426,plain,
    ( ~ product(X0,e_1,X1)
    | ~ product(X0,e_4,X1) ),
    inference(resolution,[status(thm)],[c_78,c_108]) ).

cnf(c_427,plain,
    ( ~ product(e_1,e_1,e_1)
    | ~ product(e_1,e_4,e_1) ),
    inference(instantiation,[status(thm)],[c_426]) ).

cnf(c_434,plain,
    ( ~ product(e_1,X0,X1)
    | ~ product(e_4,X0,X1) ),
    inference(resolution,[status(thm)],[c_78,c_109]) ).

cnf(c_435,plain,
    ( ~ product(e_1,e_1,e_1)
    | ~ product(e_4,e_1,e_1) ),
    inference(instantiation,[status(thm)],[c_434]) ).

cnf(c_442,plain,
    ( ~ product(X0,X1,e_1)
    | ~ product(X0,X1,e_5) ),
    inference(resolution,[status(thm)],[c_79,c_107]) ).

cnf(c_449,plain,
    ( ~ product(X0,e_1,X1)
    | ~ product(X0,e_5,X1) ),
    inference(resolution,[status(thm)],[c_79,c_108]) ).

cnf(c_450,plain,
    ( ~ product(e_1,e_1,e_1)
    | ~ product(e_1,e_5,e_1) ),
    inference(instantiation,[status(thm)],[c_449]) ).

cnf(c_457,plain,
    ( ~ product(e_1,X0,X1)
    | ~ product(e_5,X0,X1) ),
    inference(resolution,[status(thm)],[c_79,c_109]) ).

cnf(c_458,plain,
    ( ~ product(e_1,e_1,e_1)
    | ~ product(e_5,e_1,e_1) ),
    inference(instantiation,[status(thm)],[c_457]) ).

cnf(c_465,plain,
    ( ~ product(X0,X1,e_1)
    | ~ product(X0,X1,e_6) ),
    inference(resolution,[status(thm)],[c_80,c_107]) ).

cnf(c_472,plain,
    ( ~ product(X0,e_1,X1)
    | ~ product(X0,e_6,X1) ),
    inference(resolution,[status(thm)],[c_80,c_108]) ).

cnf(c_473,plain,
    ( ~ product(e_1,e_1,e_1)
    | ~ product(e_1,e_6,e_1) ),
    inference(instantiation,[status(thm)],[c_472]) ).

cnf(c_480,plain,
    ( ~ product(e_1,X0,X1)
    | ~ product(e_6,X0,X1) ),
    inference(resolution,[status(thm)],[c_80,c_109]) ).

cnf(c_481,plain,
    ( ~ product(e_1,e_1,e_1)
    | ~ product(e_6,e_1,e_1) ),
    inference(instantiation,[status(thm)],[c_480]) ).

cnf(c_498,plain,
    ( ~ product(X0,e_2,X1)
    | ~ product(X0,e_3,X1) ),
    inference(resolution,[status(thm)],[c_82,c_108]) ).

cnf(c_506,plain,
    ( ~ product(e_2,X0,X1)
    | ~ product(e_3,X0,X1) ),
    inference(resolution,[status(thm)],[c_82,c_109]) ).

cnf(c_514,plain,
    ( ~ product(X0,X1,e_2)
    | ~ product(X0,X1,e_4) ),
    inference(resolution,[status(thm)],[c_83,c_107]) ).

cnf(c_521,plain,
    ( ~ product(X0,e_2,X1)
    | ~ product(X0,e_4,X1) ),
    inference(resolution,[status(thm)],[c_83,c_108]) ).

cnf(c_529,plain,
    ( ~ product(e_2,X0,X1)
    | ~ product(e_4,X0,X1) ),
    inference(resolution,[status(thm)],[c_83,c_109]) ).

cnf(c_537,plain,
    ( ~ product(X0,X1,e_2)
    | ~ product(X0,X1,e_5) ),
    inference(resolution,[status(thm)],[c_84,c_107]) ).

cnf(c_544,plain,
    ( ~ product(X0,e_2,X1)
    | ~ product(X0,e_5,X1) ),
    inference(resolution,[status(thm)],[c_84,c_108]) ).

cnf(c_552,plain,
    ( ~ product(e_2,X0,X1)
    | ~ product(e_5,X0,X1) ),
    inference(resolution,[status(thm)],[c_84,c_109]) ).

cnf(c_560,plain,
    ( ~ product(X0,X1,e_2)
    | ~ product(X0,X1,e_6) ),
    inference(resolution,[status(thm)],[c_85,c_107]) ).

cnf(c_567,plain,
    ( ~ product(X0,e_2,X1)
    | ~ product(X0,e_6,X1) ),
    inference(resolution,[status(thm)],[c_85,c_108]) ).

cnf(c_575,plain,
    ( ~ product(e_2,X0,X1)
    | ~ product(e_6,X0,X1) ),
    inference(resolution,[status(thm)],[c_85,c_109]) ).

cnf(c_589,plain,
    ( ~ product(X0,X1,e_3)
    | ~ product(X0,X1,e_4) ),
    inference(resolution,[status(thm)],[c_88,c_107]) ).

cnf(c_596,plain,
    ( ~ product(X0,e_3,X1)
    | ~ product(X0,e_4,X1) ),
    inference(resolution,[status(thm)],[c_88,c_108]) ).

cnf(c_604,plain,
    ( ~ product(e_3,X0,X1)
    | ~ product(e_4,X0,X1) ),
    inference(resolution,[status(thm)],[c_88,c_109]) ).

cnf(c_612,plain,
    ( ~ product(X0,X1,e_3)
    | ~ product(X0,X1,e_5) ),
    inference(resolution,[status(thm)],[c_89,c_107]) ).

cnf(c_619,plain,
    ( ~ product(X0,e_3,X1)
    | ~ product(X0,e_5,X1) ),
    inference(resolution,[status(thm)],[c_89,c_108]) ).

cnf(c_627,plain,
    ( ~ product(e_3,X0,X1)
    | ~ product(e_5,X0,X1) ),
    inference(resolution,[status(thm)],[c_89,c_109]) ).

cnf(c_642,plain,
    ( ~ product(X0,e_3,X1)
    | ~ product(X0,e_6,X1) ),
    inference(resolution,[status(thm)],[c_90,c_108]) ).

cnf(c_650,plain,
    ( ~ product(e_3,X0,X1)
    | ~ product(e_6,X0,X1) ),
    inference(resolution,[status(thm)],[c_90,c_109]) ).

cnf(c_667,plain,
    ( ~ product(X0,X1,e_4)
    | ~ product(X0,X1,e_5) ),
    inference(resolution,[status(thm)],[c_94,c_107]) ).

cnf(c_674,plain,
    ( ~ product(X0,e_4,X1)
    | ~ product(X0,e_5,X1) ),
    inference(resolution,[status(thm)],[c_94,c_108]) ).

cnf(c_682,plain,
    ( ~ product(e_4,X0,X1)
    | ~ product(e_5,X0,X1) ),
    inference(resolution,[status(thm)],[c_94,c_109]) ).

cnf(c_690,plain,
    ( ~ product(X0,X1,e_4)
    | ~ product(X0,X1,e_6) ),
    inference(resolution,[status(thm)],[c_95,c_107]) ).

cnf(c_697,plain,
    ( ~ product(X0,e_4,X1)
    | ~ product(X0,e_6,X1) ),
    inference(resolution,[status(thm)],[c_95,c_108]) ).

cnf(c_705,plain,
    ( ~ product(e_4,X0,X1)
    | ~ product(e_6,X0,X1) ),
    inference(resolution,[status(thm)],[c_95,c_109]) ).

cnf(c_732,plain,
    ( ~ product(X0,e_5,X1)
    | ~ product(X0,e_6,X1) ),
    inference(resolution,[status(thm)],[c_100,c_108]) ).

cnf(c_740,plain,
    ( ~ product(e_5,X0,X1)
    | ~ product(e_6,X0,X1) ),
    inference(resolution,[status(thm)],[c_100,c_109]) ).

cnf(c_1439,plain,
    ( ~ product(e_1,X0,e_4)
    | ~ product(e_2,X0,e_1)
    | product(e_2,e_1,e_4) ),
    inference(instantiation,[status(thm)],[c_110]) ).

cnf(c_1440,plain,
    ( ~ product(e_1,X0,e_5)
    | ~ product(e_2,X0,e_1)
    | product(e_2,e_1,e_5) ),
    inference(instantiation,[status(thm)],[c_110]) ).

cnf(c_1441,plain,
    ( ~ product(e_1,X0,e_6)
    | ~ product(e_2,X0,e_1)
    | product(e_2,e_1,e_6) ),
    inference(instantiation,[status(thm)],[c_110]) ).

cnf(c_1457,plain,
    ( ~ product(e_1,X0,e_4)
    | ~ product(e_2,X0,e_1)
    | product(e_2,e_1,e_4) ),
    inference(instantiation,[status(thm)],[c_110]) ).

cnf(c_1458,plain,
    ( ~ product(e_2,X0,e_1)
    | ~ product(e_1,X0,e_4) ),
    inference(global_subsumption_just,[status(thm)],[c_1457,c_338,c_1439]) ).

cnf(c_1459,plain,
    ( ~ product(e_1,X0,e_4)
    | ~ product(e_2,X0,e_1) ),
    inference(renaming,[status(thm)],[c_1458]) ).

cnf(c_1460,plain,
    ( ~ product(e_1,X0,e_5)
    | ~ product(e_2,X0,e_1)
    | product(e_2,e_1,e_5) ),
    inference(instantiation,[status(thm)],[c_110]) ).

cnf(c_1461,plain,
    ( ~ product(e_2,X0,e_1)
    | ~ product(e_1,X0,e_5) ),
    inference(global_subsumption_just,[status(thm)],[c_1460,c_342,c_1440]) ).

cnf(c_1462,plain,
    ( ~ product(e_1,X0,e_5)
    | ~ product(e_2,X0,e_1) ),
    inference(renaming,[status(thm)],[c_1461]) ).

cnf(c_1901,plain,
    ( ~ group_element(X0)
    | ~ group_element(e_1)
    | product(e_1,X0,e_1)
    | product(e_1,X0,e_2)
    | product(e_1,X0,e_3)
    | product(e_1,X0,e_4)
    | product(e_1,X0,e_5)
    | product(e_1,X0,e_6) ),
    inference(instantiation,[status(thm)],[c_106]) ).

cnf(c_1902,plain,
    ( ~ group_element(X0)
    | product(e_1,X0,e_1)
    | product(e_1,X0,e_2)
    | product(e_1,X0,e_3)
    | product(e_1,X0,e_4)
    | product(e_1,X0,e_5)
    | product(e_1,X0,e_6) ),
    inference(global_subsumption_just,[status(thm)],[c_1901,c_70,c_1901]) ).

cnf(c_1904,plain,
    ( ~ group_element(X0)
    | ~ group_element(e_2)
    | product(e_2,X0,e_1)
    | product(e_2,X0,e_2)
    | product(e_2,X0,e_3)
    | product(e_2,X0,e_4)
    | product(e_2,X0,e_5)
    | product(e_2,X0,e_6) ),
    inference(instantiation,[status(thm)],[c_106]) ).

cnf(c_1905,plain,
    ( ~ group_element(e_1)
    | ~ group_element(e_2)
    | product(e_2,e_1,e_1)
    | product(e_2,e_1,e_2)
    | product(e_2,e_1,e_3)
    | product(e_2,e_1,e_4)
    | product(e_2,e_1,e_5)
    | product(e_2,e_1,e_6) ),
    inference(instantiation,[status(thm)],[c_1904]) ).

cnf(c_1906,plain,
    ( ~ group_element(X0)
    | product(e_2,X0,e_1)
    | product(e_2,X0,e_2)
    | product(e_2,X0,e_3)
    | product(e_2,X0,e_4)
    | product(e_2,X0,e_5)
    | product(e_2,X0,e_6) ),
    inference(global_subsumption_just,[status(thm)],[c_1904,c_71,c_1904]) ).

cnf(c_1909,plain,
    ( ~ group_element(X0)
    | ~ group_element(e_3)
    | product(e_3,X0,e_1)
    | product(e_3,X0,e_2)
    | product(e_3,X0,e_3)
    | product(e_3,X0,e_4)
    | product(e_3,X0,e_5)
    | product(e_3,X0,e_6) ),
    inference(instantiation,[status(thm)],[c_106]) ).

cnf(c_1910,plain,
    ( ~ group_element(e_1)
    | ~ group_element(e_3)
    | product(e_3,e_1,e_1)
    | product(e_3,e_1,e_2)
    | product(e_3,e_1,e_3)
    | product(e_3,e_1,e_4)
    | product(e_3,e_1,e_5)
    | product(e_3,e_1,e_6) ),
    inference(instantiation,[status(thm)],[c_1909]) ).

cnf(c_1911,plain,
    ( ~ group_element(X0)
    | product(e_3,X0,e_1)
    | product(e_3,X0,e_2)
    | product(e_3,X0,e_3)
    | product(e_3,X0,e_4)
    | product(e_3,X0,e_5)
    | product(e_3,X0,e_6) ),
    inference(global_subsumption_just,[status(thm)],[c_1909,c_72,c_1909]) ).

cnf(c_1913,plain,
    ( ~ group_element(e_1)
    | product(e_3,e_1,e_1)
    | product(e_3,e_1,e_2)
    | product(e_3,e_1,e_3)
    | product(e_3,e_1,e_4)
    | product(e_3,e_1,e_5)
    | product(e_3,e_1,e_6) ),
    inference(instantiation,[status(thm)],[c_1911]) ).

cnf(c_1914,plain,
    ( ~ group_element(X0)
    | ~ group_element(e_4)
    | product(e_4,X0,e_1)
    | product(e_4,X0,e_2)
    | product(e_4,X0,e_3)
    | product(e_4,X0,e_4)
    | product(e_4,X0,e_5)
    | product(e_4,X0,e_6) ),
    inference(instantiation,[status(thm)],[c_106]) ).

cnf(c_1915,plain,
    ( ~ group_element(e_1)
    | ~ group_element(e_4)
    | product(e_4,e_1,e_1)
    | product(e_4,e_1,e_2)
    | product(e_4,e_1,e_3)
    | product(e_4,e_1,e_4)
    | product(e_4,e_1,e_5)
    | product(e_4,e_1,e_6) ),
    inference(instantiation,[status(thm)],[c_1914]) ).

cnf(c_1916,plain,
    ( ~ group_element(X0)
    | product(e_4,X0,e_1)
    | product(e_4,X0,e_2)
    | product(e_4,X0,e_3)
    | product(e_4,X0,e_4)
    | product(e_4,X0,e_5)
    | product(e_4,X0,e_6) ),
    inference(global_subsumption_just,[status(thm)],[c_1914,c_73,c_1914]) ).

cnf(c_1918,plain,
    ( ~ group_element(e_1)
    | product(e_4,e_1,e_1)
    | product(e_4,e_1,e_2)
    | product(e_4,e_1,e_3)
    | product(e_4,e_1,e_4)
    | product(e_4,e_1,e_5)
    | product(e_4,e_1,e_6) ),
    inference(instantiation,[status(thm)],[c_1916]) ).

cnf(c_1919,plain,
    ( ~ group_element(X0)
    | ~ group_element(e_5)
    | product(e_5,X0,e_1)
    | product(e_5,X0,e_2)
    | product(e_5,X0,e_3)
    | product(e_5,X0,e_4)
    | product(e_5,X0,e_5)
    | product(e_5,X0,e_6) ),
    inference(instantiation,[status(thm)],[c_106]) ).

cnf(c_1921,plain,
    ( ~ group_element(X0)
    | product(e_5,X0,e_1)
    | product(e_5,X0,e_2)
    | product(e_5,X0,e_3)
    | product(e_5,X0,e_4)
    | product(e_5,X0,e_5)
    | product(e_5,X0,e_6) ),
    inference(global_subsumption_just,[status(thm)],[c_1919,c_74,c_1919]) ).

cnf(c_1923,plain,
    ( ~ group_element(e_1)
    | product(e_5,e_1,e_1)
    | product(e_5,e_1,e_2)
    | product(e_5,e_1,e_3)
    | product(e_5,e_1,e_4)
    | product(e_5,e_1,e_5)
    | product(e_5,e_1,e_6) ),
    inference(instantiation,[status(thm)],[c_1921]) ).

cnf(c_1924,plain,
    ( ~ group_element(X0)
    | ~ group_element(e_6)
    | product(e_6,X0,e_1)
    | product(e_6,X0,e_2)
    | product(e_6,X0,e_3)
    | product(e_6,X0,e_4)
    | product(e_6,X0,e_5)
    | product(e_6,X0,e_6) ),
    inference(instantiation,[status(thm)],[c_106]) ).

cnf(c_1926,plain,
    ( ~ group_element(X0)
    | product(e_6,X0,e_1)
    | product(e_6,X0,e_2)
    | product(e_6,X0,e_3)
    | product(e_6,X0,e_4)
    | product(e_6,X0,e_5)
    | product(e_6,X0,e_6) ),
    inference(global_subsumption_just,[status(thm)],[c_1924,c_75,c_1924]) ).

cnf(c_1928,plain,
    ( ~ group_element(e_1)
    | product(e_6,e_1,e_1)
    | product(e_6,e_1,e_2)
    | product(e_6,e_1,e_3)
    | product(e_6,e_1,e_4)
    | product(e_6,e_1,e_5)
    | product(e_6,e_1,e_6) ),
    inference(instantiation,[status(thm)],[c_1926]) ).

cnf(c_1929,plain,
    ( ~ product(X0,X1,e_1)
    | ~ product(e_1,X1,e_2)
    | product(X0,e_1,e_2) ),
    inference(instantiation,[status(thm)],[c_110]) ).

cnf(c_1930,plain,
    ( ~ product(X0,X1,e_2)
    | ~ product(e_1,X1,e_2)
    | equalish(e_1,X0) ),
    inference(instantiation,[status(thm)],[c_109]) ).

cnf(c_1931,plain,
    ( ~ product(e_1,X0,e_2)
    | ~ product(e_1,X1,e_2)
    | equalish(X0,X1) ),
    inference(instantiation,[status(thm)],[c_108]) ).

cnf(c_1934,plain,
    ( ~ product(X0,X1,e_2)
    | ~ product(e_2,X1,e_2)
    | product(X0,e_2,e_2) ),
    inference(instantiation,[status(thm)],[c_110]) ).

cnf(c_1937,plain,
    ( ~ product(e_2,X0,e_2)
    | ~ product(e_2,X1,e_2)
    | equalish(X0,X1) ),
    inference(instantiation,[status(thm)],[c_108]) ).

cnf(c_1938,plain,
    ( ~ product(e_2,X0,X1)
    | ~ product(e_2,X0,e_2)
    | equalish(e_2,X1) ),
    inference(instantiation,[status(thm)],[c_107]) ).

cnf(c_1939,plain,
    ( ~ product(e_2,e_1,e_1)
    | ~ product(e_2,e_1,e_2)
    | equalish(e_2,e_1) ),
    inference(instantiation,[status(thm)],[c_1938]) ).

cnf(c_1944,plain,
    ( ~ product(e_3,X0,e_2)
    | ~ product(e_3,X1,e_2)
    | equalish(X0,X1) ),
    inference(instantiation,[status(thm)],[c_108]) ).

cnf(c_1945,plain,
    ( ~ product(e_3,X0,X1)
    | ~ product(e_3,X0,e_2)
    | equalish(e_2,X1) ),
    inference(instantiation,[status(thm)],[c_107]) ).

cnf(c_1946,plain,
    ( ~ product(e_3,e_1,e_1)
    | ~ product(e_3,e_1,e_2)
    | equalish(e_2,e_1) ),
    inference(instantiation,[status(thm)],[c_1945]) ).

cnf(c_1949,plain,
    ( ~ product(X0,X1,e_4)
    | ~ product(e_4,X1,e_2)
    | product(X0,e_4,e_2) ),
    inference(instantiation,[status(thm)],[c_110]) ).

cnf(c_1951,plain,
    ( ~ product(e_4,X0,e_2)
    | ~ product(e_4,X1,e_2)
    | equalish(X0,X1) ),
    inference(instantiation,[status(thm)],[c_108]) ).

cnf(c_1965,plain,
    ( ~ product(e_6,X0,e_1)
    | ~ product(e_6,X1,e_1)
    | equalish(X0,X1) ),
    inference(instantiation,[status(thm)],[c_108]) ).

cnf(c_1968,plain,
    ( ~ product(e_1,X0,e_2)
    | ~ product(e_6,X0,e_1)
    | product(e_6,e_1,e_2) ),
    inference(instantiation,[status(thm)],[c_1929]) ).

cnf(c_1969,plain,
    ( ~ product(e_1,e_1,e_2)
    | ~ product(e_6,e_1,e_1)
    | product(e_6,e_1,e_2) ),
    inference(instantiation,[status(thm)],[c_1968]) ).

cnf(c_1970,plain,
    ( ~ product(e_1,X0,e_2)
    | ~ product(e_2,X0,e_2)
    | equalish(e_1,e_2) ),
    inference(instantiation,[status(thm)],[c_1930]) ).

cnf(c_1972,plain,
    ( ~ product(e_2,X0,e_2)
    | ~ product(e_1,X0,e_2) ),
    inference(global_subsumption_just,[status(thm)],[c_1970,c_76,c_1970]) ).

cnf(c_1973,plain,
    ( ~ product(e_1,X0,e_2)
    | ~ product(e_2,X0,e_2) ),
    inference(renaming,[status(thm)],[c_1972]) ).

cnf(c_1975,plain,
    ( ~ product(e_1,X0,e_2)
    | ~ product(e_3,X0,e_2)
    | equalish(e_1,e_3) ),
    inference(instantiation,[status(thm)],[c_1930]) ).

cnf(c_1977,plain,
    ( ~ product(e_3,X0,e_2)
    | ~ product(e_1,X0,e_2) ),
    inference(global_subsumption_just,[status(thm)],[c_1975,c_77,c_1975]) ).

cnf(c_1978,plain,
    ( ~ product(e_1,X0,e_2)
    | ~ product(e_3,X0,e_2) ),
    inference(renaming,[status(thm)],[c_1977]) ).

cnf(c_1990,plain,
    ( ~ product(e_1,X0,e_2)
    | ~ product(e_6,X0,e_2)
    | equalish(e_1,e_6) ),
    inference(instantiation,[status(thm)],[c_1930]) ).

cnf(c_1991,plain,
    ( ~ product(e_1,e_1,e_2)
    | ~ product(e_6,e_1,e_2)
    | equalish(e_1,e_6) ),
    inference(instantiation,[status(thm)],[c_1990]) ).

cnf(c_2028,plain,
    ( ~ product(e_1,e_3,e_2)
    | ~ product(e_1,e_5,e_2)
    | equalish(e_3,e_5) ),
    inference(instantiation,[status(thm)],[c_1931]) ).

cnf(c_2031,plain,
    ( ~ product(e_1,e_3,e_2)
    | ~ product(e_1,e_6,e_2)
    | equalish(e_3,e_6) ),
    inference(instantiation,[status(thm)],[c_1931]) ).

cnf(c_2032,plain,
    ( ~ product(e_1,e_6,e_2)
    | ~ product(e_1,e_3,e_2) ),
    inference(global_subsumption_just,[status(thm)],[c_2031,c_90,c_2031]) ).

cnf(c_2033,plain,
    ( ~ product(e_1,e_3,e_2)
    | ~ product(e_1,e_6,e_2) ),
    inference(renaming,[status(thm)],[c_2032]) ).

cnf(c_2047,plain,
    ( ~ product(e_1,e_5,e_2)
    | ~ product(e_1,e_6,e_2)
    | equalish(e_5,e_6) ),
    inference(instantiation,[status(thm)],[c_1931]) ).

cnf(c_2048,plain,
    ( ~ product(e_1,e_6,e_2)
    | ~ product(e_1,e_5,e_2) ),
    inference(global_subsumption_just,[status(thm)],[c_2047,c_100,c_2047]) ).

cnf(c_2049,plain,
    ( ~ product(e_1,e_5,e_2)
    | ~ product(e_1,e_6,e_2) ),
    inference(renaming,[status(thm)],[c_2048]) ).

cnf(c_2057,plain,
    ( ~ product(X0,X1,e_2)
    | ~ product(e_2,X1,e_3)
    | product(X0,e_2,e_3) ),
    inference(instantiation,[status(thm)],[c_110]) ).

cnf(c_2058,plain,
    ( ~ product(e_1,e_1,e_2)
    | ~ product(e_2,e_1,e_3)
    | product(e_1,e_2,e_3) ),
    inference(instantiation,[status(thm)],[c_2057]) ).

cnf(c_2064,plain,
    ( ~ product(e_2,e_1,e_2)
    | ~ product(e_2,e_2,e_2)
    | equalish(e_1,e_2) ),
    inference(instantiation,[status(thm)],[c_1937]) ).

cnf(c_2083,plain,
    ( ~ product(e_2,e_2,e_2)
    | ~ product(e_2,e_4,e_2)
    | equalish(e_2,e_4) ),
    inference(instantiation,[status(thm)],[c_1937]) ).

cnf(c_2084,plain,
    ( ~ product(e_2,e_4,e_2)
    | ~ product(e_2,e_2,e_2) ),
    inference(global_subsumption_just,[status(thm)],[c_2083,c_83,c_2083]) ).

cnf(c_2085,plain,
    ( ~ product(e_2,e_2,e_2)
    | ~ product(e_2,e_4,e_2) ),
    inference(renaming,[status(thm)],[c_2084]) ).

cnf(c_2086,plain,
    ( ~ product(e_2,e_2,e_2)
    | ~ product(e_2,e_5,e_2)
    | equalish(e_2,e_5) ),
    inference(instantiation,[status(thm)],[c_1937]) ).

cnf(c_2089,plain,
    ( ~ product(e_2,e_2,e_2)
    | ~ product(e_2,e_6,e_2)
    | equalish(e_2,e_6) ),
    inference(instantiation,[status(thm)],[c_1937]) ).

cnf(c_2090,plain,
    ( ~ product(e_2,e_6,e_2)
    | ~ product(e_2,e_2,e_2) ),
    inference(global_subsumption_just,[status(thm)],[c_2089,c_85,c_2089]) ).

cnf(c_2091,plain,
    ( ~ product(e_2,e_2,e_2)
    | ~ product(e_2,e_6,e_2) ),
    inference(renaming,[status(thm)],[c_2090]) ).

cnf(c_2094,plain,
    ( ~ product(e_2,e_3,e_2)
    | ~ product(e_2,e_4,e_2)
    | equalish(e_3,e_4) ),
    inference(instantiation,[status(thm)],[c_1937]) ).

cnf(c_2095,plain,
    ( ~ product(e_2,e_4,e_2)
    | ~ product(e_2,e_3,e_2) ),
    inference(global_subsumption_just,[status(thm)],[c_2094,c_88,c_2094]) ).

cnf(c_2096,plain,
    ( ~ product(e_2,e_3,e_2)
    | ~ product(e_2,e_4,e_2) ),
    inference(renaming,[status(thm)],[c_2095]) ).

cnf(c_2124,plain,
    ( ~ product(X0,X1,e_3)
    | ~ product(e_3,X1,e_3)
    | equalish(e_3,X0) ),
    inference(instantiation,[status(thm)],[c_109]) ).

cnf(c_2129,plain,
    ( ~ product(X0,X1,e_2)
    | ~ product(e_2,X1,X0)
    | product(e_2,X0,e_2) ),
    inference(instantiation,[status(thm)],[c_110]) ).

cnf(c_2130,plain,
    ( ~ product(e_1,e_1,e_2)
    | ~ product(e_2,e_1,e_1)
    | product(e_2,e_1,e_2) ),
    inference(instantiation,[status(thm)],[c_2129]) ).

cnf(c_2132,plain,
    ( ~ product(X0,X1,e_2)
    | ~ product(e_3,X1,X0)
    | product(e_3,X0,e_2) ),
    inference(instantiation,[status(thm)],[c_110]) ).

cnf(c_2133,plain,
    ( ~ product(e_1,e_1,e_2)
    | ~ product(e_3,e_1,e_1)
    | product(e_3,e_1,e_2) ),
    inference(instantiation,[status(thm)],[c_2132]) ).

cnf(c_2146,plain,
    ( ~ product(e_1,X0,e_4)
    | ~ product(e_2,X0,e_1)
    | product(e_2,e_1,e_4) ),
    inference(instantiation,[status(thm)],[c_110]) ).

cnf(c_2147,plain,
    ( ~ product(e_2,X0,e_1)
    | ~ product(e_1,X0,e_4) ),
    inference(global_subsumption_just,[status(thm)],[c_2146,c_1459]) ).

cnf(c_2148,plain,
    ( ~ product(e_1,X0,e_4)
    | ~ product(e_2,X0,e_1) ),
    inference(renaming,[status(thm)],[c_2147]) ).

cnf(c_2149,plain,
    ( ~ product(e_1,X0,e_5)
    | ~ product(e_2,X0,e_1)
    | product(e_2,e_1,e_5) ),
    inference(instantiation,[status(thm)],[c_110]) ).

cnf(c_2150,plain,
    ( ~ product(e_2,X0,e_1)
    | ~ product(e_1,X0,e_5) ),
    inference(global_subsumption_just,[status(thm)],[c_2149,c_1462]) ).

cnf(c_2151,plain,
    ( ~ product(e_1,X0,e_5)
    | ~ product(e_2,X0,e_1) ),
    inference(renaming,[status(thm)],[c_2150]) ).

cnf(c_2152,plain,
    ( ~ product(e_1,X0,e_6)
    | ~ product(e_2,X0,e_1)
    | product(e_2,e_1,e_6) ),
    inference(instantiation,[status(thm)],[c_110]) ).

cnf(c_2153,plain,
    ( ~ product(e_2,X0,e_1)
    | ~ product(e_1,X0,e_6) ),
    inference(global_subsumption_just,[status(thm)],[c_2152,c_346,c_1441]) ).

cnf(c_2154,plain,
    ( ~ product(e_1,X0,e_6)
    | ~ product(e_2,X0,e_1) ),
    inference(renaming,[status(thm)],[c_2153]) ).

cnf(c_2167,plain,
    ( ~ product(e_3,e_1,e_2)
    | ~ product(e_3,e_2,e_2)
    | equalish(e_1,e_2) ),
    inference(instantiation,[status(thm)],[c_1944]) ).

cnf(c_2168,plain,
    ( ~ product(e_3,e_2,e_2)
    | ~ product(e_3,e_1,e_2) ),
    inference(global_subsumption_just,[status(thm)],[c_2167,c_76,c_2167]) ).

cnf(c_2169,plain,
    ( ~ product(e_3,e_1,e_2)
    | ~ product(e_3,e_2,e_2) ),
    inference(renaming,[status(thm)],[c_2168]) ).

cnf(c_2170,plain,
    ( ~ product(e_3,e_1,e_2)
    | ~ product(e_3,e_3,e_2)
    | equalish(e_1,e_3) ),
    inference(instantiation,[status(thm)],[c_1944]) ).

cnf(c_2171,plain,
    ( ~ product(e_3,e_3,e_2)
    | ~ product(e_3,e_1,e_2) ),
    inference(global_subsumption_just,[status(thm)],[c_2170,c_77,c_2170]) ).

cnf(c_2172,plain,
    ( ~ product(e_3,e_1,e_2)
    | ~ product(e_3,e_3,e_2) ),
    inference(renaming,[status(thm)],[c_2171]) ).

cnf(c_2186,plain,
    ( ~ product(e_3,e_2,e_2)
    | ~ product(e_3,e_4,e_2)
    | equalish(e_2,e_4) ),
    inference(instantiation,[status(thm)],[c_1944]) ).

cnf(c_2228,plain,
    ( ~ product(X0,X1,X2)
    | ~ product(X2,X1,e_4)
    | product(X0,X2,e_4) ),
    inference(instantiation,[status(thm)],[c_110]) ).

cnf(c_2229,plain,
    ( ~ product(X0,X1,e_2)
    | ~ product(e_4,X1,X0)
    | product(e_4,X0,e_2) ),
    inference(instantiation,[status(thm)],[c_110]) ).

cnf(c_2230,plain,
    ( ~ product(e_1,e_1,e_2)
    | ~ product(e_4,e_1,e_1)
    | product(e_4,e_1,e_2) ),
    inference(instantiation,[status(thm)],[c_2229]) ).

cnf(c_2234,plain,
    ( ~ product(e_4,e_1,e_2)
    | ~ product(e_4,e_3,e_2)
    | equalish(e_1,e_3) ),
    inference(instantiation,[status(thm)],[c_1951]) ).

cnf(c_2235,plain,
    ( ~ product(e_4,e_3,e_2)
    | ~ product(e_4,e_1,e_2) ),
    inference(global_subsumption_just,[status(thm)],[c_2234,c_77,c_2234]) ).

cnf(c_2236,plain,
    ( ~ product(e_4,e_1,e_2)
    | ~ product(e_4,e_3,e_2) ),
    inference(renaming,[status(thm)],[c_2235]) ).

cnf(c_2237,plain,
    ( ~ product(e_4,e_1,e_2)
    | ~ product(e_4,e_4,e_2)
    | equalish(e_1,e_4) ),
    inference(instantiation,[status(thm)],[c_1951]) ).

cnf(c_2240,plain,
    ( ~ product(e_4,e_1,e_2)
    | ~ product(e_4,e_5,e_2)
    | equalish(e_1,e_5) ),
    inference(instantiation,[status(thm)],[c_1951]) ).

cnf(c_2243,plain,
    ( ~ product(e_4,e_1,e_2)
    | ~ product(e_4,e_6,e_2)
    | equalish(e_1,e_6) ),
    inference(instantiation,[status(thm)],[c_1951]) ).

cnf(c_2261,plain,
    ( ~ product(e_4,e_3,e_2)
    | ~ product(e_4,e_4,e_2)
    | equalish(e_3,e_4) ),
    inference(instantiation,[status(thm)],[c_1951]) ).

cnf(c_2267,plain,
    ( ~ product(e_4,e_3,e_2)
    | ~ product(e_4,e_6,e_2)
    | equalish(e_3,e_6) ),
    inference(instantiation,[status(thm)],[c_1951]) ).

cnf(c_2292,plain,
    ( ~ product(X0,X1,X2)
    | ~ product(X2,X1,e_5)
    | product(X0,X2,e_5) ),
    inference(instantiation,[status(thm)],[c_110]) ).

cnf(c_2293,plain,
    ( ~ product(X0,X1,e_2)
    | ~ product(e_5,X1,X0)
    | product(e_5,X0,e_2) ),
    inference(instantiation,[status(thm)],[c_110]) ).

cnf(c_2294,plain,
    ( ~ product(e_1,e_1,e_2)
    | ~ product(e_5,e_1,e_1)
    | product(e_5,e_1,e_2) ),
    inference(instantiation,[status(thm)],[c_2293]) ).

cnf(c_2356,plain,
    ( ~ product(X0,X1,X2)
    | ~ product(X2,X1,e_6)
    | product(X0,X2,e_6) ),
    inference(instantiation,[status(thm)],[c_110]) ).

cnf(c_2358,plain,
    ( ~ product(e_6,e_1,e_1)
    | ~ product(e_6,e_2,e_1)
    | equalish(e_1,e_2) ),
    inference(instantiation,[status(thm)],[c_1965]) ).

cnf(c_2359,plain,
    ~ product(e_6,e_1,e_1),
    inference(global_subsumption_just,[status(thm)],[c_2358,c_70,c_80,c_113,c_322,c_326,c_330,c_334,c_481,c_1969,c_1991]) ).

cnf(c_2425,plain,
    ( ~ product(X0,X1,e_1)
    | ~ product(X0,X1,e_2)
    | equalish(e_1,e_2) ),
    inference(instantiation,[status(thm)],[c_107]) ).

cnf(c_2426,plain,
    ( ~ product(X0,X1,e_2)
    | ~ product(X0,X1,e_1) ),
    inference(global_subsumption_just,[status(thm)],[c_2425,c_372]) ).

cnf(c_2427,plain,
    ( ~ product(X0,X1,e_1)
    | ~ product(X0,X1,e_2) ),
    inference(renaming,[status(thm)],[c_2426]) ).

cnf(c_2428,plain,
    ( ~ product(X0,X1,e_1)
    | ~ product(X0,X1,e_3)
    | equalish(e_1,e_3) ),
    inference(instantiation,[status(thm)],[c_107]) ).

cnf(c_2429,plain,
    ( ~ product(X0,X1,e_3)
    | ~ product(X0,X1,e_1) ),
    inference(global_subsumption_just,[status(thm)],[c_2428,c_396]) ).

cnf(c_2430,plain,
    ( ~ product(X0,X1,e_1)
    | ~ product(X0,X1,e_3) ),
    inference(renaming,[status(thm)],[c_2429]) ).

cnf(c_2485,plain,
    ( ~ product(X0,e_1,X1)
    | ~ product(X0,e_2,X1)
    | equalish(e_1,e_2) ),
    inference(instantiation,[status(thm)],[c_108]) ).

cnf(c_2486,plain,
    ( ~ product(X0,e_2,X1)
    | ~ product(X0,e_1,X1) ),
    inference(global_subsumption_just,[status(thm)],[c_2485,c_380]) ).

cnf(c_2487,plain,
    ( ~ product(X0,e_1,X1)
    | ~ product(X0,e_2,X1) ),
    inference(renaming,[status(thm)],[c_2486]) ).

cnf(c_2488,plain,
    ( ~ product(X0,e_1,X1)
    | ~ product(X0,e_3,X1)
    | equalish(e_1,e_3) ),
    inference(instantiation,[status(thm)],[c_108]) ).

cnf(c_2489,plain,
    ( ~ product(X0,e_3,X1)
    | ~ product(X0,e_1,X1) ),
    inference(global_subsumption_just,[status(thm)],[c_2488,c_403]) ).

cnf(c_2490,plain,
    ( ~ product(X0,e_1,X1)
    | ~ product(X0,e_3,X1) ),
    inference(renaming,[status(thm)],[c_2489]) ).

cnf(c_2491,plain,
    ( ~ product(X0,e_1,X1)
    | ~ product(X0,e_4,X1)
    | equalish(e_1,e_4) ),
    inference(instantiation,[status(thm)],[c_108]) ).

cnf(c_2492,plain,
    ( ~ product(X0,e_4,X1)
    | ~ product(X0,e_1,X1) ),
    inference(global_subsumption_just,[status(thm)],[c_2491,c_426]) ).

cnf(c_2493,plain,
    ( ~ product(X0,e_1,X1)
    | ~ product(X0,e_4,X1) ),
    inference(renaming,[status(thm)],[c_2492]) ).

cnf(c_2494,plain,
    ( ~ product(X0,e_1,X1)
    | ~ product(X0,e_5,X1)
    | equalish(e_1,e_5) ),
    inference(instantiation,[status(thm)],[c_108]) ).

cnf(c_2495,plain,
    ( ~ product(X0,e_5,X1)
    | ~ product(X0,e_1,X1) ),
    inference(global_subsumption_just,[status(thm)],[c_2494,c_449]) ).

cnf(c_2496,plain,
    ( ~ product(X0,e_1,X1)
    | ~ product(X0,e_5,X1) ),
    inference(renaming,[status(thm)],[c_2495]) ).

cnf(c_2497,plain,
    ( ~ product(X0,e_1,X1)
    | ~ product(X0,e_6,X1)
    | equalish(e_1,e_6) ),
    inference(instantiation,[status(thm)],[c_108]) ).

cnf(c_2498,plain,
    ( ~ product(X0,e_6,X1)
    | ~ product(X0,e_1,X1) ),
    inference(global_subsumption_just,[status(thm)],[c_2497,c_472]) ).

cnf(c_2499,plain,
    ( ~ product(X0,e_1,X1)
    | ~ product(X0,e_6,X1) ),
    inference(renaming,[status(thm)],[c_2498]) ).

cnf(c_2501,plain,
    ( ~ product(X0,e_2,X1)
    | ~ product(X0,e_3,X1)
    | equalish(e_2,e_3) ),
    inference(instantiation,[status(thm)],[c_108]) ).

cnf(c_2502,plain,
    ( ~ product(X0,e_3,X1)
    | ~ product(X0,e_2,X1) ),
    inference(global_subsumption_just,[status(thm)],[c_2501,c_498]) ).

cnf(c_2503,plain,
    ( ~ product(X0,e_2,X1)
    | ~ product(X0,e_3,X1) ),
    inference(renaming,[status(thm)],[c_2502]) ).

cnf(c_2504,plain,
    ( ~ product(X0,e_2,X1)
    | ~ product(X0,e_4,X1)
    | equalish(e_2,e_4) ),
    inference(instantiation,[status(thm)],[c_108]) ).

cnf(c_2505,plain,
    ( ~ product(X0,e_4,X1)
    | ~ product(X0,e_2,X1) ),
    inference(global_subsumption_just,[status(thm)],[c_2504,c_521]) ).

cnf(c_2506,plain,
    ( ~ product(X0,e_2,X1)
    | ~ product(X0,e_4,X1) ),
    inference(renaming,[status(thm)],[c_2505]) ).

cnf(c_2507,plain,
    ( ~ product(X0,e_2,X1)
    | ~ product(X0,e_5,X1)
    | equalish(e_2,e_5) ),
    inference(instantiation,[status(thm)],[c_108]) ).

cnf(c_2508,plain,
    ( ~ product(X0,e_5,X1)
    | ~ product(X0,e_2,X1) ),
    inference(global_subsumption_just,[status(thm)],[c_2507,c_544]) ).

cnf(c_2509,plain,
    ( ~ product(X0,e_2,X1)
    | ~ product(X0,e_5,X1) ),
    inference(renaming,[status(thm)],[c_2508]) ).

cnf(c_2510,plain,
    ( ~ product(X0,e_2,X1)
    | ~ product(X0,e_6,X1)
    | equalish(e_2,e_6) ),
    inference(instantiation,[status(thm)],[c_108]) ).

cnf(c_2511,plain,
    ( ~ product(X0,e_6,X1)
    | ~ product(X0,e_2,X1) ),
    inference(global_subsumption_just,[status(thm)],[c_2510,c_567]) ).

cnf(c_2512,plain,
    ( ~ product(X0,e_2,X1)
    | ~ product(X0,e_6,X1) ),
    inference(renaming,[status(thm)],[c_2511]) ).

cnf(c_2515,plain,
    ( ~ product(X0,e_3,X1)
    | ~ product(X0,e_4,X1)
    | equalish(e_3,e_4) ),
    inference(instantiation,[status(thm)],[c_108]) ).

cnf(c_2516,plain,
    ( ~ product(X0,e_4,X1)
    | ~ product(X0,e_3,X1) ),
    inference(global_subsumption_just,[status(thm)],[c_2515,c_596]) ).

cnf(c_2517,plain,
    ( ~ product(X0,e_3,X1)
    | ~ product(X0,e_4,X1) ),
    inference(renaming,[status(thm)],[c_2516]) ).

cnf(c_2521,plain,
    ( ~ product(X0,e_3,X1)
    | ~ product(X0,e_6,X1)
    | equalish(e_3,e_6) ),
    inference(instantiation,[status(thm)],[c_108]) ).

cnf(c_2522,plain,
    ( ~ product(X0,e_6,X1)
    | ~ product(X0,e_3,X1) ),
    inference(global_subsumption_just,[status(thm)],[c_2521,c_642]) ).

cnf(c_2523,plain,
    ( ~ product(X0,e_3,X1)
    | ~ product(X0,e_6,X1) ),
    inference(renaming,[status(thm)],[c_2522]) ).

cnf(c_2530,plain,
    ( ~ product(X0,e_4,X1)
    | ~ product(X0,e_6,X1)
    | equalish(e_4,e_6) ),
    inference(instantiation,[status(thm)],[c_108]) ).

cnf(c_2531,plain,
    ( ~ product(X0,e_6,X1)
    | ~ product(X0,e_4,X1) ),
    inference(global_subsumption_just,[status(thm)],[c_2530,c_697]) ).

cnf(c_2532,plain,
    ( ~ product(X0,e_4,X1)
    | ~ product(X0,e_6,X1) ),
    inference(renaming,[status(thm)],[c_2531]) ).

cnf(c_2537,plain,
    ( ~ product(X0,e_5,X1)
    | ~ product(X0,e_6,X1)
    | equalish(e_5,e_6) ),
    inference(instantiation,[status(thm)],[c_108]) ).

cnf(c_2538,plain,
    ( ~ product(X0,e_6,X1)
    | ~ product(X0,e_5,X1) ),
    inference(global_subsumption_just,[status(thm)],[c_2537,c_732]) ).

cnf(c_2539,plain,
    ( ~ product(X0,e_5,X1)
    | ~ product(X0,e_6,X1) ),
    inference(renaming,[status(thm)],[c_2538]) ).

cnf(c_2545,plain,
    ( ~ product(e_1,X0,X1)
    | ~ product(e_2,X0,X1)
    | equalish(e_1,e_2) ),
    inference(instantiation,[status(thm)],[c_109]) ).

cnf(c_2546,plain,
    ( ~ product(e_2,X0,X1)
    | ~ product(e_1,X0,X1) ),
    inference(global_subsumption_just,[status(thm)],[c_2545,c_388]) ).

cnf(c_2547,plain,
    ( ~ product(e_1,X0,X1)
    | ~ product(e_2,X0,X1) ),
    inference(renaming,[status(thm)],[c_2546]) ).

cnf(c_2551,plain,
    ( ~ product(e_1,X0,X1)
    | ~ product(e_4,X0,X1)
    | equalish(e_1,e_4) ),
    inference(instantiation,[status(thm)],[c_109]) ).

cnf(c_2552,plain,
    ( ~ product(e_4,X0,X1)
    | ~ product(e_1,X0,X1) ),
    inference(global_subsumption_just,[status(thm)],[c_2551,c_434]) ).

cnf(c_2553,plain,
    ( ~ product(e_1,X0,X1)
    | ~ product(e_4,X0,X1) ),
    inference(renaming,[status(thm)],[c_2552]) ).

cnf(c_2557,plain,
    ( ~ product(e_1,X0,X1)
    | ~ product(e_6,X0,X1)
    | equalish(e_1,e_6) ),
    inference(instantiation,[status(thm)],[c_109]) ).

cnf(c_2558,plain,
    ( ~ product(e_6,X0,X1)
    | ~ product(e_1,X0,X1) ),
    inference(global_subsumption_just,[status(thm)],[c_2557,c_480]) ).

cnf(c_2559,plain,
    ( ~ product(e_1,X0,X1)
    | ~ product(e_6,X0,X1) ),
    inference(renaming,[status(thm)],[c_2558]) ).

cnf(c_2561,plain,
    ( ~ product(e_2,X0,X1)
    | ~ product(e_3,X0,X1)
    | equalish(e_2,e_3) ),
    inference(instantiation,[status(thm)],[c_109]) ).

cnf(c_2562,plain,
    ( ~ product(e_3,X0,X1)
    | ~ product(e_2,X0,X1) ),
    inference(global_subsumption_just,[status(thm)],[c_2561,c_506]) ).

cnf(c_2563,plain,
    ( ~ product(e_2,X0,X1)
    | ~ product(e_3,X0,X1) ),
    inference(renaming,[status(thm)],[c_2562]) ).

cnf(c_2564,plain,
    ( ~ product(e_2,X0,X1)
    | ~ product(e_4,X0,X1)
    | equalish(e_2,e_4) ),
    inference(instantiation,[status(thm)],[c_109]) ).

cnf(c_2565,plain,
    ( ~ product(e_4,X0,X1)
    | ~ product(e_2,X0,X1) ),
    inference(global_subsumption_just,[status(thm)],[c_2564,c_529]) ).

cnf(c_2566,plain,
    ( ~ product(e_2,X0,X1)
    | ~ product(e_4,X0,X1) ),
    inference(renaming,[status(thm)],[c_2565]) ).

cnf(c_2567,plain,
    ( ~ product(e_2,X0,X1)
    | ~ product(e_5,X0,X1)
    | equalish(e_2,e_5) ),
    inference(instantiation,[status(thm)],[c_109]) ).

cnf(c_2568,plain,
    ( ~ product(e_5,X0,X1)
    | ~ product(e_2,X0,X1) ),
    inference(global_subsumption_just,[status(thm)],[c_2567,c_552]) ).

cnf(c_2569,plain,
    ( ~ product(e_2,X0,X1)
    | ~ product(e_5,X0,X1) ),
    inference(renaming,[status(thm)],[c_2568]) ).

cnf(c_2570,plain,
    ( ~ product(e_2,X0,X1)
    | ~ product(e_6,X0,X1)
    | equalish(e_2,e_6) ),
    inference(instantiation,[status(thm)],[c_109]) ).

cnf(c_2571,plain,
    ( ~ product(e_6,X0,X1)
    | ~ product(e_2,X0,X1) ),
    inference(global_subsumption_just,[status(thm)],[c_2570,c_575]) ).

cnf(c_2572,plain,
    ( ~ product(e_2,X0,X1)
    | ~ product(e_6,X0,X1) ),
    inference(renaming,[status(thm)],[c_2571]) ).

cnf(c_2575,plain,
    ( ~ product(e_3,X0,X1)
    | ~ product(e_4,X0,X1)
    | equalish(e_3,e_4) ),
    inference(instantiation,[status(thm)],[c_109]) ).

cnf(c_2576,plain,
    ( ~ product(e_4,X0,X1)
    | ~ product(e_3,X0,X1) ),
    inference(global_subsumption_just,[status(thm)],[c_2575,c_604]) ).

cnf(c_2577,plain,
    ( ~ product(e_3,X0,X1)
    | ~ product(e_4,X0,X1) ),
    inference(renaming,[status(thm)],[c_2576]) ).

cnf(c_2578,plain,
    ( ~ product(e_3,X0,X1)
    | ~ product(e_5,X0,X1)
    | equalish(e_3,e_5) ),
    inference(instantiation,[status(thm)],[c_109]) ).

cnf(c_2579,plain,
    ( ~ product(e_5,X0,X1)
    | ~ product(e_3,X0,X1) ),
    inference(global_subsumption_just,[status(thm)],[c_2578,c_627]) ).

cnf(c_2580,plain,
    ( ~ product(e_3,X0,X1)
    | ~ product(e_5,X0,X1) ),
    inference(renaming,[status(thm)],[c_2579]) ).

cnf(c_2581,plain,
    ( ~ product(e_3,X0,X1)
    | ~ product(e_6,X0,X1)
    | equalish(e_3,e_6) ),
    inference(instantiation,[status(thm)],[c_109]) ).

cnf(c_2582,plain,
    ( ~ product(e_6,X0,X1)
    | ~ product(e_3,X0,X1) ),
    inference(global_subsumption_just,[status(thm)],[c_2581,c_650]) ).

cnf(c_2583,plain,
    ( ~ product(e_3,X0,X1)
    | ~ product(e_6,X0,X1) ),
    inference(renaming,[status(thm)],[c_2582]) ).

cnf(c_2587,plain,
    ( ~ product(e_4,X0,X1)
    | ~ product(e_5,X0,X1)
    | equalish(e_4,e_5) ),
    inference(instantiation,[status(thm)],[c_109]) ).

cnf(c_2588,plain,
    ( ~ product(e_5,X0,X1)
    | ~ product(e_4,X0,X1) ),
    inference(global_subsumption_just,[status(thm)],[c_2587,c_682]) ).

cnf(c_2589,plain,
    ( ~ product(e_4,X0,X1)
    | ~ product(e_5,X0,X1) ),
    inference(renaming,[status(thm)],[c_2588]) ).

cnf(c_2590,plain,
    ( ~ product(e_4,X0,X1)
    | ~ product(e_6,X0,X1)
    | equalish(e_4,e_6) ),
    inference(instantiation,[status(thm)],[c_109]) ).

cnf(c_2591,plain,
    ( ~ product(e_6,X0,X1)
    | ~ product(e_4,X0,X1) ),
    inference(global_subsumption_just,[status(thm)],[c_2590,c_705]) ).

cnf(c_2592,plain,
    ( ~ product(e_4,X0,X1)
    | ~ product(e_6,X0,X1) ),
    inference(renaming,[status(thm)],[c_2591]) ).

cnf(c_2597,plain,
    ( ~ product(e_5,X0,X1)
    | ~ product(e_6,X0,X1)
    | equalish(e_5,e_6) ),
    inference(instantiation,[status(thm)],[c_109]) ).

cnf(c_2598,plain,
    ( ~ product(e_6,X0,X1)
    | ~ product(e_5,X0,X1) ),
    inference(global_subsumption_just,[status(thm)],[c_2597,c_740]) ).

cnf(c_2599,plain,
    ( ~ product(e_5,X0,X1)
    | ~ product(e_6,X0,X1) ),
    inference(renaming,[status(thm)],[c_2598]) ).

cnf(c_2626,plain,
    ( ~ product(X0,X1,X2)
    | ~ product(X2,X1,e_2)
    | product(X0,X2,e_2) ),
    inference(instantiation,[status(thm)],[c_110]) ).

cnf(c_2627,plain,
    ( ~ product(e_2,X0,e_3)
    | ~ product(e_6,X0,e_2)
    | product(e_6,e_2,e_3) ),
    inference(instantiation,[status(thm)],[c_2057]) ).

cnf(c_2628,plain,
    ( ~ product(e_2,e_1,e_3)
    | ~ product(e_6,e_1,e_2)
    | product(e_6,e_2,e_3) ),
    inference(instantiation,[status(thm)],[c_2627]) ).

cnf(c_2630,plain,
    ( ~ product(X0,X1,X2)
    | ~ product(X2,X1,e_3)
    | product(X0,X2,e_3) ),
    inference(instantiation,[status(thm)],[c_110]) ).

cnf(c_2666,plain,
    ( ~ product(X0,X1,X2)
    | ~ product(e_2,X1,X0)
    | product(e_2,X0,X2) ),
    inference(instantiation,[status(thm)],[c_110]) ).

cnf(c_2691,plain,
    ( ~ group_element(e_2)
    | product(e_2,e_2,e_1)
    | product(e_2,e_2,e_2)
    | product(e_2,e_2,e_3)
    | product(e_2,e_2,e_4)
    | product(e_2,e_2,e_5)
    | product(e_2,e_2,e_6) ),
    inference(instantiation,[status(thm)],[c_1906]) ).

cnf(c_2692,plain,
    ( product(e_2,e_2,e_1)
    | product(e_2,e_2,e_2)
    | product(e_2,e_2,e_3)
    | product(e_2,e_2,e_4)
    | product(e_2,e_2,e_5)
    | product(e_2,e_2,e_6) ),
    inference(global_subsumption_just,[status(thm)],[c_2691,c_71,c_2691]) ).

cnf(c_2697,plain,
    ( ~ group_element(e_4)
    | product(e_2,e_4,e_1)
    | product(e_2,e_4,e_2)
    | product(e_2,e_4,e_3)
    | product(e_2,e_4,e_4)
    | product(e_2,e_4,e_5)
    | product(e_2,e_4,e_6) ),
    inference(instantiation,[status(thm)],[c_1906]) ).

cnf(c_2698,plain,
    ( product(e_2,e_4,e_1)
    | product(e_2,e_4,e_2)
    | product(e_2,e_4,e_3)
    | product(e_2,e_4,e_4)
    | product(e_2,e_4,e_5)
    | product(e_2,e_4,e_6) ),
    inference(global_subsumption_just,[status(thm)],[c_2697,c_73,c_2697]) ).

cnf(c_2700,plain,
    ( ~ group_element(e_5)
    | product(e_2,e_5,e_1)
    | product(e_2,e_5,e_2)
    | product(e_2,e_5,e_3)
    | product(e_2,e_5,e_4)
    | product(e_2,e_5,e_5)
    | product(e_2,e_5,e_6) ),
    inference(instantiation,[status(thm)],[c_1906]) ).

cnf(c_2701,plain,
    ( product(e_2,e_5,e_1)
    | product(e_2,e_5,e_2)
    | product(e_2,e_5,e_3)
    | product(e_2,e_5,e_4)
    | product(e_2,e_5,e_5)
    | product(e_2,e_5,e_6) ),
    inference(global_subsumption_just,[status(thm)],[c_2700,c_74,c_2700]) ).

cnf(c_2703,plain,
    ( ~ group_element(e_6)
    | product(e_2,e_6,e_1)
    | product(e_2,e_6,e_2)
    | product(e_2,e_6,e_3)
    | product(e_2,e_6,e_4)
    | product(e_2,e_6,e_5)
    | product(e_2,e_6,e_6) ),
    inference(instantiation,[status(thm)],[c_1906]) ).

cnf(c_2704,plain,
    ( product(e_2,e_6,e_1)
    | product(e_2,e_6,e_2)
    | product(e_2,e_6,e_3)
    | product(e_2,e_6,e_4)
    | product(e_2,e_6,e_5)
    | product(e_2,e_6,e_6) ),
    inference(global_subsumption_just,[status(thm)],[c_2703,c_75,c_2703]) ).

cnf(c_2707,plain,
    ( ~ product(e_2,X0,e_2)
    | product(e_2,e_2,e_2) ),
    inference(instantiation,[status(thm)],[c_1934]) ).

cnf(c_2708,plain,
    ( ~ product(e_2,e_1,e_2)
    | product(e_2,e_2,e_2) ),
    inference(instantiation,[status(thm)],[c_2707]) ).

cnf(c_2766,plain,
    ( ~ product(X0,X1,e_1)
    | ~ product(e_4,X1,X0)
    | product(e_4,X0,e_1) ),
    inference(instantiation,[status(thm)],[c_110]) ).

cnf(c_2772,plain,
    ( ~ product(e_2,X0,e_3)
    | ~ product(e_3,X0,e_2)
    | product(e_2,e_3,e_2) ),
    inference(instantiation,[status(thm)],[c_2129]) ).

cnf(c_2773,plain,
    ( ~ product(e_2,e_1,e_3)
    | ~ product(e_3,e_1,e_2)
    | product(e_2,e_3,e_2) ),
    inference(instantiation,[status(thm)],[c_2772]) ).

cnf(c_2848,plain,
    ( ~ product(e_2,X0,e_1)
    | ~ product(e_2,X0,e_3) ),
    inference(instantiation,[status(thm)],[c_2430]) ).

cnf(c_2872,plain,
    ( ~ product(e_2,e_1,e_3)
    | ~ product(e_2,e_2,e_3) ),
    inference(instantiation,[status(thm)],[c_2487]) ).

cnf(c_2884,plain,
    ( ~ product(X0,X1,e_4)
    | ~ product(e_4,X1,X2)
    | product(X0,e_4,X2) ),
    inference(instantiation,[status(thm)],[c_110]) ).

cnf(c_2886,plain,
    ( ~ product(e_2,e_1,e_3)
    | ~ product(e_2,e_4,e_3) ),
    inference(instantiation,[status(thm)],[c_2493]) ).

cnf(c_2893,plain,
    ( ~ product(e_2,e_1,e_3)
    | ~ product(e_2,e_5,e_3) ),
    inference(instantiation,[status(thm)],[c_2496]) ).

cnf(c_2900,plain,
    ( ~ product(e_2,e_1,e_3)
    | ~ product(e_2,e_6,e_3) ),
    inference(instantiation,[status(thm)],[c_2499]) ).

cnf(c_2908,plain,
    ( ~ product(e_3,e_2,e_3)
    | ~ product(e_3,e_3,e_3) ),
    inference(instantiation,[status(thm)],[c_2503]) ).

cnf(c_2909,plain,
    ( ~ product(e_4,e_2,e_3)
    | ~ product(e_4,e_3,e_3) ),
    inference(instantiation,[status(thm)],[c_2503]) ).

cnf(c_2916,plain,
    ( ~ product(e_4,e_2,e_3)
    | ~ product(e_4,e_4,e_3) ),
    inference(instantiation,[status(thm)],[c_2506]) ).

cnf(c_2923,plain,
    ( ~ product(e_4,e_2,e_3)
    | ~ product(e_4,e_5,e_3) ),
    inference(instantiation,[status(thm)],[c_2509]) ).

cnf(c_2930,plain,
    ( ~ product(e_4,e_2,e_3)
    | ~ product(e_4,e_6,e_3) ),
    inference(instantiation,[status(thm)],[c_2512]) ).

cnf(c_2980,plain,
    ( ~ product(e_1,X0,e_3)
    | ~ product(e_4,X0,e_3) ),
    inference(instantiation,[status(thm)],[c_2553]) ).

cnf(c_2984,plain,
    ( ~ product(e_1,X0,e_3)
    | ~ product(e_6,X0,e_3) ),
    inference(instantiation,[status(thm)],[c_2559]) ).

cnf(c_2986,plain,
    ( ~ product(e_2,X0,e_3)
    | ~ product(e_3,X0,e_3) ),
    inference(instantiation,[status(thm)],[c_2563]) ).

cnf(c_2987,plain,
    ( ~ product(e_2,e_1,e_3)
    | ~ product(e_3,e_1,e_3) ),
    inference(instantiation,[status(thm)],[c_2986]) ).

cnf(c_2989,plain,
    ( ~ product(e_2,X0,e_3)
    | ~ product(e_4,X0,e_3) ),
    inference(instantiation,[status(thm)],[c_2566]) ).

cnf(c_2990,plain,
    ( ~ product(e_2,e_1,e_3)
    | ~ product(e_4,e_1,e_3) ),
    inference(instantiation,[status(thm)],[c_2989]) ).

cnf(c_2992,plain,
    ( ~ product(e_2,X0,e_3)
    | ~ product(e_5,X0,e_3) ),
    inference(instantiation,[status(thm)],[c_2569]) ).

cnf(c_2993,plain,
    ( ~ product(e_2,e_1,e_3)
    | ~ product(e_5,e_1,e_3) ),
    inference(instantiation,[status(thm)],[c_2992]) ).

cnf(c_2995,plain,
    ( ~ product(e_2,X0,e_3)
    | ~ product(e_6,X0,e_3) ),
    inference(instantiation,[status(thm)],[c_2572]) ).

cnf(c_2996,plain,
    ( ~ product(e_2,e_1,e_3)
    | ~ product(e_6,e_1,e_3) ),
    inference(instantiation,[status(thm)],[c_2995]) ).

cnf(c_2998,plain,
    ( ~ product(e_3,X0,e_3)
    | ~ product(e_4,X0,e_3) ),
    inference(instantiation,[status(thm)],[c_2577]) ).

cnf(c_3001,plain,
    ( ~ product(e_3,X0,e_3)
    | ~ product(e_5,X0,e_3) ),
    inference(instantiation,[status(thm)],[c_2580]) ).

cnf(c_3007,plain,
    ( ~ product(e_4,X0,e_3)
    | ~ product(e_5,X0,e_3) ),
    inference(instantiation,[status(thm)],[c_2589]) ).

cnf(c_3010,plain,
    ( ~ product(e_4,X0,e_3)
    | ~ product(e_6,X0,e_3) ),
    inference(instantiation,[status(thm)],[c_2592]) ).

cnf(c_3013,plain,
    ( ~ product(e_5,X0,e_3)
    | ~ product(e_6,X0,e_3) ),
    inference(instantiation,[status(thm)],[c_2599]) ).

cnf(c_3022,plain,
    ( ~ product(X0,X1,e_6)
    | ~ product(e_6,X1,e_3)
    | product(X0,e_6,e_3) ),
    inference(instantiation,[status(thm)],[c_2630]) ).

cnf(c_3024,plain,
    ( ~ product(e_3,X0,X1)
    | ~ product(e_2,X0,e_3)
    | product(e_2,e_3,X1) ),
    inference(instantiation,[status(thm)],[c_2666]) ).

cnf(c_3026,plain,
    ( ~ product(e_2,e_1,e_1)
    | ~ product(e_2,e_2,e_1) ),
    inference(instantiation,[status(thm)],[c_2487]) ).

cnf(c_3027,plain,
    ~ product(e_2,e_1,e_1),
    inference(global_subsumption_just,[status(thm)],[c_3026,c_70,c_81,c_113,c_322,c_326,c_330,c_334,c_389,c_1939,c_2130]) ).

cnf(c_3032,plain,
    ( ~ product(e_1,e_2,e_6)
    | ~ product(e_2,e_2,e_1) ),
    inference(instantiation,[status(thm)],[c_2154]) ).

cnf(c_3033,plain,
    ( ~ product(e_1,e_2,e_5)
    | ~ product(e_2,e_2,e_1) ),
    inference(instantiation,[status(thm)],[c_2151]) ).

cnf(c_3034,plain,
    ( ~ product(e_1,e_2,e_4)
    | ~ product(e_2,e_2,e_1) ),
    inference(instantiation,[status(thm)],[c_2148]) ).

cnf(c_3036,plain,
    ( ~ product(e_1,e_2,e_2)
    | ~ product(e_2,e_2,e_1)
    | product(e_2,e_1,e_2) ),
    inference(instantiation,[status(thm)],[c_2129]) ).

cnf(c_3037,plain,
    ( ~ product(e_2,e_2,e_1)
    | ~ product(e_1,e_2,e_2) ),
    inference(global_subsumption_just,[status(thm)],[c_3036,c_76,c_2064,c_2708,c_3036]) ).

cnf(c_3038,plain,
    ( ~ product(e_1,e_2,e_2)
    | ~ product(e_2,e_2,e_1) ),
    inference(renaming,[status(thm)],[c_3037]) ).

cnf(c_3054,plain,
    ( ~ product(e_1,e_4,e_6)
    | ~ product(e_2,e_4,e_1) ),
    inference(instantiation,[status(thm)],[c_2154]) ).

cnf(c_3055,plain,
    ( ~ product(e_1,e_4,e_5)
    | ~ product(e_2,e_4,e_1) ),
    inference(instantiation,[status(thm)],[c_2151]) ).

cnf(c_3058,plain,
    ( ~ product(e_1,e_4,e_2)
    | ~ product(e_2,e_4,e_1)
    | product(e_2,e_1,e_2) ),
    inference(instantiation,[status(thm)],[c_2129]) ).

cnf(c_3059,plain,
    ( ~ product(e_2,e_4,e_1)
    | ~ product(e_1,e_4,e_2) ),
    inference(global_subsumption_just,[status(thm)],[c_3058,c_76,c_2064,c_2708,c_3058]) ).

cnf(c_3060,plain,
    ( ~ product(e_1,e_4,e_2)
    | ~ product(e_2,e_4,e_1) ),
    inference(renaming,[status(thm)],[c_3059]) ).

cnf(c_3067,plain,
    ( ~ group_element(e_2)
    | product(e_1,e_2,e_1)
    | product(e_1,e_2,e_2)
    | product(e_1,e_2,e_3)
    | product(e_1,e_2,e_4)
    | product(e_1,e_2,e_5)
    | product(e_1,e_2,e_6) ),
    inference(instantiation,[status(thm)],[c_1902]) ).

cnf(c_3068,plain,
    ( product(e_1,e_2,e_2)
    | product(e_1,e_2,e_3)
    | product(e_1,e_2,e_4)
    | product(e_1,e_2,e_5)
    | product(e_1,e_2,e_6) ),
    inference(global_subsumption_just,[status(thm)],[c_3067,c_71,c_70,c_81,c_76,c_113,c_322,c_326,c_330,c_334,c_338,c_342,c_346,c_381,c_389,c_1905,c_1939,c_2058,c_2064,c_2130,c_2708,c_3067]) ).

cnf(c_3070,plain,
    ( ~ group_element(e_3)
    | product(e_1,e_3,e_1)
    | product(e_1,e_3,e_2)
    | product(e_1,e_3,e_3)
    | product(e_1,e_3,e_4)
    | product(e_1,e_3,e_5)
    | product(e_1,e_3,e_6) ),
    inference(instantiation,[status(thm)],[c_1902]) ).

cnf(c_3071,plain,
    ( product(e_1,e_3,e_1)
    | product(e_1,e_3,e_2)
    | product(e_1,e_3,e_3)
    | product(e_1,e_3,e_4)
    | product(e_1,e_3,e_5)
    | product(e_1,e_3,e_6) ),
    inference(global_subsumption_just,[status(thm)],[c_3070,c_72,c_3070]) ).

cnf(c_3073,plain,
    ( ~ group_element(e_4)
    | product(e_1,e_4,e_1)
    | product(e_1,e_4,e_2)
    | product(e_1,e_4,e_3)
    | product(e_1,e_4,e_4)
    | product(e_1,e_4,e_5)
    | product(e_1,e_4,e_6) ),
    inference(instantiation,[status(thm)],[c_1902]) ).

cnf(c_3074,plain,
    ( product(e_1,e_4,e_1)
    | product(e_1,e_4,e_2)
    | product(e_1,e_4,e_3)
    | product(e_1,e_4,e_4)
    | product(e_1,e_4,e_5)
    | product(e_1,e_4,e_6) ),
    inference(global_subsumption_just,[status(thm)],[c_3073,c_73,c_3073]) ).

cnf(c_3079,plain,
    ( ~ group_element(e_5)
    | product(e_1,e_5,e_1)
    | product(e_1,e_5,e_2)
    | product(e_1,e_5,e_3)
    | product(e_1,e_5,e_4)
    | product(e_1,e_5,e_5)
    | product(e_1,e_5,e_6) ),
    inference(instantiation,[status(thm)],[c_1902]) ).

cnf(c_3080,plain,
    ( product(e_1,e_5,e_1)
    | product(e_1,e_5,e_2)
    | product(e_1,e_5,e_3)
    | product(e_1,e_5,e_4)
    | product(e_1,e_5,e_5)
    | product(e_1,e_5,e_6) ),
    inference(global_subsumption_just,[status(thm)],[c_3079,c_74,c_3079]) ).

cnf(c_3082,plain,
    ( ~ group_element(e_6)
    | product(e_1,e_6,e_1)
    | product(e_1,e_6,e_2)
    | product(e_1,e_6,e_3)
    | product(e_1,e_6,e_4)
    | product(e_1,e_6,e_5)
    | product(e_1,e_6,e_6) ),
    inference(instantiation,[status(thm)],[c_1902]) ).

cnf(c_3083,plain,
    ( product(e_1,e_6,e_1)
    | product(e_1,e_6,e_2)
    | product(e_1,e_6,e_3)
    | product(e_1,e_6,e_4)
    | product(e_1,e_6,e_5)
    | product(e_1,e_6,e_6) ),
    inference(global_subsumption_just,[status(thm)],[c_3082,c_75,c_3082]) ).

cnf(c_3089,plain,
    ( ~ product(e_3,X0,e_4)
    | ~ product(e_4,X0,e_2)
    | product(e_3,e_4,e_2) ),
    inference(instantiation,[status(thm)],[c_1949]) ).

cnf(c_3090,plain,
    ( ~ product(e_3,e_1,e_4)
    | ~ product(e_4,e_1,e_2)
    | product(e_3,e_4,e_2) ),
    inference(instantiation,[status(thm)],[c_3089]) ).

cnf(c_3094,plain,
    ( ~ group_element(e_2)
    | product(e_3,e_2,e_1)
    | product(e_3,e_2,e_2)
    | product(e_3,e_2,e_3)
    | product(e_3,e_2,e_4)
    | product(e_3,e_2,e_5)
    | product(e_3,e_2,e_6) ),
    inference(instantiation,[status(thm)],[c_1911]) ).

cnf(c_3097,plain,
    ( ~ group_element(e_3)
    | product(e_3,e_3,e_1)
    | product(e_3,e_3,e_2)
    | product(e_3,e_3,e_3)
    | product(e_3,e_3,e_4)
    | product(e_3,e_3,e_5)
    | product(e_3,e_3,e_6) ),
    inference(instantiation,[status(thm)],[c_1911]) ).

cnf(c_3098,plain,
    ( product(e_3,e_3,e_1)
    | product(e_3,e_3,e_2)
    | product(e_3,e_3,e_3)
    | product(e_3,e_3,e_4)
    | product(e_3,e_3,e_5)
    | product(e_3,e_3,e_6) ),
    inference(global_subsumption_just,[status(thm)],[c_3097,c_72,c_3097]) ).

cnf(c_3116,plain,
    ( ~ group_element(e_2)
    | product(e_4,e_2,e_1)
    | product(e_4,e_2,e_2)
    | product(e_4,e_2,e_3)
    | product(e_4,e_2,e_4)
    | product(e_4,e_2,e_5)
    | product(e_4,e_2,e_6) ),
    inference(instantiation,[status(thm)],[c_1916]) ).

cnf(c_3117,plain,
    ( product(e_4,e_2,e_1)
    | product(e_4,e_2,e_2)
    | product(e_4,e_2,e_3)
    | product(e_4,e_2,e_4)
    | product(e_4,e_2,e_5)
    | product(e_4,e_2,e_6) ),
    inference(global_subsumption_just,[status(thm)],[c_3116,c_71,c_3116]) ).

cnf(c_3119,plain,
    ( ~ group_element(e_3)
    | product(e_4,e_3,e_1)
    | product(e_4,e_3,e_2)
    | product(e_4,e_3,e_3)
    | product(e_4,e_3,e_4)
    | product(e_4,e_3,e_5)
    | product(e_4,e_3,e_6) ),
    inference(instantiation,[status(thm)],[c_1916]) ).

cnf(c_3120,plain,
    ( product(e_4,e_3,e_1)
    | product(e_4,e_3,e_2)
    | product(e_4,e_3,e_3)
    | product(e_4,e_3,e_4)
    | product(e_4,e_3,e_5)
    | product(e_4,e_3,e_6) ),
    inference(global_subsumption_just,[status(thm)],[c_3119,c_72,c_3119]) ).

cnf(c_3122,plain,
    ( ~ group_element(e_4)
    | product(e_4,e_4,e_1)
    | product(e_4,e_4,e_2)
    | product(e_4,e_4,e_3)
    | product(e_4,e_4,e_4)
    | product(e_4,e_4,e_5)
    | product(e_4,e_4,e_6) ),
    inference(instantiation,[status(thm)],[c_1916]) ).

cnf(c_3123,plain,
    ( product(e_4,e_4,e_1)
    | product(e_4,e_4,e_2)
    | product(e_4,e_4,e_3)
    | product(e_4,e_4,e_4)
    | product(e_4,e_4,e_5)
    | product(e_4,e_4,e_6) ),
    inference(global_subsumption_just,[status(thm)],[c_3122,c_73,c_3122]) ).

cnf(c_3125,plain,
    ( ~ product(e_3,X0,e_4)
    | ~ product(e_4,X0,e_4) ),
    inference(instantiation,[status(thm)],[c_2577]) ).

cnf(c_3128,plain,
    ( ~ product(e_3,e_1,e_4)
    | ~ product(e_4,e_1,e_4) ),
    inference(instantiation,[status(thm)],[c_3125]) ).

cnf(c_3145,plain,
    ( ~ group_element(e_4)
    | product(e_5,e_4,e_1)
    | product(e_5,e_4,e_2)
    | product(e_5,e_4,e_3)
    | product(e_5,e_4,e_4)
    | product(e_5,e_4,e_5)
    | product(e_5,e_4,e_6) ),
    inference(instantiation,[status(thm)],[c_1921]) ).

cnf(c_3146,plain,
    ( product(e_5,e_4,e_1)
    | product(e_5,e_4,e_2)
    | product(e_5,e_4,e_3)
    | product(e_5,e_4,e_4)
    | product(e_5,e_4,e_5)
    | product(e_5,e_4,e_6) ),
    inference(global_subsumption_just,[status(thm)],[c_3145,c_73,c_3145]) ).

cnf(c_3148,plain,
    ( ~ product(e_4,X0,e_4)
    | ~ product(e_5,X0,e_4) ),
    inference(instantiation,[status(thm)],[c_2589]) ).

cnf(c_3149,plain,
    ( ~ product(e_3,X0,e_4)
    | ~ product(e_5,X0,e_4) ),
    inference(instantiation,[status(thm)],[c_2580]) ).

cnf(c_3152,plain,
    ( ~ product(e_3,e_1,e_4)
    | ~ product(e_5,e_1,e_4) ),
    inference(instantiation,[status(thm)],[c_3149]) ).

cnf(c_3153,plain,
    ( ~ product(e_4,e_1,e_4)
    | ~ product(e_5,e_1,e_4) ),
    inference(instantiation,[status(thm)],[c_3148]) ).

cnf(c_3171,plain,
    ( ~ group_element(e_4)
    | product(e_6,e_4,e_1)
    | product(e_6,e_4,e_2)
    | product(e_6,e_4,e_3)
    | product(e_6,e_4,e_4)
    | product(e_6,e_4,e_5)
    | product(e_6,e_4,e_6) ),
    inference(instantiation,[status(thm)],[c_1926]) ).

cnf(c_3172,plain,
    ( product(e_6,e_4,e_1)
    | product(e_6,e_4,e_2)
    | product(e_6,e_4,e_3)
    | product(e_6,e_4,e_4)
    | product(e_6,e_4,e_5)
    | product(e_6,e_4,e_6) ),
    inference(global_subsumption_just,[status(thm)],[c_3171,c_73,c_3171]) ).

cnf(c_3174,plain,
    ( ~ product(e_5,X0,e_5)
    | ~ product(e_6,X0,e_5) ),
    inference(instantiation,[status(thm)],[c_2599]) ).

cnf(c_3175,plain,
    ( ~ product(e_4,X0,e_5)
    | ~ product(e_6,X0,e_5) ),
    inference(instantiation,[status(thm)],[c_2592]) ).

cnf(c_3179,plain,
    ( ~ product(e_4,e_1,e_5)
    | ~ product(e_6,e_1,e_5) ),
    inference(instantiation,[status(thm)],[c_3175]) ).

cnf(c_3180,plain,
    ( ~ product(e_5,e_1,e_5)
    | ~ product(e_6,e_1,e_5) ),
    inference(instantiation,[status(thm)],[c_3174]) ).

cnf(c_3188,plain,
    ( ~ product(X0,e_2,e_3)
    | ~ product(e_3,e_2,e_3)
    | equalish(e_3,X0) ),
    inference(instantiation,[status(thm)],[c_2124]) ).

cnf(c_3193,plain,
    ( ~ product(e_1,e_2,e_3)
    | ~ product(e_3,e_2,e_3)
    | equalish(e_3,e_1) ),
    inference(instantiation,[status(thm)],[c_3188]) ).

cnf(c_3198,plain,
    ( ~ product(e_2,X0,e_3)
    | ~ product(e_3,X0,e_2)
    | product(e_3,e_2,e_3) ),
    inference(instantiation,[status(thm)],[c_2057]) ).

cnf(c_3199,plain,
    ( ~ product(e_2,e_1,e_3)
    | ~ product(e_3,e_1,e_2)
    | product(e_3,e_2,e_3) ),
    inference(instantiation,[status(thm)],[c_3198]) ).

cnf(c_3200,plain,
    ( ~ product(e_2,X0,e_3)
    | ~ product(e_4,X0,e_2)
    | product(e_4,e_2,e_3) ),
    inference(instantiation,[status(thm)],[c_2057]) ).

cnf(c_3201,plain,
    ( ~ product(e_2,e_1,e_3)
    | ~ product(e_4,e_1,e_2)
    | product(e_4,e_2,e_3) ),
    inference(instantiation,[status(thm)],[c_3200]) ).

cnf(c_3202,plain,
    ( ~ product(e_2,X0,e_3)
    | ~ product(e_5,X0,e_2)
    | product(e_5,e_2,e_3) ),
    inference(instantiation,[status(thm)],[c_2057]) ).

cnf(c_3203,plain,
    ( ~ product(e_2,e_1,e_3)
    | ~ product(e_5,e_1,e_2)
    | product(e_5,e_2,e_3) ),
    inference(instantiation,[status(thm)],[c_3202]) ).

cnf(c_3234,plain,
    ( ~ product(e_2,e_4,e_1)
    | ~ product(e_2,e_4,e_2) ),
    inference(instantiation,[status(thm)],[c_2427]) ).

cnf(c_3248,plain,
    ( ~ product(e_4,e_1,e_5)
    | ~ product(e_4,e_6,e_5) ),
    inference(instantiation,[status(thm)],[c_2499]) ).

cnf(c_3288,plain,
    ( ~ product(e_4,e_3,e_5)
    | ~ product(e_4,e_6,e_5) ),
    inference(instantiation,[status(thm)],[c_2523]) ).

cnf(c_3303,plain,
    ( ~ product(e_2,e_4,e_1)
    | ~ product(e_2,e_6,e_1) ),
    inference(instantiation,[status(thm)],[c_2532]) ).

cnf(c_3307,plain,
    ( ~ product(e_4,e_5,e_5)
    | ~ product(e_4,e_6,e_5) ),
    inference(instantiation,[status(thm)],[c_2539]) ).

cnf(c_3318,plain,
    ( ~ product(e_2,e_2,e_4)
    | ~ product(e_4,e_2,e_2)
    | product(e_2,e_4,e_2) ),
    inference(instantiation,[status(thm)],[c_2626]) ).

cnf(c_3336,plain,
    ( ~ product(e_2,e_3,e_4)
    | ~ product(e_4,e_3,e_2)
    | product(e_2,e_4,e_2) ),
    inference(instantiation,[status(thm)],[c_2626]) ).

cnf(c_3344,plain,
    ( ~ product(e_1,e_3,e_4)
    | ~ product(e_2,e_3,e_4) ),
    inference(instantiation,[status(thm)],[c_2547]) ).

cnf(c_3347,plain,
    ( ~ product(e_4,e_3,X0)
    | ~ product(e_2,e_3,e_4)
    | product(e_2,e_4,X0) ),
    inference(instantiation,[status(thm)],[c_2666]) ).

cnf(c_3349,plain,
    ( ~ product(e_2,e_3,e_4)
    | ~ product(e_4,e_3,e_1)
    | product(e_2,e_4,e_1) ),
    inference(instantiation,[status(thm)],[c_3347]) ).

cnf(c_3350,plain,
    ( ~ product(X0,e_3,e_2)
    | ~ product(e_2,e_3,e_4)
    | product(X0,e_2,e_4) ),
    inference(instantiation,[status(thm)],[c_2228]) ).

cnf(c_3351,plain,
    ( ~ product(e_1,e_3,e_2)
    | ~ product(e_2,e_3,e_4)
    | product(e_1,e_2,e_4) ),
    inference(instantiation,[status(thm)],[c_3350]) ).

cnf(c_3354,plain,
    ( ~ product(e_3,e_1,e_4)
    | ~ product(e_3,e_3,e_4) ),
    inference(instantiation,[status(thm)],[c_2490]) ).

cnf(c_3355,plain,
    ( ~ product(e_4,e_1,e_5)
    | ~ product(e_4,e_3,e_5) ),
    inference(instantiation,[status(thm)],[c_2490]) ).

cnf(c_3356,plain,
    ( ~ group_element(e_1)
    | product(e_5,e_1,e_1)
    | product(e_5,e_1,e_2)
    | product(e_5,e_1,e_3)
    | product(e_5,e_1,e_4)
    | product(e_5,e_1,e_5)
    | product(e_5,e_1,e_6) ),
    inference(instantiation,[status(thm)],[c_1921]) ).

cnf(c_3357,plain,
    ( product(e_5,e_1,e_2)
    | product(e_5,e_1,e_3)
    | product(e_5,e_1,e_4)
    | product(e_5,e_1,e_5)
    | product(e_5,e_1,e_6) ),
    inference(global_subsumption_just,[status(thm)],[c_3356,c_71,c_70,c_81,c_76,c_113,c_322,c_326,c_330,c_334,c_338,c_342,c_346,c_389,c_458,c_1905,c_1923,c_1939,c_2064,c_2130,c_2294,c_2708,c_2993]) ).

cnf(c_3359,plain,
    ( product(e_5,e_1,e_2)
    | product(e_5,e_1,e_4)
    | product(e_5,e_1,e_5)
    | product(e_5,e_1,e_6) ),
    inference(global_subsumption_just,[status(thm)],[c_3357,c_71,c_70,c_81,c_76,c_113,c_322,c_326,c_330,c_334,c_338,c_342,c_346,c_389,c_1905,c_1939,c_2064,c_2130,c_2708,c_2993,c_3357]) ).

cnf(c_3377,plain,
    ( ~ group_element(e_5)
    | product(e_5,e_5,e_1)
    | product(e_5,e_5,e_2)
    | product(e_5,e_5,e_3)
    | product(e_5,e_5,e_4)
    | product(e_5,e_5,e_5)
    | product(e_5,e_5,e_6) ),
    inference(instantiation,[status(thm)],[c_1921]) ).

cnf(c_3386,plain,
    ( ~ group_element(e_1)
    | product(e_6,e_1,e_1)
    | product(e_6,e_1,e_2)
    | product(e_6,e_1,e_3)
    | product(e_6,e_1,e_4)
    | product(e_6,e_1,e_5)
    | product(e_6,e_1,e_6) ),
    inference(instantiation,[status(thm)],[c_1926]) ).

cnf(c_3387,plain,
    ( product(e_6,e_1,e_2)
    | product(e_6,e_1,e_4)
    | product(e_6,e_1,e_5)
    | product(e_6,e_1,e_6) ),
    inference(global_subsumption_just,[status(thm)],[c_3386,c_71,c_70,c_81,c_76,c_113,c_322,c_326,c_330,c_334,c_338,c_342,c_346,c_389,c_1905,c_1928,c_1939,c_2064,c_2130,c_2359,c_2708,c_2996]) ).

cnf(c_3403,plain,
    ( ~ product(e_5,X0,e_4)
    | ~ product(e_6,X0,e_4) ),
    inference(instantiation,[status(thm)],[c_2599]) ).

cnf(c_3405,plain,
    ( ~ product(e_3,X0,e_4)
    | ~ product(e_6,X0,e_4) ),
    inference(instantiation,[status(thm)],[c_2583]) ).

cnf(c_3408,plain,
    ( ~ product(e_3,e_1,e_4)
    | ~ product(e_6,e_1,e_4) ),
    inference(instantiation,[status(thm)],[c_3405]) ).

cnf(c_3410,plain,
    ( ~ product(e_5,e_1,e_4)
    | ~ product(e_6,e_1,e_4) ),
    inference(instantiation,[status(thm)],[c_3403]) ).

cnf(c_3440,plain,
    ( ~ product(e_1,e_2,e_5)
    | ~ product(e_2,e_2,e_5) ),
    inference(instantiation,[status(thm)],[c_2547]) ).

cnf(c_3446,plain,
    ( ~ product(X0,e_2,e_2)
    | ~ product(e_2,e_2,e_5)
    | product(X0,e_2,e_5) ),
    inference(instantiation,[status(thm)],[c_2292]) ).

cnf(c_3447,plain,
    ( ~ product(e_1,e_2,e_2)
    | ~ product(e_2,e_2,e_5)
    | product(e_1,e_2,e_5) ),
    inference(instantiation,[status(thm)],[c_3446]) ).

cnf(c_3448,plain,
    ( ~ product(e_1,e_5,e_2)
    | ~ product(e_2,e_5,e_1)
    | product(e_2,e_1,e_2) ),
    inference(instantiation,[status(thm)],[c_2626]) ).

cnf(c_3449,plain,
    ( ~ product(e_2,e_5,e_1)
    | ~ product(e_1,e_5,e_2) ),
    inference(global_subsumption_just,[status(thm)],[c_3448,c_76,c_2064,c_2708,c_3448]) ).

cnf(c_3450,plain,
    ( ~ product(e_1,e_5,e_2)
    | ~ product(e_2,e_5,e_1) ),
    inference(renaming,[status(thm)],[c_3449]) ).

cnf(c_3462,plain,
    ( ~ product(e_1,e_5,e_6)
    | ~ product(e_2,e_5,e_1) ),
    inference(instantiation,[status(thm)],[c_2154]) ).

cnf(c_3463,plain,
    ( ~ product(e_1,e_5,e_5)
    | ~ product(e_2,e_5,e_1) ),
    inference(instantiation,[status(thm)],[c_2151]) ).

cnf(c_3464,plain,
    ( ~ product(e_1,e_5,e_4)
    | ~ product(e_2,e_5,e_1) ),
    inference(instantiation,[status(thm)],[c_2148]) ).

cnf(c_3467,plain,
    ( ~ product(e_2,e_6,e_2)
    | product(e_2,e_2,e_2) ),
    inference(instantiation,[status(thm)],[c_2626]) ).

cnf(c_3468,plain,
    ~ product(e_2,e_6,e_2),
    inference(global_subsumption_just,[status(thm)],[c_3467,c_2091,c_3467]) ).

cnf(c_3485,plain,
    ( ~ product(e_2,e_4,e_1)
    | ~ product(e_4,e_4,e_2)
    | product(e_4,e_2,e_1) ),
    inference(instantiation,[status(thm)],[c_2766]) ).

cnf(c_3490,plain,
    ( ~ product(e_2,e_4,e_1)
    | ~ product(e_2,e_4,e_3) ),
    inference(instantiation,[status(thm)],[c_2848]) ).

cnf(c_3491,plain,
    ~ product(e_2,e_4,e_3),
    inference(global_subsumption_just,[status(thm)],[c_3490,c_71,c_70,c_81,c_76,c_113,c_322,c_326,c_330,c_334,c_338,c_342,c_346,c_389,c_1905,c_1939,c_2064,c_2130,c_2708,c_2886]) ).

cnf(c_3493,plain,
    ( ~ product(e_2,e_5,e_1)
    | ~ product(e_2,e_5,e_3) ),
    inference(instantiation,[status(thm)],[c_2848]) ).

cnf(c_3494,plain,
    ~ product(e_2,e_5,e_3),
    inference(global_subsumption_just,[status(thm)],[c_3493,c_71,c_70,c_81,c_76,c_113,c_322,c_326,c_330,c_334,c_338,c_342,c_346,c_389,c_1905,c_1939,c_2064,c_2130,c_2708,c_2893]) ).

cnf(c_3513,plain,
    ( ~ product(X0,e_2,e_4)
    | ~ product(e_4,e_2,e_3)
    | product(X0,e_4,e_3) ),
    inference(instantiation,[status(thm)],[c_2884]) ).

cnf(c_3514,plain,
    ( ~ product(e_1,e_2,e_4)
    | ~ product(e_4,e_2,e_3)
    | product(e_1,e_4,e_3) ),
    inference(instantiation,[status(thm)],[c_3513]) ).

cnf(c_3529,plain,
    ( ~ product(e_2,e_2,e_6)
    | ~ product(e_2,e_6,e_6) ),
    inference(instantiation,[status(thm)],[c_2512]) ).

cnf(c_3533,plain,
    ( ~ product(e_1,e_2,e_6)
    | ~ product(e_2,e_2,e_6) ),
    inference(instantiation,[status(thm)],[c_2547]) ).

cnf(c_3538,plain,
    ( ~ product(X0,e_2,e_2)
    | ~ product(e_2,e_2,e_6)
    | product(X0,e_2,e_6) ),
    inference(instantiation,[status(thm)],[c_2356]) ).

cnf(c_3539,plain,
    ( ~ product(e_1,e_2,e_2)
    | ~ product(e_2,e_2,e_6)
    | product(e_1,e_2,e_6) ),
    inference(instantiation,[status(thm)],[c_3538]) ).

cnf(c_3553,plain,
    ( ~ product(e_1,e_2,e_3)
    | ~ product(e_4,e_2,e_3) ),
    inference(instantiation,[status(thm)],[c_2980]) ).

cnf(c_3558,plain,
    ( ~ product(e_1,e_2,e_3)
    | ~ product(e_6,e_2,e_3) ),
    inference(instantiation,[status(thm)],[c_2984]) ).

cnf(c_3563,plain,
    ( ~ product(e_3,e_2,e_3)
    | ~ product(e_4,e_2,e_3) ),
    inference(instantiation,[status(thm)],[c_2998]) ).

cnf(c_3564,plain,
    ( ~ product(e_3,e_2,e_3)
    | ~ product(e_5,e_2,e_3) ),
    inference(instantiation,[status(thm)],[c_3001]) ).

cnf(c_3566,plain,
    ( ~ product(e_4,e_2,e_3)
    | ~ product(e_5,e_2,e_3) ),
    inference(instantiation,[status(thm)],[c_3007]) ).

cnf(c_3567,plain,
    ( ~ product(e_4,e_2,e_3)
    | ~ product(e_6,e_2,e_3) ),
    inference(instantiation,[status(thm)],[c_3010]) ).

cnf(c_3568,plain,
    ( ~ product(e_5,e_2,e_3)
    | ~ product(e_6,e_2,e_3) ),
    inference(instantiation,[status(thm)],[c_3013]) ).

cnf(c_3573,plain,
    ( ~ product(X0,e_2,e_6)
    | ~ product(e_6,e_2,e_3)
    | product(X0,e_6,e_3) ),
    inference(instantiation,[status(thm)],[c_3022]) ).

cnf(c_3574,plain,
    ( ~ product(e_1,e_2,e_6)
    | ~ product(e_6,e_2,e_3)
    | product(e_1,e_6,e_3) ),
    inference(instantiation,[status(thm)],[c_3573]) ).

cnf(c_3575,plain,
    ( ~ product(e_2,X0,e_3)
    | ~ product(e_3,X0,e_4)
    | product(e_2,e_3,e_4) ),
    inference(instantiation,[status(thm)],[c_3024]) ).

cnf(c_3576,plain,
    ( ~ product(e_2,e_1,e_3)
    | ~ product(e_3,e_1,e_4)
    | product(e_2,e_3,e_4) ),
    inference(instantiation,[status(thm)],[c_3575]) ).

cnf(c_3588,plain,
    ( ~ product(e_2,e_3,e_4)
    | ~ product(e_2,e_4,e_4) ),
    inference(instantiation,[status(thm)],[c_2517]) ).

cnf(c_3597,plain,
    ( ~ group_element(X0)
    | ~ group_element(e_1)
    | product(e_1,X0,e_1)
    | product(e_1,X0,e_2)
    | product(e_1,X0,e_3)
    | product(e_1,X0,e_4)
    | product(e_1,X0,e_5)
    | product(e_1,X0,e_6) ),
    inference(instantiation,[status(thm)],[c_106]) ).

cnf(c_3598,plain,
    ( ~ group_element(X0)
    | product(e_1,X0,e_1)
    | product(e_1,X0,e_2)
    | product(e_1,X0,e_3)
    | product(e_1,X0,e_4)
    | product(e_1,X0,e_5)
    | product(e_1,X0,e_6) ),
    inference(global_subsumption_just,[status(thm)],[c_3597,c_70,c_1901]) ).

cnf(c_3600,plain,
    ( ~ group_element(X0)
    | ~ group_element(e_2)
    | product(e_2,X0,e_1)
    | product(e_2,X0,e_2)
    | product(e_2,X0,e_3)
    | product(e_2,X0,e_4)
    | product(e_2,X0,e_5)
    | product(e_2,X0,e_6) ),
    inference(instantiation,[status(thm)],[c_106]) ).

cnf(c_3601,plain,
    ( ~ group_element(X0)
    | product(e_2,X0,e_1)
    | product(e_2,X0,e_2)
    | product(e_2,X0,e_3)
    | product(e_2,X0,e_4)
    | product(e_2,X0,e_5)
    | product(e_2,X0,e_6) ),
    inference(global_subsumption_just,[status(thm)],[c_3600,c_1906]) ).

cnf(c_3606,plain,
    ( ~ group_element(X0)
    | ~ group_element(e_4)
    | product(e_4,X0,e_1)
    | product(e_4,X0,e_2)
    | product(e_4,X0,e_3)
    | product(e_4,X0,e_4)
    | product(e_4,X0,e_5)
    | product(e_4,X0,e_6) ),
    inference(instantiation,[status(thm)],[c_106]) ).

cnf(c_3607,plain,
    ( ~ group_element(X0)
    | product(e_4,X0,e_1)
    | product(e_4,X0,e_2)
    | product(e_4,X0,e_3)
    | product(e_4,X0,e_4)
    | product(e_4,X0,e_5)
    | product(e_4,X0,e_6) ),
    inference(global_subsumption_just,[status(thm)],[c_3606,c_73,c_1914]) ).

cnf(c_3616,plain,
    ( ~ product(X0,X1,e_2)
    | ~ product(e_1,X1,e_2)
    | equalish(e_1,X0) ),
    inference(instantiation,[status(thm)],[c_109]) ).

cnf(c_3621,plain,
    ( ~ product(e_2,X0,e_3)
    | ~ product(e_2,X1,e_3)
    | equalish(X0,X1) ),
    inference(instantiation,[status(thm)],[c_108]) ).

cnf(c_3625,plain,
    ( ~ product(e_3,X0,e_4)
    | ~ product(e_3,X1,e_4)
    | equalish(X0,X1) ),
    inference(instantiation,[status(thm)],[c_108]) ).

cnf(c_3626,plain,
    ( ~ product(e_3,X0,X1)
    | ~ product(e_3,X0,e_4)
    | equalish(e_4,X1) ),
    inference(instantiation,[status(thm)],[c_107]) ).

cnf(c_3628,plain,
    ( ~ product(X0,X1,e_4)
    | ~ product(e_4,X1,e_5)
    | product(X0,e_4,e_5) ),
    inference(instantiation,[status(thm)],[c_110]) ).

cnf(c_3629,plain,
    ( ~ product(X0,X1,e_5)
    | ~ product(e_4,X1,e_5)
    | equalish(e_4,X0) ),
    inference(instantiation,[status(thm)],[c_109]) ).

cnf(c_3630,plain,
    ( ~ product(e_4,X0,e_5)
    | ~ product(e_4,X1,e_5)
    | equalish(X0,X1) ),
    inference(instantiation,[status(thm)],[c_108]) ).

cnf(c_3631,plain,
    ( ~ product(e_4,X0,X1)
    | ~ product(e_4,X0,e_5)
    | equalish(e_5,X1) ),
    inference(instantiation,[status(thm)],[c_107]) ).

cnf(c_3633,plain,
    ( ~ product(X0,X1,e_5)
    | ~ product(e_5,X1,e_6)
    | product(X0,e_5,e_6) ),
    inference(instantiation,[status(thm)],[c_110]) ).

cnf(c_3635,plain,
    ( ~ product(e_5,X0,e_6)
    | ~ product(e_5,X1,e_6)
    | equalish(X0,X1) ),
    inference(instantiation,[status(thm)],[c_108]) ).

cnf(c_3638,plain,
    ( ~ product(X0,X1,e_6)
    | ~ product(e_6,X1,e_6)
    | product(X0,e_6,e_6) ),
    inference(instantiation,[status(thm)],[c_110]) ).

cnf(c_3640,plain,
    ( ~ product(e_6,X0,e_6)
    | ~ product(e_6,X1,e_6)
    | equalish(X0,X1) ),
    inference(instantiation,[status(thm)],[c_108]) ).

cnf(c_3643,plain,
    ( ~ product(e_1,X0,e_2)
    | ~ product(e_2,X0,e_2)
    | equalish(e_1,e_2) ),
    inference(instantiation,[status(thm)],[c_3616]) ).

cnf(c_3644,plain,
    ( ~ product(e_2,X0,e_2)
    | ~ product(e_1,X0,e_2) ),
    inference(global_subsumption_just,[status(thm)],[c_3643,c_1973]) ).

cnf(c_3645,plain,
    ( ~ product(e_1,X0,e_2)
    | ~ product(e_2,X0,e_2) ),
    inference(renaming,[status(thm)],[c_3644]) ).

cnf(c_3646,plain,
    ( ~ product(e_1,X0,e_2)
    | ~ product(e_3,X0,e_2)
    | equalish(e_1,e_3) ),
    inference(instantiation,[status(thm)],[c_3616]) ).

cnf(c_3647,plain,
    ( ~ product(e_3,X0,e_2)
    | ~ product(e_1,X0,e_2) ),
    inference(global_subsumption_just,[status(thm)],[c_3646,c_1978]) ).

cnf(c_3648,plain,
    ( ~ product(e_1,X0,e_2)
    | ~ product(e_3,X0,e_2) ),
    inference(renaming,[status(thm)],[c_3647]) ).

cnf(c_3741,plain,
    ( ~ product(e_2,e_1,e_3)
    | ~ product(e_2,e_6,e_3)
    | equalish(e_1,e_6) ),
    inference(instantiation,[status(thm)],[c_3621]) ).

cnf(c_3742,plain,
    ~ product(e_2,e_6,e_3),
    inference(global_subsumption_just,[status(thm)],[c_3741,c_71,c_70,c_81,c_76,c_113,c_322,c_326,c_330,c_334,c_338,c_342,c_346,c_389,c_1905,c_1939,c_2064,c_2130,c_2708,c_2900]) ).

cnf(c_3777,plain,
    ( ~ product(e_3,e_1,e_4)
    | ~ product(e_3,e_2,e_4)
    | equalish(e_1,e_2) ),
    inference(instantiation,[status(thm)],[c_3625]) ).

cnf(c_3778,plain,
    ( ~ product(e_3,e_2,e_4)
    | ~ product(e_3,e_1,e_4) ),
    inference(global_subsumption_just,[status(thm)],[c_3777,c_76,c_3777]) ).

cnf(c_3779,plain,
    ( ~ product(e_3,e_1,e_4)
    | ~ product(e_3,e_2,e_4) ),
    inference(renaming,[status(thm)],[c_3778]) ).

cnf(c_3839,plain,
    ( ~ product(e_3,e_2,e_3)
    | ~ product(e_3,e_2,e_4)
    | equalish(e_4,e_3) ),
    inference(instantiation,[status(thm)],[c_3626]) ).

cnf(c_3840,plain,
    ( ~ product(e_3,e_2,e_4)
    | ~ product(e_3,e_2,e_3) ),
    inference(global_subsumption_just,[status(thm)],[c_3839,c_71,c_70,c_93,c_81,c_76,c_113,c_322,c_326,c_330,c_334,c_338,c_342,c_346,c_350,c_354,c_389,c_412,c_1905,c_1913,c_1939,c_1946,c_2064,c_2130,c_2133,c_2708,c_2987,c_3199,c_3777,c_3839]) ).

cnf(c_3841,plain,
    ( ~ product(e_3,e_2,e_3)
    | ~ product(e_3,e_2,e_4) ),
    inference(renaming,[status(thm)],[c_3840]) ).

cnf(c_3842,plain,
    ( ~ product(e_3,X0,e_4)
    | ~ product(e_4,X0,e_5)
    | product(e_3,e_4,e_5) ),
    inference(instantiation,[status(thm)],[c_3628]) ).

cnf(c_3843,plain,
    ( ~ product(e_3,e_1,e_4)
    | ~ product(e_4,e_1,e_5)
    | product(e_3,e_4,e_5) ),
    inference(instantiation,[status(thm)],[c_3842]) ).

cnf(c_3846,plain,
    ( ~ product(e_4,e_1,e_5)
    | ~ product(e_4,e_2,e_5)
    | equalish(e_1,e_2) ),
    inference(instantiation,[status(thm)],[c_3630]) ).

cnf(c_3847,plain,
    ( ~ product(e_4,e_2,e_5)
    | ~ product(e_4,e_1,e_5) ),
    inference(global_subsumption_just,[status(thm)],[c_3846,c_76,c_3846]) ).

cnf(c_3848,plain,
    ( ~ product(e_4,e_1,e_5)
    | ~ product(e_4,e_2,e_5) ),
    inference(renaming,[status(thm)],[c_3847]) ).

cnf(c_3852,plain,
    ( ~ product(e_4,e_1,e_5)
    | ~ product(e_4,e_4,e_5)
    | equalish(e_1,e_4) ),
    inference(instantiation,[status(thm)],[c_3630]) ).

cnf(c_3908,plain,
    ( ~ product(e_4,e_2,e_3)
    | ~ product(e_4,e_2,e_5)
    | equalish(e_5,e_3) ),
    inference(instantiation,[status(thm)],[c_3631]) ).

cnf(c_3909,plain,
    ( ~ product(e_4,e_2,e_5)
    | ~ product(e_4,e_2,e_3) ),
    inference(global_subsumption_just,[status(thm)],[c_3908,c_98,c_3908]) ).

cnf(c_3910,plain,
    ( ~ product(e_4,e_2,e_3)
    | ~ product(e_4,e_2,e_5) ),
    inference(renaming,[status(thm)],[c_3909]) ).

cnf(c_3911,plain,
    ( ~ product(e_4,X0,e_5)
    | ~ product(e_5,X0,e_6)
    | product(e_4,e_5,e_6) ),
    inference(instantiation,[status(thm)],[c_3633]) ).

cnf(c_3912,plain,
    ( ~ product(e_4,e_1,e_5)
    | ~ product(e_5,e_1,e_6)
    | product(e_4,e_5,e_6) ),
    inference(instantiation,[status(thm)],[c_3911]) ).

cnf(c_3926,plain,
    ( ~ product(e_5,e_1,e_6)
    | ~ product(e_5,e_4,e_6)
    | equalish(e_1,e_4) ),
    inference(instantiation,[status(thm)],[c_3635]) ).

cnf(c_3929,plain,
    ( ~ product(e_5,e_1,e_6)
    | ~ product(e_5,e_5,e_6)
    | equalish(e_1,e_5) ),
    inference(instantiation,[status(thm)],[c_3635]) ).

cnf(c_3986,plain,
    ( ~ product(e_6,X0,e_6)
    | product(e_6,e_6,e_6) ),
    inference(instantiation,[status(thm)],[c_3638]) ).

cnf(c_3987,plain,
    ( ~ product(e_6,e_1,e_6)
    | product(e_6,e_6,e_6) ),
    inference(instantiation,[status(thm)],[c_3986]) ).

cnf(c_4003,plain,
    ( ~ product(e_6,e_1,e_6)
    | ~ product(e_6,e_6,e_6)
    | equalish(e_1,e_6) ),
    inference(instantiation,[status(thm)],[c_3640]) ).

cnf(c_4004,plain,
    ~ product(e_6,e_1,e_6),
    inference(global_subsumption_just,[status(thm)],[c_4003,c_80,c_3987,c_4003]) ).

cnf(c_4013,plain,
    ( ~ product(e_6,e_2,e_6)
    | ~ product(e_6,e_5,e_6)
    | equalish(e_2,e_5) ),
    inference(instantiation,[status(thm)],[c_3640]) ).

cnf(c_4014,plain,
    ( ~ product(e_6,e_5,e_6)
    | ~ product(e_6,e_2,e_6) ),
    inference(global_subsumption_just,[status(thm)],[c_4013,c_84,c_4013]) ).

cnf(c_4015,plain,
    ( ~ product(e_6,e_2,e_6)
    | ~ product(e_6,e_5,e_6) ),
    inference(renaming,[status(thm)],[c_4014]) ).

cnf(c_4033,plain,
    ( ~ product(e_6,e_4,e_6)
    | ~ product(e_6,e_5,e_6)
    | equalish(e_4,e_5) ),
    inference(instantiation,[status(thm)],[c_3640]) ).

cnf(c_4034,plain,
    ( ~ product(e_6,e_5,e_6)
    | ~ product(e_6,e_4,e_6) ),
    inference(global_subsumption_just,[status(thm)],[c_4033,c_94,c_4033]) ).

cnf(c_4035,plain,
    ( ~ product(e_6,e_4,e_6)
    | ~ product(e_6,e_5,e_6) ),
    inference(renaming,[status(thm)],[c_4034]) ).

cnf(c_4061,plain,
    ( ~ group_element(e_4)
    | product(e_1,e_4,e_1)
    | product(e_1,e_4,e_2)
    | product(e_1,e_4,e_3)
    | product(e_1,e_4,e_4)
    | product(e_1,e_4,e_5)
    | product(e_1,e_4,e_6) ),
    inference(instantiation,[status(thm)],[c_3598]) ).

cnf(c_4062,plain,
    ( product(e_1,e_4,e_2)
    | product(e_1,e_4,e_3)
    | product(e_1,e_4,e_4)
    | product(e_1,e_4,e_5)
    | product(e_1,e_4,e_6) ),
    inference(global_subsumption_just,[status(thm)],[c_4061,c_73,c_72,c_71,c_70,c_86,c_81,c_80,c_76,c_113,c_322,c_326,c_330,c_334,c_338,c_342,c_346,c_350,c_354,c_358,c_389,c_412,c_427,c_435,c_1905,c_1910,c_1918,c_1939,c_1946,c_2058,c_2064,c_2130,c_2133,c_2230,c_2628,c_2708,c_2987,c_2990,c_3073,c_3128,c_3179,c_3193,c_3199,c_3201,c_3387,c_3408,c_3553,c_3558,c_3987,c_4003]) ).

cnf(c_4064,plain,
    ( ~ group_element(e_5)
    | product(e_1,e_5,e_1)
    | product(e_1,e_5,e_2)
    | product(e_1,e_5,e_3)
    | product(e_1,e_5,e_4)
    | product(e_1,e_5,e_5)
    | product(e_1,e_5,e_6) ),
    inference(instantiation,[status(thm)],[c_3598]) ).

cnf(c_4065,plain,
    ( product(e_1,e_5,e_2)
    | product(e_1,e_5,e_3)
    | product(e_1,e_5,e_4)
    | product(e_1,e_5,e_5)
    | product(e_1,e_5,e_6) ),
    inference(global_subsumption_just,[status(thm)],[c_4064,c_74,c_72,c_71,c_70,c_86,c_81,c_80,c_76,c_113,c_322,c_326,c_330,c_334,c_338,c_342,c_346,c_350,c_354,c_358,c_389,c_412,c_435,c_450,c_1905,c_1910,c_1918,c_1939,c_1946,c_2058,c_2064,c_2130,c_2133,c_2230,c_2628,c_2708,c_2987,c_2990,c_3079,c_3128,c_3179,c_3193,c_3199,c_3201,c_3387,c_3408,c_3553,c_3558,c_3987,c_4003]) ).

cnf(c_4067,plain,
    ( ~ group_element(e_6)
    | product(e_1,e_6,e_1)
    | product(e_1,e_6,e_2)
    | product(e_1,e_6,e_3)
    | product(e_1,e_6,e_4)
    | product(e_1,e_6,e_5)
    | product(e_1,e_6,e_6) ),
    inference(instantiation,[status(thm)],[c_3598]) ).

cnf(c_4068,plain,
    ( product(e_1,e_6,e_2)
    | product(e_1,e_6,e_3)
    | product(e_1,e_6,e_4)
    | product(e_1,e_6,e_5)
    | product(e_1,e_6,e_6) ),
    inference(global_subsumption_just,[status(thm)],[c_4067,c_72,c_71,c_70,c_86,c_81,c_80,c_76,c_113,c_322,c_326,c_330,c_334,c_338,c_342,c_346,c_350,c_354,c_358,c_389,c_412,c_435,c_473,c_1905,c_1910,c_1918,c_1939,c_1946,c_2058,c_2064,c_2130,c_2133,c_2230,c_2628,c_2708,c_2987,c_2990,c_3083,c_3128,c_3179,c_3193,c_3199,c_3201,c_3387,c_3408,c_3553,c_3558,c_3987,c_4003]) ).

cnf(c_4082,plain,
    ( ~ product(X0,X1,X2)
    | ~ product(X2,X1,e_3)
    | product(X0,X2,e_3) ),
    inference(instantiation,[status(thm)],[c_110]) ).

cnf(c_4083,plain,
    ( ~ product(X0,X1,X2)
    | ~ product(X2,X1,e_4)
    | product(X0,X2,e_4) ),
    inference(instantiation,[status(thm)],[c_110]) ).

cnf(c_4084,plain,
    ( ~ product(X0,X1,X2)
    | ~ product(X2,X1,e_5)
    | product(X0,X2,e_5) ),
    inference(instantiation,[status(thm)],[c_110]) ).

cnf(c_4085,plain,
    ( ~ product(X0,X1,X2)
    | ~ product(X2,X1,e_6)
    | product(X0,X2,e_6) ),
    inference(instantiation,[status(thm)],[c_110]) ).

cnf(c_4086,plain,
    ( ~ product(X0,X1,X2)
    | ~ product(e_2,X1,X0)
    | product(e_2,X0,X2) ),
    inference(instantiation,[status(thm)],[c_110]) ).

cnf(c_4087,plain,
    ( ~ product(X0,X1,X2)
    | ~ product(e_3,X1,X0)
    | product(e_3,X0,X2) ),
    inference(instantiation,[status(thm)],[c_110]) ).

cnf(c_4088,plain,
    ( ~ product(X0,X1,X2)
    | ~ product(e_4,X1,X0)
    | product(e_4,X0,X2) ),
    inference(instantiation,[status(thm)],[c_110]) ).

cnf(c_4089,plain,
    ( ~ product(X0,X1,X2)
    | ~ product(e_5,X1,X0)
    | product(e_5,X0,X2) ),
    inference(instantiation,[status(thm)],[c_110]) ).

cnf(c_4090,plain,
    ( ~ product(X0,X1,X2)
    | ~ product(e_6,X1,X0)
    | product(e_6,X0,X2) ),
    inference(instantiation,[status(thm)],[c_110]) ).

cnf(c_4095,plain,
    ( ~ product(e_1,X0,e_3)
    | ~ product(e_3,X0,e_2)
    | product(e_1,e_3,e_2) ),
    inference(instantiation,[status(thm)],[c_110]) ).

cnf(c_4109,plain,
    ( ~ product(X0,X1,e_2)
    | ~ product(e_1,X1,X0)
    | product(e_1,X0,e_2) ),
    inference(instantiation,[status(thm)],[c_110]) ).

cnf(c_4115,plain,
    ( ~ product(X0,X1,X2)
    | ~ product(X2,X1,e_2)
    | product(X0,X2,e_2) ),
    inference(instantiation,[status(thm)],[c_110]) ).

cnf(c_4172,plain,
    ( ~ group_element(e_2)
    | product(e_2,e_2,e_1)
    | product(e_2,e_2,e_2)
    | product(e_2,e_2,e_3)
    | product(e_2,e_2,e_4)
    | product(e_2,e_2,e_5)
    | product(e_2,e_2,e_6) ),
    inference(instantiation,[status(thm)],[c_3601]) ).

cnf(c_4173,plain,
    ( product(e_2,e_2,e_2)
    | product(e_2,e_2,e_4)
    | product(e_2,e_2,e_5)
    | product(e_2,e_2,e_6) ),
    inference(global_subsumption_just,[status(thm)],[c_4172,c_72,c_71,c_70,c_86,c_81,c_80,c_76,c_113,c_322,c_326,c_330,c_334,c_338,c_342,c_346,c_350,c_354,c_358,c_389,c_412,c_435,c_1905,c_1910,c_1918,c_1939,c_1946,c_2064,c_2130,c_2133,c_2230,c_2628,c_2691,c_2708,c_2872,c_2987,c_2990,c_3034,c_3033,c_3032,c_3038,c_3068,c_3128,c_3179,c_3193,c_3199,c_3201,c_3387,c_3408,c_3553,c_3558,c_3987,c_4003]) ).

cnf(c_4188,plain,
    ( ~ group_element(e_6)
    | product(e_2,e_6,e_1)
    | product(e_2,e_6,e_2)
    | product(e_2,e_6,e_3)
    | product(e_2,e_6,e_4)
    | product(e_2,e_6,e_5)
    | product(e_2,e_6,e_6) ),
    inference(instantiation,[status(thm)],[c_3601]) ).

cnf(c_4189,plain,
    ( product(e_2,e_6,e_1)
    | product(e_2,e_6,e_4)
    | product(e_2,e_6,e_5)
    | product(e_2,e_6,e_6) ),
    inference(global_subsumption_just,[status(thm)],[c_4188,c_71,c_70,c_81,c_76,c_113,c_322,c_326,c_330,c_334,c_338,c_342,c_346,c_389,c_1905,c_1939,c_2064,c_2130,c_2704,c_2708,c_2900,c_3468]) ).

cnf(c_4191,plain,
    ( ~ product(e_2,e_3,e_4)
    | ~ product(e_4,e_3,e_5)
    | product(e_2,e_4,e_5) ),
    inference(instantiation,[status(thm)],[c_3628]) ).

cnf(c_4259,plain,
    ( ~ group_element(e_5)
    | product(e_4,e_5,e_1)
    | product(e_4,e_5,e_2)
    | product(e_4,e_5,e_3)
    | product(e_4,e_5,e_4)
    | product(e_4,e_5,e_5)
    | product(e_4,e_5,e_6) ),
    inference(instantiation,[status(thm)],[c_3607]) ).

cnf(c_4263,plain,
    ( ~ group_element(e_6)
    | product(e_4,e_6,e_1)
    | product(e_4,e_6,e_2)
    | product(e_4,e_6,e_3)
    | product(e_4,e_6,e_4)
    | product(e_4,e_6,e_5)
    | product(e_4,e_6,e_6) ),
    inference(instantiation,[status(thm)],[c_3607]) ).

cnf(c_4264,plain,
    ( product(e_4,e_6,e_1)
    | product(e_4,e_6,e_2)
    | product(e_4,e_6,e_3)
    | product(e_4,e_6,e_4)
    | product(e_4,e_6,e_5)
    | product(e_4,e_6,e_6) ),
    inference(global_subsumption_just,[status(thm)],[c_4263,c_75,c_4263]) ).

cnf(c_4289,plain,
    ( ~ product(e_4,X0,e_5)
    | ~ product(e_5,X0,e_5)
    | equalish(e_4,e_5) ),
    inference(instantiation,[status(thm)],[c_3629]) ).

cnf(c_4290,plain,
    ( ~ product(e_4,e_1,e_5)
    | ~ product(e_5,e_1,e_5)
    | equalish(e_4,e_5) ),
    inference(instantiation,[status(thm)],[c_4289]) ).

cnf(c_4291,plain,
    ( ~ product(e_5,X0,e_5)
    | ~ product(e_4,X0,e_5) ),
    inference(global_subsumption_just,[status(thm)],[c_4289,c_94,c_4289]) ).

cnf(c_4292,plain,
    ( ~ product(e_4,X0,e_5)
    | ~ product(e_5,X0,e_5) ),
    inference(renaming,[status(thm)],[c_4291]) ).

cnf(c_4293,plain,
    ( ~ product(e_4,e_1,e_5)
    | ~ product(e_5,e_1,e_5) ),
    inference(instantiation,[status(thm)],[c_4292]) ).

cnf(c_4331,plain,
    ( ~ product(X0,X1,e_1)
    | ~ product(X0,X1,e_2)
    | equalish(e_1,e_2) ),
    inference(instantiation,[status(thm)],[c_107]) ).

cnf(c_4332,plain,
    ( ~ product(X0,X1,e_2)
    | ~ product(X0,X1,e_1) ),
    inference(global_subsumption_just,[status(thm)],[c_4331,c_372]) ).

cnf(c_4333,plain,
    ( ~ product(X0,X1,e_1)
    | ~ product(X0,X1,e_2) ),
    inference(renaming,[status(thm)],[c_4332]) ).

cnf(c_4334,plain,
    ( ~ product(X0,X1,e_1)
    | ~ product(X0,X1,e_3)
    | equalish(e_1,e_3) ),
    inference(instantiation,[status(thm)],[c_107]) ).

cnf(c_4335,plain,
    ( ~ product(X0,X1,e_3)
    | ~ product(X0,X1,e_1) ),
    inference(global_subsumption_just,[status(thm)],[c_4334,c_396]) ).

cnf(c_4336,plain,
    ( ~ product(X0,X1,e_1)
    | ~ product(X0,X1,e_3) ),
    inference(renaming,[status(thm)],[c_4335]) ).

cnf(c_4337,plain,
    ( ~ product(X0,X1,e_1)
    | ~ product(X0,X1,e_4)
    | equalish(e_1,e_4) ),
    inference(instantiation,[status(thm)],[c_107]) ).

cnf(c_4338,plain,
    ( ~ product(X0,X1,e_4)
    | ~ product(X0,X1,e_1) ),
    inference(global_subsumption_just,[status(thm)],[c_4337,c_419]) ).

cnf(c_4339,plain,
    ( ~ product(X0,X1,e_1)
    | ~ product(X0,X1,e_4) ),
    inference(renaming,[status(thm)],[c_4338]) ).

cnf(c_4340,plain,
    ( ~ product(X0,X1,e_1)
    | ~ product(X0,X1,e_5)
    | equalish(e_1,e_5) ),
    inference(instantiation,[status(thm)],[c_107]) ).

cnf(c_4341,plain,
    ( ~ product(X0,X1,e_5)
    | ~ product(X0,X1,e_1) ),
    inference(global_subsumption_just,[status(thm)],[c_4340,c_442]) ).

cnf(c_4342,plain,
    ( ~ product(X0,X1,e_1)
    | ~ product(X0,X1,e_5) ),
    inference(renaming,[status(thm)],[c_4341]) ).

cnf(c_4343,plain,
    ( ~ product(X0,X1,e_1)
    | ~ product(X0,X1,e_6)
    | equalish(e_1,e_6) ),
    inference(instantiation,[status(thm)],[c_107]) ).

cnf(c_4344,plain,
    ( ~ product(X0,X1,e_6)
    | ~ product(X0,X1,e_1) ),
    inference(global_subsumption_just,[status(thm)],[c_4343,c_465]) ).

cnf(c_4345,plain,
    ( ~ product(X0,X1,e_1)
    | ~ product(X0,X1,e_6) ),
    inference(renaming,[status(thm)],[c_4344]) ).

cnf(c_4350,plain,
    ( ~ product(X0,X1,e_2)
    | ~ product(X0,X1,e_4)
    | equalish(e_2,e_4) ),
    inference(instantiation,[status(thm)],[c_107]) ).

cnf(c_4351,plain,
    ( ~ product(X0,X1,e_4)
    | ~ product(X0,X1,e_2) ),
    inference(global_subsumption_just,[status(thm)],[c_4350,c_514]) ).

cnf(c_4352,plain,
    ( ~ product(X0,X1,e_2)
    | ~ product(X0,X1,e_4) ),
    inference(renaming,[status(thm)],[c_4351]) ).

cnf(c_4353,plain,
    ( ~ product(X0,X1,e_2)
    | ~ product(X0,X1,e_5)
    | equalish(e_2,e_5) ),
    inference(instantiation,[status(thm)],[c_107]) ).

cnf(c_4354,plain,
    ( ~ product(X0,X1,e_5)
    | ~ product(X0,X1,e_2) ),
    inference(global_subsumption_just,[status(thm)],[c_4353,c_537]) ).

cnf(c_4355,plain,
    ( ~ product(X0,X1,e_2)
    | ~ product(X0,X1,e_5) ),
    inference(renaming,[status(thm)],[c_4354]) ).

cnf(c_4356,plain,
    ( ~ product(X0,X1,e_2)
    | ~ product(X0,X1,e_6)
    | equalish(e_2,e_6) ),
    inference(instantiation,[status(thm)],[c_107]) ).

cnf(c_4357,plain,
    ( ~ product(X0,X1,e_6)
    | ~ product(X0,X1,e_2) ),
    inference(global_subsumption_just,[status(thm)],[c_4356,c_560]) ).

cnf(c_4358,plain,
    ( ~ product(X0,X1,e_2)
    | ~ product(X0,X1,e_6) ),
    inference(renaming,[status(thm)],[c_4357]) ).

cnf(c_4361,plain,
    ( ~ product(X0,X1,e_3)
    | ~ product(X0,X1,e_4)
    | equalish(e_3,e_4) ),
    inference(instantiation,[status(thm)],[c_107]) ).

cnf(c_4362,plain,
    ( ~ product(X0,X1,e_4)
    | ~ product(X0,X1,e_3) ),
    inference(global_subsumption_just,[status(thm)],[c_4361,c_589]) ).

cnf(c_4363,plain,
    ( ~ product(X0,X1,e_3)
    | ~ product(X0,X1,e_4) ),
    inference(renaming,[status(thm)],[c_4362]) ).

cnf(c_4364,plain,
    ( ~ product(X0,X1,e_3)
    | ~ product(X0,X1,e_5)
    | equalish(e_3,e_5) ),
    inference(instantiation,[status(thm)],[c_107]) ).

cnf(c_4365,plain,
    ( ~ product(X0,X1,e_5)
    | ~ product(X0,X1,e_3) ),
    inference(global_subsumption_just,[status(thm)],[c_4364,c_612]) ).

cnf(c_4366,plain,
    ( ~ product(X0,X1,e_3)
    | ~ product(X0,X1,e_5) ),
    inference(renaming,[status(thm)],[c_4365]) ).

cnf(c_4373,plain,
    ( ~ product(X0,X1,e_4)
    | ~ product(X0,X1,e_5)
    | equalish(e_4,e_5) ),
    inference(instantiation,[status(thm)],[c_107]) ).

cnf(c_4374,plain,
    ( ~ product(X0,X1,e_5)
    | ~ product(X0,X1,e_4) ),
    inference(global_subsumption_just,[status(thm)],[c_4373,c_667]) ).

cnf(c_4375,plain,
    ( ~ product(X0,X1,e_4)
    | ~ product(X0,X1,e_5) ),
    inference(renaming,[status(thm)],[c_4374]) ).

cnf(c_4376,plain,
    ( ~ product(X0,X1,e_4)
    | ~ product(X0,X1,e_6)
    | equalish(e_4,e_6) ),
    inference(instantiation,[status(thm)],[c_107]) ).

cnf(c_4377,plain,
    ( ~ product(X0,X1,e_6)
    | ~ product(X0,X1,e_4) ),
    inference(global_subsumption_just,[status(thm)],[c_4376,c_690]) ).

cnf(c_4378,plain,
    ( ~ product(X0,X1,e_4)
    | ~ product(X0,X1,e_6) ),
    inference(renaming,[status(thm)],[c_4377]) ).

cnf(c_4391,plain,
    ( ~ product(X0,e_1,X1)
    | ~ product(X0,e_2,X1)
    | equalish(e_1,e_2) ),
    inference(instantiation,[status(thm)],[c_108]) ).

cnf(c_4392,plain,
    ( ~ product(X0,e_2,X1)
    | ~ product(X0,e_1,X1) ),
    inference(global_subsumption_just,[status(thm)],[c_4391,c_380]) ).

cnf(c_4393,plain,
    ( ~ product(X0,e_1,X1)
    | ~ product(X0,e_2,X1) ),
    inference(renaming,[status(thm)],[c_4392]) ).

cnf(c_4394,plain,
    ( ~ product(X0,e_1,X1)
    | ~ product(X0,e_3,X1)
    | equalish(e_1,e_3) ),
    inference(instantiation,[status(thm)],[c_108]) ).

cnf(c_4395,plain,
    ( ~ product(X0,e_3,X1)
    | ~ product(X0,e_1,X1) ),
    inference(global_subsumption_just,[status(thm)],[c_4394,c_403]) ).

cnf(c_4396,plain,
    ( ~ product(X0,e_1,X1)
    | ~ product(X0,e_3,X1) ),
    inference(renaming,[status(thm)],[c_4395]) ).

cnf(c_4397,plain,
    ( ~ product(X0,e_1,X1)
    | ~ product(X0,e_4,X1)
    | equalish(e_1,e_4) ),
    inference(instantiation,[status(thm)],[c_108]) ).

cnf(c_4398,plain,
    ( ~ product(X0,e_4,X1)
    | ~ product(X0,e_1,X1) ),
    inference(global_subsumption_just,[status(thm)],[c_4397,c_426]) ).

cnf(c_4399,plain,
    ( ~ product(X0,e_1,X1)
    | ~ product(X0,e_4,X1) ),
    inference(renaming,[status(thm)],[c_4398]) ).

cnf(c_4407,plain,
    ( ~ product(X0,e_2,X1)
    | ~ product(X0,e_3,X1)
    | equalish(e_2,e_3) ),
    inference(instantiation,[status(thm)],[c_108]) ).

cnf(c_4408,plain,
    ( ~ product(X0,e_3,X1)
    | ~ product(X0,e_2,X1) ),
    inference(global_subsumption_just,[status(thm)],[c_4407,c_498]) ).

cnf(c_4409,plain,
    ( ~ product(X0,e_2,X1)
    | ~ product(X0,e_3,X1) ),
    inference(renaming,[status(thm)],[c_4408]) ).

cnf(c_4410,plain,
    ( ~ product(X0,e_2,X1)
    | ~ product(X0,e_4,X1)
    | equalish(e_2,e_4) ),
    inference(instantiation,[status(thm)],[c_108]) ).

cnf(c_4411,plain,
    ( ~ product(X0,e_4,X1)
    | ~ product(X0,e_2,X1) ),
    inference(global_subsumption_just,[status(thm)],[c_4410,c_521]) ).

cnf(c_4412,plain,
    ( ~ product(X0,e_2,X1)
    | ~ product(X0,e_4,X1) ),
    inference(renaming,[status(thm)],[c_4411]) ).

cnf(c_4413,plain,
    ( ~ product(X0,e_2,X1)
    | ~ product(X0,e_5,X1)
    | equalish(e_2,e_5) ),
    inference(instantiation,[status(thm)],[c_108]) ).

cnf(c_4414,plain,
    ( ~ product(X0,e_5,X1)
    | ~ product(X0,e_2,X1) ),
    inference(global_subsumption_just,[status(thm)],[c_4413,c_544]) ).

cnf(c_4415,plain,
    ( ~ product(X0,e_2,X1)
    | ~ product(X0,e_5,X1) ),
    inference(renaming,[status(thm)],[c_4414]) ).

cnf(c_4416,plain,
    ( ~ product(X0,e_2,X1)
    | ~ product(X0,e_6,X1)
    | equalish(e_2,e_6) ),
    inference(instantiation,[status(thm)],[c_108]) ).

cnf(c_4417,plain,
    ( ~ product(X0,e_6,X1)
    | ~ product(X0,e_2,X1) ),
    inference(global_subsumption_just,[status(thm)],[c_4416,c_567]) ).

cnf(c_4418,plain,
    ( ~ product(X0,e_2,X1)
    | ~ product(X0,e_6,X1) ),
    inference(renaming,[status(thm)],[c_4417]) ).

cnf(c_4421,plain,
    ( ~ product(X0,e_3,X1)
    | ~ product(X0,e_4,X1)
    | equalish(e_3,e_4) ),
    inference(instantiation,[status(thm)],[c_108]) ).

cnf(c_4422,plain,
    ( ~ product(X0,e_4,X1)
    | ~ product(X0,e_3,X1) ),
    inference(global_subsumption_just,[status(thm)],[c_4421,c_596]) ).

cnf(c_4423,plain,
    ( ~ product(X0,e_3,X1)
    | ~ product(X0,e_4,X1) ),
    inference(renaming,[status(thm)],[c_4422]) ).

cnf(c_4424,plain,
    ( ~ product(X0,e_3,X1)
    | ~ product(X0,e_5,X1)
    | equalish(e_3,e_5) ),
    inference(instantiation,[status(thm)],[c_108]) ).

cnf(c_4425,plain,
    ( ~ product(X0,e_5,X1)
    | ~ product(X0,e_3,X1) ),
    inference(global_subsumption_just,[status(thm)],[c_4424,c_619]) ).

cnf(c_4426,plain,
    ( ~ product(X0,e_3,X1)
    | ~ product(X0,e_5,X1) ),
    inference(renaming,[status(thm)],[c_4425]) ).

cnf(c_4427,plain,
    ( ~ product(X0,e_3,X1)
    | ~ product(X0,e_6,X1)
    | equalish(e_3,e_6) ),
    inference(instantiation,[status(thm)],[c_108]) ).

cnf(c_4428,plain,
    ( ~ product(X0,e_6,X1)
    | ~ product(X0,e_3,X1) ),
    inference(global_subsumption_just,[status(thm)],[c_4427,c_642]) ).

cnf(c_4429,plain,
    ( ~ product(X0,e_3,X1)
    | ~ product(X0,e_6,X1) ),
    inference(renaming,[status(thm)],[c_4428]) ).

cnf(c_4433,plain,
    ( ~ product(X0,e_4,X1)
    | ~ product(X0,e_5,X1)
    | equalish(e_4,e_5) ),
    inference(instantiation,[status(thm)],[c_108]) ).

cnf(c_4434,plain,
    ( ~ product(X0,e_5,X1)
    | ~ product(X0,e_4,X1) ),
    inference(global_subsumption_just,[status(thm)],[c_4433,c_674]) ).

cnf(c_4435,plain,
    ( ~ product(X0,e_4,X1)
    | ~ product(X0,e_5,X1) ),
    inference(renaming,[status(thm)],[c_4434]) ).

cnf(c_4436,plain,
    ( ~ product(X0,e_4,X1)
    | ~ product(X0,e_6,X1)
    | equalish(e_4,e_6) ),
    inference(instantiation,[status(thm)],[c_108]) ).

cnf(c_4437,plain,
    ( ~ product(X0,e_6,X1)
    | ~ product(X0,e_4,X1) ),
    inference(global_subsumption_just,[status(thm)],[c_4436,c_697]) ).

cnf(c_4438,plain,
    ( ~ product(X0,e_4,X1)
    | ~ product(X0,e_6,X1) ),
    inference(renaming,[status(thm)],[c_4437]) ).

cnf(c_4443,plain,
    ( ~ product(X0,e_5,X1)
    | ~ product(X0,e_6,X1)
    | equalish(e_5,e_6) ),
    inference(instantiation,[status(thm)],[c_108]) ).

cnf(c_4444,plain,
    ( ~ product(X0,e_6,X1)
    | ~ product(X0,e_5,X1) ),
    inference(global_subsumption_just,[status(thm)],[c_4443,c_732]) ).

cnf(c_4445,plain,
    ( ~ product(X0,e_5,X1)
    | ~ product(X0,e_6,X1) ),
    inference(renaming,[status(thm)],[c_4444]) ).

cnf(c_4451,plain,
    ( ~ product(e_1,X0,X1)
    | ~ product(e_2,X0,X1)
    | equalish(e_1,e_2) ),
    inference(instantiation,[status(thm)],[c_109]) ).

cnf(c_4452,plain,
    ( ~ product(e_2,X0,X1)
    | ~ product(e_1,X0,X1) ),
    inference(global_subsumption_just,[status(thm)],[c_4451,c_388]) ).

cnf(c_4453,plain,
    ( ~ product(e_1,X0,X1)
    | ~ product(e_2,X0,X1) ),
    inference(renaming,[status(thm)],[c_4452]) ).

cnf(c_4454,plain,
    ( ~ product(e_1,X0,X1)
    | ~ product(e_3,X0,X1)
    | equalish(e_1,e_3) ),
    inference(instantiation,[status(thm)],[c_109]) ).

cnf(c_4455,plain,
    ( ~ product(e_3,X0,X1)
    | ~ product(e_1,X0,X1) ),
    inference(global_subsumption_just,[status(thm)],[c_4454,c_411]) ).

cnf(c_4456,plain,
    ( ~ product(e_1,X0,X1)
    | ~ product(e_3,X0,X1) ),
    inference(renaming,[status(thm)],[c_4455]) ).

cnf(c_4457,plain,
    ( ~ product(e_1,X0,X1)
    | ~ product(e_4,X0,X1)
    | equalish(e_1,e_4) ),
    inference(instantiation,[status(thm)],[c_109]) ).

cnf(c_4458,plain,
    ( ~ product(e_4,X0,X1)
    | ~ product(e_1,X0,X1) ),
    inference(global_subsumption_just,[status(thm)],[c_4457,c_434]) ).

cnf(c_4459,plain,
    ( ~ product(e_1,X0,X1)
    | ~ product(e_4,X0,X1) ),
    inference(renaming,[status(thm)],[c_4458]) ).

cnf(c_4460,plain,
    ( ~ product(e_1,X0,X1)
    | ~ product(e_5,X0,X1)
    | equalish(e_1,e_5) ),
    inference(instantiation,[status(thm)],[c_109]) ).

cnf(c_4461,plain,
    ( ~ product(e_5,X0,X1)
    | ~ product(e_1,X0,X1) ),
    inference(global_subsumption_just,[status(thm)],[c_4460,c_457]) ).

cnf(c_4462,plain,
    ( ~ product(e_1,X0,X1)
    | ~ product(e_5,X0,X1) ),
    inference(renaming,[status(thm)],[c_4461]) ).

cnf(c_4463,plain,
    ( ~ product(e_1,X0,X1)
    | ~ product(e_6,X0,X1)
    | equalish(e_1,e_6) ),
    inference(instantiation,[status(thm)],[c_109]) ).

cnf(c_4464,plain,
    ( ~ product(e_6,X0,X1)
    | ~ product(e_1,X0,X1) ),
    inference(global_subsumption_just,[status(thm)],[c_4463,c_480]) ).

cnf(c_4465,plain,
    ( ~ product(e_1,X0,X1)
    | ~ product(e_6,X0,X1) ),
    inference(renaming,[status(thm)],[c_4464]) ).

cnf(c_4467,plain,
    ( ~ product(e_2,X0,X1)
    | ~ product(e_3,X0,X1)
    | equalish(e_2,e_3) ),
    inference(instantiation,[status(thm)],[c_109]) ).

cnf(c_4468,plain,
    ( ~ product(e_3,X0,X1)
    | ~ product(e_2,X0,X1) ),
    inference(global_subsumption_just,[status(thm)],[c_4467,c_506]) ).

cnf(c_4469,plain,
    ( ~ product(e_2,X0,X1)
    | ~ product(e_3,X0,X1) ),
    inference(renaming,[status(thm)],[c_4468]) ).

cnf(c_4470,plain,
    ( ~ product(e_2,X0,X1)
    | ~ product(e_4,X0,X1)
    | equalish(e_2,e_4) ),
    inference(instantiation,[status(thm)],[c_109]) ).

cnf(c_4471,plain,
    ( ~ product(e_4,X0,X1)
    | ~ product(e_2,X0,X1) ),
    inference(global_subsumption_just,[status(thm)],[c_4470,c_529]) ).

cnf(c_4472,plain,
    ( ~ product(e_2,X0,X1)
    | ~ product(e_4,X0,X1) ),
    inference(renaming,[status(thm)],[c_4471]) ).

cnf(c_4473,plain,
    ( ~ product(e_2,X0,X1)
    | ~ product(e_5,X0,X1)
    | equalish(e_2,e_5) ),
    inference(instantiation,[status(thm)],[c_109]) ).

cnf(c_4474,plain,
    ( ~ product(e_5,X0,X1)
    | ~ product(e_2,X0,X1) ),
    inference(global_subsumption_just,[status(thm)],[c_4473,c_552]) ).

cnf(c_4475,plain,
    ( ~ product(e_2,X0,X1)
    | ~ product(e_5,X0,X1) ),
    inference(renaming,[status(thm)],[c_4474]) ).

cnf(c_4481,plain,
    ( ~ product(e_3,X0,X1)
    | ~ product(e_4,X0,X1)
    | equalish(e_3,e_4) ),
    inference(instantiation,[status(thm)],[c_109]) ).

cnf(c_4482,plain,
    ( ~ product(e_4,X0,X1)
    | ~ product(e_3,X0,X1) ),
    inference(global_subsumption_just,[status(thm)],[c_4481,c_604]) ).

cnf(c_4483,plain,
    ( ~ product(e_3,X0,X1)
    | ~ product(e_4,X0,X1) ),
    inference(renaming,[status(thm)],[c_4482]) ).

cnf(c_4484,plain,
    ( ~ product(e_3,X0,X1)
    | ~ product(e_5,X0,X1)
    | equalish(e_3,e_5) ),
    inference(instantiation,[status(thm)],[c_109]) ).

cnf(c_4485,plain,
    ( ~ product(e_5,X0,X1)
    | ~ product(e_3,X0,X1) ),
    inference(global_subsumption_just,[status(thm)],[c_4484,c_627]) ).

cnf(c_4486,plain,
    ( ~ product(e_3,X0,X1)
    | ~ product(e_5,X0,X1) ),
    inference(renaming,[status(thm)],[c_4485]) ).

cnf(c_4487,plain,
    ( ~ product(e_3,X0,X1)
    | ~ product(e_6,X0,X1)
    | equalish(e_3,e_6) ),
    inference(instantiation,[status(thm)],[c_109]) ).

cnf(c_4488,plain,
    ( ~ product(e_6,X0,X1)
    | ~ product(e_3,X0,X1) ),
    inference(global_subsumption_just,[status(thm)],[c_4487,c_650]) ).

cnf(c_4489,plain,
    ( ~ product(e_3,X0,X1)
    | ~ product(e_6,X0,X1) ),
    inference(renaming,[status(thm)],[c_4488]) ).

cnf(c_4493,plain,
    ( ~ product(e_4,X0,X1)
    | ~ product(e_5,X0,X1)
    | equalish(e_4,e_5) ),
    inference(instantiation,[status(thm)],[c_109]) ).

cnf(c_4494,plain,
    ( ~ product(e_5,X0,X1)
    | ~ product(e_4,X0,X1) ),
    inference(global_subsumption_just,[status(thm)],[c_4493,c_682]) ).

cnf(c_4495,plain,
    ( ~ product(e_4,X0,X1)
    | ~ product(e_5,X0,X1) ),
    inference(renaming,[status(thm)],[c_4494]) ).

cnf(c_4496,plain,
    ( ~ product(e_4,X0,X1)
    | ~ product(e_6,X0,X1)
    | equalish(e_4,e_6) ),
    inference(instantiation,[status(thm)],[c_109]) ).

cnf(c_4497,plain,
    ( ~ product(e_6,X0,X1)
    | ~ product(e_4,X0,X1) ),
    inference(global_subsumption_just,[status(thm)],[c_4496,c_705]) ).

cnf(c_4498,plain,
    ( ~ product(e_4,X0,X1)
    | ~ product(e_6,X0,X1) ),
    inference(renaming,[status(thm)],[c_4497]) ).

cnf(c_4503,plain,
    ( ~ product(e_5,X0,X1)
    | ~ product(e_6,X0,X1)
    | equalish(e_5,e_6) ),
    inference(instantiation,[status(thm)],[c_109]) ).

cnf(c_4504,plain,
    ( ~ product(e_6,X0,X1)
    | ~ product(e_5,X0,X1) ),
    inference(global_subsumption_just,[status(thm)],[c_4503,c_740]) ).

cnf(c_4505,plain,
    ( ~ product(e_5,X0,X1)
    | ~ product(e_6,X0,X1) ),
    inference(renaming,[status(thm)],[c_4504]) ).

cnf(c_4569,plain,
    ( ~ product(X0,e_4,e_1)
    | ~ product(e_1,e_4,e_3)
    | product(X0,e_1,e_3) ),
    inference(instantiation,[status(thm)],[c_4082]) ).

cnf(c_4575,plain,
    ( ~ product(X0,e_3,e_2)
    | ~ product(e_2,e_3,e_4)
    | product(X0,e_2,e_4) ),
    inference(instantiation,[status(thm)],[c_4083]) ).

cnf(c_4580,plain,
    ( ~ product(X0,e_4,e_3)
    | ~ product(e_3,e_4,e_5)
    | product(X0,e_3,e_5) ),
    inference(instantiation,[status(thm)],[c_4084]) ).

cnf(c_4614,plain,
    ( ~ product(e_4,e_3,X0)
    | ~ product(e_2,e_3,e_4)
    | product(e_2,e_4,X0) ),
    inference(instantiation,[status(thm)],[c_4086]) ).

cnf(c_4620,plain,
    ( ~ product(e_5,X0,X1)
    | ~ product(e_4,X0,e_5)
    | product(e_4,e_5,X1) ),
    inference(instantiation,[status(thm)],[c_4088]) ).

cnf(c_4626,plain,
    ( ~ product(e_2,X0,X1)
    | ~ product(e_6,X0,e_2)
    | product(e_6,e_2,X1) ),
    inference(instantiation,[status(thm)],[c_4090]) ).

cnf(c_4636,plain,
    ( ~ product(X0,X1,e_6)
    | ~ product(e_6,X1,e_2)
    | product(X0,e_6,e_2) ),
    inference(instantiation,[status(thm)],[c_4115]) ).

cnf(c_4653,plain,
    ( ~ product(e_1,e_2,e_2)
    | ~ product(e_2,e_2,e_2) ),
    inference(instantiation,[status(thm)],[c_3645]) ).

cnf(c_4662,plain,
    ( ~ product(e_5,e_4,X0)
    | ~ product(e_2,e_4,e_5)
    | product(e_2,e_5,X0) ),
    inference(instantiation,[status(thm)],[c_4086]) ).

cnf(c_4663,plain,
    ( ~ product(e_2,e_4,e_5)
    | ~ product(e_5,e_4,e_1)
    | product(e_2,e_5,e_1) ),
    inference(instantiation,[status(thm)],[c_4662]) ).

cnf(c_4664,plain,
    ( ~ product(X0,e_4,e_2)
    | ~ product(e_2,e_4,e_5)
    | product(X0,e_2,e_5) ),
    inference(instantiation,[status(thm)],[c_4084]) ).

cnf(c_4674,plain,
    ( ~ product(e_1,e_6,X0)
    | ~ product(e_2,e_6,e_1)
    | product(e_2,e_1,X0) ),
    inference(instantiation,[status(thm)],[c_4086]) ).

cnf(c_4716,plain,
    ( ~ product(e_2,e_2,X0)
    | ~ product(e_4,e_2,e_2)
    | product(e_4,e_2,X0) ),
    inference(instantiation,[status(thm)],[c_4088]) ).

cnf(c_4732,plain,
    ( ~ product(e_6,e_4,X0)
    | ~ product(e_4,e_4,e_6)
    | product(e_4,e_6,X0) ),
    inference(instantiation,[status(thm)],[c_4088]) ).

cnf(c_4733,plain,
    ( ~ product(e_4,e_4,e_6)
    | ~ product(e_6,e_4,e_1)
    | product(e_4,e_6,e_1) ),
    inference(instantiation,[status(thm)],[c_4732]) ).

cnf(c_4734,plain,
    ( ~ product(X0,e_4,e_4)
    | ~ product(e_4,e_4,e_6)
    | product(X0,e_4,e_6) ),
    inference(instantiation,[status(thm)],[c_4085]) ).

cnf(c_4735,plain,
    ( ~ product(e_1,e_4,e_4)
    | ~ product(e_4,e_4,e_6)
    | product(e_1,e_4,e_6) ),
    inference(instantiation,[status(thm)],[c_4734]) ).

cnf(c_4748,plain,
    ( ~ product(X0,e_6,e_4)
    | ~ product(e_4,e_6,e_6)
    | product(X0,e_4,e_6) ),
    inference(instantiation,[status(thm)],[c_4085]) ).

cnf(c_4749,plain,
    ( ~ product(e_1,e_6,e_4)
    | ~ product(e_4,e_6,e_6)
    | product(e_1,e_4,e_6) ),
    inference(instantiation,[status(thm)],[c_4748]) ).

cnf(c_4755,plain,
    ( ~ product(X0,e_2,e_6)
    | ~ product(e_6,e_2,e_3)
    | product(X0,e_6,e_3) ),
    inference(instantiation,[status(thm)],[c_4082]) ).

cnf(c_4759,plain,
    ( ~ product(e_3,e_2,X0)
    | ~ product(e_6,e_2,e_3)
    | product(e_6,e_3,X0) ),
    inference(instantiation,[status(thm)],[c_4090]) ).

cnf(c_4764,plain,
    ( ~ product(e_1,e_2,e_1)
    | ~ product(e_1,e_2,e_2) ),
    inference(instantiation,[status(thm)],[c_4333]) ).

cnf(c_4765,plain,
    ~ product(e_1,e_2,e_1),
    inference(global_subsumption_just,[status(thm)],[c_4764,c_72,c_71,c_70,c_86,c_81,c_80,c_76,c_113,c_322,c_326,c_330,c_334,c_338,c_342,c_346,c_350,c_354,c_358,c_381,c_389,c_412,c_435,c_1905,c_1910,c_1918,c_1939,c_1946,c_2058,c_2064,c_2130,c_2133,c_2230,c_2628,c_2708,c_2987,c_2990,c_3128,c_3179,c_3193,c_3199,c_3201,c_3387,c_3408,c_3553,c_3558,c_3987,c_4003]) ).

cnf(c_4775,plain,
    ( ~ product(e_1,e_4,e_1)
    | ~ product(e_1,e_4,e_3) ),
    inference(instantiation,[status(thm)],[c_4336]) ).

cnf(c_4776,plain,
    ~ product(e_1,e_4,e_1),
    inference(global_subsumption_just,[status(thm)],[c_4775,c_72,c_71,c_70,c_86,c_81,c_80,c_76,c_113,c_322,c_326,c_330,c_334,c_338,c_342,c_346,c_350,c_354,c_358,c_389,c_412,c_427,c_435,c_1905,c_1910,c_1918,c_1939,c_1946,c_2058,c_2064,c_2130,c_2133,c_2230,c_2628,c_2708,c_2987,c_2990,c_3128,c_3179,c_3193,c_3199,c_3201,c_3387,c_3408,c_3553,c_3558,c_3987,c_4003]) ).

cnf(c_4778,plain,
    ( ~ product(e_1,e_5,e_1)
    | ~ product(e_1,e_5,e_3) ),
    inference(instantiation,[status(thm)],[c_4336]) ).

cnf(c_4779,plain,
    ~ product(e_1,e_5,e_1),
    inference(global_subsumption_just,[status(thm)],[c_4778,c_72,c_71,c_70,c_86,c_81,c_80,c_76,c_113,c_322,c_326,c_330,c_334,c_338,c_342,c_346,c_350,c_354,c_358,c_389,c_412,c_435,c_450,c_1905,c_1910,c_1918,c_1939,c_1946,c_2058,c_2064,c_2130,c_2133,c_2230,c_2628,c_2708,c_2987,c_2990,c_3128,c_3179,c_3193,c_3199,c_3201,c_3387,c_3408,c_3553,c_3558,c_3987,c_4003]) ).

cnf(c_4787,plain,
    ( ~ product(e_4,X0,e_1)
    | ~ product(e_4,X0,e_5) ),
    inference(instantiation,[status(thm)],[c_4342]) ).

cnf(c_4789,plain,
    ( ~ product(e_1,e_3,e_1)
    | ~ product(e_1,e_3,e_5) ),
    inference(instantiation,[status(thm)],[c_4342]) ).

cnf(c_4790,plain,
    ~ product(e_1,e_3,e_1),
    inference(global_subsumption_just,[status(thm)],[c_4789,c_72,c_71,c_70,c_86,c_81,c_80,c_76,c_113,c_322,c_326,c_330,c_334,c_338,c_342,c_346,c_350,c_354,c_358,c_389,c_404,c_412,c_435,c_1905,c_1910,c_1918,c_1939,c_1946,c_2058,c_2064,c_2130,c_2133,c_2230,c_2628,c_2708,c_2987,c_2990,c_3128,c_3179,c_3193,c_3199,c_3201,c_3387,c_3408,c_3553,c_3558,c_3987,c_4003]) ).

cnf(c_4795,plain,
    ( ~ product(e_1,e_6,e_1)
    | ~ product(e_1,e_6,e_6) ),
    inference(instantiation,[status(thm)],[c_4345]) ).

cnf(c_4796,plain,
    ~ product(e_1,e_6,e_1),
    inference(global_subsumption_just,[status(thm)],[c_4795,c_72,c_71,c_70,c_86,c_81,c_80,c_76,c_113,c_322,c_326,c_330,c_334,c_338,c_342,c_346,c_350,c_354,c_358,c_389,c_412,c_435,c_473,c_1905,c_1910,c_1918,c_1939,c_1946,c_2058,c_2064,c_2130,c_2133,c_2230,c_2628,c_2708,c_2987,c_2990,c_3128,c_3179,c_3193,c_3199,c_3201,c_3387,c_3408,c_3553,c_3558,c_3987,c_4003]) ).

cnf(c_4824,plain,
    ( ~ product(e_4,e_2,e_2)
    | ~ product(e_4,e_2,e_5) ),
    inference(instantiation,[status(thm)],[c_4355]) ).

cnf(c_4829,plain,
    ( ~ product(e_4,e_2,e_2)
    | ~ product(e_4,e_2,e_6) ),
    inference(instantiation,[status(thm)],[c_4358]) ).

cnf(c_4850,plain,
    ( ~ product(e_4,X0,e_4)
    | ~ product(e_4,X0,e_5) ),
    inference(instantiation,[status(thm)],[c_4375]) ).

cnf(c_4868,plain,
    ( ~ product(X0,X1,e_2)
    | ~ product(e_2,X1,X2)
    | product(X0,e_2,X2) ),
    inference(instantiation,[status(thm)],[c_110]) ).

cnf(c_4875,plain,
    ( ~ product(e_2,e_1,e_2)
    | ~ product(e_2,e_2,e_2) ),
    inference(instantiation,[status(thm)],[c_4393]) ).

cnf(c_4876,plain,
    ~ product(e_2,e_1,e_2),
    inference(global_subsumption_just,[status(thm)],[c_4875,c_76,c_2064,c_2708]) ).

cnf(c_4885,plain,
    ( ~ product(e_3,e_1,e_1)
    | ~ product(e_3,e_2,e_1) ),
    inference(instantiation,[status(thm)],[c_4393]) ).

cnf(c_4886,plain,
    ~ product(e_3,e_1,e_1),
    inference(global_subsumption_just,[status(thm)],[c_4885,c_70,c_81,c_113,c_322,c_326,c_330,c_334,c_412,c_1946,c_2133]) ).

cnf(c_4894,plain,
    ( ~ product(e_6,e_1,e_2)
    | ~ product(e_6,e_3,e_2) ),
    inference(instantiation,[status(thm)],[c_4396]) ).

cnf(c_4903,plain,
    ( ~ product(X0,X1,e_4)
    | ~ product(e_4,X1,X2)
    | product(X0,e_4,X2) ),
    inference(instantiation,[status(thm)],[c_110]) ).

cnf(c_4922,plain,
    ( ~ product(X0,X1,e_5)
    | ~ product(e_5,X1,X2)
    | product(X0,e_5,X2) ),
    inference(instantiation,[status(thm)],[c_110]) ).

cnf(c_4954,plain,
    ( ~ product(e_2,e_2,e_4)
    | ~ product(e_2,e_3,e_4) ),
    inference(instantiation,[status(thm)],[c_4409]) ).

cnf(c_4964,plain,
    ( ~ product(e_2,e_2,e_5)
    | ~ product(e_2,e_4,e_5) ),
    inference(instantiation,[status(thm)],[c_4412]) ).

cnf(c_4965,plain,
    ( ~ product(e_1,e_2,e_3)
    | ~ product(e_1,e_4,e_3) ),
    inference(instantiation,[status(thm)],[c_4412]) ).

cnf(c_4966,plain,
    ~ product(e_1,e_2,e_3),
    inference(global_subsumption_just,[status(thm)],[c_4965,c_72,c_71,c_70,c_86,c_81,c_80,c_76,c_113,c_322,c_326,c_330,c_334,c_338,c_342,c_346,c_350,c_354,c_358,c_389,c_412,c_435,c_1905,c_1910,c_1918,c_1939,c_1946,c_2064,c_2130,c_2133,c_2230,c_2628,c_2708,c_2987,c_2990,c_3128,c_3179,c_3193,c_3199,c_3201,c_3387,c_3408,c_3553,c_3558,c_3987,c_4003]) ).

cnf(c_4968,plain,
    ( ~ product(e_3,e_2,e_5)
    | ~ product(e_3,e_4,e_5) ),
    inference(instantiation,[status(thm)],[c_4412]) ).

cnf(c_4979,plain,
    ( ~ product(e_4,e_2,e_6)
    | ~ product(e_4,e_5,e_6) ),
    inference(instantiation,[status(thm)],[c_4415]) ).

cnf(c_5001,plain,
    ( ~ product(e_3,e_3,e_5)
    | ~ product(e_3,e_4,e_5) ),
    inference(instantiation,[status(thm)],[c_4423]) ).

cnf(c_5002,plain,
    ( ~ product(e_4,e_3,e_6)
    | ~ product(e_4,e_4,e_6) ),
    inference(instantiation,[status(thm)],[c_4423]) ).

cnf(c_5010,plain,
    ( ~ product(e_2,e_3,e_4)
    | ~ product(e_2,e_5,e_4) ),
    inference(instantiation,[status(thm)],[c_4426]) ).

cnf(c_5011,plain,
    ( ~ product(e_1,e_3,e_3)
    | ~ product(e_1,e_5,e_3) ),
    inference(instantiation,[status(thm)],[c_4426]) ).

cnf(c_5012,plain,
    ( ~ product(e_4,e_3,e_6)
    | ~ product(e_4,e_5,e_6) ),
    inference(instantiation,[status(thm)],[c_4426]) ).

cnf(c_5024,plain,
    ( ~ product(e_4,e_3,e_6)
    | ~ product(e_4,e_6,e_6) ),
    inference(instantiation,[status(thm)],[c_4429]) ).

cnf(c_5033,plain,
    ( ~ product(e_1,e_4,e_3)
    | ~ product(e_1,e_5,e_3) ),
    inference(instantiation,[status(thm)],[c_4435]) ).

cnf(c_5034,plain,
    ( ~ product(e_4,e_4,e_6)
    | ~ product(e_4,e_5,e_6) ),
    inference(instantiation,[status(thm)],[c_4435]) ).

cnf(c_5044,plain,
    ( ~ product(e_1,e_4,e_6)
    | ~ product(e_1,e_6,e_6) ),
    inference(instantiation,[status(thm)],[c_4438]) ).

cnf(c_5055,plain,
    ( ~ product(e_1,e_5,e_6)
    | ~ product(e_1,e_6,e_6) ),
    inference(instantiation,[status(thm)],[c_4445]) ).

cnf(c_5057,plain,
    ( ~ product(e_4,e_5,e_6)
    | ~ product(e_4,e_6,e_6) ),
    inference(instantiation,[status(thm)],[c_4445]) ).

cnf(c_5073,plain,
    ( ~ product(e_1,X0,e_5)
    | ~ product(e_4,X0,e_5) ),
    inference(instantiation,[status(thm)],[c_4459]) ).

cnf(c_5076,plain,
    ( ~ product(e_1,e_4,e_6)
    | ~ product(e_4,e_4,e_6) ),
    inference(instantiation,[status(thm)],[c_4459]) ).

cnf(c_5078,plain,
    ( ~ product(e_1,e_6,e_6)
    | ~ product(e_4,e_6,e_6) ),
    inference(instantiation,[status(thm)],[c_4459]) ).

cnf(c_5092,plain,
    ( ~ product(e_2,X0,e_5)
    | ~ product(e_4,X0,e_5) ),
    inference(instantiation,[status(thm)],[c_4472]) ).

cnf(c_5093,plain,
    ( ~ product(e_2,e_2,e_2)
    | ~ product(e_4,e_2,e_2) ),
    inference(instantiation,[status(thm)],[c_4472]) ).

cnf(c_5094,plain,
    ( ~ product(e_2,e_3,e_4)
    | ~ product(e_4,e_3,e_4) ),
    inference(instantiation,[status(thm)],[c_4472]) ).

cnf(c_5097,plain,
    ( ~ product(e_2,e_6,e_6)
    | ~ product(e_4,e_6,e_6) ),
    inference(instantiation,[status(thm)],[c_4472]) ).

cnf(c_5099,plain,
    ( ~ product(e_2,X0,e_6)
    | ~ product(e_5,X0,e_6) ),
    inference(instantiation,[status(thm)],[c_4475]) ).

cnf(c_5104,plain,
    ( ~ product(e_3,X0,e_5)
    | ~ product(e_4,X0,e_5) ),
    inference(instantiation,[status(thm)],[c_4483]) ).

cnf(c_5116,plain,
    ( ~ product(e_3,e_3,e_3)
    | ~ product(e_4,e_3,e_3) ),
    inference(instantiation,[status(thm)],[c_4483]) ).

cnf(c_5120,plain,
    ( ~ product(e_3,e_3,X0)
    | ~ product(e_4,e_3,e_3)
    | product(e_4,e_3,X0) ),
    inference(instantiation,[status(thm)],[c_4088]) ).

cnf(c_5121,plain,
    ( ~ product(e_3,e_3,e_1)
    | ~ product(e_4,e_3,e_3)
    | product(e_4,e_3,e_1) ),
    inference(instantiation,[status(thm)],[c_5120]) ).

cnf(c_5129,plain,
    ( ~ product(e_4,e_2,e_4)
    | ~ product(e_4,e_4,e_4) ),
    inference(instantiation,[status(thm)],[c_4412]) ).

cnf(c_5133,plain,
    ( ~ product(e_1,e_4,e_4)
    | ~ product(e_4,e_4,e_4) ),
    inference(instantiation,[status(thm)],[c_4459]) ).

cnf(c_5143,plain,
    ( ~ product(e_1,e_6,e_4)
    | ~ product(e_4,e_6,e_4) ),
    inference(instantiation,[status(thm)],[c_4459]) ).

cnf(c_5146,plain,
    ( ~ product(e_4,e_4,e_4)
    | ~ product(e_4,e_6,e_4) ),
    inference(instantiation,[status(thm)],[c_4438]) ).

cnf(c_5148,plain,
    ( ~ product(e_4,e_2,e_4)
    | ~ product(e_4,e_6,e_4) ),
    inference(instantiation,[status(thm)],[c_4418]) ).

cnf(c_5155,plain,
    ( ~ product(e_3,X0,e_2)
    | ~ product(e_6,X0,e_2) ),
    inference(instantiation,[status(thm)],[c_4489]) ).

cnf(c_5156,plain,
    ( ~ product(e_3,e_1,e_2)
    | ~ product(e_6,e_1,e_2) ),
    inference(instantiation,[status(thm)],[c_5155]) ).

cnf(c_5161,plain,
    ( ~ product(e_4,X0,e_2)
    | ~ product(e_6,X0,e_2) ),
    inference(instantiation,[status(thm)],[c_4498]) ).

cnf(c_5162,plain,
    ( ~ product(e_4,e_1,e_2)
    | ~ product(e_6,e_1,e_2) ),
    inference(instantiation,[status(thm)],[c_5161]) ).

cnf(c_5172,plain,
    ( ~ product(e_1,e_4,e_3)
    | ~ product(e_1,e_4,e_4) ),
    inference(instantiation,[status(thm)],[c_4363]) ).

cnf(c_5174,plain,
    ( ~ product(e_1,e_4,e_4)
    | ~ product(e_4,e_4,e_5)
    | product(e_1,e_4,e_5) ),
    inference(instantiation,[status(thm)],[c_3628]) ).

cnf(c_5205,plain,
    ( ~ product(e_2,e_3,e_4)
    | ~ product(e_3,e_3,e_2)
    | product(e_3,e_2,e_4) ),
    inference(instantiation,[status(thm)],[c_4575]) ).

cnf(c_5206,plain,
    ~ product(e_3,e_3,e_2),
    inference(global_subsumption_just,[status(thm)],[c_5205,c_72,c_71,c_70,c_81,c_76,c_113,c_322,c_326,c_330,c_334,c_338,c_342,c_346,c_350,c_354,c_389,c_412,c_1905,c_1910,c_1939,c_1946,c_2064,c_2130,c_2133,c_2172,c_2708,c_2987,c_3576,c_3777,c_5205]) ).

cnf(c_5227,plain,
    ( ~ product(e_5,e_1,e_4)
    | ~ product(e_5,e_3,e_4) ),
    inference(instantiation,[status(thm)],[c_4396]) ).

cnf(c_5228,plain,
    ~ product(e_5,e_1,e_4),
    inference(global_subsumption_just,[status(thm)],[c_5227,c_73,c_71,c_70,c_81,c_80,c_76,c_113,c_322,c_326,c_330,c_334,c_338,c_342,c_346,c_350,c_354,c_358,c_389,c_412,c_435,c_1905,c_1913,c_1915,c_1939,c_1946,c_2058,c_2064,c_2130,c_2133,c_2708,c_2987,c_2990,c_3152,c_3153,c_3179,c_3199,c_3201,c_3387,c_3410,c_3563,c_3987,c_4003,c_4966,c_5156]) ).

cnf(c_5244,plain,
    ( ~ product(e_5,e_2,e_3)
    | ~ product(e_5,e_4,e_3) ),
    inference(instantiation,[status(thm)],[c_4412]) ).

cnf(c_5248,plain,
    ~ product(e_5,e_2,e_3),
    inference(global_subsumption_just,[status(thm)],[c_5244,c_73,c_72,c_71,c_70,c_86,c_81,c_80,c_76,c_113,c_322,c_326,c_330,c_334,c_338,c_342,c_346,c_350,c_354,c_358,c_389,c_412,c_435,c_1905,c_1910,c_1915,c_1918,c_1939,c_1946,c_2058,c_2064,c_2130,c_2133,c_2230,c_2628,c_2708,c_2987,c_2990,c_3128,c_3179,c_3193,c_3199,c_3201,c_3387,c_3408,c_3553,c_3558,c_3564,c_3566,c_3568,c_3987,c_4003]) ).

cnf(c_5250,plain,
    ( ~ product(e_5,e_4,e_3)
    | ~ product(e_6,e_4,e_3) ),
    inference(instantiation,[status(thm)],[c_4505]) ).

cnf(c_5254,plain,
    ( ~ product(e_1,e_4,e_3)
    | ~ product(e_5,e_4,e_3) ),
    inference(instantiation,[status(thm)],[c_4462]) ).

cnf(c_5256,plain,
    ( ~ product(X0,e_4,e_5)
    | ~ product(e_5,e_4,e_3)
    | product(X0,e_5,e_3) ),
    inference(instantiation,[status(thm)],[c_4082]) ).

cnf(c_5257,plain,
    ( ~ product(e_1,e_4,e_5)
    | ~ product(e_5,e_4,e_3)
    | product(e_1,e_5,e_3) ),
    inference(instantiation,[status(thm)],[c_5256]) ).

cnf(c_5266,plain,
    ( ~ product(e_4,e_5,e_1)
    | ~ product(e_5,e_5,e_1) ),
    inference(instantiation,[status(thm)],[c_4495]) ).

cnf(c_5309,plain,
    ( ~ product(e_1,e_4,e_3)
    | ~ product(e_1,e_6,e_3) ),
    inference(instantiation,[status(thm)],[c_4438]) ).

cnf(c_5310,plain,
    ( ~ product(e_1,e_3,e_3)
    | ~ product(e_1,e_6,e_3) ),
    inference(instantiation,[status(thm)],[c_4429]) ).

cnf(c_5330,plain,
    ( ~ product(e_3,e_2,e_4)
    | ~ product(e_3,e_2,e_6) ),
    inference(instantiation,[status(thm)],[c_4378]) ).

cnf(c_5336,plain,
    ~ product(e_3,e_2,e_4),
    inference(global_subsumption_just,[status(thm)],[c_5330,c_71,c_70,c_81,c_76,c_113,c_322,c_326,c_330,c_334,c_338,c_342,c_346,c_350,c_354,c_389,c_412,c_1905,c_1913,c_1939,c_1946,c_2064,c_2130,c_2133,c_2708,c_2987,c_3199,c_3779,c_3841]) ).

cnf(c_5399,plain,
    ( ~ product(e_4,e_3,e_2)
    | ~ product(e_4,e_3,e_5) ),
    inference(instantiation,[status(thm)],[c_4355]) ).

cnf(c_5408,plain,
    ( ~ product(e_2,e_3,e_2)
    | ~ product(e_4,e_3,e_2) ),
    inference(instantiation,[status(thm)],[c_4472]) ).

cnf(c_5416,plain,
    ( ~ product(e_2,e_3,e_4)
    | ~ product(e_4,e_3,e_2)
    | product(e_4,e_2,e_4) ),
    inference(instantiation,[status(thm)],[c_4575]) ).

cnf(c_5417,plain,
    ( ~ product(e_4,e_3,e_2)
    | product(e_4,e_2,e_4) ),
    inference(global_subsumption_just,[status(thm)],[c_5416,c_72,c_71,c_70,c_81,c_76,c_113,c_322,c_326,c_330,c_334,c_338,c_342,c_346,c_350,c_354,c_389,c_412,c_1905,c_1910,c_1939,c_1946,c_2064,c_2130,c_2133,c_2708,c_2773,c_2987,c_3576,c_5408,c_5416]) ).

cnf(c_5419,plain,
    ( ~ product(e_2,e_3,e_4)
    | ~ product(e_4,e_3,e_2)
    | product(e_2,e_4,e_2) ),
    inference(instantiation,[status(thm)],[c_4614]) ).

cnf(c_5420,plain,
    ( ~ product(e_4,e_3,e_2)
    | product(e_2,e_4,e_2) ),
    inference(global_subsumption_just,[status(thm)],[c_5419,c_72,c_71,c_70,c_81,c_76,c_113,c_322,c_326,c_330,c_334,c_338,c_342,c_346,c_350,c_354,c_389,c_412,c_1905,c_1910,c_1939,c_1946,c_2064,c_2130,c_2133,c_2708,c_2773,c_2987,c_3336,c_3576,c_5408]) ).

cnf(c_5429,plain,
    ( ~ product(e_4,e_2,e_1)
    | ~ product(e_4,e_2,e_4) ),
    inference(instantiation,[status(thm)],[c_4339]) ).

cnf(c_5432,plain,
    ( ~ product(e_4,e_1,e_4)
    | ~ product(e_4,e_2,e_4) ),
    inference(instantiation,[status(thm)],[c_4393]) ).

cnf(c_5435,plain,
    ( ~ product(e_2,e_2,e_4)
    | ~ product(e_4,e_2,e_4) ),
    inference(instantiation,[status(thm)],[c_4472]) ).

cnf(c_5436,plain,
    ( ~ product(e_1,e_2,e_4)
    | ~ product(e_4,e_2,e_4) ),
    inference(instantiation,[status(thm)],[c_4459]) ).

cnf(c_5441,plain,
    ( ~ product(e_4,e_3,e_1)
    | ~ product(e_4,e_4,e_1) ),
    inference(instantiation,[status(thm)],[c_4423]) ).

cnf(c_5453,plain,
    ( ~ product(e_1,e_4,X0)
    | ~ product(e_4,e_4,e_1)
    | product(e_4,e_1,X0) ),
    inference(instantiation,[status(thm)],[c_4088]) ).

cnf(c_5460,plain,
    ( ~ product(e_1,e_6,e_3)
    | ~ product(e_4,e_6,e_3) ),
    inference(instantiation,[status(thm)],[c_4459]) ).

cnf(c_5479,plain,
    ( ~ product(e_4,e_4,e_5)
    | ~ product(e_5,e_4,e_3)
    | product(e_4,e_5,e_3) ),
    inference(instantiation,[status(thm)],[c_4620]) ).

cnf(c_5519,plain,
    ( ~ product(e_4,e_5,X0)
    | ~ product(e_5,e_5,e_4)
    | product(e_5,e_4,X0) ),
    inference(instantiation,[status(thm)],[c_4089]) ).

cnf(c_5520,plain,
    ( ~ product(e_4,e_5,e_1)
    | ~ product(e_5,e_5,e_4)
    | product(e_5,e_4,e_1) ),
    inference(instantiation,[status(thm)],[c_5519]) ).

cnf(c_5557,plain,
    ( ~ product(e_2,e_4,e_6)
    | ~ product(e_6,e_4,e_2)
    | product(e_6,e_2,e_6) ),
    inference(instantiation,[status(thm)],[c_4626]) ).

cnf(c_5558,plain,
    ( ~ product(e_1,e_4,e_6)
    | ~ product(e_2,e_4,e_6) ),
    inference(instantiation,[status(thm)],[c_4453]) ).

cnf(c_5563,plain,
    ( ~ product(e_6,e_4,X0)
    | ~ product(e_2,e_4,e_6)
    | product(e_2,e_6,X0) ),
    inference(instantiation,[status(thm)],[c_4086]) ).

cnf(c_5564,plain,
    ( ~ product(e_2,e_4,e_6)
    | ~ product(e_6,e_4,e_1)
    | product(e_2,e_6,e_1) ),
    inference(instantiation,[status(thm)],[c_5563]) ).

cnf(c_5576,plain,
    ( ~ product(e_2,e_3,e_4)
    | ~ product(e_2,e_6,e_4) ),
    inference(instantiation,[status(thm)],[c_4429]) ).

cnf(c_5594,plain,
    ( ~ product(e_1,e_2,e_4)
    | ~ product(e_1,e_2,e_5) ),
    inference(instantiation,[status(thm)],[c_4375]) ).

cnf(c_5629,plain,
    ( ~ product(e_2,e_2,e_6)
    | ~ product(e_6,e_2,e_3)
    | product(e_2,e_6,e_3) ),
    inference(instantiation,[status(thm)],[c_4755]) ).

cnf(c_5655,plain,
    ( ~ product(e_3,e_2,e_2)
    | ~ product(e_6,e_2,e_3)
    | product(e_6,e_3,e_2) ),
    inference(instantiation,[status(thm)],[c_4759]) ).

cnf(c_5656,plain,
    ~ product(e_3,e_2,e_2),
    inference(global_subsumption_just,[status(thm)],[c_5655,c_73,c_72,c_71,c_70,c_86,c_83,c_81,c_80,c_76,c_113,c_322,c_326,c_330,c_334,c_338,c_342,c_346,c_350,c_354,c_358,c_389,c_412,c_435,c_481,c_1905,c_1910,c_1915,c_1918,c_1928,c_1939,c_1946,c_1969,c_1991,c_2058,c_2064,c_2130,c_2133,c_2169,c_2186,c_2230,c_2628,c_2708,c_2987,c_2990,c_2996,c_3090,c_3128,c_3179,c_3193,c_3199,c_3201,c_3387,c_3408,c_3553,c_3558,c_3987,c_4003,c_4894,c_5655]) ).

cnf(c_5682,plain,
    ( ~ product(e_1,e_4,e_4)
    | ~ product(e_4,e_4,e_2)
    | product(e_1,e_4,e_2) ),
    inference(instantiation,[status(thm)],[c_4109]) ).

cnf(c_5712,plain,
    ( ~ product(e_6,X0,e_3)
    | ~ product(e_6,X0,e_4) ),
    inference(instantiation,[status(thm)],[c_4363]) ).

cnf(c_5713,plain,
    ( ~ product(e_6,X0,e_1)
    | ~ product(e_6,X0,e_4) ),
    inference(instantiation,[status(thm)],[c_4339]) ).

cnf(c_5733,plain,
    ( ~ product(e_4,X0,e_4)
    | ~ product(e_6,X0,e_4) ),
    inference(instantiation,[status(thm)],[c_4498]) ).

cnf(c_5740,plain,
    ( ~ product(e_4,X0,X1)
    | ~ product(e_6,X0,e_4)
    | product(e_6,e_4,X1) ),
    inference(instantiation,[status(thm)],[c_4090]) ).

cnf(c_5761,plain,
    ( ~ product(e_2,e_6,e_1)
    | ~ product(e_4,e_6,e_1) ),
    inference(instantiation,[status(thm)],[c_4472]) ).

cnf(c_5765,plain,
    ( ~ product(e_4,e_4,e_1)
    | ~ product(e_4,e_6,e_1) ),
    inference(instantiation,[status(thm)],[c_4438]) ).

cnf(c_5766,plain,
    ( ~ product(e_4,e_3,e_1)
    | ~ product(e_4,e_6,e_1) ),
    inference(instantiation,[status(thm)],[c_4429]) ).

cnf(c_5780,plain,
    ( ~ product(e_1,e_2,e_6)
    | ~ product(e_1,e_3,e_6) ),
    inference(instantiation,[status(thm)],[c_4409]) ).

cnf(c_5783,plain,
    ( ~ product(X0,e_3,e_1)
    | ~ product(e_1,e_3,e_6)
    | product(X0,e_1,e_6) ),
    inference(instantiation,[status(thm)],[c_4085]) ).

cnf(c_5786,plain,
    ( ~ product(e_5,e_4,e_4)
    | ~ product(e_5,e_4,e_5) ),
    inference(instantiation,[status(thm)],[c_4375]) ).

cnf(c_5796,plain,
    ( ~ product(e_4,e_4,e_5)
    | ~ product(e_5,e_4,e_5) ),
    inference(instantiation,[status(thm)],[c_4495]) ).

cnf(c_5798,plain,
    ( ~ product(e_2,e_4,e_5)
    | ~ product(e_5,e_4,e_5) ),
    inference(instantiation,[status(thm)],[c_4475]) ).

cnf(c_5799,plain,
    ( ~ product(e_1,e_4,e_5)
    | ~ product(e_5,e_4,e_5) ),
    inference(instantiation,[status(thm)],[c_4462]) ).

cnf(c_5813,plain,
    ( ~ product(e_4,e_2,e_4)
    | ~ product(e_4,e_2,e_5) ),
    inference(instantiation,[status(thm)],[c_4850]) ).

cnf(c_5822,plain,
    ( ~ product(e_5,e_4,e_5)
    | ~ product(e_5,e_5,e_5) ),
    inference(instantiation,[status(thm)],[c_4435]) ).

cnf(c_5859,plain,
    ( ~ product(e_3,e_2,X0)
    | ~ product(e_3,e_2,e_3)
    | product(e_3,e_3,X0) ),
    inference(instantiation,[status(thm)],[c_4087]) ).

cnf(c_5880,plain,
    ( ~ product(e_2,X0,e_2)
    | ~ product(e_3,X0,e_2) ),
    inference(instantiation,[status(thm)],[c_4469]) ).

cnf(c_5895,plain,
    ( ~ product(e_1,e_5,e_2)
    | ~ product(e_1,e_5,e_5) ),
    inference(instantiation,[status(thm)],[c_4355]) ).

cnf(c_5917,plain,
    ( ~ product(e_1,e_6,e_4)
    | ~ product(e_4,e_6,e_5)
    | product(e_1,e_4,e_5) ),
    inference(instantiation,[status(thm)],[c_3628]) ).

cnf(c_5944,plain,
    ( ~ product(e_4,e_2,e_1)
    | ~ product(e_4,e_3,e_1) ),
    inference(instantiation,[status(thm)],[c_4409]) ).

cnf(c_5952,plain,
    ( ~ product(e_1,e_3,X0)
    | ~ product(e_4,e_3,e_1)
    | product(e_4,e_1,X0) ),
    inference(instantiation,[status(thm)],[c_4088]) ).

cnf(c_5963,plain,
    ( ~ product(e_1,e_4,e_3)
    | ~ product(e_4,e_4,e_3) ),
    inference(instantiation,[status(thm)],[c_4459]) ).

cnf(c_5969,plain,
    ( ~ product(X0,e_4,e_4)
    | ~ product(e_4,e_4,e_3)
    | product(X0,e_4,e_3) ),
    inference(instantiation,[status(thm)],[c_4082]) ).

cnf(c_5970,plain,
    ( ~ product(e_1,e_4,e_4)
    | ~ product(e_4,e_4,e_3)
    | product(e_1,e_4,e_3) ),
    inference(instantiation,[status(thm)],[c_5969]) ).

cnf(c_5972,plain,
    ( ~ product(e_3,e_4,e_5)
    | ~ product(e_4,e_4,e_3)
    | product(e_4,e_3,e_5) ),
    inference(instantiation,[status(thm)],[c_4580]) ).

cnf(c_6035,plain,
    ( ~ product(e_4,e_4,X0)
    | ~ product(e_1,e_4,e_4)
    | product(e_1,e_4,X0) ),
    inference(instantiation,[status(thm)],[c_4903]) ).

cnf(c_6036,plain,
    ( ~ product(e_1,e_4,e_4)
    | ~ product(e_4,e_4,e_1)
    | product(e_1,e_4,e_1) ),
    inference(instantiation,[status(thm)],[c_6035]) ).

cnf(c_6037,plain,
    ( ~ product(e_4,e_6,X0)
    | ~ product(e_1,e_6,e_4)
    | product(e_1,e_4,X0) ),
    inference(instantiation,[status(thm)],[c_4903]) ).

cnf(c_6038,plain,
    ( ~ product(e_1,e_6,e_4)
    | ~ product(e_4,e_6,e_1)
    | product(e_1,e_4,e_1) ),
    inference(instantiation,[status(thm)],[c_6037]) ).

cnf(c_6049,plain,
    ( ~ product(e_1,e_6,e_5)
    | ~ product(e_2,e_6,e_5) ),
    inference(instantiation,[status(thm)],[c_4453]) ).

cnf(c_6052,plain,
    ( ~ product(e_2,e_4,e_5)
    | ~ product(e_2,e_6,e_5) ),
    inference(instantiation,[status(thm)],[c_4438]) ).

cnf(c_6058,plain,
    ( ~ product(X0,e_6,e_2)
    | ~ product(e_2,e_6,e_5)
    | product(X0,e_2,e_5) ),
    inference(instantiation,[status(thm)],[c_4084]) ).

cnf(c_6059,plain,
    ( ~ product(e_1,e_6,e_2)
    | ~ product(e_2,e_6,e_5)
    | product(e_1,e_2,e_5) ),
    inference(instantiation,[status(thm)],[c_6058]) ).

cnf(c_6086,plain,
    ( ~ product(e_3,e_4,e_2)
    | ~ product(e_5,e_4,e_2) ),
    inference(instantiation,[status(thm)],[c_4486]) ).

cnf(c_6116,plain,
    ( ~ product(X0,e_5,e_5)
    | ~ product(e_5,e_5,e_3)
    | product(X0,e_5,e_3) ),
    inference(instantiation,[status(thm)],[c_4082]) ).

cnf(c_6117,plain,
    ( ~ product(e_1,e_5,e_5)
    | ~ product(e_5,e_5,e_3)
    | product(e_1,e_5,e_3) ),
    inference(instantiation,[status(thm)],[c_6116]) ).

cnf(c_6151,plain,
    ( ~ product(e_2,e_2,e_6)
    | ~ product(e_4,e_2,e_2)
    | product(e_4,e_2,e_6) ),
    inference(instantiation,[status(thm)],[c_4716]) ).

cnf(c_6232,plain,
    ( ~ product(e_2,e_4,e_5)
    | ~ product(e_2,e_5,e_5) ),
    inference(instantiation,[status(thm)],[c_4435]) ).

cnf(c_6313,plain,
    ( ~ product(e_2,e_6,X0)
    | ~ product(e_1,e_6,e_2)
    | product(e_1,e_2,X0) ),
    inference(instantiation,[status(thm)],[c_4868]) ).

cnf(c_6321,plain,
    ( ~ product(e_1,e_6,e_2)
    | ~ product(e_2,e_6,e_1)
    | product(e_1,e_2,e_1) ),
    inference(instantiation,[status(thm)],[c_6313]) ).

cnf(c_6354,plain,
    ( ~ product(e_3,e_2,e_1)
    | ~ product(e_4,e_2,e_1) ),
    inference(instantiation,[status(thm)],[c_4483]) ).

cnf(c_6379,plain,
    ( ~ product(e_2,e_2,e_5)
    | ~ product(e_4,e_2,e_2)
    | product(e_4,e_2,e_5) ),
    inference(instantiation,[status(thm)],[c_4716]) ).

cnf(c_6380,plain,
    ~ product(e_4,e_2,e_2),
    inference(global_subsumption_just,[status(thm)],[c_6379,c_71,c_70,c_81,c_76,c_113,c_322,c_326,c_330,c_334,c_338,c_342,c_346,c_350,c_354,c_389,c_412,c_1905,c_1913,c_1939,c_1946,c_2064,c_2096,c_2130,c_2133,c_2708,c_2773,c_2987,c_3318,c_3576,c_4173,c_4824,c_4829,c_4954,c_5093,c_6151,c_6379]) ).

cnf(c_6442,plain,
    ( ~ product(e_3,e_2,e_6)
    | ~ product(e_3,e_3,e_6) ),
    inference(instantiation,[status(thm)],[c_4409]) ).

cnf(c_6452,plain,
    ( ~ product(e_3,e_3,e_6)
    | ~ product(e_4,e_3,e_3)
    | product(e_4,e_3,e_6) ),
    inference(instantiation,[status(thm)],[c_5120]) ).

cnf(c_6601,plain,
    ( ~ product(e_4,e_4,e_4)
    | ~ product(e_4,e_5,e_4) ),
    inference(instantiation,[status(thm)],[c_4435]) ).

cnf(c_6613,plain,
    ( ~ product(e_1,e_4,e_4)
    | ~ product(e_1,e_4,e_5) ),
    inference(instantiation,[status(thm)],[c_4375]) ).

cnf(c_6614,plain,
    ( ~ product(e_1,e_4,e_3)
    | ~ product(e_1,e_4,e_5) ),
    inference(instantiation,[status(thm)],[c_4366]) ).

cnf(c_6618,plain,
    ( ~ product(e_1,e_3,e_5)
    | ~ product(e_1,e_4,e_5) ),
    inference(instantiation,[status(thm)],[c_4423]) ).

cnf(c_6619,plain,
    ( ~ product(e_1,e_2,e_5)
    | ~ product(e_1,e_4,e_5) ),
    inference(instantiation,[status(thm)],[c_4412]) ).

cnf(c_6662,plain,
    ( ~ product(e_1,e_5,e_5)
    | ~ product(e_5,e_5,e_2)
    | product(e_1,e_5,e_2) ),
    inference(instantiation,[status(thm)],[c_4109]) ).

cnf(c_6664,plain,
    ( ~ product(e_5,e_5,e_2)
    | ~ product(e_1,e_5,e_5) ),
    inference(global_subsumption_just,[status(thm)],[c_6662,c_5895,c_6662]) ).

cnf(c_6665,plain,
    ( ~ product(e_1,e_5,e_5)
    | ~ product(e_5,e_5,e_2) ),
    inference(renaming,[status(thm)],[c_6664]) ).

cnf(c_6693,plain,
    ( ~ product(X0,e_3,e_5)
    | ~ product(e_4,e_3,e_5)
    | equalish(e_4,X0) ),
    inference(instantiation,[status(thm)],[c_3629]) ).

cnf(c_6694,plain,
    ( ~ product(e_1,e_3,e_5)
    | ~ product(e_4,e_3,e_5)
    | equalish(e_4,e_1) ),
    inference(instantiation,[status(thm)],[c_6693]) ).

cnf(c_6797,plain,
    ( ~ product(e_5,X0,e_6)
    | ~ product(e_6,X0,e_5)
    | product(e_6,e_5,e_6) ),
    inference(instantiation,[status(thm)],[c_3633]) ).

cnf(c_6799,plain,
    ( ~ product(e_5,e_1,e_6)
    | ~ product(e_6,e_1,e_5)
    | product(e_6,e_5,e_6) ),
    inference(instantiation,[status(thm)],[c_6797]) ).

cnf(c_7005,plain,
    ( ~ product(e_1,e_3,e_6)
    | ~ product(e_4,e_3,e_6) ),
    inference(instantiation,[status(thm)],[c_4459]) ).

cnf(c_7150,plain,
    ( ~ product(e_4,e_4,X0)
    | ~ product(e_5,e_4,e_4)
    | product(e_5,e_4,X0) ),
    inference(instantiation,[status(thm)],[c_4903]) ).

cnf(c_7152,plain,
    ( ~ product(e_5,e_4,e_1)
    | ~ product(e_5,e_4,e_4) ),
    inference(instantiation,[status(thm)],[c_4339]) ).

cnf(c_7153,plain,
    ( ~ product(e_4,e_4,e_5)
    | ~ product(e_5,e_4,e_4)
    | product(e_5,e_4,e_5) ),
    inference(instantiation,[status(thm)],[c_3628]) ).

cnf(c_7157,plain,
    ( ~ product(e_4,e_4,e_1)
    | ~ product(e_5,e_4,e_4)
    | product(e_5,e_4,e_1) ),
    inference(instantiation,[status(thm)],[c_7150]) ).

cnf(c_7163,plain,
    ( ~ product(e_4,e_4,e_4)
    | ~ product(e_5,e_4,e_4) ),
    inference(instantiation,[status(thm)],[c_4495]) ).

cnf(c_7182,plain,
    ( ~ product(e_2,e_4,e_5)
    | ~ product(e_3,e_4,e_2)
    | product(e_3,e_2,e_5) ),
    inference(instantiation,[status(thm)],[c_4664]) ).

cnf(c_7211,plain,
    ( ~ product(e_1,e_4,e_2)
    | ~ product(e_1,e_4,e_4) ),
    inference(instantiation,[status(thm)],[c_4352]) ).

cnf(c_7216,plain,
    ~ product(e_1,e_4,e_4),
    inference(global_subsumption_just,[status(thm)],[c_7211,c_72,c_71,c_70,c_86,c_81,c_80,c_76,c_113,c_322,c_326,c_330,c_334,c_338,c_342,c_346,c_350,c_354,c_358,c_389,c_412,c_427,c_435,c_1905,c_1910,c_1918,c_1939,c_1946,c_2058,c_2064,c_2130,c_2133,c_2230,c_2628,c_2708,c_2987,c_2990,c_3123,c_3128,c_3179,c_3193,c_3199,c_3201,c_3387,c_3408,c_3553,c_3558,c_3987,c_4003,c_4735,c_5076,c_5133,c_5174,c_5172,c_5682,c_5970,c_6036,c_6613,c_7211]) ).

cnf(c_7222,plain,
    ( ~ product(e_1,e_4,e_2)
    | ~ product(e_3,e_4,e_2) ),
    inference(instantiation,[status(thm)],[c_3648]) ).

cnf(c_7237,plain,
    ( ~ product(e_1,e_5,e_5)
    | ~ product(e_1,e_6,e_5) ),
    inference(instantiation,[status(thm)],[c_4445]) ).

cnf(c_7242,plain,
    ( ~ product(e_1,e_6,e_5)
    | ~ product(e_4,e_6,e_5) ),
    inference(instantiation,[status(thm)],[c_5073]) ).

cnf(c_7244,plain,
    ( ~ product(e_1,e_6,e_5)
    | ~ product(e_2,e_6,e_1)
    | product(e_2,e_1,e_5) ),
    inference(instantiation,[status(thm)],[c_4674]) ).

cnf(c_7245,plain,
    ( ~ product(e_2,e_6,e_1)
    | ~ product(e_1,e_6,e_5) ),
    inference(global_subsumption_just,[status(thm)],[c_7244,c_342,c_7244]) ).

cnf(c_7246,plain,
    ( ~ product(e_1,e_6,e_5)
    | ~ product(e_2,e_6,e_1) ),
    inference(renaming,[status(thm)],[c_7245]) ).

cnf(c_7363,plain,
    ( ~ product(e_6,e_1,e_5)
    | ~ product(e_6,e_4,e_5) ),
    inference(instantiation,[status(thm)],[c_4399]) ).

cnf(c_7482,plain,
    ( ~ product(e_4,e_3,e_2)
    | ~ product(e_4,e_6,e_2) ),
    inference(instantiation,[status(thm)],[c_4429]) ).

cnf(c_7485,plain,
    ~ product(e_4,e_3,e_2),
    inference(global_subsumption_just,[status(thm)],[c_7482,c_75,c_73,c_72,c_71,c_70,c_94,c_90,c_88,c_86,c_81,c_80,c_78,c_76,c_113,c_322,c_326,c_330,c_334,c_338,c_342,c_346,c_350,c_354,c_358,c_381,c_389,c_412,c_435,c_458,c_481,c_1905,c_1910,c_1913,c_1915,c_1918,c_1923,c_1928,c_1939,c_1946,c_1969,c_1991,c_2058,c_2064,c_2085,c_2096,c_2130,c_2133,c_2230,c_2236,c_2261,c_2267,c_2628,c_2692,c_2708,c_2773,c_2872,c_2900,c_2987,c_2990,c_2993,c_2996,c_3034,c_3033,c_3032,c_3038,c_3067,c_3068,c_3117,c_3122,c_3128,c_3152,c_3153,c_3179,c_3193,c_3199,c_3201,c_3203,c_3248,c_3318,c_3387,c_3408,c_3410,c_3440,c_3447,c_3553,c_3558,c_3563,c_3564,c_3566,c_3567,c_3568,c_3574,c_3576,c_3843,c_3852,c_3912,c_3987,c_4003,c_4173,c_4263,c_4290,c_4824,c_4829,c_4954,c_4979,c_5034,c_5057,c_5093,c_5129,c_5148,c_5156,c_5399,c_5408,c_5417,c_5420,c_5429,c_5432,c_5436,c_5435,c_5460,c_5629,c_5765,c_5813,c_5972,c_6151,c_6379]) ).

cnf(c_7535,plain,
    ( ~ product(e_1,e_4,e_3)
    | ~ product(e_3,e_4,e_2)
    | product(e_1,e_3,e_2) ),
    inference(instantiation,[status(thm)],[c_4095]) ).

cnf(c_7574,plain,
    ( ~ product(e_3,e_2,e_3)
    | product(e_3,e_3,e_3) ),
    inference(instantiation,[status(thm)],[c_5859]) ).

cnf(c_7575,plain,
    ~ product(e_3,e_2,e_3),
    inference(global_subsumption_just,[status(thm)],[c_7574,c_2908,c_7574]) ).

cnf(c_7618,plain,
    ( ~ product(e_2,e_5,e_6)
    | ~ product(e_5,e_5,e_6) ),
    inference(instantiation,[status(thm)],[c_5099]) ).

cnf(c_7619,plain,
    ~ product(e_5,e_5,e_6),
    inference(global_subsumption_just,[status(thm)],[c_7618,c_73,c_72,c_71,c_70,c_86,c_81,c_80,c_79,c_76,c_113,c_322,c_326,c_330,c_334,c_338,c_342,c_346,c_350,c_354,c_358,c_389,c_412,c_435,c_458,c_481,c_1905,c_1910,c_1913,c_1915,c_1918,c_1923,c_1928,c_1939,c_1946,c_1969,c_1991,c_2058,c_2064,c_2130,c_2133,c_2230,c_2628,c_2708,c_2908,c_2987,c_2990,c_2993,c_2996,c_3128,c_3152,c_3153,c_3179,c_3180,c_3193,c_3199,c_3201,c_3203,c_3387,c_3408,c_3410,c_3553,c_3558,c_3563,c_3564,c_3566,c_3568,c_3929,c_3987,c_4003,c_4293,c_5156,c_5162,c_7574]) ).

cnf(c_7773,plain,
    ( ~ product(e_1,e_2,e_5)
    | ~ product(e_3,e_2,e_5) ),
    inference(instantiation,[status(thm)],[c_4456]) ).

cnf(c_7779,plain,
    ( ~ product(e_3,e_2,e_5)
    | ~ product(e_4,e_2,e_5) ),
    inference(instantiation,[status(thm)],[c_5104]) ).

cnf(c_7780,plain,
    ~ product(e_4,e_2,e_5),
    inference(global_subsumption_just,[status(thm)],[c_7779,c_72,c_71,c_70,c_86,c_81,c_80,c_76,c_113,c_322,c_326,c_330,c_334,c_338,c_342,c_346,c_350,c_354,c_358,c_389,c_412,c_435,c_1905,c_1910,c_1918,c_1939,c_1946,c_2058,c_2064,c_2130,c_2133,c_2230,c_2628,c_2708,c_2908,c_2987,c_2990,c_3128,c_3179,c_3193,c_3199,c_3201,c_3387,c_3408,c_3553,c_3558,c_3848,c_3910,c_3987,c_4003,c_7574]) ).

cnf(c_7878,plain,
    ( ~ product(e_2,e_3,e_4)
    | ~ product(e_4,e_3,e_6)
    | product(e_2,e_4,e_6) ),
    inference(instantiation,[status(thm)],[c_4614]) ).

cnf(c_7879,plain,
    ( ~ product(e_4,e_3,e_6)
    | product(e_2,e_4,e_6) ),
    inference(global_subsumption_just,[status(thm)],[c_7878,c_72,c_71,c_70,c_81,c_76,c_113,c_322,c_326,c_330,c_334,c_338,c_342,c_346,c_350,c_354,c_389,c_412,c_1905,c_1910,c_1939,c_1946,c_2064,c_2130,c_2133,c_2708,c_2908,c_2987,c_3199,c_3576,c_7574,c_7878]) ).

cnf(c_7918,plain,
    ( ~ product(e_1,e_2,e_4)
    | ~ product(e_1,e_5,e_4) ),
    inference(instantiation,[status(thm)],[c_4415]) ).

cnf(c_7944,plain,
    ( ~ product(e_1,e_3,e_2)
    | ~ product(e_2,e_3,e_4)
    | product(e_1,e_2,e_4) ),
    inference(instantiation,[status(thm)],[c_4575]) ).

cnf(c_7945,plain,
    ( ~ product(e_1,e_3,e_2)
    | product(e_1,e_2,e_4) ),
    inference(global_subsumption_just,[status(thm)],[c_7944,c_72,c_71,c_70,c_81,c_76,c_113,c_322,c_326,c_330,c_334,c_338,c_342,c_346,c_350,c_354,c_389,c_412,c_1905,c_1910,c_1939,c_1946,c_2064,c_2130,c_2133,c_2708,c_2908,c_2987,c_3199,c_3351,c_3576,c_7574]) ).

cnf(c_7996,plain,
    ( ~ product(e_2,e_4,e_2)
    | ~ product(e_3,e_4,e_2) ),
    inference(instantiation,[status(thm)],[c_5880]) ).

cnf(c_7997,plain,
    ~ product(e_2,e_4,e_2),
    inference(global_subsumption_just,[status(thm)],[c_7996,c_75,c_73,c_72,c_71,c_70,c_94,c_90,c_88,c_86,c_81,c_80,c_78,c_76,c_113,c_322,c_326,c_330,c_334,c_338,c_342,c_346,c_350,c_354,c_358,c_381,c_389,c_412,c_435,c_458,c_481,c_1905,c_1910,c_1913,c_1915,c_1918,c_1923,c_1928,c_1939,c_1946,c_1969,c_1991,c_2058,c_2064,c_2085,c_2096,c_2130,c_2133,c_2172,c_2230,c_2236,c_2261,c_2267,c_2628,c_2692,c_2708,c_2773,c_2872,c_2900,c_2908,c_2987,c_2990,c_2993,c_2996,c_3034,c_3033,c_3032,c_3038,c_3067,c_3068,c_3090,c_3098,c_3117,c_3120,c_3122,c_3128,c_3152,c_3153,c_3179,c_3193,c_3199,c_3201,c_3203,c_3234,c_3248,c_3318,c_3349,c_3354,c_3355,c_3387,c_3408,c_3410,c_3440,c_3447,c_3553,c_3558,c_3563,c_3564,c_3566,c_3567,c_3568,c_3574,c_3576,c_3777,c_3843,c_3852,c_3912,c_3987,c_4003,c_4173,c_4263,c_4290,c_4824,c_4829,c_4954,c_4979,c_5001,c_5012,c_5034,c_5057,c_5093,c_5094,c_5116,c_5121,c_5129,c_5148,c_5156,c_5205,c_5399,c_5408,c_5417,c_5420,c_5429,c_5432,c_5436,c_5435,c_5460,c_5629,c_5765,c_5813,c_5972,c_6151,c_6379,c_6452,c_7574,c_7996]) ).

cnf(c_8016,plain,
    ( ~ product(e_4,e_2,e_1)
    | ~ product(e_4,e_2,e_3) ),
    inference(instantiation,[status(thm)],[c_4336]) ).

cnf(c_8019,plain,
    ~ product(e_4,e_2,e_1),
    inference(global_subsumption_just,[status(thm)],[c_8016,c_73,c_72,c_71,c_70,c_94,c_86,c_81,c_80,c_76,c_113,c_322,c_326,c_330,c_334,c_338,c_342,c_346,c_350,c_354,c_358,c_389,c_412,c_435,c_458,c_1905,c_1910,c_1913,c_1915,c_1918,c_1923,c_1939,c_1946,c_2058,c_2064,c_2130,c_2133,c_2230,c_2628,c_2708,c_2908,c_2987,c_2990,c_2993,c_3094,c_3097,c_3120,c_3128,c_3152,c_3153,c_3179,c_3193,c_3199,c_3201,c_3203,c_3354,c_3355,c_3387,c_3408,c_3410,c_3553,c_3558,c_3563,c_3564,c_3566,c_3568,c_3576,c_3843,c_3912,c_3987,c_4003,c_4290,c_4968,c_5001,c_5012,c_5094,c_5116,c_5121,c_5156,c_5206,c_5336,c_5656,c_5944,c_6354,c_6442,c_7485,c_7574,c_8016]) ).

cnf(c_8046,plain,
    ( ~ product(e_1,e_3,e_2)
    | ~ product(e_1,e_3,e_6) ),
    inference(instantiation,[status(thm)],[c_4358]) ).

cnf(c_8062,plain,
    ( ~ product(e_1,e_3,e_2)
    | ~ product(e_4,e_3,e_1)
    | product(e_4,e_1,e_2) ),
    inference(instantiation,[status(thm)],[c_5952]) ).

cnf(c_8063,plain,
    ( ~ product(e_4,e_3,e_1)
    | product(e_4,e_1,e_2) ),
    inference(global_subsumption_just,[status(thm)],[c_8062,c_73,c_72,c_71,c_70,c_94,c_86,c_81,c_80,c_78,c_76,c_113,c_322,c_326,c_330,c_334,c_338,c_342,c_346,c_350,c_354,c_358,c_389,c_412,c_427,c_435,c_458,c_481,c_1905,c_1910,c_1913,c_1915,c_1918,c_1923,c_1928,c_1939,c_1946,c_1969,c_1991,c_2058,c_2064,c_2130,c_2133,c_2230,c_2628,c_2708,c_2908,c_2987,c_2990,c_2993,c_2996,c_3055,c_3054,c_3060,c_3074,c_3117,c_3122,c_3128,c_3152,c_3153,c_3179,c_3193,c_3199,c_3201,c_3203,c_3349,c_3387,c_3408,c_3410,c_3485,c_3553,c_3558,c_3563,c_3564,c_3566,c_3567,c_3568,c_3576,c_3852,c_3912,c_3987,c_4003,c_4290,c_4979,c_5034,c_5129,c_5156,c_5441,c_5963,c_6380,c_7216,c_7574,c_7780,c_8019]) ).

cnf(c_8065,plain,
    product(e_4,e_1,e_2),
    inference(global_subsumption_just,[status(thm)],[c_8063,c_73,c_72,c_71,c_70,c_94,c_86,c_81,c_80,c_76,c_113,c_322,c_326,c_330,c_334,c_338,c_342,c_346,c_350,c_354,c_358,c_389,c_412,c_435,c_458,c_1905,c_1910,c_1913,c_1915,c_1918,c_1923,c_1939,c_1946,c_2058,c_2064,c_2130,c_2133,c_2230,c_2628,c_2708,c_2908,c_2987,c_2990,c_2993,c_3097,c_3120,c_3128,c_3152,c_3153,c_3179,c_3193,c_3199,c_3201,c_3203,c_3354,c_3355,c_3387,c_3408,c_3410,c_3553,c_3558,c_3563,c_3564,c_3566,c_3568,c_3576,c_3843,c_3912,c_3987,c_4003,c_4290,c_5001,c_5012,c_5094,c_5116,c_5121,c_5156,c_5206,c_6452,c_7485,c_7574,c_8063]) ).

cnf(c_8074,plain,
    ( ~ product(e_4,e_4,e_6)
    | ~ product(e_6,e_4,e_2)
    | product(e_4,e_6,e_2) ),
    inference(instantiation,[status(thm)],[c_4636]) ).

cnf(c_8103,plain,
    ( ~ product(e_4,e_4,e_6)
    | ~ product(e_5,e_4,e_4)
    | product(e_5,e_4,e_6) ),
    inference(instantiation,[status(thm)],[c_4734]) ).

cnf(c_8104,plain,
    ~ product(e_5,e_4,e_4),
    inference(global_subsumption_just,[status(thm)],[c_8103,c_75,c_73,c_72,c_71,c_70,c_94,c_90,c_88,c_86,c_81,c_80,c_78,c_76,c_113,c_322,c_326,c_330,c_334,c_338,c_342,c_346,c_350,c_354,c_358,c_381,c_389,c_412,c_435,c_458,c_481,c_1905,c_1910,c_1913,c_1915,c_1918,c_1923,c_1928,c_1939,c_1946,c_1969,c_1991,c_2058,c_2064,c_2085,c_2096,c_2130,c_2133,c_2172,c_2230,c_2236,c_2237,c_2261,c_2267,c_2628,c_2692,c_2708,c_2773,c_2872,c_2900,c_2908,c_2916,c_2987,c_2990,c_2993,c_2996,c_3034,c_3033,c_3032,c_3038,c_3067,c_3068,c_3097,c_3117,c_3120,c_3122,c_3128,c_3152,c_3153,c_3179,c_3180,c_3193,c_3199,c_3201,c_3203,c_3248,c_3318,c_3354,c_3355,c_3387,c_3408,c_3410,c_3440,c_3447,c_3553,c_3558,c_3563,c_3564,c_3566,c_3567,c_3568,c_3574,c_3576,c_3777,c_3843,c_3852,c_3912,c_3926,c_3987,c_4003,c_4173,c_4263,c_4290,c_4824,c_4829,c_4954,c_4979,c_5001,c_5012,c_5034,c_5057,c_5093,c_5094,c_5116,c_5121,c_5129,c_5148,c_5156,c_5162,c_5205,c_5399,c_5408,c_5417,c_5420,c_5429,c_5432,c_5436,c_5435,c_5460,c_5629,c_5765,c_5786,c_5813,c_5972,c_6151,c_6379,c_6452,c_7153,c_7152,c_7157,c_7163,c_7574,c_8063,c_8103]) ).

cnf(c_8121,plain,
    ( ~ product(e_1,e_3,e_6)
    | ~ product(e_4,e_3,e_1)
    | product(e_4,e_1,e_6) ),
    inference(instantiation,[status(thm)],[c_5783]) ).

cnf(c_8123,plain,
    ~ product(e_1,e_3,e_6),
    inference(global_subsumption_just,[status(thm)],[c_8121,c_75,c_73,c_72,c_71,c_70,c_94,c_90,c_88,c_86,c_81,c_80,c_78,c_76,c_113,c_322,c_326,c_330,c_334,c_338,c_342,c_346,c_350,c_354,c_358,c_381,c_389,c_412,c_435,c_458,c_481,c_1905,c_1910,c_1913,c_1915,c_1918,c_1923,c_1928,c_1939,c_1946,c_1969,c_1991,c_2058,c_2064,c_2085,c_2096,c_2130,c_2133,c_2172,c_2230,c_2236,c_2261,c_2267,c_2628,c_2692,c_2708,c_2773,c_2872,c_2900,c_2908,c_2909,c_2987,c_2990,c_2993,c_2996,c_3034,c_3033,c_3032,c_3038,c_3067,c_3068,c_3090,c_3097,c_3117,c_3120,c_3122,c_3128,c_3152,c_3153,c_3179,c_3193,c_3199,c_3201,c_3203,c_3248,c_3318,c_3354,c_3355,c_3387,c_3408,c_3410,c_3440,c_3447,c_3514,c_3539,c_3553,c_3558,c_3563,c_3564,c_3566,c_3567,c_3568,c_3574,c_3576,c_3777,c_3843,c_3852,c_3912,c_3987,c_4003,c_4173,c_4191,c_4263,c_4290,c_4653,c_4824,c_4829,c_4954,c_4964,c_4979,c_5001,c_5012,c_5034,c_5057,c_5093,c_5094,c_5116,c_5121,c_5129,c_5148,c_5156,c_5205,c_5399,c_5408,c_5417,c_5420,c_5429,c_5432,c_5436,c_5435,c_5460,c_5629,c_5765,c_5780,c_5813,c_5972,c_6151,c_6379,c_6452,c_7005,c_7182,c_7535,c_7574,c_7773,c_8046,c_8063,c_8121]) ).

cnf(c_8144,plain,
    ( ~ product(e_2,e_3,e_4)
    | ~ product(e_4,e_3,e_1)
    | product(e_2,e_4,e_1) ),
    inference(instantiation,[status(thm)],[c_4614]) ).

cnf(c_8145,plain,
    ( ~ product(e_4,e_3,e_1)
    | product(e_2,e_4,e_1) ),
    inference(global_subsumption_just,[status(thm)],[c_8144,c_72,c_71,c_70,c_81,c_76,c_113,c_322,c_326,c_330,c_334,c_338,c_342,c_346,c_350,c_354,c_389,c_412,c_1905,c_1910,c_1939,c_1946,c_2064,c_2130,c_2133,c_2708,c_2908,c_2987,c_3199,c_3349,c_3576,c_7574]) ).

cnf(c_8193,plain,
    ( ~ product(e_2,e_6,e_5)
    | ~ product(e_4,e_6,e_5) ),
    inference(instantiation,[status(thm)],[c_5092]) ).

cnf(c_8214,plain,
    ( ~ product(e_1,e_4,e_3)
    | ~ product(e_6,e_4,e_3) ),
    inference(instantiation,[status(thm)],[c_4465]) ).

cnf(c_8306,plain,
    ( ~ product(e_1,e_6,e_6)
    | ~ product(e_2,e_6,e_6) ),
    inference(instantiation,[status(thm)],[c_4453]) ).

cnf(c_8308,plain,
    ( ~ product(e_2,e_5,e_6)
    | ~ product(e_2,e_6,e_6) ),
    inference(instantiation,[status(thm)],[c_4445]) ).

cnf(c_8309,plain,
    ( ~ product(e_2,e_4,e_6)
    | ~ product(e_2,e_6,e_6) ),
    inference(instantiation,[status(thm)],[c_4438]) ).

cnf(c_8365,plain,
    ( ~ product(e_1,e_2,e_5)
    | ~ product(e_5,e_2,e_2)
    | product(e_1,e_5,e_2) ),
    inference(instantiation,[status(thm)],[c_4109]) ).

cnf(c_8367,plain,
    ~ product(e_1,e_2,e_5),
    inference(global_subsumption_just,[status(thm)],[c_8365,c_75,c_73,c_72,c_71,c_70,c_94,c_90,c_88,c_86,c_81,c_80,c_78,c_76,c_113,c_322,c_326,c_330,c_334,c_338,c_342,c_346,c_350,c_354,c_358,c_381,c_389,c_412,c_427,c_435,c_458,c_481,c_1905,c_1910,c_1913,c_1915,c_1918,c_1923,c_1928,c_1939,c_1946,c_1969,c_1991,c_2058,c_2064,c_2085,c_2096,c_2130,c_2133,c_2172,c_2230,c_2236,c_2261,c_2267,c_2628,c_2692,c_2697,c_2708,c_2773,c_2872,c_2886,c_2900,c_2908,c_2987,c_2990,c_2993,c_2996,c_3034,c_3033,c_3032,c_3038,c_3054,c_3067,c_3068,c_3074,c_3090,c_3097,c_3098,c_3117,c_3120,c_3122,c_3123,c_3128,c_3152,c_3153,c_3179,c_3193,c_3199,c_3201,c_3203,c_3234,c_3248,c_3318,c_3349,c_3351,c_3354,c_3355,c_3387,c_3408,c_3410,c_3440,c_3447,c_3553,c_3558,c_3563,c_3564,c_3566,c_3567,c_3568,c_3574,c_3576,c_3588,c_3777,c_3843,c_3852,c_3912,c_3987,c_4003,c_4173,c_4263,c_4290,c_4735,c_4824,c_4829,c_4954,c_4979,c_5001,c_5012,c_5034,c_5057,c_5076,c_5093,c_5094,c_5116,c_5121,c_5129,c_5133,c_5148,c_5156,c_5174,c_5172,c_5205,c_5399,c_5408,c_5417,c_5420,c_5429,c_5432,c_5436,c_5435,c_5460,c_5558,c_5594,c_5629,c_5682,c_5765,c_5813,c_5970,c_5972,c_6036,c_6151,c_6379,c_6452,c_6613,c_6619,c_7182,c_7211,c_7222,c_7535,c_7574,c_7773,c_7996,c_8063]) ).

cnf(c_8377,plain,
    ( ~ product(e_1,e_2,e_2)
    | ~ product(e_5,e_2,e_2) ),
    inference(instantiation,[status(thm)],[c_4462]) ).

cnf(c_8379,plain,
    ~ product(e_1,e_2,e_2),
    inference(global_subsumption_just,[status(thm)],[c_8377,c_72,c_71,c_70,c_86,c_81,c_80,c_76,c_113,c_322,c_326,c_330,c_334,c_338,c_342,c_346,c_350,c_354,c_358,c_389,c_412,c_435,c_1905,c_1910,c_1918,c_1939,c_1946,c_2064,c_2130,c_2133,c_2230,c_2628,c_2691,c_2708,c_2872,c_2908,c_2987,c_2990,c_3034,c_3033,c_3032,c_3038,c_3068,c_3128,c_3179,c_3193,c_3199,c_3201,c_3387,c_3408,c_3447,c_3533,c_3539,c_3553,c_3558,c_3576,c_3987,c_4003,c_4653,c_4954,c_7574,c_8367]) ).

cnf(c_8402,plain,
    ( ~ product(e_2,e_4,e_1)
    | ~ product(e_5,e_4,e_1) ),
    inference(instantiation,[status(thm)],[c_4475]) ).

cnf(c_8407,plain,
    ( ~ product(X0,e_4,e_5)
    | ~ product(e_5,e_4,e_1)
    | product(X0,e_5,e_1) ),
    inference(instantiation,[status(thm)],[c_4922]) ).

cnf(c_8408,plain,
    ( ~ product(e_1,e_4,e_5)
    | ~ product(e_5,e_4,e_1)
    | product(e_1,e_5,e_1) ),
    inference(instantiation,[status(thm)],[c_8407]) ).

cnf(c_8411,plain,
    ( ~ product(e_1,e_4,e_3)
    | ~ product(e_5,e_4,e_1)
    | product(e_5,e_1,e_3) ),
    inference(instantiation,[status(thm)],[c_4569]) ).

cnf(c_8412,plain,
    ~ product(e_5,e_4,e_1),
    inference(global_subsumption_just,[status(thm)],[c_8411,c_75,c_73,c_72,c_71,c_70,c_94,c_91,c_90,c_88,c_86,c_81,c_80,c_78,c_76,c_113,c_322,c_326,c_330,c_334,c_338,c_342,c_346,c_350,c_354,c_358,c_381,c_389,c_404,c_412,c_427,c_435,c_450,c_458,c_481,c_1905,c_1910,c_1913,c_1915,c_1918,c_1923,c_1928,c_1939,c_1946,c_1969,c_1991,c_2058,c_2064,c_2085,c_2096,c_2130,c_2133,c_2172,c_2230,c_2236,c_2261,c_2267,c_2628,c_2692,c_2698,c_2708,c_2773,c_2872,c_2886,c_2900,c_2908,c_2909,c_2987,c_2990,c_2993,c_2996,c_3034,c_3033,c_3032,c_3038,c_3067,c_3068,c_3071,c_3074,c_3090,c_3097,c_3117,c_3120,c_3122,c_3123,c_3128,c_3152,c_3153,c_3179,c_3193,c_3199,c_3201,c_3203,c_3248,c_3318,c_3344,c_3349,c_3351,c_3354,c_3355,c_3387,c_3408,c_3410,c_3440,c_3447,c_3450,c_3464,c_3463,c_3462,c_3514,c_3553,c_3558,c_3563,c_3564,c_3566,c_3567,c_3568,c_3574,c_3576,c_3588,c_3777,c_3843,c_3852,c_3912,c_3987,c_4003,c_4065,c_4173,c_4263,c_4290,c_4663,c_4735,c_4824,c_4829,c_4954,c_4979,c_5001,c_5011,c_5012,c_5034,c_5057,c_5076,c_5093,c_5094,c_5116,c_5121,c_5129,c_5133,c_5148,c_5156,c_5174,c_5172,c_5205,c_5399,c_5408,c_5417,c_5420,c_5429,c_5432,c_5436,c_5435,c_5460,c_5558,c_5629,c_5682,c_5765,c_5813,c_5970,c_5972,c_6036,c_6151,c_6379,c_6452,c_6613,c_6694,c_7211,c_7222,c_7574,c_7878,c_7997,c_8063,c_8123,c_8402,c_8408,c_8411]) ).

cnf(c_8446,plain,
    ( ~ product(e_4,e_4,e_1)
    | ~ product(e_4,e_4,e_5) ),
    inference(instantiation,[status(thm)],[c_4787]) ).

cnf(c_8447,plain,
    ~ product(e_4,e_4,e_5),
    inference(global_subsumption_just,[status(thm)],[c_8446,c_75,c_73,c_72,c_71,c_70,c_94,c_90,c_88,c_86,c_81,c_80,c_78,c_76,c_113,c_322,c_326,c_330,c_334,c_338,c_342,c_346,c_350,c_354,c_358,c_381,c_389,c_412,c_435,c_458,c_481,c_1905,c_1910,c_1913,c_1915,c_1918,c_1923,c_1928,c_1939,c_1946,c_1969,c_1991,c_2058,c_2064,c_2085,c_2096,c_2130,c_2133,c_2172,c_2230,c_2236,c_2261,c_2267,c_2628,c_2692,c_2708,c_2773,c_2872,c_2900,c_2908,c_2923,c_2987,c_2990,c_2993,c_2996,c_3034,c_3033,c_3032,c_3038,c_3067,c_3068,c_3090,c_3097,c_3117,c_3120,c_3122,c_3128,c_3146,c_3152,c_3153,c_3179,c_3180,c_3193,c_3199,c_3201,c_3203,c_3248,c_3318,c_3354,c_3355,c_3387,c_3408,c_3410,c_3440,c_3447,c_3553,c_3558,c_3563,c_3564,c_3566,c_3567,c_3568,c_3574,c_3576,c_3777,c_3843,c_3852,c_3912,c_3926,c_3987,c_4003,c_4173,c_4263,c_4290,c_4824,c_4829,c_4954,c_4979,c_5001,c_5012,c_5034,c_5057,c_5093,c_5094,c_5116,c_5121,c_5129,c_5148,c_5156,c_5162,c_5205,c_5399,c_5408,c_5417,c_5420,c_5429,c_5432,c_5436,c_5435,c_5460,c_5479,c_5629,c_5765,c_5796,c_5813,c_5972,c_6086,c_6151,c_6379,c_6452,c_7574,c_8063,c_8104,c_8412]) ).

cnf(c_8450,plain,
    ( ~ product(e_1,e_4,e_3)
    | ~ product(e_4,e_4,e_1)
    | product(e_4,e_1,e_3) ),
    inference(instantiation,[status(thm)],[c_4569]) ).

cnf(c_8489,plain,
    ( ~ product(e_1,e_4,e_5)
    | ~ product(e_4,e_4,e_1)
    | product(e_4,e_1,e_5) ),
    inference(instantiation,[status(thm)],[c_5453]) ).

cnf(c_8490,plain,
    ~ product(e_1,e_4,e_5),
    inference(global_subsumption_just,[status(thm)],[c_8489,c_75,c_73,c_72,c_71,c_70,c_94,c_91,c_90,c_88,c_86,c_81,c_80,c_78,c_76,c_113,c_322,c_326,c_330,c_334,c_338,c_342,c_346,c_350,c_354,c_358,c_381,c_389,c_404,c_412,c_427,c_435,c_450,c_458,c_481,c_1905,c_1910,c_1913,c_1915,c_1918,c_1923,c_1928,c_1939,c_1946,c_1969,c_1991,c_2058,c_2064,c_2085,c_2096,c_2130,c_2133,c_2172,c_2230,c_2236,c_2237,c_2261,c_2267,c_2628,c_2692,c_2698,c_2708,c_2773,c_2872,c_2886,c_2900,c_2908,c_2909,c_2916,c_2987,c_2990,c_2993,c_2996,c_3034,c_3033,c_3032,c_3038,c_3067,c_3068,c_3071,c_3074,c_3090,c_3097,c_3098,c_3117,c_3120,c_3122,c_3123,c_3128,c_3145,c_3152,c_3153,c_3179,c_3180,c_3193,c_3199,c_3201,c_3203,c_3234,c_3248,c_3318,c_3344,c_3349,c_3351,c_3354,c_3355,c_3387,c_3408,c_3410,c_3440,c_3447,c_3450,c_3464,c_3463,c_3462,c_3514,c_3539,c_3553,c_3558,c_3563,c_3564,c_3566,c_3567,c_3568,c_3574,c_3576,c_3588,c_3777,c_3843,c_3852,c_3912,c_3926,c_3987,c_4003,c_4065,c_4173,c_4191,c_4263,c_4290,c_4653,c_4663,c_4735,c_4824,c_4829,c_4954,c_4964,c_4979,c_5001,c_5011,c_5012,c_5034,c_5057,c_5076,c_5093,c_5094,c_5116,c_5121,c_5129,c_5133,c_5148,c_5156,c_5162,c_5174,c_5172,c_5205,c_5257,c_5399,c_5408,c_5417,c_5420,c_5429,c_5432,c_5436,c_5435,c_5460,c_5558,c_5629,c_5682,c_5765,c_5780,c_5786,c_5799,c_5813,c_5970,c_5972,c_6036,c_6086,c_6151,c_6379,c_6452,c_6614,c_6613,c_6618,c_6694,c_7005,c_7153,c_7152,c_7157,c_7163,c_7182,c_7211,c_7222,c_7535,c_7574,c_7773,c_7878,c_7996,c_8046,c_8063,c_8103,c_8121,c_8402,c_8408,c_8411]) ).

cnf(c_8543,plain,
    ( ~ product(e_4,e_4,X0)
    | ~ product(e_6,e_4,e_4)
    | product(e_6,e_4,X0) ),
    inference(instantiation,[status(thm)],[c_5740]) ).

cnf(c_8547,plain,
    ( ~ product(e_4,e_4,e_4)
    | ~ product(e_6,e_4,e_4) ),
    inference(instantiation,[status(thm)],[c_5733]) ).

cnf(c_8550,plain,
    ( ~ product(e_6,e_4,e_1)
    | ~ product(e_6,e_4,e_4) ),
    inference(instantiation,[status(thm)],[c_5713]) ).

cnf(c_8551,plain,
    ( ~ product(e_6,e_4,e_3)
    | ~ product(e_6,e_4,e_4) ),
    inference(instantiation,[status(thm)],[c_5712]) ).

cnf(c_8552,plain,
    ~ product(e_6,e_4,e_3),
    inference(global_subsumption_just,[status(thm)],[c_8551,c_75,c_73,c_72,c_71,c_70,c_94,c_91,c_90,c_88,c_86,c_81,c_80,c_78,c_76,c_113,c_322,c_326,c_330,c_334,c_338,c_342,c_346,c_350,c_354,c_358,c_381,c_389,c_404,c_412,c_427,c_435,c_450,c_458,c_481,c_1905,c_1910,c_1913,c_1915,c_1918,c_1923,c_1928,c_1939,c_1946,c_1969,c_1991,c_2058,c_2064,c_2085,c_2096,c_2130,c_2133,c_2172,c_2230,c_2236,c_2237,c_2261,c_2267,c_2628,c_2692,c_2697,c_2698,c_2708,c_2773,c_2872,c_2886,c_2900,c_2908,c_2909,c_2916,c_2987,c_2990,c_2993,c_2996,c_3034,c_3033,c_3032,c_3038,c_3054,c_3067,c_3068,c_3071,c_3074,c_3090,c_3097,c_3098,c_3117,c_3120,c_3122,c_3123,c_3128,c_3146,c_3152,c_3153,c_3179,c_3180,c_3193,c_3199,c_3201,c_3203,c_3234,c_3248,c_3318,c_3344,c_3349,c_3351,c_3354,c_3355,c_3387,c_3408,c_3410,c_3440,c_3447,c_3450,c_3464,c_3463,c_3462,c_3514,c_3539,c_3553,c_3558,c_3563,c_3564,c_3566,c_3567,c_3568,c_3574,c_3576,c_3588,c_3777,c_3843,c_3852,c_3912,c_3926,c_3987,c_4003,c_4065,c_4173,c_4191,c_4263,c_4290,c_4653,c_4663,c_4735,c_4824,c_4829,c_4954,c_4964,c_4979,c_5001,c_5011,c_5012,c_5034,c_5057,c_5076,c_5093,c_5094,c_5116,c_5121,c_5129,c_5133,c_5148,c_5156,c_5162,c_5174,c_5172,c_5205,c_5250,c_5399,c_5408,c_5417,c_5420,c_5429,c_5432,c_5436,c_5435,c_5460,c_5558,c_5629,c_5682,c_5765,c_5780,c_5786,c_5798,c_5813,c_5970,c_5972,c_6036,c_6086,c_6151,c_6379,c_6452,c_6613,c_6694,c_7005,c_7153,c_7152,c_7157,c_7163,c_7182,c_7211,c_7222,c_7535,c_7574,c_7773,c_7878,c_7996,c_8046,c_8063,c_8103,c_8121,c_8214,c_8402,c_8408,c_8411,c_8490]) ).

cnf(c_8556,plain,
    ( ~ product(e_4,e_4,e_1)
    | ~ product(e_6,e_4,e_4)
    | product(e_6,e_4,e_1) ),
    inference(instantiation,[status(thm)],[c_8543]) ).

cnf(c_8559,plain,
    ( ~ product(e_4,e_4,e_6)
    | ~ product(e_6,e_4,e_4)
    | product(e_6,e_4,e_6) ),
    inference(instantiation,[status(thm)],[c_4734]) ).

cnf(c_8560,plain,
    ~ product(e_6,e_4,e_4),
    inference(global_subsumption_just,[status(thm)],[c_8559,c_72,c_71,c_70,c_78,c_338,c_342,c_346,c_350,c_354,c_1905,c_1910,c_2237,c_2916,c_2987,c_3027,c_3123,c_3180,c_3199,c_3201,c_3203,c_3359,c_3387,c_3408,c_4004,c_4035,c_4876,c_4886,c_5162,c_5228,c_5248,c_6799,c_7575,c_8065,c_8447,c_8550,c_8547,c_8556,c_8559]) ).

cnf(c_8648,plain,
    ( ~ product(e_1,e_6,e_4)
    | ~ product(e_2,e_6,e_1)
    | product(e_2,e_1,e_4) ),
    inference(instantiation,[status(thm)],[c_4674]) ).

cnf(c_8690,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_8648,c_8560,c_8552,c_8490,c_8450,c_8447,c_8412,c_8379,c_8367,c_8308,c_8309,c_8306,c_8193,c_8145,c_8123,c_8104,c_8074,c_8065,c_7997,c_7945,c_7918,c_7879,c_7878,c_7619,c_7575,c_7535,c_7485,c_7363,c_7246,c_7242,c_7237,c_7222,c_7216,c_6799,c_6694,c_6665,c_6601,c_6321,c_6232,c_6117,c_6086,c_6059,c_6052,c_6049,c_6038,c_5917,c_5822,c_5798,c_5766,c_5761,c_5576,c_5564,c_5557,c_5558,c_5520,c_5309,c_5310,c_5266,c_5254,c_5248,c_5228,c_5162,c_5146,c_5143,c_5097,c_5094,c_5078,c_5055,c_5044,c_5033,c_5024,c_5012,c_5011,c_5010,c_5002,c_4966,c_4964,c_4954,c_4886,c_4876,c_4796,c_4790,c_4779,c_4776,c_4765,c_4749,c_4733,c_4264,c_4263,c_4259,c_4191,c_4189,c_4173,c_4068,c_4065,c_4062,c_4035,c_4015,c_4004,c_3926,c_3742,c_3588,c_3576,c_3533,c_3529,c_3514,c_3494,c_3491,c_3468,c_3462,c_3463,c_3464,c_3450,c_3408,c_3387,c_3377,c_3359,c_3351,c_3349,c_3344,c_3307,c_3303,c_3288,c_3203,c_3201,c_3199,c_3180,c_3172,c_3171,c_3146,c_3122,c_3120,c_3119,c_3090,c_3083,c_3080,c_3074,c_3071,c_3068,c_3054,c_3027,c_2990,c_2987,c_2930,c_2923,c_2916,c_2909,c_2704,c_2701,c_2700,c_2698,c_2243,c_2240,c_2237,c_2086,c_2049,c_2033,c_2028,c_1910,c_1905,c_354,c_350,c_346,c_342,c_338,c_78,c_79,c_80,c_84,c_89,c_91,c_70,c_71,c_72,c_73,c_74,c_75]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : GRP128-2.006 : TPTP v8.1.2. Released v1.2.0.
% 0.03/0.11  % Command  : run_iprover %s %d THM
% 0.12/0.32  % Computer : n029.cluster.edu
% 0.12/0.32  % Model    : x86_64 x86_64
% 0.12/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32  % Memory   : 8042.1875MB
% 0.12/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32  % CPULimit : 300
% 0.12/0.32  % WCLimit  : 300
% 0.12/0.32  % DateTime : Fri May  3 00:16:07 EDT 2024
% 0.12/0.32  % CPUTime  : 
% 0.18/0.43  Running first-order theorem proving
% 0.18/0.43  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 7.42/1.63  % SZS status Started for theBenchmark.p
% 7.42/1.63  % SZS status Unsatisfiable for theBenchmark.p
% 7.42/1.63  
% 7.42/1.63  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 7.42/1.63  
% 7.42/1.63  ------  iProver source info
% 7.42/1.63  
% 7.42/1.63  git: date: 2024-05-02 19:28:25 +0000
% 7.42/1.63  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 7.42/1.63  git: non_committed_changes: false
% 7.42/1.63  
% 7.42/1.63  ------ Parsing...successful
% 7.42/1.63  
% 7.42/1.63  
% 7.42/1.63  
% 7.42/1.63  ------ Preprocessing... sf_s  rm: 0 0s  sf_e  pe_s  pe:1:0s pe:2:0s pe_e  sf_s  rm: 0 0s  sf_e  pe_s  pe_e 
% 7.42/1.63  
% 7.42/1.63  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 7.42/1.63  ------ Proving...
% 7.42/1.63  ------ Problem Properties 
% 7.42/1.63  
% 7.42/1.63  
% 7.42/1.63  clauses                                 51
% 7.42/1.63  conjectures                             1
% 7.42/1.63  EPR                                     51
% 7.42/1.63  Horn                                    50
% 7.42/1.63  unary                                   46
% 7.42/1.63  binary                                  0
% 7.42/1.63  lits                                    66
% 7.42/1.63  lits eq                                 0
% 7.42/1.63  fd_pure                                 0
% 7.42/1.63  fd_pseudo                               0
% 7.42/1.63  fd_cond                                 0
% 7.42/1.63  fd_pseudo_cond                          0
% 7.42/1.63  AC symbols                              0
% 7.42/1.63  
% 7.42/1.63  ------ Input Options Time Limit: Unbounded
% 7.42/1.63  
% 7.42/1.63  
% 7.42/1.63  ------ 
% 7.42/1.63  Current options:
% 7.42/1.63  ------ 
% 7.42/1.63  
% 7.42/1.63  
% 7.42/1.63  
% 7.42/1.63  
% 7.42/1.63  ------ Proving...
% 7.42/1.63  
% 7.42/1.63  
% 7.42/1.63  % SZS status Unsatisfiable for theBenchmark.p
% 7.42/1.63  
% 7.42/1.63  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 8.12/1.64  
% 8.12/1.64  
%------------------------------------------------------------------------------