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CSE_E---1.7.SAT-Sat.s

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%------------------------------------------------------------------------------
% File     : CSE_E---1.7
% Problem  : GRP125-2.004 : TPTP v9.2.1. Released v1.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d

% Computer : n021.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 : Tue May  5 04:23:58 PM UTC 2026

% Result   : Satisfiable 1.28s 1.73s
% Output   : Saturation 1.28s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
cnf(no_redundancy,axiom,
    ( ~ product(X1,e_1,X2)
    | ~ next(X1,X3)
    | ~ greater(X2,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',no_redundancy) ).

cnf(e_4_greater_e_3,axiom,
    greater(e_4,e_3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_greater_e_3) ).

cnf(e_2_is_not_e_1,axiom,
    ~ equalish(e_2,e_1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_1) ).

cnf(product_left_cancellation,axiom,
    ( equalish(X1,X4)
    | ~ product(X1,X2,X3)
    | ~ product(X4,X2,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_left_cancellation) ).

cnf(product_total_function1,axiom,
    ( product(X1,X2,e_1)
    | product(X1,X2,e_2)
    | product(X1,X2,e_3)
    | product(X1,X2,e_4)
    | ~ group_element(X1)
    | ~ group_element(X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_total_function1) ).

cnf(element_1,axiom,
    group_element(e_1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_1) ).

cnf(e_2_then_e_3,axiom,
    next(e_2,e_3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_then_e_3) ).

cnf(product_idempotence,axiom,
    product(X1,X1,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_idempotence) ).

cnf(element_4,axiom,
    group_element(e_4),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_4) ).

cnf(e_4_is_not_e_2,axiom,
    ~ equalish(e_4,e_2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_is_not_e_2) ).

cnf(e_4_is_not_e_1,axiom,
    ~ equalish(e_4,e_1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_is_not_e_1) ).

cnf(product_right_cancellation,axiom,
    ( equalish(X2,X4)
    | ~ product(X1,X2,X3)
    | ~ product(X1,X4,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_right_cancellation) ).

cnf(element_2,axiom,
    group_element(e_2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_2) ).

cnf(element_3,axiom,
    group_element(e_3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_3) ).

cnf(e_3_is_not_e_1,axiom,
    ~ equalish(e_3,e_1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_1) ).

cnf(e_3_is_not_e_2,axiom,
    ~ equalish(e_3,e_2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_2) ).

cnf(e_4_is_not_e_3,axiom,
    ~ equalish(e_4,e_3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_is_not_e_3) ).

cnf(qg3,negated_conjecture,
    ( product(X3,X4,X1)
    | ~ product(X1,X2,X3)
    | ~ product(X2,X1,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg3) ).

cnf(product_total_function2,axiom,
    ( equalish(X3,X4)
    | ~ product(X1,X2,X3)
    | ~ product(X1,X2,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_total_function2) ).

cnf(e_3_greater_e_2,axiom,
    greater(e_3,e_2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_greater_e_2) ).

cnf(e_4_greater_e_2,axiom,
    greater(e_4,e_2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_greater_e_2) ).

cnf(e_2_greater_e_1,axiom,
    greater(e_2,e_1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_greater_e_1) ).

cnf(e_3_greater_e_1,axiom,
    greater(e_3,e_1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_greater_e_1) ).

cnf(e_4_greater_e_1,axiom,
    greater(e_4,e_1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_greater_e_1) ).

cnf(e_1_then_e_2,axiom,
    next(e_1,e_2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_then_e_2) ).

cnf(e_3_is_not_e_4,axiom,
    ~ equalish(e_3,e_4),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_4) ).

cnf(e_2_is_not_e_4,axiom,
    ~ equalish(e_2,e_4),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_4) ).

cnf(e_2_is_not_e_3,axiom,
    ~ equalish(e_2,e_3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_3) ).

cnf(e_1_is_not_e_4,axiom,
    ~ equalish(e_1,e_4),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_4) ).

cnf(e_1_is_not_e_3,axiom,
    ~ equalish(e_1,e_3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_3) ).

cnf(e_1_is_not_e_2,axiom,
    ~ equalish(e_1,e_2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_2) ).

cnf(e_3_then_e_4,axiom,
    next(e_3,e_4),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_then_e_4) ).

cnf(c_0_32,axiom,
    ( ~ product(X1,e_1,X2)
    | ~ next(X1,X3)
    | ~ greater(X2,X3) ),
    no_redundancy,
    [final] ).

cnf(c_0_33,axiom,
    greater(e_4,e_3),
    e_4_greater_e_3,
    [final] ).

cnf(c_0_34,axiom,
    ~ equalish(e_2,e_1),
    e_2_is_not_e_1,
    [final] ).

cnf(c_0_35,axiom,
    ( equalish(X1,X4)
    | ~ product(X1,X2,X3)
    | ~ product(X4,X2,X3) ),
    product_left_cancellation,
    [final] ).

cnf(c_0_36,axiom,
    ( product(X1,X2,e_1)
    | product(X1,X2,e_2)
    | product(X1,X2,e_3)
    | product(X1,X2,e_4)
    | ~ group_element(X1)
    | ~ group_element(X2) ),
    product_total_function1,
    [final] ).

cnf(c_0_37,axiom,
    group_element(e_1),
    element_1,
    [final] ).

cnf(c_0_38,plain,
    ( ~ product(X1,e_1,e_4)
    | ~ next(X1,e_3) ),
    inference(spm,[status(thm)],[c_0_32,c_0_33]),
    [final] ).

cnf(c_0_39,axiom,
    next(e_2,e_3),
    e_2_then_e_3,
    [final] ).

cnf(c_0_40,plain,
    ( ~ product(e_1,X1,X2)
    | ~ product(e_2,X1,X2) ),
    inference(spm,[status(thm)],[c_0_34,c_0_35]),
    [final] ).

cnf(c_0_41,axiom,
    product(X1,X1,X1),
    product_idempotence,
    [final] ).

cnf(c_0_42,axiom,
    group_element(e_4),
    element_4,
    [final] ).

cnf(c_0_43,axiom,
    ~ equalish(e_4,e_2),
    e_4_is_not_e_2,
    [final] ).

cnf(c_0_44,axiom,
    ~ equalish(e_4,e_1),
    e_4_is_not_e_1,
    [final] ).

cnf(c_0_45,axiom,
    ( equalish(X2,X4)
    | ~ product(X1,X2,X3)
    | ~ product(X1,X4,X3) ),
    product_right_cancellation,
    [final] ).

cnf(c_0_46,plain,
    ( product(X1,e_1,e_4)
    | product(X1,e_1,e_3)
    | product(X1,e_1,e_2)
    | product(X1,e_1,e_1)
    | ~ group_element(X1) ),
    inference(spm,[status(thm)],[c_0_36,c_0_37]),
    [final] ).

cnf(c_0_47,axiom,
    group_element(e_2),
    element_2,
    [final] ).

cnf(c_0_48,plain,
    ~ product(e_2,e_1,e_4),
    inference(spm,[status(thm)],[c_0_38,c_0_39]),
    [final] ).

cnf(c_0_49,plain,
    ~ product(e_2,e_1,e_1),
    inference(spm,[status(thm)],[c_0_40,c_0_41]),
    [final] ).

cnf(c_0_50,plain,
    ( product(X1,e_4,e_4)
    | product(X1,e_4,e_3)
    | product(X1,e_4,e_2)
    | product(X1,e_4,e_1)
    | ~ group_element(X1) ),
    inference(spm,[status(thm)],[c_0_36,c_0_42]),
    [final] ).

cnf(c_0_51,plain,
    ( ~ product(e_2,X1,X2)
    | ~ product(e_4,X1,X2) ),
    inference(spm,[status(thm)],[c_0_43,c_0_35]),
    [final] ).

cnf(c_0_52,plain,
    ( ~ product(X1,e_1,X2)
    | ~ product(X1,e_4,X2) ),
    inference(spm,[status(thm)],[c_0_44,c_0_45]),
    [final] ).

cnf(c_0_53,plain,
    ( product(e_2,e_1,e_2)
    | product(e_2,e_1,e_3) ),
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]),c_0_49]) ).

cnf(c_0_54,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) ),
    inference(spm,[status(thm)],[c_0_50,c_0_47]) ).

cnf(c_0_55,plain,
    ~ product(e_2,e_4,e_4),
    inference(spm,[status(thm)],[c_0_51,c_0_41]),
    [final] ).

cnf(c_0_56,plain,
    ( ~ product(X1,e_1,X2)
    | ~ product(X1,e_2,X2) ),
    inference(spm,[status(thm)],[c_0_34,c_0_45]),
    [final] ).

cnf(c_0_57,plain,
    ( product(e_2,e_1,e_2)
    | ~ product(e_2,e_4,e_3) ),
    inference(spm,[status(thm)],[c_0_52,c_0_53]),
    [final] ).

cnf(c_0_58,axiom,
    group_element(e_3),
    element_3,
    [final] ).

cnf(c_0_59,axiom,
    ~ equalish(e_3,e_1),
    e_3_is_not_e_1,
    [final] ).

cnf(c_0_60,axiom,
    ~ equalish(e_3,e_2),
    e_3_is_not_e_2,
    [final] ).

cnf(c_0_61,axiom,
    ~ equalish(e_4,e_3),
    e_4_is_not_e_3,
    [final] ).

cnf(c_0_62,plain,
    ( product(e_2,e_4,e_3)
    | product(e_2,e_4,e_2)
    | product(e_2,e_4,e_1) ),
    inference(sr,[status(thm)],[c_0_54,c_0_55]) ).

cnf(c_0_63,plain,
    ~ product(e_2,e_4,e_3),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_41])]),
    [final] ).

cnf(c_0_64,plain,
    ( product(X1,e_3,e_4)
    | product(X1,e_3,e_3)
    | product(X1,e_3,e_2)
    | product(X1,e_3,e_1)
    | ~ group_element(X1) ),
    inference(spm,[status(thm)],[c_0_36,c_0_58]),
    [final] ).

cnf(c_0_65,plain,
    ( ~ product(X1,e_1,X2)
    | ~ product(X1,e_3,X2) ),
    inference(spm,[status(thm)],[c_0_59,c_0_45]),
    [final] ).

cnf(c_0_66,plain,
    ( ~ product(e_2,X1,X2)
    | ~ product(e_3,X1,X2) ),
    inference(spm,[status(thm)],[c_0_60,c_0_35]),
    [final] ).

cnf(c_0_67,plain,
    ( ~ product(X1,e_3,X2)
    | ~ product(X1,e_4,X2) ),
    inference(spm,[status(thm)],[c_0_61,c_0_45]),
    [final] ).

cnf(c_0_68,plain,
    ( product(e_2,e_4,e_1)
    | product(e_2,e_4,e_2) ),
    inference(sr,[status(thm)],[c_0_62,c_0_63]) ).

cnf(c_0_69,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) ),
    inference(spm,[status(thm)],[c_0_64,c_0_37]) ).

cnf(c_0_70,plain,
    ~ product(e_1,e_3,e_1),
    inference(spm,[status(thm)],[c_0_65,c_0_41]),
    [final] ).

cnf(c_0_71,plain,
    ( product(e_2,e_3,e_1)
    | product(e_2,e_3,e_2)
    | product(e_2,e_3,e_3)
    | product(e_2,e_3,e_4) ),
    inference(spm,[status(thm)],[c_0_64,c_0_47]) ).

cnf(c_0_72,plain,
    ~ product(e_2,e_3,e_3),
    inference(spm,[status(thm)],[c_0_66,c_0_41]),
    [final] ).

cnf(c_0_73,plain,
    ( ~ product(X1,e_2,X2)
    | ~ product(X1,e_4,X2) ),
    inference(spm,[status(thm)],[c_0_43,c_0_45]),
    [final] ).

cnf(c_0_74,plain,
    ( product(e_2,e_4,e_2)
    | ~ product(e_2,e_3,e_1) ),
    inference(spm,[status(thm)],[c_0_67,c_0_68]),
    [final] ).

cnf(c_0_75,plain,
    ( product(e_1,e_3,e_4)
    | product(e_1,e_3,e_3)
    | product(e_1,e_3,e_2) ),
    inference(sr,[status(thm)],[c_0_69,c_0_70]) ).

cnf(c_0_76,plain,
    ( product(e_2,e_3,e_4)
    | product(e_2,e_3,e_2)
    | product(e_2,e_3,e_1) ),
    inference(sr,[status(thm)],[c_0_71,c_0_72]) ).

cnf(c_0_77,plain,
    ~ product(e_2,e_3,e_1),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_41])]),
    [final] ).

cnf(c_0_78,plain,
    ( product(e_1,e_3,e_2)
    | product(e_1,e_3,e_3)
    | ~ product(e_2,e_3,e_4) ),
    inference(spm,[status(thm)],[c_0_40,c_0_75]) ).

cnf(c_0_79,plain,
    ( product(e_2,e_3,e_2)
    | product(e_2,e_3,e_4) ),
    inference(sr,[status(thm)],[c_0_76,c_0_77]) ).

cnf(c_0_80,plain,
    ( ~ product(e_1,X1,X2)
    | ~ product(e_3,X1,X2) ),
    inference(spm,[status(thm)],[c_0_59,c_0_35]),
    [final] ).

cnf(c_0_81,plain,
    ( product(e_2,e_3,e_2)
    | product(e_1,e_3,e_3)
    | product(e_1,e_3,e_2) ),
    inference(spm,[status(thm)],[c_0_78,c_0_79]) ).

cnf(c_0_82,plain,
    ( ~ product(e_1,X1,X2)
    | ~ product(e_4,X1,X2) ),
    inference(spm,[status(thm)],[c_0_44,c_0_35]),
    [final] ).

cnf(c_0_83,plain,
    ~ product(e_4,e_3,e_4),
    inference(spm,[status(thm)],[c_0_67,c_0_41]),
    [final] ).

cnf(c_0_84,plain,
    ( product(e_1,e_3,e_2)
    | product(e_2,e_3,e_2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_41])]) ).

cnf(c_0_85,plain,
    ~ product(e_4,e_1,e_1),
    inference(spm,[status(thm)],[c_0_82,c_0_41]),
    [final] ).

cnf(c_0_86,plain,
    ( product(e_4,e_3,e_1)
    | product(e_4,e_3,e_2)
    | product(e_4,e_3,e_3) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_42]),c_0_83]) ).

cnf(c_0_87,plain,
    ~ product(e_4,e_3,e_2),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_84]),c_0_51]),
    [final] ).

cnf(c_0_88,plain,
    ( product(e_4,e_1,e_2)
    | product(e_4,e_1,e_3)
    | product(e_4,e_1,e_4) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_42]),c_0_85]) ).

cnf(c_0_89,plain,
    ( ~ product(X1,e_2,X2)
    | ~ product(X1,e_3,X2) ),
    inference(spm,[status(thm)],[c_0_60,c_0_45]),
    [final] ).

cnf(c_0_90,plain,
    ( product(e_4,e_3,e_3)
    | product(e_4,e_3,e_1) ),
    inference(sr,[status(thm)],[c_0_86,c_0_87]) ).

cnf(c_0_91,plain,
    ( product(e_4,e_1,e_3)
    | product(e_4,e_1,e_2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_88]),c_0_41])]) ).

cnf(c_0_92,plain,
    ( product(X1,e_2,e_4)
    | product(X1,e_2,e_3)
    | product(X1,e_2,e_2)
    | product(X1,e_2,e_1)
    | ~ group_element(X1) ),
    inference(spm,[status(thm)],[c_0_36,c_0_47]),
    [final] ).

cnf(c_0_93,plain,
    ~ product(e_4,e_2,e_4),
    inference(spm,[status(thm)],[c_0_73,c_0_41]),
    [final] ).

cnf(c_0_94,plain,
    ( ~ product(e_3,X1,X2)
    | ~ product(e_4,X1,X2) ),
    inference(spm,[status(thm)],[c_0_61,c_0_35]),
    [final] ).

cnf(c_0_95,plain,
    ( product(e_4,e_3,e_3)
    | ~ product(e_4,e_2,e_1) ),
    inference(spm,[status(thm)],[c_0_89,c_0_90]),
    [final] ).

cnf(c_0_96,plain,
    ( product(e_4,e_1,e_2)
    | ~ product(e_4,e_2,e_3) ),
    inference(spm,[status(thm)],[c_0_56,c_0_91]) ).

cnf(c_0_97,plain,
    ( product(e_4,e_2,e_1)
    | product(e_4,e_2,e_2)
    | product(e_4,e_2,e_3) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_42]),c_0_93]) ).

cnf(c_0_98,plain,
    ~ product(e_4,e_2,e_1),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_41])]),
    [final] ).

cnf(c_0_99,negated_conjecture,
    ( product(X3,X4,X1)
    | ~ product(X1,X2,X3)
    | ~ product(X2,X1,X4) ),
    qg3,
    [final] ).

cnf(c_0_100,plain,
    ( ~ product(e_2,e_1,e_2)
    | ~ product(e_4,e_2,e_3) ),
    inference(spm,[status(thm)],[c_0_51,c_0_96]) ).

cnf(c_0_101,plain,
    ( product(e_4,e_2,e_3)
    | product(e_4,e_2,e_2) ),
    inference(sr,[status(thm)],[c_0_97,c_0_98]) ).

cnf(c_0_102,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) ),
    inference(spm,[status(thm)],[c_0_50,c_0_37]) ).

cnf(c_0_103,plain,
    ~ product(e_1,e_4,e_1),
    inference(spm,[status(thm)],[c_0_52,c_0_41]),
    [final] ).

cnf(c_0_104,negated_conjecture,
    ( product(e_2,e_4,e_2)
    | product(X1,e_1,e_4)
    | ~ product(e_4,e_2,X1) ),
    inference(spm,[status(thm)],[c_0_99,c_0_68]) ).

cnf(c_0_105,plain,
    ( product(e_4,e_2,e_2)
    | ~ product(e_2,e_1,e_2) ),
    inference(spm,[status(thm)],[c_0_100,c_0_101]),
    [final] ).

cnf(c_0_106,plain,
    ( product(e_1,e_4,e_4)
    | product(e_1,e_4,e_3)
    | product(e_1,e_4,e_2) ),
    inference(sr,[status(thm)],[c_0_102,c_0_103]) ).

cnf(c_0_107,negated_conjecture,
    ~ product(e_2,e_1,e_2),
    inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_105]),c_0_48]),c_0_52]),
    [final] ).

cnf(c_0_108,plain,
    ( product(e_4,e_1,e_2)
    | ~ product(e_2,e_1,e_3) ),
    inference(spm,[status(thm)],[c_0_51,c_0_91]) ).

cnf(c_0_109,plain,
    ( product(e_1,e_4,e_2)
    | product(e_1,e_4,e_3) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_106]),c_0_41])]) ).

cnf(c_0_110,plain,
    product(e_2,e_1,e_3),
    inference(sr,[status(thm)],[c_0_53,c_0_107]),
    [final] ).

cnf(c_0_111,negated_conjecture,
    ( product(X1,e_2,e_1)
    | ~ product(e_2,e_1,e_3)
    | ~ product(e_1,e_4,X1) ),
    inference(spm,[status(thm)],[c_0_99,c_0_108]) ).

cnf(c_0_112,negated_conjecture,
    ( product(e_1,e_4,e_2)
    | product(X1,e_3,e_4)
    | ~ product(e_4,e_1,X1) ),
    inference(spm,[status(thm)],[c_0_99,c_0_109]) ).

cnf(c_0_113,plain,
    product(e_4,e_1,e_2),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_108,c_0_110])]),
    [final] ).

cnf(c_0_114,plain,
    ( product(e_2,e_4,e_2)
    | ~ product(e_2,e_2,e_1) ),
    inference(spm,[status(thm)],[c_0_73,c_0_68]),
    [final] ).

cnf(c_0_115,axiom,
    ( equalish(X3,X4)
    | ~ product(X1,X2,X3)
    | ~ product(X1,X2,X4) ),
    product_total_function2,
    [final] ).

cnf(c_0_116,negated_conjecture,
    ( product(X1,e_2,e_1)
    | ~ product(e_1,e_4,X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_111,c_0_110])]),
    [final] ).

cnf(c_0_117,negated_conjecture,
    ( product(e_2,e_3,e_4)
    | product(e_1,e_4,e_2) ),
    inference(spm,[status(thm)],[c_0_112,c_0_113]) ).

cnf(c_0_118,plain,
    ~ product(e_2,e_2,e_1),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_114]),c_0_41])]),
    [final] ).

cnf(c_0_119,plain,
    ( ~ product(X1,X2,e_2)
    | ~ product(X1,X2,e_4) ),
    inference(spm,[status(thm)],[c_0_43,c_0_115]),
    [final] ).

cnf(c_0_120,negated_conjecture,
    product(e_2,e_3,e_4),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_117]),c_0_118]),
    [final] ).

cnf(c_0_121,plain,
    ( product(e_3,e_4,e_1)
    | product(e_3,e_4,e_2)
    | product(e_3,e_4,e_3)
    | product(e_3,e_4,e_4) ),
    inference(spm,[status(thm)],[c_0_50,c_0_58]) ).

cnf(c_0_122,plain,
    ~ product(e_3,e_4,e_4),
    inference(spm,[status(thm)],[c_0_94,c_0_41]),
    [final] ).

cnf(c_0_123,negated_conjecture,
    ~ product(e_2,e_3,e_2),
    inference(spm,[status(thm)],[c_0_119,c_0_120]),
    [final] ).

cnf(c_0_124,plain,
    ( ~ product(e_4,e_2,e_2)
    | ~ product(e_2,e_1,e_3) ),
    inference(spm,[status(thm)],[c_0_56,c_0_108]) ).

cnf(c_0_125,plain,
    ( product(e_3,e_4,e_3)
    | product(e_3,e_4,e_2)
    | product(e_3,e_4,e_1) ),
    inference(sr,[status(thm)],[c_0_121,c_0_122]) ).

cnf(c_0_126,negated_conjecture,
    ( product(e_1,e_4,e_2)
    | product(e_3,e_2,e_1) ),
    inference(spm,[status(thm)],[c_0_116,c_0_109]) ).

cnf(c_0_127,plain,
    product(e_1,e_3,e_2),
    inference(sr,[status(thm)],[c_0_84,c_0_123]),
    [final] ).

cnf(c_0_128,plain,
    ( product(e_1,e_4,e_2)
    | ~ product(e_3,e_4,e_3) ),
    inference(spm,[status(thm)],[c_0_80,c_0_109]),
    [final] ).

cnf(c_0_129,plain,
    ( ~ product(e_3,e_1,e_2)
    | ~ product(e_4,e_2,e_3) ),
    inference(spm,[status(thm)],[c_0_94,c_0_96]) ).

cnf(c_0_130,plain,
    ~ product(e_1,e_2,e_1),
    inference(spm,[status(thm)],[c_0_56,c_0_41]),
    [final] ).

cnf(c_0_131,plain,
    ( product(e_1,e_4,e_2)
    | ~ product(e_1,e_2,e_3) ),
    inference(spm,[status(thm)],[c_0_73,c_0_109]),
    [final] ).

cnf(c_0_132,plain,
    ~ product(e_4,e_2,e_2),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_124,c_0_110])]),
    [final] ).

cnf(c_0_133,plain,
    ( product(e_3,e_4,e_2)
    | product(e_3,e_4,e_3)
    | ~ product(e_3,e_2,e_1) ),
    inference(spm,[status(thm)],[c_0_73,c_0_125]) ).

cnf(c_0_134,negated_conjecture,
    product(e_3,e_2,e_1),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_126]),c_0_127])]),
    [final] ).

cnf(c_0_135,negated_conjecture,
    ~ product(e_3,e_4,e_3),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_128]),c_0_118]),
    [final] ).

cnf(c_0_136,plain,
    ~ product(e_3,e_1,e_1),
    inference(spm,[status(thm)],[c_0_80,c_0_41]),
    [final] ).

cnf(c_0_137,plain,
    ( product(e_4,e_2,e_2)
    | ~ product(e_3,e_1,e_2) ),
    inference(spm,[status(thm)],[c_0_129,c_0_101]),
    [final] ).

cnf(c_0_138,plain,
    ( product(e_1,e_2,e_2)
    | product(e_1,e_2,e_3)
    | product(e_1,e_2,e_4) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_37]),c_0_130]) ).

cnf(c_0_139,negated_conjecture,
    ~ product(e_1,e_2,e_3),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_131]),c_0_118]),
    [final] ).

cnf(c_0_140,plain,
    ~ product(e_1,e_2,e_2),
    inference(spm,[status(thm)],[c_0_89,c_0_127]),
    [final] ).

cnf(c_0_141,plain,
    product(e_4,e_2,e_3),
    inference(sr,[status(thm)],[c_0_101,c_0_132]),
    [final] ).

cnf(c_0_142,plain,
    product(e_3,e_4,e_2),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_133,c_0_134])]),c_0_135]),
    [final] ).

cnf(c_0_143,plain,
    ( product(e_3,e_4,e_2)
    | product(e_3,e_4,e_3)
    | ~ product(e_2,e_4,e_1) ),
    inference(spm,[status(thm)],[c_0_66,c_0_125]) ).

cnf(c_0_144,plain,
    ( product(e_3,e_1,e_2)
    | product(e_3,e_1,e_3)
    | product(e_3,e_1,e_4) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_58]),c_0_136]) ).

cnf(c_0_145,plain,
    ~ product(e_3,e_1,e_2),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_137]),c_0_41])]),
    [final] ).

cnf(c_0_146,negated_conjecture,
    ( product(X1,e_3,e_1)
    | ~ product(e_1,e_2,X1) ),
    inference(spm,[status(thm)],[c_0_99,c_0_110]),
    [final] ).

cnf(c_0_147,plain,
    product(e_1,e_2,e_4),
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_138,c_0_139]),c_0_140]),
    [final] ).

cnf(c_0_148,negated_conjecture,
    ( product(e_3,e_1,e_4)
    | product(e_2,e_4,e_2) ),
    inference(spm,[status(thm)],[c_0_104,c_0_141]) ).

cnf(c_0_149,plain,
    ~ product(e_2,e_4,e_2),
    inference(spm,[status(thm)],[c_0_66,c_0_142]),
    [final] ).

cnf(c_0_150,negated_conjecture,
    ( product(e_2,e_3,e_2)
    | product(X1,e_4,e_3)
    | ~ product(e_3,e_2,X1) ),
    inference(spm,[status(thm)],[c_0_99,c_0_79]) ).

cnf(c_0_151,plain,
    ( product(e_2,e_4,e_2)
    | product(e_3,e_4,e_3)
    | product(e_3,e_4,e_2) ),
    inference(spm,[status(thm)],[c_0_143,c_0_68]) ).

cnf(c_0_152,plain,
    ( product(e_3,e_1,e_4)
    | product(e_3,e_1,e_3) ),
    inference(sr,[status(thm)],[c_0_144,c_0_145]) ).

cnf(c_0_153,axiom,
    greater(e_3,e_2),
    e_3_greater_e_2,
    [final] ).

cnf(c_0_154,axiom,
    greater(e_4,e_2),
    e_4_greater_e_2,
    [final] ).

cnf(c_0_155,negated_conjecture,
    product(e_4,e_3,e_1),
    inference(spm,[status(thm)],[c_0_146,c_0_147]),
    [final] ).

cnf(c_0_156,negated_conjecture,
    product(e_3,e_1,e_4),
    inference(sr,[status(thm)],[c_0_148,c_0_149]),
    [final] ).

cnf(c_0_157,plain,
    product(e_2,e_4,e_1),
    inference(sr,[status(thm)],[c_0_68,c_0_149]),
    [final] ).

cnf(c_0_158,negated_conjecture,
    product(e_1,e_4,e_3),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_134]),c_0_123]),
    [final] ).

cnf(c_0_159,plain,
    ( ~ product(e_1,e_3,e_2)
    | ~ product(e_1,e_2,e_3) ),
    inference(spm,[status(thm)],[c_0_67,c_0_131]) ).

cnf(c_0_160,plain,
    ( ~ product(e_1,e_3,e_2)
    | ~ product(e_3,e_4,e_3) ),
    inference(spm,[status(thm)],[c_0_67,c_0_128]) ).

cnf(c_0_161,plain,
    ( product(e_4,e_1,e_2)
    | ~ product(e_3,e_1,e_3) ),
    inference(spm,[status(thm)],[c_0_94,c_0_91]) ).

cnf(c_0_162,plain,
    ( product(e_4,e_1,e_2)
    | ~ product(e_4,e_3,e_3) ),
    inference(spm,[status(thm)],[c_0_65,c_0_91]) ).

cnf(c_0_163,plain,
    ( product(e_3,e_4,e_2)
    | product(e_2,e_4,e_2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_151]),c_0_41])]) ).

cnf(c_0_164,plain,
    ( product(e_1,e_4,e_2)
    | ~ product(e_2,e_4,e_3) ),
    inference(spm,[status(thm)],[c_0_40,c_0_109]),
    [final] ).

cnf(c_0_165,plain,
    ( product(e_1,e_4,e_2)
    | ~ product(e_1,e_3,e_3) ),
    inference(spm,[status(thm)],[c_0_67,c_0_109]),
    [final] ).

cnf(c_0_166,axiom,
    greater(e_2,e_1),
    e_2_greater_e_1,
    [final] ).

cnf(c_0_167,axiom,
    greater(e_3,e_1),
    e_3_greater_e_1,
    [final] ).

cnf(c_0_168,axiom,
    greater(e_4,e_1),
    e_4_greater_e_1,
    [final] ).

cnf(c_0_169,plain,
    ( ~ product(X1,X2,e_1)
    | ~ product(X1,X2,e_3) ),
    inference(spm,[status(thm)],[c_0_59,c_0_115]),
    [final] ).

cnf(c_0_170,plain,
    ( ~ product(X1,X2,e_3)
    | ~ product(X1,X2,e_4) ),
    inference(spm,[status(thm)],[c_0_61,c_0_115]),
    [final] ).

cnf(c_0_171,plain,
    ( product(e_3,e_1,e_3)
    | ~ product(e_3,e_3,e_4) ),
    inference(spm,[status(thm)],[c_0_65,c_0_152]),
    [final] ).

cnf(c_0_172,plain,
    ( ~ product(X1,X2,e_2)
    | ~ product(X1,X2,e_3) ),
    inference(spm,[status(thm)],[c_0_60,c_0_115]),
    [final] ).

cnf(c_0_173,plain,
    ( ~ product(X1,X2,e_1)
    | ~ product(X1,X2,e_2) ),
    inference(spm,[status(thm)],[c_0_34,c_0_115]),
    [final] ).

cnf(c_0_174,plain,
    ( ~ product(X1,X2,e_1)
    | ~ product(X1,X2,e_4) ),
    inference(spm,[status(thm)],[c_0_44,c_0_115]),
    [final] ).

cnf(c_0_175,plain,
    ( product(e_4,e_3,e_3)
    | ~ product(e_3,e_3,e_1) ),
    inference(spm,[status(thm)],[c_0_94,c_0_90]),
    [final] ).

cnf(c_0_176,plain,
    ( product(e_2,e_3,e_2)
    | ~ product(e_2,e_2,e_4) ),
    inference(spm,[status(thm)],[c_0_89,c_0_79]),
    [final] ).

cnf(c_0_177,plain,
    ( product(e_2,e_1,e_2)
    | ~ product(e_2,e_2,e_3) ),
    inference(spm,[status(thm)],[c_0_56,c_0_53]),
    [final] ).

cnf(c_0_178,plain,
    ( ~ product(X1,e_1,e_3)
    | ~ next(X1,e_2) ),
    inference(spm,[status(thm)],[c_0_32,c_0_153]),
    [final] ).

cnf(c_0_179,axiom,
    next(e_1,e_2),
    e_1_then_e_2,
    [final] ).

cnf(c_0_180,plain,
    ( ~ product(X1,e_1,e_4)
    | ~ next(X1,e_2) ),
    inference(spm,[status(thm)],[c_0_32,c_0_154]),
    [final] ).

cnf(c_0_181,negated_conjecture,
    ( product(X1,e_1,e_3)
    | ~ product(e_3,e_4,X1) ),
    inference(spm,[status(thm)],[c_0_99,c_0_155]),
    [final] ).

cnf(c_0_182,negated_conjecture,
    ( product(X1,e_4,e_2)
    | ~ product(e_2,e_1,X1) ),
    inference(spm,[status(thm)],[c_0_99,c_0_147]),
    [final] ).

cnf(c_0_183,negated_conjecture,
    ( product(X1,e_4,e_1)
    | ~ product(e_1,e_3,X1) ),
    inference(spm,[status(thm)],[c_0_99,c_0_156]),
    [final] ).

cnf(c_0_184,negated_conjecture,
    ( product(X1,e_1,e_4)
    | ~ product(e_4,e_2,X1) ),
    inference(spm,[status(thm)],[c_0_99,c_0_157]),
    [final] ).

cnf(c_0_185,negated_conjecture,
    ( product(X1,e_3,e_4)
    | ~ product(e_4,e_1,X1) ),
    inference(spm,[status(thm)],[c_0_99,c_0_158]),
    [final] ).

cnf(c_0_186,negated_conjecture,
    ( product(X1,e_2,e_4)
    | ~ product(e_4,e_3,X1) ),
    inference(spm,[status(thm)],[c_0_99,c_0_142]),
    [final] ).

cnf(c_0_187,negated_conjecture,
    ( product(X1,e_1,e_2)
    | ~ product(e_2,e_3,X1) ),
    inference(spm,[status(thm)],[c_0_99,c_0_134]),
    [final] ).

cnf(c_0_188,negated_conjecture,
    ( product(X1,e_2,e_3)
    | ~ product(e_3,e_1,X1) ),
    inference(spm,[status(thm)],[c_0_99,c_0_127]),
    [final] ).

cnf(c_0_189,negated_conjecture,
    ( product(X1,e_4,e_3)
    | ~ product(e_3,e_2,X1) ),
    inference(spm,[status(thm)],[c_0_99,c_0_120]),
    [final] ).

cnf(c_0_190,plain,
    ( product(e_3,e_1,e_3)
    | ~ product(e_3,e_2,e_4) ),
    inference(spm,[status(thm)],[c_0_56,c_0_152]),
    [final] ).

cnf(c_0_191,negated_conjecture,
    ( product(X1,e_3,e_2)
    | ~ product(e_2,e_4,X1) ),
    inference(spm,[status(thm)],[c_0_99,c_0_141]),
    [final] ).

cnf(c_0_192,negated_conjecture,
    ( product(e_2,e_4,e_2)
    | ~ product(e_3,e_1,e_2) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_137]),c_0_48]),
    [final] ).

cnf(c_0_193,plain,
    ( product(e_2,e_3,e_2)
    | ~ product(e_1,e_2,e_3) ),
    inference(spm,[status(thm)],[c_0_159,c_0_84]),
    [final] ).

cnf(c_0_194,plain,
    ( product(e_2,e_3,e_2)
    | ~ product(e_3,e_4,e_3) ),
    inference(spm,[status(thm)],[c_0_160,c_0_84]),
    [final] ).

cnf(c_0_195,plain,
    ( product(e_2,e_3,e_2)
    | ~ product(e_1,e_2,e_2) ),
    inference(spm,[status(thm)],[c_0_89,c_0_84]),
    [final] ).

cnf(c_0_196,plain,
    ( ~ product(e_2,e_1,e_2)
    | ~ product(e_3,e_1,e_3) ),
    inference(spm,[status(thm)],[c_0_51,c_0_161]),
    [final] ).

cnf(c_0_197,plain,
    ( ~ product(e_4,e_2,e_2)
    | ~ product(e_3,e_1,e_3) ),
    inference(spm,[status(thm)],[c_0_56,c_0_161]),
    [final] ).

cnf(c_0_198,plain,
    ( ~ product(e_4,e_3,e_2)
    | ~ product(e_3,e_1,e_3) ),
    inference(spm,[status(thm)],[c_0_65,c_0_161]),
    [final] ).

cnf(c_0_199,plain,
    ( ~ product(e_2,e_1,e_2)
    | ~ product(e_4,e_3,e_3) ),
    inference(spm,[status(thm)],[c_0_51,c_0_162]),
    [final] ).

cnf(c_0_200,plain,
    ( ~ product(e_3,e_1,e_2)
    | ~ product(e_4,e_3,e_3) ),
    inference(spm,[status(thm)],[c_0_94,c_0_162]),
    [final] ).

cnf(c_0_201,plain,
    ( ~ product(e_4,e_2,e_2)
    | ~ product(e_4,e_3,e_3) ),
    inference(spm,[status(thm)],[c_0_56,c_0_162]),
    [final] ).

cnf(c_0_202,plain,
    ( product(e_2,e_4,e_2)
    | ~ product(e_3,e_2,e_2) ),
    inference(spm,[status(thm)],[c_0_73,c_0_163]),
    [final] ).

cnf(c_0_203,negated_conjecture,
    ( product(X1,e_2,e_4)
    | ~ product(e_3,e_4,e_3)
    | ~ product(e_4,e_1,X1) ),
    inference(spm,[status(thm)],[c_0_99,c_0_128]),
    [final] ).

cnf(c_0_204,plain,
    ( ~ product(e_1,e_2,e_2)
    | ~ product(e_2,e_4,e_3) ),
    inference(spm,[status(thm)],[c_0_73,c_0_164]),
    [final] ).

cnf(c_0_205,plain,
    ( ~ product(e_2,e_4,e_2)
    | ~ product(e_3,e_4,e_3) ),
    inference(spm,[status(thm)],[c_0_40,c_0_128]),
    [final] ).

cnf(c_0_206,plain,
    ( ~ product(e_1,e_2,e_2)
    | ~ product(e_3,e_4,e_3) ),
    inference(spm,[status(thm)],[c_0_73,c_0_128]),
    [final] ).

cnf(c_0_207,negated_conjecture,
    ( product(X1,e_2,e_4)
    | ~ product(e_1,e_2,e_3)
    | ~ product(e_4,e_1,X1) ),
    inference(spm,[status(thm)],[c_0_99,c_0_131]),
    [final] ).

cnf(c_0_208,negated_conjecture,
    ( product(X1,e_2,e_4)
    | ~ product(e_1,e_3,e_3)
    | ~ product(e_4,e_1,X1) ),
    inference(spm,[status(thm)],[c_0_99,c_0_165]),
    [final] ).

cnf(c_0_209,plain,
    ( ~ product(e_2,e_4,e_2)
    | ~ product(e_1,e_2,e_3) ),
    inference(spm,[status(thm)],[c_0_40,c_0_131]),
    [final] ).

cnf(c_0_210,plain,
    ( ~ product(e_2,e_4,e_2)
    | ~ product(e_1,e_3,e_3) ),
    inference(spm,[status(thm)],[c_0_40,c_0_165]),
    [final] ).

cnf(c_0_211,plain,
    ( ~ product(e_1,e_2,e_2)
    | ~ product(e_1,e_3,e_3) ),
    inference(spm,[status(thm)],[c_0_73,c_0_165]),
    [final] ).

cnf(c_0_212,plain,
    ( product(e_4,e_3,e_3)
    | product(e_4,e_3,e_2)
    | ~ product(e_2,e_3,e_1) ),
    inference(spm,[status(thm)],[c_0_51,c_0_86]),
    [final] ).

cnf(c_0_213,negated_conjecture,
    ( product(X1,X2,X2)
    | ~ product(X2,X2,X1) ),
    inference(spm,[status(thm)],[c_0_99,c_0_41]),
    [final] ).

cnf(c_0_214,plain,
    ( ~ product(X1,e_1,e_2)
    | ~ next(X1,e_1) ),
    inference(spm,[status(thm)],[c_0_32,c_0_166]),
    [final] ).

cnf(c_0_215,plain,
    ( ~ product(X1,e_1,e_3)
    | ~ next(X1,e_1) ),
    inference(spm,[status(thm)],[c_0_32,c_0_167]),
    [final] ).

cnf(c_0_216,plain,
    ( ~ product(X1,e_1,e_4)
    | ~ next(X1,e_1) ),
    inference(spm,[status(thm)],[c_0_32,c_0_168]),
    [final] ).

cnf(c_0_217,negated_conjecture,
    ~ product(e_4,e_3,e_3),
    inference(spm,[status(thm)],[c_0_169,c_0_155]),
    [final] ).

cnf(c_0_218,negated_conjecture,
    ~ product(e_3,e_1,e_3),
    inference(spm,[status(thm)],[c_0_170,c_0_156]),
    [final] ).

cnf(c_0_219,plain,
    ~ product(e_3,e_3,e_4),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_171]),c_0_41])]),
    [final] ).

cnf(c_0_220,negated_conjecture,
    ~ product(e_1,e_4,e_2),
    inference(spm,[status(thm)],[c_0_172,c_0_158]),
    [final] ).

cnf(c_0_221,negated_conjecture,
    ~ product(e_3,e_2,e_2),
    inference(spm,[status(thm)],[c_0_173,c_0_134]),
    [final] ).

cnf(c_0_222,negated_conjecture,
    ~ product(e_3,e_2,e_4),
    inference(spm,[status(thm)],[c_0_174,c_0_134]),
    [final] ).

cnf(c_0_223,negated_conjecture,
    ~ product(e_1,e_3,e_3),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_165]),c_0_118]),
    [final] ).

cnf(c_0_224,plain,
    ~ product(e_3,e_3,e_1),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_175]),c_0_41])]),
    [final] ).

cnf(c_0_225,plain,
    ~ product(e_2,e_2,e_4),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_176]),c_0_41])]),
    [final] ).

cnf(c_0_226,plain,
    ~ product(e_2,e_2,e_3),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_177]),c_0_41])]),
    [final] ).

cnf(c_0_227,plain,
    ~ product(e_3,e_2,e_3),
    inference(spm,[status(thm)],[c_0_89,c_0_41]),
    [final] ).

cnf(c_0_228,plain,
    ~ product(e_1,e_1,e_2),
    inference(spm,[status(thm)],[c_0_173,c_0_41]),
    [final] ).

cnf(c_0_229,plain,
    ~ product(e_3,e_3,e_2),
    inference(spm,[status(thm)],[c_0_172,c_0_41]),
    [final] ).

cnf(c_0_230,plain,
    ~ product(e_4,e_4,e_2),
    inference(spm,[status(thm)],[c_0_119,c_0_41]),
    [final] ).

cnf(c_0_231,plain,
    ~ product(e_4,e_4,e_3),
    inference(spm,[status(thm)],[c_0_170,c_0_41]),
    [final] ).

cnf(c_0_232,plain,
    ~ product(e_1,e_1,e_3),
    inference(spm,[status(thm)],[c_0_178,c_0_179]),
    [final] ).

cnf(c_0_233,plain,
    ~ product(e_1,e_1,e_4),
    inference(spm,[status(thm)],[c_0_180,c_0_179]),
    [final] ).

cnf(c_0_234,axiom,
    ~ equalish(e_3,e_4),
    e_3_is_not_e_4,
    [final] ).

cnf(c_0_235,axiom,
    ~ equalish(e_2,e_4),
    e_2_is_not_e_4,
    [final] ).

cnf(c_0_236,axiom,
    ~ equalish(e_2,e_3),
    e_2_is_not_e_3,
    [final] ).

cnf(c_0_237,axiom,
    ~ equalish(e_1,e_4),
    e_1_is_not_e_4,
    [final] ).

cnf(c_0_238,axiom,
    ~ equalish(e_1,e_3),
    e_1_is_not_e_3,
    [final] ).

cnf(c_0_239,axiom,
    ~ equalish(e_1,e_2),
    e_1_is_not_e_2,
    [final] ).

cnf(c_0_240,axiom,
    next(e_3,e_4),
    e_3_then_e_4,
    [final] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : GRP125-2.004 : TPTP v9.2.1. Released v1.2.0.
% 0.00/0.12  % Command    : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33  % Computer : n021.cluster.edu
% 0.16/0.33  % Model    : x86_64 x86_64
% 0.16/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33  % Memory   : 8042.1875MB
% 0.16/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33  % CPULimit   : 300
% 0.16/0.33  % WCLimit    : 300
% 0.16/0.33  % DateTime   : Mon May  4 18:23:40 EDT 2026
% 0.16/0.33  % CPUTime    : 
% 0.16/0.34  % start to proof: theBenchmark
% 1.28/1.73  % Version  : CSE_E---1.7
% 1.28/1.73  % Problem  : theBenchmark.p
% 1.28/1.73  % SZS status Satisfiable for theBenchmark.p
% 1.28/1.73  % SZS output start Saturation
% See solution above
% 1.28/1.73  % Total time : 1.372s
%------------------------------------------------------------------------------