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CSE_E---1.7.UNS-CRf.s

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%------------------------------------------------------------------------------
% File     : CSE_E---1.7
% Problem  : GRP134-2.003 : TPTP v9.2.1. Released v1.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d

% Computer : n024.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 04:24:32 PM UTC 2026

% Result   : Unsatisfiable 1.13s 1.62s
% Output   : CNFRefutation 1.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   25
%            Number of leaves      :   14
% Syntax   : Number of clauses     :  110 (  27 unt;  38 nHn; 110 RR)
%            Number of literals    :  243 (   0 equ; 107 neg)
%            Maximal clause size   :    5 (   2 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    6 (   5 usr;   1 prp; 0-3 aty)
%            Number of functors    :    3 (   3 usr;   3 con; 0-0 aty)
%            Number of variables   :   68 (   0 sgn)

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

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

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

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

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

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

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

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

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

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

cnf(qg4,negated_conjecture,
    ( product(X3,X4,X2)
    | ~ product(X1,X2,X3)
    | ~ product(X2,X1,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg4) ).

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

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

cnf(c_0_14,axiom,
    ( ~ product(X1,e_1,X2)
    | ~ next(X1,X3)
    | ~ greater(X2,X3) ),
    no_redundancy ).

cnf(c_0_15,axiom,
    greater(e_3,e_2),
    e_3_greater_e_2 ).

cnf(c_0_16,axiom,
    ( product(X1,X2,e_1)
    | product(X1,X2,e_2)
    | product(X1,X2,e_3)
    | ~ group_element(X1)
    | ~ group_element(X2) ),
    product_total_function1 ).

cnf(c_0_17,axiom,
    group_element(e_1),
    element_1 ).

cnf(c_0_18,plain,
    ( ~ product(X1,e_1,e_3)
    | ~ next(X1,e_2) ),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_19,axiom,
    next(e_1,e_2),
    e_1_then_e_2 ).

cnf(c_0_20,axiom,
    ~ equalish(e_2,e_1),
    e_2_is_not_e_1 ).

cnf(c_0_21,axiom,
    ( equalish(X1,X4)
    | ~ product(X1,X2,X3)
    | ~ product(X4,X2,X3) ),
    product_left_cancellation ).

cnf(c_0_22,plain,
    ( 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_16,c_0_17]) ).

cnf(c_0_23,plain,
    ~ product(e_1,e_1,e_3),
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_24,axiom,
    ~ equalish(e_3,e_1),
    e_3_is_not_e_1 ).

cnf(c_0_25,plain,
    ( ~ product(e_1,X1,X2)
    | ~ product(e_2,X1,X2) ),
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_26,plain,
    ( product(e_1,e_1,e_1)
    | product(e_1,e_1,e_2) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_17]),c_0_23]) ).

cnf(c_0_27,axiom,
    group_element(e_3),
    element_3 ).

cnf(c_0_28,axiom,
    ( equalish(X2,X4)
    | ~ product(X1,X2,X3)
    | ~ product(X1,X4,X3) ),
    product_right_cancellation ).

cnf(c_0_29,axiom,
    ~ equalish(e_3,e_2),
    e_3_is_not_e_2 ).

cnf(c_0_30,plain,
    ( ~ product(e_1,X1,X2)
    | ~ product(e_3,X1,X2) ),
    inference(spm,[status(thm)],[c_0_24,c_0_21]) ).

cnf(c_0_31,plain,
    ( product(e_1,e_1,e_2)
    | ~ product(e_2,e_1,e_1) ),
    inference(spm,[status(thm)],[c_0_25,c_0_26]) ).

cnf(c_0_32,plain,
    ( 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_16,c_0_27]) ).

cnf(c_0_33,plain,
    ( ~ product(X1,e_1,X2)
    | ~ product(X1,e_3,X2) ),
    inference(spm,[status(thm)],[c_0_24,c_0_28]) ).

cnf(c_0_34,plain,
    ( ~ product(e_2,X1,X2)
    | ~ product(e_3,X1,X2) ),
    inference(spm,[status(thm)],[c_0_29,c_0_21]) ).

cnf(c_0_35,plain,
    ( product(e_3,e_1,e_1)
    | product(e_3,e_1,e_2)
    | product(e_3,e_1,e_3) ),
    inference(spm,[status(thm)],[c_0_22,c_0_27]) ).

cnf(c_0_36,plain,
    ( ~ product(e_3,e_1,e_2)
    | ~ product(e_2,e_1,e_1) ),
    inference(spm,[status(thm)],[c_0_30,c_0_31]) ).

cnf(c_0_37,negated_conjecture,
    ( product(X3,X4,X2)
    | ~ product(X1,X2,X3)
    | ~ product(X2,X1,X4) ),
    qg4 ).

cnf(c_0_38,plain,
    ( product(e_3,e_3,e_1)
    | product(e_3,e_3,e_2)
    | product(e_3,e_3,e_3) ),
    inference(spm,[status(thm)],[c_0_32,c_0_27]) ).

cnf(c_0_39,axiom,
    group_element(e_2),
    element_2 ).

cnf(c_0_40,plain,
    ( ~ product(X1,e_1,X2)
    | ~ product(X1,e_2,X2) ),
    inference(spm,[status(thm)],[c_0_20,c_0_28]) ).

cnf(c_0_41,plain,
    ( product(e_1,e_1,e_2)
    | ~ product(e_1,e_3,e_1) ),
    inference(spm,[status(thm)],[c_0_33,c_0_26]) ).

cnf(c_0_42,plain,
    ( product(e_3,e_1,e_3)
    | ~ product(e_2,e_1,e_1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]) ).

cnf(c_0_43,negated_conjecture,
    ( product(e_3,e_3,e_3)
    | product(e_3,e_3,e_2)
    | product(X1,e_1,e_3)
    | ~ product(e_3,e_3,X1) ),
    inference(spm,[status(thm)],[c_0_37,c_0_38]) ).

cnf(c_0_44,plain,
    ( ~ product(X1,e_2,X2)
    | ~ product(X1,e_3,X2) ),
    inference(spm,[status(thm)],[c_0_29,c_0_28]) ).

cnf(c_0_45,plain,
    ( product(e_1,e_3,e_1)
    | product(e_1,e_3,e_2)
    | product(e_1,e_3,e_3) ),
    inference(spm,[status(thm)],[c_0_32,c_0_17]) ).

cnf(c_0_46,plain,
    ( 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_16,c_0_39]) ).

cnf(c_0_47,plain,
    ( ~ product(e_1,e_2,e_2)
    | ~ product(e_1,e_3,e_1) ),
    inference(spm,[status(thm)],[c_0_40,c_0_41]) ).

cnf(c_0_48,plain,
    ( ~ product(e_3,e_3,e_3)
    | ~ product(e_2,e_1,e_1) ),
    inference(spm,[status(thm)],[c_0_33,c_0_42]) ).

cnf(c_0_49,negated_conjecture,
    ( product(e_3,e_3,e_2)
    | product(e_3,e_3,e_3) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_38]),c_0_23]) ).

cnf(c_0_50,plain,
    ( product(e_1,e_3,e_3)
    | product(e_1,e_3,e_2)
    | ~ product(e_1,e_2,e_1) ),
    inference(spm,[status(thm)],[c_0_44,c_0_45]) ).

cnf(c_0_51,plain,
    ( product(e_1,e_2,e_1)
    | product(e_1,e_2,e_2)
    | product(e_1,e_2,e_3) ),
    inference(spm,[status(thm)],[c_0_46,c_0_17]) ).

cnf(c_0_52,plain,
    ( product(e_1,e_3,e_3)
    | ~ product(e_1,e_2,e_2) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_45]),c_0_44]) ).

cnf(c_0_53,negated_conjecture,
    ( product(e_3,e_3,e_2)
    | ~ product(e_2,e_1,e_1) ),
    inference(spm,[status(thm)],[c_0_48,c_0_49]) ).

cnf(c_0_54,plain,
    ( product(e_1,e_2,e_3)
    | product(e_1,e_3,e_2)
    | product(e_1,e_3,e_3) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52]) ).

cnf(c_0_55,negated_conjecture,
    ( ~ product(e_2,e_3,e_2)
    | ~ product(e_2,e_1,e_1) ),
    inference(spm,[status(thm)],[c_0_34,c_0_53]) ).

cnf(c_0_56,plain,
    ( product(e_2,e_1,e_1)
    | product(e_2,e_1,e_2)
    | product(e_2,e_1,e_3) ),
    inference(spm,[status(thm)],[c_0_22,c_0_39]) ).

cnf(c_0_57,plain,
    ( product(e_1,e_1,e_2)
    | ~ product(e_1,e_2,e_1) ),
    inference(spm,[status(thm)],[c_0_40,c_0_26]) ).

cnf(c_0_58,plain,
    ( product(e_1,e_3,e_2)
    | product(e_1,e_2,e_3)
    | ~ product(e_3,e_3,e_3) ),
    inference(spm,[status(thm)],[c_0_30,c_0_54]) ).

cnf(c_0_59,axiom,
    ( equalish(X3,X4)
    | ~ product(X1,X2,X3)
    | ~ product(X1,X2,X4) ),
    product_total_function2 ).

cnf(c_0_60,negated_conjecture,
    ( product(e_2,e_1,e_3)
    | ~ product(e_2,e_3,e_2) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_33]) ).

cnf(c_0_61,plain,
    ( ~ product(e_1,e_3,e_2)
    | ~ product(e_1,e_2,e_1) ),
    inference(spm,[status(thm)],[c_0_33,c_0_57]) ).

cnf(c_0_62,negated_conjecture,
    ( product(e_3,e_3,e_2)
    | product(e_1,e_2,e_3)
    | product(e_1,e_3,e_2) ),
    inference(spm,[status(thm)],[c_0_58,c_0_49]) ).

cnf(c_0_63,plain,
    ( ~ product(X1,X2,e_1)
    | ~ product(X1,X2,e_3) ),
    inference(spm,[status(thm)],[c_0_24,c_0_59]) ).

cnf(c_0_64,plain,
    ( ~ product(X1,X2,e_2)
    | ~ product(X1,X2,e_3) ),
    inference(spm,[status(thm)],[c_0_29,c_0_59]) ).

cnf(c_0_65,negated_conjecture,
    ( product(X1,e_3,e_2)
    | ~ product(e_2,e_3,e_2)
    | ~ product(e_1,e_2,X1) ),
    inference(spm,[status(thm)],[c_0_37,c_0_60]) ).

cnf(c_0_66,negated_conjecture,
    ( product(e_3,e_3,e_2)
    | ~ product(e_1,e_2,e_1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_63]) ).

cnf(c_0_67,negated_conjecture,
    ( product(e_3,e_3,e_2)
    | ~ product(e_1,e_2,e_2) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_62]),c_0_64]) ).

cnf(c_0_68,plain,
    ( product(e_3,e_2,e_1)
    | product(e_3,e_2,e_2)
    | product(e_3,e_2,e_3) ),
    inference(spm,[status(thm)],[c_0_46,c_0_27]) ).

cnf(c_0_69,plain,
    ( product(e_2,e_3,e_1)
    | product(e_2,e_3,e_2)
    | product(e_2,e_3,e_3) ),
    inference(spm,[status(thm)],[c_0_32,c_0_39]) ).

cnf(c_0_70,negated_conjecture,
    ~ product(e_2,e_3,e_2),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_62]),c_0_65]),c_0_34]) ).

cnf(c_0_71,negated_conjecture,
    ( product(e_1,e_2,e_3)
    | product(e_3,e_3,e_2) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_51]),c_0_67]) ).

cnf(c_0_72,plain,
    ( product(e_2,e_2,e_1)
    | product(e_2,e_2,e_2)
    | product(e_2,e_2,e_3) ),
    inference(spm,[status(thm)],[c_0_46,c_0_39]) ).

cnf(c_0_73,negated_conjecture,
    ( product(e_3,e_2,e_3)
    | product(e_3,e_2,e_2)
    | product(X1,e_1,e_3)
    | ~ product(e_2,e_3,X1) ),
    inference(spm,[status(thm)],[c_0_37,c_0_68]) ).

cnf(c_0_74,plain,
    ( product(e_2,e_3,e_3)
    | product(e_2,e_3,e_1) ),
    inference(sr,[status(thm)],[c_0_69,c_0_70]) ).

cnf(c_0_75,negated_conjecture,
    ( product(e_3,e_3,e_2)
    | ~ product(e_2,e_2,e_3) ),
    inference(spm,[status(thm)],[c_0_25,c_0_71]) ).

cnf(c_0_76,negated_conjecture,
    ( product(e_2,e_2,e_3)
    | product(e_2,e_2,e_2)
    | product(X1,e_1,e_2)
    | ~ product(e_2,e_2,X1) ),
    inference(spm,[status(thm)],[c_0_37,c_0_72]) ).

cnf(c_0_77,negated_conjecture,
    ( product(e_2,e_3,e_3)
    | product(e_3,e_2,e_2)
    | product(e_3,e_2,e_3) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_23]) ).

cnf(c_0_78,negated_conjecture,
    ( ~ product(e_3,e_2,e_2)
    | ~ product(e_2,e_2,e_3) ),
    inference(spm,[status(thm)],[c_0_44,c_0_75]) ).

cnf(c_0_79,negated_conjecture,
    ( product(e_1,e_1,e_2)
    | product(e_2,e_2,e_2)
    | product(e_2,e_2,e_3) ),
    inference(spm,[status(thm)],[c_0_76,c_0_72]) ).

cnf(c_0_80,negated_conjecture,
    ~ product(e_2,e_2,e_3),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_77]),c_0_78]),c_0_44]) ).

cnf(c_0_81,plain,
    ( product(e_1,e_3,e_3)
    | product(e_1,e_3,e_2)
    | ~ product(e_2,e_3,e_1) ),
    inference(spm,[status(thm)],[c_0_25,c_0_45]) ).

cnf(c_0_82,negated_conjecture,
    ( product(e_2,e_2,e_2)
    | product(e_1,e_1,e_2) ),
    inference(sr,[status(thm)],[c_0_79,c_0_80]) ).

cnf(c_0_83,plain,
    ( product(e_2,e_3,e_3)
    | product(e_1,e_3,e_2)
    | product(e_1,e_3,e_3) ),
    inference(spm,[status(thm)],[c_0_81,c_0_74]) ).

cnf(c_0_84,negated_conjecture,
    ( product(e_2,e_2,e_2)
    | ~ product(e_1,e_3,e_2) ),
    inference(spm,[status(thm)],[c_0_33,c_0_82]) ).

cnf(c_0_85,plain,
    ( product(e_1,e_3,e_2)
    | ~ product(e_3,e_3,e_3) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_83]),c_0_34]) ).

cnf(c_0_86,negated_conjecture,
    ( product(e_1,e_3,e_3)
    | product(e_1,e_3,e_2)
    | product(X1,e_1,e_1)
    | ~ product(e_3,e_1,X1) ),
    inference(spm,[status(thm)],[c_0_37,c_0_45]) ).

cnf(c_0_87,plain,
    ( ~ product(e_1,e_3,e_2)
    | ~ product(e_2,e_1,e_1) ),
    inference(spm,[status(thm)],[c_0_33,c_0_31]) ).

cnf(c_0_88,plain,
    ( product(e_2,e_1,e_3)
    | product(e_2,e_1,e_2)
    | ~ product(e_2,e_3,e_1) ),
    inference(spm,[status(thm)],[c_0_33,c_0_56]) ).

cnf(c_0_89,negated_conjecture,
    ( product(e_2,e_2,e_2)
    | ~ product(e_3,e_3,e_3) ),
    inference(spm,[status(thm)],[c_0_84,c_0_85]) ).

cnf(c_0_90,negated_conjecture,
    ( product(e_1,e_3,e_3)
    | ~ product(e_2,e_1,e_1) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_42]),c_0_34]),c_0_87]) ).

cnf(c_0_91,negated_conjecture,
    ~ product(e_2,e_1,e_2),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_82]),c_0_40]) ).

cnf(c_0_92,plain,
    ( product(e_2,e_3,e_3)
    | product(e_2,e_1,e_2)
    | product(e_2,e_1,e_3) ),
    inference(spm,[status(thm)],[c_0_88,c_0_74]) ).

cnf(c_0_93,negated_conjecture,
    ~ product(e_1,e_2,e_2),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_82]),c_0_25]) ).

cnf(c_0_94,negated_conjecture,
    ( product(e_3,e_3,e_2)
    | product(e_2,e_2,e_2) ),
    inference(spm,[status(thm)],[c_0_89,c_0_49]) ).

cnf(c_0_95,negated_conjecture,
    ( ~ product(e_2,e_3,e_3)
    | ~ product(e_2,e_1,e_1) ),
    inference(spm,[status(thm)],[c_0_25,c_0_90]) ).

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

cnf(c_0_97,plain,
    ( product(e_2,e_1,e_3)
    | product(e_2,e_3,e_3) ),
    inference(sr,[status(thm)],[c_0_92,c_0_91]) ).

cnf(c_0_98,plain,
    ( ~ product(e_3,e_1,e_2)
    | ~ product(e_1,e_2,e_1) ),
    inference(spm,[status(thm)],[c_0_30,c_0_57]) ).

cnf(c_0_99,plain,
    ( product(e_1,e_2,e_3)
    | product(e_1,e_2,e_1) ),
    inference(sr,[status(thm)],[c_0_51,c_0_93]) ).

cnf(c_0_100,negated_conjecture,
    ~ product(e_3,e_2,e_2),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_94]),c_0_34]) ).

cnf(c_0_101,negated_conjecture,
    product(e_2,e_1,e_3),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_97]) ).

cnf(c_0_102,plain,
    ( product(e_1,e_2,e_3)
    | ~ product(e_3,e_1,e_2) ),
    inference(spm,[status(thm)],[c_0_98,c_0_99]) ).

cnf(c_0_103,negated_conjecture,
    ( product(e_3,e_2,e_3)
    | product(e_2,e_3,e_3) ),
    inference(sr,[status(thm)],[c_0_77,c_0_100]) ).

cnf(c_0_104,negated_conjecture,
    ~ product(e_2,e_3,e_3),
    inference(spm,[status(thm)],[c_0_33,c_0_101]) ).

cnf(c_0_105,plain,
    ( ~ product(e_3,e_2,e_3)
    | ~ product(e_3,e_1,e_2) ),
    inference(spm,[status(thm)],[c_0_30,c_0_102]) ).

cnf(c_0_106,negated_conjecture,
    product(e_3,e_2,e_3),
    inference(sr,[status(thm)],[c_0_103,c_0_104]) ).

cnf(c_0_107,negated_conjecture,
    ( product(e_2,e_3,e_3)
    | product(X1,e_1,e_2)
    | ~ product(e_3,e_2,X1) ),
    inference(spm,[status(thm)],[c_0_37,c_0_74]) ).

cnf(c_0_108,plain,
    ~ product(e_3,e_1,e_2),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_105,c_0_106])]) ).

cnf(c_0_109,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_106]),c_0_104]),c_0_108]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06  % Problem    : GRP134-2.003 : TPTP v9.2.1. Released v1.2.0.
% 0.00/0.06  % Command    : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.07/0.24  % Computer : n024.cluster.edu
% 0.07/0.24  % Model    : x86_64 x86_64
% 0.07/0.24  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.24  % Memory   : 8042.1875MB
% 0.07/0.24  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.07/0.24  % CPULimit   : 300
% 0.07/0.24  % WCLimit    : 300
% 0.07/0.24  % DateTime   : Mon May  4 13:24:56 EDT 2026
% 0.07/0.24  % CPUTime    : 
% 0.07/0.25  % start to proof: theBenchmark
% 1.13/1.62  % Version  : CSE_E---1.7
% 1.13/1.62  % Problem  : theBenchmark.p
% 1.13/1.62  % SZS status Unsatisfiable for theBenchmark.p
% 1.13/1.62  % SZS output start CNFRefutation
% See solution above
% 1.13/1.62  % Total time : 1.360s
%------------------------------------------------------------------------------