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CSE_E---1.7.UNS-CRf.s

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%------------------------------------------------------------------------------
% File     : CSE_E---1.7
% Problem  : FLD041-4 : TPTP v9.2.1. Bugfixed v2.1.0.
% 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 : n008.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 04:18:21 PM UTC 2026

% Result   : Unsatisfiable 14.42s 11.53s
% Output   : CNFRefutation 14.52s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   24
%            Number of leaves      :   23
% Syntax   : Number of clauses     :  100 (  39 unt;   3 nHn; 100 RR)
%            Number of literals    :  230 (   0 equ; 131 neg)
%            Maximal clause size   :    5 (   2 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :    8 (   8 usr;   5 con; 0-2 aty)
%            Number of variables   :  181 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(associativity_multiplication_1,axiom,
    ( product(X1,X2,X3)
    | ~ product(X1,X4,X5)
    | ~ product(X4,X6,X2)
    | ~ product(X5,X6,X3) ),
    file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',associativity_multiplication_1) ).

cnf(product_6,negated_conjecture,
    product(a,b,c),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_6) ).

cnf(existence_of_identity_multiplication,axiom,
    ( product(multiplicative_identity,X1,X1)
    | ~ defined(X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',existence_of_identity_multiplication) ).

cnf(a_is_defined,hypothesis,
    defined(a),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).

cnf(distributivity_2,axiom,
    ( product(X1,X2,X3)
    | ~ sum(X4,X5,X1)
    | ~ product(X4,X2,X6)
    | ~ product(X5,X2,X7)
    | ~ sum(X6,X7,X3) ),
    file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',distributivity_2) ).

cnf(sum_7,negated_conjecture,
    sum(additive_identity,c,additive_identity),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_7) ).

cnf(commutativity_multiplication,axiom,
    ( product(X1,X2,X3)
    | ~ product(X2,X1,X3) ),
    file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',commutativity_multiplication) ).

cnf(existence_of_identity_addition,axiom,
    ( sum(additive_identity,X1,X1)
    | ~ defined(X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',existence_of_identity_addition) ).

cnf(c_is_defined,hypothesis,
    defined(c),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_is_defined) ).

cnf(associativity_multiplication_2,axiom,
    ( product(X1,X2,X3)
    | ~ product(X4,X5,X1)
    | ~ product(X5,X2,X6)
    | ~ product(X4,X6,X3) ),
    file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',associativity_multiplication_2) ).

cnf(well_definedness_of_additive_identity,axiom,
    defined(additive_identity),
    file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',well_definedness_of_additive_identity) ).

cnf(distributivity_1,axiom,
    ( sum(X1,X2,X3)
    | ~ sum(X4,X5,X6)
    | ~ product(X6,X7,X3)
    | ~ product(X4,X7,X1)
    | ~ product(X5,X7,X2) ),
    file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',distributivity_1) ).

cnf(commutativity_addition,axiom,
    ( sum(X1,X2,X3)
    | ~ sum(X2,X1,X3) ),
    file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',commutativity_addition) ).

cnf(totality_of_multiplication,axiom,
    ( product(X1,X2,multiply(X1,X2))
    | ~ defined(X1)
    | ~ defined(X2) ),
    file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',totality_of_multiplication) ).

cnf(associativity_addition_2,axiom,
    ( sum(X1,X2,X3)
    | ~ sum(X4,X5,X1)
    | ~ sum(X5,X2,X6)
    | ~ sum(X4,X6,X3) ),
    file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',associativity_addition_2) ).

cnf(b_is_defined,hypothesis,
    defined(b),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_is_defined) ).

cnf(well_definedness_of_multiplication,axiom,
    ( defined(multiply(X1,X2))
    | ~ defined(X1)
    | ~ defined(X2) ),
    file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplication) ).

cnf(well_definedness_of_multiplicative_identity,axiom,
    defined(multiplicative_identity),
    file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplicative_identity) ).

cnf(existence_of_inverse_multiplication,axiom,
    ( product(multiplicative_inverse(X1),X1,multiplicative_identity)
    | sum(additive_identity,X1,additive_identity)
    | ~ defined(X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',existence_of_inverse_multiplication) ).

cnf(not_sum_5,negated_conjecture,
    ~ sum(additive_identity,b,additive_identity),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_sum_5) ).

cnf(existence_of_inverse_addition,axiom,
    ( sum(additive_inverse(X1),X1,additive_identity)
    | ~ defined(X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',existence_of_inverse_addition) ).

cnf(associativity_addition_1,axiom,
    ( sum(X1,X2,X3)
    | ~ sum(X1,X4,X5)
    | ~ sum(X4,X6,X2)
    | ~ sum(X5,X6,X3) ),
    file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',associativity_addition_1) ).

cnf(not_sum_4,negated_conjecture,
    ~ sum(additive_identity,a,additive_identity),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_sum_4) ).

cnf(c_0_23,axiom,
    ( product(X1,X2,X3)
    | ~ product(X1,X4,X5)
    | ~ product(X4,X6,X2)
    | ~ product(X5,X6,X3) ),
    associativity_multiplication_1 ).

cnf(c_0_24,negated_conjecture,
    product(a,b,c),
    product_6 ).

cnf(c_0_25,negated_conjecture,
    ( product(X1,X2,c)
    | ~ product(X3,b,X2)
    | ~ product(X1,X3,a) ),
    inference(spm,[status(thm)],[c_0_23,c_0_24]) ).

cnf(c_0_26,negated_conjecture,
    ( product(X1,c,c)
    | ~ product(X1,a,a) ),
    inference(spm,[status(thm)],[c_0_25,c_0_24]) ).

cnf(c_0_27,axiom,
    ( product(multiplicative_identity,X1,X1)
    | ~ defined(X1) ),
    existence_of_identity_multiplication ).

cnf(c_0_28,hypothesis,
    defined(a),
    a_is_defined ).

cnf(c_0_29,axiom,
    ( product(X1,X2,X3)
    | ~ sum(X4,X5,X1)
    | ~ product(X4,X2,X6)
    | ~ product(X5,X2,X7)
    | ~ sum(X6,X7,X3) ),
    distributivity_2 ).

cnf(c_0_30,negated_conjecture,
    sum(additive_identity,c,additive_identity),
    sum_7 ).

cnf(c_0_31,axiom,
    ( product(X1,X2,X3)
    | ~ product(X2,X1,X3) ),
    commutativity_multiplication ).

cnf(c_0_32,negated_conjecture,
    product(multiplicative_identity,c,c),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28])]) ).

cnf(c_0_33,negated_conjecture,
    ( product(X1,X2,additive_identity)
    | ~ product(X3,X2,c)
    | ~ product(X4,X2,additive_identity)
    | ~ sum(X4,X3,X1) ),
    inference(spm,[status(thm)],[c_0_29,c_0_30]) ).

cnf(c_0_34,negated_conjecture,
    product(c,multiplicative_identity,c),
    inference(spm,[status(thm)],[c_0_31,c_0_32]) ).

cnf(c_0_35,negated_conjecture,
    ( product(X1,multiplicative_identity,additive_identity)
    | ~ product(X2,multiplicative_identity,additive_identity)
    | ~ sum(X2,c,X1) ),
    inference(spm,[status(thm)],[c_0_33,c_0_34]) ).

cnf(c_0_36,axiom,
    ( sum(additive_identity,X1,X1)
    | ~ defined(X1) ),
    existence_of_identity_addition ).

cnf(c_0_37,hypothesis,
    defined(c),
    c_is_defined ).

cnf(c_0_38,axiom,
    ( product(X1,X2,X3)
    | ~ product(X4,X5,X1)
    | ~ product(X5,X2,X6)
    | ~ product(X4,X6,X3) ),
    associativity_multiplication_2 ).

cnf(c_0_39,negated_conjecture,
    ( product(c,multiplicative_identity,additive_identity)
    | ~ product(additive_identity,multiplicative_identity,additive_identity) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37])]) ).

cnf(c_0_40,plain,
    ( product(X1,multiplicative_identity,X1)
    | ~ defined(X1) ),
    inference(spm,[status(thm)],[c_0_31,c_0_27]) ).

cnf(c_0_41,axiom,
    defined(additive_identity),
    well_definedness_of_additive_identity ).

cnf(c_0_42,axiom,
    ( sum(X1,X2,X3)
    | ~ sum(X4,X5,X6)
    | ~ product(X6,X7,X3)
    | ~ product(X4,X7,X1)
    | ~ product(X5,X7,X2) ),
    distributivity_1 ).

cnf(c_0_43,plain,
    ( product(X1,X2,X3)
    | ~ product(X4,multiplicative_identity,X1)
    | ~ product(X4,X2,X3)
    | ~ defined(X2) ),
    inference(spm,[status(thm)],[c_0_38,c_0_27]) ).

cnf(c_0_44,negated_conjecture,
    product(c,multiplicative_identity,additive_identity),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41])]) ).

cnf(c_0_45,axiom,
    ( sum(X1,X2,X3)
    | ~ sum(X2,X1,X3) ),
    commutativity_addition ).

cnf(c_0_46,negated_conjecture,
    ( sum(X1,X2,c)
    | ~ product(X3,b,X2)
    | ~ product(X4,b,X1)
    | ~ sum(X4,X3,a) ),
    inference(spm,[status(thm)],[c_0_42,c_0_24]) ).

cnf(c_0_47,negated_conjecture,
    ( product(additive_identity,X1,X2)
    | ~ product(c,X1,X2)
    | ~ defined(X1) ),
    inference(spm,[status(thm)],[c_0_43,c_0_44]) ).

cnf(c_0_48,axiom,
    ( product(X1,X2,multiply(X1,X2))
    | ~ defined(X1)
    | ~ defined(X2) ),
    totality_of_multiplication ).

cnf(c_0_49,axiom,
    ( sum(X1,X2,X3)
    | ~ sum(X4,X5,X1)
    | ~ sum(X5,X2,X6)
    | ~ sum(X4,X6,X3) ),
    associativity_addition_2 ).

cnf(c_0_50,negated_conjecture,
    sum(c,additive_identity,additive_identity),
    inference(spm,[status(thm)],[c_0_45,c_0_30]) ).

cnf(c_0_51,negated_conjecture,
    ( sum(X1,c,c)
    | ~ product(X2,b,X1)
    | ~ sum(X2,a,a) ),
    inference(spm,[status(thm)],[c_0_46,c_0_24]) ).

cnf(c_0_52,negated_conjecture,
    ( product(additive_identity,X1,multiply(c,X1))
    | ~ defined(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_37])]) ).

cnf(c_0_53,hypothesis,
    defined(b),
    b_is_defined ).

cnf(c_0_54,negated_conjecture,
    ( sum(X1,additive_identity,X2)
    | ~ sum(X3,additive_identity,X2)
    | ~ sum(X3,c,X1) ),
    inference(spm,[status(thm)],[c_0_49,c_0_50]) ).

cnf(c_0_55,plain,
    ( sum(X1,additive_identity,X1)
    | ~ defined(X1) ),
    inference(spm,[status(thm)],[c_0_45,c_0_36]) ).

cnf(c_0_56,negated_conjecture,
    ( sum(multiply(c,b),c,c)
    | ~ sum(additive_identity,a,a) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_53])]) ).

cnf(c_0_57,negated_conjecture,
    ( sum(X1,additive_identity,X2)
    | ~ defined(X2)
    | ~ sum(X2,c,X1) ),
    inference(spm,[status(thm)],[c_0_54,c_0_55]) ).

cnf(c_0_58,negated_conjecture,
    sum(multiply(c,b),c,c),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_36]),c_0_28])]) ).

cnf(c_0_59,negated_conjecture,
    ( product(X1,X2,additive_identity)
    | ~ product(X3,X2,additive_identity)
    | ~ product(X4,X2,c)
    | ~ sum(X4,X3,X1) ),
    inference(spm,[status(thm)],[c_0_29,c_0_50]) ).

cnf(c_0_60,negated_conjecture,
    ( sum(c,additive_identity,multiply(c,b))
    | ~ defined(multiply(c,b)) ),
    inference(spm,[status(thm)],[c_0_57,c_0_58]) ).

cnf(c_0_61,axiom,
    ( defined(multiply(X1,X2))
    | ~ defined(X1)
    | ~ defined(X2) ),
    well_definedness_of_multiplication ).

cnf(c_0_62,negated_conjecture,
    ( product(X1,multiplicative_identity,additive_identity)
    | ~ product(X2,multiplicative_identity,c)
    | ~ sum(X2,additive_identity,X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_40]),c_0_41])]) ).

cnf(c_0_63,negated_conjecture,
    sum(c,additive_identity,multiply(c,b)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_53]),c_0_37])]) ).

cnf(c_0_64,negated_conjecture,
    product(multiply(c,b),multiplicative_identity,additive_identity),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_34])]) ).

cnf(c_0_65,plain,
    ( product(X1,multiplicative_identity,X2)
    | ~ product(X3,X4,X2)
    | ~ product(X3,X4,X1)
    | ~ defined(X4) ),
    inference(spm,[status(thm)],[c_0_38,c_0_40]) ).

cnf(c_0_66,axiom,
    defined(multiplicative_identity),
    well_definedness_of_multiplicative_identity ).

cnf(c_0_67,plain,
    ( product(X1,X2,X3)
    | ~ product(X4,multiply(X5,X2),X3)
    | ~ product(X4,X5,X1)
    | ~ defined(X2)
    | ~ defined(X5) ),
    inference(spm,[status(thm)],[c_0_38,c_0_48]) ).

cnf(c_0_68,negated_conjecture,
    product(multiplicative_identity,multiply(c,b),additive_identity),
    inference(spm,[status(thm)],[c_0_31,c_0_64]) ).

cnf(c_0_69,plain,
    ( product(X1,multiplicative_identity,X2)
    | ~ product(X2,multiplicative_identity,X1)
    | ~ defined(X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_40]),c_0_66])]) ).

cnf(c_0_70,plain,
    ( product(X1,X2,X3)
    | ~ product(X1,X4,multiplicative_identity)
    | ~ product(X4,X3,X2)
    | ~ defined(X3) ),
    inference(spm,[status(thm)],[c_0_23,c_0_27]) ).

cnf(c_0_71,axiom,
    ( product(multiplicative_inverse(X1),X1,multiplicative_identity)
    | sum(additive_identity,X1,additive_identity)
    | ~ defined(X1) ),
    existence_of_inverse_multiplication ).

cnf(c_0_72,negated_conjecture,
    ( product(X1,b,additive_identity)
    | ~ product(multiplicative_identity,c,X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_53]),c_0_37])]) ).

cnf(c_0_73,negated_conjecture,
    ( sum(X1,c,X2)
    | ~ sum(X3,additive_identity,X2)
    | ~ sum(X3,additive_identity,X1) ),
    inference(spm,[status(thm)],[c_0_49,c_0_30]) ).

cnf(c_0_74,negated_conjecture,
    product(additive_identity,multiplicative_identity,c),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_44]),c_0_37])]) ).

cnf(c_0_75,plain,
    ( product(multiplicative_inverse(X1),X2,X3)
    | sum(additive_identity,X1,additive_identity)
    | ~ product(X1,X3,X2)
    | ~ defined(X3)
    | ~ defined(X1) ),
    inference(spm,[status(thm)],[c_0_70,c_0_71]) ).

cnf(c_0_76,negated_conjecture,
    product(b,a,c),
    inference(spm,[status(thm)],[c_0_31,c_0_24]) ).

cnf(c_0_77,negated_conjecture,
    ~ sum(additive_identity,b,additive_identity),
    not_sum_5 ).

cnf(c_0_78,negated_conjecture,
    product(c,b,additive_identity),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_27]),c_0_37])]) ).

cnf(c_0_79,negated_conjecture,
    ( sum(X1,c,X2)
    | ~ defined(X2)
    | ~ sum(X2,additive_identity,X1) ),
    inference(spm,[status(thm)],[c_0_73,c_0_55]) ).

cnf(c_0_80,axiom,
    ( sum(additive_inverse(X1),X1,additive_identity)
    | ~ defined(X1) ),
    existence_of_inverse_addition ).

cnf(c_0_81,negated_conjecture,
    ( product(X1,multiplicative_identity,X2)
    | ~ product(X3,c,X2)
    | ~ product(X3,additive_identity,X1) ),
    inference(spm,[status(thm)],[c_0_38,c_0_74]) ).

cnf(c_0_82,negated_conjecture,
    product(multiplicative_inverse(b),c,a),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_28]),c_0_53])]),c_0_77]) ).

cnf(c_0_83,negated_conjecture,
    product(b,c,additive_identity),
    inference(spm,[status(thm)],[c_0_31,c_0_78]) ).

cnf(c_0_84,negated_conjecture,
    sum(additive_identity,c,c),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_50]),c_0_37])]) ).

cnf(c_0_85,axiom,
    ( sum(X1,X2,X3)
    | ~ sum(X1,X4,X5)
    | ~ sum(X4,X6,X2)
    | ~ sum(X5,X6,X3) ),
    associativity_addition_1 ).

cnf(c_0_86,plain,
    ( sum(X1,additive_inverse(X1),additive_identity)
    | ~ defined(X1) ),
    inference(spm,[status(thm)],[c_0_45,c_0_80]) ).

cnf(c_0_87,negated_conjecture,
    ( sum(X1,X2,c)
    | ~ product(X3,multiplicative_identity,X2)
    | ~ product(X4,multiplicative_identity,X1)
    | ~ sum(X4,X3,c) ),
    inference(spm,[status(thm)],[c_0_42,c_0_34]) ).

cnf(c_0_88,negated_conjecture,
    ( product(X1,multiplicative_identity,a)
    | ~ product(multiplicative_inverse(b),additive_identity,X1) ),
    inference(spm,[status(thm)],[c_0_81,c_0_82]) ).

cnf(c_0_89,negated_conjecture,
    product(multiplicative_inverse(b),additive_identity,c),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_83]),c_0_37]),c_0_53])]),c_0_77]) ).

cnf(c_0_90,negated_conjecture,
    sum(c,additive_identity,c),
    inference(spm,[status(thm)],[c_0_45,c_0_84]) ).

cnf(c_0_91,plain,
    ( sum(X1,X2,additive_identity)
    | ~ defined(X3)
    | ~ sum(X4,additive_inverse(X3),X2)
    | ~ sum(X1,X4,X3) ),
    inference(spm,[status(thm)],[c_0_85,c_0_86]) ).

cnf(c_0_92,negated_conjecture,
    ( sum(X1,c,c)
    | ~ product(X2,multiplicative_identity,X1)
    | ~ sum(X2,c,c) ),
    inference(spm,[status(thm)],[c_0_87,c_0_34]) ).

cnf(c_0_93,negated_conjecture,
    product(c,multiplicative_identity,a),
    inference(spm,[status(thm)],[c_0_88,c_0_89]) ).

cnf(c_0_94,negated_conjecture,
    sum(c,c,c),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_90]),c_0_37])]) ).

cnf(c_0_95,plain,
    ( sum(X1,additive_identity,additive_identity)
    | ~ defined(X2)
    | ~ sum(X1,X2,X2) ),
    inference(spm,[status(thm)],[c_0_91,c_0_86]) ).

cnf(c_0_96,negated_conjecture,
    sum(a,c,c),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_94])]) ).

cnf(c_0_97,negated_conjecture,
    sum(a,additive_identity,additive_identity),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_37])]) ).

cnf(c_0_98,negated_conjecture,
    ~ sum(additive_identity,a,additive_identity),
    not_sum_4 ).

cnf(c_0_99,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_97]),c_0_98]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.30  % Problem    : FLD041-4 : TPTP v9.2.1. Bugfixed v2.1.0.
% 0.07/0.30  % 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
% 0.13/0.54  % Computer : n008.cluster.edu
% 0.13/0.54  % Model    : x86_64 x86_64
% 0.13/0.54  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.54  % Memory   : 8042.1875MB
% 0.13/0.54  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.54  % CPULimit   : 300
% 0.13/0.54  % WCLimit    : 300
% 0.13/0.54  % DateTime   : Mon May  4 17:28:44 EDT 2026
% 0.15/0.55  % CPUTime    : 
% 0.15/0.58  % start to proof: theBenchmark
% 14.42/11.53  % Version  : CSE_E---1.7
% 14.42/11.53  % Problem  : theBenchmark.p
% 14.42/11.53  % SZS status Unsatisfiable for theBenchmark.p
% 14.42/11.53  % SZS output start CNFRefutation
% See solution above
% 14.52/11.60  % Total time : 8.491s
%------------------------------------------------------------------------------