CSE_E---1.7.UNS-CRf.s

%------------------------------------------------------------------------------
% File     : CSE_E---1.7
% Problem  : RNG001-5 : TPTP v9.2.1. Released v1.0.0.
% 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 05:04:56 PM UTC 2026

% Result   : Unsatisfiable 4.43s 5.62s
% Output   : CNFRefutation 5.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   30
% Syntax   : Number of clauses     :  518 ( 314 unt;   0 nHn; 272 RR)
%            Number of literals    :  960 (   0 equ; 519 neg)
%            Maximal clause size   :    5 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   : 1223 (   2 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(distributivity2,axiom,
    ( product(X1,X6,X7)
    | ~ product(X1,X2,X3)
    | ~ product(X1,X4,X5)
    | ~ sum(X2,X4,X6)
    | ~ sum(X3,X5,X7) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity2) ).

cnf(distributivity4,axiom,
    ( product(X6,X2,X7)
    | ~ product(X1,X2,X3)
    | ~ product(X4,X2,X5)
    | ~ sum(X1,X4,X6)
    | ~ sum(X3,X5,X7) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity4) ).

cnf(distributivity3,axiom,
    ( sum(X3,X5,X7)
    | ~ product(X1,X2,X3)
    | ~ product(X4,X2,X5)
    | ~ sum(X1,X4,X6)
    | ~ product(X6,X2,X7) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity3) ).

cnf(distributivity1,axiom,
    ( sum(X3,X5,X7)
    | ~ product(X1,X2,X3)
    | ~ product(X1,X4,X5)
    | ~ sum(X2,X4,X6)
    | ~ product(X1,X6,X7) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity1) ).

cnf(associativity_of_multiplication1,axiom,
    ( product(X1,X5,X6)
    | ~ product(X1,X2,X3)
    | ~ product(X2,X4,X5)
    | ~ product(X3,X4,X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_multiplication1) ).

cnf(associativity_of_multiplication2,axiom,
    ( product(X3,X4,X6)
    | ~ product(X1,X2,X3)
    | ~ product(X2,X4,X5)
    | ~ product(X1,X5,X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_multiplication2) ).

cnf(associativity_of_addition1,axiom,
    ( sum(X1,X5,X6)
    | ~ sum(X1,X2,X3)
    | ~ sum(X2,X4,X5)
    | ~ sum(X3,X4,X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_addition1) ).

cnf(associativity_of_addition2,axiom,
    ( sum(X3,X4,X6)
    | ~ sum(X1,X2,X3)
    | ~ sum(X2,X4,X5)
    | ~ sum(X1,X5,X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_addition2) ).

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

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

cnf(product_substitution1,axiom,
    ( product(X2,X3,X4)
    | ~ equalish(X1,X2)
    | ~ product(X1,X3,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_substitution1) ).

cnf(product_substitution2,axiom,
    ( product(X3,X2,X4)
    | ~ equalish(X1,X2)
    | ~ product(X3,X1,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_substitution2) ).

cnf(product_substitution3,axiom,
    ( product(X3,X4,X2)
    | ~ equalish(X1,X2)
    | ~ product(X3,X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_substitution3) ).

cnf(sum_substitution1,axiom,
    ( sum(X2,X3,X4)
    | ~ equalish(X1,X2)
    | ~ sum(X1,X3,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_substitution1) ).

cnf(sum_substitution2,axiom,
    ( sum(X3,X2,X4)
    | ~ equalish(X1,X2)
    | ~ sum(X3,X1,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_substitution2) ).

cnf(sum_substitution3,axiom,
    ( sum(X3,X4,X2)
    | ~ equalish(X1,X2)
    | ~ sum(X3,X4,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_substitution3) ).

cnf(commutativity_of_addition,axiom,
    ( sum(X2,X1,X3)
    | ~ sum(X1,X2,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_addition) ).

cnf(multiply_substitution1,axiom,
    ( equalish(multiply(X1,X3),multiply(X2,X3))
    | ~ equalish(X1,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_substitution1) ).

cnf(add_substitution1,axiom,
    ( equalish(add(X1,X3),add(X2,X3))
    | ~ equalish(X1,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',add_substitution1) ).

cnf(closure_of_multiplication,axiom,
    product(X1,X2,multiply(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_multiplication) ).

cnf(closure_of_addition,axiom,
    sum(X1,X2,add(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_addition) ).

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

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

cnf(left_inverse,axiom,
    sum(additive_inverse(X1),X1,additive_identity),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).

cnf(right_inverse,axiom,
    sum(X1,additive_inverse(X1),additive_identity),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_inverse) ).

cnf(additive_identity1,axiom,
    sum(additive_identity,X1,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity1) ).

cnf(additive_identity2,axiom,
    sum(X1,additive_identity,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity2) ).

cnf(additive_inverse_substitution,axiom,
    ( equalish(additive_inverse(X1),additive_inverse(X2))
    | ~ equalish(X1,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse_substitution) ).

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

cnf(reflexivity,axiom,
    equalish(X1,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).

cnf(i_0_30,axiom,
    ( product(X1,X6,X7)
    | ~ product(X1,X2,X3)
    | ~ product(X1,X4,X5)
    | ~ sum(X2,X4,X6)
    | ~ sum(X3,X5,X7) ),
    distributivity2,
    [final] ).

cnf(i_0_31,axiom,
    ( product(X6,X2,X7)
    | ~ product(X1,X2,X3)
    | ~ product(X4,X2,X5)
    | ~ sum(X1,X4,X6)
    | ~ sum(X3,X5,X7) ),
    distributivity4,
    [final] ).

cnf(i_0_32,axiom,
    ( sum(X3,X5,X7)
    | ~ product(X1,X2,X3)
    | ~ product(X4,X2,X5)
    | ~ sum(X1,X4,X6)
    | ~ product(X6,X2,X7) ),
    distributivity3,
    [final] ).

cnf(i_0_33,axiom,
    ( sum(X3,X5,X7)
    | ~ product(X1,X2,X3)
    | ~ product(X1,X4,X5)
    | ~ sum(X2,X4,X6)
    | ~ product(X1,X6,X7) ),
    distributivity1,
    [final] ).

cnf(i_0_34,axiom,
    ( product(X1,X5,X6)
    | ~ product(X1,X2,X3)
    | ~ product(X2,X4,X5)
    | ~ product(X3,X4,X6) ),
    associativity_of_multiplication1,
    [final] ).

cnf(i_0_35,axiom,
    ( product(X3,X4,X6)
    | ~ product(X1,X2,X3)
    | ~ product(X2,X4,X5)
    | ~ product(X1,X5,X6) ),
    associativity_of_multiplication2,
    [final] ).

cnf(i_0_36,axiom,
    ( sum(X1,X5,X6)
    | ~ sum(X1,X2,X3)
    | ~ sum(X2,X4,X5)
    | ~ sum(X3,X4,X6) ),
    associativity_of_addition1,
    [final] ).

cnf(i_0_37,axiom,
    ( sum(X3,X4,X6)
    | ~ sum(X1,X2,X3)
    | ~ sum(X2,X4,X5)
    | ~ sum(X1,X5,X6) ),
    associativity_of_addition2,
    [final] ).

cnf(i_0_38,axiom,
    ( equalish(X3,X4)
    | ~ product(X1,X2,X3)
    | ~ product(X1,X2,X4) ),
    multiplication_is_well_defined,
    [final] ).

cnf(i_0_39,axiom,
    ( equalish(X3,X4)
    | ~ sum(X1,X2,X3)
    | ~ sum(X1,X2,X4) ),
    addition_is_well_defined,
    [final] ).

cnf(i_0_40,axiom,
    ( product(X2,X3,X4)
    | ~ equalish(X1,X2)
    | ~ product(X1,X3,X4) ),
    product_substitution1,
    [final] ).

cnf(i_0_41,axiom,
    ( product(X3,X2,X4)
    | ~ equalish(X1,X2)
    | ~ product(X3,X1,X4) ),
    product_substitution2,
    [final] ).

cnf(i_0_42,axiom,
    ( product(X3,X4,X2)
    | ~ equalish(X1,X2)
    | ~ product(X3,X4,X1) ),
    product_substitution3,
    [final] ).

cnf(i_0_43,axiom,
    ( sum(X2,X3,X4)
    | ~ equalish(X1,X2)
    | ~ sum(X1,X3,X4) ),
    sum_substitution1,
    [final] ).

cnf(i_0_44,axiom,
    ( sum(X3,X2,X4)
    | ~ equalish(X1,X2)
    | ~ sum(X3,X1,X4) ),
    sum_substitution2,
    [final] ).

cnf(i_0_45,axiom,
    ( sum(X3,X4,X2)
    | ~ equalish(X1,X2)
    | ~ sum(X3,X4,X1) ),
    sum_substitution3,
    [final] ).

cnf(i_0_46,axiom,
    ( sum(X2,X1,X3)
    | ~ sum(X1,X2,X3) ),
    commutativity_of_addition,
    [final] ).

cnf(i_0_47,axiom,
    ( equalish(multiply(X1,X3),multiply(X2,X3))
    | ~ equalish(X1,X2) ),
    multiply_substitution1,
    [final] ).

cnf(i_0_48,axiom,
    ( equalish(add(X1,X3),add(X2,X3))
    | ~ equalish(X1,X2) ),
    add_substitution1,
    [final] ).

cnf(i_0_49,axiom,
    product(X1,X2,multiply(X1,X2)),
    closure_of_multiplication,
    [final] ).

cnf(i_0_50,axiom,
    sum(X1,X2,add(X1,X2)),
    closure_of_addition,
    [final] ).

cnf(i_0_51,negated_conjecture,
    ~ product(a,additive_identity,additive_identity),
    prove_multiplicative_identity_axiom,
    [final] ).

cnf(i_0_52,axiom,
    ( equalish(X1,X3)
    | ~ equalish(X1,X2)
    | ~ equalish(X2,X3) ),
    transitivity,
    [final] ).

cnf(i_0_53,axiom,
    sum(additive_inverse(X1),X1,additive_identity),
    left_inverse,
    [final] ).

cnf(i_0_54,axiom,
    sum(X1,additive_inverse(X1),additive_identity),
    right_inverse,
    [final] ).

cnf(i_0_55,axiom,
    sum(additive_identity,X1,X1),
    additive_identity1,
    [final] ).

cnf(i_0_56,axiom,
    sum(X1,additive_identity,X1),
    additive_identity2,
    [final] ).

cnf(i_0_57,axiom,
    ( equalish(additive_inverse(X1),additive_inverse(X2))
    | ~ equalish(X1,X2) ),
    additive_inverse_substitution,
    [final] ).

cnf(i_0_58,axiom,
    ( equalish(X2,X1)
    | ~ equalish(X1,X2) ),
    symmetry,
    [final] ).

cnf(i_0_59,axiom,
    equalish(X1,X1),
    reflexivity,
    [final] ).

cnf(i_0_60,plain,
    sum(X1,X2,add(X2,X1)),
    inference(scs_inference,[],[i_0_50,i_0_46]) ).

cnf(i_0_61,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X2,X1,X3) ),
    inference(rename_variables,[],[i_0_46]) ).

cnf(i_0_62,plain,
    equalish(X1,add(additive_identity,X1)),
    inference(scs_inference,[],[i_0_55,i_0_50,i_0_46,i_0_39]) ).

cnf(i_0_63,plain,
    sum(X1,X2,add(X1,X2)),
    inference(rename_variables,[],[i_0_50]) ).

cnf(i_0_64,plain,
    ( ~ sum(X1,X2,X3)
    | equalish(X4,X3)
    | ~ sum(X1,X2,X4) ),
    inference(rename_variables,[],[i_0_39]) ).

cnf(i_0_65,plain,
    ~ equalish(multiply(a,additive_identity),additive_identity),
    inference(scs_inference,[],[i_0_51,i_0_55,i_0_49,i_0_50,i_0_46,i_0_39,i_0_42]) ).

cnf(i_0_66,plain,
    product(X1,X2,multiply(X1,X2)),
    inference(rename_variables,[],[i_0_49]) ).

cnf(i_0_67,plain,
    ( ~ product(X1,X2,X3)
    | product(X1,X2,X4)
    | ~ equalish(X3,X4) ),
    inference(rename_variables,[],[i_0_42]) ).

cnf(i_0_68,plain,
    sum(additive_identity,add(X1,additive_inverse(X1)),additive_identity),
    inference(scs_inference,[],[i_0_51,i_0_55,i_0_49,i_0_50,i_0_63,i_0_54,i_0_46,i_0_39,i_0_42,i_0_36]) ).

cnf(i_0_69,plain,
    sum(X1,additive_inverse(X1),additive_identity),
    inference(rename_variables,[],[i_0_54]) ).

cnf(i_0_70,plain,
    sum(additive_identity,X1,X1),
    inference(rename_variables,[],[i_0_55]) ).

cnf(i_0_71,plain,
    sum(X1,X2,add(X1,X2)),
    inference(rename_variables,[],[i_0_50]) ).

cnf(i_0_72,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ sum(X4,X6,X1)
    | ~ sum(X6,X2,X5) ),
    inference(rename_variables,[],[i_0_36]) ).

cnf(i_0_73,plain,
    sum(multiply(additive_identity,X1),multiply(additive_identity,X1),multiply(additive_identity,X1)),
    inference(scs_inference,[],[i_0_51,i_0_55,i_0_70,i_0_49,i_0_66,i_0_50,i_0_63,i_0_54,i_0_46,i_0_39,i_0_42,i_0_36,i_0_32]) ).

cnf(i_0_74,plain,
    product(X1,X2,multiply(X1,X2)),
    inference(rename_variables,[],[i_0_49]) ).

cnf(i_0_75,plain,
    product(X1,X2,multiply(X1,X2)),
    inference(rename_variables,[],[i_0_49]) ).

cnf(i_0_76,plain,
    product(X1,X2,multiply(X1,X2)),
    inference(rename_variables,[],[i_0_49]) ).

cnf(i_0_77,plain,
    sum(additive_identity,X1,X1),
    inference(rename_variables,[],[i_0_55]) ).

cnf(i_0_78,plain,
    ( ~ product(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ product(X6,X2,X4)
    | ~ product(X7,X2,X5)
    | ~ sum(X6,X7,X1) ),
    inference(rename_variables,[],[i_0_32]) ).

cnf(i_0_79,plain,
    sum(multiply(X1,additive_identity),multiply(X1,additive_identity),multiply(X1,additive_identity)),
    inference(scs_inference,[],[i_0_51,i_0_55,i_0_70,i_0_77,i_0_49,i_0_66,i_0_76,i_0_50,i_0_63,i_0_54,i_0_46,i_0_39,i_0_42,i_0_36,i_0_32,i_0_33]) ).

cnf(i_0_80,plain,
    product(X1,X2,multiply(X1,X2)),
    inference(rename_variables,[],[i_0_49]) ).

cnf(i_0_81,plain,
    product(X1,X2,multiply(X1,X2)),
    inference(rename_variables,[],[i_0_49]) ).

cnf(i_0_82,plain,
    product(X1,X2,multiply(X1,X2)),
    inference(rename_variables,[],[i_0_49]) ).

cnf(i_0_83,plain,
    sum(additive_identity,X1,X1),
    inference(rename_variables,[],[i_0_55]) ).

cnf(i_0_84,plain,
    ( ~ product(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ product(X1,X6,X4)
    | ~ product(X1,X7,X5)
    | ~ sum(X6,X7,X2) ),
    inference(rename_variables,[],[i_0_33]) ).

cnf(i_0_85,plain,
    equalish(add(additive_identity,X1),X1),
    inference(scs_inference,[],[i_0_51,i_0_55,i_0_70,i_0_77,i_0_49,i_0_66,i_0_76,i_0_50,i_0_63,i_0_54,i_0_46,i_0_39,i_0_42,i_0_36,i_0_32,i_0_33,i_0_58]) ).

cnf(i_0_86,plain,
    ( ~ equalish(X1,X2)
    | equalish(X2,X1) ),
    inference(rename_variables,[],[i_0_58]) ).

cnf(i_0_87,plain,
    ~ equalish(multiply(a,additive_identity),add(additive_identity,additive_identity)),
    inference(scs_inference,[],[i_0_51,i_0_55,i_0_70,i_0_77,i_0_49,i_0_66,i_0_76,i_0_50,i_0_63,i_0_54,i_0_46,i_0_39,i_0_42,i_0_36,i_0_32,i_0_33,i_0_58,i_0_52]) ).

cnf(i_0_88,plain,
    ( ~ equalish(X1,X2)
    | equalish(X3,X2)
    | ~ equalish(X3,X1) ),
    inference(rename_variables,[],[i_0_52]) ).

cnf(i_0_89,plain,
    product(X1,multiply(X1,X1),multiply(multiply(X1,X1),X1)),
    inference(scs_inference,[],[i_0_51,i_0_55,i_0_70,i_0_77,i_0_49,i_0_66,i_0_76,i_0_82,i_0_81,i_0_50,i_0_63,i_0_54,i_0_46,i_0_39,i_0_42,i_0_36,i_0_32,i_0_33,i_0_58,i_0_52,i_0_34]) ).

cnf(i_0_90,plain,
    product(X1,X2,multiply(X1,X2)),
    inference(rename_variables,[],[i_0_49]) ).

cnf(i_0_91,plain,
    product(X1,X2,multiply(X1,X2)),
    inference(rename_variables,[],[i_0_49]) ).

cnf(i_0_92,plain,
    product(X1,X2,multiply(X1,X2)),
    inference(rename_variables,[],[i_0_49]) ).

cnf(i_0_93,plain,
    ( ~ product(X1,X2,X3)
    | product(X4,X5,X3)
    | ~ product(X4,X6,X1)
    | ~ product(X6,X2,X5) ),
    inference(rename_variables,[],[i_0_34]) ).

cnf(i_0_94,plain,
    ( product(multiply(X1,X2),X3,multiply(X1,X2))
    | ~ product(X2,X3,X2) ),
    inference(scs_inference,[],[i_0_51,i_0_55,i_0_70,i_0_77,i_0_49,i_0_66,i_0_76,i_0_82,i_0_90,i_0_81,i_0_50,i_0_63,i_0_54,i_0_46,i_0_39,i_0_42,i_0_36,i_0_32,i_0_33,i_0_58,i_0_52,i_0_34,i_0_35]) ).

cnf(i_0_95,plain,
    ( ~ product(X1,X2,X3)
    | product(X4,X5,X3)
    | ~ product(X1,X6,X4)
    | ~ product(X6,X5,X2) ),
    inference(rename_variables,[],[i_0_35]) ).

cnf(i_0_96,plain,
    ( equalish(multiply(multiply(X1,X2),X3),multiply(X1,X2))
    | ~ product(X2,X3,X2) ),
    inference(scs_inference,[],[i_0_51,i_0_55,i_0_70,i_0_77,i_0_49,i_0_66,i_0_76,i_0_82,i_0_90,i_0_81,i_0_92,i_0_50,i_0_63,i_0_54,i_0_46,i_0_39,i_0_42,i_0_36,i_0_32,i_0_33,i_0_58,i_0_52,i_0_34,i_0_35,i_0_38]) ).

cnf(i_0_97,plain,
    product(X1,X2,multiply(X1,X2)),
    inference(rename_variables,[],[i_0_49]) ).

cnf(i_0_98,plain,
    ( ~ product(X1,X2,X3)
    | equalish(X4,X3)
    | ~ product(X1,X2,X4) ),
    inference(rename_variables,[],[i_0_38]) ).

cnf(i_0_99,plain,
    sum(X1,X2,add(X1,X2)),
    inference(rename_variables,[],[i_0_50]) ).

cnf(i_0_100,plain,
    sum(additive_identity,X1,X1),
    inference(rename_variables,[],[i_0_55]) ).

cnf(i_0_101,plain,
    sum(additive_identity,X1,X1),
    inference(rename_variables,[],[i_0_55]) ).

cnf(i_0_102,plain,
    sum(additive_identity,X1,X1),
    inference(rename_variables,[],[i_0_55]) ).

cnf(i_0_103,plain,
    ( product(additive_identity,add(X1,X2),multiply(additive_identity,X2))
    | ~ product(X2,X3,X2)
    | ~ product(additive_identity,X1,additive_identity) ),
    inference(scs_inference,[],[i_0_51,i_0_55,i_0_70,i_0_77,i_0_83,i_0_100,i_0_49,i_0_66,i_0_76,i_0_82,i_0_90,i_0_81,i_0_92,i_0_50,i_0_63,i_0_71,i_0_54,i_0_46,i_0_39,i_0_42,i_0_36,i_0_32,i_0_33,i_0_58,i_0_52,i_0_34,i_0_35,i_0_38,i_0_30,i_0_31]) ).

cnf(i_0_104,plain,
    sum(add(X1,additive_inverse(X1)),additive_identity,additive_identity),
    inference(scs_inference,[],[i_0_68,i_0_46]) ).

cnf(i_0_105,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X2,X1,X3) ),
    inference(rename_variables,[],[i_0_46]) ).

cnf(i_0_106,plain,
    ~ sum(add(additive_identity,additive_identity),additive_identity,multiply(a,additive_identity)),
    inference(scs_inference,[],[i_0_56,i_0_87,i_0_68,i_0_46,i_0_39]) ).

cnf(i_0_107,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_56]) ).

cnf(i_0_108,plain,
    ( ~ sum(X1,X2,X3)
    | equalish(X4,X3)
    | ~ sum(X1,X2,X4) ),
    inference(rename_variables,[],[i_0_39]) ).

cnf(i_0_109,plain,
    ~ equalish(multiply(a,additive_identity),add(additive_identity,add(additive_identity,additive_identity))),
    inference(scs_inference,[],[i_0_56,i_0_87,i_0_85,i_0_68,i_0_46,i_0_39,i_0_52]) ).

cnf(i_0_110,plain,
    equalish(add(additive_identity,X1),X1),
    inference(rename_variables,[],[i_0_85]) ).

cnf(i_0_111,plain,
    ( ~ equalish(X1,X2)
    | equalish(X3,X2)
    | ~ equalish(X3,X1) ),
    inference(rename_variables,[],[i_0_52]) ).

cnf(i_0_112,plain,
    ~ sum(multiply(a,additive_identity),additive_inverse(additive_identity),add(additive_identity,additive_identity)),
    inference(scs_inference,[],[i_0_56,i_0_107,i_0_53,i_0_87,i_0_85,i_0_68,i_0_46,i_0_39,i_0_52,i_0_37]) ).

cnf(i_0_113,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_56]) ).

cnf(i_0_114,plain,
    sum(additive_inverse(X1),X1,additive_identity),
    inference(rename_variables,[],[i_0_53]) ).

cnf(i_0_115,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ sum(X1,X6,X4)
    | ~ sum(X6,X5,X2) ),
    inference(rename_variables,[],[i_0_37]) ).

cnf(i_0_116,plain,
    ~ sum(add(additive_identity,additive_identity),additive_inverse(additive_identity),multiply(a,additive_identity)),
    inference(scs_inference,[],[i_0_56,i_0_107,i_0_113,i_0_53,i_0_114,i_0_87,i_0_85,i_0_68,i_0_46,i_0_39,i_0_52,i_0_37,i_0_36]) ).

cnf(i_0_117,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_56]) ).

cnf(i_0_118,plain,
    sum(additive_inverse(X1),X1,additive_identity),
    inference(rename_variables,[],[i_0_53]) ).

cnf(i_0_119,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ sum(X4,X6,X1)
    | ~ sum(X6,X2,X5) ),
    inference(rename_variables,[],[i_0_36]) ).

cnf(i_0_120,plain,
    ~ equalish(add(additive_identity,additive_identity),multiply(a,additive_identity)),
    inference(scs_inference,[],[i_0_56,i_0_107,i_0_113,i_0_117,i_0_53,i_0_114,i_0_87,i_0_85,i_0_68,i_0_46,i_0_39,i_0_52,i_0_37,i_0_36,i_0_45]) ).

cnf(i_0_121,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_56]) ).

cnf(i_0_122,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X1,X2,X4)
    | ~ equalish(X3,X4) ),
    inference(rename_variables,[],[i_0_45]) ).

cnf(i_0_123,plain,
    ~ product(a,additive_identity,add(additive_identity,additive_identity)),
    inference(scs_inference,[],[i_0_56,i_0_107,i_0_113,i_0_117,i_0_53,i_0_114,i_0_87,i_0_85,i_0_68,i_0_49,i_0_46,i_0_39,i_0_52,i_0_37,i_0_36,i_0_45,i_0_38]) ).

cnf(i_0_124,plain,
    product(X1,X2,multiply(X1,X2)),
    inference(rename_variables,[],[i_0_49]) ).

cnf(i_0_125,plain,
    ( ~ product(X1,X2,X3)
    | equalish(X4,X3)
    | ~ product(X1,X2,X4) ),
    inference(rename_variables,[],[i_0_38]) ).

cnf(i_0_126,plain,
    ( product(multiply(multiply(X1,X1),X1),X2,multiply(X1,X3))
    | ~ product(multiply(X1,X1),X2,X3) ),
    inference(scs_inference,[],[i_0_89,i_0_56,i_0_107,i_0_113,i_0_117,i_0_53,i_0_114,i_0_87,i_0_85,i_0_68,i_0_49,i_0_124,i_0_46,i_0_39,i_0_52,i_0_37,i_0_36,i_0_45,i_0_38,i_0_35]) ).

cnf(i_0_127,plain,
    product(X1,X2,multiply(X1,X2)),
    inference(rename_variables,[],[i_0_49]) ).

cnf(i_0_128,plain,
    ( ~ product(X1,X2,X3)
    | product(X4,X5,X3)
    | ~ product(X1,X6,X4)
    | ~ product(X6,X5,X2) ),
    inference(rename_variables,[],[i_0_35]) ).

cnf(i_0_129,plain,
    ( product(X1,multiply(multiply(X1,X1),X2),multiply(X1,X3))
    | ~ product(multiply(X1,X1),X2,X3) ),
    inference(scs_inference,[],[i_0_89,i_0_56,i_0_107,i_0_113,i_0_117,i_0_53,i_0_114,i_0_87,i_0_85,i_0_68,i_0_49,i_0_124,i_0_127,i_0_46,i_0_39,i_0_52,i_0_37,i_0_36,i_0_45,i_0_38,i_0_35,i_0_34]) ).

cnf(i_0_130,plain,
    product(X1,X2,multiply(X1,X2)),
    inference(rename_variables,[],[i_0_49]) ).

cnf(i_0_131,plain,
    ( ~ product(X1,X2,X3)
    | product(X4,X5,X3)
    | ~ product(X4,X6,X1)
    | ~ product(X6,X2,X5) ),
    inference(rename_variables,[],[i_0_34]) ).

cnf(i_0_132,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_56]) ).

cnf(i_0_133,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_56]) ).

cnf(i_0_134,plain,
    product(X1,X2,multiply(X1,X2)),
    inference(rename_variables,[],[i_0_49]) ).

cnf(i_0_135,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_56]) ).

cnf(i_0_136,plain,
    product(X1,X2,multiply(X1,X2)),
    inference(rename_variables,[],[i_0_49]) ).

cnf(i_0_137,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_56]) ).

cnf(i_0_139,plain,
    product(add(additive_identity,X1),multiply(X1,X1),multiply(multiply(X1,X1),X1)),
    inference(scs_inference,[],[i_0_89,i_0_62,i_0_40]) ).

cnf(i_0_140,plain,
    product(X1,multiply(X1,X1),multiply(multiply(X1,X1),X1)),
    inference(rename_variables,[],[i_0_89]) ).

cnf(i_0_141,plain,
    ( ~ product(X1,X2,X3)
    | product(X4,X2,X3)
    | ~ equalish(X1,X4) ),
    inference(rename_variables,[],[i_0_40]) ).

cnf(i_0_142,plain,
    product(X1,add(additive_identity,X2),multiply(X1,X2)),
    inference(scs_inference,[],[i_0_89,i_0_62,i_0_49,i_0_40,i_0_41]) ).

cnf(i_0_143,plain,
    product(X1,X2,multiply(X1,X2)),
    inference(rename_variables,[],[i_0_49]) ).

cnf(i_0_144,plain,
    ( ~ product(X1,X2,X3)
    | product(X1,X4,X3)
    | ~ equalish(X2,X4) ),
    inference(rename_variables,[],[i_0_41]) ).

cnf(i_0_145,plain,
    sum(add(additive_identity,additive_inverse(X1)),X1,additive_identity),
    inference(scs_inference,[],[i_0_89,i_0_53,i_0_62,i_0_49,i_0_40,i_0_41,i_0_43]) ).

cnf(i_0_146,plain,
    equalish(X1,add(additive_identity,X1)),
    inference(rename_variables,[],[i_0_62]) ).

cnf(i_0_147,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X2,X3)
    | ~ equalish(X1,X4) ),
    inference(rename_variables,[],[i_0_43]) ).

cnf(i_0_148,plain,
    sum(X1,add(additive_identity,additive_identity),X1),
    inference(scs_inference,[],[i_0_89,i_0_56,i_0_53,i_0_62,i_0_146,i_0_49,i_0_40,i_0_41,i_0_43,i_0_44]) ).

cnf(i_0_149,plain,
    equalish(X1,add(additive_identity,X1)),
    inference(rename_variables,[],[i_0_62]) ).

cnf(i_0_150,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X1,X4,X3)
    | ~ equalish(X2,X4) ),
    inference(rename_variables,[],[i_0_44]) ).

cnf(i_0_151,plain,
    sum(additive_inverse(X1),X1,add(additive_identity,additive_identity)),
    inference(scs_inference,[],[i_0_89,i_0_56,i_0_53,i_0_62,i_0_146,i_0_149,i_0_49,i_0_40,i_0_41,i_0_43,i_0_44,i_0_45]) ).

cnf(i_0_152,plain,
    equalish(X1,add(additive_identity,X1)),
    inference(rename_variables,[],[i_0_62]) ).

cnf(i_0_153,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X1,X2,X4)
    | ~ equalish(X3,X4) ),
    inference(rename_variables,[],[i_0_45]) ).

cnf(i_0_154,plain,
    ~ sum(additive_identity,additive_identity,multiply(a,additive_identity)),
    inference(scs_inference,[],[i_0_89,i_0_56,i_0_53,i_0_62,i_0_146,i_0_149,i_0_65,i_0_49,i_0_40,i_0_41,i_0_43,i_0_44,i_0_45,i_0_39]) ).

cnf(i_0_155,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_56]) ).

cnf(i_0_156,plain,
    ( ~ sum(X1,X2,X3)
    | equalish(X4,X3)
    | ~ sum(X1,X2,X4) ),
    inference(rename_variables,[],[i_0_39]) ).

cnf(i_0_157,plain,
    ~ sum(add(additive_identity,additive_identity),additive_inverse(additive_inverse(additive_identity)),multiply(a,additive_identity)),
    inference(scs_inference,[],[i_0_89,i_0_56,i_0_155,i_0_53,i_0_62,i_0_146,i_0_149,i_0_65,i_0_112,i_0_49,i_0_40,i_0_41,i_0_43,i_0_44,i_0_45,i_0_39,i_0_37]) ).

cnf(i_0_158,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_56]) ).

cnf(i_0_159,plain,
    sum(additive_inverse(X1),X1,additive_identity),
    inference(rename_variables,[],[i_0_53]) ).

cnf(i_0_160,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ sum(X1,X6,X4)
    | ~ sum(X6,X5,X2) ),
    inference(rename_variables,[],[i_0_37]) ).

cnf(i_0_161,plain,
    ~ sum(additive_inverse(multiply(a,additive_identity)),add(additive_identity,additive_identity),additive_inverse(additive_identity)),
    inference(scs_inference,[],[i_0_89,i_0_56,i_0_155,i_0_53,i_0_55,i_0_54,i_0_62,i_0_146,i_0_149,i_0_65,i_0_112,i_0_49,i_0_40,i_0_41,i_0_43,i_0_44,i_0_45,i_0_39,i_0_37,i_0_36]) ).

cnf(i_0_162,plain,
    sum(additive_identity,X1,X1),
    inference(rename_variables,[],[i_0_55]) ).

cnf(i_0_163,plain,
    sum(X1,additive_inverse(X1),additive_identity),
    inference(rename_variables,[],[i_0_54]) ).

cnf(i_0_164,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ sum(X4,X6,X1)
    | ~ sum(X6,X2,X5) ),
    inference(rename_variables,[],[i_0_36]) ).

cnf(i_0_165,plain,
    sum(add(additive_identity,additive_identity),additive_identity,additive_identity),
    inference(scs_inference,[],[i_0_89,i_0_56,i_0_155,i_0_53,i_0_55,i_0_54,i_0_62,i_0_146,i_0_149,i_0_65,i_0_112,i_0_49,i_0_40,i_0_41,i_0_43,i_0_44,i_0_45,i_0_39,i_0_37,i_0_36,i_0_46]) ).

cnf(i_0_166,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X2,X1,X3) ),
    inference(rename_variables,[],[i_0_46]) ).

cnf(i_0_167,plain,
    ( product(multiply(additive_identity,X1),X2,multiply(additive_identity,X1))
    | ~ product(multiply(additive_identity,X1),X2,multiply(additive_identity,X1)) ),
    inference(scs_inference,[],[i_0_89,i_0_56,i_0_155,i_0_53,i_0_73,i_0_55,i_0_54,i_0_62,i_0_146,i_0_149,i_0_65,i_0_112,i_0_49,i_0_40,i_0_41,i_0_43,i_0_44,i_0_45,i_0_39,i_0_37,i_0_36,i_0_46,i_0_31]) ).

cnf(i_0_168,plain,
    ( ~ sum(X1,X2,X3)
    | ~ sum(X4,X5,X6)
    | product(X3,X7,X6)
    | ~ product(X1,X7,X4)
    | ~ product(X2,X7,X5) ),
    inference(rename_variables,[],[i_0_31]) ).

cnf(i_0_169,plain,
    ( product(multiply(additive_identity,X1),X2,add(additive_identity,multiply(additive_identity,X1)))
    | ~ product(multiply(additive_identity,X1),X2,multiply(additive_identity,X1)) ),
    inference(scs_inference,[],[i_0_89,i_0_56,i_0_155,i_0_53,i_0_73,i_0_55,i_0_54,i_0_62,i_0_146,i_0_149,i_0_152,i_0_65,i_0_112,i_0_49,i_0_40,i_0_41,i_0_43,i_0_44,i_0_45,i_0_39,i_0_37,i_0_36,i_0_46,i_0_31,i_0_42]) ).

cnf(i_0_170,plain,
    equalish(X1,add(additive_identity,X1)),
    inference(rename_variables,[],[i_0_62]) ).

cnf(i_0_171,plain,
    ( ~ product(X1,X2,X3)
    | product(X1,X2,X4)
    | ~ equalish(X3,X4) ),
    inference(rename_variables,[],[i_0_42]) ).

cnf(i_0_172,plain,
    ( product(additive_identity,multiply(multiply(X1,X1),X1),multiply(additive_identity,X1))
    | ~ product(multiply(additive_identity,X1),multiply(X1,X1),multiply(additive_identity,X1)) ),
    inference(scs_inference,[],[i_0_89,i_0_140,i_0_56,i_0_155,i_0_53,i_0_73,i_0_55,i_0_54,i_0_62,i_0_146,i_0_149,i_0_152,i_0_65,i_0_112,i_0_49,i_0_143,i_0_40,i_0_41,i_0_43,i_0_44,i_0_45,i_0_39,i_0_37,i_0_36,i_0_46,i_0_31,i_0_42,i_0_34]) ).

cnf(i_0_173,plain,
    product(X1,X2,multiply(X1,X2)),
    inference(rename_variables,[],[i_0_49]) ).

cnf(i_0_174,plain,
    ( ~ product(X1,X2,X3)
    | product(X4,X5,X3)
    | ~ product(X4,X6,X1)
    | ~ product(X6,X2,X5) ),
    inference(rename_variables,[],[i_0_34]) ).

cnf(i_0_175,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_56]) ).

cnf(i_0_176,plain,
    product(X1,X2,multiply(X1,X2)),
    inference(rename_variables,[],[i_0_49]) ).

cnf(i_0_177,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_56]) ).

cnf(i_0_178,plain,
    product(X1,X2,multiply(X1,X2)),
    inference(rename_variables,[],[i_0_49]) ).

cnf(i_0_179,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_56]) ).

cnf(i_0_181,plain,
    sum(X1,additive_inverse(X1),add(additive_identity,additive_identity)),
    inference(scs_inference,[],[i_0_151,i_0_46]) ).

cnf(i_0_182,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X2,X1,X3) ),
    inference(rename_variables,[],[i_0_46]) ).

cnf(i_0_183,plain,
    product(X1,add(additive_identity,X2),multiply(add(additive_identity,X1),X2)),
    inference(scs_inference,[],[i_0_85,i_0_151,i_0_142,i_0_46,i_0_40]) ).

cnf(i_0_184,plain,
    product(X1,add(additive_identity,X2),multiply(X1,X2)),
    inference(rename_variables,[],[i_0_142]) ).

cnf(i_0_185,plain,
    ( ~ product(X1,X2,X3)
    | product(X4,X2,X3)
    | ~ equalish(X1,X4) ),
    inference(rename_variables,[],[i_0_40]) ).

cnf(i_0_186,plain,
    product(X1,X2,multiply(X1,add(additive_identity,X2))),
    inference(scs_inference,[],[i_0_85,i_0_151,i_0_142,i_0_49,i_0_46,i_0_40,i_0_41]) ).

cnf(i_0_187,plain,
    product(X1,X2,multiply(X1,X2)),
    inference(rename_variables,[],[i_0_49]) ).

cnf(i_0_188,plain,
    ( ~ product(X1,X2,X3)
    | product(X1,X4,X3)
    | ~ equalish(X2,X4) ),
    inference(rename_variables,[],[i_0_41]) ).

cnf(i_0_189,plain,
    sum(additive_inverse(add(additive_identity,X1)),X1,additive_identity),
    inference(scs_inference,[],[i_0_53,i_0_85,i_0_151,i_0_142,i_0_49,i_0_46,i_0_40,i_0_41,i_0_44]) ).

cnf(i_0_190,plain,
    sum(additive_inverse(X1),X1,additive_identity),
    inference(rename_variables,[],[i_0_53]) ).

cnf(i_0_191,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X1,X4,X3)
    | ~ equalish(X2,X4) ),
    inference(rename_variables,[],[i_0_44]) ).

cnf(i_0_192,plain,
    sum(X1,X2,add(X2,add(additive_identity,X1))),
    inference(scs_inference,[],[i_0_53,i_0_60,i_0_85,i_0_151,i_0_142,i_0_49,i_0_46,i_0_40,i_0_41,i_0_44,i_0_43]) ).

cnf(i_0_193,plain,
    sum(X1,X2,add(X2,X1)),
    inference(rename_variables,[],[i_0_60]) ).

cnf(i_0_194,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X2,X3)
    | ~ equalish(X1,X4) ),
    inference(rename_variables,[],[i_0_43]) ).

cnf(i_0_195,plain,
    ~ equalish(multiply(a,add(additive_identity,additive_identity)),additive_identity),
    inference(scs_inference,[],[i_0_51,i_0_53,i_0_60,i_0_85,i_0_151,i_0_142,i_0_49,i_0_46,i_0_40,i_0_41,i_0_44,i_0_43,i_0_42]) ).

cnf(i_0_196,plain,
    ( ~ product(X1,X2,X3)
    | product(X1,X2,X4)
    | ~ equalish(X3,X4) ),
    inference(rename_variables,[],[i_0_42]) ).

cnf(i_0_197,plain,
    ~ product(a,add(additive_identity,additive_identity),add(additive_identity,additive_identity)),
    inference(scs_inference,[],[i_0_51,i_0_53,i_0_60,i_0_85,i_0_151,i_0_120,i_0_142,i_0_184,i_0_49,i_0_46,i_0_40,i_0_41,i_0_44,i_0_43,i_0_42,i_0_38]) ).

cnf(i_0_198,plain,
    product(X1,add(additive_identity,X2),multiply(X1,X2)),
    inference(rename_variables,[],[i_0_142]) ).

cnf(i_0_199,plain,
    ( ~ product(X1,X2,X3)
    | equalish(X4,X3)
    | ~ product(X1,X2,X4) ),
    inference(rename_variables,[],[i_0_38]) ).

cnf(i_0_200,plain,
    ~ equalish(additive_identity,multiply(a,additive_identity)),
    inference(scs_inference,[],[i_0_51,i_0_53,i_0_55,i_0_60,i_0_85,i_0_151,i_0_120,i_0_142,i_0_184,i_0_154,i_0_49,i_0_46,i_0_40,i_0_41,i_0_44,i_0_43,i_0_42,i_0_38,i_0_45]) ).

cnf(i_0_201,plain,
    sum(additive_identity,X1,X1),
    inference(rename_variables,[],[i_0_55]) ).

cnf(i_0_202,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X1,X2,X4)
    | ~ equalish(X3,X4) ),
    inference(rename_variables,[],[i_0_45]) ).

cnf(i_0_203,plain,
    ~ sum(multiply(a,additive_identity),additive_identity,add(additive_identity,additive_identity)),
    inference(scs_inference,[],[i_0_51,i_0_56,i_0_53,i_0_55,i_0_60,i_0_85,i_0_151,i_0_120,i_0_142,i_0_184,i_0_154,i_0_49,i_0_46,i_0_40,i_0_41,i_0_44,i_0_43,i_0_42,i_0_38,i_0_45,i_0_39]) ).

cnf(i_0_204,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_56]) ).

cnf(i_0_205,plain,
    ( ~ sum(X1,X2,X3)
    | equalish(X4,X3)
    | ~ sum(X1,X2,X4) ),
    inference(rename_variables,[],[i_0_39]) ).

cnf(i_0_206,plain,
    ~ sum(additive_identity,additive_inverse(additive_inverse(additive_identity)),multiply(a,additive_identity)),
    inference(scs_inference,[],[i_0_51,i_0_56,i_0_53,i_0_55,i_0_201,i_0_60,i_0_193,i_0_85,i_0_151,i_0_120,i_0_142,i_0_184,i_0_157,i_0_154,i_0_49,i_0_46,i_0_40,i_0_41,i_0_44,i_0_43,i_0_42,i_0_38,i_0_45,i_0_39,i_0_37]) ).

cnf(i_0_207,plain,
    sum(additive_identity,X1,X1),
    inference(rename_variables,[],[i_0_55]) ).

cnf(i_0_208,plain,
    sum(X1,X2,add(X2,X1)),
    inference(rename_variables,[],[i_0_60]) ).

cnf(i_0_209,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ sum(X1,X6,X4)
    | ~ sum(X6,X5,X2) ),
    inference(rename_variables,[],[i_0_37]) ).

cnf(i_0_210,plain,
    ~ sum(additive_inverse(multiply(a,additive_identity)),additive_identity,additive_inverse(additive_identity)),
    inference(scs_inference,[],[i_0_51,i_0_56,i_0_53,i_0_55,i_0_201,i_0_60,i_0_193,i_0_208,i_0_85,i_0_54,i_0_151,i_0_120,i_0_142,i_0_184,i_0_157,i_0_154,i_0_112,i_0_49,i_0_46,i_0_40,i_0_41,i_0_44,i_0_43,i_0_42,i_0_38,i_0_45,i_0_39,i_0_37,i_0_36]) ).

cnf(i_0_211,plain,
    sum(X1,X2,add(X2,X1)),
    inference(rename_variables,[],[i_0_60]) ).

cnf(i_0_212,plain,
    sum(X1,additive_inverse(X1),additive_identity),
    inference(rename_variables,[],[i_0_54]) ).

cnf(i_0_213,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ sum(X4,X6,X1)
    | ~ sum(X6,X2,X5) ),
    inference(rename_variables,[],[i_0_36]) ).

cnf(i_0_214,plain,
    ( product(multiply(multiply(X1,X1),X1),X2,multiply(X1,X3))
    | ~ product(multiply(X1,X1),X2,add(additive_identity,X3)) ),
    inference(scs_inference,[],[i_0_51,i_0_89,i_0_56,i_0_53,i_0_55,i_0_201,i_0_60,i_0_193,i_0_208,i_0_85,i_0_54,i_0_151,i_0_120,i_0_142,i_0_184,i_0_198,i_0_157,i_0_154,i_0_112,i_0_49,i_0_46,i_0_40,i_0_41,i_0_44,i_0_43,i_0_42,i_0_38,i_0_45,i_0_39,i_0_37,i_0_36,i_0_35]) ).

cnf(i_0_215,plain,
    product(X1,add(additive_identity,X2),multiply(X1,X2)),
    inference(rename_variables,[],[i_0_142]) ).

cnf(i_0_216,plain,
    ( ~ product(X1,X2,X3)
    | product(X4,X5,X3)
    | ~ product(X1,X6,X4)
    | ~ product(X6,X5,X2) ),
    inference(rename_variables,[],[i_0_35]) ).

cnf(i_0_217,plain,
    ( product(X1,multiply(multiply(X1,X1),X2),multiply(X1,X3))
    | ~ product(multiply(X1,X1),add(additive_identity,X2),add(additive_identity,X3)) ),
    inference(scs_inference,[],[i_0_51,i_0_89,i_0_56,i_0_53,i_0_55,i_0_201,i_0_60,i_0_193,i_0_208,i_0_85,i_0_54,i_0_151,i_0_120,i_0_142,i_0_184,i_0_198,i_0_215,i_0_157,i_0_154,i_0_112,i_0_49,i_0_46,i_0_40,i_0_41,i_0_44,i_0_43,i_0_42,i_0_38,i_0_45,i_0_39,i_0_37,i_0_36,i_0_35,i_0_34]) ).

cnf(i_0_218,plain,
    product(X1,add(additive_identity,X2),multiply(X1,X2)),
    inference(rename_variables,[],[i_0_142]) ).

cnf(i_0_219,plain,
    ( ~ product(X1,X2,X3)
    | product(X4,X5,X3)
    | ~ product(X4,X6,X1)
    | ~ product(X6,X2,X5) ),
    inference(rename_variables,[],[i_0_34]) ).

cnf(i_0_220,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_56]) ).

cnf(i_0_221,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_56]) ).

cnf(i_0_222,plain,
    product(X1,add(additive_identity,X2),multiply(X1,X2)),
    inference(rename_variables,[],[i_0_142]) ).

cnf(i_0_223,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_56]) ).

cnf(i_0_224,plain,
    product(X1,add(additive_identity,X2),multiply(X1,X2)),
    inference(rename_variables,[],[i_0_142]) ).

cnf(i_0_225,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_56]) ).

cnf(i_0_227,plain,
    sum(add(additive_identity,additive_identity),X1,X1),
    inference(scs_inference,[],[i_0_148,i_0_46]) ).

cnf(i_0_228,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X2,X1,X3) ),
    inference(rename_variables,[],[i_0_46]) ).

cnf(i_0_229,plain,
    product(add(additive_identity,X1),X2,multiply(X1,add(additive_identity,X2))),
    inference(scs_inference,[],[i_0_62,i_0_148,i_0_186,i_0_46,i_0_40]) ).

cnf(i_0_230,plain,
    product(X1,X2,multiply(X1,add(additive_identity,X2))),
    inference(rename_variables,[],[i_0_186]) ).

cnf(i_0_231,plain,
    ( ~ product(X1,X2,X3)
    | product(X4,X2,X3)
    | ~ equalish(X1,X4) ),
    inference(rename_variables,[],[i_0_40]) ).

cnf(i_0_232,plain,
    product(X1,add(additive_identity,add(additive_identity,X2)),multiply(X1,X2)),
    inference(scs_inference,[],[i_0_62,i_0_148,i_0_186,i_0_142,i_0_46,i_0_40,i_0_41]) ).

cnf(i_0_233,plain,
    equalish(X1,add(additive_identity,X1)),
    inference(rename_variables,[],[i_0_62]) ).

cnf(i_0_234,plain,
    ( ~ product(X1,X2,X3)
    | product(X1,X4,X3)
    | ~ equalish(X2,X4) ),
    inference(rename_variables,[],[i_0_41]) ).

cnf(i_0_235,plain,
    sum(multiply(X1,additive_identity),add(additive_identity,multiply(X1,additive_identity)),multiply(X1,additive_identity)),
    inference(scs_inference,[],[i_0_79,i_0_62,i_0_233,i_0_148,i_0_186,i_0_142,i_0_46,i_0_40,i_0_41,i_0_44]) ).

cnf(i_0_236,plain,
    equalish(X1,add(additive_identity,X1)),
    inference(rename_variables,[],[i_0_62]) ).

cnf(i_0_237,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X1,X4,X3)
    | ~ equalish(X2,X4) ),
    inference(rename_variables,[],[i_0_44]) ).

cnf(i_0_238,plain,
    sum(add(additive_identity,multiply(X1,additive_identity)),multiply(X1,additive_identity),multiply(X1,additive_identity)),
    inference(scs_inference,[],[i_0_79,i_0_62,i_0_233,i_0_236,i_0_148,i_0_186,i_0_142,i_0_46,i_0_40,i_0_41,i_0_44,i_0_43]) ).

cnf(i_0_239,plain,
    equalish(X1,add(additive_identity,X1)),
    inference(rename_variables,[],[i_0_62]) ).

cnf(i_0_240,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X2,X3)
    | ~ equalish(X1,X4) ),
    inference(rename_variables,[],[i_0_43]) ).

cnf(i_0_241,plain,
    ~ equalish(multiply(add(additive_identity,a),additive_identity),add(additive_identity,additive_identity)),
    inference(scs_inference,[],[i_0_183,i_0_79,i_0_62,i_0_233,i_0_236,i_0_148,i_0_186,i_0_197,i_0_142,i_0_46,i_0_40,i_0_41,i_0_44,i_0_43,i_0_42]) ).

cnf(i_0_242,plain,
    product(X1,add(additive_identity,X2),multiply(add(additive_identity,X1),X2)),
    inference(rename_variables,[],[i_0_183]) ).

cnf(i_0_243,plain,
    ( ~ product(X1,X2,X3)
    | product(X1,X2,X4)
    | ~ equalish(X3,X4) ),
    inference(rename_variables,[],[i_0_42]) ).

cnf(i_0_244,plain,
    ~ product(a,add(additive_identity,additive_identity),additive_identity),
    inference(scs_inference,[],[i_0_183,i_0_79,i_0_62,i_0_233,i_0_236,i_0_148,i_0_186,i_0_197,i_0_200,i_0_142,i_0_46,i_0_40,i_0_41,i_0_44,i_0_43,i_0_42,i_0_38]) ).

cnf(i_0_245,plain,
    product(X1,add(additive_identity,X2),multiply(X1,X2)),
    inference(rename_variables,[],[i_0_142]) ).

cnf(i_0_246,plain,
    ( ~ product(X1,X2,X3)
    | equalish(X4,X3)
    | ~ product(X1,X2,X4) ),
    inference(rename_variables,[],[i_0_38]) ).

cnf(i_0_247,plain,
    sum(multiply(X1,additive_identity),multiply(X1,additive_identity),add(additive_identity,multiply(X1,additive_identity))),
    inference(scs_inference,[],[i_0_183,i_0_79,i_0_62,i_0_233,i_0_236,i_0_239,i_0_148,i_0_186,i_0_197,i_0_200,i_0_142,i_0_46,i_0_40,i_0_41,i_0_44,i_0_43,i_0_42,i_0_38,i_0_45]) ).

cnf(i_0_248,plain,
    equalish(X1,add(additive_identity,X1)),
    inference(rename_variables,[],[i_0_62]) ).

cnf(i_0_249,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X1,X2,X4)
    | ~ equalish(X3,X4) ),
    inference(rename_variables,[],[i_0_45]) ).

cnf(i_0_250,plain,
    ~ sum(multiply(a,additive_identity),multiply(a,additive_identity),additive_identity),
    inference(scs_inference,[],[i_0_183,i_0_79,i_0_62,i_0_233,i_0_236,i_0_239,i_0_148,i_0_186,i_0_197,i_0_200,i_0_142,i_0_46,i_0_40,i_0_41,i_0_44,i_0_43,i_0_42,i_0_38,i_0_45,i_0_39]) ).

cnf(i_0_251,plain,
    sum(multiply(X1,additive_identity),multiply(X1,additive_identity),multiply(X1,additive_identity)),
    inference(rename_variables,[],[i_0_79]) ).

cnf(i_0_252,plain,
    ( ~ sum(X1,X2,X3)
    | equalish(X4,X3)
    | ~ sum(X1,X2,X4) ),
    inference(rename_variables,[],[i_0_39]) ).

cnf(i_0_253,plain,
    ~ sum(additive_inverse(multiply(a,additive_identity)),additive_identity,multiply(a,additive_identity)),
    inference(scs_inference,[],[i_0_183,i_0_79,i_0_251,i_0_62,i_0_233,i_0_236,i_0_239,i_0_181,i_0_148,i_0_186,i_0_197,i_0_106,i_0_200,i_0_142,i_0_46,i_0_40,i_0_41,i_0_44,i_0_43,i_0_42,i_0_38,i_0_45,i_0_39,i_0_37]) ).

cnf(i_0_254,plain,
    sum(multiply(X1,additive_identity),multiply(X1,additive_identity),multiply(X1,additive_identity)),
    inference(rename_variables,[],[i_0_79]) ).

cnf(i_0_255,plain,
    sum(X1,additive_inverse(X1),add(additive_identity,additive_identity)),
    inference(rename_variables,[],[i_0_181]) ).

cnf(i_0_256,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ sum(X1,X6,X4)
    | ~ sum(X6,X5,X2) ),
    inference(rename_variables,[],[i_0_37]) ).

cnf(i_0_257,plain,
    ~ sum(multiply(a,additive_identity),multiply(a,additive_identity),additive_inverse(additive_identity)),
    inference(scs_inference,[],[i_0_183,i_0_56,i_0_79,i_0_251,i_0_53,i_0_62,i_0_233,i_0_236,i_0_239,i_0_181,i_0_148,i_0_186,i_0_197,i_0_106,i_0_200,i_0_142,i_0_46,i_0_40,i_0_41,i_0_44,i_0_43,i_0_42,i_0_38,i_0_45,i_0_39,i_0_37,i_0_36]) ).

cnf(i_0_258,plain,
    sum(additive_inverse(X1),X1,additive_identity),
    inference(rename_variables,[],[i_0_53]) ).

cnf(i_0_259,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_56]) ).

cnf(i_0_260,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ sum(X4,X6,X1)
    | ~ sum(X6,X2,X5) ),
    inference(rename_variables,[],[i_0_36]) ).

cnf(i_0_261,plain,
    ( product(X1,multiply(a,additive_identity),multiply(a,additive_identity))
    | ~ product(X1,a,a) ),
    inference(scs_inference,[],[i_0_183,i_0_56,i_0_79,i_0_251,i_0_53,i_0_62,i_0_233,i_0_236,i_0_239,i_0_181,i_0_148,i_0_186,i_0_197,i_0_106,i_0_200,i_0_142,i_0_46,i_0_40,i_0_41,i_0_44,i_0_43,i_0_42,i_0_38,i_0_45,i_0_39,i_0_37,i_0_36,i_0_34]) ).

cnf(i_0_262,plain,
    ( ~ product(X1,X2,X3)
    | product(X4,X5,X3)
    | ~ product(X4,X6,X1)
    | ~ product(X6,X2,X5) ),
    inference(rename_variables,[],[i_0_34]) ).

cnf(i_0_263,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_56]) ).

cnf(i_0_264,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_56]) ).

cnf(i_0_265,plain,
    product(X1,add(additive_identity,X2),multiply(X1,X2)),
    inference(rename_variables,[],[i_0_142]) ).

cnf(i_0_266,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_56]) ).

cnf(i_0_267,plain,
    product(X1,add(additive_identity,X2),multiply(X1,X2)),
    inference(rename_variables,[],[i_0_142]) ).

cnf(i_0_268,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_56]) ).

cnf(i_0_269,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_56]) ).

cnf(i_0_270,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_56]) ).

cnf(i_0_272,plain,
    sum(X1,X2,add(X1,add(additive_identity,X2))),
    inference(scs_inference,[],[i_0_192,i_0_46]) ).

cnf(i_0_273,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X2,X1,X3) ),
    inference(rename_variables,[],[i_0_46]) ).

cnf(i_0_274,plain,
    product(X1,X2,multiply(add(additive_identity,X1),add(additive_identity,X2))),
    inference(scs_inference,[],[i_0_85,i_0_192,i_0_186,i_0_46,i_0_40]) ).

cnf(i_0_275,plain,
    product(X1,X2,multiply(X1,add(additive_identity,X2))),
    inference(rename_variables,[],[i_0_186]) ).

cnf(i_0_276,plain,
    ( ~ product(X1,X2,X3)
    | product(X4,X2,X3)
    | ~ equalish(X1,X4) ),
    inference(rename_variables,[],[i_0_40]) ).

cnf(i_0_277,plain,
    product(X1,X2,multiply(add(additive_identity,X1),X2)),
    inference(scs_inference,[],[i_0_183,i_0_85,i_0_192,i_0_186,i_0_46,i_0_40,i_0_41]) ).

cnf(i_0_278,plain,
    product(X1,add(additive_identity,X2),multiply(add(additive_identity,X1),X2)),
    inference(rename_variables,[],[i_0_183]) ).

cnf(i_0_279,plain,
    ( ~ product(X1,X2,X3)
    | product(X1,X4,X3)
    | ~ equalish(X2,X4) ),
    inference(rename_variables,[],[i_0_41]) ).

cnf(i_0_280,plain,
    sum(multiply(additive_identity,X1),add(additive_identity,multiply(additive_identity,X1)),multiply(additive_identity,X1)),
    inference(scs_inference,[],[i_0_183,i_0_73,i_0_85,i_0_62,i_0_192,i_0_186,i_0_46,i_0_40,i_0_41,i_0_44]) ).

cnf(i_0_281,plain,
    equalish(X1,add(additive_identity,X1)),
    inference(rename_variables,[],[i_0_62]) ).

cnf(i_0_282,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X1,X4,X3)
    | ~ equalish(X2,X4) ),
    inference(rename_variables,[],[i_0_44]) ).

cnf(i_0_283,plain,
    ~ equalish(additive_inverse(additive_identity),additive_inverse(multiply(a,additive_identity))),
    inference(scs_inference,[],[i_0_183,i_0_56,i_0_73,i_0_85,i_0_62,i_0_192,i_0_210,i_0_186,i_0_46,i_0_40,i_0_41,i_0_44,i_0_43]) ).

cnf(i_0_284,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_56]) ).

cnf(i_0_285,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X2,X3)
    | ~ equalish(X1,X4) ),
    inference(rename_variables,[],[i_0_43]) ).

cnf(i_0_286,plain,
    ~ equalish(multiply(add(additive_identity,a),additive_identity),additive_identity),
    inference(scs_inference,[],[i_0_183,i_0_278,i_0_56,i_0_73,i_0_85,i_0_62,i_0_192,i_0_210,i_0_244,i_0_186,i_0_46,i_0_40,i_0_41,i_0_44,i_0_43,i_0_42]) ).

cnf(i_0_287,plain,
    product(X1,add(additive_identity,X2),multiply(add(additive_identity,X1),X2)),
    inference(rename_variables,[],[i_0_183]) ).

cnf(i_0_288,plain,
    ( ~ product(X1,X2,X3)
    | product(X1,X2,X4)
    | ~ equalish(X3,X4) ),
    inference(rename_variables,[],[i_0_42]) ).

cnf(i_0_289,plain,
    ~ product(a,add(additive_identity,add(additive_identity,additive_identity)),add(additive_identity,additive_identity)),
    inference(scs_inference,[],[i_0_183,i_0_278,i_0_56,i_0_73,i_0_85,i_0_62,i_0_192,i_0_232,i_0_210,i_0_244,i_0_186,i_0_120,i_0_46,i_0_40,i_0_41,i_0_44,i_0_43,i_0_42,i_0_38]) ).

cnf(i_0_290,plain,
    product(X1,add(additive_identity,add(additive_identity,X2)),multiply(X1,X2)),
    inference(rename_variables,[],[i_0_232]) ).

cnf(i_0_291,plain,
    ( ~ product(X1,X2,X3)
    | equalish(X4,X3)
    | ~ product(X1,X2,X4) ),
    inference(rename_variables,[],[i_0_38]) ).

cnf(i_0_292,plain,
    sum(multiply(additive_identity,X1),multiply(additive_identity,X1),add(additive_identity,multiply(additive_identity,X1))),
    inference(scs_inference,[],[i_0_183,i_0_278,i_0_56,i_0_73,i_0_85,i_0_62,i_0_281,i_0_192,i_0_232,i_0_210,i_0_244,i_0_186,i_0_120,i_0_46,i_0_40,i_0_41,i_0_44,i_0_43,i_0_42,i_0_38,i_0_45]) ).

cnf(i_0_293,plain,
    equalish(X1,add(additive_identity,X1)),
    inference(rename_variables,[],[i_0_62]) ).

cnf(i_0_294,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X1,X2,X4)
    | ~ equalish(X3,X4) ),
    inference(rename_variables,[],[i_0_45]) ).

cnf(i_0_295,plain,
    ~ sum(multiply(a,additive_identity),multiply(a,additive_identity),add(additive_identity,additive_identity)),
    inference(scs_inference,[],[i_0_183,i_0_278,i_0_56,i_0_73,i_0_79,i_0_85,i_0_62,i_0_281,i_0_192,i_0_232,i_0_210,i_0_244,i_0_186,i_0_120,i_0_46,i_0_40,i_0_41,i_0_44,i_0_43,i_0_42,i_0_38,i_0_45,i_0_39]) ).

cnf(i_0_296,plain,
    sum(multiply(X1,additive_identity),multiply(X1,additive_identity),multiply(X1,additive_identity)),
    inference(rename_variables,[],[i_0_79]) ).

cnf(i_0_297,plain,
    ( ~ sum(X1,X2,X3)
    | equalish(X4,X3)
    | ~ sum(X1,X2,X4) ),
    inference(rename_variables,[],[i_0_39]) ).

cnf(i_0_298,plain,
    ~ sum(multiply(a,additive_identity),multiply(a,additive_identity),additive_inverse(multiply(a,additive_identity))),
    inference(scs_inference,[],[i_0_183,i_0_278,i_0_56,i_0_284,i_0_73,i_0_79,i_0_296,i_0_85,i_0_62,i_0_281,i_0_192,i_0_232,i_0_210,i_0_253,i_0_244,i_0_186,i_0_120,i_0_46,i_0_40,i_0_41,i_0_44,i_0_43,i_0_42,i_0_38,i_0_45,i_0_39,i_0_37]) ).

cnf(i_0_299,plain,
    sum(multiply(X1,additive_identity),multiply(X1,additive_identity),multiply(X1,additive_identity)),
    inference(rename_variables,[],[i_0_79]) ).

cnf(i_0_300,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_56]) ).

cnf(i_0_301,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ sum(X1,X6,X4)
    | ~ sum(X6,X5,X2) ),
    inference(rename_variables,[],[i_0_37]) ).

cnf(i_0_302,plain,
    ~ sum(additive_inverse(multiply(a,additive_identity)),additive_identity,additive_identity),
    inference(scs_inference,[],[i_0_183,i_0_278,i_0_56,i_0_284,i_0_73,i_0_79,i_0_296,i_0_85,i_0_62,i_0_281,i_0_60,i_0_54,i_0_192,i_0_232,i_0_210,i_0_203,i_0_253,i_0_244,i_0_186,i_0_120,i_0_46,i_0_40,i_0_41,i_0_44,i_0_43,i_0_42,i_0_38,i_0_45,i_0_39,i_0_37,i_0_36]) ).

cnf(i_0_303,plain,
    sum(X1,X2,add(X2,X1)),
    inference(rename_variables,[],[i_0_60]) ).

cnf(i_0_304,plain,
    sum(X1,additive_inverse(X1),additive_identity),
    inference(rename_variables,[],[i_0_54]) ).

cnf(i_0_305,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ sum(X4,X6,X1)
    | ~ sum(X6,X2,X5) ),
    inference(rename_variables,[],[i_0_36]) ).

cnf(i_0_306,plain,
    ( product(multiply(multiply(X1,X1),X1),X2,multiply(X1,X3))
    | ~ product(multiply(X1,X1),X2,add(additive_identity,add(additive_identity,X3))) ),
    inference(scs_inference,[],[i_0_89,i_0_183,i_0_278,i_0_56,i_0_284,i_0_73,i_0_79,i_0_296,i_0_85,i_0_62,i_0_281,i_0_60,i_0_54,i_0_192,i_0_232,i_0_290,i_0_210,i_0_203,i_0_253,i_0_244,i_0_186,i_0_120,i_0_46,i_0_40,i_0_41,i_0_44,i_0_43,i_0_42,i_0_38,i_0_45,i_0_39,i_0_37,i_0_36,i_0_35]) ).

cnf(i_0_307,plain,
    product(X1,add(additive_identity,add(additive_identity,X2)),multiply(X1,X2)),
    inference(rename_variables,[],[i_0_232]) ).

cnf(i_0_308,plain,
    ( ~ product(X1,X2,X3)
    | product(X4,X5,X3)
    | ~ product(X1,X6,X4)
    | ~ product(X6,X5,X2) ),
    inference(rename_variables,[],[i_0_35]) ).

cnf(i_0_309,plain,
    ( ~ sum(a,a,additive_identity)
    | ~ product(additive_identity,add(additive_identity,add(additive_identity,additive_identity)),additive_identity) ),
    inference(scs_inference,[],[i_0_89,i_0_183,i_0_278,i_0_56,i_0_284,i_0_300,i_0_73,i_0_79,i_0_296,i_0_85,i_0_62,i_0_281,i_0_60,i_0_54,i_0_192,i_0_232,i_0_290,i_0_307,i_0_250,i_0_210,i_0_203,i_0_253,i_0_244,i_0_186,i_0_120,i_0_46,i_0_40,i_0_41,i_0_44,i_0_43,i_0_42,i_0_38,i_0_45,i_0_39,i_0_37,i_0_36,i_0_35,i_0_31,i_0_32]) ).

cnf(i_0_310,plain,
    product(X1,add(additive_identity,add(additive_identity,X2)),multiply(X1,X2)),
    inference(rename_variables,[],[i_0_232]) ).

cnf(i_0_311,plain,
    product(X1,add(additive_identity,add(additive_identity,X2)),multiply(X1,X2)),
    inference(rename_variables,[],[i_0_232]) ).

cnf(i_0_312,plain,
    ( ~ product(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ product(X6,X2,X4)
    | ~ product(X7,X2,X5)
    | ~ sum(X6,X7,X1) ),
    inference(rename_variables,[],[i_0_32]) ).

cnf(i_0_313,plain,
    product(X1,add(additive_identity,X2),multiply(X1,X2)),
    inference(rename_variables,[],[i_0_142]) ).

cnf(i_0_314,plain,
    sum(additive_identity,X1,X1),
    inference(rename_variables,[],[i_0_55]) ).

cnf(i_0_315,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_56]) ).

cnf(i_0_317,plain,
    sum(add(additive_identity,multiply(additive_identity,X1)),multiply(additive_identity,X1),multiply(additive_identity,X1)),
    inference(scs_inference,[],[i_0_280,i_0_46]) ).

cnf(i_0_318,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X2,X1,X3) ),
    inference(rename_variables,[],[i_0_46]) ).

cnf(i_0_319,plain,
    ~ equalish(multiply(a,additive_identity),additive_inverse(additive_inverse(additive_identity))),
    inference(scs_inference,[],[i_0_55,i_0_280,i_0_206,i_0_46,i_0_44]) ).

cnf(i_0_320,plain,
    sum(additive_identity,X1,X1),
    inference(rename_variables,[],[i_0_55]) ).

cnf(i_0_321,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X1,X4,X3)
    | ~ equalish(X2,X4) ),
    inference(rename_variables,[],[i_0_44]) ).

cnf(i_0_322,plain,
    ~ equalish(additive_identity,additive_inverse(multiply(a,additive_identity))),
    inference(scs_inference,[],[i_0_56,i_0_55,i_0_280,i_0_206,i_0_302,i_0_46,i_0_44,i_0_43]) ).

cnf(i_0_323,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_56]) ).

cnf(i_0_324,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X2,X3)
    | ~ equalish(X1,X4) ),
    inference(rename_variables,[],[i_0_43]) ).

cnf(i_0_325,plain,
    ~ equalish(multiply(add(additive_identity,a),add(additive_identity,additive_identity)),additive_identity),
    inference(scs_inference,[],[i_0_51,i_0_274,i_0_56,i_0_55,i_0_280,i_0_206,i_0_302,i_0_46,i_0_44,i_0_43,i_0_42]) ).

cnf(i_0_326,plain,
    product(X1,X2,multiply(add(additive_identity,X1),add(additive_identity,X2))),
    inference(rename_variables,[],[i_0_274]) ).

cnf(i_0_327,plain,
    ( ~ product(X1,X2,X3)
    | product(X1,X2,X4)
    | ~ equalish(X3,X4) ),
    inference(rename_variables,[],[i_0_42]) ).

cnf(i_0_328,plain,
    ~ product(a,add(additive_identity,add(additive_identity,additive_identity)),additive_identity),
    inference(scs_inference,[],[i_0_51,i_0_274,i_0_56,i_0_55,i_0_280,i_0_206,i_0_302,i_0_232,i_0_200,i_0_46,i_0_44,i_0_43,i_0_42,i_0_38]) ).

cnf(i_0_329,plain,
    product(X1,add(additive_identity,add(additive_identity,X2)),multiply(X1,X2)),
    inference(rename_variables,[],[i_0_232]) ).

cnf(i_0_330,plain,
    ( ~ product(X1,X2,X3)
    | equalish(X4,X3)
    | ~ product(X1,X2,X4) ),
    inference(rename_variables,[],[i_0_38]) ).

cnf(i_0_331,plain,
    ~ equalish(add(multiply(a,additive_identity),multiply(a,additive_identity)),add(additive_identity,additive_identity)),
    inference(scs_inference,[],[i_0_51,i_0_274,i_0_56,i_0_55,i_0_50,i_0_295,i_0_280,i_0_206,i_0_302,i_0_232,i_0_200,i_0_46,i_0_44,i_0_43,i_0_42,i_0_38,i_0_45]) ).

cnf(i_0_332,plain,
    sum(X1,X2,add(X1,X2)),
    inference(rename_variables,[],[i_0_50]) ).

cnf(i_0_333,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X1,X2,X4)
    | ~ equalish(X3,X4) ),
    inference(rename_variables,[],[i_0_45]) ).

cnf(i_0_334,plain,
    ~ sum(additive_inverse(X1),X1,multiply(add(additive_identity,a),additive_identity)),
    inference(scs_inference,[],[i_0_51,i_0_274,i_0_56,i_0_55,i_0_53,i_0_50,i_0_295,i_0_280,i_0_206,i_0_286,i_0_302,i_0_232,i_0_200,i_0_46,i_0_44,i_0_43,i_0_42,i_0_38,i_0_45,i_0_39]) ).

cnf(i_0_335,plain,
    ( ~ sum(X1,X2,X3)
    | equalish(X4,X3)
    | ~ sum(X1,X2,X4) ),
    inference(rename_variables,[],[i_0_39]) ).

cnf(i_0_336,plain,
    ~ sum(additive_identity,additive_inverse(multiply(a,additive_identity)),multiply(a,additive_identity)),
    inference(scs_inference,[],[i_0_51,i_0_274,i_0_56,i_0_55,i_0_320,i_0_53,i_0_50,i_0_295,i_0_280,i_0_206,i_0_286,i_0_302,i_0_151,i_0_232,i_0_200,i_0_46,i_0_44,i_0_43,i_0_42,i_0_38,i_0_45,i_0_39,i_0_37]) ).

cnf(i_0_337,plain,
    sum(additive_identity,X1,X1),
    inference(rename_variables,[],[i_0_55]) ).

cnf(i_0_338,plain,
    sum(additive_inverse(X1),X1,add(additive_identity,additive_identity)),
    inference(rename_variables,[],[i_0_151]) ).

cnf(i_0_339,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ sum(X1,X6,X4)
    | ~ sum(X6,X5,X2) ),
    inference(rename_variables,[],[i_0_37]) ).

cnf(i_0_340,plain,
    ~ sum(multiply(a,additive_identity),multiply(a,additive_identity),additive_inverse(additive_inverse(additive_identity))),
    inference(scs_inference,[],[i_0_51,i_0_274,i_0_56,i_0_79,i_0_55,i_0_320,i_0_337,i_0_53,i_0_50,i_0_295,i_0_280,i_0_206,i_0_286,i_0_302,i_0_151,i_0_232,i_0_200,i_0_46,i_0_44,i_0_43,i_0_42,i_0_38,i_0_45,i_0_39,i_0_37,i_0_36]) ).

cnf(i_0_341,plain,
    sum(multiply(X1,additive_identity),multiply(X1,additive_identity),multiply(X1,additive_identity)),
    inference(rename_variables,[],[i_0_79]) ).

cnf(i_0_342,plain,
    sum(additive_identity,X1,X1),
    inference(rename_variables,[],[i_0_55]) ).

cnf(i_0_343,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ sum(X4,X6,X1)
    | ~ sum(X6,X2,X5) ),
    inference(rename_variables,[],[i_0_36]) ).

cnf(i_0_344,plain,
    ( product(multiply(X1,additive_identity),X2,multiply(X1,additive_identity))
    | ~ product(multiply(X1,additive_identity),X2,multiply(X1,additive_identity)) ),
    inference(scs_inference,[],[i_0_51,i_0_274,i_0_56,i_0_79,i_0_341,i_0_55,i_0_320,i_0_337,i_0_53,i_0_50,i_0_295,i_0_280,i_0_206,i_0_286,i_0_302,i_0_151,i_0_232,i_0_200,i_0_46,i_0_44,i_0_43,i_0_42,i_0_38,i_0_45,i_0_39,i_0_37,i_0_36,i_0_31]) ).

cnf(i_0_345,plain,
    ( ~ sum(X1,X2,X3)
    | ~ sum(X4,X5,X6)
    | product(X3,X7,X6)
    | ~ product(X1,X7,X4)
    | ~ product(X2,X7,X5) ),
    inference(rename_variables,[],[i_0_31]) ).

cnf(i_0_346,plain,
    ( product(multiply(X1,additive_identity),X2,multiply(X1,additive_identity))
    | ~ product(multiply(X1,additive_identity),add(additive_identity,X2),multiply(X1,additive_identity)) ),
    inference(scs_inference,[],[i_0_51,i_0_274,i_0_56,i_0_79,i_0_341,i_0_55,i_0_320,i_0_337,i_0_53,i_0_85,i_0_50,i_0_295,i_0_280,i_0_206,i_0_286,i_0_302,i_0_151,i_0_232,i_0_200,i_0_46,i_0_44,i_0_43,i_0_42,i_0_38,i_0_45,i_0_39,i_0_37,i_0_36,i_0_31,i_0_41]) ).

cnf(i_0_347,plain,
    ( ~ product(X1,X2,X3)
    | product(X1,X4,X3)
    | ~ equalish(X2,X4) ),
    inference(rename_variables,[],[i_0_41]) ).

cnf(i_0_348,plain,
    ( product(add(additive_identity,multiply(X1,additive_identity)),add(additive_identity,X2),multiply(X1,additive_identity))
    | ~ product(multiply(X1,additive_identity),add(additive_identity,X2),multiply(X1,additive_identity)) ),
    inference(scs_inference,[],[i_0_51,i_0_274,i_0_56,i_0_79,i_0_341,i_0_55,i_0_320,i_0_337,i_0_53,i_0_85,i_0_50,i_0_62,i_0_295,i_0_280,i_0_206,i_0_286,i_0_302,i_0_151,i_0_232,i_0_200,i_0_46,i_0_44,i_0_43,i_0_42,i_0_38,i_0_45,i_0_39,i_0_37,i_0_36,i_0_31,i_0_41,i_0_40]) ).

cnf(i_0_349,plain,
    equalish(X1,add(additive_identity,X1)),
    inference(rename_variables,[],[i_0_62]) ).

cnf(i_0_350,plain,
    ( ~ product(X1,X2,X3)
    | product(X4,X2,X3)
    | ~ equalish(X1,X4) ),
    inference(rename_variables,[],[i_0_40]) ).

cnf(i_0_351,plain,
    product(X1,add(additive_identity,add(additive_identity,X2)),multiply(X1,X2)),
    inference(rename_variables,[],[i_0_232]) ).

cnf(i_0_352,plain,
    product(X1,add(additive_identity,X2),multiply(X1,X2)),
    inference(rename_variables,[],[i_0_142]) ).

cnf(i_0_353,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_56]) ).

cnf(i_0_354,plain,
    product(X1,add(additive_identity,X2),multiply(X1,X2)),
    inference(rename_variables,[],[i_0_142]) ).

cnf(i_0_355,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_56]) ).

cnf(i_0_356,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_56]) ).

cnf(i_0_357,plain,
    ( ~ product(a,additive_inverse(X1),additive_identity)
    | ~ product(multiply(X2,additive_identity),add(additive_identity,X3),multiply(X2,additive_identity))
    | ~ product(a,X1,additive_identity) ),
    inference(scs_inference,[],[i_0_51,i_0_89,i_0_274,i_0_56,i_0_323,i_0_353,i_0_355,i_0_79,i_0_341,i_0_55,i_0_320,i_0_337,i_0_53,i_0_85,i_0_50,i_0_62,i_0_295,i_0_280,i_0_206,i_0_286,i_0_302,i_0_151,i_0_232,i_0_329,i_0_200,i_0_142,i_0_352,i_0_46,i_0_44,i_0_43,i_0_42,i_0_38,i_0_45,i_0_39,i_0_37,i_0_36,i_0_31,i_0_41,i_0_40,i_0_30]) ).

cnf(i_0_358,plain,
    sum(X1,additive_inverse(add(additive_identity,X1)),additive_identity),
    inference(scs_inference,[],[i_0_189,i_0_46]) ).

cnf(i_0_359,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X2,X1,X3) ),
    inference(rename_variables,[],[i_0_46]) ).

cnf(i_0_360,plain,
    ~ equalish(add(multiply(a,additive_identity),multiply(a,additive_identity)),additive_identity),
    inference(scs_inference,[],[i_0_62,i_0_331,i_0_189,i_0_46,i_0_52]) ).

cnf(i_0_361,plain,
    equalish(X1,add(additive_identity,X1)),
    inference(rename_variables,[],[i_0_62]) ).

cnf(i_0_362,plain,
    ( ~ equalish(X1,X2)
    | equalish(X3,X2)
    | ~ equalish(X3,X1) ),
    inference(rename_variables,[],[i_0_52]) ).

cnf(i_0_363,plain,
    ~ equalish(multiply(a,additive_identity),additive_inverse(multiply(a,additive_identity))),
    inference(scs_inference,[],[i_0_55,i_0_62,i_0_331,i_0_336,i_0_189,i_0_46,i_0_52,i_0_44]) ).

cnf(i_0_364,plain,
    sum(additive_identity,X1,X1),
    inference(rename_variables,[],[i_0_55]) ).

cnf(i_0_365,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X1,X4,X3)
    | ~ equalish(X2,X4) ),
    inference(rename_variables,[],[i_0_44]) ).

cnf(i_0_366,plain,
    ~ equalish(additive_inverse(multiply(a,additive_identity)),multiply(a,additive_identity)),
    inference(scs_inference,[],[i_0_55,i_0_62,i_0_53,i_0_331,i_0_336,i_0_189,i_0_250,i_0_46,i_0_52,i_0_44,i_0_43]) ).

cnf(i_0_367,plain,
    sum(additive_inverse(X1),X1,additive_identity),
    inference(rename_variables,[],[i_0_53]) ).

cnf(i_0_368,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X2,X3)
    | ~ equalish(X1,X4) ),
    inference(rename_variables,[],[i_0_43]) ).

cnf(i_0_369,plain,
    ~ equalish(multiply(add(additive_identity,a),add(additive_identity,additive_identity)),add(additive_identity,additive_identity)),
    inference(scs_inference,[],[i_0_183,i_0_55,i_0_62,i_0_53,i_0_331,i_0_336,i_0_289,i_0_189,i_0_250,i_0_46,i_0_52,i_0_44,i_0_43,i_0_42]) ).

cnf(i_0_370,plain,
    product(X1,add(additive_identity,X2),multiply(add(additive_identity,X1),X2)),
    inference(rename_variables,[],[i_0_183]) ).

cnf(i_0_371,plain,
    ( ~ product(X1,X2,X3)
    | product(X1,X2,X4)
    | ~ equalish(X3,X4) ),
    inference(rename_variables,[],[i_0_42]) ).

cnf(i_0_372,plain,
    ~ equalish(additive_inverse(additive_identity),multiply(add(additive_identity,a),additive_identity)),
    inference(scs_inference,[],[i_0_183,i_0_56,i_0_55,i_0_62,i_0_53,i_0_331,i_0_334,i_0_336,i_0_289,i_0_189,i_0_250,i_0_46,i_0_52,i_0_44,i_0_43,i_0_42,i_0_45]) ).

cnf(i_0_373,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_56]) ).

cnf(i_0_374,plain,
    ~ sum(additive_inverse(X1),X1,multiply(add(additive_identity,a),additive_identity)),
    inference(rename_variables,[],[i_0_334]) ).

cnf(i_0_375,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X1,X2,X4)
    | ~ equalish(X3,X4) ),
    inference(rename_variables,[],[i_0_45]) ).

cnf(i_0_376,plain,
    ~ sum(additive_inverse(X1),X1,multiply(add(additive_identity,a),add(additive_identity,additive_identity))),
    inference(scs_inference,[],[i_0_183,i_0_56,i_0_55,i_0_62,i_0_53,i_0_367,i_0_331,i_0_334,i_0_336,i_0_289,i_0_189,i_0_325,i_0_250,i_0_46,i_0_52,i_0_44,i_0_43,i_0_42,i_0_45,i_0_39]) ).

cnf(i_0_377,plain,
    ( ~ sum(X1,X2,X3)
    | equalish(X4,X3)
    | ~ sum(X1,X2,X4) ),
    inference(rename_variables,[],[i_0_39]) ).

cnf(i_0_378,plain,
    ~ sum(additive_inverse(multiply(a,additive_identity)),multiply(a,additive_identity),multiply(a,additive_identity)),
    inference(scs_inference,[],[i_0_183,i_0_56,i_0_79,i_0_55,i_0_62,i_0_53,i_0_367,i_0_331,i_0_334,i_0_336,i_0_289,i_0_189,i_0_325,i_0_250,i_0_46,i_0_52,i_0_44,i_0_43,i_0_42,i_0_45,i_0_39,i_0_37]) ).

cnf(i_0_379,plain,
    sum(additive_inverse(X1),X1,additive_identity),
    inference(rename_variables,[],[i_0_53]) ).

cnf(i_0_380,plain,
    sum(multiply(X1,additive_identity),multiply(X1,additive_identity),multiply(X1,additive_identity)),
    inference(rename_variables,[],[i_0_79]) ).

cnf(i_0_381,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ sum(X1,X6,X4)
    | ~ sum(X6,X5,X2) ),
    inference(rename_variables,[],[i_0_37]) ).

cnf(i_0_382,plain,
    ~ sum(multiply(a,additive_identity),multiply(a,additive_identity),additive_inverse(add(additive_identity,additive_identity))),
    inference(scs_inference,[],[i_0_183,i_0_56,i_0_373,i_0_79,i_0_55,i_0_62,i_0_53,i_0_367,i_0_331,i_0_334,i_0_336,i_0_289,i_0_189,i_0_325,i_0_250,i_0_46,i_0_52,i_0_44,i_0_43,i_0_42,i_0_45,i_0_39,i_0_37,i_0_36]) ).

cnf(i_0_383,plain,
    sum(additive_inverse(add(additive_identity,X1)),X1,additive_identity),
    inference(rename_variables,[],[i_0_189]) ).

cnf(i_0_384,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_56]) ).

cnf(i_0_385,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ sum(X4,X6,X1)
    | ~ sum(X6,X2,X5) ),
    inference(rename_variables,[],[i_0_36]) ).

cnf(i_0_386,plain,
    ~ product(additive_identity,additive_identity,additive_inverse(multiply(a,additive_identity))),
    inference(scs_inference,[],[i_0_229,i_0_183,i_0_56,i_0_373,i_0_79,i_0_55,i_0_62,i_0_53,i_0_367,i_0_49,i_0_331,i_0_272,i_0_334,i_0_336,i_0_289,i_0_189,i_0_325,i_0_250,i_0_46,i_0_52,i_0_44,i_0_43,i_0_42,i_0_45,i_0_39,i_0_37,i_0_36,i_0_32]) ).

cnf(i_0_387,plain,
    product(add(additive_identity,X1),X2,multiply(X1,add(additive_identity,X2))),
    inference(rename_variables,[],[i_0_229]) ).

cnf(i_0_388,plain,
    product(X1,X2,multiply(X1,X2)),
    inference(rename_variables,[],[i_0_49]) ).

cnf(i_0_389,plain,
    sum(X1,X2,add(X1,add(additive_identity,X2))),
    inference(rename_variables,[],[i_0_272]) ).

cnf(i_0_390,plain,
    ( ~ product(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ product(X6,X2,X4)
    | ~ product(X7,X2,X5)
    | ~ sum(X6,X7,X1) ),
    inference(rename_variables,[],[i_0_32]) ).

cnf(i_0_391,plain,
    product(add(additive_identity,additive_identity),add(X1,X1),multiply(additive_identity,add(additive_identity,X1))),
    inference(scs_inference,[],[i_0_229,i_0_387,i_0_183,i_0_73,i_0_56,i_0_373,i_0_79,i_0_55,i_0_62,i_0_53,i_0_367,i_0_50,i_0_49,i_0_331,i_0_272,i_0_334,i_0_336,i_0_289,i_0_189,i_0_325,i_0_250,i_0_46,i_0_52,i_0_44,i_0_43,i_0_42,i_0_45,i_0_39,i_0_37,i_0_36,i_0_32,i_0_30]) ).

cnf(i_0_392,plain,
    sum(X1,X2,add(X1,X2)),
    inference(rename_variables,[],[i_0_50]) ).

cnf(i_0_393,plain,
    sum(multiply(additive_identity,X1),multiply(additive_identity,X1),multiply(additive_identity,X1)),
    inference(rename_variables,[],[i_0_73]) ).

cnf(i_0_394,plain,
    product(add(additive_identity,X1),X2,multiply(X1,add(additive_identity,X2))),
    inference(rename_variables,[],[i_0_229]) ).

cnf(i_0_395,plain,
    product(add(additive_identity,X1),X2,multiply(X1,add(additive_identity,X2))),
    inference(rename_variables,[],[i_0_229]) ).

cnf(i_0_396,plain,
    ( ~ sum(X1,X2,X3)
    | ~ sum(X4,X5,X6)
    | product(X7,X3,X6)
    | ~ product(X7,X1,X4)
    | ~ product(X7,X2,X5) ),
    inference(rename_variables,[],[i_0_30]) ).

cnf(i_0_397,plain,
    product(additive_identity,add(X1,X1),multiply(additive_identity,add(additive_identity,X1))),
    inference(scs_inference,[],[i_0_229,i_0_387,i_0_183,i_0_73,i_0_56,i_0_373,i_0_85,i_0_79,i_0_55,i_0_62,i_0_53,i_0_367,i_0_50,i_0_49,i_0_331,i_0_272,i_0_334,i_0_336,i_0_289,i_0_189,i_0_325,i_0_250,i_0_46,i_0_52,i_0_44,i_0_43,i_0_42,i_0_45,i_0_39,i_0_37,i_0_36,i_0_32,i_0_30,i_0_40]) ).

cnf(i_0_398,plain,
    equalish(add(additive_identity,X1),X1),
    inference(rename_variables,[],[i_0_85]) ).

cnf(i_0_399,plain,
    ( ~ product(X1,X2,X3)
    | product(X4,X2,X3)
    | ~ equalish(X1,X4) ),
    inference(rename_variables,[],[i_0_40]) ).

cnf(i_0_400,plain,
    ~ product(a,add(additive_identity,additive_identity),additive_inverse(additive_identity)),
    inference(scs_inference,[],[i_0_229,i_0_387,i_0_183,i_0_370,i_0_73,i_0_56,i_0_373,i_0_85,i_0_79,i_0_55,i_0_62,i_0_53,i_0_367,i_0_50,i_0_49,i_0_331,i_0_272,i_0_334,i_0_336,i_0_289,i_0_189,i_0_325,i_0_250,i_0_46,i_0_52,i_0_44,i_0_43,i_0_42,i_0_45,i_0_39,i_0_37,i_0_36,i_0_32,i_0_30,i_0_40,i_0_38]) ).

cnf(i_0_401,plain,
    product(X1,add(additive_identity,X2),multiply(add(additive_identity,X1),X2)),
    inference(rename_variables,[],[i_0_183]) ).

cnf(i_0_402,plain,
    ( ~ product(X1,X2,X3)
    | equalish(X4,X3)
    | ~ product(X1,X2,X4) ),
    inference(rename_variables,[],[i_0_38]) ).

cnf(i_0_403,plain,
    ( ~ product(add(additive_identity,a),additive_identity,additive_inverse(multiply(a,additive_identity)))
    | ~ product(add(additive_identity,a),additive_identity,multiply(a,additive_identity)) ),
    inference(scs_inference,[],[i_0_229,i_0_387,i_0_183,i_0_370,i_0_73,i_0_56,i_0_373,i_0_384,i_0_85,i_0_79,i_0_55,i_0_62,i_0_53,i_0_367,i_0_50,i_0_49,i_0_186,i_0_331,i_0_272,i_0_334,i_0_336,i_0_289,i_0_189,i_0_325,i_0_250,i_0_46,i_0_52,i_0_44,i_0_43,i_0_42,i_0_45,i_0_39,i_0_37,i_0_36,i_0_32,i_0_30,i_0_40,i_0_38,i_0_33]) ).

cnf(i_0_404,plain,
    product(X1,X2,multiply(X1,add(additive_identity,X2))),
    inference(rename_variables,[],[i_0_186]) ).

cnf(i_0_405,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_56]) ).

cnf(i_0_406,plain,
    ( ~ product(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ product(X1,X6,X4)
    | ~ product(X1,X7,X5)
    | ~ sum(X6,X7,X2) ),
    inference(rename_variables,[],[i_0_33]) ).

cnf(i_0_407,plain,
    sum(X1,add(additive_identity,additive_inverse(X1)),additive_identity),
    inference(scs_inference,[],[i_0_145,i_0_46]) ).

cnf(i_0_408,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X2,X1,X3) ),
    inference(rename_variables,[],[i_0_46]) ).

cnf(i_0_409,plain,
    ~ equalish(add(additive_identity,additive_identity),additive_inverse(multiply(a,additive_identity))),
    inference(scs_inference,[],[i_0_227,i_0_378,i_0_145,i_0_46,i_0_43]) ).

cnf(i_0_410,plain,
    sum(add(additive_identity,additive_identity),X1,X1),
    inference(rename_variables,[],[i_0_227]) ).

cnf(i_0_411,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X2,X3)
    | ~ equalish(X1,X4) ),
    inference(rename_variables,[],[i_0_43]) ).

cnf(i_0_412,plain,
    sum(X1,X2,add(add(additive_identity,X2),X1)),
    inference(scs_inference,[],[i_0_85,i_0_60,i_0_227,i_0_378,i_0_145,i_0_46,i_0_43,i_0_44]) ).

cnf(i_0_413,plain,
    sum(X1,X2,add(X2,X1)),
    inference(rename_variables,[],[i_0_60]) ).

cnf(i_0_414,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X1,X4,X3)
    | ~ equalish(X2,X4) ),
    inference(rename_variables,[],[i_0_44]) ).

cnf(i_0_415,plain,
    ~ product(a,add(additive_identity,additive_identity),additive_inverse(multiply(a,additive_identity))),
    inference(scs_inference,[],[i_0_142,i_0_85,i_0_60,i_0_227,i_0_378,i_0_366,i_0_145,i_0_46,i_0_43,i_0_44,i_0_38]) ).

cnf(i_0_416,plain,
    product(X1,add(additive_identity,X2),multiply(X1,X2)),
    inference(rename_variables,[],[i_0_142]) ).

cnf(i_0_417,plain,
    ( ~ product(X1,X2,X3)
    | equalish(X4,X3)
    | ~ product(X1,X2,X4) ),
    inference(rename_variables,[],[i_0_38]) ).

cnf(i_0_418,plain,
    ~ equalish(additive_inverse(additive_identity),multiply(add(additive_identity,a),add(additive_identity,additive_identity))),
    inference(scs_inference,[],[i_0_56,i_0_142,i_0_85,i_0_60,i_0_227,i_0_378,i_0_366,i_0_376,i_0_145,i_0_46,i_0_43,i_0_44,i_0_38,i_0_45]) ).

cnf(i_0_419,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_56]) ).

cnf(i_0_420,plain,
    ~ sum(additive_inverse(X1),X1,multiply(add(additive_identity,a),add(additive_identity,additive_identity))),
    inference(rename_variables,[],[i_0_376]) ).

cnf(i_0_421,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X1,X2,X4)
    | ~ equalish(X3,X4) ),
    inference(rename_variables,[],[i_0_45]) ).

cnf(i_0_422,plain,
    ~ sum(additive_inverse(X1),X1,add(multiply(a,additive_identity),multiply(a,additive_identity))),
    inference(scs_inference,[],[i_0_56,i_0_142,i_0_85,i_0_53,i_0_60,i_0_227,i_0_378,i_0_366,i_0_376,i_0_145,i_0_360,i_0_46,i_0_43,i_0_44,i_0_38,i_0_45,i_0_39]) ).

cnf(i_0_423,plain,
    ( ~ sum(X1,X2,X3)
    | equalish(X4,X3)
    | ~ sum(X1,X2,X4) ),
    inference(rename_variables,[],[i_0_39]) ).

cnf(i_0_424,plain,
    ~ sum(multiply(a,additive_identity),additive_identity,additive_identity),
    inference(scs_inference,[],[i_0_56,i_0_142,i_0_85,i_0_55,i_0_53,i_0_50,i_0_60,i_0_227,i_0_378,i_0_366,i_0_376,i_0_145,i_0_360,i_0_203,i_0_46,i_0_43,i_0_44,i_0_38,i_0_45,i_0_39,i_0_37]) ).

cnf(i_0_425,plain,
    sum(X1,X2,add(X1,X2)),
    inference(rename_variables,[],[i_0_50]) ).

cnf(i_0_426,plain,
    sum(additive_identity,X1,X1),
    inference(rename_variables,[],[i_0_55]) ).

cnf(i_0_427,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ sum(X1,X6,X4)
    | ~ sum(X6,X5,X2) ),
    inference(rename_variables,[],[i_0_37]) ).

cnf(i_0_428,plain,
    ~ sum(additive_identity,multiply(a,additive_identity),additive_identity),
    inference(scs_inference,[],[i_0_56,i_0_419,i_0_142,i_0_85,i_0_55,i_0_53,i_0_50,i_0_60,i_0_227,i_0_378,i_0_366,i_0_376,i_0_145,i_0_360,i_0_302,i_0_203,i_0_46,i_0_43,i_0_44,i_0_38,i_0_45,i_0_39,i_0_37,i_0_36]) ).

cnf(i_0_429,plain,
    sum(additive_inverse(X1),X1,additive_identity),
    inference(rename_variables,[],[i_0_53]) ).

cnf(i_0_430,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_56]) ).

cnf(i_0_431,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ sum(X4,X6,X1)
    | ~ sum(X6,X2,X5) ),
    inference(rename_variables,[],[i_0_36]) ).

cnf(i_0_432,plain,
    ~ product(additive_identity,add(additive_identity,additive_identity),additive_inverse(multiply(a,additive_identity))),
    inference(scs_inference,[],[i_0_56,i_0_419,i_0_142,i_0_416,i_0_85,i_0_55,i_0_426,i_0_53,i_0_50,i_0_60,i_0_227,i_0_378,i_0_366,i_0_376,i_0_145,i_0_360,i_0_302,i_0_203,i_0_46,i_0_43,i_0_44,i_0_38,i_0_45,i_0_39,i_0_37,i_0_36,i_0_32]) ).

cnf(i_0_433,plain,
    product(X1,add(additive_identity,X2),multiply(X1,X2)),
    inference(rename_variables,[],[i_0_142]) ).

cnf(i_0_434,plain,
    sum(additive_identity,X1,X1),
    inference(rename_variables,[],[i_0_55]) ).

cnf(i_0_435,plain,
    ( ~ product(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ product(X6,X2,X4)
    | ~ product(X7,X2,X5)
    | ~ sum(X6,X7,X1) ),
    inference(rename_variables,[],[i_0_32]) ).

cnf(i_0_436,plain,
    ~ product(a,additive_identity,additive_inverse(multiply(a,additive_identity))),
    inference(scs_inference,[],[i_0_56,i_0_419,i_0_142,i_0_416,i_0_433,i_0_85,i_0_55,i_0_426,i_0_434,i_0_53,i_0_50,i_0_60,i_0_227,i_0_378,i_0_366,i_0_376,i_0_145,i_0_360,i_0_302,i_0_203,i_0_46,i_0_43,i_0_44,i_0_38,i_0_45,i_0_39,i_0_37,i_0_36,i_0_32,i_0_33]) ).

cnf(i_0_437,plain,
    product(X1,add(additive_identity,X2),multiply(X1,X2)),
    inference(rename_variables,[],[i_0_142]) ).

cnf(i_0_438,plain,
    sum(additive_identity,X1,X1),
    inference(rename_variables,[],[i_0_55]) ).

cnf(i_0_439,plain,
    ( ~ product(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ product(X1,X6,X4)
    | ~ product(X1,X7,X5)
    | ~ sum(X6,X7,X2) ),
    inference(rename_variables,[],[i_0_33]) ).

cnf(i_0_440,plain,
    ( product(X1,multiply(additive_identity,X2),multiply(additive_identity,X2))
    | ~ product(X1,multiply(additive_identity,X2),multiply(additive_identity,X2)) ),
    inference(scs_inference,[],[i_0_73,i_0_56,i_0_419,i_0_142,i_0_416,i_0_433,i_0_85,i_0_55,i_0_426,i_0_434,i_0_53,i_0_50,i_0_60,i_0_227,i_0_378,i_0_366,i_0_376,i_0_145,i_0_360,i_0_302,i_0_203,i_0_46,i_0_43,i_0_44,i_0_38,i_0_45,i_0_39,i_0_37,i_0_36,i_0_32,i_0_33,i_0_30]) ).

cnf(i_0_441,plain,
    ( ~ sum(X1,X2,X3)
    | ~ sum(X4,X5,X6)
    | product(X7,X3,X6)
    | ~ product(X7,X1,X4)
    | ~ product(X7,X2,X5) ),
    inference(rename_variables,[],[i_0_30]) ).

cnf(i_0_442,plain,
    ( product(X1,add(additive_identity,multiply(additive_identity,X2)),multiply(additive_identity,X2))
    | ~ product(X1,multiply(additive_identity,X2),multiply(additive_identity,X2)) ),
    inference(scs_inference,[],[i_0_73,i_0_56,i_0_419,i_0_142,i_0_416,i_0_433,i_0_85,i_0_55,i_0_426,i_0_434,i_0_62,i_0_53,i_0_50,i_0_60,i_0_227,i_0_378,i_0_366,i_0_376,i_0_145,i_0_360,i_0_302,i_0_203,i_0_46,i_0_43,i_0_44,i_0_38,i_0_45,i_0_39,i_0_37,i_0_36,i_0_32,i_0_33,i_0_30,i_0_41]) ).

cnf(i_0_443,plain,
    equalish(X1,add(additive_identity,X1)),
    inference(rename_variables,[],[i_0_62]) ).

cnf(i_0_444,plain,
    ( ~ product(X1,X2,X3)
    | product(X1,X4,X3)
    | ~ equalish(X2,X4) ),
    inference(rename_variables,[],[i_0_41]) ).

cnf(i_0_445,plain,
    ( product(X1,multiply(additive_identity,X2),multiply(additive_identity,X2))
    | ~ product(add(additive_identity,X1),multiply(additive_identity,X2),multiply(additive_identity,X2)) ),
    inference(scs_inference,[],[i_0_73,i_0_56,i_0_419,i_0_142,i_0_416,i_0_433,i_0_85,i_0_55,i_0_426,i_0_434,i_0_62,i_0_53,i_0_50,i_0_60,i_0_227,i_0_378,i_0_366,i_0_376,i_0_145,i_0_360,i_0_302,i_0_203,i_0_46,i_0_43,i_0_44,i_0_38,i_0_45,i_0_39,i_0_37,i_0_36,i_0_32,i_0_33,i_0_30,i_0_41,i_0_40]) ).

cnf(i_0_446,plain,
    ( ~ product(X1,X2,X3)
    | product(X4,X2,X3)
    | ~ equalish(X1,X4) ),
    inference(rename_variables,[],[i_0_40]) ).

cnf(i_0_447,plain,
    ( product(add(additive_identity,X1),multiply(additive_identity,X2),add(additive_identity,multiply(additive_identity,X2)))
    | ~ product(add(additive_identity,X1),multiply(additive_identity,X2),multiply(additive_identity,X2)) ),
    inference(scs_inference,[],[i_0_73,i_0_56,i_0_419,i_0_142,i_0_416,i_0_433,i_0_85,i_0_55,i_0_426,i_0_434,i_0_62,i_0_443,i_0_53,i_0_50,i_0_60,i_0_227,i_0_378,i_0_366,i_0_376,i_0_145,i_0_360,i_0_302,i_0_203,i_0_46,i_0_43,i_0_44,i_0_38,i_0_45,i_0_39,i_0_37,i_0_36,i_0_32,i_0_33,i_0_30,i_0_41,i_0_40,i_0_42]) ).

cnf(i_0_448,plain,
    equalish(X1,add(additive_identity,X1)),
    inference(rename_variables,[],[i_0_62]) ).

cnf(i_0_449,plain,
    ( ~ product(X1,X2,X3)
    | product(X1,X2,X4)
    | ~ equalish(X3,X4) ),
    inference(rename_variables,[],[i_0_42]) ).

cnf(i_0_450,plain,
    product(X1,add(additive_identity,add(additive_identity,X2)),multiply(X1,X2)),
    inference(rename_variables,[],[i_0_232]) ).

cnf(i_0_451,plain,
    ( product(additive_identity,multiply(additive_identity,X1),multiply(additive_identity,X1))
    | ~ product(add(additive_identity,additive_inverse(X2)),multiply(additive_identity,X1),multiply(additive_identity,X1))
    | ~ product(X2,multiply(additive_identity,X1),multiply(additive_identity,X1)) ),
    inference(scs_inference,[],[i_0_391,i_0_73,i_0_56,i_0_419,i_0_142,i_0_416,i_0_433,i_0_85,i_0_55,i_0_426,i_0_434,i_0_62,i_0_443,i_0_53,i_0_429,i_0_232,i_0_50,i_0_60,i_0_227,i_0_378,i_0_366,i_0_376,i_0_145,i_0_360,i_0_302,i_0_203,i_0_46,i_0_43,i_0_44,i_0_38,i_0_45,i_0_39,i_0_37,i_0_36,i_0_32,i_0_33,i_0_30,i_0_41,i_0_40,i_0_42,i_0_31]) ).

cnf(i_0_452,plain,
    sum(X1,X2,add(add(additive_identity,X1),X2)),
    inference(scs_inference,[],[i_0_412,i_0_46]) ).

cnf(i_0_453,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X2,X1,X3) ),
    inference(rename_variables,[],[i_0_46]) ).

cnf(i_0_454,plain,
    product(add(additive_identity,X1),add(additive_identity,X2),multiply(X1,add(additive_identity,X2))),
    inference(scs_inference,[],[i_0_229,i_0_62,i_0_412,i_0_46,i_0_41]) ).

cnf(i_0_455,plain,
    product(add(additive_identity,X1),X2,multiply(X1,add(additive_identity,X2))),
    inference(rename_variables,[],[i_0_229]) ).

cnf(i_0_456,plain,
    ( ~ product(X1,X2,X3)
    | product(X1,X4,X3)
    | ~ equalish(X2,X4) ),
    inference(rename_variables,[],[i_0_41]) ).

cnf(i_0_457,plain,
    sum(X1,add(additive_identity,X2),add(X1,X2)),
    inference(scs_inference,[],[i_0_229,i_0_62,i_0_50,i_0_412,i_0_46,i_0_41,i_0_44]) ).

cnf(i_0_458,plain,
    sum(X1,X2,add(X1,X2)),
    inference(rename_variables,[],[i_0_50]) ).

cnf(i_0_459,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X1,X4,X3)
    | ~ equalish(X2,X4) ),
    inference(rename_variables,[],[i_0_44]) ).

cnf(i_0_460,plain,
    ~ equalish(additive_inverse(additive_identity),multiply(a,additive_identity)),
    inference(scs_inference,[],[i_0_229,i_0_62,i_0_53,i_0_50,i_0_412,i_0_424,i_0_46,i_0_41,i_0_44,i_0_43]) ).

cnf(i_0_461,plain,
    sum(additive_inverse(X1),X1,additive_identity),
    inference(rename_variables,[],[i_0_53]) ).

cnf(i_0_462,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X2,X3)
    | ~ equalish(X1,X4) ),
    inference(rename_variables,[],[i_0_43]) ).

cnf(i_0_463,plain,
    product(add(additive_identity,X1),add(additive_identity,X2),multiply(X1,X2)),
    inference(scs_inference,[],[i_0_229,i_0_62,i_0_142,i_0_53,i_0_50,i_0_412,i_0_424,i_0_46,i_0_41,i_0_44,i_0_43,i_0_40]) ).

cnf(i_0_464,plain,
    product(X1,add(additive_identity,X2),multiply(X1,X2)),
    inference(rename_variables,[],[i_0_142]) ).

cnf(i_0_465,plain,
    ( ~ product(X1,X2,X3)
    | product(X4,X2,X3)
    | ~ equalish(X1,X4) ),
    inference(rename_variables,[],[i_0_40]) ).

cnf(i_0_466,plain,
    ~ product(a,add(additive_identity,add(additive_identity,additive_identity)),additive_inverse(additive_identity)),
    inference(scs_inference,[],[i_0_183,i_0_229,i_0_62,i_0_142,i_0_53,i_0_50,i_0_412,i_0_418,i_0_424,i_0_46,i_0_41,i_0_44,i_0_43,i_0_40,i_0_38]) ).

cnf(i_0_467,plain,
    product(X1,add(additive_identity,X2),multiply(add(additive_identity,X1),X2)),
    inference(rename_variables,[],[i_0_183]) ).

cnf(i_0_468,plain,
    ( ~ product(X1,X2,X3)
    | equalish(X4,X3)
    | ~ product(X1,X2,X4) ),
    inference(rename_variables,[],[i_0_38]) ).

cnf(i_0_469,plain,
    ~ equalish(multiply(add(additive_identity,a),additive_identity),additive_inverse(additive_identity)),
    inference(scs_inference,[],[i_0_183,i_0_467,i_0_229,i_0_62,i_0_142,i_0_53,i_0_50,i_0_412,i_0_400,i_0_418,i_0_424,i_0_46,i_0_41,i_0_44,i_0_43,i_0_40,i_0_38,i_0_42]) ).

cnf(i_0_470,plain,
    product(X1,add(additive_identity,X2),multiply(add(additive_identity,X1),X2)),
    inference(rename_variables,[],[i_0_183]) ).

cnf(i_0_471,plain,
    ( ~ product(X1,X2,X3)
    | product(X1,X2,X4)
    | ~ equalish(X3,X4) ),
    inference(rename_variables,[],[i_0_42]) ).

cnf(i_0_472,plain,
    ~ equalish(multiply(a,additive_identity),additive_inverse(add(additive_identity,additive_identity))),
    inference(scs_inference,[],[i_0_183,i_0_467,i_0_229,i_0_79,i_0_62,i_0_142,i_0_53,i_0_50,i_0_382,i_0_412,i_0_400,i_0_418,i_0_424,i_0_46,i_0_41,i_0_44,i_0_43,i_0_40,i_0_38,i_0_42,i_0_45]) ).

cnf(i_0_473,plain,
    sum(multiply(X1,additive_identity),multiply(X1,additive_identity),multiply(X1,additive_identity)),
    inference(rename_variables,[],[i_0_79]) ).

cnf(i_0_474,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X1,X2,X4)
    | ~ equalish(X3,X4) ),
    inference(rename_variables,[],[i_0_45]) ).

cnf(i_0_475,plain,
    ~ sum(additive_inverse(X1),X1,multiply(a,add(additive_identity,additive_identity))),
    inference(scs_inference,[],[i_0_183,i_0_467,i_0_229,i_0_79,i_0_62,i_0_142,i_0_53,i_0_461,i_0_50,i_0_382,i_0_195,i_0_412,i_0_400,i_0_418,i_0_424,i_0_46,i_0_41,i_0_44,i_0_43,i_0_40,i_0_38,i_0_42,i_0_45,i_0_39]) ).

cnf(i_0_476,plain,
    ( ~ sum(X1,X2,X3)
    | equalish(X4,X3)
    | ~ sum(X1,X2,X4) ),
    inference(rename_variables,[],[i_0_39]) ).

cnf(i_0_477,plain,
    ~ sum(additive_inverse(X1),X1,multiply(a,additive_identity)),
    inference(scs_inference,[],[i_0_183,i_0_467,i_0_229,i_0_79,i_0_62,i_0_56,i_0_142,i_0_53,i_0_461,i_0_50,i_0_382,i_0_195,i_0_412,i_0_400,i_0_418,i_0_424,i_0_46,i_0_41,i_0_44,i_0_43,i_0_40,i_0_38,i_0_42,i_0_45,i_0_39,i_0_37]) ).

cnf(i_0_478,plain,
    sum(additive_inverse(X1),X1,additive_identity),
    inference(rename_variables,[],[i_0_53]) ).

cnf(i_0_479,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ sum(X1,X6,X4)
    | ~ sum(X6,X5,X2) ),
    inference(rename_variables,[],[i_0_37]) ).

cnf(i_0_480,plain,
    ~ sum(multiply(a,additive_identity),additive_identity,additive_inverse(additive_identity)),
    inference(scs_inference,[],[i_0_183,i_0_467,i_0_229,i_0_79,i_0_62,i_0_56,i_0_142,i_0_53,i_0_461,i_0_478,i_0_50,i_0_382,i_0_195,i_0_412,i_0_400,i_0_418,i_0_424,i_0_46,i_0_41,i_0_44,i_0_43,i_0_40,i_0_38,i_0_42,i_0_45,i_0_39,i_0_37,i_0_36]) ).

cnf(i_0_481,plain,
    sum(additive_inverse(X1),X1,additive_identity),
    inference(rename_variables,[],[i_0_53]) ).

cnf(i_0_482,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_56]) ).

cnf(i_0_483,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ sum(X4,X6,X1)
    | ~ sum(X6,X2,X5) ),
    inference(rename_variables,[],[i_0_36]) ).

cnf(i_0_484,plain,
    ( product(X1,multiply(X2,X3),multiply(X2,X3))
    | ~ product(X1,add(additive_identity,X2),add(additive_identity,X2)) ),
    inference(scs_inference,[],[i_0_183,i_0_467,i_0_229,i_0_79,i_0_62,i_0_56,i_0_142,i_0_53,i_0_461,i_0_478,i_0_50,i_0_382,i_0_195,i_0_412,i_0_400,i_0_418,i_0_424,i_0_46,i_0_41,i_0_44,i_0_43,i_0_40,i_0_38,i_0_42,i_0_45,i_0_39,i_0_37,i_0_36,i_0_34]) ).

cnf(i_0_485,plain,
    ( ~ product(X1,X2,X3)
    | product(X4,X5,X3)
    | ~ product(X4,X6,X1)
    | ~ product(X6,X2,X5) ),
    inference(rename_variables,[],[i_0_34]) ).

cnf(i_0_486,plain,
    ( product(multiply(X1,X2),X3,multiply(X1,X2))
    | ~ product(add(additive_identity,X2),X3,add(additive_identity,X2)) ),
    inference(scs_inference,[],[i_0_183,i_0_467,i_0_229,i_0_79,i_0_62,i_0_56,i_0_142,i_0_53,i_0_461,i_0_478,i_0_50,i_0_382,i_0_195,i_0_412,i_0_400,i_0_418,i_0_424,i_0_46,i_0_41,i_0_44,i_0_43,i_0_40,i_0_38,i_0_42,i_0_45,i_0_39,i_0_37,i_0_36,i_0_34,i_0_35]) ).

cnf(i_0_487,plain,
    ( ~ product(X1,X2,X3)
    | product(X4,X5,X3)
    | ~ product(X1,X6,X4)
    | ~ product(X6,X5,X2) ),
    inference(rename_variables,[],[i_0_35]) ).

cnf(i_0_488,plain,
    ( product(X1,multiply(X2,additive_identity),multiply(X2,additive_identity))
    | ~ product(X1,multiply(X2,additive_identity),multiply(X2,additive_identity)) ),
    inference(scs_inference,[],[i_0_183,i_0_467,i_0_229,i_0_79,i_0_473,i_0_62,i_0_56,i_0_142,i_0_53,i_0_461,i_0_478,i_0_50,i_0_382,i_0_195,i_0_412,i_0_400,i_0_418,i_0_424,i_0_46,i_0_41,i_0_44,i_0_43,i_0_40,i_0_38,i_0_42,i_0_45,i_0_39,i_0_37,i_0_36,i_0_34,i_0_35,i_0_30]) ).

cnf(i_0_489,plain,
    ( ~ sum(X1,X2,X3)
    | ~ sum(X4,X5,X6)
    | product(X7,X3,X6)
    | ~ product(X7,X1,X4)
    | ~ product(X7,X2,X5) ),
    inference(rename_variables,[],[i_0_30]) ).

cnf(i_0_490,plain,
    sum(add(additive_identity,X1),X2,add(X2,X1)),
    inference(scs_inference,[],[i_0_457,i_0_46]) ).

cnf(i_0_491,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X2,X1,X3) ),
    inference(rename_variables,[],[i_0_46]) ).

cnf(i_0_492,plain,
    product(add(additive_identity,X1),add(additive_identity,add(additive_identity,X2)),multiply(X1,X2)),
    inference(scs_inference,[],[i_0_463,i_0_62,i_0_457,i_0_46,i_0_41]) ).

cnf(i_0_493,plain,
    equalish(X1,add(additive_identity,X1)),
    inference(rename_variables,[],[i_0_62]) ).

cnf(i_0_494,plain,
    ( ~ product(X1,X2,X3)
    | product(X1,X4,X3)
    | ~ equalish(X2,X4) ),
    inference(rename_variables,[],[i_0_41]) ).

cnf(i_0_495,plain,
    ~ equalish(multiply(a,additive_identity),additive_inverse(additive_identity)),
    inference(scs_inference,[],[i_0_463,i_0_62,i_0_56,i_0_477,i_0_457,i_0_46,i_0_41,i_0_43]) ).

cnf(i_0_496,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_56]) ).

cnf(i_0_497,plain,
    ~ sum(additive_inverse(X1),X1,multiply(a,additive_identity)),
    inference(rename_variables,[],[i_0_477]) ).

cnf(i_0_498,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X2,X3)
    | ~ equalish(X1,X4) ),
    inference(rename_variables,[],[i_0_43]) ).

cnf(i_0_499,plain,
    sum(X1,add(additive_identity,X2),add(X2,X1)),
    inference(scs_inference,[],[i_0_463,i_0_62,i_0_493,i_0_56,i_0_60,i_0_477,i_0_457,i_0_46,i_0_41,i_0_43,i_0_44]) ).

cnf(i_0_500,plain,
    sum(X1,X2,add(X2,X1)),
    inference(rename_variables,[],[i_0_60]) ).

cnf(i_0_501,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X1,X4,X3)
    | ~ equalish(X2,X4) ),
    inference(rename_variables,[],[i_0_44]) ).

cnf(i_0_502,plain,
    product(add(additive_identity,add(additive_identity,X1)),add(additive_identity,X2),multiply(X1,X2)),
    inference(scs_inference,[],[i_0_463,i_0_62,i_0_493,i_0_56,i_0_60,i_0_477,i_0_457,i_0_46,i_0_41,i_0_43,i_0_44,i_0_40]) ).

cnf(i_0_503,plain,
    equalish(X1,add(additive_identity,X1)),
    inference(rename_variables,[],[i_0_62]) ).

cnf(i_0_504,plain,
    ( ~ product(X1,X2,X3)
    | product(X4,X2,X3)
    | ~ equalish(X1,X4) ),
    inference(rename_variables,[],[i_0_40]) ).

cnf(i_0_505,plain,
    ~ product(add(additive_identity,add(additive_identity,a)),additive_identity,additive_inverse(additive_identity)),
    inference(scs_inference,[],[i_0_229,i_0_463,i_0_62,i_0_493,i_0_56,i_0_60,i_0_477,i_0_457,i_0_418,i_0_46,i_0_41,i_0_43,i_0_44,i_0_40,i_0_38]) ).

cnf(i_0_506,plain,
    product(add(additive_identity,X1),X2,multiply(X1,add(additive_identity,X2))),
    inference(rename_variables,[],[i_0_229]) ).

cnf(i_0_507,plain,
    ( ~ product(X1,X2,X3)
    | equalish(X4,X3)
    | ~ product(X1,X2,X4) ),
    inference(rename_variables,[],[i_0_38]) ).

cnf(i_0_508,plain,
    ~ equalish(multiply(add(additive_identity,a),add(additive_identity,additive_identity)),additive_inverse(additive_identity)),
    inference(scs_inference,[],[i_0_229,i_0_506,i_0_463,i_0_62,i_0_493,i_0_56,i_0_60,i_0_477,i_0_457,i_0_418,i_0_46,i_0_41,i_0_43,i_0_44,i_0_40,i_0_38,i_0_42]) ).

cnf(i_0_509,plain,
    product(add(additive_identity,X1),X2,multiply(X1,add(additive_identity,X2))),
    inference(rename_variables,[],[i_0_229]) ).

cnf(i_0_510,plain,
    ( ~ product(X1,X2,X3)
    | product(X1,X2,X4)
    | ~ equalish(X3,X4) ),
    inference(rename_variables,[],[i_0_42]) ).

cnf(i_0_511,plain,
    ~ equalish(additive_inverse(add(additive_identity,additive_identity)),multiply(a,additive_identity)),
    inference(scs_inference,[],[i_0_229,i_0_506,i_0_463,i_0_62,i_0_493,i_0_56,i_0_148,i_0_60,i_0_477,i_0_497,i_0_457,i_0_418,i_0_46,i_0_41,i_0_43,i_0_44,i_0_40,i_0_38,i_0_42,i_0_45]) ).

cnf(i_0_512,plain,
    sum(X1,add(additive_identity,additive_identity),X1),
    inference(rename_variables,[],[i_0_148]) ).

cnf(i_0_513,plain,
    ~ sum(additive_inverse(X1),X1,multiply(a,additive_identity)),
    inference(rename_variables,[],[i_0_477]) ).

cnf(i_0_514,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X1,X2,X4)
    | ~ equalish(X3,X4) ),
    inference(rename_variables,[],[i_0_45]) ).

cnf(i_0_515,plain,
    ~ sum(additive_identity,additive_identity,multiply(add(additive_identity,a),add(additive_identity,additive_identity))),
    inference(scs_inference,[],[i_0_229,i_0_506,i_0_463,i_0_62,i_0_493,i_0_56,i_0_148,i_0_50,i_0_60,i_0_477,i_0_497,i_0_369,i_0_457,i_0_418,i_0_46,i_0_41,i_0_43,i_0_44,i_0_40,i_0_38,i_0_42,i_0_45,i_0_39]) ).

cnf(i_0_516,plain,
    sum(X1,X2,add(X1,X2)),
    inference(rename_variables,[],[i_0_50]) ).

cnf(i_0_517,plain,
    ( ~ sum(X1,X2,X3)
    | equalish(X4,X3)
    | ~ sum(X1,X2,X4) ),
    inference(rename_variables,[],[i_0_39]) ).

cnf(i_0_518,plain,
    ~ sum(additive_identity,additive_identity,additive_inverse(multiply(a,additive_identity))),
    inference(scs_inference,[],[i_0_229,i_0_506,i_0_463,i_0_62,i_0_493,i_0_55,i_0_56,i_0_148,i_0_50,i_0_60,i_0_477,i_0_497,i_0_513,i_0_369,i_0_457,i_0_418,i_0_46,i_0_41,i_0_43,i_0_44,i_0_40,i_0_38,i_0_42,i_0_45,i_0_39,i_0_37]) ).

cnf(i_0_519,plain,
    sum(additive_identity,X1,X1),
    inference(rename_variables,[],[i_0_55]) ).

cnf(i_0_520,plain,
    ~ sum(additive_inverse(X1),X1,multiply(a,additive_identity)),
    inference(rename_variables,[],[i_0_477]) ).

cnf(i_0_521,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ sum(X1,X6,X4)
    | ~ sum(X6,X5,X2) ),
    inference(rename_variables,[],[i_0_37]) ).

cnf(i_0_522,plain,
    $false,
    inference(scs_inference,[],[i_0_229,i_0_506,i_0_463,i_0_62,i_0_493,i_0_55,i_0_519,i_0_79,i_0_56,i_0_53,i_0_148,i_0_50,i_0_60,i_0_477,i_0_497,i_0_513,i_0_520,i_0_369,i_0_457,i_0_418,i_0_46,i_0_41,i_0_43,i_0_44,i_0_40,i_0_38,i_0_42,i_0_45,i_0_39,i_0_37,i_0_36]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : RNG001-5 : TPTP v9.2.1. Released v1.0.0.
% 0.00/0.12  % 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
% 0.15/0.33  % Computer : n008.cluster.edu
% 0.15/0.33  % Model    : x86_64 x86_64
% 0.15/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33  % Memory   : 8042.1875MB
% 0.15/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33  % CPULimit   : 300
% 0.15/0.33  % WCLimit    : 300
% 0.15/0.33  % DateTime   : Tue May  5 01:44:58 EDT 2026
% 0.15/0.33  % CPUTime    : 
% 0.15/0.34  % start to proof: theBenchmark
% 4.43/5.62  % Version  : CSE_E---1.7
% 4.43/5.62  % Problem  : theBenchmark.p
% 4.43/5.62  % SZS status Unsatisfiable for theBenchmark.p
% 4.43/5.62  % SZS output start CNFRefutation
% See solution above
% 5.14/6.36  % Total time : 5.272s
%------------------------------------------------------------------------------