CSE_E---1.7.UNS-CRf.s

%------------------------------------------------------------------------------
% File     : CSE_E---1.7
% Problem  : RNG006-1 : TPTP v9.2.1. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d

% Computer : n007.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 05:04:57 PM UTC 2026

% Result   : Unsatisfiable 2.81s 2.62s
% Output   : CNFRefutation 4.00s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named 85)

% 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/sandbox2/benchmark/Axioms/RNG001-0.ax',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/sandbox2/benchmark/Axioms/RNG001-0.ax',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/sandbox2/benchmark/Axioms/RNG001-0.ax',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/sandbox2/benchmark/Axioms/RNG001-0.ax',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/sandbox2/benchmark/Axioms/RNG001-0.ax',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/sandbox2/benchmark/Axioms/RNG001-0.ax',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/sandbox2/benchmark/Axioms/RNG001-0.ax',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/sandbox2/benchmark/Axioms/RNG001-0.ax',associativity_of_addition2) ).

cnf(multiplication_is_well_defined,axiom,
    ( X3 = X4
    | ~ product(X1,X2,X3)
    | ~ product(X1,X2,X4) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',multiplication_is_well_defined) ).

cnf(addition_is_well_defined,axiom,
    ( X3 = X4
    | ~ sum(X1,X2,X3)
    | ~ sum(X1,X2,X4) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',addition_is_well_defined) ).

cnf(product_lemma3,axiom,
    ( product(additive_inverse(X1),additive_inverse(X2),X3)
    | ~ product(X1,X2,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_lemma3) ).

cnf(product_lemma2,axiom,
    ( product(additive_inverse(X1),X2,additive_inverse(X3))
    | ~ product(X1,X2,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_lemma2) ).

cnf(product_lemma1,axiom,
    ( product(X1,additive_inverse(X2),additive_inverse(X3))
    | ~ product(X1,X2,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_lemma1) ).

cnf(commutativity_of_addition,axiom,
    ( sum(X2,X1,X3)
    | ~ sum(X1,X2,X3) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',commutativity_of_addition) ).

cnf(closure_of_multiplication,axiom,
    product(X1,X2,multiply(X1,X2)),
    file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',closure_of_multiplication) ).

cnf(closure_of_addition,axiom,
    sum(X1,X2,add(X1,X2)),
    file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',closure_of_addition) ).

cnf(prove_a_times_bS_Ic_is_aPb_S__IaPc,negated_conjecture,
    ~ product(a,bS_Ic,aPb_S_IaPc),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_times_bS_Ic_is_aPb_S__IaPc) ).

cnf(left_inverse,axiom,
    sum(additive_inverse(X1),X1,additive_identity),
    file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',left_inverse) ).

cnf(right_inverse,axiom,
    sum(X1,additive_inverse(X1),additive_identity),
    file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',right_inverse) ).

cnf(aPb_plus_IaPc,hypothesis,
    sum(aPb,additive_inverse(aPc),aPb_S_IaPc),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aPb_plus_IaPc) ).

cnf(b_plus_inverse_c,hypothesis,
    sum(b,additive_inverse(c),bS_Ic),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_plus_inverse_c) ).

cnf(additive_identity1,axiom,
    sum(additive_identity,X1,X1),
    file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',additive_identity1) ).

cnf(additive_identity2,axiom,
    sum(X1,additive_identity,X1),
    file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',additive_identity2) ).

cnf(a_times_c,hypothesis,
    product(a,c,aPc),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_c) ).

cnf(a_times_b,hypothesis,
    product(a,b,aPb),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_b) ).

cnf(i_0_25,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_26,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_27,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_28,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_29,axiom,
    ( product(X1,X5,X6)
    | ~ product(X1,X2,X3)
    | ~ product(X2,X4,X5)
    | ~ product(X3,X4,X6) ),
    associativity_of_multiplication1,
    [final] ).

cnf(i_0_30,axiom,
    ( product(X3,X4,X6)
    | ~ product(X1,X2,X3)
    | ~ product(X2,X4,X5)
    | ~ product(X1,X5,X6) ),
    associativity_of_multiplication2,
    [final] ).

cnf(i_0_31,axiom,
    ( sum(X1,X5,X6)
    | ~ sum(X1,X2,X3)
    | ~ sum(X2,X4,X5)
    | ~ sum(X3,X4,X6) ),
    associativity_of_addition1,
    [final] ).

cnf(i_0_32,axiom,
    ( sum(X3,X4,X6)
    | ~ sum(X1,X2,X3)
    | ~ sum(X2,X4,X5)
    | ~ sum(X1,X5,X6) ),
    associativity_of_addition2,
    [final] ).

cnf(i_0_33,axiom,
    ( X3 = X4
    | ~ product(X1,X2,X3)
    | ~ product(X1,X2,X4) ),
    multiplication_is_well_defined,
    [final] ).

cnf(i_0_34,axiom,
    ( X3 = X4
    | ~ sum(X1,X2,X3)
    | ~ sum(X1,X2,X4) ),
    addition_is_well_defined,
    [final] ).

cnf(i_0_35,axiom,
    ( product(additive_inverse(X1),additive_inverse(X2),X3)
    | ~ product(X1,X2,X3) ),
    product_lemma3,
    [final] ).

cnf(i_0_36,axiom,
    ( product(additive_inverse(X1),X2,additive_inverse(X3))
    | ~ product(X1,X2,X3) ),
    product_lemma2,
    [final] ).

cnf(i_0_37,axiom,
    ( product(X1,additive_inverse(X2),additive_inverse(X3))
    | ~ product(X1,X2,X3) ),
    product_lemma1,
    [final] ).

cnf(i_0_38,axiom,
    ( sum(X2,X1,X3)
    | ~ sum(X1,X2,X3) ),
    commutativity_of_addition,
    [final] ).

cnf(i_0_39,axiom,
    product(X1,X2,multiply(X1,X2)),
    closure_of_multiplication,
    [final] ).

cnf(i_0_40,axiom,
    sum(X1,X2,add(X1,X2)),
    closure_of_addition,
    [final] ).

cnf(i_0_41,negated_conjecture,
    ~ product(a,bS_Ic,aPb_S_IaPc),
    prove_a_times_bS_Ic_is_aPb_S__IaPc,
    [final] ).

cnf(i_0_42,axiom,
    sum(additive_inverse(X1),X1,additive_identity),
    left_inverse,
    [final] ).

cnf(i_0_43,axiom,
    sum(X1,additive_inverse(X1),additive_identity),
    right_inverse,
    [final] ).

cnf(i_0_44,hypothesis,
    sum(aPb,additive_inverse(aPc),aPb_S_IaPc),
    aPb_plus_IaPc,
    [final] ).

cnf(i_0_45,hypothesis,
    sum(b,additive_inverse(c),bS_Ic),
    b_plus_inverse_c,
    [final] ).

cnf(i_0_46,axiom,
    sum(additive_identity,X1,X1),
    additive_identity1,
    [final] ).

cnf(i_0_47,axiom,
    sum(X1,additive_identity,X1),
    additive_identity2,
    [final] ).

cnf(i_0_48,hypothesis,
    product(a,c,aPc),
    a_times_c,
    [final] ).

cnf(i_0_49,hypothesis,
    product(a,b,aPb),
    a_times_b,
    [final] ).

cnf(i_0_50,axiom,
    X1 = X1 ).

cnf(i_0_51,axiom,
    ( X1 = X2
    | X2 != X1 ) ).

cnf(i_0_52,axiom,
    ( X1 = X2
    | X1 != X3
    | X3 != X2 ) ).

cnf(i_0_53,axiom,
    ( X1 != X2
    | ~ product(X1,X3,X4)
    | product(X2,X3,X4) ) ).

cnf(i_0_54,axiom,
    ( X1 != X2
    | ~ product(X3,X1,X4)
    | product(X3,X2,X4) ) ).

cnf(i_0_55,axiom,
    ( X1 != X2
    | ~ product(X3,X4,X1)
    | product(X3,X4,X2) ) ).

cnf(i_0_56,axiom,
    ( X1 != X2
    | ~ sum(X1,X3,X4)
    | sum(X2,X3,X4) ) ).

cnf(i_0_57,axiom,
    ( X1 != X2
    | ~ sum(X3,X1,X4)
    | sum(X3,X2,X4) ) ).

cnf(i_0_58,axiom,
    ( X1 != X2
    | ~ sum(X3,X4,X1)
    | sum(X3,X4,X2) ) ).

cnf(i_0_50_001,axiom,
    X1 = X1 ).

cnf(i_0_51_002,axiom,
    ( X1 = X2
    | X2 != X1 ) ).

cnf(i_0_52_003,axiom,
    ( X1 = X2
    | X1 != X3
    | X3 != X2 ) ).

cnf(i_0_53_004,axiom,
    ( X1 != X2
    | ~ product(X1,X3,X4)
    | product(X2,X3,X4) ) ).

cnf(i_0_54_005,axiom,
    ( X1 != X2
    | ~ product(X3,X1,X4)
    | product(X3,X2,X4) ) ).

cnf(i_0_55_006,axiom,
    ( X1 != X2
    | ~ product(X3,X4,X1)
    | product(X3,X4,X2) ) ).

cnf(i_0_56_007,axiom,
    ( X1 != X2
    | ~ sum(X1,X3,X4)
    | sum(X2,X3,X4) ) ).

cnf(i_0_57_008,axiom,
    ( X1 != X2
    | ~ sum(X3,X1,X4)
    | sum(X3,X2,X4) ) ).

cnf(i_0_58_009,axiom,
    ( X1 != X2
    | ~ sum(X3,X4,X1)
    | sum(X3,X4,X2) ) ).

cnf(i_0_59,plain,
    sum(X1,X2,add(X2,X1)),
    inference(scs_inference,[],[i_0_40,i_0_38]) ).

cnf(i_0_60,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X2,X1,X3) ),
    inference(rename_variables,[],[i_0_38]) ).

cnf(i_0_61,plain,
    X1 = add(additive_identity,X1),
    inference(scs_inference,[],[i_0_46,i_0_40,i_0_38,i_0_34]) ).

cnf(i_0_62,plain,
    sum(X1,X2,add(X1,X2)),
    inference(rename_variables,[],[i_0_40]) ).

cnf(i_0_63,plain,
    ( ~ sum(X1,X2,X3)
    | X4 = X3
    | ~ sum(X1,X2,X4) ),
    inference(rename_variables,[],[i_0_34]) ).

cnf(i_0_64,plain,
    multiply(a,bS_Ic) != aPb_S_IaPc,
    inference(scs_inference,[],[i_0_41,i_0_46,i_0_39,i_0_40,i_0_38,i_0_34,i_0_55]) ).

cnf(i_0_65,plain,
    product(X1,X2,multiply(X1,X2)),
    inference(rename_variables,[],[i_0_39]) ).

cnf(i_0_66,plain,
    sum(additive_identity,add(X1,additive_inverse(X1)),additive_identity),
    inference(scs_inference,[],[i_0_41,i_0_46,i_0_39,i_0_40,i_0_62,i_0_43,i_0_38,i_0_34,i_0_55,i_0_31]) ).

cnf(i_0_67,plain,
    sum(X1,additive_inverse(X1),additive_identity),
    inference(rename_variables,[],[i_0_43]) ).

cnf(i_0_68,plain,
    sum(additive_identity,X1,X1),
    inference(rename_variables,[],[i_0_46]) ).

cnf(i_0_69,plain,
    sum(X1,X2,add(X1,X2)),
    inference(rename_variables,[],[i_0_40]) ).

cnf(i_0_70,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ sum(X4,X6,X1)
    | ~ sum(X6,X2,X5) ),
    inference(rename_variables,[],[i_0_31]) ).

cnf(i_0_71,plain,
    sum(multiply(additive_identity,X1),multiply(additive_identity,X1),multiply(additive_identity,X1)),
    inference(scs_inference,[],[i_0_41,i_0_46,i_0_68,i_0_39,i_0_65,i_0_40,i_0_62,i_0_43,i_0_38,i_0_34,i_0_55,i_0_31,i_0_27]) ).

cnf(i_0_72,plain,
    product(X1,X2,multiply(X1,X2)),
    inference(rename_variables,[],[i_0_39]) ).

cnf(i_0_73,plain,
    product(X1,X2,multiply(X1,X2)),
    inference(rename_variables,[],[i_0_39]) ).

cnf(i_0_74,plain,
    product(X1,X2,multiply(X1,X2)),
    inference(rename_variables,[],[i_0_39]) ).

cnf(i_0_75,plain,
    sum(additive_identity,X1,X1),
    inference(rename_variables,[],[i_0_46]) ).

cnf(i_0_76,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_27]) ).

cnf(i_0_77,plain,
    sum(multiply(X1,additive_identity),multiply(X1,additive_identity),multiply(X1,additive_identity)),
    inference(scs_inference,[],[i_0_41,i_0_46,i_0_68,i_0_75,i_0_39,i_0_65,i_0_74,i_0_40,i_0_62,i_0_43,i_0_38,i_0_34,i_0_55,i_0_31,i_0_27,i_0_28]) ).

cnf(i_0_78,plain,
    product(X1,X2,multiply(X1,X2)),
    inference(rename_variables,[],[i_0_39]) ).

cnf(i_0_79,plain,
    product(X1,X2,multiply(X1,X2)),
    inference(rename_variables,[],[i_0_39]) ).

cnf(i_0_80,plain,
    product(X1,X2,multiply(X1,X2)),
    inference(rename_variables,[],[i_0_39]) ).

cnf(i_0_81,plain,
    sum(additive_identity,X1,X1),
    inference(rename_variables,[],[i_0_46]) ).

cnf(i_0_82,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_28]) ).

cnf(i_0_83,plain,
    add(additive_identity,X1) = X1,
    inference(scs_inference,[],[i_0_41,i_0_46,i_0_68,i_0_75,i_0_39,i_0_65,i_0_74,i_0_40,i_0_62,i_0_43,i_0_38,i_0_34,i_0_55,i_0_31,i_0_27,i_0_28,i_0_51]) ).

cnf(i_0_84,plain,
    ~ product(add(additive_identity,a),bS_Ic,aPb_S_IaPc),
    inference(scs_inference,[],[i_0_41,i_0_46,i_0_68,i_0_75,i_0_39,i_0_65,i_0_74,i_0_40,i_0_62,i_0_43,i_0_38,i_0_34,i_0_55,i_0_31,i_0_27,i_0_28,i_0_51,i_0_53]) ).

cnf(i_0_85,plain,
    ( X1 != bS_Ic
    | ~ product(a,X1,aPb_S_IaPc) ),
    inference(scs_inference,[],[i_0_41,i_0_46,i_0_68,i_0_75,i_0_39,i_0_65,i_0_74,i_0_40,i_0_62,i_0_43,i_0_38,i_0_34,i_0_55,i_0_31,i_0_27,i_0_28,i_0_51,i_0_53,i_0_54]) ).

cnf(i_0_86,plain,
    product(X1,multiply(X1,X1),multiply(multiply(X1,X1),X1)),
    inference(scs_inference,[],[i_0_41,i_0_46,i_0_68,i_0_75,i_0_39,i_0_65,i_0_74,i_0_80,i_0_79,i_0_40,i_0_62,i_0_43,i_0_38,i_0_34,i_0_55,i_0_31,i_0_27,i_0_28,i_0_51,i_0_53,i_0_54,i_0_29]) ).

cnf(i_0_87,plain,
    product(X1,X2,multiply(X1,X2)),
    inference(rename_variables,[],[i_0_39]) ).

cnf(i_0_88,plain,
    product(X1,X2,multiply(X1,X2)),
    inference(rename_variables,[],[i_0_39]) ).

cnf(i_0_89,plain,
    product(X1,X2,multiply(X1,X2)),
    inference(rename_variables,[],[i_0_39]) ).

cnf(i_0_90,plain,
    ( ~ product(X1,X2,X3)
    | product(X4,X5,X3)
    | ~ product(X4,X6,X1)
    | ~ product(X6,X2,X5) ),
    inference(rename_variables,[],[i_0_29]) ).

cnf(i_0_91,plain,
    product(multiply(X1,X1),X1,multiply(X1,multiply(X1,X1))),
    inference(scs_inference,[],[i_0_41,i_0_46,i_0_68,i_0_75,i_0_39,i_0_65,i_0_74,i_0_80,i_0_87,i_0_79,i_0_89,i_0_40,i_0_62,i_0_43,i_0_38,i_0_34,i_0_55,i_0_31,i_0_27,i_0_28,i_0_51,i_0_53,i_0_54,i_0_29,i_0_30]) ).

cnf(i_0_92,plain,
    product(X1,X2,multiply(X1,X2)),
    inference(rename_variables,[],[i_0_39]) ).

cnf(i_0_93,plain,
    product(X1,X2,multiply(X1,X2)),
    inference(rename_variables,[],[i_0_39]) ).

cnf(i_0_94,plain,
    product(X1,X2,multiply(X1,X2)),
    inference(rename_variables,[],[i_0_39]) ).

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_30]) ).

cnf(i_0_96,plain,
    sum(additive_identity,X1,X1),
    inference(rename_variables,[],[i_0_46]) ).

cnf(i_0_97,plain,
    sum(additive_identity,X1,X1),
    inference(rename_variables,[],[i_0_46]) ).

cnf(i_0_98,plain,
    ( aPb_S_IaPc != bS_Ic
    | product(X1,X2,X1)
    | ~ product(a,additive_identity,additive_identity)
    | ~ product(additive_identity,X2,additive_identity)
    | ~ product(X1,X2,X1) ),
    inference(scs_inference,[],[i_0_41,i_0_46,i_0_68,i_0_75,i_0_81,i_0_97,i_0_39,i_0_65,i_0_74,i_0_80,i_0_87,i_0_79,i_0_89,i_0_40,i_0_62,i_0_43,i_0_38,i_0_34,i_0_55,i_0_31,i_0_27,i_0_28,i_0_51,i_0_53,i_0_54,i_0_29,i_0_30,i_0_25,i_0_26]) ).

cnf(i_0_99,plain,
    ~ product(a,bS_Ic,aPb_S_IaPc),
    inference(equality_inference,[],[85]) ).

cnf(i_0_100,plain,
    sum(additive_inverse(aPc),aPb,aPb_S_IaPc),
    inference(scs_inference,[],[i_0_44,i_0_38]) ).

cnf(i_0_101,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X2,X1,X3) ),
    inference(rename_variables,[],[i_0_38]) ).

cnf(i_0_102,plain,
    multiply(a,bS_Ic) != add(additive_identity,aPb_S_IaPc),
    inference(scs_inference,[],[i_0_44,i_0_83,i_0_64,i_0_38,i_0_52]) ).

cnf(i_0_103,plain,
    add(additive_identity,X1) = X1,
    inference(rename_variables,[],[i_0_83]) ).

cnf(i_0_104,plain,
    ~ sum(aPb_S_IaPc,additive_identity,multiply(a,bS_Ic)),
    inference(scs_inference,[],[i_0_47,i_0_44,i_0_83,i_0_64,i_0_38,i_0_52,i_0_34]) ).

cnf(i_0_105,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_47]) ).

cnf(i_0_106,plain,
    ( ~ sum(X1,X2,X3)
    | X4 = X3
    | ~ sum(X1,X2,X4) ),
    inference(rename_variables,[],[i_0_34]) ).

cnf(i_0_107,plain,
    ~ product(a,add(additive_identity,bS_Ic),aPb_S_IaPc),
    inference(scs_inference,[],[i_0_41,i_0_47,i_0_44,i_0_83,i_0_103,i_0_64,i_0_38,i_0_52,i_0_34,i_0_54]) ).

cnf(i_0_108,plain,
    add(additive_identity,X1) = X1,
    inference(rename_variables,[],[i_0_83]) ).

cnf(i_0_109,plain,
    ~ product(a,bS_Ic,add(additive_identity,aPb_S_IaPc)),
    inference(scs_inference,[],[i_0_41,i_0_47,i_0_44,i_0_83,i_0_103,i_0_108,i_0_64,i_0_38,i_0_52,i_0_34,i_0_54,i_0_55]) ).

cnf(i_0_110,plain,
    add(additive_identity,X1) = X1,
    inference(rename_variables,[],[i_0_83]) ).

cnf(i_0_111,plain,
    ~ sum(multiply(a,bS_Ic),additive_inverse(additive_identity),aPb_S_IaPc),
    inference(scs_inference,[],[i_0_41,i_0_47,i_0_105,i_0_42,i_0_44,i_0_83,i_0_103,i_0_108,i_0_64,i_0_38,i_0_52,i_0_34,i_0_54,i_0_55,i_0_32]) ).

cnf(i_0_112,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_47]) ).

cnf(i_0_113,plain,
    sum(additive_inverse(X1),X1,additive_identity),
    inference(rename_variables,[],[i_0_42]) ).

cnf(i_0_114,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ sum(X1,X6,X4)
    | ~ sum(X6,X5,X2) ),
    inference(rename_variables,[],[i_0_32]) ).

cnf(i_0_115,plain,
    ~ sum(aPb_S_IaPc,additive_inverse(additive_identity),multiply(a,bS_Ic)),
    inference(scs_inference,[],[i_0_41,i_0_47,i_0_105,i_0_112,i_0_42,i_0_113,i_0_44,i_0_83,i_0_103,i_0_108,i_0_64,i_0_38,i_0_52,i_0_34,i_0_54,i_0_55,i_0_32,i_0_31]) ).

cnf(i_0_116,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_47]) ).

cnf(i_0_117,plain,
    sum(additive_inverse(X1),X1,additive_identity),
    inference(rename_variables,[],[i_0_42]) ).

cnf(i_0_118,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ sum(X4,X6,X1)
    | ~ sum(X6,X2,X5) ),
    inference(rename_variables,[],[i_0_31]) ).

cnf(i_0_119,plain,
    ~ sum(add(additive_identity,aPb_S_IaPc),additive_identity,multiply(a,bS_Ic)),
    inference(scs_inference,[],[i_0_41,i_0_47,i_0_105,i_0_112,i_0_42,i_0_113,i_0_44,i_0_83,i_0_103,i_0_108,i_0_110,i_0_64,i_0_38,i_0_52,i_0_34,i_0_54,i_0_55,i_0_32,i_0_31,i_0_56]) ).

cnf(i_0_120,plain,
    add(additive_identity,X1) = X1,
    inference(rename_variables,[],[i_0_83]) ).

cnf(i_0_121,plain,
    ~ sum(aPb_S_IaPc,add(additive_identity,additive_identity),multiply(a,bS_Ic)),
    inference(scs_inference,[],[i_0_41,i_0_47,i_0_105,i_0_112,i_0_42,i_0_113,i_0_44,i_0_83,i_0_103,i_0_108,i_0_110,i_0_120,i_0_64,i_0_38,i_0_52,i_0_34,i_0_54,i_0_55,i_0_32,i_0_31,i_0_56,i_0_57]) ).

cnf(i_0_122,plain,
    add(additive_identity,X1) = X1,
    inference(rename_variables,[],[i_0_83]) ).

cnf(i_0_123,plain,
    ~ sum(aPb_S_IaPc,additive_identity,add(additive_identity,multiply(a,bS_Ic))),
    inference(scs_inference,[],[i_0_41,i_0_47,i_0_105,i_0_112,i_0_42,i_0_113,i_0_44,i_0_83,i_0_103,i_0_108,i_0_110,i_0_120,i_0_122,i_0_64,i_0_38,i_0_52,i_0_34,i_0_54,i_0_55,i_0_32,i_0_31,i_0_56,i_0_57,i_0_58]) ).

cnf(i_0_124,plain,
    add(additive_identity,X1) = X1,
    inference(rename_variables,[],[i_0_83]) ).

cnf(i_0_125,plain,
    ~ product(add(additive_identity,a),add(additive_identity,bS_Ic),aPb_S_IaPc),
    inference(scs_inference,[],[i_0_41,i_0_47,i_0_105,i_0_112,i_0_42,i_0_113,i_0_44,i_0_83,i_0_103,i_0_108,i_0_110,i_0_120,i_0_122,i_0_124,i_0_64,i_0_38,i_0_52,i_0_34,i_0_54,i_0_55,i_0_32,i_0_31,i_0_56,i_0_57,i_0_58,i_0_53]) ).

cnf(i_0_126,plain,
    add(additive_identity,X1) = X1,
    inference(rename_variables,[],[i_0_83]) ).

cnf(i_0_127,plain,
    ( product(X1,aPc,aPc)
    | ~ product(X1,a,a) ),
    inference(scs_inference,[],[i_0_41,i_0_47,i_0_105,i_0_112,i_0_42,i_0_113,i_0_44,i_0_83,i_0_103,i_0_108,i_0_110,i_0_120,i_0_122,i_0_124,i_0_64,i_0_48,i_0_38,i_0_52,i_0_34,i_0_54,i_0_55,i_0_32,i_0_31,i_0_56,i_0_57,i_0_58,i_0_53,i_0_29]) ).

cnf(i_0_128,plain,
    ( ~ product(X1,X2,X3)
    | product(X4,X5,X3)
    | ~ product(X4,X6,X1)
    | ~ product(X6,X2,X5) ),
    inference(rename_variables,[],[i_0_29]) ).

cnf(i_0_129,plain,
    ( multiply(aPc,multiply(aPc,aPc)) = aPc
    | ~ product(multiply(aPc,aPc),a,a) ),
    inference(scs_inference,[],[i_0_41,i_0_91,i_0_47,i_0_105,i_0_112,i_0_42,i_0_113,i_0_44,i_0_83,i_0_103,i_0_108,i_0_110,i_0_120,i_0_122,i_0_124,i_0_64,i_0_48,i_0_38,i_0_52,i_0_34,i_0_54,i_0_55,i_0_32,i_0_31,i_0_56,i_0_57,i_0_58,i_0_53,i_0_29,i_0_33]) ).

cnf(i_0_130,plain,
    product(multiply(X1,X1),X1,multiply(X1,multiply(X1,X1))),
    inference(rename_variables,[],[i_0_91]) ).

cnf(i_0_131,plain,
    ( ~ product(X1,X2,X3)
    | X4 = X3
    | ~ product(X1,X2,X4) ),
    inference(rename_variables,[],[i_0_33]) ).

cnf(i_0_132,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_47]) ).

cnf(i_0_133,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_47]) ).

cnf(i_0_134,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_47]) ).

cnf(i_0_135,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_47]) ).

cnf(i_0_136,plain,
    ( sum(aPc,aPc,aPc)
    | ~ product(multiply(aPc,aPc),a,a)
    | ~ product(c,X1,c)
    | ~ product(multiply(aPc,aPc),additive_identity,additive_identity)
    | ~ product(additive_identity,X1,additive_identity)
    | ~ sum(c,c,c) ),
    inference(scs_inference,[],[i_0_41,i_0_91,i_0_47,i_0_105,i_0_112,i_0_116,i_0_133,i_0_42,i_0_113,i_0_44,i_0_83,i_0_103,i_0_108,i_0_110,i_0_120,i_0_122,i_0_124,i_0_64,i_0_48,i_0_38,i_0_52,i_0_34,i_0_54,i_0_55,i_0_32,i_0_31,i_0_56,i_0_57,i_0_58,i_0_53,i_0_29,i_0_33,i_0_30,i_0_25,i_0_26,i_0_28]) ).

cnf(i_0_137,plain,
    sum(additive_inverse(c),b,bS_Ic),
    inference(scs_inference,[],[i_0_45,i_0_38]) ).

cnf(i_0_138,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X2,X1,X3) ),
    inference(rename_variables,[],[i_0_38]) ).

cnf(i_0_139,plain,
    additive_inverse(additive_identity) = additive_identity,
    inference(scs_inference,[],[i_0_45,i_0_47,i_0_42,i_0_38,i_0_34]) ).

cnf(i_0_140,plain,
    sum(additive_inverse(X1),X1,additive_identity),
    inference(rename_variables,[],[i_0_42]) ).

cnf(i_0_141,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_47]) ).

cnf(i_0_142,plain,
    ( ~ sum(X1,X2,X3)
    | X4 = X3
    | ~ sum(X1,X2,X4) ),
    inference(rename_variables,[],[i_0_34]) ).

cnf(i_0_143,plain,
    multiply(a,bS_Ic) != add(additive_identity,add(additive_identity,aPb_S_IaPc)),
    inference(scs_inference,[],[i_0_45,i_0_47,i_0_42,i_0_102,i_0_83,i_0_38,i_0_34,i_0_52]) ).

cnf(i_0_144,plain,
    add(additive_identity,X1) = X1,
    inference(rename_variables,[],[i_0_83]) ).

cnf(i_0_145,plain,
    ~ sum(add(additive_identity,aPb_S_IaPc),add(additive_identity,additive_identity),multiply(a,bS_Ic)),
    inference(scs_inference,[],[i_0_45,i_0_47,i_0_42,i_0_102,i_0_121,i_0_83,i_0_144,i_0_38,i_0_34,i_0_52,i_0_56]) ).

cnf(i_0_146,plain,
    add(additive_identity,X1) = X1,
    inference(rename_variables,[],[i_0_83]) ).

cnf(i_0_147,plain,
    ~ sum(multiply(a,bS_Ic),add(additive_identity,additive_inverse(additive_identity)),aPb_S_IaPc),
    inference(scs_inference,[],[i_0_45,i_0_47,i_0_42,i_0_102,i_0_121,i_0_111,i_0_83,i_0_144,i_0_146,i_0_38,i_0_34,i_0_52,i_0_56,i_0_57]) ).

cnf(i_0_148,plain,
    add(additive_identity,X1) = X1,
    inference(rename_variables,[],[i_0_83]) ).

cnf(i_0_149,plain,
    ~ sum(aPb_S_IaPc,add(additive_identity,additive_identity),add(additive_identity,multiply(a,bS_Ic))),
    inference(scs_inference,[],[i_0_45,i_0_47,i_0_42,i_0_102,i_0_121,i_0_111,i_0_83,i_0_144,i_0_146,i_0_148,i_0_38,i_0_34,i_0_52,i_0_56,i_0_57,i_0_58]) ).

cnf(i_0_150,plain,
    add(additive_identity,X1) = X1,
    inference(rename_variables,[],[i_0_83]) ).

cnf(i_0_151,plain,
    ~ product(a,add(additive_identity,bS_Ic),add(additive_identity,aPb_S_IaPc)),
    inference(scs_inference,[],[i_0_45,i_0_47,i_0_42,i_0_102,i_0_121,i_0_111,i_0_109,i_0_83,i_0_144,i_0_146,i_0_148,i_0_150,i_0_38,i_0_34,i_0_52,i_0_56,i_0_57,i_0_58,i_0_54]) ).

cnf(i_0_152,plain,
    add(additive_identity,X1) = X1,
    inference(rename_variables,[],[i_0_83]) ).

cnf(i_0_153,plain,
    ~ product(add(additive_identity,a),bS_Ic,add(additive_identity,aPb_S_IaPc)),
    inference(scs_inference,[],[i_0_84,i_0_45,i_0_47,i_0_42,i_0_102,i_0_121,i_0_111,i_0_109,i_0_83,i_0_144,i_0_146,i_0_148,i_0_150,i_0_152,i_0_38,i_0_34,i_0_52,i_0_56,i_0_57,i_0_58,i_0_54,i_0_55]) ).

cnf(i_0_154,plain,
    add(additive_identity,X1) = X1,
    inference(rename_variables,[],[i_0_83]) ).

cnf(i_0_155,plain,
    ~ product(add(additive_identity,a),add(additive_identity,bS_Ic),add(additive_identity,aPb_S_IaPc)),
    inference(scs_inference,[],[i_0_84,i_0_45,i_0_47,i_0_42,i_0_102,i_0_121,i_0_111,i_0_109,i_0_83,i_0_144,i_0_146,i_0_148,i_0_150,i_0_152,i_0_154,i_0_38,i_0_34,i_0_52,i_0_56,i_0_57,i_0_58,i_0_54,i_0_55,i_0_53]) ).

cnf(i_0_156,plain,
    add(additive_identity,X1) = X1,
    inference(rename_variables,[],[i_0_83]) ).

cnf(i_0_157,plain,
    ~ sum(multiply(a,bS_Ic),additive_inverse(add(additive_identity,additive_identity)),aPb_S_IaPc),
    inference(scs_inference,[],[i_0_84,i_0_45,i_0_47,i_0_141,i_0_42,i_0_140,i_0_102,i_0_121,i_0_111,i_0_109,i_0_83,i_0_144,i_0_146,i_0_148,i_0_150,i_0_152,i_0_154,i_0_38,i_0_34,i_0_52,i_0_56,i_0_57,i_0_58,i_0_54,i_0_55,i_0_53,i_0_32]) ).

cnf(i_0_158,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_47]) ).

cnf(i_0_159,plain,
    sum(additive_inverse(X1),X1,additive_identity),
    inference(rename_variables,[],[i_0_42]) ).

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_32]) ).

cnf(i_0_161,plain,
    sum(b,add(additive_inverse(c),additive_identity),bS_Ic),
    inference(scs_inference,[],[i_0_84,i_0_45,i_0_47,i_0_141,i_0_158,i_0_42,i_0_140,i_0_59,i_0_102,i_0_121,i_0_111,i_0_109,i_0_83,i_0_144,i_0_146,i_0_148,i_0_150,i_0_152,i_0_154,i_0_38,i_0_34,i_0_52,i_0_56,i_0_57,i_0_58,i_0_54,i_0_55,i_0_53,i_0_32,i_0_31]) ).

cnf(i_0_162,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_47]) ).

cnf(i_0_163,plain,
    sum(X1,X2,add(X2,X1)),
    inference(rename_variables,[],[i_0_59]) ).

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_31]) ).

cnf(i_0_165,plain,
    additive_identity = additive_inverse(additive_identity),
    inference(scs_inference,[],[i_0_84,i_0_45,i_0_47,i_0_141,i_0_158,i_0_42,i_0_140,i_0_59,i_0_102,i_0_121,i_0_111,i_0_109,i_0_83,i_0_144,i_0_146,i_0_148,i_0_150,i_0_152,i_0_154,i_0_38,i_0_34,i_0_52,i_0_56,i_0_57,i_0_58,i_0_54,i_0_55,i_0_53,i_0_32,i_0_31,i_0_51]) ).

cnf(i_0_166,plain,
    ( product(aPb,X1,aPb)
    | ~ product(b,X1,b) ),
    inference(scs_inference,[],[i_0_84,i_0_45,i_0_47,i_0_141,i_0_158,i_0_42,i_0_140,i_0_59,i_0_102,i_0_121,i_0_111,i_0_109,i_0_49,i_0_83,i_0_144,i_0_146,i_0_148,i_0_150,i_0_152,i_0_154,i_0_38,i_0_34,i_0_52,i_0_56,i_0_57,i_0_58,i_0_54,i_0_55,i_0_53,i_0_32,i_0_31,i_0_51,i_0_30]) ).

cnf(i_0_167,plain,
    ( ~ product(X1,X2,X3)
    | product(X4,X5,X3)
    | ~ product(X1,X6,X4)
    | ~ product(X6,X5,X2) ),
    inference(rename_variables,[],[i_0_30]) ).

cnf(i_0_168,plain,
    ( product(a,multiply(multiply(b,b),b),aPb)
    | ~ product(b,multiply(b,b),b) ),
    inference(scs_inference,[],[i_0_86,i_0_84,i_0_45,i_0_47,i_0_141,i_0_158,i_0_42,i_0_140,i_0_59,i_0_102,i_0_121,i_0_111,i_0_109,i_0_49,i_0_83,i_0_144,i_0_146,i_0_148,i_0_150,i_0_152,i_0_154,i_0_38,i_0_34,i_0_52,i_0_56,i_0_57,i_0_58,i_0_54,i_0_55,i_0_53,i_0_32,i_0_31,i_0_51,i_0_30,i_0_29]) ).

cnf(i_0_169,plain,
    product(X1,multiply(X1,X1),multiply(multiply(X1,X1),X1)),
    inference(rename_variables,[],[i_0_86]) ).

cnf(i_0_170,plain,
    ( ~ product(X1,X2,X3)
    | product(X4,X5,X3)
    | ~ product(X4,X6,X1)
    | ~ product(X6,X2,X5) ),
    inference(rename_variables,[],[i_0_29]) ).

cnf(i_0_171,plain,
    ( sum(aPb,aPb,aPb)
    | ~ product(b,multiply(b,b),b)
    | ~ sum(a,a,a) ),
    inference(scs_inference,[],[i_0_86,i_0_84,i_0_45,i_0_47,i_0_141,i_0_158,i_0_42,i_0_140,i_0_59,i_0_102,i_0_121,i_0_111,i_0_109,i_0_49,i_0_83,i_0_144,i_0_146,i_0_148,i_0_150,i_0_152,i_0_154,i_0_38,i_0_34,i_0_52,i_0_56,i_0_57,i_0_58,i_0_54,i_0_55,i_0_53,i_0_32,i_0_31,i_0_51,i_0_30,i_0_29,i_0_27]) ).

cnf(i_0_172,plain,
    sum(add(X1,additive_inverse(X1)),additive_identity,additive_identity),
    inference(scs_inference,[],[i_0_66,i_0_38]) ).

cnf(i_0_173,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X2,X1,X3) ),
    inference(rename_variables,[],[i_0_38]) ).

cnf(i_0_174,plain,
    ~ sum(aPb,additive_inverse(aPc),multiply(a,bS_Ic)),
    inference(scs_inference,[],[i_0_44,i_0_66,i_0_64,i_0_38,i_0_34]) ).

cnf(i_0_175,plain,
    ( ~ sum(X1,X2,X3)
    | X4 = X3
    | ~ sum(X1,X2,X4) ),
    inference(rename_variables,[],[i_0_34]) ).

cnf(i_0_176,plain,
    ~ sum(add(additive_identity,aPb_S_IaPc),add(additive_identity,additive_identity),add(additive_identity,multiply(a,bS_Ic))),
    inference(scs_inference,[],[i_0_44,i_0_149,i_0_66,i_0_83,i_0_64,i_0_38,i_0_34,i_0_56]) ).

cnf(i_0_177,plain,
    add(additive_identity,X1) = X1,
    inference(rename_variables,[],[i_0_83]) ).

cnf(i_0_178,plain,
    ~ sum(add(additive_identity,aPb_S_IaPc),additive_identity,add(additive_identity,multiply(a,bS_Ic))),
    inference(scs_inference,[],[i_0_44,i_0_119,i_0_149,i_0_66,i_0_83,i_0_177,i_0_64,i_0_38,i_0_34,i_0_56,i_0_58]) ).

cnf(i_0_179,plain,
    add(additive_identity,X1) = X1,
    inference(rename_variables,[],[i_0_83]) ).

cnf(i_0_180,plain,
    ~ sum(add(additive_identity,aPb_S_IaPc),additive_inverse(additive_identity),multiply(a,bS_Ic)),
    inference(scs_inference,[],[i_0_44,i_0_119,i_0_149,i_0_66,i_0_139,i_0_83,i_0_177,i_0_64,i_0_38,i_0_34,i_0_56,i_0_58,i_0_57]) ).

cnf(i_0_181,plain,
    ~ sum(multiply(a,bS_Ic),additive_inverse(add(additive_identity,additive_identity)),add(additive_identity,aPb_S_IaPc)),
    inference(scs_inference,[],[i_0_44,i_0_47,i_0_42,i_0_145,i_0_119,i_0_149,i_0_66,i_0_139,i_0_83,i_0_177,i_0_64,i_0_38,i_0_34,i_0_56,i_0_58,i_0_57,i_0_32]) ).

cnf(i_0_182,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_47]) ).

cnf(i_0_183,plain,
    sum(additive_inverse(X1),X1,additive_identity),
    inference(rename_variables,[],[i_0_42]) ).

cnf(i_0_184,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ sum(X1,X6,X4)
    | ~ sum(X6,X5,X2) ),
    inference(rename_variables,[],[i_0_32]) ).

cnf(i_0_185,plain,
    sum(additive_inverse(c),add(b,additive_identity),bS_Ic),
    inference(scs_inference,[],[i_0_44,i_0_47,i_0_182,i_0_42,i_0_145,i_0_119,i_0_149,i_0_66,i_0_139,i_0_137,i_0_59,i_0_83,i_0_177,i_0_64,i_0_38,i_0_34,i_0_56,i_0_58,i_0_57,i_0_32,i_0_31]) ).

cnf(i_0_186,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_47]) ).

cnf(i_0_187,plain,
    sum(X1,X2,add(X2,X1)),
    inference(rename_variables,[],[i_0_59]) ).

cnf(i_0_188,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ sum(X4,X6,X1)
    | ~ sum(X6,X2,X5) ),
    inference(rename_variables,[],[i_0_31]) ).

cnf(i_0_189,plain,
    ( product(aPc,X1,aPc)
    | ~ product(c,X1,c) ),
    inference(scs_inference,[],[i_0_44,i_0_47,i_0_182,i_0_42,i_0_145,i_0_119,i_0_149,i_0_66,i_0_139,i_0_137,i_0_59,i_0_83,i_0_177,i_0_64,i_0_48,i_0_38,i_0_34,i_0_56,i_0_58,i_0_57,i_0_32,i_0_31,i_0_30]) ).

cnf(i_0_190,plain,
    ( ~ product(X1,X2,X3)
    | product(X4,X5,X3)
    | ~ product(X1,X6,X4)
    | ~ product(X6,X5,X2) ),
    inference(rename_variables,[],[i_0_30]) ).

cnf(i_0_191,plain,
    ( product(a,multiply(multiply(c,c),c),aPc)
    | ~ product(c,multiply(c,c),c) ),
    inference(scs_inference,[],[i_0_86,i_0_44,i_0_47,i_0_182,i_0_42,i_0_145,i_0_119,i_0_149,i_0_66,i_0_139,i_0_137,i_0_59,i_0_83,i_0_177,i_0_64,i_0_48,i_0_38,i_0_34,i_0_56,i_0_58,i_0_57,i_0_32,i_0_31,i_0_30,i_0_29]) ).

cnf(i_0_192,plain,
    product(X1,multiply(X1,X1),multiply(multiply(X1,X1),X1)),
    inference(rename_variables,[],[i_0_86]) ).

cnf(i_0_193,plain,
    ( ~ product(X1,X2,X3)
    | product(X4,X5,X3)
    | ~ product(X4,X6,X1)
    | ~ product(X6,X2,X5) ),
    inference(rename_variables,[],[i_0_29]) ).

cnf(i_0_194,plain,
    product(X1,X2,multiply(X1,X2)),
    inference(rename_variables,[],[i_0_39]) ).

cnf(i_0_195,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_47]) ).

cnf(i_0_196,plain,
    ( product(aPb_S_IaPc,X1,aPb_S_IaPc)
    | ~ product(aPb,X1,aPb)
    | ~ product(c,multiply(c,c),c)
    | ~ product(additive_inverse(aPc),X1,additive_inverse(aPc)) ),
    inference(scs_inference,[],[i_0_86,i_0_44,i_0_47,i_0_182,i_0_186,i_0_42,i_0_145,i_0_119,i_0_149,i_0_66,i_0_139,i_0_137,i_0_59,i_0_39,i_0_83,i_0_177,i_0_64,i_0_48,i_0_38,i_0_34,i_0_56,i_0_58,i_0_57,i_0_32,i_0_31,i_0_30,i_0_29,i_0_26]) ).

cnf(i_0_197,plain,
    sum(add(additive_inverse(c),additive_identity),b,bS_Ic),
    inference(scs_inference,[],[i_0_161,i_0_38]) ).

cnf(i_0_198,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X2,X1,X3) ),
    inference(rename_variables,[],[i_0_38]) ).

cnf(i_0_199,plain,
    ~ sum(additive_inverse(aPc),aPb,multiply(a,bS_Ic)),
    inference(scs_inference,[],[i_0_161,i_0_100,i_0_64,i_0_38,i_0_34]) ).

cnf(i_0_200,plain,
    ( ~ sum(X1,X2,X3)
    | X4 = X3
    | ~ sum(X1,X2,X4) ),
    inference(rename_variables,[],[i_0_34]) ).

cnf(i_0_201,plain,
    ~ sum(add(additive_identity,aPb_S_IaPc),additive_inverse(additive_identity),add(additive_identity,multiply(a,bS_Ic))),
    inference(scs_inference,[],[i_0_161,i_0_100,i_0_180,i_0_83,i_0_64,i_0_38,i_0_34,i_0_58]) ).

cnf(i_0_202,plain,
    add(additive_identity,X1) = X1,
    inference(rename_variables,[],[i_0_83]) ).

cnf(i_0_203,plain,
    ~ sum(add(additive_identity,aPb),additive_inverse(aPc),multiply(a,bS_Ic)),
    inference(scs_inference,[],[i_0_161,i_0_100,i_0_180,i_0_174,i_0_83,i_0_202,i_0_64,i_0_38,i_0_34,i_0_58,i_0_56]) ).

cnf(i_0_204,plain,
    add(additive_identity,X1) = X1,
    inference(rename_variables,[],[i_0_83]) ).

cnf(i_0_205,plain,
    ~ sum(aPb,add(additive_identity,additive_inverse(aPc)),multiply(a,bS_Ic)),
    inference(scs_inference,[],[i_0_161,i_0_100,i_0_180,i_0_174,i_0_83,i_0_202,i_0_204,i_0_64,i_0_38,i_0_34,i_0_58,i_0_56,i_0_57]) ).

cnf(i_0_206,plain,
    add(additive_identity,X1) = X1,
    inference(rename_variables,[],[i_0_83]) ).

cnf(i_0_207,plain,
    sum(additive_inverse(additive_identity),additive_inverse(additive_identity),additive_identity),
    inference(scs_inference,[],[i_0_47,i_0_42,i_0_161,i_0_100,i_0_180,i_0_174,i_0_43,i_0_83,i_0_202,i_0_204,i_0_64,i_0_38,i_0_34,i_0_58,i_0_56,i_0_57,i_0_32]) ).

cnf(i_0_208,plain,
    sum(additive_inverse(X1),X1,additive_identity),
    inference(rename_variables,[],[i_0_42]) ).

cnf(i_0_209,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_47]) ).

cnf(i_0_210,plain,
    sum(X1,additive_inverse(X1),additive_identity),
    inference(rename_variables,[],[i_0_43]) ).

cnf(i_0_211,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ sum(X1,X6,X4)
    | ~ sum(X6,X5,X2) ),
    inference(rename_variables,[],[i_0_32]) ).

cnf(i_0_212,plain,
    sum(additive_inverse(additive_inverse(additive_identity)),additive_identity,additive_identity),
    inference(scs_inference,[],[i_0_47,i_0_209,i_0_42,i_0_208,i_0_161,i_0_100,i_0_180,i_0_174,i_0_43,i_0_210,i_0_83,i_0_202,i_0_204,i_0_64,i_0_38,i_0_34,i_0_58,i_0_56,i_0_57,i_0_32,i_0_31]) ).

cnf(i_0_213,plain,
    sum(additive_inverse(X1),X1,additive_identity),
    inference(rename_variables,[],[i_0_42]) ).

cnf(i_0_214,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_47]) ).

cnf(i_0_215,plain,
    sum(X1,additive_inverse(X1),additive_identity),
    inference(rename_variables,[],[i_0_43]) ).

cnf(i_0_216,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ sum(X4,X6,X1)
    | ~ sum(X6,X2,X5) ),
    inference(rename_variables,[],[i_0_31]) ).

cnf(i_0_217,plain,
    ( product(X1,aPb,aPb)
    | ~ product(X1,a,a) ),
    inference(scs_inference,[],[i_0_47,i_0_209,i_0_42,i_0_208,i_0_49,i_0_161,i_0_100,i_0_180,i_0_174,i_0_43,i_0_210,i_0_83,i_0_202,i_0_204,i_0_64,i_0_38,i_0_34,i_0_58,i_0_56,i_0_57,i_0_32,i_0_31,i_0_29]) ).

cnf(i_0_218,plain,
    ( ~ product(X1,X2,X3)
    | product(X4,X5,X3)
    | ~ product(X4,X6,X1)
    | ~ product(X6,X2,X5) ),
    inference(rename_variables,[],[i_0_29]) ).

cnf(i_0_219,plain,
    ( sum(multiply(additive_identity,multiply(additive_identity,additive_identity)),aPb,aPb)
    | ~ product(multiply(additive_identity,additive_identity),a,a) ),
    inference(scs_inference,[],[i_0_91,i_0_47,i_0_209,i_0_42,i_0_208,i_0_49,i_0_161,i_0_100,i_0_180,i_0_174,i_0_43,i_0_210,i_0_46,i_0_83,i_0_202,i_0_204,i_0_64,i_0_38,i_0_34,i_0_58,i_0_56,i_0_57,i_0_32,i_0_31,i_0_29,i_0_28]) ).

cnf(i_0_220,plain,
    product(multiply(X1,X1),X1,multiply(X1,multiply(X1,X1))),
    inference(rename_variables,[],[i_0_91]) ).

cnf(i_0_221,plain,
    sum(additive_identity,X1,X1),
    inference(rename_variables,[],[i_0_46]) ).

cnf(i_0_222,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_28]) ).

cnf(i_0_223,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_47]) ).

cnf(i_0_224,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_47]) ).

cnf(i_0_225,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_47]) ).

cnf(i_0_226,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_47]) ).

cnf(i_0_228,plain,
    sum(add(b,additive_identity),additive_inverse(c),bS_Ic),
    inference(scs_inference,[],[i_0_185,i_0_38]) ).

cnf(i_0_229,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X2,X1,X3) ),
    inference(rename_variables,[],[i_0_38]) ).

cnf(i_0_230,plain,
    ~ sum(additive_identity,add(additive_identity,aPb_S_IaPc),multiply(a,bS_Ic)),
    inference(scs_inference,[],[i_0_143,i_0_185,i_0_40,i_0_38,i_0_34]) ).

cnf(i_0_231,plain,
    sum(X1,X2,add(X1,X2)),
    inference(rename_variables,[],[i_0_40]) ).

cnf(i_0_232,plain,
    ( ~ sum(X1,X2,X3)
    | X4 = X3
    | ~ sum(X1,X2,X4) ),
    inference(rename_variables,[],[i_0_34]) ).

cnf(i_0_233,plain,
    ~ sum(aPb_S_IaPc,additive_inverse(additive_identity),add(additive_identity,multiply(a,bS_Ic))),
    inference(scs_inference,[],[i_0_115,i_0_143,i_0_185,i_0_40,i_0_83,i_0_38,i_0_34,i_0_58]) ).

cnf(i_0_234,plain,
    add(additive_identity,X1) = X1,
    inference(rename_variables,[],[i_0_83]) ).

cnf(i_0_235,plain,
    ~ sum(add(additive_identity,aPb),add(additive_identity,additive_inverse(aPc)),multiply(a,bS_Ic)),
    inference(scs_inference,[],[i_0_115,i_0_143,i_0_205,i_0_185,i_0_40,i_0_83,i_0_234,i_0_38,i_0_34,i_0_58,i_0_56]) ).

cnf(i_0_236,plain,
    add(additive_identity,X1) = X1,
    inference(rename_variables,[],[i_0_83]) ).

cnf(i_0_237,plain,
    ~ sum(additive_inverse(aPc),add(additive_identity,aPb),multiply(a,bS_Ic)),
    inference(scs_inference,[],[i_0_115,i_0_143,i_0_205,i_0_185,i_0_199,i_0_40,i_0_83,i_0_234,i_0_236,i_0_38,i_0_34,i_0_58,i_0_56,i_0_57]) ).

cnf(i_0_238,plain,
    add(additive_identity,X1) = X1,
    inference(rename_variables,[],[i_0_83]) ).

cnf(i_0_239,plain,
    sum(additive_inverse(additive_identity),add(X1,additive_inverse(X1)),additive_identity),
    inference(scs_inference,[],[i_0_47,i_0_42,i_0_115,i_0_143,i_0_205,i_0_185,i_0_199,i_0_66,i_0_40,i_0_83,i_0_234,i_0_236,i_0_38,i_0_34,i_0_58,i_0_56,i_0_57,i_0_32]) ).

cnf(i_0_240,plain,
    sum(additive_inverse(X1),X1,additive_identity),
    inference(rename_variables,[],[i_0_42]) ).

cnf(i_0_241,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_47]) ).

cnf(i_0_242,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ sum(X1,X6,X4)
    | ~ sum(X6,X5,X2) ),
    inference(rename_variables,[],[i_0_32]) ).

cnf(i_0_243,plain,
    sum(additive_inverse(c),add(add(b,additive_identity),additive_identity),bS_Ic),
    inference(scs_inference,[],[i_0_47,i_0_241,i_0_42,i_0_115,i_0_143,i_0_205,i_0_185,i_0_199,i_0_66,i_0_59,i_0_40,i_0_83,i_0_234,i_0_236,i_0_38,i_0_34,i_0_58,i_0_56,i_0_57,i_0_32,i_0_31]) ).

cnf(i_0_244,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_47]) ).

cnf(i_0_245,plain,
    sum(X1,X2,add(X2,X1)),
    inference(rename_variables,[],[i_0_59]) ).

cnf(i_0_246,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ sum(X4,X6,X1)
    | ~ sum(X6,X2,X5) ),
    inference(rename_variables,[],[i_0_31]) ).

cnf(i_0_247,plain,
    ( sum(aPb,aPb,aPb)
    | ~ sum(a,a,a) ),
    inference(scs_inference,[],[i_0_47,i_0_241,i_0_42,i_0_49,i_0_115,i_0_143,i_0_205,i_0_185,i_0_199,i_0_66,i_0_59,i_0_40,i_0_83,i_0_234,i_0_236,i_0_38,i_0_34,i_0_58,i_0_56,i_0_57,i_0_32,i_0_31,i_0_27]) ).

cnf(i_0_248,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_27]) ).

cnf(i_0_249,plain,
    ( sum(aPb,aPb,aPb)
    | ~ sum(b,b,b) ),
    inference(scs_inference,[],[i_0_47,i_0_241,i_0_42,i_0_49,i_0_115,i_0_143,i_0_205,i_0_185,i_0_199,i_0_66,i_0_59,i_0_40,i_0_83,i_0_234,i_0_236,i_0_38,i_0_34,i_0_58,i_0_56,i_0_57,i_0_32,i_0_31,i_0_27,i_0_28]) ).

cnf(i_0_250,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_28]) ).

cnf(i_0_251,plain,
    ( product(additive_identity,additive_identity,additive_identity)
    | ~ product(additive_identity,additive_identity,additive_identity) ),
    inference(scs_inference,[],[i_0_47,i_0_241,i_0_244,i_0_42,i_0_49,i_0_115,i_0_143,i_0_205,i_0_185,i_0_199,i_0_66,i_0_59,i_0_40,i_0_83,i_0_234,i_0_236,i_0_38,i_0_34,i_0_58,i_0_56,i_0_57,i_0_32,i_0_31,i_0_27,i_0_28,i_0_25,i_0_26]) ).

cnf(i_0_252,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_47]) ).

cnf(i_0_253,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_47]) ).

cnf(i_0_254,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_26]) ).

cnf(i_0_255,plain,
    sum(add(X1,additive_inverse(X1)),additive_inverse(additive_identity),additive_identity),
    inference(scs_inference,[],[i_0_239,i_0_38]) ).

cnf(i_0_256,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X2,X1,X3) ),
    inference(rename_variables,[],[i_0_38]) ).

cnf(i_0_257,plain,
    ~ sum(additive_identity,aPb_S_IaPc,multiply(a,bS_Ic)),
    inference(scs_inference,[],[i_0_239,i_0_102,i_0_40,i_0_38,i_0_34]) ).

cnf(i_0_258,plain,
    sum(X1,X2,add(X1,X2)),
    inference(rename_variables,[],[i_0_40]) ).

cnf(i_0_259,plain,
    ( ~ sum(X1,X2,X3)
    | X4 = X3
    | ~ sum(X1,X2,X4) ),
    inference(rename_variables,[],[i_0_34]) ).

cnf(i_0_260,plain,
    ~ sum(additive_inverse(aPc),add(additive_identity,aPb),add(additive_identity,multiply(a,bS_Ic))),
    inference(scs_inference,[],[i_0_237,i_0_239,i_0_102,i_0_40,i_0_83,i_0_38,i_0_34,i_0_58]) ).

cnf(i_0_261,plain,
    add(additive_identity,X1) = X1,
    inference(rename_variables,[],[i_0_83]) ).

cnf(i_0_262,plain,
    ~ sum(add(additive_identity,additive_inverse(aPc)),add(additive_identity,aPb),multiply(a,bS_Ic)),
    inference(scs_inference,[],[i_0_237,i_0_239,i_0_102,i_0_40,i_0_83,i_0_261,i_0_38,i_0_34,i_0_58,i_0_56]) ).

cnf(i_0_263,plain,
    add(additive_identity,X1) = X1,
    inference(rename_variables,[],[i_0_83]) ).

cnf(i_0_264,plain,
    ~ sum(multiply(a,bS_Ic),additive_identity,aPb_S_IaPc),
    inference(scs_inference,[],[i_0_165,i_0_237,i_0_239,i_0_102,i_0_111,i_0_40,i_0_83,i_0_261,i_0_38,i_0_34,i_0_58,i_0_56,i_0_57]) ).

cnf(i_0_265,plain,
    ~ sum(multiply(a,bS_Ic),additive_identity,add(additive_identity,aPb_S_IaPc)),
    inference(scs_inference,[],[i_0_165,i_0_47,i_0_178,i_0_237,i_0_239,i_0_102,i_0_111,i_0_59,i_0_40,i_0_83,i_0_261,i_0_38,i_0_34,i_0_58,i_0_56,i_0_57,i_0_32]) ).

cnf(i_0_266,plain,
    sum(X1,X2,add(X2,X1)),
    inference(rename_variables,[],[i_0_59]) ).

cnf(i_0_267,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_47]) ).

cnf(i_0_268,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ sum(X1,X6,X4)
    | ~ sum(X6,X5,X2) ),
    inference(rename_variables,[],[i_0_32]) ).

cnf(i_0_269,plain,
    sum(add(b,additive_identity),add(additive_inverse(c),additive_identity),bS_Ic),
    inference(scs_inference,[],[i_0_165,i_0_47,i_0_267,i_0_178,i_0_237,i_0_239,i_0_228,i_0_102,i_0_111,i_0_59,i_0_266,i_0_40,i_0_83,i_0_261,i_0_38,i_0_34,i_0_58,i_0_56,i_0_57,i_0_32,i_0_31]) ).

cnf(i_0_270,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_47]) ).

cnf(i_0_271,plain,
    sum(X1,X2,add(X2,X1)),
    inference(rename_variables,[],[i_0_59]) ).

cnf(i_0_272,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ sum(X4,X6,X1)
    | ~ sum(X6,X2,X5) ),
    inference(rename_variables,[],[i_0_31]) ).

cnf(i_0_273,plain,
    ( sum(aPc,aPc,aPc)
    | ~ sum(a,a,a) ),
    inference(scs_inference,[],[i_0_48,i_0_165,i_0_47,i_0_267,i_0_178,i_0_237,i_0_239,i_0_228,i_0_102,i_0_111,i_0_59,i_0_266,i_0_40,i_0_83,i_0_261,i_0_38,i_0_34,i_0_58,i_0_56,i_0_57,i_0_32,i_0_31,i_0_27]) ).

cnf(i_0_274,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_27]) ).

cnf(i_0_275,plain,
    ( sum(aPc,aPc,aPc)
    | ~ sum(c,c,c) ),
    inference(scs_inference,[],[i_0_48,i_0_165,i_0_47,i_0_267,i_0_178,i_0_237,i_0_239,i_0_228,i_0_102,i_0_111,i_0_59,i_0_266,i_0_40,i_0_83,i_0_261,i_0_38,i_0_34,i_0_58,i_0_56,i_0_57,i_0_32,i_0_31,i_0_27,i_0_28]) ).

cnf(i_0_276,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_28]) ).

cnf(i_0_277,plain,
    ( product(aPb_S_IaPc,X1,aPb_S_IaPc)
    | ~ product(aPb,X1,aPb)
    | ~ product(additive_inverse(aPc),X1,additive_inverse(aPc)) ),
    inference(scs_inference,[],[i_0_48,i_0_165,i_0_44,i_0_47,i_0_267,i_0_178,i_0_237,i_0_239,i_0_228,i_0_102,i_0_111,i_0_59,i_0_266,i_0_40,i_0_83,i_0_261,i_0_38,i_0_34,i_0_58,i_0_56,i_0_57,i_0_32,i_0_31,i_0_26]) ).

cnf(i_0_278,plain,
    sum(additive_identity,additive_inverse(additive_inverse(additive_identity)),additive_identity),
    inference(scs_inference,[],[i_0_212,i_0_38]) ).

cnf(i_0_279,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X2,X1,X3) ),
    inference(rename_variables,[],[i_0_38]) ).

cnf(i_0_280,plain,
    ~ sum(add(additive_identity,aPb),additive_inverse(aPc),add(additive_identity,multiply(a,bS_Ic))),
    inference(scs_inference,[],[i_0_203,i_0_212,i_0_83,i_0_38,i_0_58]) ).

cnf(i_0_281,plain,
    add(additive_identity,X1) = X1,
    inference(rename_variables,[],[i_0_83]) ).

cnf(i_0_282,plain,
    ~ sum(additive_inverse(additive_identity),add(additive_identity,aPb_S_IaPc),multiply(a,bS_Ic)),
    inference(scs_inference,[],[i_0_139,i_0_203,i_0_230,i_0_212,i_0_83,i_0_38,i_0_58,i_0_56]) ).

cnf(i_0_283,plain,
    ~ sum(additive_inverse(aPc),aPb,add(additive_identity,multiply(a,bS_Ic))),
    inference(scs_inference,[],[i_0_61,i_0_139,i_0_203,i_0_230,i_0_260,i_0_212,i_0_83,i_0_38,i_0_58,i_0_56,i_0_57]) ).

cnf(i_0_284,plain,
    X1 = add(additive_identity,X1),
    inference(rename_variables,[],[i_0_61]) ).

cnf(i_0_285,plain,
    sum(b,add(additive_inverse(bS_Ic),additive_inverse(c)),additive_identity),
    inference(scs_inference,[],[i_0_61,i_0_139,i_0_45,i_0_203,i_0_230,i_0_260,i_0_212,i_0_43,i_0_59,i_0_83,i_0_38,i_0_58,i_0_56,i_0_57,i_0_31]) ).

cnf(i_0_286,plain,
    sum(X1,additive_inverse(X1),additive_identity),
    inference(rename_variables,[],[i_0_43]) ).

cnf(i_0_287,plain,
    sum(X1,X2,add(X2,X1)),
    inference(rename_variables,[],[i_0_59]) ).

cnf(i_0_288,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ sum(X4,X6,X1)
    | ~ sum(X6,X2,X5) ),
    inference(rename_variables,[],[i_0_31]) ).

cnf(i_0_289,plain,
    ( ~ sum(aPb,X1,multiply(a,bS_Ic))
    | ~ sum(X1,additive_inverse(add(additive_identity,additive_identity)),additive_inverse(aPc)) ),
    inference(scs_inference,[],[i_0_61,i_0_139,i_0_45,i_0_44,i_0_157,i_0_203,i_0_230,i_0_260,i_0_212,i_0_43,i_0_59,i_0_83,i_0_38,i_0_58,i_0_56,i_0_57,i_0_31,i_0_32]) ).

cnf(i_0_290,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ sum(X1,X6,X4)
    | ~ sum(X6,X5,X2) ),
    inference(rename_variables,[],[i_0_32]) ).

cnf(i_0_291,plain,
    ( ~ product(a,b,aPb_S_IaPc)
    | ~ product(a,additive_inverse(c),additive_identity) ),
    inference(scs_inference,[],[i_0_61,i_0_139,i_0_45,i_0_44,i_0_104,i_0_157,i_0_203,i_0_230,i_0_260,i_0_212,i_0_39,i_0_43,i_0_59,i_0_83,i_0_38,i_0_58,i_0_56,i_0_57,i_0_31,i_0_32,i_0_28]) ).

cnf(i_0_292,plain,
    product(X1,X2,multiply(X1,X2)),
    inference(rename_variables,[],[i_0_39]) ).

cnf(i_0_293,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_28]) ).

cnf(i_0_294,plain,
    ( product(bS_Ic,X1,bS_Ic)
    | ~ product(b,X1,b)
    | ~ product(additive_inverse(c),X1,additive_inverse(c)) ),
    inference(scs_inference,[],[i_0_61,i_0_139,i_0_45,i_0_44,i_0_104,i_0_157,i_0_203,i_0_230,i_0_260,i_0_212,i_0_39,i_0_43,i_0_59,i_0_83,i_0_38,i_0_58,i_0_56,i_0_57,i_0_31,i_0_26]) ).

cnf(i_0_295,plain,
    sum(add(additive_inverse(c),additive_identity),add(b,additive_identity),bS_Ic),
    inference(scs_inference,[],[i_0_269,i_0_38]) ).

cnf(i_0_296,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X2,X1,X3) ),
    inference(rename_variables,[],[i_0_38]) ).

cnf(i_0_297,plain,
    add(X1,additive_inverse(X1)) = additive_identity,
    inference(scs_inference,[],[i_0_40,i_0_269,i_0_43,i_0_38,i_0_34]) ).

cnf(i_0_298,plain,
    sum(X1,additive_inverse(X1),additive_identity),
    inference(rename_variables,[],[i_0_43]) ).

cnf(i_0_299,plain,
    sum(X1,X2,add(X1,X2)),
    inference(rename_variables,[],[i_0_40]) ).

cnf(i_0_300,plain,
    ( ~ sum(X1,X2,X3)
    | X4 = X3
    | ~ sum(X1,X2,X4) ),
    inference(rename_variables,[],[i_0_34]) ).

cnf(i_0_301,plain,
    ~ sum(additive_identity,aPb_S_IaPc,add(additive_identity,multiply(a,bS_Ic))),
    inference(scs_inference,[],[i_0_40,i_0_257,i_0_269,i_0_43,i_0_83,i_0_38,i_0_34,i_0_58]) ).

cnf(i_0_302,plain,
    add(additive_identity,X1) = X1,
    inference(rename_variables,[],[i_0_83]) ).

cnf(i_0_303,plain,
    ~ sum(additive_inverse(additive_identity),aPb_S_IaPc,multiply(a,bS_Ic)),
    inference(scs_inference,[],[i_0_139,i_0_40,i_0_257,i_0_269,i_0_43,i_0_83,i_0_38,i_0_34,i_0_58,i_0_56]) ).

cnf(i_0_304,plain,
    ~ sum(add(additive_identity,additive_inverse(aPc)),aPb,multiply(a,bS_Ic)),
    inference(scs_inference,[],[i_0_61,i_0_139,i_0_40,i_0_257,i_0_262,i_0_269,i_0_43,i_0_83,i_0_38,i_0_34,i_0_58,i_0_56,i_0_57]) ).

cnf(i_0_305,plain,
    X1 = add(additive_identity,X1),
    inference(rename_variables,[],[i_0_61]) ).

cnf(i_0_306,plain,
    sum(additive_inverse(X1),add(additive_identity,X1),additive_identity),
    inference(scs_inference,[],[i_0_61,i_0_139,i_0_42,i_0_47,i_0_40,i_0_299,i_0_257,i_0_262,i_0_269,i_0_43,i_0_83,i_0_38,i_0_34,i_0_58,i_0_56,i_0_57,i_0_31]) ).

cnf(i_0_307,plain,
    sum(additive_inverse(X1),X1,additive_identity),
    inference(rename_variables,[],[i_0_42]) ).

cnf(i_0_308,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_47]) ).

cnf(i_0_309,plain,
    sum(X1,X2,add(X1,X2)),
    inference(rename_variables,[],[i_0_40]) ).

cnf(i_0_310,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ sum(X4,X6,X1)
    | ~ sum(X6,X2,X5) ),
    inference(rename_variables,[],[i_0_31]) ).

cnf(i_0_311,plain,
    additive_identity = add(X1,additive_inverse(X1)),
    inference(scs_inference,[],[i_0_61,i_0_139,i_0_42,i_0_47,i_0_40,i_0_299,i_0_257,i_0_262,i_0_269,i_0_43,i_0_83,i_0_38,i_0_34,i_0_58,i_0_56,i_0_57,i_0_31,i_0_51]) ).

cnf(i_0_312,plain,
    additive_inverse(additive_identity) = add(X1,additive_inverse(X1)),
    inference(scs_inference,[],[i_0_61,i_0_139,i_0_42,i_0_47,i_0_40,i_0_299,i_0_257,i_0_262,i_0_269,i_0_43,i_0_83,i_0_38,i_0_34,i_0_58,i_0_56,i_0_57,i_0_31,i_0_51,i_0_52]) ).

cnf(i_0_313,plain,
    ( ~ sum(aPb,X1,multiply(a,bS_Ic))
    | ~ sum(X1,add(additive_identity,additive_inverse(additive_identity)),additive_inverse(aPc)) ),
    inference(scs_inference,[],[i_0_61,i_0_139,i_0_44,i_0_42,i_0_47,i_0_40,i_0_299,i_0_257,i_0_262,i_0_269,i_0_147,i_0_43,i_0_83,i_0_38,i_0_34,i_0_58,i_0_56,i_0_57,i_0_31,i_0_51,i_0_52,i_0_32]) ).

cnf(i_0_314,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ sum(X1,X6,X4)
    | ~ sum(X6,X5,X2) ),
    inference(rename_variables,[],[i_0_32]) ).

cnf(i_0_315,plain,
    ( ~ product(a,bS_Ic,add(additive_identity,aPb))
    | ~ product(additive_identity,bS_Ic,add(additive_identity,additive_inverse(aPc))) ),
    inference(scs_inference,[],[i_0_61,i_0_139,i_0_44,i_0_42,i_0_47,i_0_308,i_0_39,i_0_40,i_0_299,i_0_235,i_0_257,i_0_262,i_0_269,i_0_147,i_0_43,i_0_83,i_0_38,i_0_34,i_0_58,i_0_56,i_0_57,i_0_31,i_0_51,i_0_52,i_0_32,i_0_27]) ).

cnf(i_0_316,plain,
    product(X1,X2,multiply(X1,X2)),
    inference(rename_variables,[],[i_0_39]) ).

cnf(i_0_317,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_47]) ).

cnf(i_0_318,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_27]) ).

cnf(i_0_319,plain,
    ( ~ product(a,bS_Ic,add(additive_identity,aPb))
    | ~ product(a,additive_identity,add(additive_identity,additive_inverse(aPc))) ),
    inference(scs_inference,[],[i_0_61,i_0_139,i_0_44,i_0_42,i_0_47,i_0_308,i_0_317,i_0_39,i_0_316,i_0_40,i_0_299,i_0_235,i_0_257,i_0_262,i_0_269,i_0_147,i_0_43,i_0_83,i_0_38,i_0_34,i_0_58,i_0_56,i_0_57,i_0_31,i_0_51,i_0_52,i_0_32,i_0_27,i_0_28]) ).

cnf(i_0_320,plain,
    product(X1,X2,multiply(X1,X2)),
    inference(rename_variables,[],[i_0_39]) ).

cnf(i_0_321,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_47]) ).

cnf(i_0_322,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_28]) ).

cnf(i_0_323,plain,
    ( ~ product(a,bS_Ic,aPb)
    | ~ product(additive_identity,bS_Ic,additive_inverse(aPc)) ),
    inference(scs_inference,[],[i_0_41,i_0_61,i_0_139,i_0_44,i_0_42,i_0_47,i_0_308,i_0_317,i_0_321,i_0_39,i_0_316,i_0_40,i_0_299,i_0_235,i_0_257,i_0_262,i_0_269,i_0_147,i_0_43,i_0_83,i_0_38,i_0_34,i_0_58,i_0_56,i_0_57,i_0_31,i_0_51,i_0_52,i_0_32,i_0_27,i_0_28,i_0_25,i_0_26]) ).

cnf(i_0_324,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_47]) ).

cnf(i_0_325,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_26]) ).

cnf(i_0_326,plain,
    sum(add(additive_identity,X1),additive_inverse(X1),additive_identity),
    inference(scs_inference,[],[i_0_306,i_0_38]) ).

cnf(i_0_327,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X2,X1,X3) ),
    inference(rename_variables,[],[i_0_38]) ).

cnf(i_0_328,plain,
    add(X1,additive_inverse(X1)) = additive_inverse(additive_identity),
    inference(scs_inference,[],[i_0_312,i_0_306,i_0_38,i_0_51]) ).

cnf(i_0_329,plain,
    ~ sum(additive_inverse(additive_identity),add(additive_identity,aPb_S_IaPc),add(additive_identity,multiply(a,bS_Ic))),
    inference(scs_inference,[],[i_0_312,i_0_282,i_0_306,i_0_83,i_0_38,i_0_51,i_0_58]) ).

cnf(i_0_330,plain,
    add(additive_identity,X1) = X1,
    inference(rename_variables,[],[i_0_83]) ).

cnf(i_0_331,plain,
    ~ sum(aPb,additive_inverse(aPc),add(additive_identity,multiply(a,bS_Ic))),
    inference(scs_inference,[],[i_0_61,i_0_280,i_0_312,i_0_282,i_0_306,i_0_83,i_0_38,i_0_51,i_0_58,i_0_56]) ).

cnf(i_0_332,plain,
    X1 = add(additive_identity,X1),
    inference(rename_variables,[],[i_0_61]) ).

cnf(i_0_333,plain,
    ~ sum(multiply(a,bS_Ic),additive_inverse(additive_identity),add(additive_identity,aPb_S_IaPc)),
    inference(scs_inference,[],[i_0_61,i_0_139,i_0_280,i_0_312,i_0_282,i_0_306,i_0_265,i_0_83,i_0_38,i_0_51,i_0_58,i_0_56,i_0_57]) ).

cnf(i_0_334,plain,
    ~ sum(multiply(a,bS_Ic),additive_inverse(additive_inverse(aPc)),aPb),
    inference(scs_inference,[],[i_0_61,i_0_139,i_0_44,i_0_42,i_0_280,i_0_312,i_0_282,i_0_306,i_0_265,i_0_264,i_0_83,i_0_38,i_0_51,i_0_58,i_0_56,i_0_57,i_0_31]) ).

cnf(i_0_335,plain,
    sum(additive_inverse(X1),X1,additive_identity),
    inference(rename_variables,[],[i_0_42]) ).

cnf(i_0_336,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ sum(X4,X6,X1)
    | ~ sum(X6,X2,X5) ),
    inference(rename_variables,[],[i_0_31]) ).

cnf(i_0_337,plain,
    ( sum(aPb_S_IaPc,X1,additive_identity)
    | ~ sum(additive_inverse(aPc),X1,additive_inverse(aPb)) ),
    inference(scs_inference,[],[i_0_61,i_0_139,i_0_44,i_0_42,i_0_280,i_0_312,i_0_282,i_0_306,i_0_265,i_0_264,i_0_43,i_0_83,i_0_38,i_0_51,i_0_58,i_0_56,i_0_57,i_0_31,i_0_32]) ).

cnf(i_0_338,plain,
    sum(X1,additive_inverse(X1),additive_identity),
    inference(rename_variables,[],[i_0_43]) ).

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_32]) ).

cnf(i_0_340,plain,
    ( aPb_S_IaPc = additive_identity
    | ~ sum(additive_inverse(aPc),additive_identity,additive_inverse(aPb)) ),
    inference(scs_inference,[],[i_0_61,i_0_139,i_0_44,i_0_42,i_0_47,i_0_280,i_0_312,i_0_282,i_0_306,i_0_265,i_0_264,i_0_43,i_0_83,i_0_38,i_0_51,i_0_58,i_0_56,i_0_57,i_0_31,i_0_32,i_0_34]) ).

cnf(i_0_341,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_47]) ).

cnf(i_0_342,plain,
    ( ~ sum(X1,X2,X3)
    | X4 = X3
    | ~ sum(X1,X2,X4) ),
    inference(rename_variables,[],[i_0_34]) ).

cnf(i_0_343,plain,
    ( add(additive_identity,aPb_S_IaPc) = additive_identity
    | ~ sum(additive_inverse(aPc),additive_identity,additive_inverse(aPb)) ),
    inference(scs_inference,[],[i_0_61,i_0_139,i_0_44,i_0_42,i_0_47,i_0_280,i_0_312,i_0_282,i_0_306,i_0_265,i_0_264,i_0_43,i_0_83,i_0_330,i_0_38,i_0_51,i_0_58,i_0_56,i_0_57,i_0_31,i_0_32,i_0_34,i_0_52]) ).

cnf(i_0_344,plain,
    add(additive_identity,X1) = X1,
    inference(rename_variables,[],[i_0_83]) ).

cnf(i_0_345,plain,
    ( ~ product(X1,X2,X3)
    | product(X4,X5,X3)
    | ~ product(X1,X6,X4)
    | ~ product(X6,X5,X2) ),
    inference(rename_variables,[],[i_0_30]) ).

cnf(i_0_346,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_47]) ).

cnf(i_0_347,plain,
    product(X1,X2,multiply(X1,X2)),
    inference(rename_variables,[],[i_0_39]) ).

cnf(i_0_348,plain,
    ( product(aPb,aPb_S_IaPc,aPb_S_IaPc)
    | ~ sum(additive_inverse(aPc),additive_identity,additive_inverse(aPb))
    | ~ product(b,aPb,b)
    | ~ product(aPb,additive_inverse(aPc),additive_inverse(aPc)) ),
    inference(scs_inference,[],[i_0_49,i_0_61,i_0_139,i_0_44,i_0_42,i_0_47,i_0_341,i_0_39,i_0_280,i_0_312,i_0_282,i_0_306,i_0_265,i_0_264,i_0_43,i_0_83,i_0_330,i_0_38,i_0_51,i_0_58,i_0_56,i_0_57,i_0_31,i_0_32,i_0_34,i_0_52,i_0_30,i_0_25]) ).

cnf(i_0_349,plain,
    sum(add(add(b,additive_identity),additive_identity),additive_inverse(c),bS_Ic),
    inference(scs_inference,[],[i_0_243,i_0_38]) ).

cnf(i_0_350,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X2,X1,X3) ),
    inference(rename_variables,[],[i_0_38]) ).

cnf(i_0_351,plain,
    add(additive_inverse(X1),X1) = additive_identity,
    inference(scs_inference,[],[i_0_40,i_0_42,i_0_243,i_0_38,i_0_34]) ).

cnf(i_0_352,plain,
    sum(additive_inverse(X1),X1,additive_identity),
    inference(rename_variables,[],[i_0_42]) ).

cnf(i_0_353,plain,
    sum(X1,X2,add(X1,X2)),
    inference(rename_variables,[],[i_0_40]) ).

cnf(i_0_354,plain,
    ( ~ sum(X1,X2,X3)
    | X4 = X3
    | ~ sum(X1,X2,X4) ),
    inference(rename_variables,[],[i_0_34]) ).

cnf(i_0_355,plain,
    ~ sum(additive_inverse(additive_identity),aPb_S_IaPc,add(additive_identity,multiply(a,bS_Ic))),
    inference(scs_inference,[],[i_0_40,i_0_42,i_0_303,i_0_243,i_0_83,i_0_38,i_0_34,i_0_58]) ).

cnf(i_0_356,plain,
    add(additive_identity,X1) = X1,
    inference(rename_variables,[],[i_0_83]) ).

cnf(i_0_357,plain,
    ~ sum(additive_identity,add(additive_identity,aPb_S_IaPc),add(additive_identity,multiply(a,bS_Ic))),
    inference(scs_inference,[],[i_0_165,i_0_40,i_0_42,i_0_329,i_0_303,i_0_243,i_0_83,i_0_38,i_0_34,i_0_58,i_0_56]) ).

cnf(i_0_358,plain,
    ~ sum(additive_inverse(aPb_S_IaPc),multiply(a,bS_Ic),additive_identity),
    inference(scs_inference,[],[i_0_165,i_0_40,i_0_353,i_0_42,i_0_123,i_0_329,i_0_303,i_0_243,i_0_43,i_0_83,i_0_38,i_0_34,i_0_58,i_0_56,i_0_31]) ).

cnf(i_0_359,plain,
    sum(X1,X2,add(X1,X2)),
    inference(rename_variables,[],[i_0_40]) ).

cnf(i_0_360,plain,
    sum(X1,additive_inverse(X1),additive_identity),
    inference(rename_variables,[],[i_0_43]) ).

cnf(i_0_361,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ sum(X4,X6,X1)
    | ~ sum(X6,X2,X5) ),
    inference(rename_variables,[],[i_0_31]) ).

cnf(i_0_362,plain,
    additive_identity = add(additive_inverse(X1),X1),
    inference(scs_inference,[],[i_0_165,i_0_40,i_0_353,i_0_42,i_0_123,i_0_329,i_0_303,i_0_243,i_0_43,i_0_83,i_0_38,i_0_34,i_0_58,i_0_56,i_0_31,i_0_51]) ).

cnf(i_0_363,plain,
    additive_inverse(additive_identity) = add(additive_inverse(X1),X1),
    inference(scs_inference,[],[i_0_165,i_0_139,i_0_40,i_0_353,i_0_42,i_0_123,i_0_329,i_0_303,i_0_243,i_0_43,i_0_83,i_0_38,i_0_34,i_0_58,i_0_56,i_0_31,i_0_51,i_0_52]) ).

cnf(i_0_364,plain,
    ~ sum(additive_inverse(aPb_S_IaPc),add(additive_identity,multiply(a,bS_Ic)),additive_identity),
    inference(scs_inference,[],[i_0_165,i_0_139,i_0_40,i_0_353,i_0_42,i_0_123,i_0_329,i_0_303,i_0_243,i_0_43,i_0_83,i_0_356,i_0_38,i_0_34,i_0_58,i_0_56,i_0_31,i_0_51,i_0_52,i_0_57]) ).

cnf(i_0_365,plain,
    add(additive_identity,X1) = X1,
    inference(rename_variables,[],[i_0_83]) ).

cnf(i_0_366,plain,
    ( ~ sum(additive_inverse(aPc),X1,multiply(a,bS_Ic))
    | ~ sum(X1,additive_inverse(add(additive_identity,additive_identity)),aPb) ),
    inference(scs_inference,[],[i_0_165,i_0_139,i_0_100,i_0_40,i_0_353,i_0_42,i_0_123,i_0_329,i_0_303,i_0_243,i_0_157,i_0_43,i_0_83,i_0_356,i_0_38,i_0_34,i_0_58,i_0_56,i_0_31,i_0_51,i_0_52,i_0_57,i_0_32]) ).

cnf(i_0_367,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ sum(X1,X6,X4)
    | ~ sum(X6,X5,X2) ),
    inference(rename_variables,[],[i_0_32]) ).

cnf(i_0_368,plain,
    ( ~ product(a,b,multiply(a,bS_Ic))
    | ~ product(additive_identity,b,additive_inverse(additive_inverse(aPc))) ),
    inference(scs_inference,[],[i_0_49,i_0_165,i_0_139,i_0_100,i_0_40,i_0_353,i_0_42,i_0_47,i_0_123,i_0_329,i_0_303,i_0_334,i_0_243,i_0_157,i_0_43,i_0_83,i_0_356,i_0_38,i_0_34,i_0_58,i_0_56,i_0_31,i_0_51,i_0_52,i_0_57,i_0_32,i_0_27]) ).

cnf(i_0_369,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_47]) ).

cnf(i_0_370,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_27]) ).

cnf(i_0_371,plain,
    ( ~ product(a,X1,additive_inverse(additive_inverse(aPc)))
    | ~ sum(bS_Ic,X1,b) ),
    inference(scs_inference,[],[i_0_49,i_0_165,i_0_139,i_0_44,i_0_100,i_0_40,i_0_353,i_0_42,i_0_47,i_0_39,i_0_123,i_0_329,i_0_303,i_0_334,i_0_243,i_0_157,i_0_43,i_0_83,i_0_356,i_0_38,i_0_34,i_0_58,i_0_56,i_0_31,i_0_51,i_0_52,i_0_57,i_0_32,i_0_27,i_0_26,i_0_28]) ).

cnf(i_0_372,plain,
    product(X1,X2,multiply(X1,X2)),
    inference(rename_variables,[],[i_0_39]) ).

cnf(i_0_373,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_28]) ).

cnf(i_0_374,plain,
    ( ~ product(add(additive_identity,a),additive_identity,aPb)
    | ~ product(add(additive_identity,a),bS_Ic,additive_inverse(aPc)) ),
    inference(scs_inference,[],[i_0_125,i_0_49,i_0_165,i_0_139,i_0_44,i_0_100,i_0_40,i_0_353,i_0_359,i_0_42,i_0_47,i_0_39,i_0_123,i_0_329,i_0_303,i_0_334,i_0_243,i_0_157,i_0_43,i_0_83,i_0_356,i_0_38,i_0_34,i_0_58,i_0_56,i_0_31,i_0_51,i_0_52,i_0_57,i_0_32,i_0_27,i_0_26,i_0_28,i_0_25]) ).

cnf(i_0_375,plain,
    sum(X1,X2,add(X1,X2)),
    inference(rename_variables,[],[i_0_40]) ).

cnf(i_0_376,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_25]) ).

cnf(i_0_377,plain,
    sum(add(additive_inverse(bS_Ic),additive_inverse(c)),b,additive_identity),
    inference(scs_inference,[],[i_0_285,i_0_38]) ).

cnf(i_0_378,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X2,X1,X3) ),
    inference(rename_variables,[],[i_0_38]) ).

cnf(i_0_379,plain,
    add(additive_inverse(X1),X1) = additive_inverse(additive_identity),
    inference(scs_inference,[],[i_0_363,i_0_285,i_0_38,i_0_51]) ).

cnf(i_0_380,plain,
    ~ sum(additive_inverse(aPb_S_IaPc),add(additive_identity,multiply(a,bS_Ic)),additive_inverse(additive_identity)),
    inference(scs_inference,[],[i_0_139,i_0_363,i_0_364,i_0_285,i_0_38,i_0_51,i_0_58]) ).

cnf(i_0_381,plain,
    ~ sum(add(additive_identity,multiply(a,bS_Ic)),additive_inverse(additive_identity),add(additive_identity,aPb_S_IaPc)),
    inference(scs_inference,[],[i_0_139,i_0_333,i_0_363,i_0_364,i_0_285,i_0_83,i_0_38,i_0_51,i_0_58,i_0_56]) ).

cnf(i_0_382,plain,
    add(additive_identity,X1) = X1,
    inference(rename_variables,[],[i_0_83]) ).

cnf(i_0_383,plain,
    ~ sum(additive_inverse(aPb_S_IaPc),multiply(a,bS_Ic),additive_inverse(additive_identity)),
    inference(scs_inference,[],[i_0_61,i_0_139,i_0_333,i_0_363,i_0_364,i_0_285,i_0_83,i_0_38,i_0_51,i_0_58,i_0_56,i_0_57]) ).

cnf(i_0_384,plain,
    X1 = add(additive_identity,X1),
    inference(rename_variables,[],[i_0_61]) ).

cnf(i_0_385,plain,
    ~ sum(additive_identity,add(additive_identity,multiply(a,bS_Ic)),aPb_S_IaPc),
    inference(scs_inference,[],[i_0_61,i_0_139,i_0_42,i_0_47,i_0_333,i_0_363,i_0_364,i_0_285,i_0_83,i_0_38,i_0_51,i_0_58,i_0_56,i_0_57,i_0_32]) ).

cnf(i_0_386,plain,
    sum(additive_inverse(X1),X1,additive_identity),
    inference(rename_variables,[],[i_0_42]) ).

cnf(i_0_387,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_47]) ).

cnf(i_0_388,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ sum(X1,X6,X4)
    | ~ sum(X6,X5,X2) ),
    inference(rename_variables,[],[i_0_32]) ).

cnf(i_0_389,plain,
    ~ sum(multiply(a,bS_Ic),additive_inverse(aPb),additive_inverse(aPc)),
    inference(scs_inference,[],[i_0_61,i_0_139,i_0_100,i_0_42,i_0_386,i_0_47,i_0_333,i_0_363,i_0_364,i_0_285,i_0_264,i_0_83,i_0_38,i_0_51,i_0_58,i_0_56,i_0_57,i_0_32,i_0_31]) ).

cnf(i_0_390,plain,
    sum(additive_inverse(X1),X1,additive_identity),
    inference(rename_variables,[],[i_0_42]) ).

cnf(i_0_391,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ sum(X4,X6,X1)
    | ~ sum(X6,X2,X5) ),
    inference(rename_variables,[],[i_0_31]) ).

cnf(i_0_392,plain,
    ( ~ product(a,bS_Ic,add(additive_identity,additive_inverse(aPc)))
    | ~ product(additive_identity,bS_Ic,aPb) ),
    inference(scs_inference,[],[i_0_61,i_0_139,i_0_100,i_0_42,i_0_386,i_0_47,i_0_387,i_0_39,i_0_333,i_0_304,i_0_363,i_0_364,i_0_285,i_0_264,i_0_83,i_0_38,i_0_51,i_0_58,i_0_56,i_0_57,i_0_32,i_0_31,i_0_27]) ).

cnf(i_0_393,plain,
    product(X1,X2,multiply(X1,X2)),
    inference(rename_variables,[],[i_0_39]) ).

cnf(i_0_394,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_47]) ).

cnf(i_0_395,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_27]) ).

cnf(i_0_396,plain,
    ( ~ product(a,bS_Ic,additive_inverse(aPc))
    | ~ product(additive_identity,bS_Ic,aPb) ),
    inference(scs_inference,[],[i_0_61,i_0_384,i_0_139,i_0_100,i_0_42,i_0_386,i_0_47,i_0_387,i_0_39,i_0_333,i_0_304,i_0_363,i_0_364,i_0_285,i_0_264,i_0_83,i_0_38,i_0_51,i_0_58,i_0_56,i_0_57,i_0_32,i_0_31,i_0_27,i_0_55]) ).

cnf(i_0_397,plain,
    X1 = add(additive_identity,X1),
    inference(rename_variables,[],[i_0_61]) ).

cnf(i_0_398,plain,
    ( ~ product(a,add(additive_identity,bS_Ic),add(additive_identity,additive_inverse(aPc)))
    | ~ product(additive_identity,bS_Ic,aPb) ),
    inference(scs_inference,[],[i_0_61,i_0_384,i_0_139,i_0_100,i_0_42,i_0_386,i_0_47,i_0_387,i_0_39,i_0_333,i_0_304,i_0_363,i_0_364,i_0_285,i_0_264,i_0_83,i_0_382,i_0_38,i_0_51,i_0_58,i_0_56,i_0_57,i_0_32,i_0_31,i_0_27,i_0_55,i_0_54]) ).

cnf(i_0_399,plain,
    add(additive_identity,X1) = X1,
    inference(rename_variables,[],[i_0_83]) ).

cnf(i_0_400,plain,
    ( ~ product(add(additive_identity,a),bS_Ic,add(additive_identity,additive_inverse(aPc)))
    | ~ product(additive_identity,bS_Ic,aPb) ),
    inference(scs_inference,[],[i_0_61,i_0_384,i_0_139,i_0_100,i_0_42,i_0_386,i_0_47,i_0_387,i_0_39,i_0_333,i_0_304,i_0_363,i_0_364,i_0_285,i_0_264,i_0_83,i_0_382,i_0_399,i_0_38,i_0_51,i_0_58,i_0_56,i_0_57,i_0_32,i_0_31,i_0_27,i_0_55,i_0_54,i_0_53]) ).

cnf(i_0_401,plain,
    add(additive_identity,X1) = X1,
    inference(rename_variables,[],[i_0_83]) ).

cnf(i_0_402,plain,
    ( ~ product(X1,X2,X3)
    | product(X4,X5,X3)
    | ~ product(X1,X6,X4)
    | ~ product(X6,X5,X2) ),
    inference(rename_variables,[],[i_0_30]) ).

cnf(i_0_403,plain,
    product(X1,X2,multiply(X1,X2)),
    inference(rename_variables,[],[i_0_39]) ).

cnf(i_0_404,plain,
    ( product(aPb,aPb_S_IaPc,aPb_S_IaPc)
    | ~ product(additive_identity,bS_Ic,aPb)
    | ~ product(b,aPb,b)
    | ~ product(aPb,additive_inverse(aPc),additive_inverse(aPc)) ),
    inference(scs_inference,[],[i_0_49,i_0_61,i_0_384,i_0_139,i_0_44,i_0_100,i_0_42,i_0_386,i_0_47,i_0_387,i_0_39,i_0_393,i_0_333,i_0_304,i_0_363,i_0_364,i_0_285,i_0_264,i_0_334,i_0_83,i_0_382,i_0_399,i_0_38,i_0_51,i_0_58,i_0_56,i_0_57,i_0_32,i_0_31,i_0_27,i_0_55,i_0_54,i_0_53,i_0_30,i_0_25]) ).

cnf(i_0_405,plain,
    ~ sum(add(additive_identity,additive_inverse(aPb_S_IaPc)),multiply(a,bS_Ic),additive_identity),
    inference(scs_inference,[],[i_0_358,i_0_83,i_0_56]) ).

cnf(i_0_406,plain,
    add(additive_identity,X1) = X1,
    inference(rename_variables,[],[i_0_83]) ).

cnf(i_0_407,plain,
    ~ sum(add(additive_identity,multiply(a,bS_Ic)),additive_inverse(additive_identity),aPb_S_IaPc),
    inference(scs_inference,[],[i_0_61,i_0_381,i_0_358,i_0_83,i_0_56,i_0_58]) ).

cnf(i_0_408,plain,
    X1 = add(additive_identity,X1),
    inference(rename_variables,[],[i_0_61]) ).

cnf(i_0_409,plain,
    ~ sum(add(additive_identity,multiply(a,bS_Ic)),additive_identity,add(additive_identity,aPb_S_IaPc)),
    inference(scs_inference,[],[i_0_61,i_0_165,i_0_381,i_0_358,i_0_83,i_0_56,i_0_58,i_0_57]) ).

cnf(i_0_410,plain,
    ~ sum(additive_inverse(aPb),add(additive_identity,multiply(a,bS_Ic)),additive_inverse(aPc)),
    inference(scs_inference,[],[i_0_61,i_0_44,i_0_165,i_0_43,i_0_381,i_0_358,i_0_385,i_0_83,i_0_56,i_0_58,i_0_57,i_0_32]) ).

cnf(i_0_411,plain,
    sum(X1,additive_inverse(X1),additive_identity),
    inference(rename_variables,[],[i_0_43]) ).

cnf(i_0_412,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ sum(X1,X6,X4)
    | ~ sum(X6,X5,X2) ),
    inference(rename_variables,[],[i_0_32]) ).

cnf(i_0_413,plain,
    sum(b,add(additive_identity,additive_inverse(c)),bS_Ic),
    inference(scs_inference,[],[i_0_61,i_0_44,i_0_165,i_0_40,i_0_45,i_0_47,i_0_43,i_0_381,i_0_358,i_0_385,i_0_83,i_0_56,i_0_58,i_0_57,i_0_32,i_0_31]) ).

cnf(i_0_414,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_47]) ).

cnf(i_0_415,plain,
    sum(X1,X2,add(X1,X2)),
    inference(rename_variables,[],[i_0_40]) ).

cnf(i_0_416,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ sum(X4,X6,X1)
    | ~ sum(X6,X2,X5) ),
    inference(rename_variables,[],[i_0_31]) ).

cnf(i_0_417,plain,
    sum(add(additive_identity,additive_inverse(c)),b,bS_Ic),
    inference(scs_inference,[],[i_0_61,i_0_44,i_0_165,i_0_40,i_0_45,i_0_47,i_0_43,i_0_381,i_0_358,i_0_385,i_0_83,i_0_56,i_0_58,i_0_57,i_0_32,i_0_31,i_0_38]) ).

cnf(i_0_418,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X2,X1,X3) ),
    inference(rename_variables,[],[i_0_38]) ).

cnf(i_0_419,plain,
    ( product(additive_identity,b,aPb_S_IaPc)
    | ~ product(additive_inverse(a),b,additive_inverse(aPc)) ),
    inference(scs_inference,[],[i_0_49,i_0_61,i_0_44,i_0_165,i_0_40,i_0_45,i_0_47,i_0_43,i_0_411,i_0_381,i_0_358,i_0_385,i_0_83,i_0_56,i_0_58,i_0_57,i_0_32,i_0_31,i_0_38,i_0_26]) ).

cnf(i_0_420,plain,
    sum(X1,additive_inverse(X1),additive_identity),
    inference(rename_variables,[],[i_0_43]) ).

cnf(i_0_421,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_26]) ).

cnf(i_0_422,plain,
    ( ~ product(additive_identity,b,multiply(a,bS_Ic))
    | ~ product(additive_inverse(a),b,additive_inverse(aPc)) ),
    inference(scs_inference,[],[i_0_49,i_0_61,i_0_44,i_0_165,i_0_40,i_0_45,i_0_47,i_0_43,i_0_411,i_0_381,i_0_358,i_0_385,i_0_64,i_0_83,i_0_56,i_0_58,i_0_57,i_0_32,i_0_31,i_0_38,i_0_26,i_0_33]) ).

cnf(i_0_423,plain,
    ( ~ product(X1,X2,X3)
    | X4 = X3
    | ~ product(X1,X2,X4) ),
    inference(rename_variables,[],[i_0_33]) ).

cnf(i_0_424,plain,
    ( ~ product(additive_identity,b,add(additive_identity,multiply(a,bS_Ic)))
    | ~ product(additive_inverse(a),b,additive_inverse(aPc)) ),
    inference(scs_inference,[],[i_0_49,i_0_61,i_0_44,i_0_165,i_0_40,i_0_45,i_0_47,i_0_43,i_0_411,i_0_381,i_0_358,i_0_385,i_0_64,i_0_83,i_0_406,i_0_56,i_0_58,i_0_57,i_0_32,i_0_31,i_0_38,i_0_26,i_0_33,i_0_55]) ).

cnf(i_0_425,plain,
    add(additive_identity,X1) = X1,
    inference(rename_variables,[],[i_0_83]) ).

cnf(i_0_426,plain,
    ( ~ product(additive_identity,add(additive_identity,b),multiply(a,bS_Ic))
    | ~ product(additive_inverse(a),b,additive_inverse(aPc)) ),
    inference(scs_inference,[],[i_0_49,i_0_61,i_0_44,i_0_165,i_0_40,i_0_45,i_0_47,i_0_43,i_0_411,i_0_381,i_0_358,i_0_385,i_0_64,i_0_83,i_0_406,i_0_425,i_0_56,i_0_58,i_0_57,i_0_32,i_0_31,i_0_38,i_0_26,i_0_33,i_0_55,i_0_54]) ).

cnf(i_0_427,plain,
    add(additive_identity,X1) = X1,
    inference(rename_variables,[],[i_0_83]) ).

cnf(i_0_428,plain,
    ( ~ product(additive_inverse(additive_identity),b,multiply(a,bS_Ic))
    | ~ product(additive_inverse(a),b,additive_inverse(aPc)) ),
    inference(scs_inference,[],[i_0_49,i_0_61,i_0_44,i_0_165,i_0_139,i_0_40,i_0_45,i_0_47,i_0_43,i_0_411,i_0_381,i_0_358,i_0_385,i_0_64,i_0_83,i_0_406,i_0_425,i_0_56,i_0_58,i_0_57,i_0_32,i_0_31,i_0_38,i_0_26,i_0_33,i_0_55,i_0_54,i_0_53]) ).

cnf(i_0_429,plain,
    ( ~ product(X1,X2,X3)
    | product(X4,X5,X3)
    | ~ product(X1,X6,X4)
    | ~ product(X6,X5,X2) ),
    inference(rename_variables,[],[i_0_30]) ).

cnf(i_0_430,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_47]) ).

cnf(i_0_431,plain,
    product(X1,X2,multiply(X1,X2)),
    inference(rename_variables,[],[i_0_39]) ).

cnf(i_0_432,plain,
    ( product(aPb,aPb_S_IaPc,aPb_S_IaPc)
    | ~ product(b,aPb,b)
    | ~ product(additive_inverse(a),b,additive_inverse(aPc))
    | ~ product(aPb,additive_inverse(aPc),additive_inverse(aPc)) ),
    inference(scs_inference,[],[i_0_49,i_0_61,i_0_44,i_0_165,i_0_139,i_0_40,i_0_45,i_0_47,i_0_414,i_0_43,i_0_411,i_0_39,i_0_381,i_0_358,i_0_385,i_0_334,i_0_64,i_0_83,i_0_406,i_0_425,i_0_56,i_0_58,i_0_57,i_0_32,i_0_31,i_0_38,i_0_26,i_0_33,i_0_55,i_0_54,i_0_53,i_0_30,i_0_25]) ).

cnf(i_0_433,plain,
    ~ sum(add(additive_identity,additive_inverse(aPb_S_IaPc)),multiply(a,bS_Ic),additive_inverse(additive_identity)),
    inference(scs_inference,[],[i_0_383,i_0_83,i_0_56]) ).

cnf(i_0_434,plain,
    add(additive_identity,X1) = X1,
    inference(rename_variables,[],[i_0_83]) ).

cnf(i_0_435,plain,
    ~ sum(add(additive_identity,multiply(a,bS_Ic)),additive_identity,aPb_S_IaPc),
    inference(scs_inference,[],[i_0_61,i_0_383,i_0_409,i_0_83,i_0_56,i_0_58]) ).

cnf(i_0_436,plain,
    X1 = add(additive_identity,X1),
    inference(rename_variables,[],[i_0_61]) ).

cnf(i_0_437,plain,
    ~ sum(additive_inverse(aPb),multiply(a,bS_Ic),additive_inverse(aPc)),
    inference(scs_inference,[],[i_0_61,i_0_436,i_0_383,i_0_409,i_0_410,i_0_83,i_0_56,i_0_58,i_0_57]) ).

cnf(i_0_438,plain,
    X1 = add(additive_identity,X1),
    inference(rename_variables,[],[i_0_61]) ).

cnf(i_0_439,plain,
    ~ sum(multiply(a,bS_Ic),additive_inverse(additive_inverse(additive_identity)),aPb_S_IaPc),
    inference(scs_inference,[],[i_0_61,i_0_436,i_0_59,i_0_42,i_0_233,i_0_383,i_0_409,i_0_410,i_0_83,i_0_56,i_0_58,i_0_57,i_0_32]) ).

cnf(i_0_440,plain,
    sum(X1,X2,add(X2,X1)),
    inference(rename_variables,[],[i_0_59]) ).

cnf(i_0_441,plain,
    sum(additive_inverse(X1),X1,additive_identity),
    inference(rename_variables,[],[i_0_42]) ).

cnf(i_0_442,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ sum(X1,X6,X4)
    | ~ sum(X6,X5,X2) ),
    inference(rename_variables,[],[i_0_32]) ).

cnf(i_0_443,plain,
    sum(additive_identity,add(additive_inverse(c),add(b,additive_identity)),bS_Ic),
    inference(scs_inference,[],[i_0_61,i_0_436,i_0_59,i_0_440,i_0_40,i_0_42,i_0_233,i_0_295,i_0_383,i_0_409,i_0_410,i_0_83,i_0_56,i_0_58,i_0_57,i_0_32,i_0_31]) ).

cnf(i_0_444,plain,
    sum(X1,X2,add(X2,X1)),
    inference(rename_variables,[],[i_0_59]) ).

cnf(i_0_445,plain,
    sum(X1,X2,add(X1,X2)),
    inference(rename_variables,[],[i_0_40]) ).

cnf(i_0_446,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ sum(X4,X6,X1)
    | ~ sum(X6,X2,X5) ),
    inference(rename_variables,[],[i_0_31]) ).

cnf(i_0_447,plain,
    ~ product(a,add(additive_inverse(c),additive_identity),additive_inverse(aPc)),
    inference(scs_inference,[],[i_0_49,i_0_61,i_0_436,i_0_59,i_0_440,i_0_40,i_0_42,i_0_39,i_0_233,i_0_295,i_0_197,i_0_383,i_0_409,i_0_410,i_0_199,i_0_83,i_0_56,i_0_58,i_0_57,i_0_32,i_0_31,i_0_28]) ).

cnf(i_0_448,plain,
    product(X1,X2,multiply(X1,X2)),
    inference(rename_variables,[],[i_0_39]) ).

cnf(i_0_449,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_28]) ).

cnf(i_0_450,plain,
    sum(add(additive_inverse(c),add(b,additive_identity)),additive_identity,bS_Ic),
    inference(scs_inference,[],[i_0_49,i_0_61,i_0_436,i_0_59,i_0_440,i_0_40,i_0_42,i_0_39,i_0_233,i_0_295,i_0_197,i_0_383,i_0_409,i_0_410,i_0_199,i_0_83,i_0_56,i_0_58,i_0_57,i_0_32,i_0_31,i_0_28,i_0_38]) ).

cnf(i_0_451,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X2,X1,X3) ),
    inference(rename_variables,[],[i_0_38]) ).

cnf(i_0_452,plain,
    ~ product(add(additive_identity,a),add(additive_inverse(c),additive_identity),additive_inverse(aPc)),
    inference(scs_inference,[],[i_0_49,i_0_61,i_0_436,i_0_59,i_0_440,i_0_40,i_0_42,i_0_39,i_0_233,i_0_295,i_0_197,i_0_383,i_0_409,i_0_410,i_0_199,i_0_83,i_0_434,i_0_56,i_0_58,i_0_57,i_0_32,i_0_31,i_0_28,i_0_38,i_0_53]) ).

cnf(i_0_453,plain,
    add(additive_identity,X1) = X1,
    inference(rename_variables,[],[i_0_83]) ).

cnf(i_0_454,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_49,i_0_61,i_0_436,i_0_59,i_0_440,i_0_40,i_0_42,i_0_39,i_0_233,i_0_295,i_0_197,i_0_71,i_0_383,i_0_409,i_0_410,i_0_199,i_0_83,i_0_434,i_0_56,i_0_58,i_0_57,i_0_32,i_0_31,i_0_28,i_0_38,i_0_53,i_0_26]) ).

cnf(i_0_455,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_26]) ).

cnf(i_0_456,plain,
    ( multiply(additive_identity,multiply(additive_identity,additive_identity)) = multiply(additive_identity,additive_identity)
    | ~ product(multiply(additive_identity,additive_identity),additive_identity,multiply(additive_identity,additive_identity)) ),
    inference(scs_inference,[],[i_0_91,i_0_49,i_0_61,i_0_436,i_0_59,i_0_440,i_0_40,i_0_42,i_0_39,i_0_233,i_0_295,i_0_197,i_0_71,i_0_383,i_0_409,i_0_410,i_0_199,i_0_83,i_0_434,i_0_56,i_0_58,i_0_57,i_0_32,i_0_31,i_0_28,i_0_38,i_0_53,i_0_26,i_0_33]) ).

cnf(i_0_457,plain,
    product(multiply(X1,X1),X1,multiply(X1,multiply(X1,X1))),
    inference(rename_variables,[],[i_0_91]) ).

cnf(i_0_458,plain,
    ( ~ product(X1,X2,X3)
    | X4 = X3
    | ~ product(X1,X2,X4) ),
    inference(rename_variables,[],[i_0_33]) ).

cnf(i_0_459,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_47]) ).

cnf(i_0_460,plain,
    ( product(aPb,aPb_S_IaPc,aPb_S_IaPc)
    | ~ product(b,aPb,b)
    | ~ product(multiply(additive_identity,additive_identity),additive_identity,multiply(additive_identity,additive_identity))
    | ~ product(aPb,additive_inverse(aPc),additive_inverse(aPc)) ),
    inference(scs_inference,[],[i_0_91,i_0_49,i_0_61,i_0_436,i_0_44,i_0_59,i_0_440,i_0_40,i_0_42,i_0_39,i_0_47,i_0_233,i_0_295,i_0_197,i_0_71,i_0_383,i_0_409,i_0_410,i_0_199,i_0_334,i_0_83,i_0_434,i_0_56,i_0_58,i_0_57,i_0_32,i_0_31,i_0_28,i_0_38,i_0_53,i_0_26,i_0_33,i_0_30,i_0_25]) ).

cnf(i_0_461,plain,
    ~ sum(add(additive_identity,multiply(a,bS_Ic)),additive_inverse(aPb),additive_inverse(aPc)),
    inference(scs_inference,[],[i_0_389,i_0_83,i_0_56]) ).

cnf(i_0_462,plain,
    add(additive_identity,X1) = X1,
    inference(rename_variables,[],[i_0_83]) ).

cnf(i_0_463,plain,
    ~ sum(multiply(a,bS_Ic),additive_inverse(aPb),add(additive_identity,additive_inverse(aPc))),
    inference(scs_inference,[],[i_0_389,i_0_83,i_0_462,i_0_56,i_0_58]) ).

cnf(i_0_464,plain,
    add(additive_identity,X1) = X1,
    inference(rename_variables,[],[i_0_83]) ).

cnf(i_0_465,plain,
    ~ sum(multiply(a,bS_Ic),add(additive_identity,additive_inverse(aPb)),additive_inverse(aPc)),
    inference(scs_inference,[],[i_0_389,i_0_83,i_0_462,i_0_464,i_0_56,i_0_58,i_0_57]) ).

cnf(i_0_466,plain,
    add(additive_identity,X1) = X1,
    inference(rename_variables,[],[i_0_83]) ).

cnf(i_0_467,plain,
    ~ sum(additive_identity,multiply(a,bS_Ic),additive_inverse(additive_inverse(aPb_S_IaPc))),
    inference(scs_inference,[],[i_0_59,i_0_43,i_0_389,i_0_405,i_0_83,i_0_462,i_0_464,i_0_56,i_0_58,i_0_57,i_0_32]) ).

cnf(i_0_468,plain,
    sum(X1,additive_inverse(X1),additive_identity),
    inference(rename_variables,[],[i_0_43]) ).

cnf(i_0_469,plain,
    sum(X1,X2,add(X2,X1)),
    inference(rename_variables,[],[i_0_59]) ).

cnf(i_0_470,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ sum(X1,X6,X4)
    | ~ sum(X6,X5,X2) ),
    inference(rename_variables,[],[i_0_32]) ).

cnf(i_0_471,plain,
    ~ sum(additive_inverse(add(additive_identity,aPb_S_IaPc)),multiply(a,bS_Ic),additive_inverse(additive_identity)),
    inference(scs_inference,[],[i_0_59,i_0_43,i_0_468,i_0_40,i_0_201,i_0_389,i_0_405,i_0_83,i_0_462,i_0_464,i_0_56,i_0_58,i_0_57,i_0_32,i_0_31]) ).

cnf(i_0_472,plain,
    sum(X1,X2,add(X1,X2)),
    inference(rename_variables,[],[i_0_40]) ).

cnf(i_0_473,plain,
    sum(X1,additive_inverse(X1),additive_identity),
    inference(rename_variables,[],[i_0_43]) ).

cnf(i_0_474,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ sum(X4,X6,X1)
    | ~ sum(X6,X2,X5) ),
    inference(rename_variables,[],[i_0_31]) ).

cnf(i_0_475,plain,
    ( ~ product(a,bS_Ic,additive_identity)
    | ~ product(additive_identity,bS_Ic,add(additive_identity,aPb_S_IaPc)) ),
    inference(scs_inference,[],[i_0_59,i_0_43,i_0_468,i_0_40,i_0_47,i_0_39,i_0_201,i_0_389,i_0_405,i_0_230,i_0_83,i_0_462,i_0_464,i_0_56,i_0_58,i_0_57,i_0_32,i_0_31,i_0_27]) ).

cnf(i_0_476,plain,
    product(X1,X2,multiply(X1,X2)),
    inference(rename_variables,[],[i_0_39]) ).

cnf(i_0_477,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_47]) ).

cnf(i_0_478,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_27]) ).

cnf(i_0_479,plain,
    ( ~ product(a,bS_Ic,additive_inverse(additive_identity))
    | ~ product(additive_identity,bS_Ic,add(additive_identity,aPb_S_IaPc)) ),
    inference(scs_inference,[],[i_0_139,i_0_59,i_0_43,i_0_468,i_0_40,i_0_47,i_0_39,i_0_201,i_0_389,i_0_405,i_0_230,i_0_83,i_0_462,i_0_464,i_0_56,i_0_58,i_0_57,i_0_32,i_0_31,i_0_27,i_0_55]) ).

cnf(i_0_480,plain,
    ( ~ product(a,add(additive_identity,bS_Ic),additive_identity)
    | ~ product(additive_identity,bS_Ic,add(additive_identity,aPb_S_IaPc)) ),
    inference(scs_inference,[],[i_0_139,i_0_59,i_0_43,i_0_468,i_0_40,i_0_47,i_0_39,i_0_201,i_0_389,i_0_405,i_0_230,i_0_83,i_0_462,i_0_464,i_0_466,i_0_56,i_0_58,i_0_57,i_0_32,i_0_31,i_0_27,i_0_55,i_0_54]) ).

cnf(i_0_481,plain,
    add(additive_identity,X1) = X1,
    inference(rename_variables,[],[i_0_83]) ).

cnf(i_0_482,plain,
    ( ~ product(add(additive_identity,a),bS_Ic,additive_identity)
    | ~ product(additive_identity,bS_Ic,add(additive_identity,aPb_S_IaPc)) ),
    inference(scs_inference,[],[i_0_139,i_0_59,i_0_43,i_0_468,i_0_40,i_0_47,i_0_39,i_0_201,i_0_389,i_0_405,i_0_230,i_0_83,i_0_462,i_0_464,i_0_466,i_0_481,i_0_56,i_0_58,i_0_57,i_0_32,i_0_31,i_0_27,i_0_55,i_0_54,i_0_53]) ).

cnf(i_0_483,plain,
    add(additive_identity,X1) = X1,
    inference(rename_variables,[],[i_0_83]) ).

cnf(i_0_484,plain,
    ( ~ product(X1,X2,X3)
    | product(X4,X5,X3)
    | ~ product(X1,X6,X4)
    | ~ product(X6,X5,X2) ),
    inference(rename_variables,[],[i_0_30]) ).

cnf(i_0_485,plain,
    product(X1,X2,multiply(X1,X2)),
    inference(rename_variables,[],[i_0_39]) ).

cnf(i_0_486,plain,
    ( product(aPb,aPb_S_IaPc,aPb_S_IaPc)
    | ~ product(additive_identity,bS_Ic,add(additive_identity,aPb_S_IaPc))
    | ~ product(b,aPb,b)
    | ~ product(aPb,additive_inverse(aPc),additive_inverse(aPc)) ),
    inference(scs_inference,[],[i_0_49,i_0_44,i_0_139,i_0_59,i_0_43,i_0_468,i_0_40,i_0_47,i_0_39,i_0_476,i_0_201,i_0_389,i_0_405,i_0_230,i_0_334,i_0_83,i_0_462,i_0_464,i_0_466,i_0_481,i_0_56,i_0_58,i_0_57,i_0_32,i_0_31,i_0_27,i_0_55,i_0_54,i_0_53,i_0_30,i_0_25]) ).

cnf(i_0_487,plain,
    ~ sum(add(additive_identity,additive_inverse(aPb)),multiply(a,bS_Ic),additive_inverse(aPc)),
    inference(scs_inference,[],[i_0_437,i_0_83,i_0_56]) ).

cnf(i_0_488,plain,
    add(additive_identity,X1) = X1,
    inference(rename_variables,[],[i_0_83]) ).

cnf(i_0_489,plain,
    ~ sum(additive_inverse(add(additive_identity,aPb_S_IaPc)),multiply(a,bS_Ic),additive_identity),
    inference(scs_inference,[],[i_0_165,i_0_471,i_0_437,i_0_83,i_0_56,i_0_58]) ).

cnf(i_0_490,plain,
    ~ sum(aPb_S_IaPc,add(X1,additive_inverse(X1)),multiply(a,bS_Ic)),
    inference(scs_inference,[],[i_0_297,i_0_165,i_0_471,i_0_437,i_0_104,i_0_83,i_0_56,i_0_58,i_0_57]) ).

cnf(i_0_491,plain,
    ~ sum(additive_identity,multiply(a,bS_Ic),aPb_S_IaPc),
    inference(scs_inference,[],[i_0_297,i_0_165,i_0_42,i_0_47,i_0_471,i_0_437,i_0_104,i_0_358,i_0_83,i_0_56,i_0_58,i_0_57,i_0_32]) ).

cnf(i_0_492,plain,
    sum(additive_inverse(X1),X1,additive_identity),
    inference(rename_variables,[],[i_0_42]) ).

cnf(i_0_493,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_47]) ).

cnf(i_0_494,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ sum(X1,X6,X4)
    | ~ sum(X6,X5,X2) ),
    inference(rename_variables,[],[i_0_32]) ).

cnf(i_0_495,plain,
    ~ sum(additive_inverse(additive_identity),multiply(a,bS_Ic),aPb_S_IaPc),
    inference(scs_inference,[],[i_0_297,i_0_165,i_0_42,i_0_43,i_0_40,i_0_47,i_0_301,i_0_471,i_0_437,i_0_104,i_0_358,i_0_83,i_0_56,i_0_58,i_0_57,i_0_32,i_0_31]) ).

cnf(i_0_496,plain,
    sum(X1,X2,add(X1,X2)),
    inference(rename_variables,[],[i_0_40]) ).

cnf(i_0_497,plain,
    sum(X1,additive_inverse(X1),additive_identity),
    inference(rename_variables,[],[i_0_43]) ).

cnf(i_0_498,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ sum(X4,X6,X1)
    | ~ sum(X6,X2,X5) ),
    inference(rename_variables,[],[i_0_31]) ).

cnf(i_0_499,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_297,i_0_165,i_0_42,i_0_43,i_0_40,i_0_47,i_0_77,i_0_301,i_0_471,i_0_437,i_0_104,i_0_358,i_0_83,i_0_56,i_0_58,i_0_57,i_0_32,i_0_31,i_0_26]) ).

cnf(i_0_500,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_26]) ).

cnf(i_0_501,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_47]) ).

cnf(i_0_502,plain,
    product(X1,X2,multiply(X1,X2)),
    inference(rename_variables,[],[i_0_39]) ).

cnf(i_0_503,plain,
    ( product(aPb,aPb_S_IaPc,aPb_S_IaPc)
    | ~ product(b,aPb,b)
    | ~ product(multiply(X1,additive_identity),X2,multiply(X1,additive_identity))
    | ~ product(aPb,additive_inverse(aPc),additive_inverse(aPc)) ),
    inference(scs_inference,[],[i_0_49,i_0_44,i_0_297,i_0_165,i_0_42,i_0_43,i_0_40,i_0_47,i_0_493,i_0_39,i_0_77,i_0_301,i_0_471,i_0_437,i_0_104,i_0_358,i_0_334,i_0_83,i_0_56,i_0_58,i_0_57,i_0_32,i_0_31,i_0_26,i_0_30,i_0_25]) ).

cnf(i_0_504,plain,
    ~ sum(add(additive_identity,aPb_S_IaPc),add(X1,additive_inverse(X1)),multiply(a,bS_Ic)),
    inference(scs_inference,[],[i_0_490,i_0_83,i_0_56]) ).

cnf(i_0_505,plain,
    add(additive_identity,X1) = X1,
    inference(rename_variables,[],[i_0_83]) ).

cnf(i_0_506,plain,
    ~ sum(multiply(a,bS_Ic),additive_inverse(additive_inverse(additive_identity)),add(additive_identity,aPb_S_IaPc)),
    inference(scs_inference,[],[i_0_490,i_0_439,i_0_83,i_0_505,i_0_56,i_0_58]) ).

cnf(i_0_507,plain,
    add(additive_identity,X1) = X1,
    inference(rename_variables,[],[i_0_83]) ).

cnf(i_0_508,plain,
    ~ sum(additive_inverse(additive_identity),add(additive_identity,multiply(a,bS_Ic)),aPb_S_IaPc),
    inference(scs_inference,[],[i_0_490,i_0_439,i_0_495,i_0_83,i_0_505,i_0_507,i_0_56,i_0_58,i_0_57]) ).

cnf(i_0_509,plain,
    add(additive_identity,X1) = X1,
    inference(rename_variables,[],[i_0_83]) ).

cnf(i_0_510,plain,
    ~ sum(additive_inverse(multiply(a,bS_Ic)),add(additive_identity,aPb_S_IaPc),additive_identity),
    inference(scs_inference,[],[i_0_59,i_0_43,i_0_357,i_0_490,i_0_439,i_0_495,i_0_83,i_0_505,i_0_507,i_0_56,i_0_58,i_0_57,i_0_32]) ).

cnf(i_0_511,plain,
    sum(X1,X2,add(X2,X1)),
    inference(rename_variables,[],[i_0_59]) ).

cnf(i_0_512,plain,
    sum(X1,additive_inverse(X1),additive_identity),
    inference(rename_variables,[],[i_0_43]) ).

cnf(i_0_513,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ sum(X1,X6,X4)
    | ~ sum(X6,X5,X2) ),
    inference(rename_variables,[],[i_0_32]) ).

cnf(i_0_514,plain,
    ~ sum(additive_inverse(additive_identity),multiply(a,bS_Ic),add(additive_identity,aPb_S_IaPc)),
    inference(scs_inference,[],[i_0_59,i_0_43,i_0_512,i_0_40,i_0_357,i_0_490,i_0_439,i_0_495,i_0_83,i_0_505,i_0_507,i_0_56,i_0_58,i_0_57,i_0_32,i_0_31]) ).

cnf(i_0_515,plain,
    sum(X1,X2,add(X1,X2)),
    inference(rename_variables,[],[i_0_40]) ).

cnf(i_0_516,plain,
    sum(X1,additive_inverse(X1),additive_identity),
    inference(rename_variables,[],[i_0_43]) ).

cnf(i_0_517,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ sum(X4,X6,X1)
    | ~ sum(X6,X2,X5) ),
    inference(rename_variables,[],[i_0_31]) ).

cnf(i_0_518,plain,
    ( product(additive_identity,X1,additive_identity)
    | ~ product(additive_inverse(additive_identity),X1,additive_inverse(additive_identity)) ),
    inference(scs_inference,[],[i_0_59,i_0_43,i_0_512,i_0_40,i_0_357,i_0_207,i_0_490,i_0_439,i_0_495,i_0_83,i_0_505,i_0_507,i_0_56,i_0_58,i_0_57,i_0_32,i_0_31,i_0_26]) ).

cnf(i_0_519,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_26]) ).

cnf(i_0_520,plain,
    ( multiply(multiply(additive_identity,additive_identity),additive_identity) = additive_identity
    | ~ product(additive_inverse(additive_identity),multiply(additive_identity,additive_identity),additive_inverse(additive_identity)) ),
    inference(scs_inference,[],[i_0_86,i_0_59,i_0_43,i_0_512,i_0_40,i_0_357,i_0_207,i_0_490,i_0_439,i_0_495,i_0_83,i_0_505,i_0_507,i_0_56,i_0_58,i_0_57,i_0_32,i_0_31,i_0_26,i_0_33]) ).

cnf(i_0_521,plain,
    product(X1,multiply(X1,X1),multiply(multiply(X1,X1),X1)),
    inference(rename_variables,[],[i_0_86]) ).

cnf(i_0_522,plain,
    ( ~ product(X1,X2,X3)
    | X4 = X3
    | ~ product(X1,X2,X4) ),
    inference(rename_variables,[],[i_0_33]) ).

cnf(i_0_523,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_47]) ).

cnf(i_0_524,plain,
    product(X1,X2,multiply(X1,X2)),
    inference(rename_variables,[],[i_0_39]) ).

cnf(i_0_525,plain,
    ( product(aPb,aPb_S_IaPc,aPb_S_IaPc)
    | ~ product(b,aPb,b)
    | ~ product(additive_inverse(additive_identity),multiply(additive_identity,additive_identity),additive_inverse(additive_identity))
    | ~ product(aPb,additive_inverse(aPc),additive_inverse(aPc)) ),
    inference(scs_inference,[],[i_0_86,i_0_49,i_0_44,i_0_59,i_0_43,i_0_512,i_0_40,i_0_39,i_0_47,i_0_357,i_0_207,i_0_490,i_0_439,i_0_495,i_0_334,i_0_83,i_0_505,i_0_507,i_0_56,i_0_58,i_0_57,i_0_32,i_0_31,i_0_26,i_0_33,i_0_30,i_0_25]) ).

cnf(i_0_526,plain,
    ~ sum(additive_identity,multiply(a,bS_Ic),add(additive_identity,aPb_S_IaPc)),
    inference(scs_inference,[],[i_0_165,i_0_514,i_0_56]) ).

cnf(i_0_527,plain,
    ~ sum(additive_inverse(additive_identity),add(additive_identity,multiply(a,bS_Ic)),add(additive_identity,aPb_S_IaPc)),
    inference(scs_inference,[],[i_0_165,i_0_514,i_0_508,i_0_83,i_0_56,i_0_58]) ).

cnf(i_0_528,plain,
    add(additive_identity,X1) = X1,
    inference(rename_variables,[],[i_0_83]) ).

cnf(i_0_529,plain,
    ~ sum(additive_inverse(multiply(a,bS_Ic)),aPb_S_IaPc,additive_identity),
    inference(scs_inference,[],[i_0_61,i_0_165,i_0_514,i_0_510,i_0_508,i_0_83,i_0_56,i_0_58,i_0_57]) ).

cnf(i_0_530,plain,
    X1 = add(additive_identity,X1),
    inference(rename_variables,[],[i_0_61]) ).

cnf(i_0_531,plain,
    ~ sum(multiply(a,bS_Ic),additive_inverse(aPb_S_IaPc),additive_inverse(additive_identity)),
    inference(scs_inference,[],[i_0_61,i_0_165,i_0_59,i_0_42,i_0_355,i_0_514,i_0_510,i_0_508,i_0_83,i_0_56,i_0_58,i_0_57,i_0_32]) ).

cnf(i_0_532,plain,
    sum(X1,X2,add(X2,X1)),
    inference(rename_variables,[],[i_0_59]) ).

cnf(i_0_533,plain,
    sum(additive_inverse(X1),X1,additive_identity),
    inference(rename_variables,[],[i_0_42]) ).

cnf(i_0_534,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ sum(X1,X6,X4)
    | ~ sum(X6,X5,X2) ),
    inference(rename_variables,[],[i_0_32]) ).

cnf(i_0_535,plain,
    sum(additive_inverse(additive_identity),bS_Ic,bS_Ic),
    inference(scs_inference,[],[i_0_61,i_0_165,i_0_59,i_0_42,i_0_533,i_0_443,i_0_355,i_0_514,i_0_510,i_0_508,i_0_83,i_0_56,i_0_58,i_0_57,i_0_32,i_0_31]) ).

cnf(i_0_536,plain,
    sum(additive_inverse(X1),X1,additive_identity),
    inference(rename_variables,[],[i_0_42]) ).

cnf(i_0_537,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ sum(X4,X6,X1)
    | ~ sum(X6,X2,X5) ),
    inference(rename_variables,[],[i_0_31]) ).

cnf(i_0_538,plain,
    sum(bS_Ic,additive_inverse(additive_identity),bS_Ic),
    inference(scs_inference,[],[i_0_61,i_0_165,i_0_59,i_0_42,i_0_533,i_0_443,i_0_355,i_0_514,i_0_510,i_0_508,i_0_83,i_0_56,i_0_58,i_0_57,i_0_32,i_0_31,i_0_38]) ).

cnf(i_0_539,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X2,X1,X3) ),
    inference(rename_variables,[],[i_0_38]) ).

cnf(i_0_540,plain,
    ( ~ product(a,b,add(additive_identity,aPb_S_IaPc))
    | ~ product(a,additive_inverse(c),add(X1,additive_inverse(X1))) ),
    inference(scs_inference,[],[i_0_61,i_0_165,i_0_59,i_0_42,i_0_533,i_0_45,i_0_39,i_0_443,i_0_355,i_0_504,i_0_514,i_0_510,i_0_508,i_0_83,i_0_56,i_0_58,i_0_57,i_0_32,i_0_31,i_0_38,i_0_28]) ).

cnf(i_0_541,plain,
    product(X1,X2,multiply(X1,X2)),
    inference(rename_variables,[],[i_0_39]) ).

cnf(i_0_542,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_28]) ).

cnf(i_0_543,plain,
    ( ~ product(a,b,aPb_S_IaPc)
    | ~ product(a,additive_inverse(c),add(X1,additive_inverse(X1))) ),
    inference(scs_inference,[],[i_0_61,i_0_530,i_0_165,i_0_59,i_0_42,i_0_533,i_0_45,i_0_39,i_0_443,i_0_355,i_0_504,i_0_514,i_0_510,i_0_508,i_0_83,i_0_56,i_0_58,i_0_57,i_0_32,i_0_31,i_0_38,i_0_28,i_0_55]) ).

cnf(i_0_544,plain,
    X1 = add(additive_identity,X1),
    inference(rename_variables,[],[i_0_61]) ).

cnf(i_0_545,plain,
    ( ~ product(a,add(additive_identity,b),add(additive_identity,aPb_S_IaPc))
    | ~ product(a,additive_inverse(c),add(X1,additive_inverse(X1))) ),
    inference(scs_inference,[],[i_0_61,i_0_530,i_0_165,i_0_59,i_0_42,i_0_533,i_0_45,i_0_39,i_0_443,i_0_355,i_0_504,i_0_514,i_0_510,i_0_508,i_0_83,i_0_528,i_0_56,i_0_58,i_0_57,i_0_32,i_0_31,i_0_38,i_0_28,i_0_55,i_0_54]) ).

cnf(i_0_546,plain,
    add(additive_identity,X1) = X1,
    inference(rename_variables,[],[i_0_83]) ).

cnf(i_0_547,plain,
    ( ~ product(add(additive_identity,a),b,add(additive_identity,aPb_S_IaPc))
    | ~ product(a,additive_inverse(c),add(X1,additive_inverse(X1))) ),
    inference(scs_inference,[],[i_0_61,i_0_530,i_0_165,i_0_59,i_0_42,i_0_533,i_0_45,i_0_39,i_0_443,i_0_355,i_0_504,i_0_514,i_0_510,i_0_508,i_0_83,i_0_528,i_0_546,i_0_56,i_0_58,i_0_57,i_0_32,i_0_31,i_0_38,i_0_28,i_0_55,i_0_54,i_0_53]) ).

cnf(i_0_548,plain,
    add(additive_identity,X1) = X1,
    inference(rename_variables,[],[i_0_83]) ).

cnf(i_0_549,plain,
    ( ~ product(X1,X2,X3)
    | product(X4,X5,X3)
    | ~ product(X1,X6,X4)
    | ~ product(X6,X5,X2) ),
    inference(rename_variables,[],[i_0_30]) ).

cnf(i_0_550,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_47]) ).

cnf(i_0_551,plain,
    ( product(aPb,aPb_S_IaPc,aPb_S_IaPc)
    | ~ product(a,additive_inverse(c),add(X1,additive_inverse(X1)))
    | ~ product(b,aPb,b)
    | ~ product(aPb,additive_inverse(aPc),additive_inverse(aPc)) ),
    inference(scs_inference,[],[i_0_49,i_0_61,i_0_530,i_0_44,i_0_165,i_0_59,i_0_42,i_0_533,i_0_45,i_0_47,i_0_39,i_0_443,i_0_355,i_0_504,i_0_514,i_0_510,i_0_508,i_0_334,i_0_83,i_0_528,i_0_546,i_0_56,i_0_58,i_0_57,i_0_32,i_0_31,i_0_38,i_0_28,i_0_55,i_0_54,i_0_53,i_0_30,i_0_25]) ).

cnf(i_0_552,plain,
    ~ sum(additive_identity,add(additive_identity,multiply(a,bS_Ic)),add(additive_identity,aPb_S_IaPc)),
    inference(scs_inference,[],[i_0_165,i_0_527,i_0_56]) ).

cnf(i_0_553,plain,
    ~ sum(multiply(a,bS_Ic),additive_inverse(aPb_S_IaPc),additive_identity),
    inference(scs_inference,[],[i_0_165,i_0_527,i_0_531,i_0_56,i_0_58]) ).

cnf(i_0_554,plain,
    ~ sum(multiply(a,bS_Ic),add(additive_identity,additive_inverse(aPb_S_IaPc)),additive_inverse(additive_identity)),
    inference(scs_inference,[],[i_0_165,i_0_527,i_0_531,i_0_83,i_0_56,i_0_58,i_0_57]) ).

cnf(i_0_555,plain,
    add(additive_identity,X1) = X1,
    inference(rename_variables,[],[i_0_83]) ).

cnf(i_0_556,plain,
    ~ sum(additive_identity,multiply(a,bS_Ic),add(additive_identity,add(additive_identity,aPb_S_IaPc))),
    inference(scs_inference,[],[i_0_165,i_0_47,i_0_306,i_0_527,i_0_489,i_0_531,i_0_83,i_0_56,i_0_58,i_0_57,i_0_32]) ).

cnf(i_0_557,plain,
    sum(additive_inverse(X1),add(additive_identity,X1),additive_identity),
    inference(rename_variables,[],[i_0_306]) ).

cnf(i_0_558,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_47]) ).

cnf(i_0_559,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ sum(X1,X6,X4)
    | ~ sum(X6,X5,X2) ),
    inference(rename_variables,[],[i_0_32]) ).

cnf(i_0_560,plain,
    ~ sum(aPc,multiply(a,bS_Ic),aPb),
    inference(scs_inference,[],[i_0_165,i_0_42,i_0_47,i_0_40,i_0_306,i_0_283,i_0_527,i_0_489,i_0_531,i_0_83,i_0_56,i_0_58,i_0_57,i_0_32,i_0_31]) ).

cnf(i_0_561,plain,
    sum(X1,X2,add(X1,X2)),
    inference(rename_variables,[],[i_0_40]) ).

cnf(i_0_562,plain,
    sum(additive_inverse(X1),X1,additive_identity),
    inference(rename_variables,[],[i_0_42]) ).

cnf(i_0_563,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ sum(X4,X6,X1)
    | ~ sum(X6,X2,X5) ),
    inference(rename_variables,[],[i_0_31]) ).

cnf(i_0_564,plain,
    ( ~ product(add(additive_identity,a),bS_Ic,aPb)
    | ~ product(add(additive_identity,a),additive_identity,additive_inverse(aPc)) ),
    inference(scs_inference,[],[i_0_125,i_0_44,i_0_165,i_0_59,i_0_42,i_0_47,i_0_40,i_0_306,i_0_283,i_0_527,i_0_489,i_0_531,i_0_83,i_0_56,i_0_58,i_0_57,i_0_32,i_0_31,i_0_25]) ).

cnf(i_0_565,plain,
    sum(X1,X2,add(X2,X1)),
    inference(rename_variables,[],[i_0_59]) ).

cnf(i_0_566,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_25]) ).

cnf(i_0_567,plain,
    ( ~ product(add(additive_identity,a),bS_Ic,add(additive_identity,aPb))
    | ~ product(add(additive_identity,a),additive_identity,additive_inverse(aPc)) ),
    inference(scs_inference,[],[i_0_125,i_0_44,i_0_165,i_0_59,i_0_42,i_0_47,i_0_40,i_0_306,i_0_283,i_0_527,i_0_489,i_0_531,i_0_83,i_0_555,i_0_56,i_0_58,i_0_57,i_0_32,i_0_31,i_0_25,i_0_55]) ).

cnf(i_0_568,plain,
    add(additive_identity,X1) = X1,
    inference(rename_variables,[],[i_0_83]) ).

cnf(i_0_569,plain,
    ( ~ product(add(additive_identity,a),add(additive_identity,bS_Ic),aPb)
    | ~ product(add(additive_identity,a),additive_identity,additive_inverse(aPc)) ),
    inference(scs_inference,[],[i_0_125,i_0_44,i_0_165,i_0_59,i_0_42,i_0_47,i_0_40,i_0_306,i_0_283,i_0_527,i_0_489,i_0_531,i_0_83,i_0_555,i_0_568,i_0_56,i_0_58,i_0_57,i_0_32,i_0_31,i_0_25,i_0_55,i_0_54]) ).

cnf(i_0_570,plain,
    add(additive_identity,X1) = X1,
    inference(rename_variables,[],[i_0_83]) ).

cnf(i_0_571,plain,
    ( ~ product(a,bS_Ic,aPb)
    | ~ product(add(additive_identity,a),additive_identity,additive_inverse(aPc)) ),
    inference(scs_inference,[],[i_0_125,i_0_61,i_0_44,i_0_165,i_0_59,i_0_42,i_0_47,i_0_40,i_0_306,i_0_283,i_0_527,i_0_489,i_0_531,i_0_83,i_0_555,i_0_568,i_0_56,i_0_58,i_0_57,i_0_32,i_0_31,i_0_25,i_0_55,i_0_54,i_0_53]) ).

cnf(i_0_572,plain,
    X1 = add(additive_identity,X1),
    inference(rename_variables,[],[i_0_61]) ).

cnf(i_0_573,plain,
    ( ~ product(X1,X2,X3)
    | product(X4,X5,X3)
    | ~ product(X1,X6,X4)
    | ~ product(X6,X5,X2) ),
    inference(rename_variables,[],[i_0_30]) ).

cnf(i_0_574,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_47]) ).

cnf(i_0_576,plain,
    ~ sum(add(X1,additive_inverse(X1)),multiply(a,bS_Ic),add(additive_identity,aPb_S_IaPc)),
    inference(scs_inference,[],[i_0_297,i_0_526,i_0_56]) ).

cnf(i_0_577,plain,
    ~ sum(multiply(a,bS_Ic),add(additive_identity,additive_inverse(aPb_S_IaPc)),additive_identity),
    inference(scs_inference,[],[i_0_297,i_0_165,i_0_526,i_0_554,i_0_56,i_0_58]) ).

cnf(i_0_578,plain,
    ~ sum(aPc,add(additive_identity,multiply(a,bS_Ic)),aPb),
    inference(scs_inference,[],[i_0_297,i_0_165,i_0_526,i_0_554,i_0_560,i_0_83,i_0_56,i_0_58,i_0_57]) ).

cnf(i_0_579,plain,
    add(additive_identity,X1) = X1,
    inference(rename_variables,[],[i_0_83]) ).

cnf(i_0_580,plain,
    ~ sum(multiply(a,bS_Ic),aPc,aPb),
    inference(scs_inference,[],[i_0_297,i_0_165,i_0_59,i_0_43,i_0_331,i_0_526,i_0_554,i_0_560,i_0_83,i_0_56,i_0_58,i_0_57,i_0_32]) ).

cnf(i_0_581,plain,
    sum(X1,X2,add(X2,X1)),
    inference(rename_variables,[],[i_0_59]) ).

cnf(i_0_582,plain,
    sum(X1,additive_inverse(X1),additive_identity),
    inference(rename_variables,[],[i_0_43]) ).

cnf(i_0_583,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ sum(X1,X6,X4)
    | ~ sum(X6,X5,X2) ),
    inference(rename_variables,[],[i_0_32]) ).

cnf(i_0_584,plain,
    ~ sum(add(additive_identity,multiply(a,bS_Ic)),aPc,aPb),
    inference(scs_inference,[],[i_0_44,i_0_297,i_0_165,i_0_59,i_0_43,i_0_582,i_0_331,i_0_435,i_0_526,i_0_554,i_0_560,i_0_83,i_0_56,i_0_58,i_0_57,i_0_32,i_0_31]) ).

cnf(i_0_585,plain,
    sum(X1,additive_inverse(X1),additive_identity),
    inference(rename_variables,[],[i_0_43]) ).

cnf(i_0_586,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ sum(X4,X6,X1)
    | ~ sum(X6,X2,X5) ),
    inference(rename_variables,[],[i_0_31]) ).

cnf(i_0_587,plain,
    ~ sum(c,bS_Ic,b),
    inference(scs_inference,[],[i_0_49,i_0_48,i_0_44,i_0_297,i_0_165,i_0_59,i_0_43,i_0_582,i_0_39,i_0_331,i_0_435,i_0_526,i_0_554,i_0_560,i_0_83,i_0_56,i_0_58,i_0_57,i_0_32,i_0_31,i_0_28]) ).

cnf(i_0_588,plain,
    product(X1,X2,multiply(X1,X2)),
    inference(rename_variables,[],[i_0_39]) ).

cnf(i_0_589,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_28]) ).

cnf(i_0_590,plain,
    ( ~ product(additive_identity,b,aPc)
    | ~ product(a,b,multiply(a,bS_Ic)) ),
    inference(scs_inference,[],[i_0_49,i_0_48,i_0_44,i_0_297,i_0_165,i_0_59,i_0_43,i_0_582,i_0_46,i_0_39,i_0_331,i_0_435,i_0_526,i_0_554,i_0_560,i_0_83,i_0_56,i_0_58,i_0_57,i_0_32,i_0_31,i_0_28,i_0_27]) ).

cnf(i_0_591,plain,
    sum(additive_identity,X1,X1),
    inference(rename_variables,[],[i_0_46]) ).

cnf(i_0_592,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_27]) ).

cnf(i_0_593,plain,
    ( ~ product(additive_identity,b,add(additive_identity,aPc))
    | ~ product(a,b,multiply(a,bS_Ic)) ),
    inference(scs_inference,[],[i_0_49,i_0_48,i_0_44,i_0_297,i_0_165,i_0_59,i_0_43,i_0_582,i_0_46,i_0_39,i_0_331,i_0_435,i_0_526,i_0_554,i_0_560,i_0_83,i_0_579,i_0_56,i_0_58,i_0_57,i_0_32,i_0_31,i_0_28,i_0_27,i_0_55]) ).

cnf(i_0_594,plain,
    add(additive_identity,X1) = X1,
    inference(rename_variables,[],[i_0_83]) ).

cnf(i_0_595,plain,
    ( ~ product(additive_identity,add(additive_identity,b),aPc)
    | ~ product(a,b,multiply(a,bS_Ic)) ),
    inference(scs_inference,[],[i_0_49,i_0_48,i_0_44,i_0_297,i_0_165,i_0_59,i_0_43,i_0_582,i_0_46,i_0_39,i_0_331,i_0_435,i_0_526,i_0_554,i_0_560,i_0_83,i_0_579,i_0_594,i_0_56,i_0_58,i_0_57,i_0_32,i_0_31,i_0_28,i_0_27,i_0_55,i_0_54]) ).

cnf(i_0_596,plain,
    add(additive_identity,X1) = X1,
    inference(rename_variables,[],[i_0_83]) ).

cnf(i_0_597,plain,
    ( ~ product(add(X1,additive_inverse(X1)),b,aPc)
    | ~ product(a,b,multiply(a,bS_Ic)) ),
    inference(scs_inference,[],[i_0_49,i_0_48,i_0_44,i_0_297,i_0_165,i_0_59,i_0_43,i_0_582,i_0_46,i_0_39,i_0_331,i_0_435,i_0_526,i_0_554,i_0_560,i_0_83,i_0_579,i_0_594,i_0_56,i_0_58,i_0_57,i_0_32,i_0_31,i_0_28,i_0_27,i_0_55,i_0_54,i_0_53]) ).

cnf(i_0_598,plain,
    ( ~ product(X1,X2,X3)
    | product(X4,X5,X3)
    | ~ product(X1,X6,X4)
    | ~ product(X6,X5,X2) ),
    inference(rename_variables,[],[i_0_30]) ).

cnf(i_0_599,plain,
    ( product(aPb,aPb_S_IaPc,aPb_S_IaPc)
    | ~ product(a,b,multiply(a,bS_Ic))
    | ~ product(b,aPb,b)
    | ~ product(aPb,additive_inverse(aPc),additive_inverse(aPc)) ),
    inference(scs_inference,[],[i_0_49,i_0_48,i_0_44,i_0_297,i_0_165,i_0_59,i_0_43,i_0_582,i_0_46,i_0_39,i_0_331,i_0_435,i_0_526,i_0_554,i_0_560,i_0_83,i_0_579,i_0_594,i_0_56,i_0_58,i_0_57,i_0_32,i_0_31,i_0_28,i_0_27,i_0_55,i_0_54,i_0_53,i_0_30,i_0_25]) ).

cnf(i_0_600,plain,
    ~ sum(add(X1,additive_inverse(X1)),multiply(a,bS_Ic),aPb_S_IaPc),
    inference(scs_inference,[],[i_0_297,i_0_491,i_0_56]) ).

cnf(i_0_601,plain,
    ~ sum(multiply(a,bS_Ic),additive_inverse(aPb_S_IaPc),add(X1,additive_inverse(X1))),
    inference(scs_inference,[],[i_0_297,i_0_491,i_0_553,i_0_56,i_0_58]) ).

cnf(i_0_602,plain,
    ~ sum(add(additive_identity,multiply(a,bS_Ic)),add(additive_identity,aPc),aPb),
    inference(scs_inference,[],[i_0_297,i_0_491,i_0_553,i_0_584,i_0_83,i_0_56,i_0_58,i_0_57]) ).

cnf(i_0_603,plain,
    add(additive_identity,X1) = X1,
    inference(rename_variables,[],[i_0_83]) ).

cnf(i_0_604,plain,
    ~ sum(additive_inverse(additive_inverse(aPb_S_IaPc)),additive_identity,multiply(a,bS_Ic)),
    inference(scs_inference,[],[i_0_297,i_0_46,i_0_306,i_0_491,i_0_577,i_0_553,i_0_584,i_0_83,i_0_56,i_0_58,i_0_57,i_0_32]) ).

cnf(i_0_605,plain,
    sum(additive_inverse(X1),add(additive_identity,X1),additive_identity),
    inference(rename_variables,[],[i_0_306]) ).

cnf(i_0_606,plain,
    sum(additive_identity,X1,X1),
    inference(rename_variables,[],[i_0_46]) ).

cnf(i_0_607,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ sum(X1,X6,X4)
    | ~ sum(X6,X5,X2) ),
    inference(rename_variables,[],[i_0_32]) ).

cnf(i_0_608,plain,
    sum(additive_identity,add(add(b,additive_identity),additive_inverse(c)),bS_Ic),
    inference(scs_inference,[],[i_0_297,i_0_59,i_0_46,i_0_40,i_0_349,i_0_306,i_0_491,i_0_577,i_0_553,i_0_584,i_0_83,i_0_56,i_0_58,i_0_57,i_0_32,i_0_31]) ).

cnf(i_0_609,plain,
    sum(X1,X2,add(X2,X1)),
    inference(rename_variables,[],[i_0_59]) ).

cnf(i_0_610,plain,
    sum(X1,X2,add(X1,X2)),
    inference(rename_variables,[],[i_0_40]) ).

cnf(i_0_611,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ sum(X4,X6,X1)
    | ~ sum(X6,X2,X5) ),
    inference(rename_variables,[],[i_0_31]) ).

cnf(i_0_612,plain,
    sum(add(add(b,additive_identity),additive_inverse(c)),additive_identity,bS_Ic),
    inference(scs_inference,[],[i_0_297,i_0_59,i_0_46,i_0_40,i_0_349,i_0_306,i_0_491,i_0_577,i_0_553,i_0_584,i_0_83,i_0_56,i_0_58,i_0_57,i_0_32,i_0_31,i_0_38]) ).

cnf(i_0_613,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X2,X1,X3) ),
    inference(rename_variables,[],[i_0_38]) ).

cnf(i_0_614,plain,
    ( ~ product(additive_identity,b,aPc)
    | ~ product(a,b,add(additive_identity,multiply(a,bS_Ic))) ),
    inference(scs_inference,[],[i_0_49,i_0_297,i_0_59,i_0_46,i_0_606,i_0_40,i_0_349,i_0_306,i_0_491,i_0_577,i_0_553,i_0_578,i_0_584,i_0_83,i_0_56,i_0_58,i_0_57,i_0_32,i_0_31,i_0_38,i_0_27]) ).

cnf(i_0_615,plain,
    sum(additive_identity,X1,X1),
    inference(rename_variables,[],[i_0_46]) ).

cnf(i_0_616,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_27]) ).

cnf(i_0_617,plain,
    ( ~ product(additive_identity,b,add(additive_identity,aPc))
    | ~ product(a,b,add(additive_identity,multiply(a,bS_Ic))) ),
    inference(scs_inference,[],[i_0_49,i_0_297,i_0_59,i_0_46,i_0_606,i_0_40,i_0_349,i_0_306,i_0_491,i_0_577,i_0_553,i_0_578,i_0_584,i_0_83,i_0_603,i_0_56,i_0_58,i_0_57,i_0_32,i_0_31,i_0_38,i_0_27,i_0_55]) ).

cnf(i_0_618,plain,
    add(additive_identity,X1) = X1,
    inference(rename_variables,[],[i_0_83]) ).

cnf(i_0_619,plain,
    ( ~ product(additive_identity,add(additive_identity,b),aPc)
    | ~ product(a,b,add(additive_identity,multiply(a,bS_Ic))) ),
    inference(scs_inference,[],[i_0_49,i_0_297,i_0_59,i_0_46,i_0_606,i_0_40,i_0_349,i_0_306,i_0_491,i_0_577,i_0_553,i_0_578,i_0_584,i_0_83,i_0_603,i_0_618,i_0_56,i_0_58,i_0_57,i_0_32,i_0_31,i_0_38,i_0_27,i_0_55,i_0_54]) ).

cnf(i_0_620,plain,
    add(additive_identity,X1) = X1,
    inference(rename_variables,[],[i_0_83]) ).

cnf(i_0_621,plain,
    ( ~ product(add(X1,additive_inverse(X1)),b,aPc)
    | ~ product(a,b,add(additive_identity,multiply(a,bS_Ic))) ),
    inference(scs_inference,[],[i_0_49,i_0_297,i_0_59,i_0_46,i_0_606,i_0_40,i_0_349,i_0_306,i_0_491,i_0_577,i_0_553,i_0_578,i_0_584,i_0_83,i_0_603,i_0_618,i_0_56,i_0_58,i_0_57,i_0_32,i_0_31,i_0_38,i_0_27,i_0_55,i_0_54,i_0_53]) ).

cnf(i_0_622,plain,
    ( ~ product(X1,X2,X3)
    | product(X4,X5,X3)
    | ~ product(X1,X6,X4)
    | ~ product(X6,X5,X2) ),
    inference(rename_variables,[],[i_0_30]) ).

cnf(i_0_623,plain,
    ( product(aPb,aPb_S_IaPc,aPb_S_IaPc)
    | ~ product(a,b,add(additive_identity,multiply(a,bS_Ic)))
    | ~ product(b,aPb,b)
    | ~ product(aPb,additive_inverse(aPc),additive_inverse(aPc)) ),
    inference(scs_inference,[],[i_0_49,i_0_48,i_0_44,i_0_297,i_0_59,i_0_46,i_0_606,i_0_40,i_0_349,i_0_306,i_0_491,i_0_577,i_0_553,i_0_578,i_0_584,i_0_83,i_0_603,i_0_618,i_0_56,i_0_58,i_0_57,i_0_32,i_0_31,i_0_38,i_0_27,i_0_55,i_0_54,i_0_53,i_0_30,i_0_25]) ).

cnf(i_0_624,plain,
    ~ sum(multiply(a,bS_Ic),add(additive_identity,aPc),aPb),
    inference(scs_inference,[],[i_0_61,i_0_602,i_0_56]) ).

cnf(i_0_625,plain,
    X1 = add(additive_identity,X1),
    inference(rename_variables,[],[i_0_61]) ).

cnf(i_0_626,plain,
    ~ sum(add(additive_identity,multiply(a,bS_Ic)),add(additive_identity,aPc),add(additive_identity,aPb)),
    inference(scs_inference,[],[i_0_61,i_0_602,i_0_83,i_0_56,i_0_58]) ).

cnf(i_0_627,plain,
    add(additive_identity,X1) = X1,
    inference(rename_variables,[],[i_0_83]) ).

cnf(i_0_628,plain,
    ~ sum(c,add(additive_identity,bS_Ic),b),
    inference(scs_inference,[],[i_0_61,i_0_602,i_0_587,i_0_83,i_0_627,i_0_56,i_0_58,i_0_57]) ).

cnf(i_0_629,plain,
    add(additive_identity,X1) = X1,
    inference(rename_variables,[],[i_0_83]) ).

cnf(i_0_630,plain,
    ~ sum(additive_inverse(additive_identity),additive_inverse(aPb_S_IaPc),additive_inverse(multiply(a,bS_Ic))),
    inference(scs_inference,[],[i_0_61,i_0_59,i_0_239,i_0_602,i_0_529,i_0_587,i_0_83,i_0_627,i_0_56,i_0_58,i_0_57,i_0_32]) ).

cnf(i_0_631,plain,
    sum(additive_inverse(additive_identity),add(X1,additive_inverse(X1)),additive_identity),
    inference(rename_variables,[],[i_0_239]) ).

cnf(i_0_632,plain,
    sum(X1,X2,add(X2,X1)),
    inference(rename_variables,[],[i_0_59]) ).

cnf(i_0_633,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ sum(X1,X6,X4)
    | ~ sum(X6,X5,X2) ),
    inference(rename_variables,[],[i_0_32]) ).

cnf(i_0_634,plain,
    sum(additive_identity,add(additive_inverse(c),b),bS_Ic),
    inference(scs_inference,[],[i_0_61,i_0_59,i_0_632,i_0_40,i_0_197,i_0_239,i_0_602,i_0_529,i_0_587,i_0_83,i_0_627,i_0_56,i_0_58,i_0_57,i_0_32,i_0_31]) ).

cnf(i_0_635,plain,
    sum(X1,X2,add(X2,X1)),
    inference(rename_variables,[],[i_0_59]) ).

cnf(i_0_636,plain,
    sum(X1,X2,add(X1,X2)),
    inference(rename_variables,[],[i_0_40]) ).

cnf(i_0_637,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ sum(X4,X6,X1)
    | ~ sum(X6,X2,X5) ),
    inference(rename_variables,[],[i_0_31]) ).

cnf(i_0_638,plain,
    sum(add(additive_inverse(c),b),additive_identity,bS_Ic),
    inference(scs_inference,[],[i_0_61,i_0_59,i_0_632,i_0_40,i_0_197,i_0_239,i_0_602,i_0_529,i_0_587,i_0_83,i_0_627,i_0_56,i_0_58,i_0_57,i_0_32,i_0_31,i_0_38]) ).

cnf(i_0_639,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X2,X1,X3) ),
    inference(rename_variables,[],[i_0_38]) ).

cnf(i_0_640,plain,
    ( ~ product(additive_identity,b,add(additive_identity,multiply(a,bS_Ic)))
    | ~ product(a,b,add(additive_identity,aPc)) ),
    inference(scs_inference,[],[i_0_49,i_0_61,i_0_59,i_0_632,i_0_46,i_0_40,i_0_197,i_0_239,i_0_602,i_0_529,i_0_587,i_0_83,i_0_627,i_0_56,i_0_58,i_0_57,i_0_32,i_0_31,i_0_38,i_0_27]) ).

cnf(i_0_641,plain,
    sum(additive_identity,X1,X1),
    inference(rename_variables,[],[i_0_46]) ).

cnf(i_0_642,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_27]) ).

cnf(i_0_643,plain,
    ( ~ product(additive_identity,b,multiply(a,bS_Ic))
    | ~ product(a,b,add(additive_identity,aPc)) ),
    inference(scs_inference,[],[i_0_49,i_0_61,i_0_625,i_0_59,i_0_632,i_0_46,i_0_40,i_0_197,i_0_239,i_0_602,i_0_529,i_0_587,i_0_83,i_0_627,i_0_56,i_0_58,i_0_57,i_0_32,i_0_31,i_0_38,i_0_27,i_0_55]) ).

cnf(i_0_644,plain,
    X1 = add(additive_identity,X1),
    inference(rename_variables,[],[i_0_61]) ).

cnf(i_0_645,plain,
    ( ~ product(additive_identity,add(additive_identity,b),add(additive_identity,multiply(a,bS_Ic)))
    | ~ product(a,b,add(additive_identity,aPc)) ),
    inference(scs_inference,[],[i_0_49,i_0_61,i_0_625,i_0_59,i_0_632,i_0_46,i_0_40,i_0_197,i_0_239,i_0_602,i_0_529,i_0_587,i_0_83,i_0_627,i_0_629,i_0_56,i_0_58,i_0_57,i_0_32,i_0_31,i_0_38,i_0_27,i_0_55,i_0_54]) ).

cnf(i_0_646,plain,
    add(additive_identity,X1) = X1,
    inference(rename_variables,[],[i_0_83]) ).

cnf(i_0_647,plain,
    ( ~ product(add(X1,additive_inverse(X1)),b,multiply(a,bS_Ic))
    | ~ product(a,b,add(additive_identity,aPc)) ),
    inference(scs_inference,[],[i_0_49,i_0_61,i_0_625,i_0_297,i_0_59,i_0_632,i_0_46,i_0_40,i_0_197,i_0_239,i_0_602,i_0_529,i_0_587,i_0_83,i_0_627,i_0_629,i_0_56,i_0_58,i_0_57,i_0_32,i_0_31,i_0_38,i_0_27,i_0_55,i_0_54,i_0_53]) ).

cnf(i_0_648,plain,
    ( ~ product(X1,X2,X3)
    | product(X4,X5,X3)
    | ~ product(X1,X6,X4)
    | ~ product(X6,X5,X2) ),
    inference(rename_variables,[],[i_0_30]) ).

cnf(i_0_649,plain,
    ( ~ product(a,additive_identity,add(additive_identity,multiply(a,bS_Ic)))
    | ~ product(a,b,add(additive_identity,aPc)) ),
    inference(scs_inference,[],[i_0_49,i_0_61,i_0_625,i_0_297,i_0_59,i_0_632,i_0_46,i_0_641,i_0_40,i_0_197,i_0_239,i_0_602,i_0_529,i_0_587,i_0_83,i_0_627,i_0_629,i_0_56,i_0_58,i_0_57,i_0_32,i_0_31,i_0_38,i_0_27,i_0_55,i_0_54,i_0_53,i_0_30,i_0_29,i_0_28]) ).

cnf(i_0_650,plain,
    sum(additive_identity,X1,X1),
    inference(rename_variables,[],[i_0_46]) ).

cnf(i_0_651,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_28]) ).

cnf(i_0_652,plain,
    ( product(aPb,aPb_S_IaPc,aPb_S_IaPc)
    | ~ product(a,b,add(additive_identity,aPc))
    | ~ product(b,aPb,b)
    | ~ product(aPb,additive_inverse(aPc),additive_inverse(aPc)) ),
    inference(scs_inference,[],[i_0_49,i_0_61,i_0_625,i_0_297,i_0_44,i_0_59,i_0_632,i_0_46,i_0_641,i_0_40,i_0_197,i_0_239,i_0_602,i_0_529,i_0_587,i_0_83,i_0_627,i_0_629,i_0_56,i_0_58,i_0_57,i_0_32,i_0_31,i_0_38,i_0_27,i_0_55,i_0_54,i_0_53,i_0_30,i_0_25]) ).

cnf(i_0_653,plain,
    ~ sum(multiply(a,bS_Ic),add(additive_identity,aPc),add(additive_identity,aPb)),
    inference(scs_inference,[],[i_0_61,i_0_626,i_0_56]) ).

cnf(i_0_654,plain,
    X1 = add(additive_identity,X1),
    inference(rename_variables,[],[i_0_61]) ).

cnf(i_0_655,plain,
    ~ sum(c,add(additive_identity,bS_Ic),add(additive_identity,b)),
    inference(scs_inference,[],[i_0_61,i_0_626,i_0_628,i_0_83,i_0_56,i_0_58]) ).

cnf(i_0_656,plain,
    add(additive_identity,X1) = X1,
    inference(rename_variables,[],[i_0_83]) ).

cnf(i_0_657,plain,
    ~ sum(add(additive_identity,multiply(a,bS_Ic)),aPc,add(additive_identity,aPb)),
    inference(scs_inference,[],[i_0_61,i_0_654,i_0_626,i_0_628,i_0_83,i_0_56,i_0_58,i_0_57]) ).

cnf(i_0_658,plain,
    X1 = add(additive_identity,X1),
    inference(rename_variables,[],[i_0_61]) ).

cnf(i_0_659,plain,
    sum(bS_Ic,add(additive_inverse(additive_identity),additive_inverse(additive_identity)),bS_Ic),
    inference(scs_inference,[],[i_0_61,i_0_654,i_0_59,i_0_538,i_0_626,i_0_628,i_0_83,i_0_56,i_0_58,i_0_57,i_0_31]) ).

cnf(i_0_660,plain,
    sum(X1,X2,add(X2,X1)),
    inference(rename_variables,[],[i_0_59]) ).

cnf(i_0_661,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ sum(X4,X6,X1)
    | ~ sum(X6,X2,X5) ),
    inference(rename_variables,[],[i_0_31]) ).

cnf(i_0_662,plain,
    sum(add(additive_inverse(additive_identity),additive_inverse(additive_identity)),bS_Ic,bS_Ic),
    inference(scs_inference,[],[i_0_61,i_0_654,i_0_59,i_0_538,i_0_626,i_0_628,i_0_83,i_0_56,i_0_58,i_0_57,i_0_31,i_0_38]) ).

cnf(i_0_663,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X2,X1,X3) ),
    inference(rename_variables,[],[i_0_38]) ).

cnf(i_0_664,plain,
    ( ~ sum(aPb,X1,add(additive_identity,multiply(a,bS_Ic)))
    | ~ sum(X1,additive_inverse(additive_identity),additive_inverse(aPc)) ),
    inference(scs_inference,[],[i_0_61,i_0_654,i_0_44,i_0_59,i_0_538,i_0_626,i_0_407,i_0_628,i_0_83,i_0_56,i_0_58,i_0_57,i_0_31,i_0_38,i_0_32]) ).

cnf(i_0_665,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ sum(X1,X6,X4)
    | ~ sum(X6,X5,X2) ),
    inference(rename_variables,[],[i_0_32]) ).

cnf(i_0_666,plain,
    ( ~ product(additive_identity,bS_Ic,additive_inverse(additive_inverse(aPb_S_IaPc)))
    | ~ product(a,bS_Ic,additive_identity) ),
    inference(scs_inference,[],[i_0_61,i_0_654,i_0_44,i_0_59,i_0_46,i_0_39,i_0_538,i_0_626,i_0_407,i_0_604,i_0_628,i_0_83,i_0_56,i_0_58,i_0_57,i_0_31,i_0_38,i_0_32,i_0_27]) ).

cnf(i_0_667,plain,
    product(X1,X2,multiply(X1,X2)),
    inference(rename_variables,[],[i_0_39]) ).

cnf(i_0_668,plain,
    sum(additive_identity,X1,X1),
    inference(rename_variables,[],[i_0_46]) ).

cnf(i_0_669,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_27]) ).

cnf(i_0_670,plain,
    ( ~ product(a,X1,add(additive_identity,aPc))
    | ~ sum(bS_Ic,X1,b) ),
    inference(scs_inference,[],[i_0_49,i_0_61,i_0_654,i_0_44,i_0_59,i_0_46,i_0_39,i_0_667,i_0_538,i_0_626,i_0_624,i_0_407,i_0_604,i_0_628,i_0_83,i_0_56,i_0_58,i_0_57,i_0_31,i_0_38,i_0_32,i_0_27,i_0_28]) ).

cnf(i_0_671,plain,
    product(X1,X2,multiply(X1,X2)),
    inference(rename_variables,[],[i_0_39]) ).

cnf(i_0_672,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_28]) ).

cnf(i_0_673,plain,
    ( product(a,additive_identity,aPb_S_IaPc)
    | ~ product(a,additive_inverse(b),additive_inverse(aPc)) ),
    inference(scs_inference,[],[i_0_49,i_0_61,i_0_654,i_0_44,i_0_43,i_0_59,i_0_46,i_0_39,i_0_667,i_0_538,i_0_626,i_0_624,i_0_407,i_0_604,i_0_628,i_0_83,i_0_56,i_0_58,i_0_57,i_0_31,i_0_38,i_0_32,i_0_27,i_0_28,i_0_26,i_0_25]) ).

cnf(i_0_674,plain,
    sum(X1,additive_inverse(X1),additive_identity),
    inference(rename_variables,[],[i_0_43]) ).

cnf(i_0_675,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_25]) ).

cnf(i_0_676,plain,
    ~ sum(multiply(a,bS_Ic),aPc,add(additive_identity,aPb)),
    inference(scs_inference,[],[i_0_61,i_0_657,i_0_56]) ).

cnf(i_0_677,plain,
    X1 = add(additive_identity,X1),
    inference(rename_variables,[],[i_0_61]) ).

cnf(i_0_678,plain,
    ~ sum(additive_inverse(aPb),multiply(a,bS_Ic),add(additive_identity,additive_inverse(aPc))),
    inference(scs_inference,[],[i_0_61,i_0_657,i_0_437,i_0_83,i_0_56,i_0_58]) ).

cnf(i_0_679,plain,
    add(additive_identity,X1) = X1,
    inference(rename_variables,[],[i_0_83]) ).

cnf(i_0_680,plain,
    ~ sum(c,bS_Ic,add(additive_identity,b)),
    inference(scs_inference,[],[i_0_61,i_0_677,i_0_657,i_0_655,i_0_437,i_0_83,i_0_56,i_0_58,i_0_57]) ).

cnf(i_0_681,plain,
    X1 = add(additive_identity,X1),
    inference(rename_variables,[],[i_0_61]) ).

cnf(i_0_682,plain,
    ~ sum(additive_inverse(aPb_S_IaPc),multiply(a,bS_Ic),additive_inverse(additive_inverse(additive_identity))),
    inference(scs_inference,[],[i_0_61,i_0_677,i_0_40,i_0_278,i_0_657,i_0_655,i_0_405,i_0_437,i_0_83,i_0_56,i_0_58,i_0_57,i_0_32]) ).

cnf(i_0_683,plain,
    sum(X1,X2,add(X1,X2)),
    inference(rename_variables,[],[i_0_40]) ).

cnf(i_0_684,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ sum(X1,X6,X4)
    | ~ sum(X6,X5,X2) ),
    inference(rename_variables,[],[i_0_32]) ).

cnf(i_0_685,plain,
    sum(additive_inverse(c),add(additive_identity,b),bS_Ic),
    inference(scs_inference,[],[i_0_61,i_0_677,i_0_59,i_0_40,i_0_683,i_0_278,i_0_417,i_0_657,i_0_655,i_0_405,i_0_437,i_0_83,i_0_56,i_0_58,i_0_57,i_0_32,i_0_31]) ).

cnf(i_0_686,plain,
    sum(X1,X2,add(X2,X1)),
    inference(rename_variables,[],[i_0_59]) ).

cnf(i_0_687,plain,
    sum(X1,X2,add(X1,X2)),
    inference(rename_variables,[],[i_0_40]) ).

cnf(i_0_688,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ sum(X4,X6,X1)
    | ~ sum(X6,X2,X5) ),
    inference(rename_variables,[],[i_0_31]) ).

cnf(i_0_689,plain,
    ~ sum(bS_Ic,c,b),
    inference(scs_inference,[],[i_0_49,i_0_48,i_0_61,i_0_677,i_0_59,i_0_40,i_0_683,i_0_39,i_0_278,i_0_417,i_0_657,i_0_655,i_0_580,i_0_405,i_0_437,i_0_83,i_0_56,i_0_58,i_0_57,i_0_32,i_0_31,i_0_28]) ).

cnf(i_0_690,plain,
    product(X1,X2,multiply(X1,X2)),
    inference(rename_variables,[],[i_0_39]) ).

cnf(i_0_691,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_28]) ).

cnf(i_0_692,plain,
    sum(add(additive_identity,b),additive_inverse(c),bS_Ic),
    inference(scs_inference,[],[i_0_49,i_0_48,i_0_61,i_0_677,i_0_59,i_0_40,i_0_683,i_0_39,i_0_278,i_0_417,i_0_657,i_0_655,i_0_580,i_0_405,i_0_437,i_0_83,i_0_56,i_0_58,i_0_57,i_0_32,i_0_31,i_0_28,i_0_38]) ).

cnf(i_0_693,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X2,X1,X3) ),
    inference(rename_variables,[],[i_0_38]) ).

cnf(i_0_694,plain,
    ( ~ product(additive_identity,b,multiply(a,bS_Ic))
    | ~ product(a,b,aPc) ),
    inference(scs_inference,[],[i_0_49,i_0_48,i_0_61,i_0_677,i_0_59,i_0_40,i_0_683,i_0_46,i_0_39,i_0_278,i_0_417,i_0_657,i_0_655,i_0_580,i_0_405,i_0_437,i_0_83,i_0_56,i_0_58,i_0_57,i_0_32,i_0_31,i_0_28,i_0_38,i_0_27]) ).

cnf(i_0_695,plain,
    sum(additive_identity,X1,X1),
    inference(rename_variables,[],[i_0_46]) ).

cnf(i_0_696,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_27]) ).

cnf(i_0_697,plain,
    ( ~ product(additive_identity,b,add(additive_identity,multiply(a,bS_Ic)))
    | ~ product(a,b,aPc) ),
    inference(scs_inference,[],[i_0_49,i_0_48,i_0_61,i_0_677,i_0_59,i_0_40,i_0_683,i_0_46,i_0_39,i_0_278,i_0_417,i_0_657,i_0_655,i_0_580,i_0_405,i_0_437,i_0_83,i_0_679,i_0_56,i_0_58,i_0_57,i_0_32,i_0_31,i_0_28,i_0_38,i_0_27,i_0_55]) ).

cnf(i_0_698,plain,
    add(additive_identity,X1) = X1,
    inference(rename_variables,[],[i_0_83]) ).

cnf(i_0_699,plain,
    ( ~ product(additive_identity,add(additive_identity,b),multiply(a,bS_Ic))
    | ~ product(a,b,aPc) ),
    inference(scs_inference,[],[i_0_49,i_0_48,i_0_61,i_0_677,i_0_59,i_0_40,i_0_683,i_0_46,i_0_39,i_0_278,i_0_417,i_0_657,i_0_655,i_0_580,i_0_405,i_0_437,i_0_83,i_0_679,i_0_698,i_0_56,i_0_58,i_0_57,i_0_32,i_0_31,i_0_28,i_0_38,i_0_27,i_0_55,i_0_54]) ).

cnf(i_0_700,plain,
    add(additive_identity,X1) = X1,
    inference(rename_variables,[],[i_0_83]) ).

cnf(i_0_701,plain,
    ( ~ product(add(X1,additive_inverse(X1)),b,multiply(a,bS_Ic))
    | ~ product(a,b,aPc) ),
    inference(scs_inference,[],[i_0_49,i_0_48,i_0_297,i_0_61,i_0_677,i_0_59,i_0_40,i_0_683,i_0_46,i_0_39,i_0_278,i_0_417,i_0_657,i_0_655,i_0_580,i_0_405,i_0_437,i_0_83,i_0_679,i_0_698,i_0_56,i_0_58,i_0_57,i_0_32,i_0_31,i_0_28,i_0_38,i_0_27,i_0_55,i_0_54,i_0_53]) ).

cnf(i_0_702,plain,
    ( ~ product(X1,X2,X3)
    | product(X4,X5,X3)
    | ~ product(X1,X6,X4)
    | ~ product(X6,X5,X2) ),
    inference(rename_variables,[],[i_0_30]) ).

cnf(i_0_703,plain,
    ( product(aPb,aPb_S_IaPc,aPb_S_IaPc)
    | ~ product(a,b,aPc)
    | ~ product(b,aPb,b)
    | ~ product(aPb,additive_inverse(aPc),additive_inverse(aPc)) ),
    inference(scs_inference,[],[i_0_49,i_0_48,i_0_297,i_0_44,i_0_61,i_0_677,i_0_59,i_0_40,i_0_683,i_0_46,i_0_39,i_0_278,i_0_417,i_0_657,i_0_655,i_0_580,i_0_405,i_0_437,i_0_83,i_0_679,i_0_698,i_0_56,i_0_58,i_0_57,i_0_32,i_0_31,i_0_28,i_0_38,i_0_27,i_0_55,i_0_54,i_0_53,i_0_30,i_0_25]) ).

cnf(i_0_704,plain,
    ~ sum(additive_identity,additive_inverse(aPb_S_IaPc),additive_inverse(multiply(a,bS_Ic))),
    inference(scs_inference,[],[i_0_165,i_0_630,i_0_56]) ).

cnf(i_0_705,plain,
    ~ sum(bS_Ic,c,add(additive_identity,b)),
    inference(scs_inference,[],[i_0_165,i_0_630,i_0_689,i_0_83,i_0_56,i_0_58]) ).

cnf(i_0_706,plain,
    add(additive_identity,X1) = X1,
    inference(rename_variables,[],[i_0_83]) ).

cnf(i_0_707,plain,
    ~ sum(bS_Ic,add(additive_identity,c),b),
    inference(scs_inference,[],[i_0_165,i_0_630,i_0_689,i_0_83,i_0_706,i_0_56,i_0_58,i_0_57]) ).

cnf(i_0_708,plain,
    add(additive_identity,X1) = X1,
    inference(rename_variables,[],[i_0_83]) ).

cnf(i_0_709,plain,
    sum(additive_identity,add(b,additive_inverse(c)),bS_Ic),
    inference(scs_inference,[],[i_0_165,i_0_59,i_0_40,i_0_228,i_0_630,i_0_689,i_0_83,i_0_706,i_0_56,i_0_58,i_0_57,i_0_31]) ).

cnf(i_0_710,plain,
    sum(X1,X2,add(X2,X1)),
    inference(rename_variables,[],[i_0_59]) ).

cnf(i_0_711,plain,
    sum(X1,X2,add(X1,X2)),
    inference(rename_variables,[],[i_0_40]) ).

cnf(i_0_712,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ sum(X4,X6,X1)
    | ~ sum(X6,X2,X5) ),
    inference(rename_variables,[],[i_0_31]) ).

cnf(i_0_713,plain,
    sum(add(b,additive_inverse(c)),additive_identity,bS_Ic),
    inference(scs_inference,[],[i_0_165,i_0_59,i_0_40,i_0_228,i_0_630,i_0_689,i_0_83,i_0_706,i_0_56,i_0_58,i_0_57,i_0_31,i_0_38]) ).

cnf(i_0_714,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X2,X1,X3) ),
    inference(rename_variables,[],[i_0_38]) ).

cnf(i_0_715,plain,
    ( ~ sum(add(additive_identity,X1),X2,additive_inverse(multiply(a,bS_Ic)))
    | ~ sum(X2,add(additive_identity,aPb_S_IaPc),additive_inverse(X1)) ),
    inference(scs_inference,[],[i_0_165,i_0_59,i_0_40,i_0_326,i_0_228,i_0_630,i_0_689,i_0_510,i_0_83,i_0_706,i_0_56,i_0_58,i_0_57,i_0_31,i_0_38,i_0_32]) ).

cnf(i_0_716,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ sum(X1,X6,X4)
    | ~ sum(X6,X5,X2) ),
    inference(rename_variables,[],[i_0_32]) ).

cnf(i_0_717,plain,
    ( ~ product(additive_identity,bS_Ic,aPb_S_IaPc)
    | ~ product(a,bS_Ic,additive_inverse(additive_identity)) ),
    inference(scs_inference,[],[i_0_165,i_0_59,i_0_40,i_0_46,i_0_39,i_0_326,i_0_228,i_0_630,i_0_689,i_0_115,i_0_510,i_0_83,i_0_706,i_0_56,i_0_58,i_0_57,i_0_31,i_0_38,i_0_32,i_0_27]) ).

cnf(i_0_718,plain,
    product(X1,X2,multiply(X1,X2)),
    inference(rename_variables,[],[i_0_39]) ).

cnf(i_0_719,plain,
    sum(additive_identity,X1,X1),
    inference(rename_variables,[],[i_0_46]) ).

cnf(i_0_720,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_27]) ).

cnf(i_0_721,plain,
    ( ~ product(a,additive_identity,aPb_S_IaPc)
    | ~ product(a,bS_Ic,additive_inverse(additive_identity)) ),
    inference(scs_inference,[],[i_0_165,i_0_59,i_0_40,i_0_46,i_0_719,i_0_39,i_0_718,i_0_326,i_0_228,i_0_630,i_0_689,i_0_115,i_0_510,i_0_83,i_0_706,i_0_56,i_0_58,i_0_57,i_0_31,i_0_38,i_0_32,i_0_27,i_0_28]) ).

cnf(i_0_722,plain,
    product(X1,X2,multiply(X1,X2)),
    inference(rename_variables,[],[i_0_39]) ).

cnf(i_0_723,plain,
    sum(additive_identity,X1,X1),
    inference(rename_variables,[],[i_0_46]) ).

cnf(i_0_724,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_28]) ).

cnf(i_0_725,plain,
    ( ~ product(a,bS_Ic,additive_inverse(additive_identity))
    | ~ product(a,additive_inverse(b),additive_inverse(aPc)) ),
    inference(scs_inference,[],[i_0_49,i_0_165,i_0_44,i_0_43,i_0_59,i_0_40,i_0_46,i_0_719,i_0_39,i_0_718,i_0_326,i_0_228,i_0_630,i_0_689,i_0_115,i_0_510,i_0_83,i_0_706,i_0_56,i_0_58,i_0_57,i_0_31,i_0_38,i_0_32,i_0_27,i_0_28,i_0_26,i_0_25]) ).

cnf(i_0_726,plain,
    sum(X1,additive_inverse(X1),additive_identity),
    inference(rename_variables,[],[i_0_43]) ).

cnf(i_0_727,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_25]) ).

cnf(i_0_728,plain,
    ~ sum(add(additive_identity,bS_Ic),c,add(additive_identity,b)),
    inference(scs_inference,[],[i_0_705,i_0_83,i_0_56]) ).

cnf(i_0_729,plain,
    add(additive_identity,X1) = X1,
    inference(rename_variables,[],[i_0_83]) ).

cnf(i_0_730,plain,
    ~ sum(bS_Ic,add(additive_identity,c),add(additive_identity,b)),
    inference(scs_inference,[],[i_0_705,i_0_707,i_0_83,i_0_729,i_0_56,i_0_58]) ).

cnf(i_0_731,plain,
    add(additive_identity,X1) = X1,
    inference(rename_variables,[],[i_0_83]) ).

cnf(i_0_732,plain,
    ~ sum(multiply(a,bS_Ic),add(X1,additive_inverse(X1)),add(additive_identity,aPb_S_IaPc)),
    inference(scs_inference,[],[i_0_297,i_0_705,i_0_707,i_0_265,i_0_83,i_0_729,i_0_56,i_0_58,i_0_57]) ).

cnf(i_0_733,plain,
    ~ sum(multiply(a,bS_Ic),additive_inverse(aPb_S_IaPc),additive_inverse(additive_inverse(additive_identity))),
    inference(scs_inference,[],[i_0_297,i_0_59,i_0_212,i_0_705,i_0_707,i_0_265,i_0_577,i_0_83,i_0_729,i_0_56,i_0_58,i_0_57,i_0_31]) ).

cnf(i_0_734,plain,
    sum(X1,X2,add(X2,X1)),
    inference(rename_variables,[],[i_0_59]) ).

cnf(i_0_735,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ sum(X4,X6,X1)
    | ~ sum(X6,X2,X5) ),
    inference(rename_variables,[],[i_0_31]) ).

cnf(i_0_736,plain,
    ( ~ sum(add(additive_inverse(bS_Ic),additive_inverse(c)),X1,multiply(a,bS_Ic))
    | ~ sum(X1,add(additive_identity,additive_inverse(aPb_S_IaPc)),b) ),
    inference(scs_inference,[],[i_0_297,i_0_59,i_0_377,i_0_212,i_0_705,i_0_707,i_0_265,i_0_577,i_0_83,i_0_729,i_0_56,i_0_58,i_0_57,i_0_31,i_0_32]) ).

cnf(i_0_737,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ sum(X1,X6,X4)
    | ~ sum(X6,X5,X2) ),
    inference(rename_variables,[],[i_0_32]) ).

cnf(i_0_738,plain,
    ( ~ product(a,additive_identity,add(additive_identity,aPb_S_IaPc))
    | ~ product(a,bS_Ic,additive_inverse(additive_identity)) ),
    inference(scs_inference,[],[i_0_297,i_0_59,i_0_46,i_0_39,i_0_377,i_0_212,i_0_705,i_0_707,i_0_180,i_0_265,i_0_577,i_0_83,i_0_729,i_0_56,i_0_58,i_0_57,i_0_31,i_0_32,i_0_28]) ).

cnf(i_0_739,plain,
    product(X1,X2,multiply(X1,X2)),
    inference(rename_variables,[],[i_0_39]) ).

cnf(i_0_740,plain,
    sum(additive_identity,X1,X1),
    inference(rename_variables,[],[i_0_46]) ).

cnf(i_0_741,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_28]) ).

cnf(i_0_742,plain,
    ( product(X1,aPb_S_IaPc,aPb_S_IaPc)
    | ~ product(X1,aPb,aPb)
    | ~ product(X1,additive_inverse(aPc),additive_inverse(aPc)) ),
    inference(scs_inference,[],[i_0_297,i_0_44,i_0_59,i_0_46,i_0_39,i_0_377,i_0_212,i_0_705,i_0_707,i_0_180,i_0_265,i_0_577,i_0_83,i_0_729,i_0_56,i_0_58,i_0_57,i_0_31,i_0_25]) ).

cnf(i_0_743,plain,
    ~ sum(add(additive_identity,bS_Ic),add(additive_identity,c),add(additive_identity,b)),
    inference(scs_inference,[],[i_0_730,i_0_83,i_0_56]) ).

cnf(i_0_744,plain,
    add(additive_identity,X1) = X1,
    inference(rename_variables,[],[i_0_83]) ).

cnf(i_0_745,plain,
    ~ sum(multiply(a,bS_Ic),add(X1,additive_inverse(X1)),aPb_S_IaPc),
    inference(scs_inference,[],[i_0_61,i_0_732,i_0_730,i_0_83,i_0_56,i_0_58]) ).

cnf(i_0_746,plain,
    X1 = add(additive_identity,X1),
    inference(rename_variables,[],[i_0_61]) ).

cnf(i_0_747,plain,
    ~ sum(additive_inverse(additive_inverse(aPc)),multiply(a,bS_Ic),aPb),
    inference(scs_inference,[],[i_0_61,i_0_100,i_0_40,i_0_732,i_0_730,i_0_600,i_0_83,i_0_56,i_0_58,i_0_32]) ).

cnf(i_0_748,plain,
    ~ sum(add(X1,additive_inverse(X1)),multiply(a,bS_Ic),aPb_S_IaPc),
    inference(rename_variables,[],[i_0_600]) ).

cnf(i_0_749,plain,
    sum(X1,X2,add(X1,X2)),
    inference(rename_variables,[],[i_0_40]) ).

cnf(i_0_750,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ sum(X1,X6,X4)
    | ~ sum(X6,X5,X2) ),
    inference(rename_variables,[],[i_0_32]) ).

cnf(i_0_751,plain,
    ~ sum(multiply(a,bS_Ic),additive_identity,additive_inverse(additive_inverse(aPb_S_IaPc))),
    inference(scs_inference,[],[i_0_61,i_0_100,i_0_42,i_0_40,i_0_46,i_0_732,i_0_730,i_0_600,i_0_553,i_0_83,i_0_56,i_0_58,i_0_32,i_0_31]) ).

cnf(i_0_752,plain,
    sum(additive_inverse(X1),X1,additive_identity),
    inference(rename_variables,[],[i_0_42]) ).

cnf(i_0_753,plain,
    sum(additive_identity,X1,X1),
    inference(rename_variables,[],[i_0_46]) ).

cnf(i_0_754,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ sum(X4,X6,X1)
    | ~ sum(X6,X2,X5) ),
    inference(rename_variables,[],[i_0_31]) ).

cnf(i_0_755,plain,
    ( ~ product(a,b,additive_inverse(additive_identity))
    | ~ product(a,additive_inverse(c),aPb_S_IaPc) ),
    inference(scs_inference,[],[i_0_61,i_0_100,i_0_42,i_0_40,i_0_45,i_0_46,i_0_39,i_0_732,i_0_730,i_0_600,i_0_303,i_0_553,i_0_83,i_0_56,i_0_58,i_0_32,i_0_31,i_0_28]) ).

cnf(i_0_756,plain,
    product(X1,X2,multiply(X1,X2)),
    inference(rename_variables,[],[i_0_39]) ).

cnf(i_0_757,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_28]) ).

cnf(i_0_758,plain,
    ( ~ product(a,b,additive_identity)
    | ~ product(a,additive_inverse(c),aPb_S_IaPc) ),
    inference(scs_inference,[],[i_0_165,i_0_61,i_0_100,i_0_42,i_0_40,i_0_45,i_0_46,i_0_39,i_0_732,i_0_730,i_0_600,i_0_303,i_0_553,i_0_83,i_0_56,i_0_58,i_0_32,i_0_31,i_0_28,i_0_55]) ).

cnf(i_0_759,plain,
    ( ~ product(a,add(additive_identity,b),additive_inverse(additive_identity))
    | ~ product(a,additive_inverse(c),aPb_S_IaPc) ),
    inference(scs_inference,[],[i_0_165,i_0_61,i_0_100,i_0_42,i_0_40,i_0_45,i_0_46,i_0_39,i_0_732,i_0_730,i_0_600,i_0_303,i_0_553,i_0_83,i_0_744,i_0_56,i_0_58,i_0_32,i_0_31,i_0_28,i_0_55,i_0_54]) ).

cnf(i_0_760,plain,
    add(additive_identity,X1) = X1,
    inference(rename_variables,[],[i_0_83]) ).

cnf(i_0_761,plain,
    ( ~ product(add(additive_identity,a),b,additive_inverse(additive_identity))
    | ~ product(a,additive_inverse(c),aPb_S_IaPc) ),
    inference(scs_inference,[],[i_0_165,i_0_61,i_0_100,i_0_42,i_0_40,i_0_45,i_0_46,i_0_39,i_0_732,i_0_730,i_0_600,i_0_303,i_0_553,i_0_83,i_0_744,i_0_760,i_0_56,i_0_58,i_0_32,i_0_31,i_0_28,i_0_55,i_0_54,i_0_53]) ).

cnf(i_0_762,plain,
    add(additive_identity,X1) = X1,
    inference(rename_variables,[],[i_0_83]) ).

cnf(i_0_763,plain,
    ( ~ product(X1,X2,X3)
    | product(X4,X5,X3)
    | ~ product(X1,X6,X4)
    | ~ product(X6,X5,X2) ),
    inference(rename_variables,[],[i_0_30]) ).

cnf(i_0_764,plain,
    sum(additive_identity,X1,X1),
    inference(rename_variables,[],[i_0_46]) ).

cnf(i_0_765,plain,
    ( product(aPb,aPb_S_IaPc,aPb_S_IaPc)
    | ~ product(a,additive_inverse(c),aPb_S_IaPc)
    | ~ product(b,aPb,b)
    | ~ product(aPb,additive_inverse(aPc),additive_inverse(aPc)) ),
    inference(scs_inference,[],[i_0_49,i_0_165,i_0_44,i_0_61,i_0_100,i_0_42,i_0_40,i_0_45,i_0_46,i_0_753,i_0_39,i_0_732,i_0_730,i_0_600,i_0_303,i_0_624,i_0_553,i_0_83,i_0_744,i_0_760,i_0_56,i_0_58,i_0_32,i_0_31,i_0_28,i_0_55,i_0_54,i_0_53,i_0_30,i_0_25]) ).

cnf(i_0_766,plain,
    ~ sum(add(additive_identity,c),bS_Ic,add(additive_identity,b)),
    inference(scs_inference,[],[i_0_680,i_0_83,i_0_56]) ).

cnf(i_0_767,plain,
    add(additive_identity,X1) = X1,
    inference(rename_variables,[],[i_0_83]) ).

cnf(i_0_768,plain,
    ~ sum(add(additive_identity,bS_Ic),c,b),
    inference(scs_inference,[],[i_0_61,i_0_728,i_0_680,i_0_83,i_0_56,i_0_58]) ).

cnf(i_0_769,plain,
    X1 = add(additive_identity,X1),
    inference(rename_variables,[],[i_0_61]) ).

cnf(i_0_770,plain,
    sum(additive_inverse(additive_identity),add(bS_Ic,additive_identity),bS_Ic),
    inference(scs_inference,[],[i_0_61,i_0_59,i_0_47,i_0_535,i_0_728,i_0_680,i_0_83,i_0_56,i_0_58,i_0_31]) ).

cnf(i_0_771,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_47]) ).

cnf(i_0_772,plain,
    sum(X1,X2,add(X2,X1)),
    inference(rename_variables,[],[i_0_59]) ).

cnf(i_0_773,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ sum(X4,X6,X1)
    | ~ sum(X6,X2,X5) ),
    inference(rename_variables,[],[i_0_31]) ).

cnf(i_0_774,plain,
    sum(add(bS_Ic,additive_identity),additive_inverse(additive_identity),bS_Ic),
    inference(scs_inference,[],[i_0_61,i_0_59,i_0_47,i_0_535,i_0_728,i_0_680,i_0_83,i_0_56,i_0_58,i_0_31,i_0_38]) ).

cnf(i_0_775,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X2,X1,X3) ),
    inference(rename_variables,[],[i_0_38]) ).

cnf(i_0_776,plain,
    ~ sum(add(additive_identity,c),add(additive_identity,bS_Ic),add(additive_identity,b)),
    inference(scs_inference,[],[i_0_61,i_0_59,i_0_47,i_0_535,i_0_728,i_0_680,i_0_83,i_0_767,i_0_56,i_0_58,i_0_31,i_0_38,i_0_57]) ).

cnf(i_0_777,plain,
    add(additive_identity,X1) = X1,
    inference(rename_variables,[],[i_0_83]) ).

cnf(i_0_778,plain,
    ( ~ sum(b,X1,additive_inverse(multiply(a,bS_Ic)))
    | ~ sum(X1,aPb_S_IaPc,add(additive_inverse(bS_Ic),additive_inverse(c))) ),
    inference(scs_inference,[],[i_0_61,i_0_59,i_0_47,i_0_285,i_0_535,i_0_728,i_0_680,i_0_529,i_0_83,i_0_767,i_0_56,i_0_58,i_0_31,i_0_38,i_0_57,i_0_32]) ).

cnf(i_0_779,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ sum(X1,X6,X4)
    | ~ sum(X6,X5,X2) ),
    inference(rename_variables,[],[i_0_32]) ).

cnf(i_0_780,plain,
    ( ~ product(a,bS_Ic,add(additive_identity,aPb))
    | ~ product(additive_identity,bS_Ic,additive_inverse(aPc)) ),
    inference(scs_inference,[],[i_0_61,i_0_59,i_0_47,i_0_771,i_0_39,i_0_285,i_0_535,i_0_728,i_0_680,i_0_203,i_0_529,i_0_83,i_0_767,i_0_56,i_0_58,i_0_31,i_0_38,i_0_57,i_0_32,i_0_27]) ).

cnf(i_0_781,plain,
    product(X1,X2,multiply(X1,X2)),
    inference(rename_variables,[],[i_0_39]) ).

cnf(i_0_782,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_47]) ).

cnf(i_0_783,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_27]) ).

cnf(i_0_784,plain,
    ( ~ product(a,X1,add(additive_identity,multiply(a,bS_Ic)))
    | ~ sum(X1,c,b) ),
    inference(scs_inference,[],[i_0_49,i_0_48,i_0_61,i_0_59,i_0_47,i_0_771,i_0_39,i_0_285,i_0_535,i_0_728,i_0_680,i_0_203,i_0_584,i_0_529,i_0_83,i_0_767,i_0_56,i_0_58,i_0_31,i_0_38,i_0_57,i_0_32,i_0_27,i_0_28]) ).

cnf(i_0_785,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_28]) ).

cnf(i_0_786,plain,
    ( ~ product(a,bS_Ic,aPb)
    | ~ product(a,additive_identity,additive_inverse(aPc)) ),
    inference(scs_inference,[],[i_0_41,i_0_49,i_0_48,i_0_44,i_0_61,i_0_59,i_0_47,i_0_771,i_0_782,i_0_39,i_0_285,i_0_535,i_0_728,i_0_680,i_0_203,i_0_584,i_0_529,i_0_83,i_0_767,i_0_56,i_0_58,i_0_31,i_0_38,i_0_57,i_0_32,i_0_27,i_0_28,i_0_26,i_0_25]) ).

cnf(i_0_787,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_47]) ).

cnf(i_0_788,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_25]) ).

cnf(i_0_789,plain,
    ~ sum(add(additive_identity,bS_Ic),add(additive_identity,c),b),
    inference(scs_inference,[],[i_0_768,i_0_83,i_0_57]) ).

cnf(i_0_790,plain,
    add(additive_identity,X1) = X1,
    inference(rename_variables,[],[i_0_83]) ).

cnf(i_0_791,plain,
    ~ sum(add(additive_identity,c),bS_Ic,b),
    inference(scs_inference,[],[i_0_587,i_0_768,i_0_83,i_0_790,i_0_57,i_0_56]) ).

cnf(i_0_792,plain,
    add(additive_identity,X1) = X1,
    inference(rename_variables,[],[i_0_83]) ).

cnf(i_0_793,plain,
    ~ sum(additive_inverse(aPb_S_IaPc),multiply(a,bS_Ic),add(X1,additive_inverse(X1))),
    inference(scs_inference,[],[i_0_297,i_0_587,i_0_358,i_0_768,i_0_83,i_0_790,i_0_57,i_0_56,i_0_58]) ).

cnf(i_0_794,plain,
    sum(additive_inverse(c),add(additive_identity,add(b,additive_identity)),bS_Ic),
    inference(scs_inference,[],[i_0_297,i_0_40,i_0_59,i_0_450,i_0_587,i_0_358,i_0_768,i_0_83,i_0_790,i_0_57,i_0_56,i_0_58,i_0_31]) ).

cnf(i_0_795,plain,
    sum(X1,X2,add(X1,X2)),
    inference(rename_variables,[],[i_0_40]) ).

cnf(i_0_796,plain,
    sum(X1,X2,add(X2,X1)),
    inference(rename_variables,[],[i_0_59]) ).

cnf(i_0_797,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ sum(X4,X6,X1)
    | ~ sum(X6,X2,X5) ),
    inference(rename_variables,[],[i_0_31]) ).

cnf(i_0_798,plain,
    sum(add(additive_identity,add(b,additive_identity)),additive_inverse(c),bS_Ic),
    inference(scs_inference,[],[i_0_297,i_0_40,i_0_59,i_0_450,i_0_587,i_0_358,i_0_768,i_0_83,i_0_790,i_0_57,i_0_56,i_0_58,i_0_31,i_0_38]) ).

cnf(i_0_799,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X2,X1,X3) ),
    inference(rename_variables,[],[i_0_38]) ).

cnf(i_0_800,plain,
    ( ~ sum(add(X1,additive_inverse(X1)),X2,additive_inverse(aPb_S_IaPc))
    | ~ sum(X2,add(additive_identity,multiply(a,bS_Ic)),additive_inverse(additive_identity)) ),
    inference(scs_inference,[],[i_0_297,i_0_40,i_0_59,i_0_450,i_0_255,i_0_587,i_0_364,i_0_358,i_0_768,i_0_83,i_0_790,i_0_57,i_0_56,i_0_58,i_0_31,i_0_38,i_0_32]) ).

cnf(i_0_801,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ sum(X1,X6,X4)
    | ~ sum(X6,X5,X2) ),
    inference(rename_variables,[],[i_0_32]) ).

cnf(i_0_802,plain,
    ( ~ product(a,b,additive_inverse(additive_identity))
    | ~ product(a,additive_inverse(c),add(additive_identity,aPb_S_IaPc)) ),
    inference(scs_inference,[],[i_0_297,i_0_40,i_0_59,i_0_45,i_0_39,i_0_450,i_0_255,i_0_282,i_0_587,i_0_364,i_0_358,i_0_768,i_0_83,i_0_790,i_0_57,i_0_56,i_0_58,i_0_31,i_0_38,i_0_32,i_0_28]) ).

cnf(i_0_803,plain,
    product(X1,X2,multiply(X1,X2)),
    inference(rename_variables,[],[i_0_39]) ).

cnf(i_0_804,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_28]) ).

cnf(i_0_806,plain,
    ~ sum(add(additive_identity,c),add(additive_identity,bS_Ic),b),
    inference(scs_inference,[],[i_0_791,i_0_83,i_0_57]) ).

cnf(i_0_807,plain,
    add(additive_identity,X1) = X1,
    inference(rename_variables,[],[i_0_83]) ).

cnf(i_0_808,plain,
    ~ sum(add(X1,additive_inverse(X1)),add(additive_identity,aPb_S_IaPc),multiply(a,bS_Ic)),
    inference(scs_inference,[],[i_0_297,i_0_230,i_0_791,i_0_83,i_0_57,i_0_56]) ).

cnf(i_0_809,plain,
    ~ sum(aPc,add(additive_identity,multiply(a,bS_Ic)),add(additive_identity,aPb)),
    inference(scs_inference,[],[i_0_297,i_0_230,i_0_578,i_0_791,i_0_83,i_0_807,i_0_57,i_0_56,i_0_58]) ).

cnf(i_0_810,plain,
    add(additive_identity,X1) = X1,
    inference(rename_variables,[],[i_0_83]) ).

cnf(i_0_811,plain,
    sum(additive_inverse(additive_identity),add(additive_identity,bS_Ic),bS_Ic),
    inference(scs_inference,[],[i_0_297,i_0_40,i_0_47,i_0_535,i_0_230,i_0_578,i_0_791,i_0_83,i_0_807,i_0_57,i_0_56,i_0_58,i_0_31]) ).

cnf(i_0_812,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_47]) ).

cnf(i_0_813,plain,
    sum(X1,X2,add(X1,X2)),
    inference(rename_variables,[],[i_0_40]) ).

cnf(i_0_814,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ sum(X4,X6,X1)
    | ~ sum(X6,X2,X5) ),
    inference(rename_variables,[],[i_0_31]) ).

cnf(i_0_815,plain,
    ~ product(a,additive_inverse(c),add(additive_identity,additive_inverse(aPc))),
    inference(scs_inference,[],[i_0_49,i_0_297,i_0_40,i_0_39,i_0_45,i_0_47,i_0_535,i_0_205,i_0_230,i_0_578,i_0_791,i_0_83,i_0_807,i_0_57,i_0_56,i_0_58,i_0_31,i_0_28]) ).

cnf(i_0_816,plain,
    product(X1,X2,multiply(X1,X2)),
    inference(rename_variables,[],[i_0_39]) ).

cnf(i_0_817,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_28]) ).

cnf(i_0_818,plain,
    sum(add(additive_identity,bS_Ic),additive_inverse(additive_identity),bS_Ic),
    inference(scs_inference,[],[i_0_49,i_0_297,i_0_40,i_0_39,i_0_45,i_0_47,i_0_535,i_0_205,i_0_230,i_0_578,i_0_791,i_0_83,i_0_807,i_0_57,i_0_56,i_0_58,i_0_31,i_0_28,i_0_38]) ).

cnf(i_0_819,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X2,X1,X3) ),
    inference(rename_variables,[],[i_0_38]) ).

cnf(i_0_820,plain,
    ~ product(a,additive_inverse(c),additive_inverse(aPc)),
    inference(scs_inference,[],[i_0_49,i_0_297,i_0_61,i_0_40,i_0_39,i_0_45,i_0_47,i_0_535,i_0_205,i_0_230,i_0_578,i_0_791,i_0_83,i_0_807,i_0_57,i_0_56,i_0_58,i_0_31,i_0_28,i_0_38,i_0_55]) ).

cnf(i_0_821,plain,
    X1 = add(additive_identity,X1),
    inference(rename_variables,[],[i_0_61]) ).

cnf(i_0_822,plain,
    ~ product(a,add(additive_identity,additive_inverse(c)),additive_inverse(aPc)),
    inference(scs_inference,[],[i_0_49,i_0_297,i_0_61,i_0_40,i_0_39,i_0_45,i_0_47,i_0_535,i_0_205,i_0_230,i_0_578,i_0_791,i_0_83,i_0_807,i_0_810,i_0_57,i_0_56,i_0_58,i_0_31,i_0_28,i_0_38,i_0_55,i_0_54]) ).

cnf(i_0_823,plain,
    add(additive_identity,X1) = X1,
    inference(rename_variables,[],[i_0_83]) ).

cnf(i_0_824,plain,
    ~ product(add(additive_identity,a),additive_inverse(c),add(additive_identity,additive_inverse(aPc))),
    inference(scs_inference,[],[i_0_49,i_0_297,i_0_61,i_0_40,i_0_39,i_0_45,i_0_47,i_0_535,i_0_205,i_0_230,i_0_578,i_0_791,i_0_83,i_0_807,i_0_810,i_0_823,i_0_57,i_0_56,i_0_58,i_0_31,i_0_28,i_0_38,i_0_55,i_0_54,i_0_53]) ).

cnf(i_0_825,plain,
    add(additive_identity,X1) = X1,
    inference(rename_variables,[],[i_0_83]) ).

cnf(i_0_826,plain,
    ( ~ sum(b,X1,additive_inverse(multiply(a,bS_Ic)))
    | ~ sum(X1,add(additive_identity,aPb_S_IaPc),add(additive_inverse(bS_Ic),additive_inverse(c))) ),
    inference(scs_inference,[],[i_0_49,i_0_297,i_0_61,i_0_40,i_0_39,i_0_45,i_0_47,i_0_285,i_0_535,i_0_205,i_0_230,i_0_510,i_0_578,i_0_791,i_0_83,i_0_807,i_0_810,i_0_823,i_0_57,i_0_56,i_0_58,i_0_31,i_0_28,i_0_38,i_0_55,i_0_54,i_0_53,i_0_32]) ).

cnf(i_0_827,plain,
    ( ~ sum(X1,X2,X3)
    | sum(X4,X5,X3)
    | ~ sum(X1,X6,X4)
    | ~ sum(X6,X5,X2) ),
    inference(rename_variables,[],[i_0_32]) ).

cnf(i_0_828,plain,
    ( ~ product(a,bS_Ic,aPb)
    | ~ product(additive_identity,bS_Ic,add(additive_identity,additive_inverse(aPc))) ),
    inference(scs_inference,[],[i_0_49,i_0_48,i_0_297,i_0_61,i_0_40,i_0_39,i_0_816,i_0_45,i_0_47,i_0_812,i_0_285,i_0_535,i_0_205,i_0_230,i_0_510,i_0_578,i_0_791,i_0_83,i_0_807,i_0_810,i_0_823,i_0_57,i_0_56,i_0_58,i_0_31,i_0_28,i_0_38,i_0_55,i_0_54,i_0_53,i_0_32,i_0_37,i_0_27]) ).

cnf(i_0_829,plain,
    product(X1,X2,multiply(X1,X2)),
    inference(rename_variables,[],[i_0_39]) ).

cnf(i_0_830,plain,
    sum(X1,additive_identity,X1),
    inference(rename_variables,[],[i_0_47]) ).

cnf(i_0_831,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_27]) ).

cnf(i_0_833,plain,
    $false,
    inference(scs_inference,[],[i_0_48,i_0_820,i_0_37]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : RNG006-1 : TPTP v9.2.1. Released v1.0.0.
% 0.00/0.12  % Command    : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33  % Computer : n007.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 01:45:24 EDT 2026
% 0.15/0.33  % CPUTime    : 
% 0.15/0.34  % start to proof: theBenchmark
% 2.81/2.62  % Version  : CSE_E---1.7
% 2.81/2.62  % Problem  : theBenchmark.p
% 2.81/2.62  % SZS status Unsatisfiable for theBenchmark.p
% 2.81/2.62  % SZS output start CNFRefutation
% See solution above
% 4.00/3.88  % Total time : 2.273s
%------------------------------------------------------------------------------