TSTP Solution File: NUM925+3 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : NUM925+3 : TPTP v8.1.2. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n024.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 10:41:29 EDT 2023

% Result   : Theorem 0.63s 1.15s
% Output   : CNFRefutation 0.63s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :  130
% Syntax   : Number of formulae    :  171 (  42 unt; 113 typ;   0 def)
%            Number of atoms       :   89 (  50 equ)
%            Maximal formula atoms :    6 (   1 avg)
%            Number of connectives :   59 (  28   ~;  22   |;   3   &)
%                                         (   2 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   2 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  121 (  68   >;  53   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :  110 ( 110 usr;  45 con; 0-3 aty)
%            Number of variables   :   48 (   5 sgn;  27   !;   1   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    is_int: $i > $o ).

tff(decl_23,type,
    abs_abs_int: $i > $i ).

tff(decl_24,type,
    minus_minus_int: ( $i * $i ) > $i ).

tff(decl_25,type,
    one_one_int: $i ).

tff(decl_26,type,
    plus_plus_int: ( $i * $i ) > $i ).

tff(decl_27,type,
    times_times_int: ( $i * $i ) > $i ).

tff(decl_28,type,
    zero_zero_int: $i ).

tff(decl_29,type,
    int: $i ).

tff(decl_30,type,
    undefined_int: $i > $i ).

tff(decl_31,type,
    is_bool: $i > $o ).

tff(decl_32,type,
    if_int: ( $i * $i * $i ) > $i ).

tff(decl_33,type,
    bit0: $i > $i ).

tff(decl_34,type,
    bit1: $i > $i ).

tff(decl_35,type,
    min: $i ).

tff(decl_36,type,
    pls: $i ).

tff(decl_37,type,
    number_number_of_int: $i > $i ).

tff(decl_38,type,
    succ: $i > $i ).

tff(decl_39,type,
    legendre: ( $i * $i ) > $i ).

tff(decl_40,type,
    fFalse: $i ).

tff(decl_41,type,
    fTrue: $i ).

tff(decl_42,type,
    hAPP_int_bool: ( $i * $i ) > $i ).

tff(decl_43,type,
    hAPP_nat_bool: ( $i * $i ) > $i ).

tff(decl_44,type,
    hAPP_nat_int: ( $i * $i ) > $i ).

tff(decl_45,type,
    hAPP_real_bool: ( $i * $i ) > $i ).

tff(decl_46,type,
    m: $i ).

tff(decl_47,type,
    m1: $i ).

tff(decl_48,type,
    s1: $i ).

tff(decl_49,type,
    s: $i ).

tff(decl_50,type,
    t: $i ).

tff(decl_51,type,
    x: $i ).

tff(decl_52,type,
    y: $i ).

tff(decl_53,type,
    ord_less_int: $i ).

tff(decl_54,type,
    hAPP_i1948725293t_bool: ( $i * $i ) > $i ).

tff(decl_55,type,
    semiri1621563631at_int: $i ).

tff(decl_56,type,
    n: $i ).

tff(decl_57,type,
    hBOOL: $i > $o ).

tff(decl_58,type,
    power_power_int: $i > $i ).

tff(decl_59,type,
    number_number_of_nat: $i > $i ).

tff(decl_60,type,
    power_power_real: $i > $i ).

tff(decl_61,type,
    hAPP_nat_real: ( $i * $i ) > $i ).

tff(decl_62,type,
    plus_plus_real: ( $i * $i ) > $i ).

tff(decl_63,type,
    zero_zero_real: $i ).

tff(decl_64,type,
    one_one_nat: $i ).

tff(decl_65,type,
    power_power_nat: $i > $i ).

tff(decl_66,type,
    hAPP_nat_nat: ( $i * $i ) > $i ).

tff(decl_67,type,
    one_one_real: $i ).

tff(decl_68,type,
    zero_zero_nat: $i ).

tff(decl_69,type,
    number267125858f_real: $i > $i ).

tff(decl_70,type,
    plus_plus_nat: ( $i * $i ) > $i ).

tff(decl_71,type,
    ord_less_nat: $i ).

tff(decl_72,type,
    hAPP_n1699378549t_bool: ( $i * $i ) > $i ).

tff(decl_73,type,
    ord_less_real: $i ).

tff(decl_74,type,
    hAPP_r1134773055l_bool: ( $i * $i ) > $i ).

tff(decl_75,type,
    semiri984289939at_nat: $i ).

tff(decl_76,type,
    semiri132038758t_real: $i ).

tff(decl_77,type,
    tn: $i ).

tff(decl_78,type,
    if_nat: ( $i * $i * $i ) > $i ).

tff(decl_79,type,
    ord_less_eq_int: $i ).

tff(decl_80,type,
    nat: $i > $i ).

tff(decl_81,type,
    minus_minus_nat: ( $i * $i ) > $i ).

tff(decl_82,type,
    ord_less_eq_real: $i ).

tff(decl_83,type,
    minus_minus_real: ( $i * $i ) > $i ).

tff(decl_84,type,
    times_times_nat: ( $i * $i ) > $i ).

tff(decl_85,type,
    times_times_real: ( $i * $i ) > $i ).

tff(decl_86,type,
    ord_less_eq_nat: $i ).

tff(decl_87,type,
    twoSqu1154269391sum2sq: $i ).

tff(decl_88,type,
    zprime: $i ).

tff(decl_89,type,
    dvd_dvd_int: $i ).

tff(decl_90,type,
    quadRes: $i > $i ).

tff(decl_91,type,
    zcong: ( $i * $i ) > $i ).

tff(decl_92,type,
    dvd_dvd_nat: $i ).

tff(decl_93,type,
    abs_abs_real: $i > $i ).

tff(decl_94,type,
    esk1_3: ( $i * $i * $i ) > $i ).

tff(decl_95,type,
    esk2_1: $i > $i ).

tff(decl_96,type,
    esk3_2: ( $i * $i ) > $i ).

tff(decl_97,type,
    esk4_2: ( $i * $i ) > $i ).

tff(decl_98,type,
    esk5_2: ( $i * $i ) > $i ).

tff(decl_99,type,
    esk6_1: $i > $i ).

tff(decl_100,type,
    esk7_1: $i > $i ).

tff(decl_101,type,
    esk8_1: $i > $i ).

tff(decl_102,type,
    esk9_1: $i > $i ).

tff(decl_103,type,
    esk10_1: $i > $i ).

tff(decl_104,type,
    esk11_1: $i > $i ).

tff(decl_105,type,
    esk12_1: $i > $i ).

tff(decl_106,type,
    esk13_1: $i > $i ).

tff(decl_107,type,
    esk14_2: ( $i * $i ) > $i ).

tff(decl_108,type,
    esk15_3: ( $i * $i * $i ) > $i ).

tff(decl_109,type,
    esk16_3: ( $i * $i * $i ) > $i ).

tff(decl_110,type,
    esk17_2: ( $i * $i ) > $i ).

tff(decl_111,type,
    esk18_0: $i ).

tff(decl_112,type,
    esk19_0: $i ).

tff(decl_113,type,
    esk20_0: $i ).

tff(decl_114,type,
    esk21_0: $i ).

tff(decl_115,type,
    esk22_2: ( $i * $i ) > $i ).

tff(decl_116,type,
    esk23_0: $i ).

tff(decl_117,type,
    esk24_0: $i ).

tff(decl_118,type,
    esk25_0: $i ).

tff(decl_119,type,
    esk26_0: $i ).

tff(decl_120,type,
    esk27_2: ( $i * $i ) > $i ).

tff(decl_121,type,
    esk28_3: ( $i * $i * $i ) > $i ).

tff(decl_122,type,
    esk29_1: $i > $i ).

tff(decl_123,type,
    esk30_0: $i ).

tff(decl_124,type,
    esk31_0: $i ).

tff(decl_125,type,
    esk32_0: $i ).

tff(decl_126,type,
    esk33_0: $i ).

tff(decl_127,type,
    esk34_2: ( $i * $i ) > $i ).

tff(decl_128,type,
    esk35_3: ( $i * $i * $i ) > $i ).

tff(decl_129,type,
    esk36_2: ( $i * $i ) > $i ).

tff(decl_130,type,
    esk37_3: ( $i * $i * $i ) > $i ).

tff(decl_131,type,
    esk38_3: ( $i * $i * $i ) > $i ).

tff(decl_132,type,
    esk39_3: ( $i * $i * $i ) > $i ).

tff(decl_133,type,
    esk40_3: ( $i * $i * $i ) > $i ).

tff(decl_134,type,
    esk41_3: ( $i * $i * $i ) > $i ).

fof(fact_809_succ__Bit0,axiom,
    ! [X22] : succ(bit0(X22)) = bit1(X22),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_809_succ__Bit0) ).

fof(fact_103_Bit0__def,axiom,
    ! [X22] : bit0(X22) = plus_plus_int(X22,X22),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_Bit0__def) ).

fof(fact_814_succ__def,axiom,
    ! [X22] : succ(X22) = plus_plus_int(X22,one_one_int),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_814_succ__def) ).

fof(conj_0,conjecture,
    hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) != zero_zero_int,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

fof(fact_767_nat__number__of__def,axiom,
    ! [X14] : number_number_of_nat(X14) = nat(number_number_of_int(X14)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_767_nat__number__of__def) ).

fof(fact_16_one__add__one__is__two,axiom,
    plus_plus_int(one_one_int,one_one_int) = number_number_of_int(bit0(bit1(pls))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_one__add__one__is__two) ).

fof(fact_97_Bit0__Pls,axiom,
    bit0(pls) = pls,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_Bit0__Pls) ).

fof(fact_231_field__power__not__zero,axiom,
    ! [X65,X66] :
      ( is_int(X66)
     => ( X66 != zero_zero_int
       => hAPP_nat_int(power_power_int(X66),X65) != zero_zero_int ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_field__power__not__zero) ).

fof(fact_98_Pls__def,axiom,
    pls = zero_zero_int,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_Pls__def) ).

fof(fact_807_int__le__0__conv,axiom,
    ! [X19] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X19)),zero_zero_int))
    <=> X19 = zero_zero_nat ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_807_int__le__0__conv) ).

fof(fact_789_zle__iff__zadd,axiom,
    ! [X26,X31] :
      ( is_int(X31)
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X26),X31))
      <=> ? [X91] : X31 = plus_plus_int(X26,hAPP_nat_int(semiri1621563631at_int,X91)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_789_zle__iff__zadd) ).

fof(gsy_c_Groups_Oplus__class_Oplus_000tc__Int__Oint,hypothesis,
    ! [X1,X2] :
      ( ( is_int(X1)
        & is_int(X2) )
     => is_int(plus_plus_int(X1,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Groups_Oplus__class_Oplus_000tc__Int__Oint) ).

fof(gsy_c_hAPP_000tc__Nat__Onat_000tc__Int__Oint,hypothesis,
    ! [X1,X2] : is_int(hAPP_nat_int(X1,X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__Int__Oint) ).

fof(gsy_c_Groups_Oone__class_Oone_000tc__Int__Oint,hypothesis,
    is_int(one_one_int),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Groups_Oone__class_Oone_000tc__Int__Oint) ).

fof(gsy_c_Groups_Ozero__class_Ozero_000tc__Int__Oint,hypothesis,
    is_int(zero_zero_int),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Groups_Ozero__class_Ozero_000tc__Int__Oint) ).

fof(fact_254_transfer__int__nat__numerals_I2_J,axiom,
    one_one_int = hAPP_nat_int(semiri1621563631at_int,one_one_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_transfer__int__nat__numerals_I2_J) ).

fof(fact_226_one__neq__zero,axiom,
    one_one_nat != zero_zero_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_one__neq__zero) ).

fof(c_0_17,plain,
    ! [X2084] : succ(bit0(X2084)) = bit1(X2084),
    inference(variable_rename,[status(thm)],[fact_809_succ__Bit0]) ).

fof(c_0_18,plain,
    ! [X535] : bit0(X535) = plus_plus_int(X535,X535),
    inference(variable_rename,[status(thm)],[fact_103_Bit0__def]) ).

fof(c_0_19,plain,
    ! [X2092] : succ(X2092) = plus_plus_int(X2092,one_one_int),
    inference(variable_rename,[status(thm)],[fact_814_succ__def]) ).

cnf(c_0_20,plain,
    succ(bit0(X1)) = bit1(X1),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_21,plain,
    bit0(X1) = plus_plus_int(X1,X1),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_22,plain,
    succ(X1) = plus_plus_int(X1,one_one_int),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

fof(c_0_23,negated_conjecture,
    hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int,
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])]) ).

fof(c_0_24,plain,
    ! [X1991] : number_number_of_nat(X1991) = nat(number_number_of_int(X1991)),
    inference(variable_rename,[status(thm)],[fact_767_nat__number__of__def]) ).

cnf(c_0_25,plain,
    plus_plus_int(one_one_int,one_one_int) = number_number_of_int(bit0(bit1(pls))),
    inference(split_conjunct,[status(thm)],[fact_16_one__add__one__is__two]) ).

cnf(c_0_26,plain,
    plus_plus_int(plus_plus_int(X1,X1),one_one_int) = bit1(X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).

cnf(c_0_27,plain,
    bit0(pls) = pls,
    inference(split_conjunct,[status(thm)],[fact_97_Bit0__Pls]) ).

fof(c_0_28,plain,
    ! [X721,X722] :
      ( ~ is_int(X722)
      | X722 = zero_zero_int
      | hAPP_nat_int(power_power_int(X722),X721) != zero_zero_int ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_231_field__power__not__zero])]) ).

cnf(c_0_29,negated_conjecture,
    hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int,
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

cnf(c_0_30,plain,
    number_number_of_nat(X1) = nat(number_number_of_int(X1)),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_31,plain,
    plus_plus_int(one_one_int,one_one_int) = number_number_of_int(plus_plus_int(plus_plus_int(plus_plus_int(pls,pls),one_one_int),plus_plus_int(plus_plus_int(pls,pls),one_one_int))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_21]),c_0_26]),c_0_26]) ).

cnf(c_0_32,plain,
    plus_plus_int(pls,pls) = pls,
    inference(rw,[status(thm)],[c_0_27,c_0_21]) ).

cnf(c_0_33,plain,
    ( X1 = zero_zero_int
    | ~ is_int(X1)
    | hAPP_nat_int(power_power_int(X1),X2) != zero_zero_int ),
    inference(split_conjunct,[status(thm)],[c_0_28]) ).

cnf(c_0_34,plain,
    pls = zero_zero_int,
    inference(split_conjunct,[status(thm)],[fact_98_Pls__def]) ).

cnf(c_0_35,negated_conjecture,
    hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),nat(number_number_of_int(plus_plus_int(plus_plus_int(plus_plus_int(pls,pls),one_one_int),plus_plus_int(plus_plus_int(pls,pls),one_one_int))))) = zero_zero_int,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_21]),c_0_30]),c_0_26]),c_0_26]) ).

cnf(c_0_36,plain,
    number_number_of_int(plus_plus_int(plus_plus_int(pls,one_one_int),plus_plus_int(pls,one_one_int))) = plus_plus_int(one_one_int,one_one_int),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32]),c_0_32]) ).

fof(c_0_37,plain,
    ! [X2083] :
      ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X2083)),zero_zero_int))
        | X2083 = zero_zero_nat )
      & ( X2083 != zero_zero_nat
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X2083)),zero_zero_int)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_807_int__le__0__conv])]) ).

fof(c_0_38,plain,
    ! [X2037,X2038,X2040] :
      ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2037),X2038))
        | X2038 = plus_plus_int(X2037,hAPP_nat_int(semiri1621563631at_int,esk14_2(X2037,X2038)))
        | ~ is_int(X2038) )
      & ( X2038 != plus_plus_int(X2037,hAPP_nat_int(semiri1621563631at_int,X2040))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2037),X2038))
        | ~ is_int(X2038) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_789_zle__iff__zadd])])])])]) ).

cnf(c_0_39,plain,
    ( X1 = pls
    | hAPP_nat_int(power_power_int(X1),X2) != pls
    | ~ is_int(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_34]),c_0_34]) ).

cnf(c_0_40,negated_conjecture,
    hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),nat(plus_plus_int(one_one_int,one_one_int))) = pls,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_32]),c_0_32]),c_0_36]),c_0_34]) ).

fof(c_0_41,hypothesis,
    ! [X406,X407] :
      ( ~ is_int(X406)
      | ~ is_int(X407)
      | is_int(plus_plus_int(X406,X407)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_Groups_Oplus__class_Oplus_000tc__Int__Oint])]) ).

fof(c_0_42,hypothesis,
    ! [X423,X424] : is_int(hAPP_nat_int(X423,X424)),
    inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__Nat__Onat_000tc__Int__Oint]) ).

cnf(c_0_43,plain,
    ( X1 = zero_zero_nat
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X1)),zero_zero_int)) ),
    inference(split_conjunct,[status(thm)],[c_0_37]) ).

cnf(c_0_44,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X1))
    | X1 != plus_plus_int(X2,hAPP_nat_int(semiri1621563631at_int,X3))
    | ~ is_int(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_38]) ).

cnf(c_0_45,negated_conjecture,
    ( plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)) = pls
    | ~ is_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))) ),
    inference(spm,[status(thm)],[c_0_39,c_0_40]) ).

cnf(c_0_46,hypothesis,
    ( is_int(plus_plus_int(X1,X2))
    | ~ is_int(X1)
    | ~ is_int(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_41]) ).

cnf(c_0_47,hypothesis,
    is_int(hAPP_nat_int(X1,X2)),
    inference(split_conjunct,[status(thm)],[c_0_42]) ).

cnf(c_0_48,hypothesis,
    is_int(one_one_int),
    inference(split_conjunct,[status(thm)],[gsy_c_Groups_Oone__class_Oone_000tc__Int__Oint]) ).

cnf(c_0_49,hypothesis,
    is_int(zero_zero_int),
    inference(split_conjunct,[status(thm)],[gsy_c_Groups_Ozero__class_Ozero_000tc__Int__Oint]) ).

cnf(c_0_50,plain,
    ( X1 = zero_zero_nat
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X1)),pls)) ),
    inference(rw,[status(thm)],[c_0_43,c_0_34]) ).

cnf(c_0_51,plain,
    one_one_int = hAPP_nat_int(semiri1621563631at_int,one_one_nat),
    inference(split_conjunct,[status(thm)],[fact_254_transfer__int__nat__numerals_I2_J]) ).

cnf(c_0_52,plain,
    one_one_nat != zero_zero_nat,
    inference(split_conjunct,[status(thm)],[fact_226_one__neq__zero]) ).

cnf(c_0_53,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),plus_plus_int(X1,hAPP_nat_int(semiri1621563631at_int,X2))))
    | ~ is_int(plus_plus_int(X1,hAPP_nat_int(semiri1621563631at_int,X2))) ),
    inference(er,[status(thm)],[c_0_44]) ).

cnf(c_0_54,hypothesis,
    plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)) = pls,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47]),c_0_48])]) ).

cnf(c_0_55,hypothesis,
    is_int(pls),
    inference(rw,[status(thm)],[c_0_49,c_0_34]) ).

cnf(c_0_56,plain,
    ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),pls)),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52]) ).

cnf(c_0_57,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_55])]),c_0_56]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : NUM925+3 : TPTP v8.1.2. Released v5.3.0.
% 0.11/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34  % Computer : n024.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Fri Aug 25 09:02:54 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.19/0.56  start to proof: theBenchmark
% 0.63/1.15  % Version  : CSE_E---1.5
% 0.63/1.15  % Problem  : theBenchmark.p
% 0.63/1.15  % Proof found
% 0.63/1.15  % SZS status Theorem for theBenchmark.p
% 0.63/1.15  % SZS output start Proof
% See solution above
% 0.63/1.16  % Total time : 0.540000 s
% 0.63/1.16  % SZS output end Proof
% 0.63/1.16  % Total time : 0.583000 s
%------------------------------------------------------------------------------