TSTP Solution File: NUM925+2 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : NUM925+2 : 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 : n019.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 10:41:28 EDT 2023

% Result   : Theorem 0.19s 0.70s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   82
% Syntax   : Number of formulae    :  109 (  30 unt;  72 typ;   0 def)
%            Number of atoms       :   50 (  37 equ)
%            Maximal formula atoms :    7 (   1 avg)
%            Number of connectives :   27 (  14   ~;   8   |;   3   &)
%                                         (   1 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   2 avg)
%            Maximal term depth    :    9 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   83 (  50   >;  33   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :   70 (  70 usr;  22 con; 0-3 aty)
%            Number of variables   :   31 (   2 sgn;  18   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    fFalse: $i ).

tff(decl_23,type,
    is_bool: $i > $o ).

tff(decl_24,type,
    fTrue: $i ).

tff(decl_25,type,
    hAPP_int_bool: ( $i * $i ) > $i ).

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

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

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

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

tff(decl_30,type,
    hAPP_i1948725293t_bool: ( $i * $i ) > $i ).

tff(decl_31,type,
    one_one_int: $i ).

tff(decl_32,type,
    plus_plus_int: $i > $i ).

tff(decl_33,type,
    semiri1621563631at_int: $i ).

tff(decl_34,type,
    n: $i ).

tff(decl_35,type,
    hAPP_nat_int: ( $i * $i ) > $i ).

tff(decl_36,type,
    hAPP_int_int: ( $i * $i ) > $i ).

tff(decl_37,type,
    hBOOL: $i > $o ).

tff(decl_38,type,
    t: $i ).

tff(decl_39,type,
    power_power_int: $i > $i ).

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

tff(decl_41,type,
    bit1: $i > $i ).

tff(decl_42,type,
    bit0: $i > $i ).

tff(decl_43,type,
    number_number_of_nat: $i > $i ).

tff(decl_44,type,
    power_power_real: $i > $i ).

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

tff(decl_46,type,
    plus_plus_real: $i > $i ).

tff(decl_47,type,
    hAPP_real_real: ( $i * $i ) > $i ).

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

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

tff(decl_50,type,
    power_power_nat: $i > $i ).

tff(decl_51,type,
    hAPP_nat_nat: ( $i * $i ) > $i ).

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

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

tff(decl_54,type,
    number_number_of_int: $i > $i ).

tff(decl_55,type,
    number267125858f_real: $i > $i ).

tff(decl_56,type,
    plus_plus_nat: $i > $i ).

tff(decl_57,type,
    ord_less_nat: $i ).

tff(decl_58,type,
    hAPP_n1699378549t_bool: ( $i * $i ) > $i ).

tff(decl_59,type,
    ord_less_real: $i ).

tff(decl_60,type,
    hAPP_r1134773055l_bool: ( $i * $i ) > $i ).

tff(decl_61,type,
    semiri984289939at_nat: $i ).

tff(decl_62,type,
    semiri132038758t_real: $i ).

tff(decl_63,type,
    m1: $i ).

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

tff(decl_65,type,
    if_nat: ( $i * $i ) > $i ).

tff(decl_66,type,
    ord_less_eq_int: $i ).

tff(decl_67,type,
    succ: $i > $i ).

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

tff(decl_69,type,
    ord_less_eq_nat: $i ).

tff(decl_70,type,
    sqrt: $i > $i ).

tff(decl_71,type,
    times_times_int: ( $i * $i ) > $i ).

tff(decl_72,type,
    esk1_3: ( $i * $i * $i ) > $i ).

tff(decl_73,type,
    esk2_1: $i > $i ).

tff(decl_74,type,
    esk3_2: ( $i * $i ) > $i ).

tff(decl_75,type,
    esk4_2: ( $i * $i ) > $i ).

tff(decl_76,type,
    esk5_2: ( $i * $i ) > $i ).

tff(decl_77,type,
    esk6_1: $i > $i ).

tff(decl_78,type,
    esk7_1: $i > $i ).

tff(decl_79,type,
    esk8_1: $i > $i ).

tff(decl_80,type,
    esk9_1: $i > $i ).

tff(decl_81,type,
    esk10_2: ( $i * $i ) > $i ).

tff(decl_82,type,
    esk11_1: $i > $i ).

tff(decl_83,type,
    esk12_1: $i > $i ).

tff(decl_84,type,
    esk13_2: ( $i * $i ) > $i ).

tff(decl_85,type,
    esk14_2: ( $i * $i ) > $i ).

tff(decl_86,type,
    esk15_1: $i > $i ).

tff(decl_87,type,
    esk16_3: ( $i * $i * $i ) > $i ).

tff(decl_88,type,
    esk17_3: ( $i * $i * $i ) > $i ).

tff(decl_89,type,
    esk18_3: ( $i * $i * $i ) > $i ).

tff(decl_90,type,
    esk19_2: ( $i * $i ) > $i ).

tff(decl_91,type,
    esk20_3: ( $i * $i * $i ) > $i ).

tff(decl_92,type,
    esk21_3: ( $i * $i * $i ) > $i ).

tff(decl_93,type,
    esk22_2: ( $i * $i ) > $i ).

fof(fact_176_number__of__is__id,axiom,
    ! [X21] : number_number_of_int(X21) = X21,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_number__of__is__id) ).

fof(conj_0,conjecture,
    hAPP_nat_int(power_power_int(hAPP_int_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_568_succ__Bit0,axiom,
    ! [X21] : succ(bit0(X21)) = bit1(X21),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_568_succ__Bit0) ).

fof(fact_103_Bit0__def,axiom,
    ! [X21] : bit0(X21) = hAPP_int_int(plus_plus_int(X21),X21),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_Bit0__def) ).

fof(fact_573_succ__def,axiom,
    ! [X21] : succ(X21) = hAPP_int_int(plus_plus_int(X21),one_one_int),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_573_succ__def) ).

fof(fact_105_zadd__0,axiom,
    ! [X17] : hAPP_int_int(plus_plus_int(zero_zero_int),X17) = X17,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_zadd__0) ).

fof(fact_35_zero__is__num__zero,axiom,
    zero_zero_int = number_number_of_int(pls),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_zero__is__num__zero) ).

fof(fact_231_field__power__not__zero,axiom,
    ! [X64,X65] :
      ( X65 != zero_zero_int
     => hAPP_nat_int(power_power_int(X65),X64) != zero_zero_int ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_field__power__not__zero) ).

fof(fact_447_zless__le,axiom,
    ! [X30,X25] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X30),X25))
    <=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X30),X25))
        & X30 != X25 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_447_zless__le) ).

fof(fact_0_n1pos,axiom,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_n1pos) ).

fof(c_0_10,plain,
    ! [X485] : number_number_of_int(X485) = X485,
    inference(variable_rename,[status(thm)],[fact_176_number__of__is__id]) ).

fof(c_0_11,negated_conjecture,
    hAPP_nat_int(power_power_int(hAPP_int_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_12,plain,
    ! [X1283] : succ(bit0(X1283)) = bit1(X1283),
    inference(variable_rename,[status(thm)],[fact_568_succ__Bit0]) ).

fof(c_0_13,plain,
    ! [X398] : bit0(X398) = hAPP_int_int(plus_plus_int(X398),X398),
    inference(variable_rename,[status(thm)],[fact_103_Bit0__def]) ).

fof(c_0_14,plain,
    ! [X1291] : succ(X1291) = hAPP_int_int(plus_plus_int(X1291),one_one_int),
    inference(variable_rename,[status(thm)],[fact_573_succ__def]) ).

fof(c_0_15,plain,
    ! [X400] : hAPP_int_int(plus_plus_int(zero_zero_int),X400) = X400,
    inference(variable_rename,[status(thm)],[fact_105_zadd__0]) ).

cnf(c_0_16,plain,
    zero_zero_int = number_number_of_int(pls),
    inference(split_conjunct,[status(thm)],[fact_35_zero__is__num__zero]) ).

cnf(c_0_17,plain,
    number_number_of_int(X1) = X1,
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

fof(c_0_18,plain,
    ! [X586,X587] :
      ( X587 = zero_zero_int
      | hAPP_nat_int(power_power_int(X587),X586) != zero_zero_int ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_231_field__power__not__zero])]) ).

cnf(c_0_19,negated_conjecture,
    hAPP_nat_int(power_power_int(hAPP_int_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_11]) ).

cnf(c_0_20,plain,
    succ(bit0(X1)) = bit1(X1),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_21,plain,
    bit0(X1) = hAPP_int_int(plus_plus_int(X1),X1),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_22,plain,
    succ(X1) = hAPP_int_int(plus_plus_int(X1),one_one_int),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_23,plain,
    hAPP_int_int(plus_plus_int(zero_zero_int),X1) = X1,
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_24,plain,
    pls = zero_zero_int,
    inference(rw,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_25,plain,
    ( X1 = zero_zero_int
    | hAPP_nat_int(power_power_int(X1),X2) != zero_zero_int ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_26,negated_conjecture,
    hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(pls),pls)),one_one_int)),hAPP_int_int(plus_plus_int(hAPP_int_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)],[inference(rw,[status(thm)],[c_0_19,c_0_20]),c_0_21]),c_0_21]),c_0_22]),c_0_22]) ).

cnf(c_0_27,plain,
    hAPP_int_int(plus_plus_int(pls),X1) = X1,
    inference(rw,[status(thm)],[c_0_23,c_0_24]) ).

fof(c_0_28,plain,
    ! [X1038,X1039] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1038),X1039))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1038),X1039)) )
      & ( X1038 != X1039
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1038),X1039)) )
      & ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1038),X1039))
        | X1038 = X1039
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1038),X1039)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_447_zless__le])])]) ).

cnf(c_0_29,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))),
    inference(split_conjunct,[status(thm)],[fact_0_n1pos]) ).

cnf(c_0_30,plain,
    ( X1 = pls
    | hAPP_nat_int(power_power_int(X1),X2) != pls ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_24]),c_0_24]) ).

cnf(c_0_31,negated_conjecture,
    hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(hAPP_int_int(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)],[inference(rw,[status(thm)],[c_0_26,c_0_27]),c_0_27]),c_0_27]),c_0_27]),c_0_24]) ).

cnf(c_0_32,plain,
    ( X1 != X2
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_28]) ).

cnf(c_0_33,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))),
    inference(rw,[status(thm)],[c_0_29,c_0_24]) ).

cnf(c_0_34,negated_conjecture,
    hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) = pls,
    inference(spm,[status(thm)],[c_0_30,c_0_31]) ).

cnf(c_0_35,plain,
    ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X1)),
    inference(er,[status(thm)],[c_0_32]) ).

cnf(c_0_36,plain,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_34]),c_0_35]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : NUM925+2 : TPTP v8.1.2. Released v5.3.0.
% 0.00/0.12  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.33  % Computer : n019.cluster.edu
% 0.14/0.33  % Model    : x86_64 x86_64
% 0.14/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33  % Memory   : 8042.1875MB
% 0.14/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33  % CPULimit   : 300
% 0.14/0.33  % WCLimit    : 300
% 0.14/0.33  % DateTime   : Fri Aug 25 13:32:58 EDT 2023
% 0.14/0.34  % CPUTime  : 
% 0.19/0.57  start to proof: theBenchmark
% 0.19/0.70  % Version  : CSE_E---1.5
% 0.19/0.70  % Problem  : theBenchmark.p
% 0.19/0.70  % Proof found
% 0.19/0.70  % SZS status Theorem for theBenchmark.p
% 0.19/0.70  % SZS output start Proof
% See solution above
% 0.19/0.71  % Total time : 0.105000 s
% 0.19/0.71  % SZS output end Proof
% 0.19/0.71  % Total time : 0.129000 s
%------------------------------------------------------------------------------