TSTP Solution File: NUM009-1 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : NUM009-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/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 10:26:07 EDT 2023

% Result   : Unsatisfiable 0.20s 0.63s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :  115
% Syntax   : Number of formulae    :  122 (   6 unt; 110 typ;   0 def)
%            Number of atoms       :   20 (   0 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   16 (   8   ~;   8   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  183 (  98   >;  85   *;   0   +;   0  <<)
%            Number of predicates  :   20 (  19 usr;   1 prp; 0-5 aty)
%            Number of functors    :   91 (  91 usr;  12 con; 0-5 aty)
%            Number of variables   :    8 (   2 sgn;   0   !;   0   ?;   0   :)

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

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

tff(decl_24,type,
    f1: ( $i * $i ) > $i ).

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

tff(decl_26,type,
    singleton_set: $i > $i ).

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

tff(decl_28,type,
    ordered_pair_predicate: $i > $o ).

tff(decl_29,type,
    f2: $i > $i ).

tff(decl_30,type,
    f3: $i > $i ).

tff(decl_31,type,
    first: $i > $i ).

tff(decl_32,type,
    f4: ( $i * $i ) > $i ).

tff(decl_33,type,
    f5: ( $i * $i ) > $i ).

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

tff(decl_35,type,
    f6: ( $i * $i ) > $i ).

tff(decl_36,type,
    f7: ( $i * $i ) > $i ).

tff(decl_37,type,
    estin: $i ).

tff(decl_38,type,
    intersection: ( $i * $i ) > $i ).

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

tff(decl_40,type,
    union: ( $i * $i ) > $i ).

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

tff(decl_42,type,
    f8: ( $i * $i ) > $i ).

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

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

tff(decl_45,type,
    rotate_right: $i > $i ).

tff(decl_46,type,
    f9: ( $i * $i ) > $i ).

tff(decl_47,type,
    f10: ( $i * $i ) > $i ).

tff(decl_48,type,
    f11: ( $i * $i ) > $i ).

tff(decl_49,type,
    flip_range_of: $i > $i ).

tff(decl_50,type,
    f12: ( $i * $i ) > $i ).

tff(decl_51,type,
    f13: ( $i * $i ) > $i ).

tff(decl_52,type,
    f14: ( $i * $i ) > $i ).

tff(decl_53,type,
    successor: $i > $i ).

tff(decl_54,type,
    empty_set: $i ).

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

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

tff(decl_57,type,
    sigma: $i > $i ).

tff(decl_58,type,
    f16: ( $i * $i ) > $i ).

tff(decl_59,type,
    subset: ( $i * $i ) > $o ).

tff(decl_60,type,
    f17: ( $i * $i ) > $i ).

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

tff(decl_62,type,
    powerset: $i > $i ).

tff(decl_63,type,
    relation: $i > $o ).

tff(decl_64,type,
    f18: $i > $i ).

tff(decl_65,type,
    single_valued_set: $i > $o ).

tff(decl_66,type,
    f19: $i > $i ).

tff(decl_67,type,
    f20: $i > $i ).

tff(decl_68,type,
    f21: $i > $i ).

tff(decl_69,type,
    function: $i > $o ).

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

tff(decl_71,type,
    f22: ( $i * $i * $i ) > $i ).

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

tff(decl_73,type,
    f23: ( $i * $i ) > $i ).

tff(decl_74,type,
    f24: $i > $i ).

tff(decl_75,type,
    f25: $i ).

tff(decl_76,type,
    f26: $i > $i ).

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

tff(decl_78,type,
    f27: ( $i * $i ) > $i ).

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

tff(decl_80,type,
    restrict: ( $i * $i ) > $i ).

tff(decl_81,type,
    one_to_one_function: $i > $o ).

tff(decl_82,type,
    apply: ( $i * $i ) > $i ).

tff(decl_83,type,
    f28: ( $i * $i * $i ) > $i ).

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

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

tff(decl_86,type,
    closed: ( $i * $i ) > $o ).

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

tff(decl_88,type,
    f29: ( $i * $i * $i ) > $i ).

tff(decl_89,type,
    f30: ( $i * $i * $i ) > $i ).

tff(decl_90,type,
    f31: ( $i * $i * $i ) > $i ).

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

tff(decl_92,type,
    f32: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_93,type,
    f33: ( $i * $i * $i * $i * $i ) > $i ).

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

tff(decl_95,type,
    f34: ( $i * $i ) > $i ).

tff(decl_96,type,
    f35: ( $i * $i ) > $i ).

tff(decl_97,type,
    f36: ( $i * $i ) > $i ).

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

tff(decl_99,type,
    f37: ( $i * $i * $i ) > $i ).

tff(decl_100,type,
    inverse: ( $i * $i * $i * $i ) > $o ).

tff(decl_101,type,
    f38: ( $i * $i * $i * $i ) > $i ).

tff(decl_102,type,
    group: ( $i * $i ) > $o ).

tff(decl_103,type,
    f39: ( $i * $i ) > $i ).

tff(decl_104,type,
    f40: ( $i * $i ) > $i ).

tff(decl_105,type,
    commutes: ( $i * $i ) > $o ).

tff(decl_106,type,
    f41: ( $i * $i ) > $i ).

tff(decl_107,type,
    f42: ( $i * $i ) > $i ).

tff(decl_108,type,
    natural_numbers: $i ).

tff(decl_109,type,
    f43: ( $i * $i ) > $i ).

tff(decl_110,type,
    f44: $i > $i ).

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

tff(decl_112,type,
    f45: ( $i * $i ) > $i ).

tff(decl_113,type,
    f46: ( $i * $i ) > $i ).

tff(decl_114,type,
    f47: ( $i * $i ) > $i ).

tff(decl_115,type,
    f48: ( $i * $i ) > $i ).

tff(decl_116,type,
    f49: $i > $i ).

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

tff(decl_118,type,
    f50: ( $i * $i ) > $i ).

tff(decl_119,type,
    f51: ( $i * $i ) > $i ).

tff(decl_120,type,
    f52: ( $i * $i ) > $i ).

tff(decl_121,type,
    f53: ( $i * $i ) > $i ).

tff(decl_122,type,
    f54: $i > $i ).

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

tff(decl_124,type,
    f55: $i > $i ).

tff(decl_125,type,
    f56: $i > $i ).

tff(decl_126,type,
    finite: $i > $o ).

tff(decl_127,type,
    f57: $i > $i ).

tff(decl_128,type,
    f58: $i > $i ).

tff(decl_129,type,
    twin_prime_numbers: $i ).

tff(decl_130,type,
    even_numbers: $i ).

tff(decl_131,type,
    f59: $i > $i ).

cnf(a2,axiom,
    ( little_set(X1)
    | ~ member(X1,X2) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',a2) ).

cnf(infinity2,axiom,
    member(empty_set,infinity),
    file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',infinity2) ).

cnf(natural_numbers6,axiom,
    ( member(X1,natural_numbers)
    | ~ member(X1,f44(X1)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/NUM003-0.ax',natural_numbers6) ).

cnf(natural_numbers4,axiom,
    ( member(X1,natural_numbers)
    | member(empty_set,f44(X1))
    | ~ little_set(X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/NUM003-0.ax',natural_numbers4) ).

cnf(prove_zero_is_a_natural,negated_conjecture,
    ~ member(empty_set,natural_numbers),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_zero_is_a_natural) ).

cnf(c_0_5,axiom,
    ( little_set(X1)
    | ~ member(X1,X2) ),
    a2 ).

cnf(c_0_6,axiom,
    member(empty_set,infinity),
    infinity2 ).

cnf(c_0_7,axiom,
    ( member(X1,natural_numbers)
    | ~ member(X1,f44(X1)) ),
    natural_numbers6 ).

cnf(c_0_8,axiom,
    ( member(X1,natural_numbers)
    | member(empty_set,f44(X1))
    | ~ little_set(X1) ),
    natural_numbers4 ).

cnf(c_0_9,plain,
    little_set(empty_set),
    inference(spm,[status(thm)],[c_0_5,c_0_6]) ).

cnf(c_0_10,negated_conjecture,
    ~ member(empty_set,natural_numbers),
    prove_zero_is_a_natural ).

cnf(c_0_11,plain,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_9])]),c_0_10]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : NUM009-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35  % Computer : n019.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Fri Aug 25 15:57:58 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.59  start to proof: theBenchmark
% 0.20/0.63  % Version  : CSE_E---1.5
% 0.20/0.63  % Problem  : theBenchmark.p
% 0.20/0.63  % Proof found
% 0.20/0.63  % SZS status Theorem for theBenchmark.p
% 0.20/0.63  % SZS output start Proof
% See solution above
% 0.20/0.64  % Total time : 0.027000 s
% 0.20/0.64  % SZS output end Proof
% 0.20/0.64  % Total time : 0.034000 s
%------------------------------------------------------------------------------