TSTP Solution File: SEU189+2 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU189+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n017.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 16:23:11 EDT 2023

% Result   : Theorem 0.19s 0.65s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   85
% Syntax   : Number of formulae    :   98 (   5 unt;  82 typ;   0 def)
%            Number of atoms       :   40 (  30 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   37 (  13   ~;  14   |;   4   &)
%                                         (   2 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  155 (  76   >;  79   *;   0   +;   0  <<)
%            Number of predicates  :   10 (   8 usr;   1 prp; 0-2 aty)
%            Number of functors    :   74 (  74 usr;   6 con; 0-5 aty)
%            Number of variables   :    6 (   0 sgn;   4   !;   0   ?;   0   :)

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

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

tff(decl_24,type,
    empty: $i > $o ).

tff(decl_25,type,
    relation: $i > $o ).

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

tff(decl_27,type,
    set_union2: ( $i * $i ) > $i ).

tff(decl_28,type,
    set_intersection2: ( $i * $i ) > $i ).

tff(decl_29,type,
    subset: ( $i * $i ) > $o ).

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

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

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

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

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

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

tff(decl_36,type,
    cartesian_product2: ( $i * $i ) > $i ).

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

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

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

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

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

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

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

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

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

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

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

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

tff(decl_49,type,
    meet_of_subsets: ( $i * $i ) > $i ).

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

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

tff(decl_52,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_53,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_54,type,
    esk3_1: $i > $i ).

tff(decl_55,type,
    esk4_3: ( $i * $i * $i ) > $i ).

tff(decl_56,type,
    esk5_2: ( $i * $i ) > $i ).

tff(decl_57,type,
    esk6_2: ( $i * $i ) > $i ).

tff(decl_58,type,
    esk7_2: ( $i * $i ) > $i ).

tff(decl_59,type,
    esk8_1: $i > $i ).

tff(decl_60,type,
    esk9_2: ( $i * $i ) > $i ).

tff(decl_61,type,
    esk10_3: ( $i * $i * $i ) > $i ).

tff(decl_62,type,
    esk11_3: ( $i * $i * $i ) > $i ).

tff(decl_63,type,
    esk12_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_64,type,
    esk13_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_65,type,
    esk14_3: ( $i * $i * $i ) > $i ).

tff(decl_66,type,
    esk15_3: ( $i * $i * $i ) > $i ).

tff(decl_67,type,
    esk16_3: ( $i * $i * $i ) > $i ).

tff(decl_68,type,
    esk17_2: ( $i * $i ) > $i ).

tff(decl_69,type,
    esk18_3: ( $i * $i * $i ) > $i ).

tff(decl_70,type,
    esk19_3: ( $i * $i * $i ) > $i ).

tff(decl_71,type,
    esk20_2: ( $i * $i ) > $i ).

tff(decl_72,type,
    esk21_2: ( $i * $i ) > $i ).

tff(decl_73,type,
    esk22_3: ( $i * $i * $i ) > $i ).

tff(decl_74,type,
    esk23_2: ( $i * $i ) > $i ).

tff(decl_75,type,
    esk24_2: ( $i * $i ) > $i ).

tff(decl_76,type,
    esk25_3: ( $i * $i * $i ) > $i ).

tff(decl_77,type,
    esk26_3: ( $i * $i * $i ) > $i ).

tff(decl_78,type,
    esk27_2: ( $i * $i ) > $i ).

tff(decl_79,type,
    esk28_2: ( $i * $i ) > $i ).

tff(decl_80,type,
    esk29_2: ( $i * $i ) > $i ).

tff(decl_81,type,
    esk30_2: ( $i * $i ) > $i ).

tff(decl_82,type,
    esk31_5: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_83,type,
    esk32_3: ( $i * $i * $i ) > $i ).

tff(decl_84,type,
    esk33_3: ( $i * $i * $i ) > $i ).

tff(decl_85,type,
    esk34_3: ( $i * $i * $i ) > $i ).

tff(decl_86,type,
    esk35_3: ( $i * $i * $i ) > $i ).

tff(decl_87,type,
    esk36_1: $i > $i ).

tff(decl_88,type,
    esk37_2: ( $i * $i ) > $i ).

tff(decl_89,type,
    esk38_0: $i ).

tff(decl_90,type,
    esk39_1: $i > $i ).

tff(decl_91,type,
    esk40_0: $i ).

tff(decl_92,type,
    esk41_0: $i ).

tff(decl_93,type,
    esk42_1: $i > $i ).

tff(decl_94,type,
    esk43_0: $i ).

tff(decl_95,type,
    esk44_1: $i > $i ).

tff(decl_96,type,
    esk45_2: ( $i * $i ) > $i ).

tff(decl_97,type,
    esk46_2: ( $i * $i ) > $i ).

tff(decl_98,type,
    esk47_2: ( $i * $i ) > $i ).

tff(decl_99,type,
    esk48_1: $i > $i ).

tff(decl_100,type,
    esk49_1: $i > $i ).

tff(decl_101,type,
    esk50_0: $i ).

tff(decl_102,type,
    esk51_1: $i > $i ).

tff(decl_103,type,
    esk52_2: ( $i * $i ) > $i ).

fof(t65_relat_1,conjecture,
    ! [X1] :
      ( relation(X1)
     => ( relation_dom(X1) = empty_set
      <=> relation_rng(X1) = empty_set ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_relat_1) ).

fof(t64_relat_1,lemma,
    ! [X1] :
      ( relation(X1)
     => ( ( relation_dom(X1) = empty_set
          | relation_rng(X1) = empty_set )
       => X1 = empty_set ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_relat_1) ).

fof(t60_relat_1,lemma,
    ( relation_dom(empty_set) = empty_set
    & relation_rng(empty_set) = empty_set ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_relat_1) ).

fof(c_0_3,negated_conjecture,
    ~ ! [X1] :
        ( relation(X1)
       => ( relation_dom(X1) = empty_set
        <=> relation_rng(X1) = empty_set ) ),
    inference(assume_negation,[status(cth)],[t65_relat_1]) ).

fof(c_0_4,lemma,
    ! [X414] :
      ( ( relation_dom(X414) != empty_set
        | X414 = empty_set
        | ~ relation(X414) )
      & ( relation_rng(X414) != empty_set
        | X414 = empty_set
        | ~ relation(X414) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t64_relat_1])])]) ).

fof(c_0_5,negated_conjecture,
    ( relation(esk50_0)
    & ( relation_dom(esk50_0) != empty_set
      | relation_rng(esk50_0) != empty_set )
    & ( relation_dom(esk50_0) = empty_set
      | relation_rng(esk50_0) = empty_set ) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).

cnf(c_0_6,lemma,
    ( X1 = empty_set
    | relation_rng(X1) != empty_set
    | ~ relation(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_7,negated_conjecture,
    ( relation_dom(esk50_0) = empty_set
    | relation_rng(esk50_0) = empty_set ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_8,negated_conjecture,
    relation(esk50_0),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_9,lemma,
    ( X1 = empty_set
    | relation_dom(X1) != empty_set
    | ~ relation(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_10,negated_conjecture,
    ( relation_dom(esk50_0) = empty_set
    | esk50_0 = empty_set ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_7]),c_0_8])]) ).

cnf(c_0_11,negated_conjecture,
    ( relation_dom(esk50_0) != empty_set
    | relation_rng(esk50_0) != empty_set ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_12,lemma,
    esk50_0 = empty_set,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_8])]) ).

cnf(c_0_13,lemma,
    relation_dom(empty_set) = empty_set,
    inference(split_conjunct,[status(thm)],[t60_relat_1]) ).

cnf(c_0_14,lemma,
    relation_rng(empty_set) = empty_set,
    inference(split_conjunct,[status(thm)],[t60_relat_1]) ).

cnf(c_0_15,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_12]),c_0_13]),c_0_12]),c_0_14])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SEU189+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n017.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Wed Aug 23 15:58:08 EDT 2023
% 0.19/0.34  % CPUTime  : 
% 0.19/0.54  start to proof: theBenchmark
% 0.19/0.65  % Version  : CSE_E---1.5
% 0.19/0.65  % Problem  : theBenchmark.p
% 0.19/0.65  % Proof found
% 0.19/0.65  % SZS status Theorem for theBenchmark.p
% 0.19/0.65  % SZS output start Proof
% See solution above
% 0.19/0.65  % Total time : 0.097000 s
% 0.19/0.65  % SZS output end Proof
% 0.19/0.65  % Total time : 0.103000 s
%------------------------------------------------------------------------------