TSTP Solution File: SET979+1 by Etableau---0.67

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%------------------------------------------------------------------------------
% File     : Etableau---0.67
% Problem  : SET979+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : etableau --auto --tsmdo --quicksat=10000 --tableau=1 --tableau-saturation=1 -s -p --tableau-cores=8 --cpu-limit=%d %s

% Computer : n015.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  : 600s
% DateTime : Tue Jul 19 01:04:14 EDT 2022

% Result   : Theorem 0.19s 0.36s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   14 (   7 unt;   0 def)
%            Number of atoms       :   21 (  20 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   15 (   8   ~;   3   |;   4   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :   24 (   0 sgn  16   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(t132_zfmisc_1,conjecture,
    ! [X1,X2,X3] :
      ( cartesian_product2(unordered_pair(X1,X2),X3) = set_union2(cartesian_product2(singleton(X1),X3),cartesian_product2(singleton(X2),X3))
      & cartesian_product2(X3,unordered_pair(X1,X2)) = set_union2(cartesian_product2(X3,singleton(X1)),cartesian_product2(X3,singleton(X2))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t132_zfmisc_1) ).

fof(t41_enumset1,axiom,
    ! [X1,X2] : unordered_pair(X1,X2) = set_union2(singleton(X1),singleton(X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_enumset1) ).

fof(t120_zfmisc_1,axiom,
    ! [X1,X2,X3] :
      ( cartesian_product2(set_union2(X1,X2),X3) = set_union2(cartesian_product2(X1,X3),cartesian_product2(X2,X3))
      & cartesian_product2(X3,set_union2(X1,X2)) = set_union2(cartesian_product2(X3,X1),cartesian_product2(X3,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t120_zfmisc_1) ).

fof(c_0_3,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( cartesian_product2(unordered_pair(X1,X2),X3) = set_union2(cartesian_product2(singleton(X1),X3),cartesian_product2(singleton(X2),X3))
        & cartesian_product2(X3,unordered_pair(X1,X2)) = set_union2(cartesian_product2(X3,singleton(X1)),cartesian_product2(X3,singleton(X2))) ),
    inference(assume_negation,[status(cth)],[t132_zfmisc_1]) ).

fof(c_0_4,negated_conjecture,
    ( cartesian_product2(unordered_pair(esk3_0,esk4_0),esk5_0) != set_union2(cartesian_product2(singleton(esk3_0),esk5_0),cartesian_product2(singleton(esk4_0),esk5_0))
    | cartesian_product2(esk5_0,unordered_pair(esk3_0,esk4_0)) != set_union2(cartesian_product2(esk5_0,singleton(esk3_0)),cartesian_product2(esk5_0,singleton(esk4_0))) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).

fof(c_0_5,plain,
    ! [X21,X22] : unordered_pair(X21,X22) = set_union2(singleton(X21),singleton(X22)),
    inference(variable_rename,[status(thm)],[t41_enumset1]) ).

cnf(c_0_6,negated_conjecture,
    ( cartesian_product2(unordered_pair(esk3_0,esk4_0),esk5_0) != set_union2(cartesian_product2(singleton(esk3_0),esk5_0),cartesian_product2(singleton(esk4_0),esk5_0))
    | cartesian_product2(esk5_0,unordered_pair(esk3_0,esk4_0)) != set_union2(cartesian_product2(esk5_0,singleton(esk3_0)),cartesian_product2(esk5_0,singleton(esk4_0))) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_7,plain,
    unordered_pair(X1,X2) = set_union2(singleton(X1),singleton(X2)),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

fof(c_0_8,plain,
    ! [X15,X16,X17] :
      ( cartesian_product2(set_union2(X15,X16),X17) = set_union2(cartesian_product2(X15,X17),cartesian_product2(X16,X17))
      & cartesian_product2(X17,set_union2(X15,X16)) = set_union2(cartesian_product2(X17,X15),cartesian_product2(X17,X16)) ),
    inference(variable_rename,[status(thm)],[t120_zfmisc_1]) ).

cnf(c_0_9,negated_conjecture,
    ( cartesian_product2(esk5_0,set_union2(singleton(esk3_0),singleton(esk4_0))) != set_union2(cartesian_product2(esk5_0,singleton(esk3_0)),cartesian_product2(esk5_0,singleton(esk4_0)))
    | cartesian_product2(set_union2(singleton(esk3_0),singleton(esk4_0)),esk5_0) != set_union2(cartesian_product2(singleton(esk3_0),esk5_0),cartesian_product2(singleton(esk4_0),esk5_0)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6,c_0_7]),c_0_7]) ).

cnf(c_0_10,plain,
    cartesian_product2(X1,set_union2(X2,X3)) = set_union2(cartesian_product2(X1,X2),cartesian_product2(X1,X3)),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_11,negated_conjecture,
    set_union2(cartesian_product2(singleton(esk3_0),esk5_0),cartesian_product2(singleton(esk4_0),esk5_0)) != cartesian_product2(set_union2(singleton(esk3_0),singleton(esk4_0)),esk5_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_10])]) ).

cnf(c_0_12,plain,
    cartesian_product2(set_union2(X1,X2),X3) = set_union2(cartesian_product2(X1,X3),cartesian_product2(X2,X3)),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SET979+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12  % Command  : etableau --auto --tsmdo --quicksat=10000 --tableau=1 --tableau-saturation=1 -s -p --tableau-cores=8 --cpu-limit=%d %s
% 0.12/0.33  % Computer : n015.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Sat Jul  9 21:18:52 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.19/0.36  # No SInE strategy applied
% 0.19/0.36  # Auto-Mode selected heuristic G_E___208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI
% 0.19/0.36  # and selection function SelectComplexExceptUniqMaxHorn.
% 0.19/0.36  #
% 0.19/0.36  # Presaturation interreduction done
% 0.19/0.36  
% 0.19/0.36  # Proof found!
% 0.19/0.36  # SZS status Theorem
% 0.19/0.36  # SZS output start CNFRefutation
% See solution above
% 0.19/0.36  # Training examples: 0 positive, 0 negative
%------------------------------------------------------------------------------