%------------------------------------------------------------------------------
% File     : Etableau---0.67
% Problem  : SET618+3 : TPTP v8.1.0. Released v2.2.0.
% 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 : n012.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 01:01:25 EDT 2022

% Result   : Theorem 0.21s 0.38s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   16 (  16 unt;   0 def)
%            Number of atoms       :   16 (  15 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    5 (   5   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    3 (   2 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   14 (   0 sgn  10   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(prove_th93,conjecture,
    ! [X1] : symmetric_difference(X1,X1) = empty_set,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th93) ).

fof(symmetric_difference_defn,axiom,
    ! [X1,X2] : symmetric_difference(X1,X2) = union(difference(X1,X2),difference(X2,X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetric_difference_defn) ).

fof(self_difference_is_empty_set,axiom,
    ! [X1] : difference(X1,X1) = empty_set,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',self_difference_is_empty_set) ).

fof(idempotency_of_union,axiom,
    ! [X1] : union(X1,X1) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotency_of_union) ).

fof(c_0_4,negated_conjecture,
    ~ ! [X1] : symmetric_difference(X1,X1) = empty_set,
    inference(assume_negation,[status(cth)],[prove_th93]) ).

fof(c_0_5,negated_conjecture,
    symmetric_difference(esk4_0,esk4_0) != empty_set,
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).

fof(c_0_6,plain,
    ! [X4,X5] : symmetric_difference(X4,X5) = union(difference(X4,X5),difference(X5,X4)),
    inference(variable_rename,[status(thm)],[symmetric_difference_defn]) ).

cnf(c_0_7,negated_conjecture,
    symmetric_difference(esk4_0,esk4_0) != empty_set,
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_8,plain,
    symmetric_difference(X1,X2) = union(difference(X1,X2),difference(X2,X1)),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

fof(c_0_9,plain,
    ! [X7] : difference(X7,X7) = empty_set,
    inference(variable_rename,[status(thm)],[self_difference_is_empty_set]) ).

cnf(c_0_10,negated_conjecture,
    union(difference(esk4_0,esk4_0),difference(esk4_0,esk4_0)) != empty_set,
    inference(rw,[status(thm)],[c_0_7,c_0_8]) ).

cnf(c_0_11,plain,
    difference(X1,X1) = empty_set,
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

fof(c_0_12,plain,
    ! [X6] : union(X6,X6) = X6,
    inference(variable_rename,[status(thm)],[idempotency_of_union]) ).

cnf(c_0_13,negated_conjecture,
    union(empty_set,empty_set) != empty_set,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_11]),c_0_11]) ).

cnf(c_0_14,plain,
    union(X1,X1) = X1,
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem  : SET618+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.13  % Command  : etableau --auto --tsmdo --quicksat=10000 --tableau=1 --tableau-saturation=1 -s -p --tableau-cores=8 --cpu-limit=%d %s
% 0.15/0.35  % Computer : n012.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit : 300
% 0.15/0.35  % WCLimit  : 600
% 0.15/0.35  % DateTime : Sun Jul 10 06:42:43 EDT 2022
% 0.15/0.35  % CPUTime  : 
% 0.21/0.38  # No SInE strategy applied
% 0.21/0.38  # Auto-Mode selected heuristic G_E___208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 0.21/0.38  # and selection function SelectComplexExceptUniqMaxHorn.
% 0.21/0.38  #
% 0.21/0.38  # Presaturation interreduction done
% 0.21/0.38  
% 0.21/0.38  # Proof found!
% 0.21/0.38  # SZS status Theorem
% 0.21/0.38  # SZS output start CNFRefutation
% See solution above
% 0.21/0.38  # Training examples: 0 positive, 0 negative
%------------------------------------------------------------------------------