%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SET617+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n027.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 14:34:52 EDT 2023

% Result   : Theorem 0.19s 0.59s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   36 (  18 unt;  11 typ;   0 def)
%            Number of atoms       :   32 (  31 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   19 (  12   ~;   5   |;   2   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   16 (   9   >;   7   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   2 con; 0-2 aty)
%            Number of variables   :   24 (   1 sgn;  16   !;   0   ?;   0   :)

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

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

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

tff(decl_25,type,
    empty_set: $i ).

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

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

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

tff(decl_29,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_30,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_31,type,
    esk3_1: $i > $i ).

tff(decl_32,type,
    esk4_0: $i ).

fof(prove_th92,conjecture,
    ! [X1] :
      ( symmetric_difference(X1,empty_set) = X1
      & symmetric_difference(empty_set,X1) = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th92) ).

fof(symmetric_difference_defn,axiom,
    ! [X1,X2] : symmetric_difference(X1,X2) = union(difference(X1,X2),difference(X2,X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetric_difference_defn) ).

fof(no_difference_with_empty_set2,axiom,
    ! [X1] : difference(empty_set,X1) = empty_set,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',no_difference_with_empty_set2) ).

fof(no_difference_with_empty_set1,axiom,
    ! [X1] : difference(X1,empty_set) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',no_difference_with_empty_set1) ).

fof(union_empty_set,axiom,
    ! [X1] : union(X1,empty_set) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_empty_set) ).

fof(commutativity_of_union,axiom,
    ! [X1,X2] : union(X1,X2) = union(X2,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_union) ).

fof(c_0_6,negated_conjecture,
    ~ ! [X1] :
        ( symmetric_difference(X1,empty_set) = X1
        & symmetric_difference(empty_set,X1) = X1 ),
    inference(assume_negation,[status(cth)],[prove_th92]) ).

fof(c_0_7,negated_conjecture,
    ( symmetric_difference(esk4_0,empty_set) != esk4_0
    | symmetric_difference(empty_set,esk4_0) != esk4_0 ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).

fof(c_0_8,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_9,negated_conjecture,
    ( symmetric_difference(esk4_0,empty_set) != esk4_0
    | symmetric_difference(empty_set,esk4_0) != esk4_0 ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_10,plain,
    symmetric_difference(X1,X2) = union(difference(X1,X2),difference(X2,X1)),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

fof(c_0_11,plain,
    ! [X8] : difference(empty_set,X8) = empty_set,
    inference(variable_rename,[status(thm)],[no_difference_with_empty_set2]) ).

cnf(c_0_12,negated_conjecture,
    ( union(difference(empty_set,esk4_0),difference(esk4_0,empty_set)) != esk4_0
    | union(difference(esk4_0,empty_set),difference(empty_set,esk4_0)) != esk4_0 ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_10]),c_0_10]) ).

cnf(c_0_13,plain,
    difference(empty_set,X1) = empty_set,
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

fof(c_0_14,plain,
    ! [X7] : difference(X7,empty_set) = X7,
    inference(variable_rename,[status(thm)],[no_difference_with_empty_set1]) ).

cnf(c_0_15,negated_conjecture,
    ( union(empty_set,difference(esk4_0,empty_set)) != esk4_0
    | union(difference(esk4_0,empty_set),empty_set) != esk4_0 ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_13]),c_0_13]) ).

cnf(c_0_16,plain,
    difference(X1,empty_set) = X1,
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

fof(c_0_17,plain,
    ! [X6] : union(X6,empty_set) = X6,
    inference(variable_rename,[status(thm)],[union_empty_set]) ).

fof(c_0_18,plain,
    ! [X12,X13] : union(X12,X13) = union(X13,X12),
    inference(variable_rename,[status(thm)],[commutativity_of_union]) ).

cnf(c_0_19,negated_conjecture,
    ( union(empty_set,esk4_0) != esk4_0
    | union(esk4_0,empty_set) != esk4_0 ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16]),c_0_16]) ).

cnf(c_0_20,plain,
    union(X1,empty_set) = X1,
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_21,plain,
    union(X1,X2) = union(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_22,negated_conjecture,
    union(empty_set,esk4_0) != esk4_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_20])]) ).

cnf(c_0_23,plain,
    union(empty_set,X1) = X1,
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_24,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SET617+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34  % Computer : n027.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Sat Aug 26 11:47:20 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.19/0.57  start to proof: theBenchmark
% 0.19/0.59  % Version  : CSE_E---1.5
% 0.19/0.59  % Problem  : theBenchmark.p
% 0.19/0.59  % Proof found
% 0.19/0.59  % SZS status Theorem for theBenchmark.p
% 0.19/0.59  % SZS output start Proof
% See solution above
% 0.19/0.59  % Total time : 0.007000 s
% 0.19/0.59  % SZS output end Proof
% 0.19/0.59  % Total time : 0.010000 s
%------------------------------------------------------------------------------