%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SET619+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 : n024.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 0.20s 0.59s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   39 (  29 unt;  10 typ;   0 def)
%            Number of atoms       :   29 (  28 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    5 (   5   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   16 (   8   >;   8   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   2 con; 0-2 aty)
%            Number of variables   :   53 (   2 sgn;  30   !;   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,
    intersection: ( $i * $i ) > $i ).

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

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

tff(decl_28,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_29,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_30,type,
    esk3_0: $i ).

tff(decl_31,type,
    esk4_0: $i ).

fof(prove_th95,conjecture,
    ! [X1,X2] : union(X1,X2) = union(symmetric_difference(X1,X2),intersection(X1,X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th95) ).

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(associativity_of_union,axiom,
    ! [X1,X2,X3] : union(union(X1,X2),X3) = union(X1,union(X2,X3)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_union) ).

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

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

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

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_7,negated_conjecture,
    ~ ! [X1,X2] : union(X1,X2) = union(symmetric_difference(X1,X2),intersection(X1,X2)),
    inference(assume_negation,[status(cth)],[prove_th95]) ).

fof(c_0_8,negated_conjecture,
    union(esk3_0,esk4_0) != union(symmetric_difference(esk3_0,esk4_0),intersection(esk3_0,esk4_0)),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).

fof(c_0_9,plain,
    ! [X4,X5] : symmetric_difference(X4,X5) = union(difference(X4,X5),difference(X5,X4)),
    inference(variable_rename,[status(thm)],[symmetric_difference_defn]) ).

fof(c_0_10,plain,
    ! [X6,X7,X8] : union(union(X6,X7),X8) = union(X6,union(X7,X8)),
    inference(variable_rename,[status(thm)],[associativity_of_union]) ).

fof(c_0_11,plain,
    ! [X9,X10] : union(X9,intersection(X9,X10)) = X9,
    inference(variable_rename,[status(thm)],[union_intersection]) ).

fof(c_0_12,plain,
    ! [X11,X12] : union(intersection(X11,X12),difference(X11,X12)) = X11,
    inference(variable_rename,[status(thm)],[union_intersection_difference]) ).

fof(c_0_13,plain,
    ! [X23,X24] : intersection(X23,X24) = intersection(X24,X23),
    inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).

cnf(c_0_14,negated_conjecture,
    union(esk3_0,esk4_0) != union(symmetric_difference(esk3_0,esk4_0),intersection(esk3_0,esk4_0)),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_15,plain,
    symmetric_difference(X1,X2) = union(difference(X1,X2),difference(X2,X1)),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

fof(c_0_16,plain,
    ! [X21,X22] : union(X21,X22) = union(X22,X21),
    inference(variable_rename,[status(thm)],[commutativity_of_union]) ).

cnf(c_0_17,plain,
    union(union(X1,X2),X3) = union(X1,union(X2,X3)),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_18,plain,
    union(X1,intersection(X1,X2)) = X1,
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_19,plain,
    union(intersection(X1,X2),difference(X1,X2)) = X1,
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_20,plain,
    intersection(X1,X2) = intersection(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_21,negated_conjecture,
    union(esk3_0,esk4_0) != union(union(difference(esk3_0,esk4_0),difference(esk4_0,esk3_0)),intersection(esk3_0,esk4_0)),
    inference(rw,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_22,plain,
    union(X1,X2) = union(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_23,plain,
    union(X1,union(intersection(X1,X2),X3)) = union(X1,X3),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_24,plain,
    union(intersection(X1,X2),difference(X2,X1)) = X2,
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_25,negated_conjecture,
    union(intersection(esk3_0,esk4_0),union(difference(esk3_0,esk4_0),difference(esk4_0,esk3_0))) != union(esk3_0,esk4_0),
    inference(rw,[status(thm)],[c_0_21,c_0_22]) ).

cnf(c_0_26,plain,
    union(intersection(X1,X2),union(difference(X1,X2),X3)) = union(X1,X3),
    inference(spm,[status(thm)],[c_0_17,c_0_19]) ).

cnf(c_0_27,plain,
    union(X1,difference(X2,X1)) = union(X1,X2),
    inference(spm,[status(thm)],[c_0_23,c_0_24]) ).

cnf(c_0_28,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_26]),c_0_27])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : SET619+3 : TPTP v8.1.2. Released v2.2.0.
% 0.13/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35  % Computer : n024.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   : Sat Aug 26 13:52:39 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.57  start to proof: theBenchmark
% 0.20/0.59  % Version  : CSE_E---1.5
% 0.20/0.59  % Problem  : theBenchmark.p
% 0.20/0.59  % Proof found
% 0.20/0.59  % SZS status Theorem for theBenchmark.p
% 0.20/0.59  % SZS output start Proof
% See solution above
% 0.20/0.60  % Total time : 0.011000 s
% 0.20/0.60  % SZS output end Proof
% 0.20/0.60  % Total time : 0.014000 s
%------------------------------------------------------------------------------