%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU137+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 : n011.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 16:22:40 EDT 2023

% Result   : Theorem 0.18s 0.58s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   23
% Syntax   : Number of formulae    :   33 (   7 unt;  20 typ;   0 def)
%            Number of atoms       :   19 (  11 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   12 (   6   ~;   2   |;   1   &)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   31 (  15   >;  16   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   16 (  16 usr;   5 con; 0-3 aty)
%            Number of variables   :   16 (   0 sgn;  12   !;   0   ?;   0   :)

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

tff(decl_23,type,
    set_union2: ( $i * $i ) > $i ).

tff(decl_24,type,
    set_intersection2: ( $i * $i ) > $i ).

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

tff(decl_26,type,
    empty_set: $i ).

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

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

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

tff(decl_30,type,
    esk1_1: $i > $i ).

tff(decl_31,type,
    esk2_3: ( $i * $i * $i ) > $i ).

tff(decl_32,type,
    esk3_2: ( $i * $i ) > $i ).

tff(decl_33,type,
    esk4_3: ( $i * $i * $i ) > $i ).

tff(decl_34,type,
    esk5_3: ( $i * $i * $i ) > $i ).

tff(decl_35,type,
    esk6_0: $i ).

tff(decl_36,type,
    esk7_0: $i ).

tff(decl_37,type,
    esk8_2: ( $i * $i ) > $i ).

tff(decl_38,type,
    esk9_2: ( $i * $i ) > $i ).

tff(decl_39,type,
    esk10_0: $i ).

tff(decl_40,type,
    esk11_0: $i ).

tff(decl_41,type,
    esk12_2: ( $i * $i ) > $i ).

fof(t45_xboole_1,conjecture,
    ! [X1,X2] :
      ( subset(X1,X2)
     => X2 = set_union2(X1,set_difference(X2,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_xboole_1) ).

fof(t39_xboole_1,lemma,
    ! [X1,X2] : set_union2(X1,set_difference(X2,X1)) = set_union2(X1,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_xboole_1) ).

fof(t12_xboole_1,lemma,
    ! [X1,X2] :
      ( subset(X1,X2)
     => set_union2(X1,X2) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_xboole_1) ).

fof(c_0_3,negated_conjecture,
    ~ ! [X1,X2] :
        ( subset(X1,X2)
       => X2 = set_union2(X1,set_difference(X2,X1)) ),
    inference(assume_negation,[status(cth)],[t45_xboole_1]) ).

fof(c_0_4,negated_conjecture,
    ( subset(esk10_0,esk11_0)
    & esk11_0 != set_union2(esk10_0,set_difference(esk11_0,esk10_0)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).

fof(c_0_5,lemma,
    ! [X93,X94] : set_union2(X93,set_difference(X94,X93)) = set_union2(X93,X94),
    inference(variable_rename,[status(thm)],[t39_xboole_1]) ).

fof(c_0_6,lemma,
    ! [X65,X66] :
      ( ~ subset(X65,X66)
      | set_union2(X65,X66) = X66 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t12_xboole_1])]) ).

cnf(c_0_7,negated_conjecture,
    esk11_0 != set_union2(esk10_0,set_difference(esk11_0,esk10_0)),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_8,lemma,
    set_union2(X1,set_difference(X2,X1)) = set_union2(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_9,lemma,
    ( set_union2(X1,X2) = X2
    | ~ subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_10,negated_conjecture,
    subset(esk10_0,esk11_0),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_11,negated_conjecture,
    set_union2(esk10_0,esk11_0) != esk11_0,
    inference(rw,[status(thm)],[c_0_7,c_0_8]) ).

cnf(c_0_12,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SEU137+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.12  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.33  % Computer : n011.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit   : 300
% 0.13/0.33  % WCLimit    : 300
% 0.13/0.33  % DateTime   : Wed Aug 23 23:13:07 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.18/0.56  start to proof: theBenchmark
% 0.18/0.58  % Version  : CSE_E---1.5
% 0.18/0.58  % Problem  : theBenchmark.p
% 0.18/0.58  % Proof found
% 0.18/0.58  % SZS status Theorem for theBenchmark.p
% 0.18/0.58  % SZS output start Proof
% See solution above
% 0.18/0.58  % Total time : 0.014000 s
% 0.18/0.58  % SZS output end Proof
% 0.18/0.58  % Total time : 0.017000 s
%------------------------------------------------------------------------------