%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU161+3 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n019.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 16:22:56 EDT 2023

% Result   : Theorem 0.21s 0.61s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   22 (   7 unt;   8 typ;   0 def)
%            Number of atoms       :   21 (  12 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   14 (   7   ~;   3   |;   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  :    6 (   4   >;   2   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :   18 (   0 sgn;  12   !;   0   ?;   0   :)

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

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

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

tff(decl_25,type,
    singleton: $i > $i ).

tff(decl_26,type,
    esk1_0: $i ).

tff(decl_27,type,
    esk2_0: $i ).

tff(decl_28,type,
    esk3_0: $i ).

tff(decl_29,type,
    esk4_0: $i ).

fof(t46_zfmisc_1,conjecture,
    ! [X1,X2] :
      ( in(X1,X2)
     => set_union2(singleton(X1),X2) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_zfmisc_1) ).

fof(commutativity_k2_xboole_0,axiom,
    ! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).

fof(l23_zfmisc_1,axiom,
    ! [X1,X2] :
      ( in(X1,X2)
     => set_union2(singleton(X1),X2) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l23_zfmisc_1) ).

fof(c_0_3,negated_conjecture,
    ~ ! [X1,X2] :
        ( in(X1,X2)
       => set_union2(singleton(X1),X2) = X2 ),
    inference(assume_negation,[status(cth)],[t46_zfmisc_1]) ).

fof(c_0_4,negated_conjecture,
    ( in(esk3_0,esk4_0)
    & set_union2(singleton(esk3_0),esk4_0) != esk4_0 ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).

fof(c_0_5,plain,
    ! [X7,X8] : set_union2(X7,X8) = set_union2(X8,X7),
    inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).

fof(c_0_6,plain,
    ! [X16,X17] :
      ( ~ in(X16,X17)
      | set_union2(singleton(X16),X17) = X17 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l23_zfmisc_1])]) ).

cnf(c_0_7,negated_conjecture,
    set_union2(singleton(esk3_0),esk4_0) != esk4_0,
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

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

cnf(c_0_9,plain,
    ( set_union2(singleton(X1),X2) = X2
    | ~ in(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_10,negated_conjecture,
    set_union2(esk4_0,singleton(esk3_0)) != esk4_0,
    inference(rw,[status(thm)],[c_0_7,c_0_8]) ).

cnf(c_0_11,plain,
    ( set_union2(X1,singleton(X2)) = X1
    | ~ in(X2,X1) ),
    inference(spm,[status(thm)],[c_0_8,c_0_9]) ).

cnf(c_0_12,negated_conjecture,
    in(esk3_0,esk4_0),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_13,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SEU161+3 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35  % Computer : n019.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Wed Aug 23 17:45:13 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.21/0.59  start to proof: theBenchmark
% 0.21/0.61  % Version  : CSE_E---1.5
% 0.21/0.61  % Problem  : theBenchmark.p
% 0.21/0.61  % Proof found
% 0.21/0.61  % SZS status Theorem for theBenchmark.p
% 0.21/0.61  % SZS output start Proof
% See solution above
% 0.21/0.61  % Total time : 0.006000 s
% 0.21/0.61  % SZS output end Proof
% 0.21/0.61  % Total time : 0.009000 s
%------------------------------------------------------------------------------