%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU150+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n022.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 16:22:48 EDT 2023

% Result   : Theorem 0.20s 0.57s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   22 (   8 unt;   5 typ;   0 def)
%            Number of atoms       :   26 (  25 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   17 (   8   ~;   5   |;   1   &)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    3 (   2   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   28 (   4 sgn;  16   !;   0   ?;   0   :)

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

tff(decl_23,type,
    singleton: $i > $i ).

tff(decl_24,type,
    esk1_0: $i ).

tff(decl_25,type,
    esk2_0: $i ).

tff(decl_26,type,
    esk3_0: $i ).

fof(t9_zfmisc_1,conjecture,
    ! [X1,X2,X3] :
      ( singleton(X1) = unordered_pair(X2,X3)
     => X2 = X3 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_zfmisc_1) ).

fof(t8_zfmisc_1,axiom,
    ! [X1,X2,X3] :
      ( singleton(X1) = unordered_pair(X2,X3)
     => X1 = X2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_zfmisc_1) ).

fof(commutativity_k2_tarski,axiom,
    ! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).

fof(c_0_3,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( singleton(X1) = unordered_pair(X2,X3)
       => X2 = X3 ),
    inference(assume_negation,[status(cth)],[t9_zfmisc_1]) ).

fof(c_0_4,plain,
    ! [X6,X7,X8] :
      ( singleton(X6) != unordered_pair(X7,X8)
      | X6 = X7 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_zfmisc_1])]) ).

fof(c_0_5,negated_conjecture,
    ( singleton(esk1_0) = unordered_pair(esk2_0,esk3_0)
    & esk2_0 != esk3_0 ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).

cnf(c_0_6,plain,
    ( X1 = X2
    | singleton(X1) != unordered_pair(X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_7,negated_conjecture,
    singleton(esk1_0) = unordered_pair(esk2_0,esk3_0),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

fof(c_0_8,plain,
    ! [X4,X5] : unordered_pair(X4,X5) = unordered_pair(X5,X4),
    inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).

cnf(c_0_9,negated_conjecture,
    ( esk1_0 = X1
    | unordered_pair(esk2_0,esk3_0) != unordered_pair(X1,X2) ),
    inference(spm,[status(thm)],[c_0_6,c_0_7]) ).

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

cnf(c_0_11,negated_conjecture,
    esk1_0 = esk2_0,
    inference(er,[status(thm)],[c_0_9]) ).

cnf(c_0_12,plain,
    ( X1 = X2
    | singleton(X1) != unordered_pair(X3,X2) ),
    inference(spm,[status(thm)],[c_0_6,c_0_10]) ).

cnf(c_0_13,negated_conjecture,
    singleton(esk2_0) = unordered_pair(esk2_0,esk3_0),
    inference(rw,[status(thm)],[c_0_7,c_0_11]) ).

cnf(c_0_14,negated_conjecture,
    ( esk2_0 = X1
    | unordered_pair(esk2_0,esk3_0) != unordered_pair(X2,X1) ),
    inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

cnf(c_0_15,negated_conjecture,
    esk2_0 != esk3_0,
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_16,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(er,[status(thm)],[c_0_14]),c_0_15]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SEU150+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n022.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Wed Aug 23 16:19:11 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.56  start to proof: theBenchmark
% 0.20/0.57  % Version  : CSE_E---1.5
% 0.20/0.57  % Problem  : theBenchmark.p
% 0.20/0.57  % Proof found
% 0.20/0.57  % SZS status Theorem for theBenchmark.p
% 0.20/0.57  % SZS output start Proof
% See solution above
% 0.20/0.57  % Total time : 0.004000 s
% 0.20/0.57  % SZS output end Proof
% 0.20/0.57  % Total time : 0.006000 s
%------------------------------------------------------------------------------