%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SET904+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n008.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 14:36:12 EDT 2023

% Result   : Theorem 0.21s 0.57s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   23 (   7 unt;   9 typ;   0 def)
%            Number of atoms       :   21 (   3 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   13 (   6   ~;   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  :    8 (   5   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   3 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,
    subset: ( $i * $i ) > $o ).

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

tff(decl_26,type,
    singleton: $i > $i ).

tff(decl_27,type,
    esk1_0: $i ).

tff(decl_28,type,
    esk2_0: $i ).

tff(decl_29,type,
    esk3_0: $i ).

tff(decl_30,type,
    esk4_0: $i ).

fof(t45_zfmisc_1,conjecture,
    ! [X1,X2] :
      ( subset(set_union2(singleton(X1),X2),X2)
     => in(X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_zfmisc_1) ).

fof(l21_zfmisc_1,axiom,
    ! [X1,X2] :
      ( subset(set_union2(singleton(X1),X2),X2)
     => in(X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l21_zfmisc_1) ).

fof(commutativity_k2_xboole_0,axiom,
    ! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).

fof(c_0_3,negated_conjecture,
    ~ ! [X1,X2] :
        ( subset(set_union2(singleton(X1),X2),X2)
       => in(X1,X2) ),
    inference(assume_negation,[status(cth)],[t45_zfmisc_1]) ).

fof(c_0_4,plain,
    ! [X17,X18] :
      ( ~ subset(set_union2(singleton(X17),X18),X18)
      | in(X17,X18) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l21_zfmisc_1])]) ).

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,negated_conjecture,
    ( subset(set_union2(singleton(esk3_0),esk4_0),esk4_0)
    & ~ in(esk3_0,esk4_0) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).

cnf(c_0_7,plain,
    ( in(X1,X2)
    | ~ subset(set_union2(singleton(X1),X2),X2) ),
    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,negated_conjecture,
    subset(set_union2(singleton(esk3_0),esk4_0),esk4_0),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_10,plain,
    ( in(X1,X2)
    | ~ subset(set_union2(X2,singleton(X1)),X2) ),
    inference(spm,[status(thm)],[c_0_7,c_0_8]) ).

cnf(c_0_11,negated_conjecture,
    subset(set_union2(esk4_0,singleton(esk3_0)),esk4_0),
    inference(rw,[status(thm)],[c_0_9,c_0_8]) ).

cnf(c_0_12,negated_conjecture,
    ~ in(esk3_0,esk4_0),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SET904+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.34  % Computer : n008.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Sat Aug 26 11:20:47 EDT 2023
% 0.14/0.34  % CPUTime  : 
% 0.21/0.56  start to proof: theBenchmark
% 0.21/0.57  % Version  : CSE_E---1.5
% 0.21/0.57  % Problem  : theBenchmark.p
% 0.21/0.57  % Proof found
% 0.21/0.57  % SZS status Theorem for theBenchmark.p
% 0.21/0.57  % SZS output start Proof
% See solution above
% 0.21/0.57  % Total time : 0.005000 s
% 0.21/0.57  % SZS output end Proof
% 0.21/0.57  % Total time : 0.008000 s
%------------------------------------------------------------------------------