%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SET903+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 : n001.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 14:36:11 EDT 2023

% Result   : Theorem 0.20s 0.58s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   27 (   7 unt;   9 typ;   0 def)
%            Number of atoms       :   76 (  75 equ)
%            Maximal formula atoms :   32 (   4 avg)
%            Number of connectives :   91 (  33   ~;  36   |;  22   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    4 (   3   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   6 con; 0-2 aty)
%            Number of variables   :   26 (   4 sgn;  12   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    set_union2: ( $i * $i ) > $i ).

tff(decl_23,type,
    empty_set: $i ).

tff(decl_24,type,
    empty: $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 ).

tff(decl_30,type,
    esk5_0: $i ).

fof(t43_zfmisc_1,axiom,
    ! [X1,X2,X3] :
      ~ ( singleton(X1) = set_union2(X2,X3)
        & ~ ( X2 = singleton(X1)
            & X3 = singleton(X1) )
        & ~ ( X2 = empty_set
            & X3 = singleton(X1) )
        & ~ ( X2 = singleton(X1)
            & X3 = empty_set ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_zfmisc_1) ).

fof(t44_zfmisc_1,conjecture,
    ! [X1,X2,X3] :
      ~ ( singleton(X1) = set_union2(X2,X3)
        & X2 != X3
        & X2 != empty_set
        & X3 != empty_set ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_zfmisc_1) ).

fof(c_0_2,plain,
    ! [X13,X14,X15] :
      ( ( X14 = singleton(X13)
        | X14 = empty_set
        | X14 = singleton(X13)
        | singleton(X13) != set_union2(X14,X15) )
      & ( X15 = empty_set
        | X14 = empty_set
        | X14 = singleton(X13)
        | singleton(X13) != set_union2(X14,X15) )
      & ( X14 = singleton(X13)
        | X15 = singleton(X13)
        | X14 = singleton(X13)
        | singleton(X13) != set_union2(X14,X15) )
      & ( X15 = empty_set
        | X15 = singleton(X13)
        | X14 = singleton(X13)
        | singleton(X13) != set_union2(X14,X15) )
      & ( X14 = singleton(X13)
        | X14 = empty_set
        | X15 = singleton(X13)
        | singleton(X13) != set_union2(X14,X15) )
      & ( X15 = empty_set
        | X14 = empty_set
        | X15 = singleton(X13)
        | singleton(X13) != set_union2(X14,X15) )
      & ( X14 = singleton(X13)
        | X15 = singleton(X13)
        | X15 = singleton(X13)
        | singleton(X13) != set_union2(X14,X15) )
      & ( X15 = empty_set
        | X15 = singleton(X13)
        | X15 = singleton(X13)
        | singleton(X13) != set_union2(X14,X15) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t43_zfmisc_1])])]) ).

fof(c_0_3,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ~ ( singleton(X1) = set_union2(X2,X3)
          & X2 != X3
          & X2 != empty_set
          & X3 != empty_set ),
    inference(assume_negation,[status(cth)],[t44_zfmisc_1]) ).

cnf(c_0_4,plain,
    ( X1 = empty_set
    | X1 = singleton(X2)
    | X1 = singleton(X2)
    | singleton(X2) != set_union2(X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

fof(c_0_5,negated_conjecture,
    ( singleton(esk3_0) = set_union2(esk4_0,esk5_0)
    & esk4_0 != esk5_0
    & esk4_0 != empty_set
    & esk5_0 != empty_set ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).

cnf(c_0_6,plain,
    ( X1 = empty_set
    | X1 = singleton(X2)
    | singleton(X2) != set_union2(X3,X1) ),
    inference(cn,[status(thm)],[c_0_4]) ).

cnf(c_0_7,negated_conjecture,
    singleton(esk3_0) = set_union2(esk4_0,esk5_0),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_8,negated_conjecture,
    esk5_0 != empty_set,
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_9,negated_conjecture,
    ( singleton(X1) = esk5_0
    | singleton(X1) != singleton(esk3_0) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_7]),c_0_8]) ).

cnf(c_0_10,plain,
    ( X1 = singleton(X2)
    | X1 = empty_set
    | X1 = singleton(X2)
    | singleton(X2) != set_union2(X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_11,negated_conjecture,
    singleton(esk3_0) = esk5_0,
    inference(er,[status(thm)],[c_0_9]) ).

cnf(c_0_12,plain,
    ( X1 = empty_set
    | X1 = singleton(X2)
    | singleton(X2) != set_union2(X1,X3) ),
    inference(cn,[status(thm)],[c_0_10]) ).

cnf(c_0_13,negated_conjecture,
    set_union2(esk4_0,esk5_0) = esk5_0,
    inference(rw,[status(thm)],[c_0_7,c_0_11]) ).

cnf(c_0_14,negated_conjecture,
    esk4_0 != empty_set,
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_15,negated_conjecture,
    ( singleton(X1) = esk4_0
    | singleton(X1) != esk5_0 ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]) ).

cnf(c_0_16,negated_conjecture,
    esk4_0 != esk5_0,
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_17,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_11]),c_0_16]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SET903+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 : n001.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 09:07:45 EDT 2023
% 0.14/0.34  % CPUTime  : 
% 0.20/0.57  start to proof: theBenchmark
% 0.20/0.58  % Version  : CSE_E---1.5
% 0.20/0.58  % Problem  : theBenchmark.p
% 0.20/0.58  % Proof found
% 0.20/0.58  % SZS status Theorem for theBenchmark.p
% 0.20/0.58  % SZS output start Proof
% See solution above
% 0.20/0.59  % Total time : 0.007000 s
% 0.20/0.59  % SZS output end Proof
% 0.20/0.59  % Total time : 0.009000 s
%------------------------------------------------------------------------------