%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SET975+1 : 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 : n032.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 14:36:29 EDT 2023

% Result   : Theorem 0.16s 0.50s
% Output   : CNFRefutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   44 (   8 unt;  13 typ;   0 def)
%            Number of atoms       :   84 (  28 equ)
%            Maximal formula atoms :   12 (   2 avg)
%            Number of connectives :   89 (  36   ~;  38   |;  10   &)
%                                         (   5 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   12 (   7   >;   5   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   6 con; 0-2 aty)
%            Number of variables   :   64 (   7 sgn;  29   !;   0   ?;   0   :)

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

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

tff(decl_24,type,
    singleton: $i > $i ).

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

tff(decl_26,type,
    empty: $i > $o ).

tff(decl_27,type,
    cartesian_product2: ( $i * $i ) > $i ).

tff(decl_28,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_29,type,
    esk2_0: $i ).

tff(decl_30,type,
    esk3_0: $i ).

tff(decl_31,type,
    esk4_0: $i ).

tff(decl_32,type,
    esk5_0: $i ).

tff(decl_33,type,
    esk6_0: $i ).

tff(decl_34,type,
    esk7_0: $i ).

fof(t128_zfmisc_1,conjecture,
    ! [X1,X2,X3,X4] :
      ( in(ordered_pair(X1,X2),cartesian_product2(singleton(X3),X4))
    <=> ( X1 = X3
        & in(X2,X4) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t128_zfmisc_1) ).

fof(l55_zfmisc_1,axiom,
    ! [X1,X2,X3,X4] :
      ( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
    <=> ( in(X1,X3)
        & in(X2,X4) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l55_zfmisc_1) ).

fof(d5_tarski,axiom,
    ! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).

fof(d1_tarski,axiom,
    ! [X1,X2] :
      ( X2 = singleton(X1)
    <=> ! [X3] :
          ( in(X3,X2)
        <=> X3 = X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).

fof(c_0_4,negated_conjecture,
    ~ ! [X1,X2,X3,X4] :
        ( in(ordered_pair(X1,X2),cartesian_product2(singleton(X3),X4))
      <=> ( X1 = X3
          & in(X2,X4) ) ),
    inference(assume_negation,[status(cth)],[t128_zfmisc_1]) ).

fof(c_0_5,plain,
    ! [X20,X21,X22,X23] :
      ( ( in(X20,X22)
        | ~ in(ordered_pair(X20,X21),cartesian_product2(X22,X23)) )
      & ( in(X21,X23)
        | ~ in(ordered_pair(X20,X21),cartesian_product2(X22,X23)) )
      & ( ~ in(X20,X22)
        | ~ in(X21,X23)
        | in(ordered_pair(X20,X21),cartesian_product2(X22,X23)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l55_zfmisc_1])])]) ).

fof(c_0_6,plain,
    ! [X16,X17] : ordered_pair(X16,X17) = unordered_pair(unordered_pair(X16,X17),singleton(X16)),
    inference(variable_rename,[status(thm)],[d5_tarski]) ).

fof(c_0_7,negated_conjecture,
    ( ( ~ in(ordered_pair(esk4_0,esk5_0),cartesian_product2(singleton(esk6_0),esk7_0))
      | esk4_0 != esk6_0
      | ~ in(esk5_0,esk7_0) )
    & ( esk4_0 = esk6_0
      | in(ordered_pair(esk4_0,esk5_0),cartesian_product2(singleton(esk6_0),esk7_0)) )
    & ( in(esk5_0,esk7_0)
      | in(ordered_pair(esk4_0,esk5_0),cartesian_product2(singleton(esk6_0),esk7_0)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])]) ).

cnf(c_0_8,plain,
    ( in(X1,X2)
    | ~ in(ordered_pair(X3,X1),cartesian_product2(X4,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_9,plain,
    ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_10,negated_conjecture,
    ( in(esk5_0,esk7_0)
    | in(ordered_pair(esk4_0,esk5_0),cartesian_product2(singleton(esk6_0),esk7_0)) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

fof(c_0_11,plain,
    ! [X9,X10,X11,X12,X13,X14] :
      ( ( ~ in(X11,X10)
        | X11 = X9
        | X10 != singleton(X9) )
      & ( X12 != X9
        | in(X12,X10)
        | X10 != singleton(X9) )
      & ( ~ in(esk1_2(X13,X14),X14)
        | esk1_2(X13,X14) != X13
        | X14 = singleton(X13) )
      & ( in(esk1_2(X13,X14),X14)
        | esk1_2(X13,X14) = X13
        | X14 = singleton(X13) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d1_tarski])])])])])]) ).

cnf(c_0_12,negated_conjecture,
    ( ~ in(ordered_pair(esk4_0,esk5_0),cartesian_product2(singleton(esk6_0),esk7_0))
    | esk4_0 != esk6_0
    | ~ in(esk5_0,esk7_0) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_13,plain,
    ( in(X1,X2)
    | ~ in(unordered_pair(unordered_pair(X3,X1),singleton(X3)),cartesian_product2(X4,X2)) ),
    inference(rw,[status(thm)],[c_0_8,c_0_9]) ).

cnf(c_0_14,negated_conjecture,
    ( in(esk5_0,esk7_0)
    | in(unordered_pair(unordered_pair(esk4_0,esk5_0),singleton(esk4_0)),cartesian_product2(singleton(esk6_0),esk7_0)) ),
    inference(rw,[status(thm)],[c_0_10,c_0_9]) ).

cnf(c_0_15,plain,
    ( in(X1,X2)
    | ~ in(ordered_pair(X1,X3),cartesian_product2(X2,X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_16,negated_conjecture,
    ( esk4_0 = esk6_0
    | in(ordered_pair(esk4_0,esk5_0),cartesian_product2(singleton(esk6_0),esk7_0)) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_17,plain,
    ( X1 = X3
    | ~ in(X1,X2)
    | X2 != singleton(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_18,negated_conjecture,
    ( esk6_0 != esk4_0
    | ~ in(esk5_0,esk7_0)
    | ~ in(unordered_pair(unordered_pair(esk4_0,esk5_0),singleton(esk4_0)),cartesian_product2(singleton(esk6_0),esk7_0)) ),
    inference(rw,[status(thm)],[c_0_12,c_0_9]) ).

cnf(c_0_19,negated_conjecture,
    in(esk5_0,esk7_0),
    inference(spm,[status(thm)],[c_0_13,c_0_14]) ).

cnf(c_0_20,plain,
    ( in(X1,X2)
    | ~ in(unordered_pair(unordered_pair(X1,X3),singleton(X1)),cartesian_product2(X2,X4)) ),
    inference(rw,[status(thm)],[c_0_15,c_0_9]) ).

cnf(c_0_21,negated_conjecture,
    ( esk6_0 = esk4_0
    | in(unordered_pair(unordered_pair(esk4_0,esk5_0),singleton(esk4_0)),cartesian_product2(singleton(esk6_0),esk7_0)) ),
    inference(rw,[status(thm)],[c_0_16,c_0_9]) ).

cnf(c_0_22,plain,
    ( X1 = X2
    | ~ in(X1,singleton(X2)) ),
    inference(er,[status(thm)],[c_0_17]) ).

cnf(c_0_23,negated_conjecture,
    ( esk6_0 != esk4_0
    | ~ in(unordered_pair(unordered_pair(esk4_0,esk5_0),singleton(esk4_0)),cartesian_product2(singleton(esk6_0),esk7_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_19])]) ).

cnf(c_0_24,negated_conjecture,
    esk6_0 = esk4_0,
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).

cnf(c_0_25,plain,
    ( in(ordered_pair(X1,X3),cartesian_product2(X2,X4))
    | ~ in(X1,X2)
    | ~ in(X3,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_26,plain,
    ( in(X1,X3)
    | X1 != X2
    | X3 != singleton(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_27,negated_conjecture,
    ~ in(unordered_pair(unordered_pair(esk4_0,esk5_0),singleton(esk4_0)),cartesian_product2(singleton(esk4_0),esk7_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_24]),c_0_24])]) ).

cnf(c_0_28,plain,
    ( in(unordered_pair(unordered_pair(X1,X3),singleton(X1)),cartesian_product2(X2,X4))
    | ~ in(X3,X4)
    | ~ in(X1,X2) ),
    inference(rw,[status(thm)],[c_0_25,c_0_9]) ).

cnf(c_0_29,plain,
    in(X1,singleton(X1)),
    inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_26])]) ).

cnf(c_0_30,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_19]),c_0_29])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem    : SET975+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.11  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.30  % Computer : n032.cluster.edu
% 0.13/0.30  % Model    : x86_64 x86_64
% 0.13/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.30  % Memory   : 8042.1875MB
% 0.13/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.30  % CPULimit   : 300
% 0.13/0.30  % WCLimit    : 300
% 0.13/0.30  % DateTime   : Sat Aug 26 12:23:58 EDT 2023
% 0.13/0.31  % CPUTime  : 
% 0.16/0.49  start to proof: theBenchmark
% 0.16/0.50  % Version  : CSE_E---1.5
% 0.16/0.50  % Problem  : theBenchmark.p
% 0.16/0.50  % Proof found
% 0.16/0.50  % SZS status Theorem for theBenchmark.p
% 0.16/0.50  % SZS output start Proof
% See solution above
% 0.16/0.50  % Total time : 0.006000 s
% 0.16/0.50  % SZS output end Proof
% 0.16/0.50  % Total time : 0.008000 s
%------------------------------------------------------------------------------