%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SET959+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n017.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 14:36:27 EDT 2023

% Result   : Theorem 0.20s 0.59s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   46 (  10 unt;  14 typ;   0 def)
%            Number of atoms       :   79 (  28 equ)
%            Maximal formula atoms :    9 (   2 avg)
%            Number of connectives :   81 (  34   ~;  28   |;  13   &)
%                                         (   3 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   14 (  10   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   4 con; 0-2 aty)
%            Number of variables   :   66 (   0 sgn;  37   !;   0   ?;   0   :)

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

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

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

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

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

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 ).

tff(decl_31,type,
    esk5_1: $i > $i ).

tff(decl_32,type,
    esk6_1: $i > $i ).

tff(decl_33,type,
    esk7_1: $i > $i ).

tff(decl_34,type,
    esk8_1: $i > $i ).

tff(decl_35,type,
    esk9_2: ( $i * $i ) > $i ).

fof(t112_zfmisc_1,conjecture,
    ! [X1,X2] :
      ( ( ! [X3] :
            ~ ( in(X3,X1)
              & ! [X4,X5] : X3 != ordered_pair(X4,X5) )
        & ! [X3] :
            ~ ( in(X3,X2)
              & ! [X4,X5] : X3 != ordered_pair(X4,X5) )
        & ! [X3,X4] :
            ( in(ordered_pair(X3,X4),X1)
          <=> in(ordered_pair(X3,X4),X2) ) )
     => X1 = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t112_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(commutativity_k2_tarski,axiom,
    ! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).

fof(t2_tarski,axiom,
    ! [X1,X2] :
      ( ! [X3] :
          ( in(X3,X1)
        <=> in(X3,X2) )
     => X1 = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).

fof(c_0_4,negated_conjecture,
    ~ ! [X1,X2] :
        ( ( ! [X3] :
              ~ ( in(X3,X1)
                & ! [X4,X5] : X3 != ordered_pair(X4,X5) )
          & ! [X3] :
              ~ ( in(X3,X2)
                & ! [X4,X5] : X3 != ordered_pair(X4,X5) )
          & ! [X3,X4] :
              ( in(ordered_pair(X3,X4),X1)
            <=> in(ordered_pair(X3,X4),X2) ) )
       => X1 = X2 ),
    inference(assume_negation,[status(cth)],[t112_zfmisc_1]) ).

fof(c_0_5,negated_conjecture,
    ! [X18,X21,X24,X25] :
      ( ( ~ in(X18,esk3_0)
        | X18 = ordered_pair(esk5_1(X18),esk6_1(X18)) )
      & ( ~ in(X21,esk4_0)
        | X21 = ordered_pair(esk7_1(X21),esk8_1(X21)) )
      & ( ~ in(ordered_pair(X24,X25),esk3_0)
        | in(ordered_pair(X24,X25),esk4_0) )
      & ( ~ in(ordered_pair(X24,X25),esk4_0)
        | in(ordered_pair(X24,X25),esk3_0) )
      & esk3_0 != esk4_0 ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])]) ).

fof(c_0_6,plain,
    ! [X10,X11] : ordered_pair(X10,X11) = unordered_pair(unordered_pair(X10,X11),singleton(X10)),
    inference(variable_rename,[status(thm)],[d5_tarski]) ).

cnf(c_0_7,negated_conjecture,
    ( in(ordered_pair(X1,X2),esk3_0)
    | ~ in(ordered_pair(X1,X2),esk4_0) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_8,plain,
    ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

fof(c_0_9,plain,
    ! [X8,X9] : unordered_pair(X8,X9) = unordered_pair(X9,X8),
    inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).

cnf(c_0_10,negated_conjecture,
    ( X1 = ordered_pair(esk7_1(X1),esk8_1(X1))
    | ~ in(X1,esk4_0) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_11,negated_conjecture,
    ( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),esk3_0)
    | ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),esk4_0) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7,c_0_8]),c_0_8]) ).

cnf(c_0_12,plain,
    unordered_pair(X1,X2) = unordered_pair(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_13,negated_conjecture,
    ( X1 = unordered_pair(unordered_pair(esk7_1(X1),esk8_1(X1)),singleton(esk7_1(X1)))
    | ~ in(X1,esk4_0) ),
    inference(rw,[status(thm)],[c_0_10,c_0_8]) ).

cnf(c_0_14,negated_conjecture,
    ( in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),esk3_0)
    | ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),esk4_0) ),
    inference(spm,[status(thm)],[c_0_11,c_0_12]) ).

cnf(c_0_15,negated_conjecture,
    ( unordered_pair(singleton(esk7_1(X1)),unordered_pair(esk7_1(X1),esk8_1(X1))) = X1
    | ~ in(X1,esk4_0) ),
    inference(rw,[status(thm)],[c_0_13,c_0_12]) ).

fof(c_0_16,plain,
    ! [X26,X27] :
      ( ( ~ in(esk9_2(X26,X27),X26)
        | ~ in(esk9_2(X26,X27),X27)
        | X26 = X27 )
      & ( in(esk9_2(X26,X27),X26)
        | in(esk9_2(X26,X27),X27)
        | X26 = X27 ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_tarski])])])]) ).

cnf(c_0_17,negated_conjecture,
    ( in(X1,esk3_0)
    | ~ in(X1,esk4_0) ),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_18,plain,
    ( in(esk9_2(X1,X2),X1)
    | in(esk9_2(X1,X2),X2)
    | X1 = X2 ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_19,negated_conjecture,
    ( in(ordered_pair(X1,X2),esk4_0)
    | ~ in(ordered_pair(X1,X2),esk3_0) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_20,negated_conjecture,
    ( X1 = ordered_pair(esk5_1(X1),esk6_1(X1))
    | ~ in(X1,esk3_0) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_21,negated_conjecture,
    ( esk4_0 = X1
    | in(esk9_2(esk4_0,X1),esk3_0)
    | in(esk9_2(esk4_0,X1),X1) ),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_22,negated_conjecture,
    esk3_0 != esk4_0,
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_23,negated_conjecture,
    ( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),esk4_0)
    | ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),esk3_0) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_8]),c_0_8]) ).

cnf(c_0_24,negated_conjecture,
    ( X1 = unordered_pair(unordered_pair(esk5_1(X1),esk6_1(X1)),singleton(esk5_1(X1)))
    | ~ in(X1,esk3_0) ),
    inference(rw,[status(thm)],[c_0_20,c_0_8]) ).

cnf(c_0_25,plain,
    ( X1 = X2
    | ~ in(esk9_2(X1,X2),X1)
    | ~ in(esk9_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_26,negated_conjecture,
    in(esk9_2(esk4_0,esk3_0),esk3_0),
    inference(sr,[status(thm)],[inference(ef,[status(thm)],[c_0_21]),c_0_22]) ).

cnf(c_0_27,negated_conjecture,
    ( in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),esk4_0)
    | ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),esk3_0) ),
    inference(spm,[status(thm)],[c_0_23,c_0_12]) ).

cnf(c_0_28,negated_conjecture,
    ( unordered_pair(singleton(esk5_1(X1)),unordered_pair(esk5_1(X1),esk6_1(X1))) = X1
    | ~ in(X1,esk3_0) ),
    inference(rw,[status(thm)],[c_0_24,c_0_12]) ).

cnf(c_0_29,negated_conjecture,
    ~ in(esk9_2(esk4_0,esk3_0),esk4_0),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_22]) ).

cnf(c_0_30,negated_conjecture,
    ( in(X1,esk4_0)
    | ~ in(X1,esk3_0) ),
    inference(spm,[status(thm)],[c_0_27,c_0_28]) ).

cnf(c_0_31,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_26])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SET959+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% 0.07/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.34  % Computer : n017.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 12:38:10 EDT 2023
% 0.14/0.34  % CPUTime  : 
% 0.20/0.57  start to proof: theBenchmark
% 0.20/0.59  % Version  : CSE_E---1.5
% 0.20/0.59  % Problem  : theBenchmark.p
% 0.20/0.59  % Proof found
% 0.20/0.59  % SZS status Theorem for theBenchmark.p
% 0.20/0.59  % SZS output start Proof
% See solution above
% 0.20/0.60  % Total time : 0.010000 s
% 0.20/0.60  % SZS output end Proof
% 0.20/0.60  % Total time : 0.012000 s
%------------------------------------------------------------------------------