%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU130+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 : n012.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 16:22:36 EDT 2023

% Result   : Theorem 0.20s 0.62s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   31 (   6 unt;  11 typ;   0 def)
%            Number of atoms       :   65 (  20 equ)
%            Maximal formula atoms :   20 (   3 avg)
%            Number of connectives :   68 (  23   ~;  30   |;   9   &)
%                                         (   3 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   12 (   6   >;   6   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   5 con; 0-3 aty)
%            Number of variables   :   47 (   0 sgn;  28   !;   0   ?;   0   :)

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

tff(decl_23,type,
    set_intersection2: ( $i * $i ) > $i ).

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

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

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

tff(decl_27,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_28,type,
    esk2_3: ( $i * $i * $i ) > $i ).

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

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

tff(decl_31,type,
    esk5_0: $i ).

tff(decl_32,type,
    esk6_0: $i ).

fof(d3_xboole_0,axiom,
    ! [X1,X2,X3] :
      ( X3 = set_intersection2(X1,X2)
    <=> ! [X4] :
          ( in(X4,X3)
        <=> ( in(X4,X1)
            & in(X4,X2) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).

fof(d3_tarski,axiom,
    ! [X1,X2] :
      ( subset(X1,X2)
    <=> ! [X3] :
          ( in(X3,X1)
         => in(X3,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).

fof(t28_xboole_1,conjecture,
    ! [X1,X2] :
      ( subset(X1,X2)
     => set_intersection2(X1,X2) = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_xboole_1) ).

fof(commutativity_k3_xboole_0,axiom,
    ! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).

fof(c_0_4,plain,
    ! [X17,X18,X19,X20,X21,X22,X23,X24] :
      ( ( in(X20,X17)
        | ~ in(X20,X19)
        | X19 != set_intersection2(X17,X18) )
      & ( in(X20,X18)
        | ~ in(X20,X19)
        | X19 != set_intersection2(X17,X18) )
      & ( ~ in(X21,X17)
        | ~ in(X21,X18)
        | in(X21,X19)
        | X19 != set_intersection2(X17,X18) )
      & ( ~ in(esk2_3(X22,X23,X24),X24)
        | ~ in(esk2_3(X22,X23,X24),X22)
        | ~ in(esk2_3(X22,X23,X24),X23)
        | X24 = set_intersection2(X22,X23) )
      & ( in(esk2_3(X22,X23,X24),X22)
        | in(esk2_3(X22,X23,X24),X24)
        | X24 = set_intersection2(X22,X23) )
      & ( in(esk2_3(X22,X23,X24),X23)
        | in(esk2_3(X22,X23,X24),X24)
        | X24 = set_intersection2(X22,X23) ) ),
    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)],[d3_xboole_0])])])])])]) ).

fof(c_0_5,plain,
    ! [X11,X12,X13,X14,X15] :
      ( ( ~ subset(X11,X12)
        | ~ in(X13,X11)
        | in(X13,X12) )
      & ( in(esk1_2(X14,X15),X14)
        | subset(X14,X15) )
      & ( ~ in(esk1_2(X14,X15),X15)
        | subset(X14,X15) ) ),
    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)],[d3_tarski])])])])])]) ).

cnf(c_0_6,plain,
    ( in(esk2_3(X1,X2,X3),X2)
    | in(esk2_3(X1,X2,X3),X3)
    | X3 = set_intersection2(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

fof(c_0_7,negated_conjecture,
    ~ ! [X1,X2] :
        ( subset(X1,X2)
       => set_intersection2(X1,X2) = X1 ),
    inference(assume_negation,[status(cth)],[t28_xboole_1]) ).

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

cnf(c_0_9,plain,
    ( set_intersection2(X1,X2) = X2
    | in(esk2_3(X1,X2,X2),X2) ),
    inference(ef,[status(thm)],[c_0_6]) ).

fof(c_0_10,negated_conjecture,
    ( subset(esk5_0,esk6_0)
    & set_intersection2(esk5_0,esk6_0) != esk5_0 ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).

cnf(c_0_11,plain,
    ( X3 = set_intersection2(X1,X2)
    | ~ in(esk2_3(X1,X2,X3),X3)
    | ~ in(esk2_3(X1,X2,X3),X1)
    | ~ in(esk2_3(X1,X2,X3),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_12,plain,
    ( set_intersection2(X1,X2) = X2
    | in(esk2_3(X1,X2,X2),X3)
    | ~ subset(X2,X3) ),
    inference(spm,[status(thm)],[c_0_8,c_0_9]) ).

cnf(c_0_13,negated_conjecture,
    subset(esk5_0,esk6_0),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

fof(c_0_14,plain,
    ! [X7,X8] : set_intersection2(X7,X8) = set_intersection2(X8,X7),
    inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).

cnf(c_0_15,plain,
    ( set_intersection2(X1,X2) = X2
    | ~ in(esk2_3(X1,X2,X2),X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_9]),c_0_9]) ).

cnf(c_0_16,negated_conjecture,
    ( set_intersection2(X1,esk5_0) = esk5_0
    | in(esk2_3(X1,esk5_0,esk5_0),esk6_0) ),
    inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

cnf(c_0_17,plain,
    set_intersection2(X1,X2) = set_intersection2(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_18,negated_conjecture,
    set_intersection2(esk5_0,esk6_0) != esk5_0,
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_19,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]),c_0_18]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SEU130+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
% 0.14/0.34  % Computer : n012.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   : Wed Aug 23 20:23:42 EDT 2023
% 0.14/0.34  % CPUTime  : 
% 0.20/0.56  start to proof: theBenchmark
% 0.20/0.62  % Version  : CSE_E---1.5
% 0.20/0.62  % Problem  : theBenchmark.p
% 0.20/0.62  % Proof found
% 0.20/0.62  % SZS status Theorem for theBenchmark.p
% 0.20/0.62  % SZS output start Proof
% See solution above
% 0.20/0.63  % Total time : 0.051000 s
% 0.20/0.63  % SZS output end Proof
% 0.20/0.63  % Total time : 0.054000 s
%------------------------------------------------------------------------------