%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU129+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 : n025.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 0.21s 0.61s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   41 (   5 unt;  12 typ;   0 def)
%            Number of atoms       :   86 (  10 equ)
%            Maximal formula atoms :   20 (   2 avg)
%            Number of connectives :   93 (  36   ~;  42   |;   9   &)
%                                         (   3 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   4 avg)
%            Maximal term depth    :    3 (   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    :    9 (   9 usr;   6 con; 0-3 aty)
%            Number of variables   :   74 (   6 sgn;  26   !;   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 ).

tff(decl_33,type,
    esk7_0: $i ).

fof(t26_xboole_1,conjecture,
    ! [X1,X2,X3] :
      ( subset(X1,X2)
     => subset(set_intersection2(X1,X3),set_intersection2(X2,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_xboole_1) ).

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(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(c_0_3,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( subset(X1,X2)
       => subset(set_intersection2(X1,X3),set_intersection2(X2,X3)) ),
    inference(assume_negation,[status(cth)],[t26_xboole_1]) ).

fof(c_0_4,plain,
    ! [X9,X10,X11,X12,X13] :
      ( ( ~ subset(X9,X10)
        | ~ in(X11,X9)
        | in(X11,X10) )
      & ( in(esk1_2(X12,X13),X12)
        | subset(X12,X13) )
      & ( ~ in(esk1_2(X12,X13),X13)
        | subset(X12,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)],[d3_tarski])])])])])]) ).

fof(c_0_5,negated_conjecture,
    ( subset(esk5_0,esk6_0)
    & ~ subset(set_intersection2(esk5_0,esk7_0),set_intersection2(esk6_0,esk7_0)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).

fof(c_0_6,plain,
    ! [X15,X16,X17,X18,X19,X20,X21,X22] :
      ( ( in(X18,X15)
        | ~ in(X18,X17)
        | X17 != set_intersection2(X15,X16) )
      & ( in(X18,X16)
        | ~ in(X18,X17)
        | X17 != set_intersection2(X15,X16) )
      & ( ~ in(X19,X15)
        | ~ in(X19,X16)
        | in(X19,X17)
        | X17 != set_intersection2(X15,X16) )
      & ( ~ in(esk2_3(X20,X21,X22),X22)
        | ~ in(esk2_3(X20,X21,X22),X20)
        | ~ in(esk2_3(X20,X21,X22),X21)
        | X22 = set_intersection2(X20,X21) )
      & ( in(esk2_3(X20,X21,X22),X20)
        | in(esk2_3(X20,X21,X22),X22)
        | X22 = set_intersection2(X20,X21) )
      & ( in(esk2_3(X20,X21,X22),X21)
        | in(esk2_3(X20,X21,X22),X22)
        | X22 = set_intersection2(X20,X21) ) ),
    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])])])])])]) ).

cnf(c_0_7,plain,
    ( in(X3,X2)
    | ~ subset(X1,X2)
    | ~ in(X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_8,negated_conjecture,
    subset(esk5_0,esk6_0),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_9,plain,
    ( in(X1,X2)
    | ~ in(X1,X3)
    | X3 != set_intersection2(X2,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_10,plain,
    ( subset(X1,X2)
    | ~ in(esk1_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_11,negated_conjecture,
    ( in(X1,esk6_0)
    | ~ in(X1,esk5_0) ),
    inference(spm,[status(thm)],[c_0_7,c_0_8]) ).

cnf(c_0_12,plain,
    ( in(X1,X2)
    | ~ in(X1,set_intersection2(X2,X3)) ),
    inference(er,[status(thm)],[c_0_9]) ).

cnf(c_0_13,plain,
    ( in(esk1_2(X1,X2),X1)
    | subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_14,plain,
    ( in(X1,X4)
    | ~ in(X1,X2)
    | ~ in(X1,X3)
    | X4 != set_intersection2(X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_15,plain,
    ( in(X1,X2)
    | ~ in(X1,X3)
    | X3 != set_intersection2(X4,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_16,negated_conjecture,
    ( subset(X1,esk6_0)
    | ~ in(esk1_2(X1,esk6_0),esk5_0) ),
    inference(spm,[status(thm)],[c_0_10,c_0_11]) ).

cnf(c_0_17,plain,
    ( subset(set_intersection2(X1,X2),X3)
    | in(esk1_2(set_intersection2(X1,X2),X3),X1) ),
    inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

cnf(c_0_18,plain,
    ( in(X1,set_intersection2(X2,X3))
    | ~ in(X1,X3)
    | ~ in(X1,X2) ),
    inference(er,[status(thm)],[c_0_14]) ).

cnf(c_0_19,plain,
    ( in(X1,X2)
    | ~ in(X1,set_intersection2(X3,X2)) ),
    inference(er,[status(thm)],[c_0_15]) ).

cnf(c_0_20,negated_conjecture,
    subset(set_intersection2(esk5_0,X1),esk6_0),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_21,plain,
    ( subset(X1,set_intersection2(X2,X3))
    | ~ in(esk1_2(X1,set_intersection2(X2,X3)),X3)
    | ~ in(esk1_2(X1,set_intersection2(X2,X3)),X2) ),
    inference(spm,[status(thm)],[c_0_10,c_0_18]) ).

cnf(c_0_22,plain,
    ( subset(set_intersection2(X1,X2),X3)
    | in(esk1_2(set_intersection2(X1,X2),X3),X2) ),
    inference(spm,[status(thm)],[c_0_19,c_0_13]) ).

cnf(c_0_23,negated_conjecture,
    ( in(X1,esk6_0)
    | ~ in(X1,set_intersection2(esk5_0,X2)) ),
    inference(spm,[status(thm)],[c_0_7,c_0_20]) ).

cnf(c_0_24,plain,
    ( subset(set_intersection2(X1,X2),set_intersection2(X3,X2))
    | ~ in(esk1_2(set_intersection2(X1,X2),set_intersection2(X3,X2)),X3) ),
    inference(spm,[status(thm)],[c_0_21,c_0_22]) ).

cnf(c_0_25,negated_conjecture,
    ( subset(set_intersection2(esk5_0,X1),X2)
    | in(esk1_2(set_intersection2(esk5_0,X1),X2),esk6_0) ),
    inference(spm,[status(thm)],[c_0_23,c_0_13]) ).

cnf(c_0_26,negated_conjecture,
    ~ subset(set_intersection2(esk5_0,esk7_0),set_intersection2(esk6_0,esk7_0)),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_27,negated_conjecture,
    subset(set_intersection2(esk5_0,X1),set_intersection2(esk6_0,X1)),
    inference(spm,[status(thm)],[c_0_24,c_0_25]) ).

cnf(c_0_28,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_27])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SEU129+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
% 0.18/0.34  % Computer : n025.cluster.edu
% 0.18/0.34  % Model    : x86_64 x86_64
% 0.18/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34  % Memory   : 8042.1875MB
% 0.18/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34  % CPULimit   : 300
% 0.18/0.34  % WCLimit    : 300
% 0.18/0.34  % DateTime   : Wed Aug 23 16:45:20 EDT 2023
% 0.18/0.35  % CPUTime  : 
% 0.21/0.55  start to proof: theBenchmark
% 0.21/0.61  % Version  : CSE_E---1.5
% 0.21/0.61  % Problem  : theBenchmark.p
% 0.21/0.61  % Proof found
% 0.21/0.61  % SZS status Theorem for theBenchmark.p
% 0.21/0.61  % SZS output start Proof
% See solution above
% 0.21/0.62  % Total time : 0.056000 s
% 0.21/0.62  % SZS output end Proof
% 0.21/0.62  % Total time : 0.059000 s
%------------------------------------------------------------------------------