TSTP Solution File: SEU119+2 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU119+2 : 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 : 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 16:22:31 EDT 2023

% Result   : Theorem 0.17s 0.59s
% Output   : CNFRefutation 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   52 (   5 unt;  12 typ;   0 def)
%            Number of atoms       :  131 (  32 equ)
%            Maximal formula atoms :   20 (   3 avg)
%            Number of connectives :  153 (  62   ~;  63   |;  23   &)
%                                         (   5 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   11 (   6   >;   5   *;   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   :   80 (   6 sgn;  30   !;   2   ?;   0   :)

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

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

tff(decl_24,type,
    empty_set: $i ).

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

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

tff(decl_27,type,
    esk1_1: $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(d1_xboole_0,axiom,
    ! [X1] :
      ( X1 = empty_set
    <=> ! [X2] : ~ in(X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).

fof(t3_xboole_0,conjecture,
    ! [X1,X2] :
      ( ~ ( ~ disjoint(X1,X2)
          & ! [X3] :
              ~ ( in(X3,X1)
                & in(X3,X2) ) )
      & ~ ( ? [X3] :
              ( in(X3,X1)
              & in(X3,X2) )
          & disjoint(X1,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_0) ).

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(d7_xboole_0,axiom,
    ! [X1,X2] :
      ( disjoint(X1,X2)
    <=> set_intersection2(X1,X2) = empty_set ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_xboole_0) ).

fof(c_0_4,plain,
    ! [X1] :
      ( X1 = empty_set
    <=> ! [X2] : ~ in(X2,X1) ),
    inference(fof_simplification,[status(thm)],[d1_xboole_0]) ).

fof(c_0_5,plain,
    ! [X9,X10,X11] :
      ( ( X9 != empty_set
        | ~ in(X10,X9) )
      & ( in(esk1_1(X11),X11)
        | X11 = empty_set ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])])]) ).

fof(c_0_6,negated_conjecture,
    ~ ! [X1,X2] :
        ( ~ ( ~ disjoint(X1,X2)
            & ! [X3] :
                ~ ( in(X3,X1)
                  & in(X3,X2) ) )
        & ~ ( ? [X3] :
                ( in(X3,X1)
                & in(X3,X2) )
            & disjoint(X1,X2) ) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t3_xboole_0])]) ).

cnf(c_0_7,plain,
    ( X1 != empty_set
    | ~ in(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

fof(c_0_8,plain,
    ! [X13,X14,X15,X16,X17,X18,X19,X20] :
      ( ( in(X16,X13)
        | ~ in(X16,X15)
        | X15 != set_intersection2(X13,X14) )
      & ( in(X16,X14)
        | ~ in(X16,X15)
        | X15 != set_intersection2(X13,X14) )
      & ( ~ in(X17,X13)
        | ~ in(X17,X14)
        | in(X17,X15)
        | X15 != set_intersection2(X13,X14) )
      & ( ~ in(esk2_3(X18,X19,X20),X20)
        | ~ in(esk2_3(X18,X19,X20),X18)
        | ~ in(esk2_3(X18,X19,X20),X19)
        | X20 = set_intersection2(X18,X19) )
      & ( in(esk2_3(X18,X19,X20),X18)
        | in(esk2_3(X18,X19,X20),X20)
        | X20 = set_intersection2(X18,X19) )
      & ( in(esk2_3(X18,X19,X20),X19)
        | in(esk2_3(X18,X19,X20),X20)
        | X20 = set_intersection2(X18,X19) ) ),
    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_9,negated_conjecture,
    ! [X31] :
      ( ( in(esk7_0,esk5_0)
        | ~ disjoint(esk5_0,esk6_0) )
      & ( in(esk7_0,esk6_0)
        | ~ disjoint(esk5_0,esk6_0) )
      & ( disjoint(esk5_0,esk6_0)
        | ~ disjoint(esk5_0,esk6_0) )
      & ( in(esk7_0,esk5_0)
        | ~ in(X31,esk5_0)
        | ~ in(X31,esk6_0) )
      & ( in(esk7_0,esk6_0)
        | ~ in(X31,esk5_0)
        | ~ in(X31,esk6_0) )
      & ( disjoint(esk5_0,esk6_0)
        | ~ in(X31,esk5_0)
        | ~ in(X31,esk6_0) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])])]) ).

cnf(c_0_10,plain,
    ~ in(X1,empty_set),
    inference(er,[status(thm)],[c_0_7]) ).

cnf(c_0_11,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_8]) ).

cnf(c_0_12,plain,
    ( in(X1,X2)
    | ~ in(X1,X3)
    | X3 != set_intersection2(X4,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_13,negated_conjecture,
    ( disjoint(esk5_0,esk6_0)
    | ~ in(X1,esk5_0)
    | ~ in(X1,esk6_0) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_14,plain,
    ( set_intersection2(X1,X2) = empty_set
    | in(esk2_3(X1,X2,empty_set),X2) ),
    inference(spm,[status(thm)],[c_0_10,c_0_11]) ).

cnf(c_0_15,plain,
    ( in(esk2_3(X1,X2,X3),X1)
    | in(esk2_3(X1,X2,X3),X3)
    | X3 = set_intersection2(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

fof(c_0_16,plain,
    ! [X22,X23] :
      ( ( ~ disjoint(X22,X23)
        | set_intersection2(X22,X23) = empty_set )
      & ( set_intersection2(X22,X23) != empty_set
        | disjoint(X22,X23) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d7_xboole_0])]) ).

cnf(c_0_17,plain,
    ( in(X1,X2)
    | ~ in(X1,set_intersection2(X3,X2)) ),
    inference(er,[status(thm)],[c_0_12]) ).

cnf(c_0_18,plain,
    ( in(esk1_1(X1),X1)
    | X1 = empty_set ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_19,plain,
    ( in(X1,X2)
    | ~ in(X1,X3)
    | X3 != set_intersection2(X2,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_20,plain,
    ( in(X1,X4)
    | ~ in(X1,X2)
    | ~ in(X1,X3)
    | X4 != set_intersection2(X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_21,negated_conjecture,
    ( set_intersection2(X1,esk6_0) = empty_set
    | disjoint(esk5_0,esk6_0)
    | ~ in(esk2_3(X1,esk6_0,empty_set),esk5_0) ),
    inference(spm,[status(thm)],[c_0_13,c_0_14]) ).

cnf(c_0_22,plain,
    ( set_intersection2(X1,X2) = empty_set
    | in(esk2_3(X1,X2,empty_set),X1) ),
    inference(spm,[status(thm)],[c_0_10,c_0_15]) ).

cnf(c_0_23,plain,
    ( set_intersection2(X1,X2) = empty_set
    | ~ disjoint(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_24,negated_conjecture,
    ( in(esk7_0,esk6_0)
    | ~ in(X1,esk5_0)
    | ~ in(X1,esk6_0) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_25,plain,
    ( set_intersection2(X1,X2) = empty_set
    | in(esk1_1(set_intersection2(X1,X2)),X2) ),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_26,plain,
    ( in(X1,X2)
    | ~ in(X1,set_intersection2(X2,X3)) ),
    inference(er,[status(thm)],[c_0_19]) ).

cnf(c_0_27,negated_conjecture,
    ( in(esk7_0,esk6_0)
    | ~ disjoint(esk5_0,esk6_0) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_28,plain,
    ( disjoint(X1,X2)
    | set_intersection2(X1,X2) != empty_set ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_29,negated_conjecture,
    ( in(esk7_0,esk5_0)
    | ~ disjoint(esk5_0,esk6_0) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_30,plain,
    ( in(X1,set_intersection2(X2,X3))
    | ~ in(X1,X3)
    | ~ in(X1,X2) ),
    inference(er,[status(thm)],[c_0_20]) ).

cnf(c_0_31,negated_conjecture,
    set_intersection2(esk5_0,esk6_0) = empty_set,
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]) ).

cnf(c_0_32,negated_conjecture,
    ( set_intersection2(X1,esk6_0) = empty_set
    | in(esk7_0,esk6_0)
    | ~ in(esk1_1(set_intersection2(X1,esk6_0)),esk5_0) ),
    inference(spm,[status(thm)],[c_0_24,c_0_25]) ).

cnf(c_0_33,plain,
    ( set_intersection2(X1,X2) = empty_set
    | in(esk1_1(set_intersection2(X1,X2)),X1) ),
    inference(spm,[status(thm)],[c_0_26,c_0_18]) ).

cnf(c_0_34,negated_conjecture,
    ( in(esk7_0,esk6_0)
    | set_intersection2(esk5_0,esk6_0) != empty_set ),
    inference(spm,[status(thm)],[c_0_27,c_0_28]) ).

cnf(c_0_35,negated_conjecture,
    ( in(esk7_0,esk5_0)
    | set_intersection2(esk5_0,esk6_0) != empty_set ),
    inference(spm,[status(thm)],[c_0_29,c_0_28]) ).

cnf(c_0_36,negated_conjecture,
    ( ~ in(X1,esk6_0)
    | ~ in(X1,esk5_0) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_10]) ).

cnf(c_0_37,negated_conjecture,
    in(esk7_0,esk6_0),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]) ).

cnf(c_0_38,negated_conjecture,
    in(esk7_0,esk5_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_31])]) ).

cnf(c_0_39,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SEU119+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.12  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.33  % Computer : n001.cluster.edu
% 0.14/0.33  % Model    : x86_64 x86_64
% 0.14/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33  % Memory   : 8042.1875MB
% 0.14/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33  % CPULimit   : 300
% 0.17/0.33  % WCLimit    : 300
% 0.17/0.33  % DateTime   : Thu Aug 24 01:51:10 EDT 2023
% 0.17/0.33  % CPUTime  : 
% 0.17/0.57  start to proof: theBenchmark
% 0.17/0.59  % Version  : CSE_E---1.5
% 0.17/0.59  % Problem  : theBenchmark.p
% 0.17/0.59  % Proof found
% 0.17/0.59  % SZS status Theorem for theBenchmark.p
% 0.17/0.59  % SZS output start Proof
% See solution above
% 0.17/0.60  % Total time : 0.010000 s
% 0.17/0.60  % SZS output end Proof
% 0.17/0.60  % Total time : 0.012000 s
%------------------------------------------------------------------------------