%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SET573+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n004.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 14:34:34 EDT 2023

% Result   : Theorem 0.19s 0.55s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   23 (   5 unt;   7 typ;   0 def)
%            Number of atoms       :   39 (   0 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   40 (  17   ~;  10   |;   8   &)
%                                         (   3 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    8 (   4   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :   26 (   0 sgn;  19   !;   1   ?;   0   :)

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

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

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

tff(decl_25,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_26,type,
    esk2_0: $i ).

tff(decl_27,type,
    esk3_0: $i ).

tff(decl_28,type,
    esk4_0: $i ).

fof(prove_th12,conjecture,
    ! [X1,X2,X3] :
      ( ( member(X1,X2)
        & disjoint(X2,X3) )
     => ~ member(X1,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th12) ).

fof(disjoint_defn,axiom,
    ! [X1,X2] :
      ( disjoint(X1,X2)
    <=> ~ intersect(X1,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',disjoint_defn) ).

fof(intersect_defn,axiom,
    ! [X1,X2] :
      ( intersect(X1,X2)
    <=> ? [X3] :
          ( member(X3,X1)
          & member(X3,X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersect_defn) ).

fof(c_0_3,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( ( member(X1,X2)
          & disjoint(X2,X3) )
       => ~ member(X1,X3) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[prove_th12])]) ).

fof(c_0_4,plain,
    ! [X1,X2] :
      ( disjoint(X1,X2)
    <=> ~ intersect(X1,X2) ),
    inference(fof_simplification,[status(thm)],[disjoint_defn]) ).

fof(c_0_5,plain,
    ! [X4,X5,X7,X8,X9] :
      ( ( member(esk1_2(X4,X5),X4)
        | ~ intersect(X4,X5) )
      & ( member(esk1_2(X4,X5),X5)
        | ~ intersect(X4,X5) )
      & ( ~ member(X9,X7)
        | ~ member(X9,X8)
        | intersect(X7,X8) ) ),
    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)],[intersect_defn])])])])])]) ).

fof(c_0_6,negated_conjecture,
    ( member(esk2_0,esk3_0)
    & disjoint(esk3_0,esk4_0)
    & member(esk2_0,esk4_0) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).

fof(c_0_7,plain,
    ! [X10,X11] :
      ( ( ~ disjoint(X10,X11)
        | ~ intersect(X10,X11) )
      & ( intersect(X10,X11)
        | disjoint(X10,X11) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])]) ).

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

cnf(c_0_9,negated_conjecture,
    member(esk2_0,esk4_0),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_10,plain,
    ( ~ disjoint(X1,X2)
    | ~ intersect(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_11,negated_conjecture,
    disjoint(esk3_0,esk4_0),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_12,negated_conjecture,
    ( intersect(X1,esk4_0)
    | ~ member(esk2_0,X1) ),
    inference(spm,[status(thm)],[c_0_8,c_0_9]) ).

cnf(c_0_13,negated_conjecture,
    member(esk2_0,esk3_0),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_14,negated_conjecture,
    ~ intersect(esk3_0,esk4_0),
    inference(spm,[status(thm)],[c_0_10,c_0_11]) ).

cnf(c_0_15,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SET573+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34  % Computer : n004.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Sat Aug 26 10:52:52 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.19/0.53  start to proof: theBenchmark
% 0.19/0.54  % Version  : CSE_E---1.5
% 0.19/0.54  % Problem  : theBenchmark.p
% 0.19/0.54  % Proof found
% 0.19/0.55  % SZS status Theorem for theBenchmark.p
% 0.19/0.55  % SZS output start Proof
% See solution above
% 0.19/0.55  % Total time : 0.004000 s
% 0.19/0.55  % SZS output end Proof
% 0.19/0.55  % Total time : 0.007000 s
%------------------------------------------------------------------------------