%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SET631+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 : n005.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 14:34:57 EDT 2023

% Result   : Theorem 0.20s 0.59s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   30 (   5 unt;   7 typ;   0 def)
%            Number of atoms       :   56 (   0 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   57 (  24   ~;  19   |;   8   &)
%                                         (   3 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    8 (   4   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   48 (   2 sgn;  26   !;   1   ?;   0   :)

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

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

tff(decl_24,type,
    intersect: ( $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(difference_defn,axiom,
    ! [X1,X2,X3] :
      ( member(X3,difference(X1,X2))
    <=> ( member(X3,X1)
        & ~ member(X3,X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_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(prove_th113,conjecture,
    ! [X1,X2,X3] :
      ( intersect(X1,difference(X2,X3))
     => intersect(X1,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th113) ).

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

fof(c_0_4,plain,
    ! [X1,X2,X3] :
      ( member(X3,difference(X1,X2))
    <=> ( member(X3,X1)
        & ~ member(X3,X2) ) ),
    inference(fof_simplification,[status(thm)],[difference_defn]) ).

fof(c_0_5,plain,
    ! [X7,X8,X10,X11,X12] :
      ( ( member(esk1_2(X7,X8),X7)
        | ~ intersect(X7,X8) )
      & ( member(esk1_2(X7,X8),X8)
        | ~ intersect(X7,X8) )
      & ( ~ member(X12,X10)
        | ~ member(X12,X11)
        | intersect(X10,X11) ) ),
    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,plain,
    ! [X4,X5,X6] :
      ( ( member(X6,X4)
        | ~ member(X6,difference(X4,X5)) )
      & ( ~ member(X6,X5)
        | ~ member(X6,difference(X4,X5)) )
      & ( ~ member(X6,X4)
        | member(X6,X5)
        | member(X6,difference(X4,X5)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).

fof(c_0_7,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( intersect(X1,difference(X2,X3))
       => intersect(X1,X2) ),
    inference(assume_negation,[status(cth)],[prove_th113]) ).

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,plain,
    ( member(esk1_2(X1,X2),X2)
    | ~ intersect(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_10,plain,
    ( member(X1,X2)
    | ~ member(X1,difference(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_11,plain,
    ( member(esk1_2(X1,X2),X1)
    | ~ intersect(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

fof(c_0_12,plain,
    ! [X13,X14] :
      ( ~ intersect(X13,X14)
      | intersect(X14,X13) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[symmetry_of_intersect])]) ).

fof(c_0_13,negated_conjecture,
    ( intersect(esk2_0,difference(esk3_0,esk4_0))
    & ~ intersect(esk2_0,esk3_0) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).

cnf(c_0_14,plain,
    ( intersect(X1,X2)
    | ~ intersect(X3,X2)
    | ~ member(esk1_2(X3,X2),X1) ),
    inference(spm,[status(thm)],[c_0_8,c_0_9]) ).

cnf(c_0_15,plain,
    ( member(esk1_2(difference(X1,X2),X3),X1)
    | ~ intersect(difference(X1,X2),X3) ),
    inference(spm,[status(thm)],[c_0_10,c_0_11]) ).

cnf(c_0_16,plain,
    ( intersect(X2,X1)
    | ~ intersect(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_17,negated_conjecture,
    intersect(esk2_0,difference(esk3_0,esk4_0)),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_18,plain,
    ( intersect(X1,X2)
    | ~ intersect(difference(X1,X3),X2) ),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_19,negated_conjecture,
    intersect(difference(esk3_0,esk4_0),esk2_0),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_20,negated_conjecture,
    intersect(esk3_0,esk2_0),
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_21,negated_conjecture,
    ~ intersect(esk2_0,esk3_0),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_22,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_20]),c_0_21]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem    : SET631+3 : TPTP v8.1.2. Released v2.2.0.
% 0.08/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35  % Computer : n005.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Sat Aug 26 09:44:23 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.58  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 : 0.007000 s
% 0.20/0.60  % SZS output end Proof
% 0.20/0.60  % Total time : 0.009000 s
%------------------------------------------------------------------------------