%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SET629+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n002.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 14:34:56 EDT 2023

% Result   : Theorem 0.20s 0.59s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   41 (  12 unt;   9 typ;   0 def)
%            Number of atoms       :   73 (   3 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   74 (  33   ~;  23   |;  11   &)
%                                         (   6 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   14 (   7   >;   7   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   2 con; 0-2 aty)
%            Number of variables   :   69 (   6 sgn;  40   !;   1   ?;   0   :)

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

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

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

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

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

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

tff(decl_28,type,
    esk2_2: ( $i * $i ) > $i ).

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

tff(decl_30,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/sandbox2/benchmark/theBenchmark.p',difference_defn) ).

fof(prove_intersection_and_difference_disjoint,conjecture,
    ! [X1,X2] : disjoint(intersection(X1,X2),difference(X1,X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_intersection_and_difference_disjoint) ).

fof(disjoint_defn,axiom,
    ! [X1,X2] :
      ( disjoint(X1,X2)
    <=> ~ intersect(X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',disjoint_defn) ).

fof(intersect_defn,axiom,
    ! [X1,X2] :
      ( intersect(X1,X2)
    <=> ? [X3] :
          ( member(X3,X1)
          & member(X3,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersect_defn) ).

fof(intersection_defn,axiom,
    ! [X1,X2,X3] :
      ( member(X3,intersection(X1,X2))
    <=> ( member(X3,X1)
        & member(X3,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_defn) ).

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

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

fof(c_0_7,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_8,negated_conjecture,
    ~ ! [X1,X2] : disjoint(intersection(X1,X2),difference(X1,X2)),
    inference(assume_negation,[status(cth)],[prove_intersection_and_difference_disjoint]) ).

fof(c_0_9,plain,
    ! [X1,X2] :
      ( disjoint(X1,X2)
    <=> ~ intersect(X1,X2) ),
    inference(fof_simplification,[status(thm)],[disjoint_defn]) ).

fof(c_0_10,plain,
    ! [X7,X8,X9] :
      ( ( member(X9,X7)
        | ~ member(X9,difference(X7,X8)) )
      & ( ~ member(X9,X8)
        | ~ member(X9,difference(X7,X8)) )
      & ( ~ member(X9,X7)
        | member(X9,X8)
        | member(X9,difference(X7,X8)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).

fof(c_0_11,plain,
    ! [X10,X11,X13,X14,X15] :
      ( ( member(esk1_2(X10,X11),X10)
        | ~ intersect(X10,X11) )
      & ( member(esk1_2(X10,X11),X11)
        | ~ intersect(X10,X11) )
      & ( ~ member(X15,X13)
        | ~ member(X15,X14)
        | intersect(X13,X14) ) ),
    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_12,plain,
    ! [X4,X5,X6] :
      ( ( member(X6,X4)
        | ~ member(X6,intersection(X4,X5)) )
      & ( member(X6,X5)
        | ~ member(X6,intersection(X4,X5)) )
      & ( ~ member(X6,X4)
        | ~ member(X6,X5)
        | member(X6,intersection(X4,X5)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intersection_defn])])]) ).

fof(c_0_13,negated_conjecture,
    ~ disjoint(intersection(esk3_0,esk4_0),difference(esk3_0,esk4_0)),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).

fof(c_0_14,plain,
    ! [X16,X17] :
      ( ( ~ disjoint(X16,X17)
        | ~ intersect(X16,X17) )
      & ( intersect(X16,X17)
        | disjoint(X16,X17) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])]) ).

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

cnf(c_0_16,plain,
    ( member(esk1_2(X1,X2),X1)
    | ~ intersect(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_17,plain,
    ( member(X1,X2)
    | ~ member(X1,intersection(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_18,plain,
    ( member(esk1_2(X1,X2),X2)
    | ~ intersect(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

fof(c_0_19,plain,
    ! [X20,X21] :
      ( ~ intersect(X20,X21)
      | intersect(X21,X20) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[symmetry_of_intersect])]) ).

cnf(c_0_20,negated_conjecture,
    ~ disjoint(intersection(esk3_0,esk4_0),difference(esk3_0,esk4_0)),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_21,plain,
    ( intersect(X1,X2)
    | disjoint(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_22,plain,
    ( ~ intersect(difference(X1,X2),X3)
    | ~ member(esk1_2(difference(X1,X2),X3),X2) ),
    inference(spm,[status(thm)],[c_0_15,c_0_16]) ).

cnf(c_0_23,plain,
    ( member(esk1_2(X1,intersection(X2,X3)),X2)
    | ~ intersect(X1,intersection(X2,X3)) ),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

fof(c_0_24,plain,
    ! [X18,X19] : intersection(X18,X19) = intersection(X19,X18),
    inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).

cnf(c_0_25,plain,
    ( intersect(X2,X1)
    | ~ intersect(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_26,negated_conjecture,
    intersect(intersection(esk3_0,esk4_0),difference(esk3_0,esk4_0)),
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_27,plain,
    ~ intersect(difference(X1,X2),intersection(X2,X3)),
    inference(spm,[status(thm)],[c_0_22,c_0_23]) ).

cnf(c_0_28,plain,
    intersection(X1,X2) = intersection(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_29,negated_conjecture,
    intersect(difference(esk3_0,esk4_0),intersection(esk3_0,esk4_0)),
    inference(spm,[status(thm)],[c_0_25,c_0_26]) ).

cnf(c_0_30,plain,
    ~ intersect(difference(X1,X2),intersection(X3,X2)),
    inference(spm,[status(thm)],[c_0_27,c_0_28]) ).

cnf(c_0_31,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[c_0_29,c_0_30]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem    : SET629+3 : TPTP v8.1.2. Released v2.2.0.
% 0.12/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n002.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Sat Aug 26 12:01:48 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.57  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
%------------------------------------------------------------------------------