%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SET183+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 : n009.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 14:33:30 EDT 2023

% Result   : Theorem 0.56s 0.61s
% Output   : CNFRefutation 0.56s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   43 (  14 unt;   7 typ;   0 def)
%            Number of atoms       :   80 (  13 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   72 (  28   ~;  29   |;   9   &)
%                                         (   3 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   10 (   5   >;   5   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   67 (   4 sgn;  30   !;   0   ?;   0   :)

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

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

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

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

tff(decl_26,type,
    esk2_2: ( $i * $i ) > $i ).

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

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

fof(prove_subset_intersection,conjecture,
    ! [X1,X2] :
      ( subset(X1,X2)
     => intersection(X1,X2) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_subset_intersection) ).

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

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

fof(equal_defn,axiom,
    ! [X1,X2] :
      ( X1 = X2
    <=> ( subset(X1,X2)
        & subset(X2,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).

fof(intersection_is_subset,axiom,
    ! [X1,X2] : subset(intersection(X1,X2),X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_is_subset) ).

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

fof(c_0_6,negated_conjecture,
    ~ ! [X1,X2] :
        ( subset(X1,X2)
       => intersection(X1,X2) = X1 ),
    inference(assume_negation,[status(cth)],[prove_subset_intersection]) ).

fof(c_0_7,plain,
    ! [X9,X10,X11,X12,X13] :
      ( ( ~ subset(X9,X10)
        | ~ member(X11,X9)
        | member(X11,X10) )
      & ( member(esk1_2(X12,X13),X12)
        | subset(X12,X13) )
      & ( ~ member(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)],[subset_defn])])])])])]) ).

fof(c_0_8,negated_conjecture,
    ( subset(esk3_0,esk4_0)
    & intersection(esk3_0,esk4_0) != esk3_0 ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).

cnf(c_0_9,plain,
    ( member(X3,X2)
    | ~ subset(X1,X2)
    | ~ member(X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_10,negated_conjecture,
    subset(esk3_0,esk4_0),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

fof(c_0_11,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])])]) ).

cnf(c_0_12,plain,
    ( subset(X1,X2)
    | ~ member(esk1_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_13,negated_conjecture,
    ( member(X1,esk4_0)
    | ~ member(X1,esk3_0) ),
    inference(spm,[status(thm)],[c_0_9,c_0_10]) ).

cnf(c_0_14,plain,
    ( member(X1,X2)
    | ~ member(X1,intersection(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_15,plain,
    ( member(esk1_2(X1,X2),X1)
    | subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_16,negated_conjecture,
    ( subset(X1,esk4_0)
    | ~ member(esk1_2(X1,esk4_0),esk3_0) ),
    inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

cnf(c_0_17,plain,
    ( subset(intersection(X1,X2),X3)
    | member(esk1_2(intersection(X1,X2),X3),X2) ),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_18,plain,
    ( member(X1,intersection(X2,X3))
    | ~ member(X1,X2)
    | ~ member(X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_19,negated_conjecture,
    subset(intersection(X1,esk3_0),esk4_0),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_20,plain,
    ( subset(X1,intersection(X2,X3))
    | ~ member(esk1_2(X1,intersection(X2,X3)),X3)
    | ~ member(esk1_2(X1,intersection(X2,X3)),X2) ),
    inference(spm,[status(thm)],[c_0_12,c_0_18]) ).

cnf(c_0_21,negated_conjecture,
    ( member(X1,esk4_0)
    | ~ member(X1,intersection(X2,esk3_0)) ),
    inference(spm,[status(thm)],[c_0_9,c_0_19]) ).

fof(c_0_22,plain,
    ! [X15,X16] :
      ( ( subset(X15,X16)
        | X15 != X16 )
      & ( subset(X16,X15)
        | X15 != X16 )
      & ( ~ subset(X15,X16)
        | ~ subset(X16,X15)
        | X15 = X16 ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_defn])])]) ).

cnf(c_0_23,plain,
    ( subset(X1,intersection(X2,X1))
    | ~ member(esk1_2(X1,intersection(X2,X1)),X2) ),
    inference(spm,[status(thm)],[c_0_20,c_0_15]) ).

fof(c_0_24,plain,
    ! [X7,X8] : subset(intersection(X7,X8),X7),
    inference(variable_rename,[status(thm)],[intersection_is_subset]) ).

cnf(c_0_25,negated_conjecture,
    ( subset(intersection(X1,esk3_0),X2)
    | member(esk1_2(intersection(X1,esk3_0),X2),esk4_0) ),
    inference(spm,[status(thm)],[c_0_21,c_0_15]) ).

cnf(c_0_26,plain,
    ( X1 = X2
    | ~ subset(X1,X2)
    | ~ subset(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

cnf(c_0_27,plain,
    subset(X1,intersection(X1,X1)),
    inference(spm,[status(thm)],[c_0_23,c_0_15]) ).

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

fof(c_0_29,plain,
    ! [X17,X18] : intersection(X17,X18) = intersection(X18,X17),
    inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).

cnf(c_0_30,negated_conjecture,
    subset(intersection(X1,esk3_0),intersection(esk4_0,intersection(X1,esk3_0))),
    inference(spm,[status(thm)],[c_0_23,c_0_25]) ).

cnf(c_0_31,plain,
    intersection(X1,X1) = X1,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28])]) ).

cnf(c_0_32,plain,
    intersection(X1,X2) = intersection(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_29]) ).

cnf(c_0_33,negated_conjecture,
    subset(esk3_0,intersection(esk3_0,esk4_0)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]) ).

cnf(c_0_34,negated_conjecture,
    intersection(esk3_0,esk4_0) != esk3_0,
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_35,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_33]),c_0_28])]),c_0_34]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem    : SET183+3 : TPTP v8.1.2. Released v2.2.0.
% 0.13/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35  % Computer : n009.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Sat Aug 26 14:02:20 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.56/0.59  start to proof: theBenchmark
% 0.56/0.61  % Version  : CSE_E---1.5
% 0.56/0.61  % Problem  : theBenchmark.p
% 0.56/0.61  % Proof found
% 0.56/0.61  % SZS status Theorem for theBenchmark.p
% 0.56/0.61  % SZS output start Proof
% See solution above
% 0.56/0.61  % Total time : 0.009000 s
% 0.56/0.61  % SZS output end Proof
% 0.56/0.61  % Total time : 0.012000 s
%------------------------------------------------------------------------------