%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SET585+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 : n017.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 14:34:37 EDT 2023

% Result   : Theorem 0.21s 0.56s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   24 (  11 unt;   9 typ;   0 def)
%            Number of atoms       :   22 (   0 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   15 (   8   ~;   5   |;   1   &)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   12 (   6   >;   6   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :   30 (   3 sgn;  20   !;   0   ?;   0   :)

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

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

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

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

tff(decl_26,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_27,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_28,type,
    esk3_0: $i ).

tff(decl_29,type,
    esk4_0: $i ).

tff(decl_30,type,
    esk5_0: $i ).

fof(prove_intersection_subset_of_union,conjecture,
    ! [X1,X2,X3] : subset(intersection(X1,X2),union(X1,X3)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_intersection_subset_of_union) ).

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

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

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

fof(c_0_4,negated_conjecture,
    ~ ! [X1,X2,X3] : subset(intersection(X1,X2),union(X1,X3)),
    inference(assume_negation,[status(cth)],[prove_intersection_subset_of_union]) ).

fof(c_0_5,plain,
    ! [X4,X5,X6] :
      ( ~ subset(X4,X5)
      | ~ subset(X5,X6)
      | subset(X4,X6) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[transitivity_of_subset])]) ).

fof(c_0_6,plain,
    ! [X7,X8] : subset(X7,union(X7,X8)),
    inference(variable_rename,[status(thm)],[subset_of_union]) ).

fof(c_0_7,negated_conjecture,
    ~ subset(intersection(esk3_0,esk4_0),union(esk3_0,esk5_0)),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).

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

cnf(c_0_9,plain,
    subset(X1,union(X1,X2)),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

fof(c_0_10,plain,
    ! [X9,X10] : subset(intersection(X9,X10),X9),
    inference(variable_rename,[status(thm)],[intersection_is_subset]) ).

cnf(c_0_11,negated_conjecture,
    ~ subset(intersection(esk3_0,esk4_0),union(esk3_0,esk5_0)),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_12,plain,
    ( subset(X1,union(X2,X3))
    | ~ subset(X1,X2) ),
    inference(spm,[status(thm)],[c_0_8,c_0_9]) ).

cnf(c_0_13,plain,
    subset(intersection(X1,X2),X1),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_14,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SET585+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
% 0.14/0.34  % Computer : n017.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Sat Aug 26 12:00:25 EDT 2023
% 0.14/0.34  % CPUTime  : 
% 0.21/0.55  start to proof: theBenchmark
% 0.21/0.56  % Version  : CSE_E---1.5
% 0.21/0.56  % Problem  : theBenchmark.p
% 0.21/0.56  % Proof found
% 0.21/0.56  % SZS status Theorem for theBenchmark.p
% 0.21/0.56  % SZS output start Proof
% See solution above
% 0.21/0.56  % Total time : 0.007000 s
% 0.21/0.56  % SZS output end Proof
% 0.21/0.56  % Total time : 0.009000 s
%------------------------------------------------------------------------------